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Vitek1552 [10]
2 years ago
3

An insurance company writes a policy to the effect that an amount of money A must be paid if some event E occurs within a year.

If the company estimates that E will occur within a year with probability p, what should it charge the customer in order that its expected profit will be 10 percent of A?
Mathematics
1 answer:
docker41 [41]2 years ago
5 0

Answer:

(0.1 + p)A

Step-by-step explanation:

The expected value paid by the insurance company is determined by the amount paid incase E happens multiplied by the likelihood of E occurring:

E(E) = p*A

The profit is given by the amount charged subtracted by the expected value of the policy, if the desired profit is 0.10A, the amount charged (C) must be:

0.10A = C - pA\\C= (0.1+p)A

The company should charge (0.1 + p)A.

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The temperature of chicken soup is 192.7°F. As it cools, the temperature of the soup decreases 2.3°F per minute. Part A What is
SIZIF [17.4K]

Answer:

Part A: option C. 135.2°F

Part B: 40 min

Step-by-step explanation:

<em>Part A:</em><em> What is the temperature in degrees Fahrenheit of the soup after 25 minutes?</em>

<u>1. Set an equation</u>:

  • Temperature = Initial temperature - decrease in temperature
  • decrease in temperature = rate of decrease × time
  • Variables:

        temperature: T

        initial temperature: To = 192.7°F

        decrease rate: 2.3°F / min

        time = t

  • Equation: T = 192.7°F - 2.3(°F/min) × t

2.<u> Substitute t = 25 min</u>

  • T = 192.7°F - 2.3 (°F/min) × 25 min = 135.2 °F

Part B. <em>How many minutes will it take for the soup to cool to 100.7°F?</em>

2.<u> Solve the equation for t</u>

  • T = 192.7°F - 2.3(°F/min) × t ⇒ t = (192.7 °F - T) / (2.3 °F/min)

3. <u>Substitute T = 100.7°F</u>

  • t = (192.7°F - 100.7°F) / (2.3 °F/min) = 40 min
7 0
2 years ago
On a coordinate plane, a curved line labeled f of x with a minimum value of (1.9, negative 5.7) and a maximum value of (0, 2), c
Vikentia [17]

Answer: 4.F(x) > 0 over the intervals (-0.7, 0.76) and (0.76, ∞).

Hope this helps :)

5 0
2 years ago
Read 2 more answers
4/9 divided by what equals 12
Dahasolnce [82]
(4/9)/x= 12

Multiply both sides by x
4/9=12x

Divide both sides by 12
(4/9)*(1/12)= 4/108
4/108= 1/27

Final answer: 1/27
5 0
2 years ago
What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (
aalyn [17]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=k or y=kx

in this problem we have

the point (5,12) is on the line of direct variation

so

Find the constant of proportionality k

y/x=k-------> substitute ------> k=12/5

the equation is

y=\frac{12}{5}x

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

<u>case A)</u> point (0,0)

x=0\ y=0

Substitute the value of x and y in the direct variation equation

0=\frac{12}{5}*0

0=0 -------> is true

therefore

the point (0,0) is on the line of direct variation

<u>case B)</u> point (2.5,6)

x=2.5\ y=6

Substitute the value of x and y in the direct variation equation

6=\frac{12}{5}*2.5

6=6 -------> is true

therefore

the point (2.5,6) is on the line of direct variation

<u>case C)</u> point (3,10)

x=3\ y=10

Substitute the value of x and y in the direct variation equation

10=\frac{12}{5}*3

10=7.2 -------> is not  true

therefore

the point (3,10) is not on the line of direct variation

<u>case D)</u> point (7.5,18)

x=7.5\ y=18

Substitute the value of x and y in the direct variation equation

18=\frac{12}{5}*7.5

18=18 -------> is true

therefore

the point (7.5,18) is on the line of direct variation

<u>case E)</u> point (12.5,24)

x=12.5\ y=24

Substitute the value of x and y in the direct variation equation

24=\frac{12}{5}*12.5

18=30 -------> is not true

therefore

the point  (12.5,24) is not on the line of direct variation

<u>case F)</u> point (15,36)

x=15\ y=36

Substitute the value of x and y in the direct variation equation

36=\frac{12}{5}*15

36=36 -------> is true

therefore

the point (15,36) is on the line of direct variation

therefore

<u>the answer is</u>

(0,0)

(2.5,6)

(7.5,18)

(15,36)


5 0
2 years ago
Read 2 more answers
Ernie earned $121.50 more than Kaylin. Tria earned $35 less than 3 times the amount Kaylin earned. Ernie, Tria, and Kaylin earne
Dvinal [7]
X - Ernie, y - Kaylin, z - Tria
x = y + 121.50
z = 3y - 35
x + y + z = 579
-------------------------
z = 3 y - 35      =>   - 3 y + z = -35
y + 121.50 + y + z = 579
---------------------------------
- 3 y + z = - 35        / · ( -1 )
 2 y + z = 457.50     (we will use the elimination method) 
---------------------------------
3 y - z = 35
2 y + z = 457.50
----------------------
5 y = 492.5,            y = 492.5 : 5 = 98.5
z = 3 · 98.5 - 35
z = 260.5
Tria earned $260.5 
8 0
2 years ago
Read 2 more answers
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