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2 years ago

Find the vertex of the graph of the equation y = 3x^2-6x+7

Mathematics

1 answer:

Masja [62]2 years ago

5 0

The vertex will be (1,4) I use a graphing calculator to find this answer

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Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and

balu736 [363]

Answer:

(a) The sample size required is 43.

(b) The sample size required is 62.

Step-by-step explanation:

The (1 - α) % confidence interval for population mean is:

$CI=\bar x\pm z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

The margin of error for this interval is:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

(a)

The information provided is:

σ = 4 minutes

MOE = 72 seconds = 1.2 minutes

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

$=[\frac{1.96\times 4}{1.2}]^{2}\\\\=42.684\\\\\approx 43$

Thus, the sample size required is 43.

(b)

The information provided is:

σ = 4 minutes

MOE = 1 minute

Confidence level = 95%

α = 5%

Compute the critical value of z for α = 5% as follows:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use a z-table.

Compute the sample size required as follows:

$MOE=z_{\alpha/2}\ \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma}{MOE} ]^{2}$

$=[\frac{1.96\times 4}{1}]^{2}\\\\=61.4656\\\\\approx 62$

Thus, the sample size required is 62.

3 0

2 years ago

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

Contact [7]

Answer:

$\dfrac{z-y}{a+b}$

Step-by-step explanation:

Given expression:

$\dfrac{z^2-y^2}{a^2-b^2}\div \dfrac{z+y}{a-b}$

Substitute

$a^2-b^2=(a-b)(a+b)\\ \\z^2-y^2=(z-y)(z+y)$

into the expression:

$\dfrac{(z-y)(z+y)}{(a-b)(a+b)}\div \dfrac{z+y}{a-b}\\ \\ \\=\dfrac{(z-y)(z+y)}{(a-b)(a+b)}\times \dfrac{a-b}{z+y}\\ \\ \\=\dfrac{z-y}{a+b}$

4 0

3 years ago

Read 2 more answers

A shop in the mall is 8 yards by 12 yards. How much would it cost to recarpet the shop with carpet that costs $2.69 per square y

valentinak56 [21]

Answer:

Step-by-step explanation:

You will first have to find the area to find the price of each square yard.

Area is 8*12 = 96. Multiply this by 2.69.

It will cost 258.24 dollars to recarpet the shop.

Let me know if this helped

7 0

2 years ago

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In an art history class there are two male students for every three female students. What is the ratio of female to male student

mylen [45]

Answer:

3:2

Step-by-step explanation:

3 females every 2 males

7 0

2 years ago

If x+3y=7 and y=2 then x equals?

Verdich [7]

X + 3y = 7
y = 2

Substitute

x + 3(2) = 7
x + 6 = 7
x = 1
Hope this helps!

7 0

3 years ago

Read 2 more answers