Find the angle measure to the nearest degree. cos(A) = 0.5878
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Instructions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).Consider the functions f(x)=x^2+9x and g(x)=1/x.
f(g(-1)) is
g(f(1/2)) is

Answers

Answer:

-8

2/19

Step-by-step explanation:

We must substitute x=-1 into g(x) and then the answer of g(x) we must substiute as x into f(x). Similarly we must substitute x=1/2 into f(x) and the answer as x into g(x):

1. x=-1 into g(x)

$=1/-1=-1$

substitute x=-1 into f(x)

$=(-1)^2+9\cdot(-1)=-8$

2. x=1/2 into f(x)

$=(1/2)^2+9\cdot(1/2)=19/2$

substitute x=19/2 into g(x)

$=1/(11/2)=2/19$

$f(g(x))=1/x^2+9/x\Rightarrow f(g(-1))=-8$

$f(g(x))=1/(x^2+9x) \Rightarrow g(f(1/2))=4/19$

Two boys and three girls are auditioning to play the piano for a school production. Two students will be chosen, one as the pianist, the other as the alternate. What is the probability that the pianist will be a boy and the alternate will be a girl? Express your answer as a percent.

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Answer: The probability that he pianist will be a boy and the alternate will be a girl is 30%.

Explanation:

Since we have given that

Number of boys are auditioning to play the piano for a school production = 2

Number of girls are auditioning to play the piano for a school production = 3

Total number of candidates is given by

$2+3=5$

Now,

Let Event A denotes pianist will be a boy.

Let Event B denotes alternate will be girl.

Since Event A and B are independent events so,

$P(\text{ A and B})=P(A)* P(B)$

So,

Probability that the pianist will be a boy and the alternate will be a girl is given by

$(2)/(5)* (3)/(4)\n\n=(6)/(20)=(3)/(10)$

Now, we have to change it into percent ,

$(3)/(10)* 100=3* 10=30\%$

Hence ,the probability that he pianist will be a boy and the alternate will be a girl is 30%.

The probability helps us to know the chances of an event occurring. The probability that the pianist will be a boy and the alternate will be a girl is 0.3.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm Probability=(Desired\ Outcomes)/(Total\ Number\ of\ outcomes\ possible)$

As there are 2 boys and 3 girls. And out of this total of 5 people, we need to know the probability of a boy being selected first. Therefore, the probability can be written as,

$\rm Probability=(Desired\ Outcomes)/(Total\ Number\ of\ outcomes\ possible)$

$\rm Probability=\frac{\text{Number of boys}}{\text{Number of people}} = (2)/(5)$

Now since one boy is already selected the number of choices will reduce to 4, therefore, the probability of selecting a girl next can be written as,

$\rm Probability=(Desired\ Outcomes)/(Total\ Number\ of\ outcomes\ possible)$

$\rm Probability=\frac{\text{Number of girls}}{\text{Number of people}} = (3)/(4)$

Thus, the probability that the pianist will be a boy and the alternate will be a girl can be written as,

$\rm Probability=\frac25 * \frac34 = (3)/(10) = 0.3$

Hence, the probability that the pianist will be a boy and the alternate will be a girl is 0.3.

Learn more about Probability:

brainly.com/question/795909

Evaluate:
90 over
-10

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Answer:

-9

Step-by-step explanation:

Answer:

-9

Step-by-step explanation:

24. Congratulations! You have just won a jet ski worth $8000. The depreciated value of the jet ski (V) after t years is given by V = 8000 − 725t , 0 ≤ t ≤ 11.a. Use a graphing utility to graph the equation. Include a t-chart with at least 5 key points with your accurate labeled graph.
b. After how many years will the jet ski be worth $5100? Show all of your work or explain how you came up with your answer.
c. What will be the value of the jet ski after 9 years? Show all of your work or explain how you came up with your answer.

Answers

So:

$V=8000-725t\quad \{ 0\le t\le 11\}$

*V (in dollars) stands for the depreciated or non depreciated value of the jet ski.

*t (in years) stands for the amount of time that has passed. t is greater or equal to 0 and less than or equal to 11.

-------------------

Question (a):

Now V is a function of t. V=f(t).

When t=0, V=0 --> Point:(0,0)

When t=2, V=6550 --> Point (2, 6550)

When t=4, V=5100 --> Point (4, 5100)

When t=6, V=3650 --> Point (6, 3650)

When t=8, V=2200 --> Point (8,2200)

When t=11, V=25 --> Point: (11, 25)

So as the graph V=8000-725t is LINEAR, we can draw a line through the points mentioned above.

------------------------

Question (b): After how many years will the jet ski be worth $5100?

$8000-725t=5100\n \n 8000-5100=725t\n \n 2900=725t\n \n \frac { 2900 }{ 725 } =t\n \n \therefore \quad t=4,\quad when\quad V=5100$

Answer: 4 years.

-----------------------

Question (c): What will be the value of the jet ski after 9 years?

$When\quad t=9,\n \n V=8000-725\left( 9 \right) \n \n =1475$

The answer is $1,475.00

a) $y=mx+c$
$m=gradient=-725$
$y(v)-intercept=8000$

b) $5100=8000-725t$
$2900=725t$
$t=4$
The value will be 5100 after 4 years.

c) $V=8000-725(9)$
$V=8000-6525$
$V=1475$
The value of the jet will be 1475 after 9 years.

Hope I helped bro, now i can sleep

Choose the correct answer.

Find the interest due on $800 at 12% for 120 days.

Answers

Answer:

$32

Step-by-step explanation:

To find the interest due, you will use an interest formula.

The formula will be: Interest= P · r · $(n)/(365)$

P represents our principal amount, R is our rate of interest, and N is the number of days (out of 365 which is a year).

In this situation,

$800 will be our P amount, 12% will be our R, and 120 will be our N.

This will give us:

Interest= 800 · 0.12 · $(120)/(365)$

Before we go on, I would like to clarify 12% goes out of a hundred. To find the decimal form, you will divide 12 over 100. By doing this, you will find yourselves having 0.12 (our rate of interest).

When you solve our new formula equation, you will get a long decimal number consisting of 31.5616... Remember a decimal will be rounded if it is 5 or above, if it less than 5 it will not be rounded. In this case, we got 31.5, so we round; getting us 32.

Our answer will then be $32

A boat takes 8 hours to go 6 miles upstream and come back to the starting point. If the speed of the boat is 4 miles per hour in still water, what is the rate of the current? Hint: total time taken = time taken to go upstream + time taken to go downstream

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Let x = velocity of the water current t1 = time taken to go downstream t2 = time taken to go upstream t1 + t2 = 8 t2 = 8 – t1 v = D/t Downstream (4 + x) = 6/ t1 t1 = 6/(4+x) Upstream (4 – x) = 6/t2 Substitute expression for t2 to obtain (4 – x) = 6/ (8-t1) Substituting the expression of t1 to make a single variable equation, obtaining 6 = (4-x)*(8 – 6/(4+x)) Solving for x, x= 3.16 m/s

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Find the angle measure to the nearest degree. cos(A) = 0.5878how do I do this?​

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Find the angle measure to the nearest degree. cos(A) = 0.5878
how do I do this?