.Exercise 1.1 1) Prove that if a b and ale, then a (b + c). [We have: baby, caci, and so b+c= a(b + c)./ 2) Suppose a, b, c eN such that a 0. Prove that ab ac if, and only if, ble. [() ab ac means that ac abd for some natural number d which, since a 0, is equivalent to cbd, that is, equivalent to be.] 3) Suppose a, b N such that b
Answers
To prove that if a ≤ b and a ≤ c, then a ≤ (b + c), we can use the transitive property of inequalities. Therefore, we have shown that ab = ac if and only if b = c.
Given: a ≤ b and a ≤ c
Since a ≤ b, we can write b = a + (b - a), where (b - a) is a non-negative number.
Similarly, since a ≤ c, we can write c = a + (c - a), where (c - a) is also a non-negative number.
Adding these two equations, we get:
b + c = (a + (b - a)) + (a + (c - a))
Simplifying, we have:
b + c = 2a + (b - a) + (c - a)
Since (b - a) and (c - a) are non-negative, their sum is also non-negative. Therefore, we have:
b + c ≥ 2a
And by rearranging the inequality, we get:
2a ≤ b + c
Since a is less than or equal to b + c, we can conclude that a ≤ (b + c).
2) To prove that ab = ac if and only if b = c, we can use the cancellation law of multiplication.
Assume ab = ac. Since a ≠ 0, we can divide both sides of the equation by a:
ab/a = ac/a
Simplifying, we have:
b = c
This shows that if ab = ac, then b = c.
Now, assume b = c. We can multiply both sides of the equation by a:
ab = ac
This shows that if b = c, then ab = ac.
Therefore, we have shown that ab = ac if and only if b = c.
3) The statement in exercise 1.1 seems to be incomplete. Please provide the complete statement or clarify the question.
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Related Questions
Please help me find the surface of the cylinder (no links please)
Answers
Answer:
A=10178.76
Step-by-step explanation:
2 x π x 30 x 24 + 2 x π x 30² = 10178.7602
= 10178.76
Question: What is the slope of the equation: x + 2y = 6
Answers:
m= -1/2
m=3
m= 1/3
if you don't know please don't Guess :(
Answers
x+2y=6
2y=-x+6
y=-1/2x+6
y=mx+b
m is slope
9/2 ÷ 3/4
Please help me
Answers
block 1 is resting on the floor with block 2 at rest on top of it. block 3, at rest on a smooth table with negligible friction, is attached to block 2 by a string that passes over a pulley, as shown above. the string and pulley have negligible mass.
Answers
The tension in the string connecting blocks 2 and 3 depends on the masses of the blocks and the acceleration of the system.
The tension in the string is determined by the net force acting on block 2. Since block 3 is on a smooth table with negligible friction, the only horizontal force acting on block 2 is the tension in the string. According to Newton's second law, the net force on an object is equal to the mass of the object multiplied by its acceleration. In this case, the acceleration of the system is determined by the weight of block 2 and block 3 and the force of static friction between block 1 and the floor. By considering the forces acting on block 2, we can set up an equation using the relationship between tension and the mass and acceleration of block 2 to solve for the tension in the string.
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"What is the significance of the invention of the printing press in the 15th century, and how did it impact the spread of knowledge and information during that time?"
Question 13
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Question text
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Bob Nale is the owner of Nale's Quick Fill. Bob would like to
estimate the mean number of gallons of gasoline sold to his
Answers
Conduct hypothesis tests or construct confidence intervals to evaluate the statistical significance of the estimate.
To estimate the mean number of gallons of gasoline sold at Nale's Quick Fill, Bob can use statistical sampling techniques. Here are the steps he can follow:
Define the population: Determine the population of interest, which in this case is all the customers who purchase gasoline at Nale's Quick Fill.
Determine the sampling method: Choose an appropriate sampling method to select a representative sample from the population. Common methods include simple random sampling, stratified sampling, or systematic sampling. The choice of sampling method should depend on the characteristics of the population and the resources available.
Determine the sample size: Decide on the desired sample size. The sample size should be large enough to provide a reliable estimate of the population mean. It can be determined based on statistical considerations, such as the desired level of confidence and margin of error. Larger sample sizes generally provide more precise estimates.
Select the sample: Use the chosen sampling method to select a random sample of customers from the population. Every customer in the population should have an equal chance of being selected to ensure representativeness.
Collect data: Gather information on the number of gallons of gasoline sold to each customer in the sample. This data can be obtained from sales records or by directly surveying customers.
Calculate the sample mean: Calculate the mean number of gallons of gasoline sold in the sample by summing up the individual values and dividing by the sample size.
Estimate the population mean: The sample mean can be considered an estimate of the population mean. It provides an approximation of the average number of gallons of gasoline sold at Nale's Quick Fill.
Assess the reliability of the estimate: Consider the variability within the sample and the potential sources of bias. Calculate the standard error of the sample mean to determine the precision of the estimate. Additionally, conduct hypothesis tests or construct confidence intervals to evaluate the statistical significance of the estimate.
By following these steps and ensuring proper sampling techniques, Bob can estimate the mean number of gallons of gasoline sold at Nale's Quick Fill. This estimation can provide valuable insights for business planning and decision-making.
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____ 13. Use Scenario 3-2. If heart disease death rate were expressed as deaths per 1,000 people instead of as deaths
per 100,000 people, how would the correlation r between wine consumption and heart disease death rate
r would not change
Answers
The correlation between two variables is an important measure that helps us understand the relationship between them. In Scenario 3-2, if the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would not change the correlation (r) between wine consumption and heart disease death rate.
The correlation coefficient (r) measures the strength and direction of the relationship between two variables. If the heart disease death rate is expressed as deaths per 1,000 people instead of as deaths per 100,000 people, it would change the units in which the death rate is expressed, but it would not change the underlying relationship between wine consumption and heart disease death rate.
In other words, regardless of the units in which the death rate is expressed, the correlation between wine consumption and heart disease death rate would remain the same. This is because the correlation measures the relationship between two variables, not the units in which they are expressed. It is important to note that expressing the death rate in different units may make it easier or more difficult to understand the relationship between two variables, but it does not change the underlying correlation.
In conclusion, the correlation (r) between wine consumption and heart disease death rate would not change if the death rate were expressed as deaths per 1,000 people instead of as deaths per 100,000 people.
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you don't have to do all of them
Answers
Answer: lol your using canvas
1. 63
2. D
3. B
4. A
Sorry for the bland explinations havin a bad day.
Step-by-step explanation:
1. The way we solve this is by adding the degrees 72 and 45. then we subtract it by 180. this is because in all triangles the angles always add up to 180 degrees.
2. Like question one what set of angles measures to 180 degrees.
3. The sides of a triangle should define the angle measurements. you can also see if its a triangle if the numbers are continues like 3,4,5 or in this case 4,5,6
4. like in questions 1 and 2 the angles of a triangle has to equal 180 degrees so 60 times 3 is 180 so each angle would have to be 60 degrees.
For an assignment, Jorge needs to translate a figure on a coordinate plane. A vertex of the figure is at (-2,5). After translation, that vertex is at (4,-2), as shown in the diagram
below.
Which steps did Jorge use for the translation?
Answers
Answer: Im so sorry but I have not done this in such a long time
Step-by-step explanation: Have a good day
Which pair of angles are vertical angles? 6 and 5 2 and 3 1 and 3 5 and 8
Answers
Answer:
1 and 3
Step-by-step explanation:
1 and 3 are vertical angles
The cylinder shown has a lateral surface area of about 60sq in. Which answer is closest to the height of the cylinder? Use 3.14 to approximate pi
Answers
Answer:3.2 inch
Step-by-step explanation:
We have the following data:
Al (lateral surface area) = 80 in²
R (ratio) = 4 in
h (height) = ? (in inches)
Adopt : π ≈ 3.14
We apply the data to the formula, we have:
Answer:We have the following data:
Al (lateral surface area) = 80 in²
R (ratio) = 4 in
h (height) = ? (in inches)
Adopt : π ≈ 3.14
We apply the data to the formula, we have:
Answer:
≈ 3.2 inches
________________________
≈ 3.2 inches
________________________
Solve the following system of equations graphically on the set of axes below
Answers
The solution is the point where the two lines intersect i.e. (-1,-7). The graph for the given system of equations is attached below wherein the blue line represents y=2x-5 and the green line represents y=-x-8.
What is system of equation?
A set or group of equations that are solved collectively is referred to as a system of equations. Both algebraic and visual solutions are possible for these equations. The intersection of two lines represents the system of equations' solution.
For solving the equations graphically, we need to find points for plotting
So, for y = 2x-5,
The y-intercept is -5, so we need to place a point on the graph at (0,-5). For the another point, put x=1, we get y= -3. So we need to place another point at (1,-3).
Similarly for y = -x-8,
The y-intercept is -8, so we need to place a point on the graph at (0,-8). For the another point, put x=1, we get y= -9. So we need to place another point at (1,-9).
The solution is the point where the two lines intersect.
When the two lines intersect,
2x-5=-x-8
3x=-3
x=-1
So, y=-7
Hence, the two lines intersect at (-1,-7).
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Your favorite team jersey is on sale for $32 this is a 36% discount what was the original price of the jersey.
Answers
I had gotten 52.48
thats what I used to figure out the answer
The u.s. federal ban on assault weapons expired in september 2004, which meant that after 10 years (since the ban was instituted in 1994) there were certain types of guns that could be manufactured legally again. a poll asked a random sample of 1,200 eligible voters (among other questions) whether they were satisfied with the fact that the law had expired. out of the 1200 voters, 142 said they were satisfited with the fact that the law had expired. ( meaning that 1200 - 142 = 1058 were not satisfied). (data were generated based on a poll conducted by nbc news/wall street journal poll).
we would like to estimate p, the proportion of u.s. eligible voters who were satisfied with the expiration of the law, with a 95% confidence interval.
problems with proportions, will generally give an x value, the number of individuals answering a certain way, and the n value, the total number of individuals in the sample.
for this problem, n=1200, and x=142, the number satisfied.
to have the calculator calculate the 95% confidence interval for p:
choose: stat → tests → a: 1-propzint
for x: enter 142
for n: enter 1200
for c_level: enter .95 for a (95%) confidence interval.
press: calculate
based on the output:
how many of the 1,200 sampled voters were satisfied?
answer = correct
what is the sample proportion (ˆpp^ )(note: ˆp=xnp^=xn) of those who were satisfied?
answer = correct (round to four decimal places)
what is the upper limit of the 95% confidence interval for p? interpret this interval.
answer = incorrect (round to four decimal places)
Answers
Answer: The percentage of eligible voters who were satisfied with the expiration of the U.S. federal ban on assault weapons is 11.83%.
The percentage of eligible voters who were satisfied with the expiration of the U.S. federal ban on assault weapons is calculated as follows:
Total number of eligible voters who were not satisfied = 1,200 - 142 = 1058.Percentage of eligible voters who were satisfied = (142 / 1,200) x 100% = 11.83%.Therefore, the percentage of eligible voters who were satisfied with the expiration of the U.S. federal ban on assault weapons is 11.83%.
Explanation :To find the percentage of eligible voters who were satisfied with the expiration of the U.S. federal ban on assault weapons, we need to divide the number of voters who were satisfied by the total number of eligible voters who participated in the poll and then multiply the result by 100%.The total number of eligible voters who participated in the poll is given as 1,200, and out of these, 142 were satisfied with the fact that the law had expired.
So, we can calculate the percentage of eligible voters who were satisfied as follows:
Percentage of eligible voters who were satisfied = (142 / 1,200) x 100% = 11.83%.Hence, the percentage of eligible voters who were satisfied with the expiration of the U.S. federal ban on assault weapons is 11.83%.
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Plz help I really need help, I’m gonna give brainlist
Answers
Answer:
angle 4 is 47 degrees....
I need help on this question, please help me!!
Answers
Answer:
1/3
Step-by-step explanation:
The simulation will say that Jeffrey collected three different toys if the numbers in a group of three are either 0 or 1, a number more than 1 and less than 6, and a number 6 or more.
The groups {3, 7, 1}, {5, 1, 7}, {9, 2, 0}, {3, 0, 6} and {4, 6, 0} all simulate collection of all three toys from three boxes of cereal. Of the 15 simulated sets of three boxes, that is a probability of 5/15, or 1/3.
_____
Additional comment
The simulated toy numbers can be grouped in different ways. For example, we could take a vertical column of numbers as representing the purchase of 3 boxes of cereal. Doing that, we find 3 different toys only for the simulated values {4, 0, 6}, the last digits in the 4th column. The probability from considering the simulation that way is 1/15.
From this group of 45 numbers, one could calculate P(car) = 10/45, P(bus) = 19/45, and P(airplane) = 16/45. These vary a little from the theoretical values. Overall, with these values, the probability of 3 different toys from 3 boxes is about 0.200, only slightly different from the theoretical probability of 0.192.
what is 5x = 35? what the answer
Answers
Answer: X = 7
Step-by-step explanation: 5x=35
5x = 35
5 5
x=7
The half-life of a radioactive kind of krypton is 3 minutes. How much will be left after 6 minutes, if you start with 32 grams of it?
Answers
Answer:
8 grams
Step-by-step explanation:
The half-life of a radioactive kind of krypton is 3 minutes. How much will be l6eft after 6 minutes, if you start with 32 grams of it?
The formula is given as
Nt = No(1/2) ^t/t½
Nt = 32 × (1/2) ^6/3
Nt = 8 grams
In the equation, 5x + 3y = 30, I want to find the intercepts. Which would
problem would I solve to get the 'y' intercept?
15x = 30
15y = 30
5x + 3(0) = 30
5(0) + 3y = 30
Answers
Answer:
the fourth one
Step-by-step explanation:
y-intercept is when x equals 0
Assume that your utility function over income, w, is given by u(w)= w
. You have been offered two wage options. In the first one, you will receive a fixed salary of $54,000. In the second one, you will only receive $4,000 as a fixed payment, plus a bonus of $100,000 if the firm is profitable. The probability that the firm goes profitable (and thus you get a total salary of $104,000 ) is 0.5, while the probability that the firm does not make enough profits is 0.5. a. Find the expected value of the lottery induced by accepting the second wage offer. b. Find the expected utility associated with the second offer. c. Using your answers from parts a and b, find the risk premium associated with the second offer.
Answers
a. Calculate the expected value of the lottery induced by the second offer.
b. Determine the expected utility associated with the second offer.
c. Find the risk premium using the answers from parts a and b.
a. To find the expected value of the lottery induced by accepting the second wage offer, we multiply the potential outcomes by their respective probabilities and sum them up. The fixed payment of $4,000 has a probability of 0.5, while the bonus of $100,000 has a probability of 0.5. Therefore, the expected value is calculated as (0.5 * $4,000) + (0.5 * $104,000) = $52,000 + $52,000 = $104,000.
b. To find the expected utility associated with the second offer, we need to calculate the utility of each potential outcome and multiply it by its respective probability. The utility function in this case is u(w) = w. The fixed payment of $4,000 has a utility of u($4,000) = $4,000, while the total salary of $104,000 has a utility of u($104,000) = $104,000. Since both outcomes have equal probabilities of 0.5, the expected utility is (0.5 * $4,000) + (0.5 * $104,000) = $2,000 + $52,000 = $54,000.
c. The risk premium associated with the second offer can be calculated as the difference between the expected value and the expected utility. In this case, it is $104,000 - $54,000 = $50,000. The risk premium represents the amount of additional money one would need to make the certain payment option (the first offer) equally attractive as the uncertain payment option (the second offer).
expected value, expected utility, and risk premium.
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A student wants to make the natural frequency of a string increase.
How could the student accomplish this?
Responses
by loosening the string
by tightening the string
by cutting the string
by decreasing the tension of the string
Answers
The natural frequency of a string increases by tightening the string. The correct option is B.
What is the natural frequency?The frequency at which a system is prone to oscillate when there is no external force acting on it. The normal mode is the oscillation pattern of a system operating at its fundamental frequency.
The sound frequency of musical instruments can be controlled by changing the settings of the strings. When the string of an instrument is stretched between two points, the tightened strings produce tension. Here, tension refers to how tightly the string is being stretched.
The tightening of the string provides higher frequency. The higher frequency vibrations are carried to the ear which considers high frequency as a high pitch.
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Tom wants to buy his wife a bouquet of flowers for their anniversary. He decides to get them delivered to her work. Tom spends 20 dollars on the roses. He is charged $1.25 per rose and an additional $5 for a card. How many roses did Tom send his wife?.
Answers
Tom sent 16 roses to his wife
Step-by-step explanation:
20/1.25=16
first you have to get the cost of each rose then divide that by 20 to get the total amount of roses received
Has the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.
Year
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Median Age
25.1
24.6
24.3
24.3
22.8
22.8
23.2
24.7
26.1
26.8
Determine the average rate of change in median age per year from 1930 to 1960.
a.
-0.5 years of age per year
b.
20 years of age per year
c.
-0.05 years of age per year
d.
+0.05 years of age per year
Answers
-0.05 is the average rate of change in median age per year from 1930 to 1960.
What is ratio?The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, a data set that gives the median age of an American man at the time of his first marriage.
Year Median age
1910 25.1
1920 24.6
1930 24.3
1940 24.3
1950 22.8
1960 22.8
1970 23.2
1980 24.7
1990 26.1
2000 26.8
The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)
The average rate of change from 1930 to 1960 = -0.05
Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.
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the process of repeatedly increasing a value by some amount is known as ____. group of answer choices
a. incrementing
b. accumulating
c. iterating
d. scaling
Answers
The question asks for the term used to describe the process of repeatedly increasing a value by some amount. The answer choices provided are incrementing, accumulating, iterating, and scaling.
The term that describes the process of repeatedly increasing a value by some amount is iterating. Iteration involves performing a series of repeated steps or operations, often with the purpose of gradually changing or updating a value. It is commonly used in programming and mathematics to implement loops or repetitive processes. The other answer choices have different meanings and do not specifically convey the concept of incrementally increasing a value over multiple iterations. Incrementing typically refers to adding a fixed amount to a value, accumulating refers to the process of gradually gathering or collecting values, and scaling typically involves proportionally resizing or changing the magnitude of a value.
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A 15-foot flagpole casts a 13 foot-shadow. At the same time, a nearby building casts a 55-foot shadow. How tall is the building?
Answers
Answer:the rule is
R% x P x T
which in this question is:
r%= 9%
p= 630
t=8
so
630 x 8 x 9% = 453.6
that's the final answer and in order to make sure make
630+453.6=1083.6
Step-by-step explanation:
help me please i dont get it :(
Answers
Answer:
d
Step-by-step explanation:
the square root of 121 is 11
the square root of 64 is 8
soooo
(11x+8y)(11x-8y) makes the most sense
Answer:
D. (11x + 8y) (11x - 8y)
Step-by-step explanation:
Step 1: Rewrite 121x² - 64y² as (11x)² - (8y)²
Step 2: The difference of squares can be factored using the rule:
a² - b² = (a - b) (a + b)
(11x - 8y) (11x + 8y)
or
you can write it as
(11x + 8y) (11x - 8y)
How much money will it cost you to drive a diesel tractor trailer truck 175.0 miles if it gets 8.500 miles per gallon and diesel fuel costs $3.599/gallon
Answers
To calculate the cost of driving a diesel tractor trailer truck for 175.0 miles, we need to determine the number of gallons of fuel required and then multiply it by the cost per gallon.
Calculate the number of gallons of fuel needed. Given that the truck gets 8.500 miles per gallon, we divide the total distance (175.0 miles) by the fuel efficiency: 175.0 miles / 8.500 miles per gallon
= 20.59 gallons (approximately)
Calculate the cost of the fuel.Since diesel fuel costs $3.599 per gallon, we multiply the number of gallons needed by the cost per gallon: 20.59 gallons x $3.599/gallon = $73.89 (approximately) Therefore, it will cost you approximately $73.89 to drive the diesel tractor trailer truck for 175.0 miles, assuming it gets 8.500 miles per gallon and diesel fuel costs $3.599 per gallon.
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f(x) = 2x+3 and g(x) = x - 7. Find f(3)
Answers
Answer:
f(3) = 9
Step-by-step explanation:
To evaluate f(3) substitute x = 3 into f(x), that is
f(3) = 2(3) + 3 = 6 + 3 = 9
Answer:
f(3) = 9
Step-by-step explanation:
f(3) = 2x + 3
input the 3 into all x values since it is f(x) basically it tells you the value of x
f(3) = 2(3) + 3
f(3) = 9
a friend rolls two dice and tells you that there is atleast one 6. what is the probability the sum of two rolls is 9?
Answers
The probability that the sum of two rolls is 9 if atleast one response is 6 is 1/6 or 0.1667.
As the question mentioned that atleast one dice will roll 6, it means, that we know the outcome of one dice. So, the probability of getting sum of 9 is dependent only on one die. The another dice can have any of the 6 number as outcome. However, only the number 3 will give sum of 9.
Thus, the probability will be 1/6, where specifically we count for the probability of 3 in second dice out of the 6 possible outcomes.
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I have 5 pens already I am given 2 packs of pens each pack contains t pens how many pens do I have now
Answers
Answer:5 + 2t
Step-by-step explanation:
Take the first 4 digits of your student number as the first number and the last 3 digits as the second number. Write the matlab code to find the greatest common divisor of these numbers using the Euclidean algorithm.
Answers
The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.
To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:
% Replace '12345678' with your actual student number
studentNumber = '12345678';
% Extract the first 4 digits as the first number
firstNumber = str2double(studentNumber(1:4));
% Extract the last 3 digits as the second number
secondNumber = str2double(studentNumber(end-2:end));
% Find the GCD using the Euclidean algorithm
gcdValue = gcd(firstNumber, secondNumber);
% Display the result
disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);
Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.
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