Distributive property to rewrite the following expression n(r + s)

A typical marathon is 26.2 miles. Allan averages 12 kilometers per hour when running in marathons. Determine how long it would t

Natali [406]

Answer:

The time taken by Allan to complete the marathon 3.5 hours

Step-by-step explanation:

Given as :

The distance cover in marathon = d = 26.2 miles

∵ 1 mile = 1.609 km

So, d = 26.2 × 1.609 km

i.e d = 42.155 kilo meter

The average speed of Allan = s = 12 km per hour

Let the time taken by Allan to complete the marathon = t hours

Now, ∵ Time = $\dfrac{\textrm Distance}{\textrm Speed}$

Or, t = $\dfrac{\textrm d}{\textrm s}$

Or, t = $\dfrac{\textrm 42.155 km}{\textrm 12 kmph}$

or, t = 3.512 hours

So , The time taken by Allan to complete the marathon = t = 3.5 hours

Hence, The time taken by Allan to complete the marathon 3.5 hours Answer

4 0

3 years ago

Find the solution of this system of equations? -8x-6y=60 5x+6y=-69

zvonat [6]

First subtract the x variable on both sides so on the first equation youll have -6y=8x+60 then divide 6 on all variables which means youll have y=8/6x+10 and in the second equation you do the same thing and youll have y=-5/6x-11.5

7 0

3 years ago

Read 2 more answers

Find the value of x so the function has the given value. t(x)=2x-4;t(x)=1/2

Klio2033 [76]

Answer:

9/4

Step-by-step explanation:

3 0

3 years ago

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.8. (Round your ans

Alenkinab [10]

Answer:

a) 0.011 = 1.1% probability that the sample mean hardness for a random sample of 17 pins is at least 51

b) 0.0001 = 0.1% probability that the sample mean hardness for a random sample of 45 pins is at least 51

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 are 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 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 $s = \frac{\sigma}{\sqrt{n}}$ .