MATHEMATICS HIGH SCHOOL

1 Suppose you choose at random a real number X from the interval [2, 10]. (a) Find the density function f(x) and the probability of an event E for this experiment, where E is a subinterval [a, b] of [2, 10]. (b) From (a), find the probability that X > 5, that 5 < X < 7, and that X2 − 12X + 35 > 0.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

Given that you choose at random a real number X from the interval [2, 10].

a) Since this is a contnuous interval with all number in between equally likely

E = probability for choosing a real number is U(2,10)

pdf of E is $(1)/(8)$

b) P(X>5) = $\int\limits^10_5 {1/8} \, dx = (5)/(8)$

$P(5<x<7) = (2)/(8) =(1)/(4)$

For

$x^2-12x+35 >0\n(x-5)(x-7)>0\nx<5 or x >7$

P(X<5 or x>7) = 1-P(5<x<7)

= $(3)/(4)$

Answer 2

Answer:

Final answer:

The density functionof a real number selected randomly within the range [2,10] is 1/8, with the probability of an event being the difference between the two values divided by 8. The probabilities that X is greater than 5, lies between 5 and 7 and that the inequality X^2 - 12X + 35 > 0 always holds are 5/8, 1/4 and 1 respectively.

Explanation:

The subject of this question is probability, particularly continuous uniform distribution. (a) A real number X selected from a certain interval [2, 10] has a continuous uniform distribution. Hence, the density function f(x) = 1/(b-a) = 1/8 for 2 ≤ x ≤ 10 and0otherwise. The probability of an event E, where E is [a,b], is the integral of f(x) from a to b, which is (b-a)/(10-2).

(b) Probability that X > 5 is the integral of f(x) from 5 to 10, which is (10-5)/8 = 5/8. Probability that 5 < X < 7 is the integral from 5 to 7, which is (7-5)/8 = 1/4. Lastly, the inequality X^2 - 12X + 35 > 0 factors out to (X-5)^2 + 10 > 0 which is always true as square number is always non-negative, thus the probability is 1.

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A book sold 38.400 copies in its first month of release. Suppose this represents 7.3% of the number of copies sold todate. How many copies have been sold to date?Round your answer to the nearest whole number

Answers

Since 38400 is 7.3% of the number of copies, then we can calculate the total number of copies with:

38400*100/7.3 = 526027.39. Rounded to the nearest whole number we have: 526027

The answer is 526027

If it takes Mark twice as long to earn $6.00 as it takes Carl to earn $4.00, what is theratio of Mark’s pay per hour to Carl’s pay per hour?

Answers

The ratio of Mark’s pay per hour to Carl’s pay per hour is 3:4 given that Mark takes twice as long as to earn $6.00 as it takes Carl to earn $4.00. This can be obtained by dividing their hourly wages.

What is the required ratio?

Given that, Mark takes twice as long as to earn $6.00 as it takes Carl to earn $4.00.

(Time taken for Mark to earn $6)=2×(Time taken for Carl to earn $4)

Time taken for Mark to earn $3 = Time taken for Carl to earn $4

This means that Mark takes the same amount of time to earn $3.00 as Carl earn $4.00.

Thus the ratio of Mark’s pay per hour to Carl’s pay per hour, 3/4 = 3:4

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If it takes Mark twice as long to make $6.00 than Carl making $4.00, this means Mark made $3.00 in the time it took Carl to make $4.00.
So the ratio is $3.00 to $4.00, or 3/4.

72 degrees is used in a pie chart to represent 4 people . How many people were there altogether ?

Answers

First lets find out the unit rate, the percent per person. Lets do it:-

72 ÷ 4 = 18
18% per person.

Lets find out how many people in the pie chart:-

100 ÷ 18 = 5.555.....

So, there are about 6 people in the pie chart together.

Hope I helped ya!! xD

72/4 = 18
100/18 = 5.555..
About 6 ppl.

Mackenzie wrote the following paragraph proof for the Vertical Angles Theorem: Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles. The sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. The sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 _________________. Angle 1 is equal to angle 3 by the subtraction property of equality. Which phrase completes the proof? by construction using a straightedge by the definition of a perpendicular bisector by the transitive property of equality. by the vertical angles theorem

Answers

by the transitive property of equality

Answer:

the transitive property of equality

Step-by-step explanation:

Rebecca sold 11 more magazine subscriptions than Chad.Laura sold 4 more than Rebecca.Laura sold 45 magazine subscriptions.How many magazine subscriptions did Chad sell?

Answers

Since Laura sold 4 more than Rebecca, you subtract 4 from 45 which is 41, and Rebecca sold 11 more than Chad, you subtract 11 from 41 which is 30.
Laura sold 45 magazine.
Rebecca sold 41 magazine.
Chad sold 30 magzine.

$45-4 = 41 \ (Rebecca) \n\ 41-11 = 30 \ (Chad)$