Write the following ratio as a fraction in lowest terms <br> 5/3to7/6

A soup kitchen makes 15 gallons of soup each day a quarter of the soup is served and the rest is saved for the next day , what i

Sophie [7]

Number of ounces left is 1120

Step-by-step explanation:

Step 1: Find number of ounces left after each day.

Given total soup prepared each day = 15 gallons

Amount served each day = 1/4 of 15 = 15/4 gallons

Amount left after each day = 15 - 15/4 = 60 - 15/4 = 35/4 gallons

Step 2: Convert gallons into ounces. 1 gallon = 128 ounces

35/4 gallons = 35/4 × 128 = 1120 ounces

5 0

4 years ago

a vender sold a combined total of 102 sodas and hot dogs. The number of sodas sold was two times the number of hot dogs sold. Fi

maxonik [38]

Answer:

34 hotdogs were sold

68 sodas sold

4 0

3 years ago

which of the following is equivalent to 3 sqrt 32x^3y^6 / 3 sqrt 2x^9y^2 where x is greater than or equal to 0 and y is greater

Nutka1998 [239]

Answer:

$\frac{\sqrt[3]{16y^4}}{x^2}$

Step-by-step explanation:

The options are missing; However, I'll simplify the given expression.

Given

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$

Required

Write Equivalent Expression

To solve this expression, we'll make use of laws of indices throughout.

From laws of indices $\sqrt[n]{a} = a^{\frac{1}{n}}$

So,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ gives

$\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}$

Also from laws of indices

$(ab)^n = a^nb^n$

So, the above expression can be further simplified to

$\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}$

Multiply the exponents gives

$\frac{(32^\frac{1}{3}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

Substitute $2^5$ for 32

$\frac{(2^{5*\frac{1}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

From laws of indices

$\frac{a^m}{a^n} = a^{m-n}$

This law can be applied to the expression above;

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$ becomes

$2^{\frac{5}{3}-\frac{1}{3}}x^{1-3}*y^{2-\frac{2}{3}}$

Solve exponents

$2^{\frac{5-1}{3}}*x^{-2}*y^{\frac{6-2}{3}}$

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$

From laws of indices,

$a^{-n} = \frac{1}{a^n}$ ; So,

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$ gives

$\frac{2^{\frac{4}{3}}*y^{\frac{4}{3}}}{x^2}$

The expression at the numerator can be combined to give

$\frac{(2y)^{\frac{4}{3}}}{x^2}$

Lastly, From laws of indices,

$a^{\frac{m}{n} = \sqrt[n]{a^m}$ ; So,

$\frac{(2y)^{\frac{4}{3}}}{x^2}$ becomes

$\frac{\sqrt[3]{(2y)}^{4}}{x^2}$

$\frac{\sqrt[3]{16y^4}}{x^2}$

Hence,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ is equivalent to $\frac{\sqrt[3]{16y^4}}{x^2}$

8 0

3 years ago

A food pantry is making packages. each package weights 64 pounds. Here are two situations. for each situation, write and solve a

alexdok [17]

Answer:

Step-by-step explanation:

5 0

3 years ago

ben earns $9 per hour and $6 for each delivery he makes. he wants to earn more than $155 in an 8-hour workday. what is the least

Ymorist [56]

First find out how much he makes in 8 hours (9x8=72). Then subtract 72 from 155 (155-72=83). Then divide 83 by 6 (83/6=13.8333). Since 83 is not evenly divisible by 6, and since he can't deliver .8333 of a delivery, we would round up, giving us 14). Ben would need to make 14 deliveries in 8 hours to make more than $155 :) Hope this helps you :)

3 0

3 years ago

Write the following ratio as a fraction in lowest terms 5/3to7/6