trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)
The 2017 balance sheet of Kerber's Tennis Shop, Inc., showed long-term debt of $5 million, and the 2018 balance sheet showed long-term debt of $5.2 million. The 2018 income statement showed an interest expense of $165,000. During 2018, the company had a cash flow to stockholders for the year was $70,000. Suppose you also know that the firm’s net capital spending for 2018 was $1,370,000, and that the firm reduced its net working capital investment by $69,000. What was the firm’s 2018 operating cash flow, or OCF?
Griffin's Goat Farm, Inc., has sales of $686,000, costs of $332,000, depreciation expense of $65,000, interest expense of $48,500, and a tax rate of 24 percent. What is the net income for this firm?
The net income for Griffin's Goat Farm, Inc., was [tex]\$184,340[/tex].
The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:
[tex]OCF = EBIT + Depreciation - Taxes + \triangle Working Capital[/tex]
where EBIT is earnings before interest and taxes.
Calculate EBIT by subtracting interest expense from operating income:
EBIT = Operating Income - Interest Expense
We do not have the information for operating income, but we can use the fact that interest expense was. [tex]\$165,000[/tex] to calculate EBIT.
EBIT = Interest Expense / (1 - Tax Rate)
= [tex]\$165,000 / (1 - 0)[/tex]
= [tex]\$165,000[/tex]
Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by [tex]\$69,000[/tex], which means that working capital increased by [tex]\$69,000[/tex].
Therefore:
[tex]\triangle Working Capital = \$69,000[/tex]
Now, we can calculate OCF:
OCF = EBIT + Depreciation - Taxes + Δ Working Capital
=[tex]\$165,000 + 0 - 0 +\ $69,000[/tex]
=[tex]\$234,000[/tex]
Therefore, the firm’s 2018 operating cash flow (OCF) was [tex]\$234,000[/tex] .
To calculate the net income for Griffin's Goat Farm, we can use the following formula:
Net Income = EBIT - Interest Expense - Taxes
where EBIT is earnings before interest and taxes. We can calculate EBIT as:
EBIT = Sales - Costs - Depreciation
= [tex]\$686,000 - \$332,000 - \$65,000[/tex]
=[tex]\$289,000[/tex]
Next, we need to calculate taxes. We are given a tax rate of 24%, so:
Taxes = Tax Rate x (EBIT - Depreciation)
= [tex]0.24 \times (\$289,000 - \$65,000)= \$56,160[/tex]
Now, we can calculate net income:
Net Income = EBIT - Interest Expense - Taxes
= [tex]\$289,000 - \$48,500 - \$56,160= \$184,340[/tex]
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There are 11 balls numbered 1 through 11 placed in a bucket. What is the probability of reaching into the bucket and randomly drawing three balls numbered 4, 9, and 7 without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth
The probability of reaching into the bucket and randomly drawing three balls numbered 4, 9, and 7 without replacement, in that order, is 1/990, which is a decimal rounded to the nearest millionth is 0.001.
The probability of drawing three balls numbered 4, 9, and 7 without replacement, in that order, can be found by multiplying the probabilities of drawing each ball in the correct order.
The probability of drawing the first ball, numbered 4, is 1/11, since there is only one ball numbered 4 out of 11 balls in the bucket.
After the first ball is drawn, there are 10 balls remaining in the bucket, and the probability of drawing the second ball, numbered 9, is 1/10, since there is only one ball numbered 9 remaining out of the 10 balls in the bucket.
After the first two balls are drawn, there are 9 balls remaining in the bucket, and the probability of drawing the third ball, numbered 7, is 1/9, since there is only one ball numbered 7 remaining out of the 9 balls in the bucket.
Therefore, the probability of drawing the balls numbered 4, 9, and 7 without replacement, in that order, is:
(1/11) * (1/10) * (1/9) = 1/990
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pamela registered her new phone number on the do not call registry. how long will her number remain on the list?
If Pamela has registered for the first time, it will remain on the Do Not Call list permanently. If she has re-registered, it will remain on the list for an additional five years from the date of re-registration.
How long do phone numbers remain on the Do Not Call Registry?The length of time that Pamela's phone number will remain on the National Do Not Call Registry depends on whether she registered her number on the Do Not Call Registry for the first time or if she has re-registered her number after it has already been on the list for a while.
If Pamela registered her phone number for the first time, it will be added to the Do Not Call Registry within 31 days of her registration date. Her phone number will remain on the list permanently, unless she requests to remove it or the number is disconnected.
If Pamela has re-registered her phone number after it has already been on the list for a while, her number's registration will be extended for another five years from the date she re-registered it.
Therefore, if Pamela registered her phone number for the first time, it will remain on the list permanently. If she has re-registered her number, it will remain on the list for an additional five years from the date of re-registration.
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Use the functions f(x)=√x+1, g(x)=2x-5, and h(x) = 3x² - 3 to complete the table.
x
4
10
20
34
52
f(g(x))
Answer:
To find the values of f(g(x)) for the given values of x, we need to first evaluate g(x) for each value of x, and then plug the result into f(x).
Using the given functions:
g(x) = 2x - 5
f(x) = √(x+1)
Therefore, we have:
f(g(x)) = √(g(x) + 1) = √(2x - 5 + 1) = √(2x - 4) = 2√(x - 2)
So, we can complete the table as follows:
x f(g(x))
4 2
10 4
20 6
34 8
52 10
Therefore, the completed table is:
x f(g(x))
4 2
10 4
20 6
34 8
52 10
a rectangular solid (with a square base) has a surface area of 433.5 square centimeters. find the dimensions that will result in a solid with maximum volume.
The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.
Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:
Surface area = area of base + area of front + area of back + area of left + area of right
Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh
We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5
We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:
Volume = area of base × height = x² × h
We can use the surface area equation to solve for h in terms of x:
x² + 8xh = 433.5
h = (433.5 - x²)/(8x)
Substituting this expression for h into the volume equation, we get:
Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8
To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:
d(Volume)/dx = (433.5 - 3x²)/8 = 0
433.5 - 3x² = 0
x² = 144.5
x = sqrt(144.5) ≈ 12.02
We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:
d²(Volume)/dx² = -3x/4
At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).
Substituting x = sqrt(144.5) into the expression for h, we get:
h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))
h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8
h = 5.01
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The dimensions of the rectangular solid that will result in a maximum volume are approximately.[tex]6.34 cm \times 9.03 cm \times 9.03 cm.[/tex]
Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.
The surface area of the rectangular solid can be expressed as:
[tex]SA = 2xy + 2xz + 2yz[/tex]
Substituting x for y and z, we get:
[tex]SA = 2x^2 + 4xy[/tex]
We are given that the surface area is 433.5 square centimeters, so:
[tex]2x^2 + 4xy = 433.5[/tex]
Simplifying, we get:
[tex]x^2 + 2xy - 216.75 = 0[/tex]
Using the quadratic formula to solve for y, we get:
[tex]y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2[/tex]
[tex]y = -x \± \sqrt (x^2 + 216.75)[/tex]
Since the base of the rectangular solid is a square, we know that y = z. So:
[tex]z = -x \± \sqrt(x^2 + 216.75)[/tex]
The volume of the rectangular solid is given by:
[tex]V = x^2y[/tex]
Substituting y for[tex]-x + \sqrt (x^2 + 216.75),[/tex] we get:
[tex]V = x^2(-x + \sqrt(x^2 + 216.75))[/tex]
Expanding and simplifying, we get:
[tex]V = -x^3 + x^2\sqrt(x^2 + 216.75)[/tex]
The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.
We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:
[tex]dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0[/tex]
Multiplying both sides by [tex]2\sqrt (x^2 + 216.75)[/tex] to eliminate the denominator, we get:
[tex]-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0[/tex]
Simplifying, we get:
[tex]x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0[/tex]
We can solve this equation numerically using a graphing calculator or computer software.
[tex]The solution is approximately x = 6.34 centimeters.[/tex]
Substituting x = 6.34 into the expression for y and z, we get:
[tex]y = z \approx 9.03 centimeters[/tex]
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The weight of oranges growing in an orchard is normally distributed with a mean weight of 4.5 oz. and a standard deviation of 1 oz. Using the empirical rule, what percentage of the oranges from the orchard weigh between 3.5 oz. and 5.5 oz.?
Therefore, we can conclude that approximately 68% of the oranges from the orchard weigh between 3.5 oz. and 5.5 oz. using the empirical rule.
The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, we want to find the percentage of oranges that weigh between 3.5 oz. and 5.5 oz., which is one standard deviation below and above the mean, respectively.
First, we need to standardize the values using the z-score formula:
z = (x - μ) / σ
where:
x is the value we want to standardize (in this case, 3.5 oz. and 5.5 oz.)
μ is the mean (4.5 oz.)
σ is the standard deviation (1 oz.)
For 3.5 oz.:
z = (3.5 - 4.5) / 1 = -1
For 5.5 oz.:
[tex]z = (5.5 - 4.5) / 1 = 1[/tex]
Now, we can use a standard normal distribution table or calculator to find the area under the curve between z = -1 and z = 1. The area between two z-scores represents the percentage of data that falls between those values.
According to the table, the area between [tex]z = -1[/tex]and [tex]z = 1[/tex]is approximately 0.6827 or 68.27%.
Therefore, we can conclude that approximately 68% of the oranges from the orchard weigh between 3.5 oz. and 5.5 oz. using the empirical rule.
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Write 35% as a fraction in lowest term
Answer:7/20
Step-by-step explanation:
35% [tex]= 0.35 = \frac{35}{100} = \frac{35/5}{100/5} = \frac{7}{20}[/tex]
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the pairs of figures that have the same volume. 3-D shape of a cone is represented. The cone has a radius of 4 units and a height of 12 units. 3-D shape of a rectangular prism is represented. The rectangular prism has a length of 18 units, a width of 6 units, a height of 6 units. 3-D shape of a rectangular prism is represented. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units. 3-D shape of a cylinder is represented. The cylinder has a radius of 3 units and a height of 8 units. 3-D shape of a cone is represented. The cone has a radius of 8 units and a height of 9 units. 3-D shape of a rectangular prism is represented. The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units. arrowBoth 3-D shape of a cylinder is represented. The cylinder has a radius of 4 units and a height of 12 units. arrowBoth 3-D shape of a cone is represented. The cone has a radius of 6 units and a height of 6 units. arrowBoth Reset Next © 2023 Edmentum. All rights reserved.
The pair of figures having same volume are:
a. The cylinder has a radius of 3 units and a height of 8 units ; The cone has a radius of 6 units and a height of 6 units.
b. The cone has a radius of 8 units and a height of 9 units ; The cylinder has a radius of 4 units and a height of 12 units.
c. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units ; The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.
What is volume of a figure?
Volume is a unit of measurement for three-dimensional space. It is usually stated quantitatively in terms of a number of imperial or US-standard units as well as SI-derived units.
i. The cone has a radius of 4 units and a height of 12 units.
⇒ Volume = π[tex]r^{2} \frac{h}{3}[/tex]
⇒ Volume = π[tex]4^{2} \frac{12}{3}[/tex]
⇒ Volume = 64 π
⇒ Volume = 201 cubic units
ii. The rectangular prism has a length of 18 units, a width of 6 units, a height of 6 units.
⇒ Volume = length * width * height
⇒ Volume = 18 * 6 * 6
⇒ Volume = 648 cubic units
iii. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units.
⇒ Volume = length * width * height
⇒ Volume = 16 * 6 * 6
⇒ Volume = 576 cubic units
iv. The cylinder has a radius of 3 units and a height of 8 units.
⇒ Volume = π[tex]r^{2}[/tex]h
⇒ Volume = π[tex]3^{2}[/tex] * 8
⇒ Volume = 72 π
⇒ Volume = 226 cubic units
v. The cone has a radius of 8 units and a height of 9 units.
⇒ Volume = π[tex]r^{2} \frac{h}{3}[/tex]
⇒ Volume = π[tex]8^{2} \frac{9}{3}[/tex]
⇒ Volume = 192 π
⇒ Volume = 603 cubic units
vi. The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.
⇒ Volume = length * width * height
⇒ Volume = 8 * 8 * 9
⇒ Volume = 576 cubic units
vii. The cylinder has a radius of 4 units and a height of 12 units.
⇒ Volume = π[tex]r^{2}[/tex]h
⇒ Volume = π[tex]4^{2}[/tex] * 12
⇒ Volume = 192 π
⇒ Volume = 603 cubic units
viii. The cone has a radius of 6 units and a height of 6 units.
⇒ Volume = π[tex]r^{2} \frac{h}{3}[/tex]
⇒ Volume = π[tex]6^{2} \frac{6}{3}[/tex]
⇒ Volume = 72 π
⇒ Volume = 226 cubic units
Hence, three pairs have the same volume.
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The missing figures have been attached below.
tell whether the ordered pair is a solution of the inequality. 2z less than 15; z =11
The ordered pair (z, 11) is not a solution of the inequality.
Explain inequality
An inequality is a statement that compares two values, expressing that one value is greater than or less than the other, or that they are not equal. Inequalities are represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). They are used to describe relationships between numbers, variables, and expressions.
According to the given information
To determine whether the ordered pair (z, 11) is a solution of the inequality 2z < 15, we need to substitute z = 11 into the inequality and see if it is true or false:
2z < 15
2(11) < 15
22 < 15 (this is false)
Since 22 is not less than 15, the ordered pair (z, 11) is not a solution to the inequality.
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an observer has determined that the time headways between successive vehicles on a section of highway are exponentially distributed and that 65% of the headways between vehicles are 9 seconds or greater. if the observer decides to count traffic in 30- second time intervals, estimate the probability of the
If observer decides to count traffic in 30-second time intervals, then the probability of observer counting exactly 1 vehicles in an interval is 0.344.
The Vehicle headway follows an exponential distribution and the vehicle arrival follows a poison distribution.
We know that that, probability of getting headway greater than or equal to 9 seconds is 65%,
So, P(h≥9) = 0.65 ...equation(1)
We know that, P(h≥t) = [tex]e^{-\lambda \times t}[/tex],
where, h is headway , t is time and λ is vehicle "arrival-rate",
So, P(h≥9) = [tex]e^{-\lambda \times 9}[/tex], ....equation(2)
Equating both equation(1) and equation(2),
We get,
⇒ [tex]e^{-\lambda \times 9}[/tex] = 0.65,
⇒ -9λ = ln(0.65),
⇒ λ = 0.047 vehicles per second.
Since, the vehicle arrival follows poison distribution,
The probability of having "n" vehicles arrive in "t" time is P(n) ,
⇒ P(n) = {(λt)ⁿ[tex]e^{-\lambda \times t}[/tex]}/n!,
where, λ = average vehicle arrival rate = 0.047,
"t" = duration of time interval is = 30,
To find the probability of getting exactly 1 vehicle, we put n = 1,
So,
⇒ P(1) = {(0.047×30)¹ [tex]e^{-0.047 \times 30}[/tex]}/1!
⇒ P(1) = 0.344.
Therefore, the required probability is 0.344.
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The given question is incomplete, the complete question is
An observer has determined that the time headways between successive vehicles on a section of highway are exponentially distributed and that 65% of the headways between vehicles are 9 seconds or greater. If the observer decides to count traffic in 30-second time intervals,
Estimate the probability of the observer counting exactly 1 vehicles in an interval.
I NEED HELP ON THIS ASAP! JUST THE QUESTION BELOW THE TABLE
The proof that the table has a constant ratio is shown below
Proving that the table has a constant ratioFrom the table of values, we have the following parameters that can be used in our computation:
f(x + 1) = ab^(x + 1)
f(x + 2) = ab^(x + 2)
f(x + 3) = ab^(x + 3)
When divided, we get the ratio r
So, we have
r = f(x + 3)/f(x + 2) = f(x + 2)/f(x + 1)
This gives
ab^(x + 3)/ab^(x + 2) = ab^(x + 2)/ab^(x + 1)
Divide through by a
b^(x + 3)/b^(x + 2) = b^(x + 2)/b^(x + 1)
Using the law of indices, we have
b^(x + 3 - x - 2) = b^(x + 2 - x - 1)
Evaluate
b^0 = b^0
This gives
1 = 1
Hence, the table has a constant ratio
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What is the value of x?
Answer:
X= 22
Step-by-step explanation:
So all the angles in a triangle will have a sum of 180°
since you already have a 90° angle you can make the equation
2x+3x-20=90
you'll add the 2x and 3x to get 5x and then you'll also add 20 on both sides
20+90=110
the equation you'll then have is 5x=110
now you'll divide five from both sides and 110/5 is 22
Checked answer: 2(22)+ 3(22)-20= 90 and then youll add that 90 ° angle from before and youll get 180°
A car travels 3 miles in 5 minutes. A subway train travels 4 miles in 6 minutes. How much longer does it take to travel 7 miles in the slower vehicle
The slower vehicle is the car, and it would take (11.67 - 10.5) = 1.17 minutes longer to travel 7 miles compared to the subway train.
To find out how much longer it would take to travel 7 miles in the slower vehicle, we need to calculate the speed of
each vehicle first.
The car travels 3 miles in 5 minutes, which means it travels at a speed of 3/5 miles per minute.
The subway train travels 4 miles in 6 minutes, which means it travels at a speed of 4/6 miles per minute. Simplifying
this, we get a speed of 2/3 miles per minute.
Now, we can calculate how long it would take each vehicle to travel 7 miles:
The car travels at a speed of 3/5 miles per minute, so it would take (7 / (3/5)) = 11.67 minutes to travel 7 miles.
The subway train travels at a speed of 2/3 miles per minute, so it would take (7 / (2/3)) = 10.5 minutes to travel 7 miles.
Therefore, the slower vehicle is the car, and it would take (11.67 - 10.5) = 1.17 minutes longer to travel 7 miles compared to the subway train.
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An article on the relation of cholesterol levels in human blood to aging reports that average cholesterol level for women aged 70-74 was found to be 230m/dl. If the standard deviation was 20mg/dl and the distribution normal, what is the probability that a given woman in this age group would have a cholesterol level
a) Less than 200mg/dl
b) More than 200mg/dl
c) Between 190mg/dl and 210mg/dl
d) Write a brief report on the guidance you would give a woman having high cholesterol level in this age group
a) The probability of a given woman in this age group having a cholesterol level less than 200mg/dl is 6.68%.
b) The probability of a given woman in this age group having a cholesterol level more than 200mg/dl is 93.32%.
c) The probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl is 15.87%.
d) If a woman in this age group has a cholesterol level higher than 230mg/dl, it is considered high and puts her at risk of heart disease
To calculate the probability of a given woman in this age group having a cholesterol level less than 200mg/dl, we need to find the z-score first. The z-score is the number of standard deviations that a given value is from the mean. The formula to calculate the z-score is:
z = (x - μ) / σ
where x is the given value, μ is the mean, and σ is the standard deviation.
For a cholesterol level of 200mg/dl, the z-score is:
z = (200 - 230) / 20 = -1.5
We can then use a z-table or calculator to find the probability of a z-score being less than -1.5, which is 0.0668 or approximately 6.68%.
Next, to find the probability of a given woman in this age group having a cholesterol level more than 200mg/dl, we can use the same process but subtract the probability of a z-score being less than -1.5 from 1 because the total probability is always 1.
So, the probability of a given woman in this age group having a cholesterol level more than 200mg/dl is:
1 - 0.0668 = 0.9332 or approximately 93.32%.
Finally, to find the probability of a given woman in this age group having a cholesterol level between 190mg/dl and 210mg/dl, we need to find the z-scores for both values.
For a cholesterol level of 190mg/dl, the z-score is:
z = (190 - 230) / 20 = -2
For a cholesterol level of 210mg/dl, the z-score is:
z = (210 - 230) / 20 = -1
We can then use the z-table or calculator to find the probability of a z-score being between -2 and -1, which is 0.1587 or approximately 15.87%.
Finally, a brief report on the guidance that you would give a woman having high cholesterol levels in this age group is:
It is essential to make lifestyle changes such as eating a healthy diet, exercising regularly, quitting smoking, and managing stress to lower cholesterol levels.
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please help thank you
A football field is a rectangle 160 ft wide and 120 ft long. The coach tells them to run from one corner to the other corner diagonally across. What is the distance?
Answer: 160.45
Step-by-step explanation:
plug in 160 for a and 120 for b and use the formula
c=[tex]\sqrt a^{2} +b^{2}[/tex]
(thats all under the sq. root sign not just a sq.
Topic 7: Tangents
For questions 19-20, determine if AB is tangent to circle C.
Based on the definition of the tangent of a circle and the Pythagorean triple of a right triangle, AB is not tangent to circle C in both question 19 and 20.
What is the Tangent of a Circle?In geometry, the tangent of a circle is a line that intersects the circle at exactly one point, which is called the point of tangency. This line is perpendicular to the radius of the circle at that point. This means that it forms a right angle at that point.
19. If AB is tangent to circle C, the lengths of the triangle ABC will form a Pythagorean triple. Let's check:
4.8² + 7.2² = 12²
74.88 = 144 [not true} Therefore, AB is not tangent to circle C.
20. Also, we will have the following:
15² + 11.2² = 6.8²
350.44 = 46.24 [not true].
AB is not tangent to circle C.
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Reasoning There are 55 vehicles in a parking lot. The frequency table
shows data about the types and colors of the vehicles. Complete a
relative frequency table to show the distribution of the data with respect to
color. Use pencil and paper. Explain why the first two numbers in each
row must add up to 100%.
Frequency Table
Type of Vehicle
Color Car Truck Total
Blue 11 14 25
Red 14 16 30
Total 25 30 55
Row Relative
Frequency Table
Type of Vehicle
Color Car Truck Total
Blue
% % 100%
Red % % 100%
Total %
% 100%
(Round to the nearest tenth as needed)
The row relative frequencies in each row sums up to 100% as they show how much part of the total event they contain in since a relative frequency indicates by what frequency a specific kind of event takes place within the total number of observations.
The row relative frequency table showing the data of the exact number of cars and trucks in their respective color is as follow,
Type of Vehicle
Color Car Truck Total
Blue 44% 56% 100%
Red 46.67% 53.33% 100%
Total 45.45% 54.55% 100%
There are 55 vehicles in a parking lot of which there are cars and trucks . The cars and trucks are either of blue or of red cars.
The frequency table showing the data of the exact number of cars and trucks in their respective color is as follow,
Type of Vehicle
Color Car Truck Total
Blue 11 14 25
Red 14 16 30
Total 25 30 55
The row relative frequency of the given data can be calculated row-wise as,
Relative frequency of row 1 of column 1 that is denoted as cars of blue color is = {( Number of blue cars) / ( Number of vehicles of blue color)}*100
= (11/ 25)*100 = 44 %
Relative frequency of row 1 of column 2 that is denoted as trucks of blue color is = {( Number of blue trucks) / ( Number of vehicles of blue color)}*100
= (14/25)*100 = 56%
Relative frequency of row 2 of column 1 that is denoted as cars of red color is = {( Number of red cars) / ( Number of vehicles of red color)}*100
= (14/30)*100 = 46.67% (approximately)
Relative frequency of row 2 of column 2 that is denoted as trucks of red color is = {( Number of red trucks) / ( Number of vehicles of red color)}*100
= (16/30)*100 = 53.33% (approximately)
Relative frequency of total blue cars with respect to total number of vehicles is = (25/55)*100 = 45.45%
Relative frequency of total red cars with respect to total number of vehicles is = (30/55)*100 = 54.55% (approximately)
A relative frequency indicates by what frequency a specific kind of event takes place within the total number of observations. Therefore the row relative frequencies in each row sums up to 100% as they show how much part of the total event they contain in.
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solve :ac all over 3c+5a
The expression ac all over 3c+5a when simplified is a * c/(3c + 5a)
Simplifying the expressionThe expression is given as
ac all over 3c+5a
So, we have
ac/(3c + 5a)
To simplify this expression, we can use the distributive property of multiplication to expand the numerator:
So, we have
ac/(3c + 5a) = a * c/(3c + 5a)
Now, we can simplify each fraction by factoring out the greatest common factor in the denominator:
ac/(3c + 5a) = a * c/(3c + 5a)
So the simplified expression is a * c/(3c + 5a)
which cannot be further simplified without additional information about the variables.
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(Please help!!!) The heights of 14 plants, in inches, are listed.
12, 14, 15, 15, 16, 16, 16, 17, 18, 18 ,19, 20, 22, 25
If another plant with a height of 13 inches is added to the data, how would the mean be impacted?
The mean would stay the same value of about 17.1 inches.
The mean would decrease in value to about 17.1 inches.
The mean would stay the same value of about 17.4 inches.
The mean would increase in value to about 17.4 inches.
As a result, the mean would be approximately **15.87** inches. The solution is **B**.
The mean would decrease in value to about 17.1 inches.
Defining Mean?The mean in mathematics is a measurement of a set of numbers' central tendency. The average is another name for it. A set of numbers are added together to determine the mean, which is then divided by the total number of values in that set.
The sum of a collection of integers divided by the total number of values in the set yields the mean of the set.
12 + 14 + 15 + 15 + 16 + 16 + 17 + 18 + 18 + 19 + 20 + 22 + 25 = **225** is the total height of the 14 plants.
Rounding to two decimal places, the mean height of these plants is 225/14, or **16.07** inches.
The revised sum of heights would be **238** if an additional plant with a height of 13 inches were to be included in the data.
238/15 = **15.87** inches (rounded to two decimal places) would be the new mean height.
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Impactation in the mean is B)The mean would decrease in value to about 17.1 inches.
Defining Mean?
The mean in mathematics is a measurement of a set of numbers' central tendency. The average is another name for it. A set of numbers are added together to determine the mean, which is then divided by the total number of values in that set.
The sum of a collection of integers divided by the total number of values in the set yields the mean of the set.
=>12 + 14 + 15 + 15 + 16 + 16 + 17 + 18 + 18 + 19 + 20 + 22 + 25 = **225** is the total height of the 14 plants.
Rounding to two decimal places, the mean height of these plants is
=> 225/14, or **16.07** inches.
The revised sum of heights would be **238** if an additional plant with a height of 13 inches were to be included in the data.
=> 238/15 = **15.87** inches (rounded to two decimal places) would be the new mean height.
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Y+5=2(x+1) what is the x and y intercepts
Answer: x-intercept is (3/2, 0), y-intercept is (0, -3)
Step-by-step explanation:
for a normal distribution, a positive value of z indicates that group of answer choices all the observations must have had positive values. the area corresponding to the z is either positive or negative. the sample mean is smaller than the population mean. the sample mean is larger than the population mean.
For a normal distribution ,a positive value of z simply means that the observation or sample mean is above the population mean this implies
none of the options provided is completely accurate.
All the observations must have had positive values,
It is not necessarily true for a positive value of z.
The value of z indicates how many standard deviations away from the mean a particular observation or sample mean is.
A positive value of z simply means that the observation or sample mean is above the population mean.
The area corresponding to the z is either positive or negative,
It is also not accurate.
The area under the normal curve corresponds to probabilities, not positive or negative values.
The area to the right of the mean corresponds to positive z-values, and the area to the left of the mean corresponds to negative z-values.
The sample mean is smaller than the population mean,
It is a possibility when the z-value is negative, indicating that the sample mean is below the population mean.
The sample mean is larger than the population mean,
It is a possibility when the z-value is positive, indicating that the sample mean is above the population mean.
Therefore, the sample mean can be either larger or smaller than the population mean depending on the direction of the z-value.
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Write a quadratic function in intercept (factored) form that passes through (-4,0), (4,0), and (−2,12).
The equation of the quadratic function is y = -x² + 16 in intercept (factored) form.
How to Write a Quadratic Function in Intercept Form?To write a quadratic function in intercept (factored) form that passes through (-4,0), (4,0), and (−2,12), we need to use the factored form of the quadratic equation:
y = a(x - r)(x - s)
where a is the leading coefficient, and r and s are the x-intercepts.
From the given points, we can see that the x-intercepts are -4 and 4, so we have:
y = a(x + 4)(x - 4)
To find the value of a, we can use the point (-2, 12) which lies on the curve. Substituting these values, we get:
12 = a(-2 + 4)(-2 - 4)
12 = a(2)(-6)
a = -1
Thus, the quadratic function in intercept (factored) form that passes through (-4,0), (4,0), and (−2,12) is:
y = -1(x + 4)(x - 4)
y = -(x²- 16)
y = -x² + 16
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Given C(2, −8), D(−6, 4), E(0, 4), U(1, −4), V(−3, 2), and W(0, 2), and that △CDE is the preimage of △UVW, represent the transformation algebraically.
Rotate triangle △C'D'E' counterclockwise by approximately -0.785 radians about the origin:
[tex]x1' = 1 \times cos(-0.785) - (-4) \times sin(-0.785) \approx 0.436[/tex]
[tex]y1' = 1 \times sin(-0.785) + (-4) \times cos(-0.785) \approx -3.678[/tex]
[tex]x2' = -7 \times cos(-0.785) - 8[/tex]
What is the coordinate of the point?The given point [tex]s C(2, -8), D(-6, 4),[/tex] and [tex]E(0, 4)[/tex] form the triangle △CDE, and the points U(1, -4), V(-3, 2), and W(0, 2) form the triangle △UVW, with △CDE being the preimage of △UVW.
To represent the transformation algebraically, we can use a combination of translations and rotations.
Translation:
To translate a point (x, y) by a vector (h, k), we add h to the x-coordinate and k to the y-coordinate of the point.
To transform triangle △CDE to triangle △UVW, we can first translate triangle △CDE by a vector (h, k) to obtain triangle △C'D'E', where C' = C + (h, k), D' = D + (h, k), and E' = E + (h, k).
Since the coordinates of C are (2, -8) and the coordinates of U are (1, -4), we can calculate the translation vector (h, k) as follows:
[tex]h = 1 - 2 = -1[/tex]
[tex]k = -4 - (-8) = 4[/tex]
So the translation vector is [tex](-1, 4).[/tex]
Rotation:
To rotate a point (x, y) by an angle θ counterclockwise about the origin, we use the following formulas:
[tex]x' = x \times \cos(\theta) - y times \sin(\theta)[/tex]
[tex]y' = x \times \sin(\theta) + y \times \cos(\theta)[/tex]
To transform triangle △C'D'E' to triangle △UVW, we can apply a rotation of angle θ counterclockwise about the origin to triangle △C'D'E', where C' = (x1', y1'), D' = (x2', y2'), and E' = (x3', y3'). Since the coordinates of C' are (2, -8) after translation, and the coordinates of U are (1, -4), we can calculate the rotation angle θ as follows:
[tex]\theta = atan2(y1' - y2', x1' - x2') - atan2(y1 - y2, x1 - x2)= atan2((-8 + 4) - (-4), (2 + 1) - (-6 + 3)) - atan2((-8) - (-4), 2 - (-6))[/tex]
Using a calculator, we can find θ to be approximately -0.785 radians.
So, the algebraic representation of the transformation that maps triangle [tex]\triangle CDE[/tex] to triangle [tex]\triangle UVW[/tex] is:
Translate triangle △CDE by the vector (-1, 4) to obtain triangle △C'D'E':
[tex]C' = (2, -8) + (-1, 4) = (1, -4)[/tex]
[tex]D' = (-6, 4) + (-1, 4) = (-7, 8)[/tex]
[tex]E' = (0, 4) + (-1, 4) = (-1, 8)[/tex]
Therefore, Rotate triangle △C'D'E' counterclockwise by approximately -0.785 radians about the origin:
[tex]x1' = 1 \times cos(-0.785) - (-4) \times sin(-0.785) \approx 0.436[/tex]
[tex]y1' = 1 \times sin(-0.785) + (-4) \times cos(-0.785) \approx -3.678[/tex]
[tex]x2' = -7 \times cos(-0.785) - 8[/tex]
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Find the perimeter of the window to the nearest tenth.
The perimeter of the window is 102.8cm²
What is the perimeter?
The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.
First, we will establish that the shape of the window is a semi-circle.
This means we must use the formula for the perimeter of a semi-circle to obtain the perimeter of the window.
The formula for the perimeter of a semi-circle is as follows:
Let the perimeter of a window or semi-circle = P
P = [ 2πr / 2 ] + 2r
Where r = radius of circle or semi-circle
From this, we will simply use the value of the radius given from the diagram in the problem and substitute it into the formula to obtain the perimeter of the window.
P = [ 2πr / 2 ] + 2r
r = 20
So,
P = [ 2π( 20 ) / 2 ] + 2( 20 )
P = 20π + 40
P = 102.83...cm²
P = 102.8cm² ( to the nearest tenth )
Therefore, the perimeter of the window is 102.8cm²
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unit 7: geometry homework 3: angle relationship and algebra
Angle relationship and algebra are closely related in geometry, as we often use algebraic expressions to represent angle measures and their ratios.
How to express the relationship between angular relations and algebra?For example, if we are given that angle A and angle B are complementary (meaning that their sum is 90 degrees), we can write an algebraic equation:
A + B = 90Similarly, if we know that angle A is three times larger than angle B, we can write:
A = 3BWe can use algebraic equations to solve for unknown angle measures or to find relationships between angles.
For example, let's say we are given that angle A is complementary to angle B, and that angle B is twice as large as angle C. We can write:
A + B = 90B = 2CWe can substitute the second equation into the first equation to get:
A + 2C = 90This equation relates the three angles A, B, and C. We can use algebra to solve for any of the unknown angles, given the measures of the others.
Therefore, algebraic equations and expressions are an important tool in understanding and analyzing angle relationships in geometry.
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Evaluate the following.
Write an exponential function of the form y = ab^x that has the given points
(−1,6 3/4), (2, 1-4)
Answer:
Step-by-step explanation:
y = abx
a is the y-intercept
y = 16bx
Now substitute 2 for x and 1296 for y
1296 = 16(b)2
81 = b2
b = 9
y = 16(9)x
1. Triangle ABC is shown with its incenter at
D. The inscribed circle's radius measures 2
units. The length of AB is 9 units. The
length of BC is 10 units. The length of AC
is 17 units.
a. What is the area of triangle AC D?
b. What is the area of triangle ABC?
a. the area of triangle ACD is 10
b. the area of triangle ABC is 12√(3)
How do we calculate?part a.
Let E be the intersection of AB and CD.
AE/EB = AC/CB = 17/10
Applying the angle bisector theorem, :
AD/DB = AC/CB = 17/10
AE/EB = AD/DB
Multiplying both sides by EB :
AE = AD*(EB/DB)
we know that AE + EB = 9,
AE = AD*(9-AD)/(DB-AD)
applying the angle bisector theorem for angle B, we can find:
BF = BD*(10-BD)/(AD-BD
DG = (AD+BD-AB)/2
CG = (AC+BC-BC)/2 = 17/2
Using the Pythagorean theorem for triangles DGC and DFC,we have :
DG^2 + CG^2 = CD^2
DF^2 + CF^2 = CD^2
AD^2*(9-AD)^2/(AD-BD)^2 + BD^2*(10-BD)^2/(BD-AD)^2 = CD^2
CD = 4
s = (AD+CD+AC)/2 = 21/2
A = √(s(s-AD)(s-CD)(s-AC))
= s√t(2152*1) = 10
b. we use Heron's formula in order to To find the area of triangle ABC,
s = (AB+BC+AC)/2 = 18
A = √t(s(s-AB)(s-BC)(s-AC))
= √(1898*1) = 12√(3)
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do students who learned english and another language simultaneously score worse on the sat critical reading exam than the general population of test takers? the mean score among all test takers on the sat critical reading exam is 501. a random sample of 100 test takers who learned english and another language simultaneously has a mean sat critical reading score of 485 with a standard deviation of 116. do these results suggest that students who learn english as well as another language simultaneously score worse on the sat critical reading exam
Therefore, while these results do suggest that there may be a difference in SAT Critical Reading scores between students who learned English and another language simultaneously and the general population, further research is needed to understand the extent and causes of this difference.
Based on the information provided, it seems that students who learned English and another language simultaneously score lower on the SAT Critical Reading exam than the general population of test takers. The mean score of the general population is 501, while the mean score of the sample of 100 test takers who learned English and another language simultaneously is 485. This is a difference of 16 points, which could be considered statistically significant.
However, it is important to note that the standard deviation of the sample is quite high at 116. This suggests that there is a lot of variability in the scores of students who learned English and another language simultaneously, which could be due to a variety of factors such as differences in language proficiency or educational background.
Therefore, while these results do suggest that there may be a difference in SAT Critical Reading scores between students who learned English and another language simultaneously and the general population, further research is needed to understand the extent and causes of this difference.
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The results do not provide sufficient evidence to suggest that students who learn English and another language simultaneously score worse on the SAT critical reading exam than the general population of test takers.
We will use the terms: mean, standard deviation, sample size, and hypothesis testing.
Mean score among all test takers: 501
Mean score of the bilingual students' sample: 485
Standard deviation of the bilingual students' sample: 116
Sample size: 100.
To determine if bilingual students score worse on the SAT critical reading exam, we will conduct a hypothesis test.
Formulate the hypotheses
Null hypothesis (H0):
Bilingual students' mean score = General population mean score
Alternative hypothesis (H1):
Bilingual students' mean score < General population mean score
Calculate the test statistic
Test statistic = (Sample mean - Population mean) / (Standard deviation / sqrt(Sample size))
Test statistic = (485 - 501) / (116 / sqrt(100))
Test statistic = -16 / 11.6
Test statistic ≈ -1.38
Determine the critical value and significance level
We'll use a one-tailed test with a significance level (α) of 0.05. Using a standard normal (Z) table, the critical value is -1.645.
Compare test statistic to critical value
Since our test statistic (-1.38) is greater than the critical value (-1.645), we fail to reject the null hypothesis.
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determine the failure rate for a 100-hr test of 11 samples, where 3 items failed at 35, 64 and 72 hrs., respectively.
The failure rate for the 100-hour test with 11 samples is 2.73%. It can be expressed as the proportion of failed samples over the total time of the test and the number of samples.
How to determine the failure rate?To determine the failure rate for a 100-hr test of 11 samples, where 3 items failed at 35, 64, and 72 hours, respectively, we can use the following formula:
Failure rate = (Number of failures / Total time of the test) * (1 / Number of samples)
Number of failures = 3
Total time of the test = 100 hours
Number of samples = 11
So, the failure rate would be:
Failure rate = (3 / 100) * (1 / 11) = 0.0273 or 2.73%
Therefore, the failure rate for this 100-hour test with 11 samples is 2.73%.
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What are the real and complex solutions of the polynomial equation? x 4 – 41 x 2 = – 400 please show work and how you got then answer
All four zeros are real solutions in the polynomial equation.
What are polynomials in equations?
A polynomial is an expression that consists of one or more variables, coefficients, and non-negative integer exponents of the variables. An equation is a mathematical statement with an equal sign between two algebraic expressions with equal values.
x⁴ – 41 x² = – 400
Adding 400 on both sides to get rid 400 from right side and set 0 on right side, we get
x⁴ - 41x² + 400 = -400 + 400
x⁴ - 41x² + 400 = 0
Factoring by product sum rule.
We need product of 400 and sum upto -41.
We can see that 400 = -25 × -16 = 400 and -25-16 = -41.
Therefore,
x⁴ - 25x² - 16x² + 400 = 0
Making it into two groups, we get
(x⁴ - 25x²) + (-16x² + 400) = 0
Factoring out GCF of each group, we get
x²(x² - 25) (x² - 16) = 0
(x² - 25) = x² - 5² = (x - 5) (x + 5)
x² - 16 = x² - 4² = (x - 4)(x + 4)
(x - 5) (x + 5) (x - 4)(x + 4) = 0
Applying zero product rule,
x-5=0
x+5=0
x-4=0 and
x+4=0.
Therefore,
x = -5, -4, 4 and 5.
All four zeros are real solutions.
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