Hey there!
<span>At
Haines Elementary, 30% of the 120 teachers were male. The following
school year, several new teachers were hired. The number of female
teachers remained the same, but the number of males increased to 40%.
How many new male teachers were hired?
Answer: 21 male teachers were hired
Hope this helps
Have a great day (:
</span>
Answer:
Step-by-step explanation:
a) Tip = 15% of bill = 15% * 21 = 0.15 * 21 = $ 3.15
Amount including tips = 21 + 3.15 = $ 24.15
b) Tip = 15% of b = 0.15b
Amount including tips = b +0.15b
Answer:
Suppose a population of rodents satisfies the differential equation dP 2 kP dt = . Initially there are P (0 2 ) = rodents, and their number is increasing at the rate of 1 dP dt = rodent per month when there are P = 10 rodents.
How long will it take for this population to grow to a hundred rodents? To a thousand rodents?
Step-by-step explanation:
Use the initial condition when dp/dt = 1, p = 10 to get k;
![\frac{dp}{dt} =kp^2\\\\1=k(10)^2\\\\k=\frac{1}{100}](https://tex.z-dn.net/?f=%5Cfrac%7Bdp%7D%7Bdt%7D%20%3Dkp%5E2%5C%5C%5C%5C1%3Dk%2810%29%5E2%5C%5C%5C%5Ck%3D%5Cfrac%7B1%7D%7B100%7D)
Seperate the differential equation and solve for the constant C.
![\frac{dp}{p^2}=kdt\\\\-\frac{1}{p}=kt+C\\\\\frac{1}{p}=-kt+C\\\\p=-\frac{1}{kt+C} \\\\2=-\frac{1}{0+C}\\\\-\frac{1}{2}=C\\\\p(t)=-\frac{1}{\frac{t}{100}-\frac{1}{2} }\\\\p(t)=-\frac{1}{\frac{2t-100}{200} }\\\\-\frac{200}{2t-100}](https://tex.z-dn.net/?f=%5Cfrac%7Bdp%7D%7Bp%5E2%7D%3Dkdt%5C%5C%5C%5C-%5Cfrac%7B1%7D%7Bp%7D%3Dkt%2BC%5C%5C%5C%5C%5Cfrac%7B1%7D%7Bp%7D%3D-kt%2BC%5C%5C%5C%5Cp%3D-%5Cfrac%7B1%7D%7Bkt%2BC%7D%20%5C%5C%5C%5C2%3D-%5Cfrac%7B1%7D%7B0%2BC%7D%5C%5C%5C%5C-%5Cfrac%7B1%7D%7B2%7D%3DC%5C%5C%5C%5Cp%28t%29%3D-%5Cfrac%7B1%7D%7B%5Cfrac%7Bt%7D%7B100%7D-%5Cfrac%7B1%7D%7B2%7D%20%20%7D%5C%5C%5C%5Cp%28t%29%3D-%5Cfrac%7B1%7D%7B%5Cfrac%7B2t-100%7D%7B200%7D%20%7D%5C%5C%5C%5C-%5Cfrac%7B200%7D%7B2t-100%7D)
You have 100 rodents when:
![100=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{100} \\\\2t=98\\\\t=49\ months](https://tex.z-dn.net/?f=100%3D-%5Cfrac%7B200%7D%7B2t-100%7D%20%5C%5C%5C%5C2t-100%3D-%5Cfrac%7B200%7D%7B100%7D%20%5C%5C%5C%5C2t%3D98%5C%5C%5C%5Ct%3D49%5C%20months)
You have 1000 rodents when:
![1000=-\frac{200}{2t-100} \\\\2t-100=-\frac{200}{1000} \\\\2t=99.8\\\\t=49.9\ months](https://tex.z-dn.net/?f=1000%3D-%5Cfrac%7B200%7D%7B2t-100%7D%20%5C%5C%5C%5C2t-100%3D-%5Cfrac%7B200%7D%7B1000%7D%20%5C%5C%5C%5C2t%3D99.8%5C%5C%5C%5Ct%3D49.9%5C%20months)
Answer:
D. 6 1/12
Step-by-step explanation:
3 2/3= 3 8/12, 1 3/4= 1 9/12, 2/3= 8/12 || add (3 8/12+ 1 9/12+ 8/12= 4 25/12= 6 1/12)
The answer is the 3rd one