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guajiro [1.7K]
3 years ago
8

2. One angle is one less than six times the measure of

Mathematics
1 answer:
Illusion [34]3 years ago
8 0

The equations used to find the measure of each angle in degrees is x + y = 90 and x = 6y - 1

The two complementary angles are 77 degrees and 13 degrees

<em><u>Solution:</u></em>

Given that two angles are complementary angles

Complementary angles are two angles whose sum is 90 degrees

Let one of the angle be "x" and the other angle be "y"

Therefore,

x + y = 90 ------ eqn 1

Also given that,

One angle is one less than six times the measure of  another

one angle = six times the other angle - 1

x = 6y - 1 ------ eqn 2

Substitute eqn 2 in eqn 1

6y - 1 + y = 90

Thus the above equation is used to find the measure of each angle in degrees

Solve the above equation

6y + y - 1 = 90

7y - 1 = 90

7y = 91

y = 13

Substitute y = 13 in eqn 2

x = 6(13) - 1

x = 78 - 1

x = 77

Thus the two complementary angles are 77 degrees and 13 degrees

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The life times of light bulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 h
Nezavi [6.7K]

Answer:

a. 1200hours

b.  σ² = 400² =160000hour

c. standard error = 133.33

d. for 9 lightbulb it is likely that 9*0.146 = 1.31 bulbs will have lives of fewer than 1,050 hours?

Step-by-step explanation:

mean of 1,200 hours

σ, a standard deviation of 400 hours.

Sample size, N =  nine bulbs,

a) mean of the sample mean lifetime: is given as 1,200 hours

b) variance of the sample mean is the square of the  σ, a standard deviation of 400 hours.

σ² = 400² =160000hours

c) What is the standard error of the sample mean?

The standard deviation of a sampling distribution of mean values is called the standard error of the means,

standard error of the means,  σx = σ √N

The formula for the standard error of the means is true for all values infinite number of sample, N.

σx = σ √N

     =400  √9 = 400/3 =133.3333

d) the probability that, on average, those nine lightbulbs have lives of fewer than 1,050 hours

The area under part of a normal probability curve is  directly proportional to probability and the value is calculated as

z = ( x₁−x) /σ

where z = propability of normal curve

x₁ = variate mean = 1050hours

x = mean of 1200hours

σ = standard deviation = 400

applying the formula,

z= (1050-1200)/400

z = 150/400 =0.375

Using a table of partial areas beneath the standardized normal curve (see Table of normal curve, a z-value of 0.375 corresponds to an area of 0.1460 between the mean value.

Thus the probability of a lightbulbs having lives of fewer than 1,050 hours is 0.1460.

for 9 lightbulb it is likely that 9*0.146 i.e. 1.31 bulbs will have lives of fewer than 1,050 hours?  

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Answer:

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Next multiply my given answer by 0.4

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Answer:

y = - x + 5 should be the answer. Hope this helps!

Step-by-step explanation:

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