PLS HELP WITH THIS MATH PROBLEM! Attached is the math problem.

Answer:

Option C

Step-by-step explanation:

f(x) can be factorised and re-written as (2x+3)(x-2)

g(x) can be re-written as (x+2)(x-2)

On dividing f(x) by g(x): (x-2) cancels out

Quotient: (2x+3)/(x+2)

After 5 years, the amount owed on the loan will be approximately $15,792.34.

What is compounding?

Compounding refers to the process where interest is earned on both the principal amount and the accumulated interest of an investment. In other words, it is the addition of interest to the principal sum of a loan or deposit, which in turn earns interest in the following periods.

To find the amount owed after 5 years, we can use the formula for compound interest:

[tex]A = P(1 + \frac{r}{n})^{n*t}[/tex]

where:

A = the amount owed after t years

P = the principal (initial amount borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

Plugging in the given values, we get:

[tex]A = $7000(1 + 0.18/1)^{1*5}[/tex]

[tex]A = $7000(1.18)^5[/tex]

A ≈ $15,792.34

Therefore, after 5 years, the amount owed on the loan will be approximately $15,792.34.

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Complete question:  Suppose Rita borrows $7000 at an interest rate of 18% compounded each year. Assume that no payments are made on the loan. find the amount owed after 5 years.

Out of 220 students, 44 would like dogs more than cats.

How to find the number of students who like dogs more than cats?

First, we know that 20 students like dogs and 12 like cats, so there are 20 - 12 = 8 more students who like dogs than cats.

We also know that there are 40 students in total, so the percentage of students who like dogs more than cats is 8/40 = 0.2.

To find the number of students who would like dogs more than cats among 220 students, we can use the same percentage:

We know that there are 220 students in total, so the number of students who would like dogs more than cats is 0.2 × 220 = 44.

Therefore, out of 220 students, 44 would like dogs more than cats.

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The angle measure of RUT is m∠RUT = 33°.

The diameter of an arc within a circle is equal to the diameter of the central angle that subtends the arc.

Therefore, if we know the length of an arc, we may calculate the length of its corresponding central angle.

In this case, we are given that the measure of the minor arc RT is 66°.

We need to find the measure of angle RUT.

We achieve this by taking use of the fact that an inscribed angle's measure is half that of its equivalent central angle.

Since angle RUT is an inscribed angle that intercepts arc RT, we have:

m∠RUT = 1/2 × m/RT

m∠RUT = 1/2 × 66°

m∠RUT = 33°.

Therefore, the measure of angle RUT is 33°.

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Answer:

(-4,8)

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

A. There will be bias with this solution as parents that attend the PTO meeting will already know the school well, and are likely to sway the vote.

B. Every 5th person creates unbias, as the Headmaster can not pick who to survey from the list. Therefore, I would argue that this is the best way to survey the parents out of the provided options.

C. We can not infer that every parent waits in the pick-up line, and therefore it would be unfair to carry out the data collection knowing that you are going to miss out on parents' opinions.

D. This completely rules out all students with uneven numbered birthdays for no reason, which is an unfair way of carrying out this survey.

First, write the coefficients of the polynomial in order of decreasing degree and include a placeholder for missing terms:

2 -8 -27 14 24

6

Bring down the leading coefficient:

2 -8 -27 14 24

6

2

Multiply the divisor by the result of the previous step and subtract from the corresponding coefficients:

2 -8 -27 14 24

6

2 -12

48

2 -12 21

-42

2 -12 21 -28

168

2 -12 21 -28 192

The result of the division is 2x³ - 12x² + 21x - 28 with a remainder of 192.

The average speed of the Moon's orbit is  593,21 km/h

The average speed is defined as the quotient between distance and time, here we know that:

distance = 384,400 km

time = 27 days = 27*(24 hours)= 648 hours.

Then the average speed will be:

S = 384,400 km/648h

S = 593,21 km/h

That is the average speed of the Moon's orbit.

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To add these two mixed numbers, we first add their whole number parts and then their fractional parts separately.

Whole number parts: 10 + 13 = 23

Fractional parts: 9/12 + 9/12 = 18/12

We can simplify 18/12 by dividing both the numerator and denominator by their greatest common factor, which is 6.

18/12 = (18 ÷ 6) / (12 ÷ 6) = 3/2

Therefore, the sum of 10 9/12 and 13 9/12 is:

23 3/2 or 23 and 1/2.

The values of  x, y, and z in the triangle are y = 7.8, z = 1.25 and x = 3.25

From the question, we have the following parameters that can be used in our computation:

the right triangle

So, we have

y^2 = 7.2^2 + 3^2

Evaluate

y = 7.8

For z, we have

3^2 = 7.2z

So, we have

z = 1.25

For x, we have

x^2 = (z + 7.2)^2 - y^2

So, we have

x^2 = (1.25 + 7.2)^2 - 7.8^2

x = 3.25

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Answer:

18

Step-by-step explanation:

[tex]x^{2}[/tex] -2x + 3      x = -3

[tex](-3)^{2}[/tex] - 2(-3) + 3

9 + 6 + 3

18

Helping in the name of Jesus.

The area of the shaded region is 83.3% of the area of the sector ONQ.

First, let's find the area of the sector ONQ:

The formula for area of a sector is;

Area of sector = (angle/360) x πr²

In this case, the angle of the sector ONQ is 120 degrees (since AOB is an equilateral triangle and each angle of an equilateral triangle is 60 degrees). So;

Area of sector ONQ = (120/360) x π(11²)

= 127.2 cm²

Next, we need to find the area of the equilateral triangle AOB:

The formula for area of an equilateral triangle is;

Area of equilateral triangle = (√3/4) x s²

where s is length of a side of the triangle.

In this case, s =7 cm, so;

Area of equilateral triangle AOB = (√3/4) x (7²) = 21.2 cm²

Now we can find the area of the shaded region (which is the area of sector ONQ minus the area of triangle AOB);

Area of shaded region = Area of sector ONQ - Area of equilateral triangle AOB

= 127.2 - 21.2

= 106 cm²

Finally, we can express the area of the shaded region as a percentage of the area of sector ONQ;

Percentage = (Area of shaded region / Area of sector ONQ) x 100%

= (106 / 127.2) x 100%

= 83.3%

Therefore, the area of the shaded region is 83.3%

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--The given question is incomplete, the complete question is

"ONQ is a sector of a circle with centre O and radius 11 cm. A is the point on ON and B is the point on OQ such that AOB is an equilateral triangle of side 7 cm. Calculate the area of the shaded region as a percentage of the area of the sector ONQ. Give your answer correct to 1 decimal place.​"--

Answer:

width = 16 in

height = 24 in

depth = 32  in

Step-by-step explanation:

Volume = height x width x depth = hwd

h = 1.5w

d = 2w

V = (1.5w)(w)(2w) = 12,288

V = 3w³ = 12,288

w³ = 12,288/3 = 4096

w = ∛4096 = 16

h = 1.5(16) = 24

d = 2(16) = 32

The expression of the given statement is 2y - 3  = -1

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. The operations of mathematics include multiplication, division, addition, and subtraction.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Let's look at how expressions are written.

The expression of the given statement is 2y - 3  = 4.

Here, let the unknown number = y

Now, product of y and 2 =  2 times  y   =   2y

Also, three less than the product   =  Product - 3

So, three less than the product  of 3 and y =  2 y - 3

Now, this above expression is equivalent to -1.

⇒2 y - 3  = -1

Hence the expression of the given statement is 2y - 3  = -1

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The sentence "Three less than the product of 2 and a number is 4" can be translated into the equation: 2x - 3 = 4

A mathematical statement that demonstrates the equivalence of two expressions is known as an equation.

It has two sides that are divided by the equals sign (=).

Variables, constants, coefficients, operators, and functions can all be used in the expressions on either side of the equation.

Here, x represents the unknown number that we are trying to solve for. The expression "the product of 2 and a number" is represented by 2x, and "three less than" is represented by the subtraction of 3 from that product. This expression is set equal to 4, which is the result given in the original sentence.

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Hence, -12×[tex]\frac{1}{2}[/tex]×13 this expression is used  Commutative property to make it easier to evaluate -12×13×[tex]\frac{1}{2}[/tex] .

According to mathematics, an arithmetic operation is commutative if switching the operands positions has no effect on the computation's outcome.

When two numbers A and B are provided, the commutative property of the numbers formula is as follows:

A+B=B+A

A×B=B×A

A-B≠B-A

A÷B≠B÷A

According to the commutative property formula, the outcome is unaffected by the sequence in which two integers are added or multiplied. However, the order of the integers matters for subtracting and dividing any two real numbers, thus it cannot be altered.

The commutativity property is used to get

-12×13×[tex]\frac{1}{2}[/tex] = -12×[tex]\frac{1}{2}[/tex]×13

such that the evaluation becomes easier, which is to get 12×[tex]\frac{1}{2}[/tex]=6.

The commutativity property is used as follows:

-12×(13×[tex]\frac{1}{2}[/tex])=-12×([tex]\frac{1}{2}[/tex]×13).

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Answer: -20

Step-by-step explanation:

The formula is written as -2 - (-8) + (-14) + 2. Using the following addition and subtraction rules for integers will allow us to simplify this expression:

1.  To add two integers with the same sign, we add their absolute values and then assign the common sign to the sum.

2.  To add two integers with different signs, we find the difference   between their absolute values and assign the sign of the integer with the greater absolute value to the sum.

3.  To subtract an integer, we add its opposite.

Using these rules, we can simplify the given expression as follows:

-2 - (-8) + (-14) + 2

= -2 + 8 - 14 + 2      (using rule 3 for the second term)

= -6 - 14              (combining like terms)

= -20

Therefore, the value of the expression is -20.

Answer:

Based on the description, Rhett's drawing of his house is a rectangular prism. A rectangular prism is a three-dimensional figure that has six faces, where each face is a rectangle. In a rectangular prism, opposite faces are congruent and parallel, and adjacent faces meet at right angles.

The function that is represented by the graph is y = - [tex]\frac{1}{x}[/tex] + 1, Option C.

Graph functions are mathematical functions that are plotted on a graph, with the input values on the horizontal axis and the corresponding output values on the vertical axis.

They are a visual representation of how the output values of the function change as the input values change.

The function is y = -(1/x) + 1 might be identifies as transformation of the reciprocal function y = 1/x.

we can start by identifying any coordinated we see for both curved lines.
The first curved line has (-1, 2)

The second curved line has (1, 0)

We can cross check if we can find y using the function y = - [tex]\frac{1}{x}[/tex] + 1,

x = -1  therefore

y = (-1/(-1)) + 1 = 2. 2 matches matches the y coordinate (-1, 2).

x = 1 therefore,

y = (-1/1) + 1 = 0. 0 matches the y coordinate (1, 0).

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The 95 percent confidence interval for the true mean metal thickness is [0.290351, 0.290649] (rounded to 4 decimal places).

Confidence level is a statistical phrase that reflects the degree of confidence or reliability associated with an estimated parameter (such as a mean or percentage) generated from a sample of data. It is frequently stated as a percentage and shows the likelihood that the real population parameter falls within a certain confidence range.

Given :

Sample mean ([tex]\mu[/tex]) = 0.2905 mm

Sample size (n) = 59

Standard deviation (σ) = 0.000586 mm

Critical value for 95% confidence level = 1.96 (rounded to two decimal places)

Now,

[tex]\text{Standard error (SE)}= \sigma /\sqrt(n)\\\\SE = 0.000586 / \sqrt(59) = 0.00007613 \;\text{(rounded to 5 decimal places)}[/tex]

Now, for confidence interval;

[tex]\text {Confidence Interval }= \mu \pm Critical \;Value * SE[/tex]

[tex]\text{Confidence Interval} = 0.2905 \pm 1.96 * 0.00007613}\\\\\text{Confidence Interval} = 0.2905 \pm 0.000149 \text{ (rounded to 6 decimal places)}[/tex]

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Part 1) The variables are y, the total cost (dependent variable), and x the charge per day (independent variable).

Part B) A linear equation in a slope-intercept form representing the cost of the campsite is y = 15 + 20x.

A linear equation is an algebraic equation.

A linear equation is written in the form of y = mx+b, where y is the dependent variable, m is the slope and b is the y-intercept or a constant.

The fixed rental fee to reserve the camping site, b = $15

The charge per day (slope), m = $20

Let the number of days the site is rented = x

Total cost, y = 15 + 20x.

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Answer:

-6

Step-by-step explanation:

Y + 8 = 2

Subtract 8 from both sides
Y = -6

The United States senate passes a bill that increases

the federal income tax rate, which then pays for the service would most likely provide the revenue to pay for this new public service.

What is revenue?

Revenue means money received in the ordinary course of business and is calculated by multiplying the average selling price by the number of items sold. This is the total amount of money from which other costs and expenses are subtracted to calculate net income.

The definition of revenue says it is the total amount of money received from a business, such as sales. This is also called sales in the income statement. This is a top-line figure because it appears first on the company's income statement. There are two types of income i.e. operating income and non-operating income.

Here, the most likely way to generate revenue to pay for a new national water pollution abatement plan is for the United States Senate to pass a bill that raises the federal income tax rate that would then pay for the service. This is because it directly increases the funds available to the federal government, which can then be allocated to a new public service. Other options, such as homeowners paying higher property taxes or states raising sales taxes, may not generate enough revenue or may not be directly related to the new public service. Furthermore, selling clean water to other countries may not be sustainable or ethical to fund a public service.

So, The United States senate passes a bill that increases the federal income tax rate, which then pays for the service would most likely provide the revenue to pay for this new public service.

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If Thabang worked for three hours and Ndivhu worked for two hours, then the total number of hours worked is five. To determine the amount Thabang will receive if they decided to share their money according to hours, we need to calculate the proportion of the total hours that Thabang worked and multiply that by the total amount of money earned.

Thabang worked for three out of five hours, which is 3/5 or 0.6 of the total time. To find out how much money he should receive, we can multiply this fraction by the total amount earned:

0.6 x R400 = R240

Therefore, Thabang should receive R240 if they decide to split the money based on hours worked.

The answer  is ,  the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.

An integer is a whole number that can be positive, negative, or zero, but does not have any fractional or decimal parts. Integers can be represented on the number line, with zero at the center and positive integers to the right and negative integers to the left.

We  use technique called "stars and bars" to solve this problem.

Using this approach, the number of positive integers less than 1000 with a digit sum of 4 is equal to the number of ways to arrange 4 stars and 3 bars. We can choose the positions of the bars in 7 ways (i.e., there are 7 places where we can place a bar), so the total number of such arrangements is 7 choose 3 (i.e., we choose 3 places for the bars out of the 7 possible places), which is:

7 choose 3 = 7! / (3! * (7-3)!) = 35

Note that we need to subtract the number of solutions that have 0 as the first digit, since we are only looking for positive integers. We can choose the positions of the bars in 6 ways (i.e., we cannot place a bar before the first star), so the number of such arrangements is 6 choose 3, which is:

6 choose 3 = 6! / (3! * (6-3)!) = 20

Therefore, the total number of positive integers less than 1000 with a digit sum of 4 is 35 - 20 = 15.

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The median would be a better measure to use for his homework grades.

What is the median?

The midway number in a set of data is known as the median. The data should first be arranged and ranked from smallest to greatest. Divide the total number of observations by two to get the midway value. The value in that location is the median if there are an odd number of observations; otherwise, round the number up.

Here, we have

Given: In his history class, Han's homework scores are:

100 100 100 100 95 100 90 100 0

The history teacher uses the mean to calculate the grade for homework.

We have to write an argument for Han.

Median would objectively fair better as a way to calculate grades. The median value doesn't rely on all of the assets that make up the dataset, unlike the mean method would.

The mean sum up every asset, which can lead to it being unreliable. The median, however, is the middle-most value within a list of numbers, which would make it a more accurate method of grading.

Overall, it would make the most sense for Han's history teacher to use the median method for grading homework.

Hence, the median would be a better measure to use for his homework grades.

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The volume of the rectangular prism is  234 cm³

The formula for calculating the volume of a rectangular prism is expressed with the equation

V = Bh

Such that the parameters are enumerated as;

From the information given, we have that;

Substitute the values into the equation

Volume = 36(6.5)

multiply the values, and expand the bracket, we get;

Volume= 234 cm³

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Answer:

To solve the inequality 40(7−5x)<7−25(8x+2), we can start by distributing the 40 on the left side and the -25 on the right side:

280 - 200x < 7 - 200x - 50

Next, we can combine like terms on both sides:

230 - 200x < -200x - 43

Now, we can add 200x to both sides:

230 < -43

This is a false statement, which means that there is no solution to the inequality. Therefore, the inequality 40(7−5x)<7−25(8x+2) is false for all values of x.