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Zolol [24]
3 years ago
15

What is the measure of an angle if it is 70 less than three times its own complement?

Mathematics
2 answers:
anzhelika [568]3 years ago
4 0
Let the angle be x.

Hence, its complement is 90 - x.

x = 3* (90 - x) - 70 = 270 - 3x - 70 = 200 - 3x

4x = 200

x = 50

Thus, the angle is 50°.
lyudmila [28]3 years ago
4 0
The complement of an angle is what you add to it to get 90 degrees

if the angle is x, then the complement is y such that x+y=90

an angle is 70 less than 3 times it's complement
x=-70+3y

hmm
x+y=90
minus x both sides
y=90-x
subsitute 90-x for y

x=-70+3y
x=-70+3(90-x)
x=-70+270-3x
x=200-3x
add 4x to both sides
4x=200
divide both sides by 4
x=50
the angle is 50°
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The tensile strength of a metal part is normally distributed with mean 40 pounds and standard deviation 5 pounds. If 50,000 part
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a) how many would you expect to fail to meet a minimum specification limit of 35-pounds tensile strength?

7933 parts

b) How many would have a tensile strength in excess of 48 pounds?

2739.95 parts

Step-by-step explanation:

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

a) how many would you expect to fail to meet a minimum specification limit of 35-pounds tensile strength?

z = (x-μ)/σ

x = 35 μ = 40 , σ = 5

z = 35 - 40/5

= -5/-5

= -1

Determining the Probability value from Z-Table:

P(x<35) = 0.15866

Converting to percentage = 15.866%

We are asked how many will fail to meet this specification

We have 50,000 parts

Hence,

15.866% of 50,000 parts will fail to meet the specification

= 15.866% of 50,000

= 7933 parts

Therefore, 7933 parts will fail to meet the specifications.

b) How many would have a tensile strength in excess of 48 pounds?

z = (x-μ)/σ

x = 48 μ = 40 , σ = 5

z = 48 - 40/5

z = 8/5

z = 1.6

P-value from Z-Table:

P(x<48) = 0.9452

P(x>48) = 1 - P(x<48)

1 - 0.9452

= 0.054799

Converting to percentage

= 5.4799%

Therefore, 5.4799% will have an excess of (or will be greater than) 48 pounds

We are asked, how many would have a tensile strength in excess of 48 pounds?

This would be 5.4799% of 50,000 parts

= 5.4799% × 50,000

= 2739.95

Therefore, 2739.95 parts will have a tensile strength excess of 48 pounds

4 0
3 years ago
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