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3 years ago

Solve the equation by completing the square. -9n^2+79+=-18n

1 answer:

6 0

Hello,
-9n²+79=-18n
==>9n²-18n-79=0
==>9(n²-2n+1-1)-79=0
==>9(n-1)²-88=0
==>[3(n-1)-2√22][3(n-1)+2√22]=0
==>3(n-1)=2√22 or 3(n-1)=-2√22
==>n-1=2/3*√22 or n-1=-2/3*√22
==>n=1+2/3*√22 or n=1-2/3*√22

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Find AuB and AnB for the sets A and B.<br> A={3, 4, 5, 6, 7), B = {4, 6, 8, 10)

kvv77 [185]

Answer:

AuB= {3,4,5,6,7,8,10}

AnB= {4,6}

7 0

3 years ago

An educator claims that the average salary of substitute teachers in school districts is less than $60 per day. A random sample

valentina_108 [34]

Answer:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

Step-by-step explanation:

Information given

60, 56, 60, 55, 70, 55, 60, and 55.

We can calculate the mean and deviation with these formulas:

$\bar X= \frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Replacing we got:

$\bar X=58.875$ represent the mean

$s=5.083$ represent the sample standard deviation for the sample

$n=8$ sample size

$\mu_o =60$ represent the value that we want to test

$\alpha=0.1$ represent the significance level

t would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to test if the true mean is less than 60, the system of hypothesis would be:

Null hypothesis: $\mu \geq 60$

Alternative hypothesis: $\mu < 60$

The statistic would be given by:

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

Replacing the info we got:

$t=\frac{58.875-60}{\frac{5.083}{\sqrt{8}}}=-0.626$

The degrees of freedom are given by:

$df=n-1=8-1=7$

The p value would be given by:

$p_v =P(t_{(7)}$

Since the p value is higher than 0.1 we have enough evidence to FAIl to reject the null hypothesis and we can't conclude that the true mean is less than 60

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3 years ago

Please solve this:<br> 6-2x=3

Westkost [7]

Answer:

-4

Step-by-step explanation:

6 - 2x = 3

-2x = 3 + 6

-2x = 8

x= $\frac{8}{-2}$

x= -4

I apologize if this isn't the right answer.

7 0

2 years ago

1. what is the product of 3/4 and - 6/7?

kari74 [83]

Multiplying fractions: multiply numerators and multiply denominators

1. 3/4 X -6/7 = -18/28 = -9/14

2. -2/7 X -3/7 = 6/49

3. 4 because 72/9 is 8. -72/-9 is 8. Two negatives makes a positive when multiplying and dividing.

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4 years ago

Write an equation of the line that passes through the given points.<br> (-1,7) and (4, -8)

djverab [1.8K]

Answer:

y=-3x+4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-8-7)/(4-(-1))

m=-15/(4+1)

m=-15/5

m=-3

y-y1=m(x-x1)

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y-7=-3(x+1)

y=-3x-3+7

y=-3x+4

3 0

3 years ago