Find the center and radius of the circle: x2 + y2 - 8x

Suppose a basketball player has made 231 out of 361 free throws. If the player makes the next 2 free throws, I will pay you $31.

statuscvo [17]

Answer:

The expected value of the proposition is of -0.29.

Step-by-step explanation:

For each free throw, there are only two possible outcomes. Either the player will make it, or he will miss it. The probability of a player making a free throw is independent of any other free throw, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Suppose a basketball player has made 231 out of 361 free throws.

This means that $p = \frac{231}{361} = 0.6399$

Probability of the player making the next 2 free throws:

This is P(X = 2) when n = 2. So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{2,2}.(0.6399)^{2}.(0.3601)^{0} = 0.4095$

Find the expected value of the proposition:

0.4095 probability of you paying $31(losing $31), which is when the player makes the next 2 free throws.

1 - 0.4059 = 0.5905 probability of you being paid $21(earning $21), which is when the player does not make the next 2 free throws. So

$E = -31*0.4095 + 21*0.5905 = -0.29$

The expected value of the proposition is of -0.29.

3 0

2 years ago

Jessica's annual salary decreased by 3800, which was a 9% decrease. what was Jessica's original salary?

Andrei [34K]

Answer:

Step-by-step explanation:

x = original salary

$3800 = (1-9%)x = (1-0.09)x = 0.91x

x = $3800/0.91 = $4175.82

7 0

3 years ago

Find the equation of a line that is parallel to the line x equals negative 1x=−1 and contains the point left parenthesis negativ

sineoko [7]

The equation of the line is given as $y-x=-1$

A straight line equation is given in the form $y=mx+c$ where $m$ is the gradient and $c$ is the y-interest.

We need to rearrange $y-x=-1$ to make $y$ the subject.
$y= x-1$ ⇒ from here we can read the gradient and the y-intercept. The gradient, $m=1$ and $c=-1$ .

A line that is parallel to $y=x-1$ will have the same gradient, $m=1$ but different y-intercept. One example of equation of a line that is parallel to $y=x-1$ is $y=x+3$

8 0

3 years ago

Which statements about the function are true? Select two

iogann1982 [59]

Answer:

The vertex of the function is at (1,-25)

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one.

Part of the graph of the function f(x) = (x + 4)(x-6) is shown below.

Which statements about the function are true? Select two

options.

The vertex of the function is at (1,-25).

The vertex of the function is at (1,-24).

The graph is increasing only on the interval -4< x < 6.

The graph is positive only on one interval, where x <-4.

The graph is negative on the entire interval

My answer:

Given the factored form of the function:

f(x) = (x + 4)(x-6)

<=> f(x) = $x^{2} - 2x -24$

We will convert to vertex form

<=> f(x) = ( $x^{2} - 2x +1$ ) - 25

<=> f(x) = $(x-1)^{2} -25$

=> the vertex of the function is: (1,-25)

We choose: a. The vertex of the function is at (1,-25)

Let analyse other possible answers:

c. The graph is increasing only on the interval -4< x < 6.

Because the parameter a =1 so the graph open up all over its domain and the vertex is the lowest point.

So the graph is increasing in the domain (1, +∞)

=> C is wrong

d. The graph is positive only on one interval, where x <-4

Wrong, The graph is positive only on one interval, where x > 6

e. The graph is negative on the entire interval

Wrong, The graph is negative only on one interval, where -4< x < 6.

7 0

3 years ago

PLZ HELP! Need this ASAP! Thx so much! Find m∠PMK Plz show ur work!

max2010maxim [7]

In ∆MKP and ∆MNP

MK = MN

PK = NP

MP = MP

SO ∆MKP AND ∆MNP ARE CONGRUENT.

SO m<PMN = m<PMK

m<NMK = 50

=> m<PMN + m<PMK = 50

=> 2 m<PMK = 50

=> m<PMK = 50/2 = 25°

3 0

3 years ago

Find the center and radius of the circle: x2 + y2 - 8x – 12y + 43 = 0