#1) 4.445 ft
#2) yes
Explanation
#1) The maximum height is the y-coordinate of the vertex. We first find the axis of symmetry, given by x=-b/2a:
x=-0.17/2(-0.005) = -0.17/-0.01 = 17
Plugging this into the equation,
y=-0.005(17²)+0.17(17)+3 = 4.445
#2) Substituting 30 into the equation,
y=-0.005(30²) + 0.17(30) + 3 = 3.6
The ball will 3.6 in the air, so yes, it will clear the 3 ft tall net.
Answer/Step-by-step explanation:
✔️Find AC using Pythagorean Theorem:
AC² = 25.2² - 11.3²
AC² = 507.35
AC = √507.35
AC = 22.5 (nearest tenth)
✔️Find m<A using trigonometric ratio:
Reference angle = A
Opp = 11.3
Hyp = 25.2
Sin(A) = opp/hyp
Sin(A) = 11.3/25.2
A = sin^{-1}(11.3/25.2)
A = 26.6° (nearest tenth)
✔️Find m<B using trigonometric ratio:
Reference angle = B
Adj = 11.3
Hyp = 25.2
Cos(A) = adj/hyp
Cos(A) = 11.3/25.2
A = cos^{-1}(11.3/25.2)
A = 63.4° (nearest tenth)
Answer:
A) 99.7% of people have an IQ between 64 and 136.
B) 5% of people have an IQ score less than 76 or greater than 124.
C) 16% of people have an IQ score greater than 112.
Step-by-step explanation:
The Empirical Rule tells us that, in a normal or 'bell-shaped' distribution, 68% of the data is one standard deviation from the mean, 95% of the data is two standard deviations from the mean, and 99.7% of the data is three standard deviations from the mean.
A) 64 and 136 are 3 standard deviations away from the mean, so 99.7% of people have an IQ between 64 and 136.
B) 76 and 124 are 2 standard devations away from the mean, but the answer is asking what percentage is not between them. 100% - 95% gives us 5%.
C) 112 is one standard deviation away from the mean. If we want to find the percentage greater, then we can do 100% - 50% (as 112 is to the left of the mean), then we can take half of 68 to get 34%, and after subtracting 50% and 34% from the 100%, we get 16%.
The length of AC is congruent to WY
d = 10
