If f(x) is continuous on [1,4] and f(1) = 10, f(4)=3 and k =15, then which statement(s) would be true regarding a c value in [1,4] where f(c)=15?
a. a c is not guaranteed to exist.
b. at least one c is guaranteed to exist.
c. there is one c value.
d. there are no c values.
e. there could be one c value.
f. there could be multiple c values.

(could be more than one answer)

a and c

step-by-step explanation:

66.666666667%

step-by-step explanation:

divide 150 by 100

divide 100 by 1.5

there you go!

decreased by 33.333333334%

it is 570

step-by-step explanation:

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)