Answer: 37.33 % of items cost less than $7.5
Step-by-step explanation:
To find the percentage of items that cost less than $7.5, we would need to know the probability distribution function of the cost per item, as well as the specific parameters of the distribution (such as the shape parameter).
Since the information provided is that the cost per item follows an exponential distribution and the mean cost per item is $10.5,
We can use the cumulative distribution function (CDF) of the exponential distribution which is
F(x) = 1 - e^(-λx)
where x is the cost of the item, λ is the rate parameter and e is the base of the natural logarithm.
We know the mean is $10.5 , and in an exponential distribution the mean and the rate parameter are equal, so we can say λ = 1/10.5
To find the percentage of items that cost less than $7.5, we need to find the probability that X < 7.5, which is the same as finding F(7.5)
So, F(7.5) = 1 - e^(-λ*7.5) = 1 - e^(-0.714)
Then, we need to convert this probability to percentage, so we need to multiply it by 100
F(7.5) = (1 - e^(-0.714)) * 100 = 37.33 %
Therefore, 37.33 % of items cost less than $7.5
Assume a total current of 2 amperes flows in a circuit with three resistorsR1 has a value of 1400 ohms, R2 has a value of 200 ohms and R3 has a value of 100 ohms , producing a total resistance of 80 ohms for the circuit. What is the amount of the current flow through resistor R3?
Answers:
(A)0.114
(B)0.800
(C)1.600
(D)0.228
1.600 amps of current flow through resistor r3 are measured.
Describe the resistor.A resistor is a passive, two-terminal electrical component used in circuits to apply electrical resistance.
Resistors are employed in electronic circuits for a variety of purposes, including reducing current flow, adjusting signal levels, dividing voltages, biassing active devices, and terminating transmission lines.
The parameters are determined by the query:
total current = 2 amperes
Total resistance = 80 ohms
Total current = voltage * Resistance
Total current = 2* 80
= 160V.
Consequently, the current passing through resistor R3 will be
V= IR (Ohms law)
where I (current)= V/R
current = 160/ 100
Current flowing through R3 =1.600 amperes.
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An object moves along a straight and horizontal path with a constant acceleration. If the velocity increases from rest to 11.53m/s in 5.44s, determine the acceleration of the object.
NO LINKS!!
1. Underline the hypothesis and circle the conclusion in the following conditional statement. Then rewrite the conditional statement in if-then form.
a. All 120° angles are obtuse angles.
2. Write the negation of the following statement:
a. It is raining
Answer:
1. Hypothesis: "All 120° angles"
Conclusion: "are obtuse angles"
If-then statement: If an angle measures 120°, then it is an obtuse angle.
2. It is not raining.
Step-by-step explanation:
Question 1Conditional statement
"If this happens, then that will happen."
Hypothesis: The part after the "if".Conclusion: The part after the "then".For the statement "All 120° angles are obtuse angles":
Hypothesis: "All 120° angles"Conclusion: "are obtuse angles"Therefore, the statement written in the if-then form is:
If an angle measures 120°, then it is an obtuse angle.Question 2Given statement:
"It is raining"The definition of a negation of a statement is the opposite of the given statement. For example, the negation of statement "p" is "not p."
Therefore, the negation of the given statement is:
"It is not raining"The quadrilateral DEFG,show. On the coordinate plane below is dilated from the origin by a space factor r= 2/3. Identify the coordinates of the dilated figure D^1 E^1 F^1 G^1 and the draw and label on the coordinate plane
The required dilated coordinates of the quadrilateral is given as,
D' {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G' (-2, 2).
The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
Initial corrdiantes
D = (-6, 3)
G = (-3, 3)
E = (-4, -3)
F = (5, -2)
Dilated coordinates of a quadrilateral with by scale factor of 2/3 is given as,
D' = (-6 × 2 / 3, 3 × 2 / 3)
D' = {-4, 2}
Similarly,
G = (-2, 2)
E = (-8/3, -2)
F = (10/3, -4/3)
Thus, the required dilated coordinates of the quadrilateral is given as,
D' {-4, 2}, E' (-8/3, -2), F' (10/3, -4/3), and G' (-2, 2).
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Find a counterexample to show that the statement is false. (Select all that apply.)
X >
none of these
X> 2
-1 < x < 0
0 < x < 1
XS-1
X> 1
X
A polling agency showed the following two statements to a random sample of 2,150 adults in the United States.
Equal pay statement: The issue of equal pay should be given priority over increasing the minimum wage.
Minimum wage statement: Increasing the minimum wage should be given priority over the issue of equal pay.
The order in which the statements were shown was selected randomly for each person in the sample. After reading the statements, each person was asked to choose the statement that was most consistent with his or her opinion. The results are shown in the table.
Percent of Sample
Equal Pay Statement Minimum Wage Statement No Preference
50% 42% 8%
Part A: Assume the conditions for inference have been met. Construct and interpret a 99% confidence interval for the proportion of all adults in the United States who would have chosen the minimum wage statement. (5 points)
Part B: One of the conditions for inference that is met is that the number of those who chose the minimum wage statement and the number of those who did not choose the minimum wage statement are both greater than 10. Explain why it is necessary to satisfy this condition.
a) The 99% confidence interval for the proportion of all adults in the United States who would have chosen the minimum wage statement is given as follows: (0.3926, 0.4474).
The interpretation is that we are 99% sure that the true population proportion is in this interval.
b) The condition has to be satisfied as the confidence interval is constructed considering an assumption of normality, and by the Central Limit Theorem, at least 10 successes and 10 failures are needed for the sampling distribution of sample proportions to be normal.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The sample size and the estimate are given as follows:
[tex]n = 2150, \pi = 0.42[/tex]
Hence the lower bound of the interval is given as follows:
[tex]0.42 - 2.575\sqrt{\frac{0.42(0.58)}{2150}} = 0.3926[/tex]
The upper bound of the interval is given as follows:
[tex]0.42 + 2.575\sqrt{\frac{0.42(0.58)}{2150}} = 0.4474[/tex]
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Write the formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input.
Answer: The formula for the mathematical function that takes as input an RGB color vector ⟨r,g,b⟩ and yields as output the RGB color vector that is the unique shade of gray whose total amount of light (r+g+b) is equal to that of the input is:
(r+g+b)/3, (r+g+b)/3, (r+g+b)/3
Step-by-step explanation: RGB color space is a way to represent colors digitally, where each color is represented by a combination of red, green, and blue values ranging from 0 to 255. To obtain a unique shade of gray whose total amount of light (r+g+b) is equal to that of the input color, we have to set all three color channels to the average value of the red, green and blue values.
To calculate this average value we use the formula: (r+g+b)/3
So the output of the function is ⟨(r+g+b)/3, (r+g+b)/3, (r+g+b)/3⟩ which is the unique shade of gray whose total amount of light is equal to that of the input color.
Note: This is one way to convert color to gray, other methods exist like using luminosity or other weights to RGB channels.
Use the commutative and :or associative properties to simplify 2/5 + 5/12 + (-2/5)
Answer:
5/12
Step-by-step explanation:
Use associative property of addition:
2/5 + 5/12 + (-2/5) = (2/5 + (-2/5)) + 5/12 ==> switch 5/12 and -2/5
(2/5 + (-2/5)) + 5/12 = ==> simplify
(2/5 - 2/5) + 5/12 =
0 + 5/12 = 5/12
Complete the regression equation below.
F(x)=
The regression equation, given the line of best fit and the points on the line, would be F ( x ) = 30x + 685
How to find the regression equation ?To find the regression equation, you first need to find two points on the line on the graph. Those two lines would be ( 3, 775) and ( 4 , 805).
The next step would be to find the slope of the line :
= ( Y₂ - Y ₁ ) / ( X ₂ - X ₁ )
= ( 805 - 775 ) / ( 4 - 3 )
= 30 / 1
= 30
Then use the points to find the y - intercept :
y = mx + y- intercept
775 = 30 ( 3 ) + y - intercept
y - intercept = 775 - 90
y - intercept = 685
The regression equation is:
F ( x ) = 30x + 685
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On April 11, George Jimerson had $6,521.37 in his savings account. The account pays 5.5% interest
compounded daily. How much interest will the money earn by June 30?
The interest George Jimerson would earn by June 30 be $83368.21
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
Let y represent the amount of money in Jimerson savings account after x days.
The account pays 5.5% interest compounded daily, hence:
y = 6521.37(1.055)ˣ
In June 30, the number of days from April 11 is 49. Hence;
y = 6521.37(1.055)⁴⁹ = 89889.58
The interest = 89889.58 - 6521.37 = 83368.21
The interest would be $83368.21
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Is this equation an identity?
k - 4 = 4 + k
Yes or No
Answer:
no
Step-by-step explanation:
An identity is an equality that is always true. An equation is an equality that is (only necessarily) conditionally true.
That is to say that for any real value inputted into a variable in an identity, an equality will result, whereas only certain values for a variable in an equation will necessarily result in an equality.
If the given equation is an identity, it should result in an equality no matter what the input for k is. So, to prove that it isn't an identity, we simply have to find one value for k that results in an inequality. To do so, we can simply plug in 0 for k and simplify.
[tex]k - 4 = 4 + k[/tex]
[tex]0 - 4 \stackrel{?}{=} 4 + 0[/tex]
[tex]-4 \ne 4[/tex]
We have found one value for k that results in an inequality. Thus, this equation is not an identity.
What can the Learning Center staff help you with?
Staff at the learning center can teach whole groups of students who need extra help or focus on working one-on-one with a specific child. They work on improving knowledge of academic subjects like biology as well as skills like reading comprehension.
What is a learning center instructor?Learning centre instructors work in programmes that assist at-risk students in strengthening their academic skills. Learning centre instructors can work for a private or public learning centre. Learning centre instructors work with students to teach them valuable skills and academic subjects no matter where they work.
Learning centre instructors can teach large groups of students who require extra assistance or work one-on-one with a specific child. They work on improving academic knowledge, such as biology, as well as skills, such as reading comprehension.
They are in charge of creating the overall curriculum and training programme. Learning centre instructors must also have excellent classroom management skills as well as patience in order to work with students who are experiencing difficulties.
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What is 1/5 x ( 7 x -4) =
Answer:
7x2−4x/5
Step-by-step explanation:
7x2−4x over 5
The triangles are similar.
What is the value of x?
Enter your answer in the box.
Answer:
x = 4
Step-by-step explanation:
We can look at the hypotenuse of both the triangles to find the factor that we multiply by. (In similar triangles, corresponding sides are always in the same ratio)
Big triangle:little triangle
25:5
5:1
So, we have to multiply the corresponding side of the little triangle by 5 to get an equivalent value.
Solve for x:
3x+8 = 4(5) [ratio!!]
3x+8 = 20
(subtract 8 from both sides)
3x = 12
(divide both sides by 3)
x = 4
Thus, we have our answer!
The cab charges in a metro city include a fixed charge plus the charges for the distance covered. Linus traveled 11 miles and paid $88. For the ride of 16 miles, he paid $108. How much would Linus have to pay to travel 6 miles?
$268.00
$128.00
$98.00
$68.00
Answer:
Step-by-step explanation:
The problem can be solved by using the information provided to set up a system of equations and then solving for the unknown variable, which in this case is the fixed charge.
Let x be the fixed charge.
We know that the total cost of the 11-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:
x + 11y = 88 (1)
We also know that the total cost of the 16-mile trip is the fixed charge plus the charge for the distance covered, so we can write the equation:
x + 16y = 108 (2)
Where y is the cost per mile
We can solve for y by subtracting equation (1) from equation (2), so:
16y - 11y = 108 - 88
5y = 20
y = 4
Now we know that cost per mile is 4$, we can substitute it in equation (1)
x + 11(4) = 88
x = 24
Now we know the fixed charge is 24$ and cost per mile is 4$, we can calculate the fare for 6 miles
24 + 6(4) = $48
Therefore, Linus would have to pay $48 to travel 6 miles.
help me pleace!!!!!!!
Step-by-step explanation:
For 60 muffins sold there are 3 boxes, because there are 20 muffins per box.
For 600 muffins sold there are 30 boxes, because there are 20 muffins per box.
For 6000 muffins sold there are 300 boxes, because there are 20 muffins per box.
Because 2×3=6
Find the median and mean of the data set
below:
7, 47, 43, 47, 25, 16, 18
Median :
Mean :
Answer:
25 median. 29 mean.
Step-by-step explanation:
7, 16, 18, 25, 43, 47, 47
25 is the middle number when ordered by value, so 25 is the median
7 + 47 + 43 + 47 + 25 + 16 + 18 = 203
203 / 7 (amount of numbers in the set) = 29
29 mean
A plumber bought some pieces of copper and plastic pipe. Each piece of copper pipe was 6
meters long and each piece of plastic pipe was 1 meter long. He bought 10 pieces of pipe.
The total length of the pipe was 35 meters. How many pieces of each type of pipe did the
plumber buy?
pieces of copper pipe
pieces of plastic pipe
Submit
The plumber bought 5 pieces of copper wire and 5 pieces of plastic wire.
What is an equation?
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign.
Length of each piece of copper wire = 6 m
Length of each piece of plastic wire = 1 m
Total number of pipes bought = 10
Total length of pipes = 35 m
Let the number of copper pipes be x.
Let the number of plastic pipes be y.
The equation for number of pipes will be -
x + y = 10...(1)
The equation for length of pipes will be -
6x + y = 35...(2)
Subtracting equation (1) from (2) -
5x = 25
x = 5
Substituting the value of x in equation (1) -
5 + y = 10
y = 10 - 5
y = 5
Therefore, the number of copper and plastic wires is 5 each.
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Factor completely 640-10x^2
Answer:
Step-by-step explanation:
640 - 10x^2 = (4x-10)(160 + 4x)
The factors of 640-10x^2 are (4x-10) and (160 + 4x).
i need help
please someone help me
Answer: 1/2 PI actually ez not gonna lie
Step-by-step explanation: We know that pi times radius squared times 45/360 equals 1/2 pi. PI*radius^2*0.125 = 1/2PI. Solve algebra to get r^2 = 4 or radius = 2. We need the diameter to find circumference. D = 2*r or D = 4. D * PI * 45/360 = answer. We get 4 * PI * 0.125 = 1/2 PI
I will give brainliest, if you get this correct
1) What is the probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the I.D's of five students from among ten students of which four are not of legal age?
Answer: The probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students from among ten students of which four are not of legal age is 0.288 or 28.8%.
Step-by-step explanation:
he probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated using the binomial probability formula.
The binomial probability formula is: P(x) = (n choose x) * p^x * (1-p)^(n-x)
Where:
x = the number of successful outcomes (in this case, the number of minors refused service)
n = the total number of trials (in this case, the number of IDs checked)
p = the probability of a successful outcome in a single trial (in this case, the probability that a randomly chosen student is a minor)
In this case:
x = 3 (the number of minors refused service)
n = 5 (the number of IDs checked)
p = 4/10 (the probability that a randomly chosen student is a minor)
So, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated as:
P(3) = (5 choose 3) * (4/10)^3 * (6/10)^2 = (10/3) * (0.16) * (0.36) = 0.288
Therefore, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students is 0.288 or 28.8%.
It's worth noting that this problem assumes that the waitress randomly chooses the 5 students, if the waitress doesn't pick them randomly the result may be different.
In triangle ABC, ZA=25°, ZC=55° and AB-60. What are the approximate measures of the remaining side lengths of
the triangle?
BCN 31, AC 72
BC 72, AC 31
BC 23, AC 87
O BC 87, AC 23
The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.
What is the sine law?The Law of Sines The law of trigonometric functions, sine law, sine formula, or sinusoidal rule is a trigonometric equation that relates the sizes of any triangle's edges to the sines of its orientations.
The sine law in the triangle ΔABC is given as,
AB / sin C = BC / sin A = AC / sin B
In triangle ABC, ∠A = 25°, ∠C = 55° and AB = 60. Then the third angle is given as,
∠A + ∠B + ∠C = 180°
25° + ∠B + 55° = 180°
∠B = 100°
Then the length of BC is given as,
60 / sin 55° = BC / sin 25°
BC = 30.955
BC ≈ 31
Then the length of AC is given as,
60 / sin 55° = AC / sin 100°
AC = 72.134
AC ≈ 72
The side length of the triangle AC and BC will be 72 and 31. Then the correct option is A.
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What happens to the perimeter of the frame
when it becomes a parallelogram?
The perimeter of the parallelogram is
less than the perimeter of the square.
The perimeter of the parallelogram is
the same as the perimeter of the square.
The perimeter of the parallelogram is
greater than the perimeter of the square.
The perimeter of the parallelogram is greater than the perimeter of the square.
What is a perimeter?
The complete length of a shape's boundary is referred to as the perimeter in geometry. The perimeter of a shape is obtained by adding up the length of all the sides and edges of the shape. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
Now, let's assume a geometric system of a square and a parallelogram having the same base and equivalent side of the square " a ".
Therefore, the respective two parallel sides of the Parallelogram will also be equal to " a ".
Now, let's rotate the one of the parallel lines with angle Φ clockwise then, the side lengths which aren't equal and parallel to the first set will get increased and it's incremental rate will be responsible for the increase in perimeter of the figures aslike , perimeter is the sum of the sides of the figure.
Now let's rotate alternate side length at maximum at angle θ , aslike it should touch the square at diagonally opposite angles ,
Now, let's calculate perimeters of both the figures -
Square of side length " a " = a + a + a + a = 4a
Parallelogram of two base side length " a " and two parallel set lines of length √2a
= a + a + √2a + √2a
= 2a + 2√2a
= 2a [ 1 + √2 ]
Hence, the acquired perimeter of Parallelogram is greater than that of square
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A trader buys some oranges at #50 each. He finds that six of them are rotten. He sells the rest at #80 each and makes a profit of #450. How many oranges did he buy?
The total number of oranges that the trader bought is 31
How to calculate the total number of oranges that the trader bought?A trader bought some oranges at the price of #50 each
He finds that Six of these oranges are rotten
He sells the remaining at #80
He makes a profit of #450
Therefore the number of oranges that the trader bought is
Let y represent the number of oranges that the trader bought
At a price of #50= 50x
6 oranges were rotten= x-6
Profit = 450
450= 80(x-6)-50x
450= 80x-480-50x
450= 80x-50x-480
450= 30x-480
450+480= 30x
930= 30x
x= 930/30
x= 31
Hence the trader bought 31 oranges
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A building has a number of floors of equal helght, as well as a thirty-foot spire above them all. If the
height of each floor In feet is h, and there are n floors in the building, which of the following represents
the building's total height In feet?
A.) n+h+30
B.)nh+30
C.)30n+h
D.)30h+n
The total height of the building would be nh + 30.
Option (B) is correct.
What is a simplification in mathematics?
In mathematics, simplification refers to the process of making an expression or equation simpler or easier to understand or work with. This can involve combining like terms, removing unnecessary terms or factors, or rearranging the order of the terms.
The building's total height in feet is represented by the sum of the height of each floor plus the height of the spire.
So if the height of each floor is h, and there are n floors in the building and the building's spire is 30 feet, the total height of the building is:
= n * h + 30
=nh + 30
This is because the height of each floor is h, and there are n floors, so the total height of the floors is n * h. Adding the height of the spire, 30 feet, to the total height of the floors gives nh + 30.
Hence, the total height of the building would be nh + 30.
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complex numbers. see picture for question!!!
Answer:
yes b is a right answer hope it will help you and please make me brainlist
I need help with this
Using the above equation 1/i is equal to 2/(9-5j^2+3k)
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Given; 2i+5j^2-3k=9
2i+5j^2-3k=9
2i=9-5j^2+3k
i=(9-5j^2+3k)/2
1/i=2/(9-5j^2+3k)
Therefore, the value of 1/i according to the given equation will be
2/(9-5j^2+3k)
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Kyle is curious on how long does it take for him to reach school from their house. With that he asked his parents what is their speed as they drive going to school. How long does it take for kyle to reach school if their speed is in constant 40 km/h as they travel 60 km going to school in the northern side of their city? Show your solution.
math/science..
Answer: To find how long it takes Kyle to reach school, we can use the formula:
Time = Distance / Speed
Given that Kyle's parents travel at a constant speed of 40 km/h and the distance from their house to school is 60 km, we can substitute these values into the formula:
Time = Distance / Speed = 60 km / 40 km/h
To convert the answer from hours to minutes we have to multiply the result by 60.
Time = (60 km / 40 km/h) * 60 = 1.5 * 60 = 90 minutes
So it takes Kyle 90 minutes to reach school from their house if their speed is constant at 40 km/h and the distance they are traveling is 60 km.
Step-by-step explanation:
The cost of 3 dozen oranges is rupee 54 how many oranges can be purchased for rupee 24 ?
Can you explain the steps plsss it’s for my assignment
Answer:
You can buy 17 oranges for rupee 24.
Step-by-step explanation:
3 dozen = 3 x 12 = 39 oranges
54 ÷ 39 = 1.38461538462
1 orange = rupee 1.38
1.38461538462 x 17 = 23.5384615385
17 oranges = rupee 23.54
If you add the cost of 1 more orange it would cost more than rupee 24 so you can only buy 17 oranges for rupee 24.
Hope this helps :)
Sarah needed to get her computer fixed. She took it to the repair store. The technician at the store worked on the computer for 4.25 hours and charged her $54 for parts. The total was $585.25. Write and solve an equation which can be used to determine xx, the cost of the labor per hour.
The cost of labor per hour is $125.
What is the cost of labor per hour?The equation that can be used to solve for the cost of labor per hour is a linear equation. A linear equation is an equation that has a single variable that is raised to the power of one.
The form of the linear equation is:
Total cost = cost of the parts + (cost per hour x total hours worked)
$585.25 = $54 + (4.25 x d)
$585.25 = $54 + 4.25d
In order to determine the value of x, take the following steps:
Combine similar terms:
$585.25 - $54 = 4.25d
Add similar terms
$531.25 = 4.25d
Divide both sides of the equation by 4.24
d = 531.25 / 4.25
d = 125
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