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3 years ago

Find the product. -2x(x2 - 3) -2 x3 - 6 x -2 x2 6 x 6 x3 -2 x3 6 x.

1 answer:

6 0

Product of two polynomials can be done by distribution of multiplication over addition. The product of $-2x(x^2 - 3)$ is $-2x^3 + 6x$

<h3>What is distributive property of multiplication over addition?</h3>

Suppose a, b and c are three numbers. Then we have:

$a(b + c) = a\times b + a\times c$

(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)

The product result of the given expression is

$-2x(x^2 - 3) = -2x^{1 + 2} + 6x = -2x^3 + 6x$

It is because when bases are same and there is multiplication, then powers add up, so we have: $a^b \times a^c = a^{b+c}$

Thus,

The product of $-2x(x^2 - 3)$ is $-2x^3 + 6x$

Learn more about product of polynomials here:

brainly.com/question/9106484

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The longest human power sporting event is the tour de France cycling race in a particular year the average speed for the winner

sergey [27]

Answer:

The winner completed the race in 96 hours and 52 minutes.

Step-by-step explanation:

Given:

Distance of the cycling race = 2292 miles

Average speed of the winner = $23.66\ mph$

We need to find time required by winner to complete the race.

Solution:

Now we know that;

Time required can be calculated by dividing Total Distance from the Average speed.

framing in equation form we get;

time required by winner to complete the race = $\frac{2292}{23.66} = 96.87\ hrs$

Now converting $0.87\ hrs$ into minutes we get;

$0.87\times 60= 52.2\approx 52\ mins$

Hence the winner completed the race in 96 hours and 52 minutes.

3 0

3 years ago

Which statements are true about the place values in the number 99.999?

dalvyx [7]

A and B are correct... reason is because hundredths is 1/10 to tenths and tenths are 10 times bigger than hundredths. C and D are wrong.

Hope this helped!

Nate

4 0

3 years ago

Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do ho

oksano4ka [1.4K]

Answer:

a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12

c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.

d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.

Step-by-step explanation:

Let the event that a student does homework regularly be H.

The event that a student passes the course be P.

- 60% of her students do homework regularly

P(H) = 60% = 0.60

- 95% of the students who do their homework regularly generally pass the course

P(P|H) = 95% = 0.95

- She also knows that 85% of her students pass the course.

P(P) = 85% = 0.85

a) The probability that a student will do homework regularly and also pass the course = P(H n P)

The conditional probability of A occurring given that B has occurred, P(A|B), is given as

P(A|B) = P(A n B) ÷ P(B)

And we can write that

P(A n B) = P(A|B) × P(B)

Hence,

P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57

b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')

From Sets Theory,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

P(H n P) = 0.57 (from (a))

Note also that

P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)

0.60 = P(H n P') + 0.57

P(H n P') = 0.60 - 0.57

Also

P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)

0.85 = P(H' n P) + 0.57

P(H' n P) = 0.85 - 0.57 = 0.28

So,

P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1

Becomes

0.03 + 0.28 + 0.57 + P(H' n P') = 1

P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12

c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.

Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,

P(A n B) = 0.

But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.

Hence, the two events aren't mutually exclusive.

d. Are the events "pass the course" and "do homework regularly" independent? Explain

Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when

P(A|B) = P(A)

P(B|A) = P(B)

P(A n B) = P(A) × P(B)

To check if the events pass the course and do homework regularly are mutually exclusive now.

P(P|H) = 0.95

P(P) = 0.85

P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671

P(H) = 0.60

P(H n P) = P(P n H)

P(P|H) = 0.95 ≠ 0.85 = P(P)

P(H|P) = 0.671 ≠ 0.60 = P(H)

P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)

None of the conditions is satisfied, hence, we can conclude that the two events are not independent.

Hope this Helps!!!

7 0

3 years ago

Érica has saved $24, which is 40% of the total amount she needs to buy a new video game. How much does she need total to buy the

d1i1m1o1n [39]

Do 40/100=24/x and cross multiply

5 0

3 years ago

-2(3x+2) is greater than or equal to -6x-4

olchik [2.2K]

The inequality would look like this:

-2 (3x + 2) $\geq$ -6x-4

To begin to find the solutions, distribute the -2 throughout the set of parenthesis on the left side of the inequality by multiplying the -2 by each term in the set of parenthesis

-2 x 3x = -6x
-2 x 2 = -4

-6x -4 $\geq$ -6x-4

Begin to isolate x by performing the opposite operation of adding -6x on both sides of the inequality

0x -4 $\geq$ -4

Next perform the opposite operation by adding 4 on both sides of the inequality

0x $\geq$ 0

Now, I'm not exactly understanding how that can possibly work. So, I guess I didn't really help you. But add a comment so that we can talk about the problem :)

8 0

3 years ago