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Jobisdone [24]
3 years ago
12

Find the exact value of each of the following. In each case, show your work and explain the steps you take to find the value.

Mathematics
1 answer:
mote1985 [20]3 years ago
4 0

Answer: a) \frac{1}{2}

b) 1

c) 2

Step-by-step explanation:

(a) sin 17π/6  

It is known that the value of sin x repeat after an interval of 2\pi\ or\ 360^{\circ}

∴ \sin\frac{17\pi}{6}=\sin2\frac{5\pi}{6}=\sin(2\pi+\frac{5}{6}\pi)=\sin{\frac{5}{6}\pi}=\sin(\pi-\frac{\pi}{6})=\sin(\frac{\pi}{6})=\frac{1}{2}

[Since the value of sin x is positive in 2nd quadrant]

(b) tan 13π/4  

It is known that the value of sin x repeat after an interval of \pi\ or\ 180^{\circ}

∴ \tan\frac{13\pi}{4}=\tan(3\pi+\frac{\pi}{4})=\tan{\frac{\pi}{4}}=1

(c) sec 11π/3

\text{Since, }\sec(x)=\frac{1}{\cos x}

\cos(\frac{11\pi}{3})=cos(\frac{5\pi}{3}+2\pi)=\cos(\frac{5\pi}{3})=\cos(6\pi-\frac{\pi}{3})=\cos(\frac{\pi}{3})=\frac{1}{2}\\\Rightarrow\sec(\frac{11\pi}{3})=\frac{1}{\cos(\frac{11\pi}{3})}=2

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please help John's age increased by 11 is 5 less than 5 times his age. How old is he? If x represents John's age, which of the f
Keith_Richards [23]
So x is John's age.
We can solve this problem by working backwards.
Since it's 5 times his age, we first do 5x.
And then since it's five less, we move on to 5x - 5
And then we add the John's age is increased by 11: 5x - 5 = x + 11
I hope this helped :)
(It should be the second one you listed)
7 0
3 years ago
Every person has blood type O, A, B, or AB. A random group of people are blood-typed, and the results are shown in the table.
Evgesh-ka [11]

Answer:

12%

Step-by-step explanation:

P=\frac{6}{22+20+6+2} =.12

6 0
3 years ago
A committee of 15 members is voting on a proposal. Each member casts a yea or nay vote. On a random voting basis, what is the pr
Igoryamba

Answer:

0.006% probability that the final vote count is unanimous.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they vote yes, or they vote no. The probability of a person voting yes or no is independent of any other person. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which 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)!}

And p is the probability of X happening.

Random voting:

So 50% of voting yes, 50% no, so p = 0.5

15 members:

This means that n = 15

What is the probability that the final vote count is unanimous?

Either all vote no(P(X = 0)) or all vote yes(P(X = 15)). So

p = P(X = 0) + P(X = 15)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{15,0}.(0.5)^{0}.(0.5)^{15} = 0.00003

P(X = 15) = C_{15,15}.(0.5)^{15}.(0.5)^{0} = 0.00003

So

p = P(X = 0) + P(X = 15) = 0.00003 + 0.00003 = 0.00006

0.006% probability that the final vote count is unanimous.

7 0
3 years ago
I WILL MARKED BRAINLIEST IF YOU COULD ANSWER THIS!
tester [92]

Answer:

s = -2400t + 17400

Step-by-step explanation:

Let's say t is the x value on a coordinate plane, and s is the y. Then, we have the points (0, 17400) and (6, 3000). The slope of these is 14400/-6 or -2400.

Now we just have the equation y = -2400x + b, and from the point (0, 17400) we can find that b is 17400. So, we have y = -2400x + 17400. Convert these back into t and s and you get your answer, s = -2400t + 17400.

6 0
3 years ago
Simplify 2/9 + 1/3 + 2/3=
Maurinko [17]
2/9 + 1/3 + 2/3
2/9 + 3/9 + 6/9
(2 + 3 + 6) /9
11/9
7 0
3 years ago
Read 2 more answers
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