Answer:
95,040 different cast are possible
Step-by-step explanation:
In this case the order in which the actors are selected for the 5 different roles is important. Therefore we use the permutations formula.
Where n is the number of items you can choose and choose r from them.
In this case 
and 
Answer:
40 mph
Step-by-step explanation:
If the speed increased by 20%, now the speed is 120% of the original speed.
48 mph is 120%, so dividing by 6 will get 8 which is 20%.
If 8 is 20%, you can multiply it by 5 to get 40, which is 100%. This means 40 mph is the original speed.
Hope this helps!
9514 1404 393
Answer:
f^-1(x) = 4+∛((x-6)/5)
Step-by-step explanation:
To find the inverse function, solve ...
x = f(y)
then write the answer in functional form.
![\displaystyle x=f(y)\\\\x=5(y-4)^3+6\\\\x-6=5(y-4)^3\\\\\frac{x-6}{5}=(y-4)^3\\\\\sqrt[3]{\frac{x-6}{5}}=y-4\\\\y=4+\sqrt[3]{\frac{x-6}{5}}\\\\\boxed{f^{-1}(x)=4+\sqrt[3]{\frac{x-6}{5}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3Df%28y%29%5C%5C%5C%5Cx%3D5%28y-4%29%5E3%2B6%5C%5C%5C%5Cx-6%3D5%28y-4%29%5E3%5C%5C%5C%5C%5Cfrac%7Bx-6%7D%7B5%7D%3D%28y-4%29%5E3%5C%5C%5C%5C%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-6%7D%7B5%7D%7D%3Dy-4%5C%5C%5C%5Cy%3D4%2B%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-6%7D%7B5%7D%7D%5C%5C%5C%5C%5Cboxed%7Bf%5E%7B-1%7D%28x%29%3D4%2B%5Csqrt%5B3%5D%7B%5Cfrac%7Bx-6%7D%7B5%7D%7D%7D)
__
The graph shows the function and its inverse to be reflections of each other in the line y=x, as they should be.
Answer:
2.25 cups
Step-by-step explanation:
15.75÷7= 2.25 cups of flour for one batch of cookie
Answer:
<em>H</em>₀: <em>μ</em> = 4 vs. <em>H
ₐ</em>: <em>μ </em>> 4
Step-by-step explanation:
A null hypothesis is a sort of hypothesis used in statistics that intends that no statistical significance exists in a set of given observations.
It is a hypothesis of no difference.
It is typically the hypothesis a scientist or experimenter will attempt to refute or discard. It is denoted by H₀.
Whereas, the alternate hypothesis is the contradicting statement to the null hypothesis.
The alternate hypothesis describes direction of the hypothesis test, i.e. if the test is left tailed, right tailed or two tailed.
It is also known as the research hypothesis and is denoted by H
ₐ.
In this case we need to test whether the amount is paid after the grace period, on average, more than 4 times in 2018.
The hypothesis can be defined as follows:
<em>H</em>₀: <em>μ</em> = 4 vs. <em>H
ₐ</em>: <em>μ </em>> 4
