Answer:
0.7493 or 74.93%
Step-by-step explanation:
We are given;
Population mean; μ = 100
Population standard deviation; σ = 12
Sample mean 1; x1¯ = 90
Sample mean 2; x2¯ = 120
Z-score formula of the data given is;
z = (x¯ - μ)/σ
z1 = (90 - 100)/12
z1 = -0.83
z2 = (120 - 100)/12
z2 = 1.67
Since we wan to Find the probability that a randomly selected bill is between $90 to $120.
Thus;
P(90 < x¯ < 120) = P(−0.83 < Z < 1.67)
Probability will be gotten from online probability with 2 z-scores calculator to get;
P = 0.7493
Answer:
Step-by-step explanation:
Answer:
5.3
Step-by-step explanation:
You use the Pythagoras theorem which is a^2+b^2=c^2.
Since you're solving for a side length that's not the hypotenuse you will manipulate the equation to c^2-a^2=b^2. From here you just plug in numbers.
8^2 - 6^2 = b^2
64 - 36 = b^2
b = sqrt(28)
b = 5.2915.... = 5.3
Answer:
=========
<h2>Given</h2>
<h3>Line 1</h3>
<h3>Line 2</h3>
- Passing through the points (4, 3) and (5, - 3)
<h2>To find</h2>
- The value of k, if the lines are perpendicular
<h2>Solution</h2>
We know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.
Find the slope of line 1 by converting the equation into slope-intercept from standard form:
<u><em>Info:</em></u>
- <em>standard form is ⇒ ax + by + c = 0, </em>
- <em>slope - intercept form is ⇒ y = mx + b, where m is the slope</em>
- 3x - ky + 7 = 0
- ky = 3x + 7
- y = (3/k)x + 7/k
Its slope is 3/k.
Find the slope of line 2, using the slope formula:
- m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6
We have both the slopes now. Find their product:
- (3/k)*(- 6) = - 1
- - 18/k = - 1
- k = 18
So when k is 18, the lines are perpendicular.
