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baherus [9]
1 year ago
10

Lulu wants to get fit. She started with 50 laps a day and she intends to add 10 laps every week. Write a mathematical expression

for this statement.
Mathematics
1 answer:
Bumek [7]1 year ago
8 0

The mathematical expression for the given statement is 50 + 10x

<h3>How to write a mathematical expression for this statement?</h3>

The given parameters are:

Initial distance = 50 laps

Rate of increment = 10 laps each week

Represent the number of weeks with x

So, we have:

Number of laps = Initial distance + Rate of increment * Number of weeks

This gives

Number of laps = 50 + 10 * x

Evaluate

Number of laps = 50 + 10x

Hence, the mathematical expression for the given statement is 50 + 10x

Read more about expressions at:

brainly.com/question/723406

#SPJ1

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A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x is used to estimat
zmey [24]

Answer:

a) 0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b) 0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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 = \frac{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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

Z = \frac{X - \mu}{s}

X = 205

Z = \frac{X - \mu}{s}

Z = \frac{205 - 200}{5}

Z = 1

Z = 1 has a pvalue of 0.8413.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{195 - 200}{5}

Z = -1

Z = -1 has a pvalue of 0.1587.

0.8413 - 0.1587 = 0.6426

0.6426 = 64.26% probability that the sample mean will be within +/- 5 of the population mean.

b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 210 subtracted by the pvalue of Z when X = 190.

X = 210

Z = \frac{X - \mu}{s}

Z = \frac{210 - 200}{5}

Z = 2

Z = 2 has a pvalue of 0.9772.

X = 195

Z = \frac{X - \mu}{s}

Z = \frac{190 - 200}{5}

Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

0.9544 = 95.44% probability that the sample mean will be within +/- 10 of the population mean.

7 0
3 years ago
I need help plzzzzz this is really confusing
Anuta_ua [19.1K]

Answer:

B. <u>x</u><u><</u><u> </u>-3

hope it helps.

<h3>stay safe healthy and happy.</h3>
5 0
3 years ago
Read 2 more answers
Please help, I really would love it
Amanda [17]

Answer:

A,C, and D I believe.

Step-by-step explanation:

3 0
3 years ago
Add the following:
PIT_PIT [208]

Step-by-step explanation:

1) 7/23 + 11/23 + 9/23

7+11+9/23

27/23

= 1 4/23

2) 2 5/7 + 9 4/7

11 9/7

= 11.12

3) 9/20 + 3/5

9+12/20

21/20

= 1 1/20 or 1.05

8 0
3 years ago
Keegan deposits into her savings account at the beginning of the year. The account earns 3% simple interest each year. She has $
fiasKO [112]

Answer:

She deposits $350 into the account at the beginning of the year.

Step-by-step explanation:

Let us assume that Keegan deposits $P into her savings account at the beginning of the year.

The account earns 3% simple interest each year and she has $360.50 in her account at the end of the year.

If Keegan did not make any additional deposits or withdrawals during the year.

So, we can write that P[1+\frac{3}{100} ]= 360.50

⇒ P = $350 (Answer)

7 0
3 years ago
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