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patriot [66]
3 years ago
12

Noah and Maggie are making a rectangular picture frame.They want the length of the frame to be three inches longer than the widt

h. If the perimeter is 42”, what are the dimensions of their frame?
Mathematics
1 answer:
zalisa [80]3 years ago
7 0

Answer:

9 inches by 12 inches

Step-by-step explanation:

So let's say <em>L</em>=length and <em>W</em>=width.

Since the problem states that the length should be 3 inches longer than the width, <em>L</em><em>=</em><em> </em>W+3

And the formula to find the perimeter of a rectangle is 2L+2W

so plug in W+3 for L and you get 2(W+3)+2W

Then distribute

2W+6+2W

Combine like-terms

4W+6

And the problem states the perimeter is 42 inches so,

4W+6=42

Subtract 6 to both sides

4W=36

Divide by 4 to both sides

W=9

So the width is 9

And to get the length, plug in 9 for W in L=W+3

L=9+3

L=12

So the length is 12

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small car pays less bigger car pays more

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Jerry is a judge. He hears 5 cases in 2 3/8 hours. How many cases does he hear per hour
Serggg [28]

Answer:

Jerry does 2.11 cases per hour (Rounded to 2 decimal places). As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.

Step-by-step explanation:

to find the number of cases per hour, we have to divide the number of cases by number of hours taken for those cases,

Number of cases per hour = \frac{5cases}{2\frac{3}{8} hours}

                                             =\frac{5}{\frac{19}{8} } \\ cases per hour

                                             =\frac{5*8}{19} cases per hour

                                             =\frac{40}{19} cases per hour

                                              =2.11 cases per hour (Rounded to 2 decimal places)

As we cannot do 0.11 cases. We can say Jerry does 2 cases per hour.

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3 years ago
F function g has the factors (x − 7) and (x + 6), what are the zeros of function g?
Allisa [31]

Answer:

Zeros are 7 and -6

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What is the place if 6 in 34.76
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3 years ago
Read 2 more answers
A simple random sample of 110 analog circuits is obtained at random from an ongoing production process in which 20% of all circu
telo118 [61]

Answer:

64.56% probability that between 17 and 25 circuits in the sample are defective.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

n = 110, p = 0.2

So

\mu = E(X) = np = 110*0.2 = 22

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{110*0.2*0.8} = 4.1952

Probability that between 17 and 25 circuits in the sample are defective.

This is the pvalue of Z when X = 25 subtrated by the pvalue of Z when X = 17. So

X = 25

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

Z = \frac{25 - 22}{4.1952}

Z = 0.715

Z = 0.715 has a pvalue of 0.7626.

X = 17

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

Z = \frac{17 - 22}{4.1952}

Z = -1.19

Z = -1.19 has a pvalue of 0.1170.

0.7626 - 0.1170 = 0.6456

64.56% probability that between 17 and 25 circuits in the sample are defective.

4 0
3 years ago
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