Answer:
3.6 qt. and 2.4 qt respectively
Step-by-step explanation:
Let x be x% of 50% saline solution. And (100-x%) be the percentage of 60% saline solution.
54=x*(50/100)+(100-x)*(60/100), solving it we will get x=60%. So we need 3.6 qt. of 50% saline solution and 2.4 qt. of 60% saline solution
Answer:
x = (i sqrt(7))/4 - 3/4 or x = -(i sqrt(7))/4 - 3/4
Step-by-step explanation:
Solve for x:
x - 1 - 2/x = 3 x + 2
Bring x - 1 - 2/x together using the common denominator x:
(x^2 - x - 2)/x = 3 x + 2
Multiply both sides by x:
x^2 - x - 2 = x (3 x + 2)
Expand out terms of the right hand side:
x^2 - x - 2 = 3 x^2 + 2 x
Subtract 3 x^2 + 2 x from both sides:
-2 x^2 - 3 x - 2 = 0
Divide both sides by -2:
x^2 + (3 x)/2 + 1 = 0
Subtract 1 from both sides:
x^2 + (3 x)/2 = -1
Add 9/16 to both sides:
x^2 + (3 x)/2 + 9/16 = -7/16
Write the left hand side as a square:
(x + 3/4)^2 = -7/16
Take the square root of both sides:
x + 3/4 = (i sqrt(7))/4 or x + 3/4 = -(i sqrt(7))/4
Subtract 3/4 from both sides:
x = (i sqrt(7))/4 - 3/4 or x + 3/4 = -(i sqrt(7))/4
Subtract 3/4 from both sides:
Answer: x = (i sqrt(7))/4 - 3/4 or x = -(i sqrt(7))/4 - 3/4
Answer:
The equation of the parabola is:
y
=
1
32
x
2
Explanation:
Please notice that we know that the parabola opens upward or downward, because the directrix is a horizontal line:
y
=
−
8
This tells use that the equation of the parabola of the form:
y
=
f
(
x
)
Not
x
=
f
(
y
)
.
Furthermore, we can see that it must open upward, because the y coordinate of the focus is above the directrix.
The vertex has the same x coordinate as the focus:
x
=
0
And its y coordinate is halfway between the focus and the directrix:
y
=
8
−
8
2
=
0
Therefore the vertex is
(
0
,
0
)
Use the vertex form of the equation of a parabola that opens upward or downward:
y
=
a
(
x
−
h
)
2
+
k
where the vertex is the point
(
h
,
k
)
.
Substitute the vertex into the equation:
y
=
a
(
x
−
0
)
2
+
0
Simplify:
y
=
a
x
2
The distance, f, from the vertex to the focus is,
f
=
8
; this allows use to find the value of
a
, using the equation:
a
=
1
4
f
a
=
1
32
The equation of the parabola is:
y
=
1
32
x
2
Step-by-step explanation:
Answer:
D. I and III only
Step-by-step explanation:
Number of first fie defects are given as 9,7,10,4 and 6.
First we have to arrange the above data in ascending order which is 4,6,7,9,10
- Now if we consider the defect in sixth car to be 3 then our data will look like: 3,4,6,7,9,10
So the mean of above data would be 
= 6.5
and Median of the above data would be = 
= 
= 6.5
Hence mean and median number of defects are same if the sixth car has 3 defects.
- Now if we consider the defect in sixth car to be 12 then our data will look like: 4,6,7,9,10,12
So the mean of above data would be 
= 8
and Median of the above data would be = = 
= 8
Hence mean and median number of defects are same if the sixth car has 12 defects.
- But Now if we consider the defect in sixth car to be 7 then our data will look like: 4,6,7,7,9,10
So the mean of above data would be 
= 7.167
and Median of the above data would be = = 7
Hence mean and median number of defects are not same if the sixth car has 7 defects.
Therefore option D is correct.
Answer:
B √8
Step-by-step explanation:
Equation of a circle is:
(x − h)² + (y − k)² = r²
where (h, k) is the center and r is the radius.
The center of the circle is (1, 6).
(x − 1)² + (y − 6)² = r²
The circle passes through the point (-1, 8).
(-1 − 1)² + (8 − 6)² = r²
4 + 4 = r²
r = √8
