Reduce a 24 cm by 36 cm photo to 3/4 original size.
The most logical way to do this is to keep the width-to-height ratio the same: It is 24/36, or 2/3. The original photo has an area of (24 cm)(36 cm) = 864 cm^2.
Let's reduce that to 3/4 size: Mult. 864 cm^2 by (3/4). Result: 648 cm^2.
We need to find new L and new W such that W/L = 2/3 and WL = 648 cm^2.
From the first equation we get W = 2L/3. Thus, WL = 648 cm^2 = (2L/3)(L).
Solve this last equation for L^2, and then for L:
2L^2/3 = 648, or (2/3)L^2 = 648. Thus, L^2 = (3/2)(648 cm^2) = 972 cm^2.
Taking the sqrt of both sides, L = + 31.18 cm. Then W must be 2/3 of that, or W = 20.78 cm.
Check: is LW = (3/4) of the original 864 cm^2? YES.
Answer:
a. E(x) = 3.730
b. c = 3.8475
c. 0.4308
Step-by-step explanation:
a.
Given
0 x < 3
F(x) = (x-3)/1.13, 3 < x < 4.13
1 x > 4.13
Calculating E(x)
First, we'll calculate the pdf, f(x).
f(x) is the derivative of F(x)
So, if F(x) = (x-3)/1.13
f(x) = F'(x) = 1/1.13, 3 < x < 4.13
E(x) is the integral of xf(x)
xf(x) = x * 1/1.3 = x/1.3
Integrating x/1.3
E(x) = x²/(2*1.13)
E(x) = x²/2.26 , 3 < x < 4.13
E(x) = (4.13²-3²)/2.16
E(x) = 3.730046296296296
E(x) = 3.730 (approximated)
b.
What is the value c such that P(X < c) = 0.75
First, we'll solve F(c)
F(c) = P(x<c)
F(c) = (c-3)/1.13= 0.75
c - 3 = 1.13 * 0.75
c - 3 = 0.8475
c = 3 + 0.8475
c = 3.8475
c.
What is the probability that X falls within 0.28 minutes of its mean?
Here we'll solve for
P(3.73 - 0.28 < X < 3.73 + 0.28)
= F(3.73 + 0.28) - F(3.73 + 0.28)
= 2*0.28/1.3 = 0.430769
= 0.4308 -- Approximated
Answer:
0.3
Step-by-step explanation:
Convert -2/5 into a decimal.
-0.4.
Then subtract the two.
-0.4-(-0.75)
-0.4+(+0.75)
0.3
Your answer would be (b.) because -2+-3=-5
Answer: 9πcm²
Step-by-step explanation: area of the square= 36cm²
Therefore, the area of one side= √area = √36 = 6cms
Since the circle is touching the sides of the square, the side of the square = the diameter of the circle
Therefore the radius of the circle= side/2 = 3cm
The formula for the ares of the circle is πr²
π*3*3 = 9πcm²
