Answer:
The correct answer would be option C
Step-by-step explanation:
3^2*3^4*3^6=531441
3^12=531441
or for a simpler way you can just add the exponents together when the problem is set up like this
Answer:
5-a=2
Step-by-step explanation:
let's firstly convert the mixed fractions to improper fractions, and then add them up.
![\bf \stackrel{mixed}{8\frac{1}{2}}\implies \cfrac{8\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{17}{2}}~\hfill \stackrel{mixed}{7\frac{2}{3}}\implies \cfrac{7\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{23}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{17}{2}+\cfrac{23}{3}\implies \stackrel{\textit{using the LCD of 6}}{\cfrac{(3)17~~+~~(2)23}{6}}\implies \cfrac{51+46}{6}\implies \cfrac{97}{6}\implies 16\frac{1}{6}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B8%5Cfrac%7B1%7D%7B2%7D%7D%5Cimplies%20%5Ccfrac%7B8%5Ccdot%202%2B1%7D%7B2%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B17%7D%7B2%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B7%5Cfrac%7B2%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7B7%5Ccdot%203%2B2%7D%7B3%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B23%7D%7B3%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B17%7D%7B2%7D%2B%5Ccfrac%7B23%7D%7B3%7D%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Busing%20the%20LCD%20of%206%7D%7D%7B%5Ccfrac%7B%283%2917~~%2B~~%282%2923%7D%7B6%7D%7D%5Cimplies%20%5Ccfrac%7B51%2B46%7D%7B6%7D%5Cimplies%20%5Ccfrac%7B97%7D%7B6%7D%5Cimplies%2016%5Cfrac%7B1%7D%7B6%7D)
<h3>1.</h3>
The equation in point-slope form: y - y₁ = m(x - x₁)
slope: m = -2
point: (4, -5) ⇒ x₁ = 4, y₁ = -5
Therefore, the equation of the line in point-slope form:
<h3>
y + 5 = -2(x - 4)</h3>
<h3>2.</h3>
The equation in slope-intercept form: y = mx + b
Parallel lines has the same slope, so:
y = 4x + 2 ⇒ a = 4
If a line passes through the point <em>(x₁, y₁) </em>then the equation y<em>₁</em> = mx<em>₁</em> + b is true.
(4, 6) ⇒ x₁ = 4, y₁ = 6
So: 6 = 4·4 + b ⇒ b = -10
Therefore the equation:
<h3>
y = 4x - 10</h3>
<h3>3.</h3>
a = 3
(-1, 1) ⇒ x₁ = -1, y₁ = 1
So: 1 = 3·(-1) + b ⇒ b = 4
The equation:
<h3>
y = 3x + 4</h3>
<h3>4. </h3>
The product of slopes of perpendicular lines is -1.
2x - 7y = 1 ⇒ 7y = -2x + 1 ⇒ y = -²/₇x + ¹/₇
-²/₇×m = -1 ⇒ m = ⁷/₂
(0, -4) ⇒ x₁ = 0, y₁ = -4
-4 = ⁷/₂·0 + b ⇒ b = -4
The equation:
<h3>
y = ⁷/₂x - 4</h3>
Answer:
0.99804932311
Step-by-step explanation:
We solve this using binomial probability
Binomial probability formula
= nCx × p^x × q^n - x
= n!/(n - x)! x!
Where n = Number of trials = 25 samples
x = Number of successes = 23
p = probability of success = 99% = 0.99
q = probability of failure = 1 - p
= 1 - 0.99
= 0.01
Hence,
p(at least 23 are properly filled) = p(X ≥ x)
= [25!/(25 - 23)! × 23! × 0.99^23 × 0.01^25 - 23 ]+ [25!/(25 - 24)! × 24! × 0.99^24 × 0.01^25 - 24 ]+ [25!/(25 - 25)! × 23! × 0.99^25 × 0.01^25 - 25]
= [300 × 0.99 ^23 × 0.01^2] + [25 × 0.99^24 × 0.01^1] + [1 × 0.99^25 + 0.01^0]
= 0.0238084285 + 0.1964195352 + 0.7778213594
= 0.99804932311
