F = {(1, 4), (2, 3), (5, 8), (4, 7)}<br> F-1 is a function.<br> True<br> False

A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics e

professor190 [17]

Answer:

$\chi^2 =\frac{15-1}{25} 16 =8.96$

The degrees of freedom are given by:

$df = n-1 = 15-1=14$

The p value for this case would be given by:

$p_v =P(\chi^2$

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes

Step-by-step explanation:

Information given

$n=15$ represent the sample size

$\alpha=0.05$ represent the confidence level

$s^2 =16$ represent the sample variance

$\sigma^2_0 =25$ represent the value that we want to verify

System of hypothesis

We want to test if the true deviation for this case is lesss than 5minutes, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \geq 25$

Alternative hypothesis: $\sigma^2$

The statistic is given by:

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

And replacing we got:

$\chi^2 =\frac{15-1}{25} 16 =8.96$

The degrees of freedom are given by:

$df = n-1 = 15-1=14$

The p value for this case would be given by:

$p_v =P(\chi^2$

Since the p value is higher than the significance level we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true deviation is not ignificantly lower than 5 minutes

6 0

3 years ago

Joey drives a golf cart when he needs to monitor the security of his neighborhood. He can cover the 40 miles of streets in his n

suter [353]

40/2=20
Therefore he can cover 20 miles in 1 hour
Hope this helps!

5 0

3 years ago

Consignment Sale. Just Between Friends is the leading pop-up consignment sales event franchise in North America. The Des Moines

natita [175]

Answer:

Just Between Friends

The percentage of consignors who receive a check for more than $370 is:

= 16%.

Step-by-step explanation:

Mean of consignor check, μ = $480

Standard deviation, σ = $110

Value of check received, x > $370

Solution: find the z-score to determine the percentage of consignors who receive a check for more than $370:

z = (x-μ)/σ

z= ($370 - $480)/$110

z = -$110/$110

z = -1.00

Percentage of consignors who receive a check for more than $370

= 0.15866

= 0.16

= 16%

7 0

3 years ago

Prove that if $w,z$ are complex numbers such that $|w|=|z|=1$ and $wz\ne -1$, then $\frac{w+z}{1+wz}$ is a real number.

mr_godi [17]

Answer:

See proof below

Step-by-step explanation:

Let $r=\frac{w+z}{1+wz}$ . If w=-z, then r=0 and r is real. Suppose that w≠-z, that is, r≠0.

Remember this useful identity: if x is a complex number then $x\bar{x}=|x|^2$ where $\bar{x}$ is the conjugate of x.

Now, using the properties of the conjugate (the conjugate of the sum(product) of two numbers is the sum(product) of the conjugates):

$\frac{r}{\bar{r}}=\frac{w+z}{1+wz} \left(\frac{1+\bar{w}\bar{z}}{\bar{w}+\bar{z}}{\right)$

= $\frac{(w+z)(1+\bar{w}\bar{z})}{(1+wz)(\bar{w}+\bar{z})}=\frac{w+z+w\bar{w}\bar{z}+z\bar{z}\bar{w}}{\bar{w}+\bar{z}+\bar{w}wz+\bar{z}zw}=\frac{w+z+w+|w|^2\bar{z}+|z|^2\bar{w}}{\bar{w}+\bar{z}+|w|^2z+|z|^2w}=\frac{w+z+\bar{z}+\bar{w}}{\bar{w}+\bar{z}+z+w}=1$

Thus $\frac{r}{\bar{r}}=1$ . From this, $r=\bar{r}$ . A complex number is real if and only if it is equal to its conjugate, therefore r is real.

3 0

3 years ago

Please solve this <br>Solve by completing the square. 4x2+8x−3=0

Greeley [361]

Step-by-step explanation:

4x2+8x−3=0

For this equation: a=4, b=8, c=-3

4x2+8x+−3=0

Step 1: Use quadratic formula with a=4, b=8, c=-3.

x=

−b±√b2−4ac

2a

x= −(8)±√(8)2−4(4)(−3)

2(4)

x= −8±√112

8 x=−1+

1 2 √7 or x=−1+

−1 2 √7

Answer: x=−1+

1 2√7 or x=−1+

−1 2 √7

7 0

2 years ago

F = {(1, 4), (2, 3), (5, 8), (4, 7)} F-1 is a function. True False