The lengths of two sides of a triangle are shown below:

...........................................................

klasskru [66]

Answer:

lollllll

Step-by-step explanation:

have a nice day!

3 0

3 years ago

Read 2 more answers

Complete the number sentence to make it true

Mila [183]

The answer is 54.609 is less than 54.69

3 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

! + 3 − 5 = 0; by completing the square

mylen [45]

Answer:

x = 1.19258 and x = −4.19258

Step-by-step explanation:

The given equation is :

$x^2+3x-5=0$

Keep x terms on the left and move the constant to the right side by adding it on both sides.

$x^2+3x=5$

Take half of the x term and square it.

$(3\times \dfrac{1}{2})^2=\dfrac{9}{4}$

then add the result to both sides

$x^2+3x+\dfrac{9}{4}=5+\dfrac{9}{4}\\\\(x+\dfrac{3}{2})^2=\dfrac{29}{4}\\\\(x+\dfrac{3}{2})=\sqrt{\dfrac{29}{4}}\\\\x=\dfrac{-3}{2}+\sqrt{\dfrac{29}{4}}\\\\x=\dfrac{-3}{2}-\sqrt{\dfrac{29}{4}}$

So,

x = 1.19258 and x = −4.19258

Hence, this is the required solution.

6 0

3 years ago

VERY IMPORTANT QUESTION I WILL GIVE 50 POINTS TO WHOEVER ANSWERS THIS QUESTION

solmaris [256]

I think it might be expression one =14 i think and number 2 is obviously is 19 but you would put parenthesis around 5+4_2+6

I think i did this right its been a while since i did this

8 0

3 years ago