Question 4 3 mi = How many feet

Let f ( ) sin(arctan ) x x = . What is the range of f ?

nikklg [1K]

So you have composed two functions,
h(x)=sin(x) and g(x)=arctan(x)
→f=h∘g
meaning
f(x)=h(g(x))
g:R→[−1;1]
h:R→[−π2;π2]
And since
[−1;1]∈R→f is defined ∀x∈R

And since arctan(x) is strictly increasing and continuous in [-1;1] ,
h(g(]−∞;∞[))=h([−1;1])=[arctan(−1);arctan(1)]
Meaning
f:R→[arctan(−1);arctan(1)]=[−π4;π4]
so there's your domain

5 0

3 years ago

A club is choosing 2 members to serve on a committee. The club has nominated 2 women and 4 men. Based on chance alone, what is t

tekilochka [14]

Answer:

53.33% probability that one woman and one man will be chosen to be on the committee

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the members are chosen is not important, so we use the combinations formula to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

What is the probability that one woman and one man will be chosen to be on the committee?

Desired outcomes:

One woman, from a set of 2, and one man, from a set of 4. So

$D = C_{2,1}*C_{4,1} = \frac{2!}{1!1!}*\frac{4!}{1!3!} = 8$

Total outcomes:

Two members from a set of 2 + 4 = 6. So

$T = C_{6,2} = \frac{6!}{2!4!} = 15$

Probability:

$p = \frac{D}{T} = \frac{8}{15} = 0.5333$

53.33% probability that one woman and one man will be chosen to be on the committee

5 0

3 years ago

For the expression, combine like terms and write an equivalent expression 3 points

Simora [160]

Answer:

5+7x

Step-by-step explanation:

1/2(6-4x) +2 +9x

3-2x+2+9x

5+7x

4 0

3 years ago

Please help me ASAP!

Snezhnost [94]

Answer:

y = 6.5

Step-by-step explanation:

When triangles are similar, we can set up a proportion to compare the sides. I will have the "left" side on the bottom of the fractions, and the side I am solving for on the top.

$\frac{y}{6} =\frac{13}{12}$

[Cross multiply]

12y = 78

y = 6.5

Have a nice day!

I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

7 0

3 years ago

What sample size should be used if we would like to estimate the mean age of the college students at a particular campus with 95

nevsk [136]

Answer: 12

Step-by-step explanation:

The formula to find the sample size is given by:-

$n=(\dfrac{z_c\cdot \sigma}{E})^2$ , where $\sigma$ is the population standard deviation, $z_c$ is the z-value for the $(1-\alpha)$ confidence interval and E is the margin of error .