Answer:
The chance of completing the entire package installation in under 12 minutes is 0.1271.
Step-by-step explanation:
We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.
To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.
Utilizing 
, we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.
Given the symmetry of the standard normal distribution density function, we ascertain 
.
Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.
The equation of the perpendicular line can be identified by determining its slope and applying the given point within the standard formula.
Standard equation: y-y1 = m(x-x1)
m*m'=-1
where m' indicates the slope of the perpendicular line
m denotes the slope of the original line
m = -coefficient of x/coefficient of y = -4/-3 = 4/3
m' = -3/4
Substituting the point (3, -2):
y+2 = -3/4*(x-3)
4y+8 = -3x+9
Thus, the equation of the perpendicular line is: 3x+4y-1=0
It is necessary for the value of m to exceed that of n. When binomials are multiplied, the middle term emerges from combining the outside and inside products. Thus, bx = –nx + mx, simplifying further leads to b = –n + m. When adding numbers that have opposite signs, we subtract their absolute values and retain the sign of the number with the larger absolute value. Since b is positive, m must indeed possess a greater absolute value.
0.027%. A bank promotes an APR of 5.5% for personal loans. To address this problem, we will utilize the Annual Percentage Yield formula. In this formula, r signifies the interest rate in decimal form, and n represents the number of compounding periods per year. First, we convert the interest rate into decimal format. Next, we will calculate APY while compounding monthly using n = 12 and r = 0.055 within the APY formula. We proceed to do the same for quarterly compounding by substituting n = 4 and r = 0.055 into the APY formula. To determine the difference, we subtract the quarterly APY from the monthly APY. Therefore, the APY for monthly compounding is 0.027% higher than for quarterly compounding.
137 paquetes de vasos, aunque el último solo tiene 7 vasos, es necesario para asegurar que no queden sin empacar.
