A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.5 months. When this computer-relay microchip malfunctions, the entire satellite is useless. A large London insurance company is going to insure the satellite for 50 million dollars. Assume that the only part of the satellite in question is the microchip. All other components will work indefinitely.
A. For how many months should the satellite be insured to be 94% confident that it will last beyond the insurance date?
B. If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends?
C. If the satellite is insured for 84 months, what is the expected loss to the insurance company?
D. If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make?
Answers
Answer:
a) The insurance should be of 84.6 months, that is, approximately 85 months.
b) 0.0436 = 4.36% probability that it will malfunction before the insurance coverage ends.
c) The expected loss to the insurance company is of 2.18 million.
d) The company should expect to make a profit of $689,200.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 90 months and a standard deviation of 3.5 months.
This means that \(\mu = 90, \sigma = 3.5\)
A. For how many months should the satellite be insured to be 94% confident that it will last beyond the insurance date?
The 100 - 94 = 6th percentile, which is X when Z has a pvalue of 0.06. So X when Z = -1.555.
\(Z = \frac{X - \mu}{\sigma}\)
\(-1.555 = \frac{X - 90}{3.5}\)
\(X - 90 = -1.555*3.5\)
\(X = 84.6\)
The insurance should be of 84.6 months, that is, approximately 85 months.
B. If the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends?
This is the pvalue of Z when X = 84. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z= \frac{84 - 90}{3.5}\)
\(Z = -1.71\)
\(Z = -1.71\) has a pvalue of 0.0436
0.0436 = 4.36% probability that it will malfunction before the insurance coverage ends.
C. If the satellite is insured for 84 months, what is the expected loss to the insurance company?
0.0436 probability of losing 50 million. So
0.0436*50 = 2.18
The expected loss to the insurance company is of 2.18 million.
D. If the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make?
1 - 0.0436 = 0.9564 probability of making 3 million.
0.0436 probability of losing 50 million
So
\(E = 0.9564*3 - 0.0436*50 = 0.6892\)
The company should expect to make a profit of 0.6892 million, that is, $689,200.
Related Questions
A cement walk 3 ft wide is placed around the outside of a circular pond with radius 17 ft. What is the total cost of the walk if the cost per square foot is $1.66 ? A. $582.73 B. $581.15 C. $579.90 D. $583.38 E. $578.87
Answers
Answer:
$578.87
Step-by-step explanation:
Find the area made by the circle made by the 3 ft. walk:
Radius = 17 + 3 = 20
Area = 22/7 x 20 x20 = 1257.14
Find the area made by the pond:
Area = 22/7 x 17 x 17 = 908.29
Subtract area 2 from area 1:
1257.14 - 908.29 = 348.85
Muliply this area by the cost er squar foot:
348.85 x $1.66 = 579.09
It depends on the value of pi used
Suppose that you are taking a course that has 4 tests. The first three tests are each worth 20% of your final grade, and the fourth test is worth 40% of the final grade. To get a B in the course, you must have an average of at least 80 percent on the 4 tests. Your scores on the first 3 tests were 63.5 %, 76 %, and 87 %. What is the minimum score you need on the fourth test to get a B for the course?. Don't round your answer.
Answers
Answer:
86.75
Step-by-step explanation:
Given test scores of 63.5, 76, and 87 that each count for 20% of your grade, you want to know the fourth test score needed for an average of 80, if the fourth test is worth 40% of your grade.
Course gradeThe grade for the course, with fourth test score x, will be ...
0.20(63.5 +76 +87) +0.40x = 80
0.40x +45.3 = 80
Solving for x, we get ...
0.40x = 34.7 . . . . subtract 45.3
x = 86.75 . . . . . . . divide by 0.4
The minimum score you need on the fourth test is 86.75.
<95141404393>
Your friend printed a picture of a regular 18-gon. She wants to cut the 18-gon into right triangles. If she divides the figure into 36 right triangles, what are the measures of the non-right angles of each triangle?
Answers
The measures of the non-right angles of each triangle are 40 degrees and 50 degrees.
The sum of the interior angles of a regular 18-gon can be found using the formula:
S = (n - 2) × 180 degrees
n is the number of sides of the polygon.
Substituting n = 18 we get:
S = (18 - 2) × 180 degrees
= 2880 degrees
The 18-gon into 36 right triangles need to draw 18 lines from the center of the polygon to its vertices dividing the polygon into 36 congruent sectors each with a central angle of 360 degrees / 18 = 20 degrees.
Each sector is an isosceles triangle with two sides of equal length radiating from the center of the polygon.
The vertex angle of each isosceles triangle is equal to twice the central angle or 40 degrees.
Since the vertex angle of a right triangle is 90 degrees the two non-right angles of each right triangle are 40 degrees and 50 degrees.
For similar questions on non-right angles
https://brainly.com/question/30571649
#SPJ11
Please help???????????????
Answers
Answer:
A
Step-by-step explanation:
if you dont feel right dont pick my answer
How do I find the line above the 2 in calculator and what is it called?
Answers
Answer:
A bar notation
Step-by-step explanation:
the line is called a bar notation
Answer:
If you have a line over a number (let's say there is a line over 0.2):
0.2, then it means that it is a repeating number.
So, a line over 0.2 would mean it is actually 0.2222222222 etc. They just don't want to right it out because it is way to long, and it is infinite.
Step-by-step explanation:
May I have Brainliest please? My next rank will be the highest one: A GENIUS! Please help me on this journey to become top of the ranks! I only need 14 more brainliest to become a genius! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
Find the length of a segment in the coordinate plane with endpoints (-4,-5) and (8, 1).
Answers
Answer:
Step-by-step explanation:
d = 13.416408
For:
(X1, Y1) = (-4, -5)
(X2, Y2) = (8, 1)
Answer:
L = 9.49 units
Step-by-step explanation:
From the 1st point to the 2nd, x changes by 12; from the 1st to the 2nd, y changes (increases) by 6. These results (12 and 6) represent the leg length of a right triangle whose diagonal length we wish to calculate using the Pythagorean Theorem:
12^2 = 144 and 6^2 = 36.
Combining these results in the length of the diagonal:
L = √(144 + 36) = √180 = 13.42 units using the Pythagorean Theorem
Rounding off, we get L = 9.49 units
Evaluate the expression 43+ [(96 = 8) ~ 5] - 42.
Answers
Answer:
233
Step-by-step explanation:
Step-by-step explanation:
43+[(96/8=12)×5]-42
=43+60-42
=103-42
=61
The diagnoal of a tv is 26 inches long . assuming that this diagonal forms a pair of 30 -60 - 90 right triangles , what are the exact length and width of the tv?
Answers
Answer: 13 inches by 13-√3 inches
Let
x-------> the length side of the TV
y-------> the width of the TV
d------> the diagonal of a TV
we know that
in a 30-60-90 right triangle
cos (30°) = √³/2
sin (30°) =1/2
d = 26 in
sin (30°) = ----> y = d * sin(30°)
cos (30°) = ----> x = d * cos (30°)
substitute the values
y = 26* = 13 in
x = 26³ = 13√√3 in
the length side of the TV is 13√3 in the width of the TV is 13 in
Answer: 13 inches by 13-√3 inches
I hope this helps! :)
Juan ramirez sells suits in a major department store on weekends he Ernst a commission of 5 percent on the first ten suits and he sells more than ten he Ernakulam additional 3 percent last weekend he sold thirteen 250 suits what was his commission?
Answers
Answer:
$185
Step-by-step explanation:
The first ten suits sold for 10×$250 = $2,500
commission = 5% of $2,500 = 0.05×$2,500 = $125
The next three suits sold for 3×$250 = $750
commission = 8% of $750 = 0.08×$750 = $60
Total commissions = $125+$60 = $185
There are several errors in the question. If you are using voice recognition, you are better off typing the question manually.
will mark as brainlyestWhat Is The Square Root Of 4?
Answers
Answer:
2
Step-by-step explanation:
Hope you don't need to summarize:) if so I will do it for you!
Work the following area application problem.
You wish to paint a storage shed. Its four walls measure 5 ft. high and 8 ft. wide each. If one gallon of paint covers 160
sq. ft., how many gallons of paint will you need?
Gallons of paint required =
a. 1
b. 2
c. 3
d. 4
Answers
Answer: a. 1
Step-by-step explanation:
There are 4 walls in total, and each wall measures 5ft high, 8ft wide
5 × 8=40 ft² for each wall
4×40=160 ft² for 4 walls
------------------
stated one gallon cover 160 ft²
160 ÷ 160=1 gallon
Hope this helps!! :)
Please let me know if you have any question
Write an algebraic expression to model the unknown number situation.
the sum of a number and one-third
Which statements are true? Select all that apply.
You can replace "a number" with a variable to represent an unknown value.
You can replace "sum" with an addition sign.
You can replace "sum" with an multiplication sign.
You can replace "one-third" with 1/3
The correct algebraic expression is 1/3 n
CHART IS BELOW
Answers
Answer:
You can replace "a number" with a variable to represent an unknown value.
You can replace "sum" with an addition sign.
You can replace "one-third" with 1/3.
Step-by-step explanation:
"the sum" means to add.
Let "a number" = x:
The sum of a number and one-third = x + 1/3.
You can replace "a number" with a variable to represent an unknown value.
You can replace "sum" with an addition sign.
You can replace "one-third" with 1/3.
3.
A coat is discounted 40% off its regular price. Which value is equivalent to 40%?
0.004
40
Answers
40% means "40 out of 100"
40 ÷ 100 = 0.40
So, 40% = 0.40 as a decimal
Which of the following statements must be true based on the diagram below? Select all that apply. (Diagram is not to scale.)
ASAPPPPP
Answers
The statements that must be true based on the diagram below are:
LM is a segment bisectorLM is a perpendicular bisectorL is a midpoint in the diagramM is a midpoint in the diagramHow to determine which of the following statements must be true based on the diagram below?From the diagram, segments that have the same mark are congruent segments
This means that:
Segments KL and HL are congruent segments
So, we have:
LM is a segment bisector
Also, because the angle at point L is a right-angle
LM is a perpendicular bisector and L is a midpoint in the diagram
Lastly, point M is a midpoint in the diagram
Read more about midpoints at
https://brainly.com/question/5566419
#SPJ1
a)Solve for x:
y = 130 − 4x
b) What is the value of x when y = 120
Answers
Answer:
\(x = \frac{5}{2}\)
Step-by-step explanation:
y = 130 - 4x
======================
120 = 130 - 4x
-10 = -4x
x = \(\frac{-10}{-4} =\frac{5}{2}\)
Jasmine has a circular swimming pool with a radius of 4.2 meters. What is the circumference of the pool? Use 3.14 for π
. Round to the nearest hundredth if necessary.
__ m
Answers
If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.
The "Circumference" of a circle is known as the distance around the boundary of a circle.
The circumference of a circle is given by the formula : 2 × π × radius,
where π (pi) is a mathematical constant approximately equal to 3.14,
We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :
⇒ Circumference = 2 × 3.14 × 4.2 meters,
⇒ Circumference ≈ 26.4 meters,
Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.
Learn more about Circumference here
https://brainly.com/question/16125353
#SPJ1
Given f(x) = x^2 + 3 , work out the value of f(4)
Answers
Answer: 19
Step-by-step explanation:
\(f(4)=(4)^2+3=16+3=19\)
Answer:
f(4) = 19
Step-by-step explanation:
f(x) = x^2 + 3
plug in 4 for the xs
f(4) = 4^2 + 3
f(4) = 16 + 3
f(4) = 19
Question 3 Write a method that solves for x in the quadratic equation. The parameters are a, b, c, and boolean flag that indicates whether it will solve the equation with addition or subtraction in the numerator. 2-4ac ㄨㄧ- 2a Source: Wikipedia The method will return the value of x
Answers
On solving the providewd question we can say that, public static double solve(double a, double b, double c, boolean flag )
What is quadratic equation?A quadratic equation is a quadratic polynomial in one variable that looks like this: x = ax2 + bx + c. a 0. This polynomial has at least one solution since it is a second-order polynomial, according to the Fundamental Theorem of Algebra. The answer can actually work or be difficult.
public static double solve(double a, double b, double c, boolean flag)
{ double d = Math.sqrt(b*b - 4*a*c); if(flag)
{ return (-b + d) / (2*a); }
else { return (-b - d) / (2*a); } }
To know more about quadratic equation visit:
https://brainly.com/question/17177510
#SPJ4
Which table represents exponential growth? A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 8, 16. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 7, 11. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 2, 4, 6, 10. HELP ME IMMEDIATELY!
Answers
The table that represents exponential growth is the second table.. The second column is labeled y with entries 2, 4, 6, 8. A 2-column table has 4 rows.
What is exponential growth?Exponential growth simply means a process that increases quantity over time. It occurs when the instantaneous rate of change of a quantity with respect to time is proportional to the quantity itself.
Exponential growth is the pattern of data which shows sharper increases over time. In finance, compounding creates exponential returns and the savings accounts with a compounding interest rate can show exponential growth.
In this case, the second table described represents an exponential function. It has a common ratio of 4, meaning that each y-value is multiplied by 4 to get to the next value. Here, every time the X's increase by 1, the Ys increase by a multiple of 4.
One of the best examples of exponential growth is observed in bacteria. Here, it takes bacteria roughly an hour to reproduce through prokaryotic fission. This illustrates exponential growth.
Learn more about exponential growth on:
brainly.com/question/4172151
Brainliest for correct answer.
Answers
Answer:
First option
V = π \(r^{2}\) h
Answer:
the first one
Step-by-step explanation:
which number line shows the solution to x + 8 > 15
Answers
7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
The given inequality is:
x + 8 > 15
Subtracting 8 on both sides of the equation:
x + 8 - 8 > 15 - 8
x > 7
Here, 7 is not included and hence it is depicted using an open dot.
Hence, option B is the correct answer.
Learn more about inequality here:
https://brainly.com/question/28823603
#SPJ1
If and is in , find cos
Answers
Answer:
9/41
Step-by-step explanation:
Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side) which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.
Suraj took a slice of pizza from the freezer and put it in the oven. The pizza's temperature (in degrees Celsius) as a function of time (in minutes) is graphed.
Answers
The time it will take the pizza to reach 0 degrees Celsius would be 0.75 minute.
What is a graph?A graph is defined as the diagram that is used to represent the variation of a variable in comparison with that of one or more other variables.
From the given graph above, the X axis is the time in minutes which is plotted against the temperature at y axis is degree Celsius.
From the graph, the time it will take the pizza to reach 0 degrees Celsius would be 0.75 minute.
Learn more about graph here:
https://brainly.com/question/25184007
#SPJ1
Find the sales tax for three CDs, if each CD is $14.29 and the sales tax is 7.25%. What is the answer?
A. $3.34
B. $3.86
C. $3.11
D. $3.08
Answers
Answer:
C
Step-by-step explanation:
An experiment was used to test a new migraine medicine. Each participant took either the new medicine or a placebo
then waited for one hour to see if the headache went away or remained. The results are compiled in the contingency
table below. Use the table to answer the questions.
Went Away| Medicine| Placebo
Remained|. 120. |. 68
18. | 44
Your answers should be exact numerical values.
There were
participants whose headache remained.
The probability of randomly selecting an individual whose headache remained is
There were
participants whose headache remained and took a placebo.
The probability of randomly selecting an individual whose headache remained and took a placebo is
Answers
1) Number of participants whose headache remained is: 62
2) The probability of randomly selecting an individual whose headache remained is: 0.4133
3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933
How to find the probability of random selection?From the table, we have the parameters as:
Number of participants that took medicine and headache went away = 120
Number of participants that took placebo and headache went away = 68
Number of participants that took and headache remained = 18
Number of participants that took placebo and headache remained = 44
1) Number of participants whose headache remained = 18 + 44 = 62
2) The probability of randomly selecting an individual whose headache remained is:
62/(62 + 120 + 68)
= 62/150
= 0.4133
3) The probability of randomly selecting an individual whose headache remained and took a placebo is:
44/150 = 0.2933
Read more about probability of random selection at: https://brainly.com/question/251701
#SPJ1
Help ASAP NEED HELP
Answers
Answer:
Its C
Step-by-step explanation:
first you would do the square which would be 3x3 which is 9 next you would do the rectangle which is 9x3 which is 27
9+27=36
Give the domain and range. On a coordinate plane, points are at (negative 2, negative 1), (0, 1), (2, 3). a. domain: {2, 0, 2}, range: {1, 1, 3} b. domain: {–1, 1, 3}, range: {–2, 0, 2} c. domain: {–2, 0, 2}, range: {–1, 1, 3} d. domain: {1, 1, 3}, range: {2, 0, 2} Please select the best answer from the choices provided A B C D
Answers
Answer:
c. domain: {-2, 0, 2}, range: {-1, 1, 3}
Step-by-step explanation:
From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.
The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.
In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.
Therefore, the correct answer is:
c. domain: {-2, 0, 2}, range: {-1, 1, 3}
If I have 100 thousand dollars in account and will add 800 dollars a month to the account plus I get 5% annual interest how much will I have in 10 years
Answers
Step-by-step explanation:
To calculate the future value of your account after 10 years, we can use the formula for compound interest:
FV = PV * (1 + r/n)^(n*t)
where:
FV is the future value of the account
PV is the present value of the account (in this case, $100,000)
r is the annual interest rate (in this case, 5%)
n is the number of times interest is compounded per year (assuming monthly compounding, n=12)
t is the number of years (in this case, 10)
Using this formula, we can calculate the future value of your account after 10 years:
FV = 100000 * (1 + 0.05/12)^(1210) + 80012*10
FV = $146,912.45
Therefore, after 10 years, with $100,000 initial investment, adding $800 per month and an annual interest rate of 5%, you will have approximately $146,912.45 in your account.
Send your answers I will check if it is correct
Answers
Answer:
285, 7392, 15708, are divisible by 3 but not by 9
Step-by-step explanation:
it's because of we add the sun of the digits, 285, 7392, 15708, they are divisible by 3. actually, except for 629, all of them are divisible by 3, but 5490 and 43695 are both divisible by 3 and 9
() Which number is closest to √5?
1.7
2.2
3.4
3.1
Answers
Answer:
Step-by-step explanation:
