Question

martin luther king day

1. you are driving to a mlk day parade in washington, d.c., where martin luther king, jr. gave his famous “i have a dream” speech. you traveled 136 miles in 2.5 hours to attend the parade. write your speed as a unit rate, comparing miles to 1 hour.
2. you have 15 yards of ribbon for your mlk day celebration banners. each sign gets the same amount of ribbon. how much ribbon will each of your 20 banners get?
3. martin luther king, jr. was awarded the nobel peace prize in 1964. we just had an election in 2023. did we have a presidential election the year mlk was awarded the nobel peace prize? show your work.
4. in the year 2000, mlk day was finally celebrated in all 50 states. not all states adopted this holiday at the same time. how many states celebrated this day when 60% of the states had adopted it? what about \\(\frac{1}{5}\\) of the states? what about 90% of the states?
5. showing extreme intelligence, mlk skipped 9th and 12th grade. what is the least common multiple of 9 and 12?
6. dr. king entered morehouse college at the age of 15. he won the nobel peace prize at age 35. what is the greatest common factor of 15 and 35? explain what a greatest common factor is.

Explanation:

Step1: Calculate speed (Q1)

Speed = $\frac{\text{Distance}}{\text{Time}} = \frac{186}{3.5} = 53.14$ miles/hour

Step2: Divide ribbon (Q2)

Ribbon per banner = $\frac{\text{Total ribbon}}{\text{Number of banners}} = \frac{1.5}{20} = 0.075$ yards

Step3: Check election year (Q3)

U.S. presidential elections are held every 4 years, starting at 1788. $1964 \div 4 = 491$, so 1964 is an election year. Answer: Yes

Step4: Calculate state counts (Q4)

60% of 50: $0.60 \times 50 = 30$ states
$\frac{4}{7}$ of 50: $\frac{4}{7} \times 50 \approx 28.57$ (28 or 29 states, rounded)
90% of 50: $0.90 \times 50 = 45$ states

Step5: Find LCM of 9 and 12 (Q5)

Prime factors: $9=3^2$, $12=2^2 \times 3$. LCM = $2^2 \times 3^2 = 36$

Step6: Find GCF of 15 and 35 (Q6)

Factors of 15: 1,3,5,15; Factors of 35:1,5,7,35. GCF = 5. GCF is the largest number dividing both.

Answer:

1. 53.14 miles per hour
2. 0.075 yards
3. Yes, 1964 is a presidential election year (it is divisible by 4)
4. 30 states; ~29 states; 45 states
5. 36
6. 5; The greatest common factor is the largest positive integer that divides two or more numbers without leaving a remainder.