Find the constant of variation for the relation and use it to write an equation for the statement.
If y varies as directly as the square of x, and y
75/8 when x = 5, find y when x = 2

The statement that "If the correlation between the growth of a stock and the growth of the economy as a whole is close to 1, then this would be a good stock to hold during a recession when the economy shrinks" is False.

If the correlation between the growth of a stock and the growth of the economy as a whole is close to 1, then this would not be a good stock to hold during a recession when the economy shrinks. The statement is false.

The correlation can be defined as the statistical relationship between two variables that shows the strength of their association.

A positive correlation is one where the two variables move in the same direction, while a negative correlation is one where the two variables move in opposite directions.

A correlation of +1 indicates a perfect positive correlation, while a correlation of -1 indicates a perfect negative correlation. A correlation of 0 indicates no correlation.

A correlation between 0 and +1 or 0 and -1 indicates a positive or negative correlation, but it is not perfect.

If a stock is positively correlated with the economy, it means that it is affected by the economy's performance. As a result, when the economy grows, the stock grows, and when the economy shrinks, the stock shrinks.

When the economy is in a recession, it is more likely that the stock will be negatively affected. As a result, holding such a stock during a recession when the economy shrinks is not recommended.

Therefore, if the correlation between the growth of a stock and the growth of the economy as a whole is close to 1, then this would not be a good stock to hold during a recession when the economy shrinks. The statement is false.

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The one-sample chi-square test is used to determine whether the distribution of a single categorical variable significantly differs from what would be expected by chance. The statement is True.

The one-sample chi-square test is a statistical test used to determine if there is a significant difference between the observed frequency and the expected frequency in a single categorical variable. It compares the observed frequency distribution of a variable to the expected frequency distribution, assuming that the null hypothesis is true.

This test compares observed frequencies to expected frequencies and calculates a chi-square statistic to assess the significance of the difference.

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Answer:

1/2 > 3/8

Step-by-step explanation:

To compare the answers, we need to change them to the same denominator.

2x4=8

So we can create an equivent fraction of 1/2 by dividing both numbers by 4:

1x4=4

2x4=8

1/4=4/8

Now we are comparing 4/8 and 3/8, and we can see clearly that 4/8 is greater than 3/8 because 4 is greater than 3.

Hope this helped!

The probability that the sample mean would differ from the population mean by less than 0.5 millimeters is 0.3970.

Given mean diameter of 145 millimeters, standard deviation of 6 millimeters.

We have to find out the probability that the sample mean would differ from the population mean by less than 0.5 millimeters.

μ=145 and ,σ=60 ,n=39 then

s=60/\(\sqrt{39}\)=0.96

By finding the probability that the sample mean would differ by less than 0.5 mm equal to p value of Z when X=145+0.5=145.5 mm subtracted by the p value of Z when X==145-0.5=144.5 mm.

When X=145.5 mm

Z=(X-μ)/σ

By central limit theorem

Z=(145.5-145)/5

=0.5/0.96

=0.52

p value of 0.52=0.6985.

When X=144.5

Z=(144.5-145)/0.96

=-0.5/0.96

=-0.52

p value of -0.52=0.5-0.1985=0.3015

Required probability=0.6985-0.3015=0.3970.

Hence the probability that the sample mean would differ from the population mean by less than 0.5 mm is 0.3970.

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Step-by-step explanation:

\(circumference = 2\pi\: r \: \\ = 2 \times 3.14 \times 86 \\ = 540.08\)

Answer:

540.08

Step-by-step explanation:

Answer:

1.23

0.067

25.34

Step-by-step explanation:

10^2 = 100

The point moves two places towards the right

Answer:

The correct answer is:

It is a continuous random variable (B)

Step-by-step explanation:

Continuous Random Variables are variables that take on a number of possibilities of values that cannot be counted. The values have infinite possibilities. In this example, the height of a Giraffe measured in meters can be an unlimited possibility if values say, 10.5m, 15.22m 12.0m etc. The possibilities are endless.

Discrete Random variables are variables that take on a number of possibility of occurrences that can be counted. For instance, if a dice is rolled, the possibilities can either be a 1, 2, 3, 4, 5 or 6. There are six values that can be gotten, nothing in-between.

I think the answer is B.

Please check to make sure.

Answer:C. 17,280

Step-by-step explanation:It this way because it cant be 3k obv or 6k. And it says 72% down not up so not d either :D

he residual value of the car be after three year is mathematically given as

R=17280

Option C

Question Parameters:

A car with a MSRP of $24,000 for three years.

After three years, the leasing company expects the car to have a value of 72%

Generally the equation for the  residual value  is mathematically given as

R=percentage of drop *original price

R=0.72*24000

R=17280

Therefore, the residual value of the car be after three years is R=17280

Option C

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Answer:

38.5 mm^2

Have a nice day!

Step-by-step explanation:

Area = πr^2

Area = π(3.5^2)

Area = π(12.25)

Area = 38.48451...

Area = 38.5

The centre line of a control chart is calculated by computing the average (mean) of the data for every period.

In control chart analysis, the centre line represents the central tendency or average value of the process being monitored. It is typically obtained by calculating the mean of the data points collected over a specific period. The purpose of the centre line is to provide a reference point against which the process performance can be compared. Any data points falling within acceptable limits around the centre line indicate that the process is stable and under control.

The calculation of the centre line involves summing up the values of the data points and dividing it by the number of data points. This average is then plotted on the control chart as the centre line. By monitoring subsequent data points and their distance from the centre line, deviations and trends in the process can be identified. Deviations beyond the control limits may indicate special causes of variation that require investigation and corrective action. Therefore, the centre line is a critical element in control chart analysis for understanding the baseline performance of a process and detecting any shifts or changes over time.

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Answer:

6 ways she can choose a course

The simplified expressions are:

1. (3a - 4)³ = 9a³ - 36a² + 144a - 64

2. (3 - a)³ = -a³ + 9a² - 27a + 27

We are given two  mathematical expressions. The expressions are algebraic. Each expression contains two terms. The expressions are binomial. Let the first and second expressions be denoted by the variables "E1" and "E2", respectively. The identity is given below.

(a - b)³ = a³ - b³ + 3ab² - 3a²b

We have to simplify the expressions. We will use the identity of cubic to expand the given expressions. The expressions are given below.

We will first simplify the first expression.

E1 = (3a - 4)³

E1 = (3a)³ - (4)³ + 3(3a)(4)² - 3(3a)²(4)

E1 = 9a³ - 64 + 144a - 36a²

E1 = 9a³ - 36a² + 144a - 64

We will now simplify the second expression.

E2 = (3 - a)³

E2 = 3³ - a³ + 3(3)(a)² - 3(3)²(a)

E2 = 27 - a³ + 9a² - 27a

E2 = -a³ + 9a² - 27a + 27

Hence, both expressions are simplified.

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Answer:

f(x)=740

Step-by-step explanation:

f(x)=45x+200

If f(12)

f(x) = 45(12) +200

f(x) = 540 +200

f(x)=740

The range is 740 and we get the range by substituting x = 12 in the given function.

Given,

John's health club has an enrollment fee of $200 and costs $45 a month. The total cost of the membership is a function of the number of months. The function is represented by f(x)=45x+200.

The domain is 12 months.

We need to find the range and explain it.

The domain is the input value and the range is the output value of the given function.

We have a function:

f(x) = x + 1

f(1) = 1 + 1 = 2

Domain = 1.

Range = 2.

Find the range of f(x) = 45x + 200.

We have,

Domain = 12 months.

x = 12.

f(12) = 45 x 12 + 200

       = 540 + 200

       = 740.

Thus the range is 740 and we get the range by substituting x = 12 in the given function.

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Answer:

120

Step-by-step explanation:

15 ⋅ 8 = 120

Answer:

Step-by-step explanation:

The area of a parallelogram is the product of the base and height.

A=bh

A=15(8)

A=120cm^2

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

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Step-by-step explanation:

You can find the area of a right triangle the same as you would any other triangle by using the following formula:

A = (1/2)bh, where A is the area of the triangle, b is the length of the base and h is the height of the triangle; However, with a right triangle, it's much more convenient in finding its area if we utilize the lengths of the two legs (the two sides that are shorter than the longest side, the hypotenuse and that are perpendicular to each other and thus form the right angle of the right triangle), that is, since the two legs of a right triangle are perpendicular to each other, when we treat one leg as the base, then, consequently, we can automatically treat the length of the other leg as the height, and if we initially know the lengths of both legs, then we can then just plug this information directly into the area formula for a triangle to find the area A of the right triangle.

For example: Find the area of a right triangle whose legs have lengths of 3 in. and 4 in.

Make the 4 in. leg the base. Since the two legs of a right triangle are perpendicular to each other, then the length of the other leg is automatically the height of the triangle; therefore, plugging this information into the formula for the area of a triangle, we have:

A = (1/2)bh

= (1/2)(4 in.)(3 in.)

= (1/2)(12 in.²)

A = 6 in.² (note: in.² means square inches)

The DC current gain (βdc) of the transistor is 73.

The DC current gain (βdc) of a transistor is the ratio of the collector current (IC) to the base current (IB) at DC conditions. Therefore, to determine the βdc of a transistor with IB = 50 µA and IC = 3.65 mA, we simply substitute these values into the equation:

βdc = IC / IB

βdc = 3.65 mA / 50 µA

βdc = 73

Therefore, the DC current gain (βdc) of the transistor is 73.

This result indicates that for every 1 µA of base current, the transistor can allow 73 µA of collector current to flow. A high βdc value indicates that the transistor can provide significant amplification in a circuit. In addition, the βdc value is essential in selecting the appropriate biasing resistors and determining the operating point of the transistor in amplifier circuits.

Thus, by determining the βdc value, we can gain valuable insights into the performance characteristics of a transistor and how it can be used in various circuit designs.

Therefore, The DC current gain (βdc) of the transistor is 73.

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The equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

What is function?

For the parent function f(x) and a constant k >0,

then, the function given by  

g(x) = kf(x) can be sketched by vertically stretching f(x) by a factor of k if k>1 (or)

if 0 < k < 1 , then it is vertically shrinking f(x) by a factor of k

As per the given statement that the graph of f(x) is stretched vertically by a factor of 3 i.e

k = 3 >1

so, by definition

g(x) = 3 f(x) = 3 . 8(3)ˣ

= 8(3)ˣ⁺¹

= 24 (3)ˣ

Hence, the equation of g(x) is 24 (3)ˣ when the graph is stretched vertically by a factor of 3 to form the graph g(x).

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Answer:

33.75 ft

Add up every time it travels both up and down.

12 + 6 + 6 + 3 + 3 + 1.5 + 1.5 + .75 = 33.75 on the fourth landing.

Step-by-step explanation:

The ball traveled a total of 12 feet vertically when it hit the ground for the fourth time.

The length along a line or line segment between two points on the line or line segment.

The ball is dropped from a height of 12 feet, so we can represent this with the point (0,12) on a coordinate plane.

The ball then bounces up to a height of 6 feet (half the height of the previous bounce), so we can represent this with the point (1,6) on the coordinate plane.

The ball then bounces down to a height of 3 feet (half the height of the previous bounce), so we can represent this with the point (2,3) on the coordinate plane.

The ball then bounces up to a height of 1.5 feet (half the height of the previous bounce), so we can represent this with the point (3,1.5) on the coordinate plane.

The ball then hits the ground for the fourth time.

The distance of the first bounce is 12 - 6 = 6 feet.

The distance of the second bounce is 6 - 3 = 3 feet.

The distance of the third bounce is 3 - 1.5 = 1.5 feet.

The distance of the fourth bounce is 1.5 - 0 = 1.5 feet

The total distance the ball traveled vertically is: 6 + 3 + 1.5 + 1.5 = 12 feet

Hence, the ball traveled a total of 12 feet vertically when it hit the ground for the fourth time.

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Answer:

sqaure root of 11

5

6

square root of 40

Step-by-step explanation:

square root of 11- 3.31

sqaure root of 40- 6.32

6

5

hope this helps :)

hello

the answer to the question is:

(√8x)(5√2x) = (2√2x)(5√2x) = 10√2x

therefore B) is the correct answer

Answer:

B) 5

Step-by-step explanation:

They have a total of 4+8+3+5 = 20 bracelets

There is 4 girls

20/4 = 5

Answer:

(7,-6)

Step-by-step explanation:

The solution of the systems of equations is the point where the lines intersect. So just looking at the graph, you can see that the point (7,-6) is where the two lines intersect.

Hope this helps! :)

Answer:

Each child gets $36666.67, each grandchild gets $18333.33

Step-by-step explanation:

220000/6= 36666.67,

36666.67/2= 18333.33

9 servings are there in 22.5 ounces of trail mix.

Given:

The weight of one serving of trail mix is 2. 5 ounces.

1 serving = 2.5 ounces

Number of servings = 22.5 ounces / 1 serving

= 22.5 / 2.5

= 225/10/25/10

= 225/25

= 9 servings.

Therefore 9 servings are there in 22.5 ounces of trail mix.

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The relative frequency of Katie losing the game is 3/5

Relative frequency is the frequency in relation to the total frequency of the given requirement. It is defined as-

Subgroup frequency/ Total frquency.

Now, coming to the given frequency-

Outcome     Frequency

Win                 2

Lose               3

Total               5

Hence, the relative frequency of losing the game = frequency of losing/ total frequency = 3/5

Hence the relative frequency is 3/5 for Katie to lose the game.

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There's a 95% chance that the true proportion is in the confidence interval.

When we want to estimate a property of a population (a population's parameter), without surveying the population, we use samples.

Then, with the information of the samples we can calculate the statistics and infere properties about a population. This inferences obviously came with some uncertainty, depending on the properties of the sample and specially the sample size.

When we talk about confidence intervals, we use the statistic of the sample (in this case, the mean) to estimate a range of values it is expected to find the true mean of the population. The width of this interval depends on the sample standard deviation and the sample size.

The value of the confidence interval (95%, 99%, etc.) represent the probability that the true mean is within this interval.

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Answer:

The answer is given below

Step-by-step explanation:

The distance from the lake to the car is 3 miles and it takes 2 hours. The velocity of the hiker is 3/2 mi/hr. Therefore f(t) which is the distance from the car t hours after 7 A.M is given by:

\(f(t)=\frac{3}{2}t\)

When coming back on Sunday morning, the distance g(t) from the car at any point in time is given by:

\(g(t)=3-\frac{3}{2}t\)

a)

\(f(t)=\frac{3}{2}t\\f(0)=\frac{3}{2}(0)=0\ mile\\f(2)=\frac{3}{2}(2)=3\ miles\)

\(g(t)=3-\frac{3}{2}t\\g(0)=3-\frac{3}{2}(0)=3\ miles\\g(2)=3-\frac{3}{2}(2)=2-2=0\ mile\\\)

b)

\(h(t)=f(t)-g(t)=\frac{3}{2}t -(3-\frac{3}{2}t)=\frac{3}{2}t -3+\frac{3}{2}t=3t-3\\h(t)=3t-3\\h(0)=3(0)-3=0-3=-3\\h(2)=3(2)-3=6-3=3\)

c)

According to Intermediate Value Theorem, there exist a point b where f(b) = g(b). i.e. f(b) - g(b) = 0

\(h(b)=f(b)-g(b)=0\\h(0)=-3,h(2)=3\)

This means there exist a point b within the interval [-3, 3] where f(b) - g(b) = 0