The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table.

A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38.

Using technology, what is the correlation coefficient?

–0.997
–0.503
0.503
0.997

The required  the average daily census for this period is 12.

A Average can be characterized as the amount of all numbers isolated by the all out number of values. A mean can be characterized as a normal of the arrangement of values in an example of information. At the end of the day, a normal is likewise called the math mean. It is known as a mean to Depict the average.

there were 2,200 inpatient service days.

Number of days between this period = 184 days

So, average daily census = 2200/184

11.95

⇒ 12 up to whole number.

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Observe from the data that a director of manufacturing must persuade management that the proposed production process cuts costs in order for the new way to be implemented.

The average cost of the present production process is $220 per hour.

What does "cost" mean?

The sum paid for anything, or its equivalent, is referred to as the price. the investment or expenditure (as of labor or sacrifice) made to obtain a thing; the average cost of a college education has increased significantly.

a)

In this instance, note how the researcher conducts experiments to ensure that the new method will function with a

mean price was under $220. Which is.µ < 220

The following is the Null and Alternative Hypothesis:

Negative hypothesis H.: The new technique will be operational at a mean cost of at least $220.

Therefore, H: µ > 220

An alternative theory. H.: The new technique will function at a mean cost that is lower than

$220

Meaning H µ < 220

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The probability, which is calculated using the hypergeometric distribution, is 0.845, or 84.5%.

Given,

The answer to this question involves using the hypergeometric distribution because the patients are randomly selected from the sample without replenishment.

Hypergeometric distribution:

The probability of x successes is given by:

P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]

The parameters are:

x is the number of successes.

N is the size of the population = 56074

n is the size of the sample = 40

k is the total number of desired outcomes = 235

The number of unique combinations of x objects from a set of n elements is provided by the following formula:

Cₙ,ₓ = n! / x! (n - x)!

The probability that none left against medical advice is P(X = 0), so:

P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]

P(X = 0) = h(0, 56074, 40, 235) = (C₂₃₅, ₀ × C₅₆₀₇₄₋₄₀, ₄₀₋₀) / C₅₆₀₇₄, ₄₀

= (C₂₃₅, ₀ × C₅₅₈₃₉, ₄₀) /  C₅₆₀₇₄, ₄₀

= 0.845

The probability is 0.845 = 84.5%.

Therefore,

The probability that none of them left the treatment center against medical advice is 0.845 = 84.5%

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The solution of x in the equation is 79/3

From the question, we have the following parameters that can be used in our computation:

y = 69

5x + 15 = y + 2x - 5

Substitute y = 69 in the equation 5x + 15 = y + 2x - 5

So, we have

5x + 15 = 69 + 2x - 5

Collect the like terms

This gives

5x - 2x =69 - 5 + 15

Evaluate the like terms

This gives

3x = 79

Divide both sides by 3

x = 79/3

Hence, the solution is 79/3

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By graphing the system of equations, we will see that the solution is x = 3 and y = -2

Here we have te following system of equations:

y = -x + 1

y = (1/3)*x - 3

To solve the system we can graph bot equation in the same coordinate axis and try to identify the intersection points between the graphs.

Below you can see the graph

We can see that the interception point is (3, - 2), then the solution to the system of equations is x = 3 and y = -2.

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Answer: 25 days

Step-by-step explanation:

We know that it takes 55 days with 15 workers, so we need to find how many days it takes with 1 worker by taking 55 timed 15 = 825 days for 1 worker.

Then we take 825 divided by 33 and get 25 days for 33 workers.

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Answer:

Sean can rub in one minute:

260 meters

Step-by-step explanation:

2600 meters ⇒ 10 minutes

A meters ⇒ 1 minute

A = 2600 meters * 1 minute / 10 minute

A = 260 meters

Answer:  The correct answer is Sean can run 260 meters in 1 minute

Step-by-step explanation:

What we know:

What we need to find out:

Divide the total meters by the total minutes to find out the meters per minute

2600 meters / 10 minutes = 260 meters per minute

Distance in 1 minute

Time * meters per minute = distance

1 * 260 = 260 meters in 1 minute

The expression 16a⁴b + 8ab³ can be written as 8ab(2a³ + b²). Option (D) is correct.

GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.

The given expression is,

16a⁴b + 8ab³

Simplify the expression, by factor method,

8 x 2 x a x a x a x a x b  + 8 x a x b x b x b

The common term is 8ab,

8ab(2a³ + b²)

The required expression is 8ab(2a³ + b²).

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answer : x≤-6

steps:

3x+2≥4x+8

-x≥6

x≤-6

Answer:

x≤−6

View graph below

Step-by-step explanation:

x≤−6

Solution Steps

3x+2≥4x+8

Subtract 4x from both sides.

3x+2−4x≥8

Combine 3x and −4x to get −x.

−x+2≥8

Subtract 2 from both sides.

−x≥8−2

Subtract 2 from 8 to get 6.

−x≥6

Divide both sides by −1. Since −1 is negative, the inequality direction is changed.

x≤−6

X could be from -6 to -infinity.

Answer:

D

Step-by-step explanation:

A simpler way to see it, of course, is that the mentioned line segments lie on the same line, so they must have the same slope.

The expression in terms of x that represents the total amount that Zoe paid is 1.2x

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

A tax of 5% is applied to the bill.

Zoe decides to leave a tip of 15% on the entire bill (including the tax).

let the bill cost $x.

So, the price after tax and tip

= x+ 5% of x+ 15% of x

= x + 0.05x + 0.15x

= x + 0.20x

= 1.2x

Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x

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Examining the function  -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0

Where a parabolic curve opens up or down in this case depends on the sign on the coefficient of the x².

The coefficient of  x² is a and in this function is -9

A negative coefficient leads to opening downwards while a positive coefficient will result to opening upwards

The y intercept

-9x² + 7x = 0

x(-9x + 7) = 0

x = 0

-9x + 7 = 0

-9x = -7

x = 7/9

the y intercept is 0 ad 7/9

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The type of pair of angles that are∠2 and angle∠11 is an alternate interior angles.

When a transversal intersects two coplanar lines, alternate interior angles are formed. They are on the inside of the parallel lines, but on the outside of the transversal.

Angles with the same size that occur on opposite sides of the transversal line are known as alternate angles. The following alternate angles are equal: By drawing a Z shape, we can frequently identify interior alternate angles: Alternate angles are classified into two types: alternate interior angles and alternate exterior angles.

To understand alternate interior angles, imagine a set of parallel lines and then a line intersecting them. The intersecting line is known as a transversal, and all of the angles formed by the parallel lines are known as interior angles.

Both angles are interior angles that lie alternately to each other on the transversal line r. Therefore, they are alternate interior angle.

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The required coupon rate of Samantha's bond is 4%.

The coupon rate is the annual income an investor can expect to receive while holding a particular bond. It is fixed when the bond is issued and is calculated by dividing the sum of the annual coupon payments by the par value. At the time it is purchased, a bond's yield to maturity and its coupon rate are the same.c

We have,

principal amount = $600

Amount after five year = $720

Interest of five year = $(720 - 600) = $120

Then,

Interest of one year = $120/5 = $24

Now,

Coupon rate = ($24/600)×100 = 4%

Thus, required coupon rate is 4%.

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The printed price of the desk on the furniture store is $173. It can be solved by the concept of cost price and selling price.

What is cost price and selling price?

Cost price is the price of the object at which it is purchaged and selling price is the price of the object at which it is sold. If cost price is more than the selling price then the seller will earn a loss. If the cost price is less than then the selling price then the seller will earn a profit.

The cost price of the furniture = $144

Now, 20% of cost price is,

[tex]=\$ 144\times\frac{20}{100}\\=\$28.8[/tex]

Now, price of furniture on the store = Cost price + 20% of cost price

                                                           = $144 + $28.8

                                                           = $172.8$

Round off the price                           = $173

Hence, the printed price of the desk on the furniture store is $173.

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a)

Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is right tailed. And null hypothesis can include equality. Further mu is not a statistics,

So option a) i.e these data comply with our rules, is correct and all other are incorrect.

b)

Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left  tailed. And null hypothesis can include equality. Further sigma is not a statistics,

So option d) is correct and all other are incorrect.

C)

Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left  tailed. And null hypothesis can include equality. Further p is not a statistics,

So option (b) is correct and all other are incorrect.

d)

Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left  tailed. And null hypothesis can include equality. Further mu1 and mu2  is not a statistics,

So option a) i.e these data comply with our rules, is correct and all other are incorrect.

e)

Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left  tailed. And null hypothesis can include equality. Further sigma is not a statistics,

So option (c) correct and all other are incorrect.

f)

Since alternative hypothesis can be of either right tailed or left tailed or a simple hypothesis. Here alternative hypothesis is a simple  hypothesis  And null hypothesis can include equality. Further mu is not a statistics,

So option a) i.e these data comply with our rules, is correct and all other are incorrect.

g)

Since alternative hypothesis can be of either right tailed or left tailed or two tailed. Here alternative hypothesis is two  tailed. And null hypothesis can include equality. Further sigma1 and sigma 2 is not a statistics,

So option a) i.e these data comply with our rules, is correct and all other are incorrect.

h)

Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left  tailed. And null hypothesis can include equality. Further p is not a statistics, and asseter value of H0 should not appear in asserted value in Ha.

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The number of different ways the prizes can be awarded is 161700

From the question, we have the following parameters that can be used in our computation:

The number of different ways the prizes can be awarded is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 100 and r = 3

Substitute the known values in the above equation

Total = ¹⁰⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 100!/97!3!

Evaluate

Total = 161700

Hence, the number of ways is 161700

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The average rate of change of f(x), represented by the table of values, over the interval [-2, 3] is: D. 0.5.

An average rate of change is sometimes referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes with respect to another quantity, over a given interval.

In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:

Average rate of change = [f(b) - f(a)]/(b - a)

Next, we would determine the average rate of change of the function f(x) over the interval [-2, 3]:

a = -2; f(a) = 2.5

b = 3; f(b) = 5

Substituting the given parameters into the formula, we have the following;

Average rate of change = (5 - 2.5)/(3 - (-2))

Average rate of change = 2.5/5

Average rate of change = 0.5.

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Using the conversion factor, we can say that each sheet of paper is 0.0012mm thick.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

So, 500 sheets of A4 paper make up a conventional ream. Each paper measures 297mm in length by 210mm broad, and one ream contains 3742.2cm of paper.

to change cm to mm

3742.2cm = 37422 mm

Sheet 1's surface

(297mm) X 210mm) = 62370mm²

1st volume sheet:

37422mm : 500 = 74.844mm

One sheet's thickness is:

74.844mm : 62370mm = 0.0012mm

Therefore, each sheet of paper is 0.0012mm thick.

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Correct question:
A ream of A4 paper contains 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm find the thickness of each sheet of paper answer in millimeters​

The amount of sales Terry must make is $1667

How to determine the amount in sales?

From the question, we have the following parameters that can be used in our computation:

Commission = 18% of sales

Commission = $300

These parameters mean that

Commission = 18% of sales

Substitute the known values in the above equation, so, we have the following representation

18% of sales = 300

Divide both sides by 18%

Sales = 1667

Hence, the amount is $1667

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Option C, which states that the sample variance is constant as the number of sample values rises when the samples are independent and regularly distributed

Each sampling distribution's variability declines as the sample size go up, becoming more and more leptokurtic. The sample distribution's range is less than the original population's range.

The margin of error & sample size has an inverse relationship, meaning that as sample size rises, sampling error falls. It is because the findings would be more accurate the more evidence you had.

The distribution's dispersion is gauged by the standard error. The dispersion decreases as the sample size increases and the distribution's mean moves closer to the population mean.

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Answer:

B

Step-by-step explanation:

Its the second one, Answer B

As per the given sample size, the shape of the population distribution when conducting t test is approximately normal.

Sampling.

in statistics, sampling refers the statistical procedure that is concerned with the selection of the individual observation; it helps us to make statistical inferences about the population.

Given,

Here we have the sample size is 81.

Now, we need to find the shape of the population distribution when conducting the t test.

Let us consider you are the manager of a restaurant for a fast-food franchise. And in last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.9 minutes.

Now, you are selecting a random sample of 81 orders.

As per the sample size, the sample mean waiting time is 3.72 minutes, with a sample standard deviation of 0.8 minute.

Now, we complete parts (a) and (b) below.

a. here at the 0.01 level of significance, is there evidence that the population mean waiting time is different from 3.9 minutes.

And state the null and alternative hypotheses.

H0: μ▼ H1: μ ▼

So, H0 is sufficient insufficient evidence to conclude that the population mean waiting time is different from 3.9 minutes .

b. According to the sample size is 81,

The shpe of the population distribution when conducting t test is approximately normal. As in the t test is appropriate for a large sample size.

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x = 111°

Interior angles of a polygon

The formula for the sum of the interior angles of a polygon with n sides is: (n-2) x 180°.

The mentioned polygon has 7 sides, so we can put this in the formula:

The sum of the interior angles = (n – 2) x 180°

                                                   = (7 – 2) x 180°

                                                   = 5 x 180°

                                                   = 900°

We already had the value of the 6 interior angles, so we can calculate the 7th angels (x) as follow:

900° = 136° + 118° + 135° + 139° + 141° + 120° + x

        = 789° + x

x = 900° – 789°

  = 111°

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Answer:

As we than it is a diagram of heptagon. so the sum of its angles is 900°

according to the diagram,

x+136°+118°+135°+139°+141°+120°=900°[total sum of heptagon angles]

or, x+ 789°=900°

or, x=900°-789°

or, x=111°

The dimensions of the rectangle should be 150 feet by 400 feet in order to enclose the maximum possible area.

To explain this step by step:

Step 1: We know that the perimeter of a rectangle is equal to 2*length + 2*width.

Step 2: Since we have 600 feet of rope, we can plug this number into the equation: 2*length + 2*width = 600

Step 3: To solve for the length and width, we can divide both sides by 2: length + width = 300

Step 4: We can then separate the equation into two equations: length = 300 - width and width = 300 - length

Step 5: Since we want to find the maximum possible area, we should set width equal to the larger number, 300, and set length equal to the smaller number, 300 - width.

Step 6: Plugging this into the equation, we get: width = 300 and length = 300 - width = 300 - 300 = 0.

Step 7: Therefore, the maximum possible area that can be enclosed with 600 feet of rope is 150 feet by 400 feet dimensions.

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The amount of time it would take for the balloon's diameter to decrease to 8 feet is 56 minutes.

What is an example of diameter?

If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.

In how long would the diameter have decreased to 8 feet?

A circle's diameter is determined by drawing a line across its center, touching both ends of its circumference.

Minutes are calculated as diameter/decline.

56 minutes from 14/0.25

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The number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.

What is integration?

It is defined as the mathematical approach to calculating the smaller parts or components.

It is given that:

A barn is 100 feet long and 40 feet wide.

Find the first derivative of the given function:

After solving the above integration:

= 20(e - 1/e)

The roofing = 100(20(e - 1/e))

= 4701 square feet

Thus, the number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.

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The cost of the book after the discount and coupon is $7.32

From the question, we have the following parameters that can be used in our computation:

Amount  = $15.40

Coupon = $5 offer

Discount = 20% off

This means that

Total amount = Amount  * (1 - Discount) - Coupon

So, we have

Total amount = 15.40 * (1 - 20%) - 5

Evaluate

Total amount = 7.32

Hence, the total amount = 7.32

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Using the equation of the proportional relationship, the number of miles she would drive on 50 gallons is: 1,660 miles.

A direct proportional relationship can be defined by the equation, y = kx, where the constant of proportionality between the variables is given as the value of k.

First, we need to write an equation that defines the table of values given. To do this, find the constant of proportionality by using any pair of values from the table, say (6, 199.2):

Number of gallons used = x

Number of miles driven = y

Constant of proportionality, k = y/x = 199.2/2

k = 33.2

To write the equation for the proportional relationship, substitute k = 33.2 into y = kx:

y = 33.2x

To find the how many miles she would drive on 50 gallons, substitute x = 50 into y = 33.2x:

y = 33.2(50)

y = 1,660 miles.

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It is untrue that it can build cause-and-effect relationships.

When the following criteria are met, a cause-and-effect relationship is asserted: the two occurrences take place at the same time and location; one event occurs right before the other; and it seems doubtful that the second event would have happened without the first event first occurring.

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