P(<em>X</em> ≤ 65) = P((<em>X</em> - 79)/7 ≤ (65 - 79)/7) = P(<em>Z</em> ≤ -2)
where <em>Z</em> follows the standard normal distribution with mean 0 and standard deviation 1.
Recall that for any normal distribution with mean <em>µ</em> and s.d. <em>σ</em>, we have
P(|<em>X</em> - <em>µ</em>| ≤ 2<em>σ</em>) ≈ 0.95
which in the case of <em>Z</em> translates to
P(-2 ≤ <em>Z</em> ≤ 2) ≈ 0.95
Now,
P(-2 ≤ <em>Z</em>) + P(-2 ≤ <em>Z</em> ≤ 2) + P(<em>Z</em> ≥ 2) = 1
==> P(-2 ≤ <em>Z</em>) + P(<em>Z</em> ≥ 2) ≈ 0.05
Any normal distribution is symmetric about its mean, so P(-2 ≤ <em>Z</em>) = P(<em>Z</em> ≥ 2), and this gives us
==> 2 P(-2 ≤ <em>Z</em>) ≈ 0.05
==> P(-2 ≤ <em>Z</em>) ≈ 0.025
Answer:
3k^2 -k+5
reason:
when adding two equations together, you combine like terms.
First, add -2 to 7 to get 5
Then, add k, or 1k, to -2k, which gives you -1k, or just -k
3k^2 stays the same because there are no like terms in the other equation to combine it with
Answer:
A. 1.65 k = 48
B. 105
Step-by-step explanation:
- If we name "k" the amount of apples that Kayla has, and "r" the amount of apples thata Richard has, we know that r + k =48 (the two of them together have 48 apples).
- In addition, we know that Kayla has 35% more apples than Richard. This means that k (1-0.35) = r (the apples of Richard are 0.35 % smaller than the apples of Kayla). Then 0.65 k = r
- Then, taking these two considerations together, r + k= 48 and 0.65 k= r, imply 0.65 k + k = 48 (I just replace the second equation into the first one). Which finally means that k= 29 (and r = 19 because r+ k=48).
- If Kayla has 162 apples, and according previous statements, she has 35% more apples than Richard, this means that 0.65 k= r, therfore if k=162, r= 162 x 0.65 = 105 (Richar has 105 apples).
Answer:
A
Step-by-step explanation:
|((experimental - theoretical) / theoretical)| x 100
5.5 - 5.62 / 5.62 = -.0213
|-.0213| = .0213
.0213 x 100 = 2.13
<u>The minimum distance is 492 meters from the house (500 - 8 = 492), and the maximum distance is 508 meters from the house (500 + 8 = 508). The dog may be slightly closer to the house, depending on how long the dog is, or if Morgan is using a leash extender.</u>