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2 years ago

9

A function and its inverse are shown on the same graph. Which statement describes the relationship between the function and its

inverse?

1 answer:

pickupchik [31]2 years ago

5 0

Answer:

D should be right

Step-by-step explanation:

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Which is the reciprocal of -13/7

Nataly [62]

The reciprocal of -13/7 should be -7/13

6 0

3 years ago

The prior probabilities for events A1 and A2 are P(A1) = 0.20 and P(A2) = 0.80. It is also known that P(A1 ∩ A2) = 0. Suppose P(

Umnica [9.8K]

Answer:

(a) $A_1$ and $A_2$ are indeed mutually-exclusive.

(b) $\displaystyle P(A_1\; \cap \; B) = \frac{1}{20}$ , whereas $\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}$ .

(c) $\displaystyle P(B) = \frac{9}{100}$ .

(d) $\displaystyle P(A_1 \; |\; B) \approx \frac{5}{9}$ , whereas $P(A_1 \; |\; B) = \displaystyle \frac{4}{9}$

Step-by-step explanation:

<h3>(a)</h3>

$P(A_1 \; \cap \; A_2) = 0$ means that it is impossible for events $A_1$ and $A_2$ to happen at the same time. Therefore, event $A_1$ and $A_2$ are mutually-exclusive.

<h3>(b)</h3>

By the definition of conditional probability:

$\displaystyle P(B \; | \; A_1) = \frac{P(B \; \cap \; A_1)}{P(B)} = \frac{P(A_1 \; \cap \; B)}{P(B)}$ .

Rearrange to obtain:

$\displaystyle P(A_1 \; \cap \; B) = P(B \; |\; A_1) \cdot P(A_1) = 0.25 \times 0.20 = \frac{1}{20}$ .

Similarly:

$\displaystyle P(A_2 \; \cap \; B) = P(B \; |\; A_2) \cdot P(A_2) = 0.80 \times 0.05 = \frac{1}{25}$ .

<h3>(c)</h3>

Note that:

$\begin{aligned}P(A_1 \; \cup \; A_2) &= P(A_1) + P(A_2) - P(A_1 \; \cap \; A_2) = 0.20 + 0.80 = 1\end{aligned}$ .

In other words, $A_1$ and $A_2$ are collectively-exhaustive. Since $A_1$ and $A_2$ are collectively-exhaustive and mutually-exclusive at the same time:

$\displaystyle P(B) = P(B \; \cap \; A_1) + P(B \; \cap \; A_2) = \frac{1}{20} + \frac{1}{25} = \frac{9}{100}$ .

<h3>(d)</h3>

By Bayes' Theorem:

$\begin{aligned} P(A_1 \; |\; B) &= \frac{P(B \; | \; A_1) \cdot P(A_1)}{P(B)} \\ &= \frac{0.25 \times 0.20}{9/100} = \frac{0.05 \times 100}{9} = \frac{5}{9}\end{aligned}$ .

Similarly:

$\begin{aligned} P(A_2 \; |\; B) &= \frac{P(B \; | \; A_2) \cdot P(A_2)}{P(B)} \\ &= \frac{0.05 \times 0.80}{9/100} = \frac{0.04 \times 100}{9} = \frac{4}{9}\end{aligned}$ .

6 0

2 years ago

What is the probability that a student eye color would be blue if their grade in physics is A? A two way table is presented belo

Zarrin [17]

The <u>correct answer</u> is:

16/45.

Explanation:

We want the probability that a student's eye color is blue if they made an A in physics. This means we look at the column for students with an A.

There are 32 students with blue eyes in the A column.

This is out of 32+58=90 students that made an A.

This makes the probability 32/90, which simplifies to 16/45.

8 0

2 years ago

Which fraction is equal to 1/4? 4/16,6/30 or 5/15

Paha777 [63]

1/4 is equal to 4/16

5 0

2 years ago

6+4×5-5² help please I keep on getting 16

Whitepunk [10]

Answer: 1

Step-by-step explanation:

6+4×5-5²

=6+20-25

=1

3 0

2 years ago

Read 2 more answers