A​ town's population is . 57,900 About 75 people move out of the town each month. Each​ month, 200 people on average move into town. A nearby town has a population of 60,600 . It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be​ equal? Write an equation to model the situation. Then solve the equation and answer the question.

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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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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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:

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 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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Answer 5795

Step-by-step explanation:

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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Answer:

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

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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Answer:

23200

Step-by-step explanation:

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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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:

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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i think the answer is 3/10

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.

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

Answer:

he uses 2.33333333333 amount of walnuts in each muffin

Step-by-step explanation:

14 divided by 6 = 2.33333333333

Have a nice day!

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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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:

C. [tex] \frac{ - 15x - 53}{ {x}^{2} + 8x + 15 }≥ 0[/tex]

Step-by-step explanation:

See attached image for explanation

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 bat colony will cover an area of 80,000 square miles in 1.612 hours.

A circle is the collection of all the points together in plane that are equally distant from the a given point known as the circle's center. A circle is represented by the symbol. A radius of a circle is a line segment that connects the center of a circle toward any point on the circle.

Now, as per the given question;

The area covered (A) by the colony, evaluated in square miles, is depicted by the mentioned geometrical formula as the bat colony emerges from a cave & spreads out in a circular pattern:

A = π R²

R = the bat's distance from the cave, calculated in miles.

Furthermore, each bat moves at a constant speed, and distance is depicted by the following kinematic formula:

R = r₀ + rΔt

r₀ = The bat's initial distance from the cave, estimated in miles.

r = Bat speed, estimated in miles per hour.

Δt = Time, expressed in hours.

Substitute the value of R in the formula of area.

A = π (r₀ + rΔt)²

(r₀ + rΔt)² = A/ π

(r₀ + rΔt) = √(A/ π)

rΔt = √(A/ π) - r₀

Δt = (√(A/ π) - r₀)/r

r =  99 miles per hour

The distance between the bat and the cave has now been substituted, and time has been cleared:

A = area of 80,000 square miles

π = 3.14

r₀ = 0 miles per hour

Substituting all the values in the A we calculate the time.

Δt = (√( 80,000/3.14) - 0)/99

On solving;

Δt = 1.612 (approx)

Thus, It will take 1.612 hours for the bat colony to cover an area of 80,000 square miles.

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The complete question is-

The Brazilian free-tailed bat can travel 99 miles per hour. after sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. how long before these bats cover an area of 80,000 square miles? use pi = 3.14.

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

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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Answer:

5 miles

Step-by-step explanation:

distance = rate times time

distance = (10 miles per hour)( 30 minutes)  30 minutes is equal to 1/2 hour

distance = [tex]\frac{10 miles}{hour}[/tex] [tex](\frac{1 hour}{2} )[/tex]  You can cancel words, like like cancelling numbers  The hours cancel out and you are left with [tex]\frac{10 miles}{2}[/tex]  which is equal to 5 miles.

Answer: 5 miles

Step-by-step explanation:

Jim runs 10 miles per hour, and 30 minutes is half an hour, so divide 10 by 2.

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