Please see photo checking my work I think it is all the students attending the college

We have to solve the equation:

The steps are:

1. Original equation

2. Distributive property

3. Substraction property of equality

4. Addition property of equality

5. Combine all terms

6. Division property of equality

7. Solution

Answer:

Step-by-step explanation:

ft7654

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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Solution

Note: Laws Of Logarithm To Use

From the question, we have

To evaluate, we have

The answer is

If 105 customers were the total, and 35% prefers cake, we must calculate 35% of 105, then we must do 105 multiplied by 35%, we can doit transforming the 35% in the fraction notation:

And the multiplication

Therefore, if we round it to the nearest whole number, the number of customers that prefer cake is 37.

37 customers prefer cake.

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.

Answer:

P = 0.5

Explanation:

The probability can be calculated as the division of the number of students that does not play on sports team by the total number of students.

Taking into account the table, there is a total of 20 students and from those 10 does not play on a sports team. Therefore, the probability is:

P = 10/20 = 0.5

S(8)=3500(1+(.047/4))^32

S(8)=$5086.40 in the account after 8 years.

a)The relative growth rate is .25, or 25%

b)at t=0, the population is 955e^.25(0)=955

c)at t=5; the population is 955*e^.25(5)=955*3.49=3333.28 bacterium.

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.

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

Answer: No real solutions

Step-by-step explanation:

[tex]14|x+14|+13=-69\\\\14|x+14|=-82\\\\|x+14|=-82/14[/tex]

Since absolute value is always non-negative, there are no real solutions.

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

the expression of the discount amount is

here x is the price

and the discount is 25%

Since x is the larger number and y is the smaller number

Since their sum is 56

That means add x and y then equate them by 56

Since the difference between them is 28

That means subtract y from x and equate the answer by 28

Look at the answer to find the correct answer

It is B

x - y = 28 and x + y = 56

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.

Answer:

1268000

Step-by-step explanation:

16000x79.25=1268000

Given: A triangular prism with base 6ft,height of triangle is 8 ft and height of prism is 12ft

Find : the volume of the prism.

Explanation: the volume of the triangular prism is equal to area of the base triangle times height of the prism.

final answer: the volume of the rectangular prism is

(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 geometric progression has the form:

We have the information about the second term, a*r:

We know that the common ratio is

So from this information we can get the coefficient a:

And we also know that the last term is 1/128, that is

From this one we can find n:

We can apply the property of the logarithm of power to get n:

Be careful, because n is not the number of terms. The number of terms is n+1, so the G.P. has 5 terms

To answer this question, we can take the coordinates (2, 4), and (3, 6) and substitute each of them in the given equation. Then, we can determine which of these ordered pairs is a solution of the equation 7x - 5 = 4y - 6. Then, we have:

1. Case: Ordered pair (2, 4):

This ordered pair is NOT a solution.

2. Case: Ordered pair (3, 6):

This ordered pair is NOT a solution.

Therefore, neither the ordered pair (2, 4) nor (3, 6) are solutions to the given equation (Option D).

Answer: 104

Step-by-step explanation:

[tex]f(-8)[/tex] represents [tex]f(x)[/tex] evaluated at [tex]x=-8[/tex].

[tex]f(-8)=3(-8)^2 +9(-8)-16\\\\=192-72-16\\\\=120-16\\\\=104[/tex]

The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m = slope

c = y intercept

The formula for finding slope is

m = (y2 - y1)/(x2 - x1)

y2 and y1 are the final and initial values of y

x2 and x1 are the final and initial values of x

From the given points ,

x1 = 8, y1 = 4

x2 = - 4, y2 = 9

m = (9 - 4)/(- 4 - 8) = 5/- 12 = - 5/12

Recall, if two lines are perpendicular, it means that the slope of one line is equal to the negative reciprocal of the slope of the other line. The negative reciprocal of - 5/12 is 12/5

Thus, the slope of the perpendicular to line FG is 12/5

First we dra a triangle:

To prove that the triangles are similar we have to do the following:

Considet triangles ABC and ACD, in this case we notice that angles ACB and ADC are equal to 90°, hence they are congruent. Furthermore angles CAD and CAB are also congruent, this means that the remaining angle in both triangles will also be congruent, therefore by the AA postulate for similarity we conclude that:

Now consider triangles ABC and BCD, in this case we notice that angles ACB and BDC are congruent since they are both equal to 90°. Furthermore angles ABC and DBC are also congruent, this means that the remaining angle in both triangles will, once again, be congruent. Hence by the AA postulate we conclude that:

With this we conclude that traingles BCD and ACD are both similar to triangle ABC, and by the transitivity property of similarity we conclude that:

Now that we know that both triangles are similar we can use the following proportion:

this comes from the fact that the ratios should be the same in similar triangles.

From this equation we can find h:

Plugging the values we have for x and y we have that h (that is the segment CD) has length:

Therefore, the length of segment CD is:

Answer:

The value of f is;

Explanation:

Given the triangle in the attached image.

Recall that;

from the given figure;

substituting the values;

Therefore, the value of f is;

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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Since both drawings are similar and have a scale factor, we can say that all sides keep the same scamle factor, if the scale drawing is in a proportion of 3:1 means that all of its sides is 3 times the real objects sides.

write this as equations

to find the respetive values for a and b we divide the sides by 3

The correct answer is D.

we know that

The unit rate is equal to

1.2 oz per mile

so

To obtain the number of ounces

multiply the unit rate by the number of miles driven

1.2*(15)=18 oz

step 2

Convert ounces to cups

Remember that

1 oz=0.125 cups

so

18 oz=18*0.125=2.25 cups

therefo

The number of batting orders that are possible for the game is 1365 orders.

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

ⁿCr = n! / ((n – r)! r!

n = the number of items.

r = how many items are taken at a time.

This will be:

15! / 11! (15 - 11)!

= 15! / 11! 4!

= 15 × 14 × 13 × 12 / 4 × 3 × 2

= 1365 orders

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Given a set of data:

6.4,6,8, 8.1,5.4, 11.1,6.7

The sum of the given data =

The number of the data = 6

so, the mean =

Rounding to the nearest tenth, so, the answer will be:

Mean = 7.4