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3 years ago

Using the distributive property simplify this -2(x-3)

Mathematics

1 answer:

Mnenie [13.5K]3 years ago

4 0

For this case we must simplify the following expression:

$-2 (x-3)$

By definition we have that the distributive property establishes that:

$a (b + c) = ab + ac$

So, if we have:

-2 (x-3)

We take into account the law of multiplication of signs:

$- * + = -\\- * - = +$

So:

$-2 (x-3) = - 2x + 2 * 3 = -2x + 6$

Answer:

$-2x + 6$

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3 years ago

A financial talk show host claims to have a 55.3 % success rate in his investment recommendations. You collect some data over th

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Answer:

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

Step-by-step explanation:

For each recommendation, there are only two possible outcomes. Either it was a success, or it was a failure. So we use the binomial probability distribution to solve this problem.

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.

In this problem we have that:

$p = 0.553, n = 10$

If the claim is correct and the performance of recommendations is independent, what is the probability that you would have observed 4 or fewer successful:

This is

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)$

In which

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

$P(X = 0) = C_{10,0}.(0.553)^{0}.(0.447)^{10} = 0.0003$

$P(X = 1) = C_{10,1}.(0.553)^{1}.(0.447)^{9} = 0.0039$

$P(X = 2) = C_{10,2}.(0.553)^{2}.(0.447)^{8} = 0.0219$

$P(X = 3) = C_{10,3}.(0.553)^{3}.(0.447)^{7} = 0.0724$

$P(X = 4) = C_{10,4}.(0.553)^{4}.(0.447)^{6} = 0.1567$

$P(X \leq 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0003 + 0.0039 + 0.0219 + 0.0724 + 0.1567 = 0.2552$

There is a 25.52% probability of observating 4 our fewer succesful recommendations.

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3 years ago

On her first quiz in social studies, Meg answered 92% of the questions correctly. On her second quiz, she answered 27 out of 30

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3 years ago

Read 2 more answers

Let

bogdanovich [222]

∇ · (|r| r) =|r| ∇ · ( r) + r ∇ · |r|

|r| =√x²+y²+z²
∇ · ( r) =dr/dx +dr/dy+dr/dz= i+j+k
so
∇ · (|r| r) =√x²+y²+z² (i+j+k) + (x i + y j + z k ) ∇ · |r|

∇ · |r|= 2(x+y+z)/√x²+y²+z²
finally

∇ · (|r| r) = |r| (i+j+k) + 2(xi+yj+zk)/ |r|=|r| (i+j+k) + 2r/|r|

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4 years ago

The denominator of a fraction is 4 more than its numerator.

alukav5142 [94]

<h3>Answer:</h3>

<h3>Step-by-step explanation:</h3>

Let n represent the numerator of the original fraction, which is n/(n+4). After adding 1/2, the value is (2(n+4)+1)/(2(n+4)), so we have ...

n/(n+4) + 1/2 = (2(n+4)+1)/(2(n+4))

Simplifying gives ...

... (2n +(n+4))/(2(n+4)) = (2n +9)/(2(n+4))

Since the denominators are the same, we can work only with the numerators.

3n +4 = 2n +9

n = 5 . . . . . . . . . . . subtract 2n+4

_____

Check

The original fraction is 5/(5+4) = 5/9. Adding 1/2 gives ...

5/9 + 1/2 = 10/18 + 9/18 = 19/18

Note the numerator of this last fraction is 1 more than the denominator, which is twice the original denominator.

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3 years ago