Eliot needs to replace a window that is in the shape of a semicircle.

£399 is shared between Ann, Bill, Chloe and Dave.

tiny-mole [99]

Answer is 4.5 Show all
Steps below

6 0

2 years ago

Jeanne wants to start collecting coins and orders a coin collection starter kit. The kit comes with three coins chosen at random

lesya692 [45]

Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes $P_B(A)$ .

The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by
$P(A|B)= \frac{P(A \cap B)}{P(B)}$

In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.

The probability of selecting one coin is $\frac{1}{3}$

Part A:
To find the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.

P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.

Thus $P(A)= \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}$

P(B) means that the first envelope contains a quarter AND the second envelope contains a quarter

Thus $P(B)= \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Therefore, $P(A|B)=\left( \frac{ \frac{1}{27} }{ \frac{1}{9} } \right)= \frac{1}{3}$

Part B:
To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.

$P(C)= \frac{3}{3} \times \frac{2}{3} \times \frac{1}{3} = \frac{6}{27} = \frac{2}{9}$

 $P(D)= \frac{1}{3}$ 

Therefore, $P(C|D)=\left( \frac{ \frac{2}{9} }{ \frac{1}{3} } \right)= \frac{2}{3}$

3 0

2 years ago

From the following figure, how can you conclude that lines l and m are parallel?

loris [4]

C. Alternate interior angles theorem

The angles labeled are on the inside of lines l and m and they are also on alternate sides of the unnamed line

:)))

4 0

2 years ago

Read 2 more answers

Three boards are placed end to end to make a walkway. The first board is 4 feet 5 inches long, the second board is 6 feet 9 inch

Kazeer [188]

Answer:

15 feet and 1 inch long

Step-by-step explanation:

add up the feet: 4+6+3= 13 feet

add up the inches: 5+9+11 = 25 inches

25/12= 2 feet 1 inch

13 feet + 2 feet + 1 inch= 15 feet 1 inch

7 0

2 years ago

In two or more complete sentences, compare the slopes of the two functions. In your comparison, include which function has the g

ziro4ka [17]

Answer:

I guess we have the table:

x f(x)

-4 7

-2 5

0 3

2 1

4 - 1

To find the slope of this, we need to select two different points (x1, y1) and (x2, y2) and use the relation:

slope = (y2 - y1)/(x2 - x1)

let´s use the first two:

(-4,7) and (-2, 5)

Slope = (5 - 7)/(-2 - (-4)) = -2/2 = -1

Now, if we want to be sure that this is a linear equation, we should do the same for other two pairs of points, now use the first and the third:

(-4, 7) and (0,3)

S = (3 - 7)/(0 -(-4)) = -4/4 = -1

Now, for the function g(x) we can see a constant line, that is parallel to the x-axis.

This means that the slope of this function is equal to zero.

This means that the slope of g(x) is bigger than the slope of f(x), because 0 > 1

6 0

2 years ago