The formula for the confidence interval is given by
Sample mean + z*[σ/√n], and
Sample mean - z*[σ/√n]
We have:
Sample mean = 23.95
n = 40
σ = 2.55
z* for 99% confidence = 2.58
Substitute these values into the formula, we have
23.95 + (2.58)(2.55÷√40) = 24.99
23.95 - (2.58)(2.55÷√40) = 22.91
So the lower interval is 22.91 and the highest interval is 24.99
Answer:
![10,962,54](https://tex.z-dn.net/?f=10%2C962%2C54)
Step-by-step explanation:
we know that
The equation of a exponential growth is equal to
![y=a(1+r)^x](https://tex.z-dn.net/?f=y%3Da%281%2Br%29%5Ex)
where
a is the initial value
r is the rate of growth
x is the time in hours
y is the value of the quantity
we have
![a=9,100\\r=0.85\%=0.85/100=0.0085](https://tex.z-dn.net/?f=a%3D9%2C100%5C%5Cr%3D0.85%5C%25%3D0.85%2F100%3D0.0085)
substitute
![y=9,100(1+0.0085)^x](https://tex.z-dn.net/?f=y%3D9%2C100%281%2B0.0085%29%5Ex)
![y=9,100(1..0085)^x](https://tex.z-dn.net/?f=y%3D9%2C100%281..0085%29%5Ex)
For x=22 hours
substitute
![y=9,100(1..0085)^{22} =10,962,54](https://tex.z-dn.net/?f=y%3D9%2C100%281..0085%29%5E%7B22%7D%20%3D10%2C962%2C54)
D.) 06.5. 20 words don’t mind these i just don’t know what else to say besides it’s D
Answer:
<h2>
![(g \: \circ \: f)(0) = 17](https://tex.z-dn.net/?f=%28g%20%5C%3A%20%5Ccirc%20%5C%3A%20f%29%280%29%20%3D%2017)
</h2>
Step-by-step explanation:
f(x) = 2x + 4
g(x) = 4x² + 1
In order to find (g ∘ f)(0) we must first find
(g ° f )(x)
To find (g ° f )(x) substitute f(x) into g(x) that's for every x in g(x) replace it with f(x)
That's
<h3>
![(g \: \circ \: f)(x) = 4( ({2x + 4})^{2} ) + 1 \\ = 4(4 {x}^{2} + 16x + 16) + 1 \\ = {16x}^{2} + 64x + 16 + 1](https://tex.z-dn.net/?f=%28g%20%5C%3A%20%5Ccirc%20%5C%3A%20f%29%28x%29%20%3D%204%28%20%28%7B2x%20%2B%204%7D%29%5E%7B2%7D%20%29%20%2B%201%20%5C%5C%20%20%3D%204%284%20%7Bx%7D%5E%7B2%7D%20%20%2B%2016x%20%2B%2016%29%20%2B%201%20%5C%5C%20%20%3D%20%20%7B16x%7D%5E%7B2%7D%20%20%2B%2064x%20%2B%2016%20%2B%201)
</h3>
We have
<h3>
![(g \: \circ \: f)(x) = {16x}^{2} + 64x + 17 \\](https://tex.z-dn.net/?f=%28g%20%5C%3A%20%5Ccirc%20%5C%3A%20f%29%28x%29%20%3D%20%20%7B16x%7D%5E%7B2%7D%20%20%2B%2064x%20%2B%2017%20%5C%5C%20)
</h3>
Now to find (g ∘ f)(0) substitute the value of x that's 0 into (g ∘ f)(0)
We have
<h3>
![(g \: \circ \: f)(0) = 16( {0})^{2} + 64(0) + 17 \\](https://tex.z-dn.net/?f=%28g%20%5C%3A%20%5Ccirc%20%5C%3A%20f%29%280%29%20%3D%2016%28%20%7B0%7D%29%5E%7B2%7D%20%20%2B%2064%280%29%20%2B%2017%20%5C%5C%20)
</h3>
We have the final answer as
<h3>
![(g \: \circ \: f)(0) = 17](https://tex.z-dn.net/?f=%28g%20%5C%3A%20%5Ccirc%20%5C%3A%20f%29%280%29%20%3D%2017)
</h3>
Hope this helps you
Answer:
the answer is 30
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