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2 years ago

Determine e, k, and identify the type of conic for r= 12/ 7- cos theta

Mathematics

1 answer:

nlexa [21]2 years ago

7 0

Answer:

The answer is (d) ⇒ e = 1/7 , k = 12 , conic ellipse

Step-by-step explanation:

∵ r = ek/(1 ± ecosФ)

∵ r = 12/(7 - cosФ) ⇒ ÷ 7 up and down

∴ r = 12/7 ÷ 1 - 1/7 (cosФ)

∴ e = 1/7

∵ 12/7 = ke ⇒ 12/7 = k(1/7)

∴ k = 12

∵ 0 < e < 1

∴ The conic is ellipse

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A student carried out an experiment to determine the amount of vitamin C in a tablet sample. He performed 5 trials to produce th

ivolga24 [154]

Answer:

There is not enough evidence to support the claim that the amount of vitamin C in a tablet sample is different from 500 mg.

P-value = 0.166.

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{5}(490+502+505+495+492)\\\\\\M=\dfrac{2484}{5}\\\\\\M=496.8\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}((490-496.8)^2+(502-496.8)^2+(505-496.8)^2+(495-496.8)^2+(492-496.8)^2)}\\\\\\s=\sqrt{\dfrac{166.8}{4}}\\\\\\s=\sqrt{41.7}=6.5\\\\\\$

Then, we can perform the hypothesis t-test for the mean.

The claim is that the amount of vitamin C in a tablet sample is different from 500 mg.

Then, the null and alternative hypothesis are:

$H_0: \mu=500\\\\H_a:\mu< 500$

The significance level is 0.05.

The sample has a size n=5.

The sample mean is M=496.8.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=6.5.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{6.5}{\sqrt{5}}=2.907$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{496.8-500}{2.907}=\dfrac{-3.2}{2.907}=-1.1$

The degrees of freedom for this sample size are:

$df=n-1=5-1=4$

This test is a left-tailed test, with 4 degrees of freedom and t=-1.1, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.166) is bigger 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 the amount of vitamin C in a tablet sample is different from 500 mg.

4 0

2 years ago

Lydia wants to find the height of a flagpole. She measures the height

Solnce55 [7]

Answer:

10 ft.

Step-by-step explanation:

8.8 ÷ 4= 2.2

22÷2.2= 10

6 0

2 years ago

What is the solution of |-1 + x| = 5

nataly862011 [7]

Answer:

6, -4

Step-by-step explanation:

abs(-1+x)=5

-1+x=5 and -1+x=-5

-------------------------

-1+x=5

x=5-(-1)=5+1=6

-------------------

-1+x=-5

x=-5-(-1)=-5+1=-4

4 0

2 years ago

A stick 7 inches long is broken into two pieces, so that one piece is twice as long as the other one. How long are the two piece

marshall27 [118]

Hello from MrBillDoesMath!

Answer:

7/3 and 14/3 inches

Discussion:

Let P1 = "Piece 1" and "P2 = Piece 2", Then P2 = 2 * P1 and

P1 + P2 = 7 => as P2 = 2 P1

P1 + 2P1 = 7 =>

3P1 = 7 => divide both sides by 7

P1 = 7/3

Then P2 = 2 P1 - 2* (7/3) = 14/3

Thank you,

MrB

7 0

2 years ago

Read 2 more answers

Can somebody help me with this?

Juli2301 [7.4K]

Answer:

E) 1/2

Step-by-step explanation:

This is no ordinary problem. It actually requires you to solve two different problems in order to figure out the correct answer.

First, we must figure out what the hypotenuse of the triangle is. We have the two small sides (5 and 12), but don't have the larger side. To find this, we must use the Pythagorean theorem: $a^{2} + b^2 =c^2$