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Kruka [31]
3 years ago
9

4 pencils and 3 crayons are 20.9 inches. 5 pencils and 4 crayons are 26.5 inches. Each pencil is the same length as the other pe

ncils, and each crayon is the same length as the other crayons. What is the length of 1 pencil? What is the length of 1 crayon?
Mathematics
1 answer:
erastova [34]3 years ago
5 0

Answer:

The length of the pencils is 4.1 inches and for the crayons 1.5 inches

Step-by-step explanation:

We can solve by means of a 2x2 system of equations, we have to:

let "x" be the length of the pencils

let "y" be the length of the crayons

4 * x + 3 * y = 20.9

5 * x + 4 * y = 26.5 => x = (26.5 - 4 * y) / 5

Replacing:

4 * (26.5 - 4 * y) / 5 + 3 * y = 20.9

21.2 - 3.2 * y + 3 * y = 20.9

-0.2 * y = 20.9 - 21.2

y = -0.3 / -0.2

y = 1.5

now for x:

x = (26.5 - 4 * 1.5) / 5

x = 4.1

This means that the length of the pencils is 4.1 inches and for the crayons 1.5 inches

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2 years ago
The Slow Fix auto shop charges $28 for parts and $48 per hour of labor. The We Work Cheaper auto shop charges $59 for parts and
Sidana [21]

Answer: 10 hours

Step-by-step explanation:

Given

Slow fix auto charge $28 for parts and $48 per hour of labor

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Suppose both works for x hours

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When these costs are the same

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3 years ago
Manufacture of a certain component requires three different machining operations. Machining time for each operation has a normal
tigry1 [53]

Answer:

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

Step-by-step explanation:

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.

Sum of normal variables:

When normal variables are added, the mean is the sum of the means while the standard deviation is the square root of the sum of the variances.

The mean values are 20, 15, and 30 min, respectively:

This means that \mu = 20 + 15 + 30 = 65

The standard deviations are 1, 2, and 1.5 min, respectively.

This means that \sigma = \sqrt{1^2 + 2^2 + 1.5^2} = 2.6926

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Mean and standard deviation are in minutes, so this is the pvalue of Z when X = 60.

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

Z = \frac{60 - 65}{2.6926}

Z = -1.86

Z = -1.86 has a pvalue of 0.0314

0.0314 = 3.14% probability that it takes at most 1 hour of machining time to produce a randomly selected component

7 0
2 years ago
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ladessa [460]

Answer:

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Step-by-step explanation:

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when we "vertically stretch" a parabola, we are increasing the value of x.

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This means that we are looking for a function with a negative x value.

So, we are looking for a negative x-value that is multiplied by a number >1

The graph that fits our requirements is g(x) = -5x²

hope this helps!!

6 0
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Negative seven plus four
gulaghasi [49]

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-3

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