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2 years ago

Simplify the expression: -2x + 3 - (5-6x)

Mathematics

1 answer:

levacccp [35]2 years ago

8 0

Answer:

4x+3

How: -2x - (-6x) = 4

3 cannot be added there you go

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2 years ago

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3 years ago

Read 2 more answers

Assume that 63% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below

mash [69]

Answer:

a. 0.9931

b. 0.3423

c. 0.3907

d. 0.2670

e. 3.15

f. 1.0796

Step-by-step explanation:

The probability of the variable that said the number of left-handed people follow a Binomial distribution, so the probability is:

$P(x)=nCx*p^{x}*(1-p)^{n-x}$

nCx is calculated as:

$nCx=\frac{n!}{x!(n-x)!}$

Where x is the number of left-handed people, n is the number of people selected at random and p is the probability that a person is left--handed. So P(x) is:

$P(x)=5Cx*0.63^{x}*(1-0.63)^{5-x}$

Then the probabilities P(0), P(1), P(2), P(3), P(4) and P(5) are:

$P(0)=5C0*0.63^{0}*(1-0.63)^{5-0}=0.0069$

$P(1)=5C1*0.63^{1}*(1-0.63)^{5-1}=0.0590$

$P(2)=5C2*0.63^{2}*(1-0.63)^{5-2}=0.2011$

$P(3)=5C3*0.63^{3}*(1-0.63)^{5-3}=0.3423$

$P(x)=5C4*0.63^{4}*(1-0.63)^{5-4}=0.2914$

$P(x)=5C5*0.63^{5}*(1-0.63)^{5-5}=0.0993$

Then, the probability P(x≥1) that there are some lefties among the 5 people is:

P(x≥1) = P(1) + P(2) + P(3) + P(4) + P(5)

P(x≥1) = 0.0590 + 0.2011 + 0.3423 + 0.2914 + 0.0993 = 0.9931

The probability P(3) that there are exactly 3 lefties in the group is:

P(3) = 0.3423

The probability P(x≥4) that there are at least 4 lefties in the group is:

P(x≥4) = P(4) + P(5) = 0.2914 + 0.0993 = 0.3907

The probability P(x≤2) that there are no more than 2 lefties in the group is:

P(x≤2) = P(0) + P(1) + P(2) = 0.0069 + 0.0590 + 0.2011 = 0.2670

On the other hand, the expected value E(x) and standard deviation S(x) of the variable that follows a binomial distribution is:

$E(x)=np=5(0.63)=3.15\\S(x)=\sqrt{np(1-p)}=\sqrt{5(0.63)(1-0.63)}=1.0796$

6 0

3 years ago

What equation results from completing the squre and then factoring x^2+10=15

nlexa [21]

For this case we must complete squares:

$x ^ 2 + 10x = 15$

We add the square of half the coefficient of the term "x",

$(\frac {b} {2a}) ^ 2$ on both sides of the equation:

$x^2+10x+(\frac {10} {2 (1)}) ^ 2 = 25 + 15\\x ^ 2 + 10x + 5 ^ 2 = 25 + 15$

According to the perfect square trinomial we have:

$(a + b) ^ 2 = a ^2 + 2ab + b ^ 2$

Rewriting the expression we have:

$a = x\\b = 5\\(x + 5) ^ 2 = 25 + 15\\(x + 5) ^ 2 = 40$

ANswer:

$(x + 5) ^ 2 = 40$

6 0

2 years ago

Write an equation of the line with slope 2/3 that goes through the point -2,5

irinina [24]

Answer:

y = 2/3x + 19/3

Step-by-step explanation:

First, this is your current equation: y = 2/3x + b. Plug in your point to the equation, it should look like this: 5 = 2/3(-2) + b. 2/3 times -2 equals -4/3. So, this is what your equation should look like: 5 = -4/3 + b. Add 4/3 to both sides of the equation to get 19/3 = b. Go back to your original equation and plug 19/3 to b. This is your final equation: y = 2/3x + 19/3. Hope this helped!

7 0

2 years ago