MATHEMATICS COLLEGE

Solve for the unknown.a) sin (x – 5°) = cos (35°)

b) sin (2x – 17°) = cos (x – 4°)

c) sin (x)= cos (x)

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Answers

Answer 1

Answer:

Step-by-step explanation:

Use shifts to write sine and cosine in terms of each other.

a) sin (x – 5°) = cos (35°)

sin (x – 5°) = sin (90° – 35°)

sin (x – 5°) = sin (55°)

x – 5° = 55°

x = 60°

b) sin (2x – 17°) = cos (x – 4°)

sin (2x – 17°) = sin (90° – (x – 4°))

sin (2x – 17°) = sin (90° – x + 4°)

sin (2x – 17°) = sin (94° – x)

2x – 17° = 94° – x

3x = 111°

x = 37°

c) sin (x) = cos (x)

sin (x) = sin (90° – x)

x = 90° – x

2x = 90°

x = 45°

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What is the answer to (2a^4/b^5)^3

Answers

I hope this helps you

Is the relationship shown in the table at the right proportional? If so, use it to complete a proportions web. If not, explain why it is not40 Points to whover answers them all

Answers

yes it would be proportional because it goes through the origin

Answer:

yes it would be proportional because it goes through the origin

Step-by-step explanation:

A farmer decided to put a fence around his property that measures 170 feet long and 120 feet wide. What is the perimeter of his property?

Answers

um about 300 frtt long

Answer: 580

Step-by-step explanation:

A fence is usually a rectangle shape in these questions

Perimeter of a rectangle is P = 2l + 2w

P = 2(170) + 2(120) = 580

There are two more assignments in your course before the semester ends, and if you get an A on at least one of them, you will get an A for the semester. Your "what-if" scenario looks like this:Event Probability

A on paper and A on presentation 0.25
A on paper only 0.10
A on presentation only 0.30
Do not get an A on either 0.35

Answer the following questions: (1 point each, except the last item, 2 points)

a. What is the probability of getting an A on the paper?
b. What is the probability of getting an A on the presentation?
c. What is the probability of getting an A in the course?
d. Are the grades on the assignments independent? Explain your answer

Answers

Answer:

Step-by-step explanation:

Hello!

Given the events:

A: "obtain an A in the paper assigment" ⇒ P(A)= 0.10

B: "obtain A in the presentation assigment" ⇒ P(B)= 0.30

Ac: "do not get an A in the paper assigment" ⇒ P(Ac)= 1 - 0.10= 0.9

Bc: "do not get an A in the presentation assigment" ⇒ P(Bc)= 1 - 0.30= 0.7

P(A∩B)= 0.25

P(Ac∩Bc)= 0.35

a. P(A)= 0.10

b. P(B)= 0.30

c. To get an A in the course you have to get an A in the paper and an A in the presentation, symbolically: P(A∩B)= 0.25

d. If the events A and B are independent, then the ocurrence of one of them doesn't affect the probability of the other ocurring, if this is so then:

P(A)= P(A/B)

$P(A/B)= (P(AnB))/(P(B)) = (0.25)/(030)= 0.83$

P(A) ≠ P(A/B) this means that "B" ocurring modifies the probability of ocurrence of A, i.e. both events are not independent.

I hope it helps!

When we expand (2x + 1/2)^6, what is the coefficient on the x^4 term?

Answers

Answer: The coefficient before x^4 is 60

Step-by-step explanation:

Hey! So I am not an expert at this, but you have to use the binomial theorem

I have attached of the Pascals Triangle (one shows the row numbering as well)

Basically in a pascal triangle, you add the two numbers above it to get the next number below

As you can see, the rows start from 0 instead of 1

The 6th row contains the numbers 1, 6, 15, 20, 15, 6, 1 which would be the coefficient terms

NOTE: the exponents always add to 6, the first term starts at 6 and decrease it's exponent by 1 each time (6, 5, 4, 3, 2, 1, 0) and the second term increases it's exponent by 1 each time (0, 1, 2, 3, 4, 5, 6)

Using this information the third term from the sixth row (15) would be where it is x^4 (I have circled it on the second image)

It would be 15 × 2^4 × (1/2)^2 = 60

The reason why it is 2^4 and (1/2)^2 is because the third term has the exponents 4 and 2 (bolded on the NOTE) which means that the first term must be put to the power of 4 and the second term must be put to the 2nd power

Sorry for the lousy explanation. I really hope this makes sense! Let me know if this helped :)

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