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ZanzabumX [31]
3 years ago
13

After 29 years Ms. Payson is getting ready to retire from teaching. As part of her employee benefits

Mathematics
1 answer:
Korolek [52]3 years ago
4 0

Answer:

\boxed{\mathbf{\$33880.70}}

Step-by-step explanation:

1. Calculate the average salary

\text{Average salary} = \dfrac{\text{Sum of salaries}}{\text{Number of salaries}} = \dfrac{\$54900 + \$55300 + \$56700}{3}\\\\= \dfrac{\$166900}{3} = \$55633.33

2. Calculate the pension

\text{Pension} = 29 \times 0.021 \times \$55633.33 = \mathbf{\$33880.70}\\\\\text{ Ms. Payson's annual pension will be $\boxed{\mathbf{\$33880.70}}$}

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Consider a multiple choice exam with 10 questions, and with 4 possible answers to each question (labeled A, B, C, and D). 1a. Wh
mrs_skeptik [129]

Answer:

(1a) 9.54e-07 (1b) 0.9437 (2) 10^8

Step-by-step explanation:

We have n = 10 questions. For each question in the multiple choice exam, we can choose the correct answer with probability p = 0.25 or an incorrect answer with probability q = 0.75 (just by guessing). Besides is reasonable to believe that questions are independent. Let X be the random variable that represents the number of correct answers (just by guessing) observed during the n = 10 questions, so, X have a binomial distribution.

(a) The probability of getting a perfect score just by guessing is

P(X = 10) = 10C10(0.25)^{10}(0.75)^{10-10} = 9.54e-07

(b) The probability of getting at least one question correct, just by guessing

P(X\geq1) = \sum_{x=1}^{x=10}10Cx(0.25)^{x}(0.75)^{(10-x)} = 0.9437

2. Each RUID is 9-digits long, there are 10 digits, each of the nine positions for a digit of the RUID has 10 posibilities except the 4th and 5th positions which must be both 0. For the multiplication rule there can be (10)^3(1)(1)(10)^5 = 10^8 different RUIDS.

3 0
3 years ago
Harriet has 3/4 tank of gas left in her car. if she needs 1/4 tank to go to her friends house and another 1/4 tank to get back h
pashok25 [27]
Ok so if you add the two 1/4's you will find how much gas she needs total to complete the trip. So do 1/4 + 1/4 and get 1/2. Next you can see that 3/4 is larger than 1/2, so she has enough gas.
Hope that helps!
3 0
3 years ago
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Triangle MNP has vertices N(2, 2) and P(0, –2). The triangle is symmetric about the y-axis. What is the approximate measure of t
Evgesh-ka [11]
Point M of the triangle is (-2,2) to make triangle MNP as shown in the attached image

Triangle MNP has a base of 4 units and a height of 4 units. We can work out the angle x and angle y using trigonometry ratio

We use tan ratio to find both angles

Tan (x) = \frac{opposite}{adjacent}
Tan(x)= \frac{4}{2}
Tan(x)=2
Tan^{-1}(2)=63.43494882
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Tan(y)= \frac{opposite}{adjacent}
Tan(y)= \frac{2}{4}
Tan^{-1}(0.5)=26.56505118
Angle y=26.6

Angle MNP = Angle NMP = 63.43 degrees (this is based on the fact that the triangle is an isosceles triangle)

Angle MPN = 2×26.6 = 53.2 degrees (we multiply by 2 as angle y is only a half of angle MPN - as shown in the diagram)

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3 years ago
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Which of the following has the most inertia, four kilograms of iron or four kilograms of cork? ...?
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3 years ago
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Goshia [24]

<t =33 since triangle  RUT is isosceles  (RU = TU)

<r + <u + <t = 180  triangle = 180

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<rus + <sut = <u

x + x = 114

2x = 114

divide by 2

x = 57

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3 years ago
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