These calculations are based on the drawing of the file enclosed.
There are three right triangles.
From the big right triangle:
a^2 + b^2 = 25^2
From the small right triangle on the left side:
(25-x)^2 + 10^2 = a^2
From the small right triangle on the right side
x^2 +10^2 = b^2
=> (25-x)^2 + 10^2 + x^2 + 10^2 = a^2 + b^2
=> (25-x)^2 + 10^2 + x^2 + 10^2 = 25^2
=> 25^2 - 50x + x^2 + 10^2 + 10^2 = 25^2
=> x^2 -50x + 100 =0
Use the quadratic formular to find the roots:
x = 2.1 and x = 47.9
Distance from back: 25 - 2.1 = 22.9 ft
Answer: 22.9 ft
Answer:
Step-by-step explanation:
(x₁, y₁) = (-2 , -5) & (x₂ , y₂) = (-3 , 1)
Midpoint = 
![=(\frac{-2 + [-3]}{2} ,\frac{-5 + 1}{2})\\\\\\=(\frac{-5}{2} , \frac{-4}{2})\\\\=(-2.5, -2)](https://tex.z-dn.net/?f=%3D%28%5Cfrac%7B-2%20%2B%20%5B-3%5D%7D%7B2%7D%20%2C%5Cfrac%7B-5%20%2B%201%7D%7B2%7D%29%5C%5C%5C%5C%5C%5C%3D%28%5Cfrac%7B-5%7D%7B2%7D%20%2C%20%5Cfrac%7B-4%7D%7B2%7D%29%5C%5C%5C%5C%3D%28-2.5%2C%20-2%29)
Answer: y = -4x + 1 or y = 1 - 4x
Step-by-step explanation:
First, we have to find the slope of the perpendicular. The slope of the line perpendicular to the other is the <u>reciprocal and opposite value</u> of the other line's slope.
This means that the slope perpendicular to y = 1/4x + 2 is -4, or -4/1.
Now we need to find the y-intercept, to do that we will use the equation y = mx + b. m = slope, b = y-intercept.
Plug in the values.
1 = -4(0) + b
Simplify.
1 = 0 + b
1 = b
Our y-intercept is 1.
Now we can form the slope-intercept equation for the line perpendicular to y = 1/4x + 2 that passes through the point (0, 1).
y = -4x + 1
probability that the persons IQ falls between 110 and 130 is 0.2286 .
<u>Step-by-step explanation:</u>
Step 1: Sketch the curve.
The probability that 110<X<130 is equal to the blue area under the curve.
Step 2:
Since μ=100 and σ=15 we have:
P ( 110 < X < 130 )=P ( 110−100 < X−μ < 130−100 )
⇒ P ( (110−100)/15< (X−μ)/σ<(130−100)/15)
Since Z = (x−μ)/σ , (110−100)/15 = 0.67 and (130−100)/15 = 2 we have:
P ( 110<X<130 ) = P ( 0.67<Z<2 )
Step 3: Use the standard normal table to conclude that:
P ( 0.67<Z<2 )=0.2286
Therefore, probability that the persons IQ falls between 110 and 130 is 0.2286 .
Answer:
a variable is a placeholder.
Step-by-step explanation:
