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kap26
3 months ago
7

3. At a local restaurant, the health inspector visits every 7 days, and the fire inspector visits every 12 days. (a) Make a tabl

e for the next 4 visits for each inspector. (b) In how many days will both inspectors visit on the same day? Show your work.
Mathematics
2 answers:
Svet_ta [12.7K]3 months ago
8 0

Answer:

They will coincide on the 84th day.

Step-by-step explanation:

Evaluating the details provided.

The health inspector comes every 7 days, while the fire inspector visits every 12 days.

Part (A) Create a table for the next 4 visits of each inspector.

The necessary table is as follows:

Health inspector: 7, 14, 21, 28

Fire inspector:    12, 24, 36, 48

Part (B) After how many days will both inspectors be present on the same day?

To solve this, we calculate the LCM of both numbers as follows:

7= 1×7

12=2×2×3

The LCM then is: 2×2×3×7=84

As a result, they will meet on the 84th day.

Leona [12.6K]3 months ago
6 0
Health inspector visits once a week.
Fire inspector comes every 12 days.

a) health inspector fire inspector.
day 7.                    day 12.   
day 14.                    day 24.
day 21.                    day 36.
day 28.                    day 48.
day 35.                    day 60.

b) 12 x 7 = 84.

Both will coincide on day 84.




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A newspaper vendor sells three papers to 135 customers, the papers are the daily times, the observer and the new Nigeria. 70 cus
AnnZ [12381]

Answer:

Three customers purchased all three newspapers.

Step-by-step explanation:

Let D, O, and N stand for the three newspapers.

D = The Daily Times

O = The Observer

N = The New Nigeria.

According to the provided information,

n(D\cup O\cup N)=135, n(D)=70,n(O)=60,n(N)=50

n(D\cap O)=17, n(O\cap N)=15, n(D\cap N)=16

We can deduce that:

n(A\cup B\cup C) = n(A) + n(B) + n(C)-n(A\cap B)-n(B\cap C)-n(C\cap A) + n(A\cap B\cap C)

Applying this formula, we discover

n(D\cup O\cup N) = n(D)+n(O) + n(N)-n(D\cap O)-n(O\cap N)-n(N\cap D) + n(D\cap O\cap N)

135 =70+60+50-17-15-16 +n(D\cap O\cap N)

135 =132+n(D\cap O\cap N)

135 -132=n(D\cap O\cap N)

3=n(D\cap O\cap N)

Hence, three customers bought all three papers.

5 0
3 months ago
Two well-known aviation training schools are being compared using random samples of their graduates. it is found that 70 of 140
zzz [12365]
In a two-tailed test where the p-value stands at 0.0275, it indicates that with a threshold of 0.025, we should dismiss the hypothesis asserting equal proportion. This conclusion follows from p = 0.0275 in line with the guideline P-value < p.
7 0
2 months ago
A rocket was launched into the air from a podium 6 feet off the ground. The rocket path is represented by the equation h(t)=-16t
lawyer [12517]

Answer:

60

Step-by-step explanation:

The function provided is:

h(t)=-16t^2+120t+6

The average rate of change of h(t) as time goes from t=a to t=b is expressed as:

\frac{h(b)-h(a)}{b-a}

This function can be reformulated as: h(t)=-16(t-3.75)^2+231

The rocket's peak height is 231, which occurs at t=3.75 seconds.

\implies h(3.75)=231

The initial launch happens at: t=0

and h(0)=-16(0)^2+120(0)+6=6

The average rate of change from launch to max height is

\frac{h(3.75)-h(0)}{3.75-0}=\frac{231-6}{3.75-0} =60

6 0
3 months ago
At an ocean-side nuclear power plant, seawater is used as part of the cooling system. This raises the temperature of the water t
Zina [12379]

Answer:

(a1) The chance that the temperature rises by less than 20°C is 0.667.

(a2) The probability of the temperature increase falling between 20°C and 22°C is 0.133.

(b) The likelihood that the temperature increase could be hazardous at any moment is 0.467.

(c) The anticipated value of the temperature rise is 17.5°C.

Step-by-step explanation:

Let X denote the temperature increase.

The random variable X is distributed uniformly over the interval [10°C, 25°C].

The probability density function for X is shown here:

f(X)=\left \{ {{\frac{1}{25-10}=\frac{1}{15};\ x\in [10, 25]} \atop {0;\ otherwise}} \right.

(a1)

The probability of the temperature increase being under 20°C can be calculated as follows:

P(X

Consequently, the chance that the temperature increase will be below 20°C is 0.667.

(a2)

The probability of the temperature rise being in the range from 20°C to 22°C is computed as follows:

P(20

This leads to the probability of the temperature increase being between 20°C and 22°C being 0.133.

(b)

To find the probability that the increase in temperature could be dangerous, we calculate:

P(X>18)=\int\limits^{25}_{18}{\frac{1}{15}}\, dx\\=\frac{1}{15}\int\limits^{25}_{18}{dx}\,\\=\frac{1}{15}[x]^{25}_{18}=\frac{1}{15}[25-18]=\frac{7}{15}\\=0.467

This results in a probability of 0.467 that the temperature rise is potentially dangerous at any time.

(c)

The expected value of the uniform random variable X is determined as follows:

E(X)=\frac{1}{2}[10+25]=\frac{35}{2}=17.5

The expected value for the temperature increase computes to 17.5°C.

7 0
3 months ago
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