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2 years ago

A cookie recipe calls for 1/4 cup of brown sugar for one batch of 24.How many cups

Mathematics

1 answer:

natali 33 [55]2 years ago

4 0

Set up a proportion and solve for x:
(1/4)/x = 24/144
24x = 36
X = 1 1/2 cups of brown sugar

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GalinKa [24]

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3 years ago

I need help for this to pass my last math class please help and show your work

Maksim231197 [3]

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2 years ago

manufacturing company produces digital cameras and claim that their products maybe 3% defective. A video company, when purchasin

alexdok [17]

Answer:

P(X>17) = 0.979

Step-by-step explanation:

Probability that a camera is defective, p = 3% = 3/100 = 0.03

20 cameras were randomly selected.i.e sample size, n = 20

Probability that a camera is working, q = 1 - p = 1 - 0.03 = 0.97

Probability that more than 17 cameras are working P ( X > 17)

This is a binomial distribution P(X = r) $nCr q^{r} p^{n-r}$

$nCr = \frac{n!}{(n-r)!r!}$

P(X>17) = P(X=18) + P(X=19) + P(X=20)

P(X=18) = $20C18 * 0.97^{18} * 0.03^{20-18}$

P(X=18) = $20C18 * 0.97^{18} * 0.03^{2}$

P(X=18) = 0.0988

P(X=19) = $20C19 * 0.97^{19} * 0.03^{20-19}$

P(X=19) = $20C19 * 0.97^{19} * 0.03^{1}$

P(X=19) = 0.3364

P(X=20) = $20C20 * 0.97^{20} * 0.03^{20-20}$

P(X=20) = $20C20 * 0.97^{20} * 0.03^{0}$

P(X=20) = 0.5438

P(X>17) = 0.0988 + 0.3364 + 0.5438

P(X>17) = 0.979

The probability that there are more than 17 working cameras should be 0.979 for the company to accept the whole batch

6 0

3 years ago

Consider the equality xy k. Write the following inverse proportion: y is inversely proportional to x. When y = 12, x=5.

skelet666 [1.2K]

Answer:

$y=\dfrac {60} {x}$ or $xy=60$ (depending on your teacher's format preference)

Step-by-step explanation:

<h3><u>Proportionality background</u></h3>

Proportionality is sometimes called "variation". (ex. " 'y' varies inversely as 'x' ")

There are two main types of proportionality/variation:

Direct
Inverse.

Every proportionality, regardless of whether it is direct or inverse, will have a constant of proportionality (I'm going to call it "k").

Below are several different examples of both types of proportionality, and how they might be stated in words:

$y=kx$ y is directly proportional to x
$y=kx^2$ y is directly proportional to x squared
$y=kx^3$ y is directly proportional to x cubed
$y=k\sqrt{x}}$ y is directly proportional to the square root of x
$y=\dfrac {k} {x}$ y is inversely proportional to x
$y=\dfrac {k} {x^2}$ y is inversely proportional to x squared

From these examples, we see that two things:

things that are <u>directly proportional</u> -- the thing is <u>multipli</u>ed to the constant of proportionality "k"
things that are <u>inversely proportional</u> -- the thing is <u>divide</u>d from the constant of proportionality "k".

<h3><u>Looking at our question</u></h3>

In our question, y is inversely proportional to x, so the equation we're looking at is the following $y=\dfrac {k} {x}$ .

It isn't yet clear what the constant of proportionality "k" is for this situation, but we are given enough information to solve for it: "When y=12, x=5."

We can substitute this known relationship pair, and find the "k" that relates this pair of numbers:

<h3><u>Solving for k, and finding the general equation</u></h3>

General Inverse variation equation...

$y=\dfrac {k} {x}$

Substituting known values...

$(12)=\dfrac {k} {(5)}$