4. You have a deck of 40 number cards: five of each number 2 to 9. You shuffle the deck, pick a card, look at it, return it to the deck, and then repeat for a second card. Determine each theoretical probability. a) sum is 12 b) difference is less than 5 c) product is odd
Answers
To determine the theoretical probabilities, we'll analyze the different possible outcomes for each case.
Total number of cards = 40 (5 cards for each number from 2 to 9)
a) Sum is 12:
There are several combinations of cards that can result in a sum of 12:
- 3 and 9
- 4 and 8
- 5 and 7
- 7 and 5
- 8 and 4
- 9 and 3
Total favorable outcomes = 6 (since there are 6 possible combinations)
Total possible outcomes (since you're drawing two cards) = 40 * 40 = 1600
Probability (sum is 12) = (Number of favorable outcomes) / (Total possible outcomes)
Probability (sum is 12) = 6 / 1600 = 0.00375
b) Difference is less than 5:
There are several combinations of cards that can result in a difference less than 5:
- 2 and 3
- 3 and 2
- 3 and 4
- 4 and 3
- 4 and 5
- 5 and 4
- 5 and 6
- 6 and 5
- 6 and 7
- 7 and 6
- 7 and 8
- 8 and 7
- 8 and 9
- 9 and 8
Total favorable outcomes = 14
Total possible outcomes = 1600
Probability (difference is less than 5) = 14 / 1600 = 0.00875
c) Product is odd:
For the product to be odd, one or both of the numbers drawn must be odd. Since there are five odd numbers (3, 5, 7, 7, 9), and each number has five cards, the total number of favorable outcomes is 5 + 5 + 5 + 5 + 5 = 25.
Total possible outcomes = 1600
Probability (product is odd) = 25 / 1600 = 0.015625
To summarize:
- a) Probability (sum is 12) ≈ 0.00375
- b) Probability (difference is less than 5) ≈ 0.00875
- c) Probability (product is odd) ≈ 0.015625
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Solve the inequality 4x-7<5
Answers
I will get rid of y. So, we can multiply the second equation by 2. This gives us
2x-2y=10
Now, we can add both equations
This gives us 7x=-14
Therefore, x = -2
Plug that into another equation.
-10 + 2y=-24
Therefore, y = -7
Hope this helped!! :D
1x - 1y = 5 ⇒ 2x - 2y = 10
7x = -14
7 7
x = -2
x - y = 5
-2 - y = 5
+ 2 + 2
-y = 7
-1 -1
y = -7
(x, y) = (-2, -7)
A = {KL}
A = {KJ, KL}
A = {KL, LK}
A = {KJ, KL, LJ}
Answers
Answer: First Option is correct.
Step-by-step explanation:
Since we have given that
There are three person : Joe, Keitaro, Luis.
And two names will be selected for he game .
Possible events will be
But we want to find the complement of the event in which Joe plays in hte first match,
As we know that complement of any events means eliminate that event from the universal set.
Event of getting Joe plays in the first match is given by
So, complement of this event that Joe plays in the first match is given by
so, First Option is correct.
{JK, JL, KL}
The events where J does not play (the first game) are: {KL}
Answer: A = {KL}
Answers
Answer:
124.2
Step-by-step explanation:
increase 92 by 35% would be to multiply 92 by 135%
92(135%)=92(1.35)=124.2
Answers
Answer:
It would require 40 teaspoons
Step-by-step explanation:
Given that;
A cookie recipe requires 3 teaspoons of baking soda for 36 cookies
The amount of teaspoons of baking soda required per cookie is;
r = 3/36 teaspoons per cookie
So, for 480 cookies i would require;
N = r × 480 cookies
Substituting r, we have;
N = 3/36 teaspoons per cookie × 480 cookies
N = 40 teaspoons
It would require 40 teaspoons
Answers
Answer:
First option on the list:
Step-by-step explanation:
Use the distributive property of exponents to get rid of parentheses in the algebraic expression, evaluate the powers of the numerical factors, and finally, cancel common factors in numerator and denominator to arrive at the final answer:
Answers
Answer:
The length and width that maximize the area are:
W = 2*√8
L = 2*√8
Step-by-step explanation:
We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.
Remember that the area of a rectangle of length L and width W, is:
A = L*W
You can see the image below to see how i will define the length and the width:
L = 2*x'
W = 2*y'
Where we have the relation:
4 = √(x'^2 + y'^2)
16 = x'^2 + y'^2
Now we can isolate one of the variables, for example, x'
16 - y'^2 = x^'2
√(16 - y'^2) = x'
Then we can write:
W = 2*y'
L = 2*√(16 - y'^2)
Then the area equation is:
A = 2*y'*2*√(16 - y'^2)
A = 4*y'*√(16 - y'^2)
If A > 1, like in our case, maximizing A is the same as maximizing A^2
Then if que square both sides:
A^2 = (4*y'*√(16 - y'^2))^2
= 16*(y'^2)*(16 - y'^2)
= 16*(y'^2)*16 - 16*y'^4
= 256*(y'^2) - 16*y'^4
Now we can define:
u = y'^2
then the equation that we want to maximize is:
f(u) = 256*u - 16*u^2
to find the maximum, we need to evaluate in the zero of the derivative:
f'(u) = 256 - 2*16*u = 0
u = -256/(-2*16) = 8
Then we have:
u = y'^2 = 8
solving for y'
y' = √8
And we know that:
x' = √(16 - y'^2) = √(16 - (√8)^2) = √8
And the dimensions was:
W = 2*y' = 2*√8
L = 2*y' = 2*√8
These are the dimensions that maximize the area.