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By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.

According to the statement, we have the equation of a fraction and we need to find the expression by simplify the former expression. In this situation we must use factor decomposition and algebra properties to make simplification effective:

42 / 49                           Given

(2 × 3 × 7) / (7 × 7)          Factor decomposition

(2 × 3) / 7 × (7 / 7)           Commutative and associative properties / Multiplication of fractions

6 / 7 × 1                           Definition of division / Existence of the multiplicative inverse

6 / 7                                 Modulative property / Result

By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.

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Both cyclist are moving apart at a speed of 9.434 mi/hr.

Velocity is the direction at which an item is moving and serves as a measure of the rate at which its location is changing as seen from a certain point of view and as measured by a specific unit of time (for example, 60 km/h northbound). In kinematics, the area of classical mechanics that deals with the motion of bodies, velocity is a basic idea. A physical vector quantity called velocity must have both a magnitude and a direction in order to be defined. Speed is the scalar absolute value (magnitude) of velocity; it is a coherent derived unit whose quantity is measured in metres per second (m/s or m/s1) in the SI (metric system).

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The value of j from the equation h-10/j=k is equal to 10/(h-k).

Given that the equation is h-10/j=k.

We are required to find the value of j from the given equation.

Equation is a relationship between two or more variables that are expressed in equal to form. It may be a linear equation,quadratic equation, cubic equation and many more depending on the power of the variables present in that equation.

The equation is h-10/j=k.

-10/j=k-h

1/j=(k-h)/-10

j=-10/(k-h)

j=10/(h-k)  

(We can eliminate the negative sign by taking negative out from the denominator.)

Hence the value of j from the equation h-10/j=k is equal to 10/(h-k).

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A line segment has the endpoints as K and L that are (0,2) and (0,6).The  midpoint M is (0,4).

Given that,

The line segment has the endpoints as K and L that are (0,2) and (0,6).

The Formula for the Midpoint of a Line Segment

Let the line segment's termination point be ([tex]a_{1}[/tex], [tex]b_{1}[/tex]) and ([tex]a_{2}[/tex], [tex]b_{2}[/tex]) respectively. The following is the midpoint formula for a line segment connecting these two points:

(a,b)=[tex](\frac{a_{1} -a_{2} }{2}, \frac{b_{1} -b_{2} }{2} )[/tex]

Where

[tex]a_{1} =0,b_{1} =2 \\and \\a_{2} =0,b_{2} =6[/tex]

[tex](a,b)=(\frac{0+0}{2},\frac{2+6}{2}) \\(a,b)=(0,4)[/tex]

Therefore, When the line segment with the endpoints k and L the midpoint M is (0,4).

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i think the answer is 3/10

Answer: 28 feet

Step-by-step explanation: The ratio of length to width is 2:1. Add the 2 numbers and it will give you 3. Then, divide 84 by 3 and it will give you 28. Times this by 1 (as the ratio of the width is 1). This will give you 28.

Step-by-step explanation:

Assume the number of double matches is x (matches)

the number of single matches is y (matches)

(Condition: x > 0 and y > 0)

Because there are 13 matches in progress, so:

x + y = 13 (1)

Because there are 38 people playing (4 people on each double match and 2 people on each single match), so:

4x + 2y = 38 (2)

A system of equation is made by combining (1) and (2):

x + y = 13 (1)

4x + 2y = 38 (2)

Take (2) - 2×(1):

=> 2x = 12

=> x = 6

Substitute the result on (1)

=> y = 7

So there are 6 double matches and 7 single matches being played

The first five term of the sequence are 42, 35, 28, 21 and 14.

According to the given question.

We have a rule for finding the terms of a sequence i.e. [tex]a_{n} = a_{n-1} -7[/tex].

Also, the first term of the sequence is a1 = 42

Therefore,

The second term of the sequence is given by

Second term [tex]a_{2}[/tex] = [tex]a_{1}[/tex] - 7

⇒ Second term = 42 - 7 = 35

Similarly,

The third term of the sequence, [tex]a_{3}[/tex] = [tex]a_{2}[/tex] - 7 = 35 - 7 = 28

Fourth term of the sequence = 28 - 7 = 21

Fifth term of the sequence = 21 - 7 = 14

Hence, the first five term of the sequence are 42, 35, 28, 21 and 14.

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We get the age of Jack is 29 years and the age of Jill is 16 years.

We are given that the sum of Jack's age and Jill's age is 45 years.

Let Jack's age be x.

Let Jill's age be y.

x + y = 45

x = 45 - y

Now, we are also given that jack's age next year will be twice Jill's age last year.

Jack's age next year = x + 1

Jill's age last year = y - 1

ATQ, We get the equation as:

x + 1 = 2( y - 1)

x + 1 = 2 y - 2

x = 2 y - 2 - 1

x = 2 y - 3

We get that:

45 - y = 2 y - 3

2 y + y = 45 + 3

3 y = 48

y = 48 / 3

y = 16 years.

x + y = 45

x + 16 = 45

x = 45 - 16

x = 29 years.

Therefore, we get the age of Jack is 29 years and the age of Jill is 16 years.

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number = x

2/3x + 18 = 23

2/3x = 5

x = 15/2 = 7.5

the variable(s) x have a value of 13.

A variable is any property, amount, or number that can be measured or counted. A data item is another name for a variable. Age, sex, business income and expenses, place of birth, capital expenditures, class grades, eye color, and car kind are only a few examples of variables.

A variable is a value that could change based on the details of an experiment or the parameters of a mathematical problem. A variable is typically identified by a single letter. The letters x, y, and z are the universal symbols for variables that are most frequently employed.

According to given value ;

4x+(7x+37)=180

sum of three angle equal to 180

4x+7x+37=180

4x+7x=180-37

11x=143

x=143/11

x=13

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The coffee reaches t ≈ 12 minutes a temperature of 150◦F.

(t) = Ts + (T0 - Ts)e-kt, according to Newton's Law of Cooling.

T(t) = temperature of the coffee cup t minutes after being placed in the roomTs is the ambient temperature.T0 indicates the coffee cup's beginning temperature.

(a).  Using the given information, we have T(t) = 70 + (160 - 70)e-kt

= 70 + 90e-kt

T(5) = 70 + 90e-k(5) = 112.5

So, 90e-5k = 42.5

e-5k = 0.47222222

-5k = ln(0.47222222)

 k = 0.15      Temperature after 10 minutes = T(10) = 70 + 90e-0.15(10)

 ≈ 90.1

-------------------------------------------------------------------------------------

(b). When will the temperature of the coffee reach 85°?

     Find t so that T(t) = 85:   70 + 90e-0.15t = 85

90e-0.15t = 15

e-0.15t = 0.16666666

-0.15t = ln(0.166666666)      

t ≈ 12 minutes

According to Newton's law of cooling, a body's rate of heat loss is inversely related to the temperature difference between it and its surroundings. The law is frequently qualified to state that the tiny temperature differential and the consistency of the heat transmission mechanism must exist. As a result, it is the same as asserting that the heat transfer coefficient, which mediates between heat losses and temperature variations, is constant. Due to the fact that the thermal conductivity of the majority of materials very slightly depends on temperature, this requirement is typically satisfied in heat conduction (where it is guaranteed by Fourier's law). Newton's Law is applied in convective heat transfer for forced air or pumped fluid cooling.

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Answer:

Step-by-step explanation:

Answer: 24

Step-by-step explanation: first we can rewrite the expression as 170%*x=40.8 (x is your answer). By solving and simplifying it, you should get 24.

The dimensions of expensive television is 32 inches through 64 inches.

This trouble may be solved if we understand the idea of fraction and a way to calculate the part of a fragment.

right here it is for the reason that the inexpensive tv is 12 inches by means of 24 inches.

Also it is given that the expensive television is [tex]\frac{8}{3}[/tex] of the cheaper one.

Now taking the length into consideration the length of the television is

  =[tex]\frac{8}{3}*12[/tex]

  = 32 inches

Now taking the width into consideration the width of the television is

 =[tex]\frac{8}{3}*24[/tex]

 = 64 inches

So, the dimension of the expensive television is 32 inches by 64 inches.

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Answer:

27

Step-by-step explanation:

27

Explanation:

"Percent" or "%" means "out of 100" or "per 100", Therefore 18% can be written as  

18 /100 .

When dealing with percentage, the word "of" means "times" or "to multiply".

Finally, lets call the number we are looking for "n".

Putting this altogether we can write this equation and solve for  "n "

while keeping the equation balanced:

n  =  18 /100  ×  150

n  =  2700 /100

n  =  27

27 is 18% of 150

Answer:

23200

Step-by-step explanation:

Answer 5795

Step-by-step explanation:

An unreliable study can occur if the test administration is inconsistent

Consistency is the key to success in anything and it implies to the studies and surveys as well. If you want the results of the study to be reliable, then you must be consistent in test administration.

Inconsistency can lead to various issues like improper representation of the feedback which may alter the results. This can lead to various problems.

For example, test performed at certain time may have a different set of people and absence of periodic tests can accommodate feedback from irrelevant people.

Therefore, a proper set schedule must be followed for the tests with consistency.

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Answer:

a. 0, -6, -18, -21, -90

b. 3, 0, -6, -18, -42

c. A starting point of any number ≥ 6 will result in a sequence of positive values

Step-by-step explanation:

Here the sequence is governed by the rule:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]
[tex]\textsf {where $a_n$ is the nth term and $a_{n-1}$ is the previous term}}[/tex]

1) Starting with a₁ = 0 we get
a₂ = 2(a₁ - 3) = 2(0 - 3) = -6
a₃ = 2(a₂ - 3) = 2(-6 -3) = 2(-9) = -18
a₄ = 2(a3 - 3) = 2(-18 - 3) = 2(-21) = -42
a₅ = 2(a₄ - 3) = 2(-42- 3) = 2(-45) = -90

So the first 5 numbers in the sequence starting with 0 are:
0, -6, -18, -21, -90

2) I will approach this slightly differently

We have the relationship:
[tex]\sf a_{n} = 2(a_{n-1} - 3)[/tex]

Expanding the brackets we get
[tex]\sf a_{n} = 2a_{n-1} - 6[/tex]

We have a₁ = 3
a₂ = 2(a₁) - 6 = 2(3) - 6 = 6 - 6 = 0
a₃ = 2(a₂) - 6 = 2(0) - 6 = -6
a₄ = 2(a₃) - 6 = 2(-6) - 6 = -18
a₅ = 2(a₄ ) - 6 = 2(-18) - 6 = -42

The sequence starting with 3 is:
3, 0, -6, -18, -42

Both methods work exactly the same, some students find expanding the brackets easier to deal with

c. We can see that as a₁ increases, the number of negative numbers decreases by 2. So, in order for all numbers to be positive (> 0) we should start with a sufficiently large number so that all numbers are positive

The smallest such number is 6.
When a₁ = 6, the sequence is all 6s because
a₂ = 2(6) - 6 = 12 - 6 = 6

So the next number is a₃ = 12(6) - 6 = 6 and so on

So any starting point ≥ 6 will yield positive values. At 5 the sequence would be: 5, 4, 2, -2, -10 so starting point of 5 will not work

The measure of the angles ( 15y - 48 )°, ( 8x - 1 )°, and ( 11x - 25 )° are 165°, 15°, and 63° respectively.

The lines j and k are parallel and lines l and m are parallel.

Consider the figure,

( 8x - 1 )° ≅ 1, corresponding angles

1 ≅ 9, corresponding angles

9 ≅ ( 11x - 25 )°, vertical angles

Therefore,

m∠ 1 = m∠ 9

m∠9 = ( 8x - 1 )°

So,

( 8x - 1 )° = ( 11x - 25 )°

Subtracting 8x from both sides of the equation.

11x - 25 - 8x = 8x - 1 - 8x

3x - 25 = - 1

Adding 25 on both sides of the equation.

3x - 25 + 25 = - 1 + 25

3x = 24

Dividing each side of the equation by 3

( 3x/3 ) = ( 24/3 )

x = 8

Now, the angle made by a straight line is 180°.

Therefore,

( 8x - 1 )° + ( 15y  - 48 )° = 180°

( 8 × 8 - 1 )° + ( 15y - 48 )° = 180°

15° + 15y - 48° = 180°

15y - 33° = 180°

Adding each side of the equation by 33°.

15y - 33° + 33° = 180° + 33°

15y = 213°

Dividing each side of the equation by 15

( 15y/15 ) = ( 213/15 )°

y = 14.2°

So, the measure of the angles are:

( 15y  - 48 )° = ( 15 × 14.2 - 48 )° = ( 213 - 48 )° = 165°

( 8x - 1 )° = ( 8 × 8 - 1 )° = 15°

( 11x - 25 )° = ( 11 × 8 - 25 )° = ( 88 - 25 )° = 63°

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The correct option is A which is Yixing should clean out the kennels, and Olivia should move the food bags.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

All the parts will be solved below:-

a. Olivia has an absolute advantage as she takes less time for completing both the tasks

b. Olivia's opportunity cost of cleaning a kennel is

= 6 ÷ 6

= 1 bag of food moved.

c. Olivia's opportunity cost of moving one bag of food is

= 6 ÷ 6

= 1 kennel cleaned

d. Yixing's opportunity cost of cleaning a kennel is

= 10 ÷ 12

= 0.83 bags of food moved.

e. Yixing's opportunity cost of moving one bag of food is

= 12 ÷ 10

= 1.2 kennels cleaned

f. From the above calculations, we can see that the opportunity cost of kennel cleaning would be less sin Yixing so here Yixing should have a comparative advantage and Olivia should have moved the food bags

The complete question is given below:-

Olivia and Yixing are volunteering at a cat rescue shelter. The shelter supervisor asks them to clean out kennels and haul bags of cat food from the donation area into storage. It takes Olivia 6 minutes to clean out a kennel and 6 minutes to move a bag of food. It takes Yixing 10 minutes to clean out a kennel and 12 minutes to move a bag of food.

A. ____has an absolute advantage in completing both tasks.

B. Olivia's opportunity cost of cleaning a kennel:___bags of food moved.

C. Olivia's opportunity cost of moving one bag of food:_____kennels cleaned.

D. Yixing's opportunity cost of cleaning a kennel:____bags of food moved.

E. Yixing's opportunity cost of moving one bag of food:____kennels cleaned.

F. Yixing says it does not matter which task each of them performs because Olivia is faster at both tasks. Is she correct?

A) No, Yixing should clean out the kennels, and Olivia should move the food bags.

B) No, Olivia should clean out the kennels, and Yixing should move the food bags.

C) Yes, Olivia should do both tasks because she is faster at both.

D) No, Yixing should do both tasks so that she can practice and become more efficient.

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The fastest vehicle is: the all terrain that can travel at a speed of 72 mi/h

To solve this problem we must perform the following algebraic operations with the given information

Information about the problem:

Calculating the velocity of the all terrain vehicle we get:

v(all terrain vehicle) =  6 * 12mi/h

v(all terrain vehicle) =  72 mi/h

By ordering the velocities from highest to lowest we have:

(all terrain vehicle)72 mi/h >(go kart)67 mi/h >(scooter)12mi/h

Due to the all terrain vehicle has the highest velocity it is the faster vehicle.

We can say that they are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

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Using a linear function, it is found that:

A linear function is modeled by the following rule:

y = mx + b

In which:

From the table, we have that:

Hence, we have that when x = 0, y = 45, meaning that:

The y-intercept is of 45.

When x increases by 5, y decays by 8, hence the slope is given as follows:

m = -8/5 = -1.6.

Then the function is:

y = -1.6x + 45.

The x-intercept is found as follows:

-1.6x + 45 = 0

1.6x = 45

x = 45/1.6

x = 28.125.

The x-intercept is of 28.125.

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Answer:

answer is ((1 × 2) + 3) × 4 × 5 + 6 - 7 - 8 + 9 = 100

Answer:

-11x + 30

Step-by-step explanation:

distribute the 5 into the parenthesis

= 4x -15x + 30

combine like terms

= -11x + 30

Answer:

-11x + 30

Step-by-step explanation:

4x + 5(-3x + 6)  Distribute the 5

4x + (5)-3x + (5)6

4x -15x + 30 Combine the x's

-11x + 30

The numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.

The largest factor of the two numbers which divides both the numbers is called as greatest common factor or GCF. In other words, the greatest common factor is the largest positive number which can be divided into given numbers evenly.

Given the number is 7 the pair of numbers having the greatest common factor is calculated below:-

For pairs 7 and 14. Both the numbers are the multiple of 7 it can be divided by 7. The greatest common factor will be 7 for pairs 7 and 14.

Similarly for pairs 7 and 28. Both the numbers are the multiple of 7 it can be divided by 7. The greatest common factor will be 7 for pairs 7 and 28.

Therefore, the numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.

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By definition of vertical angles, the value of the variable x behind the geometric system is equal to 12. The measure of the labeled angle is 48°.

The image shows a geometric system generated by two non-parallel lines that intersect each other and consequently two pairs of vertical angles are therefore created. In geometry, two vertical angles are opposite to each other and have the same measure. Then, the following mathematical relationship is found:

4 · x = 48

In addition, we must clear the variable x within the equation:

4 · x = 48                                   Given

x = 48 / 4                                   Compatibility with multiplication / Commutative, associative and modulative properties / Existence of multiplication

x = 12                                         Definition of division / Result

The value of the variable x behind the geometric system is equal to 12.

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