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3 years ago

Write the equation of a horizontal ellipse with a major axis of 30, a minor axis of 14, and a center at (-9, -7

1 answer:

7 0

Recall that the major axis is "a + a" or 2a, whilst the minor axis is "b + b" or 2b.

so if the major axis is 30, then a = 15, and if the minor one is 14, b = 7.

$\bf \textit{ellipse, horizontal major axis}
\\\\
\cfrac{(x-{{ h}})^2}{{{ a}}^2}+\cfrac{(y-{{ k}})^2}{{{ b}}^2}=1
\qquad 
\begin{cases}
center\ ({{ h}},{{ k}})\\
vertices\ ({{ h}}\pm a, {{ k}})
\end{cases}\\\\
-------------------------------\\\\
\textit{we know that }
\begin{cases}
a=\frac{30}{2}\\
b=\frac{14}{2}\\
h=-9\\
k=-7
\end{cases}\implies \cfrac{[x-(-9)]^2}{15^2}+\cfrac{[y-(-7)]^2}{7^2}=1
\\\\\\
\cfrac{(x+9)^2}{225}+\cfrac{(y+7)^2}{49}=1$

You might be interested in

Find the area of the figure. Round to the nearest tenth if necessary.

baherus [9]

Hello!

First of all, let's find the triangle. As we can see, it is eight units long and four units tall. We can use the triangle formula and half the product.

4(8)=32

32/2=16

Now we need to find the area of the semicircle. We can use circle formulas and half our final answer. We will find the area using A= $\pi$ r².

We know that the diameter of this circle is eight. Therefore our radius is 4.

A= $4\pi$ ²

A= $16\pi$

Now we multiply.

16 $\pi$ ≈50.27

Now we add our triangle.

50.27+16=66.27

The nearest answer to this is B)66.2. It may have been a bit over as we used $\pi$ , not 3.14.

I hope this helps!

3 0

3 years ago

Katie is getting her laundry done it cost $2.25 per square foot of flowers added to the yard if she wants 12.4 ft.² of flowers h

7nadin3 [17]

Answer:

Katie needs to pay $27.9.

Step-by-step explanation:

Given;

Cost of per foot = $2.25

Number of flowers in her yard = 12.4 square foot

We need to find how much she needs to pay.

Solution:

Now we know that;

$1\ ft^2 = \$2.25$

So for $12.4 ft^2$ = Cost for $12.4 ft^2$ .

By using Unitary method we get;

Cost for $12.4 ft^2$ = $2.25\times12.4= \$27.9$

Hence Katie needs to pay $27.9.

5 0

2 years ago

What is the slope of the line on the graph? Enter your answer in the box.

slava [35]

Y= mx+B is the formula

5 0

2 years ago

Read 2 more answers

Bottles of water sell for $1.50 each.

anyanavicka [17]

Y axis is 1.5 and x axis is 1 and make them meet in the middle and add and repeat the process

4 0

2 years ago

A company wants to find out if the average response time to a request differs across its two servers. Say µ1 is the true mean/ex

lorasvet [3.4K]

Answer:

a) The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

Test statistic t=0.88

The P-value is obtained from a t-table, taking into acount the degrees of freedom (419) and the type of test (two-tailed).

b) A P-value close to 1 means that a sample result have a high probability to be obtained due to chance, given that the null hypothesis is true. It means that there is little evidence in favor of the alternative hypothesis.

c) The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

d) The consequences of the confidence interval containing 0 means that the hypothesis that there is no difference between the response time (d=0) is not a unprobable value for the true difference.

This relate to the previous conclusion as there is not enough evidence to support that there is significant difference between the response time, as the hypothesis that there is no difference is not an unusual value for the true difference.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that there is significant difference in the time response for the two servers.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is 0.05.

The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.

The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

$M_d=M_1-M_2=12.5-12.2=0.3$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{3^2}{196}+\dfrac{4^2}{225}}\\\\\\s_{M_d}=\sqrt{0.046+0.071}=\sqrt{0.117}=0.342$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{0.3-0}{0.342}=\dfrac{0.3}{0.342}=0.88$

The degrees of freedom for this test are:

$df=n_1+n_2-1=196+225-2=419$

This test is a two-tailed test, with 419 degrees of freedom and t=0.88, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=2\cdot P(t>0.88)=0.381$

As the P-value (0.381) is greater than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that there is significant difference in the time response for the two servers.

<u>Confidence interval </u>

We have to calculate a 95% confidence interval for the difference between means.

The sample 1, of size n1=196 has a mean of 12.5 and a standard deviation of 3.

The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

The estimated standard error of the difference is s_Md=0.342.

The critical t-value for a 95% confidence interval and 419 degrees of freedom is t=1.966.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_{M_d}=1.966 \cdot 0.342=0.672$

Then, the lower and upper bounds of the confidence interval are:

$LL=M_d-t \cdot s_{M_d} = 0.3-0.672=-0.372\\\\UL=M_d+t \cdot s_{M_d} = 0.3+0.672=0.972$

The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

7 0

3 years ago