Which expression is equivalent to 5x +10y-15?

mart [117]

Your answer is D 6561 multiply each number 3 and your answer will be this

5 0

2 years ago

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

Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the

strojnjashka [21]

The answer is C) y=14(0.9)ˣ and it's an exponential function

PROOF

Give to x the respective values of x & calculate y, using y = 14(0.9)ˣ

x | y
---------|---------
0 | 14(0.9)⁰ = 14
1 | 14(0.9)¹ = 12.6
2 | 14(0.9)² = 11.34
3 | 14(0.9)³ = 10.206
4 | 14(09)⁴ = 9.1845

4 0

3 years ago

What step is wrong -12=4(f-6) step 1 12=4f step 2 4=f step 3

kirza4 [7]

Answer:

Step(iii)

The value of 'f' = 3

Step-by-step explanation:

Step(i):-

Given - 12 = 4(f-6)

Multiply

- 12 = 4 f - 24

Step(ii):-

- 12 = 4 f - 24

Adding '12' on both sides, we get

- 12 + 12 = 4 f - 24 + 12

0 = 4 f - 12

4f - 12 =0

4 f = 12

Step(iii):-

Dividing '4' on both sides, we get

f = 3

3 0

3 years ago

Can somebody help me with this!?

Daniel [21]

Answer:

24 $\pi$ /5

Step-by-step explanation:

The way I think about areas of sectors is a fraction of the pie. You know what percentage of the "pie" (in this case, circle) you want, because they give you the angle of the sector and you know a circle always has 360°. So technically, you're trying to find 48/360 th of the entire area (36 $\pi$ ). If you're using a calculator, it doesn't matter if you simplify the fraction, but if you're doing it by hand simplifying makes everything a lot easier.

The equation will be:

Area = 24/180 × 36 $\pi$

= 2/15 × 36 $\pi$

= 72 $\pi$ /15

= 24 $\pi$ /5

I hope this helped! Also, in Khan Academy, when you get an answer wrong/right, you can view their explanation by clicking "hint" or sometimes "see how we did it" shows up.

4 0

3 years ago