Answer:
<u>Yes they are equivalent.</u>
Step-by-step explanation:
Use PEMDAS: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction
Distribute or multiply -3 with 2p and 4 to get -6p and -12.
You will then have 18-6p-12-3p, simplify to get 6-9p
For the second equation multiply 3 with 2 and -3p, you will then get 6-9p as well.
They are equal, hope the helps ;)
The z-value that corresponds to a two-tailed 95% confidence interval is z = +/- 1.96. Then the bounds of the confidence interval can be determined as:
Lower bound = mean - z*SD/sqrt(n) = 20 - 1.96*2/sqrt(100) = 20 - 0.12 = 19.88 hours
Upper bound = mean + z*SD/sqrt(n) = 20 + 1.96*2/sqrt(100) = 20 + 0.12 = 20.12 hours
So the first choice is the correct answer: 19.88-20.12 hours
- Make an equation representing the number of vehicles needed.
We have six drivers so
x + y ≤ 6
That's not really an equation; it's an inequality. We want to use all our drivers so we can use the small vans, so
x + y = 6
- Make an equation representing the total number of seats in vehicles for the orchestra members.
s = 25x + 12y
That's how many seats total; it has to be at least 111 so again an inequality,
25x + 12y ≥ 111
We solve it like a system of equations.
x + y = 6
y = 6 - x
111 = 25x + 12y = 25x + 12(6-x)
111 = 25x + 72 - 12x
111 - 72 = 13 x
39 = 13 x
x = 3
Look at that, it worked out exactly. It didn't have to.
y = 6 - x = 3
Answer: 3 buses, 3 vans
L = building side
W = non-building side
P = 2W + L = 42 (note only one L because the other L is the building itself)
Solve for L:
L = 42 - 2W
Area = l*w
Area = (42-2W)W = 42W - 2W2
Let area be y, so y = -2W2 +42W
Note this is a parabola pointing down because the coefficient of the W2 is negative. That makes the vertex the maximum for which we are searching.
Vertex of this parabola is at W=-b/2a, if the quadratic is aW2 + bW + c = 0
a = -2
b = 42
W = -42/(2*-2) = -42/-4 = 10.5
W = 10.5
L = 42-2(10.5) = 42-21 = 21
Area = L*W = 21 * 10.5
A = 220.5 ft2
There is an infinite number of chords in a circle