Check attachment for picture but please help with extraneous solution:

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

sashaice [31]

Answer:

θ = 60° or θ = 120°, which in radians is equivalent to θ = π/3 rad or θ = 2π/3 rad.

Explanation:

The given equation is sin θ = (√3)/2

Solving that equation is finding the value of the angle, θ, whose sine is (√3)/2.

The function that returns the value of the angle whose sine is (√3)/2 is the inverse function of the sine and it has a special name: arc sine or arcsin.

Hence, θ = arcsin (√3)/2.

You can use your knowledge of the notable angles to solve for that equation.

1) The function sine is positive in first and second quadrants.

2) The angles in the first quadrant go from 0° to 90°.

3) The sine of 60° (√3)/2, Hence the first value of θ is 60°

4) The angles in the second quatrant go from 90° to 120°. 60° is the reference angle in the second quadrant, and the angle searched is

180° - reference angle = 180° - 60° = 120°. So, 120° is the other solution of the equation.

5) You can convert both angles to radians using the equivalence

π radians = 180° ⇒ 1 = π rad / 180°

60° = 60° × π rad / 180° = π/ 3 rad

120° = 120° × π rad / 180° = 2π/3 rad

6) You can verify that sin 60° = (√3)/2 = sin 120° .

4 0

3 years ago

50 POINTS !

Mademuasel [1]

Answer:

cap it's only 5

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Not Answered Country Financial, a financial services company, uses surveys of adults age 18 and older to determine if personal f

ehidna [41]

Answer:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

$z=\frac{0.410-0.350}{\sqrt{0.382(1-0.382)(\frac{1}{1000}+\frac{1}{900})}}=2.688$

$p_v =2*P(Z>2.688)= 0.0072$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.

Step-by-step explanation:

Data given and notation

$X_{1}=410$ represent the number of people indicating that their financial security was more than fair in 2012

$X_{2}=315$ represent the number of people indicating that their financial security was more than fair in 2010

$n_{1}=1000$ sample 1 selected

$n_{2}=900$ sample 2 selected

$p_{1}=\frac{410}{1000}=0.410$ represent the proportion estimated of people indicating that their financial security was more than fair in 2012

$p_{2}=\frac{315}{900}=0.350$ represent the proportion estimated of people indicating that their financial security was more than fair in 2010

$\hat p$ represent the pooled estimate of p

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

Part a: Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference between the two proportions, the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

Hypothesis testing

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{410+315}{1000+900}=0.382$

z-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.

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.410-0.350}{\sqrt{0.382(1-0.382)(\frac{1}{1000}+\frac{1}{900})}}=2.688$

Statistical decision

Since is a two sided test the p value would be:

$p_v =2*P(Z>2.688)= 0.0072$

Comparing the p value with the significance level assumed $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to to reject the null hypothesis, and we can say that the proportions analyzed are significantly different at 5% of significance.

3 0

4 years ago

What lists all integer solutions of the inequality |x|<2

Nookie1986 [14]

Answer:

The solution to that inequality is (-2,2).

Step-by-step explanation:

Given the inequality |x|<2, we have two possibilities

1) x<2 or

2) -x<2 ⇒ x> -2.

Then the intersection between solutions is (-2, 2).

4 0

3 years ago

781 books second = books minute

hram777 [196]

34,860

You take 781 books a second and multiply that by 60 since there’s 60 seconds in a minute

8 0

2 years ago