Answer:
0 < y <= 6
Step-by-step explanation:
Given:
√(x² - 6x + 9)
if -3 <= x < 3
you can write (x² - 6x + 9)
as (x-3) * (x- 3) which is (x-3)²
so now you have √{(x-3)²}, which is the same as the absolute value of x-3. In mathematics it is written as:
| x - 3 |
So √(x² - 6x + 9) = | x - 3 |
See the graph in the attachment.
for -3 <= x < 3
you get the y values bigger then ( but not equal to) 0 and smaller then or equal to 6.
This is written as 0 < y <= 6
Let
x----------> the length of the rectangle
y---------> the width of the rectangle
we know that
perimeter of rectangle=2*[x+y]
area of rectangle=x*y
P=81 ft
so
81=2*[x+y]-----------> 40.5=[x+y]
case <span>A) 20.25 feet × 20.25 feet
P=2*[20.25+20.25]-----> 81 ft----------> the perimeter is ok
A=20.25*20.25-----> 410.06 ft</span>²
case <span>B) 11 feet × 29.5 feet
</span>P=2*[11+29.5]-----> 81 ft----------> the perimeter is ok
A=11*29.5-----> 324.5 ft²
case <span>C) 9 feet × 9 feet
</span>P=2*[9+9]-----> 36 ft----------> the perimeter is not 81
A=9*9-----> 81 ft²
case <span>D) 17.5 feet × 23 feet
</span>P=2*[17.5+23]-----> 81 ft----------> the perimeter is ok
A=17.5*23-----> 402.5 ft²
the answer is
case A) 20.25 feet × 20.25 feet
11.5x+22 equal to -13x+218
11.5x+22=-13x+218
Now you have an equation. Solve for x:
11.5x+22+13x=-13x+13x+218 (add 13x to both sides)
24.5x+22=218
24.5x+22-22=218-22 (subtract 22 from both sides)
24.5x=196
x=196÷24.5
x=8
After 8 weeks their balances would be the same.
Their balances will be:
11.5x+22=11.5(8)+22=114$
and
-13x+218=-13(8)+218=114$
So, 114$ each.
Hope this was helpful.
Answer:
Step-by-step explanation:
Data provided
represent the sample mean in mg per deciliter of cholesterol level
represent the sample standard deviation
sample size
represent the value that we want to test
t would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the mean is higher than 53 mg per deciliter, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
Calculate the statistic
Replacing into the formula we got:
P-value
We need to find first the degrees of freedom:
The p value for this case since we have a right tailed test is:
3/12 is a rational number because rational numbers can be written in the form of a/b
When you simplify 3/12, you get 1/4, which is a fraction
