Maggie is considering two investments. Investment A Investment B Principal $10,000 $8,000 Interest rate 3% 2.8% Time in years 5
2 answers:
To determine this, we will apply the simple interest formula: 
where
signifies the total amount.
indicates the principal amount.
represents the interest rate in decimal.
denotes the time period in years.
Investment A. The initial investment amount is $10,000, so
. The investment period is 5 years, meaning 
. To express the interest rate in decimal, divide it by 100%
Now, we can substitute these values into our formula to find:
Investment B.
, 
, and 
.
In conclusion, investment A will yield a greater value than investment B at the investment period's conclusion.
where
Investment A. The initial investment amount is $10,000, so
Now, we can substitute these values into our formula to find
Investment B.
In conclusion, investment A will yield a greater value than investment B at the investment period's conclusion.
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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:
(a1)
The probability of the temperature increase being under 20°C can be calculated as follows:
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:
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:
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:
The expected value for the temperature increase computes to 17.5°C.
Response:
Refer to the figure attached.
Step-by-step explanation:
Each portion is treated as a function.
Let x represent the hours worked in a day
The company packs 80 boxes of toys each hour during the first three hours. Thus, y₁ = 80x, for x ∈ [0,3]
After three hours, the total boxes packed = 80 * 3 = 240
They pause packaging for two hours for a training session. Therefore, y₂ = 240, for x ∈ [3,5]
Next, for the subsequent four hours, they pack 20 boxes of toys hourly
y₃ = 20x + c, for x ∈ [5,9]
To determine c, equate y₂ and y₃ at x = 5
∴ 240 = 20 * 5 + c
∴ c = 240 - 20 * 5 = 240 - 100 = 140
∴ y₃ = 20x + 140, for x ∈ [5,9]
Consequently,
y₁ = 80x, for x ∈ [0,3]
y₂ = 240, for x ∈ [3,5]
y₃ = 20x + 140, for x ∈ [5,9]
The graph plotting the piecewise function that depicts the described situation is shown in the attached illustration.
