The kite is approximately 78.80 feet off of the ground.
Explanation: If we assume that the string his held taut without any swag, we can use a right triangle to solve for the height of the kite. sin
θ
=
o
p
p
h
y
p
sin
52
o
=
h
100
f
t
100
sin
52
o
=
h
100
(
0.7880
)
=
h
78.80
f
t
=
h
Answer:
<u>4 weeks</u>
Step-by-step explanation:
Remaining money (per week) :
- Net income - Expenses
- $400 - $380
- $20
No. of weeks to buy shoes :
- Cost of shoes / Remaining money (per week)
- $70/$20
- 3.5 ≈ <u>4 weeks</u> (nearest whole week)
There may be more than one way in which to answer this question. I will assume that the "equation" is a linear one: f(x) = mx + b.
Then (16/3) = m(1) + b
This is one equation in two unknowns, so it does not have a unique solution. Was there more to this problem than you have shared?
If we assume that the y-intercept (b) is zero, then y = mx, and
16/3 = 1m, so that m = 16/3, and so y = (16/3)x.
Answer:
The system is consistent because the rightmost column of the augmented matrix is not a pivot column.
Step-by-step explanation:
It is given that the coefficient of the matrix of a linear equation has a pivot position in every row.
It is provided by the Existence and Uniqueness theorem that linear system is said to be consistent when only the column in the rightmost of the matrix which is augmented is not a pivot column.
When the linear system is considered consistent, then every solution set consists of either unique solution where there will be no any variables which are free or infinitely many solutions, when there is at least one free variable. This explains why the system is consistent.
For any m x n augmented matrix of any system, if its co-efficient matrix has a pivot position in every row, then there will never be a row of the form [0 .... 0 b].
Answer:
Step-by-step explanation:
From the information given,
Number of personnel sampled, n = 85
Mean or average = 6.5
Standard deviation of the sample = 1.7
We want to determine the confidence interval for the mean number of years that personnel spent in a particular job before being promoted.
For a 95% confidence interval, the confidence level is 1.96. This is the z value and it is determined from the normal distribution table. We will apply the following formula to determine the confidence interval.
z×standard deviation/√n
= 1.96 × 6.5/√85
= 1.38
The confidence interval for the mean number of years spent before promotion is
The lower end of the interval is 6.5 - 1.38 = 5.12 years
The upper end is 6.5 + 1.38 = 7.88 years
Therefore, with 95% confidence interval, the mean number of years spent before being promoted is between 5.12 years and 7.88 years
