Answers
1. The characters in "The Town Mouse and the Country Mouse" are two mice who are cousins. The town mouse is described as elegant, refined, and sophisticated, while the country mouse is simple and unsophisticated.
2. The main idea of the story is that one should be content with their simple life rather than crave for a luxurious life full of dangers and uncertainties.
What is The Town Mouse and The Country Mouse?"The Town Mouse and the Country Mouse" is a fable, a short story that teaches a moral or lesson. It tells the story of two cousins, a town mouse and a country mouse, who visit each other's homes and experience each other's way of life. The town mouse lives in luxury and eats rich food, but is always in danger from the cat, while the country mouse lives a simple life but is safe and content.
3. The sequence of events in the story is as follows:
The country mouse invites the town mouse to visit him in the countryside.The town mouse accepts the invitation and visits the country mouse.The country mouse serves the town mouse simple food, which the town mouse finds unappetizing.The town mouse invites the country mouse to visit him in the town.The country mouse accepts the invitation and visits the town.The town mouse serves the country mouse luxurious food, but they both get scared and run away when the cat appears.The country mouse returns to his simple life, realizing that it's better to be safe and content than to live in luxury but in constant danger.4. Important details in the story include the description of the town and country mice, the differences in their lifestyles, and their reactions to each other's homes. These details are important because they emphasize the theme of the story, which is that it's better to be content with one's simple life than to crave for a luxurious but dangerous life.
5. I think "The Town Mouse and the Country Mouse" is a great story because it teaches an important lesson in a fun and engaging way. The characters are well-developed, and the plot is entertaining, making it easy for readers to understand the message.
6. One question I have about the writing is whether the author intended the story to be a commentary on social class and wealth.
7. A fable is a short story that teaches a moral or lesson. Fables usually feature animals or other non-human characters that can talk and behave like humans.
8. The moral of "The Town Mouse and the Country Mouse" is that it's better to be content with a simple life than to crave for luxury and danger. The story shows that the country mouse is happier and safer in his simple life than the town mouse, who is always in danger despite his luxurious lifestyle. This lesson teaches readers to be satisfied with what they have rather than always craving for more.
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town mouse and country mouse are cousins, the town mouse is working hard, (keep up the good work bud,) and the city mouse is relaxing, one day, town mouse was invited to city mouse’s city, they were relaxing, and then, a dog almost killed the mouses.
Related Questions
An automatic machine in a manufacturing process is operating groperly if the iengths of an important subcomponent are normally distributed with a mean of izal cri and a otandard deviation of 5.6 cm. A. Find the probability that one selected subcomponent is longer than 122 cm, Probability = B3. Find the probability that if 3 subcomponents are randomly selected, their mean length exceeds 122 cm. Probability win C. Find the probabilify that if 3 are randomly selected, ail 3 have lengths that exceed 122 cm. Probability =
Answers
A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.
z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)
Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.
B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.
The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.
Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm
Now we can calculate the z-score for a mean length of 122 cm:
z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)
Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.
C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.
Probability = (0.9999)^3 ≈ 0.9997
Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.
Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.
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Which ordered pairs are in the solution set of system of linear inequalities?
A:(5,-2),(3,1),(-4,2)
B:(5,-2),(3,-1),(4,-3)
C:(5,-2),(3,1),(4,2)
D:(5,-2),(-3,1),(4,2)
Answers
Answer:
Option (3)
Step-by-step explanation:
There are two inequalities graphed in the figure attached.
1). Solid line having shaded above the solid line (passing through origin) will be represented by the equation,
\(y\geq -\frac{1}{2}x\)
2). Another dotted line having shaded area below the line will be represented by the inequality,
\(y<\frac{1}{2}x+1\)
Common shaded area of these inequalities will be the solution area.
All the ordered pairs lying in this area will be the answer.
In the given options,
Ordered pairs given in Option (3) lie in the common shaded area.
Answer:
C
Step-by-step explanation:
got it right
A box of cereal contains 10 cups. If each bowl holds 1 1/4 cups of cereal, how many bowls of cereal will you get out of the box?
Answers
Answer:
8
Step-by-step explanation:
Answer: 8
Step-by-step explanation: 10 / 1.25 = 8
A standard showerhead in Marty's house dispenses 7 gallons of water per minute. Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y = 3x How much water does Marty save each day with the change in showerheads if he uses the shower for 8 minutes each day? 4 gallons 12 gallons 32 gallons 53 gallons
Answers
Answer:
32 gallons
Step-by-step explanation:
A standard showerhead in Marty's house dispenses 7 gallons of water per minute. If he showers for 8 minutes, he uses:
1 minute = 7 gallons
8 minutes = x
x = 7 × 8 minutes = 56 gallons of water
We are told that:
Marty changed this showerhead to an energy-saving one. The equation shows the amount of water dispensed, y, as a function of the number of minutes, x, for the new showerhead. y = 3x
The equation for the energy saving shower:
y = 3x
Where x is the number of minutes spent in the shower
For 8 minutes
y = 3 × 8
y = 24 gallons
The gallons of water Marty saved each day with the change in showerheads if he uses the shower for 8 minutes each day is calculated as:
56 gallons - 24 gallons
= 32 gallons
Find the indefinite integral. (Use C for the constant of integration.) sin^4 (5θ) dθ
Answers
The indefinite integral of sin^4(5θ) dθ is (1/4)[θ - sin(10θ)/5 + (θ/2) + (1/40)sin(20θ)] + C.
An indefinite integral is the reverse operation of differentiation. Given a function f(x), its indefinite integral is another function F(x) such that the derivative of F(x) with respect to x is equal to f(x), that is:
F'(x) = f(x)
The symbol used to denote the indefinite integral of a function f(x) is ∫ f(x) dx. The integral sign ∫ represents the process of integration, and dx indicates the variable of integration. The resulting function F(x) is also called the antiderivative or primitive of f(x), and it is only unique up to a constant of integration. Therefore, we write:
∫ f(x) dx = F(x) + C
where C is an arbitrary constant of integration. Note that the indefinite integral does not have upper and lower limits of integration, unlike the definite integral.
We can use the identity \(sin^2(x)\) = (1/2)(1 - cos(2x)) to simplify the integrand:
\(sin^4\)(5θ) = (\(sin^2\)(5θ)\()^2\)
= [(1/2)(1 - cos(10θ))\(]^2\) (using \(sin^2\)(x) = (1/2)(1 - cos(2x)))
= (1/4)(1 - 2cos(10θ) +\(cos^2\)(10θ))
Expanding the square and integrating each term separately, we get:
∫ \(sin^4\)(5θ) dθ = (1/4)∫ (1 - 2cos(10θ) + \(cos^2\)(10θ)) dθ
= (1/4)[θ - sin(10θ)/5 + (1/2)∫ (1 + cos(20θ)) dθ] + C
= (1/4)[θ - sin(10θ)/5 + (θ/2) + (1/40)sin(20θ)] + C
Therefore, the indefinite integral of sin^4(5θ) dθ is (1/4)[θ - sin(10θ)/5 + (θ/2) + (1/40)sin(20θ)] + C.
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To indirectly measure the distance across a river, Madeline stands on one side of the river and uses sight-lines to a landmark on the opposite bank. Madeline draws the diagram below to show the lengths and angles that she measured. Find PRPR, the distance across the river. Round your answer to the nearest foot.it was 5.94 seconds(time at max)
Answers
The distance across the river, PR, is approximately 243 feet, rounded to the nearest foot, based on the diagram provided by Madeline and using trigonometry to calculate the length of PR.
To determine the length of PR, we can use the trigonometric relationship of tangent, which is the ratio of the opposite side to the adjacent side of a right triangle. In this case, we have a right triangle with angle QPR as the right angle, PQ as the opposite side, and QR as the adjacent side. Using the tangent of angle QPR, we can calculate the length of PR as follows:
tan(QPR) = PQ/QR
tan(57) = 110/QR
QR = 110/tan(57)
QR ≈ 146.77 feet
Next, we can use the trigonometric relationship of sine, which is the ratio of the opposite side to the hypotenuse of a right triangle, to find the length of PR. In this case, we have a right triangle with angle RQP as the right angle, PQ as the opposite side, and PR as the hypotenuse. Using the sine of angle RQP, we can calculate the length of PR as follows:
sin(RQP) = PQ/PR
sin(33) = 110/PR
PR = 110/sin(33)
PR ≈ 242.69 feet
Rounding to the nearest foot, we get PR ≈ 243 feet as the distance across the river.
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The distance across the river, PR, is approximately 243 feet, rounded to the nearest foot, based on the diagram provided by Madeline and using trigonometry to calculate the length of PR.
To determine the length of PR, we can use the trigonometric relationship of tangent, which is the ratio of the opposite side to the adjacent side of a right triangle. In this case, we have a right triangle with angle QPR as the right angle, PQ as the opposite side, and QR as the adjacent side. Using the tangent of angle QPR, we can calculate the length of PR as follows:
tan(QPR) = PQ/QR
tan(57) = 110/QR
QR = 110/tan(57)
QR ≈ 146.77 feet
Next, we can use the trigonometric relationship of sine, which is the ratio of the opposite side to the hypotenuse of a right triangle, to find the length of PR. In this case, we have a right triangle with angle RQP as the right angle, PQ as the opposite side, and PR as the hypotenuse. Using the sine of angle RQP, we can calculate the length of PR as follows:
sin(RQP) = PQ/PR
sin(33) = 110/PR
PR = 110/sin(33)
PR ≈ 242.69 feet
Rounding to the nearest foot, we get PR ≈ 243 feet as the distance across the river.
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???????????????????????
Answers
Answer:
0.040 "<" 0.207
Step-by-step explanation:
0.040
0.207
We can see that there is a 2 in 0.207 in the tenths spot, which automatically makes it larger than 0.040.
Write an inequality using the "<" sign:
0.040 < 0.207.
Hope this helps!
A _ is an assignment of probabilities to each distinct value of a discrete random variable or to each interval of values of a continuous random variable. random variable binomial experiment probability distribution binomial probability distribution
Answers
A probability distribution is an assignment of probabilities to each distinct value of a discrete random variable or to each interval of values of a continuous random variable.
A probability distribution is a mathematical function that assigns probabilities to all possible outcomes of a random variable. It describes the likelihood of each possible value or range of values occurring.
For a discrete random variable, which takes on distinct values, the probability distribution assigns probabilities to each possible value. It specifies the probability of observing each value of the random variable.
For a continuous random variable, which takes on a range of values, the probability distribution assigns probabilities to intervals or ranges of values. Since there are infinitely many possible values within a range, the probability of observing a specific value is usually zero. Instead, the probability distribution provides probabilities for intervals of values, indicating the likelihood of the random variable falling within those intervals.
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Candy icing for the trim around a cookie cost $7.50 for 6 ft. How much wouldyou pay for 25 feet of icing at this rate?
Answers
The icing costs $7.50 every 6 feet
To calculate how much will 25 feet of icing cost, you can use cross multiplication
6feet_____$7.50
25feet____$x
\(\begin{gathered} \frac{7.50}{6}=\frac{x}{25} \\ x=(\frac{7.50}{6})\cdot25 \\ x=31.25 \end{gathered}\)25 feet of icing costs $31.25
libgen extending the linear model with r : generalized linear, mixed effects and nonparametric regression models, second edition
Answers
This book provides a comprehensive guide to extending the linear model in R, allowing for more flexible and powerful analyses.The book "libgen extending the linear model with r: generalized linear, mixed effects and nonparametric regression models, second edition" explores different ways to expand the linear model in R. It covers three main topics: generalized linear models, mixed effects models, and nonparametric regression models.
Generalized linear models (GLMs) are an extension of the linear model that allows for different types of response variables, such as binary or count data. GLMs use a link function to relate the linear predictor to the response variable.
Mixed effects models combine fixed effects (predictors that are constant across all subjects) and random effects (predictors that vary across subjects) to model hierarchical or clustered data. They are useful when there is a nested or hierarchical structure in the data.
Nonparametric regression models do not assume a specific functional form for the relationship between predictors and the response variable. Instead, they estimate the relationship from the data without making assumptions about the underlying distribution.
Overall, this book provides a comprehensive guide to extending the linear model in R, allowing for more flexible and powerful analyses.
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27/2 divided by 9 what is the answer
Answers
Answer:
1.5
Step-by-step explanation:
I'm thinking of a even number 1 to 29. What is the probability that you will guess it
Answers
Answer:14/29
Step-by-step explanation:
There are 14 even numbers and there are 29 numbers.
So it would equal 14/29
Which polynomial function has zeros at -3, 0, and 4?
f(x) = (x + 3)(x2 + 4)
f(x) = (x2 - 3)(x - 4)
f(x) = x(x + 3)(x - 4)
f(x) = x(x - 3)(x + 4)
Answers
Answer:
If 5 is zero then (x - 5) is a factor.
Only 4. has this factor.
Step-by-step explanation:
1. It's either B or D
Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $0.42.
A. c(p) = p + 0.42
B. c(p) = 42p
C. c(p) = p/0.42
D. c(p) = 0.42p
Answers
Answer:
D. c(p) = 0.42p
Step-by-step explanation:
total cost = .42(P)
Example: 5 lbs
$2.10 = $.42(5)
c(p) = 0.42p <== ur function
Since a pound of sugar increases proportionally to the total cost of sugar bought, then the function can be written as:
c(p) = 0.42p
Where: c(p) = total cost of sugar bought
p = pounds of sugar
c(p) is a function of p, because c(p) depends on p.
Answer: The function rule that gives the total cost is given by
Step-by-step explanation:
Let the number of pounds of sugar be 'p'.
Let the total cost would be C(p).
Cost of each pound = $0.42
So, the function rule would be
Hence, the function rule that gives the total cost is given by
Write an expression for 88 added to v
Answers
Answer:
\(\mathrm{88 + v}\)
What is 8397 divided by 27 in partial quotients?
Answers
Answer:
8397 divided by 27 in partial quotients is 311
Step-by-step explanation:
Decide if each statement below is true or false. "Explain how you know". please help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! :(
a. -19+7=-7+19
b. 4/5 · 1=4/5
c. 3/2 ·2/3=1
d. 5·7-5 · 1/5=34
Answers
Therefore , the solution of the given problem of expression comes out to be the multiplication is done first using the sequence of operations: 57=35 and 51/5=1. 35 is then reduced by 1 to yield 34.
Define expression.Mathematical processes such as multiplying, dividing, adding, and even deleting are necessary. If they were combined, the following statement would result: An equation, some statistics, and a mathematical formula Values, components, and mathematical processes like additions, subtractions, algebraic expressions, and divisions make up a statement of truth. Words and sentences can be analysed and ranked.
Here,
a. Accurate. The commutative property of addition says that the sum remains constant regardless of the addends' order. As a result, -19+7 is equivalent to 7-19, which is equivalent to -12+19.
b. True. Any integer is itself when multiplied by 1. As a result, 4/5 + 1 equals 4/5.
c. Accurate. One is obtained by multiplying two reciprocals. As a result, 3/2 2/3 equals 32 23, which is reduced to 1.
d. Correct. The multiplication is done first using the sequence of operations: 57=35 and 51/5=1. 35 is then reduced by 1 to yield 34.
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hi help and you get 100 points
Answers
I know all but 14. and 14. but number 10. is -1.89 11. is 1.86 and 12. is 6.24.
Answer:
Okay so 2+2 = 4
Step-by-step explanation: 349609658959603589657045863408w8024306835+1=349609658959603589657045863408w8024306836
If i toss a fair coin five times and the outcomes are ttttt, then the probability that tails appears on the next toss is.
Answers
The probability that tails appears on the next toss is 0.5
Given,
In the question:
If I toss a fair coin five times and the outcomes are TTTTT,
To find the probability that tails appears on the next toss is.
Now, According to the question:
The possible ordered outcomes are listed as elements in a sample space, which is commonly indicated using set notation.
A sequence of five fair coin flips has a sample space that contains all potential outcomes. \(2^3\) {H, T} is the sample of a fair coin toss. {HHHHH, HHHHT, HHHTH, HHTHH, HTHHH,...…TTTTT} .
The probability of a tails result on the next flip is always equal to 0.5 It makes no difference if previous outcomes were {TTTTT} , {HHHHH} or {THTHT} In each of these and all other circumstances, the probability of the next being tails is still 0.5
Hence, the probability that tails appears on the next toss is 0.5
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Pre Calc question, thanks for the help! Question linked in photo below.
Answers
The valid solution for the positive demand is (6,3)
How to determine the valid solutions?The equation of the function is given as:
\(C(t) = -\sqrt{t^2 - 4t - 12} + 3\)
Next, we test the options::
Option (a): (t, C(t)) = (2,3)
This gives
\(-\sqrt{2^2 - 4*2 - 12} + 3 = 3\)
Evaluate the radicand
\(-\sqrt{-16} + 3 = 3\) ---- this is not true (square root of -16 is a complex number)
Option (b): (t, C(t)) = (6,3)
This gives
\(-\sqrt{6^2 - 4*6 - 12} + 3 = 3\)
Evaluate the radicand
\(-\sqrt{0} + 3 = 3\)
Evaluate the root
0 + 3 = 3
Evaluate the sum
3 = 3 ---- this is true
Hence, the valid solution for the positive demand is (6,3)
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help asap if you can pls!!!!!
Answers
Answer:
SAS, because vertical angles are congruent.
Which function rule would help you find the values in the table n=2,4,6 m=-6,-12,-18
Answers
In the given table, we have values for two variables: n and m.
For n, we have the values 2, 4, and 6.
For m, we have the corresponding values -6, -12, and -18.
To find the relationship between n and m, we can observe the pattern in how the values change.
When we increase n by 2 from 2 to 4, the corresponding value of m decreases by 6 from -6 to -12. Similarly, when we increase n by 2 from 4 to 6, the corresponding value of m decreases by 6 from -12 to -18.
This pattern suggests that there is a linear relationship between n and m, where the value of m decreases by 6 units for every increase of 2 units in n.
In terms of a function rule, we can express this relationship as:
m = -6n
This means that the value of m can be determined by multiplying the value of n by -6. The negative sign indicates that as n increases, m decreases.
So, for any value of n, if we substitute it into the function rule m = -6n, we can find the corresponding value of m.
For example:
When n = 2, m = -6(2) = -12
When n = 4, m = -6(4) = -24
When n = 6, m = -6(6) = -36
Therefore, the function rule m = -6n describes the relationship between the values of n and m in the given table.
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Round 95.9153055893 to the nearest tenth
Answers
Answer:
100
Step-by-step explanation:
Use the Distributive property to write each expression as an equivalent algebraic expression.
7(-2x + 6)
Answers
Answer:
Step-by-step explanation:
we will use distributive property to write an equivalent expression:
7(-2x)+7(6)
PLEASE HELP DUE SOONNNNN SIMPLE ADVANCED MIDDLE SCHOOL MATH AKA FACTORING
Answers
Answer:
28. x(x+2)(x+5)
29. 2(2x+1)(x-2)
30. y(a+5)^2
Step-by-step explanation:
30. y(a+5)(a+5)
The equation of a rational function does not have to contain a expression.O A. True O B. False
Answers
Answer: B = False
Step-by-step explanation: Doesn't need one mainly because a rational function has an equation and no expression, most rational functions may have one. For example 2x + 7 x + 5x = ???
What is the equation of the line that contains the point (-1, 4) and has a slope of 3?
Answers
Suppose that X is a random variable with mean 20 and standard deviation 4. Also suppose that Y is a random variable with mean 40 and standard deviation 7. Find the mean and the variance of the random variable Z for each of the following cases. Be sure to show your work.
(a) Z = 40 - 5X
(b) Z = 15X - 20
(c) Z = X + Y
(d) Z = X - Y
(e) Z = -2X + 3Y
Answers
(a) The mean of Z in case (a) is -60 and the variance is 400.
(b) The mean of Z in case (b) is 280 and the variance is 3600.
(c) The mean of Z in case (c) is 60 and the variance is 65.
(d) The mean of Z in case (d) is -20 and the variance is 65.
(e) The mean of Z in case (e) is 80 and the variance is 505.
To find the mean and variance of the random variable Z for each case, we can use the properties of means and variances.
(a) Z = 40 - 5X
Mean of Z:
E(Z) = E(40 - 5X) = 40 - 5E(X) = 40 - 5 * 20 = 40 - 100 = -60
Variance of Z:
Var(Z) = Var(40 - 5X) = Var(-5X) = (-5)² * Var(X) = 25 * Var(X) = 25 * (4)² = 25 * 16 = 400
Therefore, the mean of Z in case (a) is -60 and the variance is 400.
(b) Z = 15X - 20
Mean of Z:
E(Z) = E(15X - 20) = 15E(X) - 20 = 15 * 20 - 20 = 300 - 20 = 280
Variance of Z:
Var(Z) = Var(15X - 20) = Var(15X) = (15)² * Var(X) = 225 * Var(X) = 225 * (4)² = 225 * 16 = 3600
Therefore, the mean of Z in case (b) is 280 and the variance is 3600.
(c) Z = X + Y
Mean of Z:
E(Z) = E(X + Y) = E(X) + E(Y) = 20 + 40 = 60
Variance of Z:
Var(Z) = Var(X + Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65
Therefore, the mean of Z in case (c) is 60 and the variance is 65.
(d) Z = X - Y
Mean of Z:
E(Z) = E(X - Y) = E(X) - E(Y) = 20 - 40 = -20
Variance of Z:
Var(Z) = Var(X - Y) = Var(X) + Var(Y) = (4)² + (7)² = 16 + 49 = 65
Therefore, the mean of Z in case (d) is -20 and the variance is 65.
(e) Z = -2X + 3Y
Mean of Z:
E(Z) = E(-2X + 3Y) = -2E(X) + 3E(Y) = -2 * 20 + 3 * 40 = -40 + 120 = 80
Variance of Z:
Var(Z) = Var(-2X + 3Y) = (-2)² * Var(X) + (3)² * Var(Y) = 4 * 16 + 9 * 49 = 64 + 441 = 505
Therefore, the mean of Z in case (e) is 80 and the variance is 505.
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a large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. use a 0.05 level og significance to test the claim that this sample comes from a population with a mean score greater than 160. use the P-value method of testing hypotheses.
Answers
Using the P-value method of testing hypotheses with a significance level of 0.05, the sample provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.
To test the claim that the mean score of job applicants from the university is greater than 160, we will perform a one-sample t-test using the P-value method. The null hypothesis (H0) assumes that the mean score is equal to 160, while the alternative hypothesis (Ha) assumes that the mean score is greater than 160.
First, we calculate the test statistic, which is the t-value. The formula for the t-value is:
t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))
Plugging in the given values, we have:
t = (183 - 160) / (12 / √(25))
= 23 / (12 / 5)
= 23 * (5 / 12)
≈ 9.58
Next, we find the P-value associated with the test statistic. The P-value represents the probability of obtaining a test statistic as extreme as the observed value, assuming the null hypothesis is true. Since the alternative hypothesis is one-sided (greater than 160), we calculate the P-value by finding the probability of the t-distribution with 24 degrees of freedom being greater than the calculated t-value.
Consulting statistical tables or using software, we find that the P-value is very small (less than 0.0001).
Since the P-value (less than 0.0001) is less than the significance level (0.05), we reject the null hypothesis. This provides strong evidence to support the claim that the mean score of job applicants from the university is greater than 160.
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State the equation of the graphed function.
Answers
The equation of the graphed function is given as follows:
f(x) = x³ + 2x² - 5x - 6.
How to obtain the equation of the function?
The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.
From the graph, the zeros of the function are:
x = -3.x = -1.x = 2.Hence the function is:
f(x) = a(x + 3)(x + 1)(x - 2).
In which a is the leading coefficient.
Expanding the product, we have that:
f(x) = a(x² + 4x + 3)(x - 2)
f(x) = a(x³ + 2x² - 5x - 6).
When x = 0, y = -6, hence the leading coefficient a is obtained as follows:
-6a = -6
a = 1.
Hence the function is:
f(x) = x³ + 2x² - 5x - 6.
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