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4 years ago

9

A recipe for making popcorn requires 2 tablespoons of butter for every 1/3 cup of popcorn kernels. At this rate, how much butter

is required if 2 cups of popcorn kernels are used?

1 answer:

PtichkaEL [24]4 years ago

7 0

Answer:

12 tablespoons of butter

Step-by-step explanation:

Create a proportion:

$\frac{2}{1/3}$ = $\frac{x}{2}$

Cross multiply:

1/3x = 4

x = 12

= 12 tablespoons of butter

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What is 14=10×14÷2

WINSTONCH [101]

Answer: 70

Step-by-step explanation:

10*14/2=140/2=70

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4 years ago

Use symbols Replace each with a number to make /24 >1/4 > 4/ a true statement

Ksenya-84 [330]

Answer:

Step-by-step explanation:

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4 years ago

A computer that originally cost $500 is on sale for $350. What is the percent discount?

laiz [17]

Answer:

30%

Step-by-step explanation:

500 - 350 = 150
Set up a proportion: $\frac{150}{500} = \frac{x}{100}$
Cross multiply, then divide: 150 × 100 = 15000, 15000 ÷ 500 = 30
Write the completed fraction: $\frac{30}{100}$
$\frac{30}{100} =$ 30%

I hope this helps!

8 0

3 years ago

Carly and janiya put some money into their money boxes every week. the amounts of money (y), in dollars, in their money boxes af

Lelu [443]

Carly : y = 60x + 40
janiya : y = 50x + 80

60x + 40 = 50x + 80
60x - 50x = 80 - 40
10x = 40
x = 40/10
x = 4 <=== so at 4 weeks, they will have the same amount of money <==
The money they have is : y = 60(4) + 40.....y = $ 280 <=

so ur answer is : 4 weeks, $ 280

8 0

3 years ago

1. Express <img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7Bx%282x%2B3%29%20%7D" id="TexFormula1" title="\frac{1}{x(2x+3) }" a

katovenus [111]

1. Let a and b be coefficients such that

$\dfrac1{x(2x+3)} = \dfrac ax + \dfrac b{2x+3}$

Combining the fractions on the right gives

$\dfrac1{x(2x+3)} = \dfrac{a(2x+3) + bx}{x(2x+3)}$

$\implies 1 = (2a+b)x + 3a$

$\implies \begin{cases}3a=1 \\ 2a+b=0\end{cases} \implies a=\dfrac13, b = -\dfrac23$

so that

$\dfrac1{x(2x+3)} = \boxed{\dfrac13 \left(\dfrac1x - \dfrac2{2x+3}\right)}$

2. a. The given ODE is separable as

$x(2x+3) \dfrac{dy}dx} = y \implies \dfrac{dy}y = \dfrac{dx}{x(2x+3)}$

Using the result of part (1), integrating both sides gives

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + C$

Given that y = 1 when x = 1, we find

$\ln|1| = \dfrac13 \left(\ln|1| - \ln|5|\right) + C \implies C = \dfrac13\ln(5)$

so the particular solution to the ODE is

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3|\right) + \dfrac13\ln(5)$

We can solve this explicitly for y :

$\ln|y| = \dfrac13 \left(\ln|x| - \ln|2x+3| + \ln(5)\right)$

$\ln|y| = \dfrac13 \ln\left|\dfrac{5x}{2x+3}\right|$

$\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|$

$\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}$

2. b. When x = 9, we get

$y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}$

8 0

3 years ago