n=39; i = 0.039; PMT = $196; PV =?

Volume is area * height

area of pentagon is 1/4 * root(5(5 + 2root(5))) a^2

a being length of 1 side

if a =2, area is 6.88

6.88 * 4 = 27.52 yards^3

The solution of the composition functions are represented as follows;

Composite functions are when the output of one function is used as the input of another.

In other words, a composite function is generally a function that is written inside another function.

Therefore,  the composite function can be solved as follows:

f(x) = √x

g(x) = - 2x + 3

Hence,

(fog)(x) = f(g(x)) = [tex]\sqrt{-2x+3}[/tex]

(g o f)(x) = g(f(x)) = - 2√x + 3 = -2√x + 3

Therefore, the composite function expression is as follows:

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Answer: 288.7 miles per minute.

Step-by-step explanation:

Considering:

Distance = Rate / Time

We are given the distance as 2309.6 miles in orbit.

We can calculate the time required to travel 2309.6 miles by doing:

End time - Start time.

In this case it would be 9:31 - 9:23 = 8 minutes.

Therefore it takes 8 minutes to travel 2309.6 miles.

Now we need to find the Rate of Change in miles per minutes.

In other words we need how many miles the shuttle traveled every minute.

Right now we have the shuttle traveled 2309.6 miles in 8 minutes. To find how many traveled in 1 minute, we need to divide.

2309.6 / 8 = 288.7 miles per minute.

The average number of text messages sent during the month by each person was 408.

The average is the total number of a data set divided by the number of items on the data set.

The average is the same as the mean, which is a central value of a data set.

The total number of text messages sent in a month in 2008 = 110.4 billion

(110,400,000,000)

The total number of people using text messaging = 270.3 million (270,300,000)

Average text messages per person = 408. 44 (110,400,000,000/270,300,000)

Thus, we can conclude that, on average, each person in the population texted 408 messages per month in 2008.

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We are given the number in scientific notation:

To convert it to decimal format, we need to move the decimal point two spaces to the left.

Since we don't have enough digits before the decimal point, we add two zeros before the 4:

Now we move the point as required:

The required number is 0.0458

Answer:

slope = 5/3

y-intercept = -4

Step-by-step explanation:

First, move the x to the other side of the equation:
-3y=-5x+12
Then, divide BOTH sides by -3, so that there is no coefficient next to y:
y=5/3x-4

Then, just look at the constant and coefficient next to x (m). The slope is 5/3 and the y-intercept is -4.

Hope this helps!

Answer:

[tex]y = \frac{5}{3}x - 4[/tex]

Step-by-step explanation:

move the 5x to a -5x

-3y= -5x+12

-3/-3= -5x÷ -3 12÷ -3

Answer

a. Vertical shrink by a factor of 1/3

Step-by-step explanation

Function transformation

• a,f(x) vertically compresses f(x) when 0 < a < 1

Given the function:

Multiplying f(x) by a = 1/3, we get:

Then, f(x) is vertically shrunk by a factor of 1/3

-2y + 1 = 3

Solving for y:

Add 2y to both sides:

-2y + 1 +

===============================================

Explanation:

x = total number of balls

x-4 = number of blue

x-4 = number of green

x-4 = number of red

3(x-4) = 3x-12 = total number of blue, green, or red

x - (3x-12) = x-3x+12 = -2x+12 = number of other colors

If there are other colors, then we want this quantity to be larger than 0, so,

-2x+12 > 0

-2x > -12

x < -12/(-2)

x < 6

There are less than 6 balls in the bag.

At the same time, we want each x-4 to be greater than zero

x-4 > 0

x > 4

------------------

We found that x > 4 and x < 6

This combines to 4 < x < 6 which has us land on x = 5

This computes x-4 = 5-4 = 1, showing there's one of each blue, green and red. There are 5-1-1-1 = 2 balls of some other color not mentioned.

------------------

If x = 6, then,

x-4 = 2 each of blue, green and red

There wouldn't be any other color since 6-2-2-2 = 0

Answer:

(-2,-5)

Step-by-step explanation:

(-5+1÷2, -9+(-1)÷2)

=(-4÷2, -10÷2)

=(-2,-5)

Answer:

The given graph is not a graph of a function because a vertical line can be drawn that will intersect this graph more than once.

Explanation:

A vertical line test is generally used to determine if a relation is a function or not by drawing a vertical line across the graph of the relation.

If the vertical line intersects the graph of the relation more than once, it means that the relation is not a function because one x-value will have more than one y-value.

If the vertical line intersects the graph just once, then we can say that the relation is a function since one x-value will be associated with only one y-value.

Looking at the given graph, we can see that a vertical line can be drawn across the graph that will intersect the graph more than once, therefore the given graph is not a graph of a function because a vertical line can be drawn that will intersect the graph more than once.

We are asked to find the probability that a student is female given that they have an A.

Since this is the case, we limit ourselves to observing the row "Has an A".

In said row, there is a total of 6 students who have an A. Out of those 6, 2 are female.

Thus, P(Female|A) = 2/6 = 1/3 = 33.33%.

Explanation:

The expression is given below as

Notice that the first term is 114 and the third term is 134, then, between the first and the third, there are 20 units of difference.

Then, the common difference between each term must be 10, thus, the complete sequence is:

we know that

the rule of the translation in this problem is 2 units at left and 3 units up

so

(x,y) ------> (x-2,y+3)

Apply the rule

(7,2) ------> (7-2,2+3)

In mathematic terms, the expression 6p is written as 6 times p.

Mathematic terms

Mathematic terms means a single mathematical expression. The terms may be a single number, a single variable, several variables multiplied but never added or subtracted. Some of the terms contain variables with a number in front of them.  Those number in front of a term is called a coefficient.

Given,

Here we have the expression 6p.

Now, we have to write it as a mathematic term.

While we looking into the expression 6p.

The only operation word in this expression is p which is multiplied with the constant that is the number 6.

So, in the verbal phrase it can be written as 6 times p.

Here p take any valid number in the real numbers.

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Using the numbers 12, 6, 6, the triangle can not be formed.

The given numbers are 12, 6 and 6.

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

Here, 6 + 6 = 12 but not greater than 12

Therefore, using the numbers 12, 6, 6, the triangle can not be formed.

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The factors of f(x) are (x-4), (x+1) and (2x-3) respectively.

To select the factors of f(x), we are to pick the functions that satisfy the conditions of the given information.

For  f(4) = 0:

The function that evaluates to 0 when x = 4 is (x - 4). That is:

f(x) = (x - 4)

f(4) = (4 - 4) = 0

For  f(-1) = 0:

The function that evaluates to 0 when x = -1 is (x + 1). That is:

f(x) = (x + 1)

f(-1) = (-1 + 1) = 0

For  f(3/2) = 0:

The function that evaluates to 0 when x = 3/2 is (2x-3). That is:

f(x) = (2x-3)

f(3/2) = (2 × 3/2 - 3) = 0

Therefore, (x-4), (x+1) and (2x-3) are the corresponding factors of f(x)

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2) y = 8x² +2x -15

(4x -5)(2x +3)

S={-3/2, 5/4}

3) y= 4x² +20x +24

(4x +8)(x +3)

S={-2,3}

1) Factoring these quadratic functions we have:

2) y = 8x² +2x -15

Let's call u, and v two factors.

Multiplying 8 by -15 = we have u*v = -120 Adding u + v= 2, so u = 12 and v =-10

12 x -10 = -120

12 +(-10) = 2

So, now we can rewrite it following this formula:

(ax² + ux) +(vx +c)

(8x² +12x) +(-10x-15) Rewriting each binomial in a factored form

4x(2x +3) -5(2x+3)

(4x -5)(2x +3)

Equating each factor to zero to find out the roots:

(4x -5) =0

4x =5

x=5/4

(2x +3) = 0

2x = -3

x= -3/2

Hence, the solution set is S={-3/2, 5/4}

3) y= 4x² +20x +24

Proceeding similarly we have:

u * v = 96

u + v = 20

So u = 12, and v =8 12x 8 = 96 12 +8= 20

Rewriting into (ax²+ux)+(vx +c)

(4x²+12x) +(8x+24) Factoring out each binomial

4x(x+3) +8(x+3) As we have a repetition we can write:

(4x +8)(x +3)

3.2) Now to find out the roots equate each factor to zero, and solve it for x:

4x +8 = 0

4x = -8

x =-2

x+3 =0

x=-3

4) Hence, the answers are:

2) y = 8x² +2x -15

(4x -5)(2x +3)

S={-3/2, 5/4}

3) y= 4x² +20x +24

(4x +8)(x +3)

S={-2,3}

Given:

The function used to compute the probability of x successes in n trials, when the trials are dependent.

Required:

To choose the correct option for the given statement.

Explanation:

The hypergeometric distribution is a discrete probability distribution. It is used when you want to determine the probability of obtaining a certain number of successes without replacement from a specific sample size.

Therefore the option c is correct.

Final Answer:

c ) hypergeometric probability function.

The amount of interest paid is $21000

What is interest?

In finance and economics, interest is the payment of an amount over repayment of the principle sum (that is, the amount borrowed) by a borrower or deposit-taking financial institution to a lender or depositor at a certain rate by a borrower or deposit-taking financial institution. It differs from a charge that the borrower may pay to the lender or a third party. Interest is also distinct from a dividend, which is given by a firm to its shareholders (owners) from its profit or reserve, but not at a fixed rate, but rather on a pro rata basis as a portion of the reward achieved by risk-taking entrepreneurs when revenue exceeds total expenditures.

Total amount paid = $11000x3 = $33000

Interest paid = $(33000-12000) = $21000

Hence, the amount of interest paid is $21000

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The function is given as.

f(x)={(8,3),(4,1),(0,-1),(-4,-3) }​

The inverse function is determined as a function, which can reverse into another function.

Therefore the inverse function g(x) is obtained as

Hence the correct option is D.

Okay, here we have this:

Considering the provided expression, we are going to prove the identity, so we obtain the following:

Given:-

Cost of blouse is $27.50

Cost of sweater is $34.99

To find the cost if laura bought :-

So since laura bought one blouse and two sweaters, we get

So the cost is $97.48 and she bought the cloths of her summer needs.

In order to find the rate of discount, calculate what is the associated percentage of 5.50 related to 12.99, just as follow:

(5.50/12.99)(100) = 42.34

5.50 is the 42.34% of 12.99.

Hence, the discount was 100% - 42.34% = 57.65%

The range of the following function is

We can also call the range of a function an image, the range or image of a function is a set, we can see this set looking at the graph and see which values of y the function have, remember that we can have the same y value for different x value, looking at our graph we can see that this function comes from high y values, have a vertex on (3,1), in other words, it stops at y = 1 and then start growing again, and go on repeated values of y, then we can say that the image (values of y that the function assumes) is all values bigger than 1, therefore {y > 1}.

Given

Data from graph

Procedure

It is more likely to rain on the first 15 days of the month

To solve this problem, we will compute the slope of the line and then we will use it to find the equation of the line.

To determine the slope of a line that passes through points (x₁,y₁), and (x₂,y₂), we can use the following formula:

Substituting

in the above formula, we get:

Now, with the above slope, we use the following formula for the equation of a line with slope m:

Finally, we substitute one of the points:

and take the equation to its slope-intercept form:

a) 84.13%

b) 2.28%

c) 15.86%

Given:

the numbers of skateboards produced per day at a certain factory were normally distributed

mean = 20, 500

standard deviation = 55

To find:

a) On what percent of the day did the factories produced 20,555 or fewer?

b) On what percent of the day did the factories produced 20,610 or fewer?

c) On what percent of the day did the factories produced 20445 or fewer?

To determine the answers, we will use the z-score formula and then use the standard normal table to get the equivalence of the z-score

The formula of score is given as: