Answer:
k = 12
Step-by-step explanation:
Given:
The equation
To find:
Value of for which the given equation has one distinct real solution.
Solution:
The given equation is a quadratic equation.
There are always two solutions of a quadratic equation.
For the equation: to have one distinct solution:
Here,
a = 2,
b = -k and
c = 18
Putting the values, we get:
The equation becomes:
And the one root is:
Answer:
True Statements are -
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
Step-by-step explanation:
Given - Ted and Jude are each saving money each month. After x months, the amount of money, in dollars, that Ted has saved is represented by the
equation T = 40x, and the amount of money that Jude has saved is represented by the equation J = 60x.
To find - Choose all of the statements that are true.
A. Each month, Jude saves two-thirds as much money as Ted saves.
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
C. The amount of money Jude saves each month is $20 more than the amount Ted saves each month.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
Proof -
Given that,
After x months,
Ted saved the amount of money, T(x) = 40x
Jude saved the amount of money, J(x) = 60x
Now,
In 1 month,
Ted saved money, T(1) = 40(1) = 40
Jude saved money, J(1) = 60(1) = 60
So,
In 1st month, Jude saved money 20 more than Ted saved.
Now,
In 2 month,
Ted saved money, T(2) = 40(2) = 80
Jude saved money, J(2) = 60(2) = 120
So,
In 2nd month, Jude saved money 40 more than Ted saved.
Now,
In 3 month,
Ted saved money, T(3) = 40(3) = 120
Jude saved money, J(3) = 60(3) = 180
So,
In 3rd month, Jude saved money 60 more than Ted saved.
So,
Option C is incorrect
Because
In 1st month, Jude saves is $20 more than the amount Ted saves
In 2nd month, Jude saves is $40 more than the amount Ted saves
Now,
In 1st month,
Ted saves = 40
and
= 26.67
So, Jude will save = 40 + 26.67 = 66.67
But Jude saves 60
So,
Option A is incorrect.
i.e. A. Each month, Jude saves two-thirds as much money as Ted saves.
Now,
We can see that,
In 3 months, Ted will have saved the money = 120
In 2 months, Jude will have saved the money = 120
So,
Option B is correct.
i.e. B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
Also,
We can see that
In 1st month, Jude saved money 20 more than Ted saved.
In 2nd month, Jude saved money 40 more than Ted saved.
In 3rd month, Jude saved money 60 more than Ted saved.
So,
Option D is correct.
i.e. D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
∴ we get
True Statements are -
B. In 3 months, Ted will have saved the same amount that Jude saved in 2 months.
D. The total amount of money Jude has saved is always $20 more than the total amount Ted has saved.
Answer:
1. The margin of error is of 66.96 square feet.
2. The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 22 - 1 = 21
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.08
The margin of error is:
In which s is the standard deviation of the sample.
The margin of error is of 66.96 square feet.
The lower end of the interval is the sample mean subtracted by M. So it is 1500 - 66.96 = 1433.04 square feet
The upper end of the interval is the sample mean added to M. So it is 1500 + 314 = 1566.96 square feet
The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet