Find the total amount of money accumulated for an initial investment of $300 at an annual rate of 6% compounded annually for 4
years.
(Notice from the wording that this is a question about compound interest, not simple interest.)
(Note: Include a dollar sign in your answer)
Amount:

Answer:

225

Step-by-step explanation:

x² -y³

Evaluate for x=3,y=−6

3²−(−6)³

3²−(−6)³

=225

The graph of the feasible region is attached

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

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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Answer: We need we need 10 pints of the second fruit juice (85% pure fruit juice). Therefore, we need

(60-10 = 50) pints of the first fruit juice (55% pure fruit juice).

Step-by-step explanation:

Let x be number of pints of the first fruit drink which is ( 55% pure fruit juice), while y will be the number of pints of second fruit drink (85% pure fruit juice).

We know that there are 60 total pints. Therefore:

x + y = 60

We also know that 60% of the 60 pints will be pure fruit juice, and the pure fruit juice will either come from

x or y.

For x pints of first juice, there is 0.55x pure fruit juice while for y pints of first juice, there is 0.85y pure fruit juice. Therefore, we get:

0.55x + 0.85y = 60 × 0.6

0.55x + 0.85y = 36

We will get rid of the decimals by multiplying through by 100. This will be:

55x + 85y = 3600

Combining both equations

x + y = 60 .......... i

55x + 85y = 3600 ........ ii

Multiply equation i by 55

Multiply equation ii by 1

55x + 55y = 3300

- 55x + 85y = 3600

Then subtract

-30y = -300

y = 10

Therefore, we need we need 10 pints of the second fruit juice (85% pure fruit juice). Therefore, we need

(60-10 = 50) pints of the first fruit juice (55% pure fruit juice).

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

The mean number of minutes per movie in the given sample is 117.

The correct answer is option E.

To find the mean number of minutes per movie, we need to calculate the average length of the 10 movies provided.

Given movie lengths: 101, 134, 149, 81, 149, 101, 134, 101, 149, 81

To find the mean, we sum up all the movie lengths and divide by the total number of movies:

Sum of movie lengths = 101 + 134 + 149 + 81 + 149 + 101 + 134 + 101 + 149 + 81 = 1170

Number of movies = 10

Mean = Sum of movie lengths / Number of movies = 1170 / 10 = 117

Therefore, the mean number of minutes per movie in the given sample is 117.

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The question probable may be:

He wants to estimate the average length, in minutes, per movie in his collection. So, I wrote down the length of 10 random movies. The lengths are listed below. 101, 134, 149, 81, 149, 101, 134, 101, 149, 81

Assuming that the sample was representative of the entire collection, what was the mean number of minutes per movie?

A. 91

B. 141.5

C. 118

D. 125

E. 117

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Answer:

780

Step-by-step explanation:

In this example we will call Original Price = y

72%=0.72

218.40=0.72*y

1-0.72=0.28

218.4÷0.28=780

The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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Answer:

100 is your answer

Step-by-step explanation:

I simply switched around the equation the answered it that way

Example: n×50=5,000

5000/50=n

500/50=100

9514 1404 393

Answer:

  46 24/25 in

Step-by-step explanation:

Opposite pairs of sides are the same length, so the total length needed is ...

  2(8 4/5 +14 17/25) = 2(8 20/25 +14 17/25) = 2(22 37/25) = 2(23 12/25)

  = 46 24/25 . . . inches

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

Brian is constructing figures inscribed in circle C.

Equilateral triangle MNQ inscribed in circle C:

This option is possible since the points M, N, and Q are labeled and they lie on circle C.

Equilateral triangle ANP inscribed in circle C:

This option is not possible. The points A and P are labeled, but the third vertex of the equilateral triangle is not specified.

Regular hexagon AMNBPQ inscribed in circle C:

This option is possible since the points A, M, N, B, P, and Q are labeled and they lie on circle C.

Square MNPQ inscribed in circle C:

This option is not possible based on the given information. The label points do not form a square.

Square ANBQ inscribed in circle C:

This option is not possible . The points A, N, B, and Q are labeled, but they do not form a square.

The correct options that could be constructed by Brian using his straightedge to draw some chords of circle C are:

Equilateral triangle MNQ inscribed in circle C

Regular hexagon AMNBPQ inscribed in circle C

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Answer:

4) Melody is 9 and her sister is 24

5) The numbers are 3 and 9

6) 14 feet per second

Step-by-step explanation:

Questions 4

There is a lot going on here.  This is probably hard to follow.  If it is, it is me and not you.

Let m = Melody and s = sister

m - 4 = 1/4(s-4)                     m + 6 = 1/2(s + 6)  Clear the fractions

4m - 16 = s -4                        2m -s = -6

Multiple the second equation by -1 and add together

4m - s = 12

-2m + s = 6

2m = 18  Divide both sides by 2

m = 9  Substitute this in to find the sister's age

2m + 12 = s + 6

2(9) +12 + s + 6

18 + 12 = s + 6

30 = s + 6  Subtract 6 from both sides

24 = s

Questions 5

x + y = 12              x = 5y - 6

Plug in 5y - 6 in the first equation for x

5y - 6 + y = 12  Combine like terms

6y - 6 = 12  Add 6 to both sides

6y = 18  Divide both sides by 6

y = 3

x + y = 12

3 + y = 12  Subtract 3 from both sides

y = 9

I am little confused by this because it says, "The value of the number..."  What number are they referring to?

Question 6

To find the rate taking into consideration the walkway rate:

\(\frac{48}{3}\) - w  Which is equivalent to 16 - w

\(\frac{24}{2}\) + w  Which is equivalent to 12 + w

Set these expression equal to each other and find the rate of the walkway

16 - w = 12 + w  Add w to both sides

16 = 12 + 2w  Subtract 12 from both sides

4 = 2w  Divide both sides by 2

2 = w

The rate of the walkway is 2 feet per second.  Subtract that from 16 or add is to the 12 to get 14 steps per second.

Answer:

1, 2, 3 and 5

Step-by-step explanation:

1. 2,23 < 2,3 < 2,44 True

2. 2,23 <2,4 < 2,44 True

3. 2 < 2,23 < 2,34 True

4. 2,83 < 3 < 3 False

5. 2,83 < 2,9 < 3 True

6. 2 < 4,5 < 2,23 False

Answer: 36 oz box

Step-by-step explanation:

3.1/12=0.258333

7.9/360.291444

Thus, the 36 oz box is the better buy

The probability that a male student chooses chocolate ice cream is 13/23.

Probability exists as the branch of mathematics that examines the possible results of given events together with the outcomes' relative likelihoods and distributions.

Probability defines the odds that a random event would occur. The odds that the event would occur lie between 0 and 1.

The probability that a male student chooses chocolate ice cream

= number of males that chose ice cream / total number of males

= 13 / 23

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Answer:

the answer is 3/22

Step-by-step explanation:

Using it's concept, the standard deviation of the data-set is of 34.2.

Having this in mind, and inserting the data-set in the calculator, it is found that:

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Step-by-step explanation:

No. of square inches of knit per hour is 14 and No. of hours spent in knitting 1 square inch is \frac{1}{14}141

Step-by-step explanation:

We are given that Lena can knit 14 square inches of a blanket in hours

So, No. of square inches of knit per hour = 14

No. of hours spent in  knitting 14 square inch = 1

No. of hours spent in knitting 1 square inch = \frac{1}{14}141

So,  No. of square inches of knit per hour is 14 and No. of hours spent in knitting 1 square inch is \frac{1}{14}141

Answer:

c) assets, liabilities, and owner's equity

Step-by-step explanation:

Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

According to the information, the graph would be as shown in the attached image (4 * 1/3 = 1 1/3)

According to the information we must take into account that a complete hexagon represents an integer. So one third of the hexagon would be the rhomboid. So, to graph this equation, we must replace the values with the corresponding figures.

In this case we must multiply the rhomboid by four, the rhomboid represents 1 of 3 elements that make up a hexagon. Therefore, if we have 4 rhomboids, we would have a hexagon and a rhomboid.

Note: This question is incomplete. Here is the complete information:

Image attached

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On solving the provided question, we can say that Therefore, you would need multiply  approximately 27.84 pounds of food each day for your horse.

One of the four mathematical operations, along with arithmetic, subtraction, and division, is multiplication. Mathematically, adding subgroups of identical size repeatedly is referred to as multiplication. The multiplication formula is multiplicand multiplier yields product. To be more precise, multiplicand: Initial number (factor). Number two as a divider (factor). The outcome is known as the result after dividing the multiplicand as well as the multiplier. Adding numbers involves making several additions. as in 5 x 4 Equals 5 x 5 x 5 x 5 = 20. 5 times by 4 is what I did. This is why the process of multiplying is sometimes called "doubling."

First, we need to convert the weight of the horse from kilograms to pounds, so:

678 kg x 2.20462 lbs/kg = 1495.69 lbs

Next, we need to calculate how many Mcal the horse needs per day:

0.0333 Mcal/kg x 678 kg = 22.58 Mcal/day

Then, we can convert the Mcal to kcal:

22.58 Mcal/day x 1000 kcal/Mcal = 22,580 kcal/day

Finally, we can divide the total daily kcal needed by the kcal per pound of food to find the total pounds of food needed:

22,580 kcal/day ÷ 810 kcal/lb = 27.84 lbs/day

Therefore, you would need approximately 27.84 pounds of food each day for your horse.

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Answer:

Step-by-step explanation:

Hello!

The researcher developed a treatment to teach social skills to youth offenders. To test if the treatment is effective in increasing empathy compared to the standard treatment she randomly selected a group of 9 offenders and applied the new treatment and to another group of 9 randomly selected youth offenders, she applied the standard treatment. (Note: the data corresponds to two samples of 9 units each, so I've used those sizes to conduct the test)

At the end of the treatment, she administers BES to measure their empathy levels. Her claim is that the offenders that received the new treatment will have higher BES scores than those who received the standard treatment.

1) Using the records obtained for both groups, she  intends to conduct an independent t-test to analyze her claim.

X₁: BES results of a youth offender treated with the new treatment.

X₂: BES results of a youth offender treated with the standard treatment.

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

α:0.05

test statistic

\(t_{H_0}= -0.32\)

p-value: 0.7517

The p-value is greater than the significance level so the decision is to not reject the null hypothesis. This means that at a 5% significance level you can conclude that there is no difference between the mean BES scores of the youth offenders treated with the new treatment and the mean BES score of  the youth offenders treated with the standard treatment. The new treatment doesn't increase the levels of social empathy of the youth offenders.

I hope this helps

(Box plot in attachment)

Answer:

53

Step-by-step explanation:

because triangle is equal to 180

the first one is 35 and there is 90 u will add them the u substraction 127 from 180 it equal to 53

hope it help

Answer:

TBH I would go with either B or D.

Step-by-step explanation:

Well first off your going to 24 miles not 96 or 99 and it doesn't say how much they went on Monday or Tuesday

Answer:

b

Step-by-step explanation:

a

0

=

4

a

i

=

a

i

−

1

+

7

XXXX

possibly with the restriction 1<=i<=4 if this is not intended to be a continuous sequence

Explanation:

This is a simple arithmetic sequence with a difference of  

7

between ascending sequence terms.

Answer:

4.24

Step-by-step explanation:

Answer: 4.24

Step-by-step explanation:

just do 7.42/ 1.75 and ur answer is 4.24

Answer:

Y= 7.9 lb

X= 10.1 lb

Step-by-step explanation:

The chef orders 2.2 lb more carrots than celery. The two orders weigh 10.8 lb combined.

Let carrot= x

Let celery= y

X+y = 18...... equation one

X= 2.2 +y.... equation two

Substituting the value of x into equation one

2.2 +y +y =18

2y= 18-2.2

2y= 15.8

Y= 7.9 lb

Substituting the value of yinto equation 2

X= 2.2 +y

X= 2.2 + 7.9

X= 10.1 lb

Answer:

P=4

Step-by-step explanation:

P(3) =12

This means that P multiplied by 3 would equal 12.

3 x 4 = 12

So, 'P' equals 4.

The investor should invest Rs 12,000 in bank deposits, Rs 8,000 in a unit trust, and Rs 10,000 in equity shares.

The investor has a total of Rs 30,000 to invest in bank deposits, equity shares, and unit trusts. According to the given conditions, the investment in equity shares should be 20% of the total investment in bank deposits and unit trusts. Also, the ratio between investment in bank deposits and unit trust should be 3:2.

Let x be the investment in bank deposits, y be the investment in a unit trust, and z be the investment in equity shares. Based on the given conditions, we can create the following system of equations:

x + y + z = 30,000 (total investment)
z = 0.2(x + y) (equity shares condition)
x/y = 3/2 (ratio condition)

Using the inverse matrix method, we can rewrite these equations as a matrix equation:

|1 1 1| |x|   |30,000|
|0.2 0.2 -1| |y| = |0      |
|3/2 -1  0 | |z|   |0      |

To solve this matrix equation, we can compute the inverse of the coefficient matrix and multiply it with the constant matrix:

A = |1 1 1|
    |0.2 0.2 -1|
    |3/2 -1  0 |

A_inv = |2/5 -1/5 -1/5|
          |-3/2 1/2 1/2|
          |5/2 1/2 -3/2|

Multiplying A_inv with the constant matrix, we get:

|x|   |12,000|
|y| = |8,000  |
|z|   |10,000|

So, the investor should invest Rs 12,000 in bank deposits, Rs 8,000 in a unit trust, and Rs 10,000 in equity shares.

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