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ch4aika [34]
3 years ago
15

A line goes through the point (6,-2) and has a slope of -3. What is the value of a if the point (a,7) lies on the line?​

Mathematics
2 answers:
Sindrei [870]3 years ago
7 0

m =  y1 - y2 / x1 x2

-3 = -2 - 7 / 6 - a

-3 = -9 / 6 - a

-3 (6 - a)=-9

-18 + 3a = -9

3a = - 9 + 18

a = 9 / 3

a = 3

Vikki [24]3 years ago
3 0

Answer:

<h2>a = 3</h2>

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

m =  \frac{ y_2 - y _ 1}{x_ 2 - x_ 1}  \\

From the question the slope is - 3

To find the value of a we have

- 3 =  \frac{7 -  - 2}{a - 6}  \\  - 3 =  \frac{7 + 2}{a - 6}  \\  - 3(a - 6) = 9 \\  - 3a + 18 = 9 \\  - 3a = 9 - 18 \\  - 3a =  - 9

Divide both sides by - 3

\frac{ - 3a}{ - 3}  =  \frac{ - 9}{ - 3}  \\

We have the final answer as

<h3>a = 3</h3>

Hope this helps you

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r-ruslan [8.4K]

Answer:

hope this helps u!

Step-by-step explanation:

8 0
2 years ago
In a​ survey, 32​% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result
adoni [48]

Answer:

z=\frac{0.29 -0.32}{\sqrt{\frac{0.32(1-0.32)}{210}}}=-0.932  

p_v =P(z  

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 proportion of  pet owners contacted by telephone is NOT significantly lower than 0.32

Step-by-step explanation:

Data given and notation

n=210 represent the random sample taken

X=61 represent the number of pet owners contacted by telephone

\hat p=\frac{61}{210}=0.29 estimated proportion of  pet owners contacted by telephone

p_o=0.32 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 proportions is lower than 0.32.:  

Null hypothesis:p \geq 0.32  

Alternative hypothesis:p < 0.32  

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 requires we can replace in formula (1) like this:  

z=\frac{0.29 -0.32}{\sqrt{\frac{0.32(1-0.32)}{210}}}=-0.932  

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  

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 proportion of  pet owners contacted by telephone is NOT significantly lower than 0.32

3 0
3 years ago
Three roads lead into a stadium's parking areas. Each road has four lanes (two in each direction) with a capacity oftwo parking
andrew-mc [135]

Answer:

Number of attendants required are 16.

10000 vehicles will take 8 hours 20 min. to enter the parking area.

Step-by-step explanation:

Attendants required to park cars for each type a lot = 2  

Attendants required to park cars for 6 type a lots = 2×6 = 12

Attendants required to park cars for each type b lot = 1

Attendants required to park cars for 4 type b lot = 4×1 = 4

So, total attendants required are  12+4 = 16.


total number of roads = 3

number of lanes for 1 road = 4

number of lanes for 3 roads = 3×4 = 12


number of vehicles one lane can park = 100 /hour

number of vehicles 12 lanes can park = 12×100 = 1200/hour


So, 1200 vehicles takes parking area for 60 min.

10000 vehicles takes parking area for  \frac{10000\times 60}{1200} min.

                                                               = 500 minutes.


60 min. = 1 hour

500 min. = \frac{500}{60} hours = 8 hours 20 min.

So, 10000 vehicles will take 8 hours 20 min. to enter the parking area.                                                    

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Answer:

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Step-by-step explanation:

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5 0
3 years ago
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