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2 years ago

Solve this inequality j/4 - 8 < 4

1 answer:

5 0

J/4 - 8 < 4
 + 8 + 8 *add 8 to both sides to cancel -8.
j/4 < 12
*4/1 *4/1 *multiply 4/1 to both sides to cancel 1/4
j < 48

j should be less than 48 to make the inequality true.

example: j = 47
j/4 - 8 < 4
47/4 - 8 < 4
11.75 - 8 < 4
3.75 < 4

Any number below 48 will end up with an answer less than 4. if j is 48 and above, the inequality is false because the answer arrived at will be equal to or greater than 4.

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Two machines are used for filling glass bottles with a soft-drink beverage. The filling process have known standard deviations s

stellarik [79]

Answer:

a. We reject the null hypothesis at the significance level of 0.05

b. The p-value is zero for practical applications

c. (-0.0225, -0.0375)

Step-by-step explanation:

Let the bottles from machine 1 be the first population and the bottles from machine 2 be the second population.

Then we have $n_{1} = 25$ , $\bar{x}_{1} = 2.04$ , $\sigma_{1} = 0.010$ and $n_{2} = 20$ , $\bar{x}_{2} = 2.07$ , $\sigma_{2} = 0.015$ . The pooled estimate is given by

$\sigma_{p}^{2} = \frac{(n_{1}-1)\sigma_{1}^{2}+(n_{2}-1)\sigma_{2}^{2}}{n_{1}+n_{2}-2} = \frac{(25-1)(0.010)^{2}+(20-1)(0.015)^{2}}{25+20-2} = 0.0001552$

a. We want to test $H_{0}: \mu_{1}-\mu_{2} = 0$ vs $H_{1}: \mu_{1}-\mu_{2} \neq 0$ (two-tailed alternative).

The test statistic is $T = \frac{\bar{x}_{1} - \bar{x}_{2}-0}{S_{p}\sqrt{1/n_{1}+1/n_{2}}}$ and the observed value is $t_{0} = \frac{2.04 - 2.07}{(0.01246)(0.3)} = -8.0257$ . T has a Student's t distribution with 20 + 25 - 2 = 43 df.

The rejection region is given by RR = {t | t < -2.0167 or t > 2.0167} where -2.0167 and 2.0167 are the 2.5th and 97.5th quantiles of the Student's t distribution with 43 df respectively. Because the observed value $t_{0}$ falls inside RR, we reject the null hypothesis at the significance level of 0.05

b. The p-value for this test is given by $2P(T$ 0 (4.359564e-10) because we have a two-tailed alternative. Here T has a t distribution with 43 df.

c. The 95% confidence interval for the true mean difference is given by (if the samples are independent)

$(\bar{x}_{1}-\bar{x}_{2})\pm t_{0.05/2}s_{p}\sqrt{\frac{1}{25}+\frac{1}{20}}$ , i.e.,

$-0.03\pm t_{0.025}0.012459\sqrt{\frac{1}{25}+\frac{1}{20}}$

where $t_{0.025}$ is the 2.5th quantile of the t distribution with (25+20-2) = 43 degrees of freedom. So

$-0.03\pm(2.0167)(0.012459)(0.3)$ , i.e.,

(-0.0225, -0.0375)

8 0

2 years ago

What 2 numbers divide to get 375 while multiplying to equal 38.4?

Rus_ich [418]

Answer:

Well, 375 is a composite number.

Prime factorization: 375 = 3 x 5 x 5 x 5, which can be written 375 = 3 x (5^3)

The exponents in the prime factorization are 1 and 3.

Factors of 375: 1, 3, 5, 15, 25, 75, 125, 375.

Factor pairs: 375 = 1 x 375, 3 x 125, 5 x 75, or 15 x 25. Good Luck!

5 0

2 years ago

I need help please

gulaghasi [49]

Answer:

Step-by-step explanation:

AO = OC

3x - 4 = 8

x = 4

7 0

2 years ago

Read 2 more answers

A BMW that cost $71,000 in 2003 depreciates in value about 15% a year. How much was it worth in 2013?

N76 [4]

100-15= 85%

2013-2003= 10 years

$71,000 * (0.85^10yrs)= $13,978.08

Did this make sense or would you like me to explain some more about something you are still not understanding? Please comment below :)

6 0

2 years ago

Help me pleaseee!!!☹️

zavuch27 [327]

Answer:

i can't understand it as well

7 0

2 years ago