Find the coordinates of the midpoint of XY for X(-2,3) and T(-8,-9)

Flying against the wind, a jet travels 2190 miles in 3 hours. Flying with the wind, the same jet travels 9520 miles in 8 hours.

dezoksy [38]

Answer:

Velocity of jet in still air is 970 miles per hour and velocity of wind is 210 miles per hour.

Step-by-step explanation:

Jet's velocity against wind is

3040/4 = 760 miles per hour and flying with wind it is

8260/7 = 1180 miles per hour.

Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.

As such its velocity against wind is x − y and with wind is x + y and therefore

x − y = 760 and x + y = 1180

Adding the two 2 x = 1940 and x = 970 and y = 1180 − 970 = 210

Hence velocity of jet in still air is 970 miles per hour and velocity of wind is

210 miles per hour.

Actual Answer:

https://socratic.org/questions/flying-against-the-wind-a-jet-travels-3040-miles-in-4-hours-flying-with-the-wind

7 0

3 years ago

On average, Christopher scores 2 goals in a soccer game but, depending on how well the opposing team is playing, his goal total

SVETLANKA909090 [29]

Given:

Christopher scores 2 goals in a soccer game.

His goal total can vary from the average by 1 goal.

To find:

The absolute value equation can be used to calculate Christopher's maximum and minimum goals per game.

Solution:

Let Christopher scores x goals in a soccer game.

Then difference between actual goals and average goals is x-2.

His goal total can vary from the average by 1 goal.

Maximum number of goals = 2+1 = 3

Minimum number of goals = 2-1 = 1

It means, the difference between actual goals and average goals is either -1 and 1.

$x-2=-1$ ...(1)

$x-2=1$ ...(2)

Using (1) and (2),we get

$|x-2|=1$

Therefore, the correct option is C.

7 0

3 years ago

A tire manufacturer is considering a newly designed tread pattern for its all-weather tires. Tests have indicated that these tir

Nataly_w [17]

Answer:

With outlier (102)

$t=\frac{126.2-125}{\frac{9.138}{\sqrt{10}}}=0.415$

$p_v =P(t_{9}>0.415)=0.344$

If we compare the p value and a significance level assumed $\alpha=0.05$ 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 higher than 125 feet at 5% of significance.

Without outlier (102)

$t=\frac{128.89-125}{\frac{3.551}{\sqrt{9}}}=3.285$

$p_v =P(t_{8}>3.285)=0.0056$

And we conclude that we reject the null hypothesis since $p_v$ . So the final conclusion would be not use the method since the value of 102 observed can be a potential outlier, removing this value we see that we reject the null hypothesis and we have a significant result that the true mean is higher than 125.

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data: 129, 128, 130, 132, 135, 123, 102, 125, 128, 130

We can calculate the mean with the following formulas:

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

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

$\bar X=126.2$ represent the sample mean

$s=9.138$ represent the sample standard deviation

n=10 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is significantly higher than 125, the system of hypothesis would be:

Null hypothesis: $\mu \leq 125$

Alternative hypothesis: $\mu > 125$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

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

t-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:

$t=\frac{126.2-125}{\frac{9.138}{\sqrt{10}}}=0.415$

P-value

First we need to calculate the degrees of freedom given by:

$df=n-1=10-1= 9$

Then since is a right tailed sided test the p value would be:

$p_v =P(t_{9}>0.415)=0.344$

Conclusion

If we compare the p value and a significance level assumed $\alpha=0.05$ 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 higher than 125 feet at 5% of significance.

Using all the data we see that we don;t have enough info to conclude that the true mean is higher than 125, but if we see careful 9 of the 10 values are over the limit of 125 feet. And if we repeat the procedure with the outlier of 102. We got this:

$\bar X=128.89$ represent the sample mean

$s=3.551$ represent the sample standard deviation

$t=\frac{128.89-125}{\frac{3.551}{\sqrt{9}}}=3.285$

First we need to calculate the degrees of freedom given by:

$df=n-1=9-1= 8$

Then since is a right tailed sided test the p value would be:

$p_v =P(t_{8}>3.285)=0.0056$

And we conclude that we reject the null hypothesis since $p_v$ . So the final conclusion would be not use the method since the value of 102 observed can be a potential outlier removing this value we see that we reject the null hypothesis and we have a significant result that the true mean is higher than 125.

8 0

3 years ago

What is the height of a trapezoid with a area of 79.2 and bases 4.2 and 9

julsineya [31]

The answer to this problem is 12. If you want me to write it out I can

8 0

3 years ago

Read 2 more answers

Which expression is equivilent to 6(3x-4)+2x

motikmotik

Answer:

44x,

Step-by-step explanation:

you can expand the brackets which equals 18x + 24 (or subtract 24 if the expression is 6(3x-4)) at the end of the equation you will add 2 which would give you 44x

4 0

2 years ago