What’s interval notation of the real numbers from 0 to 25

frez [133]

Answer: 1875

Hope this helps!

6 0

2 years ago

Given sinθ=- 3/5 and cscθ=-5/3 in quadrant III, find the value of other trigonometric functions using a Pythagorean Identity. Sh

Yakvenalex [24]

Let ABC be a triangle in the 3rd quadrant, right-angled at B.
So, AB-> Perpendicular BC -> Base AC -> Hypotenuse.
Given: sinÎ¸=-3/5 cosecÎ¸=-5/3
According to Pythagorean theorem, square of the hypotenuse is equal to the sum of square of the other two sides.
Therefore in triangle ABC, ă€–ACă€—^2=ă€–ABă€—^2+ă€–BCă€—^2 ------
--(1)
Since sinÎ¸=Perpendicular/Hypotenuse ,
AC=5 and AB=3
Substituting these values in equation (1)

ă€–BCă€—^2=ă€–ACă€—^2-ă€–ABă€—^2

ă€–BCă€—^2=5^2-3^2

ă€–BCă€—^2=25-9

ă€–BCă€—^2=16

BC=4 units

Since the triangle is in the 3rd quadrant, all trigonometric ratios, except tan
and cot are negative.
So,cosÎ¸=Base/Hypotenuse CosÎ¸=-4/5
secÎ¸=Hypotnuse/Base secÎ¸=-5/4
tanÎ¸=Perpendicular/Base tanÎ¸=3/4
cotÎ¸=Base/Perpendicular cotÎ¸=4/3

4 0

2 years ago

Can someone answer my questions please ._.

tekilochka [14]

Answer:

wheres the question?

Step-by-step explanation:

6 0

2 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

2 years ago

Whats the answer can someone answer please

tatuchka [14]

Answer:

both are c

Step-by-step explanation:

4 0

2 years ago