Decrease £36 by 21%
1 answer:
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Answer: 114°
Step-by-step explanation:
<h2>Concept: </h2>Here, we need to know the idea of the "Exterior Angle theorem".
<u>The exterior angle theorem</u> states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles of the triangle.
If you are still confused, then refer to the attachment below for a graphical explanation.
<h2>Solve:</h2>Given
24 + (2x + 18) = 3x + 6
Put like terms together
24 + 18 + 2x = 3x + 6
Combine like terms
42 + 2x = 3x + 6
Subtract 6 on both sides
42 + 2x - 6 = 3x + 6 - 6
36 + 2x = 3x
Subtract 2x on both sides
36 + 2x - 2x = 3x - 2x
x = 36
Exterior angle = 3x + 6 = 3(36) + 6 = 114°
Hope this helps!! :)
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Answer:
μ = 5.068 oz
Step-by-step explanation:
Normal distribution formula to use the table attached
Z = (x - μ)/σ
where μ is mean, σ is standard deviation, Z is on x-axis and x is a desired point.
98% of 6-oz. cups will not overflow means that the area below the curve is equal to 0.49; note that the curve is symmetrical respect zero, so, 98% of the cases relied between the interval (μ - some value) and (μ + some value)].
From table attached, area = 0.49 when Z = 2.33. From data, σ = 0.4 oz and x = 6 oz (maximum capacity of the cup). Isolating x from the formula gives
Z = (x - μ)/σ
2.33 = (6 - μ)/0.4
μ = 6 - 2.33*0.4
μ = 5.068
This means that with a mean of 5 oz and a standard deviation of 0.4 oz, the machine will discharge a maximum of 6 oz in the 98% of the cases.
