How much principal must be deposited to earn $2,179 in simple interest at a rate of 3 2/3% for 60 months

The labor fee is $13.55 and each quart of oil is $2.25

Step-by-step explanation:

Let,

x be the amount of each quart of oil

y be the amount of labor fee

According to given statement;

5x+y=24.80        Eqn 1

7x+y=29.30        Eqn 2

Subtracting Eqn 1 from Eqn 2

[tex](7x+y)-(5x+y)=29.30-24.80\\7x+y-5x-y=4.50\\2x=4.50[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{4.50}{2}\\x=2.25[/tex]

Putting x=2.25 in Eqn 1

[tex]5(2.25)+y=24.80\\11.25+y=24.80\\y=24.80-11.25\\y=13.55[/tex]

The labor fee is $13.55 and each quart of oil is $2.25

Keywords: linear equation, subtraction

Learn more about subtraction at:

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Final answer:

Stefan spent $120 originally to buy the bike and helmet and made $36 by selling them to Jin.

Explanation:

To find out how much Stefan spent originally, we need to divide the total cost for Jin by 130%.

Let's call the original amount x.

Jin's total cost is 130% of x, which can be expressed as 1.3x.

We know that the total cost for Jin is $140 for the bike + $16 for the helmet = $156.

So we have the equation 1.3x = $156. To solve for x, divide both sides of the equation by 1.3. x = $156 / 1.3 = $120.

Therefore, Stefan spent $120 originally to buy the bike and helmet.

To find out how much money Stefan made by selling the bike and helmet, we subtract the original amount spent from the total cost for Jin.

Money made = $156 - $120 = $36.

Greater Than!

First make the denominator (the bottom number) the same for both fractions. So you can multiply the 1/2 by 5 and the 4/5 by 2.

This will make them 5/10 and 8/10.

Then, you see that 8/10 (4/5) is greater than 5/10 (1/2)

Hope that’s makes sense! :)

The fraction 4/5 is greater than 1/2. This conclusion can be reached by converting the fractions to decimal form, where 4/5 becomes 0.8 and 1/2 becomes 0.5, highlighting that 0.8 is indeed greater than 0.5.

The question is whether the fractional value of 4/5 is greater than, less than, or equal to 1/2. To compare these fractions, it may be helpful to first convert them to decimal form, as this is often easier to understand than comparing fractions directly. 4/5 as a decimal is 0.8 and 1/2 as a decimal is 0.5. Hence, 0.8 is greater than 0.5. Therefore, 4/5 is greater than 1/2.

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The answer to this one would be 2.

Answer: 2

Step-by-step explanation:

1 1/2 divided 3/4

First make all a fraction

3/2 divided 3/4

3/2*4/3 inverted

2

Answer:

36x + 12y + 24 = T

Step-by-step explanation:

If Sahil has 36 packs of x pencils, then x would equal the number of pencils in each pack. Same thing goes for y. 12 packs of y pencils and y will be the number of crayons in each pack.

36(x) = Total number of pencils.

12(y) = Total number of crayons.

24 = The numbers of erasers which is given.

36x + 12y + 24 = Total numbers of items.

Answer:

Step-by-step explanation:

5) D  2000/200 = 10

6) C 90/9 = 10

7) B 80/8 = 10

8) A)   10 times 2 =10*2 = 20

Answer:

Less than:  1/4, 1/8, 1/16,...

Greater than: 5/8, 3/4, 1,...

Hope this helps :)

Answer: y = -3x + 8

Step-by-step explanation:

The formula for finding equation of line when two points are given is :

[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = 1

[tex]x_{2}[/tex] = -2

[tex]y_{1}[/tex] = 5

[tex]y_{2}[/tex] = 14

Substituting the values , we have

[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{14-5}{-2-1}[/tex]

[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{9}{-3}[/tex]

[tex]\frac{y-5}{x-1}[/tex] = [tex]\frac{-3}{1}[/tex]

y-5 = -3(x-1)

y -5 = -3x + 3

writing the equation in slope - intercept form , we will make y the subject of the formula:

y = -3x + 3 + 5

y = -3x + 8

Answer:

y = - [tex]\frac{3}{2}[/tex] x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{2}{3}[/tex] x + 2 ← is in slope- intercept form

with slope m = [tex]\frac{2}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex], thus

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

To find c substitute (2, - 4) into the partial equation

- 4 = - 3 + c ⇒ c = - 4 + 3 = - 1

y = - [tex]\frac{3}{2}[/tex] x - 1 ← equation of perpendicular line

Answer:

n = 14

Step-by-step explanation:

Write the equation in algebraic (numbers and symbols) form

[tex]\frac{238}{n}[/tex] = n + 3              Rearrange the equation

[tex]n\frac{238}{n}[/tex] = n(n + 3)           Multiply both sides by 'n'

238 = n(n + 3)          On the left, multiplying and dividing by 'n' cancels out

238 = n² + 3n           Distributed right side

0 = n² + 3n - 238        Rearranged to standard form for quadratic equations

Remember standard form for quadratic equations is: ax² + bx + c = 0

State the variables a, b and c:

a = 1; b = 3; c = -238

When a quadratic equation is in standard form, you can use the quadratic formula to solve for 'n'. (Usually, you see the variable 'x', but the quadratic formula can solve for 'n' as if it is 'x', as long as it's in standard form.)

[tex]n = \frac{-b±\sqrt{b^{2}-4ac}}{2a}[/tex]  (ignore the Â, it's a formatting error)

[tex]n = \frac{-(3)±\sqrt{(3)^{2}-4(1)(-238)}}{2(1)}[/tex]  Substitute the values for 'a', 'b' and 'c' from the equation

[tex]n = \frac{-3±\sqrt{9-(-952)}}{2}[/tex]     In the root, two negatives make a positive

[tex]n = \frac{-3±\sqrt{9+952}}{2}[/tex]     Add inside the root

[tex]n = \frac{-3±\sqrt{961}}{2}[/tex]       Find the square root of 961

[tex]n = \frac{-3±{31}{2}[/tex]     Split the equation at the ±

Split for adding:

[tex]n = \frac{-3+31}{2}[/tex]    Simplify

n = 14

Split for subtracting:

[tex]n = \frac{-3-31}{2}[/tex]      Simplify

n = -17

You get the answers 14 and -17 for 'n'. Decide which one is 'inadmissible', meaning it can't be right even if it solves the equation.

The problem says 'n' is a natural number. Natural numbers are all non-partial numbers count up from 1. (Non-partial means as a fraction, they are reduced to a number over 1). Since -17 is less than 1, it is inadmissible because it is not a natural number.

Therefore, 'n' is 14.

Answer:

The AP is, 1 , 6, 11, 16, 21, 26, 31, .....................

Step-by-step explanation:

From the question;

We are required to find the AP;

nth term = a + (n-1) d , where a is the first term and d is the common difference

5th term = a + 4d

7th term = a + 6d

5th term + 7th term = 2a + 10d = 52  ..........eqn 1

10th term = a + 9d

2a + 10d = 52

a + 9d = 46

Multiplying the second equation by 2, we get;

2a + 10d = 52

2a + 18d = 92

Eliminating a by subtracting the two equations; we get;

-8d = -40

   d = 5

Solving for a

a + 9d = 46

   a = 46 - 9d

      = 46 - 9(5)

      = 46 - 45

   a  = 1

Thus, the first term, a= 1 and the common difference, d= 5

Therefore;

First term = a = 1

Second term = a + d = 1 + 5 = 6

Third term = a + 2d = 1 + 2(5) = 11

Fourth term = a + 3d = 1 + 3(5) =16

Fifth term = a + 4d = 1 + 4(5) = 21

Sixth term = 1 + 5d = 1 + 5(5) = 26

Seventh term = 1 + 6d = 1 + 6(5) = 31

Thus,

The AP is, 1 , 6, 11, 16, 21, 26, 31, .....................

A submarine hovers at 66 and 2/3 yards below sea level. If it ascends 24 and 1/8 yards and then descends again 78 and 3/4 yards, what is the submarine’s new position, in yards, below sea level?

Answer:

The submarine's new position is [tex]-121\frac{7}{24}\text{ yards}[/tex] below sea level.

Solution:

Given that a submarine hovers at [tex]66\frac{2}{3}[/tex] yards below sea level. This means that the position of submarine is negative

Therefore, we get [tex]-66\frac{2}{3}[/tex]

Also given that it ascend [tex]24\frac{1}{8}[/tex] yards

So we have to add [tex]-66\frac{2}{3}[/tex] and [tex]24\frac{1}{8}[/tex]

[tex]\rightarrow -66\frac{2}{3} + 24\frac{1}{8}\\\\\text{Convert mixed fractions to improper fractions }\\\\\rightarrow -\frac{66 \times 3+2}{3} + \frac{24 \times 8+1}{8} = \frac{-200}{3} + \frac{193}{8}\\\\\rightarrow \frac{-200 \times 8}{3 \times 8} + \frac{193 \times 3}{8 \times 3}\\\\\text{Simplify the above expression }\\\\\rightarrow \frac{-1600}{24} + \frac{579}{24} = \frac{-1021}{24}[/tex]

The submarine descends again 78 and 3/4 yards

This means we need to subtract [tex]-78\frac{3}{4}\text{ yards from } -\frac{1021}{24}\text{ yards}[/tex]

[tex]\rightarrow \frac{-1021}{24} -(78\frac{3}{4})\\\\\rightarrow \frac{-1021}{24} - \frac{78 \times 4 + 3}{4}\\\\\rightarrow \frac{-1021}{24} - \frac{315}{4} = \frac{-1021}{24} - \frac{315 \times 6}{4 \times 6}\\\\\rightarrow \frac{-1021 -1890}{24} = \frac{-2911}{24}\\\\\text{Simplify the expression }\\\\\rightarrow \frac{-2911}{24} = -121\frac{7}{24}[/tex]

Therefore, the submarine's new position is [tex]-121\frac{7}{24}\text{ yards}[/tex] below sea level.

Answer:

The answer-121 and 7/24

Hope this helps

:D

If I'm wrong sorry

And sorry that I'm super late

Answer:

  $10,000

Step-by-step explanation:

Let x represent the amount invested in the 5.5% bond.

For an annual income of $1800, we want ...

  (5.5%)x + (6.25%)(30,000-x) = 1800

  (-0.75%)x + 1875 = 1800

  -0.0075x = -75 . . . . . . . . . subtract 1875

  x = 10,000 . . . . . . . . . . . . . divide by -0.0075

At most $10,000 should be invested at 5.5% to obtain at least $1800 in interest.

Answer:

See below.

Step-by-step explanation:

The equation is already solved for p.

p = 75 + 45h

Final answer:

To solve for the fluid density 'p', use the hydrostatic pressure formula P = pgh. By rearranging the formula to p = P / (gh) and inputting the known values for P (atmospheric pressure) and h (height of the water column), the density can be calculated.

Explanation:

To solve for density 'p' when given the equation P = 75 + 45h, where P represents atmospheric pressure and h is the height of a column of fluid, we need to incorporate the concept of hydrostatic pressure. The formula for hydrostatic pressure is P = pgh, where 'p' is the fluid density, 'g' is the acceleration due to gravity, and 'h' is the height of the fluid column. If we know the value of 'P' and the value of 'h', we can isolate 'p' by rearranging the equation to p = P / (gh). This calculation assumes that 'g', the acceleration due to gravity, is a known constant.

Let's assume 'P' is given as 1.00 atm (standard atmospheric pressure) for a water column which is the fluid we're working with. The density 'p' of water that creates this pressure can be calculated by inserting the known values into the expression for 'h'. For instance, if 'h' is 10 meters, the equation would be p = 1.00 atm / (9.81 m/s² × 10 m). To get 'p' in appropriate units, we would convert atm to pascals, and the result will provide the density in kg/m³.

Answer:

Step-by-step explanation:

If he reads 80 pages in 2 hours, that means he reads 80 pages in 120 minutes. 80 pages/120 minutes simplifies to 2 pages/3 minutes. It also means it takes him 1 and a half minutes to read each page.

Answer:

a is the answer or 320 ft

Step-by-step explanation:

95*65=6175 ft^ for area

95+95+65+65=320 ft

Answer:

Please Mark Brainliest!

Step-by-step explanation:

i think it would be 14 bananas if u take 3 divided by 42

hope that is right.

he rides for 7 min and waits in line for 20 min, if he was to wait in line for 60 min then he would ride for 21 min, if you divide 20/60 then you'll get 3. Multiply the 7 with that 3 and you'll get "21".

120

Answer:

the first loan is cheaper

Step-by-step explanation:

convert percent values to decimals

8.5/100=.085

7.75/100=.0775

find the value for the first loan

1550*.085*4=527

find the value for the first loan

1550*.0775*5=600.625

compare

Belle would pay $5100 in interest for the 4-year loan at 8.5% and $5812.50 for the 5-year loan at 7.75%. Therefore, less interest would be paid with the 4-year loan.

To calculate the simple interest, we use the formula I = P*R*T, where P is the principal amount, R is the interest rate, and T is the time in years.

For the 4-year loan at 8.5%, interest would be: I = $15,000 * 8.5/100 * 4 = $5100

For the 5-year loan at 7.75%, interest would be: I = $15,000 * 7.75/100 * 5 = $5,812.50.

So, the 4-year loan at 8.5% will require less interest payment.

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Answer:

0.36 or [tex]\frac{9}{25}[/tex]

Step-by-step explanation:

9/20=.45

4/5=.8

Answer: .36

Answer: $74

Step-by-step explanation:

cost for an hour = $10

since she worked for 6 hours , this means that she made $(6x10) = $60

Also , she made 4% commission on her sale and she sold $350 , this means that she made 4% of 350 =$14

Therefore: she made $ 60 + $14 for the day. Thai is , she made $74 for the day

Answer:?

Step-by-step explanation:

not sure..

Answer:

Pizza is pretty good tbh. Also the answer is 4.

Answer:

Pizza is great

Step-by-step explanation:

And 8/2 is 4. Pls mark brainliest thx! :)

if each person had to run 1/25 of a mile then you would need to have 5 people per team. it takes 5/25 to equal 1/5. So your answer is 5!!

Hope this helps! :)

Answer:

18 to the 8th power

Step-by-step explanation:

Answer:

7,800

Step-by-step explanation:

Because the 3 goes down.

Answer:

321 300 20 1

Step-by-step explanation:

In written for: Three hundred twenty-one

Expanded form: 300 + 20 + 1

Standard form: 321

Fraction form: 321/1

Decimal form: 321.00

Answer: 6000+200+10+9

Step-by-step explanation:

The ones place multiplies by 1 so 9*1=9

The tens place multiplies by 10 so 10*1=10

The hundreds place multiply by 100 so 100+2=100

The thousands place multiply by 1000 so 1000*6=6000

Hope This Helps!!!

Answer:

30 centimeters

Step-by-step explanation:

since the width is 4 centimeters more than 3/10 of the length, then 13 is 4 centimeters more than 3/10 of the length. 4 less than 13 is 9, so nine is 3/10 of the length. if 9 is 3/10, then 3 is 1/10 because 3/10 is three times 1/10. If 3 is 1/10, that means that 30 is the length because 1/10 multiplied by 10 is 10 tenths, or 1.