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2 years ago

11

Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal plac

es where appropriate).
4 sin(2θ) − 2 sin(θ) = 0

1 answer:

storchak [24]2 years ago

4 0

Answer:

θ = πk, 1.318+2πk, 4.965+2πk

Step-by-step explanation:

4sin(2θ) − 2sin(θ) = 0

8sin(θ)cos(θ) - 2sin(θ) = 0

2sin(θ)[4cos(θ)-1] = 0

2sin(θ) = 0

sin(θ) = 0

θ = πk

4cos(θ)-1 = 0

4cos(θ) = 1

cos(θ) = 1/4

θ ≈ 1.318+2πk, 4.965+2πk

Therefore, θ = πk, 1.318+2πk, 4.965+2πk

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What is the simplified of this?

masha68 [24]

It is the second option, let me know if you got it right

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3 years ago

Lashonda purchased a prepaid phone card for $20. Long distance calls cost 8 cents a minute using this card. Lashonda used her ca

Gre4nikov [31]

We know that

• Lashonda purchased a prepaid phone card for $20.

,

• Long-distance calls cost 8 cents a minute.

,

• The remaining credit on her card is $17.12.

This problem can be expressed as

$20-0.08x=17.12$

Where <em>x</em> is the number of minutes.

We solve the equation for <em>x</em>

$\begin{gathered} -0.08x=17.12-20 \\ -0.08x=-2.88 \end{gathered}$

Then, we divide by -0.08 the equation

$\begin{gathered} \frac{-0.08x}{-0.08}=\frac{-2.88}{-0.08} \\ x=36 \end{gathered}$ <h2>Therefore, Lashonda's call last 36 minutes.</h2>

8 0

1 year ago

A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

For this problem, we consider that we want it to be within 4%.

Item a:

The sample size is <u>n for which M = 0.04.</u>

There is no estimate, hence $\pi = 0.5$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2$

$n = 600.25$

Rounding up:

A sample of 601 is needed.

Item b:

The estimate is $\pi = 0.96$ , hence:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}$

$\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2$

$n = 92.2$

Rounding up:

A sample of 93 is needed.

Item c:

The closer the estimate is to $\pi = 0.5$ , the larger the sample size needed, hence, the correct option is A.

For more on the z-distribution, you can check brainly.com/question/25404151

8 0

2 years ago

The fraction: 340 | 3/4

Effectus [21]

Answer:

It's A I hope that helps

Step-by-step explanation:

8 0

3 years ago

See the question attached. Please help

Lelu [443]

Answer:

1) 36

2) 190

3) 72 units

Step-by-step explanation:

1) 2x4 = 8 units area for rectangle

(4-2) x4 /2 = 4 units

6 x 4 = 24 units

8 + 4 + 24 = 36

2) 3 x 10 / 2 = 15 units

5 x 10 /2 = 25 units

15 x 10 = 150 units

150 + 25 + 15 = 190 units

3) 6 x 3 / 2 = 9 units

6 x 9 = 54 units

6 x 3 / 2 = 9 units

9 + 9 + 54 = 18 + 54 = 72 units

3 0

2 years ago

Read 2 more answers