full-time high school students spend approximately 30 hours per week in class, and full-time college students only spend about half of that in class. true or false: full-time high school students spend more time per week on their courses than full-time college students.

The mean absolute deviation (MAD) of the given set of data is 3.875.

To calculate the mean absolute deviation, we first need to find the mean of the data set by adding up all the numbers and dividing by the total number of values:

Mean = (12 + 10 + 12 + 6 + 8 + 4 + 2 + 12) / 8

Mean = 8

Next, we find the absolute deviation of each number from the mean. To do this, we subtract the mean from each number and take the absolute value:

|12 - 8| = 4

|10 - 8| = 2

|12 - 8| = 4

|6 - 8| = 2

|8 - 8| = 0

|4 - 8| = 4

|2 - 8| = 6

|12 - 8| = 4

Then, we find the mean of the absolute deviations:

Mean absolute deviation = (4 + 2 + 4 + 2 + 0 + 4 + 6 + 4) / 8

Mean absolute deviation = 26 / 8

Mean absolute deviation = 3.875

Therefore, the mean absolute deviation of the given set of data is 3.875.

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Complete Question:

what is the mean absolute deviation of the following set of data 12 10 12 6 8 4 2 12.

The coordinates for the dilated triangle is obtained as A'(-1, 8), B'(-7, 6), and C'(-7, -4).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

The coordinates point of the triangle is given as -

A (-1,6)

B (-4,5)

C (-4,0)

To dilate triangle ABC by a scale factor of 2 about the point (-1, 4), we can follow these steps -

Translate the triangle so that the center of dilation is at the origin.

We can do this by subtracting (-1, 4) from each vertex -

A' = (-1, 6) - (-1, 4) = (0, 2)

B' = (-4, 5) - (-1, 4) = (-3, 1)

C' = (-4, 0) - (-1, 4) = (-3, -4)

Dilate the translated triangle by multiplying the coordinates of each vertex by the scale factor of 2 -

A'' = 2(0, 2) = (0, 4)

B'' = 2(-3, 1) = (-6, 2)

C'' = 2(-3, -4) = (-6, -8)

Translate the dilated triangle back to its original position by adding (-1, 4) to each vertex -

A'B'C' = A'' + (-1, 4) = (-1, 8)

B'' + (-1, 4) = (-7, 6)

C'' + (-1, 4) = (-7, -4)

Therefore, the coordinates of the dilated triangle A'B'C' are (-1, 8), (-7, 6), and (-7, -4).

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Step-by-step explanation:

[tex]{ \tt{h(x) = {x}^{2} + 4x - 7 }}[/tex]

Substitute for x as -2;

[tex]{ \tt{h( - 2) = {( - 2)}^{2} + 4( - 2) - 7}} \\ \\ { \tt{h( - 2) = 4 - 8 - 7}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ { \tt{h( - 2) = - 11}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

Answer:-9

Step-by-step explanation:

h(-2)=h(x)

it symbolize that x=-2;

so, we'll replace every x with -2:

-2^2+3*(-2)-7=4-6-7=-9

The plant is growing 0.89 feet per month.

To calculate how much a plant grows per month, you need to first convert the measurements into one unit of measurement.

Since the plant is growing 2/3 of a foot every 3/4 of a month,

we can first convert the fractions of a foot and a month into decimal equivalents.

2/3 of a foot is 0.67 feet, and 3/4 of a month is 0.75 months.

We can then calculate the amount of growth per month by dividing the amount of growth per 3/4 of a month by the amount of time that is 3/4 of a month (0.75).

The equation is 0.67 feet / 0.75 months = 0.89 feet per month.

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Answer:

Step-by-step explanation:

(g * h)(24)

gh*24

24gh

Based on the given information, the scout should choose Player A if they are looking for consistency.

What are range and standard deviation?

Range is the difference between the highest and lowest scores in the set.

Standard deviation measures how spread out the scores are from the mean.

To determine which player is more consistent, we need to look at the variability in their scores. One way to measure variability is to calculate the range and the standard deviation of each player's scores.

The smaller the range, the more consistent the player's scores are.

A smaller standard deviation indicates that the scores are closer together, which means the player is more consistent.

Using the data provided, we can calculate the range and standard deviation for both players:

Player A:

Range = 21 - 0 = 21

Standard deviation = 5.70

Player B:

Range = 48 - 3 = 45

Standard deviation = 10.89

From these calculations, we can see that Player A has a smaller range and a smaller standard deviation, which means that their scores are more consistent than Player B's. Therefore, the scout should choose Player A if they are looking for consistency.

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The correct option is the second one, your supervisor did not divide by the total number of bags.

Here we can see a table with the size of each bag (in grams) and the number of sold bags.

Now, remember that for a set of N numbers {x₁, ..., xₙ} the mean is:

M = (x₁ + x₂ + ...)/N

So the denominator is the amount of elements in the set.

Then here in the denominator we should see the total number of bags sold, which is:

25 + 32 + 40 + 18 = 115

That number should be in the denominator instead of the sum of the masses.

Then the correct option is the second one.

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The constant of proportionality is calculated as:

Option D: 8.5

The constant of proportionality is defined as the constant value of the ratio between two proportional quantities.

Now, we are given a table of values and as such, we can find the constant of proportionality from the formula:

k = y/x

From the table, we have:

k = 25.50/3

k = 8.5

k = 42.5/5

k = 8.5

k = 59.50/7

k = 8.5

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P(strawberry or cherry) = P (strawberry) + P (cherry) = 1/2 + 1/2 = 1

The probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is the same and is equal to 50%. This is because there are an equal number of strawberry chews (10) and cherry chews (10) in the bag of candy. Therefore, the probability of her selecting one of either is 1/2 = 0.5 = 50%.
The word or phrase that describes the probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is "either/or probability".Explanation:The candy bag of Kadeesha contains 10 strawberry chews and 10 cherry chews. This means there are two flavors of candies in the bag. The probability that she picks a strawberry chew at random without looking will be 10/20, which can be simplified to 1/2. Similarly, the probability of picking a cherry chew at random without looking will be 10/20, which can also be simplified to 1/2. When considering either of the probabilities, it implies that the probability that she reaches in without looking and pulls out a strawberry or a cherry chew is the sum of the probability of picking a strawberry chew and the probability of picking a cherry chew.i.e. P (strawberry or cherry) = P (strawberry) + P (cherry) = 1/2 + 1/2 = 1Therefore, the probability that Kadeesha reaches in without looking and pulls out a strawberry or a cherry chew is 1, which implies that it is a sure event. Hence, the word or phrase that describes the probability that she reaches in without looking and pulls out a strawberry or a cherry chew is "either/or probability".

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The probability of selecting 46 students out of a college population where 65% still need to take another math class is 0.05433 or 5.433%.

The probability of selecting 46 students out of a college population of which 65% still need to take another math class can be calculated using the binomial probability formula. To calculate the probability, the following information is needed:

Using the binomial probability formula, we can calculate the probability of selecting 46 students out of a college population where 65% still need to take another math class as follows:

[tex]P(X=46) = (N!/((N-r)! * r!)) * (p^r) * (1-p)^(N-r)[/tex]

[tex]= (100!/((100-46)! * 46!)) * (0.65^46) * (1-0.65)^(100-46)[/tex]
[tex]= 0.05433[/tex]

Therefore, the probability of selecting 46 students out of a college population where 65% still need to take another math class is 0.05433 or 5.433%.

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The answer choice that is the most appropriate is B. A one-sample z-interval for estimating a population proportion

This is the most appropriate method because you are trying to estimate the proportion of all registered voters who have a favorable impression of Candidate A based on the sample data.

A one-sample z-interval is used when you want to estimate a population proportion using a sample proportion.

To calculate the one-sample z-interval for estimating a population proportion, you can use the following formula:

Confidence Interval = p ± Z * sqrt((p * (1 - p)) / n)

where:

Using this method, you will calculate a confidence interval that estimates the true proportion of registered voters who have a favorable impression of Candidate A, based on the sample data.

This is the most appropriate method because it focuses on estimating a single population proportion and incorporates the sample data and sample size into the calculation.

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Answer: The cost of each small candle is $3 and the cost of each large candle is $6.

Step-by-step explanation:

Let's use variables to represent the cost of each small candle and each large candle. Let's call the cost of each small candle "x" and the cost of each large candle "y".

We can set up two equations based on the information given:

4x + 1y = 18 (equation 1)

5x + 2y = 27 (equation 2)

We can solve for one variable in terms of the other by using one equation to eliminate one variable. Let's solve for "y" in terms of "x" by multiplying equation 1 by 2 and subtracting it from equation 2:

5x + 2y = 27

(8x + 2y = 36)

-3x = -9

Dividing both sides by -3, we get:

x = 3

Now that we know the cost of each small candle is $3, we can substitute that value into one of the equations to solve for the cost of each large candle. Let's use equation 1:

4x + 1y = 18

4(3) + 1y = 18

12 + y = 18

y = 6

Therefore, the cost of each small candle is $3 and the cost of each large candle is $6.

Answer:

Interpolation and extrapolation are two methods used to estimate data points within or beyond a given set of values.Interpolation is the process of estimating a data point within the given range of values, based on the relationship between the known data points. For example, suppose we have the following data points: (1, 3), (2, 5), and (4, 9). If we want to estimate the value of y for x = 3, we can use interpolation to calculate it based on the trend of the data points within the given range. In this case, we can see that the slope of the line between (2, 5) and (4, 9) is the same as the slope of the line between (1, 3) and (2, 5). Therefore, we can estimate the value of y for x = 3 to be 7, using the trend of the known data points.Extrapolation, on the other hand, is the process of estimating a data point beyond the given range of values, based on the trend of the known data points. For example, suppose we have the same data points as before: (1, 3), (2, 5), and (4, 9). If we want to estimate the value of y for x = 5, we can use extrapolation to calculate it based on the trend of the known data points. In this case, we can see that the slope of the line between (2, 5) and (4, 9) is the same as the slope of the line between (1, 3) and (2, 5). Therefore, we can estimate the value of y for x = 5 to be 11, assuming that the trend of the known data points continues beyond the given range.Here is a graph that shows both interpolation and extrapolation:

{graph attached below}

In the graph, the blue dots represent the known data points. The red line represents the trend of the known data points, which can be used for interpolation and extrapolation. The green dot represents an interpolated data point, while the purple dot represents an extrapolated data point.In summary, interpolation and extrapolation are similar in that they both involve estimating data points based on the trend of the known data points. However, they differ in that interpolation estimates data points within the given range of values, while extrapolation estimates data points beyond the given range of values.

hope this helps!

To find the surface area of the volume generated when the curve y = x^2 revolves around the y-axis from x = 0 to x = 2, we will use the surface area formula for revolution:

Surface Area = 2 * pi * ∫[x * sqrt(1 + (dy/dx)^2)] dx from x = 0 to x = 2.

First, find the derivative dy/dx:
y = x^2
dy/dx = 2x

Now, plug in the derivative and simplify the expression inside the integral:
sqrt(1 + (2x)^2) = sqrt(1 + 4x^2)

Now, set up the integral with the surface area formula:
Surface Area = 2 * pi * ∫[x * sqrt(1 + 4x^2)] dx from x = 0 to x = 2.

Next, we will approximate the integral using a calculator:
Approximate Integral ≈ 9.8433

Finally, multiply by 2 * pi:
Surface Area ≈ 2 * pi * 9.8433 ≈ 61.9362

So, the surface area of the volume generated when the curve revolves around the y-axis is approximately 61.9362 (rounded to four decimal places).

a) There are three values of x, namely -3, -2, and -1, for which g(x) = 0.

b) The absolute minimum value of g on the interval -7 ≤ x ≤ 9 is 20, and the absolute maximum value of g is 90

a. To check if there is a value of x for -3 ≤ x ≤ 2 such that g(x) = 0, we can plug in each value in the interval and see if any of them make g(x) equal to 0:

g(-3) = -3² + 5(-3) + 6 = 0

g(-2) = -2² + 5(-2) + 6 = 0

g(-1) = -1² + 5(-1) + 6 = 0

g(0) = 0² + 5(0) + 6 = 6

g(1) = 1² + 5(1) + 6 = 12

g(2) = 2² + 5(2) + 6 = 20

So, we can see that there are three values of x, namely -3, -2, and -1, for which g(x) = 0.

b. To find the absolute minimum and maximum values of g on the interval -7 ≤ x ≤ 9, we can first find the critical points of g by taking its derivative:

g'(x) = -2x + 5

Setting g'(x) = 0, we get:

-2x + 5 = 0

-2x = -5

x = 5/2

So, the only critical point of g is x = 5/2.

We can now check the values of g at the endpoints of the interval and the critical point:

g(-7) = -7² + 5(-7) + 6 = 20

g(9) = 9² + 5(9) + 6 = 90

g(5/2) = (5/2)² + 5(5/2) + 6 = 43.25

Therefore, the absolute minimum value of g on the interval -7 ≤ x ≤ 9 is 20, which occurs at x = -7, and the absolute maximum value of g is 90, which occurs at x = 9.

We can justify this by noting that g is a quadratic function with a negative leading coefficient, which means that it opens downward and has a maximum value at its vertex (which occurs at x = 5/2). Since the vertex is within the given interval, and the function is decreasing on the left and increasing on the right of the vertex, the maximum and minimum values of g must occur at the endpoints of the interval.

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We have 6 red and 1 blue marble thus the probability of drawing blue marble = 1/7

To understand probability as a concept, pay attention to the steps below.

Step 1. Multiply the individual probabilities to obtain the chance of numerous separate events.

Step 2. As there are two separate events in this scenario, double the probabilities of each.

Step 3. Add the individual probabilities to obtain the chance of several events that are mutually exclusive.

In this bag of 7 marbles, there is 1 blue one. Assume that each is marked with a number. Choosing blue-1 has a 1/7 chance of happening. (Why? As there are 7 marbles that may be chosen, each with an equal probability, and since those 7 occurrences are mutually exclusive, the 7 probabilities total up to 1.)

The probability of choosing blue-2 is similarly 1/7; the same goes for blue-3,..., and blue-8. To determine the likelihood of picking a blue, add those up (and blue).

Step 4. Do the same for red next.

Thus the probability of drawing blue marble =  1/7

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The required sides of kite are √61, √61, √221 and √221 units.

According to the Pythagoras theorem, the square of the hypotenuse in a right-angled triangle equals the total of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two sides. Pythagoras theory triangles are another name for these triangles.

In ΔAOD

AD = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units

In ΔAOB

AB = [tex]\sqrt{5^2+6^2} = \sqrt{61}[/tex] units

In ΔBOC

BC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units

In ΔDOC

DC = [tex]\sqrt{5^2+14^2} = \sqrt{221}[/tex] units

Thus, required sides of kite are √61, √61, √221 and √221 units.

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Answer:

14

Step-by-step explanation:

all you have to do to find difference is subtract the small number from the bigger number, 18 - 4 = 14

Answer:

14

Step-by-step explanation:

The difference of 18 and 4

18 - 4

14

The quadratic function to represent the total area of the park and its path is given by: f(x) = 2x² + 18x + 36.

In this problem, we are given that the length of a rectangular park is twice its width, and it is surrounded by a 3-foot wide path.

We are required to write a quadratic function to represent the total area of the park and its path.

The rectangular park can be represented as follows:

Length = 2x (twice the width)

Width = x

Therefore, the total length of the park including the 3-foot wide path can be represented as (2x + 2*3),

and the total width of the park including the 3-foot wide path can be represented as (x + 2*3).

The area of the park is given by the product of its length and width.

Thus, the area of the park can be represented as follows: Area of the park = (2x + 6)(x + 6)

To represent this as a quadratic function,

we can simplify the above expression using the distributive property.

Area of the park = 2x² + 6x + 12x + 36 = 2x² + 18x + 36.

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Answer: 1287

Step-by-step explanation:

The missing value is approximately 64.12 degrees, which is closest to option D: 21.25 using inverse cos.

The inverse cosine (or arccosine) of both sides of the equation must be taken in order to locate the missing value in the equation cos = 7/18 to the closest tenth. We will then be able to convert the value of to degrees and round it to the closest hundredth using the value of the radian that is produced.

cos θ = 7/18

= arccos(7, 18, 7)

A 1.1181 radian angle

We can use the conversion factor /180 to convert radians to degrees.

θ = 1.1181 × 180/π

64.12 degrees.

As a result, the figure that is lacking is roughly 64.12 degrees, which is closest to choice D: 21.25.

Due to the periodic nature of the cosine function, there are often two solutions when determining the inverse cosine of a value. But, since the problem states that we should round to the closest hundredth, which suggests a single answer, we can disregard the second option in this instance. By reinserting the value we discovered into the original equation and making sure it equals 7/18, we can further confirm that the result is accurate.

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The college instructor is most concerned with equity standards.

Equity standards are when an instructor adjusts grades to ensure fairness to all students regardless of their individual performances.

This means that if a class as a whole does not do as well as last year, the instructor will alter the distribution of grades so that the overall grades reflect the effort put in by the class.

For example, if the class average is a C, the instructor may raise some grades to a B or even A in order to ensure that the grades are fair to all students in the class.

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The missing side length for the triangle is given as follows:

[tex]x = \frac{16\sqrt{3}}{3}[/tex]

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 60º on the triangle, we have that:

The tangent of 60º is equals to the square root of 3, hence the value of x is obtained as follows:

tan(60º) = 16/x

[tex]\sqrt{3} = \frac{16}{x}[/tex]

[tex]x = \frac{16}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}[/tex]

[tex]x = \frac{16\sqrt{3}}{3}[/tex]

The triangle is given by the image presented at the end of the answer.

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Answer:  The area of the smaller circle is [tex]65.6cm^{2}[/tex].

Step-by-step explanation:

A = [tex]\pi r^{2}[/tex], r is the radius.

1. Find out the diameter of the small circle.

[tex]\frac{1}{3}(27)= 9[/tex]

2) Find out the radius, r.

[tex]radius = \frac{diameter}{2} =\frac{9}{2} =4.5[/tex]

3) We plugin r = 4.5 into the formula to solve the area of the smaller circle.

[tex]A=\pi r^{2}=\pi (4.5)^{2} =65.6cm^{2}[/tex]

The distance between the two people is changing at a rate of 24.884 mi/h after 15 minutes.

We can use the Pythagorean theorem to determine the distance between the two people as a function of time. Let x be the distance traveled by the person walking east, and y be the distance traveled by the person walking northeast. Then, after 15 minutes (or 0.25 hours), we have:

x = (9 mi/h) * (0.25 h) = 2.25 mi

y = (8 mi/h) * (0.25 h) = 2 mi

The distance between the two people is given by:

[tex]d = sqrt(x^2 + y^2)[/tex]

Taking the derivative with respect to time t, we get:

[tex]d' = (2x dx/dt + 2y dy/dt) / (2sqrt(x^2 + y^2))[/tex]

Substituting the values we found earlier, we get:

[tex]d' = (2(2.25)(9) + 2(2)(8)) / (2sqrt((2.25)^2 + (2)^2))= 24.884 mi/h[/tex]

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The solution to the system of equations is x = 5 and y = -3.

We can use the elimination method by multiplying the second equation by 2 and adding it to the first equation to eliminate y:

= -4y + 11x - 67 + 2(2y + 5x - 19) = 0

-4y + 11x - 67 + 4y + 10x - 38 = 0

21x - 105 = 0

Dividing both sides by 21, we get:

x - 5 = 0

So x = 5.

Now we can substitute x = 5 into either of the original equations:

2y + 5x - 19 = 0

2y + 5(5) - 19 = 0

y = -3

Thus, the solution to the system of equations is:

x = 5, and y = -3.

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The simplified form of the expression the sum of 6. 6 and 3. 2 all divided by 5 times the quantity of the squared difference of 2 minus 5 plus 6 is -0.3267

To simplify this expression, we'll work from the inside out, using the order of arithmetic operation

First, we'll evaluate the expression inside the parentheses:

(2 - 5 + 6) = 3

Next, we'll calculate the squared difference of 2 and 5:

(2 - 5)^2 = (-3)^2 = 9

Then, we'll subtract the result from step 2 from the result of step 1:

3 - 9 = -6

Next, we'll calculate the sum of 6.6 and 3.2:

6.6 + 3.2 = 9.8

Finally, we'll divide the result from step 4 by 5 times the result from step 3:

9.8 / (5 × -6) = 9.8 / -30

= -0.3267 (rounded to four decimal places)

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Answer:

1440000

Step-by-step explanation:

Since for every mile, there are 12 people, we have 120000 miles. If we multiply 12 by 120000, we get 1440000.

The percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

Percent error is a measure of the difference between an actual value and an estimated or measured value, expressed as a percentage of the actual value. It is used to evaluate the accuracy of measurements or calculations.

To calculate the percent error for Jason's measurement, we first need to find the absolute error, which is the difference between his measurement and the actual value:

Actual value minus measured value equals absolute error.

Absolute error = |14 - 13|

Absolute error = 1 inch

Next, we can use the formula for percent error:

(Absolute error / Actual Value) x 100% equals the percent of error.

Percent error = (1 / 14) x 100%

Percent error = 0.0714 x 100%

Percent error = 7.14%

Therefore, the percent error for Jason's measurement is 7.14%. This means that his measurement was off by 7.14% compared to the actual value.

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