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3 years ago

A company makes batteries with an average life span of 300

Mathematics

1 answer:

aksik [14]3 years ago

3 0

Answer:

a) P(z<-0.66) = 0.2546

b) P(-1<z<1) = 0.6826

c) P(z>1.33) = 0.9082

Step-by-step explanation:

Mean = 300

Standard Deviation = 75

a) Less than 250 hours

P(X<250)=?

z = x - mean/ standard deviation

z = 250 - 300 / 75

z = -50/75

z = -0.66

P(X<250) = P(z<-0.66)

Looking for value of z = -0.66 from z score table

P(z<-0.66) = 0.2546

b. Between 225 and 375 hours

P(225<X<375)=?

z = x - mean/ standard deviation

z = 225-300/75

z = -75/75

z = -1

z = x - mean/ standard deviation

z = 375-300/75

z = 75/75

z = 1

P(225<X<375) = P(-1<z<1)

Looking for values from z score table

P(-1<z<1) = P(z<1) - P(z<-1)

P(-1<z<1) = 0.8413 - 0.1587

P(-1<z<1) = 0.6826

c. More than 400 hours

P(X>400) =?

z = x - mean/ standard deviation

z = 400-300/75

z = 100/75

z = 1.33

P(X>400) = P(z>1.33)

Looking for value of z = 1.33 from z-score table

P(z>1.33) = 0.9082

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Step-by-step explanation:

Let

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Total pages read = 31/45x + 42/180x

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If he still has 14 pages left to read on Friday

Total read from Monday to Thursday + Friday

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3 years ago

An airplane needs to reach a velocity of 203.0 km/h to take off. On a 2000 m runway, what is the minimum acceleration necessary

Aliun [14]

Answer:

1.59 m/s²

Step-by-step explanation:

Acceleration = change in Velocity over time. Mathematically it is represented as Δv/Δt

Given values in the question:

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distance 2000 m
Initial velocity is 0 m/s

To use the equation for acceleration time is needed.

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(203/3.6) = 2000/time mltiplying both sides by time

(203/3.6) x time = 2000 making time subject of the formula

time = 2000/(203/3.6)

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Substituting into the acceleration equation

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$\displaystyle \large{w(x) = {x}^{2} + 1 }$

Since we want to find w(x+3), the input would be x+3.

Substitute x = x+3 in.

$\displaystyle \large{w(x + 3) = {(x + 3)}^{2} + 1 }$

Alternate Solution

The answer above works if you want it in vertex form. For this alternate solution, I will convert the function in standard form.

As we know:

$\displaystyle \large{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }$

Therefore:

$\displaystyle \large{ {(x + 3)}^{2} = {x}^{2} + 2(x)(3) + {3}^{2} } \\ \displaystyle \large{ {(x + 3)}^{2} = {x}^{2} + 6x+ 9}$

Now for function w:

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Hence:

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