Answer: option (a) and option (e).
Step-by-step explanation:
Answer:
(a) and (e) are correct
Step-by-step explanation:
(a) x² + (y - 3)² = 6²
(b) x² + (y - 5)² = (√6)²
(c) (x - 4)² + y² = 6²
(d) (x + 6)² + y² = 12²
(e) x² + (y + 8)² = 6²
The general equation of a circle is:
(x - a)² + (y - b)² = r², where (a, b) represents the x-y coordinates of the centre, and r represents the radius.
Hence, by process of elimination, the options that have a diameter of 12 units and therefore, a radius of 6 units, are (a), (c), and (e).
Therefore, the correct choices are (a), and (e), as (c) has a circle centre of (4,0) and does not lie on the y-axis.
An African mousebird is 2 feet tall. A camel is 4 times as tall as the mousebird. How tall is the camel in inches?
someone help me plsss
The fraction of the panel left after cutting the hole is 11/12.
The correct answer choice is option C
What is the fraction of the panel is left?Fraction left = (area of panel) - (area of hole) / (area of panel
Area of panel = 3 feet × 2 feet
= 6 square feet
Area of hole = 1 foot × ½ foot
= ½ square foot
So,
Fraction left = (area of panel) - (area of hole) / (area of panel
= (6) - (½) / (6)
= (5½) / (6)
= 11/2 ÷ 6
multiply by the reciprocal of 6
= 11/2 × 1/6
= 11/12
Ultimately, the fraction left is 11/12
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Use the graph to answer the question.
graph of polygon ABCD with vertices at 1 comma 5, 3 comma 1, 7 comma 1, 5 comma 5 and a second polygon A prime B prime C prime D prime with vertices at 8 comma 5, 10 comma 1, 14 comma 1, 12 comma 5
Determine the translation used to create the image.
7 units to the right
7 units to the left
3 units to the right
3 units to the left
The pre-image ABCD was translated into the picture A'B'C'D' by moving 7 units to the right. answer is option (a).
What is a translation transformation?A translation transformation is one in which the pre-image's size and orientation are maintained while the position of the points on the pre-image changes.
The polygon ABCD's vertices are located at these coordinates (1, 5), (3, 1), (7, 1), (5, 5)
The polygon's vertices are located at these coordinates: (8, 5), (10, 1), (14, 1), (12, 5)
where the preimage's and image's vertices are;
A(1, 5), B(3, 1), C(7, 1), D(5, 5), and A'(8, 5), B'(10, 1), C'(14, 1), D'(12, 5),
the x and y values disagree, which shows;
A' - A = (8 - 1, 5 - 5) = (7, 0)
B' - B = (10 - 3, 1 - 1) = (7, 0)
C' - C = (14 - 7, 1 - 1) = (7, 0)
D' - D = (12 - 5, 5 - 5) = (7, 0)
In view of this, the transformation employed to produce the image A'B'C'D' from the pre-image, ABCD, is a translation, 7 units to the right.
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Answer:
7 units to the right
Step-by-step explanation:
Identify the correct equation of the graph
Answer:
The correct function is
[tex]f(b) = {b}^{2} - 4[/tex]
How can I solve this math problem within 5 minutes
The equation a² + b² = c² represents the Pythagorean theorem.
What is the Pythagorean theorem?This is a theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
The Pythagorean theorem is used to find the length of one of the sides of a right-angled triangle when the lengths of the other two sides are known.
To solve the problem, you need to have at least two side lengths given. Then, you can use the equation to find the length of the third side. For example:
If you know the lengths of sides a and b and need to find the length of the hypotenuse (c):
Plug in the known values for a and b into the equation and solve for c.
Example: If a = 3 and b = 4, then 3² + 4² = c², which gives 9 + 16 = c², so c² = 25, and c = sqrt(25) = 5.
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Select the point on the number line that best approximates the location of √14
Answer:
To approximate the location of the square root of 14 on a number line, we can first find the two integers that √14 is between. We know that:
3^2 = 9 < 14 < 16 = 4^2
So √14 is between 3 and 4. We can divide the distance between 3 and 4 into equal parts and estimate the location of √14 based on where it falls in that interval.
Dividing the interval into 10 equal parts, we get:
3.0 - 3.1 - 3.2 - 3.3 - 3.4 - 3.5 - 3.6 - 3.7 - 3.8 - 3.9 - 4.0
Since √14 is closer to 3 than to 4, we can estimate its location as being closer to 3.4 than to 3.5. Therefore, a good approximation for the location of √14 on the number line is 3.7.
HELP PLSZZZZSZZZZZZZZZZ need asap
Answer:
thursday
Step-by-step explanation:
there are 7 days in a week, and the multiple of 7 closest to 100 is 14, so after 98 days, it will be a monday. 3 days after monday is thursday, which is your answer. I hope this helps!
Consider the line shown on the graph.
Enter the equation of the line in the form v = mx + b
where m is the slope and b is the y-intercept.
An equation of this line in slope-intercept form is equal to y = 2x + 7.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (7 + 1)/(0 + 4)
Slope (m) = 8/4
Slope (m) = 2
At data point (0, 7) and a slope of 2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 7 = 2(x - 0)
y - 7 = 2x
y = 2x + 7
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I need help with this please
Answer:
To find out how many more feet Peyton needs to walk to reach her goal of 10,000 steps, we can multiply the remaining number of steps by the average distance per step.
Total steps Peyton needs to reach her goal = 10,000 - 7,338 = 2,662 steps
Average distance per step = 2.5 feet
Total distance Peyton needs to cover = Total steps × Average distance per step
= 2,662 × 2.5
= 6,655 feet
Therefore, Peyton needs to walk 6,655 more feet to reach her goal of 10,000 steps.
Answer:
peyton needs to walk a total of 6655feets more
A waiter made $288 in tips after waiting on 12 tables. What was the waiter’s average tip per table?
A$24
B$13
C$15
D$16
Answer:
24
Step-by-step explanation:
Answer:
A. $24
Step-by-step explanation:
Given:
total of $288number of values is 12 tablesSolve for average tip:
Average is the same as the meanTo solve you have add up the total and divide by the total number of values288 / 12 = 24Answer:
Thus, the waiter's average tip per table is $24.
The answer is A.
7. Can the following be the lengths of the sides of a triangle?
a. 20 cm, 40 cm, 50 cm
b. 20 cm, 40 cm, 60 cm
c. 41 cm, 250 mm, 12 cm
Answer:
B
Step-by-step explanation:
THE TWO SMALLER SIDES = THE LARGER SIDE HENCE ITS A TRIANGLE
Find the logarithm
The value of the logarithm expression is Logₐ(13.3) is 2.598.
What is Logarithm?Logarithm is the exponent or power to which a base must be raised to yield a given number.
To find logₐ(13.5), we use the following techniques below
Given:
Logₐ² = 0.693Logₐ³ = 1.097But,
Logₐ(13.3) = Logₐ(27/2) = Logₐ(3³/2)Applying the law of logarithm,
Logₐ(3³/2) = Logₐ3³-Logₐ2Logₐ(3³/2) = 3Logₐ3-logₐ2........................ Equation 1Substitute the values above into equation 1
Logₐ(13.3) = 3(1.097)-0.693Logₐ(13.3) = 3.291-0.693Logₐ(13.3) = 2.598Learn more about logarithm here: https://brainly.com/question/25993029
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1 5/8x5 3/4
PLS HELP
Answer:
Answer as an improper fraction: 299/32
Answer as a mixed number: 9 11/32
Step-by-step explanation:
Change 1 5/8 and 5 3/4 to improper fractions. See image. You get
13/8 × 23/4
Multiply fractions. You do this straight across: top×top and bottom×bottom
This gives you 299/32.
Simplify if possible. This is not possible to simplify. Sometimes you need to change it back to a mixed number. See image.
299/32 is 9 11/32.
see image.
Also some calculators have a D》F and F》D button. That changes decimals to fractions and fractions to decimals.
Problem Walk-Through
Stocks A and B have the following probability distributions of expected future returns:
Probability
0.1
0.2
0.5
0.1
0.1
A
(7%)
6
14
23
31
B
(39%)
0
23
25
45
a. Calculate the expected rate of return, FB, for Stock B (A = 12.90%.) Do not round Intermediate calculations. Round your answer to two decimal places.
%
b. Calculate the standard deviation of expected returns, GA, for Stock A (08= 21.64 %.) Do not round intermediate calculations. Round your answer to two decimal places.
%
Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. Round your answer to two decimal places.
Is it possible that most investors might regard Stock B as being less risky than Stock A?
I. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
II. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
III. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
IV. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
V. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
-Select-
c. Assume the risk-free rate is 1.5%. What are the Sharpe ratios for Stocks A and B? Do riot round intermediate calculations. Round your answers to four decimal places.
Stock A:
Stock B:
Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?
I. In a stand-alone risk sense A is less risky than B. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and
hence be more risky in a portfolio sense.
II. In a stand-alone risk sense A is more risky than B. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and
hence be less risky in a portfolio sense.
A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market than Stock A.
What is Expeced return?The profit or loss an investor can anticipate realising from an investment is known as the expected return. Calculating an expected return involves multiplying possible outcomes by their likelihood before adding the results. The expected return is computed by summing the results of multiplying all possible outcomes by the likelihood that each one will occur (as illustrated below).
Expeced return=Sum(probability*return)
Standard Deviation=[tex]\sqrt{sum(probability*(return-expected\ return)^2}[/tex]
Coefficient of Variation=Standard Deviation/Expected Return
1. Expected Returns:
Stock B=0.1*(-38%)+0.2*0%+0.5*21%+0.1*26%+0.1*36%=12.900%
2. Standard Deviation:
Stock A=[tex]\sqrt{(0.1*(-11\%-11.3\%)^2+0.2*(5\%-11.3\% +0.5*(13\%-11.3\%)^2+)^2 0.1*(18\%-11.3\%)^2} \\+0.1*(31\%-11.3\%)^2)[/tex]
= 10.120%
3. Coefficient of Variation:
Stock B=19.892%/12.9%=1.5420
4. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio if it has a lower correlation to the market
than Stock A.
5. Sharpe Ratio:
Stock A=(11.3%-3.5%)/10.120%=0.7708
Stock B=(12.9%-3.5%)/19.892%=0.4726
6. A is riskier than B in terms of pure risk. Stock B may have a lower beta than Stock A and so be less hazardous in the context of a portfolio
if it has a lower correlation to the market than Stock A.
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On a standardized test with a normal distribution, the mean was 64.3 and the standard deviation was 5.4.
Approximately what percent of those taking this exam had scores between 58.9 and 69.7?
Responses
A 68.3%
B 38.2%
C 60.0%
D 34.1%
The percent of those taking this exam had scores between 58.9 and 69.7 is 34.1%
What is standardized test?To find the number of standard deviations 58.9 and 69.7 are above and below the mean, find the difference between these two numbers and the mean, then divide by the standard deviation 5.4:
z1 = (58.9 - 64.3) / 5.4 = -0.996
z2 = (69.7 - 64.3) / 5.4 = 1.004
Since the absolute values of the z-scores are almost equal, we can approximate the area between them as half of the total area between -1 and 1 standard deviations.
Therefore, the approximate percentage of those taking the exam with scores between 58.9 and 69.7 is:
68% / 2 = 34%
Therefore, the correct option is D 34.1%.
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Round your answer to the nearest tenth of a degree
Answer:
57.8°
Step-by-step explanation:
SohCahToa
use sin^1 to get angle
sin^1(11/13)=57.7957725
to the nearest tenth=57.8°
hat is the volume of the cylinder below if it has a height of 22 yards and diameter of 8 yards? (Use 3.14 for)
Cylinder
1408.0 yd
1105.3 yd
4423.3 yd
2211.7 yd
A boat traveled 350 miles each way downstream and back. The trip downstream took 14 hours.
The trip back took 70 hours. What is the speed of the boat in still water? What is the speed of
the current?
Answer:
The speed of the boat in still water is 15 mi/hr while the speed of the current is 10 mi/hr.
Step-by-step explanation:
Given: d = 350 miles
[tex]t_{ds}[/tex] = 14 hours
[tex]t_{us}[/tex] = 70 hours
Asked: Speed of the boat [tex]V_b[/tex] in still water and speed of the current [tex]V_c[/tex]
Solve:
Note that when the boat is going downstream, the current is helping the boat to speed up and when the boat is going upstream, the current is slowing it down.
Get the speed downstream
[tex]V_{ds} = V_b + V_c[/tex]
350mi/14hrs = [tex]V_b + V_c[/tex]
25 mi/hr = [tex]V_b + V_c[/tex]
Transpose to get the value of Vb
25 mi/hr - Vc = Vb ---equation 1
Get the speed upstream
[tex]V_{us} = V_b - V_c[/tex]
350mi/70hrs = Vb - Vc
5 mi/hr = Vb - Vc
Transpose to get the value of Vb
5 mi/hr + Vc = Vb ----equation 2
Equate equations 1 and 2
25 mi/hr - Vc = 5 mi/hr + Vc
Transpose
25 mi/hr - 5 mi/hr = Vc + Vc
20 mi/hr = 2 Vc
Divide both sides of the equation by 2
10 mi/hr = Vc
Vc = 10 mi/hr
From 25 mi/hr = [tex]V_b + V_c[/tex] we then solve the speed of the boat
25 mi/hr = Vb + 10 mi/hr
25 mi/hr - 10 mi/hr = Vb
15 mi/hr = Vb
Vb = 15 mi/hr
If <2 is equivalent to (2x-8)• what is the value of c?
A 62•
B 35•
C 28•
D 18•
Reason:
[tex]\angle 1 = 62^{\circ}[/tex] because of the vertical angles theorem.
Then angle 1 and angle 2 add to 90 degrees (the angles are complementary).
[tex]\angle 1 + \angle 2 = 90\\\\62 + (2x-8) = 90\\\\2x + 54 = 90\\\\2x = 90 - 54\\\\2x = 36\\\\x = 36/2\\\\x = 18\\\\[/tex]
Alexandra is a head librarian in a city with a population of 1.8×106 residents. When her library system conducted a survey, they found that the average resident visits a library 1.5 times per year. How many total library visits per year does that work out to?
Write your answer in standard form. Do not use exponents. THE ANSWER IS 2,700,000 YOUR WELCOME...
The total number of library visits per year is 2.7 million, written in standard form as 2.7×106.
What is average?Average refers to the central tendency or typical value of a set of numerical data, which is obtained by dividing the sum of the values by the total number of values. It is a commonly used statistical measure that helps to represent the general trend or level of a dataset. The average can be calculated for various types of data, such as income, age, weight, and test scores, among others.
According to the given information:
To calculate the total number of library visits per year, we need to multiply the average number of visits per resident by the total population:
Total number of library visits per year = average visits per resident x total population
Substituting the given values, we get:
Total number of library visits per year = 1.5 x 1.8×106
Multiplying, we get:
Total number of library visits per year = 2.7×106
Therefore, the total number of library visits per year is 2.7 million, written in standard form as 2.7×106.
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solve the equation x^2+4x-11=0 by completing the square
To solve the equation x^2 + 4x - 11 = 0 by completing the square, we can follow these steps:
Move the constant term to the right side of the equation:
x^2 + 4x = 11
Complete the square by adding the square of half the coefficient of x to both sides of the equation:
x^2 + 4x + (4/2)^2 = 11 + (4/2)^2
Simplifying the left side:
x^2 + 4x + 4 = 11 + 4
Factor the perfect square on the left side of the equation:
(x + 2)^2 = 15
Take the square root of both sides of the equation:
x + 2 = ±√15
Solve for x by subtracting 2 from both sides:
x = -2 ± √15
Therefore, the solutions to the equation x^2 + 4x - 11 = 0 by completing the square are x = -2 + √15 and x = -2 - √15.
find the factors to this polynomials i need help SHOW YOUR WORK.
Answer:
hope this will help you...
Larry Mitchell invested part of his $20,000 advance at 3% annual simple interest and the rest at 6% annual simple interest. If his total yearly interest from both accounts was $990, find the amount invested at each rate.
Larry Mitchell invested $ [tex]7000[/tex] at [tex]3[/tex]% annual simple interest and $[tex]13000[/tex] at [tex]6[/tex]% annual simple interest.
What is the annual simple interest?Let's denote the amount Larry Mitchell invested at 3% annual simple interest as "x" (in dollars) and the amount he invested at 6% annual simple interest as [tex]"20,000 - x"[/tex] (since he invested the rest of the advance amount).
The formula for simple interest is:
Simple Interest (SI) = Principal (P) * Rate (R) * Time (T)
Given that the total yearly interest from both accounts was $990, we can set up the following equation:
3% of x + 6% of [tex](20,000 - x) = 990[/tex]
Converting the percentages to decimals, we get:
[tex]0.03x + 0.06(20,000 - x) = 990[/tex]
Now, we can solve for x by simplifying the equation and isolating x on one side:
[tex]0.03x + 1200 - 0.06x = 990[/tex]
[tex]-0.03x = 990 - 1200[/tex]
[tex]-0.03x = -210[/tex]
Dividing both sides by -0.03, we get:
x = (-210)/(-0.03)
[tex]x = 7000[/tex]
So, Larry Mitchell invested $7000 at 3% annual simple interest.
Substituting the value of x back into the equation, we can find the amount he invested at 6% annual simple interest:
[tex]20,000 - x = 20,000 - 7000 = 13000[/tex]
Therefore, Larry Mitchell invested $ [tex]7000[/tex] at [tex]3[/tex]% annual simple interest and $[tex]13000[/tex] at [tex]6[/tex]% annual simple interest.
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If P(A)=0.3, P(B)=0.2 and P(A∩B)=0.2 determine the following probabilities:
(a) P(A')
(b) P(A∪B)
(c) P(A'∩B)
(d) P(A∩B')
(e) P[(A∪B)']
The probabilities are as follows:
(a) P(A')= 0.7
(b) P(A∪B) = 0.3
(c) P(A'∩B) = 0
(d) P(A∩B') = 0.1
(e) P[(A∪B)'] = 0.7
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
(a) P(A') = 1 - P(A) = 1 - 0.3 = 0.7
(b) P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.2 - 0.2 = 0.3
(c) P(A'∩B) = P(B) - P(A∩B) = 0.2 - 0.2 = 0
(d) P(A∩B') = P(A) - P(A∩B) = 0.3 - 0.2 = 0.1
(e) P[(A∪B)'] = 1 - P(A∪B) = 1 - 0.3 = 0.7
Note: P(A) represents the probability of event A occurring, P(B) represents the probability of event B occurring, and P(A∩B) represents the probability of both events A and B occurring simultaneously. The symbol '∪' represents the union of two events, and the symbol '∩' represents the intersection of two events. The complement of an event A is represented by A'.
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Help with math problems
1. The solution to the system of equations is v = -3 and w = 4.
2. The solution to the system of equations is y = 6 and z = -2.
How to solve for -v + w = 7; v + w = 1?To eliminate v, we can add the two equations:
(-v + w) + (v + w) = 7 + 1
2w = 8
w = 4
Substitute w = 4 into one of the equations to solve for v:
v + 4 = 1
v = -3
How to solve for y + z = 4; y - z = 8?To eliminate z, we can add the two equations:
(y + z) + (y - z) = 4 + 8
2y = 12
y = 6
Substitute y = 6 into one of the equations to solve for z:
6 + z = 4
z = -2.
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Malachi asks students in his class, "How long does it take you to get to school?" The histogram shows the data. Which statement best describes the distribution?
The data from the distribution shows a symmetric distribution.
When is the data from a distribution symmetric?The data from a distribution can be described as symmetric when the values of the data are evenly distributed around its center point. This mans that if the data is folded along its center point and the two halves overlap perfectly, then the distribution is said to be symmetric.
In the histogram, we see an example of symmetric data because the center value that has the frequency of 10 ahs even distribution on both sides.
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Find the area, to the nearest thousandth, of the indicated region of the standard normal distribution. The region where z >1.42
The area to the right of [tex]1.42[/tex] in the standard normal distribution is approximately [tex]0.0793[/tex] .
What is the standard normal distribution?The region where [tex]z > 1.42[/tex] in the standard normal distribution corresponds to the area under the curve to the right of [tex]1.42[/tex] on the z-axis.
To find this area, we can use a standard normal distribution table or a calculator with a cumulative distribution function (CDF) for the standard normal distribution.
Using a calculator with a CDF for the standard normal distribution, we can input 1.42 and calculate the area to the left of 1.42. Then, we subtract this area from 1 to get the area to the right of 1.42. Here's the calculation:
[tex]P(Z > 1.42) = 1 - P(Z < 1.42)[/tex]
Using a standard normal distribution table or a calculator, we find that [tex]P(Z < 1.42)[/tex] is approximately 0.9207. Subtracting this value from 1, we get:
[tex]P(Z > 1.42) \approx 1 - 0.9207 \approx 0.0793[/tex]
Therefore, the area to the right of [tex]1.42[/tex] in the standard normal distribution is approximately [tex]0.0793[/tex].
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[4x2+(5+1)]÷2 can I please get help :)
he solution to the system of equations shown is (2, 0).
3x − 2y = 6
x + 4y = 2
When the first equation is multiplied by 2, the sum of the two equations is equivalent to 7x = 14
.
Which system of equations will also have a solution of (2, 0)?
Answer:
Multiplying the first equation by 2, we get:
6x - 4y = 12
Adding the second equation, we get:
6x - 4y + x + 4y = 2 + 12
Simplifying, we get:
7x = 14
This is the same equation given in the problem statement. So any system of equations that has this equation and the second equation will also have the solution (2, 0). For example:
3x - 2y = 6
7x = 14
Helppppppppppppppppppppp
