The 100 feet per second rate at which rocket is rising vertically upwards and the 50 feet distance of the observation position from the launch, indicates;
A) The height of the rocket after exactly 2 seconds is 200 feet
B) The rate of the angular motion at which to scan upwards to keep track of the rocket is 2/17 radians per second
What is an angular motion?Angular motion is a circular motion of an object about a fixed axis, described in radians per second.
The rate at which the rocket is rising up in the air = 100 feet per second
The horizontal distance from the point of launch to the observer = 50 feet
The time at which the height of the rocket is required = 2 seconds
A) The height of the rocket after 2 seconds, h = 2 s × 100 ft/s = 200 ft
B) The angle of elevation of the line of sight to the rocket = θ
tan(θ) = h/50
sec²(θ)·(dθ/dt) = (1/50)·(dh/dt)
(dθ/dt) = (1/50) × (dh/dt)/sec²(θ) = (1/50)×(dh/dt)×(cos²(θ))
At time, t = 2 seconds, the height of the rocket = 200 feet
Therefore;
tan(θ) = 200/50 = 4
θ = arctan(4)
dh/dt = The vertical velocity of the rocket = 100 ft/s
(dθ/dt) = (1/50)× 100 ×(cos²(arctan(4))) = 2/17
The rate at which the eyes is scanning upwards is 2/17 radians per second
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ç
Radius
Diameter
Circumference
help asap, whats the answer?
The function f, in the slope-intercept form is f= -3x+6.
What is a slope?The slope or gradient of the line is a numerical value used to describe a line's steepness and direction in mathematics. It was first used to describe slope in O'Brien's (1844) and Todhunter's (1888) versions of the equation for a straight line, which are both written as "y = mx + b" and "y = mx + c," respectively. The choice of the letter m for slope has no apparent justification.
Calculating slope involves comparing the "vertical change" to the "horizontal change" between any two points on a line, or any two points. The ratio, which provides the same number for each, is occasionally given as a quotient ("rise over run").
Here given,
For a linear function f,
f(2)=0 and f(4)=-6
So, from the given hint the points are (2, 0) and (4, -6)
Here slope m=(-6-0)/(4-2)
m=-6/2
m= -3
We know that the equation of the function in slope-intercept form is:
f=mx +c
By substituting the point (2, 0) and m= -3 in the function we get,
0= -3(2)+c
c=6
Now, by substituting m= -3 and c=6 in the function, we get
f= -3x+6
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What type of number is 15.301i?
Choose all answers that apply:
Real
Imaginary
Complex
The number 15.031i is an Imaginary number.
What is a complex number?
Complex numbers are those that are expressed as a + ib, where a and b are actual numbers and i is a fictitious number called a "iota." i has the value (√-1).
What is a real number?
A real number is a number that can be used to represent a continuous one-dimensional quantity in mathematics, such as a temperature, duration, or distance. Continuous in this context suggests that values may vary by arbitrary little amounts. An infinite decimal expansion can nearly always represent any real number.
Given number is 15.031i.
Iota is denoted by i which is an imaginary number.
Since no real number is not added with given number, it is not a real number.
Since iota presents in the given number, it is an imaginary number.
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PLEASE HELP ASAP!
On a number line, point A is located at 4, point C is located at 11, and point B lies between points A and C. What is the location of B such that the ratio of AB:BC is 2:3?
8.2
6.8
5.9
5.6
The location of B under the Line Segment Partition is 6.8
What is Line Segment Partition?
A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.
Given in the question that on a number line AC;
Location of Point A = 4
Location of point C = 11
point B lies between points A and C
So, B divides line AC in the ratio AB: BC = 2:3.
Thus;
BC = 3/5 of the total length of the AC
AB = 2/5 the total length of the AC
Then, total length of AC = 11-4 = 7
BC = 3/5 * 7 = 4.2
AB = 2/5 * 7 = 2.8
Thus, the location of point B is; 4 + 2.8 = 6.8
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Does dilation affect driving?
Yes, dilation affects the driving.
When you get your eyes dilated, your doctor uses special drops to open your pupils wide. This let them get a look at your whole eye, including all the nerves and blood vessels at the back, to check for signs of diseases
When dilated, the pupil is unable to get smaller, and thus block out light in bright areas. This causes glare in your vision so you can't see things clearly.
The drops also make it difficult to focus on things up close, but usually don't affect distance vision.
So, Your eyesight will be impaired, so some experts say you should play it safe and not get behind the wheel will leds to affecting your driving
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7/1 in simplest form
Answer:
7
Step-by-step explanation:
hope it helps!
Answer:
7
Step-by-step explanation:
7 over one is a whole number
Estimate a 15% tip on a dinner bill of 48.71 by first rounding the bill amount to the nearest ten dollars.
The 15 percent tip on a dinner bill of 48.71 dollars is 7.3 dollars
How to find the estimation of a dinner bill?The dinner bill is 48.71 dollars. Let's estimate a 15 percent tip on the dinner bill as follows:
In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100.
In other words, Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Therefore, let's estimate the 15% tip on the dinner bill of 48.71 dollars.
dinner tip = 15% of 48.71
dinner tip = 15 / 100 × 48.71
Hence, the estimated 15% tips of the dinner bill is as follows:
dinner tip = 7.3065 dollars
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Greta is mailing a care package to her little sister at college. After packing the box, she weighs it on her bathroom scale to estimate the mailing cost. The scale shows the package weighing 3 pounds. At the post office, the clerk weighs the package on a more precise scale, and it weighs 3.25 pounds. What is the percent error for Greta's scale's measurement?
Answer: 7.7%
Step-by-step explanation:
So the answer is 7.7
To find the percent error, start by listing the key information from the problem.
Greta's scale shows the package weighing 3 pounds.
The scale at the post office shows the package weighing 3.25 pounds.
First, find the amount of error. It is the difference between 3.25 and 3, which is 0.25.
Now, use the formula to find the percent error.
percent error =
amount of error
correct amount = 0.25
3.25
= 0.0769…
You can rewrite this as a percent rounded to the tenths place, 7.7%. So, the percent error for Greta's scale measurement is about 7.7
theorem: there is no smallest positive rational number. a proof by contradiction of the theorem starts by assuming which fact?
that there is no smallest positive rational number is proven below.
What is Rational Number?
Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.
So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have commonly divisible.
Let r be any reasonable number.
We can infer that r/2 is rational because r is a rational number.
There is no smallest rational number so we can assume that r/2 r because r/2 is rational.
Hence, proved that here is no smallest positive rational number.
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what is 4 + X ≤ - 28?
Answer:
x≤−32
Step-by-step explanation:
Help!! Show your work please!
Answer:
62 degrees
Step-by-step explanation:
first we find angle C by subtracting 116 from 180
180-116
64 degrees is angle c
Sum of all three angles of a triangle is 180 degrees
(3x-13)+(2x+4)+64=180
5x-9+64=180
5x+55=180
-55. -55
5x=125
/5. /5
x=25
Now we know x we can find angle A
3(25)-13
75-13
62 degrees
Hopes this helps please mark brainliest
According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting time of 11 minutes before an IRS telephone assister answers. Based on data from past years, you can assume that the standard deviation of waiting times is 8 minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day is significantly less that the overall mean waiting time of 13 minutes? Use alpha=0.05
Calculate the test statistic
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis.
What is test statistic?A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.
A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.
The alternative and null hypotheses are listed below.
Lack of hypothesis H0: μ = 13
Ha: 13 Alternative Hypothesis
Statistical test, z = (xbar - mu)/(sigma/sqrt(n))
z = (11 - 13)/(8/sqrt(50))
z = -1.77
Region of Rejection
For α= 0.05, this is a left-tailed test.
Z has a critical value of -1.645.
Therefore, if z -1.645, reject H0 and accept the null hypothesis.
P-value Approach
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis
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which car is ahead after three minutes? car a car b explain your reasoning. the area under curve a is greater than the area under curve b. the area under curve b is greater than the area under curve a. (b) what is the meaning of the area of the shaded region in the context of this problem? it is how much faster a is traveling than b after 3 minutes. it is how much faster b is traveling than a after 3 minutes. it is the distance by which a is ahead of b after 3 minutes. it is the distance by which b is ahead of a after 3 minutes. (c) which car is ahead after six minutes? car a car b explain your reasoning. the area under curve a is greater than the area under curve b. the area under curve b is greater than the area under curve a.
a) car A is ahead of car B after 3 minutes.
b) Velocity is the shaded region.
c) the area under curve b is greater than the area under curve a.
a) The total distance represented by the shaded region A, the area under the graph of v(t).
(c) A is a triangle, so its area is
A =1/2(base)(height)
= 1/2(5 sec)(80 ft/s) = 200 ft
b) The meaning of area of the shaded region in this problem is: Velocity
Velocity is the directional velocity of a moving object as an indicator of the rate of change of position, observed from a certain frame of reference and measured at a certain time reference (eg 60 km/h northward).
c) The distance travelled will be represented by the area
under the velocity graph.
However, first convert everything to meters and seconds:
320 km/h = 1000
Now,
60·60 320 m/s ≈ 88.89 m/s.
A =1/2(base)(height)
= 1/2(30 sec)(88.89 m/s) ≈ 1333.3m
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Use numerals instead of words. if necessary, use / for the fraction bar. if p − 1 is a factor of p4 + p2 p − k, the value of k is:____.
Use / for the fraction bar if necessary. if p − 1 is a factor of p^4 + p^2 + p - k , the value of k is 1 + p^2 + p^4.
A fraction bar is a graphic representation of fractions that is useful for fraction comparison and fraction operations. Part-to-whole representational models like fraction bars or fraction strips are used. One unit out of a whole is represented by each segment of a fraction bar.
To comprehend the value of a fraction, utilize fraction bars. They can also be utilized for comparing fractions and, subsequently, adding and removing fractions. The ability to visualize a fraction bar for just any fraction is crucial.
p - 1 = p^4 + p^2 + p - k
k = 1 + p^2 + p^4
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Solve the problems.
Pedro has a stand where he sells tea and lemonade. He sells lemonade for $2 per
cup and tea for $4 per cup. This weekend, Pedro sold 5 times as much lemonade
as he did tea. He earned a total of $120. What do the expressions 4t and 20
represent in the system of equations?
4t+ 2 = 120
l = 5t
SOLUTION
The terms 4t and 120 represents the cost of 4 cups of tea and total cost respectively.
What is a system of equations?A system of equation is defined as the group of equations having the same degree and same number of variables.
The given system can have one or more than one or no solutions at all.
The system having no solutions are called inconsistent while the ones having them are called consistent.
The given problem can be solved as follows,
Suppose the number of cups of tea and lemonade be t and l respectively.
Then, the following equations can be formed for the given case,
The equation for total cost is given as,
4t + 2l = 120 (1)
And, the equation for the number of cups is given as,
l = 5t (2)
Now, the term 4t in equation (1) represents the cost for 4 cups of tea and 120 represents the total cost.
Hence, the given terms represent the cost of 4 cups of tea and the total cost of tea and lemonade.
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7. A farmer wants to start raising cows, horses, goats, and sheep, and desires to have a rectangular pasture for the animals to graze in. However, no two different kinds of animals can graze together. In order to minimize the amount of fencing she will need, she has decided to enclose a large rectangular area and then divide it into four equally sized pens by adding three segments of fence inside the large rectangle that are parallel to two existing sides. She has decided to purchase 7500 ft of fencing. What is the maximum possible area that each of the four pens will enclose?
Having a rectangular pasture for the animals to graze in is something a farmer wants in order to start growing cows, horses, goats, and sheep. She has decided to purchase 7500 ft of fencing. 1875 square feet is the maximum possible area that each of the four pens will enclose.
The maximum possible area of each pen is 1875 square feet. To calculate this, first calculate the total area of the large rectangle that the farmer is enclosing. To do this, multiply the total length of the fencing (7500 feet) by the width of the fence (1 foot). This gives us 7500 square feet as the area of the large rectangle.
Next, divide the area of the large rectangle by 4 to get the area of each pen. This gives us 1875 square feet as the maximum area of each pen.
Total Area of Large Rectangle = 7500 ft x 1 ft = 7500 sq ft
Area of Each Pen = 7500 sq ft / 4 = 1875 sq ft
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a wooden artifact from an ancient temple has a 14c activity of 38.0 counts per minute as compared with an activity of 58.2 counts per minute for a standard at zero age. the half-life of 14c is 5715 years. what is the age of the artifact?
The age of the artifact is 3523.77 years.
What is radioactive decay?
The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.
Here,
The half-life of the reaction is defined as the time required by a substance to reach half its initial concentration. It is represented by t(1/2)
All radioactive decay processes follow the first-order reaction.
The equation for the half-life for first-order reaction follows:
t(1/2) = 0.693/k....(1)
where,
k = rate constant of a first-order reaction
Given value:
t(1/2) = 5715 years
Put the value of t in equation (1), and we get
k = 0.693/5715
k = 1.21×10⁻⁴yr
The integrated rate law expression for first-order reaction follows:
t = 2.303/k×㏒(a/(a-x))
where,
t = time period
a = initial concentration of the reactant = 58.2 counts per minute
(a-x) = Concentration of reactant left after time t = 38.0 counts per minute
k = rate constant of a first-order reaction
Put the values in the equation and we get
t = 2.303/1.21×10⁻⁴㏒58.2/38
t = 3523.77 years.
Hence, the age of the artifact is 3523.77 years.
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Solve 5x−14 = 14−2x . Check your solution.
two boxes of Apples the sum of their weight is 54 kilograms the first has 12kg more than the second so the number of kilograms in the second box is....... kg.
Answer:
If the first box of apples weighs 12 kilograms more than the second box, then the weight of the second box is 54 - 12 = <<54-12=42>>42 kilograms.
Geometry-Need help
.......
After solving for angles, the value of p in the given angles is 44°.
What are angles?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex.
The name "angel" comes from the Latin word "angulus," which means "corner."
Angles are also produced when two planes intersect.
These are what are known as dihedral angles.
So, we know that ∠CAD = 90°.
And since ∠CAB is s straight angle. Then,
∠CAD + ∠DAB = 180
90 + p + 46 = 180
p + 136 = 180
p = 180 - 136
p = 44°
Therefore, after solving for angles, the value of p in the given angles is 44°.
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Write (-2^6) as repeated addition and evaluate. Is the answer negative or positive?
Answer:
to write (-2)^6 as repeated addition, we can write it as -2 + -2 + -2 + -2 + -2 + -2 + -2. When we evaluate this expression, we get -128. Therefore, the answer is negative
Serenity has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 210 square meters. Solve for the dimensions (length and width) of the field.
The dimensions of the rectangular field is 15 meters long and 14 meters wide.
A rectangle is a two-dimensional figure that has 2 pair of parallel sides that are of the same length. The corners made by these sides are right triangles.
Let x = length of the rectangular field
y = width of the rectangular field
If the area of the land is 210 square meters, then the product of its length and width is equal to 210 square meters.
A = l x w
210 = xy
x = 210/y
Serenity has 58 m of fencing for the perimeter of the rectangular field.. Hence,
P = 2l + 2w
58 = 2x + 2y
Substitute the expression of x and solve for y.
58 = 2x + 2y
58 = 2(210/y) + 2y
58 = 420/y + 2y
Multiply both sides by y and divide by 2.
29y = 210 + y²
y² - 29y + 210 = 0
(y - 14)(y - 15) = 0
y = 14 ; y = 15
Hence, y = 14.
Substitute the value of y and solve for x.
x = 210/y
x = 210/14
x = 15
Hence, the length and width of the field is 15 meters and 14 meters, respectively.
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Give the slope between the points (-5,-2)(-2,-7)
Step-by-step explanation:
Give the slope between the points (-5,-2)(-2,-7)
slope = change in y / change in x
slope = (-2 - (-7)) / (-5 - (-2))
slope = ( -2 + 7) / ( -5 + 2)
slope = 5/-3
slope = -5/3 or -1.667
Deb is searching online for airline tickets. Two weeks ago, the cost to fly from Denver to Hartford was $250. Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer:
1/ 42% increased
2/ 62%
Step-by-step explanation:
Let's find the answer to the first question
Take 355 divided by 250, then times 100% = 142%
142% - 100% = 42% increase
So the percent increase is 42%
Now let's find the answer to the second question
First, find the total cost by 355 + 50 = $405
Take 405 divided by 250, then times 100% = 162%
162% - 100% = 62%
It increases by 62% if the airline charges ann additional $50 baggage fee!
Which function has a domain of all real numbers?
A. y = (1 + 2)
B. y = -2(3r)
C. y = (20) - 7
D. y = - +
+5
On solving the following question, the function that has domain of all real numbers is - [tex]y = -2(3X)^{\frac{1}{6} }[/tex]
What are real numbers?All numbers that we can recall are real numbers except complex numbers. The union of the set of rational numbers and the set of irrational numbers is the set of real numbers denoted by the symbol R.
What are rational numbers?A rational number is any number that can be expressed as the ratio p/q. The fraction's denominator is denoted by "q," while the numerator is represented by "p." "q" is not zero.
Both 5 and 1/2 are actual figures. X also defines a number, but since it's negative, it's an integer because it's rational.
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Helppppppppppppppppppppppppp
A i think maybe
:>..,.h,j.
Ms.Miller decides to give a test worth 120 points and contains 36 questions. Multiple-choice questions are worth 3 points and open response questions are worth 5 points. How many of each type of question are there?
The number of multiple-choice questions is 30.
The number of open-response questions is 6.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
Number of multiple choice questions = M
Number of open response questions = N
We can make two equations.
M + N = 36 _______(1)
3M + 5N = 120 ______(2)
From (1) we get,
M = 36 - N ______(3)
Putting (3) in (2) we get,
3(36 - N) + 5N = 120
108 - 3N + 5N = 120
2N = 120 - 108
2N = 12
N = 6
Now,
Putting N = 6 in (3) we get,
M = 36 - 6
M = 30
Thus,
The number of multiple-choice questions and open-response questions is 30 and 6.
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1 what is recursion? a problem solution defined in terms of a list. a problem solution defined without function calls. a problem solution defined in terms of itself. a problem solution defined iteratively.
Recursion is defined as "defining an issue in terms of itself" or "solving a problem via the solution of smaller subproblems (smaller versions of the same problem)". This concept is frequently utilized in algorithms and data structures to tackle difficult issues by partitioning them into simpler ones.
What is recursion, according to this image? a list-based definition of a problem-solving approach. a solution to a problem that does not need using functions. a solution to a problem that is specified by itself. an incrementally specified solution to a problem.
A straightforward illustration of a recursive function is the factorial, which multiplies a number by itself while lowering it slowly. Recursive functions can relate to a wide variety of self-referencing looping operations, such as those where n = n + 1 given an operational range.
Hence recursion is a problem solution defined in terms of itself.
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spam: a researcher reported that 71.8% of all email sent in a recent month was spam. a system manager at a large corporation believes that the percentage at his company may be 70% . he examines a random sample of 500 emails received at an email server, and finds that 373 of the messages are spam. can you conclude that the percentage of emails that are spam is greater than 70% ? use both
There is sufficient proof to presume that under 77% of messages are spam.
Explain hypothesis test.A statistical hypothesis test is a technique for measurable induction used to conclude whether the information within reach adequately support a specific theory. Speculation testing permits us to offer probabilistic expressions about populace boundaries.
According to question:Given the information in the inquiry;
Test size n = 500
x = 361
p₀ = 77% = 0.77
q₀ = 1 - p₀ = 1 - 0.77 = 0.23
p = x/n = 361/500 = 0.722
Speculation;
Null hypothesis H₀ : p ≥ 77% or 0.77
Alternative hypothesis Hₐ : p ≥ 77% or 0.77
Test Measurement
z = ( p - p₀ )/√( ( p₀ × q₀ )/n )
so we substitute
z = ( 0.722 - 0.77 )/√( ( 0.77 × 0.23 )/500 )
z = - 0.048/√( 0.1771/500 )
z = - 0.048/√0.0003542
z = - 0.048/0.01882
z = - 2.55
so our p-worth will be;
p-value = p( z < - 2.55 ) {from table }
p-value = 0.0054
at 0.05 degree of importance ∝
p-value ( 0.0054 ) is not as much as importance level ∝ ( 0.05 )
Accordingly we Reject Null hypothesis H₀
Thus, there is sufficient proof to presume that under 77% of messages are spam.
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The following year Tiffany gets $25 and 1 box of candy. Todd gets $20 and 5 boxes of candy. Their grandmother assures them that she spent the same amount on each gift. What is the price of a box of candy?
The price of a box of candy will be $1.25.
What is an expression?Expression in math's is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
Tiffany gets $25 and 1 box of candy.
And, Todd gets $20 and 5 boxes of candy.
Now,
Since, Tiffany gets $25 and 1 box of candy.
And, Todd gets $20 and 5 boxes of candy.
Let price of box of candy = x
So, We can formulate;
⇒ $25 + x = $20 + 5x
Solve for x as;
⇒ $25 - $20 = 5x - x
⇒ $5 = 4x
⇒ x = 5/4
⇒ x = $1.25
Thus, The price of a box of candy = $1.25
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