AutoTrader would like to estimate the number of years owners keep the cars that they purchased as a new vehicle. The following data shows the age of seven vehicles that were sold for the first time by their owners. Using this sample, the 90% confidence interval that estimates the average age of cars sold for the first time is ________. Group of answer choices (2. 56, 10. 30) (5. 14, 7. 72) (1. 27, 11. 59) (3. 93, 8. 93)

Answers

Answer 1

The 90% confidence interval that estimates the average age of cars sold for the first time is (2.56, 10.30).

To calculate the confidence interval, we can use the formula:

CI =$\bar{X}$ ± tα/2 * (s/√n)

where $\bar{X}$ is the sample mean, s is the sample standard deviation, n is the sample size, tα/2 is the critical value from the t-distribution table with (n-1) degrees of freedom and a confidence level of 90%.

Using the given data, we find that the sample mean is 6.43 years and the sample standard deviation is 2.69 years. With a sample size of 7, the critical value from the t-distribution table is 1.895.

Plugging in these values, we get:

CI = 6.43 ± 1.895 * (2.69/√7)

Simplifying this expression gives us the confidence interval (2.56, 10.30). Therefore, we can say with 90% confidence that the average age of cars sold for the first time is between 2.56 and 10.30 years.

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Related Questions

If x is positive, which of the following could be correct ordering of 1x 1 � , 2x 2 � , and x2 � 2 ? I. x2<2x<1x � 2 < 2 � < 1 � II. x2<1x<2x � 2 < 1 � < 2 � III. 2x

Answers

The correct ordering, assuming x is positive, is III: 2x < x² < 2 < 1/x²< 1.

Let's evaluate each option one by one:

I. x² < 2x < 1/x² < 2 < 1

If x is positive, x² will always be greater than 1/x². Therefore, this ordering is not possible.

II. x² < 1/x² < 2x < 1 < 2

Similarly, x² will always be greater than 1/x². Therefore, this ordering is also not possible.

III. 2x < x² < 2 < 1/x² < 1

For this ordering to be true, we need to confirm that 2x is indeed less than x². Since x is positive, we can divide both sides of the inequality by x to preserve the inequality direction. This gives us 2 < x. As long as x is greater than 2, this ordering holds true. Therefore, the correct ordering, assuming x is positive, is III: 2x < x² < 2 < 1/x²< 1.

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Find the equation of the line pecified. The lope i 7, and it pae through ( 8, 6). A. Y = 7x - 50
b. Y = 14x - 50
c. Y= 7x 6
d. Y = 7x 62

Answers

That the equation of the line is y = 7x - 50.

The equation of a line with slope m passing through the point (x1, y1) is given by: y - y1 = m(x - x1).

In this case, the line has a slope of 7 and passes through (8, 6). Therefore, we can plug in the values for m, x1, and y1 into the equation above to find the desired equation.

Substituting in 7 for m, 8 for x1, and 6 for y1, we can rewrite the equation as: y - 6 = 7(x - 8).

Simplifying, we find that the equation of the line is y = 7x - 50.

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A farmers has 17 sheep and all but nine die. How many are left?

Answers

Answer:

9 sheeps.

Step-by-step explanation:

Note the usage of words.

If you remove "but nine", you will be left with "all... die", which means that he will have 0 sheep. However, the usage of 9 implies that there are some remaining; The number attached suggest the amount left.

9 sheep are left.

Answer:

Step-by-step explanation:

What is the conversion of 720 hours to days?

Answers

720 hours is equal to 30 days.

One hour contains 60 minutes or 3,600 seconds.

In one day there are 24 hours.

Earth requires 24 hours to complete one rotation.

It is defined as exactly 86,400 seconds.

1 Hour equal to 0.041666667 Days

We have to convert 720 hours to days,

We have to divide the number of given hours by the number of hours in one day.

There are 24 hours in a day,

so we can write it as:

720 hours / 24 hours/day = 30 days

Hence, After conversion we get 720 hours is exactly equal to 30 days.

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Amanda's parents had a birthday dinner for her at Sushi Yama restaurant. The bill came to $74 before the tip. They left an 18% tip. What was the total cost of Amanda's birthday dinner?

Answers

Answer:

$87.32

Step-by-step explanation:

Step one:

given data

we are told that the initial bill is $74

thereafter they gave a tip worth 18% of the bill

let us compute what 18% of $74 will amount to

Step two:

=18/100*74

=0.18*74

=$13.32

The added expenses is $13.32

Hence the total cost is

the initial bill plus the tip

=74+13.32

=$87.32

What's the correct math expression for 25 less than 32

Answers

25>32

less than = >
less than or equal to = >

1. Find the perimeter of a square whose diagonal √14

Answers

Answer:

P = 4 sqrt(7)

Step-by-step explanation:

The diagonal is sqrt(14)

The triangle is 45 - 45 -90

The side lengths would then be the hypotenuse divided by sqrt(2)

sqrt(14)/sqrt(2) = sqrt(7)

The perimeter of a square is

P =4 s where s is the side length

P = 4 sqrt(7)

Helppppp, I don’t know what to do, I just really need the answer

Answers

The completed statement on the exponential model that fits the data in the question is presented as follows;

The exponential model indicates that the plastic production has a 7.88% growth per year. The model predicts that the production 15 years after 1960 was closest to 30 million metric tons, because the correlation coefficient indicates a strong correlation between the model and the data, this prediction is correct.

What is a correlation coefficient?

The correlation coefficient is an indication of the level at which the variables are interdependent.

The table of values in the question can be entered into a spreadsheet application as follows;

In the spreadsheet application, enter Year since 1960 values in a column, and the Plastic Production in an adjacent columnSelect the all the data entered into the spreadsheet document such as MS Excel, then select the Insert tabIn the charts section select scatter plot to create a scatter plot of the dataIn the Design tab, that appears when the chart is selected, select the Add Chart Element button access the Trendline functionSelect the Exponential trendline from the menu for trendlinesThe exponential trendline is then created by the spreadsheet application

The equation for the trendline obtained from MS Excel is presented as follows; f(x) = 9.2179·e^(0.0788·x)

The growth rate from the above exponential function is 7·88% per year

The production 15 years after 1960 is therefore;

f(15) = 9.2179·e^(0.0788 × 15) ≈30.06

The number of plastic produced 15 years after 1960 is about 30 million metric tons

The correlation coefficient obtained from MS Excel is R² = 0,9157, which indicates a strong correlation between the data and the model

The prediction is correct based on the strong correlation between the year and the number of plastic produced.

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true or false: if you are given a graph with two shiftable lines, the correct answer will always require you to move both lines.

Answers

False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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Student X and Student Y are both studying for a test. Student X studies 2 hours every day, while Student Y starts studying 4 days after Student X and studies 3 hours each day. Define a variable and write an equation that represents the information given. Determine the number of days after Student X starts studying when both students will have studied the same number of hours.

Answers

Answer:

Let's define the variable "d" to represent the number of days after Student X starts studying when both students will have studied the same number of hours.

Student X will study for d days, and since they study 2 hours each day, they will have studied a total of:

2d hours

Student Y will start studying 4 days after Student X, so by the time Student Y starts studying, Student X will have already studied for d + 4 days.

Student Y will study for d days, and since they study 3 hours each day, they will have studied a total of:

3d hours

To find the number of days when both students will have studied the same number of hours, we can set the two expressions for total hours equal to each other and solve for d:

2d = 3d - 12

Adding 12 to both sides:

2d + 12 = 3d

Subtracting 2d from both sides:

12 = d

Therefore, both students will have studied the same number of hours 12 days after Student X starts studying.

Step-by-step explanation:

Answer: Let's define the variable t as the number of days after Student X starts studying.

Then the equation that represents the total number of hours each student has studied in terms of t is:

For Student X: Hx = 2t

For Student Y: Hy = 3(t-4)

Note that we subtract 4 from t for Student Y since they start studying 4 days after Student X.

To find the number of days after Student X starts studying when both students will have studied the same number of hours, we can set the two equations equal to each other and solve for t:

2t = 3(t-4)

2t = 3t - 12

t = 12

Therefore, it will take 12 days after Student X starts studying for both students to have studied the same number of hours.

Step-by-step explanation:

A and B are oppoite vertice of a regular ix-ide hape, the point C and D are the midpoint of two oppoite ide. The area of the regular ix-ided hape i 60. Determine the product of the length of the line AB and CD!

Answers

The product of AB and CD in a regular hexagon with an area of 60 is (40 / √3) / 2.

To find the product of the length of AB and CD in a regular hexagon, we have to initially calculate the length of one side of the hexagon and later use that information to find the length of AB and CD.

Let us say that the length of one side of the hexagon = s.

W.k.t the area of the hexagon = 60, so we can use the formula for the area of a regular hexagon:

Area = (3 * √3) / 2 * $s^2$

Making this equal to 60 and solving s:

60 = (3 * √3) / 2 * $s^2$

120 = 3 * √3 * $s^2$

40 = √3 * $s^2$

(40 / √3) = $s^2$

Taking the square root of both sides:

s = (40 / √3)^(1/2)

Now that we found the length of one side of the hexagon, So we can use that to find the length of AB and CD.

AB = the length of one side of the hexagon times the square root of 3, CD = the length of one side of the hexagon divided by 2.

So,

AB = s * √3

CD = s / 2

Now, we can find the product of AB and CD by multiplying them together:

AB * CD = s * √3 * s / 2

AB * CD = (s^2 * √3) / 2

AB * CD = (40 / √3) / 2

So the product of AB and CD in a regular hexagon with an area of 60 is equal to (40 / √3) / 2.

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Kellie ran 3 laps around the high school track if the total distancekellie ran was 7 1/3 miles how long is each lap around the track

Answers

Answer:

22 miles.

Step-by-step explanation:

7 1/3 ×3=22

Find the first five terms. Please solve

Answers

Answer:

a1=3, a2=6, a3=12, a4=24, a5=48

Step-by-step explanation:

a7=a*r^6=192

a10=a*r^9=1536, r^3=8, r=2 and a=3

a1=3, a2=6, a3=12, a4=24, a5=48

which expression is equivalent to (4 square root 5 to the power of 3) to the power of 1/2?

Answers

the answer is on the photo

Solve the system of equations by graphing.y = 1/2x + 1 y = 1/2x - 2

Answers

Answer:

The given system of equations has no solution

Explanation:

Given the pair of equations:

$\begin{gathered} y=\frac{1}{2x}+1\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(1) \\ \\ y=\frac{1}{2x}-2\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}$

From equations (1) and (2), we can write:

$\frac{1}{2x}+1=\frac{1}{2x}-2$

Subtrac 1/2x from both sides, we are left with no variable x, therefore, the system has no solution

6 = a divided by 4 + 2

Answers

Answer:

Step-by-step explanation:

36 is the answer hope this helped!

What is the product of (2i) and (5+3i)?
Group of answer choices

-6 + 10i

10 + 6i

16i

10 - 6i

Answers

The value of the product expression given as product of (2i) and (5+3i) is 10i -6

How to determine the product?

The product expression is given as:

product of (2i) and (5+3i)

Rewrite the expression as:

(2i) * (5+3i)

Open the brackets

(2i) * (5+3i) = 10i + 6i^2

Evaluate

(2i) * (5+3i) = 10i + 6(-1)

This gives

(2i) * (5+3i) = 10i -6

Hence, the value of the product expression given as product of (2i) and (5+3i) is 10i -6

Answers

The length of the rectangular garden is x + 7 units and the width = x + 5 units.

Area of a ractangle= length X breadth

Here it is given that the area = x² + 12x + 35

Therefore, length X width = x² + 12x + 35

Therefore, to get the length and width of the rectangular plots we need to factorize the expression x² + 12x + 35.

x² + 12x + 35

Here the constant is 35.

First, we need to find such 2 numbers whose product is 35 but the sum or difference is 12.

This can be achieved by 5 and 7

5 X 7 = 35

5 + 7 = 12

Now we break 12x up in 5x + 7x to get

x² + 5x + 7x + 35

Now we take x common from the first 2 terms and 7 common from the last 2 terms.

x(x + 5) + 7(x + 5)

(x + 5)(x + 7)

Hence we get x +5 and x + 7 units.

By convention, length is the larger value while the width is the smaller one. Hence we get, length = x + 7 units and width = x + 5 units

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There is a population of 50 bacteria in a colony. If the number of bacteria doubles every 280
hours, what will the population be 560 hours from now?

Answers

I think its 100 at 280 then 200 at 560 since it doubles. sooo 560

$Simplify:\sqrt{64x^8y^2z^1^2}$

Answers

Answer:

theres nothing here....

Which expressions are equivalent to 2 ( 4 f + 2 g ) Choose 3 answers

Answers

Answer:

Since there are no choices to choose from, I'll make it up.

8f + 4g

8(f + 1/2g)

4(2f + g)

Hope this helps!! Please mark as brainliest if you don't mind! Thanks ^^

Please help im so confused rn :((

Answers

Answer:

7/12/14/6

7/12*1/14*1/6

1/12*1/2*1/6

1/144, should be your answer.

Answer:

1/144

Step-by-step explanation:

7/12÷14÷6=

Write an equivalent expression for 12^3 • 12^9 • 12^4 • 12^2

Answers

9514 1404 393

Answer:

12^18

Step-by-step explanation:

Each exponent tells you the number of times 12 is repeated as a factor. The total number of repetitions of 12 as a factor in this product is ...

3 +9 +4 +2 = 18

The equivalent expression is 12¹⁸.

Suppose the market is competitive. Sketch the supply and demand and state the equilibrium quantity.
Suppose the market is competitive. Sketch the supply and demand and state the equilibrium quantity. 1.) Using the multipoint drawing tool, graph the market demand from the four hospitals. Label your line 'Demand'. (Use the "Esc" key after you have placed your last point to exit the drawing tool.) 2.) Using the multipoint drawing tool, graph the market supply of the four producers. Label your line 'Supply'. (Use the "Esc" key after you have placed your last point to exit the drawing tool.) The equilibrium quantity of ventilators sold is units. Carefully follow the instructions above and only draw the required pbjects.

Answers

In a competitive market, we need to graph the market demand and supply curves and determine the equilibrium quantity. The equilibrium quantity represents the quantity at which the demand and supply curves intersect.

To sketch the supply and demand curves, we first need to gather information on the market demand and supply. The demand curve represents the quantity of ventilators that the four hospitals are willing to purchase at different prices, while the supply curve represents the quantity of ventilators that the four producers are willing to sell at different prices.

Using the multipoint drawing tool, we can plot the market demand curve based on the data provided for the hospitals. Label this line as 'Demand'. Next, using the same tool, we can plot the market supply curve based on the data provided for the producers. Label this line as 'Supply'.

The equilibrium quantity is determined at the point where the demand and supply curves intersect. It represents the quantity of ventilators that will be sold in the market. To find this point, we identify the quantity at which the demand and supply curves meet on the graph.

By following the instructions and accurately plotting the demand and supply curves, we can determine the equilibrium quantity of ventilators sold in the market.

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A student solves the following equation and determines that the solution is −2. Is the student correct? Explain. 3 a 2 − 6a a2 − 4 =.

Answers

Answer:

3a²-6a=a²-4

2a²-6a-4=0

a²-3a-2=0

a=2 or a=1

marcio is playing a video game. the number of minutes, x, marcio plays is related to the number of points, y, he earns. How many points does he earn per minute

Answers

Answer:

85 points per minute

Step-by-step explanation:

the points earned per minute is calculated as

$\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₂, y₂) = (200, 17007) and (x₁, y₁ ) = (100,8507) ← 2 ordered pairs from table

points earned per minute = $\frac{17007-8507}{200-100}$ = $\frac{8500}{100}$ = 85

Find the exact value of each.
Find the exact value of each. MUST SHOW WORK 8) 1+tan 42°tan 12°/ tan 42° - tan 12°

Answers

Given expression is;1+tan 42°tan 12°/ tan 42° - tan 12°.

To find the exact value of given expression.

First, find the value of tan (42)° + tan (12)°tan (42)° + tan (12)° = tan (42+12)°tan (42)° + tan (12)° = tan (54)°

Now, put the value in the expression.1+tan 42°tan 12°/ tan 42° - tan 12°= 1 + tan (42)° + tan (12)°/tan (42)° - tan (12)° = 1 + tan 54° / tan (42-12)° = 1 + tan 54° / tan 30°.

Now, put the value of tan 54° and tan 30°= 1 + (1.37638192047) / (0.57735026919)= 3.73205The main answer is 3.73205.

The summary: To find the exact value of given expression, First, find the value of tan (42)° + tan (12)°tan (42)° + tan (12)° = tan (42+12)°tan (42)° + tan (12)° = tan (54)°Now, put the value in the expression.1+tan 42°tan 12°/ tan 42° - tan 12°= 1 + tan (42)° + tan (12)°/tan (42)° - tan (12)° = 1 + tan 54° / tan (42-12)° = 1 + tan 54° / tan 30°Now, put the value of tan 54° and tan 30°= 1 + (1.37638192047) / (0.57735026919)= 3.73205.

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A fashion blog has 22,000 page views so far. In addition, that number grows 25% every week. Which function can be used to determine the number of page views the blog will have after x weeks?

Answers

Answer: 22,000 * 1.25^ x

Step-by-step explanation:

The number of pages grows at 25% every week. This number is based on the previous week's number of pages so the increase in page number is being compounded.

Use the future value equation to determine the number of pages after x weeks.

FV = Amount * ( 1 + rate of increase) ^ time

= 22,000 * ( 1 + 25%) ^ x

= 22,000 * 1.25^x

50 points
you can just draw a line or something

Answers

______________________

for the simple harmonic motion equation d=9 cos(pi/2t) what is the period

Answers

The period of the simple harmonic motion described by the equation d = 9 cos(pi/2t) is 4 seconds. The period is the time it takes for the motion to complete one full cycle, and in this case, it takes 4 seconds to do so.

To understand why the period is 4 seconds, let's examine the equation. The cosine function has a period of 2π radians or 360 degrees. In this equation, the argument of the cosine function is (π/2)t. To find the period, we need to determine the value of t that corresponds to one full cycle of the cosine function.

Since the argument is (π/2)t, one full cycle occurs when (π/2)t increases by 2π radians or 360 degrees. Solving for t, we have:

(π/2)t = 2π

Dividing both sides by π/2, we get:

t = 4

Therefore, the value of t that corresponds to one full cycle is 4 seconds, which is the period of the simple harmonic motion described by the equation.

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