The function h(x) shown is the result of adding two functions, f(x) and g(x).

Which statement could be used to describe the functions?

The following function models the population of rabbits, in thousands, in a state x years after 1990.

What is the approximate population of rabbits in 2012?

Count the number of years after 1990 to 2012.

That's 22 years so we have x = 22

Let us substitute x = 22 into the above function

That is approximately 120 thousands or 120,000

The Solution:

Representing the given in a diagram, we have

By similarity theorem, we have that:

So,

Substituting these values in the formula above, we get

Solving for x:

We shall cross multiply,

Dividing both sides by o.21, we get

The height of the tower is

Therefore, the correct answer is 138 meters.

The width of the television is 23 in.

A rectangle is a closed 2-D shape, having 4 sides, 4 corners, and 4 right angles. The opposite sides of a rectangle are equal and parallel.

Given that, A television's length is 3 inches more than twice its width the perimeter of the television is 144 inches

Perimeter of a rectangle = 2(length+width)

According to question,

l = 3+2w

Therefore,

Perimeter = 2(w + 3+2w) = 144

3w + 3 = 72

3w = 69

w = 23

Hence, The width of the television is 23 in.

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Amount sold = $800

Commission = 3.5%

To calculate the commission amount, multiply $800 by the commission percentage in decimal form (divided by 100)

800 x (3.5/100)= 800 x 0.035 = $28

We know that

• Henry started with 3 packages of pencils.

• He used 4 pencils each week.

• The school year is 36 weeks.

Assuming that each package of pencils has 8, he would have

Henry has 24 pencils in total. But he uses 4 pencils each week, so let's divide

From the definition, it must have symmetry in the present figure. It seems to be a vertical line going through the middle of the drawing. From this, we can say that:

Now, we can solve it.

Hello there. To solve this question, we have to remember some properties about logarithms.

Given the logarithmic equation:

We want to determine the value of x.

For this, remember the following rule:

Such that, in this case, the logarithm has base 10, therefore

This power of 10 can be easily found :

It has 5 digits after the decimal place, being the fifth digit a 1.

This is the answer contained in the option B.

Answer

P(Z and T)= 8/121

Explanation

The total out come in group 1 = 11

The number of z = 4

Probability of picking a Z in group 1 = 4 / 11

Group 2

The total out comes = 11

Number of T outcomes = 2

Probability of picking a T = 2/11

Therefore, P( Z and T) = P(Z) x P(T)

P(Z and T) = P(Z) x P(T)

P(Z) = 4/11

P(T) = 2/11

P(Z and T) = 4/11 x 2/11

P(z and T) = 8/121

Therefore, the probability of picking a Z and aT is 8/121

The length of the block = 1ft.

The volume of the length of the side of blocks = 1ft^3

The 3 on the one feet means raised to power 3.

So, 1ft raised to power 3:

To get the length, we would assume the block is a cube

The volume of a cube = length^3

1 ft^3 = length^3

Hence, the length of the block = 1ft.

We can see that there are 24/8 in 3 units, so we have then that there are 8 times 3/8 in 3 units.

So, the answer is there are 8 times.

Explanation

Step 1

multiply each side by 3

Step 2

divide both sides by

The total commission salesperson earned is $394.5.

What is commission?

Commissions are a type of variable-pay compensation for provided services or sold goods. Commissions are a typical method of encouraging and rewarding salespeople. It is also possible to create commissions to promote particular sales behaviours. For instance, while offering significant reductions, commissions might be decreased.

Given:  A jewelry salesperson earns 5 1/5 % commission on all sales. Today he sold $7,310 in jewelry.

We have to find the commission earned on $7310.

Here, [tex]5\frac{1}{5} = \frac{(5)(5)+2}{5} =\frac{27}{5}[/tex]

5 1/5% = 27/5%

Today he sold $7310 in Jwellary.

So, the commission is,

[tex]\frac{(7310)(27)}{(5)(100)} = 394.5[/tex]

Hence, the total commission of $7310 is $394.5.

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Given

the constant speed.

the points 1 (1,8)

Point 2 (1.5, 10.1) ​

Procedure

y=mx+b

the equation is: y=4.2x+3.8

The statements that are true are:

B. The rate of the change of the function is 4.2

D. The toy boat's speed on the lake is 4.2 feet per second

E. the toy boat is originally 3.8 feet from the shore of the lake

It is given that the amount invested is $3000 with an interest rate of 4.1% compounded monthly.

It is required to find the amount in 1 year and the annual percentage yield.

The formula for Compound Interest is:

Where:

• A= final amount

• P= amount invested initially

• r= interest rate

• n= number of times interest is compounded in a year

• t= number of years

Substitute P=3000, r=4.1%=0.041, n=12 (compounded monthly), and t=1 into the formula:

The formula for the Annual Percentage Yield is given as:

Substitute r=0.041, n=12 into the formula:

Answers:

Amount = $3125.34

APY = 4.18%

x + z = 180 (Because it is a Rhombus and angles across from each other equal 180)

x = 97

y = 83

Given:

Points A(-2,-3),B(-2,4),and C(3,6) are three vertices of parallelogram ABCD.

As we know, the opposite sides of the parallelogram are parallel and congruent

To draw the parallelogram, we will draw the points and connect the sides

AB, AC, and BC

then, draw two lines parallel to AB from C and BC from A, the intersection will give the point D

The graph of the parallelogram will be as shown in the following picture

As shown the coordinates of the fourth point D = (3, -1)

Answer:

322.5 square centimeters

Explanation:

To convert from square inches to square centimeters, we need to multiply the number by the conversion factor 6.45, so 50 in² are equivalent to:

50 in² x 6.45 = 322.5 cm²

Therefore, the answer is 322.5 square centimeters.

From the question, we have a linear function for the cost of each pumpkin, and this function is:

As we can see, the cost for one pumpkin is:

Now, to find the cost for 25 pumpkins, we need to substitute the value of x = 25 into the function, since this is a function that gives us the cost as a function of the number of pumpkins:

As we can see, we multiply 2.75 times 25, and we got 68.75.

Therefore, in summary, it will cost $68.75 for 25 pumpkins.

ANSWER:

The equivalent expressions are

STEP-BY-STEP EXPLANATION:

We have the following expression:

If we factor we have:

if we separate the value we have

You can identify that the following is a Decimal number:

In order to convert a Decimal number to an Equivalent fraction, you can follow the steps shown below:

1. You need to write the Decimal number 0.005 as the numerator of the fraction and the denominator must be 1:

2. Now you can multiply the numerator and the denominator by 1,000, in order to remove the decimal places of the numerator (notice that it has three decimal places):

3. Finally, you have to reduce the fraction. Notice that you can divide the numerator and the denominator by 5. Then, you get:

The answer is:

we are given the following system of equations:

Equation (2) can be rewritten dividing by 5 on both sides as:

Solving the operations:

Since equation (2) is the same equation as equation(1), this means that the system has infinite solutions.

sixth power is the exponent of 1.

To obtain the result, multiply 1 by itself 6 times:

1x1x1x1x1x1=1

1^6 = 1

,Given the table of values we can find the equation that will represent the total price in dollars for the bannana by using the equation of a line.

Explanation

The equation of a line is given as

We can then remodel the equation above to fit the given table of values. This would give;

Next, we will pick some random points to represent the variables in the equation

Then we insert the variables into the formula.

Answer: The equation is given as p = 0.59n

Solution

We are given the pair of simultaneous equation

we solve using elimination method

equation (1) x 2

Equation (2) - equation (1)

We have

Which is impossible because 0 (zero) can never be equal to 18

Therefore, the simultaneous is not consistent or it degenerate and thus, there is no solution

95% of the data is represented as 69 to 93 (option G)

Given:

mean of data = 81

standard deviation = 6

To find:

The option that represents 95% of the data

To determine the right option, we will apply the empirical rule (68-95-99.7%):

68% of the data will fall within 1 standard deviation

95% of the data will fall within 2 standard deviation

99.5% of the data will fall within 3 standard deviation

substitute the values:

This problem is about geometric sequence, which is a sequence formed by multiplying (or dividing) a constant factor.

In this case, we can observe that each new day has greater power, specifically, its exponent increases by one. This is because each day, the number of amoebas increases by a multiplying factor of 2.

Having said that, we can deduct that the fourth day is going to have a power with exponent 4, because as we said before, each day the exponent increases by 1.

So, the power of the fourth day is

A 95% confidence interval for the percentage of voters who choose Candidate A is (0.3,0.3).

Given that,

1750 American voters were chosen at random to participate in a poll on their presidential candidate preferences. 28% of those polled indicated they favored Candidate A.

We have to find determine a 95% confidence interval for the percentage of voters who choose Candidate A.

We have a sample size=1750

28% preferred candidate A.

Margin of error = Z[tex]\sqrt{P(1-P)/n}[/tex]

Where, z=1.96 at 95%

P=0.28

n=1750

ME = 1.96[tex]\sqrt{0.28(1-0.28)/1750}[/tex]

ME = 1.96[tex]\sqrt{0.28(0.72)/1750}[/tex]

ME = 1.96[tex]\sqrt{0.2016/1750}[/tex]

ME = 1.96[tex]\sqrt{0.000152}[/tex]

ME = 0.021

For confidence interval is

CI= 0.28±0.021

CI= (0.28+0.021,0.28-0.021)

CI = (0.301, 0.259)

For the nearest tenth,

CI = (0.3,0.3)

Therefore, A 95% confidence interval for the percentage of voters who choose Candidate A is (0.3,0.3).

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distributing:

the expression is equivalent to 1/2x - 1