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3 years ago

7

How much money should be deposited today in an account that earns 7% compounded semiannually so that it will accumulate to $11,0

00 in three years?
The amount of money that should be deposited is $ N
(Round up to the nearest cent.)

1 answer:

Alona [7]3 years ago

7 0

Answer:

$8950.37

Step-by-step explanation:

Use the compound amount formula A = P(1 + r/n)^(nt), in which P is the initial amount of money (the principal), r is the interest rate as a decimal fraction, n is the number of times per year that interest is compounded, and t is the number of years.

Here we have A = $11,000, n = 2, r = 0.07 and t = 3, and so:

$11,000 = P(1 + 0.07/2)^(2*3), or

$11,000 = P (1.035)^6

$11,000 $11,000

Solving for P, we get P = ---------------- = ------------- = $8950.37

1.035^6 1.229

Depositing $8950.37 with terms as follows will result in an accumulation of $11,000 after 3 years.

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Maci and I are making a small kite. Two sides are 10". Two sides are 5". The shorter diagonal is 6". Round all your answers to t

Art [367]

Answer:

A. 4".

B. Approximately 9.54".

C. Approximately 13.54".

Step-by-step explanation:

Please find the attachment.

Let x be the distance from the peak of the kite to the intersection of the diagonals and y be the distance from the peak of the kite to the intersection of the diagonals.

We have been given that two sides of a kite are 10 inches and two sides are 5 inches. The shorter diagonal is 6 inches.

A. Since we know that the diagonals of a kite are perpendicular and one diagonal (the main diagonal) is the perpendicular bisector of the shorter diagonal.

We can see from our attachment that point O is the intersection of both diagonals. In triangle AOD the side length AD will be hypotenuse and side length DO will be one leg.

We can find the value of x using Pythagorean theorem as:

$(AO)^2=(AD)^2-(DO)^2$

$x^{2}=5^2-3^2$

$x^{2}=25-9$

$x^{2}=16$

Upon taking square root of both sides of our equation we will get,

$x=\sqrt{16}$

$x=\pm 4$

Since distance can not be negative, therefore, the distance from the peak of the kite to the intersection of the diagonals is 4 inches.

B. We can see from our attachment that point O is the intersection of both diagonals. In triangle DOC the side length DC will be hypotenuse and side length DO will be one leg.

We can find the value of y using Pythagorean theorem as:

$(OC)^2=(DC)^2-(DO)^2$

Upon substituting our given values we will get,

$y^2=10^2-3^2$

$y^2=100-9$

$y^2=91$

Upon taking square root of both sides of our equation we will get,

$y=\sqrt{91}$

$y\pm 9.539392$

$y\pm\approx 9.54$

Since distance can not be negative, therefore, the distance from intersection of the diagonals to the top of the tail is approximately 9.54 inches.

C. We can see from our diagram that the length of longer diagram will be the sum of x and y.

$\text{The length of the longer diagonal}=x+y$

$\text{The length of the longer diagonal}=4+9.54$

$\text{The length of the longer diagonal}=13.54$

Therefore, the length of longer diagonal is approximately 13.54 inches.

3 0

3 years ago

What is your sister’s total cost under each of the two plans?2. Suppose your sister doubles her monthly usage to 3,500 minutes a

chubhunter [2.5K]

Answer:

(1) The total cost under Plan A is <u>$92</u> and the total cost under Plan B is <u>$515</u>.

(2) The total cost under Plan A is <u>$92</u> and the total cost under Plan B is <u>$1,030</u>.

Step-by-step explanation:

<u><em>The question is incomplete, so the complete question is below:</em></u>

$A\ cell \ phone \ company\ offers\ two \ different \ plans.$

$Plan\ A\ costs\ \$92\ per\ month\ for\ unlimited\ talk\ and\ text.\ Plan\ B\ costs \ $0.20\ per\ minute\ plus\ \$0.10\ per\ text\ message\ sent.$ $You\ need \ to\ purchase \ a \ plan \ for\ your \ 14-year-old \ sister$ $.Your\ sister\ currently \ uses\ 1,750 \ minutes\ and \ sends\ 1,650 \ texts\ each \ month.$ $(1) What\ is\ your \ sister's\ total\ cost\ under \ each\ of\ the\ two\ plans?$

$(2) Suppose\ your\ sister\ doubles\ her\ monthly\ usage \ to\ 3,500\ minutes \ and\ sends\ 3,300 \ texts.$ $What \ is \ your \ sister's \ total \ cost \ under \ each \ of \ the \ two \ plans?$

Now, to find (1) total cost for each of the two plans. (2) Total cost under each of the two plans, if sister doubles her monthly usage to 3,500 minutes and sends 3,300 texts.

<h3>(1) </h3>

As, the Plan A is for unlimited talk and text

Cost of the Plan A = $92.

<u><em>Now, to find the cost under Plan B:</em></u>

According to question:

Rate of call per minute is $0.20 and per text is $0.10.

Calls she uses currently is 1,750 minutes and text 1,650.

<u><em>So, to get the cost of Plan B:</em></u>

$0.20\times 1750+0.10\times 1650$

$=350+165$

$=515.$

Thus, Plan B costs $515.

<h3>(2)</h3>

<u><em>Now, to get the total cost as, sister doubles her monthly usage to 3,500 minutes and sends 3,300 texts.</em></u>

As, the Plan A is same in both cases and is for unlimited text and calls.

So, cost of Plan A = $92.

As, the monthly usage is double.

Calls in minutes are 3,500.

Texts are 3,300.

<u><em>Now, to get the total cost under Plan B:</em></u>

$0.20\times 3500+0.10\times 3300$

$=700+330$

$=1030.$

Hence, the cost of Plan B = $1,030.

Therefore, (1) The total cost under Plan A is $92 and the total cost under Plan B is $515.

(2) The total cost under Plan A is $92 and the total cost under Plan B is $1,030.

7 0

3 years ago

30 students : 2 teachers<br> please help this is due today

tankabanditka [31]

Answer:

It’s a ratio

Step-by-step explanation:

Is that the whole question?

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3 years ago

Based on the housing data below, which equation can be used to calculate

Nuetrik [128]

Answer: y= 0.074x + 50.48

Step-by-step explanation:

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3 years ago

5-7 Please explain how to do step by step. 85 points ;) max

AleksandrR [38]

5a: To find the slope, you would divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. So coordinates (15,1.5) and (5,0.5). You would subtract 1.5 form 0.5 which gives you neagtive one. (-1) Then subtract 15 from 5 which is -10. (negative ten) -1 divided by -10 is one tenths. 1/10 is your answer to part a.

5b. To find the slope, you would divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. (Not sure what you meant by "interpret".

5c. The phone bill will increase by $0.50 if you talk for 5 extra minutes.

5d. You talked for 30 minutes if the phone bill costs $3.

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6a. I can't really graph it but I'll interpret the slope. Y would basically be 7.5 times as much as x.

6b. I'm kinda stuck on how to get from 7.5 to 1. Sorry. OnO

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7a. Hamburgers sell faster because there are 60 minutes in a hour. If 2.5 wraps are sold in one minute. Then there would be 150 wraps sold in 60 minutes which is also one hour. Hamburgers sell ten more than wraps per hour.

7b. The equation for wraps is: y=2.5x

The equation for hamburgers is y=2.6667x

Goodnight and hope it helps.~ RIP my sleep...

8 0

3 years ago

Read 2 more answers