The answer is 1/4
If you reply I might explain why.
\(\text{First we need to convert "top 26%" to a z-score}\\ \text{We do this by using a table or software of the }\\ \text{CDF of the standard normal distribution}\\ \text{We find that 74% has a corresponding z-score of }\\ z=0.643345\)
\(\text{We then use the mean and deviation to convert this z-score into a value}\\ d= \mu + \sigma z = 4 + 0.643345\cdot 0.375 = 4.24125 \Rightarrow 4.24ft\)
\(x = c y\\ x = \dfrac d z\)
\(x=3, y=3 \Rightarrow c = 2\\ x = 3, z=4 \Rightarrow d = 12\)
\(y=3 \Rightarrow x = 6 \Rightarrow z=2\)
The problem says the ratio of the amount they spent on tacos, 6T, to the amount they spent on burritos, 2B, is 7:4.
You have the ratio of the price of tacos, to the price of burritos as 7:4.
I suppose it's a poorly worded problem.
This problem leads to a negative price for tacos. If you ever find this please let me know.
\(\dfrac{\dfrac{n!}{k!(n-k)!}}{\dfrac{n!}{(k+1)!(n-k-1)!}} = \\ \dfrac{(k+1)!(n-k-1)!}{k!(n-k)!}=\\ \dfrac{k+1}{n-k}=\dfrac{4}{11}\)
\(11k+11=4n-4k\\ 4n-15k=11\)
\(\text{We can use the Euclidean algorithm to find }n=14,~k=3\)
\(\text{Let }\Phi(x) \text{ be the CDF of the standard normal, (that thing you have the table for)}\\ P[\text{response between 400 and 500 seconds}] = \\ \Phi\left(\dfrac{500-450}{50}\right) - \Phi\left(\dfrac{400-450}{50}\right)=\\ \Phi(1)-\Phi(-1) \approx 0.683\\ 0.683 \times 160 \approx 109.23\)
\(\dfrac{d}{dx} \displaystyle \int_{a(x)}^{b(x)}f(t)~dt = \\ f(b(x))\dfrac{db}{dx} - f(a(x))\dfrac{da}{dx}\)
\(\dfrac{d}{dx} \displaystyle \int_3^{x^2}\dfrac{\sqrt{1+2t}}{t}~dt = \\ \dfrac{\sqrt{1+2x^2}}{x^2}\cdot 2x - \dfrac{\sqrt{1+2(3)}}{3}\cdot 0 = \\ \dfrac{2\sqrt{1+2x^2}}{x}\)
\(\text{a linear factor is of the form }(x-a)\)
\(f(x) = x^3 + 24x^2 - 2x + 6 \text{ (I'm assuming what was written was a typo)}\\ \text{This doesn't seem to have any linear factors} \)
\(f(x) = x^{16}+72x^6 + x = x(x^{15}+72x^5+1)\\ \text{This has one linear factor, }x\)
\(f(x)=(x+2)\text{ clearly has a single linear factor which is itself}\)
I can't really agree with the answer given. We have no idea what the form of f(x) is so trying to cast it as linear or quadratic is confusing.
3a) All we have to do here is take the graph of f(x) and shift it 4 units up the y axis.
3b) Here we shift f(x) 2 units to the right along the x-axis, and then 2 units up the y axis