relation and functionFunction OperationComposition of functionsymmetryfunction Inversesrate of change scartterplotsMINIMUM STEPS PLEASE!

SOLUTION

Given:

Now substitute these given into the expression above:

Simplifying further:

The answer therefore is:

The table would look like this;

We are told that Of the 125 students that made the honor roll 64% had cheese pizza.

64% of 125 is 80 students, therefore, 80 students in total had cheese pizza.

Let's fill that in.

We now know that those who had pepperoni pizza are 125 - 80 = 45 in number.

There were 48 students that had cheese pizza and a coke, let's fill that in too, we have.

This means that the number of students that had a cheese and sprite is 80 - 48 = 32 students.

We are also told that 5 more students chose to have a coke than a sprite.

Let the total number that chose coke be x.

Then the total who chose sprite would be x - 5.

But these total must add up to 125.

So;

Therefore, 65 students took coke in total and 60 took sprite, let's fill that in too.

We can now fill in the pepperoni column.

For pepperoni and coke, we subtract 48 from 65 to obtain 17

For pepperoni and sprite, we subtract 32 from 60 to obtain 28

ii. The joint relative frequency of the students who had a sprite and pepperoni pizza.

From the table, the joint relative frequency of those who had a sprite and a pepperoni pizza is

i.e 28/45 or 0.6 of those who had pepperoni pizza, took sprite.

9.

Alternative interior angles are congruent

Therefore;

5x + 42 = 18x -12

collect like term

5x - 18x = -12 - 42

-13 x = -54

Divide both-side of the equation by -13

x=4.15

Solution

Note: Laws Of Logarithm To Use

From the question, we have

To evaluate, we have

The answer is

The perimeter of a quadrilateral is given by the sum of all the sides.

In order to add mixed numbers, let's rewrite them as a sum of the integer part and the fraction part.

So we have:

Therefore the perimeter is 9 1/3 ft.

Using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.

Recall:

Perimeter of a rectangle (P) = 2(L + W) (relationship between the width, length and perimeter)

Given:

Width (W) = 3.6 cm

Perimeter (P) = 48 cm

Length (L) = ?

Using the relationship between the dimension of a rectangle and its perimeter, the following equation would be derived:

48 = 2(L + 3.6)

Solve for the value of L

48 = 2L + 7.2

Subtract 7.2 from each side

48 - 7.2 = 2L

40.8 = 2L

Divide both sides by 2

20.4 = L

L = 20.4 cm

Therefore, using the relationship between the dimension of a rectangle and its perimeter, given its perimeter and width, the length is: 20.4 cm.

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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant.

The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area.

Ratio = cost / area

750 / 500 = 1.50

1500 / 1000 = 1.50

2,250 / 1500 = 1.50

3000 / 2000 = 1.50

Since the ratios are constant, the relationship is proportional.

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The correct statement is the relationship is proportional because the ratio of the area to the cost is constant. Is the relationship proportional?The first step is to determine if the ratio of the area of the carpet and its cost is proportional. The ratio is proportional, if the ratio is constant for all the areas and costs provided in the question. The ratio can be determined by dividing cost by the area. Ratio = cost / area 750 / 500 = 1.50 1500 / 1000 = 1.502,250 / 1500 = 1.503000 / 2000 = 1.50 Since the ratios are constant, the relationship is proportional.

For the given equation: x² + y² = 400, the required values of dy/dt and dx/dt are [(-28)/3] and 4 respectively.

What are differentiable functions?
If the derivative f '(a) exists at each point in its domain, then f(x) is said to be differentiable at the point x = a. Given two functions g and h, where y = g(u) and u = h(x). A function is referred to as a composite function if its definition is y = g [h (x)] or goh(x). Therefore, fog is also differentiable and (fog)'(x) = f'(g(x) if g (x) and h (x) are two differentiable functions. g’(x).

Given, the equation for x and y is: x² + y² = 400
Differentiating the equation above with respect to t using chain rule, we have: (2x)(dx/dt) + (2y)(dy/dt) = 0 -(i)
Rearranging (i) for dy/dt, we have: dy/dt = (-x/y)(dx/dt)   - (ii)
Again, rearranging (i) for dx/dt, we have: dx/dt = (-y/x)(dy/dt)   - (iii)
For (a), x = 16, y = 12 and dx/dt = 7, thus dy/dt using (ii) can be written as:
dy/dt = (-x/y)(dx/dt) = (-16/12)*7 = (-4/3)*7 = (-28)/3
For (b), x = 16, y = 12 and dy/dt = -3, thus dx/dt using (iii) can be written as:
dx/dt = (-y/x)(dy/dt) = (-12/16)*(-3) = (4/(-3))*(-3) = 4
Therefore, for the given equation: x² + y² = 400, the required values of dy/dt and dx/dt are [(-28)/3] and 4 respectively.

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(a) To find the area of the kitchen floor, we just have to multiply

(b) To find the number of tiles needed, we have to find the area of each tile, which is

Then, we divide the total area of the kitchen floor by the area of each tile.

Hence, David will need 80 tiles to cover the floor.

the expression of the discount amount is

here x is the price

and the discount is 25%

We have to calculate the volume of the cone.

The volume of the cone is 1/3 of the area of the base times the height.

As the base has diameter D = 16 yd, we can calculate the area of the base as:

Knowing the height is h = 14 yd, we then can calculate the volume as:

Answer: the volume is 937.81 cubic yards.

we have the equation

H = -16t^2 + 36t + 56

This equation represents a vertical parabola open downward, which means, the vertex is a maximum

The time t when the ball reaches its maximum value corresponds to the x-coordinate of the vertex

so

Convert the given equation into vertex form

H=a(t-h)^2+k

where

(h,k) is the vertex

step 1

Complete the square

H = -16t^2 + 36t + 56

Factor -16

H=-16(t^2-36/16t)+56

H=-16(t^2-36/16t+81/64)+56+81/4

Rewrite as perfect squares

H=-16(t-9/8)^2+76.25

the vertex is (9/8,76.25)

therefore

From the given graph the line is passing through the points (-2,0) and (0,3).

Let,

From the option the equation of the line is y=2x+3

Since on subtituting (0,3) in the above expression the condition satisfys, also on substituting (-1.5,0) in the given expression the condition satisfys.

Thus, the correct option is option A.

The coordinate of the x-intercept and y-intercept will be (-3, 0) and (0, -2), respectively.

A connection between a set of variables results in a linear system when presented on a graph. The variable will have a degree of only one.

The linear equation is given below

- 2x - 3y = 6

For the x-intercept, the value of the y will the zero. Then we have

- 2x - 3(0) = 6

-2x = 6

x = -3

The x-intercept is at (-3, 0).

For the y-intercept, the value of the x will the zero. Then we have

- 2(0) - 3y = 6

-3y = 6

x = -2

The y-intercept is at (0, -2).

Thus, the coordinate of the x-intercept and y-intercept will be (-3, 0) and (0, -2), respectively.

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The heptagon is a polygon of 7 sides and 7 angles

The heptagon is a closed figure formed from 7 sides

Since every 2 sides connected to form an angle, then

It contains also 7 angles

Then the answer is :

Angles: 7

Sides: 7

Step-by-step explanation:

due to AB being parallel to XZ, we know that ABY and XZY are similar triangles.

therefore, they have the same angles, and there is one common scale factor for all side lengths from one triangle to the other.

so,

AY / XY = AB / XZ

XY = AY + AX = 7 + 6 = 13

7/13 = 14/XZ

XZ×7/13 = 14

XZ×7 = 14×13

XZ = 14×13/7 = 2×13 = 26

For the given question, let the size of the original field = x

Ninety percent of a large field is cleared for planting

So, the size of the cleared land = 90% of x = 0.9x

50 percent is planted with blueberry plants and 40 percent is planted with strawberry plants.

So, the size of the land planted with blueberry plants and strawberry plants =

The remaining will be = 0.9x - 0.81x = 0.09x

Given: the remaining 360 acres of cleared land is planted with gooseberry plants

so,

divide both sides by (0.09) to find x:

So, the answer will be:

The size of the original field = 4,000 acres

Using the Empirical Rule, the correct option regarding the skewness of the distribution is given as follows:

(A) No, the distribution is skewed to the right.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is given as follows:

In the context of this problem, the mean and the standard deviation are given as follows:

A huge percentage is within one standard deviation of the mean, and the distribution is not symmetric, hence it is not normal.

Since most values are at the lower bounds of the histogram, the distribution is right skewed and option a is correct.

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ANSWER

1.5(x)

EXPLANATION

The tree is originally x feet tall. If it grows 1/2 this height it means that now it is 1/2x taller, or we can express this as a decimal, 0.5x. If we add these two heights we'll have the new height of the tree:

From the figure, we have the coordinates of the vertices:

ABC ==> A(2, 1), B(5, 1), C(1, 5)

A'B'C' ==> A'(-2, 1), B'(-5, 1), C(-1, 5)

Let's determine the type of transformation that occured here.

Apply the rules of rotation.

For a rotation acorss the y-axis, only the x-coordinates of the points will change to the opposite. i.e from negative to positive or from positive to negative.

For a rotation across the y-axis, we have:

(x, y) ==> (-x, y)

From the given graph, we can see that the only the x-coordinates changed from positive to negative.

Therefore, the transformation that occured here is the reflection across the y-axis.

ANSWER:

B) Reflection across the y-axis.

Let x represent Mikhail's age.

Since Gabrielle is 8 years older than Mikhail, it means that Gabrielle's age is

x + 8

If the sum of their ages is 104, it means that

x + x + 8 = 104

2x = 104 - 8

2x = 96

x = 96/2

x = 48

Mikhail's age is 48

Answer:

Step-by-step explanation:

Given a function f(x), a new function g(x) = cf(x), where c is a constant, is a vertical stretch of f(x) when c > 1.

In our case the function f(x) is stretched by a factor of 3.

It means c = 3 and therefore:

Correct choice is B

Answer:11

Step-by-step explanation:

1.

It means multiply f(x) and g(x) and then put "2" into it. The solution is what we are looking for. So,

2.

For this we subtract f from g and put -1 into the expression. So

3.

We simply add f and g and put 2 into the final expression.

4.

We divide f by g and put -1 in the final expression. Shown below:

Now, please match each answer with each choice.

Answer:

your answer is B

Step-by-step explanation:

Germany, Austria-Hungary, Bulgaria, and the Ottoman Empire

The inequality given is

Collecting like terms we will have

With the above solution, we can conclude that y=10 is not a solution to the inequality because the values of y are less than 8

Hence, The answer is NO

SOLUTION

We want to perform the following division using synthetic division

This becomes

First we write the problem in a division format as shown below

Next take the following step to perform the division

Now, we have completed the table and we obtained the following coefficients, 1, -1, 1, -1, 4

Note that the first four ( 1, -1, 1, -1) are coefficients of the quotient, while the last one (4) is the coefficient of the remainder.

Hence the quotient is

And the remainder is 4.

Hence

If we sum both equations, we have the next result:

Since we have this, we can say that the system has infinite solutions. We sum both equations, and we finally get that 0 = 0. In this case, the system has infinite solutions.

All these solutions are expressed by (solving for y):

For example, for a value of x = 1, y is a function of x; then, y = 1 + 5 = 6, or (1, 6), and so on.

For the next system of equations:

Adding both equations, we finally have:

Then, solving for x, we have (using the first equation):

Then, this last system has a unique solution, which is (3, 5) or x = 3 and y = 5.

We are given a graph that shows the depth in meters (y) as a function of the time in minutes (x).

Part A:

Points A, B, and their projection in the point (2, 110) form a similar triangle with the triangle formed by points A, C, and the point (2, 66).

Hello there. To solve this question, we'll have to remember some properties about inequalities and its graphs.

First, we have to determine the equation of the line. For this, we have to find, by inspection, two points contained in that line:

We can easily find the points (0, -6) and (2, -2).

With this, we can find the equation of the line using the point-slope formula:

Where (x0, y0) is a point of the line, as well as (x1, y1) and the slope m is given by:

Plugging the coordinates of the points, we get:

Such that:

Rearranging it in the ax + by = c form,

Multiply both sides of the equation by a factor of 2

Finally, notice that the values of y in the shaded region are greater than the values in the line, which means that the inequality we're looking for is:

All the point (x, y) satisfying this inequality are contained in the shaded region.