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never [62]
3 years ago
7

On a normal day, I can walk from my house to school in three quarters of an hour. The return trip takes me the same amount of ti

me. My mom, driving our car, covers that distance in about a quarter of the time that it takes me. If I go to school five days a week and there are thirty-seven weeks in the school year,
how many hours would I save every year if my mom agreed to drive me to and from school?
Give your answer as a mixed number.
Mathematics
1 answer:
Likurg_2 [28]3 years ago
4 0

Answer:

  208 1/8 hours

Step-by-step explanation:

The amount of time saved on each trip is ...

  (3/4 h) - (1/4)(3/4 h) = (3/4)(3/4 h) = 9/16 h

There are 2×5×37 = 370 trips in the school year, so the total savings in time is about ...

  370×(9/16 h) = 208 1/8 h

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Judith has \$70 in a savings account that earns 5% interest , compounded annually .
Firlakuza [10]

Answer:

$81.03

Step-by-step explanation:

Given

n = 1 --- annually

t =3 --- time

r = 5\% --- rate

PV = \$70 ---- Present value

Required

The future value

This is calculated as:

FV = PV * (1 + \frac{r}{n})^{nt}

This gives:

FV = 70 * (1 + \frac{5\%}{1})^{1*3}

FV = 70 * (1 + 5\%)^3

FV = 70 * (1.05)^3

FV = 70 * 1.157625

FV = 81.03375

<em>The future value to the nearest cent is: $81.03</em>

4 0
2 years ago
On the 40th birthday, Mr. Ramos decided to buy a pension plan for himself. This plan will allow him to claim
Mama L [17]

Answer:

The amount of one-time payment should he make on his 40th birthday to pay off his pension plan is P32,880.77.

Step-by-step explanation:

Step 1: Calculation of present value on 3 months after his 60th birthday

The present value on 3 months after his 60th birthday can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV60 = Q * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV60 = present value on 3 months after his 60th birthday = ?

Q = quarterly claim = P10,000

r = quarterly interest rate = annual interest rate / 4 = 8% / 4 = 0.08 / 4 = 0.02

n = number of quarters = number of years * Number of quarters in a year = 5 * 4 = 20

Substitute the values into equation (1), we have:

PV60 =  P10,000 * ((1 - (1 / (1 + 0.02))^20) / 0.02)

PV60 = P10,000 * 16.3514333445971

PV60 = P163,514.33  

Step 2: Calculation of one-time payment on his 40th birthday

The one-time payment can be calculated using the formula the following formula:

PV = PV60 / (1 + r)^n ........................ (2)

Where;

PV = Present value or One-time payment = ?

PV60 = present value on 3 months after his 60th birthday = P163,514.33

r = quarterly interest rate = annual interest rate / 4 = 8% / 4 = 0.08 / 4 = 0.02

n = number of quarters from 40th to 3 months after his 60th birthday = (number of years * Number of quarters in a year) + One quarter = (20 * 4) + 1 = 81

Substitute the values into equation (2), we have:

PV = P163,514.33 / (1 + 0.02)^81 = P32,880.77

Therefore, the amount of one-time payment should he make on his 40th birthday to pay off his pension plan is P32,880.77.

7 0
3 years ago
Factor the expression: x^6-729. Show your work Please.
Brut [27]

Answer:

  • (x + 3)(x - 3)(x^2 -3x + 9)(x^2 + 3x + 9)

Step-by-step explanation:

<u><em>Use of formulas:</em></u>

  • <em>a^2 - b^2 = (a + b)(a -b)</em>
  • <em>a^3 + b^3 = (a + b)(a^2 - ab + b^2)</em>
  • <em>a^3 - b^3 = (a - b)(a^2 + ab + b^2)</em>

<u>Given the expression: </u>

  • x^6-729

<u>Factoring 729</u>

  • 729 = 3*3*3*3*3*3 = 3^6

<u>Factoring the expression </u>

  • x^6 - 3^6 =
  • (x^3)^2 - (3^3)^2 =
  • (x^3 + 3^3)(x^3 - 3^3) =
  • (x + 3)(x^2 -3x + 9)(x - 3)(x^2 + 3x + 9) =
  • (x + 3)(x - 3)(x^2 -3x + 9)(x^2 + 3x + 9)
7 0
3 years ago
Chris is splitting 6 quarts of ice cream with 9 members of the team. If the ice cream is split evenly. How many cups will each p
vodka [1.7K]
Each person gets 2 2/3 cups of ice-cream
Step-by-step explanation:
First, you convert 6 quarts to cups. For every quart, there are 4 cups so you do 6 times 4 and you get 24 then you divide 24 by 9 and you get 2 2/3
4 0
2 years ago
What is 1/3 of 3?? I can't seem to figure it out lol
raketka [301]
1/3*3
1

1 is 1/3 of 3 hope that helps
6 0
3 years ago
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