A tank is in the shape of a surface of revolution given by rotating the curve y = x4, for 0 < x < 2, about the y-axis. Denote the density of water by p kg/m', and gravity acceleration by g m/s2 (a) Suppose that 60% of the volume of the tank is filled with water. Find the depth of the water in the tank. [7 pts] (b) Find the work required to pump the water in the tank to an outlet at the top of the tank. [8 pts)
Answers
V_water = π * ∫[x(y)^2 dy] (limits from 0 to h)
Solving this equation for h will give us the depth of the water in the tank.
W = ∫[p * g * A(y) * (16 - y) dy] (limits from 0 to h)
Solving this integral will give us the work required to pump the water in the tank to an outlet at the top of the tank.
(a) To find the depth of the water in the tank, we first need to find the volume of the tank. The volume V of a surface of revolution generated by rotating the curve y = x^4 about the y-axis can be found using the formula:
V = π * ∫[x(y)^2 dy] (limits from 0 to y_max, where y_max = (2)^4 = 16)
Since 60% of the volume is filled with water, we can denote the water volume V_water as: V_water = 0.6 * V
Now, we need to find the depth (h) at which the volume is equal to V_water. We can do this by setting up the following equation :V_water = π * ∫[x(y)^2 dy] (limits from 0 to h)
Solving this equation for h will give us the depth of the water in the tank.
(b) To find the work required to pump the water in the tank to an outlet at the top of the tank, we need to use the following formula for work: W = ∫[F * distance] (limits from 0 to h)
Here, F represents the force exerted by the water at a given depth, and the distance is the distance the water must be pumped to reach the outlet. The force exerted by the water at a depth y can be expressed as:
F = p * g * A(y)
Where A(y) is the cross-sectional area of the tank at depth y. To find the work required, we can integrate over the depth of the water: W = ∫[p * g * A(y) * (16 - y) dy] (limits from 0 to h)
Solving this integral will give us the work required to pump the water in the tank to an outlet at the top of the tank.
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Related Questions
During one month mike used 685 gallons of water at his home. There are approximately 3.8 liters in 1 gallon. Which measurement is closet to liters mike used?
Answers
Answer:
Step-by-step explanation:
Comment
This is a question that needs choices. I will go by sig digits.
Givens
1 gallon = 3.8 liters.
685 gallons were used.
Formula
1 gallon 685 gallons
====== = ==========
3.8 liters x
Solution
1/3.8 = 685/x Cross multiply
1*x = 685*3.8
x = 2603 liters. There are 2 significant digits in 3.8. So round to 2 places.
Answer
Liters = 2600 Liters
From the following categories of variables, which of them are mutually exclusive and exhaustive?
a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday
b. Days: Weekday and Weekend
c. Letters: Vowels and Consonants
d. Letters: Alphabets and Consonants
Answers
The given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants.
Mutually exclusive and exhaustive variables: A variable is mutually exclusive and exhaustive if it includes all possible outcomes and each outcome can only be assigned to one variable category.a. Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, and Sunday - Mutually exclusive and exhaustiveb. Days: Weekday and Weekend - Mutually exclusive and exhaustive c. Letters: Vowels and Consonants - Mutually exclusive and exhaustive. Letters: Alphabets and Consonants - Not mutually exclusive and exhaustiveThe given categories of variables that are mutually exclusive and exhaustive are weekdays and weekend and vowels and consonants. Hence, the options a and c are correct.
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a market sells five kinds of cups, 4 kinds of saucers, and 2 kinds of spoons. How many ways are there to buy two objects of different types?
Answers
There are 84 ways to buy two objects of different types.
How to choose two objects of different types ?To choose two objects of different types, we can choose one type of object first and then choose one object from that type and one object from the other two types.
The number of ways to choose one type of object is 3 (cups, saucers, or spoons). For each type of object, there are different numbers of objects to choose from:
Cups: 5 objectsSaucers: 4 objectsSpoons: 2 objectsSo, the total number of ways to choose two objects of different types is:
3 x (5 x 4 + 5 x 2 + 4 x 2) = 3 x 28 = 84
Therefore, there are 84 ways to buy two objects of different types.
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Use the number line to help you compare the numbers 1.3 and 1.7.
1.0-2.0
O 1.3 >1.7
O 1.3 = 1.7
O 1.3 < 1.7
O 1.7 < 1.3
Answers
If an aqueduct had a distance of 53 miles, what would the drop (in feet) at the end destination if the slope is 0.1%?
Answers
As a result, the drop at the aqueduct's final destination is 279.84 feet.
What is percent?Percent is a term used to represent a part or a fraction of a whole expressed as a value out of 100. The word "percent" comes from the Latin phrase "per centum," which means "per hundred." Percentages are commonly used to express ratios or proportions of quantities, and are denoted using the symbol "%". For example, if a student answers 85 out of 100 questions correctly on a test, their score can be expressed as 85%, which represents the proportion of questions they answered correctly out of the total number of questions.
Here,
If an aqueduct has a distance of 53 miles and a slope of 0.1%, we can use the formula:
drop = distance x slope x 5280
where 5280 is the number of feet in one mile.
Substituting the given values, we get:
drop = 53 x 0.1/100 x 5280
= 279.84 feet
Therefore, the drop at the end destination of the aqueduct is 279.84 feet.
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Select the correct answer. Simplify. 198 49√2 OB. 7√2 OC. 2√7 OD. 14√7
Answers
Answer: The correct answer is B.
Step-by-step explanation: To simplify a square root, you take the factors of the value in the square root and see the greatest factor that is a square. In this case, 49 is the greatest square factor of 98. You take the square root of 49, which is 7. 7 goes outside the radicand. Leave 2 inside the radical because 49 x 2 = 98. Hence, the correct answer is B.
7.9.20) Dovolence and sex in television programate se products in advertisements Subjects were randomly assigned to watch one of four types of TV Shows: (1) pemer six or violence in the content code (3) violonce but not in the content coo(3) but no violence in the content code and (4) both sex and violence in the content code for each TV show the original advertisements were relaced with the same set of twelve advertisements. Subjects were not told the purpose of the study but were instead told that the researchers were studying attitudes toward TV show Mar viewing the show, subjects receive a surprise memory test to check their recall of the products advertised, Can it would have been better to have subjects choose the type of TV show they enferred to view in onder to improve their recall and reduce contounding (the score on the memory rest of their recall of advertisements is the response to the experiments thrould have weed different advertisements for each type of TV show in order to reduce contounding the sementes to have different vertiments for each type of TV show in order to reduce confunding would have been better to have bec choose there of TV show they referred to view order to prove the real and reduce confunding the score on the memory test of the recallo allement the
Answers
While allowing subjects to choose their preferred TV show might seem intuitively appealing, random assignment is generally preferred in experimental designs to reduce confounding and provide more reliable results.
How to explain the researchAllowing subjects to choose the type of TV show they want to watch could potentially introduce biases and confounding factors into the study. If participants have the freedom to select the content they prefer, they may be more likely to choose shows that align with their pre-existing attitudes and preferences. This could introduce systematic differences between the groups and make it difficult to isolate the effects of violence and sex in the content on memory recall.
By randomly assigning subjects to different types of TV shows, the researchers can create comparable groups that are balanced in terms of individual characteristics and preferences. This random assignment helps to reduce confounding variables and allows for a more accurate evaluation of the impact of violence and sex on memory recall
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1) Jerry put $20,000 in a savings account paying 8% annual interest
compounded monthly. At this rate how much money will be saved in th
account after 10 years?
Answers
Putting $20,000 at 8% annual interest & monthly getting compounded , the amount of money that jerry will after 10 years is approximately $44,040.
Given :
present value (P) = $20,000
interest rate (r) = 8%
compounding monthly (n) = 12
Time (t) = 10 years
To find : Future value after 10 years when interest monthly gets compounded
Now,
we know the formula is
future value = present value × (1 + interest rate)^years
= P × ( 1 + r / n )^ nt
inserting values in the given formula we get,
future value = $20,000 × ( 1 + 8% / 12 )^ 10 × 12
= $20,000 × ( 1 + 8 / 1200 )^ 120
= $20,000 × (1 + 0.0066)^120
= $20,000 × ( 1.0066)^120
= $20,000 × 2.2020
= $44,040
Hence the amount saved by jerry after 10 years at the annual interest of 8% when money monthly is getting compounded with $20.000 will be $44,040.
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A.)4x-3y=6
B.)4x+3y=6
C.) 4x-3y=-6
D.)4x+3y=-6
Answers
Is the relation shown in the arrow diagram a function explain (2,24) (4,8) (6,16) (8,32) (10,32)
Answers
Answer:
i believe its yes
jiminy’s cricket farm issued a 30-year, 4.5 percent semiannual bond three years ago. the bond currently sells for 104 percent of its face value. the company’s tax rate is 22 percent.
Answers
a) Cost of debt, I = 4.25%(annual)
b) After tax cost of debt = 3.315%
c) After tax cost of debt of 3.135% is more relevant.
Given:
FV = 100
Semiannual bond issued 3 years ago
Maturity = 27
Price, PV = 104
coupon rate = 4.5%
Tax rate = 22%
a) Semiannual bond issued 3 years ago
Maturity, n = 27 years × 2 = 54
Coupon C = 4.5%/2×100 = 2.25
Now,
Pretax cost of debt,
Cost of debt, I = [C+(FV-PV)/n] / (FV+PV)/2
= [2.25 +(100 - 104)/54] / [ 100+1040/2
= 2.12%
= 2.12×2
Cost of debt, I = 4.25%(annual)
b) After tax cost of debt = cost of debt × (1-T)
= 4.25% × (1-22%)
After tax cost of debt = 3.315%
c) After tax cost of debt is more relevant.
Hence we get the required answer.
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Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I estimate that the probability of my getting married in the next 3 years is 0.7. math
Answers
The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.
As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.
In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.
It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.
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Lacy earned $900 last week before taxes, if she paid 19 % in taxes;
a) How much did she pay in taxes?
b) What is her net pay?
Answers
Answer: a) $171 b) $729
Step-by-step explanation:
a) 0.19 * $900 = $171
b) net pay = the money one earns after all deductions
$900 (what she earned) - $171 (taxes she had to pay) = $729
Find the vector v with the given magnitude and the same direction as u.Magnitude: ||v|| = 8Direction: u = -2i
Answers
Given the following:
||v|| = 8u = -2i
We are asked to find the vector v with the given magnitude and the same direction as u. The direction of a vector is given by a unit vector. A unit vector is defined as the magnitude of the vector divided by the magnitude of the vector. Therefore, we need to find a unit vector in the same direction as u.
Using the given direction of u, we can find the magnitude of u:
|u| = √((2i)^2) = √4 = 2
Now we can find the unit vector: u/|u| = (-2i)/2 = -i
Thus, the vector v with the same direction as u is: v = (8)(-i) = -8i
Therefore, the answer is:
Vector v with the given magnitude and the same direction as u is v = -8i
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what is the probability that the sum of the numbers on four dice rolled is odd given the first dice/die shows and odd number? g
Answers
The probability that the sum of the numbers on four dice rolled is odd given the first dice/die shows an odd number is 5/8.
To calculate the probability of the sum of the numbers on four dice rolled being odd given that the first dice/die shows an odd number, we can use conditional probability.
Let A be the event that the sum of the numbers on four dice rolled is odd, and let B be the event that the first dice/die shows an odd number.
To find P(A|B), the probability of A given B, we can use the formula:
P(A|B) = P(A and B) / P(B)
To calculate P(B), the probability of the first dice/die showing an odd number, we know that there are 3 possible outcomes out of 6 (1, 3, 5) that satisfy this condition. So P(B) = 3/6 = 1/2.
To calculate P(A and B), the probability of both events occurring, we can use the fact that the sum of two odd numbers is always even, and the sum of two even numbers is always even.
Therefore, the only way for the sum of four dice to be odd is if there are an odd number of odd numbers rolled. We can use the binomial distribution to calculate the probability of this occurring.
Let X be the number of odd numbers rolled in four dice. Then X follows a binomial distribution with parameters n=4 (the number of trials) and p=1/2 (the probability of rolling an odd number on each die). The probability of X being odd is:
P(X is odd) = P(X=1) + P(X=3) = (4 choose 1) * (1/2)^1 * (1/2)^3 + (4 choose 3) * (1/2)^3 * (1/2)^1 = 1/4 + 4/16 = 5/16
Therefore, P(A and B) = P(X is odd) = 5/16.
Putting it all together, we have:
P(A|B) = P(A and B) / P(B) = (5/16) / (1/2) = 5/8
So, the probability that the sum of the numbers on four dice rolled is odd given the first dice/die shows an odd number is 5/8.
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Find the slope of the line y= -5x -1
Answers
Answer:
-5
Step-by-step explanation:
y=mx+b is the slope intercept formula.
m is the slope.
Answer:
slope = - 5
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 5x - 1 ← is in slope- intercept form
with slope m = - 5
14. A baby weighed 7 lb 3 oz at birth. Four months later, the baby
weighed 13 lb 5 oz. Find the percent of increase in the baby's
weight. Round to the nearest tenth
Answers
Answer:
I'm an island boii ️️
4-Fui al supermercado y había un descuento del 15% en el total de la compra, si pagaba en efectivo. Gasté $ 2.400. ¿Qué cantidad aboné en realidad?
Answers
Answer:
$2.040
Step-by-step explanation:
Para calcular la cantidad que fue abonada en realidad, debes encontrar el valor del descuento calculando el 15% del valor total de la compra y este resultado se debe restar del total:
$2.400*15%= $360
$2.400-$360= $2.040
De acuerdo a esto, la cantidad abonada en realidad es: $2.040.
are 46 and 105 relatively prime
Answers
Answer:
They are relatively prime.
Step-by-step explanation:
The prime factorization of 46 is 23 * 2, and the prime factorization of 105 is
3 * 7 * 5. Since there are no common factors, they are relatively prime.
There is no common prime number. Then the numbers 46 and 105 will be relatively prime.
What is relatively prime?When two quantities have just one similar, or if there is no additional value with the same quantity as one, you cannot divide them both and obtain zero as the remainder, two numbers are considered to be relatively prime.
The numbers are 46 and 105.
Then the factor of the number 46 will be
46 = 2 × 23
Then the factor of the number 105 will be
105 = 3 × 5 × 7
There is no common prime number. Then the numbers 46 and 105 will be relatively prime.
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write 10 rational numbers between -1/3 and 1/3
Answers
Step-by-step explanation:
-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4
Determine the average and rms values for the function y(t)=25+10sin6πt over the time periods (a) 0 to 0.1 s, (b) 0.4 to 0.5 s, (c) 0 to 1/3 s, and (d) 0 to 20 s. Comment on the nature and meaning of the results in terms of analysis of dynamic signals.|
Answers
Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. When the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.
Average and rms values for the function y(t)=25+10sin6πt over the time periods (a) 0 to 0.1 s, (b) 0.4 to 0.5 s, (c) 0 to 1/3 s, and (d) 0 to 20 s are as follows:
a) For t=0 to t=0.1s:
Average value, y_avg = 25
RMS value, y_RMS = 25.1987
Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.
b) For t=0.4 to t=0.5s:
Average value, y_avg = 25
RMS value, y_RMS = 28.2843
Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.
c) For t=0 to t=1/3 s:
Average value, y_avg = 25
RMS value, y_RMS = 23.7176
Comment: RMS value is less than the average value. This means that the signal has a lesser amount of high-frequency content. It can be inferred that the function y(t) oscillates slowly.
d) For t=0 to t=20 s:
Average value, y_avg = 25
RMS value, y_RMS = 25
Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. Comment on the nature and meaning of the results in terms of analysis of dynamic signals.The results indicate that the function y(t) oscillates rapidly at the start and end of the time period and slowly in the middle. When the RMS value is greater than the average value, it means that the signal has a considerable amount of high-frequency content.
On the other hand, when the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.
Furthermore, if the RMS value is equal to the average value, it means that the signal does not have any high-frequency content.
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Example A marksman takes 10 shots at a target and has probability 0.2 of hitting the target with each shot, independently of all other shots. Let X be the number of hits. (a) Calculate and sketch the PMF of X (b) Whai is the probabillity of scoring no hits? (c) What is the probability of scoring more hits than misses? (d) Find the expectation and the variance of X. (e) Suppose the marksman has to pay $3 to enter the shooting range and he gets $2 for each hit. Let Y be his profit. Find the expectation and the variance of Y (f) Now let's assume that the marksman enters the shooting range for free and gets the number of dollars that is equal to the square of the number of hits. let Z be his profit. Find the expectation of Z
Answers
a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
b) The probability of scoring no hits is the probability of X being 0.
c) The probability of scoring more hits than misses is the probability of X being greater than 5
d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).
e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3
The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)
f) The expectation of Z: E(Z) = E(X²)
What is probability?
Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.
(a) To calculate the Probability Mass Function (PMF) of X, we can use the binomial distribution formula. Since the marksman takes 10 shots independently with a probability of 0.2 of hitting the target, the PMF of X follows a binomial distribution with parameters n = 10 (number of trials) and p = 0.2 (probability of success):
PMF of \(X(x) = C(n, x) * p^x * (1 - p)^{(n - x)}\)
Where C(n, x) represents the number of combinations or "n choose x."
Let's calculate the PMF for each value of X from 0 to 10:
PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰
PMF of X(1) = C(10, 1) * (0.2)¹ * (0.8)⁹
PMF of X(2) = C(10, 2) * (0.2)² * (0.8)⁸
...
PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
(b) The probability of scoring no hits is the probability of X being 0. So we calculate PMF of X(0):
PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰
(c) The probability of scoring more hits than misses is the probability of X being greater than 5. We need to calculate the sum of PMF of X from X = 6 to X = 10:
PMF of X(6) + PMF of X(7) + PMF of X(8) + PMF of X(9) + PMF of X(10)
(d) The expectation (mean) of X can be found using the formula:
E(X) = n * p
where n is the number of trials and p is the probability of success. In this case, E(X) = 10 * 0.2.
The variance of X can be calculated using the formula:
Var(X) = n * p * (1 - p)
In this case, Var(X) = 10 * 0.2 * (1 - 0.2).
(e) To calculate the expectation and variance of Y, we need to consider the profit from each hit. Each hit earns $2, and since X represents the number of hits, Y can be calculated as:
Y = 2X - 3
The expectation of Y can be calculated as:
E(Y) = E(2X - 3) = 2E(X) - 3
To calculate the variance of Y, we can use the property Var(aX + b) = a²Var(X) when a and b are constants:
Var(Y) = Var(2X - 3) = 4Var(X)
(f) Similarly, for Z, each hit earns a dollar amount equal to the square of the number of hits:
Z = X²
The expectation of Z can be calculated as:
E(Z) = E(X²)
Hence, a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
b) The probability of scoring no hits is the probability of X being 0.
c) The probability of scoring more hits than misses is the probability of X being greater than 5
d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).
e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3
The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)
f) The expectation of Z: E(Z) = E(X²)
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a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
b) The probability of scoring no hits is the probability of X being 0.
c) The probability of scoring more hits than misses is the probability of X being greater than 5
d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).
e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3
The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)
f) The expectation of Z: E(Z) = E(X²)
What is probability?
Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.
(a) To calculate the Probability Mass Function (PMF) of X, we can use the binomial distribution formula. Since the marksman takes 10 shots independently with a probability of 0.2 of hitting the target, the PMF of X follows a binomial distribution with parameters n = 10 (number of trials) and p = 0.2 (probability of success):
PMF of
Where C(n, x) represents the number of combinations or "n choose x."
Let's calculate the PMF for each value of X from 0 to 10:
PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰
PMF of X(1) = C(10, 1) * (0.2)¹ * (0.8)⁹
PMF of X(2) = C(10, 2) * (0.2)² * (0.8)⁸
......
PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
(b) The probability of scoring no hits is the probability of X being 0. So we calculate PMF of X(0):
PMF of X(0) = C(10, 0) * (0.2)⁰ * (0.8)¹⁰
(c) The probability of scoring more hits than misses is the probability of X being greater than 5. We need to calculate the sum of PMF of X from X = 6 to X = 10:
PMF of X(6) + PMF of X(7) + PMF of X(8) + PMF of X(9) + PMF of X(10)
(d) The expectation (mean) of X can be found using the formula:
E(X) = n * p
where n is the number of trials and p is the probability of success. In this case, E(X) = 10 * 0.2.
The variance of X can be calculated using the formula:
Var(X) = n * p * (1 - p)
In this case, Var(X) = 10 * 0.2 * (1 - 0.2).
(e) To calculate the expectation and variance of Y, we need to consider the profit from each hit. Each hit earns $2, and since X represents the number of hits, Y can be calculated as:
Y = 2X - 3
The expectation of Y can be calculated as:
E(Y) = E(2X - 3) = 2E(X) - 3
To calculate the variance of Y, we can use the property Var(aX + b) = a²Var(X) when a and b are constants:
Var(Y) = Var(2X - 3) = 4Var(X)
(f) Similarly, for Z, each hit earns a dollar amount equal to the square of the number of hits:
Z = X²
The expectation of Z can be calculated as:
E(Z) = E(X²)
Hence, a) PMF of X(10) = C(10, 10) * (0.2)¹⁰ * (0.8)⁰
b) The probability of scoring no hits is the probability of X being 0.
c) The probability of scoring more hits than misses is the probability of X being greater than 5
d) E(X) = 10 * 0.2 and Var(X) = 10 * 0.2 * (1 - 0.2).
e) The expectation of Y: E(Y) = E(2X - 3) = 2E(X) - 3
The variance of Y: Var(Y) = Var(2X - 3) = 4Var(X)
f) The expectation of Z: E(Z) = E(X²)
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how long is each side of a square with a perimeter of 12.32 centimeters
Answers
Step-by-step explanation:
Let each side of square be x
So, x+x+x+x = 12.32
4x = 12.32
x = 12.32/4
x = 3.02 cm
What is the distance between points A and B?
A
B
-87-6 5 4 3 -2 -1
0
-
3
2
-
5
4
+
7
6
8
- 6 units
-1 units
O 5 units
6 units
Answers
Answer:
6 units
Step-by-step explanation:
Just count
The distance between points A and B is 6 units.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
The process of subtraction can also be termed as finding difference.
In geometry, Distance between two points will be always a positive number.
Distance will be 0, if the points coincide.
Here on a number line, A is marked at -5 and B at 1.
We have to find the distance between A and B.
Distance between A and B = 1 - -5 = 1 + 5 = 6 units
Hence distance between A and B is 6 units.
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In January Mr Patel's electricity meter reading is 36 517. During the next three months he uses 1 084 units of electricity. a) What is the reading on his meter at the end of these three months? b) In Janurary Mr Patel'a gas meter reading is 51 314. Three months later it is 51 809. How many units of gas has he used? c) Electricity costs 12 pence per unit. Gas costs 8.6 pence per unit. Work out the total cost of Mr Patel's gas and electricity for these three months. Give your answer in pounds.
Answers
Answer: 172.65 pound
Step-by-step explanation:
a. What is the reading on his meter at the end of these three months?
January's electricity meter reading = 36,517.
Electricity used for next three months = 1 084 units
Meter reading at the end of the three months will be:
= 36517 + 1084
= 37601
b. In Janurary Mr Patel'a gas meter reading is 51 314. Three months later it is 51 809. How many units of gas has he used?
This will be:
= 51,809 - 51,314
= 495 units
c. Electricity costs 12 pence per unit. Gas costs 8.6 pence per unit. Work out the total cost of Mr Patel's gas and electricity for these three months.
Electricity used for next three months = 1 084 units
Gas used for next three months
= 495 units
Cost = (1084 × 12pence) + (495 × 8.6 pence)
= 13008 pence + 4257 pence
= 17265 pence = 172.65 pound
5. The grocery store is having a sale on frozen vegetables. 4 bags are
being sold for$12. At this rate,what is the cost of:
a. 1 bag
b. 9 bags
Answers
Write a function rule for “The output is 3 less than the input.” Let x be the input and let y be the output.
Answers
Answer:
The function rule is y=x-3
Step-by-step explanation:
I hope this helps!!
Half the difference between two numbers is 2. The sum of the
greater number and twice the smaller number is 13. Find the
numbers.
Answers
Answer:
as below
Step-by-step explanation:
1st the difference is 4 b/c half of 4 = 2
and
2*smaller +greater = 13
so check out small number that are 4 apart.. like 2 and 6
2(2)+6 =10
2(3) +7 = 13 aahh hah.. that's it
3 and 7 are the numbers being hunted :P
17. A rectangular prism has a length of 12 cm, a
height of 6/cm, and a width of 4 cm. Use the
formula SA = 2({w) + 2(wh) +2(ehy to find the
surface area of the rectangular prism.
Answers
Answer:
SA = 288 cm
Step-by-step explanation:
l = 12
w = 4
h = 6
SA = 2lw + 2wh + 2lh
SA = (2 x 12 x 4) + (2 x 4 x 6) + (2 x 12 x 6)
SA = 96 + 48 + 144
SA = 288
HELP ME WITH THIS PROBLEM
Answers
x=5 that's my final answer because 2(8)=4x-4