Answers
In both cases considered below, we have either x = m or m ∉ x. Therefore, m is an ∈-minimal element of X.
Let's consider a nonempty subset X ⊆ ℕ.
To prove that X has an ∈-minimal element, we can follow the given hint: pick an arbitrary n ∈ X and look at the intersection of X with the set {0, 1, 2, ..., n}.
Let's denote this intersection as Y = X ∩ {0, 1, 2, ..., n}.
We can observe the following:
Y is a nonempty subset of ℕ: Since X is nonempty, and we are intersecting it with a nonempty set {0, 1, 2, ..., n}, the resulting set Y = X ∩ {0, 1, 2, ..., n} will also be nonempty.
Y is a finite subset of ℕ: The set {0, 1, 2, ..., n} is finite, and the intersection of any two finite sets is also finite. Therefore, Y is a finite subset of ℕ.
Since Y is a nonempty and finite subset of ℕ, it must have a minimal element with respect to the element hood relation ∈.
Let's denote this minimal element as m, where m ∈ Y.
Now, we need to show that m is an ∈-minimal element of X, i.e., for any x ∈ X, either x = m or m ∉ x.
Consider an arbitrary element x ∈ X. We know that x ∈ Y because Y is defined as the intersection of X with {0, 1, 2, ..., n}. Since m is the minimal element of Y, we have two cases:
Case 1: If x = m, then we have x = m, satisfying the condition.
Case 2: If x ≠ m, then x ∈ Y implies that x ∉ {0, 1, 2, ..., n} \ {m}. In other words, x ∉ {0, 1, 2, ..., n} or x = m. But x ≠ m, so x ∉ {0, 1, 2, ..., n} must hold. Since x ∉ {0, 1, 2, ..., n}, we can conclude that m ∉ x.
In both cases, we have either x = m or m ∉ x. Therefore, m is an ∈-minimal element of X.
Since we picked an arbitrary n ∈ X and showed that X ∩ {0, 1, 2, ..., n} has an ∈-minimal element, we have demonstrated that every nonempty subset X ⊆ ℕ has an ∈-minimal element.
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Related Questions
Form a sequence that has one arithmetic mean between 35 and 45
Answers
Answer: 40 is the arithmetic mean
Step-by-step explanation:
Triangle PQR has vertices P(3, 5), Q(-2, 6) and R(8, -1). Give the translation rule (x, y) → (x + 4, y – 5). What will Q’ (__, __) be
Answers
To find the image of point Q after applying the given translation rule, we need to apply the rule to the coordinates of point Q(-2, 6).
Using the translation rule (x, y) → (x + 4, y - 5), we can apply the rule to the coordinates of point Q:
Q' = (-2 + 4, 6 - 5)
= (2, 1)
Therefore, the image of point Q after the translation is Q'(2, 1).
If you plan to buy a phone but first you check out on all the brands available: iPhone,
Samsung, Motorola, and Nokia
What can be an example of an empty set in this sample scenario?
a. buying an Iphone
b. buying a phone of each brand
c. not buying any phone
d. buying a Samsung
Answers
Answer: C. not buying any phone
(q18) The average time to get your order at a restaurant is 15 minutes. What is probability that you will receive your order in the first 10 minutes?
Answers
The correct answer is option (C): 0.487
How to solveIf the typical duration for a customer to receive their food in a dining establishment is 15 minutes, it is possible to utilize the exponential function to estimate the likelihood of obtaining the meal within the initial 10 minutes.
The probability density function (PDF) that characterizes the exponential distribution is expressed as f(x) = (1/µ) * e^(-x/µ), where µ denotes the mean or average value.
The average duration in this scenario is 15 minutes, denoted as µ. Our goal is to determine the probability of X falling between the limits of a and b, where a is set at 0 and b is set at 10.
To calculate this probability, we need to integrate the PDF from a to b:
P(0 ≤ X ≤ 10) = ∫[tex][0 to 10] (1/15) * e^(-x/15) dx[/tex]
Integrating this expression gives us:
P(0 ≤ X ≤ 10) = [tex][-e^(-x/15)] from 0 to 10[/tex]
Plugging in the values, we get:
P(0 ≤ X ≤ 10) = [tex][-e^(-10/15)] - [-e^(0/15)][/tex]
Simplifying further:
P(0 ≤ X ≤ 10) = [tex]-e^(-2/3) + 1[/tex]
Using a calculator, we can evaluate this expression:
P(0 ≤ X ≤ 10) ≈ 0.487
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PRESS ON THE QUESTION IF YOU DON'T UNDERSTAND
[tex] \frac{ - 2.5 \div 5 + 6.25 \times 2}{2.4 \div (1.2 - 2.4} [/tex]
[tex] - 2 \frac{3}{4} \div 1 \frac{3}{8} + ( \frac{2}{5} + \frac{3}{10}) \times 2 \frac{1}{7} [/tex]
show the formula using BEDMAS
Answers
The final simplified form of the equation using BEDMAS is:
76 + (55555co)/12 + TO + 47
To simplify the equation using the order of operations (BEDMAS), we'll follow these steps:
-12 - 11 - 10 - 9 - 8 - 7 + 6 + 5 + (co ÷ 12) × 55555 + 11 + 10 + 9 - 2 - 1 - TO - 9 - 10 - 11 + "12 × (4 ÷ 4) + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12
Let's simplify this step by step:
-12 - 11 - 10 - 9 - 8 - 7 = -57
-57 + 6 + 5 = -46
co ÷ 12 = co/12
co/12 × 55555 = (55555co)/12
(55555co)/12 + 11 + 10 + 9 = (55555co)/12 + 30
-2 - 1 = -3
TO - 9 - 10 - 11 = TO - 30
"12 × (4 ÷ 4) = 12
12 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 80
Now we can simplify the entire equation:
-46 + (55555co)/12 + 30 - 3 + TO - 30 + 80
To further simplify the equation:
46 + (55555co)/12 + 30 - 3 + TO - 30 + 80
Let's simplify the expression:
46 + (55555co)/12 + 30 - 3 + TO - 30 + 80
= 76 + (55555co)/12 + TO + 47
The final simplified form of the equation is:
76 + (55555co)/12 + TO + 47
Simplifying further depends on the value or expression assigned to "co" and "TO." Without specific values or expressions, we cannot provide a final simplified form of the equation.
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A company has budgeted 6 2/3 hours to complete a project, with 1/4 of the time spent on research. How much time does the company plan to spend on research? Express your answer as a mixed number.
Answers
Answer:
1 2/3
Step-by-step explanation:
If the company has budgeted 6 2/3 hours to complete a project, and 1/4 of that time is spent on research, we can find the amount of time spent on research as follows:
Total time for the project = 6 2/3 hours
Time spent on research = (1/4) * (6 2/3) hours
We can simplify 6 2/3 to an improper fraction as follows:
6 2/3 = (6 x 3 + 2) / 3 = 20/3
Substituting this value into the equation above, we get:
Time spent on research = (1/4) * (20/3) hours
Multiplying the fractions, we get:
Time spent on research = 5/3 hours
We can convert this improper fraction to a mixed number as follows:
5/3 = 1 2/3
Therefore, the company plans to spend 1 2/3 hours on research.
Show your work please please
Answers
Answer:
[tex]9\frac{2}{3}[/tex]
Step-by-step explanation:
[tex]\displaystyle 1\frac{1}{4}+\biggr(3\frac{2}{3}+5\frac{3}{4}\biggr)\\\\1\frac{3}{12}+3\frac{8}{12}+5\frac{9}{12}\\\\(1+3+5)+\biggr(\frac{3}{12}+\frac{8}{12}+\frac{9}{12}\biggr)\\\\9+\frac{20}{12}\\\\9+1\frac{8}{12}\\\\9+\frac{2}{3}\\\\9\frac{2}{3}[/tex]
Again, least common denominator is 3*4=12
Step-by-step explanation:
1 1/4 + ( 3 2/3 + 5 3/4)
First change them from mixed fractions to normal fractions.
= 5/4 + ( 11/3 + 23/4)
Then Find the LCM(lowest common factor) of 4 and 3 which is 12 so we'll multiply both 4 and 3 to the number so the answer would be 12. and also if we multiply the denominator we do the same to the numerator.
= 5/4 + (44/12 + 69/12)
add them.
= 5/4 + (44 + 69/12)
now find their LCM and do the same to them since 4 is a factor of 12 we'll multiply it by 3 to get 12 as a denominator to add.
= 5/4 + 113/12
= 15/4 + 113/12
= 15 + 113/12
add them.
= 128/12
Divide both numerator and the denominator by the LCM.
= 64/6
= 32/3
Answer: 32/3 or in mixed fraction: 10 2/3
sin45+cos67-4554+97+64555+755577652-6622
Answers
The value of the given expression sin(45°) + cos(67°) - 4554 + 97 + 64555 + 755577652 - 6622 is approximately 755,642,129.099.
To find the value of the expression sin(45°) + cos(67°) - 4554 + 97 + 64555 + 755577652 - 6622, we can start by evaluating the trigonometric functions and then simplifying the arithmetic operations.
First, let's find the values of sin(45°) and cos(67°).
sin(45°) is equal to √2/2, approximately 0.7071, and cos(67°) is equal to 0.3919 (rounded to four decimal places).
Now, we can substitute these values into the expression:
0.7071 + 0.3919 - 4554 + 97 + 64555 + 755577652 - 6622
Next, let's perform the arithmetic operations:
0.7071 + 0.3919 = 1.099 (rounded to three decimal places)
1.099 - 4554 + 97 + 64555 + 755577652 - 6622
Simplifying further:
-4554 + 97 + 64555 = 60098
60098 + 755577652 - 6622 = 755642128
Finally, we have:
1.099 + 755642128 = 755642129.099
Note: The answer has been rounded to three decimal places for intermediate steps and provided as an approximate value due to rounding in trigonometric functions.
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Help fill this out please.
Answers
Step-by-step explanation:
Tess's expression is NOT equivalent because she forgot to include the - sign when multiplying -7 and -4.
Bernette's expression is NOT equivalent because she did 2-7 first which is not correct. Since the -7 is connected to the parenthesis, she needs to fully distribute the -7 into the parenthesis before including the 2.
Lucy's expression IS equivalent because she factored it correctly and distributed the -7 into the parenthesis.
PLEASE LOOK AT SCREEN SHOT
Answers
Answer:
The answers are
Emperor Penguin and Artatic wolf
Combine the areas to finf the total surface areas. Total surface area?
Answers
The surface area of the rectangular cuboid is S = 426 feet²
Given data ,
Let the surface area of the cuboid be S
Let the length of the rectangular cuboid be L = 12 feet
Let the width of the rectangular cuboid be W = 9 feet
Let the height of the rectangular cuboid be H = 5 feet
Now , The total surface area of the cuboid is given by the formula
Surface Area = 2 ( LH + LW + HW )
So, S = 2 ( 12 x 5 + 12 x 9 + 5 x 9 )
S = 2 ( 60 + 108 + 45 )
S = 2 x 213
S = 426 feet²
Hence , the surface area is S = 426 feet²
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Mano you new wom a) Divide 70,756 by 19. b) Subtract 940 from your answer to part a).
Answers
The solution of the expression is,
a) 3,724
b) 2,784
We have to given that,
a) Divide 70,756 by 19.
b) Subtract 940 from your answer to part a).
Now, We can simplify as,
a) Divide 70,756 by 19.
⇒ 70,756 ÷ 19
⇒ 3,724
And, Subtract 940 from your answer to part a). that is, 3724
⇒ 3724 - 940
⇒ 2,784
Therefore, The solution of the expression is,
a) 3,724
b) 2,784
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Review the points versus no points chart to answer the question:
Loan Terms Example 1 (No Points) Example 2 (One Point)
Loan Principal (after down payment) $292,670.00 $292,670.00
APR: fixed 4.1% 3.85%
Discount Points No points 1 point = $2,927.00
Total Interest over 30-Year Term $216,370.00 $201,250.00
Calculate the percent increase of total interest paid between purchasing one point and purchasing no points. Round the final answer to the nearest tenth.
6.0%
6.9%
8.9%
9.2%
Answers
The percent increase of total interest paid between purchasing one point and purchasing no points is approximately [tex]6.9[/tex]%.
To calculate the percent increase of total interest paid between purchasing one point and purchasing no points, we need to find the difference in total interest and then calculate the percentage increase.
For Example 1 (No Points), the total interest paid is $[tex]216,370.00[/tex].
For Example 2 (One Point), the total interest paid is $[tex]201,250.00[/tex].
The difference in total interest is $[tex]216,370.00[/tex] - $[tex]201,250.00[/tex] = $[tex]15,120.00[/tex].
To calculate the percentage increase, we divide the difference by the total interest of Example 1 and multiply by [tex]100[/tex]:
[tex]\[\frac{15,120.00}{216,370.00} \times 100 \approx 6.9\%\][/tex]
Therefore, it can be said that the percent increase of total interest paid between purchasing one point and purchasing no points is approximately [tex]6.9[/tex]% (rounded to the nearest tenth).
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Target Business is interested in buying a piece of equipment for $150,000.
The average useful life
of the equipment is 5 years, with projected annual cash flow of $22,000
Calculate the net present value of the equipment at 8%. no salvage value.
Answers
The net present value of the equipment is, $7,564.56.
Now, Based on the information , the net present value (NPV) of the equipment can be calculated using the formula:
NPV = (-Initial Investment) + (CF1 / (1+r)) + (CF2 / (1+r)) + ... + (CFn / (1+r)^n)
Where:
Initial Investment = $150,000
CF₁ - CFn = $22,000
r = 8%
Plugging in these values, we get:
NPV = (-$150,000) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08)) + ($22,000 / (1+0.08))
Simplifying the equation, we get:
NPV = -$150,000 + $20,370.37 + $18,828.67 + $17,405.10 + $16,088.71 + $14,871.71
Therefore, the net present value of the equipment is $7,564.56.
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3. Determine the total cost of the automobile after down payment and finance cost. Round your answer to the nearest penny, do not use commas in your answer.
price of car: $46,890.00, percent down: 26%, finance cost: $792.00 per month for 60 months
answer: $___
Answers
The cost of the car is $59,711.4.
Since, A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100.
Given here:
Price of the car = $46,890.00,
percent down: 26%,
finance cost: $792.00 per month for 60 months
Thus Total cost= $46,890.00×0.26+60×792
= $12191.4 + $47520
= $59,711.4
Hence, The cost of the car is $59,711.4
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For a population of scores, the sum of the deviation scores is equal to EX. True or False?
Answers
It is false that for a population of scores, the sum of the deviation scores is equal to expected value.
Are the sum of deviation scores equal to EX?The sum of deviation scores is not equal to the expected value (EX) of a population of scores. The expected value represents the average value that we expect to obtain if we were to repeatedly sample from the population.
The sum of deviation scores is the sum of the differences between each score and the mean of the population. It provides information about the total variability in the data. While both concepts are related to the distribution of scores, they serve different purposes and are calculated differently.
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The 25 members of a basketball team are trying to raise at least $1460.00 to cover the traveling cost for a holiday tournament. If they have already raised $461.00, at least how much should each member still raise, on average, to meet the goal?
Answers
Each member should still raise, on average, at least $39.96 to meet the goal.
What's the slope-intercept form of the equation of the line graphed in this figure?
A) y = –3∕5x + 1
B) y = –5∕ x – 1
C) y = 5∕3x + 1
D) y = 3∕5x + 1
Answers
Answer:
Option D
Step-by-step explanation:
Slope intercept form:(-5, -2) ; x₁ = -5 & y₁ = -2
(5 , 4) ; x₂ = 5 & y₂ = 4
Plugin the points in the below mentioned formula and find the slope.
[tex]\boxed{\bf slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{4-[-2]}{5-[-5]}\\\\\\=\dfrac{4+2}{5+5}\\\\=\dfrac{6}{10}\\\\=\dfrac{3}{5}[/tex]
Equation of slope-intercept form: y =mx + b
Here, m is the slope and b is the y-intercept.
[tex]\sf y = \dfrac{3}{5}x + b[/tex]
The line is passing through (5, 4). So, substitute the points in the equation and find the y-intercept.
[tex]4 =\dfrac{3}{5}*5 + b\\\\\\4=3+b\\\\[/tex]
4 - 3 = b
b = 1
Slope intercept form of the equation:
[tex]\sf y = \dfrac{3}{5}x + 1[/tex]
Please help me with this proof.
Answers
Answer:
See below
Step-by-step explanation:
For the second step, [tex]\angle T\cong\angle R[/tex] by Alternate Interior Angles. The rest of the steps appear to be correct.
I really need answer asap option D is 11.75 it didn't include in the photo
Answers
Hello!
16 - (2.5 + 4.25) = 9.25
the answer is 9.25How do I rewrite x^2+5x+6 as equivalent to x^2+rx+sx+6
Answers
To rewrite equation [tex]x^2 + 5x + 6[/tex] as[tex]x^2 + rx + sx + 6[/tex], we need to choose suitable values for r and s that satisfy r + s = 5.
To rewrite the quadratic expression[tex]x^2 + 5x + 6[/tex] as equivalent to[tex]x^2 + rx + sx + 6[/tex] , we need to find the values of r and s that satisfy the equation.
Let's start by expanding [tex]x^2 + rx + sx + 6:[/tex]
[tex]x^2 + rx + sx + 6 = x^2 + (r + s)x + 6[/tex]
We can see that the coefficient of x in the original expression is 5, and in the rewritten expression, it is (r + s). Therefore, we want to find values for r and s such that r + s = 5.
Next, we need to consider the constant term. In the original expression, the constant term is 6, and in the rewritten expression, it is also 6. Therefore, we want r, s, and 6 to satisfy the equation.
Since r + s = 5, we can solve for one variable in terms of the other. For example, if we choose r = 3, then s = 2 to satisfy the equation. Alternatively, we could choose r = 4 and s = 1, or any other combination that adds up to 5.
So, rewriting [tex]x^2 + 5x + 6[/tex] as [tex]x^2 + rx + sx + 6[/tex]can be achieved by choosing suitable values for r and s that satisfy r + s = 5.
For example, if we choose r = 3 and s = 2, the equivalent expression would be [tex]x^2 + 3x + 2x + 6.[/tex]
In summary, to rewrite[tex]x^2 + 5x + 6[/tex]as [tex]x^2 + rx + sx + 6[/tex], we need to choose suitable values for r and s that satisfy r + s = 5.
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Sophia throws a dart at this square-shaped target:
A square is shown with sides labeled 9. A shaded circle is shown in the center of the square. The diameter of the circle is 3.
Part A: Is the probability of hitting the black circle inside the target closer to 0 or 1? Explain your answer and show your work. (5 points)
Part B: Is the probability of hitting the white portion of the target closer to 0 or 1? Explain your answer and show your work. (5 points)
PLS DO THE STEPS MARKING BRAINLESTTT
Answers
The probability of hitting the black circle as required is closer to 0 than. it is to 1.
The probability of hitting the white portion of the target as required is closer to 1 than it is to 0.
What is the probability of hitting each section of the target?It follows from the task content that the probability of hitting the circle is dependent on the area of the black circle and the square shaped target.
Since the area of the square is; 9² = 81.
The area of the black circle is; π(1.5)² = 7.07.
Since the area of the black circle is less than half the area of the square; it follows that the the probability are as stated in the answer section above.
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help please
due today
Answers
Answer: 38.4 + 216 = 254.4
Step-by-step explanation: The volume of the block at the top is 38.4 and the volume of the block at the bottom is 216 so add them together to make 254.4
Hope it helped :D
(05.03 MC)
A system of equations is given.
-5y = 10 - 5x
-2y = 8 - 4x
Solve for (x, y) using the elimination method. Show all work.
Answers
Answer:
(x,y)=(2,0)
Step-by-step explanation:
Multiply top equation by 4 and bottom equation by 5
-5y = 10 - 5x --> -20y = 40 - 20x
-2y = 8 - 4x --> -10y = 40 - 20x
Subtract both equations
-10y = 0
y = 0
Substitute y=0 into one of the original equations to find x
-5y = 10 - 5x
-5(0) = 10 - 5x
0 = 10 - 5x
5x = 10
x = 2
Therefore, the solution is (x,y)=(2,0)
A triangle has side lengths of 5 cm, 8 cm and 10 cm. Determine the perimeter of the triangle and the area.
Answers
Answer:
[tex]\mathrm{23cm,19.81cm^2}[/tex]
Step-by-step explanation:
[tex]\mathrm{Solution:}\\\mathrm{Let\ a=5cm,\ b=8cm\ and\ c=10cm}\\\mathrm{Let\ "P"\ denote\ the\ perimeter\ and\ "A"\ denote\ the\ area\ of\ the\ triangle.}\\\mathrm{Then,\ P=a+b+c=5+8+10=23cm}\\\mathrm{Also,\ Semiperimeter(s)=\frac{P}{2}=\frac{23}{2}=11.5}\\[/tex]
[tex]\mathrm{Now,}\\\mathrm{Area\ of\ triangle=\sqrt{s(s-a)(s-b)(s-c)}}\\\mathrm{=\sqrt{11.5(11.5-5)(11.5-8)(11.5-10)}}\\\mathrm{=\sqrt{11.5\times 6.5\times 3.5\times 1.5}}\\\mathrm{=19.81cm^2}\\\mathrm{So,\ the\ perimeter\ of \ the\ triangle\ is\ 23cm\ and\ area\ is\ 19.81cm^2.}[/tex]
Dakota walked the dog for 14 minutes and then completed chores for 48 minutes. If she finished the chores at 1:32 p.m. what time did she start walking the dog?
Answers
He started walking the dog at the time 12:30 p.m.
We know that Dakota completed hera chores at 1:32 p.m. and that she spent a total of 48 minutes doing them.
That means she must have started her chores at:
⇒ 1:32 p.m. - 48 minutes = 12:44 p.m.
We know that she walked the dog for 14 minutes.
We want to find out what time she started walking the dog,
so subtract 14 minutes from the time she started doing chores,
⇒ 12:44 p.m. - 14 minutes = 12:30 p.m.
Therefore,
Dakota started walking the dog at 12:30 p.m.
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Find a pair of values that make the linear equation 14x−y=−14 a true statement by filling in the boxes with a valid value of x and y.
Answers
To find a pair of values that make the linear equation 14x - y = -14 a true statement, we can choose any value for x and calculate the corresponding value of y.
Let's choose x = 2:
14(2) - y = -14
28 - y = -14
Now, we can solve for y:
-y = -14 - 28
-y = -42
Dividing both sides by -1 (to isolate y):
y = 42
Therefore, the pair of values (x, y) that make the equation true is (2, 42).
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[tex]2x {}^{2} + 2y {}^{2} - 6y - 12y = 3 [/tex]
I need help
Answers
what is the sum 3/x+9+5/x-9
Answers
Answer:
[tex]\frac{8}{x}[/tex]
Step-by-step explanation:
what is the sum 3/x+9+5/x-9
[tex]\frac{3}{x} + 9 + \frac{5}{x} - 9 =[/tex] (add [tex]\frac{3}{x}[/tex] and [tex]\frac{5}{x}[/tex])
[tex]\frac{8}{x} + 9 - 9 =[/tex] (solve 9 - 9 = 0)
[tex]\frac{8}{x}[/tex] ( your answer)
Identify the part, percent and base.
A discount of $1.92 on a $6.40 item that is on sale for 30% off.
Part:
Percent:
Base:
Answers
Part: $1.92 (the discount amount)
Percent: 30% (the discount percentage)
Base: The original price of the item before the discount and sale, which we can calculate as follows:
Let x be the original price of the item.
The discount of $1.92 represents 30% of the original price, so we can write:
0.30x = 1.92
Solving for x, we get:
x = 1.92 / 0.30
x = 6.40
Therefore, the base is $6.40 (the original price of the item before the discount and sale).
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