Answer:So first, I found the length of the sides and the diagonal of the square, which are 18−−√ and 6 respectively. By graphing, I know the solution is (0,−1). Then, I assume that since the length between (3,2) and (−3,2) is the diagonal, then the distance between (0,5) and the remaining vertex must be the diagonal too. And since the length of the side is 6, then the distance between the vertex and either (3,2) or (−3,2) must be 6. So:
(x−3)2+(y−2)2−−−−−−−−−−−−−−−√=18−−√
(x−0)2+(y−5)2−−−−−−−−−−−−−−−√=6
Which gives (after a bit of cleaning up):
x2+y2−10y=11
x2−6x+y2−4y=5
Then, replacing the second expression into the first one:
x2−6x+y2−4y=5⇒x2=5+6x−y2+4y
5+6x−y2+4y+y2−10y=11
5+6x+4y−10y=11
6x−6y+6
x−y=1
x=1+y
Up to this point, I know I'm not entirely wrong because the expression is true for the actual coordinates of the vertex, because 0=1+(−1) is true. But I wouldn't know how to proceed if I hadn't known the answer beforehand. I need to find both x and y, is there a linear equation I'm missing to find the exact coordinates of the last vertex? Is my process okay or is there a simpler way to do it?
Step-by-step explanation:
The probability that a randomly selected x-value from the distribution will be in the interval:
- P(35 < x < 45) = 0.6827 and,
- P(30 < x < 40) = 0.47725
<h3>What is the probability of a normal distribution?</h3>
The probability of a normal distribution can be determined from the symmetrical curve between 1 to 100%.
From the information given:
- Mean = 40
- Standard deviation = 5
To determine the probability that a randomly selected x-value is in the given interval:
![\mathbf{P(35 < x < 45) = P[Z\le 1] -P[Z\le -1]}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%2835%20%3C%20x%20%3C%2045%29%20%3D%20P%5BZ%5Cle%201%5D%20-P%5BZ%5Cle%20-1%5D%7D)
Using normal distribution table:
P(35 < x < 45) = 0.8414 - 0.1587
P(35 < x < 45) = 0.6827
![\mathbf{P(30 < x < 40) = P[Z\le0]-P[Z\le -2]}](https://tex.z-dn.net/?f=%5Cmathbf%7BP%2830%20%3C%20x%20%3C%2040%29%20%3D%20P%5BZ%5Cle0%5D-P%5BZ%5Cle%20-2%5D%7D)
Using normal distribution table:
P(30 < x < 40) = 0.5 - 0.02275
P(30 < x < 40) = 0.47725
Learn more about the probability of a normal distribution here:
brainly.com/question/4079902
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They will need 8 cups/pints for the milk shakes
Let x be the number of children and t, the number of adults.
x + y =153
5.2x + 8.4y = 1013.2
Solving those equation will give:
x = 85 tickets sold to the kids ( and 68 tickets for adults)
Answer:
8 grams
Step-by-step explanation:
if 5/5 is 40 grams, you divide 40 by 5 to get 1/5
