The factorial ! just means we multiply by every natural number less that the value so
6! =6×5×4×3×2×1= 720

for permutations we use the formula n!/(n-r)!
so we have 8!/(8-5)!=8!/3!=8×7×6×5×4

for combinations s we have n!/(n-r)!r!
so we have 12!/(12-4)!4!=12!/8!4!=12×11×10×9/4×3×2=11×10×9/2=99×5

7 0

2 years ago

Shanti began to draw a Venn diagram comparing refracting and reflecting telescopes. 2 overlapping circles. The left circle label

iren2701 [21]

The label could be written in the area marked X as "Uses a convex eyepiece lens". Then the correct option is D.

Sets are the collection of well-defined elements. A set is represented by a capital letter symbol and the number of elements in the finite set is shown as curly bracket {..}.

<h3>What is the Venn diagram?</h3>

It is the representation of the sets by the diagram. And shows the condition that is generated between them by the overlapping of the circle.

Shanti began to draw a Venn diagram comparing refracting and reflecting telescopes. The two overlapping circles.

The left circle is labeled Refracting telescopes.

The right circle is labeled Reflecting Telescopes.

An X in the overlap. Both as a label below and outside the overlap.

From the figure, we can say that the label could be written in the area marked X as "Uses a convex eyepiece lens".

Then the correct option is D.

More about the set link is given below.

brainly.com/question/8053622

7 0

1 year ago

In a simple regression analysis for a given data set, if the null hypothesis β = 0 is rejected, then the null hypothesis ρ = 0 i

kati45 [8]

Answer:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

$t=\frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$

And is distributed with n-2 degrees of freedom

And the statistic to check the significance of a coeffcient in a regression is given by:

$t_1 = \frac{\hat{\beta_1} -0}{S.E (\hat{\beta_1})}$

For this case is importantto remember that t1 and p value for test of slope coefficient is the same test statistic and p value for the correlation test so then the answer would be:

Always

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis: