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enot [183]
2 years ago
14

ZABD and DBC are supplementary angles

Mathematics
2 answers:
Papessa [141]2 years ago
8 0

<x=102°

Step-by-step explanation:

<x+78=180 being supplementary

<x=180-78=102

Levart [38]2 years ago
5 0

Answer:

f

Step-by-step explanation:

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How can subtracting the equations help you solve the system?
devlian [24]

System of equations subtraction method

In the addition/subtraction method, the two equations in the system are added or subtracted to create a new equation with only one variable. ... Substitute the variable back into one of the equations and solve for the other variable. Check the solution--it should satisfy both equations.

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3 years ago
Read 2 more answers
the letter "T" makes up an estimated 8% of a certain language. Assume this still correct. A random sample of 1000 letters is tak
rusak2 [61]

Answer:

0.242

Step-by-step explanation:

p = 0.08, q = 1 − p = 0.92, and n = 1000.

The mean and standard deviation are:

μ = p = 0.08

σ = √(pq/n) = 0.00858

The z score is:

z = (x − μ) / σ = -0.70

Using a calculator or z score table, the probability is:

P(Z < -0.70) = 0.242

8 0
3 years ago
In the rectangle below, E1=2x -2, FH=3x+6, and m 4IHG =35°.Find Gl and m LIEH
Tpy6a [65]

Recall that the diagonals of a rectangle bisect each other and are congruent, therefore:

\begin{gathered} FH=2EI, \\ GI=EI. \end{gathered}

Substituting the given expression for each segment in the first equation, we get:

3x+6=2(2x-2).

Solving the above equation for x, we get:

\begin{gathered} 3x+6=4x-4, \\ 3x+6+4=4x, \\ 3x+10=4x, \\ 4x-3x=10, \\ x=10. \end{gathered}

Substituting x=10 in the equation for segment EI, we get:

EI=2*10-2=20-2=18.

Therefore:

GI=18.

Now, to determine the measure of angle IEH, we notice that:

\Delta HFG\cong\Delta GEH,

therefore,

\measuredangle GHF\cong\measuredangle HGE.

Using the facts that the triangles are right triangles and that the interior angles of a triangle add up to 180° we get:

m\measuredangle IEH=90^{\circ}-35^{\circ}=55^{\circ}.

<h2>Answer: </h2>\begin{gathered} m\operatorname{\measuredangle}IEH=55^{\operatorname{\circ}}, \\ GI=18. \\  \end{gathered}

4 0
1 year ago
In a study of the accuracy of fast food drive-through orders, McDonald’s had 33 orders that were not accurate among 362 orders o
melomori [17]

Answer:

A. We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.

B. Null hypothesis:p=0.1  

Alternative hypothesis:p \neq 0.1  

C. z=\frac{0.0912 -0.1}{\sqrt{\frac{0.1(1-0.1)}{362}}}=-0.558  

D. z_{\alpha/2}=-1.96  z_{1-\alpha/2}=1.96

E. Fail to the reject the null hypothesis

F. So the p value obtained was a very high value and using the significance level given \alpha=0.05 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 true proportion of inaccurate orders is not significantly different from 0.1.  

Step-by-step explanation:

Data given and notation

n=362 represent the random sample taken

X=33 represent the number of orders not accurate

\hat p=\frac{33}{363}=0.0912 estimated proportion of orders not accurate

p_o=0.10 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)  

A: Write the claim as a mathematical statement involving the population proportion p

We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.

B: State the null (H0) and alternative (H1) hypotheses

Null hypothesis:p=0.1  

Alternative hypothesis:p \neq 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.

C: Find the test statistic

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

z=\frac{0.0912 -0.1}{\sqrt{\frac{0.1(1-0.1)}{362}}}=-0.558  

D: Find the critical value(s)

Since is a bilateral test we have two critical values. We need to look on the normal standard distribution a quantile that accumulates 0.025 of the area on each tail. And for this case we have:

z_{\alpha/2}=-1.96  z_{1-\alpha/2}=1.96

P value

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 bilateral test the p value would be:  

p_v =2*P(z  

E: Would you Reject or Fail to Reject the null (H0) hypothesis.

Fail to the reject the null hypothesis

F: Write the conclusion of the test.

So the p value obtained was a very high value and using the significance level given \alpha=0.05 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 true proportion of inaccurate orders is not significantly different from 0.1.  

6 0
3 years ago
-c = 3abc-a; solve for c
emmainna [20.7K]

Answer:

C= 12

Step-by-step explanation:

8 0
3 years ago
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