At a certain fire station, false alarms are received at a mean rate of .2 per day. In a year, what is the probability that fewer than 60 false alarms are received?

0.064

Step-by-step explanation:

Number of days in a year = 365

Mean rate of false alarm in a year = λ = 365 * 0.2 = 73

Standard deviation, σ = sqrt(λ) = sqrt(73) = 8.54 (for large λ value)

Using the relation :

P(x < 60): (60 - 73) / 8.54

P(x < 60) = - 1.52

P(Z < - 1.52) = 0.06426 (Z probability calculator

= 0.064

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°

- both graphs increase on their domain.

- the graphs of both functions have the same x-intercept.

- neither graph has a y-intercept.