Find the midpoint of the line segment with the given endpoints. ( 1, -10),
(-7, 7).

The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approx b). 0.9428.

The intelligence quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. The standard deviation of the mean of a sample of 50 adults can be calculated as the population standard deviation divided by the square root of the sample size, or 15/√50 = 1.58.

Using a standard normal distribution table, the probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 can be calculated as the area under the standard normal curve between the z-scores corresponding to 98 and 103. These z-scores can be calculated using the formula z = (x - mean) / standard deviation, where x is the value of interest and mean is the population mean. The z-score for 98 is (98 - 100) / 1.58 = -1.27, and the z-score for 103 is (103 - 100) / 1.58 = 2.53.

The area under the standard normal curve between -1.27 and 2.53 can be found using a standard normal distribution table or a calculator with normal distribution functions. The probability of selecting a sample of 50 adults and finding that the mean of this sample is between 98 and 103 is approximately 0.9228, which is closest to the answer choice b. 0.9428.

Find out more about probability

brainly.com/question/14987010

#SPJ4

Answer:

1/7

Step-by-step explanation:

Answer:

The probability of flipping tails is 1/2

Answer:

c)  3 grams

Step-by-step explanation:

Left side of hanger:

Total mass of circles: 6 (2 circles x 3 gram)

Total mass of squares: 10 (5 squares x 2 gram)

Total mass of triangles: 6 (2 triangles x 3 gram)

Makes a total of 22 grams

Right side of hanger:

Total mass of circles: 3 (1 circle x 3 gram)

Total mass of squares: 4 (2 squares x 2 gram)

Total mass of triangles: 15 (5 triangles x 3 gram)

Makes a total of 22 grams.

Answer:

Step-by-step explanation:

Answer:

6

y2-2y+6

since y= 2

22-22+6

=6

Consequently, this student's quiz results have a median, or "middle," value of 16.

When a dataset is ordered, the median value is the one that appears exactly in the middle of the dataset. The difference between the lowest and highest 50% of data is a measure of central tendency or average. Depending on whether you have an odd or even number of data points, the procedures for determining the median , mode change.

Here,

the median, or "middle" value in a data set. Your data must be in numerical order in order to calculate the median.

Exam results:

9, 13, 20, 15, 18, 17

Number the rows and columns.

9, 13, 15, 17, 18, 20

Calculate the "middle" value:

9, 13, 15, 17, 18, 20

If there are two middle values, put them together and divide by two.

15 + 17 = 32

32/2 = 16

Consequently, this student's quiz results have a median, or "middle," value of 16.

To know more about median , visit

https://brainly.com/question/28060453

#SPJ1

Stan's average speed for the total trip is 55 miles per hour.

Given,

Stan drove 300 miles in 5 hours 20 minutes

Again, Stan drove 360 miles in 6 hours 40 minutes

To find,

Stan's average speed in miles per hour for the total trip

Solution

We can start the problem by calculating the total distance and the total time for the trip. Then we can use the formula for average speed which is;

Average speed = Total distance / Total time

First, let's calculate the total distance covered by Stan in the entire trip;

Total distance covered = 300 + 360= 660 miles

Now, let's calculate the total time taken by Stan in the entire trip;

Total time taken = 5 hours 20 minutes + 6 hours 40 minutes= 12 hours

Now, let's use the formula for average speed and calculate the average speed for the entire trip;

Average speed = Total distance / Total time= 660 / 12= 55 miles per hour

Therefore, Stan's average speed for the total trip is 55 miles per hour.

learn more about average speed here:

https://brainly.com/question/13318003

#SPJ11

Answer:

(1 , 4)

Step-by-step explanation:

x=1

y=4

We have three points that represent the vertices of the triangle

- A( -1, 5 )

- B( 4, 5 )

- C( -1, 1 )

We need to calculate the distances between the points to calculate the perimeter

To calculate the distances we must use the next equation

Distance for AB:

Distance for BC:

Distance for AC:

Finally, the perimeter is

So, the answer is

If you save $2,015.82 every year at an interest rate of 8%, you can retire in 30 years and live another 25 years while still having enough money to spend $80,000 per year.

To calculate the amount you need to save per year for the next 30 years, we can use the future value of an ordinary annuity formula.

The future value of an ordinary annuity formula is:

\(FV = P \cdot \left(\frac{(1 + r)^n - 1}{r}\right)\)

Where:

FV = Future value of the annuity

P = Payment amount per period

r = Interest rate per period

n = Number of periods

In this case:

P = Amount you need to save per year

r = 8% = 0.08 (annual interest rate)

n = 30 (number of years)

We want the future value (FV) to be equal to the amount needed to spend per year during retirement, which is $80,000.

Using the formula, we can calculate the amount you need to save per year:

\(\$80,000 = P \cdot \left[\left(1 + 0.08\right)^{30} - 1\right] / 0.08\$\)

Simplifying the equation:

\($80000 = P \cdot [1.08^{30} - 1] / 0.08$\)

$80,000 * 0.08 = P * [1.08³⁰ - 1]

$6,400 = P * [1.08³⁰ - 1]

Dividing both sides by [1.08³⁰ - 1]:

\($P = \dfrac{\$6400}{1.08^{30} - 1}$\)

Calculating [1.08³⁰ - 1]:

[1.08³⁰ - 1] ≈ 3.172024

Dividing $6,400 by 3.172024:

P ≈ \($\frac{6,400}{3.172024} \approx$ $2,015.82\) (rounded to the nearest cent)

Therefore, you need to save approximately $2,015.82 per year into your investment account at the end of each year for the next 30 years.

To know more about the interest rate refer here,

https://brainly.com/question/30007732#

#SPJ11

9514 1404 393

Answer:

  a) $336

  b) $1036

Step-by-step explanation:

a) The interest is computed using the formula ...

  I = Prt

where P is the amount invested at rate r for t years.

  I = $700·0.08·6 = $336

The interest earned is $336.

__

b) The balance of the account is the sum of the original amount and the interest earned:

  balance = $700 +336 = $1036

The balance of the account is $1036.

Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).

We would need 453 more observations to increase your confidence level to 95% certainty.

To determine the required number of observations to be 90% sure of being within ±2.5% of the population mean for an activity occurring 30% of the time, we'll use the sample size formula for proportions:

n = (Z^2 * p * (1-p)) / E^2

Here, n is the sample size, Z is the z-score corresponding to the desired confidence level, p is the proportion (30% or 0.30), and E is the margin of error (±2.5% or 0.025).

For a 90% confidence level, the z-score (Z) is 1.645. Plugging the values into the formula:

n = (1.645^2 * 0.30 * (1-0.30)) / 0.025^2
n ≈ 1023.44

So, you would need approximately 1024 observations to be 90% sure of being within ±2.5% of the population mean.

To increase the confidence level to 95%, the z-score (Z) changes to 1.96. Using the same formula:

n = (1.96^2 * 0.30 * (1-0.30)) / 0.025^2
n ≈ 1476.07

So, you would need approximately 1477 observations for a 95% confidence level.

To find the additional number of observations needed, subtract the initial sample size from the new sample size:

1477 - 1024 = 453

Therefore, you would need 453 more observations to increase your confidence level to 95% certainty.

Visit here to learn more about population mean  : https://brainly.com/question/30727743
#SPJ11

Answer:

(6/2)² = 3² = 9

6²/2² = 36/4 = 9

Answer:

9

Step-by-step explanation:

6/2 is 3

squaring three we get 3 to  the power of two or 3x3

3x3=9

3 squared is 9

Anais, who bought a ribbon of length \(2 \dfrac 12 \) yards, and she trimming a curtain from it. From substraction, length of ribbon used in curtain is equals to 72 inches.

Word problems express in mathematical form. In subtraction, keywords that could signal the operation are lesser, less than, removed from. However, there are times when the idea of subtraction or taking away is inferred from the problem itself. In the problem, total length of ribbon Anais bought

= \(2 \dfrac 12 \) yards

The length of ribbon left after trimming some curtains = 1 feet 6 inches

We have to determine inches of ribbon Anais use to trim the curtains. Let it will be equal to x inches . We may notice in the provide values that they all have different units. We can convert the all different units into inches. Using uint conversation, 1 yard = 36 inches

=> \(2 \dfrac 12 \)

yards =\( 36 × \frac{ 5}{2} \)

= 90 inches

Similarly, 1 feet = 12 inches, then 1 feet + 6 inches = 12 + 6 = 18 inches

Thus, the left ribbon length = 18 inches

Using substraction method, the length in inches of ribbon that anais use to trim the curtains = total length - left length of ribbon = 90 - 18

= 72 inches.

Hence, required value is 72 inches.

For more information about substraction, visit :

https://brainly.com/question/22520797

#SPJ4

Complete question:

Anais bought

\(2 \dfrac 12 \)

yards of ribbon. She had 1 feet 6 inches of ribbon left after trimming some curtains. How many inches of ribbon did Anais use to trim the curtains?

The probability of type II error will decrease if the level of significance of a hypothesis test is raised from 0.005 to 0.2.

A type II error occurs when a false null hypothesis is not rejected or a true alternative hypothesis is mistakenly rejected.

It is denoted by 'β'. The power of the hypothesis is given by '1 - β'.

The relation between type II error and the significance level(α):

From this, it is known that when the significance level of the given hypothesis test is raised from 0.005 to 0.2, the probability of type II error will decrease.

Learn more about type II error of a hypothesis test here:

https://brainly.com/question/15221256

#SPJ4

Answer:

Roadhouse

Step-by-step explanation:

Because

Answer:

  A.  x ≈ 25/16

Step-by-step explanation:

You want the solution to 5^(-x) +7 = 2x +4 using 3 iterations of successive approximation.

There are many methods of successive approximation. We presume from the answer choices that you want to use the bisection method. Here, it can start with the interval [1, 2], bounded by the integers either side of the x-coordinate of the point where the curves intersect.

The bisection method has you evaluate the function at the midpoint of the interval. The midpoint of the interval will replace the endpoint whose function value has the same sign, thus reducing the interval width by half.

The attached table shows the intervals containing the solution to the equation are reduced after 3 iterations to ...

  [1, 2] ⇒ [3/2, 2] ⇒ [3/2, 7/4] ⇒ [3/2, 13/8]

The midpoint of this last interval is (12/8 +13/8)/2 = 25/16. This is our approximation of the solution.

  x ≈ 25/16

__

Additional comment

We find it convenient to rewrite the equation to the form f(x) = 0. Then we are looking for the x-intercept of the function f(x). For the function we have chosen, the function value is positive at the left end of the interval, and negative at the right end. Thus, we can choose which interval bound to replace based on the sign of the function value. This simplifies the mental effort required.

If you do the arithmetic using separate functions for the left- and right-sides of the equation, then you need to compare those values and choose the interval end to change based on that comparison. We find that to be extra work.

The bisection method, on average, adds about 1/3 of a decimal place to the precision of the solution with each iteration. Other iteration methods can converge much more quickly. For example, Newton's method iteration can get a 6 decimal place answer in two iterations starting from x ≈ 1.5.

<95141404393>

Answer:

Step-by-step explanation:

An equation in point-slope form of the line passing through point P(x₁, y₁) with slope m:   y - y₁ = m(x - x₁)

m = -2

P(-3, 6)  ⇒   x₁ = -3,  y₁ = 6

y - 6 = -2(x - (-3))

y - 6 = -2(x + 3)  ←    point-slope form

y - 6 = -2x - 6        {add 6 to both sides}

y = - 2x                 ←    slope-intercept form {intercept=0}

Triangle ABC, we are given the measure of angle A as 30 degrees, the length of side AC as 10.7 cm, and the length of side BC as 6.5 cm.

To work out the value of sin(ABC), we can use the trigonometric ratio of the sine function.

The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.

In the given information, we don't have a right triangle or the length of the side opposite angle ABC.

Without this information, it is not possible to calculate the value of sin(ABC) accurately.

If you have any other information regarding the triangle, such as the length of side AB or the measure of angle B or C, please provide it so that I can assist you further in calculating sin(ABC).

We may utilise the sine function's trigonometric ratio to get the value of sin(ABC).

The sine function connects the ratio of the hypotenuse length of a right triangle to the length of the side opposite an angle.

A right triangle or the length of the side opposite angle ABC are absent from the provided information.

The value of sin(ABC) cannot be reliably calculated without these information.

Please share any more information you may have about the triangle, such as the length of side AB or the size of angles B or C, so I can help you with the calculation of sin(ABC).

For similar questions on Triangle

https://brainly.com/question/1058720

#SPJ8

Answer:

Step-by-step explanation:

x + 2x + 6 = 27

3x + 6 = 27

x + 2 = 9

x = 9 - 2

x = 7

2 × 7 = 14

14 + 6 = 20

To determine the number of different ways a group of twenty people can be selected for the positions of President, Vice President, Treasurer, and Secretary, we can use the concept of permutations.

For the position of President, there are 20 candidates to choose from. After selecting the President, there are 19 remaining candidates for the position of Vice President. Similarly, after selecting both the President and Vice President, there are 18 candidates remaining for the position of Treasurer. Finally, after selecting the President, Vice President, and Treasurer, there are 17 candidates remaining for the position of Secretary. The total number of different ways to select the group is obtained by multiplying the number of choices at each step:

20 choices for President × 19 choices for Vice President × 18 choices for Treasurer × 17 choices for Secretary = 116,280 different ways. Therefore, there are 116,280 different ways to select a group of twenty people for the positions of President, Vice President, Treasurer, and Secretary.

Learn more about permutations here:

https://brainly.com/question/29990226

#SPJ11

To convert an annual interest rate to a daily interest rate based on simple interest, divide the annual interest rate by 365, the number of days in a year.

This way,

The daily interest rate is 0.05%

To get the simple interest in a 30 day period, we use the formula for simple interest and get:

The interest for a 30 day period is $23.15

5.48% of the people in line waited for more than 28 minutes

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

In a set with mean  and standard deviation , the z-score of a measure X

Given Mean waiting time of 20 minutes with a standard deviation of 5 minutes.

This means that percentage of the people in line waited for more than 28 minutes.

The proportion is 1 subtracted by the p-value of Z when X = 28. So

Z = 1.6

This has a p-value of 0.9452.

1 - 0.9452 = 0.0548.

As a percentage,

0.0548*100% = 5.48%

Thus 5.48% of the people in line waited for more than 28 minutes

Learn more about standard deviation and variance:

https://brainly.com/question/11448982

#SPJ1

Answer:

B

Step-by-Step Explanation:

Architects often create scale models before the actual building is constructed. if a scale model has a length of 24 inches and a width of 36 in., 2:3 the dimensions are geometrically similar to the model buildings

Geometrically similar to the model buildings are those whose ratio of corresponding dimensions are the same as those of the model.

The ratio of the dimensions of the scale model is:

length:width = 24:36 = 2:3

There are two ratios to compare in a building with dimensions L and W:

length : width = L:W and

width : length = W:L

The ratio of the dimensions of a building must be in proportion to the ratio of the dimensions of the scale model for geometric similarity.

Since the dimensions of the model are 2:3, the dimensions of the building must also be in a 2:3 ratio.

Therefore, we have: L : W = 2:3

L = (2/3)W

The ratio of the length to the width of the building is 2:3.

For similar question on dimensions

https://brainly.com/question/28107004

#SPJ11

The directional derivative of the function at the given point in the direction of the vector v are as follows :

\(\[D_{\mathbf{u}} f(\mathbf{a}) = \nabla f(\mathbf{a}) \cdot \mathbf{u}\]\)

Where:

- \(\(D_{\mathbf{u}} f(\mathbf{a})\) represents the directional derivative of the function \(f\) at the point \(\mathbf{a}\) in the direction of the vector \(\mathbf{u}\).\)

- \(\(\nabla f(\mathbf{a})\) represents the gradient of \(f\) at the point \(\mathbf{a}\).\)

- \(\(\cdot\) represents the dot product between the gradient and the vector \(\mathbf{u}\).\)

Now, let's substitute the values into the formula:

Given function: \(\(f(x, y) = 7e^x \sin y\)\)

Point: \(\((0, \frac{\pi}{3})\)\)

Vector: \(\(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Gradient of \(\(f\)\) at the point  \(\((0, \frac{\pi}{3})\):\)

\(\(\nabla f(0, \frac{\pi}{3}) = \begin{bmatrix} \frac{\partial f}{\partial x} (0, \frac{\pi}{3}) \\ \frac{\partial f}{\partial y} (0, \frac{\pi}{3}) \end{bmatrix}\)\)

To find the partial derivatives, we differentiate \(\(f\)\) with respect to \(\(x\)\) and \(\(y\)\) separately:

\(\(\frac{\partial f}{\partial x} = 7e^x \sin y\)\)

\(\(\frac{\partial f}{\partial y} = 7e^x \cos y\)\)

Substituting the values \(\((0, \frac{\pi}{3})\)\) into the partial derivatives:

\(\(\frac{\partial f}{\partial x} (0, \frac{\pi}{3}) = 7e^0 \sin \frac{\pi}{3} = \frac{7\sqrt{3}}{2}\)\)

\(\(\frac{\partial f}{\partial y} (0, \frac{\pi}{3}) = 7e^0 \cos \frac{\pi}{3} = \frac{7}{2}\)\)

Now, calculating the dot product between the gradient and the vector \(\(\mathbf{v}\)):

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \begin{bmatrix} \frac{7\sqrt{3}}{2} \\ \frac{7}{2} \end{bmatrix} \cdot \begin{bmatrix} -5 \\ 12 \end{bmatrix}\)\)

Using the dot product formula:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = \left(\frac{7\sqrt{3}}{2} \cdot -5\right) + \left(\frac{7}{2} \cdot 12\right)\)\)

Simplifying:

\(\(\nabla f(0, \frac{\pi}{3}) \cdot \mathbf{v} = -\frac{35\sqrt{3}}{2} + \frac{84}{2} = -\frac{35\sqrt{3}}{2} + 42\)\)

So, the directional derivative \(\(D_{\mathbf{u}} f(0 \frac{\pi}{3})\) in the direction of the vector \(\mathbf{v} = \begin{bmatrix} -5 \\ 12 \end{bmatrix}\) is \(-\frac{35\sqrt{3}}{2} + 42\).\)

To know more about derivative visit-

brainly.com/question/31422048

#SPJ11

The expected value of the "Buy New" option is 724732.60.

Decision Tree:

To solve the given problem, the first step is to create a decision tree. The decision tree for the given problem is shown below:

Expected Value Calculation: The expected value of the "Buy New" option can be calculated using the following formula:

Expected Value = (Prob. of Prosperity * Payoff for Prosperity) + (Prob. of Recession * Payoff for Recession)

Substituting the given values in the above formula, we get:

Expected Value for "Buy New" = (0.7 * 1,035,332) + (0.3 * -150,000)Expected Value for "Buy New" = 724,732.60

Therefore, the expected value of the "Buy New" option is 724,732.60.

Conclusion:

To conclude, the decision tree is an effective tool used in decision making, especially when the consequences of different decisions are unclear. It helps individuals understand the costs and benefits of different choices and decide the best possible action based on their preferences and probabilities.

The expected value of the "Buy New" option is 724,732.60.

For more questions on expected value

https://brainly.com/question/14723169

#SPJ8