Can someone help with this???

Mathematics

1 answer:

Sedbober [7]3 years ago

3 0

Answer:

x=7

Step-by-step explanation:

The pattern is: i^1 = i, i^2 = −1, i^3 = −i, i^4 = 1, i^5 = i, i^6 = −1 and repeats again, so x = 7 would be i^20 = $(i^{4} )^{5}$ = 1^5 = 1

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Peter leaves Mitchell's house traveling 30 mph. Mitchell leaves 15 min later, trying to catch up to peter, going 40 mph. if they

UkoKoshka [18]

Answer:

45 minutes

Step-by-step explanation:

At 30 mph for 1/4 hour, Peter has a 7.5 mile head start. After he leaves, Mitchell closes that gap at the rate of 40-30 = 10 miles per hour. It will take him ...

t = d/s

t = (7.5 mi)/(10 mi/h) = 0.75 h

to catch Peter.

Mitchell will catch Peter in 45 minutes.

<em>Alternate Solution</em>

Another way to look at it is that Mitchell's 10 mph advantage is 1/3 of Peter's speed, so it will take 1/(1/3) = 3 times the period of Peter's head start:

3 × 15 minutes = 45 minutes . . . for Mitchell to catch Peter

_____

You can write equations involving time and distance and see where the distances traveled become the same. You need to be careful choosing the time reference, since you're concerned with Mitchell's travel time. I personally prefer to work "head start" problems by considering the differences in time and speed, as above. This is where you end up using the equations approach, anyway.

4 0

3 years ago

Heated-treated parts are specified to have a hardness of at least 45 (lower specification limit). Any parts that are below 45 ar

Nataly_w [17]

Answer:

$P(X$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

The figure shows the calculation for this case.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the hardness of a population, and for this case we know the distribution for X is given by:

$X \sim N(48.5,2)$