The number 72 lies between the perfect squares . So, the square root of 72 lies between the numbers , which means 72 is number.

Emma Drew 13 hearts and 20 circles what is the ratio of hearts to all shape

wariber [46]

9514 1404 393

Answer:

13 : 33

Step-by-step explanation:

hearts : all shapes = hearts : (hearts + circles) = 13 : (13 +20) = 13 : 33

4 0

3 years ago

2.A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation

Vesna [10]

Answer:

Step-by-step explanation:

Given that:

population mean = 10

standard deviation = 0.1

sample mean = 9.8 < x > 10.2

The z score can be computed as:

$z = \dfrac{\bar x - \mu}{\sigma}$

if x > 10.2

$z = \dfrac{10.2- 10}{0.1}$

$z = \dfrac{0.2}{0.1}$

z = 2

If x < 9.8

$z = \dfrac{9.8- 10}{0.1}$

$z = \dfrac{-0.2}{0.1}$

z = -2

The p-value = P (z ≤ 2) + P (z ≥ 2)

The p-value = P (z ≤ 2) + ( 1 - P (z ≥ 2)

p-value = 0.022750 +(1 - 0.97725)

p-value = 0.022750 + 0.022750

p-value = 0.0455

Therefore; the probability of defectives = 4.55%

the probability of acceptable = 1 - the probability of defectives

the probability of acceptable = 1 - 0.0455

the probability of acceptable = 0.9545

the probability of acceptable = 95.45%

4.55% are defective or 95.45% is acceptable.

sampling distribution of proportions:

sample size n=1000

p = 0.0455

The z - score for this distribution at most 5% of the items is;

$z = \dfrac{0.05 - 0.0455}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}$

$z = \dfrac{0.0045}{\sqrt{\dfrac{0.04342975}{1000}}}$

$z = \dfrac{0.0045}{\sqrt{4.342975 \times 10^{-5}}}$

z = 0.6828

The p-value = P(z ≤ 0.6828)

From the z tables

p-value = 0.7526

Thus, the probability that at most 5% of the items in a given batch will be defective = 0.7526

The z - score for this distribution for at least 85% of the items is;

$z = \dfrac{0.85 - 0.9545}{\sqrt{\dfrac{0.0455\times 0.9545}{1000}}}$

$z = \dfrac{-0.1045}{\sqrt{\dfrac{0.04342975}{1000}}}$

z = −15.86

p-value = P(z ≥ -15.86)

p-value = 1 - P(z < -15.86)

p-value = 1 - 0

p-value = 1

Thus, the probability that at least 85% of these items in a given batch will be acceptable = 1

6 0

3 years ago

Find the simple interest and amount when principal = Rs. 6000, rate = 6% per annum and time = 4 years

Alinara [238K]

Given:

Principal = Rs. 6000

Rate of simple interest = 6% per annum.

Time = 4 years

To find:

The simple interest and amount.

Solution:

Formula for simple interest:

$I=\dfrac{P\times r\times t}{100}$

Where, P is principal, r is the rate of interest and t is the number of years.

Putting P=6000, r=6 and t=4, we get

$I=\dfrac{6000\times 6\times 4}{100}$

$I=60\times 6\times 4$

$I=1440$

Now,

$Amount=Principal+Interest$

$Amount=6000+1440$

$Amount=7440$

Therefore, the simple interest is Rs. 7440 and the amount is Rs 7440.

7 0

3 years ago

What is the solution of the system? 7x+5y=19 and -7x-2y=-16 Need help ASAP

Stells [14]

Answer:

x = 2, y = 1

Step-by-step explanation:

7x + 5y = 19
-7x - 2y = -16

Use the elimination method to solve the system of equations. Add the terms from top to bottom. 7x and -7x cancel out.

0 + 3y = 3

Divide both sides by 3.

y = 1

Substitute 1 for y into the first equation.

7x + 5(1) = 19

7x + 5 = 19

Subtract 5 from both sides.

7x = 14

Divide both sides by 7.

x = 2

3 0

4 years ago

A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean

Dovator [93]

Answer:

B) 0.0069

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 normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes 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 $s = \frac{\sigma}{\sqrt{n}}$ .