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WARRIOR [948]
3 years ago
11

What is 35\42 in simplest form

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
4 0
To put a fraction into simplest form, you need to divide both the numerator and the denominator by the GCF of both of these numbers.

35 and 42 have a GCF of 7.  

So, if we divide
35/7=5
42/7=6

Therefore, 35/42 in simplest form is 5/6
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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 is the length of AB?<br> .<br> A9<br> B. 3<br> C.<br> 0.<br> D. 12
Tpy6a [65]

Answer:

D

Step-by-step explanation:

4X =2 X +6

=>X =  3

6 0
2 years ago
Read 2 more answers
Ed takes five 100-point tests in his algebra class. He scores 87, 85 and 87 points on the first three tests. If the scores of hi
trasher [3.6K]

Answer:

Step-by-step explanation:

When we take an average of something, we have to add up all the data on the somethings and then divide by the number of somethings we have. Ed takes 5 tests, and we have scores for them; we also have his current average. What we don't know for sure are 2 of the 5 test scores, but we have enough to determine what they are.

If one test has a score of x, and the other test is 3 points less than that, the score on that last test is x - 3. Putting all of that together into an average problem:

\frac{87+85+87+x+(x-3)}{5}=90 and simplfiying a bit:

\frac{256+2x}{5}=90. Multiply both sides by 5 to get

256 + 2x = 450; subtract 256 from both sides to get

2x = 194 and divide by 2:

x = 97

The one test score was a 97 and the other one, which was 3 less than that, was a 94.

3 0
3 years ago
The product of x and 6 is less than or equal to 24.
iren2701 [21]

Answer:

x= 4 or <

Step-by-step explanation:

5 0
3 years ago
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If each cube in the rectangular prism measures 1 cubic inch, what is the volume of the prism?
algol13
The answer for that is A. 40 cubic in
3 0
3 years ago
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