Solve the inequality and how do i graph ?

Answer:

A. 200

B. 500

Step-by-step explanation:

          1000x²

R(x) = --------------

           x² + 4

x = years

A. the first year = 1

         1000(1)²

R(1) = --------------

           (1)² + 4

            1000

R(1) = --------------

             1 + 4

            1000

R(1) = --------------

               5

R(1) = 200

B.  years = 2

           1000(2)²

R(2) = --------------

           (2)² + 4

           1000(4)

R(2) = --------------

             4 + 4

            4000

R(2) = --------------

                8

R(2) = 500

I hope this helps!

Answer:

a) r = 0.79%

b)

c) 6.6 million people

d) 2046

Explanation:

We'll use the below formula for exponential growth;

where a = initial amount

r = growth rate

t = number of time intervals

a) From the question, we have that

a = 5.17 million

P(t)= 6.05 million

t = 20 years

Let's go ahead and substitute these values into our formula, and solve for r as shown below;

b) The exponential model can be written as shown below;

c) When t = 31 years, let's go ahead and find P as shown below;

d) When P = 7.5 million, let's go ahead and solve for t as shown below;

So to get the particular year all we need to do is add 47 years to the initial year. That will us 1999 + 47 = 2046

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:

The expressions that represent a quadratic expression in factored form is (x + 1)(x − 2).

Quadratic expression  can be described as the mathematical expression that posses  the variable which have highest power of 2.

It should be noted that the quadratic equation is usually expressed in the form ax^2 + bx + c where the abc are the known numbers in the equation  that will be used in the calculation of the factors of the equation and in the quadratic equation the number a will not be equal to zero in the equation.

Therefore, option C is correct.

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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:-

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.

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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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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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%.

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.

-2y + 1 = 3

Solving for y:

Add 2y to both sides:

-2y + 1 +

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 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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Explanation

We are asked to simplify the given question

To simplify the terms, we will follow the steps below

Step 1: simplify the terms in the bracket using the exponential rule

Thus for the terms in the parentheses

Hence

Simplifying further

Step 2: substitute the value obtained above in step 1 into the parentheses, so that

Step 3: Simplify further, we will apply the rule

so that

Simplifying further

Hence, our final answer 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)

Okay, here we have this:

The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides.

This mean that the statement is true.

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%

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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Given

Data from graph

Procedure

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

The ratio of the volume of cube B to the volume of cube A is 1/64

The volume of cube A is 8^3 = 512 cubic inches

The volume if cube B is 2^3 = 8 cubic inches

The ratio of the volume of cube B to the volume of cube A is:

8/512 = 1/64

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.

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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ANSWER

23/8

EXPLANATION

To solve this, first, we have to do the operations in the parenthesis. The first one is a subtraction between a mixed number and a fraction, so before doing the subtraction, we have to convert the number to an improper fraction by adding the parts,

So the subtraction is,

Then we divide the second term using the KCF rule:

• K,eep the first fraction

• C,hange the division sign for a multiplication sign

• F,lip the second fraction

Now, we add these two results,

Hence, the answer is 23/8.

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:

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

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: Hi that would be (r+16) since they are generally the same thing, hope this is what you are asking for!

Step-by-step explanation:

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.

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.

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: