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3 years ago

Use distributive property to remove parentheses -6(-5y+3x-2)

Mathematics

2 answers:

Sergio [31]3 years ago

6 0

Answer:

When using distributive property just take the outside number and multiply it by all the numbers inside the parentheses

30y-18x+12

NISA [10]3 years ago

3 0

Answer:

30y - 18x +12

Step-by-step explanation:

Distribute (multiply) -6 to all terms within the parenthesis. Remember to follow the sign rules: negative x negative = positive ; negative x positive = negative

-6(-5y) = 30y

-6(3x) = -18x

-6(-2) = 12

Combine:

30y - 18x + 12 is your answer

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Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that 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.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

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

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

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

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

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

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

8 0

3 years ago

Help me please, asap i’m so confused :(

amm1812

What is the lalalallalalalaa

8 0

2 years ago

Can someone plz help me I don’t understand how to do this and I am really struggling with the online stuff

sweet [91]

Answer:

Step-by-step explanation:

x=6.28111...

100 x=628.111...

1000x=6281.111...

subtract

900x=5653

x=5653/900

density of iodine=785×5653/900≈4930.672222...

Here 2 is repeating .

3 0

3 years ago

A Web music store offers two versions of a popular song. The size of the standard version is 2.4 megabytes (MB). The size of the

Margarita [4]

Answer:

880 high-quality version

Step-by-step explanation:

I think the below is your full question:

<em>A Web music store offers two versions of a popular song. The size of the standard version is 2.1megabytes (MB). The size of the high-quality version is 4.5 MB. Yesterday, there were 1290 downloads of the song, for a total download size of 4821 MB. How many downloads of the high-quality version were there?</em>

Here is my answer:

Let x is the number of high-quality version

So the number of standard version= 1290 - x

We also know: total download size of 4821 MB. which means:

4.5x + 2.1(1290-x) = 4821

<=> 4.5x+2709-2.1x=4821

<=> 2.4x=2112

<=> x=880

So there were 880 high-quality version

5 0

3 years ago

Read 2 more answers

Determine if a triangle can be formed with the given lengths. If it can, classify it as acute,

lisabon 2012 [21]

Answer:

steps below

Step-by-step explanation:

1. It can be formed a triangle: sum of any two sides is greater than the 3rd side

2. It can't be an obtuse triangle: 5² + 7² = 74 < 10²

the triangle is an obtuse-angled triangle if the square of the longest side (c²) is greater than the sum of the square of other two sides (c²>a²+b²)

6 0

3 years ago