MATHEMATICS COLLEGE

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 1

Answer:

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!

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Which fraction is bigger 7/36, or 4/9

Answers

Answer:

4/9 is bigger

Step-by-step explanation:

For the 1st fraction, since 9 × 4 = 36,

4/9 = 4 × 4

9 × 4 = 16/36

Likewise, for the 2nd fraction, since 36 × 1 = 36,

7/36= 7 × 1

36 × 1 = 7/36

Since the denominators are now the same, the fraction with the bigger numerator is the greater fraction

16/36> 7/36 or 4/9 > 7/36

7/36 is bigger
7 goes into 36 5 times
and 4 goes in 9 only 4 times

A Popsicle store at the beach is comparing their monthly revenue with the sunglasses store next door. The shop owners find that their monthly revenue is positive correlated. This means that eating Popsicles causes people to buy sunglasses.True or False

Answers

Answer:

False

Step-by-step explanation:

Correlation is not causation.

It may mean that eating popsicles and buying sunglasses have a common cause: sunny days.

Use the binomial theorem to expand the expression :(3x + y)^5 and simplify.
(b) find the middle term in the expansion of
(1/x+√x)^4 and simplify your unswer.
(c) determine the coefficient of x^11 in the expansion of (x^2 +1/x)^10, simplify your answer.

Answers

Answer:

a) $(3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5$ .

b) The middle term in the expansion is $(6)/(x)$ .

c) The coefficient of $x^(11)$ is 120.

Step-by-step explanation:

Remember that the binomial theorem say that $(x+y)^n=\sum_(k=0)^(n) \binom{n}{k}x^(n-k)y^(k)$

a) $(3x+y)^5=\sum_(k=0)^5\binom{5}{k}3^(n-k)x^(n-k)y^k$

Expanding we have that

$\binom{5}{0}3^5x^5+\binom{5}{1}3^4x^4y+\binom{5}{2}3^3x^3y^2+\binom{5}{3}3^2x^2y^3+\binom{5}{4}3xy^4+\binom{5}{5}y^5$

symplifying,

$(3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5$ .

b) The middle term in the expansion of $((1)/(x) +√(x))^4=\sum_(k=0)^(4)\binom{4}{k}(1)/(x^(4-k))x^{(k)/(2)}$ correspond to k=2. Then $\binom{4}{2}(1)/(x^2)x^{(2)/(2)}=(6)/(x)$ .

c) $(x^2+(1)/(x))^(10)=\sum_(k=0)^(10)\binom{10}{k}x^(2(10-k))(1)/(x^k)=\sum_(k=0)^(10)\binom{10}{k}x^(20-2k)(1)/(x^k)=\sum_(k=0)^(10)\binom{10}{k}x^(20-3k)$