Answer:
Step-by-step explanation:
Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.
We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.
First, we differentiate the volume equation with respect to time t:
V = x^3
dV/dt = d(x^3)/dt
Using the chain rule:
dV/dt = 3x^2 * (dx/dt)
Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:
56 = 3 * (6)^2 * (dx/dt)
Solving for dx/dt:
56 = 108 * (dx/dt)
dx/dt = 56 / 108
dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)
So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.
Michelle is a dentist. One-third of her patients are under the age of 12. Five-twelfths of her patients are over the age of 65. What fraction of Michelle’s patients are 12 to 65 years old?
A: 1/6
B: 3/4
C: 3/5
D: 1/4
Simplifying this fraction gives us 1/4. The answer is (D) 1/4.
What is arithmetic sequence?
An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.
Let's start by finding the fraction of Michelle's patients who are under 12 or over 65. We know that one-third of her patients are under 12, so two-thirds must be 12 or older. Similarly, five-twelfths of her patients are over 65, so seven-twelfths must be 65 or younger.
Now, we want to find the fraction of Michelle's patients who are between 12 and 65. To do this, we need to subtract the fraction of patients who are under 12 or over 65 from 1 (since these are the only two age groups we're considering).
Fraction of patients under 12: 1/3
Fraction of patients over 65: 5/12
Fraction of patients 12 to 65: 1 - 1/3 - 5/12
We can simplify this expression by finding a common denominator:
Fraction of patients 12 to 65: 12/12 - 4/12 - 5/12
Fraction of patients 12 to 65: 3/12
Simplifying this fraction gives us 1/4. Therefore, the answer is (D) 1/4.
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What is the height, h, of the rectangular prism shown below?
Round your answer to the nearest tenth.
h
The height is
4
√34
units.
3
The height is 3 units.
We have,
l = 4 and b= 3
Using Pythagoras theorem
d² = l² + b²
d² = 4² + 3²
d² = 16 + 9
d² = 25
d= 5 unit
let h be the height.
Again, using Pythagoras theorem
34 = 25 + h²
h² = 9
h= 3 unit
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Use the image to determine the direction and angle of rotation.
graph of triangle ABC in quadrant 4 and a second polygon A prime B prime C prime in quadrant 3
90° clockwise rotation
90° counterclockwise rotation
180° clockwise rotation
360° counterclockwise rotation
The direction and angle of rotation include the following: B. 90° counterclockwise rotation.
What is a transformation?In Mathematics and Geometry, a transformation is the movement of a point from its initial position to a new location. This ultimately implies that, when a geometric figure or object is transformed, all of its points would also be transformed;
What is a rotation?In Mathematics, a rotation refers to a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
By critically observing the geometric figures, we can reasonably infer and logically deduce that the pre-image was rotated counterclockwise to produce the image.
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Let u = 4i-j, v = 5i + j. and w=i+6j.
Find the specified scalar
U*V+U*W
To find the specified scalar, we need to first find the dot product of U and V, and then the dot product of U and W, and add these two dot products together:
U·V + U·W
where U·V denotes the dot product of U and V, and U·W denotes the dot product of U and W.
The dot product of two vectors a = (a1, a2) and b = (b1, b2) is given by:
a · b = a1b1 + a2b2
Using this formula, we can find the dot product of U and V:
U · V = (4i - j) · (5i + j) = 4i · 5i + 4i · j - j · 5i - j · j = 20i^2 + (4i · j - 5i · j) - j^2 = 20 + (-i · j) - 1 = 19 - i · j
Next, we can find the dot product of U and W:
U · W = (4i - j) · (i + 6j) = 4i · i + 4i · 6j - j · i - j · 6j = 4i^2 + (4i · 6j - j · i) - 6j^2 = 4 + (24i · j) - 6 = -2 + 24i · j
Now we can substitute these values into the original expression:
U·V + U·W = (19 - i·j) + (-2 + 24i·j) = 17 + 23i·j
Therefore, the specified scalar is 17 + 23i·j.
What is the degree of -4x to the power of 3 + 6x to the power of 4 -1
what is one of the zeros of the function shown in this graph?
Answer:
x = -3 and x = 1 are the two zeroes of this function. Choose one of them for your answer.
Tina pet sits to earn extra money. She charges a flat service fee of $20, plus $15 per day. If one of her customers spent less than $125, which of the following inequalities could be used to solve for x, the number of days the customer paid for pet sitting?
Therefore, **x < 7** is the inequality that may be utilized to find x
What is inequality?A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).
For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".
Let x represent how many days the client paid for pet sitting.
$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.
We are aware that the customer's purchase was under $125. Consequently, we can write:
20 + 15x < 125
Putting this disparity simply:
15x < 105
x < 7
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which of the following describes the graph
Therefore, the graph of the given set is: closed circles on 1 and 4 with a line segment between.
How should an equation be set up to determine the value of x?A common form for an algebraic expression is one of the following: addition, subtraction, multiplication, or division. Simplify the values to determine the result.
The expression (x I x ≤ 1) U (x I x ≥ 24) represents the set of all values of x that are less than or equal to 1 or greater than or equal to 24.
the graph of this set will have a closed circle at x=1 and a closed circle at x=24
The arrows pointing outward indicate that the set continues indefinitely in both directions.
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PLEASE HELP ON QUESTION!!!
A rectangular field has a perimeter of 150cm
Field is 15 m longer than it is wide . The width of field is a meters.
A) write down equation for this information.
If answers correct I'll rate 5 stars , a thanks and maybe brainliest.
4. Assuming that the rectangles have whole number side lengths, why is it possible to draw two different rectangles that have an area of 30 square inches but not possible to draw two rectangles with an area of 7 square inches?
Answer:
hm
Step-by-step explanation:
The reason why it is possible to draw two different rectangles that have an area of 30 square inches is that there are multiple pairs of whole numbers that multiply to 30. For example, a rectangle with dimensions 5 inches by 6 inches has an area of 30 square inches, and so does a rectangle with dimensions 2 inches by 15 inches.
However, the number 7 is a prime number, which means it can only be divided evenly by 1 and itself. Therefore, the only way to get an area of 7 square inches for a rectangle is by multiplying 1 and 7, which means the dimensions of the rectangle would be 1 inch by 7 inches. Since there are no other pairs of whole numbers that multiply to 7, it is not possible to draw two different rectangles with an area of 7 square inches.
A stainless steel patio heater is a square pyramid. The length of one side of the base is 22.6 in. The slant height of the pyramid is 88.9 in. What is the height of the pyramid?
NEED AN ANSWER ASAP! IT'S DUE TOMORROW
Select all equations that have n = 6 as a solution. 2 + n = 6 n + 6 = 12 4 • n = 24 n • 3 = 2
The only equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.
How do equations work?An equation is a collection of variables, constants, and mathematical operations like addition, subtraction, multiplication, or division that are balanced by the equal sign. The equation's right-hand side (RHS) is on the right, and its left-hand side (LHS) is on the left.
To check if a given equation has n = 6 as a solution, we simply substitute n = 6 into the equation and see if it is true.
2 + n = 6 : 2 + 6 = 8, not true for n = 6.
n + 6 = 12 : 6 + 6 = 12, true for n = 6.
4 • n = 24 : 4 • 6 = 24, true for n = 6.
n • 3 = 2 : 6 • 3 = 18, not true for n = 6.
Therefore, only the equations n + 6 = 12 and 4 • n = 24 have n = 6 as a solution.
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What’s the length of side AB?
tan = 1/√3= perpendicular/ base
1/√3 = AB / AC
AB / 6 = 1/√3
AB = 6/√3
You own 23 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
The probability that the CDs are in alphabetical order is
The probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.
What is combination?
In mathematics, a combination is a way of selecting objects from a larger group of objects, where the order of selection is not important. A combination is a subset of objects that are chosen from a larger set without regard to the order in which they are selected.
The formula is given by:
C(n, r) = [tex]\frac{n!}{r!* (n - r)!}[/tex]
The total number of ways to choose 5 CDs from a collection of 23 CDs is given by the combination formula:
C(23, 5) = [tex]\frac{23!}{5!* (23 - 5)!}[/tex]
= 33649
This means there are 33649 different ways to arrange 5 CDs out of the 23 CDs.
Out of these 33649 ways, only one arrangement is alphabetical. For this to happen, the first CD chosen must be the first one alphabetically, the second CD chosen must be the second one alphabetically, and so on.
The first CD can be any of the 23 CDs. However, once the first CD is chosen, there is only one CD that can be the second one alphabetically, two CDs that can be the third one alphabetically, and so on. Therefore, the probability of choosing 5 CDs in alphabetical order is:
P = 1 / C(23, 5)
P = 1 / 33649
P ≈ 0.00003
So the probability of choosing 5 CDs in alphabetical order out of a collection of 23 CDs is approximately 0.00003 or 0.003%.
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[tex]What is the logarithmic form of the exponential equation 4^{3} =(5x+4)[/tex]
The logarithmic form of the given exponential equation in the question, 4³ = (5x + 4) is Log₄ (5x + 4) = 3.
How to convert exponential equation to logarithmic form.The exponential-to-logarithmic format is useful because it makes it easy to compute large numeric expressions. Expressions involving exponential multiplication and division can be converted to addition and subtraction by applying logarithms. Logarithmic exponential form is a common means of converting mathematical expressions in one form to another form.
The exponential form aˣ = N is transformed and written logarithmically as LogₐN = x.
The exponential form of a for the exponent of x equal to N is converted to the logarithm of the number N in base a, equal to x.
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On the Y axis, we have the profit from the trucking company and on the X axis, we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
The correct answer is: A. Y intercept will be less and X will be less.
What is slope?A linear function's slope is a gauge of how steep the line is. Between any two points on the line, it is the ratio of the change in the y-coordinate to the change in the x-coordinate. The formula is used to compute it:
slope equals (y2 - y1)/. (x2 - x1)
where any two points on the line (x1, y1) and (x2, y2) are.
The company's expenses will rise once it begins paying a driver at a rate of 0.25 cents per mile, which means its profit will decline. The profit curve on the y-axis will go vertically downward as a result of this. But, because the cost of paying the driver is fixed per mile and has no impact on the profit per mile, the slope of the line—which reflects the profit per mile—will stay the same.
Hence, A. Y intercept will be less and X will be less is correct.
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A hamster runs at a speed of 16 centimeters per second in a wheel of radius 15 centimeters.
a) What is the angular velocity of the wheel? (in radians/sec)
b) How fast will the wheel spin in revolutions per minute?
a) The angular velocity of the wheel is approximately 1.0667 radians per second. b) The wheel will spin at approximately 10.16 revolutions per minute.
What is angular velocity?Angular velocity is a measure of how quickly an object rotates or revolves around a fixed point, such as an axis or a center of rotation. It is a vector quantity that describes the rate of change of an object's angular position with respect to time, and is usually expressed in units of radians per second (rad/s) or degrees per second (deg/s).
According to given information:a) To find the angular velocity of the wheel, we can use the formula:
angular velocity = linear velocity / radius
In this case, the linear velocity of the hamster is 16 centimeters per second, and the radius of the wheel is 15 centimeters. So, we have:
angular velocity = 16 / 15
angular velocity = 1.0667 radians per second
Therefore, the angular velocity of the wheel is approximately 1.0667 radians per second.
b) To find the speed of the wheel in revolutions per minute, we need to convert the angular velocity from radians per second to revolutions per minute. There are 2π radians in one revolution, and 60 seconds in one minute. So, we can use the following formula:
angular velocity (in revolutions per minute) = angular velocity (in radians per second) * 60 / 2π
Plugging in the angular velocity we found in part (a), we get:
angular velocity (in revolutions per minute) = 1.0667 * 60 / 2π
angular velocity (in revolutions per minute) ≈ 10.16 revolutions per minute
Therefore, the wheel will spin at approximately 10.16 revolutions per minute.
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When is M equals to T
Basically M will be equal to T if the value of M is assigned to T or vice-versa.
Understanding equality of two variablesThe equality of numbers refers to a mathematical concept that indicates that two numbers are the same. When two numbers are equal, they represent the same quantity, and we can use the symbol "=" to indicate this relationship. For example, "2 + 3 = 5" indicates that the sum of 2 and 3 is equal to 5. Similarly, "7 = 7" indicates that the number 7 is equal to itself.
The concept of equality is a fundamental concept in mathematics and is used extensively in various mathematical operations and equations. We can use the concept of equality to compare two or more numbers, variables, expressions, and equations.
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Verify that segments with lengths of 21 inches, 72 inches, and 75 inches form a triangle. If so, determine whether they form a right triangle.
A. triangle, right triangle
B. triangle, isosceles triangle
C. triangle, obtuse triangle
D. triangle, acute triangle
Answer:
it would be C
Step-by-step explanation:
In which
situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf
The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.
What is expression?Expression in mathematics is a combination of symbols and numbers, often using an operation, such as addition, subtraction, multiplication, or division. It can represent a number, a variable, a function, or a mathematical statement. It can also represent a combination of these things. Expressions are used to describe relationships between numbers, variables, and mathematical concepts.
The expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and there are 2 shelves in total. This expression can be used to calculate the total number of head wraps on the shelves by multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves). As such, the expression 8×2 can be used to find the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total, resulting in a total of 16 head wraps.
In conclusion, the expression 8x2 can be used to calculate the total number of head wraps on the shelf when there are 8 head wraps per shelf and 2 shelves in total. By multiplying 8 (the number of head wraps per shelf) by 2 (the number of shelves), the total number of head wraps on the shelf can be found, resulting in a total of 16 head wraps.
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Complete questions as follows-
In which situation can the Expression
on 8×2 be used to find the total number of head wraps on the shelf?
Circle B is shown, with GHJK inscribed in the circle. The mGHJ = (3x+50)°, and mzHJK = (4x)° and mLGK] = (4x-10)°.
Find HGK and JHG
The value of
m∠GHJ = (3(20°)+50)° = 110°.
m∠GkJ = (4(20°)-10)° = 70°
m∠HJK = (4(20°))° = 80°
What is an angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Here, we have
Given: Circle B is shown, with GHJK inscribed in the circle. The m∠GHJ = (3x+50)°, and m∠HJK = (4x)° and mLGK] = (4x-10)°.
we have to find the value of HJK and JHG.
We know that
m∠GHJ + m∠GkJ = 180°
(3x+50)° + (4x-10)° = 180°
7x + 40 = 180°
7x = 140°
x = 20°
Hence, the value of
m∠GHJ = (3(20°)+50)° = 110°.
m∠GkJ = (4(20°)-10)° = 70°
m∠HJK = (4(20°))° = 80°
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A diamond merchant received a shipment of 7/10 of a pound of diamonds. He divided the diamonds into 7 equal lots and sold them to jewelers for making rings and necklaces. What was the weight of the diamonds in each lot? Write your answer as a fraction or as a whole or mixed number.
The weight of the diamonds in each lot is 4.9 pounds.
What is the fractional idea?Here, the fractional idea can be used. A fraction represents a portion of a total. A fraction is a numerical figure that designates a portion of a whole. A fraction is a component or section taken from a whole, which can be any number, a certain value, or an object.
A cargo of half a pound's worth of diamonds was received by a diamond trader. He separated the stones into 4 equal lots and sold them to jewelers so they could be used to make necklaces and rings.
Total shipment = 7/10 pound
number of equal lots = 7
then, 7 x weight = 7/10
weight = 4.9
Therefore, the weight of each lot is 4.9 pounds.
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A certain college had 3,000 students enrolled in
2015. The college predicts that after 2015, the
number of students enrolled each year will be 2%
less than the number of students enrolled the year
before. Which of the following functions models the
relationship between the number of students
enrolled, f (x), and the number of years after 2015,
x?
A. f(x) = 0.02x(3000)*
B. f(x) = 0.98x(3000)*
C. f(x) = 3000(0.02)*
D. f(x) = 3000(0.98)*
The function that models the relationship between the number of students enrolled, f(x) and the number of years after 2015, x, is D. f(x) = 3000(0.98)*.
What is a function?Mathematically, a function defines a mathematical relationship or an algebraic expression involving one variable (the independent variable) and another variable (the dependent variable).
There are four main types of mathematical functions, including:
Constant Function, example, the polynomial function of degree zero.Linear Function, for example, the polynomial function of degree one.Quadratic Function, for example, the polynomial function of degree two.Cubic Function, the polynomial function of degree three.The number of students enrolled in 2015 = 3,000
The annual decrease in students enrollment = 2%
Let f(x) the model modeling the relationship between the number of students enrolled and the number of years after 2015.
Let the number of years after 2015 = x.
Thus, the correction function is D. f(x) = 3000(0.98)*.
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A ski club charges $70 for a lift ticket and $20 per hour to ski. Jim paid at least $130 last week to ski. How many hours would he have skied.
Answer:
Step-by-step explanation: $130-$70 lift = $60/$20 per hour= 3 hours ski time
Find the probability for each problem. Then, drag the problem to the correct column.
1.) The probability of rolling two even numbers would be = 1/4
2.) The probability of rolling one even and one odd number = 1/2
3.) The probability of flipping tails on a coin and by rolling a factor of 6 on a six sided die would be = 1/3
How to calculate the probability of the various given events?To calculate the probability the formula that should be used is given as follows;
probability = possible outcome/sample space
For question 1.):
Sample space when two dice are thrown = 36
possible outcome = (2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)= 9
Probability = 9/36 = 1/4
For question 2.)
Sample space when two dice are thrown = 36
possible outcome = 18
probability = 18/36 = 1/2
for question 3.)
Sample space when two dice are thrown = 12
possible outcome = 4
probability = 4/12 = 1/3
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Write the quadratic equation whose roots are 6 and -5, and whose leading coefficient is 2.
(Use the letter .x to represent the variable.)
=0
Step-by-step explanation:
x = 6 x = -5
x - 6 = 0 x + 5 = 0
f(x) = 2(x-6)(x+5)
f(x) = 2(x² +5x - 6x - 30)
f(x) = 2(x² - x - 30)
f(x) = 2x² - 2x - 60
Mark me as brainliest
I need help with this please
Answer:
Step-by-step explanation:
just add the two numbers up 576x1 1/2= 864
A car travels at an average speed of 64 mph. how long does it take to travel 304 miles 
Assuming the time begins after the car is fully accelerated to 64 mph, 4 hours 45 minutes
IG:whis.sama_ent
Carlita surveyed all the students in her grade and reported the fraction of students who liked each type of pet.
Three-sevenths liked hamsters.
Five-sixths liked dogs.
One-half liked cats.
liked snakes.
Which list has the animals in order from least liked to most liked?
A. dogs, cats, snakes, hamsters
B. snakes, dogs, cats, hamsters
C. dogs, cats, hamsters, snakes
D. snakes, hamsters, cats, dogs
On the basis of data reported by Carlita in form of fractions , on comparing the given fractions order of animals from least liked to most liked is option-D:Snakes, hamsters, cats, dogs.
What are fractions?
A fraction represents a portion of a total. This entire may refer to a place or a group of places. The Latin word "fractio," which meaning "to break," is the source of the English term "fraction." It is simpler to identify the greater or smaller fraction when comparing fractions with the same or similar denominators. We must change fractions with dislike or different denominators to fractions with like or the same denominators in order to compare them. To do this, we must determine the denominators' Least Common Multiple (LCM). We can compare fractions simply when the denominators are made the same or similar.
Given data collected by Carlita:
Fraction of students who like hamsters= [tex]\frac{3}{7}[/tex]
Fraction of students who like dogs = [tex]\frac{5}{6}[/tex]
Fraction of students who like cats= [tex]\frac{1}{2}[/tex]
Fraction of students who like hamsters= [tex]\frac{1}{9}[/tex]
To compare all four fractions [tex]\frac{3}{7}[/tex] , [tex]\frac{5}{6}[/tex] , [tex]\frac{1}{2}[/tex] & [tex]\frac{1}{9}[/tex]
We find LCM of denominators 2,6,7 & 9
prime factors:
2=2
6=2 x 3
7=7
9= 3 x 3
LCM=2 x 3 x 3 x 7
=126
Equivalent fractions with denominator 126:
[tex]\frac{3}{7}[/tex] = [tex]\frac{3}{7}[/tex] × [tex]\frac{18}{18}[/tex] = [tex]\frac{54}{126}[/tex]
[tex]\frac{5}{6}[/tex] = [tex]\frac{5}{6}[/tex] × [tex]\frac{21}{21}[/tex] = [tex]\frac{105}{126}[/tex]
[tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] × [tex]\frac{63}{63}[/tex] = [tex]\frac{63}{126}[/tex]
[tex]\frac{1}{9}[/tex] = [tex]\frac{1}{9}[/tex] × [tex]\frac{14}{14}[/tex] = [tex]\frac{14}{126}[/tex]
On arranging least to most [tex]\frac{54}{126}[/tex], [tex]\frac{105}{126}[/tex], [tex]\frac{63}{126}[/tex] & [tex]\frac{14}{126}[/tex] we get
[tex]\frac{14}{126}[/tex] < [tex]\frac{54}{126}[/tex] < [tex]\frac{63}{126}[/tex] < [tex]\frac{105}{126}[/tex]
snakes<hamsters<cats<dogs
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Refer to the attachment for the complete question.
1. If it takes you 2¹/2 hours to assemble one unit, how many units will you complete in 15 hours?
(Note: Change 2¹/2 to an improper fraction before calculating.)
Answer:
Step-by-step explanation:
Make a chart.
units hours
2 5
4 10
6 15