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4 years ago

NEED HELP ASAP!!!!!!!!!!!

Mathematics

2 answers:

liubo4ka [24]4 years ago

5 0

Answer:

Step-by-step explanation:

I took the test on E2020.

zhenek [66]4 years ago

4 0

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC ⇒ 2nd answer

Step-by-step explanation:

Let us revise the trigonometry ratios in the right triangle ABC, where B is the right angle, AC is the hypotenuse, AB and BC are the legs of the triangle

The trigonometry ratios of the ∠BAC, the opposite side to this angle is BC and the adjacent side to it is AB are

$sin(BAC)=\frac{opposite}{hypotenuse}=\frac{BC}{AC}$
$cos(BAC)=\frac{adjacent}{hypotenuse}=\frac{AB}{AC}$
$tan(BAC)=\frac{opposite}{adjacent}=\frac{BC}{AB}$

In Δ ABC

∵ ∠ BCA is a right angle

∴ The hypotenuse is AB

∵ The adjacent side to ∠CAB is AC

∵ The opposite side to ∠CAB is BC

∵ AB = 13 units ⇒ hypotenuse

∵ CB = 12 units ⇒ opposite

∵ AC = 5 units ⇒ adjacent

- Let us find the trigonometry ratios of angle BAC

∵ m∠CAB is x

∵ $sin(x)=\frac{BC}{AB}$

∴ $sin(x)=\frac{12}{13}$

∴ $x=sin^{-1}(\frac{12}{13})$

∵ $cos(x)=\frac{AC}{AB}$

∴ $cos(x)=\frac{5}{13}$

∴ $x=cos^{-1}(\frac{5}{13})$

∵ $tan(x)=\frac{BC}{AC}$

∴ $tan(x)=\frac{12}{5}$

∴ $x=tan^{-1}(\frac{12}{5})$

The equation $x=tan^{-1}(\frac{12}{5})$ can be used to find the measure of ∠BAC

Learn more:

You can learn more about the trigonometry ratios in brainly.com/question/4924817

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A manufacturer of nickel-hydrogen batteries randomly selects 100 nickel plates for test cells, cycles them a specified number of

kolezko [41]

Answer:

a) Parameter of interest $p$ representing the true proportion of the plates have blistered.

b) Null hypothesis: $p\leq 0.1$

Alternative hypothesis: $p > 0.1$

c) $z=\frac{0.14 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=1.33$

d) For this case we need to find a value in the normal standard distribution that accumulates 0.1 of the area in the right tail and for this case is:

$z_{critc}= 1.28$

e) For this case since our calculated value is higher than the critical value 1.33>1.28 we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly higher than 0.1

f) $p_v =P(z>1.33)=0.0917$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 10% of significance the true proportion is higher than 0.1 or 10%

Step-by-step explanation:

Data given and notation

n=100 represent the random sample taken

Part a

Parameter of interest $p$ representing the true proportion of the plates have blistered.

X=14 represent the number of the plates have blistered.

$\hat p=\frac{14}{100}=0.14$ estimated proportion of the plates have blistered.

$p_o=0.1$ is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

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

Part b: Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that more than 10% of all plates blister under such circumstances.:

Null hypothesis: $p\leq 0.1$

Alternative hypothesis: $p > 0.1$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Part c: Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.14 -0.1}{\sqrt{\frac{0.1(1-0.1)}{100}}}=1.33$

Part d: Rejection region

For this case we need to find a value in the normal standard distribution that accumulates 0.1 of the area in the right tail and for this case is:

$z_{critc}= 1.28$

Part e

For this case since our calculated value is higher than the critical value 1.33>1.28 we have enough evidence to reject the null hypothesis and we can conclude that the true proportion is significantly higher than 0.1

Part f

Since is a right taild test the p value would be:

$p_v =P(z>1.33)=0.0917$

7 0

3 years ago

Line I is a perpendicular bisector

kolezko [41]

Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the Perpendicular Bisector Theorem below.

<h3>What is the perpendicular bisector theorem?</h3>

According to the theorem of perpendicular bisector, any locus on the perpendicular bisector is equidistant from the terminal points of the line segment on which it is created.

Thus, Line I is a perpendicular bisector because it bisects another line at right angles via the point of intersection or midpoint. See the attached image.

Learn more about perpendicular bisectors at:
brainly.com/question/11006922
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