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3 years ago

2. Write AND simplify an expression showing how many times farther

Mathematics

1 answer:

lora16 [44]3 years ago

6 0

Answer: Neptune is the farthest, with an average distance of 2.8 × 109miles from the Sun.

Step-by-step explanation:

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A cafe sells drink in 3 sizes: small,medium and a large. The small cup cost $0.89 and holds 9 ounces. The medium cost $1.29 and

KatRina [158]

The large cup is best to buy. This is because it costs 11 cents per ounce for the medium cup and 11 cents for the large cup as well. You get almost double the amount for the same price with the large cup.

3 0

3 years ago

A rectangular prism has a width of 51 ft and a volume of 144 ft3. Find the volume of a similar prism with a width of 17 ft. Roun

meriva

Answer:

$5.3\ ft^3$

Step-by-step explanation:

Similar shapes with scale factor $k$ have proportional volumes with coefficient $k^3$ i.e.

$\dfrac{V_{large}}{V_{small}}=k^3,$

where

$k=\dfrac{\text{width of large prism}}{\text{width of small prism}}.$

Since

$\text{width of large prism}=51\ ft,\\ \\\text{width of small prism}=17\ ft,$

then

$k=\dfrac{51}{17}=3.$

Hence,

$\dfrac{144}{V_{small}}=3^3\Rightarrow V_{small}=\dfrac{144}{27}=\dfrac{16}{3}=5\dfrac{1}{3}\approx 5.3\ ft^3.$

7 0

3 years ago

Lou’s Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50

patriot [66]

The easiest way to think of these is to put them in terms of percentages. Obviously, if you are SAVING 25%, you are SPENDING 75%. So if she SPENDS 13.50, we can easily use the 75% in an equation. $13.50 = .75x, with x being what the shoes cost originally. The .75 indicates that she is spending 75% of what the original cost is. You don't have any examples to pick from, but this is the best way to explain what one of the equations could be. You could also base it on money saved, but the equation is not quite as neat.

4 0

4 years ago

Read 2 more answers

You deposit $300 in a savings account that pays 6% interest compounded semiannually. How much will you have at the middle of the

Otrada [13]

Answer:

Please check the explanation.

Step-by-step explanation:

a) How much will you have at the middle of the first year?

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 0.5 years

Total amount = A = ?

Using the formula

$A\:=\:P\left(1+\frac{r}{n}\right)^{nt}$

substituting the values

$A=300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(0.5\right)}$

$A=300\cdot \frac{2.06}{2}$

$A=\frac{618}{2}$

$A=309$ $

Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 0.5 years is $ 309.00.

Part b) How much at the end of one year?

Principle P = $300

Annual rate r = 6% = 0.06 per year

Compound n = Semi-Annually = 2

Time (t in years) = 1 years

Total amount = A = ?

Using the formula

$A\:=\:P\left(1+\frac{r}{n}\right)^{nt}$

so substituting the values

$A\:=\:300\left(1+\frac{0.06}{2}\right)^{\left(2\right)\left(1\right)}$

$A=300\cdot \frac{2.06^2}{2^2}$

$A=318.27$ $

Therefore, the total amount accrued, principal plus interest, from compound interest on an original principal of $ 300.00 at a rate of 6% per year compounded 2 times per year over 1 year is $ 318.27.

7 0

3 years ago

X + 2y = 5 3x + 5y = 14 Solve the system of equations. (3.1) (7.-1) (2.3/2)

son4ous [18]

Answer:

(3,1) because x is 3 and y is 1.

Step-by-step explanation:

x+2y=5

3x+5y=14

Multiply first equation by 3:

3x+6y=15

3x+5y=14

Subtract 3x:

1y=1

Therefore, y = 1

Plug it back into 1st equation:

x+2(1)=5

x+2=5

Therefore, x = 3

Judging from your answers, it looks like (3,1) because x is 3 and y is 1.

I hope this helped!

5 0

3 years ago