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2 years ago

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Mathematics

1 answer:

pychu [463]2 years ago

6 0

The equation of a hyperbola is $x^{2}$ /9 - $y^{2}$ /4 = 1

What are the steps to Hyperbola equation ?

To find the equation of hyperbola, the following steps must be taken. You need to identify;

The coordinate of the center

The coordinate of the vertices

The coordinate of the foci

The general equation of a hyperbola can be expressed as

$x^{2}$ / $a^{2}$ - $y^{2}$ / $b^{2}$ = 1

From the graph, we have the following parameters

a = 3

$a^{2}$ = $3^{2}$ = 9

b = 2

$b^{2}$ = $2^{2}$ = 4

The equation of a hyperbola can be expressed as

$x^{2}$ /9 - $y^{2}$ /4 = 1

The vertices = V(+/-a,0) = (+/-3,0)

The center = C(0,0)

The focus = F(+/-C, 0)

Where $C^{2}$ = $a^{2}$ + $b^{2}$

C = $\sqrt{9 + 4}$

C = $\sqrt{13}$

Focus = F(+/- $\sqrt{13}$ , 0)

The general equation for asymptote = +/- b/a X

= +/-2/3X

Therefore, the equation of a hyperbola can be expressed as

$x^{2}$ /9 - $y^{2}$ /4 = 1

Learn more about hyperbola here: brainly.com/question/3405939

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The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first deter

JulsSmile [24]

Answer:

1) n=114

2) n=59

3) On this case no, because if we survey just the adults of the nearest college that would be a convenience sample. And when we use "convenience sample" we have some problems associated to bias. This methodology it's not appropiate in order to have a good estimation of the parameter of interest. It's better use a random, cluster or stratified sampling.

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 80% of confidence, our significance level would be given by $\alpha=1-0.80=0.2$ and $\alpha/2 =0.1$ . And the critical value would be given by:

$z_{\alpha/2}=-1.28, z_{1-\alpha/2}=1.28$

Part 1

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.06$ or 6% points, and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have a prior estimate of $\het p$ we can use 0.5 as a good estimate, replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.06}{1.28})^2}=113.77$

And rounded up we have that n=114

Part 2

On this case we have a prior estimate for the population proportion and is $\hat p =0.85$ so replacing the values into equation (b) we got:

$n=\frac{0.85(1-0.85)}{(\frac{0.06}{1.28})^2}=58.027$

And rounded up we have that n=59

Part 3

On this case no, because if we survey just the adults of the nearest college that would be a convenience sample. And when we use "convenience sample" we have some problems associated to bias. This methodology it's not appropiate in order to have a good estimation of the parameter of interest. It's better use a random, cluster or stratified sampling.

5 0

3 years ago

Simple interest rate earned after 12 years on 1350 at an interest rate of 8%

Mademuasel [1]

Answer:

1296

Step-by-step explanation:

Simple interest is

I = PRT where I is the interest P is the principle, r is the rate and t is the time

I = 1350 * .08 * 12

I = 1296

8 0

3 years ago

3.) Simplify the expression by combining like

Evgesh-ka [11]

$45s^2-19-s^2+16\\=45s^2-s^2-19+16\\=s^2(45-1)-19+16\\=44s^2+(-19+16)\\=44s^2-3$

Hope that helps and hope you get better!

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3 years ago

How do I factor this polynomial? q^2-121

Tresset [83]

$q^2-121 =q^2-11^2=(q-11)(q+11)\\ \\ \\a^2-b^2 =(a-b)(a+b)$

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3 years ago

Which of the following must be true?

Ilya [14]

The answer is C, when numbers or variables are between "|" (also called bars) it means to remove any negative symbols and think of it as a positive number. If the number is already positive you keep it a positive number.

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3 years ago