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swat32
1 year ago
7

A college student takes the same number of credits each semester. They had 5 credits when they started, and after 2 semesters, t

hey had 31 credits.
Express the rate at which they are earning credits.
Mathematics
1 answer:
gogolik [260]1 year ago
5 0

The rate at which the college student earns credit is 13 credits per semester.

<h3>What is an equation?</h3>

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let the credit earned each semester be x.

This will be illustrated as:

5 + 2x = 31

Collect like terms

2x = 31 - 5

2x = 26

Divide

x = 26/2

x = 13

The rate is 13 credits per semester.

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

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When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 55 bat
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The probability of accepting this shipment is 98%.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Almost all such shipments will be accepted because the probability of having a sample with more than 3 defective batteries is very low.

The shipment will be accepted if at most 3 batteries don't meet specifications.

This can be modeled as a binomial distribution, where the sample size is n=55 and the probability of not meeting the specifications of any battery is p=0.02.

The shipment will be accepted if D ≤ 3.

The probability of this event is:

P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)

P(D=X) = n!/(x!(n-x)!) pˣ(1-p)ⁿ⁻ˣ

P(D=0) = 55!/(0!(55-0)!) 0.02⁰(1-0.02)⁵⁵⁻⁰ = 1× 1 × 0.32 = 0.32

P(D=1) = 55!/(1!(55-1)!) 0.02¹(1-0.02)⁵⁴ = 54 × 0.02 × 0.33= 0.35

P(D=2) = 55!/(2!(55-2)!) 0.02²(1-0.02)⁵³ = 55 ×27 × 0.0004 × 0.34= 0.20

P(D=3) = 55!/(3!(55-3)!) 0.02³(1-0.02)⁵² = 25740× 0.0000008 × 0.35= 0.07

Then,

P( D ≤ 3) = P(D=0) + P(D=1) + P(D=2) + P(D=3)

P( D ≤ 3) = 0.32 + 0.35 + 0.20 + 0.07

P( D ≤ 3) = 0.98

Hence, the probability of accepting this shipment is 98%.

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