The supplementary angle of 100.6° is

What characteristics are easily found when given a quadratic equation in Standard form and/or in vertex form?

labwork [276]

In vertex form the value of the vertex is easily identified in the equation. I’m standard form the value of the x intercepts are evident.

3 0

2 years ago

Sarah is paid $20 an hour at her new job. She wishes to graph her total pay T, as a function of the number of hours, h. She want

Hatshy [7]

1 is 400 and 2 is 20 i did this before

4 0

2 years ago

Which of the following are valid names for the given triangle? Check all that apply V ALOM BNLMZ C.PAMLZ DXZML WENZMO 72 FRAZMD

crimeas [40]

The answer is C.pamlz dxzml

8 0

2 years ago

Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→1 1 − x + l

AfilCa [17]

$\displaystyle\lim_{x\to1}\frac{1-x+\ln x}{1+\cos5\pi x}$

Evaluating the limand directly at $x=1$ gives an indeterminate form $\dfrac00$ . Apply L'Hospital's rule once and we get

$\displaystyle\lim_{x\to1}\frac{-1+\frac1x}{-5\pi\sin5\pi x}$

Again, plugging in $x=1$ returns $\dfrac00$ . Apply the rule once more:

$\displaystyle\lim_{x\to1}\frac{-\frac1{x^2}}{-25\pi^2\cos5\pi x}=\frac1{25\pi^2}\lim_{x\to1}\frac1{x^2\cos5\pi x}$

Now, in the denominator, when $x=1$ we get $x^2\cos5\pi x=-1$ , so the limit is $-\dfrac1{25\pi^2}$ .

3 0

3 years ago

Assume that we have two events, and , that are mutually exclusive. Assume further that we know and . If an amount is zero, enter

sweet [91]

Answer:

Explained below.

Step-by-step explanation:

The complete question is:

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.

What is P(A and B)?

What is P(A | B)?

Is P(A | B) equal to P(A)?

Are events A and B dependent or independent?

A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?

What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Solution:

The probability of the two events <em>A</em> and <em>B</em> are:

P(A) = 0.30 and P(B) =0.40

(a)

Compute the value of P (A ∩ B) as follows:

$P(A\cap B)=0$

This is because mutually exclusive events are those events that cannot occur together.

(b)

Compute the value of P (A | B) as follows:

$P(A|B)=\frac{P(A\cap B)}{P(B)}=\frac{0}{0.40}=0$

Thus, the value of P (A | B) is 0.

(c)

No, P (A | B) is not equal to the P (A).

(d)

As mentioned in part (a), mutually exclusive events are those events which cannot occur together.

That is, $P(A\cap B)=0$ .

Events A and B are independent if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.

That is, $P(A\cap B)=P(A)\times P(B)$ .

The concepts of mutually exclusive events and independent events are not the same.

(e)

As the it is provided that A and B are mutually exclusive events, we know that $P(A\cap B)=0$ .

Now compute the value of $P(A)\times P(B)$ as follows:

$P(A)\times P(B)=0.30\times 0.40=0.12\neq 0$

Thus, the events A and B are not independent.

Thus, if two events are mutually exclusive events they cannot be independent.

4 0

3 years ago