Answer:
And we can find the probability with the complement rule and the normal standard distirbution and we got:
Step-by-step explanation:
Let X the random variable that represent the time spent reading of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And we can use the z score formula given by:
Using this formula we got:
And we can find the probability with the complement rule and the normal standard distirbution and we got:
129
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Answer:
- m∠A ≈ 53.13°
- m∠B ≈ 73.74°
- m∠C ≈ 53.13°
Step-by-step explanation:
An altitude to AC bisects it and creates two congruent right triangles. This lets you find ∠A = ∠C = arccos(6/10) ≈ 53.13°.
Since the sum of angles of a triangle is 180°, ∠B is the supplement of twice this angle, so is about 73.74°.
m∠A = m∠C ≈ 53.13°
m∠B ≈ 73.74°
_____
The mnemonic SOH CAH TOA reminds you of the relation between the adjacent side, hypotenuse, and trig function of an angle:
Cos = Adjacent/Hypotenuse
If the altitude from B bisects AC at X, triangle AXB is a right triangle with side AX adjacent to the angle A, and side AB as the hypotenuse. AX is half of AC, so has length 12/2 = 6, telling you the cosine of angle A is AX/AB = 6/10.
A diagram does not have to be sophisticated to be useful.
Answer: the solutions are
x = 3 or x = - 11
Step-by-step explanation:
The given quadratic equation is expressed as
y = 2x² + 16x - 66 = 0
The equation is already in the standard form of ax² + bx + c
The general formula for solving quadratic equations is expressed as
x = [- b ± √(b² - 4ac)]/2a
From the equation given,
a = 2
b = 16
c = - 66
Therefore,
x = [- 16 ± √(16² - 4 × 2 × - 66)]/2 × 2
x = [- 16 ± √(256 + 528)]/4
x = [- 16 ± √784]/4
x = (- 16 + 28)/4 or x = (- 16 - 28)/4
x = 12/4 or x = - 44/4
x = 3 or x = - 11