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skelet666 [1.2K]
3 years ago
8

3) The average age of students at XYZ University is 24 years with a standard deviation of 8 years. Number of students at the uni

versity is 7500. A random sample of 36 students is selected. What is the probability that the sample mean will be between 25.5 and 27 years
Mathematics
1 answer:
otez555 [7]3 years ago
3 0

Answer:

0.1875

Step-by-step explanation:

σM=σ/√N

=8/√7500

=8/86.608

=0.092

Z=(x-μ)/σ/√N

=(25.5-36)/8/√7500

=-10.5/0.0092=-1141.304

Z score = -1.3125

=(27-36)/8/√7500 =

=9/0.0092=978.261

Z score= -1.125

-1.125-(-1.3125)=-1.125+1.3125)= 0.1875

The probability that the sample mean will be between 25.5 and 27 years

P(between 25.5 and 27) = 0.1875

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Nikitich [7]

The acceleration of the particle is given by the formula mentioned below:

a=\frac{d^2s}{dt^2}

Differentiate the position vector with respect to t.

\begin{gathered} \frac{ds(t)}{dt}=\frac{d}{dt}\sqrt[]{\mleft(t^3+1\mright)} \\ =-\frac{1}{2}(t^3+1)^{-\frac{1}{2}}\times3t^2 \\ =\frac{3}{2}\frac{t^2}{\sqrt{(t^3+1)}} \end{gathered}

Differentiate both sides of the obtained equation with respect to t.

\begin{gathered} \frac{d^2s(t)}{dx^2}=\frac{3}{2}(\frac{2t}{\sqrt[]{(t^3+1)}}+t^2(-\frac{3}{2})\times\frac{1}{(t^3+1)^{\frac{3}{2}}}) \\ =\frac{3t}{\sqrt[]{(t^3+1)}}-\frac{9}{4}\frac{t^2}{(t^3+1)^{\frac{3}{2}}} \end{gathered}

Substitute t=2 in the above equation to obtain the acceleration of the particle at 2 seconds.

\begin{gathered} a(t=1)=\frac{3}{\sqrt[]{2}}-\frac{9}{4\times2^{\frac{3}{2}}} \\ =1.32ft/sec^2 \end{gathered}

The initial position is obtained at t=0. Substitute t=0 in the given position function.

\begin{gathered} s(0)=-23\times0+65 \\ =65 \end{gathered}

8 0
1 year ago
I don’t get this :(
muminat
Ok so for the first one it’s super simple I’m gonna do it as less complicated so it can help you :)


So first we need to convert the mixed number to an improper fraction


1 4/5 = 9/5


Now we need to reduce the numbers greatest common divisor which is 3

3/5 x 6

Now multiply the numbers


Your answer is 18/5 I hoped this help



Now for the second one

this one is a little more complicated and I don’t know how to make it sound easier so I’m gonna tell you the answer which is 580/21


The last one is the same steps we did for the first one which is 27/20



I hoped this helped you it is a little difficult but you’ll get the hang of it :)

5 0
3 years ago
Rachel has 20 marbles in a jar. This table shows the number of blue, black, red, orange, and green marbles. What is the probabil
Tema [17]
Assuming the numbers are percents, the answer is 25%, because 5/20 is 1/4, then convert the fraction to a percentage and you get 25%.
5 0
3 years ago
Read 2 more answers
You know the measure of the exterior angle which forms a linear pair with the vertex angle. Describe two ways you can find measu
aev [14]

Answer:

Step-by-step explanation:

A linear pair are two given angles whose sum is equal to 180^{o}.

Let the exterior angle be represented by x^{o}, and the three interior angles of the triangle be represented by a^{o}, b^{o} and c^{o}.

Assume that the vertex angle c^{o} is the linear pair to the exterior angle x^{o}.

i.e            x^{o} + c^{o} = 180^{o}  (sum of angles on a straight line)

Thus,

i. a^{o} +  b^{o} = x^{o}  (sum of two opposite interior angles is equal to an exterior angle)

⇒ a^{o}  = x^{o} - b^{o}

Also,

b^{o}  = x^{o} - a^{o}

But,

a^{o} + b^{o} + c^{o} = 180^{o}   (sum of angles in a triangle)

⇒ c^{o} = 180^{o} - (a^{o} +  b^{o})

and

a^{o} + b^{o} = 180^{o} - c^{o}

ii. a^{o} + b^{o} + c^{o} = 180^{o}   (sum of angles in a triangle)

a^{o} = 180^{o} - (b^{o} + c^{o})

Also,

a^{o} +  b^{o} = x^{o}

⇒ b^{o} = x^{o} - a^{o}

c^{o} = 180^{o} - x^{o}

8 0
3 years ago
PLEASE HELP THIS IS DUE BY 10 MINUTES
garri49 [273]

Answer:

Both 10 and 2

Step-by-step explanation:

Hope this helpsss

3 0
2 years ago
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