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ankoles [38]
3 years ago
6

Buddy the elf and Jovie are planning to start running together for a few days per week. In order to estimate how far they could

run together in a amount of time, they each time a 1/2 mile solo run. Buddy the elf ran the 1/2 mile in 5 minutes, 30 seconds, while Jovie ran the 1/2 mile in 5 minutes, 15 seconds.
a) What is the unit rate for each number? Explain what unit rate means
b) What is the maximum number of miles Buddy the Elf and Jovie can run together in an hour if the run at Buddy the Elf's pace?
Mathematics
1 answer:
eduard3 years ago
3 0

Answer:

a) Buddy's Unit rate is 11 minutes per 1 mile.

Jovie's unit rate is 10 minutes and 30 seconds or 10.5 per 1 mile.

A unit rate is the amount per one unit.

b) 5 miles. Or if Buddy and Jovie count their miles separately then 10 miles together since each runs 5 miles.

Step-by-step explanation:

a) A unit rate is the amount per one unit. At a grocery store, the unit rate is dollar cost per 1 unit bought. In a race, the unit race is the time it takes to one 1 mile.

Since Buddy can run 1/2 a mile in 5 minutes and 30 seconds, we can double his time for a full mile. 2*5 min is 10 minutes and 2*30 sec is 60 seconds or 1 minute. Buddy runs 11 minutes per mile.

Since Jovie can run 1/2 a mile in 5 minutes and 15 seconds, we can double the time for a full mile. 2*5 min is 10 minutes and 2*15 sec is 30 seconds. Jovie runs 10 minutes and 30 seconds per mile. This can also be written as 10.5 mins per mile.

b) Because we know how long it takes to run 1 mile, we can calculate how many miles can be run in a specific time frame by dividing it by the unit rate. An hour has 60 minutes. Divide 60 by Buddy's unit rate. 11 minutes per 1 mile. 11 divides into 60 to give 5.4545454....miles. We round up or down to the nearest mile to give 5 miles completed in 1 hour. If each runs 5 miles then together they run 10 miles.



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The College Board reports that 2% of students who take the SAT each year receive special accommodations because of documented di
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Answer:

(a) P(X=1) = 0.3079

(b) P(X≥1) = 0.3965

(c) P(X≥2) = 0.0886

(d) P(X≤1.9) = 0.9114

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Step-by-step explanation:

We have,

p = 0.02

n = 25

q = 1-p

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We will use the binomial distribution formula to solve this question. The formula is:

P(X=x) = ⁿCₓ pˣ qⁿ⁻ˣ

where n = total no. of trials

           x = no. of successful trials

           p = probability of success

           q = probability of failure

Let X be the number of students who received a special accommodation.

(a) P(X=1) = ²⁵C₁ (0.02)¹ (0.98)²⁵⁻¹

          = 25*0.02*0.61578

P(X=1) = 0.3079

(b) P(X≥1) = 1 - P(X<1)

               = 1 - P(X=0)

               = 1 - (²⁵C₀ (0.02)⁰ (0.98)²⁵⁻⁰)

              = 1 - 0.6035

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(c)  P(X≥2) = 1 - P(X<2)

                 = 1 - [P(X=0) + P(X=1)]

                 = 1 - (0.6035 + 0.3079)

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(d) The probability that the number among 25 who received a special accommodation is within 2 standard deviations of the expected number of accommodations. This means we need to compute the probability P(X-μ≤2σ). For this we need to calculate the mean and standard deviation of this distribution.

μ = np = (25)*(0.02) = 0.5

σ = \sqrt{npq} = √(25)*(0.02)*(0.98) = √0.49 = 0.7

P(X-μ≤2σ) = P(X - 0.5≤ 2(0.7)) = P(X≤ 1.4 + 0.5) = P(X≤1.9)

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             = 0.6035 + 0.3079

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(e) Student who does not receive a special accommodation i.e. X=0 is given 3 hours for the exam whereas an accommodated student P(X>0) is given 4.5 hours. The expected average number of hours given on the exam can be calculated as:

Expected no. of hours = ∑x*P(x)

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                                     = 1.8105 + 4.5(1 - 0.6035)

                                     = 1.8105 + 1.78425

Expected no. of hours = 3.594 hours

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