What is the equation in slope-intercept form for graph shown?

Which of the following is an equation of a circle in

DaniilM [7]

Answer:

$x^2 + (y - 4)^2 = \dfrac{25}{9}$

Step-by-step explanation:

The equation of a circle with center at (h, k) and radius r is

$(x - h)^2 + (y - k)^2 = r^2$

You have center (0, 4).

We get:

$(x - 0)^2 + (y - 4)^2 = r^2$

$x^2 + (y - 4)^2 = r^2$

To find the radius, we use the distance formula to find the distance from the center of the circle to the given point on the circle.

$r = d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

$r = \sqrt{(\dfrac{4}{3} - 0)^2 + (5 - 4)^2}$

$r = \sqrt{(\dfrac{4}{3})^2 + 1^2}$

$r = \sqrt{\dfrac{16}{9} + \dfrac{9}{9}}$

$r = \sqrt{\dfrac{25}{9}}$

We need r^2 in the equation of the circle, so

$r^2 = \dfrac{25}{9}$

The equation of the circle is

$x^2 + (y - 4)^2 = \dfrac{25}{9}$

7 0

4 years ago

There are 36 gold cards and 36 silver cards in a deck. The gold cards are numbered 1,3,5,... 71 and the silver cards are numbere

Andrei [34K]

A) multiples of 12 up to 72 ( 72 total cards)

12, 24, 36, 48, 60, 72 = 6 cards.

36 are gold.

Total gold cards and multiple of 12 = 36 + 6 =42

Probability of getting one of them is 42/72, which reduces to 7/12

B) 36 silver cards

Multiples of 9: 9, 18, 27, 36, 45, 54,63 = 7 cards

Silver cards are even and there is 3 even cards that are also multiples of 9, so subtract 3 from 7 to get 4.

Total silver cards and multiples of 9 = 36 + 4 = 40

Probability = 40/72 which reduces to 5/9

8 0

3 years ago

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You are given the information that P(A) = 0.30 and P(B) = 0.40.

Ad libitum [116K]

Answer:

1.B. No. You need to know the value of P(A and B). 2.C. Yes P(A and B) =0, so P(A or B) = P(A) + P(B).

Step-by-step explanation:

We can solve this question considering the following:

For two mutually exclusive events:

$\\ A_{1}\;and\;A_{2}$

$\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2})$ (1)

An extension of the former expression is:

$\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2}) - P(A_{1} and A_{2})$ (2)

In mutually exclusive events, P(A and B) = 0, that is, the events are independent one of the other, and we know the probability that both events happen at the same time is zero (P(A and B) = 0). There are some other cases in which if event A happens, event B too, so they are not mutually exclusive because P(A and B) is some number different from zero. Notice the difference between OR and AND. The latter implies that both events happen at the same time.

In other words, notice that the formula (2) provides an extension of formula (1) for those events that are not mutually exclusive, that is, there are some cases in which the events share the same probabilities in a way that these probabilities must be subtracted from the total, so those probabilities in common do not "inflate" the actual probability.

For instance, imagine a person going to a gas station and ask for checking both a tire and lube oil of his/her car. The probability for checking a tire is P(A)=0.16, for checking lube oil is P(B)=0.30, and for both P(A and B) = 0.07.

The number 0.07 represents the probability that both events occur at the same time, so the probability that this person ask for checking a tire or the lube oil of his/her car is:

P(A or B) = 0.16 + 0.30 - 0.07 = 0.39.

That is why we cannot simply add some given probabilities without acknowledging if the events are or not mutually exclusive, whereas we can certainly add the probabilities in question when we know that both probabilities are mutually exclusive since P(A and B) = 0.

In conclusion, knowing the events are mutually exclusive does provide extra information and we can proceed to simply add the probabilities of either event; thus, the answers are those in which we need to previously know the value of P(A and B).

7 0

3 years ago

Solve the proportion for x

KengaRu [80]

I got as the final answer x=13

8 0

3 years ago

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briannas jump rope is 13 feet long. alyssas jump rope is 168 inches long. alyssa says her jump rope is much longer because 168 i

oksano4ka [1.4K]

Alyssa is right because her jump rope is 14 feet long.

7 0

3 years ago

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