MATHEMATICS COLLEGE

When proving a statement using mathematical induction, part of the process is assuming that the statement is true for the nth case. (True or False).

Answers

Answer 1

Answer:

Answer:

True

Step-by-step explanation:

We assume that is true for the nth case and prove it for the n+1 case

and show that it is true for the case when n=1

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2) Zoe was practicing for a marathon. She practiced for six days, runningfour miles each day. How many miles did Zoe run altogether?
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After writing a $800 check to pay a bill, a student had a balance of $350 in his account. How muchdid he have in the account before he wrote the check?a) Let X = his balance before writing the check. Write the equation you would use to solve thisproblem.

A high school student took two college entrance exams, scoring 1070 on the SAT and 25 on the ACT. Suppose that SAT scores have a mean of 950 and a standard deviation of 155 while the ACT scores have a mean of 22 and a standard deviation of 4. Assuming the performance on both tests follows a normal distribution, determine which test the student did better on.

Answers

Answer:

Due to the higher z-score, he did better on the SAT.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Determine which test the student did better on.

He did better on whichever test he had the higher z-score.

SAT:

Scored 1070, so $X = 1070$

SAT scores have a mean of 950 and a standard deviation of 155. This means that $\mu = 950, \sigma = 155$ .

$Z = (X - \mu)/(\sigma)$

$Z = (1070 - 950)/(155)$

$Z = 0.77$

ACT:

Scored 25, so $X = 25$

ACT scores have a mean of 22 and a standard deviation of 4. This means that $\mu = 22, \sigma = 4$

$Z = (X - \mu)/(\sigma)$

$Z = (25 - 22)/(4)$

$Z = 0.75$

Due to the higher z-score, he did better on the SAT.

Grace's walking rate is 1.5 meters per second. Her house is 90 meters from the fountain. How many seconds will it take her to reach the fountain?

Answers

Grace's walking rate is 1.5 meters per second. Her house is 90 meters from the fountain. How many seconds will it take her to reach the fountain?

Answer: We know that Grace's walking rate is 1.5 meters per second

Number of meters Grace's house is from fountain is 90 meters.

Therefore, the time it will take Grace to reach the fountain is:

$(Distance-between-House-and-fountain)/(Grace's-walking-rate)$

$(90)/(1.5) =60 seconds$

Therefore, it will take Grace 60 seconds to reach fountain

Speed=1.5

Distance=90 meters

Time=?

Distance= time × speed

Thus,

T=distance/speed

=90/1.5

= 60 second

= 1 minute

The product of two numbers is 16/3 if one of the number is 48/5 what is the other one?

Answers

Answer:

The other number is 5/9.

Step-by-step explanation:

16/3 = 48/5 * x

x = 5/9

3 less than a number b divided by 2

Answers

Answer:

The equation would be written as fallowed

f(d)=d/2-3

Step-by-step explanation:

The expression 3a + 2b + c / d gives the average number of points a team earns in d games by winning a games in regulation, b games in overtime and losing c games in overtime. What is the average number of points earned for a team that wins 10 games in regulation, wins 8 in overtime, loses 6 in overtime, and loses 4 in regulation?

Answers

Answer:

Step-by-step explanation:

10+8-6-4=8

Use the following to answer Sean takes two 250 mg chewable calcium tablets each day, 6) How many milligrams of calcium will Sean take in a week?
7) How many grams of calcium will Sean take in a week?

Answers

6. 1,750 mg in a week 7. 1.75 g in a week

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