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3 years ago

Help fast please???

Mathematics

2 answers:

Makovka662 [10]3 years ago

5 0

There is a rule that specifies whether or not the triangle exist.

Rule: When added, the two smaller sides of the triangle must be greater than the longest side.

In this case answer C fits the choice.

Since the small sides are 8cm and 15cm

8 + 15 = 23

And the biggest side of the triangle is 22

23 > 22

Answer = C. 8cm, 5cm, 10cm

blagie [28]3 years ago

4 0

The answer would be C. 8 cm, 15 cm, 22cm.
The rule is that the two smaller sides when added, have to be bigger than the largest side. 8 + 15= 23 and the largest side is 22. 23 is greater than 22. The other options do not work with this rule

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Vinvika [58]

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Step-by-step explanation:

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3 years ago

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Step-by-step explanation:

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3 years ago

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3 years ago

The viscosity of a liquid detergent is supposed to average 800 centistokes at 25° C. A random sample of 16 batches of detergent

meriva

Answer:

a) Null hypothesis: $\mu = 800$

Alternative hypothesis: $\mu \neq 800$

b) $z=\frac{812-800}{\frac{25}{\sqrt{16}}}=1.92$

c) $p_v =2*P(z>1.92)=0.0548$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not different from the value of 800.

d) $812- 1.96 \frac{25}{\sqrt{16}}=799.75$

$812+ 1.96 \frac{25}{\sqrt{16}}=824.25$

Since the confidence interval contains the value 800 this result agrees with the result obtained in the hypothesis test we fail to reject the null hypothesis that the true mean is 800

Step-by-step explanation:

Data given and notation

$\bar X=812$ represent the mean for the sample

$\sigma=25$ represent the standard deviation for the population

$n=16$ sample size

$\mu_o =800$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

a) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the true mean is different from 800 centistokes:

Null hypothesis: $\mu = 800$

Alternative hypothesis: $\mu \neq 800$

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

b) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{812-800}{\frac{25}{\sqrt{16}}}=1.92$

c) Calculate the P-value

Since is a two tailed test the p value would be:

$p_v =2*P(z>1.92)=0.0548$

Conclusion

d) Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing we got:

$812- 1.96 \frac{25}{\sqrt{16}}=799.75$

$812+ 1.96 \frac{25}{\sqrt{16}}=824.25$

Since the confidence interval contains the value 800 this result agrees with the result obtained in the hypothesis test we fail to reject the null hypothesis that the true mean is 800

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4 years ago