Answer:
Mrs. Cook has to grade 63 tests.
Step-by-step explanation:
In order to find the answer, first you have to calculate 80% of the number of tests Ms. Morris has:
35*80%= 28
Then, you have to add the number that represents 80% to the number of tests Ms. Morris has to grade:
35+28=63
According to this, the answer is that Mrs. Cook has to grade 63 tests.
Recall the logarithm rules :
a^y = x is the same as log_a x = y
In this case,
a = 18
y = r - 10
x = 93
So,
18^ (r-10) = 93
is the same as
log_18 93 = r - 10
Solve for r to get :
10 + log_18 93 = r
Answer:
the probability is 50% or 1/2 (equally likely and equally unlikely)
That is because it does not state the amount of socks inside the draw; meaning the answer has to be theoretical.
If the probability is the same, than it has to equal to 100
so we can conclude that 1/2 of the drawer is blue socks and 1/2 is white socks.
Answer:
<h2>210</h2>
Step-by-step explanation:
list of prime #s between 12 and 42:
13, 17, 19, 23, 29, 31, 37, 41
now add them up:
13+17+<em>19</em>+<u>23</u>+<em>29+31</em>+<u>37</u>+<em>41</em>
30+60+60+60
90+120
210
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
