Use long division to rewrite the following rational expression.

Solution

For this case we can use the following formula:

where

A= future value, P= present value= 400800.00

r= 5.5%=0.055, n =1 , t= 4 years

n= represent the number of times that the interest is compounded each year =1 for this case

Replacing we got:

then we can find the interest in the following way:

Answer:

Step-by-step explanation:

1. j

2. k

3. L

4. Lj

5. kL

6. jk

The "ordered-pair" which is the solution to the equation "5x + 7y = 6" is : (d) (4, -2).

The equation for which we have to find the solutions is 5x + 7y = 6,

We substitute the values of x and y into the equation to check if it holds true for each ordered pair.

Option (a) : the point is : (1, -1),

⇒ 5(1) + 7(-1) = 5 - 7 = -2 ≠ 6.

Option (b) : the point is : (2, 1),

⇒ 5(2) + 7(1) = 10 + 7 = 17 ≠ 6.

Option (c) : the point is : (3, 3),

⇒ 5(3) + 7(3) = 15 + 21 = 36 ≠ 6.

Option (d) : the point is : (4, -2),

⇒ 5(4) + 7(-2) = 20 - 14 = 6 (Correct),

Therefore, The correct answer is (d) (4, -2), because it is the only ordered pair that satisfies the equation 5x + 7y = 6.

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The given question is incomplete, the complete question is

Which ordered pairs are solutions to the equation 5x+7y=6?

(a) (1, -1)

(b) (2, 1)

(c) (3, 3)

(d) (4, -2).

According to the information, we can infer that Mazibane must pay R3640 into the account on 30 June to have no debt.

To calculate the amount Mazibane must pay on 30 June to have no debt in the account, we need to consider the initial debt, the interest, and the previous payment.

Initial Debt:

Interest Calculation:

Previous Payment:

To determine the remaining debt on 1 June, we subtract the payment from the initial debt:

From 1 June to 30 June, a period of one month, interest is charged on the remaining debt.

To calculate the interest for one month, we use the formula:

where the principal is the remaining debt, the rate is the monthly interest rate (16%/12), and the time is the number of months (1).

To find the total debt on 30 June, we add the remaining debt on 1 June and the interest for one month:

To have no debt on 30 June, Mazibane must pay the total debt amount:

Calculating the interest and summing up the values, we find that Mazibane must pay approximately R3640 into the account on 30 June to have no debt.

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Answer:

24.5%

Step-by-step explanation:

Given

P(Off-Campus) = 0.30

P(Part-Time Job | Off-Campus) = 0.62

P(Part-Time Job | On-Campus) = 0.65

Inferred

P(On-Campus) = 0.70

P(No Part-Time Job | Off-Campus) = 0.38

P(No Part-Time Job | On-Campus) = 0.35

Calculation

P(No Part-Time Job | On-Campus) = P(No Part-Time Job ∩ On-Campus)/P(On-Campus)

0.35 = P(No Part-Time Job ∩ On-Campus)/0.70

0.245 = P(No Part-Time Job ∩ On-Campus)

Therefore, 24.5% of students that live on campus do not have a part-time job.

Juliet will earn the same amount of money whether she chooses a monthly salary of ​$1900 from the company or a base salary of ​$1800 plus a ​5% commission on furniture sales if her sales amount to $2000.

To find the amount of sales for which the two salary choices are equal, we set the equation for the base salary plus commission equal to the equation for the flat monthly salary. The equation can be written as:

1800 + 0.05x = 1900

where x is the amount of furniture sales in dollars.

Simplifying and solving for x, we get:

0.05x = 100

x = 2000

If she sells less than $2000 of furniture, she will earn more with the flat monthly salary of $1900. If she sells more than $2000 of furniture, she will earn more with the base salary plus commission. This calculation provides an important decision-making tool for Juliet, as she can tailor her salary choice based on her expected sales for the month.

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Answer:

4x25/100=1

Step-by-step explanation:

How I came up with it

4÷100=25

25÷25=1

Julie will only get a 1% discount

Hope it helps

Answer:

400

Step-by-step explanation:

\(100 + 200 + 300 + 400 + 500 + 600 + 700 = 2800 \)

There are 7 numbers ( No. of cakes in a month)

Therefore, we should divide it by sum of the cakes

\(2800 \div 7 = 400\)

SO MEAN NUMBER IS 400//

Answer:

34% decrease

Step-by-step explanation:

(V1-V2)/V1x100

450-297=153

153/450=0.34

0.34 x 100=34

34% decrease

Step-by-step explanation:

Let x represent the first number, and y be the second number.

The first statement can be modeled as

\( {x}^{2} - {y}^{2} = 15\)

The second statement can modeled as

\(2 {x}^{2} - {y}^{2} = 30\)

If we multiply 2 both sides of the first equation,

\(2( {x}^{2} - {y}^{2} ) = 15 \times 2\)

\(2 {x}^{2} - 2 {y}^{2} = 30\)

Subsitue this for 30 in second equation,

\(2 {x}^{2} - {y}^{2} = 2 {x}^{2} - {2y}^{2} \)

\( {y}^{2} = 0\)

\(y = 0\)

Subsitue this for y in either equation,

\( {x}^{2} = 15\)So our answer is

plus or minus sqr root of 15, 0).

\((± \sqrt{15} ,0)\)

\(x = \sqrt{15} \)

or

\(x = - \sqrt{15} \)

Answer:

B. )The graph of g(x) is a translation of the graph of f(x) right 6 units.

Step-by-step explanation:

When a positive number is directly added to an "x" variable (usually inside of parentheses), the graph is shifted to the left that many units.

When a negative number is directly added to an "x" variable, the graph is shifted to the right that many units.

A graph shifts up or down when a positive or negative number is added to the overall function. For example, if the -6 were outside of the parentheses, the graph would be translated 6 units downwards.

Answer: Dawn's score is 4

Answer: 4

brainlist pls???

Step-by-step explanation:

7-21=14

14-10=4

Answer: \(9\pi\) meters; \(20.25\pi\) square meters

Step-by-step explanation:

The length of the string of lights is the circumference, which is \(2\pi(4.5)=9\pi\).

The amount of carpet is the area, which is \(\pi(4.5^2)=20.25\pi\)

Answer:

x-intercept: (-5,0) , y-intercept: (0,15)

Step-by-step explanation:

0=3x+15

-3x=15

x=-5

Answer:

\(f(x)=\frac{4x+1}{x^2-5}\)

Step-by-step explanation:

What (f/g)(x) is asking us to do is divided function f(x) by function g(x).

Answer:

OK so he gets 3000 a year

so 3000t is what we need. thats 3000 times the number of years.

His starting salary is 41250, so we would add that on.  

K = 3000t + 41250.

Step-by-step explanation:

Answer:

\((-\infty,2)\)

Step-by-step explanation:

Since \(-3x+6\nless 0\), then \(x\ngtr 2\), therefore, the domain of the function is \((-\infty,2)\).

The probability that two cards will be drawn at random, without replacement, is 13/18.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

According to our answer-

P(at least 1 green) = 1 - P(no green)

P(no green) = draw yellow on both draws

= P(draw yellow on 1st draw) * P( draw yellow on 2nd draw, given draw yellow on 1st draw)

= 5/9 * 4/8 = 20/72 = 5/18

P(at least 1 green) = 1 - 5/18

= 13/18

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Answer:

This one is easy I did this one before its A

Answer:

the answer is c

you times the radius with the 2 and the pi

Note that the coordinates of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4). (Option B)

To rotate a point 90 degrees  clockwise about a given point,we can follow these steps -

Translate the coordinates   of the given point so that the center of rotation is at the origin.   In this case,we subtract the coordinates   of the center (0,1) from the coordinates of point A (5,4) to get (-5, 3).

Perform the rotation by swapping the x and y coordinates and changing the sign of the   new x coordinate. In this case,we  swap the x and y coordinates of (-5, 3)   to  get (3, -5).

Translate the coordinates back to their original position   by adding the coordinates of the center (0,1)  to the result from step 2. In   this case, we add (0,1) to (3, -5) to get (3, -4).

Therefore, the coordinates   of the point A' after rotating 90 degrees clockwise about the point (0,1) are (3, -4).

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Answer:

hello your question is incomplete attached below is the complete question

answer : The population mean LDL level after six months is same for all four treatments

Step-by-step explanation:

A null hypothesis represents a no difference in the question. therefore the correct option is The population mean LDL level after six months is same for all four treatments

Answer:

12.5%

Step-by-step explanation:

Answer:

Have a good day yall

Step-by-step explanation:

i dont know the answer but good luck

The baker can only make peanut butter cookies and cannot make any chocolate chip cookies with the given amount of ingredients.

Let's denote the number of batches of peanut butter cookies as "x" and the number of batches of chocolate chip cookies as "y."

From the given information, we can set up the following system of equations:

For the flour:

2x + 3y = 26

For the butter:

34x + y = 9

To solve this system of equations, we can use the substitution method or the elimination method. Let's use the elimination method:

Multiply the first equation by 17 (to make the coefficients of x in both equations the same):

34x + 51y = 442

Now we have the system of equations:

34x + y = 9

34x + 51y = 442

Subtract the first equation from the second equation:

34x + 51y - (34x + y) = 442 - 9

50y = 433

Divide both sides by 50:

y = 433/50

Since the number of batches of cookies cannot be fractional, we need to find a whole number solution for y. However, in this case, y is a fraction, indicating that the given amount of butter is not sufficient to make even one batch of chocolate chip cookies.

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The median of the given set of numbers is determined by rearranging them in ascending or descending order and selecting the middle number. Since the number of responses are even, we would find the mean of the two middle numbers. Rearranging the numbers in ascending order, it becomes

6, 12, 12, 13, 13, 15

The median = (12 + 13)/2 = 12.5

Mean = sumof responses/number of responses

Mean = (6 + 12 + 12 + 13 + 13 + 15)/6

Mean = 9.3

Answer:

A.) Chord CD must not only bisect but must also be perpendicular to diameter AB.

Step-by-step explanation:

The error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.

Geometric construction is method todraw any sketch lines, angles, and other geometric forms and figures only using a compass and a straightedge. It generally is done without employing precise measurements of length, angle, etc.

Now the steps taken by Makayle are,

→draw diameter AB

→use a compass and a straightedge to find chord CD that bisects diameter AB.

→use a straightedge to draw the four chords that make up the square: chords AC, AD, BC, and BD.

Now here the error she is making is that the required chords will be AB, BC, CD, and DA, not AC, AD, BC, and BD.

Hence,the error, Makayla is making in her instructions to Rodney is that the chords that make up the square are chords AB, BC, CD, and DA.

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Answer:

96 or 20

Step-by-step explanation:

12 x 8 = 96 and 12 + 8 = 20

Answer:

Domain: x ≥ -2

Range: y ≥ -4

Step-by-step explanation:

Since the dot is filled in, it means that the values of domain and range will be greater than or equal. The domain is represents all the values of x, and range is of y, shown in the graph. The smallest value of x is -2, and it continues to the right, increasing. The smallest value of y is -4, and it continues its way up, also increasing.

Based on the given information, we have a square pyramid with points M and N being the midpoints of the edges of one face. and forms a parallelogram. Option D

Since the base of the pyramid is a square, the cross section will consist of a square shape. Additionally, since the slice is made through the midpoints of the edges of the face, the resulting cross section will have parallel sides.

Considering these characteristics, we can conclude that the shape of the resulting cross section is a parallelogram. A parallelogram is a quadrilateral with opposite sides parallel. In this case, the opposite sides of the square cross section will be parallel, as the slice passes through the midpoints of the edges.

Therefore, the correct answer is D. parallelogram.

It's important to note that a triangular prism is not the correct answer because a triangular prism is a three-dimensional figure with two triangular bases and three rectangular faces. The cross section resulting from the given slice will not have the characteristics of a triangular prism. Option D.

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Answer:

I think it would 12 and 14