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3 years ago

If 101! = (99!)x, then x = ?

Mathematics

1 answer:

beks73 [17]3 years ago

5 0

$99!x=101!\ \ \ /:99!\\\\x=\frac{101!}{99!}\\\\x=\frac{99!\cdot100\cdot101}{99!}\\\\x=100\cdot101\\\\x=10\ 100$

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Factor? for 6xy−3x−8y+4

forsale [732]

6xy -3x -8y +4
3x (2y - 1 ) - 4 (2y -1)
(2y-1) (3x-4)

3 0

3 years ago

Read 2 more answers

The quality control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance

lisabon 2012 [21]

Answer:

The 95% confidence interval for the variance in the pounds of impurities would be $3.829 \leq \sigma^2 \leq 14.121$ .

Step-by-step explanation:

1) Data given and notation

$s^2 =6.62$ represent the sample variance

s=2.573 represent the sample standard deviation

$\bar x$ represent the sample mean

n=20 the sample size

Confidence=95% or 0.95

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical values.

The excel commands would be: "=CHISQ.INV(0.025,19)" "=CHISQ.INV(0.975,19)". so for this case the critical values are:

$\chi^2_{\alpha/2}=32.852$

$\chi^2_{1- \alpha/2}=8.907$

And replacing into the formula for the interval we got:

$\frac{(19)(6.62)}{32.852} \leq \sigma^2 \frac{(19)(6.62)}{8.907}$

$3.829 \leq \sigma^2 \leq 14.121$

So the 95% confidence interval for the variance in the pounds of impurities would be $3.829 \leq \sigma^2 \leq 14.121$ .

4 0

3 years ago

What is the value of the rate of change when we put a glass of water at room temperature in the freezer for 15 minutes, what is

alexgriva [62]

Answer:

Step-by-step explanation:

I do not understand your question very well but I think that the state of the glass of the water would be liquid and solid at the same time since the water would not freeze 100% and would be with small pieces of solid and some parts liquid, in terms of temperature, I think that at 5 minutes it would be 5 ° C and at 10 it would be 3-4 ° C the longer it is in the freezer the less its temperature will be

(All of that is my point of view)

Average temperature 30 °

So :

30 ÷ 15 = 2 °

30 ÷ 10 = 3 °

30 ÷ 5 = 6 °

3 0

3 years ago

The distance that a spring will stretch varies directly as the force applied to the spring. A force of 6060 pounds is needed to

Anestetic [448]

Answer:

Forced need to stretch 1414 inches = 129830.91 pounds

Step-by-step explanation:

Force ∝ Distance

F = KD where K is constant of proportionality

K = F/D = 6060/66 = 91.818182

Hence Force needed to stretch 1414 inches =

F = 6060/66 x 1414 = 129830.91 pounds

8 0

3 years ago

What multiples of 4 are not factors of 48?

drek231 [11]

48 = 48 * 1 = 24 * 2 = 16 * 3 = 12 * 4 = 8 * 6
So the factors of 48 are: 1, 2, 3, 4, 6, 89, 12, 16, 24 and 48.
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48,...
Answer:
Multiples of 4 that are not factors of 48 are: 20, 28, 32, 36, 40, 44.

3 0

3 years ago

Read 2 more answers