Answer:24
Step-by-step explanation:
Since the numbers in the middle are 21 and 27, you add both and divide by 2 to get the number in the middle of those 2.
Simplifying
5n + 3 = 2(n + 2) + 3n
Reorder the terms:
3 + 5n = 2(n + 2) + 3n
Reorder the terms:
3 + 5n = 2(2 + n) + 3n
3 + 5n = (2 * 2 + n * 2) + 3n
3 + 5n = (4 + 2n) + 3n
Combine like terms: 2n + 3n = 5n
3 + 5n = 4 + 5n
Add '-5n' to each side of the equation.
3 + 5n + -5n = 4 + 5n + -5n
Combine like terms: 5n + -5n = 0
3 + 0 = 4 + 5n + -5n
3 = 4 + 5n + -5n
Combine like terms: 5n + -5n = 0
3 = 4 + 0
3 = 4
Solving
3 = 4
The left and right sides are not equal, therefore there is no solution.
<h2>60,47,73</h2>
Step-by-step explanation:
Let the first angle be
degrees
Let the second angle be
degrees
Let the third angle be
degrees
It is given that sum of angles is
degrees.
so,
...(i)
It is given that sum of the measures of the second and third angles is two times the measure of the first angle.
...(ii)
It is given that the third angle is 26 more than the second.
...(iii)
using (ii) and (iii),


using (i),(ii) and (iii),





Answer:
aₙ = 4(-1)ⁿ⁻¹(3)ⁿ⁻¹
Step-by-step explanation:
The formula for the nth term of a geometric sequence is
aₙ = a₁rⁿ⁻¹
We can get the value for r by dividing aₙ by aₙ₋₁.
a₄/a₃ = -108/36
a₄/a₃ = -3
r = -3
aₙ = 4(-3)ⁿ⁻¹
aₙ = 4(-1)ⁿ⁻¹(3)ⁿ⁻¹
The (-1)ⁿ⁻¹ term makes even-numbered terms negative.
Answer:
16% is the percent of wooden shipping boxes will have breaking strengths greater than 520 pounds per square inch.
Step-by-step explanation:
We are given the following information:
Mean = 500 pounds
Standard Deviation = 20 pounds
Empirical rule:
- The empirical rule also known as the three-sigma rule or 68-95-99.7 rule
- It is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ).
- It shows that 68% falls within the first standard deviation that is

- About 95% of the data lies within the first two standard deviations that is

- About 99.7% of the data lies within the first three standard deviations that is

We have to find the percent of its wooden shipping boxes that will have breaking strengths greater than 520 pounds per square inch.
Now,

According to empirical rule around 68% of the data will lie between 
Thus, 34% of data lies between 500 and 520.
Data lying above 520 = 50% - 34% = 16%
16% is the percent of wooden shipping boxes will have breaking strengths greater than 520 pounds per square inch.