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2 years ago

Solve the right triangle. Round your answers to the nearest tenth.

Mathematics

1 answer:

madam [21]2 years ago

5 0

Answer:

B = 44°

c = 27.8

b = 19.3

Step-by-step explanation:

m∡B = 180 - (90 + 46)

sin46° = 20/c

c = 20 / sin 46°

c = 27.8

b² + 20² = 27.8²

b² + 400 = 772.84

b² = 372.84

b = $\sqrt{372.84}$

b = 19.3

You might be interested in

A corner of a rectangle is cut, creating a trapezoid.

forsale [732]

Answer:

the last option of 135°.

Step-by-step explanation:

The total degree of the rectangle is 360°. But it was sliced, so with the remaining measurements, subtract each of them from 360°.

90°+90°+45°+x°=360°

225°+x°=360° add all of the values on the left side, then subtract 225 on both sides to solve for the value of x°.

x°=135°

4 0

2 years ago

23. A certain type of gasoline is supposed to have a mean octane rating of at least 90. Suppose measurements are taken on of 5 r

Nostrana [21]

Answer:

a) $p_v =P(Z$

b) Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

c) $P(\bar X >90)=1-P(Z$

$1-P(Z$

d) For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

Step-by-step explanation:

Previous concepts and data given

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

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}$

$\bar X=88.96$ represent the sample mean

$s=1.011$ represent the sample standard deviation

n=5 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is less than 90, the system of hypothesis would be:

Null hypothesis: $\mu \geq 90$

Alternative hypothesis: $\mu < 90$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t 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".

Calculate the statistic

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

$z=\frac{88.96-90}{\frac{0.8}{\sqrt{5}}}=-2.907$

Part a

P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=5-1 = 4$

Then since is a left tailed test the p value would be:

$p_v =P(Z$

Part b

Since $p_v$ we can reject the null hypothesis at the significance level given. So based on this we can commit type of Error I.

Because Type I error " is the rejection of a true null hypothesis".

Part c

We want this probability:

$P(\bar X$

The best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}$

If we apply this formula to our probability we got this:

$P(\bar X >90)=1-P(Z$

$1-P(Z$

Part d

For this case we need a z score that accumulates 0.02 of the area on the right tail and 0.98 on the left tail and this value is z=2.054

And we can use this formula:

$2.054=\frac{90-89}{\frac{0.8}{\sqrt{n}}}$

And if we solve for n we got:

$n = (\frac{2.054 *0.8}{1})^2=2.7 \approx 3$

7 0

2 years ago

Which of the following describes the graph of {x | 2 < x < 2}? just a closed circle on 2 the entire number line an open ci

julia-pushkina [17]

Answer: the correct answer would be no solution.

5 0

2 years ago

Read 2 more answers

Judges in some figure skating

kykrilka [37]

Answer:

4 jumps

Step-by-step explanation:

5 points per jump and 20 points in total.

20/5 = 4

5 0

2 years ago

. Using the rounding off technique, find the rough estimated difference of the given decimals.

nikitadnepr [17]

Answer:

19. 188

20. 18

21. 5

21. 4

Step-by-step explanation:

634.58 would round up to 635 and 436.79 would round up to 437.

20. 37.86 would round up to 38 and 19.92 would round up to 20.

21. 14.49 would round to 14 and 8.59 would round up to 9.

22. 7.45 would round down to 7 and 2.93 would round up to 3.

3 0

2 years ago