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Pepsi [2]
2 years ago
12

Figure ABCD is a parallelogram. What is the product of xy?

Mathematics
1 answer:
Andrei [34K]2 years ago
5 0

Answer:

A) 2695.

Step-by-step explanation:

Opposite angels of a parallelogram are equal.

Also (x - y) = 42   (interior alternate angles)

So we have the system of equations:

x + y = 112

x - y = 42       Adding the 2 equations:

2x = 154

x = 77.

Plug x = 77 in the first equation:

77 + y = 112

y = 112 - 77 = 35.

and

xy =  77 * 35 =  2695.

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Answer:

Coordinates: (2, -1)

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Good luck!

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Find the measure of angle X.
densk [106]

Answer:

x = 23 degrees

Because if you look at diagram x is vertical to angle FBC, and angle FEC and angle EBA are alternate interior angles so they are equal to each other, and AC is a straight line which means it equals to 180 degrees.

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aleksandrvk [35]
The answer is 10w.

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6 0
3 years ago
The Damon family owns a large grape vineyard in western New York along Lake Erie. The grapevines must be sprayed at the beginnin
vazorg [7]

Answer:

z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784    

p_v =2*P(Z>1.784) =0.074  

Comparing the p value with 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 say that the two proportions differes at 10% of significance.

Step-by-step explanation:

Data given and notation  

X_{1}=42 represent the number of infested vines for Pernod5

X_{2}=22 represent the number of infested vines for Action

n_{1}=440 sample of Pernod5

n_{2}=360 sample of Action

\hat p_{1}=\frac{42}{440}=0.0955 represent the proportion of residents of  infested vines for Pernod5

\hat p_{2}=\frac{22}{360}=0.0611 represent the proportion of infested vines for Action

z would represent the statistic (variable of interest)  

p_v represent the value for the test (variable of interest)  

\alpha=0.1 significance level given

Concepts and formulas to use  

We need to conduct a hypothesis in order to check if is there is a difference between thw two population proportions, the system of hypothesis would be:  

Null hypothesis:p_{1} - p_{2}=0  

Alternative hypothesis:p_{1} - p_{2} \neq 0  

We need to apply a z test to compare proportions, and the statistic is given by:  

z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{1}})}}   (1)  

Where \hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{42+22}{440+360}=0.08  

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.  

Calculate the statistic  

Replacing in formula (1) the values obtained we got this:  

z=\frac{0.0955-0.0611}{\sqrt{0.08(1-0.08)(\frac{1}{440}+\frac{1}{360})}}=1.784    

Statistical decision

Since is a two sided test the p value would be:  

p_v =2*P(Z>1.784) =0.074  

Comparing the p value with 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 say that the two proportions differes at 10% of significance.

4 0
4 years ago
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