The statements that would be true if the length of each side of the square increased by one unit is that the area of the square would be a rational number and the area of the square would be a perfect square.
What is a perfect square?A perfect square is defined as the number that can be expressed as the product of two equal integers.
The area of the square given = 400
The sides of the square = 20
When an additional unit is added= 21
The new area = 441
This is a perfect square and equally a rational number because it's a real number.
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The Bureau of Labor Statistics generally uses 90% confidence levels in its reports. One
report gives a 90% confidence interval for the mean hourly earnings of American workers in
2000 as $15.49 to $16.11. If the null hypothesis states that the mean hourly earnings of all
workers in 2000 was $16.15, would this hypothesis be rejected in a two-tailed test if a = .10?
What about a null hypothesis stating that the mean was $15.50? Explain your reasoning.
For a two-tailed test with a 90% confidence interval and a significance level of 0.10, the null hypothesis of $16.15 would be rejected, but the null hypothesis of $15.50 would not be rejected.
How to check if null hypothesis will be rejected?Identify the given information, including confidence level, confidence interval, null hypothesis, and significance level (alpha).Check if the null hypothesis values fall within the confidence interval.If the null hypothesis values fall within the confidence interval, we do not have enough evidence to reject the null hypotheses at the given significance level.If the null hypothesis values fall outside the confidence interval, we have enough evidence to reject the null hypotheses at the given significance level.Consider the significance level (alpha) to determine the level of significance for rejecting the null hypotheses.Conclude whether the null hypotheses should be rejected or not at the given significance level.Given:
Confidence level: 90%
Confidence interval for American employees' mean hourly wages in 2000: $15.49 to $16.11
Null hypothesis 1: Mean hourly earnings of all workers in 2000 was $16.15
Null hypothesis 2: Mean hourly earnings of all workers in 2000 was $15.50
Significance level (alpha): 0.10
For a two-tailed test with a 90% confidence interval and a significance level (alpha) of 0.10:
Null hypothesis 1:
In this case, since the null hypothesis value of $16.15 falls outside the confidence interval of $15.49 to $16.11, we would have enough evidence to reject the null hypothesis at the given significance level of 0.10. This means that we can reject the null hypothesis and conclude that the mean hourly earnings of all workers in 2000 is significantly different from $16.15.
Null Hypothesis 2:
In this case, since the null hypothesis value of $15.50 falls within the confidence interval of $15.49 to $16.11, we do not have enough evidence to reject the null hypothesis at the given significance level of 0.10. This means that we would not reject the null hypothesis and cannot conclude that the mean hourly earnings of all workers in 2000 is significantly different from $15.50.
Thus, the null hypothesis stating that the mean hourly earnings of all workers in 2000 is $16.15 would be rejected, while the null hypothesis stating that the mean hourly earnings of all workers in 2000 is $15.50 would not be rejected, based on a two-tailed test with a 90% confidence interval and a significance level of 0.10.
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Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
n = 130, x = 69; 90% confidence
0.458 < p < 0.604
0.463 < p < 0.599
0.459 < p < 0.603
0.461 < p < 0.601
The confidence interval for the population proportion is 0.458 < p < 0.604, with an error in the upper bound due to rounding.
Option A is correct
How do we calculate?The formula for calculating a confidence interval for a population proportion is:
p ± z*√[(p(1-p))/n]
Given information:
the sample size is n = 130,
the sample proportion is x/n = 69/130 = 0.531, and
the desired level of confidence is 90%.
The critical value for a 90% confidence interval is z* = 1.645.
Substituting the values into the formula, we have :
p ± z*√[(p(1-p))/n]
0.531 ± 1.645√[(0.531(1-0.531))/130]
0.531 ± 0.080
In conclusion, the 90% confidence interval for the population proportion is:
0.531 - 0.080 < p < 0.531 + 0.080
0.451 < p < 0.611
we then round off to 3 decimal places:
0.458 < p < 0.614
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A Ferris wheel is 21 meters in diameter and completes 1 full revolution in 12 minutes.
A Ferris wheel is 21 meters in diameter and boarded from a platform that is 1 meter above the ground.
The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1
full revolution in 12 minutes. The function h (t) gives a person's height in meters above the ground t
minutes after the wheel begins to turn.
Part A: I need to find the amplitude, midline, and period of h(t).
Part B: Assume the person had just boarded the Ferris wheel from the platform and that the Ferris wheel starts spinning at time t=0. Find a formula for the height function h(t).
Part C: If the Ferris wheel continues to turn, how high off the ground is a person after 33 minutes?
The person is approximately 10.68 meters above the ground after 33 minutes.
Part A:
The amplitude of h(t) is half the vertical distance between the highest and lowest points on the Ferris wheel. The highest point occurs when the person is at the top of the wheel, which is 21/2 = 10.5 meters above the midline. The lowest point occurs when the person is at the bottom of the wheel, which is 1 meter above the midline. Therefore, the amplitude is [tex]10.5 - 1 = 9.5[/tex] meters.
The midline of h(t) is the average of the highest and lowest points, which is [tex](10.5 + 1)/2 = 5.75[/tex] meters.
The period of h(t) is the time it takes for one complete revolution of the Ferris wheel, which is 12 minutes.
Part B:
The height function h(t) can be modeled by a sinusoidal function of the form:
h(t) = A sin(B(t - C)) + D
where A is the amplitude, B is the frequency (in radians per minute), C is the phase shift (in minutes), and D is the midline.
Using the values from Part A, we have:
A = 9.5
D = 5.75
The frequency can be found by dividing 2π by the period:
[tex]B = 2\pi /12 = \pi /6[/tex]
The phase shift is the time it takes for the Ferris wheel to complete one-quarter of a revolution from the starting position (at t=0), which is 3 minutes. Therefore, C = 3.
Putting it all together, the formula for the height function is:
[tex]h(t) = 9.5 sin(\pi /6 (t - 3)) + 5.75[/tex]
Part C:
To find the height of a person after 33 minutes, we simply substitute t = 33 into the height function:
h(33) = 9.5 sin(π/6 (33 - 3)) + 5.75
≈ 10.68 meters
Therefore, the person is approximately 10.68 meters above the ground after 33 minutes.
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Office Innovations LLC is aiming for a net profit of $1,500,000 on its new desk top mini-shredder. The fixed costs for the production are $984,000 while variable costs are $14.50 per unit. The estimated unit sales are 480,000 units. What selling price should the company try in dollars? Round to the nearest hundredth.
The selling price that the company should aim for to achieve a net profit of $1,500,000 is $19.67 per unit.
Define Selling PriceSelling price refers to the amount at which a product or service is offered for sale to the customer. It is the price that the customer pays to purchase the product or service from the seller.
To calculate the selling price for the mini-shredder that will achieve a net profit of $1,500,000, we can use the following formula:
Selling Price = (Total Fixed Costs + Total Variable Costs + Desired Profit) / Number of Units Sold
where:
Total Fixed Costs = $984,000
Variable Costs per unit = $14.50
Number of Units Sold = 480,000
Desired Profit = $1,500,000
Plugging in the given values, we get:
Selling Price = (984,000 + (14.50 x 480,000) + 1,500,000) / 480,000
Selling Price = (984,000 + 6,960,000 + 1,500,000) / 480,000
Selling Price = 9,444,000 / 480,000
Selling Price = $19.67
Therefore, the selling price that the company should aim for to achieve a net profit of $1,500,000 is $19.67 per unit.
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Which of the following is a rational function?
O O O
A. F(x)= x-x² +8
OB. F(x) = -7x+15
O C. F(x)=
xả +5x-6
3x
OD. F(x)=√√2x-1+9
Out of the given options, option C is a rational function because it can be expressed as the ratio of two polynomial functions:
F(x) = (x² + 5x - 6) / 3x
What is rational function?A function that is the ratio of polynomials is referred to as rational. When a function of one variable, x, can be written as f (x) = p (x)/q (x), where p (x) and q (x) are polynomials with q (x) 0, the function is said to be rational.
A rational function is a function that can be expressed as the ratio of two polynomial functions, where the denominator is not equal to zero.
Out of the given options, option C is a rational function because it can be expressed as the ratio of two polynomial functions:
F(x) = (x² + 5x - 6) / 3x
The numerator of the function is a polynomial of degree 2 and the denominator is a polynomial of degree 1, so it satisfies the definition of a rational function.
Option A and B are not rational functions because they cannot be expressed as the ratio of two polynomial functions.
Option D is also not a rational function because it contains a square root function, which is not a polynomial function.
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In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student chosen randomly from the class plays neither a sport nor an instrument? Plays an instrument Does not play an instrument Plays a sport 3 2 Does not play a sport 7 15
Answer:
play an instrument and a sport: 2
play an instrument but does not play a sport: 8
does not play an instrument but plays a sport: 10
does not play an instrument or a sport: 4
BRAINLIEST to whoever shows work
The value of side BC of square is [tex]13{\sqrt{2}[/tex] and the value of x through which the relation is satisfied x = 7 .
What about square ?
A square is a regular quadrilateral with all four sides of equal length and all four angles of equal measure (i.e., 90 degrees). It can be thought of as a special case of a rectangle, where all four sides are equal in length.
The properties of a square include:
- All four sides are equal in length.
- All four angles are right angles (i.e., 90 degrees).
- Opposite sides are parallel and congruent.
- Diagonals bisect each other at right angles.
- The diagonals of a square are congruent.
According to the given information:
For (18) as we know all sides of square are equal
Hence AB = BC = X
[tex]x^{2} + x^{2} = 26^{2} \\\\2x^{2} = 26^{2} \\\\x = 13\sqrt{2}[/tex]
BC = [tex]13\sqrt{2}[/tex]
In the same way the diagonal bisect the angle of triangle so, m ∠BCE =
m ∠CBE and m ∠BEC = 90 degree.
[tex](11x - 32) + (11x - 32) + 90 = 180\\\\2(11x -32) = 90 \\\\11x -32 = 45\\\\x = 7[/tex]
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The degree of one polynomial is m. The degree of a second polynomial is n. the two polynomials are multiplied together. what is the degree of the resulting polynomial? Explain.
Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.
What is polynomial?A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.
Here,
When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.
This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.
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This is about scatter plots and association i just need number 1
The form of association that would be found in the variables would be:
Positive association No association Negative association How to find the association ?As the number of hours spent playing a video game increases, the player is likely to reach higher levels within the game. So positive association.
The number of letters in a person's name and the last digit of their phone number are likely to be unrelated and randomly distributed. There is no association.
As the temperature of the drink decreases, the number of ice cubes in the drink is likely to increase, and vice versa. This is therefore negative association.
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How do I do 2,000,001 divided by 9
2,000,001 divided by 9 is 222,222 with a remainder of 3, which can be expressed as 222,222 R 3. This result can be verified by multiplying the quotient (222,222) by 9 and adding the remainder (3). The total is equal to the dividend (2,000,001)
What is number?Number is a mathematical concept used to quantify a group of objects or to measure a physical quantity. It can be used to count, measure, label, order, or compare items. It is also used to describe relationships between objects, to perform calculations, and to compare values. Numbers are used in almost all aspects of life, from counting money and measuring meals to calculating distances and constructing buildings.
To divide 2,000,001 by 9, we can use the long division method.
First, we divide the number 2,000,001 into groups of 9.
2,000,001 ÷ 9
2 | 222,222
Next, we divide the first group of 9 into 9.
2 | 222,222
2 | 24,691
Next, we subtract the first group of 9 (2) from the first group of 9 (2) and bring down the next group of 9 (222,222).
2 | 222,222
2 | 24,691
-2
0 | 222,220
Now, we divide the second group of 9 (222,220) into 9.
0 | 222,220
0 | 24,691
Next, we subtract the first group of 9 (0) from the second group of 9 (0) and bring down the next group of 9 (24,691).
0 | 222,220
0 | 24,691
-0
0 | 24,691
Now, we divide the third group of 9 (24,691) into 9.
0 | 24,691
0 | 2,743
Next, we subtract the first group of 9 (0) from the third group of 9 (0) and bring down the next group of 9 (2,743).
0 | 24,691
0 | 2,743
-0
0 | 2,743
Now, we divide the fourth group of 9 (2,743) into 9.
0 | 2,743
0 | 305
Next, we subtract the first group of 9 (0) from the fourth group of 9 (0) and bring down the next group of 9 (305).
0 | 2,743
0 | 305
-0
0 | 305
Now, we divide the fifth group of 9 (305) into 9.
0 | 305
0 | 34
Next, we subtract the first group of 9 (0) from the fifth group of 9 (0) and bring down the next group of 9 (34).
0 | 305
0 | 34
-0
0 | 34
Finally, we divide the sixth group of 9 (34) into 9.
0 | 34
0 | 3
We can conclude that 2,000,001 divided by 9 is 222,222 with a remainder of 3.
In conclusion, 2,000,001 divided by 9 is 222,222 with a remainder of 3, which can be expressed as 222,222 R 3. This result can be verified by multiplying the quotient (222,222) by 9 and adding the remainder (3). The total is equal to the dividend (2,000,001).
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complete questions as follows-
How do I do 2,000,001 divided by 9?
In the diagram below of circle O, chords AD and BC intersect at E, and chords AB and CD are drawn.
Which statement must always be true?
PLEASE HELP!
The correct answer is (C) [tex]\angle B \cong \angle C.[/tex] when In the diagram below of circle O, chords AD and BC intersect at E.
What is a circle ?
A circle is a two-dimensional geometric shape that consists of all the points in a plane that are at a fixed distance from a given point, called the center.
In the given diagram, we have a circle O with chords AB, CD, AD, and BC. The chords AD and BC intersect at point E.
Based on the diagram, we can see that the opposite angles in the quadrilateral AEDC are supplementary (i.e., they add up to 180 degrees). Therefore, we have:
[tex]\angle A + \angle C = 180^\circ[/tex]
Similarly, the opposite angles in the quadrilateral BEFC are supplementary. Thus,
[tex]\angle B + \angle C = 180^\circ[/tex]
We can rewrite the second equation as:
[tex]\angle C = 180^\circ - \angle B[/tex]
Substituting this value of \angle C into the first equation, we get:
[tex]\angle A + 180^\circ - \angle B = 180^\circ[/tex]
Simplifying, we get:
[tex]\angle A = \angle B[/tex]
Therefore, the correct answer is (C) [tex]\angle B \cong \angle C.[/tex]
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how do I do 10% of 8,000
Answer:
800
Step-by-step explanation:
10% = 0.1
8000 · 0.1 = 800
So, 10% of 8000 is 800
A ball is hit straight up in the air from a certain height from the ground. The height of the ball from the ground, H (t), in feet, as a function of time, t, in seconds, can be modeled by the equation shown
H(t)=-4t^2+16t+1
Select all true statements
The ball reaches the maximum height at t- 1 seconds
The ball reaches the maximum height at t- 2 seconds
The maximum height reached by the ball is 13 feet from the ground
The maximum height reached by the ball is 17 feet from the ground.
The ball is hit straight up in the air from 1 feet height from the ground
The ball is hit straight up in the air from 4 feet height from the ground
The true statements are:The ball reaches the maximum height at t = 2 seconds.The maximum height reached by the ball is 17 feet from the ground.The ball is hit straight up in the air from 1 feet height from the ground.
How to deal with moving object?To find the maximum height reached by the ball, we need to find the vertex of the parabolic function, which occurs at[tex]t = \frac{-b}{2a} = \frac{-16}{2*8} = 2[/tex]
So, the ball reaches the maximum height at t = 2 seconds.To find the maximum height, we substitute t = 2 in the given equation:
[tex]H(2) = -4(2)^2 + 16(2) + 1 = 17[/tex]
So, the maximum height reached by the ball is 17 feet from the ground.Therefore, the true statements are:The ball reaches the maximum height at t = 2 seconds.The maximum height reached by the ball is 17 feet from the ground.The ball is hit straight up in the air from 1 feet height from the ground.
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Solve the system
y = x^2 + 2x - 2
y = x + 10
Answer:
x1 = -4,
y1 = 6,
x2 = 3,
y2 = 13
Step-by-step explanation:
{y = x^2 + 2x - 2,
{y = x + 10;
Since both equations are equal to y, they are equal to one another aswell:
[tex] {x}^{2} + 2x - 2 = x + 10[/tex]
Collect like-terms:
[tex] {x}^{2} + x - 12 = 0[/tex]
a = 1, b = 1, c = -12
Let's solve this quadratic equation:
[tex]d = {b}^{2} - 4ac = {1}^{2} - 4 \times 1 \times ( - 12) = 1 + 48 = 49 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{ - 1 - 7}{2 \times 1} = \frac{ - 8}{2} = - 4[/tex]
[tex]x2 = \frac{ - b + \sqrt{d} }{2a} = \frac{ - 1 + 7}{2 \times 1} = \frac{6}{2} = 3[/tex]
{x1 = -4,
{y1 = -4 + 10 = 6;
{x2 = 3,
{y2 = 3 + 10 = 13
Answer:
(- 4, 6 ) , (3, 13 )
Step-by-step explanation:
y = x² + 2x - 2 → (1)
y = x + 10 → (2)
substitute y = x² + 2x - 2 into (2)
x² + 2x - 2 = x + 10 ← subtract x + 10 from both sides
x² + x - 12 = 0 ← in standard form
(x + 4)(x - 3) = 0 ← in factored form
equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 3 = 0 ⇒ x = 3
substitute these values into (2) for corresponding values of y
x = - 4 : y = - 4 + 10 = 6 ⇒ (- 4, 6 )
x = 3 : y = 3 + 10 = 13 ⇒ (3, 13 )
Solve this equation
2v+18=16-4(v+7)
Answer:
v = -5
Step-by-step explanation:
Answer:
2v + 18 = 16 - 4(v+7)
2v +18 = 16 -4v -28
6v = -30
v = -5
Hope this answers your question :)
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What is the probability that the total of two dice is greater than 9, given that the first die is a 5? Give your answer as a fraction in simplest form.
Let A = first die is 5
Let B = total of two dice is greater than 9
[tex]\text{P(A)}= \dfrac{1}{6}[/tex]
Possible outcomes for A and B : {(5,5), (5,6)}
[tex]\text{P(A and B)}=\dfrac{2}{36} =\dfrac{1}{18}[/tex]
[tex]\text{P}\text{(B}|\text{A})=\dfrac{\text{P}(\text{A}\cap \text{B})}{\text{P(A)}}[/tex]
[tex]=\dfrac{1}{18} \times6= \dfrac{1}{3}[/tex]
With the info, solve for m
Answer:35 or 115
Step-by-step explanation
combine like terms
Which expression is equivalent to 65x0.15
Since I didn't see any options : 6.5 × 1.5
The equivalent value of the expression is A = ( 65 x 0.1 ) + ( 65 x 0.05 )
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
A = 65 x 0.15
From the distributive property , we get
A = 65 x ( 0.1 + 0.05 )
On simplifying , we get
A = ( 65 x 0.1 ) + ( 65 x 0.05 )
Hence , the expression is A = ( 65 x 0.1 ) + ( 65 x 0.05 )
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The complete question is attached below :
Which expression is equivalent to 65x0.15
Which unit of measurement is part of the metric system?
O quart
O kilogram
O foot
O pound
Answer:
2. kilograms
Step-by-step explanation:
Find the surface area of the cone in terms of π.
180π cm2
108π cm2
144π cm2
90π cm2
Answer:
[tex]54\pi \: {cm}^{2} [/tex]
Step-by-step explanation:
Given:
A cone
l = 15 cm
r (radius) = 3 cm
Find: A (surface area) - ?
[tex]a(surface) = \pi {r}^{2} + \pi \times r \times l[/tex]
[tex]a(surface) = \pi \times {3}^{2} + \pi \times 3 \times 15 = 9\pi + 45\pi = 54\pi \: {cm}^{2} [/tex]
Need help with these please I would really appreciate it!
2. Walter received $83220 from the sale.. from the stated percentage.
3. He made $657.50 in commission
4. The seller received $3780 from the sale.
5. The store received $738.
6. The rancher received $30080 from the sale.
7. Miss Coffey received $1178 from the sale.
Sales commissions calculations.2. The real estate agent's commission is 5% of the sale price, which is 0.05 x $87600 = $4380.
Therefore, Walter received $87600 - $4380 = $83220 from the sale.
3. The salesman's commission is 12.5% of the total sales, which is 0.125 x $5260 = $657.50.
Therefore, he made $657.50 in commission.
4. The real estate agent's commission is 10% of the sale price, which is 0.1 x $4200 = $420.
Therefore, the seller received $4200 - $420 = $3780 from the sale.
5. The total sales for the stoves and radios is $345 x 2 + $65 x 2 = $820. The sales clerk's commission is 10% of the total sales, which is 0.1 x $820 = $82.
Therefore, the store received $820 - $82 = $738.
6. The commission house's commission is 6% of the sale price, which is 0.06 x $32000 = $1920.
Therefore, the rancher received $32000 - $1920 = $30080 from the sale.
7. The auctioneer's commission is 5% of the sale price, which is 0.05 x $1240 = $62.
Therefore, Miss Coffey received $1240 - $62 = $1178 from the sale.
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I also need help with this one if do then thank you a lot
3 is the Value of x and A = 38° , B = 44°, C = 25° , D = 54° , E = 34° , G = 39° are angles in the polygon .
Describe polygons using an example?
Any two-dimensional object formed by a series of straight lines is referred to as a polygon. Some examples of polygons are triangles, hexagons, pentagons, and quadrilaterals.
Any object that is constructed in two dimensions using straight lines is called a polygon. Polygons include shapes like hexagons, triangles, pentagons, and quadrilaterals. The number of sides of the form is indicated by the name. As an illustration, a triangle has three sides while a quadrilateral has four.
in polygon,
no = 7
= 7 * 180
= 1260
(n-2)x180 = 1260
n = 9
A = x + 29 = 9 + 29 = 38
B = X + 35 = 9 + 35 = 44
C = x + 16 = 9 + 16 = 25
D = x + 20 = 9 + 20 = 25
E = x + 45 = 9 + 45 = 54
F = X + 25 = 9 + 25 = 34
G = X + 30 = 9 + 30 = 39
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Here are 6 celebrities with some of the highest net worths (in millions of dollars) in a recent year: George Lucas (5500).
Steven Spielberg (3700), Oprah Winfrey (3200), Paul McCartney (1200), J. K. Rowling (1000), and Jerry Seinfeld (950)
Find the range, variance, and standard deviation for the sample data. What do the results tell us about the
population of all celebrities? Based on the nature of the amounts, what can be inferred about their precision?
What do the results tell us about the population of all the celebrities?
The range of this data set is quite large, ranging from $950 million to $5.5 billion.
Find the range, variance, and standard deviation for the sample data. What do the results tell us about the
population of all celebrities? Based on the nature of the amounts, what can be inferred about their precision?
What do the results tell us about the population of all the celebrities?
To find the range, variance, and standard deviation for this sample data, we can use the following formulas:
Range = maximum value - minimum value
Variance = sum of (each value minus the mean) squared, divided by the sample size
Standard deviation = the square root of the variance
Using these formulas, we can calculate the following:
[tex]Range = 5500 - 950 = 4550[/tex]
[tex]Mean = (5500 + 3700 + 3200 + 1200 + 1000 + 950) / 6 = 2466.67[/tex]
[tex]Variance = [(5500 - 2466.67)^2 + (3700 - 2466.67)^2 + (3200 - 2466.67)^2 + (1200 - 2466.67)^2 + (1000 - 2466.67)^2 + (950 - 2466.67)^2] / 5 = 3031191.11[/tex]
[tex]Standard deviation = sqrt(3031191.11) = 1742.41[/tex]
The range of this data set is quite large, ranging from $950 million to $5.5 billion. The variance and standard deviation are also quite large, indicating that there is a wide range of net worths among celebrities. These results suggest that the population of all celebrities likely has a large variation in net worth, with some celebrities being extremely wealthy and others having much lower net worths.
Given the nature of these amounts, it is likely that they are precise to the nearest million dollars. It is possible that the true net worths of these celebrities are slightly higher or lower than the reported values, but the reported values are likely accurate to within a few million dollars.
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The figure below is a net for a triangular pyramid.
12 in length of 1 of 4 triangles.
10.39 in height of 1 of 4 triangles.
If all the triangles are equilateral, what is the surface area of the pyramid, in square inches?
The surface area of the triangular pyramid is approximately 256.224 square inches.
How do we calculate the surface area?The surface area of a triangular pyramid can be calculated by summing the areas of its four triangular faces.
Given that one of the triangular faces has a length of 12 inches and a height of 10.39 inches, we can calculate its area using the formula for the area of an equilateral triangle:
Area = (1/2) * base * height
For the given triangular face:
Base = 12 inches
Height = 10.39 inches
Plugging in these values, we get:
Area of one triangular face:
= (1/2) * 12 * 10.39
= 64.056 square inches
Since there are four triangular faces in a triangular pyramid, the total surface area of the pyramid is:
= 4 * Area of one triangular face
= 4 * 64.056
= 256.224 square inches.
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Given the vertices, determine the quadrilateral's most specific classification.
A(5, -3) B(7, 1) C(9, -3) D(-7, 7)
Indicate whether each expression in the table is equivalent to 1/2x-1, equivalent to x-1/2
1. The expression 2/3 (3/4 x - 3/2) is equivalent to x - 1/2. not equivalent to 1/2x - 1 and the third option. 2. The expression (2x + 1) - (x + 3/2) is equivalent to x - 1/2, not equivalent to 1/2x - 1 and the third option.
What is equation and expression?An expression is a mathematical sentence that may or may not have an equal sign, whereas an equation is a declaration that two expressions are equal. The equal sign in an equation indicates whether the result is true or false, depending on the values of the variables. On the other hand, while expressions can be assessed or sped up, they cannot be true or untrue. Expressions are used to represent quantities or operations, whereas equations are used to find the values of variables that the equation requires.
For the given expressions simplifying we get:
1. 2/3 (3/4 x - 3/2)
= 1/2 x - 1
This expression is equivalent to x - 1/2.
2. (2x + 1) - (x + 3/2)
= x - 1/2
This expression is equivalent to x - 1/2.
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What is the volume of this cylinder? 40yd 11yd
Use ≈ 3.14 and round your answer to the nearest hundredth.
Volume of the cylinder is 15197.60(to the nearest hundredth).
What is cylinder?
In mathematics, Cylinder is the basic 3d shapes, which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center which is called height of the cylinder.
Given that the radius of the cylinder is 11yd.
and the height of the cylinder is 40yd.
Formula for the volume of cylinder is π × r² × h where π=3.14, r= radius and h= height.
Putting the values we get,
Volume of the cylinder is = 3.14 × (11)² × 40 cubic yd.
= 15197.6
Hence, Volume of the cylinder is 15197.60(to the nearest hundredth).
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Omar made $216 for 18 hours of work.
At the same rate, how much would he make for 12 hours of work?
Answer:144
Step-by-step explanation:$216 for 18 hours is $12 an hour
12 times 12 = $144
eight third is is an improper fraction, which mixed number is equal to?
A pyramid has a rectangular base of length (3x + 1)cm and width xcm.
It also has a perpendicular height of 12 cm.
The volume of the pyramid is 96 cm³.
Given that the volume of a pyramid is one third of the area of the base
multiplied by the perpendicular height, find the dimensions of the base
of the pyramid.
Optional working
width: Answer
length: Answer
cm
cm
The width of the rectangular base of the pyramid is approximately 3.74 cm, and the length is approximately 11.22 cm (since it is given as 3x+1).
What is base of a pyramid?The base of a pyramid can be any polygon, such as a square or a triangle, but the height must always be measured perpendicular to the base.
Define the term dimensions?Dimensions refer to the number of coordinates needed to specify the location of an object in space.
Based on the given information, we can set up an equation to solve for x, which is the width of the rectangular base of the pyramid:
Volume of pyramid = 1/3 × base area ×height
96 = 1/3 ×(3x+1) × x ×12
Simplifying the equation:
96 = 4x² + (4/3)x
Multiplying both sides by 3 to eliminate the fraction:
288 = 12x² + 4x
Rearranging the equation into a quadratic form:
12x² + 4x - 288 = 0
Dividing both sides by 4 to simplify the equation:
3x² + x - 72 = 0
We can then use the quadratic formula to solve for x:
x = (-b ± [tex]\sqrt{(b^2-4ac)}/2a[/tex]
where a = 3, b = 1, and c = -72.
Plugging in the values:
x=(-1±[tex]\sqrt{1^2-4(3)(-72)} /2(3)[/tex])
x=(-1±[tex]\sqrt{1+864} /6[/tex])
x = (-1 ±[tex]\sqrt{865} /6[/tex] )
Since the width of the base cannot be negative, we take the positive solution:
x = (-1 + √(865) / 6
Therefore, the width of the rectangular base of the pyramid is approximately 3.74 cm, and the length is approximately 11.22 cm (since it is given as 3x+1).
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