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The standard deviation of the sampling distribution of sample means is 4.5.

What is standard deviation?

Standard deviation is commonly used to describe the spread or distribution of a data set and is often used in inferential statistics to assess the significance of differences between groups or to estimate the precision of measurements.

To find the standard deviation of the sampling distribution of sample means, we can use the formula σ_[tex]\bar{x}[/tex] = σ/√n, where σ is the population standard deviation, n is the sample size, and σ_[tex]\bar{x}[/tex] is the standard deviation of the sampling distribution of sample means.

In this case, we are given that the population mean is μ = 47 and the population standard deviation is σ = 9, and we want to find the standard deviation of the sampling distribution of sample means for a sample size of n = 4. Applying the formula, we get:

σ_[tex]\bar{x}[/tex]=σ/√n = 9/√4 = 4.5

Therefore, the standard deviation of the sampling distribution of sample means is 4.5.

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With a frequency of 6, the value 40 in this instance appears the most frequently. Therefore: mean = 38.16

median = 38.5

mode = 40

The mean, commonly referred to as the average, is a statistic that expresses central tendency and is calculated by dividing all values in either a dataset by all the data point observations. A dataset's mean is determined by adding up all of its values and dividing the total by the dataset's total number of observations. Take the following dataset, for instance: The mean can be impacted by outliers or extremely high or low values in the information, which can skew the outcome. Use of a different central tendency measure, like the median or mode, may be preferable in these circumstances.

given

To calculate the mean, multiply the sum of all frequencies by the corresponding values, then divide by the total number of frequencies. Therefore:

mean = (363 + 374 + 384 + 393 + 40*6) / (3+4+4+3+6) = 38.16

The middle value in the data set, when placed in order, is what we need to locate to get the median.

Since there are exactly as many data points as there are data points, we must take the average of the two middle values, which in this instance are 38 and 39. Therefore:

median = (38 + 39) / 2 = 38.5

The value that appears the most frequently in the data set must be determined in order to determine the mode.

With a frequency of 6, the value 40 in this instance appears the most frequently. Therefore: mode = 40

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It should be noted that the composite function for hg(x) = -1 + (3/2)x^4.

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.  Each input has only one output.  The function is the description of how the inputs relate to the output.

(a) (i) To find g(-2), we substitute -2 for x in the expression for g(x):

g(-2) = 2 - 3(-2)^4 = 2 - 3(16) = 2 - 48 = -46

(ii) To express the composite function hg in the form hg(x), we need to find h(g(x)) and simplify the expression.

h(g(x)) = h(2 - 3x^4) = 3(2 - 3x^4)/2 - (2 - 3x^4) = 3 - 9x^4/2 - 2 + 3x^4 = -1 + (3/2)x^4

Therefore, hg(x) = -1 + (3/2)x^4.

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The area bounded by y = x² + 5 and the x axis from x = 0 to x = 5 is .66.67 square units

To solve for the bounded area, we us

∫(x² + 5) dx = (1/3x³ + 5x +C). This is known as the antiderivative of the function.

When we input the figures, it will be

∫[(1/3)(5³) + 5(5)] - [(1/3)(0) + 5(0)}

[(1/3)(125) + 25] -[0]

= 125/3 + 25

convert 25 into a fraction

= 125/3 + 75/3

= 200/3

= 66.67

The question as seen in the picture is;

Below is the graph y = x² + 5

The area bounded by y = x² + 5 and the x axis from x = 0 to x = 5 is ........

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g(x) has a larger y-intercept than f(x).-

The y-intercept is what we get when we evaluate in x = 0.

For f(x) = 4*(3)^x

We evaluate this in x = 0 to get:

f(0) = 4*(3)^0

f(0) = 4*1 = 4

For the other function we have a table, we can see that it is a power of 3, such that:

g(-1) = 27

g(1) = 3

g(3) = 1/3

This function is:

g(x) = (3)^(-x + 2)

So the y-intercept is:

g(0) =3^(2) = 9

g(x) has a larger y-intercept.

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The fraction written in 3 different forms is:

6/8 = 3/4 = 0.75

We want a fraction that is greater than five-eighths and less than thirteen-eighths. Then if our fraction is x:

5/8 < x < 13/8

So we can write the fraction such that the denominator is also 8, but the numerator is between 5 and 13, then we could use 6/8

5/8 < 6/8 < 13/8

To write the fraction in other forms we can simplify it:

6/8 = 3/4 = 0.75

There are 3 ways.

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Answer:

The second choice and the fifth choice are correct.

Step-by-step explanation:

y = x + 3  The rate of change for this equation is the number before the x.  Since we do not see a number before the x, we assume that the number is 1, so the rate of change for this equation is 1.

Not the first choice:

To find the rate of change, you find the change in y over the change in x.  You find the change by subtracting.

(-2,-7)(3,-2)  The y values are -2 and-7.  The x values are 3 and-2

[tex]\frac{-2-(-7)}{3 - (-2)}[/tex] = [tex]\frac{-2 + 7}{3 + 2}[/tex] = [tex]\frac{5}{5}[/tex] = 1

This has the same rate of change as the equation (1)

The second choice is correct.

Select two points on the line. I have selected the points (0,1) and (1,3)  To go from the first point to the second point, you need to go up 2 and left 1.  This would be the rate of change of [tex]\frac{2}{1}[/tex] = 2.  You will see people use the phrase rise over run.  We rose 2 and we ran 1.

The rate of change is 2 which is greater than the rate of change in the equation of 1.

The Third choice in not correct.

The y is increasing by 1 and the x is increasing by 3.  That gives a rate of change of [tex]\frac{1}{3}[/tex] which is less than 1.

The Fourth choice is not correct.

The rise is 1 and the run is 2.  The rate of change is [tex]\frac{1}{2}[/tex] which is less than 1.

The Fifth choice is correct.

The y is changing by 9 and the x is changing by 6.  [tex]\frac{9}{6}[/tex] is greater than 1.

Helping in the name of Jesus.

If a rectangular prism has a length of 2 meters, a width of 4 meters, and a height of 2 meters. The volume of the prism is 16 cubic meters.

The volume of a rectangular prism is given by the formula:

Volume = length x width x height

Substituting the given values, we get:

Volume = 2 meters x 4 meters x 2 meters

Simplifying this expression, we get:

Volume = 16 cubic meters

Therefore, the volume of the prism is 16 cubic meters.

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The mean for the given data items in the given frequency distribution is 2.818

From the question, we are to determine the mean for the given data items

The given frequency distribution is:

Score, x           : 1, 2, 3, 4, 5, 6, 7, 8

Frequency, f   : 3, 6, 5, 5, 4, 5, 3, 2

To find the mean, we need to first calculate the sum of the products of each score and its frequency, and then divide by the total frequency.

(1 x 3) + (2 x 6) + (3 x 5) + (4 x 5) + (5 x 4) + (6 x 5) + (7 x 3) + (8 x 2) = 93

Total frequency = 3 + 6 + 5 + 5 + 4 + 5 + 3 + 2 = 33

Thus,

Mean = Sum of (x * f) / Total frequency

= 93 / 33

= 2.818

Hence, the mean of the scores is 2.818

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Answer: Sussy initially deposited $31.61.

Step-by-step explanation: 5% interest rate for 6 months with $32.45 earned, we can use the compound interest formula A=P(1 + r/n)^nt where A is the final amount, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year and t is the time in years.

In this case, we know that P is what we are looking for, r=5%, n=2 (since it’s compounded twice a year), t=6/12=0.5 years and A=P+$32.45.

Substituting these values into the formula gives us:

A=P(1 + r/n)^nt + $32.45

$32.45=P(1 + 0.05/2)^(2*0.5)

$32.45=P(1 + 0.025)^1

$32.45=P(1.025)

P=$31.61

The cost of ordering food service is $0.14, which is closest to option D: $1.64.

Interest is a periodically paid interest amount related to the amount borrowed, deposited or borrowed (the so-called capital amount).

To find out how much more you paid instead of  cash, you need to add one year's interest expense and  divide it by 12 to get one month's interest expense.

The annual interest  is 16.99%, i.e. the monthly interest  is 16.99% / 12 = 1.41%.  The total price for the grocery delivery service is $115.99 per year, so the monthly price is $115.99 / 12 = $9.67.  

If the subscriber pays for the service by credit card, the monthly interest is:

$9.67 x 1.41% = $0.14

Therefore, if the balance is paid  after one month's interest is paid, the total cost for the first month is:

$9.67× $0.14 = $9.81

The difference between the total cost of a credit card and the total cost of using cash is:

$9.81 - $9.67 = $0.14

So the answer is $0.14, which is closest to choice D: $1.64.

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The circles are similar because you can translate circle 1 using the transformation rule (x + 10, y) and then dilate it using a scale factor of 2/5.

First analyze the centers, the original center is at (-3, 5) and the new center is at (7, 5)

The change is in the x-value, the change is:

7 - (-3) = 10

So there is a translation of 10 units to the right,

And the original radius is R = 10, the new one is R' = 4

if the scale factor of the dilation is k we can write:

10*k = 4

k = 4/10 = 2/5

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The measure of the two interior angles on the same side of the transversal are 78 degrees and 102 degrees, respectively, when the lines are parallel.

When two parallel lines are intersected by a transversal, the interior angles on the same side of the transversal are supplementary, which means they add up to 180 degrees. So, we can set up the following equation:

(5x + 3) + (6x + 12) = 180

Simplifying and solving for x, we have:

11x + 15 = 180

11x = 165

x = 15

Now that we know x, we can find the measure of each angle:

The first angle measures 5x + 3 = 5(15) + 3 = 78 degrees.

The second angle measures 6x + 12 = 6(15) + 12 = 102 degrees.

Therefore, the measure of the two interior angles on the same side of the transversal are 78 degrees and 102 degrees, respectively, when the lines are parallel.

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Complete question

Two interior angles on the same side of the transversal measure 5x+3 and 6x + 12°. Find x and  the measure of each angle if the lines are parallel

Both representations are equivalent and describe the same function.the function rule for this table is:   f(x) = -1/2 x 2

The slope or gradient of a line is a number that describes both the direction and the steepness of the line. A slope of a line is the change in y coordinate with respect to the change in x coordinate.

To write a function rule for a given array, we need to determine how the values ​​in the output column (y) relate to the values ​​in the input column (x).

Looking at the given data, we notice that the output values ​​decrease by 1 every time the input value increases by 2. This suggests that the function is linear and that we can use the slope-intercept form of a linear equation to represent it. .

The slope-intercept form of a linear equation is y = mx b, where m is the slope and b is the y-intercept. In this case, the slope m is -1/2 because the output values ​​decrease by 1 every time the input values ​​increase by 2. The y-intercept b is 2 because the output value is 2 when the input value is 0.

Therefore, the function rule for this table is:

f(x) = -1/2 x 2

where x is the input value and f(x) is the output value.

Alternatively, we can also represent the function in table entries, for example:

f(0) = 2

f(2) = 1

f(4) = 0

f(6) = -1

Both representations are equivalent and describe the same function.

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The growth factor of the credit card balance is 1.0142. The Option B is correct.

The growth factor is equal to the slope of the line representing a linear relationship. To calculate the growth factor of the credit card balance, we need to add the monthly interest rate to 1.

Monthly interest rate = 1.42% = 0.0142

The Growth factor will be:

= 1 + monthly interest rate

= 1 + 0.0142

= 1.0142.

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Ahab's total change to funds is -$175, which means he spent more than he gained.

Ahab spent 3 tires at $50 each, which is a total of 3 x $50 = $150.

Later, he returned one tire, so he gets $50 back.

He also found a $5 bill, so he has an extra $5.

He then bought 2 jackets at $40 each, which is a total of 2 x $40 = $80.

The total amount Ahab spent is $150 + $80 = $230.

However, he also received $50 back and found $5, so his total change to funds is $50 + $5 - $230 = -$175.

Therefore, Ahab's total change to funds is -$175, which means he spent more than he gained.

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Answer:

it will take about 7,851,057 full rotations for each tire to travel 10,000 miles.

Step-by-step explanation:

To answer this question, you need to know the circumference of each tire. The circumference of a tire is the distance around the outside of the tire. You can find the circumference of a tire by multiplying the diameter of the tire by pi, which is approximately 3.14. The diameter of a tire is the distance from one side of the tire to the other. You can find the diameter of a tire by adding the rim diameter and twice the sidewall height. The rim diameter and the sidewall height are given on the tire’s sidewall. and To find out how many full rotations it will take for each tire to travel 10,000 miles, you need to convert the circumference from millimeters to feet, and then divide 52,800,000 feet by that number. One millimeter is equal to 0.00328084 feet, so 2051.2 millimeters is equal to 6.726 feet. Then, 52,800,000 feet divided by 6.726 feet is equal to 7,851,057 rotations.

Answer:

c. 4

Step-by-step explanation:

for this problem, you would have to set up a division equation, which would be

total number of cups

———————————————

unit rate amount for one dumpling

in this case, your equation would be

2

—

.5

when you solve 2/.5 you get 4 total dumplings

Answer: width is 12 m

Step-by-step explanation:

Let [tex]x[/tex] be the length of the rectangle. Then the width is [tex]x-4.[/tex] The area of a rectangle is base times height, so our variable [tex]x[/tex] satisfies the equation:

[tex]x(x-4)=192.[/tex]

After a bit of algebraic manipulation, we get [tex]x^2-4x-192=0,[/tex] and we can solve this using the quadratic formula.

This gives us [tex]x = \frac{4 \pm \sqrt{16+4\times192}}{2} = \frac{4 \pm 28}{2} = 2 \pm 14.[/tex] However, we must take the positive solution, as lengths in geometry are always positive. Hence, [tex]x = 2+14=16,[/tex] and width is just [tex]x-4[/tex] which is equal to [tex]\boxed{12}[/tex].

a. The probability that a male passenger can fit through the doorway without bending is approximately 0.9994.

The probability of an event happening is the likelihood that it will. It does not reveal what will occur; it only indicates how likely an event is to occur. An event has an equal chance of occurring (happening or not occurring).

a. To determine if a male passenger can fit through the doorway without bending, we need to find the probability that his height is less than or equal to 78 inches.

We can use the normal distribution formula to standardize the height of the male passenger:

z = (x - μ) / σ

where x is the height of the male passenger, μ is the mean height of men, and σ is the standard deviation of men's heights.

Substituting the given values, we have:

z = (78 - 69) / 2.8 = 3.21

Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is less than or equal to 3.21:

P(Z ≤ 3.21) ≈ 0.9994

Therefore, the probability that a male passenger can fit through the doorway without bending is approximately 0.9994.

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The fraction expression 9 ÷ 2 is 4.5

To evaluate an expression like (9/2), we need to perform the arithmetic operation indicated by the mathematical operator, which in this case is the division symbol "/".

So, we divide the number 9 by the number 2:

9 ÷ 2 = 4.5

The quotient we obtain from this division is 4.5, which means that (9/2) is equal to 4.5.

Therefore, the correct answer to the given question is D. 4.5.

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Answer: 594 Rabbits

Step-by-step explanation:

To solve this problem, we can use the formula for exponential growth:

A = P(1 + r)^t

where A is the final amount, P is the initial amount, r is the monthly growth rate (as a decimal), and t is the number of months.

In this case, we know that the initial amount (in July) is 260, the monthly growth rate is 9% or 0.09, and we want to find the final amount after 12 months (from July to next July).

So we have:

A = 260(1 + 0.09)^12

A ≈ 593.87

Rounding to the nearest whole number, we get:

A ≈ 594

Therefore, we can expect about 594 rabbits by next July.

The term formula for a geometric progression where the second term is 54, the fourth term is 6, and the common ratio is 0.5 is Un = 108 * (0.5)n-1.

In a Geometric Progression (G.P.), each term is the product of the previous term and a constant multiplier (known as the common ratio). To begin, identify the common ratio (r) by using the formula r = Un / Un-1. If the second term is 54 and the fourth term is 6, then the common ratio (r) is √(6/54) = 0.5.

Once we have established the common ratio, we can find an arbitrary term of the progression using the formula Un = U1 * r(n-1). However, since we don't know the first term, we can derive it from U1 = U2 / r, substituting our given values, we find U1 = 54 / 0.5 = 108.

Now, we can substitute U1 and r into our term formula to find any term (n) in the series: Un = 108 * (0.5)n-1.

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The surface area of the square pyramid, to the nearest whole number is: 131 m².

The surface area of the composite solid can be found by using the formula below:

Surface area = 8(area of 8 triangular faces)

= 8(1/2 * a * l)

Where:

a = base length of the square pyramid=

l = slant height of the square pyramid

We are given:

a = 4 m

l = √(8² + 2²) = [based on Pythagorean Theorem]

l = 8.2 m

Therefore:

Surface area = 8(1/2 * a * l) = 8(1/2 * 4 * 8.2)

≈ 131 m²

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Answer:

Step-by-step explanation:

The standard deviation of the sampling distribution of sample means is given by the formula:

standard deviation = population standard deviation / sqrt(sample size)

Here, the population standard deviation is 0.8 years, and the sample size is 38. Substituting these values into the formula, we get:

standard deviation = 0.8 / sqrt(38)

standard deviation ≈ 0.13

Rounding to two decimal places, the standard deviation of the sampling distribution of sample means is approximately 0.13 years.

Which involves calculating the square root of the sum of the squares of the differences between the coordinates of its endpoints.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles.

The concept you are describing is that of a line segment, which is a part of a straight line that is defined by two endpoints and includes all the points between those endpoints. A line segment has a finite length, which is the distance between its endpoints, but it contains an infinite number of points in one dimension, which means that it can be divided into an infinite number of smaller segments or points.

The length of a line segment can be measured using various methods, including the Pythagorean theorem, which involves calculating the square root of the sum of the squares of the differences between the coordinates of its endpoints.

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Answer:

4

Step-by-step explanation: