Which sum of difference is equivalent to the following expression? 5-3x/5

For which value of theta is cot theta equal to cos theta?

Oksi-84 [34.3K]

Answer:

$\frac{cos \theta}{sin \theta}= cos \theta$

If we multiply by cross we got:

$cos \theta = sin \theta cos \theta$

We can divide both sides of the last equation by $cos \theta$ and we got:

$sin \theta = 1$

And if we apply arcsin in both sides we got:

$\theta = arcsin (1) = \frac{\pi}{2}$

And the best solution would be:

C) pi/2

Step-by-step explanation:

For this case we want to solve the following equation:

$cot \theta = cos \theta$

And we know that by definition $cot \theta = \frac{cos \theta}{\sin \theta}$

And replacing we got:

$\frac{cos \theta}{sin \theta}= cos \theta$

If we multiply by cross we got:

$cos \theta = sin \theta cos \theta$

We can divide both sides of the last equation by $cos \theta$ and we got:

$sin \theta = 1$

And if we apply arcsin in both sides we got:

$\theta = arcsin (1) = \frac{\pi}{2}$

And the best solution would be:

C) pi/2

8 0

3 years ago

Calculate the difference in the proportion of males and the proportion of females that smoke. Give your answer to 2 decimal plac

Xelga [282]

The difference in the proportion of males and the proportion of females that smoke is 0.08

<h3>Missing information </h3>

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

<h3>How to determine the proportion difference?</h3>

The given parameters are:

Male Female

Sample 61 48

Smokers 15 8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

Read more about proportion at:

brainly.com/question/16828793

#SPJ12

7 0

2 years ago

A recent study showed that women who lived near a freeway had an unusually high rate of rheumatoid arthritis. Sarah said, “They

Artemon [7]

Answer:

they should move away from the freeway

6 0

3 years ago

What is the slope of the line through (6,9) and (7,1)

suter [353]

Slope of (6, 9) & (7, 1)

To find the slope, we use the equation : m = y₂-y₁ / x₂-x₁

**Remember : m = slope**

Let's say that (6, 9) is our first set of points, and (7, 1) is our second.

If those are our first and second points, then we now know this :

x₁ = 6, x₂ = 7, y₁ = 9, y₂ = 1

Now that we know that, we can simply plug those points into our slope equation.

m = y₂ - y₁ / x₂ - x₁

m = (1 - 9) / (7 - 6 )

Simplify.

m = -8 / 1

Simplify.

m = -8

So, our slope is -8.

~Hope I helped!~

6 0

3 years ago

The article "Influence of Penetration Rate on Penetrometer Resistance" (see textbook for reference) presents measures of penetra

snow_tiger [21]

Answer:

The 95% of confidence interval for the mean penetration resistance for this soil is (2.0823, 3.1977).

Step-by-step explanation:

The sample size is 15.

The first step to solve this problem is finding how many degrees of freedom there are, that is, the sample size subtracted by 1. So

$df = 15-1 = 14$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 14 and 0.025 in the t-distribution table, we have $T = 2.145$ .

Now, we need to find the standard deviation of the sample. That is:

$s = \frac{1.02}{\sqrt{15}} = 0.26$

Now, we multiply T and s

$M = T*s = 2.145*0.26 = 0.5577$

For the lower end of the interval, we subtract the mean by M. So 2.64 - 0.5577 = 2.0823

For the upper end of the interval, we add the mean to M. So 2.64 + 0.5577 = 3.1977

The 95% of confidence interval for the mean penetration resistance for this soil is (2.0823, 3.1977).

7 0

3 years ago