The two numbers are 6 and 2.
Let's assume the first number is x and the second number is y.
From the first statement, we can write the equation x = y + 4.
From the second statement, we can write the equation 2x = 4y + 2.
Now, we can substitute x in terms of y from the first equation into the second equation:
2(y + 4) = 4y + 2
Simplifying this equation, we get:
2y + 8 = 4y + 2
2y = 6
y = 3
Substituting y = 3 in the first equation, we get:
x = y + 4 = 3 + 4 = 7
Therefore, 6 and 2 are the two numbers,
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solve for x, using a tangent and secant line
Check the picture below.
[tex]x^2=(8+2)(2)\implies x^2=20\implies x=\sqrt{20}\implies x\approx 4.5[/tex]
The value of x is 4.5 rounded to the nearest tenth.
What is Tangent and Secant of a Circle?Tangent of a circle is defined as the line which passes through exactly one point on the circle.
Secant of a circle is the line which passes through two points on the circle.
Secant-Tangent Rule states that if a tangent and a secant are drawn to a circle from the same point outside the circle, then the square of the length of the tangent segment is equal to the product of the lengths of secant and the segment of secant outside the circle.
Using the theorem, we can say here that,
(8 + 2) 2 = x²
x² = 10 × 2
x² = 20
x = √20
x = 4.472 ≈ 4.5
Hence the value of x is 4.5.
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Determine weather the series is arithmetic or geometric,then find the indicated sum
The series, based on the general terms, can be found to be arithmetic. The indicated sum is - 544.
How to determine if a series is arithmetic or geometric ?To determine if the series is arithmetic or geometric, we must first find the common difference (arithmetic) or common ratio (geometric).
Term 1 (p=1): 19 - 2(1) = 17
Term 2 (p=2): 19 - 2(2) = 15
Term 3 (p=3): 19 - 2(3) = 13
There is a common difference of -2 so this is arithmetic.
The formula for the sum of an arithmetic series is:
Sum = (n x (a1 + an)) / 2
The series is: ∑ (p = 1 to 34) (19 - 2p)
To find the last term, we plug in p = 34:
an = 19 - 2(34)
= 19 - 68
= -49
The sum is therefore:
Sum = (34 x (17 + (-49))) / 2
Sum = -544
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Mary bought 8 blouses and 3 skirts for a total of $120.00. Kristy bought 5 blouses and 5 skirts at the same prices for a total of $112.50. What is the cost of each blouse and each skirt?
After solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.
What are equations?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation.
As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
So, the cost of each blouse and skirt:
x be the price of one blouse and y is the price of one skirt.
For a total of $215, Carol purchased 3 skirts and 5 blouses.
5x + 3y = 215
For a total of $135, Ellen purchased 2 skirts and 3 blouses.
3x + 2y = 135
By resolving the equations in the system:
5x + 3y = 215
3x + 2y = 135
We will obtain:
x = $25
y = $30
Therefore, after solving the equations we know that the price of each blouse and each skirt is $25 and $30 respectively.
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Correct question:
Carol bought 5 blouses and 3 skirts for a total of $215. At the same time, her sister Ellen bought 3 blouses and 2 skirts for a total of $135. What was the price of each blouse and each skirt?
Can you please answer this question
Answer:
9/14
Step-by-step explanation:
add them
For what values of x and y is PQRS a parallelogram?
P x+9 Q x+7 R 2x-1 S y
The values for the variables x and y in the parallelogram are equal to 10 and 17 respectively.
How to evaluate for the variables x and y in the parallelogramThe parallelogram OPSR have two pairs of parallel sides hence OP = RS and PS = OR.
We shall evaluate for variables x and y as follows:
2x - 1 = x + 9
2x - x = 9 + 1 {collect like terms}
x = 10
y = x + 7
y = 10 + 7 {substituting 10 for x}
y = 17
Therefore, the values for the variable x and y in the parallelogram are equal to 10 and 17 respectively.
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Xavier receives a paycheck of $2250. First, he spends 20% of his paycheck to buy a new mattress. Then, he spends 29 of the remaining amount to fix a leak in his kitchen. After Xavier pays these two expenses, how much will be left over from his paycheck?
Answer:
Step-by-step explanation:
he's rich
Xavier will have $1278 left over from his paycheck after spending 20% on a new mattress and 29% on fixing a leak.
Explanation:To find out how much will be left over from Xavier's paycheck after he spends 20% on a new mattress and 29% on fixing a leak, we can follow these steps:
Calculate 20% of $2250, which is $450.Subtract $450 from $2250 to find the remaining amount after buying the mattress, which is $1800.Calculate 29% of $1800, which is $522.Subtract $522 from $1800 to find the amount left over after fixing the leak, which is $1278.Therefore, Xavier will have $1278 left over from his paycheck.
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Jacqui wants to prove that figures abc and def are similar. Which series of transformations would prove that these two figures are similar
One figure should be rotated to match the other's alignment. Expand one figure till it is the same size as another.
what is transformations ?A figure or object in a coordinate plane can be transformed to create a new figure or object that has been relocated, flipped, or altered in some other way. Translations, rotations, and reflections are the three primary forms of transformations. Moving a figure horizontally or vertically without altering its size or shape is known as translation. Rotation entails angling a figure around a fixed point, often known as the rotational center.
given
The subsequent transformations must be used in order to demonstrate similarity between two figures:
Translation (moving the figures to the same spot) (moving the figures to the same position)
Rotation (rotation one figure to fit the other) (rotating one figure to match the other)
Dilation (resizing the figures such that they have the same shape, but maybe different sizes) (resizing the figures so that they have the same shape, but possibly different sizes)
Consequently, the following set of transformations should be used to demonstrate that the figures abc and def are similar.
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Are the ratios 4:3 and 5:4 equivalent?
Answer:
They're not promise
Step-by-step explanation:
I did it on the calculator
I hope this helps youuu
Have a good day <3
the points on the graph show how much chee pays for different amounts of noodles, complete the statement about the graph
Using graphs,
The ordered pair, (6,15) represents here the cost of 6 pounds of noodles that is $15.
What are graphs?A structured representation of the data is all that the graph is. It assists us in comprehending the info. Data are the numerical details gathered by observation. Data is a derivative of the Latin term datum, which means "something provided."
Data is continuously gathered through observation once a research question has been formulated. After that, it is arranged, condensed, and categorised before being graphically portrayed.
Here in the question,
As we can see that the graph is a relation between the number of noodles in pounds and the cost of noodles in dollars has been given and compared.
So, as per the question,
The ordered pair that represents here the cost of 6 pounds of noodles is (6,15).
As, from the graph:
When noodles in pounds is 6, cost in dollars is 15.
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The complete question is:
the points on the graph show how much chee pays for different amounts of noodles, complete the statement about the graph
If f(1) = 10, and f(n) = f(n-1) + 4, then find the value of
ƒ (4).
The value of f(4) using recursive formula f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2 is 22
Finding the Value of f(4) Using Recursive FormulaGiven that f(1) = 10 and f(n) = f(n-1) + 4 for n ≥ 2.
To find the value of f(4), we can use the recursive formula to work our way up from f(1) to f(4):
Using the above as a guide, we have the following:
f(2) = f(1) + 4 = 10 + 4 = 14
Next, we have
f(3) = f(2) + 4 = 14 + 4 = 18
Next, we have
f(4) = f(3) + 4 = 18 + 4 = 22
Therefore, the value of f(4) is 22.
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50 POINTS PLEASE HELP
IN YOUR OWN WORDS PLEASE:)
The purpose of filling out a W-4 is to make it easier for individuals to meet their tax liability by
paying income taxes as they earn income. Paying anticipated taxes from each paycheck
reduces the amount an individual owes when filing taxes and can even result in a tax refund.
To guarantee or increase the refund, individuals sometimes claim fewer allowances (to have
more income tax withheld) or request a specific additional amount to be withheld from each
paycheck.
Daniel's employer will automatically deduct taxes from Daniel's pay using the information on
the W-4 form that Daniel completed on his first day. From his W-4 form, Daniel's employer
determined that $75 needs to be withheld from each of Daniel's weekly paychecks, totaling
$3,900 for the year.
Compare Daniel's tax liability from part B, question 3, with the total amount withheld from his
check: $3,900 for the year. If Daniel wants a refund when he files his taxes, should he have
filled out his W-4 differently? Explain your reasoning.
Answer:
To determine if Daniel should have filled out his W-4 form differently to receive a refund, we need to compare his tax liability with the total amount withheld from his paychecks for the year.
If Daniel's tax liability for the year is less than $3,900, he will receive a refund when he files his taxes. If his tax liability is more than $3,900, he will owe additional taxes when he files his taxes.
If Daniel's tax liability is exactly $3,900, he will neither owe additional taxes nor receive a refund when he files his taxes.
Therefore, to determine if Daniel should have filled out his W-4 form differently, we need to compare his tax liability with $3,900.
If Daniel's tax liability from part B, question 3, is less than $3,900, he will receive a refund when he files his taxes, as the total amount withheld from his paychecks is more than his tax liability. In this case, Daniel may want to consider filling out his W-4 form differently to reduce the amount withheld from his paychecks and increase his take-home pay.
On the other hand, if Daniel's tax liability from part B, question 3, is more than $3,900, he will owe additional taxes when he files his taxes, as the total amount withheld from his paychecks is less than his tax liability. In this case, Daniel may want to consider filling out his W-4 form differently to increase the amount withheld from his paychecks and reduce the amount he will owe when he files his taxes.
If Daniel's tax liability from part B, question 3, is exactly $3,900, he will neither owe additional taxes nor receive a refund when he files his taxes, and his W-4 form is correctly filled out for his tax situation.
In summary, whether or not Daniel should have filled out his W-4 form differently to receive a refund depends on his tax liability compared to the total amount withheld from his paychecks. If his tax liability is less than the total amount withheld, he may want to reduce the amount withheld to increase his take-home pay. If his tax liability is more than the total amount withheld, he may want to increase the amount withheld to reduce the amount he will owe when he files his taxes. If his tax liability is exactly equal to the total amount withheld, his W-4 form is correctly filled out for his tax situation.
The formula for finding the surface area of a rectangular solid with length 1, width w, ~ and height h is SA = 2/w + 21h + 2wh. Find the surface area of a rectangular solid with length 5 inches, width 2 inches, and height 4 inches. A. 28 square inches B. 36 square inches C. 72 square inches D. 76 square inches
The surface area of the rectangular solid with length 5 inches, width 2 inches, and height 4 inches is 76 sq inch. The answer is D.
What is surface area of rectangular solid ?
The surface area of a rectangular solid (also known as a rectangular prism) is the total area of all its faces. It can be calculated using the formula:
SA = 2lw + 2lh + 2wh
where l is the length of the rectangular solid, w is its width, and h is its height.
The rectangular solid has six faces: a top face, a bottom face, a front face, a back face, a left side face, and a right side face. The formula above accounts for the area of each of these faces.
According to the question:
The formula for the surface area of a rectangular solid is:
SA = 2lw + 2lh + 2wh
We are given that the length (l) of the solid is 5 inches, the width (w) is 2 inches, and the height (h) is 4 inches. Substituting these values into the formula, we get:
SA = 2(5)(2) + 2(5)(4) + 2(2)(4)
= 20 + 40 + 16
= 76 square inches
Therefore, the surface area of the rectangular solid with length 5 inches, width 2 inches, and height 4 inches is 76 square inches. The answer is D.
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suppose that x is the number of cars per minute that pass through a certain intersection, and that x has the poisson distribution. what can be the smallest value of x? enter your answer in accordance to the question statemententer your answer in accordance to the question statement
The smallest value of x in the Poisson distribution is 0, which means that no cars can pass through the intersection in a given minute.
For explain further, a Poisson distribution is a statistical model that describes the probability of a given number of events occurring in a fixed period of time, such as cars passing through an intersection in a minute.
In a Poisson distribution, the probability of x events occurring in a given minute is given by the equation P(x) = e-λλx/x!, where λ is the average number of events in a given minute. In this case, λ would be the average number of cars that pass through the intersection per minute.
The probability of 0 cars passing through the intersection in a given minute is e-λλ0/0! = 1, which is the highest probability in the distribution. Therefore, the smallest value of x in a Poisson distribution is 0.
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Solve for x 5x
-2(x+1)=10
Step-by-step explanation:
5x-2(x+1)=10
5x-2x+2=10
3x+2=10
3x=10-2
3x=8
8/3
2.7 if you do round it
2.666666667 before you do
x=2.7
(I think it's right Because I've already been taught this if not just tell me.)
Find one solution for the equation, (2x-3)(3x+5)=0.
The two solutions to the equation (2x - 3)(3x + 5) = 0 when solved are x = 3/2 and x = -5/3
How to determine the solution to the equationGiven that, we have the following equation
(2x - 3)(3x + 5) = 0
The above equation means that
2x - 3 = 0 and 3x + 5 = 0
When the equations are evaluated, the equations becoms
2x = 3 and 3x = -5
Lastly, we divide both sides of the equation by the coefficent of x i.e 2 and 3
So, we have
x = 3/2 and x = -5/3
So, the values of the solutions to the equation are x = 3/2 and x = -5/3
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(04.03 MC)
Find the area of the polygon.
A 41 square units
B 44 square units
C 52 square units
D 56 square units
The area of given polygon is 44 square units from the given graph.
What is Polygon ?
A polygon is a 2-dimensional geometric shape that is formed by joining a finite number of straight line segments to form a closed shape.
The area of each triangle can be found by using the formula:
Area = (base * height)/2
Triangle 1: Base = 4 units, Height = 5 units
Area of Triangle 1 = (4*5)/2 = 10 square units
Triangle 2: Base = 8 units, Height = 3 units
Area of Triangle 2 = (8*3)/2 = 12 square units
The area of the trapezoid can be found by using the formula:
Area = (Sum of parallel sides * Height)/2
Trapezoid: Height = 4 units, Parallel side 1 = 3 units, Parallel side 2 = 7 units
Area of Trapezoid = ((3+7)*4)/2 = 20 square units
Therefore, the total area of the polygon is:
Total Area = Area of Triangle 1 + Area of Triangle 2 + Area of Trapezoid
Total Area = 10 + 14 + 20 = 44 square units
Hence, The area of given polygon is 44 square units from the given graph.
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Solve for x. Round to the nearest tenth of a degree, if necessary.
please help me I will give brainliest to whoever helps me
Answer: x= 71
Step-by-step explanation:
Since each triangle has a sun of all the angles to equal 180, we can figure what is X.
At rolling hills middle school the ratio of the total number of students to the number of students with pets is 3 to 1 if there are 243 students at the school how many students have pets
If there are 243 students at the school, then there are 81 students at Rolling Hills Middle School who have pets.
If the ratio of the total number of students to the number of students with pets at Rolling Hills Middle School is 3 to 1, this means that for every 3 students at the school, there is 1 student with a pet.
Let's represent the total number of students at the school as "3x" (since the ratio is 3 to 1, we can use any multiple of 3 as a placeholder for the total number of students), and the number of students with pets as "x". Therefore, we can write the following equation:
3x : x = 3 : 1
To solve for x, we can cross-multiply:
3x * 1 = x * 3
3x = 3x
We can see that the equation is true for any value of x, which means that there are many possible solutions. However, since we know that the total number of students at the school is 243, we can use this information to solve for x:
3x = 243
x = 81
Therefore, there are 81 students at Rolling Hills Middle School who have pets.
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HARD 30 points please help me :(
A liner function goes through the points (1, 2) and (-3, 5) Calculate the slope of the line in simplest form
M = Y2 - Y1
X2 - X1
Show your work, please
Slope (m) =
Answer:
To calculate the slope of the line that passes through the points (1, 2) and (-3, 5), we use the slope formula:
m = (Y2 - Y1) / (X2 - X1)
where (X1, Y1) = (1, 2) and (X2, Y2) = (-3, 5).
Substituting the values into the formula, we get:
m = (5 - 2) / (-3 - 1)
m = 3 / (-4)
Simplifying the fraction by dividing both the numerator and denominator by their greatest common factor of 1, we get:
m = -3/4
Therefore, the slope of the line in simplest form is -3/4.
Please help and please hurry
what is an equivalent expression to 4x(2x-3)-5(3x-4)
Answer:4x + 3x + 2x - 4 - 3
Step-by-step explanation:Hope this helps
Kathy is adding a new slide to her swing set. The slide is 5 feet long, and the ladder is 4 feet high. How
many feet away is the base of the ladder from the end of the slide, g, as shown below?
5 ft
g
4ft
The number of feet away is the base of the ladder from the end of the slide, g, as shown is 3 ft.
How many feet away is the base of the ladder from the end of the slide?The base of the ladder from the end of the slide forms a right triangle.
Hypotenuse² = opposite² + adjacent²
Hypotenuse = 5 ft
Opposite = 4 ft
Adjacent = g
So,
Hypotenuse² = opposite² + adjacent²
5² = 4² + g²
25 = 16 + g²
subtract 16 from both sides
25 - 16 = g²
9 = g²
find the square root of both sides
√9 = g
g = 3 ft
In conclusion, the base of the ladder is 3 ft away from the end of the slide.
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a bank pin is a string of seven digits, each digit 0-9. five of the digits {0, 2, 4, 6, 8} are even and five of the digits {1, 3, 5, 7, 9} are odd. how many pins are there with at least one odd digit?
three and seven tenths times five
the adaptive-response-rate single exponential smoothing model is best applied to time series data that are multiple choice non stationary. stationary and non seasonal. seasonal. stationary and seasonal. seasonal and nonstationary.
The adaptive-response-rate single exponential smoothing model is best applied to time series data that are non stationary and seasonal which means option D is the right answer.
The adaptive response rate single exponential smoothing model is used to demonstrate the changes in the forecasting data and the fluctuation in data values with respect to time which are smoothened by a coefficient. The larger the coefficient, the greater the smoothing effect.
This kind of model is ineffective for stationary time series as it takes into account the smoothing of the information. Adaptive smoothing is computationally difficult. Exponential smoothing produces accurate forecasts. The forecast shows projected demand and actual demand.
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Determine a series of transformations that would map Figure D onto Figure E.
Figure E is a rotated and reflected version of Figure D that has been shifted to the right and up as a result of this transformation sequence.
What is a transformation sequence called?The sequence transformation (which may be dependent on n). This is known as a linear sequence transformation. Nonlinear sequence transformations are nonlinear sequence transformations.
We can use the following transformations to map Figure D onto Figure E:
Figure D should be translated 4 units to the right and 1 unit up.
Figure D should be rotated 90 degrees clockwise around the origin.
Cross the y-axis with the resulting figure.
This transformation sequence results in Figure E, which is a rotated and reflected version of Figure D that has been shifted to the right and up.
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describe the technique used to count the rational numbers (1-1 correspondence with the natural number
Yet because we can compare the set of positive rational numbers exactly to the collection of natural numerals, we may infer that the set of positive rational must have a number of clusters of 0, or n(Q+)=0. Due to the fact that these two numbers must equal one another, 02 = 0.
Since they may be arranged in a one-to-one correspondence with the natural numbers (the integers, such as 1, 2, and 3), Cantor showed in 1873 that the rational numbers, although being infinite, are countable (or denumerable).
How are the rational numbers counted as a group?
To achieve this, we take into account the this double integers grid upon that positive orthogonal. If p and q are positive natural numbers, then p/q may be used to represent any positive valid value.
Simply put, we establish the following values: h(0) = 0, h(2n) = f(n), for all natural numbers n > 0, and h(2n-1) = g(n) = -f(n), for all natural numbers n > 0.
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carlos and juan take 5 hours to do a job. carlos alone takes 8 hours to do the same job. how long would it take juan to do the same job alone?
13.33 hrs long would it take juan to do the same job alone.
Here, we have,
given that,
carlos and juan take 5 hours to do a job.
carlos alone takes 8 hours to do the same job.
let, x hr long would it take juan to do the same job alone.
now, we have,
1 hr work of carlos = 1/8
1 hr work of juan = 1/x
1 hr work of both = 1/8 + 1/x = (x+8)/8x
we have,
So they together can do this job in = 5 hours
so, ATQ, we get,
(x+8)/8x = 1/5
or, (5x+40) = 8x
or, 3x = 40
or. x = 13.33
Hence, 13.33 hrs long would it take juan to do the same job alone.
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Unit 10: Circles Homework 6: Tangent Lines (Can I please have this rounded to the nearest tenth Thank You)
A tangent line is a straight line that intersects a circle at only one point, and it is perpendicular to the radius that goes through that point.
Tangent lines are important because they help us determine the relationship between circles and other geometric shapes.
To find the tangent line to a circle, we need to first identify the point of intersection between the circle and the line.
A tangent line to a circle is a line that intersects the circle at exactly one point, called the point of tangency. The tangent line is perpendicular to the radius that intersects the point of tangency.
m = [tex]\frac{-1}{r}[/tex]
where m is the slope of the tangent line, and r is the radius of the circle.
The equation of a tangent line to a circle can be found using the point-slope form of the equation:
y - y1 = m(x - x1)
where (x1, y1) is the point of tangency and m is the slope of the tangent line.
The length of the tangent segment from the point of tangency to the point of intersection with a secant line can be found using the formula:
[tex]t^2[/tex] = s1 * s2
where t is the length of the tangent segment, and s1 and s2 are the lengths of the two segments of the secant line that intersect the circle.
In terms of calculating the tangent line, we can use the point-slope formula.
Let's say we have a circle with equation [tex]x^2[/tex] + [tex]y^2[/tex] = [tex]r^2[/tex] and we want to find the tangent line at the point (a,b).
We can start by taking the derivative of the equation with respect to x, which gives us 2x + 2yy' = 0.
Solving for y', we get y' = -x/y.
Then, we substitute the values of x and y at the point of intersection (a,b) to get the slope of the radius at that point.
Finally, we take the negative reciprocal of that slope to get the slope of the tangent line, and use the point-slope formula to find the equation of the tangent line.
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how many ways can rudy choose 5 pizza toppings from a menu of 20 toppings if each topping can only be chosen once?
the population of a community is known to increase at a rate proportional to the number of people present at time t. if an initial population p0 has doubled in 5 years, how long will it take to triple? to quadruple?
It will take 7.5 years for the population to triple, and 10 years for the population to quadruple.
The population of a community is known to increase at a rate proportional to the number of people present at time t. This means that the rate of increase is directly proportional to the population.
If an initial population of p0 has doubled in 5 years, we can calculate how long it will take to triple or quadruple the population.
To triple the population, we use the equation: t = (5 years x 3) / 2, where t is the amount of time it takes for the population to triple. This gives us t = 7.5 years.
To quadruple the population, we use the equation: t = (5 years x 4) / 2, giving us t = 10 years.
In summary, it will take 7.5 years for the population to triple, and 10 years for the population to quadruple.
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