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Nitella [24]
3 years ago
14

How do I solve this equation: -5/6b + 3/4 = 1/2b - 2/3 ?

Mathematics
1 answer:
Gre4nikov [31]3 years ago
3 0
First get like things on the same side:
-5/6b - 1/2b= -2/3 - 3/4

Then find equivalent fractions to make the equation easier to solve.
-5/6b - 3/6b= -8/12 - 9/12

Then just add things together and solve.
-8/6b= -17/12
-8b= 6(-17/12)
-8b= -17/2
b= (-17/2)/-8
b= 17/16

You can then plug the answer back into the original question to make sure it is the correct answer.
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6 0
2 years ago
A student who is trying to write a paper for a course has a choice of two topics, A and B. If topic A is chosen, the student wil
algol13

Answer:

P(Topic A) = 0.91

P(Topic B) = 0.9163

The student should choose Topic B to maximize the probability of writing a good paper because P(Topic B)>P(Topic A).

Step-by-step explanation:

If Topic A is chosen, 2 books will be ordered (n=2)

If topic B is chosen, 4 books will be ordered (n=4)

Probability that a book arrives in time (p) = 0.7

Probability that a book does not arrive in time (q) = 1 - p = 1 - 0.7 = 0.3

We will <u>use the binomial distribution</u> to find out which topic should the student choose to maximize the probability of writing a good paper. The binomial distribution formula is:

P(X=x) = ⁿCˣ pˣ qⁿ⁻ˣ

where p = probability of success

           q = probability of failure

           n = total no. of trials

           x = no. of successful trials

For Topic A, n = 2, p=0.7 and q=0.3. If topic A is chosen, the student will use at least half the books i.e. he will use either 1 or 2 books. So,

P(Topic A) = P(X=1) + P(X=2)

                 =²C₁ (0.7)¹(0.3)²⁻¹ + ²C₂ (0.7)²(0.3)²⁻²

                 = 0.42 + 0.49

P(Topic A) = 0.91

For topic B, n=4, p=0.7 and q=0.3. If topic B is chosen, the student will choose 2 or more books i.e. 2, 3 or 4 books.

P(Topic B) = P(X=2) + P(X=3) + P(X=4)

                  = ⁴C₂ (0.7)²(0.3)⁴⁻² + ⁴C₃ (0.7)³(0.3)⁴⁻³ + ⁴C₄ (0.7)⁴(0.3)⁴⁻⁴

                  = 0.2646 + 0.4116 + 0.2401

P(Topic B) = 0.9163

The student should choose Topic B to maximize the probability of writing a good paper because P(Topic B)>P(Topic A) as calculated above.

3 0
3 years ago
Answers?? With work please
Naya [18.7K]
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7 0
3 years ago
The length of the flower garden is 3 times as great as the width. What are the dimensions? The area is 48 sq m
Rudiy27
The correct answer is 144
8 0
3 years ago
What is the value of x?​
WINSTONCH [101]

Answer:

\large\boxed{x=8\sqrt2}

Step-by-step explanation:

\bold{METHOD\ 1}\\\\\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=8,\ leg=8,\ hypotenuse=x.\\\text{Substitute:}\\\\x^2=8^2+8^2\\\\x^2=2(8^2)\to x=\sqrt{2(8^2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\sqrt2\cdot\sqrt{8^2}\qquad\text{use}\ \sqrt{a^2}=a\\\\x=8\sqrt2

\bold{METHOD\ 2}\\(look\ at\ the\ picture)\\\\\text{We have}\ a=8.\ \text{Therefore}\ a\sqrt2=8\sqrt2

5 0
3 years ago
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