Lisa's work finding the value of the expression 9 + 2(1-7) is shown below. Determine whether or not her work is correct. If it is incorrect, show Lisa how to find the correct value. Problem: 9 + 2(1-7) Step 1: Step 2: Answer: 9+2(-6) 11(-6) -66​

Answers

Answer 1

Answer:

9 + 2(1 - 7)

= 9 + 2(-6)           Simplify the subtraction expression inside the parenthesis.

= 9 - 12                Multiply.

= -3                      Subtract.


Related Questions

a plane begins its takeoff at 2:00 p.m. on a 2250-mile flight. after 4.7 hours, the plane arrives at its destination. explain why there are at least two times during the flight when the speed of the plane is 100 miles per hour.

Answers

We may deduce from the average speed that the aircraft must have at least once during the flight attained a speed of 478.72or higher.

This implies that the aircraft must have surpassed 100 mph once while descending to its average speed following takeoff.

So,

We can write,

The speed of the aircraft decreased throughout the arrival from its usual speed to 100 miles per hour before returning to zero at the destination.

Based on the given conditions,

Total distance of the flight = 2250 miles

Flight takeoff time = 2:00 pm

Arrival time of the flight = 7:40 pm

So,

The total time taken by the flight to cover 2250 = 4 hours 40 minutes

The total time is taken by the flight to cover 2250 = 4.7 hours

Then,

The average speed of the plane =Total distance/ total time

We can substitute values,

total distance = 2250,

total time = 4.7 hours

The average speed of the plane = 2250÷4.7

The average speed of the plane  is 478.72 miles per hour

From the average speed we can analyze that the plane must have reached the speed of 478.72 or more at least once during the journey this also concludes that the plane must have reached the speed of 100 miles per hour once while reaching to the average speed after the takeoff.

Hence,

During the arrival, the speed of the plane also reached went from the average speed to 100 miles per hour and then zero at the arrival destination

Therefore,

There were at least two times during the flight when the speed of the plane was 100 miles per hour.

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Help pleaseeeeeeeeeee

Help pleaseeeeeeeeeee

Answers

Answer: A

Step-by-step explanation:

-7+4x>-3 ; isolate x

4x>-3+7

4x>4; divide 4

x>1

> is a opened circle and greater than goes to the right side, therefore, the answer is A.

Answer:

Answer 1

Step-by-step explanation:

\(-7+4x>-3\\4x>-3+7\\4x>4\\x>1\\\)

Identify all the expressions that are equivalent to 43.
A
12
B.
64
C
4x4x4
D
34
E
82
F
26

Identify all the expressions that are equivalent to 43.A12B.64C4x4x4D34E82F26

Answers

Answer:

4*4*4, 64, 8^2, 2^6

Step-by-step explanation:

4^3=4*4*4

=64

4^3=2^(2*3)=2^6

=8^2

the slope of the ladder making an angle 30 degree with the floor is dash​

Answers

Since, Ladder makes an angle 60

with the floor as shown in figure.

∴ ladder makes 120

angle with the positive direction of x-axis.

⇒ slope of ladder =tan120

=tan(90

+30

)=−cot30

=−

3

An integer is three more than another integer. Twice the larger integer is two less
than the square of the smaller integer. Find the two integers.

Answers

Answer:

The integers are 4 and 7 or -2 and 1.

Step-by-step explanation:

You can make a system of equations with the description of the two integers.

1. x = y + 3

2. 2x + 2 = y^2

The simplest and the fastest way to solve this system in this case is substitution. You can substitute x for y + 3 in the second equation.

1. x = y + 3

2. 2(y + 3) + 2 = y^2

Now simplify and solve the second one. For convenience, I will just disregard the first equation for now.

2y + 6 + 2 = y^2

y^2 - 2y - 8 = 0

You can factor this equation to solve for y.

(y - 4) (y + 2) = 0

y = 4, y = -2

Now we can substitute the value of y for x in the first equation.

x = 7, x = 1

The two expressions to find the value of the two integers.

M = 3N

2M = N² - 2

N = 6.3 and M = 18.9

The two integers are 6.3 and 18.9

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Smaller integer = M

Larger integer = N

Now,

An integer is three more than another integer.

This can be written as,

M = 3N ____(1)

Twice the larger integer is two less than the square of the smaller integer.

This can be written as,

2M = N² - 2 ______(2)

From (1) and (2) we get,

2(3N) = N² - 2

6N = N² - 2

N² - 2 - 6N = 0

N² - 6N - 2 = 0

This is a quadratic equation.

The roots of this quadratic equation are 6.32 and -0.31 (neglected)

N = 6.32

N = 6.3

Now,

M = 3N

M = 3 x 6.3

M = 18.9

Thus,

The two integers are 6.3 and 18.9

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Recent difficult economic times have caused an increase in the foreclosure rate of home mortgages. Statistics from the Penn Bank and Trust Company show their monthly foreclosure rate is now one loan out of every 136 loans. Last month the bank approved 300 loans. What is the probability of exactly two foreclosures? (upto 2 decimal places)

Answers

The probability of exactly two foreclosures is 0.09.

If one loan out of every 136 loans is foreclosed, the probability of a loan being foreclosed is 1/136. Therefore, the probability of a loan not being foreclosed is 135/136.

Since the bank approved 300 loans last month, the number of loans that can be foreclosed ranges from 0 to 300. We can use the binomial probability formula to calculate the probability of exactly 2 foreclosures in 300 loans:

P(X = 2) = (300 choose 2) * (1/136)^2 * (135/136)^298

Using a calculator, we can evaluate this expression to get:

P(X = 2) ≈ 0.091

Therefore, the probability of exactly two foreclosures is 0.09 (rounded to two decimal places).

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a grain silo consists of a cylindrical main section and a hemispherical roof of the total volume of the silo (including the part inside the roof section) is 10,000 find.the.cylindrical part is 30 ft tall, what is the radius of the silo, correct to the nearest tenth of a foot?

Answers

The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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Harrison steps outside his house to see the hot air balloon pass by. He raises his eyes at a 35° angle to view the balloon. If the balloon is 5,000 feet above the ground, about how far is it from Harrison? Note: Harrison's eye level is 5.2 feet from the ground.

A 6,100 feet
B 8700 feet
C 7100 feet
D 2900 feet

Answers

If the balloon is 5,000 feet above the ground, then the Harrison is 7100 feet away (option c)

To solve for the adjacent side, we can use the tangent function, which relates the opposite and adjacent sides of a right triangle to the angle between them.

Tangent of an angle = opposite side / adjacent side

In this case, the tangent of 35° can be written as:

tan(35°) = height of balloon / distance between Harrison and balloon

We can rearrange this equation to solve for the distance between Harrison and the balloon:

distance between Harrison and balloon = height of balloon / tan(35°)

Substituting the given values, we get:

distance between Harrison and balloon = 5000 / tan(35°)

Using a calculator, we can find that the tangent of 35° is approximately 0.7002. Substituting this value, we get:

distance between Harrison and balloon = 5000 / 0.7002

Simplifying this expression, we get:

distance between Harrison and balloon ≈ 7,100 feet

Therefore, the answer is (C) 7,100 feet.

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% what is the general relationship between the probability function (or probability % density), f(t), and its associated cumulative probaility function, f(t)?

Answers

The PDF describes the rate at which probability is accumulating around a given point, while the CDF gives the probability that the random variable takes on a value less than or equal to a given value.

The probability density function (PDF) and cumulative distribution function (CDF) are two different ways of representing the same information about a probability distribution.

The PDF gives the probability density of a continuous random variable at a particular point in its domain. In other words, the PDF gives the rate at which the probability is accumulating around a given point. The area under the PDF curve between two points represents the probability of the random variable taking on a value between those two points.

On the other hand, the CDF gives the probability that a random variable is less than or equal to a given value. The CDF is the integral of the PDF from negative infinity up to that value.

Therefore, the CDF and PDF are related by integration: The CDF is the integral of the PDF, and the PDF is the derivative of the CDF.

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The given question is incomplete, the complete question is:

What is the relationship between the cumulative distribution function and the probability density function?

(1) Using the Black/Scholes Option Pricing Model, calculate the value of the call option given: S=74; X=70;T=6 months; σ2=.50 Rf​=10% (2) What is the intrinsic value of the call? (3) What stock price is necessary to break-even? 4 If volatility were to decrease, the value of the call would (5 If the exercise price would increase, the value of the call would ? 6 If the time to maturity were 3-months, the value of the call would ? 77 If the stock price were $62, the value of the call would ? 8 What is the maximum value that a call can take? Why?

Answers

(1) Using the Black/Scholes Option Pricing Model, the value of the call option is $7.70.

(2) The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

(3) The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.

(4) If volatility were to decrease, the value of the call would decrease.

(5) If the exercise price would increase, the value of the call would decrease.

(6) If the time to maturity were 3-months, the value of the call would decrease.

(7) If the stock price were $62, the value of the call would be zero.

(8) The maximum value that a call option can take is unlimited.

In the Black/Scholes option pricing model, the value of a call option can be calculated using the formula:

C = S*N(d1) - X*e^(-rT)*N(d2)

where S is the stock price, X is the exercise price, r is the risk-free rate, T is the time to maturity, and σ2 is the variance of the stock's return.

Using the given values, we can calculate d1 and d2:

d1 = [ln(S/X) + (r + σ2/2)T]/(σ2T^(1/2))

   = [ln(74/70) + (0.10 + 0.50/2)*0.5]/(0.50*0.5^(1/2))

   = 0.9827

d2 = d1 - σ2T^(1/2) = 0.7327

Using these values, we can calculate the value of the call option:

C = S*N(d1) - X*e^(-rT)*N(d2)

= 74*N(0.9827) - 70*e^(-0.10*0.5)*N(0.7327)

= $7.70

The intrinsic value of the call is the difference between the stock price and the strike price of the option. Therefore, it is $4.

The stock price required to break-even is the sum of the strike price and the option premium. Therefore, it is $74.If volatility were to decrease, the value of the call would decrease. This is because the option's value is directly proportional to the volatility of the stock.

If the exercise price would increase, the value of the call would decrease. This is because the option's value is inversely proportional to the exercise price of the option.

If the time to maturity were 3-months, the value of the call would decrease. This is because the option's value is inversely proportional to the time to maturity of the option.If the stock price were $62, the value of the call would be zero. This is because the intrinsic value of the call is zero when the stock price is less than the strike price.

The maximum value that a call option can take is unlimited. This is because the value of a call option is directly proportional to the stock price. As the stock price increases, the value of the call option also increases.

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Determine the domain of the following graph

Determine the domain of the following graph

Answers

Answer:

-1

Step-by-step explanation:

I got -1 by getting two points from the graph where the line touches. The two points I got were (0,-3) and (1, -4). When it asks you to find the domain it's asking you to find for the slope. The domain and the slope are the same thing. To find slope you use the slope formula which is y2-y1 over x2-x1. Once you set up your equation you should get -4-(-3) over 1-0. When you solve it you should get -1/1 and -1 divided by 1 is -1. So then the slope is -1....
(hope you were able to understand it... I might've not chosen the right points but hopefully I did...I'm sorry if you get it wrong)

List the numbers from greatest to least 4/9, 0.44%, 0.4,

Answers

Answer:
4/9 > 0.4 > 0.44%

please help, thanks!

please help, thanks!

Answers

Answer:

a) 10.5cm

b) 1520cm³ (3 s.f.)

c) 1270cm² (3 s.f.)

Step-by-step explanation:

Please see the attached picture for full solution.

please help, thanks!

Please help me with this geometry question

Please help me with this geometry question

Answers

Answer:

You put a point at -4,-8 and mark it A and put a point at 2,-2 and mark it B please mark brainlist thank you and God bless

Answer:

Midpoints:

A=-6

B=0

Step-by-step explanation:

(-5, -4) is the midpoint on the coordinate plane.

Please help me with this geometry question

For problem #4, identify the indicated side length or angle measurement.

For problem #4, identify the indicated side length or angle measurement.

Answers

SOLUTION:

We are to find the measurement of angle A.

Since the three sides are known, we just pick any of the two sides.

Considering

Using the trigonometric ratio:

\(\begin{gathered} \sin \theta\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \\ \sin \text{ A = }\frac{8}{10} \\ \\ \sin \text{ A = 0.8} \\ A\text{ = }\sin ^{-1}\text{ (0.8)} \\ A=53.13^o \end{gathered}\)

The measurement of angle A is 53.13 degrees.

how can jamie rewrite the expression 1/1-sin theta so that the fraction has cos^2 theta in the denominator
0 she can multiply the numerator and denominator by cos theta
0 she can mulitply the numerator and denominator by tan theta
0 she can mulitply the numerator and denominator by 1- cos theta
0 she can multiply the numerator and denominator by 1+ sin theta

Answers

As a result, Jamie could rewrite the equation as (1+sin theta)/cos² theta by multiplying both the denominator and the numerator by (1+sin theta), and then replacing 1-sin² theta with cos² theta.

What exactly is a fraction in mathematics?

A ²is part of a whole. The number is expressed mathematically as a quotient, which divides the denominator and the numerator. Both are integers in a simple fraction. A complicated fraction contains a fraction in the numerator or denominator. The denominator of a correct fraction is greater than the numerator

Jamie can double the numerator and write 1/(1-sin theta) to ensure that the fraction's denominator is cos² theta. Neither 1-cos theta nor any other option, but the numerator by (1+sin theta):

1/(1-sin theta) × (1+sin theta)/(1+sin theta) = (1+sin theta)/(1-sin² theta)

We may replace cos² theta for 1-sin² theta using the identity sin² theta + cos² theta = 1:

(1+sin theta)/cos² theta

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Please find below five research case studies. Each case study can be classified under one of following four Research Methods Review of historical data [Review] Field survey [Survey] Natural observation [Nat obs] Field/laboratory experiment [Exp.] Note: all research methods may not be represented in this task In no more than 20 words, identify the correct research method and justify using a single sentence explanation. Study # 3 "Why do so many people believe fake cyberspace news?" This research tests a possible answer to this question: previous encounters on multiple social media platforms allows consumers to become familiar with false news [last exposure to fake news confirms earlier presentations. This study included 1,455 participants [42% were male and groups average age was 27 years - with a range of 18 to 39 years]. The instrument of this study were 24 false news stories. One group were exposed to multiple versions of fake news while the second group were only exposed to each news story once. The findings of a familiarity effect were significant. That is, the familiarized news was rated more accurate [and believable] than the non-familiarized news. The current study also showed that the effect of familiarized news lasted for up to a month.

Answers

The correct research method for the study mentioned in the question is a Field survey.

Field survey can be defined as a research method used to collect data from a target population. In this study, researchers used a survey questionnaire to gather data from participants. The research aimed to test the theory that the exposure to multiple versions of fake news on various social media platforms made people believe the news.

The researchers surveyed 1,455 participants with an average age of 27, and 42% were male. The participants were exposed to 24 false news stories, and one group was exposed to multiple versions of fake news, while the other group was only exposed to each news story once.

The findings suggested that the more familiar the news was, the more accurate and believable it was. This familiarity effect lasted for up to a month. Hence, the research method used in this study was a field survey.

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estimate the area of the circle to the nearest unit.

estimate the area of the circle to the nearest unit.

Answers

Answer:

Step-by-step explanation: We know that ,

Area of circle =πr² and

r = radius of circle.

Now,

Diameter of circle =56 cm [given]

So, radius of circle=D/2=56/2

Radius of circle=28

Now,

Area of circle=πr²

Area of circle=22/7 ×(28)² [π=22/7]

Area of circle=22×4×28

Area of circle=2464cm²

Hence, Area of circle is 2464cm²

I hope it's help you.

Answer:

48 cm²

Step-by-step explanation:

Area of circle formula:  A = πr²

                                          = π (d/2)²

                                          = 3.14 * (4)²

                                          = 50.24

The area of the circle is closest to Option D, 48 cm²

when there are few data, we often fall back on personal probability. there had been just 2424 space shuttle launches, all successful, before the challenger disaster in january 1986. the shuttle program management thought the chances of such a failure were only 11 in 100,000.in 100,000. suppose 11 in 100,000100,000 is a correct estimate of the chance of such a failure. if a shuttle was launched every day, about how many failures would one expect in 300 years?300 years? round your answer to the nearest whole number.

Answers

If a shuttle was launched every day, about 1 failures would one expect in 300 years.

What is estimate?

Finding an estimate or approximation—a value that can be used for a purpose despite the possibility of incomplete, uncertain, or unstable input data—is the process of estimation. Despite this, the value is still useful because it was created using the most up-to-date data.

Here,

There are about 110,000 days in 300 years, so the expected number of failures is about 10/11 ≈ 1.

This assumes the launch conditions are identical for each of the launches, or that whatever variation there might be has no effect on the probability. These are bad assumptions.

If a shuttle was launched every day, one might anticipate one failure every 300 years.

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Given the matrix [\begin{array}{ccc}4&2&-2\\4&3&4\\5&-1&1\end{array}\right]. find its determinant. Do not use a calculator. The determinant is :

Answers

The determinant of the given matrix is 22.

To calculate the determinant of the matrix, we can use the Laplace expansion along the first row.

Using this method, we get:

det = 4 * det\[\begin{array}{ccc}3&4\\-1&1\end{array}\] - 2 * det\[\begin{array}{ccc}4&4\\-1&1\end{array}\] - 2 * det\[\begin{array}{ccc}4&3\\-1&1\end{array}\]

To calculate each of the 2x2 determinants, we can again use the

Laplace expansion

along the first row. This gives:

det\[\begin{array}{ccc}3&4\\-1&1\end{array}\] = 3 * 1 - 4 * (-1) = 7

det\[\begin{array}{ccc}4&4\\-1&1\end{array}\] = 4 * 1 - 4 * (-1) = 8

det\[\begin{array}{ccc}4&3\\-1&1\end{array}\] = 4 * 1 - 3 * (-1) = 7

Substituting these values back into the original formula for the determinant, we get:

det = 4 * 7 - 2 * 8 - 2 * 7 = 28 - 16 - 14 = -2

Therefore, the determinant of the given matrix is -2.

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1. the surface area of the rectangular prism
5 cm
20 cm
4cm

Answers

Answer:

430 cm^2

thankuhh

have a nice day

400cm^2

Please mark brainliest!

7. 4x +7= 15 when x= 2.

Answers

Answer:

15

Step-by-step explanation:

4(2)+7=15

8+7=15

15=15

Answer:

The solution is given below:

Step-by-step explanation:

4x +7= 15

As we know that the value x is 2

therefore the equation will be

4 × 2 + 7 = 15

8 + 7 = 15

15 = 15

−3.3 ÷ 2.2
Find the quotient. Write your answer as a decimal.

Answers

-1.5 is the answer why I took the test

Answer:

-1.5

Step-by-step explanation:

Factor the numerator and denominators and cancel the common factors.

Relate the area of the square to the length of each side.

Relate the area of the square to the length of each side.

Answers

The area of a square can be found by using the following expression:

\(A=l^2\)

where "A" is the area and "l" is the length of each side of the square. The square on this problem has an area of 9 cm², so we can find the sides by replacing A for 9 on the expression above.

\(\begin{gathered} 9=l^2 \\ l^2=9 \end{gathered}\)

To solve it we need to take the square root on both sides of the equation.

\(\begin{gathered} \sqrt[]{l^2}=\sqrt[]{9} \\ l=\sqrt[]{9} \\ l=3\text{ cm} \end{gathered}\)

Each side of the square has a length of 3 cm, so the sides are 3 cm x 3 cm.

HELP PLEASE.

What's 6 x 183?

A. 1023
B. 1639
C. 1089
D. 1098

Answers

Answer:

D

........................

Answer:

D. 1098 is the right answer.

Step-by-step explanation:

\((6 \times 183 )= 1098\)

HELP PLEASE. What's 6 x 183?A. 1023B. 1639C. 1089D. 1098

If you translate B(-4,-6) 4 units to the right and 8 units down, where is B'?

Answers

Answer:

(0, 2).

Step-by-step explanation:

B' = ((-4+4), (-6+8))

= (0, 2).

What is the equation of the line that
passes through the point (-7, -8) and
has a slope of 0?

Answers

The equation of line is: y = 7

What is point-slope form?For linear equations, the typical form is y-y1=m(x-x1). It highlights the line's slope and a line point (that is not the y-intercept). When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation. One of the three ways we can express a straight line is using the point slope form, also known as the point-gradient form. By merely knowing one point on the line and the slope of the line, we may use this form to get the equation of the line.

The equation of line is:\($y=7$\)

Step-by-step explanation:

- point\($=(-8,7)$\)

- slope\($=0$\)

Using the point-slope form

\($$y-y_1=m\left(x-x_1\right)$$\)

where m is the slope, and \($\left(x_1, y_1\right)$\) is the point substituting the values m=0 and the point (-8,7)

\(& y-y_1=m\left(x-x_1\right) \\\)

\(& y-7=0(x-(-8)) \\\)

\(& y-7=0 \\\)

\(& y=7\)

Thus, the equation of line is: \($y=7$\)

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Given a pre-image and image, determine if the scale factor is greater than 1, less than 1, or equal to 1.
a. less than 1
b. greater than 1
c. equal to 1
*see attached image for the pre image and image

Given a pre-image and image, determine if the scale factor is greater than 1, less than 1, or equal to

Answers

The scale factor is greater than 1.

Determine if the scale factor is greater than 1, less than 1, or equal to 1?The pre-image and image provided can be used to determine the scale factor between the two shapes.A scale factor is the ratio of the lengths of two corresponding sides of two similar figures.To determine the scale factor, the length of the two corresponding sides must be compared.Looking at the pre-image and image, it can be seen that the pre-image has a longer length than the image.This indicates that the scale factor is less than 1, as the length of the corresponding side in the image is shorter than the pre-image.To confirm this, the lengths of the corresponding sides must be compared.The pre-image has a length of 8 units and the image has a length of 6 units.The ratio of 8/6 is equal to 4/3, which is less than 1.Therefore, the scale factor between the pre-image and image is less than 1.

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A new car cost $28,950. It loses 15% of its value each year. The formula V(t) = 28,950(1-0.15) models this situation. What does V(t) represent?​

Answers

Answer:

the answer is 67789 because he will have enough money for the car to play

1.0- ! 0.8- 8 8 Chance.of.Admit 0.6- 8 : 8 0.4- 290 310 320 330 340 GRE. Score 300 Confidence Level for Slope and Intercept: Regression Analysis of Chance.of.Admit (Y) explained by GRE.Score (X) Coefficient Table: Estimate Std. Error t value Prl>[t]) Cl Lower Bound (Intercept) -2.44 0.12 -20.68 0.00 -2.67 GRE.Score 0.01 0.00 26.84 0.00 0.01 R-squared: 0.6441835 sigma: 0.08517377 CI Upper Bound -2.20 0.01 8. Is the linearity condition met? Yes, the residual plot is normal. Yes, there is no megaphone pattern found in the scatterplot Yes, the scatterplot shows a linear pattern in the data Yes, there is no megaphone pattern in the residual plot. 9. Select "Proceed to Regression Analysis". Refer to the table. If we perform at test for the slope of the regression line, what is the test statistic and p-value for this procedure? t = -20.68, p-value = -2.67 t = 26.84, p-value = 0.00 t = 26.84, p-value = 0.01 t = -20.68, p-value = 0.00 10. Calculate a 95% confidence interval for the slope on the line. Assuming that a = 0.05, can we use this interval as evidence that there is a linear relationship between GRE score and chance of admission? No. We don't know the alternative hypothesis, so we cannot make a conclusion on the relationship between GRE score and chance of admission. Yes. Because our alternative hypothesis is one-sided and O is not found in the confidence interval, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and chance of admission. No. Confidence intervals cannot be used to make conclusions for hypothesis tests. Yes. Because our alternative hypothesis is two-sided and O is not found in the confidence interval, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and chance of admission.

Answers

The test statistic and p-value for the slope of the regression line are t = 26 and p-value = 0.00.

Based on the given information, the analysis is focused on determining whether there is a linear relationship between GRE score and the chance of admission. The pattern observed in the scatterplot shows a linear pattern in the data, indicating a potential linear relationship between the two variables.

To test this hypothesis, a regression analysis was performed, which yielded a coefficient table with estimates for the intercept and slope of the regression line. The p-value for the slope test was found to be 0.00, which suggests strong evidence for a significant linear relationship between GRE score and the chance of admission.

Furthermore, a 95% confidence interval for the slope was calculated, which did not include the null value of zero. This means that we can reject the null hypothesis and conclude that there is a linear relationship between the GRE score and the chance of admission.

In summary, based on the analysis and statistical tests performed, there is evidence to support a linear relationship between the GRE score and the chance of admission.
The test statistic and p-value for the slope of the regression line are t = 26. ,an  p-value = 0.00.
A 95% confidence interval for the slope on the line is (0.01, 0.01). Since 0 is not found in the confidence interval and our alternative hypothesis is two-sided, we reject the null hypothesis and conclude that there is a linear relationship between GRE score and the chance of admission.

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