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3 years ago

How do you do proofs

Mathematics

1 answer:

AnnyKZ [126]3 years ago

8 0

Answer:

you can watch YT videos or search online. search: How to solve proofs. Also search up proof theorems. This will help you even more towards solving more complex proof problems.

Step-by-step explanation:

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The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacemen

mamaluj [8]

<h2>Answer:</h2>

(a)

The probability is : 1/2

(b)

The probability is : 1/2

<h2>Step-by-step explanation:</h2>

The numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement.

The total combinations that are possible are:

(1,2) (1,3) (1,4) (1,5)

(2,1) (2,3) (2,4) (2,5)

(3,1) (3,2) (3,4) (3,5)

(4,1) (4,2) (4,3) (4,5)

(5,1) (5,2) (5,3) (5,4)

i.e. the total outcomes are : 20

(a)

Let A denote the event that the first number is 4.

and B denote the event that the sum is: 9.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

We know that it could be calculated by using the formula:

$P(A|B)=\dfrac{P(A\bigcap B)}{P(B)}$

Hence, based on the data we have:

$P(A\bigcap B)=\dfrac{1}{20}$

( Since, out of a total of 20 outcomes there is just one outcome which comes in A∩B and it is: (4,5) )

and

$P(B)=\dfrac{2}{20}$

( since, there are just two outcomes such that the sum is: 9

(4,5) and (5,4) )

Hence, we have:

$P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}$

(b)

Let A denote the event that the first number is 3.

and B denote the event that the sum is: 8.

Let P denote the probability of an event.

We are asked to find:

P(A|B)

Hence, based on the data we have:

$P(A\bigcap B)=\dfrac{1}{20}$

( since, the only outcome out of 20 outcomes is: (3,5) )

and

$P(B)=\dfrac{2}{20}$

( since, there are just two outcomes such that the sum is: 8

(3,5) and (5,3) )

Hence, we have:

$P(A|B)=\dfrac{\dfrac{1}{20}}{\dfrac{2}{20}}\\\\i.e.\\\\P(A|B)=\dfrac{1}{2}$

7 0

3 years ago

Cscx/secx = cotx<br><br> Verify with steps please :)

Dovator [93]

Csc(x) = 1/sin(x)
sec(x) = 1/cos(x)
cot(x) = [1/sin(x)] / [1/cos(x)]
cot(x) = 1/sin(x) * cos(x)/1
cot(x) = cos(x) / sin(x)
cot(x) = cot(x)

6 0

3 years ago

Mark is in training for a bicycle race. He needs to ride 50 kilometers a week as part of his training. He rode 18.23 kilometers

Nikitich [7]

Answer:

The answer is B, 17.83 km.

Step-by-step explanation:

To solve this, we need to first find out how many kilometers he rode for both Monday and Wednesday. To do this, add 13.94 and 18.23 together. The answer is 32.17 kilometers. Since we know he has to ride 50 kilometers for the week, we can subtract 32.17 from 50 to find the answer. Note that I didn't attempt to convert 32.17 to kilometers since that was the unit of measure it was already in. Now, after you have done 50-32.17, you will get 17.83. Put this in kilometers. This gives us our answer, which is 17.83 km. Mark needs to ride for 17.83 more kilometers to complete his training for the week.

7 0

3 years ago

Ax-c=2x+5 solve for x

Dmitriy789 [7]

Ax - c = 2x + 5
ax - c + c = 2x + 5 + c
ax = 2x + 5 + c
ax - 2x = 2x - 2x + 5 + c

ax - 2x = c + 5
X(a - 2) = c + 5
X(a - 2)/(a - 2) = c+5/(a-2)

X = c+5/a-2

I believe this would be the solution.

8 0

3 years ago

A number cube with the numbers 1 through 6 is rolled. What is the probability of the number cube showing an even number or a num

inna [77]

Answer:

Step-by-step explanation:

The correct answer is 5/6 = 83.3%

I really hope this helps!

8 0

3 years ago