Question

in 2010, the enrollment at an after - school childcare program was approximately 2500 students. in 2014, the enrollment had increased to 3250 students. if the enrollment continues to change at this constant rate, what is a reasonable projection of the after - school enrollment for 2022?
a4750
b5750
c6500
d4000
yesterday:
what was its average speed in miles per hour if a plane flew 1839.1 miles in 5.3 hours?
released staar questions:
fernando recorded the weather for 90 days. the statements shown summarize some of his records:
. it was sunny for 1/2 of the days.
. it rained during 1/3 of the days.
. it snowed during the remaining days.
how many days did it snow out of the 90 days?
(a) 45 days
(b) 30 days
(c) 15 days
(d) 75 days

Explanation:

Step1: Find the rate of change of enrollment

The time - period from 2010 to 2014 is $2014 - 2010=4$ years. The change in enrollment is $3250 - 2500 = 750$ students. So the rate of change $r=\frac{3250 - 2500}{2014 - 2010}=\frac{750}{4}=187.5$ students per year.

Step2: Find the number of years from 2014 to 2022

The number of years from 2014 to 2022 is $2022 - 2014 = 8$ years.

Step3: Calculate the projected enrollment in 2022

The enrollment in 2014 is 3250 students. The increase in enrollment from 2014 to 2022 is $187.5\times8=1500$ students. So the projected enrollment in 2022 is $3250+1500 = 4750$ students.

Step4: Calculate the average speed of the plane

The formula for average speed $v$ is $v=\frac{d}{t}$, where $d$ is the distance and $t$ is the time. Given $d = 1839.1$ miles and $t = 5.3$ hours. Then $v=\frac{1839.1}{5.3}=347$ miles per hour.

Step5: Calculate the number of snowy days

The fraction of sunny days is $\frac{1}{2}$ of 90 days, so the number of sunny days is $\frac{1}{2}\times90 = 45$ days. The fraction of rainy days is $\frac{1}{3}$ of 90 days, so the number of rainy days is $\frac{1}{3}\times90=30$ days. The fraction of snowy days is $1-\frac{1}{2}-\frac{1}{3}=\frac{6 - 3-2}{6}=\frac{1}{6}$. The number of snowy days is $\frac{1}{6}\times90 = 15$ days.

Answer:

1. A. 4750
2. 347 miles per hour
3. C. 15 days