For each quadratic function, find the domain range vertex and axis of symmetry y=(x-1) squared +1

1 answer:

3 0

$y=(x-1)^2 +1 \\ \\ For \ the \ quadratic \ function \\ \\ f(x) =a(x-h)^2+k \\ \\ where \ a, \ h \ and \ k \ are \ real \ numbers \ with \ a \neq 0 , \\ \\ the \ vertex \ is \ (h,k) =(1,1) \\ \\ a \ symmetry \ about \ the \ vertical \ line \ x = h \\ \\ x= 1$

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t is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desir

PtichkaEL [24]

Answer:

The sample size needed to be taken is approximately 74.

Step-by-step explanation:

To get alpha; we have 1 - 0.95 = 0.05

Therefore, $z_{\frac{a}{2} } = \frac{0.05}{2} = 0.025$

The we look up z* in a Standard Normal table where α = 0.025 area in each tail.

From the table, z* = 1.96

From the question variance is 484, then the standard deviation is 22

Standard deviation = $\sqrt{Var(x)} = \sqrt{484} = 22$

And margin of error is 5 or less

The formula for margin of error is given as:

margin of error = $\frac{(z^{*}) (SD)}{\sqrt{n} }$

$5 = \frac{1.96 * 22}{\sqrt{n} } \\5 = \frac{43.12}{\sqrt{n} } \\5 * \sqrt{n} = 43.12\\(5)^{2} * (\sqrt{n} )^{2} = (43.12)^2\\25 * n = 1859.3344\\25n = 1859.3344\\\frac{25n}{25} = \frac{1859.3344}{25} \\n = 74.373376\\n = 74$

The approximate value of n is 74.

3 0

3 years ago

F(x)=4x+7 Place the steps for finding f -1(x) in the correct order.

dybincka [34]

X=4x+7

X=4y+7

X-7=4y

X-7/4=y

F-1(x)=x-7/4

6 0

4 years ago

Determine the sum of the first 9 terms in the geometric series where r= -0.25 and a1= 256.

Damm [24]

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=-0.25\\ a_1=256\\ n=9 \end{cases}$

$\bf S_9=256\left(\cfrac{1-(-0.25)^9}{1-(-0.25)} \right)\implies S_9=256\left( \cfrac{1+0.25^9}{1+0.25} \right) \\\\\\ S_9=256\left( \cfrac{52429}{65536}\right)\implies S_9=\cfrac{52429}{256}\implies S_9=204.80078125$