Answer:
3 grams
Step-by-step explanation:
We are going to take the mass of a bunch of little strips below the triangle "roof." To do this, we must figure out what formula for the mass we'll use, in this case, we'll use:
Mass of strip = denisty * area = (1+x)*y*deltax grams
now, because the "roof" of the triangle contains two different integrals (it completely changes direction), we will use TWO integrals!
**pretend ∈ is the sum symbol
Mass of left part = lim x->0 ∈ (1+x)*y*deltax = inegral -1 to 0 of (1+x)*3*(x+1) = 3 * integral -1 to 0 of (x^2 + 2x + 1) = 3 * 1/3 = 1
Mass of left part = lim x->0 ∈ (1+x)*y*deltax = inegral 0 to 1 of (1+x)*3*(-x+1) = 3 * integral 0 to 1 of (-x^2 + 1) = 3 * 2/3 = 2
Total mass = mass left + mass right = 1 + 2 = 3 grams
Answer:
15 years and 8 months
Step-by-step explanation:
I used the formula for compound interest as shown below and solved for the unknown, time.
Since our interest is compounded annually (So once a year) our m value is 1.
Answer:
7x=-5x
Step-by-step explanation:
Answer:
And the 68% confidence interval is given by (91.1186, 97.2814)
Step-by-step explanation:
For this case we know that mean time that visitors stay at a museum is given by:
The standard deviation is given by:
And the standard error is given by:
And we want to interval captures 68% of the means for random samples of 25 scores and for this case the critical value can be founded like this using the normal standard distribution or excel:
We can find the interval like this:
And replacing we got:
And the 68% confidence interval is given by (91.1186, 97.2814)
a = 30
a = 16
-a² + 46a -480 = 0
(-a + 30) (a -16) = 0
(-a)(a) + (-a)(-16) + 30(a) + 30(-16) = 0
-a² + 16a + 30a -480 = 0
-a² + 46a - 480 = 0
(-a + 30) = 0 ; (a - 16) = 0
-a = -30 ; a = 16
a = 30
To check:
a = 30
-(30)² + 46(30) - 480 = 0
-900 + 1380 - 480 = 0
480 - 480 = 0
0 = 0
a = 16
-(16)² + 46(16) - 480 = 0
-256 + 736 - 480 = 0
480 - 480 = 0
0 = 0
