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kap26 [50]
1 year ago
11

Karen recorded her walking pace in the table below. what equation best represents this relationship

Mathematics
1 answer:
REY [17]1 year ago
8 0

Given Data:

The table given here shows time taken in the first column and the distance travelled in the second column.

First check the ration of distance /time to verify if the speed of the man is constant or not.

\begin{gathered} \frac{8.75\text{ m}}{2.5\text{ h}}=3.5\text{ m/h} \\ \frac{14\text{ m}}{4\text{ h}}=3.5\text{ m/h} \end{gathered}

As both ratios are same it means the speed of the man is constant and the distance travelled is directly proportional to the time taken and varies linealy with the time.

Now to determine the relationship between <em>m</em> and <em>h </em>we will use the same ratio of <em>m</em> and <em>h</em> which comes in the previous step.

\begin{gathered} \frac{m}{h}=3.5 \\ m=3.5h \end{gathered}

Thus, option (D) is the required solution.

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The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 48,564 miles, with a standard
DerKrebs [107]

Answer:

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

Step-by-step explanation:

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

Normal probability distribution:

Problems of normally distributed samples can be solved using 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 random variable X, with mean \mu and standard deviation \sigma, the sample means with size n of at least 30 can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\mu = 48564, \sigma = 3293, n = 281, s = \frac{3293}{\sqrt{281}} = 196.44

What is the probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct?

This is the pvalue of Z when X = 48101. So

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

By the Central Limit Theorem

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

Z = \frac{48101 - 48564}{196.44}

Z = -2.36

Z = -2.36 has a pvalue of 0.0091

0.0091 = 0.91% probability that the sample mean would be less than 48,101 miles in a sample of 281 tires if the manager is correct

6 0
3 years ago
Find the least common multiple of 10 and 16.
hammer [34]
I'm pretty sure its 80, if this isnt for school i suggest Calculator Soup's LCM calculator (:
7 0
3 years ago
Read 2 more answers
CAN YOU SOLVE THIS MATH PROBLEM 20 POINTS
Zolol [24]
The correct answer is A. x=22

Since the angles of a rectangle are right angles (90 degrees) you would set it up as 90=5x-20. Then combine like terms and solve the equation. (If you need me to show you how step by step tell me)
7 0
2 years ago
Read 2 more answers
Find the unknown side length, x. Write your answer in simplest radical form.
Mama L [17]

<span>The correct answer between all the choices given is the second choice or letter B. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.</span>

4 0
3 years ago
Which characteristics will prove that ΔDEF is an acute, isosceles triangle?
ololo11 [35]

Answer:

  a.  segment DE and segment EF are congruent to each other but not to segment DF, and their slopes are not related.

Step-by-step explanation:

In order for a triangle to be isosceles, two of the line segments must be congruent. (eliminates choices C and D)

If the slopes of the congruent segments are negative reciprocals of each other, the triangle is a right triangle, not an acute triangle. (eliminates choice B)

With choices B, C, D eliminated, we are left with choice A.

__

However, <em>that necessary description is not sufficient</em> to constrain the triangle to be an acute triangle. In order for the triangle to be acute, the third side must be less than √2 times the length of either of the congruent sides.

The correct answer is "none of the above."

3 0
3 years ago
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