find sin(alpha-beta) if sin alpha =-5/13 with alpha between pi and 3pi/2; cos beta=2/5 with beta between 3pi/2 and 2pi

Answers

Answer 1

Answer: sin(α) = ⁻⁵/₁₃
sin⁻¹[sin(α)] = sin⁻¹(⁻⁵/₁₃)
α ≈ 1.1256π

cos(β) = ²/₅
cos⁻¹[cos(β)] = cos⁻¹(²/₅)
β ≈ 1.6311π

sin(α - β) = sin(1.1256π - 1.6311π)
sin(α - β) = sin(-0.5055π)
sin(α - β) = -sin(0.5055π)
sin(α - β) = -sin(90.99)
sin(α - β) ≈ -0.116

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A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week. To test the belief, the scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28, and the resulting hypothesis test had a p-value of 0.061. The computation of the p- value assumes which of the following is true? (A) The population proportion of adults who watch 15 or fewer hours of television per week is 0.28. Submit

(B) The population proportion of adults who watch 15 or fewer hours of television per week is 0.30.

(C) The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

(D) The population mean number of hours adults spend watching television per week is 15.

(E) The population mean number of hours adults spend watching television per week is less than 15.

Answers

The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

Given that,

A social scientist believed that less than 30 percent of adults in the United States watch 15 or fewer hours of television per week.

The scientist randomly selected 1,250 adults in the United States. The sample proportion of adults who watch 15 or fewer hours of television per week was 0.28,

And the resulting hypothesis test had a p-value of 0.061.

We have to determine,

The computation of the p- value assumes which of the following is true.

According to the question,

Let, The proportion of adults watching televisionless than or equal to 15% be = x

Null Hypothesis [H0] : x = 30% = 0.30

Alternate Hypothesis [H1] : x < 30% , or x < 0.30

P value is calculated at z value :

$= P_1- \sqrt(p_o(1-p_o))/(n)}$

Where p' = 0.28, $P_0$ = 0.30, $P_1$ = 0.70 ;

Then,

$= 0.70- \sqrt(0.30(1-0.30))/(1250)}\n\n= 0.70- \sqrt{(0.30 * 0.70 )/(1250) }\n\n= 0.70 - 0.012\n\n= 0.61$

Assuming 10% level of significance, p = 0.10

Therefore, p value 0.061 < 0.10, reject H0 & accept H1. This implies that we conclude that 'x i.e. proportion of adults watching television less than or equal to 15% < 30% or 0.30'

Hence, The population proportion of adults who watch 15 or fewer hours of television per week is less than 0.30.

To know more about Sample proportion click the link given below.

brainly.com/question/13846904

Answer:

Step-by-step explanation:

Let the proportion of adults watching television less than or equal to 15% be = x

Null Hypothesis [H0] : x = 30% = 0.30
Alternate Hypothesis [H1] : x < 30% , or x < 0.30

P value is calculated at z value : p' - [ √ { p0 (1- p0) } / n ] ;

where p' = 0.28, p0 = 0.30, p1 = 0.70 ; ∴ p ( z < -1.543) = 0.061

Assuming 10% level of significance, p = 0.10

As p value 0.061 < 0.10, we reject H0 & accept H1. This implies that we conclude that 'x ie proportion of adults watching television less than or equal to 15% < 30% or 0.30'

An advertising company designs a campaign to introduce a new product to a metropolitan area of population 3 Million people. Let P(t) denote the number of people (in millions) who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one was aware of the product at the beginning of the campaign, and that 50% of the people were aware of the product after 50 days of advertising. The number of people who become aware of the product at time t is:

Answers

Answer:

$P(t)=3,000,000-3,000,000e^(0.0138t)$

Step-by-step explanation:

Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have

$P'(t)=K(3,000,000-P(t))$

Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising

P(0) = 0 and P(50) = 1,500,000

We have and ordinary differential equation of first order that we can write

$P'(t)+KP(t)= 3,000,000K$

The integrating factor is

$e^(Kt)$

Multiplying both sides of the equation by the integrating factor

$e^(Kt)P'(t)+e^(Kt)KP(t)= e^(Kt)3,000,000*K$

Hence

$(e^(Kt)P(t))'=3,000,000Ke^(Kt)$

Integrating both sides

$e^(Kt)P(t)=3,000,000K \int e^(Kt)dt +C$

$e^(Kt)P(t)=3,000,000K((e^(Kt))/(K))+C$

$P(t)=3,000,000+Ce^(-Kt)$

But P(0) = 0, so C = -3,000,000

and P(50) = 1,500,000

$e^(-50K)=(1)/(2)\Rightarrow K=-(log(0.5))/(50)=0.0138$

And the equation that models the number of people (in millions) who become aware of the product by time t is

$P(t)=3,000,000-3,000,000e^(0.0138t)$

PLEASE HELP ASAP :))) 1. Consider the following standard:

Understand that polynomials form a system analogous to the integers, namely, they
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Answer the questions in the picture please

Answers

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1) angle 2 and 4

2)angle 2 and 3

3)angle 1 and 4

Hope it helps

D=G+Grt solve for t. Show work

Answers

G + Grt = D
Subtract G
Grt = D - G
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Use the following to answer Sean takes two 250 mg chewable calcium tablets each day, 6) How many milligrams of calcium will Sean take in a week?
7) How many grams of calcium will Sean take in a week?

Answers

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