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Find (w ∘ w)(−1) for w(x)=3x^2+3x−3.
Answer: (w ∘ w)(−1)=

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

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)

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.

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%.

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 Solution.

By formula, the volume of the planet (sphere) is given as below:

In this case,

Substitting these given values into the formula above, we can solve for r, the radius of the planet.

Dividing both sides by

We get

Taking the cube root of both sides, we have

Thus, the correct answer is 1060784.418km.

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

Explanation:

The expression is given below as

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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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}.

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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Answer:

(-2,-5)

Step-by-step explanation:

(-5+1÷2, -9+(-1)÷2)

=(-4÷2, -10÷2)

=(-2,-5)

Question: the line that passes through the point (-1,4) and point (6,y) has a slope of 5/7. find y.

Solution:

By definition, the slope of a line is given by the formula:

where m is the slope of the line and (X1,Y1), (X2,Y2) are any two points on the line. In this case, we have that:

(X1,Y1) = (-1,4)

(X2,Y2) = (6,y)

m = 5/7

thus, replacing the above data into the slope equation, we get:

this is equivalent to:

By cross-multiplication, this is equivalent to:

solving for y, we get:

then, we can conclude that the correct answer is:

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}

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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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.

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

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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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.

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:

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.

Okay, here we have this:

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

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

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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The function f is given by:

If a quadratic function is written in the form:

Then the function has a minimum point at (h,k)

And the minimum is k

In this case,

Therefore, the minimum of the function f is at (0.25, 5.875)

The minimum of the function given by the table is at (-1, -6).

Therefore, the required horizontal distance is given by:

Therefore, the horizontal distance is 1.25

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.

Answer

Explanation

Given:

A bug is moving along a straight path with velocity

What to find:

The total distance traveled by the bug over interval [0, 6].

Solution:

To find the total distance traveled by the bug over interval [0, 6], you first integrate v(t)= t² - 6t + 8

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 are going to use the formula for the compound interest, which is

A = the future value of the investment

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = the time the money is invested or borrowed for

Replacing the values in the first question we have:

Answer for the first question is : $7140

Then, replacing the values in the second question we have:

Answer for the second question is : $8497