The average of 8 numbers is 86.2. What is the total of the 8 numbers? (30 points​

The man threw the basketball from 30 inches above the ground. It traveled 45 inches to the floor, then 40 inches to the boy, who caught it. The angles formed by the path were congruent. The distance from the floor to the boy catching the ball was 85 inches.

Distance from man to floor: 30 in. + 45 in. = 75 in.

Distance from floor to boy: 40 in.

Total distance: 75 in. + 40 in. = 115 in.

Distance from floor to boy catching the ball: 115 in. - 30 in. = 85 in.

The man threw the basketball from 30 inches above the ground. This is the distance from the man to the floor. The basketball then traveled 45 inches from the man to the floor, making the total distance 75 inches. It then traveled 40 inches from the floor to the boy who caught it. This makes the total distance 115 inches. To find the distance from the floor to the boy catching the ball, we subtract the distance from the man to the floor (30 inches) from the total distance (115 inches). This gives us a result of 85 inches, which is the distance from the floor to the boy catching the ball.

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Preparing more for the AP test is associated with higher scores on the AP test.

Jen's data suggests that there is a correlation between the amount of time spent preparing for the AP test and the score that a student receives. This implies that there is a relationship between the two variables, and that increased preparation for the AP test is associated with higher scores. It is important to note, however, that this correlation does not necessarily imply causation. It is possible that students who are more likely to do well on the test are also more likely to put in more effort into preparing for it. Additional research would be needed to determine the exact nature of the relationship between the two variables.

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So on solving the provided question, we can say that volume of cuboid = l X b X h; V = 1200 cubic cm

A cuboid is a solid or three-dimensional form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic:

In contrast to a cube, which has rectangular faces, a cube has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

volume of cuboid = l X b X h

V = 10 *10*12

V = 1200 cubic cm

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The product of expression (3a⁴ + 4)² is 9a⁸ + 24a⁴ + 16

In this question we have been given an expression (3a⁴ + 4)²

We need to find the product  (3a⁴ + 4)².

Consider given expression

 (3a⁴ + 4)²

We use the formula (a + b)² = a² + 2ab + b²

So, (3a⁴ + 4)²

= (3a⁴)² + 2(3a⁴)(4) + (4)²                      ...............(1)

We know that the exponents property that, for any non-zero numbers p, q, r;

[tex](p^q)^r = p^{(q \times r)}[/tex]

So, from expression (1),

(3a⁴)² + 2(3a⁴)(4) + (4)²

= 9a⁽⁴ ˣ ²⁾ + (2 × 3 × 4)a⁴ + 16

= 9a⁸ + 24a⁴ + 16

Therefore, the product (3a⁴ + 4)² = 9a⁸ + 24a⁴ + 16

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If the base ten blocks shown are to be divided into 6 equal groups, you should first Exchange the 3 hundred flats for 30 ten rods. Option D

Generally, A cube is a three-dimensional solid object that is defined in geometry as having six square faces, facets, or sides, with three of these faces meeting at each vertex.

It has the appearance of a hexagon when seen from one of the corners, and the net is often represented as a cross. In addition to being one of the five Platonic solids, the cube is also the only regular hexahedron.

To divide the base ten blocks into 6 equal groups, you should first exchange the 3 hundred flats for 30 ten rods.

This will give you a total of 30 ten rods, which you can then divide into 6 equal groups of 5 ten rods each.

Alternatively, you could exchange the 3 hundred flats for 300 unit cubes and then divide the unit cubes into 6 equal groups.

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The line of the equation should be y = 20x + 320 and travelers will spend about $620 billion in the year 2008. So, the option c is correct.

In the given question, we have to write an equation for the line of best fit and then predict how much money travelers will spend in 2008.

The graph of the question is given below:

From the graph the points are (1.5, 350) and (4, 400)

As we know that the formula of the equation of line is:

y-y(1) = {y(2)-y(1)}/{x(2)-x(1)} (x-x(1))

x(1) = 1.5, y(1) = 350, x(2) = 4 and y(2) = 400

Now putting the values

y-350 = (400-350)/(4-1.5) (x-1.5)

y-350 = 50/2.5 (x-1.5)

y-350 = 20(x-1.5)

y-350 = 20x-30

Add 350 on both side, we get

y = 20x + 320

So, the line of the equation should be y = 20x + 320.

So that travelers will spend about $620 billion in the year 2008.

Hence, the option c is correct.

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An equation for the boiling point of this liquid is y = -0.001845x + 214.37. Also, the boiling point of this liquid at 2600 ft is equal to 209.573°F.

In order to write an equation for the boiling point of this liquid, we would have to first calculate its slope because the relationship between altitude and the boiling point of this liquid is linear.

Mathematically, the slope of any linear equation can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided about the altitudes and boiling points of this liquid, we have the following parameters:

Point (x, y) = (8300, 199.06)

Point (x, y) = (4300, 206.44)

Substituting the given points into the formula, we have;

Slope, m = (206.44 - 199.06)/(4300 - 8300)

Slope, m = 7.38/-4000

Slope, m = -0.001845

At point (8300, 199.06), the equation of this line is given by:

y - y₁ = m(x - x₁)

Where:

y - 199.06 = -0.001845(x - 8300)

y - 199.06 = -0.001845x + 15.31

y = -0.001845x + 15.31 + 199.06

y = -0.001845x + 214.37

Now, we can calculate the boiling point of this liquid at 2600 ft:

y = -0.001845(2600) + 214.37

y = -4.797 + 214.37

y = 209.573°F.

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Complete Question:

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8300 ft, the liquid boils at 199.06°F. At an altitude of 4200 ft, the liquid boils at 206.44°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2600 ft?

To put this expression in order from least to greatest, we first need to combine like terms.

-2y - 5 + 6y² + 5y³ - 5y² + 2y³ + 4y

= (-2y - 5 + 4y) + (6y² - 5y²) + (5y³ + 2y³)

= 2y - 5 + 6y² - 5y² + 7y³

Then, we can arrange the terms in order of increasing degree:

-2y - 5 + 6y² + 5y³ - 5y² + 2y³ + 4y= -5 + 2y + y² + 7y³

So the expression in order from least to greatest is: -5, 2y, y², 7y³

If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, the length of the straw is 13.5 inches.

The question is addressing the rectangular box of lengths 10 by  9 by 3

The lengths to be used are the length and the height of the rectangular box

Using the Pythagoras rule that says that in a roght angled triangle, the square on the hypothenuse side is equal to the sum of the squares on the other two sides

This implies that

d² = 10²+9²

d²=100+81

d²=181

d=√181

d=13.5 inches

Therefore, the length of the straw is 13.5 inch

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Answer:

C

Step-by-step explanation:

The solution for each system of equations is given as follows:

1. x = -4, y = 0.

2. x = 7, y = -2.

The first system of equations is defined as follows:

By the substitution method, using the first equation, we have that:

y = 2x + 8.

Replacing in the second, we have that:

-3x + 4(2x + 8) = 12.

-3x + 8x + 32 = 12

5x = -20

x = -20/5

x = -4.

Hence the solution for y is given as follows:

y = 2(-4) + 8 = -8 + 8 = 0.

The second system of equations is defined as follows:

Multiplying the first equation by -1, we have that:

Adding the two equations, the solution for y is obtained as follows:

y = -2.

Then the solution for x is calculated as follows:

3x + 6(-2) = 9

3x = 21

x = 21/3

x = 7.

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Answer:

where x=0 , y=-3

where x=2 ,y =-3

where x= -2 ,y =5

where x= 4 , y = 5

Answer:

10

Step-by-step explanation:

the least number of 2,5,10 is 10 .so we can cut red and blue pieces into 10 pieces each but green pieces stays the same. so we have total of 30 pieces.

The minimum of the absolute value function:

y = |x + 3| - 2

is y = -2.

Here we want to find the minimum value of the absolute value function:

y = |x + 3| - 2

Now, this is an absolute value function that opens upwards, then the minimum is at the vertex.

Remember that for an absolute value function:

y = |x - a| + b

The vertex is at (a, b)

So for our function:

y = |x + 3| - 2

The vertex is at (-3, -2)

And the minimum is the y-value of that point, so the minimum of the function is y = -2

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Answer:

The resulting coordinate of △ D'E'F' is translated by the vector is (8, 5),  (12,3), and (10, 0)

Given the coordinates of vertices of △ DEF as D (2, 5), E (6, 3), and F (4, 0).

If the coordinate of the vertices is translated by the vector (6, 0), the resulting coordinates of △ D'E'F' will be expressed as:

D'= (2+6, 5 + 0) = (8, 5)

E' = (6 + 6, 3 + 0) = (12, 3)

F' = (4 + 6, 0 + 0) = (10, 0)

The graph of both triangles is as attached;

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Step-by-step explanation:

The speed of the airplane is 728.5km/hr. The speed of the wind is 56 km/hr.

Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.

Let the speed of the airplane in still air being [tex]v_{a} kmh^{-2}[/tex]

Let the speed of the wind be   [tex]v_{a} kmh^{-2}[/tex]

Therefore, the ongoing speed is [tex]v_{a} - v_{m}= 4707/7 .......................(i)[/tex]

And the return journey is [tex]v_{a} - v_{m}= 4707/6 .......................(ii)[/tex]

Solving equations (i) and (ii) we get,

[tex]2v_{a} = 4707/7 - 4707/6 = 4707(\frac{1}{7} +\frac{1}{6} )[/tex]

[tex]v_{a} = 728.5kmh^{-1}[/tex]

Thus, The speed of the airplane is 728.5km/hr.

Hence, [tex]2v_{w} = 4707/6 - 4707/7 = 4707(\frac{1}{6} +\frac{1}{7} )[/tex]

[tex]v_{m} = 56.0kmh^{-1}[/tex]

The speed of the wind is 56 km/hr.

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As per the given distance, the rate of the jet in still air is 728 km/h and the rate of the wind is 56 km/h

Here we have given that a jet takes 7 hours to travel a distance of 4704 miles against the wind. The return trip takes 6 hours with the wind.

Here let us consider that L1 refers speed of the airplane in still air be and L2 refers the speed of the wind be.

Then the on going speed is written as,

=> L1 - L2 = 4704/7

And the return journey is written as,

=> L1 + L2 = 4704/6

When we Solving equations, then we get,

=> 2L1 = 4704/7 + 4704/6

=> 84L1 = (6 x 4704) + (4704 x 7)

=> 84L1 = 61152

=> L1 = 728

Then the value of L2 is

=> L2 = 4704/6 - 728

=> L2 = 336/6

=> L2 = 56

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The accurate statement based on the information is that B. The author compares building a debate team to building a house to help readers understand the importance of each step in the process.

From the information, to strong debate team, Mr. Gonzalez starts with a strong foundation: He recruits students who are interested in current events and are willing to put in the necessary time and effort. He then forms the framework by providing students with the tools they need to construct solid arguments.

Based on the analogy, the author compares building a debate team to building a house to help readers understand the importance of each step in the process. The correct option is B.

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Complete question

In a small-group discussion, Leo is trying to explain to his classmates the purpose of the analogy in the following excerpt from an article:

To build a strong debate team, Mr. Gonzalez starts with a strong foundation: He recruits students who are interested in current events and are willing to put in the necessary time and effort. He then forms the framework by providing students with the tools they need to construct solid arguments.

Which of the following statements is accurate?

A.

The author compares building a debate team to building a house to help readers understand the challenge of recruiting eligible students.

B.

The author compares building a debate team to building a house to help readers understand the importance of each step in the process.

C.

The author compares building a debate team to building a house to help readers understand the similarities between building and debating.

D.

The author compares building a debate team to building a house to help readers understand the contrast between literal tools and figurative tools

Answer:

Option B (3/2) and E (7/2)

Step-by-step explanation:

Given function [tex]f(x) = \frac{x}{2} + \frac{3}{2} = \frac{(x + 3)}{2}[/tex]

so,

(A) [tex]f(\frac{-1}{2}) = \frac{\frac{-1}{2}+3 }{2} = \frac{\frac{5}{2} }{2} = \frac{5}{4}[/tex]       (Incorrect)

(B) [tex]f(\frac{-1}{2}) = \frac{0+3 }{2} = \frac{3}{2}[/tex]                 (Correct)

(C) [tex]f(\frac{-1}{2}) = \frac{1+3 }{2} = \frac{4}{2} = 2[/tex]          (Incorrect)

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

(E) [tex]f(\frac{-1}{2}) = \frac{4+3 }{2} = \frac{7}{2}[/tex]                  (Correct)

If a school wants to build a rectangular playground that will have a diagonal length of 75 yards. The wide of the playground be if the length has to be 30 yards is: 68.7.

Using Pythagoreans theorem to find the width of the playground

c² = √a² - b²

Where:

c = Width

a = 75 yards

c = 30 yards

So,

c² = √75² - 30²

c² = √5,625 -900

c² = √4,725

c= 68.7

Therefore we can conclude that the width is 68.7.

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Using Pythagoras theorem, the width is 68.74 yards

The Pythagorean Theorem is a fundamental mathematical principle that states that in a right triangle (a triangle with one angle equal to 90 degrees), the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

It can be expressed mathematically as:

c^2 = a^2 + b^2

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

To solve this problem, we have to take the diagonal as the hypothenuse and the length as one of the legs.

75² = 30² + b²

b² = 75² - 30²

b = 68.74yds

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Answer:

what do you need help on?

The commission the sales man was paid is 101

A sales commission is a sum of money paid to an employee upon completion of a task, usually selling a certain amount of goods or services. Employers sometimes use sales commissions as incentives to increase worker productivity. A commission may be paid in addition to a salary or instead of a salary.

For example, if a man is to be given a commission of 10%. And he made a sales of $10000. Therefore his commission is 10/100× 10000 = $1000

The commission of the sales man is 5% of his total sales

His total sales is 2020

Therefore the commission the sales man will be paid is 5/100× 2020

= 10100/100

= 101

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Answer:

3

Step-by-step explanation:

2+1 = 3

Answer:

3 ( 1 + 2 = 3)

Step-by-step explanation:

How did i get the answer 3?

Simple for example if you have 1 cookie's and your other two friend's have cookie's to. but they decide they don't want them so they give it to you well if you have 1 cookie and you get 2 more your adding more cookies to you collection.

what does it look like in problem form?

It look's like this:

1 + 2 = 3

in total you will have 3 cookies.

The correct answer is (Option B): Observations with values of 200 are included in the class frequency.

When a class interval is expressed as "100 up to 200," it means that the class includes all observations with values greater than or equal to 100 and less than or equal to 200. So observations with a value of 200 would be included in the class frequency.

A. Observations with values of 100 are excluded from the class frequency - This is incorrect, as a class interval typically includes the lower value but not the upper value. For example, if the class interval is 100 up to 200, then observations with values of 100 would be included in the class frequency.

B. Observations with values of 200 are included in the class frequency - This is correct, as a class interval typically includes the lower value but not the upper value. For example, if the class interval is 100 up to 200, then observations with values of 200 would be included in the class frequency.

C. Observations with values of 200 are excluded from the class frequency - This is incorrect, as a class interval typically includes the lower value but not the upper value. For example, if the class interval is 100 up to 200, then observations with values of 200 would be included in the class frequency.

D. The class interval is 99 - This is incorrect, as the class interval is specified as 100 up to 200, not 99. The class interval is the range of values that are grouped together for the purpose of counting the frequency of observations.

Therefore, The correct answer is (Option B): Observations with values of 200 are included in the class frequency.

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Answer:

[tex]\displaystyle {\frac{sec^8(x)}{8}-\frac{sec^6(x)}{6}+C}[/tex]

Step-by-step explanation:

[tex]\displaystyle \int {\tan^3(x)\sec^6(x)} \, dx\\\\=\int {\tan^2(x)\sec^5(x)\tan(x)\sec(x)} \, dx\\=\int {\bigr(\sec^2(x)-1\bigr)\sec^5(x)\tan(x)\sec(x)} \, dx\\[/tex]

Now let [tex]u=\sec(x)[/tex] and [tex]du=\tan(x)\sec(x)dx[/tex]:

[tex]\displaystyle \int {\bigr(u^2-1\bigr)u^5} \, du\\\\=\int {u^7-u^5} \, du\\\\=\frac{u^8}{8}-\frac{u^6}{6}+C\\\\=\bold{\frac{sec^8(x)}{8}-\frac{sec^6(x)}{6}+C}[/tex]

So, because the tangent term was odd and the secant term was even, we had to break it up so we could have the factor sec(x)tan(x), and then turn tan²(x) into sec²(x)-1. Also, because the derivative of sec(x) is sec(x)tan(x), the substitution becomes really simple as you see above.

The correct constraints for the oranges would be 3x + y <= 50.

What is the linear equality in two variables?

Linear equality in two variables is an equation that uses a linear function to describe a relationship between two variables (x and y). A linear function is of the form:

ax + by = c

Where a, b, and c are constants, and x and y are the variables.

The correct constraint for the oranges used in the Refresher and Super-Duper juice would be:

3x + y <= 50

This represents the maximum number of oranges that can be used, given the number of Refreshers (x) and Super-Dupers (y) that the juice stand is making. It says that the total number of oranges used in the Refreshers (3 oranges per Refresher) plus the total number of oranges used in the Super-Dupers (1 orange per Super-Duper) must be less than or equal to the total number of oranges the juice stand has on hand (50 oranges).

Hence, the correct constraints for the oranges would be 3x + y <= 50.

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The number of integers that are divisible by 9, given the arithmetic sequence beginning with 36 and ending with 405, is 42 integers

To find the integers that would be divisible by 9, in an arithmetic sequence beginning with 36 and ending with 405, find the multiples of 9 between 36 and 405.

This is because only the multiples of 9 are divisible by 9 and so the multiples of 9 between 36 and 405 would be the integers divisible by 9.

The multiples of 9 between 36 and 405 are :
36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405

This means that the number of integers divisible by 9 in the sequence would be :

42 integers

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what is the value of m

10 (the answer)

30

70

150

Answer:

Step-by-step explanation:

We have to assume that a "piece of fruit" is either a bunch of bananas or a pound of apples. Without that assumption, there is insufficient information to work the problem.

Let B represent the number of bunches of bananas. Then 13-B is the number of pounds of apples. The total cost is ...

6B +8(13 -B) = 92

-2B + 104 = 92 . . . . . eliminate parentheses

B = -12/-2 = 6 . . . . . . subtract 104, then divide by the coefficient of B

13-B = 7 . . . . . . . . . . . the number of pounds of apples

The customer bought 6 bunches of bananas and 7 pounds of apples.

Hoped This Helped!

Answer:

W = 59 degree

Y = 59 degree

Z = 53 degree

x = 121 degree

v = 121 degree

Step-by-step explanation:

W = 59 degrees because a triangle has a total of 180 degrees, and we know 2 of the angles, one is 31 degrees and the other is 90 degrees, so

90 + 31 = 121

180 - 121 = 59 degrees

So, W = 59 degrees

Y = 59 degrees because w and y are vertical angles.

z = 53 degrees because

68 + 59 = 127

180 - 127 = 53 degree

So, z = 53 degree

x = 121 degree, y = 121 degree because w, x, y, v add up to 360 degree

59 + 59 = 118

360 - 118 = 242

242 / 2 = 118 degree

So, x and y equal to 118 degrees.

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