Answer:
5,040 different passwords are possible
Step-by-step explanation:
Assuming that 4-digit means using only numeric values.
This is a permutations problem.
n = number of values used with number values only this is 10
r = the number used in each case without repeating in this case 4
nPr = n! / (n - r)!
nPr = 10! / (10-4)!
nPr = 10! / 6!
The ! means factorial. For example 4! = 4 x 3 x 2 x 1 = 24
A quick hack for dividing factorials is to use cancelling.
10! / 6! = 10 x 9 x 8 x 7 (because 6 to 1 are cancelled by 6!)
= 5040
Answer:
y = -4x+14
Step-by-step explanation:
First find the slope
m = (y2-y1)/(x2-x1)
m = (2-10)/(3-1)
=-8/2
= -4
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
y = -4x+b
Substitute a point into the equation
10 = -4(1)+b
Add 4 to each side
14 = b
y = -4x+14
Answer:
1 cookie = $1.25 1 cake = $15
Step-by-step explanation:
set up a system of equations:
let x = 1 cookie
let y = 1 cake
3x + 5y = 78.75
8x + 2y = 40
I multiplied the first equation by 2 to get: 6x + 10y = 157.50
I multiplied the second equation by -5 to get: -40x - 10y = -200.00
If you add both equations, the y-terms will be eliminated
-34x = -42.50
x = 1.25
Plug in 1.25 into equation to find value of y: 8(1.25) + 2y = 40
10 + 2y = 40
2y = 30
y = 15
Answer:
The answer is D because on the picture it shows them going threw extreme heat and pressure.
We are given the following variables:
μ = the sample mean = 152 pounds
σ = the standard deviation = 26 pounds
x = the sample value we want to test = 180 pounds
n = the sample size = unknown
MOE = margin of error = 4% = 0.04
Confidence level = 96%
The first thing we can do is to find for the value of z
using the formula:
z = (x – μ) / σ
z = (180 – 152) / 26
z = 1.0769 = 1.08
Since we are looking for the people who weigh more than
180 pounds, therefore this is a right tailed z test. The p value is:
p = 0.1401
Then we can use the formula below to solve for n:
n = z^2 * p * (1 – p) / (MOE)^2
n = 1.08^2 * 0.1401 * (1 – 0.1401) / (0.04)^2
n = 87.82 = 88
Therefore around 88 people must be surveyed.
