Place values and whole number

The complement of an angle is one-sixth the measure of the supplement of the angle. What is the measure of the complement angle?

cestrela7 [59]

Answer:

The measure of the complement angle is $18\°$

Step-by-step explanation:

Let

x-----> the angle

we know that

The complement of an angle is equal to $(90-x)\°$

The supplement of an angle is equal to $(180-x)\°$

we have

The complement of an angle is one-sixth the measure of the supplement of the angle

$(90-x)\°=(1/6)(180-x)\°$

solve for x

$(540-6x)\°=(180-x)\°$

$(6x-x)=(540-180)\°$

$(5x)=(360)\°$

$x=72\°$

Find the measure of the complement angle

$(90-x)\°$ ------> $(90-72)=18\°$

7 0

3 years ago

Read 2 more answers

What is 5/12 of 2/5 i need help

Marianna [84]

Answer:10/60

If need to simply it is 1/6.

Step-by-step explanation: Mutiply 5/12 by 2/5 .

5 0

3 years ago

Zoe goes out to lunch. The bill

DanielleElmas [232]

Answer:

$60

Step-by-step explanation:

To find how much Zoe paid before the sales tax and tip, we first need to consider the amount she paid in sales tax and tips.

Sales tax + Tips = $18.60

Let x = original price

Sales tax = 11% * original price

Sales tax = 0.11 * x

x= 0.11x

Tips = 20% * original price

Tips = 0.20 * x

x = 0.2x

Now that we have a value for both the sales tax and tips, we can then proceed to find the original price by:

0.11x + 0.2x = 18.60

0.31x = 18.60

Now we need to divide both sides by 0.31 to find x.

x = 60

Zoe's dinner before the sales tax and tips was $60.

5 0

3 years ago

Read 2 more answers

Estion

dalvyx [7]

Using the Poisson distribution, it is found that there is a 0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

<h3>What is the Poisson distribution?</h3>

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

The parameters are:

x is the number of successes

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

Considering the average of 15 birds every 2 hours during daylight hours, the mean for a 45-minute period is given by:

$\mu = 15 \times \frac{45}{120} = 5.625$

The probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours is given by:

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)$

In which:

$P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}$

$P(X = 0) = \frac{e^{-5.625}(5.625)^{0}}{(0)!} = 0.004$

$P(X = 1) = \frac{e^{-5.625}(5.625)^{1}}{(1)!} = 0.02$

$P(X = 2) = \frac{e^{-5.625}(5.625)^{2}}{(2)!} = 0.057$

$P(X = 3) = \frac{e^{-5.625}(5.625)^{3}}{(3)!} = 0.107$

$P(X = 4) = \frac{e^{-5.625}(5.625)^{4}}{(4)!} = 0.150$

$P(X = 5) = \frac{e^{-5.625}(5.625)^{5}}{(5)!} = 0.169$

Then:

$P(X \leq 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.004 + 0.02 + 0.057 + 0.107 + 0.15 + 0.169 = 0.507$

0.507 = 50.7% probability that the bird feeder will be visited by at most 5 birds in a 45 minute period during daylight hours.

More can be learned about the Poisson distribution at brainly.com/question/13971530

#SPJ1

3 0

2 years ago

1. The 2006 General Social Survey contains information on the number of hours worked by a respondent each week. The mean number

Vilka [71]

Answer:

A)σ_M = 1.2634

B) CI = (36.564, 41.516)

C) σ_M = 0.1151

Step-by-step explanation:

A) Formula for standard error is;

σ_M = σ/√n

We are given;

Mean; x¯ = 39.04

Standard deviation; σ = 11.51

Sample size; n = 83

Thus;

Standard error; σ_M = 11.51/√83

σ_M = 1.2634

B) formula for confidence interval is;

CI = x¯ ± z(σ_M)

z is critical value

At 95% Confidence interval, z = 1.96

Thus;

CI = 39.04 ± 1.96(1.2634)

CI = (39.04 + 2.476) and (39.04 - 2.476)

CI = (36.564, 41.516)

C) sample size is now increased to 10000

Thus,standard error is calculated as;

σ_M = 11.51/√10000

σ_M = 0.1151

8 0

3 years ago