Answer: There is convincing evidence at the the significance level that the DMV's claim is incorrect.
Step-by-step explanation:
Since we have given that
Hypothesis:
Probability of teens pass their drivers test on the first attempt = 60% = 0.60
Number of teens = 125
Number of them passed the tests on their first try = 86
So, the value of test statistic would be
At α = 0.05% level of significance, critical value = 1.645
Since 1.645 < 2.01
So, we will reject the null hypothesis.
Hence, there is convincing evidence at the the significance level that the DMV's claim is incorrect.
![\bf f(x)=(x-6)e^{-3x}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=1\cdot e^{-3x}+(x-6)-3e^{-3x}\implies \cfrac{dy}{dx}=e^{-3x}[1-3(x-6)] \\\\\\ \cfrac{dy}{dx}=e^{-3x}(19-3x)\implies \cfrac{dy}{dx}=\cfrac{19-3x}{e^{3x}}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%28x-6%29e%5E%7B-3x%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3D1%5Ccdot%20e%5E%7B-3x%7D%2B%28x-6%29-3e%5E%7B-3x%7D%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3De%5E%7B-3x%7D%5B1-3%28x-6%29%5D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3De%5E%7B-3x%7D%2819-3x%29%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B19-3x%7D%7Be%5E%7B3x%7D%7D)
set the derivative to 0, solve for "x" to get any critical points
keep in mind, setting the denominator to 0, also gives us critical points, however, in this case, the denominator will never be 0, so... no critical points from there
there's only 1 critical point anyway, and do a first-derivative test on it, check a number before it and after it, to see what sign the derivative has, and thus, whether the graph is going up or down, to check for any extrema
Answer:
B. 
Step-by-step explanation:
![\displaystyle x^2 = -8x - 7 → x^2 + 8x + 7 \\ \\ x^2 + 8x + 7 \\ [x + 1][x + 7]; -1, -7 = x](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E2%20%3D%20-8x%20-%207%20%E2%86%92%20x%5E2%20%2B%208x%20%2B%207%20%5C%5C%20%5C%5C%20x%5E2%20%2B%208x%20%2B%207%20%5C%5C%20%5Bx%20%2B%201%5D%5Bx%20%2B%207%5D%3B%20-1%2C%20-7%20%3D%20x)
I am joyous to assist you at any time.
The answer is x equals 24
you set up a proportion new over old
so for red cars 40 over 5
since we don’t know the new for blue cars we’ll use x
so x over 3
we then make them equal to each other
40 x
—- = —-
5 3
cross multiply, then we get
120=5x
isolate the x by dividing 5 from both sides to get 24
