X is an integer Write down all the solutions of inequality 3<2x +1 < 13

Mathematics

1 answer:

BaLLatris [955]3 years ago

6 0

Answer:

1<x<6

Step-by-step explanation:

subtract 1 from every side: 2<2x<12

divide 2 every side: 1<x<6

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Suppose that two teams play a series of games that ends when one of them has won ???? games. Also suppose that each game played

Musya8 [376]

Answer:

(a) E(X) = -2p² + 2p + 2; d²/dp² E(X) at p = 1/2 is less than 0

(b) 6p⁴ - 12p³ + 3p² + 3p + 3; d²/dp² E(X) at p = 1/2 is less than 0

Step-by-step explanation:

(a) when i = 2, the expected number of played games will be:

E(X) = 2[p² + (1-p)²] + 3[2p² (1-p) + 2p(1-p)²] = 2[p²+1-2p+p²] + 3[2p²-2p³+2p(1-2p+p²)] = 2[2p²-2p+1] + 3[2p² - 2p³+2p-4p²+2p³] = 4p²-4p+2-6p²+6p = -2p²+2p+2.

If p = 1/2, then:

d²/dp² E(X) = d/dp (-4p + 2) = -4 which is less than 0. Therefore, the E(X) is maximized.

(b) when i = 3;

E(X) = 3[p³ + (1-p)³] + 4[3p³(1-p) + 3p(1-p)³] + 5[6p³(1-p)² + 6p²(1-p)³]

Simplification and rearrangement lead to:

E(X) = 6p⁴-12p³+3p²+3p+3

if p = 1/2, then:

d²/dp² E(X) at p = 1/2 = d/dp (24p³-36p²+6p+3) = 72p²-72p+6 = 72(1/2)² - 72(1/2) +6 = 18 - 36 +8 = -10

Therefore, E(X) is maximized.

6 0

3 years ago

Can you plz answer this for 10pt

Harrizon [31]

Round to the nearest thousands

8,276 = 8,000
2,451 = 2,000

8,000 + 2,000 = 10,000

answer
Maya traveled by plane about 10.000 miles

7 0

3 years ago

In a survey of 248 people, 156 are married, 70 are self-employed, and 25 percent of those who are married are self-employed. If

MatroZZZ [7]

Answer:

The probability of selecting a person which is self-employed but not married equals 1/8.

Step-by-step explanation:

Here, the given survey says:

Total number of people surveyed = 248

Number of people married = 156

The number of people are self employed = 70

Now, 25% of people who are married are SELF EMPLOYED.

Now, calculating 25% of 156 , we get:

$\frac{25}{100} \times 156 = 39$

⇒ out of total 156 married people, 39 are self employed.

So, number of self employed people but not married

= Self employed people - Self employed people PLUS married

= 70 - 39 = 31.

So, the probability that the person selected will be self-employed but not married = $\frac{\textrm{The total number of people self-employed but not married}}{\textrm{Total Number of people}}$ = $\frac{31}{248} = \frac{1}{8}$