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sdas [7]
2 years ago
6

determine the equation of the straight line which passes through the point 1 and 5 and is perpendicular to the line 3x + y is eq

ual to 4​
Mathematics
1 answer:
xenn [34]2 years ago
7 0

The straight line is perpendicular to y = -3x + 4.

Therefore, the gradient of the straight line must be 3.

The equation of the straight line is y = 3x + 2.

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Josh has 36 postcards from national parks he visited. He wants to put them in a
Salsk061 [2.6K]

Answer:

He needs 9 pages

Step-by-step explanation:

8 will be full and 1 will have 2 extra

36 divided by 4

8 with 2 left over so 9 pages

6 0
2 years ago
Read 2 more answers
Solve the equation 4s2+32s=60 by completing the square
lord [1]

Answer:

s = -4 ± √31

Step-by-step explanation:

Given 4s^{2} + 32s = 60

divide by 4 throughout

s^{2}  + 8s = 15\\s^{2} + 8s + (\frac{8}{2}) ^{2}  = 15 + (\frac{8}{2}) ^{2}

 (s + 4)^{2}  = 31\\s + 4 = \sqrt{31}

s = -4 ± √31

7 0
3 years ago
Solve 5n^2=5 with the quadratic formula
Yanka [14]

Answer:

n = 1

Step-by-step explanation:

First, rearrange the equation to standard form 0 = ax² + bx + c, when everything equals 0.

5n² = 5

5n² - 5 = 0

State the variables a, b and c.

a = 5;  b = 0;  c = -5

Substitute a, b, and c into the quadratic formula.

n = \frac{-b ±\sqrt{b^{2}-4ac} }{2a}

n = \frac{-0 ±\sqrt{0^{2}-4(5)(-5)} }{2(5)}   Substitute

n = \frac{\sqrt{100} }{10}   Simplify inside the √ and bottom

n = \frac{10}{10}  Simplify the top

n = 1  Final answer

Therefore the solution is n = 1.

The quadratic formula usually is written with x, but it can be solved with any variable in standard form.

3 0
3 years ago
A machine that puts corn flakes into boxes is adjusted to put an average of 15.6 ounces into each box, with standard deviation o
Anastaziya [24]

Answer:

\chi^2 =\frac{15-1}{0.0676} 0.1521 =31.5

p_v =P(\chi^2_{14} >31.5)=0.0047

If we compare the p value and the significance level assumed of 0.05 we see that p_v so on this case we have enough evidence in order to reject the null hypothesis at the significance level provided. And that means that the population variance is significantly higher than 0.26^2=0.0676.

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

n=15 represent the sample size

\alpha represent the confidence level  

s^2 =0.39^2 =0.1521 represent the sample variance obtained

\sigma^2_0 =0.26^2 =0.0676 represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is violated, so the system of hypothesis would be:

Null Hypothesis: \sigma^2 \leq 0.0676

Alternative hypothesis: \sigma^2 >0.0676

Calculate the statistic  

For this test we can use the following statistic:

\chi^2 =\frac{n-1}{\sigma^2_0} s^2

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

\chi^2 =\frac{15-1}{0.0676} 0.1521 =31.5

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case df=15-1=14. And since is a right tailed test the p value would be given by:

p_v =P(\chi^2_{14} >31.5)=0.0047

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(31.5,14,TRUE)"

Conclusion

If we compare the p value and the significance level assumed of 0.05 we see that p_v so on this case we have enough evidence in order to reject the null hypothesis at the significance level provided. And that means that the population variance is significantly higher than 0.26^2=0.0676.

4 0
2 years ago
You would like to join a fitness center. Fit-N-Trim charges $80 per month. Fit-For-Life charges a one tim e membership fee of $7
maksim [4K]
Y=80x
y=55x+75
They are not parallel
6 0
3 years ago
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