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3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Mathematics

2 answers:

just olya [345]3 years ago

8 0

Answer:

I would answer but I'm missing information

Step-by-step explanation:

4vir4ik [10]3 years ago

3 0

Answer:

There is no question.

Step-by-step explanation:

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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 $\displaystyle P(A_2\; \cap \; B) = \frac{1}{25}$ .

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

Step-by-step explanation:

$P(A_1 \; \cap \; A_2) = 0$ 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.

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:

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

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:

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

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

3 years ago

The measure of the angles of a triangle are in the extended ratio 17 : 16 : 12. what is the measure of the largest angle?

murzikaleks [220]

17x + 16x + 12x =180
45x = 180
x = 4
Largest angle = 17*4 = 68 degrees

8 0

3 years ago

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Round of 0.016668correct to three significant figures

Dmitry_Shevchenko [17]

0.0167

Since the decimal is present, start from the left side of the number and move to the right until you hit the first Non-Zero number. That number will be the first significant figure, and the number you will start counting from. That’s the first, the second is next, and lastly the third. You round the LAST significant figure, in this case a 6 followed by a 6, meaning you round UP.

6 0

2 years ago

Macy’s buys a pair of Cole Haan dress shoes wholesale for $90. If Macy’s marks up the price 20%, and tax is 9%, how much did Nor

stich3 [128]

Answer:

Norman bought the shoes for $117.72

Step-by-step explanation:

In order to find the answer to this question, start by multiplying the cost by the markup.

$90 * 20% = $18.

Now we add the $18 to the original price.

$90 + $18 = $108

Now that we have the mark up price, we need to do the same using the tax.

$108 * 9% = $9.72

Finally, we add that to the previous total.

$108 + $9.72 = $117.72

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3 years ago

Juan analyzes the amount of radioactive material remaining in a medical waste container over time. He writes the function f(x) =

Misha Larkins [42]

Rounded to the nearest tenth would remain is 8.2 units is the answer. Just took the test.

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3 years ago

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