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3 years ago

Write the equation of a parabola with a vertex and (-5, 2) and a directrix y = -1

Mathematics

1 answer:

mrs_skeptik [129]3 years ago

4 0

Answer:

y=(x+5)²/6 + 1/3

Step-by-step explanation:

Use the distance formula to plug in the values you know:

√(y+1)² =√(x+5)² +( y-2)²

the square roots cancel out

(y+1) ²= (x+5)² +(y-2)²

(y+1) (y-1)= (x+5)² + (y-2) (y-2)

y²+2y+1= (x+5)² + y² -4y+4

the y² cancel out

2y+ 4y = (x+5)² + 4-1

6y= (x+5)² +3

y= (x+5)² /6+ 1/3

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One quarter of Steve's baseball cards are from his dad's collection. Another 0.2 are from his uncle , and 0.5 are from his broth

irina [24]

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3 years ago

Which of the following ratios are proportional? 9/12 12/15 16/20 20/24 24/35

8_murik_8 [283]

9/12 is the correct answer

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3 years ago

A restaurant chain has two locations in a medium-sized town and, believing that it has oversaturated the market for its food, is

scoray [572]

Answer:

Yes, since the test statistic value is greater than the critical value.

Step-by-step explanation:

Data given and notation

$\bar X_{1}=360000$ represent the mean for the downtown restaurant

$\bar X_{2}=340000$ represent the mean for the freeway restaurant

$s_{1}=50000$ represent the sample standard deviation for downtown

$s_{2}=40000$ represent the sample standard deviation for the freeway

$n_{1}=36$ sample size for the downtown restaurant

$n_{2}=36$ sample size for the freeway restaurant

t would represent the statistic (variable of interest)

$\alpha=0.05$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the true mean of revenue for downtown is higher than for freeway restaurant, the system of hypothesis would be:

Null hypothesis: $\mu_{1}\leq \mu_{2}$

Alternative hypothesis: $\mu_{1} > \mu_{2}$

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Determine the critical value.

Based on the significance level $\alpha=0.05$ and $\alpha/2=0.025$ we can find the critical values from the t distribution dith degrees of freedom df=36+36-2=55+88-2=70, we are looking for values that accumulates 0.025 of the area on the right tail on the t distribution.

For this case the value is $t_{1-\alpha/2}=1.66$

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

$t=\frac{360000-340000}{\sqrt{\frac{50000^2}{36}+\frac{40000^2}{36}}}}=1.874$

What is the p-value for this hypothesis test?

Since is a right tailed test the p value would be:

$p_v =P(t_{70}>1.874)=0.033$

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we reject the null hypothesis, and the true mean for the downtown revenue restaurant seems higher than the true mean revenue for the freeway restaurant.

The best option would be:

Yes, since the test statistic value is greater than the critical value.

5 0

3 years ago

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andrew11 [14]

Answer:hiiiiiiiii

Step-by-step explanation:

8 0

3 years ago

The height of an ostrich is 20 inches more than 4 times the height of a kiwi. If an ostrich is 108 inches tall, how tall is a ki

pishuonlain [190]

Let the height of the kiwi be x, then the height of the ostrich is 20 + 4x.
20 + 4x = 108
4x = 108 - 20 = 88
x = 88/4 = 22
The height of the kiwi is 22 inches.

6 0

3 years ago