9514 1404 393
Answer:
x = 30
Step-by-step explanation:
In an arithmetic sequence, any given term is the average of the two terms that come before and after. The middle term of this sequence must be ...
2sin(3x) = (-11 +15)/2
sin(3x) = 1 . . . . . . . . . . simplify and divide by 2
Then the value of 3x must be 90°, so ...
x = 90/3 = 30
There is one value of x in the interval [0, 90] that makes this sequence arithmetic: x = 30.
The variance is the total of the squared distances of the given data from the mean.
This can be calculated through the equation,
σ² = summation of X² / N - μ²
where σ² is the variance X's are the data, N is the number of terms, and μ is the mean.
summation of X² = 100² + 100² + 120² + 120² + 180² = 81200
N = 5
μ = (100 + 100 + 120 + 120 + 180) / 5
μ = 124
Substituting these values to the equation for variance,
σ² = (81200/5) - 124² = 864
Thus, the variance is equal to 864.
Answer:
r = 4
General Formulas and Concepts:
<u>Pre-Alg</u>
- Order of Operations: BPEMDAS
- Equality Properties
Step-by-step explanation:
<u>Step 1: Define equation</u>
-5 + 22 = r - 4 + 3r + 5
<u>Step 2: Solve for </u><em><u>r</u></em>
- Combine like terms: 17 = 4r + 1
- Subtract 1 on both sides: 16 = 4r
- Divide 4 on both sides: 4 = r
- Rewrite: r = 4
<u>Step 3: Check</u>
<em>Plug in r to verify it's a solution.</em>
- Substitute: -5 + 22 = 4 - 4 + 3(4) + 5
- Add/Subtract: 17 = 3(4) + 5
- Multiply: 17 = 12 + 5
- Add: 17 = 17
Answer:
radius = √5 = 2.24 to nearest hundredth.
Step-by-step explanation:
(x + 3)^2 + (y + 3)^2 = 5 comparing with the standard form
(x - h)^2 + (y - k)^2 = r^2
-h = 2 so h = -3, -k = 3 so k = -3.
r^2 = 5 so r = √5.
Factor f(t) and you can identify the values of t for which the height is zero.
.. f(t) = -16t(t -3)
The projectile lands after 3 seconds in the air. (selection A)
