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Sliva [168]
3 years ago
10

Find the length of the midsegment.

Mathematics
1 answer:
STALIN [3.7K]3 years ago
7 0

Answer:

50

Step-by-step explanation:

The length of the midsegment is half the length of the base segment, so you have ...

... 2(6x +2) = 2x +84

... 10x = 80 . . . . . . . . . simplify, subtract 2x+4

... x = 8

The length of the midsegment is 6·8+2 = 50.

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The midpoint of RS¯¯¯¯¯¯¯ is M. Use the given endpoint R(23, 14) and midpoint M(13, 8) to find the coordinates of the other endp
Oksanka [162]

The coordinates of other endpoint S is (3, 2)

<h3><u>Solution:</u></h3>

Given that midpoint of RS is M

Given endpoint R(23, 14) and midpoint M(13, 8)

To find: coordinates of the other endpoint S

<em><u>The formula for midpoint is given as:</u></em>

For a line containing containing two points (x_1, y_1) and (x_2, y_2) midpoint is given as:

m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)

Here in this problem,

m(x, y) = (13, 8)

(x_1, y_1) = (23, 14)\\\\(x_2, y_2) = ?

Substituting the given values in above formula, we get

(13,8)=\left(\frac{23+x_{2}}{2}, \frac{14+y_{2}}{2}\right)

Comparing both the sides we get,

\begin{aligned}&13=\frac{23+x_{2}}{2} \text { and } 8=\frac{14+y_{2}}{2}\\\\&26=23+x_{2} \text { and } 16=14+y_{2}\\\\&x_{2}=3 \text { and } y_{2}=2\end{aligned}

Thus the coordinates of other endpoint S is (3, 2)

8 0
3 years ago
The manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour. (a-1) At α = .05 i
fenix001 [56]

Answer:

Null hypothesis:\mu \geq 250        

Alternative hypothesis:\mu < 250  

p_v =P(t_{15}    

If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not significantly lower than 530 at 5% of significance.      

Step-by-step explanation:

1) Data given and notation        

\bar X=510 represent the mean for the sample    

s=50 represent the standard deviation for the sample  

n=16 sample size        

\mu_o =530 represent the value that we want to test  

\alpha represent the significance level for the hypothesis test.      

t would represent the statistic (variable of interest)        

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

2) State the null and alternative hypotheses.        

We need to conduct a hypothesis in order to determine if the claim thet the handle on average is 530 bags per hour:      

Null hypothesis:\mu \geq 530        

Alternative hypothesis:\mu < 530        

We don't know the population deviation and the sample size is lees than 30, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:        

t=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)        

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

3) Calculate the statistic        

We can replace in formula (1) the info given like this:        

t=\frac{510-530}{\frac{50}{\sqrt{16}}}=-1.60        

4) Calculate the critical value

We need to begin calculating the degrees of freedom

df=n-1=16-1=15

The critical value for this case would be :

P(t_{15}

The value of a that satisfy this on the normal standard distribution is a=-1.75 and would be the critical value on this case zc=-1.75

5) Calculate the P-value        

Since is a one-side upper test the p value would be:        

p_v =P(t_{15}    

6) Conclusion        

If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we FAIL to reject the null hypothesis, and the the actual mean is not significantly lower than 530 at 5% of significance.      

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Write 0.624 as a percent and as a simplified fraction.
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The function f(x) = x^2 - 2x + 8 is transformed such that g(x) = f(x-2). Find the vertex of g(x).
Serjik [45]

Answer:

Step-by-step explanation:

Since g(x) is f(x-2), every time there is a "x" in the f(x) equation, substitute "x-2". So g(x) would be (x-2)^2-2(x-2)+8. Use the method of trial and error: substitute x as 1,-1, and 3, until you found the right vertex. The answer is B (3,7).

7 0
3 years ago
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