How many gallons of a 20% salt solution must be mixed with 4 gallons of a 30% salt solution to make a 25% salt solution?
1 answer:
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Answer:
a. 0.82%
b. 71.11%
c. 0.564 micrometer
Step-by-step explanation:
To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.
The equation for z is:
z = (x - m) / (sd)
Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.
a.
For 0.62 copies, we calculate:
z = (0.62 - 0.5) / (0.05)
z = 2.4
This translates to 0.9918.
Therefore, p (x > 0.62) = 1 - 0.9918
p (x > 0.62) = 0.0082 = 0.82%
b.
For 0.47 copies, we have:
z = (0.47 - 0.5) / (0.05)
z = -0.6, which equates to 0.2742.
For 0.63 copies:
z = (0.63 - 0.5) / (0.05)
z = -2.6, which yields 0.9953.
Hence, p (0.47 > x > 0.63) = 0.9953 - 0.2742
p (0.47 > x > 0.63) = 0.7211 = 72.11 %
c.
For x copies, we find:
p = 0.9 corresponds to z = 1.28.
Thus, 1.28 = (x - 0.5) / (0.05)
From which we derive:
x = 1.28*0.05 + 0.5
x = 0.564 micrometer
Answer:
Step-by-step explanation:
Given that lines l and m are parallel and there is a transversal cutting through these lines.
5). (9x + 2)° = 119° [by alternate interior angles]
9x = 117 ⇒ x = 13
6). (12x - 8)° + 104° = 180°
12x = 180 - 96
x = ⇒ x = 7
7). (5x + 7) = (8x - 71) [by alternate exterior angles]
8x - 5x = 71 + 7
3x = 78
x = 26
8). (4x - 7) = (7x - 61) [by corresponding angles]
7x - 4x = -7 + 61
3x = 54
x = 18
9). (9x + 25) = (13x - 19) [by corresponding angles]
13x - 9x = 25 + 19
4x = 44
x = 11
(13x - 19)° + (17y + 5)° = 180° [linear pairs of angles sum to supplementary]
(13×11) - 19 + 17y + 5 = 180
129 + 17y = 180
17y = 180 - 129
y = 3
10). (3x - 29) + (8y + 17) = 180 [linear pairs of angles sum to supplementary]
3x + 8y = 180 + 12
3x + 8y = 192 -----(1)
(8y + 17) = (6x - 7) [by alternate exterior angles]
6x - 8y = 24
3x - 4y = 12 -----(2)
From equation (1) subtract equation (2)
(3x + 8y) - (3x - 4y) = 192 - 12
12y = 180
y = 15
Plugging into equation (1),
3x + 8(15) = 192
3x + 120 = 192
x = 24
11). (3x + 49)° = (7x - 23)° [by corresponding angles]
7x - 3x = 49 + 23
4x = 72 ⇒ x = 18
(11y - 1)° = (3x)° [by corresponding angles]
11y = 3×18 + 1
11y = 55 ⇒ y = 5
12). (5x - 38)° = (3x - 4)° [by corresponding angles]
5x - 3x = 38 - 4
2x = 34
x = 17
(7y - 20)° + (5x - 38)° + 90° = 180°
[The angles within a triangle sum to 180°]
7y + 5x - 58 = 90
5x + 7y = 148
5×17 + 7y = 148
85 + 7y = 148
7y = 148 - 85
y =