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3 years ago

The function g is defined by g(x)=ax−7, where a is a constant. Find a, if the graph of g passes through the point ( 1/3,−2).

Mathematics

1 answer:

sattari [20]3 years ago

7 0

Answer:

a = 15

Step-by-step explanation:

g(x) is the same thing as "y". Our point gives us an x and y value, so we will sub those into the equation and solve for a:

-2 = a(1/3) - 7 and

-2 = 1/3a - 7 and

5 = 1/3a so

a = 15

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The measures of two supplementary angles are (3x + 9)° and (2x + 2)°. What is the measure of the smaller angle? A. 16.6° B. 69.6

s344n2d4d5 [400]

Answer:

Step-by-step explanation:

Supplementary angles sum to 180°, hence

3x + 9 + 2x + 2 = 180, that is

5x + 11 = 180 ( subtract 11 from both sides )

5x = 169 ( divide both sides by 5 )

x = 33.8

Hence the smaller angle has a measure of

2x + 2 = (2 × 33.8) + 2 = 67.6 + 2 = 69.6° → B

3 0

2 years ago

10(8r+23) =1430 <br> HELP PLS ITS FOR MY HW PLS PLS PLS

Mademuasel [1]

Answer:

r = 15

Step-by-step explanation:

10(8r + 23) = 1430

Divide both sides by 10.

8r + 23 = 143

Subtract 23 from both sides.

8r = 120

Divide both sides by 8.

r = 15

7 0

3 years ago

What is u^+6u-27 factoring

MissTica

U² + 6u - 27
u² + 9u - 3u - 27
(u - 3)(u + 9)

7 0

3 years ago

What is the gradient of the line (-4, 10) to (-2, 6)<br>

Andre45 [30]

Answer:

（2,-4）

Step-by-step explanation:

-4＋2＝-2

10＋-4＝10-4＝6

6 0

2 years ago

You work in the HR department at a large franchise. you want to test whether you have set your employee monthly allowances corre

ra1l [238]

Answer:

1) Null hypothesis: $\mu \leq 500$

Alternative hypothesis: $\mu > 500$

$z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90$

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:

$z_{crit}= 2.33$

For this case we see that the calculated value is higher than the critical value

Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level

2) Since is a right tailed test the p value would be:

$p_v =P(z>5.90)=1.82x10^{-9}$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1

Step-by-step explanation:

Part 1

Data given

$\bar X=640$ represent the sample mean

$\sigma=150$ represent the population standard deviation

$n=40$ sample size

$\mu_o =500$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

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

Step1:State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is higher than 500, the system of hypothesis would be:

Null hypothesis: $\mu \leq 500$

Alternative hypothesis: $\mu > 500$

Step 2: Calculate the statistic

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

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

$z=\frac{640-500}{\frac{150}{\sqrt{40}}}=5.90$

Step 3: Calculate the critical value

For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.01 of the area in the right and we got:

$z_{crit}= 2.33$

Step 4: Compare the statistic with the critical value

For this case we see that the calculated value is higher than the critical value

Step 5: Decision

Since the calculated value is higher than the critical value we have enugh evidence to reject the null hypothesis at 1% of significance level

Part 2

P-value

Since is a right tailed test the p value would be:

$p_v =P(z>5.90)=1.82x10^{-9}$

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, same conclusion for part 1

7 0

3 years ago