One investigator takes a sample of 100 men age 18-24 in a certain town. Another takes a sample of 1,000 such men. a) Which investigator will get a bigger average for the heights of the men in his sample? or should the averages be about the same? b) Which investigator will get a bigger SD for the heights of the men in his sample? or should the SDs be about the same? c) Which investigator is likely to get the tallest of the sample men? or are the chances about the same for both investigators? d) Which investigator is likely to get the shortest of the sample men? or are the chances about the same for both investigators?

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity is equal to the number of total observations (N) minus the number of groups (k). So, it can be represented as (N - k).

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity depend on the sample size and the number of groups being compared.

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Answer:

\(\sqrt{70\times70}\)

\(70\times70=4900\)

\(=\sqrt{4900}\)

\(=70^2\)

\(=\sqrt{70^{2} }\)

\(=70\)

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The amount earned is $88,709.68

It is a payroll tax that is paid on wages earned by employees.

We have,

We will assume the current Social Security tax rate for employees as 6.2%.

Now,

The amount earned.

= 5,500 / 6.2%

= 5500 / 0.062

= $88,709.68

Thus,

The amount earned is $88,709.68

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The car travels 45.84 meters in 3 seconds.

To solve this problem, we need to convert the speed of the car from kilometers per hour to meters per second since the time given is in seconds.
To do this, we can use the conversion factor that 1 kilometer is equal to 1000 meters and 1 hour is equal to 3600 seconds.
So, 55 kilometers per hour is equal to (55 x 1000) / 3600 = 15.28 meters per second.
Now, we can use the formula: distance = speed x time
Plugging in the values, we get distance = 15.28 meters per second x 3 seconds = 45.84 meters.
Therefore, the car travels 45.84 meters in 3 seconds.

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According to the question Square meters will be available to plant are 86.4 square meters.

To calculate the area of the trapezoid-shaped garden, we can use the formula for the area of a trapezoid:

Given information:

Height of the trapezoid \((\(h\))\) = 6.4 m

Length of the bases:

Base 1 \((\(b_1\))\) = 15.1 m

Base 2 ( \(\(b_2\)\) ) = 11.9 m

To find the area of the trapezoid \((\(A\))\) , we can use the formula:

\(\[A = \frac{1}{2} \times (b_1 + b_2) \times h\]\)

Substituting the given values into the formula, we get:

\(\[A = \frac{1}{2} \times (15.1 + 11.9) \times 6.4\]\)

Simplifying the expression, we have:

\(\[A = \frac{1}{2} \times 27 \times 6.4\]\)

Calculating the result, we find:

\(\[A = 86.4\]\)

Therefore, the available area to plant is 86.4 square meters.

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Answer:

y

Step-by-step explanation:

y needs to provide a number

The value of x in the triangle is,

⇒ x = 4

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Triangle is shown in image,

Now, By definition of triangle trigonometry;

⇒ sin 30° = Opposite / Hypotenuse

⇒ sin 30° = x / 8

⇒ 1/2 = x / 8

⇒ x = 8/2

⇒ x = 4

Thus, The value of x in the triangle is,

⇒ x = 4

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The verbal expressions A. half of five more than a number, C. five more than half a number, and D. half of five less than a number represent the given algebraic expression when assigned with a variable. The expressions are 1/2(x + 5), 5 + 1/2x, and 1/2(x - 5).

The verbal expressions that represent the algebraic expressions are A. half of five more than a number, C. five more than half a number, and D. half of five less than a number. To convert these expressions into algebraic form, we need to assign a variable, say x, to the unknown number.

A. Half of five more than a number can be expressed algebraically as 1/2(x + 5). B. Twice a number and five can be written algebraically as 2x + 5. C. Five more than half a number can be expressed algebraically as 5 + 1/2x. D. Half of five less than a number can be written algebraically as 1/2(x - 5).

Therefore, the expressions that represent the given algebraic expression are A. half of five more than a number, C. five more than half a number, and D. half of five less than a number. Expression B represents a different algebraic expression altogether.

To summarize, three of the given verbal expressions represent the given algebraic expression, which can be converted to algebraic form by assigning a variable to the unknown number. These expressions are 1/2(x + 5), 5 + 1/2x, and 1/2(x - 5).

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Any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

Within 2 standard deviations of the mean refers to the range that includes data points within two units of standard deviation from the mean. In this case, the mean is 180 and the standard deviation is 35.

To find the range within 2 standard deviations of the mean, we need to calculate the upper and lower bounds.

The upper bound can be found by adding 2 standard deviations (2 * 35 = 70) to the mean: 180 + 70 = 250.

The lower bound can be found by subtracting 2 standard deviations (2 * 35 = 70) from the mean: 180 - 70 = 110.

Therefore, any value between 110 and 250 is within 2 standard deviations of the mean. In other words, any data point between 110 and 250 is considered within this range.

It's important to note that this answer is specific to the given mean and standard deviation. If the mean and standard deviation were different, the range within 2 standard deviations would also be different.

Always calculate the upper and lower bounds based on the provided mean and standard deviation to determine the range within 2 standard deviations accurately.

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Answer:

36 pi

Step-by-step explanation:

The radius is 6

A = pi r^2

A = pi 36

Answer:

Area of circle = 36 π square unit

Step-by-step explanation:

To calculate area of circle simplify formula area of circle . we have given radius of circle which is 6.

Area of circle = π × r²

where,

substitute the value

Area of circle = π × ( 6 ) ²

expand the exponent

Area of circle = π × 36

multiply

Area of circle = 36 π square unit

Answer:

14

Step-by-step explanation:

To find the length of the rectangle, we can use the formula for the perimeter of a rectangle, which is:

P = 2L + 2W

where P is the perimeter, L is the length, and W is the width.

By substituting the given values, we get:

60 = 2L + 2(16)

Simplifying the right-hand side, we get:

60 = 2L + 32

Subtracting 32 from both sides, we get:

28 = 2L

Dividing both sides by 2, we get:

L = 14

Therefore, the length of the rectangle is 14 inches.

The variable other than the ones being studied that could affect the outcome of an experiment if not controlled is known as the extraneous variable. An extraneous variable is defined as any variable that is not under investigation, which may impact the dependent variable (DV) and lead to inaccurate findings.

Experiments should be designed to control as many extraneous variables as possible to get accurate results of the relationship between the independent variable and dependent variable. In most cases, extraneous variables are an issue in experimental studies because researchers cannot control all variables in a real-world setting. In a perfect world, the only difference between the experimental and control groups is the independent variable (IV), which is the only variable that the researcher manipulates to test the effects on the dependent variable.

Unfortunately, real-world experiments are more complex, and many other factors may impact the dependent variable, making it difficult to establish a cause-and-effect relationship between the independent variable and dependent variable. The challenge for the researcher is to identify the extraneous variables and control them to the best of their ability to get the most accurate findings.

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Answer:

true

Step-by-step explanation:

Answer:true

Step-by-step explanation:

Dakota rode his bike for 60 km. He understood that he could have been there 16 hours earlier if he had traveled 12 mph quicker. Dakota's actual speed during the bike ride was approximately 41.8 mph.

Let's assume that Dakota's actual speed during the bike ride was x miles per hour.

Using the distance formula:

distance = speed x time

We can calculate the time it took Dakota to complete the ride at his actual speed as:

60 = x * t

where t is the time in hours.

Now, according to the problem, if he had gone 12 mph faster, he would have arrived 16 hours sooner. This means that he would have covered the same distance in less time.

So we can set up another equation:

60 = (x + 12) * (t - 16)

Simplifying this equation:

60 = xt - 16x + 12t - 192

76 = xt - 16x + 12t

Substituting the value of t from the first equation, we get:

76 = 60 - 16x + 12(60/x)

Simplifying this equation:

\(16x^2 - 720x + 7200 = 0\)

Dividing both sides by 16:

\(x^2 - 45x + 450 = 0\)

Solving this quadratic equation using the quadratic formula:

\($x = \frac{45 \pm \sqrt{45^2 - 41450}}{2}$\)

\($x = 22.5 \pm 7.5\sqrt{5}$\)

We can reject the negative root because it doesn't make sense in the context of the problem.

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Answer:

B

Step-by-step explanation:

Did on freckle

Answer:

9

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Hope this helps!

The SSS(Side-Side-Side) Triangle congruency is proven by following rule.

In SSS (Side-Side-Side) condition the two triangles are said to be congruent if the three sides of one triangle are equivalent to the corresponding three sides of the second triangle.

In mathematics, the term "congruent" refers to figures and shapes that can be flipped or rearranged to match up with other ones. These forms can be mirrored to produce related shapes. A triangle is a closed polygon with three line segments that intersect at each of its three angles.

Two shapes are congruent if their sizes and forms are comparable. Additionally, if two shapes are congruent, then their mirror images are likewise congruent.

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Therefore, the order-reversed integral is:

∫ba∫dcsin(x^2) dydx, where a= 0, b= 3, c= √(3y), and d= √(9y).

We have:

∫30∫3ysin(x^2) dxdy

To reverse the order of integration, we need to express the limits of integration as inequalities of x and y:

3y ≤ x^2 ≤ 9y

√(3y) ≤ x ≤ √(9y)

0 ≤ y ≤ 1

So, we have:

∫30∫√(9y)√(3y)sin(x^2) dxdy

Integrating with respect to x first, we get:

∫√(9y)√(3y) [-cos(x^2)/2] |_0^(√(3y)) dy

= ∫30 [-cos(3y)/2 + cos(y)/2] dy

= [-sin(3y)/6 + sin(y)/2] |_0^3

= (-sin(9)/6 + sin(3)/2) - (0 - 0)

= (-sin(9)/6 + sin(3)/2)

Therefore, the order-reversed integral is:

∫ba∫dcsin(x^2) dydx, where a= 0, b= 3, c= √(3y), and d= √(9y).

Note: We can also check the answer by evaluating the original integral and comparing it with the answer obtained by reversing the order of integration.

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Answer:

Step-by-step explanation:

The inequality shaded in the graph is given as follows:

y ≥ 5x/2 + 3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:

b = 3.

When x increases by 2, y increases by 5, hence the slope m is given as follows:

m = 5/2.

Then the equation of the line is given as follows:

y = 5x/2 + 3.

The line is a solid line, and values above it are plotted, hence the inequality is given as follows:

y ≥ 5x/2 + 3.

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The dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

To determine the dimensions of the can that minimize the cost of the material, we need to find the dimensions that minimize the surface area of the can.

Let's assume the can has a height of h and a radius of r.

The volume of a cylinder is given by:

V = πr²h

Given that the can should hold 500 cubic centimeters of liquid, we have:

500 = πr²h

We want to minimize the cost, which depends on the surface area of the can.

The surface area of the can is the sum of the areas of the top, bottom, and side surfaces.

The cost of the top and bottom surfaces is twice as expensive per square centimeter as the sides.

Let's assume the cost per square centimeter of the sides is c, so the cost per square centimeter of the top and bottom surfaces is 2c.

The surface area of the sides of the cylinder is given by:

A_sides = 2πrh

The surface area of the top and bottom surfaces (each) is given by:

A_top_bottom = 2πr²

The total surface area (cost) is given by:

Cost = 2(2c)A_top_bottom + cA_sides

= 4cπr² + 2c(2πrh)

= 4cπr² + 4cπrh

To minimize the cost, we need to minimize the surface area. To do this, we can express the surface area in terms of a single variable, such as the radius (r) or the height (h).

From the volume equation, we have:

h = 500 / (πr²)

Substituting this value of h into the surface area equation, we get:

Cost = 4cπr² + 4cπr(500 / (πr²))

= 4cπr² + 2000c/r

Now, we can take the derivative of the cost function with respect to r, set it equal to zero, and solve for r to find the critical points:

dCost/dr = 8cπr - 2000c/r² = 0

8cπr = 2000c/r²

8πr³ = 2000

r³ = 250 / π

r ≈ 6.324

Now, we can substitute this value of r back into the equation for h:

h = 500 / (π(6.324)²)

≈ 3.984

So, the dimensions of the can that minimize the cost of the material are approximately:

Radius (r) ≈ 6.324 cm

Height (h) ≈ 3.984 cm

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Answer:

To find the width of the garden, we need to use the formula for the area of a rectangle, which is:

Area = length x width

In this case, we know the length is 1 yard and the area is 5 square yards. We can substitute these values into the formula and solve for the width:

5 = 1 x width

width = 5/1

width = 5

Therefore, the garden should be 5 yards wide.

Answer: 525

Step-by-step explanation:

if your looking for 150 percent of 350, the answer is 525 because....

150 x 350/ 100 =525

The correlation coefficient that best represents a moderate relationship showing fewer anxiety symptoms is a negative correlation coefficient.

In a negative correlation, as one variable increases, the other variable decreases. In the context of anxiety symptoms, a negative correlation would indicate that as one factor (e.g., a particular intervention, treatment, or activity) increases, the number or severity of anxiety symptoms decreases. This suggests a moderate relationship between the two variables, indicating that the higher the value of the independent variable, the lower the value of the dependent variable (in this case, fewer anxiety symptoms).

The correlation coefficient ranges from -1 to 1, with -1 representing a perfect negative correlation, 0 representing no correlation, and 1 representing a perfect positive correlation. A correlation coefficient close to -1, but not reaching -1, would be indicative of a moderate negative correlation and would best represent a moderate relationship showing fewer anxiety symptoms.

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The answer  is that the graph corresponding to the map of the postal worker's route would likely be a line graph.

This is because the route follows a linear path along the road, with the postal worker delivering mail to both sides of the road as she goes.

A line graph is a type of graph that is used to represent data that changes over time or along a continuous line. In the case of the postal worker's route, the line graph would show the distance traveled along the road as the independent variable on the x-axis, with the number of mail deliveries made on each side of the road as the dependent variable on the y-axis.

The postal worker is likely aiming to solve a graph problem related to optimizing her route and maximizing efficiency in delivering mail to all the houses along the road. By using a line graph to visualize the data of her route, she can analyze patterns in mail delivery and adjust her strategy as needed to improve her efficiency and accuracy.

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The equation to determine the velocities of boxes is given by, v² = 2*a*d

To determine the velocities of the boxes when they move a distance d down the slope after being released from rest, we can use the following terms: velocity, box, and distance (d). Here's a step-by-step explanation:

1. Since the boxes are released from rest, their initial velocity (v0) is 0.
2. Let's assume the slope has an angle (θ) and the acceleration due to gravity (g) is 9.81 m/s².
3. Calculate the acceleration (a) of the boxes down the slope using the formula: a = g * sin(θ).
4. To find the final velocity (v) of the boxes after traveling a distance (d) down the slope, we can use the equation: v² = v0² + 2*a*d.

Since the boxes are released from rest, v0 is 0. Therefore, the equation simplifies to:

v² = 2*a*d

Now, substitute the acceleration (a) and distance (d) into the equation and solve for the final velocity (v) of the boxes.

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Answer:

32n = 100 - 20

n = 2.5

he purchased 2 sweaters

Step-by-step explanation:

32n = 100 - 20

If Favian originally had $100 but spent $20 on a belt, he only had 80 left, meaning that 80 = 32n which means that he was able to but 2 sweaters and got $16 back. Therefore the formula would be 32n = 100 - 20

The formula for the number of sweaters will be 32n = 100 – 20.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Favian received a $100 gift card to a clothing store.

Using only the gift card, he was able to purchase n sweaters that cost $32 each and 1 belt for $20.

If there was no tax on the sweaters and belt,

Then the equation will be

32n + 1 x 20 = 100

    32n + 20 = 100

             32n = 80

                 n = 2.5 ≈ 2

If Favian originally had $100 but spent $20 on a belt, he only had 80 left, meaning that 80 = 32n, which means that he was able to but 2 sweaters and got $16 back.

Therefore, the formula would be 32n = 100 – 20.

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Eight cattle spend the entire day inside the barn because they weren't among the herd that went outside to graze. So the correct option is C)

There were eight cattle present inside the barn the entire time. All but eight of the 23 cattle that Mr. González had in his stable left to go graze outside for six hours. We initially discover that 15 cattle were out grazing for six hours before calculating how many cattle were inside the barn all day.

We can presume that the eight cattle who didn't go outside to graze spent the entire day inside the barn because the problem provides no information on them. 8 cattle are so present within the barn all day.

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