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Yakvenalex [24]
3 years ago
9

Jeremiah wants to estimate the mean age of students at his large university. He'll sample n students and make a 95%, percent con

fidence interval for the mean age. He is willing to use σ=3 years as an estimate of the standard deviation, and he wants the margin of error to be no more than 1 year. Which of these is the smallest approximate sample size required to obtain the desired margin of error?
Mathematics
2 answers:
ANEK [815]3 years ago
7 0

Answer:

Hint: 95% is close to a whole for example 0.95 is 95% of 1

Step-by-step explanation:

Gnoma [55]3 years ago
5 0

Answer:

35 students

Step-by-step explanation:

khan

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Find the volume of a cylinder whose base is an ellipse with axes of 12 inches and 7 inches. The altitude of the cylinder is 21 i
Tpy6a [65]

if the ellipse has a major axis of 12 inches, that means its major radius is half that, or 6, and if its minor axis is 7, then its minor radius is half that, 3.5.


\bf \textit{volume of an elliptical cylinder}\\\\
V=\pi ab h~~
\begin{cases}
a=\textit{major axis radius}\\
b=\textit{minor axis radius}\\
h=height\\[-0.5em]
\hrulefill\\
a=6\\
b=3.5\\
h=21
\end{cases}
\\\\\\
V=\pi (6)(3.5)(21)\implies V\approx 1385.44236023309881816203

3 0
3 years ago
A drawer has some red, green, and blue marbles. There are 33 marbles in all. Thete are 4 times as many red marbles as green marb
Vinvika [58]
Let:
x - green marbles
4x - red marbles
x/2 - blue marbles

x+4x+\frac{x}{2}=33|\cdot2\\
2x+8x+x=66\\
11x=66\\
\boxed{x=6}\\\\
\boxed{4x=24}\\\\
\boxed{\frac{x}{2}=3}

6 0
3 years ago
Eric wants to send a package to his mother. If he chooses UPS, the fixed express fee is 10 dollars and each kilogram costs 2 dol
o-na [289]

Answer:

10kg

Step-by-step explanation:

For UPS;

express fee = $10

If one kg costs $2, then x kg of package will coat $2x

Total cost of shipping xkg of package will be 10+2x

For FedEx;

Fixed express fee = $20

If one kg costs $1, then x kg of package will coat $1x

Total cost of shipping x kg of package is 20+x

If the total costs of the two options are the same, then;

10+2x = 20+x

2x-x = 20-10

x = 10.

Hence Eric sent 10kg of package

8 0
3 years ago
Write a number between 80 and 100 that has exactly 3 factors, one of which is a 5
Flura [38]
Answer:

answer is 90

Explanation:

Here 5 is one of the 4 prime factors, so dividing the lower (80) and upper limit (100) by 5 we have new lower limit 16 and new upper limit 20.

So the product of other 3 factors should be greater than 16 and less than 20.

And we can have it from 18 only. Hence the number is 90.

The numbers between 80 and 100 having factor 5 are

<span>80,85,90,95,100</span>

<span>16=<span>24</span></span>

<span>17=17</span>

<span>18=2×3×3</span>

<span>19=19</span>

<span>20=<span>22</span>×5</span>

<span>90=2×<span>32</span>×<span>5</span></span>

<span><span>
</span></span>

5 0
4 years ago
Find the solution of the differential equation that satisfies the given initial condition. y' tan x = 3a + y, y(π/3) = 3a, 0 &lt
Paladinen [302]

Answer:

y(x)=4a\sqrt{3}* sin(x)-3a

Step-by-step explanation:

We have a separable equation, first let's rewrite the equation as:

\frac{dy(x)}{dx} =\frac{3a+y}{tan(x)}

But:

\frac{1}{tan(x)} =cot(x)

So:

\frac{dy(x)}{dx} =cot(x)*(3a+y)

Multiplying both sides by dx and dividing both sides by 3a+y:

\frac{dy}{3a+y} =cot(x)dx

Integrating both sides:

\int\ \frac{dy}{3a+y} =\int\cot(x) \, dx

Evaluating the integrals:

log(3a+y)=log(sin(x))+C_1

Where C1 is an arbitrary constant.

Solving for y:

y(x)=-3a+e^{C_1} sin(x)

e^{C_1} =constant

So:

y(x)=C_1*sin(x)-3a

Finally, let's evaluate the initial condition in order to find C1:

y(\frac{\pi}{3} )=3a=C_1*sin(\frac{\pi}{3})-3a\\ 3a=C_1*\frac{\sqrt{3} }{2} -3a

Solving for C1:

C_1=4a\sqrt{3}

Therefore:

y(x)=4a\sqrt{3}* sin(x)-3a

3 0
4 years ago
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