Answer:
Move the decimal place over to the left two spaces
.75--> 7.5--> 75%
and reverse
75%--> 7.5--> .75
Step-by-step explanation:
brainliest plz
Answer:
75%
Step-by-step explanation:
"Percent" means "per 100" or "over 100". So, to convert 0.75 to percent we rewrite 0.75 in terms of "per 100" or over 100.
Multiply 0.75 by 100/100. Since 100/100 = 1, we are only multiplying by 1 and not changing the value of our number.
0.75 100 75
-------- x -------- = -------- which equals to 75%
1 100 100
Hope this helps
can i have brainliest plz
cual es el resultado de esta ecuacion 8x+9=25
Answer:
x=2
Step-by-step explanation:
Hope I helped and I hope you get it correct
If you flip a coin three times in the air, what is the probability that tails lands up all three times? A. 1/2 B. 1/8 C. 1/4 D. 1/6
Answer: A) 1/2
Step-by-step explanation:
Answer:
If you flip a coin three times in the air, what is the probability that tails lands up all three times?
Step-by-step explanation:
1/2
Solve the formula 6x+5y=13 for y.
Answer:
13/5 - 6x/5
Step-by-step explanation:
Please help me! Thank you so much (question inserted below)
Answer:
838.08 in³
Step-by-step explanation:
volume of tank = (36×24×24)+(½×3.14×12²×24)
= 20,736 + 5,425.92
= 26,161.92 in³
the remaining water = 27,000 - 26,161.92
= 838.08 in³
Policies Current Attempt in Progress On May 1, 2021, Sheffield Company sells office furniture for $300000 cash. The office furniture originally cost $746800 when purchased on January 1, 2014. Depreciation is recorded by the straight-line method over 10 years with a salvage value of $80200. What gain should be recognized on the sale? (Hint: Use 7.333333 for years used in calculation.) O $44540. O $22220. O $84080. O $42040. Save for Later -/5 = 1 Attempts: 0 of 1 used Submit Answer
To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.
First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.
Depreciation per year = (Cost - Salvage Value) / Useful Life
Depreciation per year = ($746,800 - $80,200) / 10 years
Depreciation per year = $66,160
Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.
Accumulated Depreciation = Depreciation per year × Years
Accumulated Depreciation = $66,160 × 7.33 years
Accumulated Depreciation = $484,444.80
Now, we can calculate the book value of the furniture:
Book Value = Cost - Accumulated Depreciation
Book Value = $746,800 - $484,444.80
Book Value = $262,355.20
Finally, we can calculate the gain on the sale:
Gain on Sale = Sale Price - Book Value
Gain on Sale = $300,000 - $262,355.20
Gain on Sale = $37,644.80
Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.
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The gain that should be recognized on the sale of the office furniture is $84,080.
The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.
Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.
For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420
Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.
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h(t) = 210 - 150
How do you find the value of t
Answer:
t = -40
Step-by-step explanation:
the value of t is just the answer. Do not let the H confuse you.
210 - 250 = -40
t = -40
Find the measure of the side indicated (x). Round to the nearest tenth. Show your work to support your answer.
Answer:
x = 13.77
Step-by-step explanation:
cos 37° = 11/x
0.7986 = 11/x
0.7986x = 11
x = 11/0.7986
x = 13.77
The value of the hypotenuse x will be 14.37.
What will be the value of the hypotenuse?Here in the triangle, it is given that
The angle between base and hypotenuse = \(37^0\)
The base =11
So from the property
\(COS\theta=\dfrac{Base}{Hypotenuse}\)
\(Cos37=\dfrac{11}{x}\)
\(x=\dfrac{11}{0.7654}\)
\(x=14.37\)
Thus the value of the hypotenuse x will be 14.37.
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What is the following product?
(~/14 - 3)(/12 +7)
O 2N/42+7N/2-6-/21
O 14-6+N7
• 26 + /21 -/15-/10
2,/42 - 21
Option A
im pretty sure when you change the sign in an equation you actually have to change all of them so the equation would be 3+5+7. Am i correct?
Answer:
1
Step-by-step explanation:
Mistake in the second step.
We must add positive numbers or negative ones.
Here he had add the positive and negative numbers and that is the mistake
\(=3-(-5)-7\\\\=3+5-7\)Here 5 is positive because -×-=+
\(=8-7\)
\(=1\)
In the second step, we must add the positives that are 3 and 5 and subtract from 7.
Hope it will help you.
answer the following, Round final answer to 4 decimal places. a.) Which of the following is the correct wording for the randon variable? r×= the percentage of all people in favor of a new building project rv= the number of people who are in favor of a new building project r N= the number of people polled r×= the number of people out of 10 who are in favor of a new building project b.) What is the probability that exactly 4 of them favor the new building project? c.) What is the probabilitv that less than 4 of them favor the new building project? d.) What is the probabilitv that more than 4 of them favor the new building project? e.) What is the probabilitv that exactly 6 of them favor the new building project? f.) What is the probability that at least 6 of them favor the new building project? 8.) What is the probabilitv that at most 6 of them favor the new building project?
In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.
a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.
b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.
c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.
d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).
e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.
f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
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Go to your math tools and open the Graph tool to graph the equation you found for calculating profit. Set the scale of the graph to go from -5 to 40 on the x-axis and from -80 to 80 on the y-axis.
Part A
What do the points on the line in quadrant IV represent in terms of the situation?
Answer:
The y-coordinates in quadrant IV are negative. Because y represents profit, negative values of y signify not making a profit. That is, negative values signify loss. The points in quadrant IV represent the baseball team losing money.
Step-by-step explanation:
I took the assignment :).
If a=-x and b=-1-5, then find the value of the a^{2}b in fully simplified form.
Simplification form of the expression is -1.5x² after plugging the values of a and b in the expression a²b
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
If a=-x and b=-1-5, then find the value of the a²b
Plug the values of a and b in the expression a²b
= (-x)²(-1.5)
= -1.5x²
Thus, simplification form of the expression is -1.5x² after plugging the values of a and b in the expression a²b
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Evaluate the expression below at x = 6.
i linked the numbers in a image
A.
606
B.
396
C.
468
D.
1,692
Answer:
B
Step-by-step explanation:
you can break the 78 into 70 and 8, and multiply them separately by 6 and then add the two answers to get 468
1. Give the formula for the forward Fourier Transform for a signal, X(jω)=F{x(t)}. 2. Give the formula for the inverse Fourier Transform of a signal, x(t)=F−1{X(jω)}. Compare this to the formula from problem 1) above and discuss similarities and differences. What is the Fourier Transform property called which refers to the similarity between the two formulas? 3. Using the defining integral of the Fourier Transform, determine the transform of the following signal: x(t)=⎣⎡−1,1,0,−1
The forward Fourier Transform formula for a signal is X(jω) = F{x(t)}. The inverse Fourier Transform formula is x(t) = F^(-1){X(jω)}. The two formulas are related by the Fourier Transform property called duality or symmetry.
1. The forward Fourier Transform formula is given by:
X(jω) = ∫[x(t) * e^(-jωt)] dt
This formula calculates the complex spectrum X(jω) of a signal x(t) by integrating the product of the signal and a complex exponential function.
2. The inverse Fourier Transform formula is given by:
x(t) = (1/2π) ∫[X(jω) * e^(jωt)] dω
This formula reconstructs the original signal x(t) from its complex spectrum X(jω) by integrating the product of the spectrum and a complex exponential function.
The similarity between these two formulas is known as the Fourier Transform property of duality or symmetry. It states that the Fourier Transform pair (X(jω), x(t)) has a symmetric relationship in the frequency and time domains. The forward transform calculates the spectrum, while the inverse transform recovers the original signal. The duality property indicates that if the spectrum is known, the inverse transform can reconstruct the original signal, and vice versa.
3. To determine the Fourier Transform of the given signal x(t) = [-1, 1, 0, -1], we apply the defining integral:
X(jω) = ∫[-1 * e^(-jωt1) + 1 * e^(-jωt2) + 0 * e^(-jωt3) - 1 * e^(-jωt4)] dt
Here, t1, t2, t3, t4 represent the respective time instants for each element of the signal.
Substituting the time values and performing the integration, we can obtain the Fourier Transform of x(t).
Note: Please note that without specific values for t1, t2, t3, and t4, we cannot provide the numerical result of the Fourier Transform for the given signal. The final answer will depend on these time instants.
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The 2013-14 roster of the Seattle Seahawks, winners of the 2014 NFL Super Bowl, included 10 defensive linemen and 9 offensive linemen. (Data set may be found here.) The weights in pounds of the defensive linemen were 254 311 297 323 260 242 300 252 303 274 and the weights of the offensive linemen were 310 315 305 318 298 301 321 332 320 (a) Make a back to back stemplot of the weights of the offensive and defensive linemen. (Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.) Find the five-number summary for the offensive line. (Enter your answers to one decimal place.) Minimum lb Q1 lb Median lb Q3 lb Maximum lb (b) Find the five-number summary for the defensive line. (Enter your answer to one decimal place.) Minimum lb Q1 lb Median lb Q3 lb Maximum lb (c) Which group of players tends to be heavier? Offensive Defensive
Answer:
Step-by-step explanation:
The weights in pounds of the defensive linemen were :
254,311, 297, 323, 260, 242, 300, 252, 303, 274
Ascending order: 242 ,252 ,254 ,260 ,274 ,297 ,300 ,303 ,311 ,323
The weights in pounds of the offensive linemen were :
310 ,315, 305, 318, 298, 301, 321, 332, 320
Ascending order:298 ,301 ,305 ,310 ,315 ,318 ,320 ,321 ,332
a)
Offensive line Stem Defensive line
24 | 2
25 | 2 , 4
26 | 0
27 | 4
8 | 29 | 7
1,5 | 30 | 0,3
0,5,8 | 31 | 1
0,1 | 32 | 3
2 | 33 |
Five number summary of offensive line:
1) minimum: 298
2) maximum: 332
3)
Lower quartile:298 ,301 ,305 ,310
Q1 is the median of lower quartile
\(Q1=\frac{301+305}{2}=303\)
4)
Upper quartile:318 ,320 ,321 ,332
Q3 is the median of upper quartile
\(Q3=\frac{320+321}{2}=320.5\)
5)
Q2 is the median
298 ,301 ,305 ,310 ,315 ,318 ,320 ,321 ,332
Mid value =\(\frac{9+1}{2}\)=5th term = 315
Q2=315
Five number summary of defensive line:
1) minimum: 242
2) maximum: 323
3)
Lower quartile:242 ,252 ,254 ,260 ,274
Q1 is the median of lower quartile
Q1=254
4)
Upper quartile:297 ,300 ,303 ,311 ,323
Q3 is the median of upper quartile
Q3=303
5)
Q2 is the median
242 ,252 ,254 ,260 ,274 ,297 ,300 ,303 ,311 ,323
Mid value =\frac{274+297}{2}=285.5
Q2=285.5
c) Mean weight of offensive line = \(\frac{298+301+305+310+315+318+320+321+332}{9}=313.33\)
Mean weight of defensive line = \(\frac{242+252+254+260+274+297+300+303+311+323}{10}=281.6\)
Mean weight of offensive line is more
So, Offensive group of players tends to be heavier
50 POINTS PLS HELP!!!
7. Write the expression as a single natural logarithm.
3 ln 6 + 4 ln x
ln (216 + x4)
ln 216x4
ln 72x
ln 18x4
The expression 3 ln 6 + 4 ln x as a single Natural logarithm,The expression 3 ln 6 + 4 ln x can be simplified as ln (216x^4).
The expression 3 ln 6 + 4 ln x as a single natural logarithm, we can use the properties of logarithms.
The property we will use is the product rule of logarithms, which states that ln(a) + ln(b) = ln(a * b).
Applying this property to the given expression, we have:
3 ln 6 + 4 ln x = ln 6^3 + ln x^4
Now, we can simplify the expression further by using the power rule of logarithms, which states that ln(a^b) = b * ln(a).
Applying this rule, we have:
ln 6^3 + ln x^4 = ln (6^3 * x^4)
Simplifying the expression inside the natural logarithm:
ln (6^3 * x^4) = ln (216 * x^4)
Now, we can simplify the expression by multiplying the constants:
ln (216 * x^4) = ln (216x^4)
Therefore, the expression 3 ln 6 + 4 ln x can be simplified as ln (216x^4).
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Last week, the price, in dollars of gasoline was g. This week, the price of gasoline was increased by 8%. Which expressions represent this week's price, in dollars, of a gallon of gasoline? Select all that apply.
The expressions represent this week's price, in dollars, of a gallon of gasoline, is g + 0.08g
Last week the price, in dollars, of a gallon of gasoline was g.
This week the price of gasoline per gallon increased by 8%.
We have to determine, the expressions that represent this week's price, in dollars, of a gallon of gasoline
According to the question,
The price of a gallon of gasoline = g in last week.
The price of gasoline increased = 5% = 0.05
The expressions represent this week's price, in dollars, of a gallon of gasoline is,
= Price of gallon last week + Price of gallon increased this week
= g + 0.08g
= (1 + 0.08)g
= 1.08g
Hence, The expressions represent this week's price, in dollars, of a gallon of gasoline, is g + 0.08g
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Use the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =
By Using the table to work out the values of a , b , c , and d. X y = 2 x + 1 − 3 a − 2 − 3 − 1 b 0 1 1 c 2 d a = b = c = d =
Therefore, The solutions are : a = -3, b = 0, c = 6, d = 9
Equation:
In mathematics, an equation is an expression that indicates equality of two expressions by connecting them with the equal sign = . The word "equation" and related words in other languages can have slightly different meanings. For example, in French an equation is defined as containing one or more variables, whereas in English a well-formed formula consisting of two expressions connected by an equal sign is an equation.
Given:
This table;
x y = 3x+3
-3 -6
-2 a
-1 b
0 3
1 c
2 d
To Find:
Values of a, b, c and d
Consider the 2nd row,
x = -2, y = a
Putting the values in the equation,
we get,
a = 3(-2) + 3
⇒ a = -3
Consider the 3rd row,
x = -1, y = b
Putting the values in the equation,
we get,
b = 3(-1) + 3
⇒ b = 0
Consider the 5th row,
x = 1, y = c
Putting the values in the equation,
c = 3(1) + 3
⇒ c = 6
Consider the 6th row,
x = 2, y = d
d = 3(2) + 3
⇒ d = 9
The final answer is,
a = -3, b = 0, c = 6, d = 9.
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help please I need help
Answer:
it should be A, but it depends on how you look at it
The 7th-grade class took a survey on their favorite ice cream. 58 people said they prefer vanilla, while 28 people said they prefer chocolate. Write a ratio comparing chocolate to vanilla. (Write it in a :b form)
PLEASE HELP THIS IS MY LAST QUESTIONNNN
- The electric company charges Dalton a monthly service fee of $30 plus $0.15 per kilowatt-hour of electricity used. This month, Dalton's bill is $105.
- How many kilowatt-hours of electricity did Dalton use?
Answer:
500 kilowatt-hours.
Step-by-step explanation:
Let k = number of kilowatt-hours.
\(0.15k+30=105\\0.15k=75\\k=500\)
Therefore, Dalton used 500 kilowatt-hours of electricity.
A parallelogram has an area of 159.6 square meters and a height of 14 meters. What is the length of the base?
Answer:
base = 11. 4 m
Step-by-step explanation:
Area of parallelogram = base * height
base * height = 159.6 square meter
base * 14 = 159.6
base = 159.6 ÷ 14
base = 11.4 m
How do you find the number of distinguishable permutations of the group of letters: A, A, G, E, E, E, M?
In order to find the number of distinguishable permutations of the group of letters A, A, G, E, E, E, M, we can use the following formula:
The number of permutations = n! / (n1! n2! ... nk!), where n is the total number of objects to be arranged, and n1, n2, ..., nk are the numbers of objects that are identical to one another.
For this problem, we have 7 letters with 2 A's, 3 E's, and 1 G and 1 M letter.
Using the formula above, we can find the number of distinguishable permutations: 7! / (2! 3! 1! 1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / [(2 × 1) × (3 × 2 × 1) × (1 × 1) × (1 × 1)] = 2520
Therefore, there are 2520 distinguishable permutations of the group of letters A, A, G, E, E, E, M.
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write out the form of the partial fraction decomposition of the function (see example). do not determine the numerical values of the coefficients. (a) x^3/ x^2 + 10x + 9
A/(x+1) + B/(x+9)
(b) 7x+1/(x+1)^3 (x^2+4)^2
A/(x+1) +B(X+1)^2 +C(X+1)^3 + DX+E/X^2+4 + fX+G/(X^2+4)^2
The form of the partial fraction decomposition of the function is x -10 + A/(x+1) + B/(x+9).
Partial fractions are fractions used to decompose a rational equation. When an algebraic expression is divided into two or more rational expressions, each portion is referred to as a partial fraction. As a result, it is essentially the inverse of rational expression addition. A partial fraction, like a fraction, has a numerator and a denominator, with the denominator representing the decomposed component of a rational function.
To avoid this complication, we must continue the task by simplifying the complicated form of the rational statement. One approach for decomposing rational statements into simpler partial fractions is partial fraction decomposition.
a) \(\frac{x^3}{x^2+10x+9} = \frac{x^3}{(x+1)(x+9)}\)
Degree on numerator is higher than degree on denominator
so, first we will divide
x³ = (x-10) (x²+10x+9) + (x+90)
\(\frac{x^3}{x^2+10x+9} = \frac{(x^2+10x+9)(x-10) +(x+90)}{x^2+10x+9}\)
= x -10 + A/(x+1) + B/(x+9)
b) \(\frac{7x+1}{(x+1)^3 (x^2+4)^2} = \frac{A}{x+1} +\frac{B}{(x+1)^2} +\frac{C}{(x+1)^3} +\frac{Dx +E}{x^2+4} +\frac{Fx+G}{(x^2+4)^2}\)
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Which angle has a negative sine value and a positive cotangent value?
sin4π/3= sin(π+π/3) = - sinπ/3
cot4π/3=cot(π+π/3)= cotπ/3
OPTION C 4π/3
Was is 9 Divided 3103
Answer:
0.003 but if you just put that in backwards, 345.
Step-by-step explanation:
Answer:
\(344\\9*344=3096\\3103-3096=7\\\\344\\Remainder = 7\)
↓ Step Breakdown ↓
How I got 344 was I asked myself, "How many times does 9 go into 3103?"
To the 1st digit manner, 9 goes into 31(03) 3 times.
Subtract.
Result is 4. Drop the 0 from the tens place to match up.
9 goes into 4(0) 4 times.
Subtract.
The result is 4. Drop the 3 from the ones place.
9 goes into 4(3) 4 times.
Final subtraction.
The final result is 7.
4 times the difference of 4
and a number is 24. What is
the number?
Answer: n=-2
Step-by-step explanation:
4(4-n)=24
16-4n=24
-4n=8
n=-2
Which is the best way to estimate 32% of 13?
1/2 x 10
1/4 x 12
1/3 x 15
1/3 x 12
Please answer quickly
Answer:
32% of 13 is 3.84
Step-by-step explanation:
but if your doing estimate one of those it would be 1/3*12
hope that helped
Assume you are taking a class and the professor tells that class that 10% of the class will receive an "A", 20% will receive a "B", 40% will receive a "C", 20% will receive a "D" and 10% will receive a "F". What type of evaluation approach is this?
A.) ranking approach
B.) forced distribution
C.) graphic rating
D.) behaviorally anchored rating scales
The evaluation approach described in the given scenario is B.) forced distribution.
Forced distribution is an evaluation approach where performance ratings are distributed among employees according to predetermined percentages. In this case, the professor has predetermined that 10% of the class will receive an "A", 20% will receive a "B", 40% will receive a "C", 20% will receive a "D", and 10% will receive an "F".
This approach imposes a forced ranking system that restricts the distribution of grades based on predetermined proportions. Forced distribution can be useful in certain contexts as it helps differentiate performance levels and prevent grade inflation or deflation.
However, it also has limitations, as it may not accurately reflect individual performance and can create a competitive environment among students. It is important for educators to carefully consider the implications and potential drawbacks of using forced distribution in educational settings.
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What is wrong with the following proof that the sum of two odd integers is even? Proof: Let a,b be two odd integers. Then a=2k+1 and b=2k+1 for some integer k. Thus a+b=(2k+1)+(2k+1)=4k+2=2(2k+1). Since 2k+1 is an integer we see that a+b=2m for some integer m. Hence a+b is even, completing the proof. A. We cannot conclude that a+b=2m for an integer m. B. The algebra is incorrect: (2k+1)+(2k+1) is not equal to 4k+2. C. We are not using the correct definition of "odd." D. The conclusion is assumed, making for circular reasoning. E. We are assuming integers a and bare EQUAL integers.
The correct answer is A. We cannot conclude that a+b=2m for an integer m.
In the given proof, the error lies in assuming that adding two odd integers will always result in an even integer. The proof correctly starts by assuming a=2k+1 and b=2k+1, where k is an integer. However, the step where it concludes a+b=4k+2 is incorrect.
The correct sum of a+b is:
a + b = (2k+1) + (2k+1) = 4k + 2k + 1 + 1 = 6k + 2.
Notice that we have 6k + 2, not 4k + 2 as stated in the incorrect proof. Since 6k + 2 is not in the form of 2m for any integer m, we cannot conclude that the sum of two odd integers is always even.
The mistake in the proof arises from incorrectly distributing the addition over the parentheses. The correct algebraic step would be:
a + b = (2k+1) + (2k+1) = 2k + 2k + 1 + 1 = 4k + 2.
However, even in this corrected step, we cannot assume that 4k + 2 is always in the form of 2m for some integer m. Therefore, the conclusion that the sum of two odd integers is always even is not valid.
This demonstrates the importance of careful reasoning and precise algebraic manipulation in mathematical proofs.
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