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coldgirl [10]
3 years ago
10

Solve the inequality 2(4+2x)≥5x+5

Mathematics
1 answer:
iris [78.8K]3 years ago
3 0
  • Answer:

<em>x ≤ 3</em>

<em>x ∈ [ 3 ; +oo )</em>

  • Step-by-step explanation:

<em>2(4 + 2x) ≥ 5x + 5</em>

<em>8 + 4x ≥ 5x + 5</em>

<em>8 - 5 ≥ 5x - 4x</em>

<em>3 ≥ x</em>

<em>x ≤ 3</em>

<em>x ∈ [ 3 ; +oo )</em>

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Five years after 650 high school seniors graduated, 400 had a college degree and 310 were married. Half of the students with a c
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Answer:

The probability that a student has a college degree or is not married is 0.8308.

Step-by-step explanation:

The information provided is:

Total number of high school seniors (<em>N</em>) = 650.

Number of seniors with a college degree (<em>n</em> (C)) = 400.

Number of seniors who were married, (<em>n</em> (M)) = 310.

Consider the Venn diagram below.

The probability of an event, say E, is the ratio of the favorable outcomes of <em>E</em> to the total number of outcomes of the experiment.

That is,

P(E)=\frac{n(E)}{N}

Here,

n (E) = favorable outcomes of <em>E</em>

N = total number of outcomes of the experiment.

The probability of the union of two events is:

P(A\cup B)=P(A)+P(B)-P(A\cap B)=\frac{n(A)+n(B)-n(A\cap B)}{N}

Compute the probability that a student has a college degree or is not married as follows:

P(C\cup M^{c})=\frac{n(C)+n(M^{c})-n(C\cap M^{c})}{N}

From the Venn diagram:

n (C) = 400

n (M^{c}) = N - n (M) = 650 - 310 = 340

n (C ∩ M^{c}) = 200

The value of P (C ∪ M^{c}) is:

P(C\cup M^{c})=\frac{n(C)+n(M^{c})-n(C\cap M^{c})}{N}=\frac{400+340-200}{650}=0.83077\approx0.8308

Thus, the probability that a student has a college degree or is not married is 0.8308.

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