The scale of the drawing is 1 cm = 4.5 m. This means that each centimeter in the drawing represents 4.5 meters in the actual field. The length of the field in the drawing is 7.2 cm, so the actual length of the field is 7.2 cm × 4.5 m/cm = 32.4 m. The width of the field in the drawing is 3 cm, so the actual width of the field is 3 cm × 4.5 m/cm = 13.5 m. The area of a rectangle is found by multiplying its length by its width, so the area of the actual field is 32.4 m × 13.5 m = 437.4 m²
Note :- I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull
solve x and y for 5x−y=44−3=−3x−y=−12
The values of the variables are;
x = 7
y = -9
How to solve for the variablesFrom the information given, we have that;
5x−y=44
−3x−y=−12
Using the elimination method of solving simultaneous equations
Subtract equation (2) from equation (1), we get;
5x - y - (-3x - y) = 44 - (-12)
Now, expand the bracket
5x - y+ 3x + y = 56
collect the like terms
5x + 3x = 56
add the terms
8x = 56
Make 'x' the subject of formula
x= 7
Now, substitute the value of x in equation (2)
-3x - y = -12
-3(7) - y = -12
expand the bracket
-21 - y= - 12
collect like terms
-y = 9
y = -9
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What is the solution to this equation? 3.1 = -0.5 + 0.3x A:x=6 B:x=3 C:x=12 C:x=0.8
Required solution of the given equation 3.1 = -0.5 + 0.3x is x = 12.
What is equation?
A mathematical statement that asserts that two expressions are equal is called equation
. It is consist of variables, constants, and mathematical operations such as , subtraction, addition, division, multiplication . We can use equations in mathematics to model real-world situations or to solve problems. It can also be used to express relationships between quantities, to find unknown values, and to test hypotheses. Equations can be written in various forms, such as linear, exponential, trigonometric ,quadratic. Equation depends on the type of relationship being modeled.
Here given equation is 3.1 = -0.5 + 0.3x.
We are Simplifying it,
[tex]3.1 + 0.5 = 0.3x \\ 0.3x = 3.6 \\ x = \frac{3.6}{0.3} \\ x = 12[/tex]
So, required solution of the given equation is 12.
Therefore, option C is the correct answer.
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Correct question is "What is the solution to this equation? 3.1 = -0.5 + 0.3x A:x=6 B:x=3 C:x=12 D:x=0.8".
If cosine = 1/7 in quadrant 1, find tangent
Answer:
What we know from the problem:
Cosine = Adjacent/Hypotenuse = 1/7If you make a triangle in the first quadrant all the sides are positivetherefore tangent will be positive.
So we know that:Adjacent Side = 1
Hypotenuse Side = 7
We need to find out:
Opposite Side = b
Using the Pythagorean Theorem: a² + b² = c²
1² + b² = 7²
b = 4√3
Lastly:
Tangent = Opposite/Adjacent
4√3 ÷ 1 = 4√3
Tangent = 4√3
American Manufacturing Incorporated operates two divisions with the following selected information for the month of February: North Division South Division Sales $ 120,000 $ 90,000 Contribution margin $ 52,000 $ 40,000 Segment margin $ 18,000 $ 12,000 North Division’s direct fixed expenses for February is:
North Division’s direct fixed expenses for February is $34000.
Segment margin = Contribution margin - Direct fixed expenses
We are given that the North Division's segment margin for February is $18,000, and its contribution margin is $52,000. Let X represent the North Division's direct fixed expenses:
$18,000 = $52,000 - X
Solving for X, we get:
X = $52,000 - $18,000
X = $34,000
Therefore, the North Division's direct fixed expenses for February is $34,000.
The answer is: Multiple Choice $34,000.
Hence, North Division’s direct fixed expenses for February is $34000.
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Complete question:
American Manufacturing Incorporated operates two divisions with the following selected information for the month of February: North Division South Division Sales $ 120,000 $ 90,000 Contribution margin $ 52,000 $ 40,000 Segment margin $ 18,000 $ 12,000 North Division’s direct fixed expenses for February is: Multiple Choice $34,000. $96,000. $60,000. $78,000.
Find the value of X
Parallel & Perpendicular Lines
The value of the angle x is 108 degrees
How to determine the valueTo determine the value, we need to note that the sum of the angles on a straight line is 180 degrees.
Also, parallel lines are lines that do not meet or intersect each other on any side of a plane
From the information given, we have that;
x + 72 = 180
now, collect the like terms in the equation, we have;
x = 180 - 72
subtract the values
x = 108 degrees
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Find the scale factor of HOPE to RSTU.
The scale factor of HOPE to RSTU is 1.5
Finding the scale factor of HOPE to RSTU.From the question, we have the following parameters that can be used in our computation:
The shape
From the shape, we have the following parameters
Side length of HOPE = 8
Corresponding side length of RSTU = 12
Using the above as a guide, we have the following:
Scale factor of the dilation = Corresponding side length of RSTU/ Side length of HOPE
So, we have
Scale factor of the dilation = 12/8
Evaluate
Scale factor of the dilation = 1.5
Hence, the scale factor of the dilation is 1.5
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Can you help me answer this question? (Explain answer please, if you can)
Mr. Perez designs a probability model to help him predict which color car his customers will want to buy. He puts equal numbers of red, black, white, gray and blue slips of paper into a bag to represent all the different possible car colors. Which of the following statements about the model are true?
A. Mr Perez will most likely not pull any black slips.
B. Mr. Perez will more likely to pull a red slip than a blue slip.
C. Adding another white slip would make this a non-uniform probability model.
D. The results of Mr. Perez’s experiment are likely to exactly math the frequency with which his costumers select each color of car.
) Emily baked a cake in 42.5 minutes. She finished making dinner 9 1/10 minutes sooner than the cake. How long did it take her to make dinner? Hint: Change the 9 1/10 to a decimal
It took Emily 33.4 minutes to make dinner.
Define a mixed number?A mixed number is a kind of fraction that also has a proper fraction and a whole number. The number of whole units is represented by the whole number, and the fraction of a unit is represented by the proper fraction.
To solve the problem, we have to convert the mixed number [tex]9 \frac{1}{10}[/tex] to a decimal number:
⇒ [tex]9 \frac{1}{10} = 9 +\frac{1}{10} = \frac{(9*10)+1}{10}[/tex]
⇒ [tex]\frac{91}{10}[/tex] = 9.1
This means that Emily finished making dinner 9.1 minutes sooner than the cake.
To find out how long it took Emily to make dinner, we can subtract 9.1 from the cake baking time:
⇒ 42.5 - 9.1 = 33.4 minutes
Therefore, it took Emily 33.4 minutes to make dinner.
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On the grid above, draw a graph of the relationship between t and d for a trip that lasted from O to 7 hours.
If the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.
What is graph?Graph is a data structure composed of nodes (vertices) and edges. It is a non-linear data structure that is used to represent relationships between objects, events, or ideas. Graphs are widely used in computer science, mathematics, engineering, and other fields for representing various types of data. Graphs can be used to represent a wide variety of data sets, including networks, social relationships, and even biological systems. Graphs can also be used to identify patterns, trends, and correlations in data.
The graph below shows the relation between time (hours) and distance (km) for a train trip that lasted from 0 to 7 hours.
The line of best fit is a linear line with a positive slope, indicating that the distance travelled increases as the time spent travelling increases. Therefore, it can be estimated that if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be calculated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis, which is approximately 90 km.
In conclusion, if the train was travelling nonstop for 5.5 hours, it would travel approximately 90 km. This can be estimated by observing the graph and finding the corresponding distance for 5.5 hours on the y-axis.
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Complete questions as follows-
On the grid below, draw a graph of the relationship between and for a trip that lasted from 0to 7 hours. 8Time (hours) If the train was traveling nonstop, how many would it travel in 5.5 hours?
When both t and d are zero, we can immediately see that c = 0 because the train begins at rest. Additionally, the rate of change is the constant speed, making m = 95. Thus, d = 95t is the necessary relationship.
What is graph?A graph is a type of data structure that consists of edges and nodes (vertices). It is a non-linear data structure intended to depict connections between things, occasions, or concepts. Graphs are frequently used to represent numerous forms of data in computer science, mathematics, engineering, and other disciplines. A wide range of data sets, including networks, social relationships, and even biological systems, can be represented using graphs. Graphs can also be used to spot trends, correlations, and patterns in data.
The necessary equation should be d = mt +c,
Where the arbitrary real constants m and c are used.
When t = 1, d = 95
so that 95= m+c ---> (1)
Also, when t=2, d = 190,
hence 190 = 2m+c ---> (2)
When the first equation is taken out and the second equation is added back in,
we get 2m+c-m-c = 190-95 or, m = 95.
When this value of m is substituted in the first equation,
we get 95 = 95+c so that c = 95-95 = 0.
Thus, the require3d equation is d = 95t. Since 95*3 = 285 and 95*4= 380, All of the given facts are satisfied by this equation.
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The complete question and graph attached below,
Simplify the expression. 1/4(13y-3)+1/8(6y+9)
Answer:
The answer in the simplest form is (32y-3)/8
Step-by-step explanation:
1/4(13y-3)+1/8(6y+3)
13y/4-3/4+6y/8+9/8
(13y-3)/4+(6y+9)/8
[2(13y-3)+(6y+9)]/8
[26y-6+6y+9]/8
C.L.T
[26y+6y-6+9]/8
(32y-3)/8
I think of a number, x, the product of my number and 5 is 65. What number am I thinking of?
Answer:
325
Step-by-step explanation:
the product being multiplication is 65 * 5
HELP!!! rewrite x^2-12x=10 in vertex form. Please clearly show your work :)
Answer:
Write
f
(
x
)
=
2
x
2
+
12
x
+
10
as an equation.
y
=
2
x
2
+
12
x
+
10
Step-by-step explanation:
Write
f
(
x
)
=
2
x
2
+
12
x
+
10
as an equation.
y
=
2
x
2
+
12
x
+
10
A circular clock face has a diameter of 7 inches. What is the area of the clock face? Round to the nearest tenth.
A. 49 in.2
B. 38.5 in.2
C. 11 in.2
D. 153.9 in.2
-10-9-8
Which inequality is graphed on the number line?
OA) x>-7
OB) x < -7
C) x ≤ -7
D) xz -7
The inequality is graphed on the number line is
A) x > -7How is inequality graphed in a number line\Inequality can be graphed on a number line by shading the appropriate region of the number line.
To graph an inequality x > -7, follow these steps:
Plot the critical points on the number line. The critical points are the values of x that make the inequality true with an equal sign. For example, to graph the inequality x > -7, we plot the critical point x = -7 on the number line.
Determine the direction of the shading or line. If the inequality is "greater than" or "greater than or equal to," shade to the right of the critical point..
If the inequality includes "or equal to," use a closed circle at the critical point. If the inequality does not include "or equal to," use an open circle at the critical point.
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In a direct proof, evidence is used to
. On the other hand, a counterexample is a single example that
.
On solving the provided question ,we can say that In order to find holes in a mathematical proof or the boundaries of a theory or hypothesis, counterexamples might be helpful.
what is a sequence?A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.
Evidence is utilised to back up a claim or argument in a direct proof. A direct proof's objective is to connect known facts or presumptions logically to the desired conclusion in order to show that a certain assertion is true. Direct proofs sometimes take the form of a series of logical stages that are combined to get the desired result.
A counterexample, on the other hand, is a solitary instance that refutes a claim or argument. A counterexample presents a particular situation in which a claim is wrong in order to demonstrate that the claim is not always true. In order to find holes in a mathematical proof or the boundaries of a theory or hypothesis, counterexamples might be helpful.
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Find the solution of the initial value problem 2
′′ − 3
′ + = 0, (0) = 2,
′
(0) = 1/2 . Then determine the maximum value of the solution and also find
the point where the solution is zero.
Determining the highest point of value for a particular solution relies heavily on the type of problem which needs to be resolved.
To address this conundrum, there are several different strategies one can follow:Evaluate equations or functions: If you possess an equation or function that symbolizes the desired answer, it is prudent to study it intensely in order to pinpoint its maximum value. For instance, taking the derivative of the equation and establishing zero as an equalizer will allow you to determine any critical points. Shortly afterward, evaluating those points alongside endpoints within its domain verifies what its maximum value is.
Optimization strategies: In cases where a particular quantity must be maximized amidst constraints, such as linear programming or quadratic programming techniques, it is useful to implement optimization strategies to resolve these kinds of problems conveniently and effectively.
Experimentation via simulation: In instances where mathematical analyses prove too difficult given the complexity involved, it becomes necessary to use simulation or experimentation techniques to investigate potential solutions thoroughly. It involves improvising input parameters while watching output meticulously with an eye to spotting the corresponding maximum value.
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Factor the following polynomial.
40x3 70x² + 30x
10x(x - [?])([? ]x - [? ]
Answer:
To factor the polynomial 40x^3 + 70x^2 + 30x, we can first factor out the greatest common factor of the terms, which is 10x:
10x(4x^2 + 7x + 3)
Next, we can factor the quadratic expression inside the parentheses. We need to find two numbers that multiply to give 4 × 3 = 12 and add to give 7. These numbers are 4 and 3:
10x(4x + 3)(x + 1)
Therefore, the factored form of the polynomial is:
10x(4x + 3)(x + 1)
DYN
MEDICIN
r
5
In the table below, fill in the empty cell with the corresponding exact measures in radian or degrees.
Angle measure in
radians
9rt/5
3π/4
Angle measure in
degrees
20
275
Angle measure in radians 9π/5 3π/4
Angle measure in degrees 324° 135°
Note:
9π/5 can also be written as 1.8π radians or 324 degrees
3π/4 can also be written as 0.75π radians or 135 degrees
The table provides values for angle measures in radians and degrees. To convert between radians and degrees, The exact measures in radians for 9rt/5 is 3π/5 and for 3π/4 is 135°. The exact measure in radians for 20 degrees is π/9 and for 275 degrees is 55π/36.
What is angle?An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is used to measure the amount of rotation between the two rays or line segments.
What is Radian?A radian is a unit of measure for angles, where the measure of the central angle is equal to the length of the corresponding arc on the unit circle. It is equal to approximately 57.3 degrees.
According to thw given information:
The table displays measures of angles in radians and degrees. Radians are a unit of measurement for angles, and they relate the length of the arc of a circle to the radius of that circle. One radian is equivalent to the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. Pi radians, or 180 degrees, represent a straight angle.
In the table, the first angle measure in radians is given as 9√5, which is an exact measure. The second angle measure in radians is given as 3π/4, which represents a quarter of the circumference of the circle, and is equal to 45 degrees. The first angle measure in degrees is given as 20°, which is the equivalent of π/9 radians, and the second angle measure in degrees is given as 275°, which is equivalent to 55π/36 radians.
Knowing how to convert between radians and degrees is important in many mathematical calculations, especially those involving trigonometry. Understanding the relationship between these units of measure can help to solve problems in many areas of mathematics and science.
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Which angle is an x-intercept for the function y = cos(x)?
Α. Ο
B. x/2
C.pie
D. 2pie
The correct option is D, the x-intercept is 2pi
Which angle is an x intercept?To find this, we need to solve the equation:
y = cos(x/2) = 0
Remember that the cosine function is zero for the arguments pi and (3/2)pi.
Then the x-intercepts are:
x/2 = pi
x/2 = (3/2)pi
Solving these:
x = 2pi
x = 3pi
From these the one that appears in the options is 2pi, at option D.
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The width of a block of wood with rectangular cross-section is x cm . it's height is two - thirds its width and it's length is 4 times its height. What is its volume in cm3
An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.3 mm, how many of these components should she consider to be 90% sure of knowing the mean will be within ± 0.3 mm
The engineer should consider a sample size of 325 electronic components to be 90% sure that the mean width will be within ± 0.3 mm.
To determine the required sample size, we can use the formula for the margin of error (ME) in the context of the normal distribution:
ME = (Z * σ) / √n
Where:
ME = Margin of error
Z = Z-score, which corresponds to the desired level of confidence (in this case, 90%)
σ = Standard deviation (3.3 mm in this problem)
n = Sample size
First, we need to find the Z-score corresponding to a 90% confidence level. This can be found using a Z-table or statistical software. The Z-score for a 90% confidence interval is approximately 1.645.
Now, we will rearrange the formula to solve for the sample size (n):
n = (Z * σ / ME)^2
We are given that the margin of error should be within ± 0.3 mm:
n = (1.645 * 3.3 / 0.3)^2
n ≈ (18.015)^2
n ≈ 324.54
Since we cannot have a fraction of a component, we round up to the nearest whole number to ensure the desired level of confidence:
n ≈ 325
The engineer should consider a sample size of 325 electronic components to be 90% sure that the mean width will be within ± 0.3 mm.
Help me solve this problem
Answer:
[tex]-i\sqrt{7}[/tex]
Step-by-step explanation:
We can write this expression as:
[tex]-\sqrt{-1 \cdot 7}[/tex]
From here, we can take the square root of negative 1 ([tex]i[/tex]):
[tex]\boxed{-i\sqrt{7}}[/tex]
No further simplification can be done.
On average, teens spend 4 hours a week using the Internet and 4 hours doing chores. They spend 10 hours listening to the radio. What percent of the total time teens spend using the Internet and doing chores is the time they spend listening to the radio?
The percent of the total time teens spend using the Internet and doing chores is the time they spend listening to the radio is 55.56%.
How the percentage is calculatedTime spent using the internet = 4 hours
Time spent doing chores = 4 hours
The time spent listening to the radio = 10 hours
The total time spent during the week is 4 + 4 + 10 = 18 hours
The percentage of this total time that is spent listening to the radio is:
(10 hours / 18 hours) x 100% =55.56%
This is basic arithmetic operations and is used in calculation of numbers.
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45% of the fruit on a table are apples and the rest are oranges. What is the probability that a piece of randomly selected fruit from the table is not an apple
Answer:
If 45% of the fruit on a table are apples, then 55% of the fruit are oranges (since the total percentage must add up to 100%).
The probability of selecting a piece of fruit that is not an apple is equal to the percentage of oranges on the table, which is 55%.
Therefore, the probability of selecting a piece of fruit that is not an apple is 55%.
Please solve with proof.
The distance from point C to A that is AC = 7.5 cm and CB = 10.5 cm.
What is distance?While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."
Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Let us suppose the distance between C to A = x.
Now, for C to B we have = 3 + x
Given, AB = 18
Thus,
AC + CB = AB
x + (x + 3) = 18
2x + 3 = 18
2x = 15
x = 7.5
Now, CB = 3 + x = 3 + 7.5 = 10.5
Hence, the distance from C to A that is AC = 7.5 cm and CB = 10.5 cm.
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Write y =x2 -4x - 32 in factored form.
Answer:
8
Step-by-step explanation:
x^2-4x=32
Subtract from both sides:
x^2-4x-32=32-32
Simplify the expression
x^2-4x-32=0
To find the coefficients, use the standard form of a quadratic equation:
ax^2+bx+c=0
x^2-4x-32=0
a coefficient =1
b coefficient =-4
c coefficient =-32
Find the factors which product equals to coefficient a multiplied by coefficient c:
a coefficient ∙ c coefficient = 1 ∙ -32 = -32
List the factors of -32:
1, 2, 4, 8, 16, 32
Because the product of coefficient a and coefficient c equals a negative number (-32) one factor needs to be positive and the other one negative.
From the list of factors, find a pair which sum equals to the b coefficient.
b coefficient = -4
This pair doesn't work.
1*-32=-32
2*-16=-32
2-16=-14
Found it - this pair does the trick:
4*-8=-32
4-8=-4
The product of 4 and -8 equals to coefficient a(1) multiplied by coefficient c (-32) and their sum equals to coefficient b (-4).
What is the slope of the line that passes through the points (-9, 7) and (8, -6)?
Answer: -13/17
Step-by-step explanation: To find the slope of the line that passes through the points (-9, 7) and (8, -6), you can use the slope formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) = (-9, 7) and (x2, y2) = (8, -6)
Substituting the values in the formula, we get:
slope = (-6 - 7) / (8 - (-9))
slope = -13 / 17
Therefore, the slope of the line that passes through the points (-9, 7) and (8, -6) is -13/17.
Answer:
[tex]\frac{-14}{17}[/tex]
Step-by-step explanation:
Slope is the change in y's (-9,7) (8,-6) over the changes in x's (-9,7)(8,-6). You find the changes by subtraction
[tex]\frac{-6-7}{8-(-9)}[/tex] = [tex]\frac{-14}{8+9}[/tex] = [tex]\frac{-14}{17}[/tex]
Helping in the name of Jesus.
I need help!!!! pleaseee
The genotype ratio is: 1 TT : 1 Tt : 0 tt
The phenotype ratio is : 4 Tall : 0 Short
100 percent of the offspring will be tall.
What is Genotypic and Phenotypic ratio?Genotypic ratio is the ratio between the genetic makeup among the offspring population.
On the other hand, the ratio between the offspring population for an observable characteristic is the phenotype ratio.
The given test cross is between a homozygous tall parent and a heterozygous tall parent.
Using a Punnett square,
The result will be as shown below.
T t
T TT Tt
T TT Tt
Genotype : 1 TT : 1 Tt : 0 tt
Phenotype : 4 Tall : 0 Short
100 percent of the offspring will be tall.
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A town has a population of 2.33 × 101 and grows at a rate of 7% every year. Which equation represents the town's population after 6 years?
The equation that represents the town's population after 6 years is:
P = 2.33 × 10¹ (1.07)⁶
What is the rate?
In mathematics, the rate is a measure of the change in one quantity with respect to another quantity. It is typically expressed as a ratio between the two quantities.
The initial population is 2.33 × 10¹.
After one year, the population will be:
P₁ = 2.33 × 10¹ + 0.07 × 2.33 × 10¹
P₁ = 2.33 × 10¹ (1 + 0.07)
After two years, the population will be:
P₂ = P₁ + 0.07 P₁
P₂ = P₁ (1 + 0.07) = 2.33 × 10¹ (1 + 0.07)²
After three years, the population will be:
P₃ = P₂ + 0.07 P₂
P₃ = P₂ (1 + 0.07) = 2.33 × 10¹ (1 + 0.07)³
And so on, until after six years:
P₆ = 2.33 × 10¹ (1 + 0.07)⁶
Simplifying the expression, we get:
P₆ = 2.33 × 10¹ (1.07)⁶
Therefore, the equation that represents the town's population after 6 years is:
P = 2.33 × 10¹ (1.07)⁶
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I'm Luke but a Helmond for $19.67 how much change should Luke receive if He pays the cashier $20 use colons and build this solove?
Answer:
To find out how much change Luke should receive if he pays the cashier $20 for a Helmond that costs $19.67, we can subtract the cost of the Helmond from the amount of money Luke pays:
$20.00 - $19.67 = $0.33
Therefore, Luke should receive $0.33 in change.
