Simplify<br> (x + 3)^8 <br> ————

In the video at the beginning of the lesson, how many 2-topping pizza combinations were there if there were 7 toppings to choose

elena-s [515]

Answer:

3 or 3 and 1/2

Step-by-step explanation:

2 toppings per pizza

2, 4, 6 and the half pizza with one topping

8 0

3 years ago

Read 2 more answers

The following data lists the ages of a random selection of actresses when they won an award in the category of Best Actress, al

Valentin [98]

Answer:

a) $p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

b) The 99% confidence interval would be given by (-21.469;2.069)

c) We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two

Step-by-step explanation:

Part a

Let put some notation

x=actor's age , y = actress's age

x: 58 41 36 36 34 33 48 37 37 43

y: 26 27 34 26 35 29 23 42 30 34

The system of hypothesis for this case are:

Null hypothesis: $\mu_y- \mu_x \geq 0$

Alternative hypothesis: $\mu_y -\mu_x$

The first step is calculate the difference $d_i=y_i-x_i$ and we obtain this:

d: -32, -14, -2, -10, 1, -4, -25, 5, -7, -9

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}= -9.7$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =11.451$

The 4 step is calculate the statistic given by :

$t=\frac{\bar d -0}{\frac{s_d}{\sqrt{n}}}=\frac{-9.7 -0}{\frac{11.451}{\sqrt{10}}}=-2.679$

The next step is calculate the degrees of freedom given by:

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

Now we can calculate the p value, since we have a left tailed test the p value is given by:

$p_v =P(t_{(9)}$

The p value is higher than the significance level given 0.01, so then we can conclude that we FAIL to reject the null hypothesis. And we can say that the true difference for Best Actresses is not significantly lower than the mean for Best Actors at 1% of significance.

Part b

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

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".

The confidence interval for the mean is given by the following formula:

$\bar d \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

Now we have everything in order to replace into formula (1):

$-9.7-3.25\frac{11.451}{\sqrt{10}}=-21.469$

$-9.7+3.25\frac{11.451}{\sqrt{10}}=2.069$

So on this case the 99% confidence interval would be given by (-21.469;2.069)

Part c

We got the same conclusion as part a, sicne the confidence interval contains the value 0, we FAIL to reject the null hypothesis that the difference between the two means is 0.

8 0

3 years ago

Consider two stocks. Stock 1 always sells for $10 or $20. If stock 1 is selling for $10 today, there is a .80 chance that it wil

Hitman42 [59]

Answer:

On stock 2 will be has an average sell of $50 for higher price.

Step-by-step explanation:

stock 1 of $10 (today)+ $10 (80% chance tommorow)=$20 stock sell price and for $20(today)+$20(90% chance tommorow)= $40 this two final of price for stock 1.

Stock 2 of $10 (today)+$10(90% chance tommorow)= $20 and of $25(today)+$25(85% chance tomorrow)= $50 this two for final of it's price for stock 2.So as for Stock 2 has the average sell higher price.

Hope this helps you

5 0

3 years ago

Help me pls and explain

posledela

Answer:

A

Step-by-step explanation:

I believe it is A because there is not any repeating X's. There is a repeating y which is 1. Therefore it is A.

7 0

3 years ago

A salesman receives a commission of $4 for every pair of dress shoes he sells. He is paid $3 for every pair of athletic shoes he

Crank

Answer: he sold 9 pairs of dress shoes.

he sold 4 pairs of athletic shoes.

Step-by-step explanation:

Let x represent the number of pairs of dress shoes that he sells.

Let y represent the number of pairs of athletic shoes that he sells.

The total number of pairs of shoes that he sold in a day is 13. It means that

x + y = 13

The salesman receives a commission of $4 for every pair of dress shoes he sells. He is paid $3 for every pair of athletic shoes he sells. The commission that he got on that day was $48. It means that

4x + 3y = 48- - - - - - - - - - 1

Substituting x = 13 - y into equation 1, it becomes

4(13 - y) + 3y = 48

52 - 4y + 3y = 48

- 4y + 3y = 48 - 52

- y = - 4

y = 4

x = 13 - y = 13 - 4

x = 9

4 0

3 years ago

Simplify (x + 3)^8 —————- (x + 3) ^5