Please help if you want points and happy ramadan if you celebrate it

Find the area of a triangle with a base length of 4 units and height of 5 units.

ruslelena [56]

Area of a Triangle = 1/2 * b * h
A = 1/2 * 4 * 5
A = 1/2 * 20
A = 10 units

In short, Your Answer would be Option C

Hope this helps!

7 0

3 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

Please answer the question step by step!

erma4kov [3.2K]

Answer:

Step-by-step explanation:

See the figure below.

This is how you graph directly from the equation in the slope-intercept form (y = mx + b) without having to create a table of x and y values.

The equation is

y = -2/3 x + 1

Compare it with

y = mx + b

b = 1

The y-intercept is 1, so mark 1 on the y-axis. (You already did.)

I placed a black dot there.

The slope is m.

m = -2/3

slope = m = rise/run

A slope of -2/3 can be though of as -2 rise and 3 run. That means start from the y-intercept, and go -2 in y (a rise of 2 down) and 3 in x (a run 3 right). Point graphed in red.

Mathematically, -2/3 is the same as 2/(-3), so starting again from the y-intercept, this slope can also be though of as rise of 2 in y (a rise of 2 up) and a run of -3 in x (a run of 3 left). Point graphed in green.

The line is graphed in blue.

5 0

2 years ago

Read 2 more answers

A right rectangular prism and an oblique triangular prism are both 12 centimeters tall and have the same volume. What Statement

Eva8 [605]

Check the picture.

The bases of the 2 prisms are on 2 parallel planes, a and b.

Let c be a third plane, between a and b, parallel to both.

Then,

the cross-sections A and B , of the 2 prisms, formed by plane c, have Equal Areas,

this is by Cavalier's Principle.

7 0

3 years ago

The cylindrical jar above has a height of 12 centimeters and a radius of 4 centimeters. The jar contains 20 spherical marbles. E

Katen [24]

The answer is 57.72 cm.

5 0

3 years ago