There are 5 blue, 5 green and 5 red books on a shelf. Two books are selected randomly. What is the probability of

Solve the system using elimination. 2x + 3y = -2 3x - 6y = 18

ohaa [14]

Answer:

dd the equations in order to solve for the first variable. Plug this value into the other equations in order to solve for the remaining variables.

Point Form:

(

2

,

−

2

)

Equation Form:

x

=

2

,

y

=

−

2

Step-by-step explanation:

8 0

3 years ago

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Which of the following is an irrational number? 5 / 4 √5 / 7 1/ 8 3 / 5

Xelga [282]

Answer: $\sqrt{5} /7$

Step-by-step explanation:

5/4 is not an irrational number because it is already in a fraction the same as 1/8 and 3/5.

The square root of 5 is not rational because it cannot be converted to a fraction or in other words is not a perfect square.

5 0

4 years ago

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Which statement follows from the given theorem? Theorem: The diagonal of a parallelogram divides it into two congruent triangles

Ivenika [448]

Answer:

SSS

Step-by-step explanation:

the dividing line would give the triangles the same length for one side, the side it divided, and then it says the triangles are congruent, meaning they are both the same triangle.

8 0

4 years ago

I need helppppp <img src="https://tex.z-dn.net/?f=%20-%2029%20%5Cleqslant%20n%20-%2016" id="TexFormula1" title=" - 29 \leqsla

EastWind [94]

Answer: where’s the question?

Step-by-step explanation:

7 0

3 years ago

Last year, a comprehensive report stated that 28% of businesses in the northeast of Ohio were considered highly profitable. This

Alik [6]

Answer:

$z=\frac{0.38 -0.28}{\sqrt{\frac{0.28(1-0.28)}{50}}}=1.575$

$p_v =2*P(z>1.575)=0.115$

So the p value obtained was a very high value and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of businesses were highly profitable is not significantly different from 0.28 or 28%.

Step-by-step explanation:

Data given and notation

n=50 represent the random sample taken

X=19 represent the businesses were highly profitable

$\hat p=\frac{19}{50}=0.38$ estimated proportion of businesses were highly profitable

$p_o=0.28$ 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 of businesses were highly profitable is different from 0.28 or no, the system of hypothesis is.:

Null hypothesis: $p=0.28$

Alternative hypothesis: $p \neq 0.28$

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 $p_o$ .

Calculate the statistic

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

$z=\frac{0.38 -0.28}{\sqrt{\frac{0.28(1-0.28)}{50}}}=1.575$

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 $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(z>1.575)=0.115$

So the p value obtained was a very high value and using the significance level given $\alpha=0.01$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of businesses were highly profitable is not significantly different from 0.28 or 28%.

4 0

4 years ago