Answer:
B. (1,5) and (5.25, 3.94)
Step-by-step explanation:
The answer is where the 2 equations intersect.
We need to solve the following system of equations:
y = -x^2 + 6x
4y = 21 - x
From the second equation:
x = 21 - 4y
Plug this into the first equation:
y = -(21 - 4y)^2 + 6(21 - 4y)
y = -(441 - 168y + 16y^2)+ 126 - 24y
y = -441 + 168y - 16y^2 + 126 - 24y
16y^2 + y - 168y + 24y + 441 - 126 = 0
16y^2 - 143y + 315 = 0
y = [-(-143) +/- sqrt ((-143)^2 - 4 * 16 * 315)]/ (2*16)
y = 5, 3.938
When y = 5:
x = 21 - 4(5) = 1
When y = 3.938
x = 21 - 4(3.938) = 5.25.
Answer:
D. Subtraction Property of Equality
Step-by-step explanation:
Hope it helps.
Answer:1.625
Step-by-step explanation:you just divide 65 and 40
Answer:
And using the z score given by:
Where:
If we find the z score for 
we got:
So we want to find this probability:
And using the complement rule and the normal standard distribution and excel we got:
Step-by-step explanation:
For this case we have the proportion of interest given 
. And we have a sample size selected n = 474
The distribution of 
is given by:
We want to find this probability:
And using the z score given by:
Where:
If we find the z score for we got:
So we want to find this probability:
And using the complement rule and the normal standard distribution and excel we got:
9514 1404 393
Answer:
nπ -π/6 . . . for any integer n
Step-by-step explanation:
tan(x) +√3 = -2tan(x) . . . . . given
3tan(x) = -√3 . . . . . . . . . . . add 2tan(x)-√3
tan(x) = -√3/3 . . . . . . . . . . divide by 3
x = arctan(-√3/3) = -π/6 . . . . use the inverse tangent function to find x
This is the value in the range (-π/2, π/2). The tangent function repeats with period π, so the set of values of x that will satisfy this equation is ...
x = n·π -π/6 . . . . for any integer n
