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g100num [7]
3 years ago
13

A random number is selected from the interval [6.35, 10]. Find the probability that the number is within a distance of 0.25 from

an even integer. (Answer as a decimal number, and round to 4 decimal places).
Mathematics
1 answer:
exis [7]3 years ago
6 0

Let <em>X</em> be a random number selected from the interval. Then the probability density for the random variable <em>X</em> is

f_X(x)=\begin{cases}\dfrac1{10-6.35}=\dfrac1{3.65}\approx0.2740&\text{if }6.35\le x\le 10\\0&\text{otherwise}\end{cases}

8 and 10 are the only even integers that fit the given criterion (6 is more than 0.25 away from 6.35), so that we're looking to compute

P(|<em>X</em> - 8| < 0.25) + P(|<em>X</em> - 10| < 0.25)

… = P(7.75 < <em>X</em> < 8.25) + P(9.75 < <em>X</em> < 10.25)

… = P(7.75 < <em>X</em> < 8.25) + P(9.75 < <em>X</em> < 10)

(since P(<em>X</em> > 10) = 0)

… = 0.2740 (8.25 - 7.75) + 0.2740 (10 - 9.75)

… = 0.2055

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Y is directly proportional to x when y=30, x=6
rosijanka [135]

Answer:

a) y = 5x

b) y = 60

Step-by-step explanation:

Since, y is directly proportional to x when y=30, x=6

\therefore \:  y \:  \alpha \:  \: x \\ \therefore \:  y =  kx ...(1) \\ plug \: y = 30 \: and \: x = 6  \: in \: eq \: (1)\\ 30 = k \times 6 \\ k =  \frac{30}{6}  \\ k = 5 \\ plug \: k = 5 \: in \: (1) \\ y = 5x....(2) \: (required \: equation) \\ plug \: x = 12 \: in \: eq \: (2) \\ y = 5 \times 12 \\  \huge \red{ \boxed{y = 60}}

4 0
3 years ago
A survey shows that 10% of the population is victimized by property crime each year. A random sample of 527 older citizens (65 y
jekas [21]

Answer:

The data provide sufficient evidence that older people are more likely to be victimized.

Step-by-step explanation:

H 0 : P = 0.10

H 1 : P > 0.10 (Right tailed test)

n = 527, P = 0.1235

The test statistics

x = P - p / \sqrt{p*(1-p) / n}

x = 0.1235 - 0.10 / \sqrt{0.10 * 0.90 / 527}

x = 0.0235 / \sqrt{0.09 / 527}

x = 0.0235 / \sqrt{0.00017077798}

x = 0.0235 / 0.0130682049264618

x = 1.798257689731729

x = 1.798

P value = [1 - p(Z > 1.7980] (Right tailed test)

P value = 0.036089

The P - Value is very small, so <u>reject H0</u>

Conclusion: The data provide sufficient evidence that older people are more likely to be victimized.

7 0
3 years ago
Please answer correctly, work is optional.
kati45 [8]

Answer: 0.845

Step-by-step explanation: 1.69 divided by two is 0.845

3 0
3 years ago
Read 2 more answers
I have a triangle with angles measuring 40, 40, and 100. Is this one a unique triangle, many triangles, or no triangle?
juin [17]

Answer:

Unique triangle.

Step-by-step explanation:

If you were to draw the triangle, you would've been able to see that one angle is open and that the other 2 were closed.

5 0
3 years ago
There are 52 cards in a deck, and 13 of them are hearts. Four cards are dealt, one at a time, off the top of a well-shuffled dec
irga5000 [103]

Answer:

10.97%

Step-by-step explanation:

There are 52 cards.

13 of them, are hearts.

Then

52 - 13 = 39 cards are not hearts.

4 cards are drawn, we want to find the percent chance that the fourth card is a heart card, but no before.

So the first card can't be a heart card.

because the deck is well-shuffled, all the cards have the same probability of being drawn.

Then the probability of not getting a heart card, is equal to the quotient between the number of non-heart cards (39) and the total number of cards (52), then the probability is:

p₁ = 39/52

The second card also can't be a heart card, the probability is calculated in the same way than above, but now there are 38 non-heart cards and a total of 51 cards (because one card was already drawn) then the probability here is:

p₂ = 38/51

For the third card the reasoning is similar to the two above cases, here the probability is:

p₃ = 37/50

The fourth card should be a hearts card, the probability is computed in the same way than above, as the quotient between the number of heart cards in the deck (13) and the total number of cards in the deck (now there are 49 cards)

then the probability is:

p₄ = 13/49

The joint probability (the probability of these 4 events happening together) is equal to the product between the individual probabilities:

P = p₁*p₂*p₃*p₄

P = (39/52)*(38/51)*(37/50)*(13/49) = 0.1097

The percent chance is the above number times 100%

Percent =  0.1097*100% = 10.97%

3 0
3 years ago
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