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3 years ago

AC = 22, BC = x + 14, and AB = x + 10.Find x.

Mathematics

2 answers:

Luden [163]3 years ago

7 0

Hi there! :)

Answer:

$\huge\boxed{x = -1}$

Given:

AC = 22

BC = x + 14

AB + x + 10

AC is equivalent to AB + BC, therefore:

AC = AB + BC

Substitute in the expressions:

22 = (x + 10) + (x + 14)

Combine like terms:

22 = 2x + 24

Subtract 24 from both sides:

-2 = 2x

Divide both sides by 2:

x = -1

Dmitry_Shevchenko [17]3 years ago

4 0

Given : AC = 22, BC = x + 14, and AB = x + 10.

$\rule{130}1$

Solution :

$:\implies\sf AB + BC = AC\:\:\:\:\Bigg\lgroup \bf{Segment\: addition\: postulate}\Bigg\rgroup \\\\\\:\implies\sf (x + 10) + (x + 14) = 22\:\:\:\:\Bigg\lgroup \bf{Substitution}\Bigg\rgroup\\\\\\:\implies\sf 2x + 24 = 22\:\:\:\:\Bigg\lgroup \bf{Simplify\:(added\:like\:term)}\Bigg\rgroup\\\\\\:\implies\sf 2x = -2\\\\\\:\implies\sf x = \dfrac{-2}{2}\\\\\\:\implies\underline{\boxed{\pink{\sf x = -1}}}$

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Read 2 more answers

A sample of 1200 computer chips revealed that 45% of the chips fail in the first 1000 hours of their use. The company's promotio

yaroslaw [1]

Answer:

$z=\frac{0.45 -0.48}{\sqrt{\frac{0.48(1-0.48)}{1200}}}=-2.08$

$p_v = P(Z$

So the p value obtained was a low value and using the significance level given $\alpha=0.05$ 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 5% of significance the proportion of chips that fail in the first 1000 hours of their use is not significantly less than 0.48.

Step-by-step explanation:

Data given and notation

n=1200 represent the random sample taken

$\hat p=0.45$ estimated proportion of chips that fail in the first 1000 hours of their use

$\mu_0 =0.48$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

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

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion si less then 0.48:

Null hypothesis: $p\geq 0.48$

Alternative hypothesis: $p < 0.48$

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 is significantly different from a hypothesized value .

Calculate the statistic

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

$z=\frac{0.45 -0.48}{\sqrt{\frac{0.48(1-0.48)}{1200}}}=-2.08$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

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

$p_v = P(Z$

6 0

4 years ago

AC = 22, BC = x + 14, and AB = x + 10.Find x.​

AC = 22, BC = x + 14, and AB = x + 10.Find x.