Answer: 37
Step-by-step explanation:
Given : Significance level : 
Critical value : 
margin of error : E= 1 mile per gallon
Population standard deviation:
miles per gallon.
We know that when the population standard deviation is known then the formula to find the sample size is given by :

[Round to the next whole number.]
Hence, the required number of automobiles should be used in the test = 37
Answer:
m < 49/12
Step-by-step explanation:
The portion of the quadratic formula under the square root sign is the discriminant.
If the discriminant is > 0 then there are two real roots.
b² -4ac > 0
-----------------------------
7² - 4(3)m > 0
49 - 12m > 0
Subtract 49 from both sides
-12m > -49
Divide both sides by -12
(when multiplying or dividing by a negative the inequality must be reversed)
m < 49/12
Answer:
its27.54 8.1×3.4 =27.54 base×height
Answer:
Step-by-step explanation:
Let the solution to
2x^2 + x -1 =0
x^2+ (1/2)x -(1/2)
are a and b
Hence a + b = -(1/2) ( minus the coefficient of x )
ab = -1/2 (the constant)
A. We want to have an equation where the roots are a +5 and b+5.
Therefore the sum of the roots is (a+5) + (b+5) = a+ b +10 =(-1/2) + 10 =19/2.
The product is (a+5)(b+5) =ab + 5(a+b) + 25 = (-1/2) + 5(-1/2) + 25 = 22.
So the equation is
x^2-(19/2)x + 22 =0
2x^2-19x + 44 =0
B. We want the roots to be 3a and 3b.
Hence (3a) + (3b) = 3(a+b) = 3(-1/2) =-3/2 and
(3a)(3b) = 9(ab) =9(-1/2)=-9/2.
So the equation is
x^2 +(3/2) x -9/2 = 0
2x^2 + 3x -9 =0.
I am going to show you how easy this is. Once you understand, you will be able to do this forever.
:
Assuming the side of the rectangle are (L) length and (W) width, the perimeter:
2L + 2W = 234
:
"the rectangle is twice as long as it is wide,", the equation for this statement:
L = 2W
:
In the first equation, we can replace L with 2W, then we have
2(2W) + 2W = 234
4W + 2W = 234
6W = 234
Divide both sides by 6
W = 234%2F6
W = 39 meters is the width
:
Remember it said the length is twice the width, therefore:
L = 2(39)
L = 78 meters is the length
:
:
Check this by finding the perimeter with these values
2(78) + 2(39) =
156 + 78 = 234