Write the equation of a parabola with a vertex at (0,0) and directrix at (0,4)

In a lottery game, a player picks six numbers from 1 to 21. If the player matches all six numbers, they win 40,000 dollars. Othe

Darina [25.2K]

Answer:

The expected value of this game is -$0.26.

Step-by-step explanation:

Expected value:

Each possible earning/loss multiplied by it's probability.

Probability:

Number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the numbers are chosen is not important. So we use the combinations formula to solve.

Combinations formula:

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

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

Probability of winning:

Desired outcomes:

The 6 correct numbers, so $D = 6$

Total outcomes:

6 numbers from a set of 21. So

$T = C_{21,6} = \frac{21!}{6!15!} = 54264$

Probability:

$p = \frac{1}{54265}$

Expected value

$\frac{1}{54265}$ probability of earning 40,000.

$\frac{54264}{54265}$ probability of losing 1. So

$E = \frac{40,000}{54265} - \frac{54264}{54265} = -0.26$

The expected value of this game is -$0.26.

7 0

3 years ago

the ratio of white pens to green pens is 2 to 8. how many green pens are there if there are 18 white pens?

NISA [10]

There are 72 green pens.

There is 9 times as many white pens from 2 to 18, so there has to be 9 times as many green pens because of the ratio. 9 times 8 is 72.

5 0

3 years ago

Please answer this with explanation. Please I really am struggling. I will mark you brainalist. Please solve it Please

Hatshy [7]

Answer:

13, 11, 4, 16, 6, 22

Step-by-step explanation:

Let the second digit be x and the last digit be y

Given:

Data set: 13, x, 4, 16, 6, y
Mean = 12
y = 2x or x = 2y

The mean of the data is the average. The average can be calculated by determining the sum of the terms and dividing it by the total digits.

$\implies \text{Mean of data:} \ \dfrac{13 + x + 4 + 16 + 6 + y}{6} = 12$

Let us substitute the value of y (2x) in the data.

$\implies \dfrac{13 + x + 4 + 16 + 6 + 2x}{6} = 12$

Now, add all the terms in the data and simplify.

$\implies \dfrac{39 + x +2x}{6} = 12$

$\implies \dfrac{39 + 3x}{6} = 12$

Distribute the denominators and simplify.

$\implies \dfrac{39}{6} + \dfrac{3x}{6} = 12$

$\implies \dfrac{13}{2} + \dfrac{x}{2} = 12$

$\implies 6.5 + \dfrac{x}{2} = 12$

Subtract 6.5 both sides and simplify.

$\implies 6.5 + \dfrac{x}{2} - 6.5 = 12 - 6.5$

$\implies \dfrac{x}{2} = 5.5$

Use cross multiplication and simplify.

$\implies x= 5.5 \times 2$

$\implies x= 11$

To determine the value of "y", simply substitute the value of "x" into the expression that represents the value of "y".

$\implies y = 2x$

$\implies y = 2(11)$

$\implies y = 22$

When the x and y values are substituted in the data, we get;

⇒ 13, 11, 4, 16, 6, 22

Therefore, the data is 13, 11, 4, 16, 6, 22.

8 0

2 years ago

Graph of a cubic polynomial that falls to the left and rises to the right with x intercepts negative 2, negative 1, and 2

xz_007 [3.2K]

Hello,

A cubic polynomial with -2,1,2 as roots is
f(x)=k*(x+2)(x+1)*(x-2)=k(x²-4)(x+1)=k(x^3+x²-4x-4)

Looking the answers ==>k=1

==>Answer A

6 0

3 years ago

Read 2 more answers

PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! Which graph represents

KATRIN_1 [288]

Answer: D

Step-by-step explanation:

Vertex form is: f(x) = a(x - h)² + k where (h, k) is the vertex.

f(x) = (x - 3)² - 5

the vertex is (3, 5).
"a" is positive (+1), so it points upward.

The only graph that matches is the last one, which I called graph D.

6 0

3 years ago