The populations of both towns would be equal in nine months.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's assume that both town's populations will be equal in x months.
After x months, the population of the first town is given by
200x - 75x + 57,900
The population of the second town after x months is given by
60,600 - 175x
In order for the population of both towns to be equal, we have
200x - 75x + 57,900 = 60,600 - 175x
This is the required equation that represents the given situation.
200x - 75x + 57,900 = 60,600 - 175x
Rearrange the likewise terms and apply arithmetic operation
200x - 75x + 175x = 60,600 - 57,900
300x = 2700
x = 2700/300
x = 9
Therefore, the populations of both towns would be equal in nine months.
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Self balancing scooter travels 12 miles per hour, all terrain vehicle can travel 6 times as fast as the scooter,a go kart can travel 67 miles per hour,which vehicle can travel the fastest
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:
v(scooter) = 12mi/hv(all terrain vehicle) = 6 * 12mi/hv(go kart) = 67 mi/hwhich is the faster=?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.
What are algebraic operations?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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(5) Set up a system of equations and solve:
38 people are playing pickle-ball in a park. 13 matches are in progress. How many double and
how many single matches are being played?
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
Find the value of the variable(s).
the variable(s) x have a value of 13.
What in mathematics is a variable?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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What are the first five terms of the following sequence a1=42, an=an-1-7
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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170% of what number is 40.8?
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.
Yo i need help asap can yall help me fast?
By factor decomposition and algebra properties we conclude that the fraction 42 / 49 is equivalent to the fraction 6 / 7.
Which pair of fractions is equivalent to each other?
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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an unreliable study can occur if the . a. survey is very clear b. survey yields consistent results c. test administration is inconsistent
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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What are the values of b and c?
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b =
C=
C
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b
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74°
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a cup of coffee at 160 degrees is placed in a room where the temperature of 70 degrees. after 5 minutes, the coffee’s temperature is 112.5 degrees.
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
what do you mean by newton's law of cooling?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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which pair of numbers have a greatest common factor of 7? select each correct answer. 7 and 14 7 and 14 28 and 7 28 and 7 7 and 1 7 and 1 21 and 3
The numbers 7 and 14, 28 and 7 have the greatest common factor. The correct options are A and B.
What is the greatest common factor?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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Here is a rule that can be used to build a sequence of numbers once a starting number is chosen: Each number is two times three less than the previous number.
a. Starting with the number 0, build a sequence of 5 numbers.
b. Starting with the number 3, build a sequence of 5 numbers.
c. Can you choose a starting point so that the first 5 numbers in your sequence are all positive? Explain your reasoning.
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
Jason considered two similar televisions at a local electronics store. the cheaper version was 12 inches by 24 inches. the more expensive version was \large \frac{8}{3} the size of the cheaper one. what are the dimensions of the expensive television? a 4.5 inches by 9 inches b 28 inches by 56 inches c 7.5 inches by 15 inches d 32 inches by 64 inches
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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A line segment has the endpoints K(0, 2) and L(0, 6). Find the coordinates of its midpoint M.
Write the coordinates as decimals or integers.
M =
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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Which statement is true for the function y = log3x
Answer:
Step-by-step explanation:
jamie is pedaling due south a 8 mi/hr. his sister, martha, is pedaling due west at 5 mi/hr. after 2 hours, how fast are the two cyclists moving apart?
Both cyclist are moving apart at a speed of 9.434 mi/hr.
What is velocity?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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Help please if u can show ur work please
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.
Yesterday Sarah read 15% of her entire book. Today she read another 17% of the entire book.
In lowest terms, what fraction of the book is left for her to read?
a) 7/25
b) 3/10
c) 17/25
d) 7/10
answer quick please!!!!
i think the answer is 3/10
Given the numbers 1,2,3,4,5,6,7,8,9 use the operations +, -,/ and * to get the answer as 100 while leaving the numbers in their respective given order
Answer:
answer is ((1 × 2) + 3) × 4 × 5 + 6 - 7 - 8 + 9 = 100
how to simplify 4x +5(-3x +6)
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
18% of the car inn the parking lot are blue . If there are 150 cars in the parking lot how many cars are blue
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
he 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 π
The bat colony will cover an area of 80,000 square miles in 1.612 hours.
What is defined as the circle?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.
every morning jim runs for 30 minutes. if jim runs 10 miles per hour, how far does he travel?
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.
Part A
JEWELRY Chloe makes necklaces and bracelets to sell at fundraisers to raise money for new band uniforms. She
has $18 to buy necklace and bracelet chains. Necklace chains cost $0.60 each, and bracelet chains cost $0.40
each. The number of bracelet chains she can purchase given the number of necklace chains that she buys are
shown in the table.
Necklace Chains
Bracelet Chains
What are the x and y intercepts of the function modeling the number of bracelet chains chloe can purchase given the number of necklace chains that she buys?
Using a linear function, it is found that:
The x-intercept is of 28.125.The y-intercept is of 45.What is a linear function?A linear function is modeled by the following rule:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, the change in y divided by the change in x.b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.From the table, we have that:
The input is the number of necklace chains.The output is the number of bracelet chains.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 equation and some of the steps used to solve the equation are shown below. One step is missing:
2(x-3) + 10x = 5(3 + x)
?
2x-5x + 10x = 15 + 6
7x = 21
x=3
Which set of statements is most likely the missing step and the property that justifies the step?
Answer choices listed in picture(Sorry for quality, taken from my laptop) (Will mark brainliest)
Answer 5795
Step-by-step explanation:
The function h=−16t^2+1936 gives an object’s height h, in feet, at t seconds. When will the object be 912 feet above the ground?
Can somebody help wit this I’m failing geometry rn and it makes no sense .
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°.
What is the measure of variable within a geometric system generated by two lines intersecting each other?
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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jack's age next year will be twice jill's age last year. their present ages total 45. how old is each no
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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Mario uses 14 pound of walnuts to make muffins. he uses the same amount of walnuts in each of 6 muffins. what is the amount of walnuts in each muffin?
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!
Help out please I don’t understand
Answer:
C. [tex] \frac{ - 15x - 53}{ {x}^{2} + 8x + 15 }≥ 0[/tex]
Step-by-step explanation:
See attached image for explanation
I hope it helps you232x100 what is the answer
Answer:
23200
Step-by-step explanation: