Calculate 15% of $490.

Solve for x. See picture for full problem. Please and thank you!

Nadya [2.5K]

Answer:

x = 16

Step-by-step explanation:

All 3 right triangles are similar, so the lengths of corresponding sides are in proportion.

8√3 / 12 = x / 8√3

12x = (8√3)²

12x = 64 × 3

4x = 64

x = 16

8 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:

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

Which number goes in the box?<br> 8 + 9 = 9 +

Ira Lisetskai [31]

Answer:

8

Step-by-step explanation:

I hope this helps you out!

7 0

3 years ago

Read 2 more answers

A number divided by 7<br><br> Select one:<br> a. 7+x<br> b. 7/x<br> c. x/7<br> d. 7x

maksim [4K]

Answer:

c. x/7

Step-by-step explanation:

seven is dividing something, and X is the placeholder in this equation.

So, since x is being divided by seven, that rules out B., because that's backwards.

A. and D. don't involve division, so they're both incorrect as well.

Thus we are left with C. x/7

7 0

2 years ago

Read 2 more answers

Complete the remaining columns in the chart by calculating the missing values for each category. Round your percentages to the n

Alenkinab [10]

Answer:

yearly cost for housing expenses = $11,400, average monthly cost for food = $650

yearly clothing cost = $900,

average monthly cost for transportation= $500,

Yearly cost for insurance & medical= $14,400

yearly cost for emergency fund = $600

average monthly college saving = $50

Step-by-step explanation:

Yearly housing = monthly cost * 12 = 950 * 12 = 11400

Food, monthly = 7800 /12 = 650

Clothing, yearly = 75 * 12 = $900

Monthly transport = 6000 / 12 = $500

Insurance and medical = 1200*12 =14400

Emergency fund = $50 * 12 = $600

College saving = $600 / 12 = $50

8 0

3 years ago

Calculate 15% of $490.​

Calculate 15% of $490.