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3 years ago

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Pete wants to mix 4 quarts of 20% orange juice concentrate with some 60% pineapple juice concentrate to get a 50% punch concentr

ate for a party. How much of the 60% pineapple juice concentrate should be used? Pete wants to mix 4 quarts of 20% orange juice concentrate with some 60% pineapple juice concentrate to get a 50% punch concentrate for a party. How much of the 60% pineapple juice concentrate should be used?

1 answer:

Tamiku [17]3 years ago

7 0

Pete starts with 4 quarts of 20% juice, which contains

0.20 • (4 quarts) = 0.8 quarts

of juice.

If he mixes this with <em>x</em> quarts of 60% juice, which contains

0.60 • (<em>x</em> quarts) = 0.6<em>x</em> quarts

of juice, then he would end up with a mixture with a volume of (<em>x</em> + 4) quarts that contains (0.8 + 0.6<em>x</em>) quarts of juice. The mix has to have a concentration of 50% juice, which means

(0.8 + 0.6<em>x</em>) / (<em>x</em> + 4) = 0.50

Solve for <em>x</em> :

0.8 + 0.6<em>x</em> = 0.50 (<em>x</em> + 4)

0.8 + 0.6<em>x</em> = 0.5<em>x</em> + 2

0.1<em>x</em> = 1.2

<em>x</em> = 12

So Pete needs 12 quarts of the 60% juice.

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Chance can wash the car in 2 hours, while Sandy can wash the same car in 4 hours. How many hours would it take for them to wash

aliya0001 [1]

Answer: First Option is correct.

Step-by-step explanation:

Since we have given that

Number of hours Chance can wash the car = 2 hours

Number of hours Sandy can wash the car = 4 hours

Work done by Chance per hour is given by

$\frac{1}{2}$

Work done by Sandy per hour is given by

$\frac{1}{4}$

Work done by altogether per hour is given by

$\frac{1}{2}+\frac{1}{4}\\\\=\frac{2+1}{4}\\\\=\frac{3}{4}$

So, Number of hours they take if they together wash the car is given by

$\frac{4}{3}$

Hence, First Option is correct.

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3 years ago

Read 2 more answers

The Office of Student Services at a large western state university maintains information on the study habits of its full-time st

Vera_Pavlovna [14]

Answer:

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 20 hours, standard deviation of 6:

This means that $\mu = 20, \sigma = 6$

Sample of 150:

This means that $n = 150, s = \frac{6}{\sqrt{150}}$

What is the probability that the mean of this sample is between 19.25 hours and 21.0 hours?

This is the p-value of Z when X = 21 subtracted by the p-value of Z when X = 19.5. So

X = 21

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{21 - 20}{\frac{6}{\sqrt{150}}}$

$Z = 2.04$

$Z = 2.04$ has a p-value of 0.9793

X = 19.5

$Z = \frac{X - \mu}{s}$

$Z = \frac{19.5 - 20}{\frac{6}{\sqrt{150}}}$

$Z = -1.02$

$Z = -1.02$ has a p-value of 0.1539

0.9793 - 0.1539 = 0.8254

0.8254 = 82.54% probability that the mean of this sample is between 19.25 hours and 21.0 hours

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kirza4 [7]

Answer:

(a)23 (b)90 (c)3

Step-by-step explanation:

The equation for the line of best fit for this situation is given as

$y=\frac{3}{10}x+8$

where x=average temperature in degrees

y=average number of hot dogs she sold,

(a) The expected number of hot dogs sold when the temperature is 50° would be___hot dogs.

When x=50°

$y=\frac{3}{10}X50+8=15+8=23$

When the temperature is 50°, the expected number of hot dogs sold would be 23.

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If y=35

$35=\frac{3}{10}x+8\\35-8=\frac{3}{10}x\\27=\frac{3}{10}x$

Multiply both sides by 10/3

$27 X \frac{10}{3}= \frac{3}{10}x X \frac{10}{3}\\x=90^{0}$

If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees.

(c) Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

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