Answer:
Part 1) 2.1 cups of cream
Part 2) 4.2 cups of dark chocolate
Step-by-step explanation:
we know that
The recipe for 20 chocolate truffles is:
I cup of cream
2 cups of dark chocolate
step 1
Find how many cups of cream are needed for 42 truffles
using proportion
Let
x-----> the number of cups of cream needed
20/1=42/x
x=42/20=2.1 cups of cream
step 2
Find how many cups of dark chocolate are needed for 42 truffles
using proportion
Let
x-----> the number of cups of dark chocolate needed
20/2=42/x
x=42*2/20=4.2 cups of dark chocolate
Answer:
Mean = 16.5
Variance = 35.55
Step-by-step explanation:
<u> x P(x) x. P(x) x² x². P(x)</u>
6 0.10 0.6 36 3.6
12 0.35 4.2 144 50.4
18 0.25 4.5 324 81
<u> 24 0.30 7.2 576 172.8</u>
∑x P (x) 16.5 ∑x² P (x) 307.8
The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.
Mean is given by E(X)= ∑x P (x) = 16.5
Similarly the variance is also calculated using the expected value of X and X².
Variance is given= E(X)²- [E(X)]²= 307.8- (16.5)²= 307.8-272.25 = 35.55
Lim ln([(x+1)/x]^3x) as x ->.infinity =lim ln([(x+1)^(3x)]/[x^(3x)]) as s->infinity =lim ln((x+1)^(3x))-ln(x^(3x)) = infinity - infinity
your answer is e3 but you can use l'hopital if you liketake the log, get 3xln(1+1/x)which is in the form ∞×0 then use the usual trick of rewriting as ln(1+1/x)/1/3x
The answer you are looking for is 12.0
Running burns the most calories folwed by aerobic
so max out the most and min the least
most running
running has no limit, so see least
aerobic, aerobic has to be at most 30 (less than 30)
rowing has to be at least 15 mins
say row=15 mins
then you have 45 mins left
max out on running (minus 1 tho to do running)
so
44mins running 1 min run, 15min row
total calories=507 calories burned
the way to do it is
x=running minutes
y=aerobic minutes
z=rowing minutes
x+y+z=60
9x+6y+7z=max calories
x≥5
y≤30
z≥15
those are the equations
not sure what the objective function is
