Bill Board is "lording" his SAT score over his friend, Rhoda Dendron, who took the ACT. "You only got a 25 in math," he chortled, "while I got a 300 in math." Given that the SAT has a μ of 500 and a σ of 100, and the ACT has a μ of 20 and a σ of 5, what is wrong with Bill’s logic (give the answer in both z scores and percentile ranks).

Answer:

a) 0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

b) 0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes

c) 0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 8.9 minutes and a standard deviation of 2.9 minutes.

This means that [tex]\mu = 8.9, \sigma = 2.9[/tex]

Sample of 37:

This means that [tex]n = 37, s = \frac{2.9}{\sqrt{37}}[/tex]

(a) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes?

320/37 = 8.64865

Sample mean below 8.64865, which is the p-value of Z when X = 8.64865. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{8.64865 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]

[tex]Z = -0.53[/tex]

[tex]Z = -0.53[/tex] has a p-value of 0.2981

0.2981 = 29.81% probability that for 37 jets on a given runway, total taxi and takeoff time will be less than 320 minutes.

(b) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes?

275/37 = 7.4324

Sample mean above 7.4324, which is 1 subtracted by the p-value of Z when X = 7.4324. So

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{7.4324 - 8.9}{\frac{2.9}{\sqrt{37}}}[/tex]

[tex]Z = -3.08[/tex]

[tex]Z = -3.08[/tex] has a p-value of 0.001

1 - 0.001 = 0.999

0.999 = 99.9% probability that for 37 jets on a given runway, total taxi and takeoff time will be more than 275 minutes.

(c) What is the probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes?

Sample mean between 7.4324 minutes and 8.64865 minutes, which is the p-value of Z when X = 8.64865 subtracted by the p-value of Z when X = 7.4324. So

0.2981 - 0.0010 = 0.2971

0.2971 = 29.71% probability that for 37 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes

Answer:

339.4cm³

Step-by-step explanation:

V

=

π

r

2

h

3

22/7×6²×9/3= 339.42

Answer:

Easton entered in 25 shows last year.

Step-by-step explanation:

Given that Easton won best in show in 60% of the shows I have entered, to determine how many show was Easton entered if he won best in show 15 times last year, the following calculation must be performed:

60 = 15

100 = X

(100 x 15) / 60 = X

1,500 / 60 = X

25 = X

Therefore, Easton entered in 25 shows last year.

Answer:

formula - 2 (wl + hl + hw)

559,872 is the answer from how I learned it.

If i'm right, please mark me brainliest ! (๑・ω-)～♥”

Answer:

Complementary Angles - 3rd one (at the bottom)

Supplementary Angles - 2nd one (at the top-right)

Vertical Angles - 1st one (at the top-left)

Feel free to mark it as brainliest :D

Answer:

x = 12

Step-by-step explanation:

First, we need to find the last interior angle of the triangle. Since we know the exterior angle next to it is 140° and they are supplementary, meaning they form a 180° angle, we can make an equation to solve for the last angle.

∠SRT + 140° = 180°

∠SRT = 40°

Now we know that the last interior angle is 40°. All triangles have a sum of 180°, therefore we can once again set up an equation to solve for x.

3x + 4 + 8x + 4 + 40 = 180

11x + 48 = 180

11x = 132

x = 12

Therefore, x = 12.

Answer:

The arm routine lasts 10 minutes, and the abs routine lasts 15 minutes.

Step-by-step explanation:

Since Oscar is trying to incorporate more exercise into his busy schedule, and he has several short exercise routines he can complete at home, and last week, he worked out for a total of 35 minutes by doing 2 arm routines and 1 abdominal routine while That this week, he has completed 4 arm routines and 1 abdominal routine and spent a total of 55 minutes exercising, to determine how long does each routine last the following calculation must be performed:

2ARM + 1ABS = 35

4ARM + 1ABS = 55

4ARM + 1ABS - 2ARM - 1ABS = 55 - 35

2ARM = 20

ARM = 20/2

ARM = 10

2 x 10 + ABS = 35

ABS = 15

Therefore, the arm routine lasts 10 minutes, and the abs routine lasts 15 minutes.

Answer:

252

Step-by-step explanation:

To answer the equation, you first need to note that it asks for surface area.

To find surface area, you use an input formula, known as SA=2lw+2lh+2hw. 'H' stands for height, 'L' stands for length, and 'W' stands for width.

Since the current height is 12, the current length is 6, and the width is 3, you need to plug them into the equation.

SA=2(6)(3)+2(6)(12)+2(12)(3)

SA=252

Quick tip! It's tempting to just multiply them all at once, but using the power of distribution is vital to solving these equations.

(nevermind srry, that was wrong)

Answer: represents the growth factor which reveals the monthly interest rate.

Step-by-step explanation:

Anthony's account balance can be modeled by the general compound interest formula shown below, where P is the initial amount, r is the annual interest rate, n is the number of times that the interest in the account is compounded per year, and t is the time period.

Consider the given expression.

1250(1+0.06/12)^12t

In the given expression, "1" represents 100% of the money in the account at the start of the month and "" represents the percentage of the account balance that gets added into the account at the end of each month. This is the monthly interest rate and the entire expression,(1+0.06/12t) , is the factor of growth.

Therefore, (1+0.06/12t)represents the growth factor which reveals the monthly interest rate.

Answer:

Step-by-step explanation:

x+2x+27=90

3x=90-27

3x=63

x=63/3

x=21

Answer:

x = 21

Step-by-step explanation:

Since ∠ PQR = 90° , then the sum of the 3 angles = 90° , that is

x + 2x + 27 = 90

3x + 27 = 90 ( subtract 27 from both sides )

3x = 63 ( divide both sides by 3 )

x = 21

Answer:

[tex]I = \frac{1}{6}\cdot \sin^{2} 3x + C[/tex]

Where [tex]C[/tex] is the integration constant.

Step-by-step explanation:

We use integration by substitution to obtain the integral, where:

[tex]u = \sin 3x[/tex], [tex]du = 3\cdot \cos 3x\,dx[/tex]

[tex]I = \int {\sin 3x\cdot \cos 3x} \, dx[/tex]

[tex]I = \frac{1}{3} \int {u} \, du[/tex]

[tex]I = \frac{1}{6}\cdot u^{2} + C[/tex]

[tex]I = \frac{1}{6}\cdot \sin^{2} 3x + C[/tex]

Where [tex]C[/tex] is the integration constant.

Answer:

There is one solution

(2, 2)

Step-by-step explanation:

The solutions are where the line and curve intersect.

The isone point of intersection and therefor one solution (2, 2)

Answer:

answer is b.) one

Step-by-step explanation:

edge 2021

Answer:

The area is 36 inches

Step-by-step explanation: 18 * 2 = 36

Answer:

[tex]\boxed {\boxed {\sf 18 \ inches^2}}[/tex]

Step-by-step explanation:

The area is the amount of space inside the shape. The area of a triangle is half the product of the base and height.

[tex]a= \frac{1}{2} bh[/tex]

The base of the triangle is 18 inches and the height is 2 inches.

Substitute the values into the formula.

[tex]a= \frac{1}{2} (18 \ in)(2 \ in)[/tex]

Multiply the numbers in parentheses.

[tex]a= \frac{1}{2}(36 \ in^2)[/tex]

Multiply by 1/2 or divide by 2.

[tex]a= 18 \ in^2[/tex]

The area of the triangle is 18 square inches.

Answer:

0.1357 = 13.57% of bolts will have a diameter greater than 1.211 inches

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 1.20 inches and a standard deviation of 0.01 inches.

This means that [tex]\mu = 1.20, \sigma = 0.01[/tex]

What proportion of bolts will have a diameter greater than 1.211 inches?

This is 1 subtracted by the p-value of Z when X = 1.211. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1.211 - 1.20}{0.01}[/tex]

[tex]Z = 1.1[/tex]

[tex]Z = 1.1[/tex] has a p-value of 0.8643.

1 - 0.8643 = 0.1357

0.1357 = 13.57% of bolts will have a diameter greater than 1.211 inches

Answer:

Step-by-step explanation:

Since we are given the coordinates of A, and we know that another coordinate on segment OA is the origin, (0, 0), we can use that information in the slope formula to find the slope of segment OA:

[tex]m_{OA}=\frac{-3-0}{6-0}=-\frac{1}{2}[/tex]

Since segment OB is perpendicular to segment OA, then its slope is the opposite reciprocal of that of segment OA. Therefore, the slope of segment OB is 2. We will use that along with the coordinate of the origin to write the equation of OB in the slope-intercept form of a line:

y = mx + b where y = 0, x = 0, m = 2

0 = 2(0) + b so

b = 0 and the equation for the line is

y = 2x

Answer:

y=-2/3x

Step-by-step explanation:

Perpendicular gradients(slopes) are negative reciprocals so first rearrange the given equation to find the gradient. y=3/2x-7/2

the gradient of the new line will be m=-2/3 then use the point (-3,-2) to find the equation of the line

y=mx+b

-2=(-2/3)(-3)+b

-2=2+b

b=0

y=-2/3x

Answer:

60 cm³

Step-by-step explanation:

Applying,

Volume (V) = Area of the base(A)×Height(h)

V = Ah................ Equation 1

From the diagram,

A =  Area of Trapezium

A = 1/2(a+b)c............. Equation 2

Substitute equation 2 into equation 1

V = [1/2(a+b)c]h........... Equation 3

Given: a = 3 cm, b = 7 cm, c = 3 cm, h = 4 cm

Substitute these values into equation 3

V = [3(3+7)/2]4

V = (3×10/2)4

V = (3×5)4

V = 15×4

V = 60 cm³

Answer:

C

Step-by-step explanation:

The answer is c because the point where they meet is -6 so it has to be all real number greater than.

Answer:

C) 86

Step-by-step explanation:

To find the mean you first add all of the numbers together. So you would add 75+90+84+95=344. Then you would divide the sum by the amount if numbers there are. So it would be 344÷4 =86

Hope this helped :)

Answer:

x = 75, 90 , 84, 95

[tex]Mean = \frac{ \sum x}{n}= \frac{75+90+84+95}{4} = 86[/tex]

Answer:

2.9

hope this helps

have a good day :)

Step-by-step explanation:

x^2 + 21^2 = 29^2

x^2 + 441 = 841

x^2 = 841 - 441

x^2 = 400

x = √400

x = 20

Answer:

20 lawyers

Step-by-step explanation:

48 ÷ 12 = 4

which means every year 4 lawyers are hired

5 × 4 = 20

so this means the law firm has hired 20 lawyers in the last 5 years

Answer:

Step-by-step explanation:

1 m =0.001 km

15m=15*0.001

=0.015 km

Answer:

[tex]a:b = 8:3[/tex]

Step-by-step explanation:

To find the ration, we want to get in equation in the form [tex]\frac{a}{b} =\frac{x}{y}[/tex].

We can start by dividing by b on both sides:

3a = 8b

÷b     ÷b

[tex]\frac{3a}{b} = 8[/tex]

Now, we can divide by 3 on both sides to get:

[tex]\frac{a}{b} = \frac{8}{3}[/tex]

We can change the format into a ratio:

[tex]a:b = 8:3[/tex]

Answer:

a) This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.

b) P-value of Z when X = 76 subtracted by the p-value of X = 68.

c) Because the underlying distribution(pulse rates of females) is normal.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].

standard deviation of beats per minute.

a. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between A beats per minute and B beats per minute.

This is the p-value of Z when X = A subtracted by the p-value of Z when X = B.

b. If 4 adult females are selected, find the probability that they have pulse rates with a mean between 68 beats per minute and 76 beats per minute.

Sample of 4 means that we have [tex]n = 4, s = \frac{\sigma}{\sqrt{4}} = 0.5\sigma[/tex]

The formula for the z-score is:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{X - \mu}{0.5\sigma}[/tex]

[tex]Z = 2\frac{X - \mu}{\sigma}[/tex]

This probability is the p-value of Z when X = 76 subtracted by the p-value of X = 68.

c. Why can the normal distribution be used in heartbeat even the sample side does not exceed 30?

Because the underlying distribution(pulse rates of females) is normal.

Answer:

(x+1)(x+3)(x+5)

Step-by-step explanation:

Answer:

the height is 599.950

Step-by-step explanation:

The computation of the  horizontal length of the line  is shown below:

The vertical distance is

= 10.20ft - 2.50ft

= 7.70 ft

Now use the pythagoreans theorem to determine the length of the line horizontally i.e presented below;

√horizontal distance^2 + √vertical distance^2 = Slope

√horizontal distance^2 + √7.7^2 = 600

So the height is 599.950

Answer:

(D)

Step-by-step explanation:

The slope of the given line is (2/3) which means that a line perpendicular to it must have a slope of (-3/2).

Answer:

Step-by-step explanation:

area of circle=π*r^2

=3.14*2.5^2

=3.14*6.25

=19.625

=19.63