some one do this giving out 100 points
Complete the sentence: Squares and rectangles both have four ______ angles.
acute
obtuse
right
uneven

Answer: I believe it is -144

We reject the null hypothesis because the test statistic (-2.91) is lower than the crucial t-value (-1.711). This shows that there is evidence to back up the assertion that largemouth bass have a shorter lifespan because of oil contamination in the ichthyologist's region.

To test the claim of a shortened life span for largemouth bass due to oil contamination, we can conduct a hypothesis test using the given sample data.

Null Hypothesis (H₀): The true average life span of largemouth bass is 16 years.

Alternative Hypothesis (H₁): The true average life span of largemouth bass is less than 16 years.

We can use a one-sample t-test to analyze the data. The test statistic is calculated by subtracting the hypothesized population mean (16 years) from the sample mean (13.2 years) and dividing it by the sample standard deviation (2.3 years), multiplied by the square root of the sample size (25).

Calculating the test statistic:

t = (13.2 - 16) / (2.3 / √25) = -2.91

With 24 degrees of freedom (n-1 = 25-1 = 24), we can consult a t-distribution table or use statistical software to find the critical t-value at a significance level of 0.05 for a one-tailed test.

The critical t-value for alpha = 0.05 with 24 degrees of freedom is approximately -1.711.

Since the test statistic (-2.91) is less than the critical t-value (-1.711), we reject the null hypothesis. This indicates that there is evidence to support the claim of a shortened life span for largemouth bass due to oil contamination in the ichthyologist's area.

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Answer:

B) 154

Step-by-step explanation:

the formula for finding volume is lengthxwidthxheight

Answer:

Volume of rectangular prism=l*b*h

11*7*2

=154 cubic units

Answer:

10 30 15 16 48 24 25 75 37.5

The simplified form of (27^(2/3)) / (27^(4/3)) is 1/9.

To simplify the expression (27^(2/3)) / (27^(4/3)), we can use the properties of exponents.

First, let's rewrite both terms with the same base, which is 27. Recall that when dividing two terms with the same base, we subtract the exponents:

27^((2/3) - (4/3))

Next, we can simplify the exponent by subtracting the fractions:

27^(-2/3)

To further simplify this expression, we can apply the property of negative exponents, which states that a^(-n) is equal to 1 / a^n:

1 / (27^(2/3))

Now, let's rewrite the exponent as a cube root:

1 / (cuberoot(27^2))

Since 27 is equal to 3^3, we can simplify further:

1 / (cuberoot((3^3)^2))

1 / (cuberoot(3^6))

Taking the cube root of 3^6:

1 / 3^2

Simplifying further:

1 / 9

Therefore, the simplified form of (27^(2/3)) / (27^(4/3)) is 1/9.

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The particle's motion along the parabola from x = -1 to x = 2 results in a work done of 13.5 units.

To find equations of parabola we compute the work done by the force field in moving a particle along a curve, we can use the line integral formula:

Work = ∫C F · dr

where F is the force field and dr is the differential displacement vector along the curve C.

Given the force field F(x, y, z) = xi + yj + zk, and the curve defined by y = 3x² and z = 0, we need to express F and dr in terms of the parameter x.

The differential displacement vector dr can be written as:

dr = dx i + dy j + dz k

Since z is constant (z = 0), dz = 0, so dr simplifies to:

dr = dx i + dy j

We can express dy in terms of dx using the equation of the parabola

y = 3x²:

dy = 6x dx

Now we can rewrite dr as:

dr = dx i + 6x dx j

Substituting F and dr into the line integral formula:

Work = ∫C (xi + yj + zk) · (dx i + 6x dx j)

Now we calculate the dot product between F and dr:

F · dr = (xi + yj + zk) · (dx i + 6x dx j)

= x dx + 6x² dx

Integrating the dot product over the curve C from x = -1 to x = 2:

Work = ∫C (x dx + 6x² dx)

= ∫[from -1 to 2] (x + 6x²) dx

Integrating with respect to x:

Work = [1/2 x² + 2x³] | from -1 to 2

= [1/2 (2)² + 2(2)³] - [1/2 (-1)² + 2(-1)³]

= [1/2 (4) + 2(8)] - [1/2 + 2(-1)]

= 2 + 16 - 1/2 - 4

= 13.5

Therefore, the work done in moving the particle along the parabola from x = -1 to x = 2 is 13.5 units.

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Answer:

A linear relationship benefits from a logarithmic transformation, in terms of data analysis.

The test statistic is approximately -0.96.

To calculate the test statistic, we will use the formula for the z-test for proportions:

z = (p' - p) / √((p * (1 - p)) / n)

where:

p' is the sample proportion of successes,

p is the hypothesized population proportion,

n is the sample size.

In this case, p'= 37/147 = 0.2517 (proportion of successes)

p = 0.29 (hypothesized proportion)

n = 147 (sample size)

Substituting these values into the formula, we get:

z = (0.2517 - 0.29) / √((0.29 * (1 - 0.29)) / 147)

Calculating the numerator:

0.2517 - 0.29 = -0.0383

Calculating the denominator:

√((0.29 * (1 - 0.29)) / 147) ≈ 0.0401

Now, we can calculate the test statistic:

z = -0.0383 / 0.0401 ≈ -0.9566

Rounding to two decimal places, the test statistic is approximately -0.96.

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The length of side RQ is 13.00 ft.

Given that a triangle RPQ, with sides RP = 8 ft, PQ = 13 ft and angle P between these sides equal to 71°, we need to find the length of side RQ which is opposite to the angle P,

To find the length of side RQ using the cosine rule, we can use the formula:

RQ² = RP² + PQ² - 2 RP PQ Cos(P)

Let's plug in the given values:

RP = 8 ft

PQ = 13 ft

angle P = 71°

Now we can calculate RQ:

RQ² = 8² + 13² - 2 × 8 × 13 × cos(71°)

Using a calculator, we can evaluate the cosine term:

RQ² = 64 + 169 - 208 × cos(71°)

RQ² ≈ 64 + 169 - 208 × 0.3072

RQ² ≈ 64 + 169 - 63.9936

RQ² ≈ 169.0064

Taking the square root of both sides:

RQ ≈ √169.0064

RQ ≈ 13.00 ft (rounded to two decimal places)

Therefore, the length of side RQ is 13.00 ft.

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Answer:

Julia had 120 peas to start .

Answer:

  120 peas

Step-by-step explanation:

Before Julia gave Vlada 15 peas, the ratio of their numbers was 3:2. Afterward, Julia still had 10 more peas. You want to know the number Julia started with.

Let j represent the initial number of peas Julia had. Then Vlada had 2/3j peas. After the transfer, the difference was ...

  (j -15) -(2/3j +15) = 10

  1/3j -30 = 10

  1/3j = 40

  j = 120

Julia had 120 peas at first.

__

Additional comment

The transfer of peas decreases the difference by 30, so if it remains 10 it must have originally been 40. The difference in initial ratio units is 3-2 = 1, so Julia's initial 3 ratio units represent 3·40 = 120 peas.

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The question is asking for the value of z that satisfies the probability that a standard normal variable z is less than z to be 0.9525. In other words, we want to find the z-score that corresponds to the 95.25th percentile of the standard normal distribution. Option (b) is the closest to the correct answer (-1.67). However, this could be due to rounding errors or differences in the table used. Therefore, the correct answer is (f) None of the above.

To solve this problem, we can use a standard normal distribution table or a calculator with a normal distribution function. Using a standard normal distribution table, we can look up the closest value to 0.9525 in the body of the table, which is 0.9515. The corresponding z-score is 1.65.

However, since the table only gives us values for the area to the left of a positive z-score, we need to subtract 1.65 from 0 (the mean of the standard normal distribution) to get the z-score that corresponds to the 95.25th percentile on the left tail. Therefore, the answer is -1.65. So none of above is correct.

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The statement which is true for Cluster analysis is: The first step in cluster analysis is to select the variables on which clustering is based.

In cluster analysis, the initial step involves selecting the variables that will be used to form clusters. These variables can be numerical or categorical, depending on the type of data being analyzed.

The choice of variables is crucial as it determines the basis for grouping similar data points together into clusters. The selected variables should capture the relevant characteristics or attributes of the data that are important for clustering.

Once the variables are chosen, the clustering algorithm is applied to partition the data into distinct groups or clusters based on the similarity or dissimilarity of the variable values. Various techniques and algorithms, such as K-means clustering or hierarchical clustering, can be employed to perform cluster analysis.

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The calculated area of the square 3 is 25

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

The shapes (see attachment)

We have

Area 1 = 169

Perimeters 2 = 48

This means that

Side length 1 = 13

Side length 2 = 12

So, we have

Area of square 3 = Side length 1² - Side length²

So, we have

Area of square 3 = 13² - 12²

Evaluate

Area of square 3 = 25

Hence, the area of the square 3 is 25

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The normal distribution is a continuous probability distribution that is symmetric around the mean. The total area under the normal curve is equal to 1. When we talk about the area under the normal curve to the left of x=30 cm, we are referring to the probability of observing a value less than 30 cm in a normally distributed population.



1. The first interpretation is that the probability of observing a value less than 30 cm is 0.5. This is because the normal distribution is symmetric around the mean, and if we assume that the mean is centered at 0, then half of the area under the curve lies to the left of the mean, and the other half lies to the right.

2. The second interpretation is that the area under the normal curve to the left of x=30 cm represents the cumulative probability of observing a value less than 30 cm.

When we talk about the area under the normal curve to the left of a certain value, we are referring to the probability of observing a value less than that value in a normally distributed population. The interpretation of this result depends on whether we are referring to a specific probability or a cumulative probability.

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The value of y which is one of the leg of the given right angled triangle to the nearest tenth is 178.3 feet.

Given a right angled triangle.

We have to find the length of y, which is one of the leg.

Length of hypotenuse = x

Length of one of the leg = y

Length of other leg = 350 feet

Also,

One of the angle = 27°

We have to find the side opposite to 27°.

Adjacent side to 27° is given which is of length 350 feet.

So, using trigonometric ratio of tangent function,

tan (27°) = opposite side / adjacent side

tan (27°) = y / 350

y = 350 × tan (27°)

y = 178.3 feet

Hence the value of y is 178.3 feet.

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The trigonometric function graphed is defined as follows:

y = 3cos(4x).

The standard definition of the cosine sine function is given as follows:

y = Acos(Bx) + C.

For which the parameters are given as follows:

The function in this problem oscillates between -3 and 3, hence the amplitude is given as follows:

A = 3.

As the function oscillates between -A and A, it has no vertical shift, hence the parameter C is given as follows:

C = 0.

The period of the function is of π - π/2 = π/2, hence the parameter B is given as follows:

2π/B = π/2

B = 4.

Hence the function is given as follows:

y = 3cos(4x).

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Answer: Linear Equations, Quadratic Equations, Polynomial Equations, Inequalities, etc.

Step-by-step explanation: Determining the number of real solutions in a math problem depends on the specific problem and the type of equation or inequality involved. It's important to note that these methods cover only a few common scenarios, and the specific problem at hand may require other techniques or approaches

The answers are A. the center of the circle is (-2, -3), B. the radius is [tex]5\sqrt2[/tex], and C. the equation for the circle is [tex](x + 2)^2 + (y + 3)^2 = 50.[/tex]

a. To find the center of the circle, we can use the midpoint formula. The midpoint is the average of the x-coordinates and the average of the y-coordinates of the endpoints of the diameter.

The x-coordinate of the center is (−7 + 3) / 2 = -2.

The y-coordinate of the center is (2 + (-8)) / 2 = -3.

Therefore, the center of the circle is (-2, -3).

b. To find the radius of the circle, we can use the distance formula. The radius is half the length of the diameter, which is the distance between the endpoints P(-7, 2) and Q(3, -8).

The distance formula is given by [tex]\sqrt {(x2 - x1)^2 + (y2 - y1)^2}[/tex].

Substituting the coordinates, we get:

Radius [tex]= 1/2 * \sqrt{(3 - (-7))^2 + (-8 - 2)^2}[/tex]

           [tex]= 1/2 * \sqrt{(3 + 7)^2 + (-8 - 2)^2}[/tex]

           [tex]= 1/2 * \sqrt{10^2 + (-10)^2}[/tex]

           [tex]= 1/2 * \sqrt{100 + 100}[/tex]

           [tex]= 1/2 * \sqrt200[/tex]

           [tex]= \sqrt50[/tex]

           [tex]= 5\sqrt2[/tex]

Hence, the radius of the circle is [tex]5\sqrt2[/tex].

c. The equation for a circle with center (h, k) and radius r is given by [tex](x - h)^2 + (y - k)^2 = r^2.[/tex]

Using the center (-2, -3) and the radius [tex]5\sqrt2[/tex], the equation for this circle is:

[tex](x - (-2))^2 + (y - (-3))^2 = (5\sqrt2)^2[/tex]

[tex](x + 2)^2 + (y + 3)^2 = 50.[/tex]

Therefore, the equation for the circle is [tex](x + 2)^2 + (y + 3)^2 = 50.[/tex]

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Given function is [tex]f(x) = 6 e - 3x[/tex]We need to find the first four nonzero terms of the Maclaurin series for the given function.

Also, we need to write the power series using summation notation and determine the interval of convergence of the series.a. The first nonzero term of the Maclaurin series is 6.

f(x) = 6 e - 3x

Now, we differentiate f(x) 4 times to get the required terms for the Maclaurin series.(1)

[tex]f(x) = 6 e - 3x(2) f'(x)[/tex]

[tex]= -18 e - 3x(3) f''(x)[/tex]

[tex]= 54 e - 3x(4) f'''(x)[/tex]

[tex]= -162 e - 3x(5) f''''(x)[/tex]

[tex]= 486 e - 3x[/tex]

When x=0, we have

[tex]f(0) = 6, f'(0) = -18,[/tex]

[tex]f''(0) = 54, f'''(0) = -162[/tex] and

[tex]f''''(0) = 486[/tex]

Therefore, the Maclaurin series is given by:

[tex]f(x) = 6 - 18x + 27x² - 81x³ + 243x⁴[/tex]

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the values of the six trigonometric functions under the given conditions are as follows: cos(θ) = 1/√(10√29)

sin(θ) = ± √((10√29 - 1)/(10√29))

tan(θ) = ± (√(10√29 - 1))

csc(θ) = √(10√29) / (10√29 - 1)

sec(θ) = √(10√29)

cot(θ) = 1 / (√(10√29 - 1))

Given that cos(2θ) = 1/√290 and 0° ≤ θ ≤ 180°, we can find the values of the six trigonometric functions using the provided information.

Since cos(2θ) = 1/√290, we can find the value of cos(θ) by taking the square root of both sides:

cos(θ) = ± √(1/√290) = ± 1/√(√290) = ± 1/√(10√29)

Since the given conditions indicate that 0° ≤ θ ≤ 180°, the value of cos(θ) must be positive. Therefore:

cos(θ) = 1/√(10√29)

To find the other trigonometric functions, we can use the relationships between the trigonometric functions:

sin(θ) = ± √(1 - cos^2(θ))

tan(θ) = sin(θ) / cos(θ)

csc(θ) = 1 / sin(θ)

sec(θ) = 1 / cos(θ)

cot(θ) = 1 / tan(θ)

Let's calculate each trigonometric function:

sin(θ) = ± √(1 - cos^2(θ)) = ± √(1 - (1/√(10√29))^2) = ± √(1 - 1/(10√29)) = ± √((10√29 - 1)/(10√29))

tan(θ) = sin(θ) / cos(θ) = ± (√((10√29 - 1)/(10√29))) / (1/√(10√29)) = ± (√(10√29 - 1))

csc(θ) = 1 / sin(θ) = 1 / (√((10√29 - 1)/(10√29))) = √(10√29) / (10√29 - 1)

sec(θ) = 1 / cos(θ) = 1 / (1/√(10√29)) = √(10√29)

cot(θ) = 1 / tan(θ) = 1 / (√(10√29 - 1))

Therefore, the values of the six trigonometric functions under the given conditions are as follows:

cos(θ) = 1/√(10√29)

sin(θ) = ± √((10√29 - 1)/(10√29))

tan(θ) = ± (√(10√29 - 1))

csc(θ) = √(10√29) / (10√29 - 1)

sec(θ) = √(10√29)

cot(θ) = 1 / (√(10√29 - 1))

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Answer:

D. 5sqrt2(cos(-pi/4)+isin(-pi/4))

Step-by-step explanation:

The polar form of a complex number z is given by r(cos(θ)+isin(θ)), where r is the magnitude of z and θ is the argument of z.

The magnitude r can be calculated as the square root of the sum of the squares of the real and imaginary parts of z.

In this case, r = sqrt(5^2 + (-5)^2) = 5sqrt(2).

The argument θ can be calculated as the arctangent of the imaginary part divided by the real part.

In this case, θ = arctan(-5/5) = -pi/4.

So, the polar form of z is 5sqrt(2)(cos(-pi/4)+isin(-pi/4)).

Answer:
2/3 is the correct answer.

Step-by-step explanation:

Create equivalent expressions in the equation that all have equal bases, then solve for x.

Answer: 0

Step-by-step explanation:

First, we need to determine the mean of the data set-

5+10+8+9+10+4+5+8+11+10 = 80      

80 / 10 = 8

now that we know the mean, we have to calculate the distance from the mean of each number by inputting it like this--->  |each number - mean|

|5 - 8|, |10 - 8|, |8 - 8|, and so on...

then after solving the distance between each number to the mean, you have to take the deviation (what you got from subtracting the mean from each number) and add them together like so:

(-3)+2+0+1+2+(-4)+(-3)+0+3+2 = 0

and now that we have added them all together, we have to divide by the number of data points

0 / 10 = 0

Therefore the MAD of shop B = 0

Answer:

im not sure

Step-by-step explanation:

Answer:

-2

use rise over run

Step-by-step explanation:

pick 2 points and count how many points vertically it took to get to the second point and horizontally to get to the second point. and if the line is going up then it is positive and if it is going down then it is negative

2 point from this graph were (0,2) and (1,0)

it took 2 lines down and one across to get to (1,0) and since the line is pointed downward it is negative

rise/run

sorry if this doesn't make sense i'm not the best at explaining things

Answer:y=2x-2

Step-by-step explanation:

y=mx+b

this is the equation for a line

m is the slope

b is where the line crosses the y-axis. AKA, y-intercept

in this case, b is 2. We can see this because when the x value is 0 (also when the line crosses the y-axis), the y value is 2. Look at the number on the y-axis that the line crosses over.

m, or slope is a little bit harder to figure out.

to find the slope we need to remember a formula- m=(change in y/change in x)

in this case, we have two points. (0,2)-y-intercept (1,0) x-intercept. so now all we have to do is figure out the change in x and the change in y. we can see that x goes up one, and y goes down 2. so then we now have

m=(-2/1)

simplified to- m=-2

slope = -2

The table of values that represents a linear function include the following: C. table C.

In Mathematics and Geometry, a linear function refers to a type of function whose equation is graphically represented by a straight line on the xy-plane or cartesian coordinate.

This ultimately implies that, a linear function has the same (constant) slope and it is typically used for uniquely mapping an input variable to an output variable, which both increases simultaneously.

In this context, we have the following table C with constant slopes:

Slope = (1 + 2)/(-1 + 3) = (4 - 1)/(0 + 2)

Slope = 3/2

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The number of shirts sold is given by the formula S = -4x^2 + 88x - 160, where x is the price of the shirts in dollars. To find the price at which the maximum number of shirts will be sold, we need to find the vertex of the quadratic function.

The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.

In this case, a = -4 and b = 88. Plugging these values into the formula, we get:

x = -88 / (2 * -4)

x = -88 / -8

x = 11

Therefore, the maximum number of shirts will be sold at a price of $11.

The correct answer is:

b) $11

At a price of 11$ per shirt, the designer can sell the maximum number of shirts.

The answer is (B) 11$

This question can be solved by using the graphical representation of the equations given.

First, we know that the general equation of a parabola is represented as

y = ax² + bx + c, which is also the general form of a quadratic equation.

(a,b,c are constants)

Number of Shirts sold (S) = -4x² + 88x - 160

Identifying general terms,

a = -4

b = 88

c = -160

x = Price of each shirt ($)

Thus, from the question, we conclude that the given formula can be represented as a downward parabola (a<0).

(Refer to Diagram)

The maximum number of shirts, as required by the designer, can be found by identifying the vertex of the parabolic function.

The vertex of the parabola of the form ax² + bx + c is defined as :

x = (- b/2a)

Thus, the vertex of our parabola is at

x = -88/[2 * (-4)]

x = -88/-8

x = 11$

Thus, the designer would sell a maximum number of shirts at a price of 11$ per shirt.

Option (b) 11$ is the correct answer.

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(Image is not drawn to scale, it is made only for a representation of the shape of a downward parabola)

Tim could fill the 18-litre bucket in 22.5 times.

To get the number of times he could fill an 18-litre bucket with the sand from the wheelbarrow, we wil set up proportion using the known information.

The amount of sand that can fill a 12-litre bucket is proportional to the number of times it can fill the bucket.

The proportion will be:

12 litres / 15 times = 18 litres / x times

12x = 15 * 18

12x = 270

x = 270 / 12

x = 22.5.

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Rounding this answer to four decimal places, we get:

p(z < -1.57) ≈ 0.0589

What is probability?

Probability is a measure or quantification of the likelihood or chance of an event occurring. It represents the ratio of the favorable outcomes to the total possible outcomes in a given situation or experiment. Probability values range from 0 to 1, where 0 indicates an event is impossible and 1 indicates an event is certain to occur.

To find the probability that a standard normal random variable, denoted by Z, is less than a specific value, we can use a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find the area/probability to the left of a given Z-score.

The Z-score of -1.57 represents the value that is 1.57 standard deviations to the left of the mean (0).

Looking up the Z-score of -1.57 in the standard normal distribution table, we find the corresponding area/probability is 0.0589.

Hence, Rounding this answer to four decimal places, we get:

p(z < -1.57) ≈ 0.0589

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The probability of not selecting a purple marble when choosing one marble from the bag is 60%.

To determine the probability of not selecting a purple marble when choosing one marble from the bag, we need to find the number of marbles that are not purple and divide it by the total number of marbles in the bag.

The number of marbles that are not purple is the sum of red, green, and yellow marbles. Therefore, the number of marbles that are not purple is 3 + 3 + 9 = 15.

The total number of marbles in the bag is the sum of all the marbles: 3 + 3 + 9 + 10 = 25.

So, the probability of not selecting a purple marble is 15/25 = 0.6, which is equivalent to 60%.

Therefore, the probability of not selecting a purple marble when choosing one marble from the bag is 60%.

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The value of the z-score is approximately 0.9804.

The z-score (also known as the standard score) represents the number of standard deviations a particular value is away from the mean of a distribution. It is calculated using the formula:

z = (x - μ) / σ

Where:

z is the z-score,

x is the value you want to standardize,

μ is the population mean, and

σ is the population standard deviation.

To determine the probability that the mean height of the 60 randomly selected men is less than 72 inches, we need to know the population means and standard deviation of the height.

Assuming we have the population mean (μ) and standard deviation (σ) of the height available, we can use the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.

In this case, since the sample size is large (n = 60), we can approximate the distribution of the sample mean as a normal distribution.

Let's suppose the population mean (μ) is 70 inches and the population standard deviation (σ) is 5 inches.

To find the value of z, which represents the number of standard deviations away from the mean, we can use the following formula:

z = (x - μ) / (σ /√n)

Substitute the above values

z = (72 - 70) / (5 / √60)

= 2 / (5 /√60)

= 2 / (5 / √60)

= 2 / (5 / 2.449)

= 2 / 2.041

≈ 0.9804

Therefore,

The value of the z-score is approximately 0.9804.

Learn more about z-score at

https://brainly.com/question/31871890

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