What is 0.0022 as a fraction show your work

A cubical house can hold 4096m of air .find the height of the house

iren2701 [21]

Answer:

16 m

Step-by-step explanation:

V = $s^{3}$

4096 = $s^{3}$

cube root of 4096 = 16

5 0

4 years ago

A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of ounces and a st

11111nata11111 [884]

Complete question is;

A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 127.9 ounces. Does the machine need to be? reset? Explain your reasoning.

(yes/no)?, it is (very unlikely/ likely) that you would have randomly sampled 35 cans with a mean equal to 127.9 ?ounces, because it (lies/ does not lie) within the range of a usual? event, namely within (1 standard deviation, 2 standard deviations 3 standard deviations) of the mean of the sample means.

Answer:

Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.

Step-by-step explanation:

We are given;

Mean: μ = 128

Standard deviation; σ = 0.2

n = 35

Now, formula for standard error of mean is given as;

se = σ/√n

se = 0.2/√35

se = 0.0338

Normally, the range of values should be within 2 standard deviations of mean. In this case, normal range of values will be;

μ ± 2se = 128 ± 0.0338

This gives; 127.9662, 128.0338

So, Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.

4 0

3 years ago

For each of the following pairs a, b of integers, find the greatest common divisor d of a and b and express d in the form ar + b

Ray Of Light [21]

Answer:

Step-by-step explanation:

We are to find gcd of a and b using linear combination algorithm

a) 7 and 11. 1= 3(7)-2(11). Hence GCD =1

b) -28 and -63:

$-63 = -2(28)-7\\28=-4(7)+0$

7=-2(-28)+(-63)

So 7 is GCD

c) $126 = 91+35\\91 = 2(35)+21\\35 = 21+14\\21 = 14+7\\14 = 2(7)$

So 7 is GCD and 7 = 7(91)-5(126)

d) 630 and 132

GCD is 6.

$630=132(4) +102\\132=102+30\\102 = 30(3)+12\\30=2(12)+6\\12=2(6)$

6=630(-9)+43(132)

e) 7245 and 4784

GCD is 23

23 = 7245(35)+4784(-53)

f) 6499 and 4288

GCD is 67

67 = 6499(-31)+4288(47)

3 0

4 years ago

A bottle maker believes that 33% of his bottles are defective. If the bottle maker is right, what is the probability that the pr

pogonyaev

Answer:

8.54% probability that the proportion of defective bottles in a sample of 730 bottles would differ from the population proportion by greater than 3%

Step-by-step explanation:

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.

For a proportion p in a sample of size n, we have that $\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}$

In this problem

$\mu = 0.33, \sigma = \sqrt{\frac{0.33*0.67}{730}} = 0.0174$

What is the probability that the proportion of defective bottles in a sample of 730 bottles would differ from the population proportion by greater than 3%

Either less than 0.33 - 0.03 = 0.3 or greater than 0.33 + 0.03 = 0.36.

Since the normal distribution is symmetric, and both these values are the same distance from the mean, we can find any of these probabilities and multiply by 2, since they are equal.

Probability of being lower than 0.3.

pvalue of Z when X = 0.3. So

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

$Z = \frac{0.3 - 0.33}{0.0174}$