Sin(2x) = 20 x cos²(x), cos(2x) = -99 x cos²(x), and tan(2x) = -20/99.
How did we get the value?To find the values of sin(2x), cos(2x), and tan(2x) using the given information, use trigonometric identities to express them in terms of tan(x) and sin(x).
Given that tan(x) = 10 and sin(x) is negative. Since tan(x) = sin(x)/cos(x), find cos(x) using the given information.
Let's solve for cos(x) first:
tan(x) = sin(x)/cos(x)
10 = sin(x)/cos(x)
Now, let's find sin(x) using the given information that sin(x) is negative:
Since tan(x) = sin(x)/cos(x) and tan(x) = 10, substitute 10 for sin(x)/cos(x):
10 = sin(x)/cos(x)
Multiplying both sides by cos(x):
10 x cos(x) = sin(x)
Now, sin(x) = 10 x cos(x).
Since sin(x) is negative, conclude that cos(x) must be positive.
Now, let's use the double-angle identities to find sin(2x), cos(2x), and tan(2x):
sin(2x) = 2 x sin(x) x cos(x)
cos(2x) = cos²(x) - sin²(x)
tan(2x) = sin(2x) / cos(2x)
Substituting sin(x) = 10 x cos(x) into the above formulas, express sin(2x), cos(2x), and tan(2x) in terms of cos(x):
sin(2x) = 2 x (10 x cos(x)) x cos(x) = 20 x cos²(x)
cos(2x) = cos²(x) - (10 x cos(x))² = cos²(x) - 100 x cos²(x) = -99 x cos²(x)
tan(2x) = sin(2x) / cos(2x) = (20 x cos²(x)) / (-99 x cos²(x)) = -20/99
Therefore, sin(2x) = 20 x cos²(x), cos(2x) = -99 x cos²(x), and tan(2x) = -20/99.
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PLEASE HELP ONLY QUESTION 8 PLEASE !! :)
Answer:
150
Step-by-step explanation:
Robert has some nickels and some dimes. He has a maximum of 29 coins worth no less than $2.20 combined. If Robert has 10 nickels, determine all possible values for the number of dimes that he could have. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Robert's dimes are anywhere between 17 and 19.
Explanation:Nickels
are worth 5 cents, and
dimes
are worth 10 cents. Since Robert has 10 nickels, he already has 50 cents. To reach a minimum of $2.20, or 220 cents, Robert needs at least 170 more cents. Because each dime is worth 10 cents, he needs a minimum of 17 dimes. If he has a maximum of 29 coins in total, subtracting the 10 nickels means that he can have up to 19 dimes. So, Robert could have anywhere between 17 and 19 dimes.
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What is the area of the figure? In Units
Answer:
Area = 40
Perimeter = 26
Step-by-step explanation:
length = 8
width = 5
Area = 8 x 5 = 40
Perimeter = 2(8 + 5) = 26
Explain where the hands of an analog clock point at 1:27.
The hands of an analog clock point at 1:27 is at 1o'clock position
How to determine the pointAt 1:27 on an analog clock, the hour hand focuses straightforwardly at the numeral "1" on the clock confront, demonstrating that it is within the 1 o'clock position.
The miniature hand, on the other hand, focuses between the numerals "2" and "3" on the clock confront, roughly midway between them.
Since there are 60 minutes in an hour and the diminutive hand moves around the clock confront at a consistent rate, it shows that 27 minutes have passed since the hour started.
Hence, the miniature hand is closer to the numeral "3" but not however at it. The moment hand may be anyplace on the clock confront, because it moves persistently.
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On an exam students are asked to list 5 historical events in the order in which they occurred. A student randomly orders the events. what is the probability that the
The probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.
How to solveIf the student randomly orders the events, there is only one correct order out of all possible permutations.
Hence, the likelihood of selecting the accurate sequence is equal to 1 over the total count of potential arrangements.
As there are 5 occurrences, the overall count of conceivable sequences is equivalent to 5 factorial (5!), amounting to 120.
Therefore, the probability that the student chooses the correct order is 1/120 or approximately 0.0083, which is equivalent to 0.83%.
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On an exam, students are asked to list 5 historical events in the order in which they occurred. A student randomly orders the events. What is the probability that the student chooses the correct order?
2
5. Many people believe that criminals who plead guilty tend to get lighter sentences than those
who are convicted in trials. The accompanying table summarizes randomly selected sample
data for defendants in burglary cases in a specific city. All of the subjects had prior prison
sentences. Use a 0.05 significance level to find the critical value needed to test the claim that
the sentence (sent to prison or not sent to prison) is independent of the plea.
Sent to prison
Not sent to prison
Guilty Plea
392
564
Not-Guilty Plea
58
14
(1 point)09.488
03.841
042.557
05.991
Answer:
Is 03.841
Step-by-step explanation:
To find the critical value needed to test the claim that the sentence is independent of the plea, we need to perform a chi-square test of independence. The critical value is based on the significance level (α) and the degrees of freedom.
In this case, the given significance level is 0.05. Since the table represents a 2x2 contingency table (two categories for plea and two categories for sentence), the degrees of freedom (df) can be calculated as (number of rows - 1) * (number of columns - 1) = (2 - 1) * (2 - 1) = 1.
To find the critical value at a significance level of 0.05 with 1 degree of freedom, we consult a chi-square distribution table or use statistical software.
The critical value for a chi-square test with 1 degree of freedom and a significance level of 0.05 is approximately 3.841.
Therefore, the correct answer is 03.841.
What is the answer to this question? Having a hard time completing and finding answer
Which expressions are equivalent to the expression 3x2 - 5a3+2y4?
Answer: There are several expressions that are equivalent to the given expression 3x^2 - 5a^3 + 2y^4. Here are a few examples:
2y^4 - 5a^3 + 3x^2-5a^3 + 3x^2 + 2y^43x^2 + 2y^4 - 5a^32y^4 + 3x^2 - 5a^3
These expressions have the same terms but may differ in the order in which the terms are written. It's important to note that the coefficients and exponents of the variables remain unchanged in each expression.
The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.
The domain and the range of the graph are Domain = (-5, -1) U (2, 5] and Range = (-4, 5]
Calculating the domain and range of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph
The above graph can be represented as a list of ordered pairs
The rule of a graph is that
The domain is the x valuesThe range is the f(x) valuesUsing the above as a guide, we have the following:
Domain = (-5, -1) U (2, 5]
Range = (-4, 5]
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A number b increased by 2 is less than -30 as an inequality
Answer:
b + 2 < -30
Step-by-step explanation:
But if it needs to be simplified the answer is b < -32
Johnson Industries purchased a metal-working lathe for $38,000. This item will be used for business 90% of the time. Accountants elected to take a $18,000 section 179 deduction and utilize the special depreciation allowance of 50%.
Prepare a depreciation schedule (in $) using MACRS.
Round all dollar amounts to the nearest cent.
The depreciation schedule (in dollars) using MACRS for the metal-working lathe is as follows:
Year 1: $1,429.00
Year 2: $2,449.00
Year 3: $1,749.00
Year 4: $1,249.00
Year 5: $893.00
Year 6: $892.00
Year 7: $893.00
What is the MACRS depreciation schedule?The depreciation schedule using the Modified Accelerated Cost Recovery System (MACRS) is prepared as follows:
Given data:
Purchase cost of the metal-working lathe: $38,000
Business use percentage: 90%
Section 179 deduction: $18,000
Special depreciation allowance: 50%
Depreciable basis = Purchase cost - Section 179 deduction
Depreciable basis = $38,000 - $18,000 = $20,000
Special depreciation allowance = $20,000 * 50%
Special depreciation allowance = $10,000
Adjusted depreciable basis = $20,000 - $10,000
Adjusted depreciable basis = $10,000
The recovery period for a metal-working lathe is 7 years.
Using MACRS, the depreciation rates for a 7-year recovery period are as follows:
Year 1: 14.29%
Year 2: 24.49%
Year 3: 17.49%
Year 4: 12.49%
Year 5: 8.93%
Year 6: 8.92%
Year 7: 8.93%
Annual depreciation expense = Adjusted depreciable basis * Depreciation rateYear 1:
Depreciation expense = $10,000 * 14.29% = $1,429.00
Year 2:
Depreciation expense = $10,000 * 24.49% = $2,449.00
Year 3:
Depreciation expense = $10,000 * 17.49% = $1,749.00
Year 4:
Depreciation expense = $10,000 * 12.49% = $1,249.00
Year 5:
Depreciation expense = $10,000 * 8.93% = $893.00
Year 6:
Depreciation expense = $10,000 * 8.92% = $892.00
Year 7:
Depreciation expense = $10,000 * 8.93% = $893.00
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A)19.0
B)10.0
Step-by-step explanation:
Using [tex]\frac{1}{2} * absin(C)[/tex]
This is used when you have an angle between two sides
Kindly check the attached image for the solution
Here, S.P. = . 1,61, 680 D%= 6%. M.P. = ?
The marked price (M.P.) is 1,72,000 when the selling price is 1,61,680 with discount of 6%.
To find the marked price (M.P.), we can use the formula:
M.P. = S.P. / (1 - D%)
Given:
S.P. = 1,61,680
D% = 6%
First, we need to convert the discount percentage to decimal form by dividing it by 100:
D% = 6/100 = 0.06
Now, we can substitute the values into the formula:
M.P. = 1,61,680 / (1 - 0.06)
M.P. = 1,61,680 / 0.94
M.P. = 1,72,000
Therefore, the marked price (M.P.) is approximately 1,72,000.
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An investment banking house conducted a survey to determine how two of its proposed investment plans for three different age categories are used. This table shows the responses they received. Plan I Plan II Neither Ages 26–35 19 14 17 Ages 36–45 14 28 8 Ages 46–55 27 21 2 What percentage of people preferring plan I are from the 36–45 age group, and what percentage of people from the 46–55 age group prefer plan II? Round your answers to the nearest whole number. A. 23% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II. B. 28% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II. C. 23% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II. D. 28% of people who prefer plan I are from the 36–45 age group, and 33% of people from the 46–55 age group prefer plan II. E. 32% of people who prefer plan I are from the 36–45 age group, and 42% of people from the 46–55 age group prefer plan II.
The Percentage of people from the 46-55 age group preferring Plan II is 42%.
The percentages, we need to calculate the ratio of people preferring Plan I in the 36-45 age group and the ratio of people preferring Plan II in the 46-55 age group.
Let's start with the first part of the question:
Percentage of people preferring Plan I from the 36-45 age group:
To calculate this percentage, we need to divide the number of people preferring Plan I in the 36-45 age group by the total number of people preferring Plan I, and then multiply by 100 to express it as a percentage.
Number of people preferring Plan I in the 36-45 age group = 14
Total number of people preferring Plan I = 14 + 28 + 21 = 63
Percentage = (14 / 63) * 100 ≈ 22.22 ≈ 22% (rounded to the nearest whole number)
So, the percentage of people preferring Plan I from the 36-45 age group is approximately 22%.
Now, let's move on to the second part of the question:
Percentage of people from the 46-55 age group preferring Plan II:
To calculate this percentage, we need to divide the number of people preferring Plan II in the 46-55 age group by the total number of people from the 46-55 age group, and then multiply by 100 to express it as a percentage.
Number of people preferring Plan II in the 46-55 age group = 21
Total number of people in the 46-55 age group = 27 + 21 + 2 = 50
Percentage = (21 / 50) * 100 = 42%
So, the percentage of people from the 46-55 age group preferring Plan II is 42%.
Based on the calculations, the correct answer is:
A. 23% of people who prefer Plan I are from the 36-45 age group, and 42% of people from the 46-55 age group prefer Plan II.
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(x−5.2)
2
+(y+3.7)
2
=49left parenthesis, x, minus, 5, point, 2, right parenthesis, squared, plus, left parenthesis, y, plus, 3, point, 7, right parenthesis, squared, equals, 49
What is its center?
What is its radius?
Step-by-step explanation:
This is the equation for a circle in the form :
(x-h)^2 + (y-k)^2 = r^2 where h,k is the center and r is the radius
center = 5.2,-3.7 and radius = sqrt (49) = 7
Any idea.???????
Here are four shapes
Rhombus and equilateral triangle will fit in regular circle and rectangle will fit in quadrilateral circle.
A Venn diagram is a diagram that helps us visualize the logical relationship between sets and their elements and helps us solve examples based on these sets. A Venn diagram typically uses intersecting and non-intersecting circles (although other closed figures like squares may be used) to denote the relationship between sets.
Here, rhombus and equilateral triangle are regular, and rectangle and triangle are not regular.
Therefore, rhombus and equilateral triangle will fit in regular circle and rectangle will fit in quadrilateral circle.
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A passenger train leaves depot 2 hours after a freight train leaves the same depot. The freight train is traveling 18 mph slower than the freight train find the rate of each train if the passenger train over, takes the freight train in 3 hours
Answer:
The passenger train is traveling at 45 mph, and the freight train is traveling at 27 mph.
Step-by-step explanation:
Let's assume the speed of the passenger train is represented by x mph.
According to the given information, the freight train leaves the depot 2 hours before the passenger train. Therefore, when the passenger train starts, the freight train has already been traveling for 2 hours.
Let's represent the speed of the freight train as (x - 18) mph, which is 18 mph slower than the passenger train.
Now, we know that the passenger train overtakes the freight train in 3 hours. This means that the passenger train traveled for 3 hours, while the freight train traveled for 3 + 2 = 5 hours.
Since speed = distance/time, we can set up the following equation based on the distances covered by each train:
Distance covered by passenger train = Distance covered by freight train
Using the formula, distance = speed × time, we get:
x × 3 = (x - 18) × 5
Simplifying the equation:
3x = 5x - 90
90 = 5x - 3x
90 = 2x
Dividing both sides by 2:
45 = x
So, the speed of the passenger train is 45 mph.
The speed of the freight train is 45 - 18 = 27 mph.
7x 2/9 what the answer
Answer:
1.55
Step-by-step explanation:
2/9=0.22 x 7 =1.55
i hope this helps!
Label the triangle sides, assuming the angle of interest is the 30-degree angle:
solve for
The side with x is the
blank side.
The side with y is the
NO SPAM I WILL REPORT YOU
blank side.
The side with 17 is the blank side
Check the picture below.
Please help i will give brainliest
The value of measure of angle 1, angle 2, and angle 3 are,
⇒ ∠1 = 106 degree
⇒ ∠2 = 74°
⇒ ∠3 = 74°
We have to given that;
Angle in figure is,
⇒ 74°
Since, From figure,
angle 1 is,
⇒ ∠1 = 180 - 74
⇒ ∠1 = 106 degree
Hence, We get;
Measure of angle 2 is,
⇒ ∠2 = 180 - 106
⇒ ∠2 = 74°
And, Measure of angle 3 is,
⇒ ∠ 3 = ∠ 2
By definition of alternate interior angle.
⇒ ∠3 = 74°
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The measure of ∠1 is 106 because it is a straight angle with 74° angles.
The measure of ∠2 is 74 because it is a vertical angle with 74° angles.
The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.
We have,
The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
Now,
∠1 + 74 = 180
∠1 = 180 - 74
∠1 = 106
And,
∠2 and 74 are vertical angles.
So,
∠2 = 74
And,
∠3 and 74 are corresponding angles.
So,
∠3 = 74
Thus,
The measure of ∠1 is 106 because it is a straight angle with 74° angles.
The measure of ∠2 is 74 because it is a vertical angle with 74° angles.
The measure of ∠3 is 74 because ∠3 and 74° are corresponding angles.
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O+O+O=30
1-3 -5 -7
9 -11 -
15
To solve the equations:
O + O + O = 30
1 - 3 - 5 - 7
9 - 11 -
15
We can start by simplifying the second equation:
1 - 3 - 5 - 7 = -14
9 - 11 - x = -14
To find the value of x, we can solve the equation:
-11 - x = -14
Adding 11 to both sides of the equation:
-11 + 11 - x = -14 + 11
Simplifying:
-x = -3
Multiplying both sides by -1:
(-1) * (-x) = (-1) * (-3)
x = 3
Now, substituting the value of x back into the second equation:
9 - 11 - 3 = -14
-5 - 3 = -14
-8 = -14
This is not a true statement. Therefore, the values provided do not satisfy the equations given.
Inputs: People at concession stand Outputs: Cost of their order
this relation a function?
it a constant function?
it a 1-1 function?
People at the concession stand as input Cost of their order's output.
(1) The relation in question is a function.
(II) This function is not constant. (Each category of concession has a different order cost.)
Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)
A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.
The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.
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Nicole and her 3 friends bought 8 pounds of candy and shared them equally. How many pounds
of candy
?
3
Answer:
Each person will get 2 pounds of candy
Step-by-step explanation:
Nicole + 3 friends = 4 total
8 pounds of candy = total
total candy / total people
8/4 = 2
Question no 59
Need solution
The area of the shaded region is 104 cm²
How to determine the areaFirst, we need to know that the area of a circle is calculated using the formula;
A = πr²
Such that the parameters of the formula are;
A is the area of the circler is the radiusFirst, let us find the area of the small circle
Area = 3.14 × 4²
Find the square value and multiply, we have;
Area = 50.24cm²
Area of the large circle = 3.14 × 7²
Find the square value and multiply
Area = 153. 86cm²
Area of the shaded region = Area of large circle - area of small circle
= 153.86 - 50.24
= 104 cm²
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round 3666042 to the nearest hundred thousand
3666042 to the nearest hundred thousand is 3,700,000
By definition, theoretical probability is equal to:
A. No. of favorable outcomes/ total no. of possible outcomes ✅️
B. No. of total outcomes/ total no. of impossible outcomes
C. No. of possible outcomes/ total no. of favorable outcomes
D. No. of total outcomes/ total no. of possible outcomes
Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes, making option A the correct answer.
The correct answer is A. Theoretical probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes. It represents the likelihood of an event occurring based on mathematical calculations and assumptions.
To provide a detailed explanation, let's break down the components of the definition:
Favorable outcomes: These are the outcomes that meet the desired criteria or event you are interested in. For example, if you are rolling a fair six-sided die and you want to find the probability of rolling a 3, the favorable outcome would be a single outcome where the die shows a 3.
Total number of possible outcomes: This refers to the complete set of all possible outcomes in the given situation. In the case of the fair six-sided die, there are six possible outcomes (numbers 1 to 6) since each face of the die represents a different number.
Theoretical probability is then calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This ratio provides an estimate of the probability of the event occurring under ideal, theoretical conditions. It assumes that each outcome is equally likely to occur.
It's worth noting that theoretical probability is based on mathematical calculations and assumptions, and it may not always reflect the actual probability observed in real-world scenarios. However, it serves as a foundation for understanding and analyzing probabilities in various contexts, such as in mathematics, statistics, and decision-making processes.
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an online store begins selling a new kind of baskelballshoe. At week zero, 30 pairs of shoes were sold.
In week 3, the store sold 240 pairs of shoes. Write an exponential model that relates the number of shoes sold to the week number, and use the model to predict how many shoes will be sold during week 7.
Answer:
3840 pairs of shoes
Step-by-step explanation:
To write an exponential model that relates the number of shoes sold to the week number, we can use the general form of an exponential function:
y = a * b^x
where:
y is the number of shoes sold,
x is the week number, and
a and b are constants to be determined.
Given the information:
In week 0, 30 pairs of shoes were sold.
In week 3, 240 pairs of shoes were sold.
We can use these two data points to determine the values of a and b.
Using the data point for week 0:
30 = a * b^0
30 = a
Using the data point for week 3:
240 = 30 * b^3
8 = b^3
b = 2 (taking the cube root of both sides)
Therefore, the exponential model that relates the number of shoes sold to the week number is:
y = 30 * 2^x
To predict the number of shoes sold during week 7, we substitute x = 7 into the model:
y = 30 * 2^7
y = 30 * 128
y = 3840
Therefore, the model predicts that 3840 pairs of shoes will be sold during week 7.
Check out this square pyramid: Find the surface area of the square pyramid (above) using its net (below).
The surface area of a square pyramid attached is
40 square units
How to find the surface area of a square pyramidThe surface area of a square pyramid is solved using the formula
= a² + 2 * a * l
where
a = side of the square
l = slant height
In the problem
a = 4
l = 3
plugging in the values
surface area of a square pyramid = 4² + 2 * 4 * 3
surface area of a square pyramid = 16 + 24
surface area of a square pyramid = 40 square units
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Which of the following represents the equation of the trigonometry function graphed below?
The equation of the trigonometric function graphed is A) f(x) = 3 sin (x) - 2.
Given a graph of the trigonometric function.
We have to find the equation of the trigonometric function.
For x = π/2, y = 1
Also, when x = 3π/2, y = -5
A) If the function is,
f(x) = 3 sin (x) - 2,
When x = π/2
f(x) = 3 sin (π/2) - 2
= 3(1) - 2
= 1
When x = 5π/2
f(x) = 3 sin (5π/2) - 2
= 3 (-1) - 2
= -5
Hence the correct option is A.
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Using digits 1to 9 fill in the boxes once write largest and smallest absolute value. Then find the decimal equivalent.
The decimal equivalent of the largest Absolute value, 987654321, is 987,654,321. the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.
The largest and smallest absolute values using the digits 1 to 9, we need to arrange them in a way that maximizes or minimizes the resulting number. Let's consider the boxes as placeholders for the digits.
To determine the largest absolute value:
We place the digit 9 in the leftmost box, as it is the largest digit among 1 to 9. Then we arrange the remaining digits, 8, 7, 6, 5, 4, 3, 2, and 1, from largest to smallest in the remaining boxes. This gives us the number 987654321, which is the largest possible number using the given digits. Therefore, the largest absolute value is 987654321.
To determine the smallest absolute value:
We place the digit 1 in the leftmost box, as it is the smallest digit among 1 to 9. Then we arrange the remaining digits, 2, 3, 4, 5, 6, 7, 8, and 9, from smallest to largest in the remaining boxes. This gives us the number 123456789, which is the smallest possible number using the given digits. Therefore, the smallest absolute value is 123456789.
To find the decimal equivalent of these numbers, we simply read the digits from left to right. The decimal equivalent of the largest absolute value, 987654321, is 987,654,321. The decimal equivalent of the smallest absolute value, 123456789, is 123,456,789.
Thus, the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.
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