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Rufina [12.5K]
3 years ago
5

Zohar is using scissors to cut a rectangle with a length of 5x – 2 and a width of 3x + 1 out of a larger piece of paper. The per

imeter of the rectangle is 2(5x – 2) + 2(3x + 1). If x = 4 centimeters, what is the total distance Zohar needs to cut with the scissors?
Mathematics
1 answer:
enot [183]3 years ago
8 0
62 cm. plug in 4 for x. 2(5(4)-2))+2(3(4)+1))= 2(18)+2(13)= 36+26=62. Hope this helps!
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adelina 88 [10]
Find common denominators
2/20+3/20
then multiply 3x4=12/20
then 2x5=15/20
last add that 27/20
5 0
3 years ago
Find an equation of a line with a slope of 4 that passes through (-8, 11)
Rasek [7]

Answer:

y=4x+25

Step-by-step explanation:

y-11=4(x+8)

y-11=4x+36

y=4x+25

3 0
2 years ago
John has 8 cards that spell the word H O M E W O R K. She shuffles them and then places them face down. Assume she returns the c
finlep [7]

Answer:

The probability that I will choose a consonant is 62.50%.

Step-by-step explanation:

Given that John has 8 cards that spell the word H O M E W O R K, and he shuffles them and then places them face down, to determine what is the probability he will choose a consonant the following calculation must be performed:

Vowels: 3

Consonants: 5

5/8 = X

0.625 = X

0.625 x 100 = 62.50

Therefore, the probability that I will choose a consonant is 62.50%.

3 0
2 years ago
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation
Wewaii [24]

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

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 establishes 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.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that \mu = 14, \sigma = 2

Sample of 100:

This means that n = 100, s = \frac{2}{\sqrt{100}} = 0.2

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

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

By the Central Limit Theorem

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

Z = \frac{14.2 - 14}{0.2}

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

6 0
3 years ago
What does the ' mean in 12 degrees and 15'
tino4ka555 [31]
The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median<span>" is the "middle" value in the list of numbers.</span>
3 0
3 years ago
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