Find the value of x.

The deck of a card game is made up of 108 cards. Twenty-five each are red, yellow, blue, and green, and eight are wild cards. Ea

Vinvika [58]

Given Information:

Total cards = 108

Red cards = 25

yellow cards = 25

Blue cards = 25

Green cards = 25

Wild cards = 8

Required Information:

Probability that a hand will contain exactly two wild cards in a seven-hand game = ?

Answer:

P = (₈C₂*₁₀₀C₅)/₁₀₈C₇

Step-by-step explanation:

The required probability is given by

P = number of ways of interest/total number of ways

The total number of ways of dealing a seven-card hand is

₁₀₈C₇

We want to select exactly 2 wild cards and the total wild cards are 8 so the number of ways of this selection is

₈C₂

Since the game is seven-card hand, we have to get the number of ways to select remaining 5 cards out of (108 - 8 = 100) cards.

₁₀₀C₅

Therefore, the setup for this problem becomes

P = number of ways of interest/total number of ways

P = (₈C₂*₁₀₀C₅)/₁₀₈C₇

This is the required setup that we can type into our calculators to get the probability of exactly two wild cards in a seven-hand card game with 8 wild cards and 108 total cards.

7 0

3 years ago

Independent random samples of vehicles traveling past a given point on an interstate highway have been observed on monday versus

quester [9]

Hi!

To compare this two sets of data, you need to use a t-student test:

You have the following data:

-Monday n1=16; x̄1=59,4 mph; s1=3,7 mph

-Wednesday n2=20; x̄2=56,3 mph; s2=4,4 mph

You need to calculate the statistical t, and compare it with the value from tables. If the value you obtained is bigger than the tabulated one, there is a statistically significant difference between the two samples.

$t= \frac{X1-X2}{ \sqrt{ \frac{(n1-1)* s1^{2}+(n2-1)* s2^{2} }{n1+n2-2}} * \sqrt{ \frac{1}{n1}+ \frac{1}{n2}} } =2,2510$

To calculate the degrees of freedom you need to use the following equation:

$df= \frac{ (\frac{ s1^{2}}{n1} + \frac{ s2^{2}}{n2})^{2}}{ \frac{(s1^{2}/n1)^{2}}{n1-1}+ \frac{(s2^{2}/n2)^{2}}{n2-1}}=33,89$ ≈34

The tabulated value at 0,05 level (using two-tails, as the distribution is normal) is 2,03. https://www.danielsoper.com/statcalc/calculator.aspx?id=10

So, as the calculated value is higher than the critical tabulated one, we can conclude that the average speed for all vehicles was higher on Monday than on Wednesday.

5 0

3 years ago

Solve for x: 4(x + 2) = 3(x − 2) A) −2 B)−4 C) −10 D) −14

BARSIC [14]

4(x+2)=3(x-2)

Multiply the first bracket by 4

Multiply the second bracket by 3

4x+8=3x-6

Move 3x to the left hand side, whenever moving a number with a letter the sign changes ( positive 3x to negative 3x)

4x-3x+8=3x-3x-6

x+8=-6

Move positive 8 to the right hand side

x+8-8=-6-8

x=-14

Check answer by using substitution method

Use x=-14 into both of the equations

4(-14+2)=3(-14-2)

-56+8=-42-6

-48=-48

Answer is -14- D)

6 0

3 years ago

Help please?!?!??!?!!!?!?!?!?!?!?!?!!?!?!?

marissa [1.9K]

Answer:

16.7%

Step-by-step explanation:

Probability is defined by the formula: the number of desirable outcomes over the total outcomes. The total number of outcomes is the sum of all shoes that he could possibly pick:

5 + 7 + 1 + 4 + 6 + 8 + 2 + 3 = 36

And the desirable outcomes are those where he picks brown boots, which is 6 outcomes.

Using the formula for probability, we get the expression: 6/36 to represent the probability. It simplifies to 1/6 which is about 16.7%

3 0

3 years ago

The length of a table is 6 feet. On a scale drawing, the length is 2 inches. Write three possible scales for the drawing.

Rus_ich [418]

A possible scale for the drawing can be
1 inches : 3 feet.
2 inches : 6 feet
or 3 inches to 9 feet
or 0.5 inches to 1.5 feet.

Hope this helps :)

6 0

3 years ago