Raj polled 100 students in his class to compare the number of hours that teen boys and girls played video games each week. the results of his survey are shown below. which statement about his data sets is true? hours of video game time per week for teen boys a box-and-whisker plot. the number line goes from 0 to 28. the whiskers range from 0 to 28, and the box ranges from 9 to 17. a line divides the box at 14.5. hours of video game time per week for teen girls a box-and-whisker plot. the number line goes from 0 to 28. the whiskers range from 0 to 28, and the box ranges from 3 to 15. a line divides the box at 6. the average boy plays 8.5 hours more per week than the average girl. the average boy plays 2 hours more per week than the average girl. the average boy plays the same amount of time per week as the average girl. the average boy plays 6 hours more per week than the average girl.

Answer:

1x + 2y = 177 (price)

x + y= 114 (rentals)

Step-by-step explanation: x= movies y= video games

Answer:

56

Step-by-step explanation:

add and then multiply

For problems 7-9, a pair of fair dice is rolled. In 7 the probability is 5/36. In 8 the probability 1/2. In 9 the probability 11/12. In 10 the probability 17/36.

7. Find the probability that the sum is at most 5.To solve this, let's find the possible outcomes that can result in a sum of 5 or less.

The possible outcomes are: {(1, 1), (1, 2), (2, 1), (1, 3), (3, 1)}

Total number of outcomes: 6 × 6 = 36

So, the probability that the sum is at most 5 is: (5 outcomes) / (36 total outcomes) = 5/36.

8. Find the probability that the sum is a multiple of 2 or a multiple of 3.To solve this, let's find the possible outcomes that can result in a sum that is a multiple of 2 or 3.

The possible outcomes are: {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6)}

Total number of outcomes: 6 × 6 = 36

So, the probability that the sum is a multiple of 2 or a multiple of 3 is: (18 outcomes) / (36 total outcomes) = 1/2.

9. Find the probability that the sum is at least 4.To solve this, let's find the possible outcomes that can result in a sum of 4 or greater.

The possible outcomes are: {(1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Total number of outcomes: 6 × 6 = 36

So, the probability that the sum is at least 4 is: (33 outcomes) / (36 total outcomes) = 11/12.

10. Find the probability that the sum is not an even number. Let's find the possible outcomes that can result in an odd number sum.

The possible outcomes are: {(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5)}

Total number of outcomes: 6 × 6 = 36

So, the probability that the sum is not an even number is: (17 outcomes) / (36 total outcomes) = 17/36.

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Answer:−(5−3m)=7m+10

m+−1(5−3m)=7m+10(Distribute the Negative Sign)

m+(−1)(5)+−1(−3m)=7m+10

m+−5+3m=7m+10

(m+3m)+(−5)=7m+10(Combine Like Terms)

4m+−5=7m+10

4m−5=7m+10

Step 2: Subtract 7m from both sides.

4m−5−7m=7m+10−7m

−3m−5=10

Step 3: Add 5 to both sides.

−3m−5+5=10+5

−3m=15

Step 4: Divide both sides by -3.

−3m

−3

=

15

−3

m=−5

Step-by-step explanation:

brainliest pleaseee

Answer:

4/11

Step-by-step explanation:

Notice that because there are 4 green marbles and 7 silver marbles, that there is a total of 11 marbles in the bag. The question is also looking at the number of green marbles and the probability of reaching into the bad and choosing a green marble. Here is a way to set the fraction up to get the right answer for these types of problems. green marbles/total

Plug in the data. The numerator is 4 and the denominator is 11. Therefore, you get 4/11

Answer:

Step-by-step explanation:

First, you will need to find out how many marbles there are total, which is 11. . Next, identify how many green marbles are in there, which is 4. You are able to identify that  With you finding probability, the total amount will be on the bottom. So, you can see that there is a 4/11 or about 36% chance that a green marble will be picked.

The volume of Preston's new step in rectangular prism shape with given length , width, and height is equals to 2,376 cubic inches

Let us consider l be the length, w is the width, and h is the height.

The volume of a rectangular prism is equal to,

V = l × w × h

In this case,

The length (l) is equals to 11 inches,

The width (w) is equals to 36 inches,

The height (h) is equals to 6 inches.

So, we can plug in these values and calculate the volume,

V = l × w × h

⇒ V = 11 inches × 36 inches × 6 inches

⇒ V = 2,376 cubic inches

Therefore, the volume of Preston's new step for given dimensions is 2,376 cubic inches.

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Answer: 1 hour and 37 mins

Step-by-step explanation: add 4 mins to 12:56 to get 1:00 then add 1:33 to get 2:33 then add 1:33+0:04.

The diagonals of the parallelogram intersect at the center. Then the value of the variable 'x' is 38.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. Its diagonals intersect in the center.

Given parallelogram A B C D below, DE = 31 If EB = x - 7.

By the definition, then the equation is given as,

EB = DE

x - 7 = 31

Simplify the equation, then we have

x - 7 = 31

x = 31 + 7

x = 38

The value of the variable 'x' is 38.

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The relation between the events Y and W prevents us from completing the analysis.

The relation between the events Y and W prevents us from completing the analysis.

Case 1: W is more likely than Y then we have the following analysis:

Z, X, Y, and W are arranged in ascending order of more likeliness.

Case 2: Y is more likely than W then we have the following analysis:

Z, X, W, and Y are arranged in ascending order of more likeliness.

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The volume of the Solid -

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

What is volume?

Volume is a measure of the amount of three-dimensional space occupied by an object or a region. It quantifies the extent or size of a solid object or a container. In simpler terms, volume is a measure of how much space an object takes up.

What is integral?

In mathematics, an integral is a fundamental concept in calculus that allows us to compute the total accumulation of a quantity over a given interval. It is used to find the area under a curve, the length of a curve, the volume of a solid, and many other applications.

To find the volume of the solid enclosed by the paraboloid z = 3x^2(y - 2)^2 and the planes z = 1, x = -2, x = 2, y = 0, and y = 2, we need to set up a triple integral over the given region.

The limits of integration for x, y, and z are as follows:

x: -2 to 2

y: 0 to 2

z: 1 to 3x^2(y - 2)^2

The volume V can be calculated as follows:

V = ∫∫∫R dz dy dx

where R represents the region defined by the given planes.

V = ∫∫∫R 3x^2(y - 2)^2 dz dy dx

To evaluate this triple integral, we integrate with respect to z first, then y, and finally x, using the given limits of integration:

V = ∫[-2,2] ∫[0,2] ∫[1,3x^2(y-2)^2] 3x^2(y - 2)^2 dz dy dx

Performing the integration:

V = ∫[-2,2] ∫[0,2] [3x^2(y - 2)^2z]∣[1,3x^2(y-2)^2] dy dx

V = ∫[-2,2] ∫[0,2] 3x^2(y - 2)^2[3x^2(y-2)^2 - 1] dy dx

V = ∫[-2,2] [x^2(y - 2)^2(3x^2(y-2)^2 - 1)]∣[0,2] dx

V = ∫[-2,2] 4x^2(2x^2 - 1)(12x^2 - 1) dx

Evaluate this integral using appropriate techniques or numerical methods, such as numerical integration or computer software, to find the volume of the solid enclosed by the paraboloid and the given planes.

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a) The expected number of customers is 61.5.

b) Olaf's expected profit for 60 sets of skis is 369.

c) Olaf's expected profit for 61 sets of skis is 378.45.

d) Olaf's expected profit for 62 sets of skis is 387.9.

e) Olaf's expected profit for 63 sets of skis is 397.35.

f) Olaf's expected profit for 64 sets of skis is 406.8.

g) The optimal number of sets of skis Olaf should have ready for rental to maximize expected profit is 62.

a) Find the expected number of customers:
This can be calculated by multiplying the probability of each customer group by the number of customers, and then adding the results together.

For example, 0.10 × 60 = 6, 0.075 × 61 = 4.575, 0.675 × 62 = 41.25, 0.075 × 63 = 4.725, and 0.075 × 64 = 4.8,

which added together results in 61.5.

b) If 60 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 369).

c) If 61 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 378.45).

d) If 62 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 387.9).

e) If 63 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 397.35).

f) If 64 sets of skis are available, compute Olaf's expected profit:
This is calculated by multiplying the expected number of customers by the daily cost for the rental of each set of skis (61.5 × 6 = 406.8).

g) How many sets of skis should Olaf have ready for rental to maximize expected profit?
This is because the highest expected profit (387.9) occurs when 62 sets of skis are available.

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Answer:

X = - 1

Y = 0

Step-by-step explanation:

The probability of selecting a defective bulb is 0.16.

Given: 8 Bulbs are defective out of 50 bulbs. To find the probability that a randomly selected item is defective.

What is probability?

Probability shows the possibility of how likely an event is happening to occur out of all the possibilities.

Let’s solve the problem:

Total number of video recorders: 50

The sample space n(S) = 50

Number of defective bulbs: 8

Let E be the event of selecting a defective bulb.

Then n(E) = 8

Therefore, the probability of selecting a defective bulb: Number of defective bulbs / Total number of bulbs

=> n(E) / n(S)

=> 8 / 50

=> 0.16

Hence the probability of selecting a defective bulb is 0.16.

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Answer:

2/3

Step-by-step explanation:

I think you meant y=2/3x+4 because what you wrote the correct equation for slope, but anyway the slope would be 2/3 because if lines are parallel, they have the same slope.

I hope this helps!

When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle.

\(x\propto \frac{1}{y} \)

We know that the area of a rectangle is given by the product of the length and width of the rectangle.

Area = Length*Width

In this given problem,

The length of the rerectanglctangle is represented by x

and the width of the rectangle is represented by y

If the area of the rectangle is represented by A now.

So by the formula,

A = x*y

When A is constant then,

x = A/y

\(\therefore x \propto \frac{1}{y}\)

So from the above calculation we can conclude that about relation between length and width that,

"When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle."

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For the system of equations to have a unique solution the value of k must not be 6

Now, According to the question:

The given equations are,

kx + 2y = 5

3x + y = 1

The above equations can be written as,

kx + 2y – 5 = 0

3x + y – 1 = 0

We need to find the value of k.

So, we know that if the two equations are \(a_1x+b_1y+c_1=0\), \(a_2x+b_2y+c_2=0\) Then we will compare the coefficients such that

\(\frac{a_1}{a_2},\frac{b_1}{b_2} and \frac{c_1}{c_2}\).

If \(\frac{a_1}{a_2}\neq \frac{b_1}{b_2}\)  then the equations have unique solution, if \(\frac{a_1}{a_2}=\frac{b_1}{b_2} = \frac{c_1}{c_2}\)

then the equations have infinitely many solutions and if \(\frac{a_1}{a_2}=\frac{b_1}{b_2} \neq \frac{c_1}{c_2}\)

then the equations have no solutions.

Here we can clearly see that,

\(a_1=k,b_1=2,c_1=-5\\\\\\a_2=3,b_2=2,c_2=-1\)

So, \(\frac{a_1}{a_2},\frac{b_1}{b_2} , \frac{c_1}{c_2}\)

\(\frac{a_1}{a_2}=\frac{k}{3}, \frac{b_1}{b_2}=\frac{2}{1} , \frac{c_1}{c_2}=\frac{5}{1}\)

We know that if the system of equation has unique solution then \(\frac{a_1}{a_2}\neq \frac{b_1}{b_2}\)

So, we solve on putting their values and we get,

\(\frac{k}{3}\neq \frac{2}{1}\)

\(k\neq 6\)

Hence, for the system of equations to have a unique solution the value of k must not be 6.

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The given question is incomplete, complete question is:

Find the value of k for which the following system of equation has the unique solution:-

kx + 2y = 5

3x + y = 1.

15.3/0.012=??????????????

Answer: 1275

Total area of quadrilateral ABCD = (-4) + (-6) = -10 square units.

To find the area of quadrilateral ABCD, we can divide it into two triangles, calculate the area of each triangle, and then add them together.

Triangle ABC:

Using the coordinates of points A(4, -3), B(6, -3), and C(9, -7), we can calculate the base and height of triangle ABC. The base is the distance between points A and B, which is 6 - 4 = 2 units. The height is the vertical distance from point C to the line containing points A and B, which is the difference in y-coordinates between points C and the y-coordinate of points A or B. So, the height is -7 - (-3) = -4 units.

Area of triangle ABC = (1/2) * base * height = (1/2) * 2 * (-4) = -4 square units.

Triangle ACD:

Using the coordinates of points A(4, -3), C(9, -7), and D(7, -7), we can calculate the base and height of triangle ACD. The base is the distance between points A and D, which is 7 - 4 = 3 units. The height is the vertical distance from point C to the line containing points A and D, which is the difference in y-coordinates between points C and the y-coordinate of points A or D. So, the height is -7 - (-3) = -4 units.

Area of triangle ACD = (1/2) * base * height = (1/2) * 3 * (-4) = -6 square units.

Adding the areas of the two triangles:

Total area of quadrilateral ABCD = (-4) + (-6) = -10 square units.

Since the area is negative, it suggests that the points are not arranged in the correct order or the order of the vertices does not form a convex quadrilateral. Double-checking the order of the vertices may be necessary to ensure the correct area calculation.

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Answer:

i think its (6,4)

Step-by-step explanation:

Answer:

Reflection

Step-by-step explanation:

Answer: -46

Step-by-step explanation:

\(A=[-3(5)-2]+[-3(9)-2]=(-15-2)+(-27-2)=-17-29=-46\)

The measure of angle ∠ACB is 70°. Then the correct option is C.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

∠ABC + ∠BCA + ∠CAB = 180°

        60° + ∠BCA + 50° = 180°

                           ∠BCA = 180° – 110°

                           ∠BCA = 70°

Then the correct option is C.

The complete question is given below.

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

The measure of ABC is 60

The measure of BAC is 50

The measure of ACB will be

a. 50

b. 60

c. 70

d. 120

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Answer:

Use the diagram showing m || n, as well as the relationships between interior and exterior angles of ΔABC, to answer the questions.

The measure of angle ABC is

✔ 60

°.

The measure of angle BAC is

✔ 50

°.

The measure of angle ACB is

✔ 70

°.

Step-by-step explanation:

Answer:

The relation is a function.

Step-by-step explanation:

Since there is one value of  y  for every value of  x  in  ( 2 , − 7 ) , ( 3 , − 7 ) , ( 4 , − 8 ) , this relation is a function.

Using function concepts, we have that:

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

That is, the input of the function is the independent variable and the output is the dependent variable.

For this problem, the volume is a function of time, hence Volume = f(Time) and:

The decay rate is constant, meaning that we have a decreasing linear function, and graph H fits this problem.

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Answer:

y = -1.5x + 3.5

Step-by-step explanation:

Slope intercept form is y=mx+b.

3x + 2y = 7

2y = -3x + 7

y = -1.5x + 3.5

Answer:

-3/2x+7/2=y

Step-by-step explanation:

Answer:

1. 2m/2n

2. 3/q + 1

3. 9/3 - 1

Step-by-step explanation:

i think this is the ans

Answer:

A graph with a slope that decreases from left to right is negative. This slope would mean as x approaches +infinity y would approach -infinity and vice versa. So as x increased y would decrease and as x decreased y would increase. This is called an inverse relationship because the values change in opposite ways.