Answer:
58%
Step-by-step explanation:
Out of 60 students who take math, 35 of them will also have science. The desired probability is ...
35/60 = 0.58333... ≈ 58%
__
More formally, ...
P(S | M) = P(S&M)/P(M)
= 35%/60% = 7/12 ≈ 58%
well you cant really be expecting us to answer all that, so make sure you specify exactly WHAT you want to be answered.
62. -2(x - 1) + 5x = 2(2x - 1)
...multiply -2
-2x + 2 + 5x = 2(2x - 1)
...multiply 2
-2x + 2 + 5x = 4x - 2
...simplify
3x + 2 = 4x - 2
...add 2
3x + 4 = 4x
...subtract 3x
4 = x
Answer:
Part a. 1400 unit²
Part b 1240 unit²
Part c 1333.33 unit²
Step-by-step explanation:
The given function is 20·x - x²
Part a.
The dimensions of the five rectangles are;
20 × 20 + 20 × 18 + 20 × 16 + 20 × 10 + 20 × 6 = 1400 unit²
Part b.
The dimensions of the ten rectangles are;
10×20 + 10×18 + 10×16 + 10×16 + 10×14 + 10×12 + 10 × 10 + 10 × 8 + 10 × 6 + 10 ×4 = 1240 unit²
Part c.
To find the area with an infinite number of rectangles, we can use limits similar to integration;
Which gives;
![\int _{0}^{20}\left (20\cdot x - x^{2} \right )dx = \left [\dfrac{20}{2}\cdot x^{2} - \dfrac{x^{3}}{3} \right ]_{0}^{20} = \left [10\cdot x^{2} - \dfrac{x^{3}}{3} \right ]_{0}^{20}](https://tex.z-dn.net/?f=%5Cint%20_%7B0%7D%5E%7B20%7D%5Cleft%20%2820%5Ccdot%20x%20-%20x%5E%7B2%7D%20%20%5Cright%20%29dx%20%3D%20%5Cleft%20%5B%5Cdfrac%7B20%7D%7B2%7D%5Ccdot%20x%5E%7B2%7D%20-%20%5Cdfrac%7Bx%5E%7B3%7D%7D%7B3%7D%20%20%5Cright%20%5D_%7B0%7D%5E%7B20%7D%20%3D%20%5Cleft%20%5B10%5Ccdot%20x%5E%7B2%7D%20-%20%5Cdfrac%7Bx%5E%7B3%7D%7D%7B3%7D%20%20%5Cright%20%5D_%7B0%7D%5E%7B20%7D)
10×20^2 - (20^3)/3 = 4000/3 = 1333.3333
Answer: length = 10 yards
Width = 4.5 yard
Step-by-step explanation:
Let the width be represented by x.
Since the length of a rectangle is 1 yd more than twice the width. This will be:
= (2 × x) + 1
= 2x+1
Area = 45
Note that length × breadth = Area
(2x + 1) × x = 45
2x² + x = 45
Equate the equation to 0
2x² + x - 45 = 0
2x² + 10x - 9x - 45 = 0
2x(x + 5) - 9(x + 5) = 0
(2x - 9) = 0
2x = 9
x = 9/2
The width is 4.5 yard
Length = 2x + 1
= 2(4.5) + 1
= 9 + 1
= 10 yard
Answer:
y = (x + 4.5)² - 13.25
Step-by-step explanation:
y = x² + 9x + 7
We need to get a perfectly squared binomial as part of the right side.
Take the '9x' term, divide it in half, square it, add <u>and also subtract it </u>on the right side, as shown below. That would be (4.5)² = 20.25 added <u>and </u>subtracted.
y = x² + 9x + 7
y = x² + 9x + 20.25 + 7 - 20.25
y = (x² + 9x + 20.25) - 13.25
y = (x + 4.5)² - 13.25
y = (x + 4.5)² - 13.25
Vertex Form is y = a(x-h)² + k, where the parabola vertex is (h, k)
So if you wrote this as y = 1(x - [-4.5] )² + (-13.25), we would see that a = 1, and h = -4.5 and k = -13.25.
Vertex = (-4.5, -13.25)
I verified on a graphing calculator that this is indeed the vertex of the parabola.
