the value of y is directly proportional to the value of x .If y = 124 when x = 8 , what is the value of y when x=

Margot is looking at some information for the obstacle course she is interested in completing. The x-coordinate is the number of

OverLord2011 [107]

Answer:

f(8) = 1.1(6.25)8; f(8) = 2561137

5 0

3 years ago

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Find all solutions in the integers of the equation ||x−3|−5| = 10, where the bars indicate absolute value.

Helga [31]

Answer:

x = 18 or x = -12.

Step-by-step explanation:

||x-3|-5| = 10 only if |x-3|-5 = 10 or |x-3|-5 = -10, i.e., if |x-3|=15 or |x-3|=-5; but |x-3| cannot be equal to -5, because |x-3| should be a non-negative value. Therefore, the first equation is true only if |x-3|=15. |x-3| = 15 only if x-3 = 15 or x-3 = -15, i.e., x = 18 or x = -12. We can verify this in the following way: ||18-3|-5|=||15|-5|=|10|=10 and ||-12-3|-5|=||-15|-5|=|15-5|=|10|=10. This verify that our solution is correct.

3 0

4 years ago

-11 greater or less than+2

kobusy [5.1K]

Less than because it is negative and 2 is positive.

8 0

3 years ago

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Solve the quadratic equation by completing the square.

vampirchik [111]

Answer:

x = -4.59, -7.41.

Step-by-step explanation:

x^2 + 12x + 34 = 0

(x + 6)^2 - 36 +34 = 0

(x + 6)^2 = 36 - 34 = 2

x + 6 = +/-√2

x = +/-√2 - 6

x = -4.59, -7.41

7 0

3 years ago

An automobile manufacturer claims that its van has a 31.3 miles/gallon (MPG) rating. An independent testing firm has been contra

Yuliya22 [10]

Answer:

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

$z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82$

$p_v =2*P(z$

If we compare the p value and the significance level given $\alpha=0.02$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is NOT significantly different from 31.3 at 2% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=31.1$ represent the sample mean

$\sigma=1.3$ represent the population standard deviation for the sample

$n=140$ sample size

$\mu_o =31.3$ represent the value that we want to test

$\alpha=0.02$ 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)

State the null and alternative hypotheses.

We can assume that we conduct a hypothesis in order to check if the true mean is equal to 31.3 , the system of hypothesis would be:

Null hypothesis: $\mu =31.3$

Alternative hypothesis: $\mu \neq 31.3$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

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

z-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".

Calculate the statistic

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

$z=\frac{31.1-31.3}{\frac{1.3}{\sqrt{140}}}=-1.82$

P-value

Since is a two-sided test the p value would be:

$p_v =2*P(z$

Conclusion

If we compare the p value and the significance level given $\alpha=0.02$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is NOT significantly different from 31.3 at 2% of signficance.

5 0

3 years ago

the value of y is directly proportional to the value of x .If y = 124 when x = 8 , what is the value of y when x= - 1/2