The scale factor of the dilation is 4.
We are given that;
The equation of line −11x=4y+4
Now,
The center of dilation is the origin (0, 0). The line given by −11x = 4y + 4 can be rewritten as y = −11/4 x − 1. This means that it passes through the points (0, −1) and (−4, 0). The image of the line after dilation is given by −11x − 4y = 16, which can be rewritten as y = −11/4 x − 4. This means that it passes through the points (0, −4) and (−16, 0).
To find the scale factor, we can use any pair of corresponding points. For example, let’s use (0, −1) and (0, −4). The distance from the center of dilation to (0, −1) is 1 unit. The distance from the center of dilation to (0, −4) is 4 units. Therefore, the scale factor is 4/1 = 4.
Therefore, by dilation the answer will be 4
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Need the correct answers for this. Can you help me?
The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.
To determine the correctness of the statements and calculate the lengths and slopes of the given quadrilateral PQRS, let's perform a coordinate proof.
Length and slope of PQ:
The coordinates of points P and Q are P(0, 2) and Q(3, -4), respectively.
Length of PQ: √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(3 - 0)² + (-4 - 2)²]
= √[9 + 36]
= √45
= 3√5 (approx.)
Slope of PQ: (y₂ - y₁) / (x₂ - x₁)
= (-4 - 2) / (3 - 0)
= -6 / 3
= -2
Therefore, the length of PQ is approximately 3√5, and its slope is -2.
Length and slope of SR:
The coordinates of points S and R are S(-2, 1) and R(1, -5), respectively.
Length of SR: √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(1 - (-2))² + (-5 - 1)²]
= √[9 + 36]
= √45
= 3√5 (approx.)
Slope of SR: (y₂ - y₁) / (x₂ - x₁)
= (-5 - 1) / (1 - (-2))
= -6 / 3
= -2
Therefore, the length of SR is approximately 3√5, and its slope is -2.
Length and slope of SP:
The coordinates of points S and P are S(-2, 1) and P(0, 2), respectively.
Length of SP: √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(0 - (-2))² + (2 - 1)²]
= √[4 + 1]
= √5
Slope of SP: (y₂ - y₁) / (x₂ - x₁)
= (2 - 1) / (0 - (-2))
= 1 / 2
Therefore, the length of SP is √5, and its slope is 1/2.
Length and slope of HQ:
The coordinates of points H and Q are H(0, 2) and Q(3, -4), respectively.
Length of HQ: √[(x₂ - x₁)² + (y₂ - y₁)²]
= √[(3 - 0)² + (-4 - 2)²]
= √[9 + 36]
= √45
= 3√5 (approx.)
Slope of HQ: (y₂ - y₁) / (x₂ - x₁)
= (-4 - 2) / (3 - 0)
= -6 / 3
= -2
Therefore, the length of HQ is approximately 3√5, and its slope is -2.
Based on the calculations, we can conclude that both statements are correct:
The quadrilateral PQRS is a parallelogram since opposite sides PQ and SR have the same lengths and slopes.
The quadrilateral PQRS is not a rectangle since the lengths of the adjacent sides PQ and SP are not equal.
Summary:
Length of PQ is approximately 3√5, and its slope is -2.
Length of SR is approximately 3√5, and its slope is -2.
Length of SP is √5, and its slope is 1/2.
Length of HQ is approximately 3√5, and its slope is -2.
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Find the area of the figure below.
Enter the answer as square inches.
Answer:
42
Step-by-step explanation:
Rectangle: A = 6 x 5 = 30
Triangle: A = 1/2(6 x 4) = 12
Area of figure: 30 + 12 = 42
5. A conical shaped pile of sand at the beach has a base circumference of 16.5 feet
and stands 10.4 feet high. The Department of Public Works is going to remove
75% of the sand. How much sand will be left in the pile after they remove 75% of
the sand?
Answer: 18.78 cubic feet
Step-by-step explanation:
The detailed analysis is attached below.
Graph the line. y=3x-8
By connecting these points with a straight line, we can graph the line y = 3x - 8.
The line should have a positive slope, rising from left to right.
To graph the line y = 3x - 8, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope of the line, and b represents the y-intercept.
Comparing the given equation with the slope-intercept form, we can see that the slope, m, is 3, and the y-intercept, b, is -8.
To plot the graph, we'll start by plotting the y-intercept, which is the point (0, -8)T.
his point represents where the line intersects the y-axis.
Next, we can use the slope to find additional points on the line. The slope of 3 means that for every increase of 1 in the x-coordinate, the y-coordinate increases by 3.
Starting from the y-intercept (0, -8), we can move 1 unit to the right and 3 units up to reach the next point (1, -5).
We can continue this pattern to plot more points.
Using this information, we can plot multiple points and then connect them to form the line:
Point 1: (0, -8)
Point 2: (1, -5)
Point 3: (2, -2)
Point 4: (-1, -11)
Point 5: (-2, -14)
By connecting these points with a straight line, we can graph the line y = 3x - 8.
The line should have a positive slope, rising from left to right.
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What is the balance after 4 years on $2000 at 4%
The balance after 4 years on $2000 at 4% is equal to $2320.
How to calculate the simple interest and future value?In Mathematics, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 2000 × 4/100 × 4
S.I = 2000 × 0.04 × 4
S.I = $320.
Next, we would calculate the future value as follows;
Future value, A = S.I + P
Future value, A = $320 + $2000
Future value, A = $2320.
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Solve the equation for the variable given. Solve for x
The solution for x, is x= (3m - b)/2. (Option-d)
To solve for x in the given equation, m=(2x+b)/3, we can start by isolating x on one side of the equation.
First, we can multiply both sides of the equation by 3 to get rid of the denominator:
3m = 2x + b
Next, we can subtract b from both sides of the equation:
3m - b = 2x
Finally, we can divide both sides of the equation by 2:
x = (3m - b)/2
It's important to note that this is a linear equation with one unknown variable, and we can use algebraic methods to solve for the unknown variable. This equation may arise in many fields of study, including physics, engineering, and economics, among others.(Option-d)
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Fill in the banks if you had this question before!!
An equation for the total cars and trucks for dealership A is: x + y = 164.
An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.
The number of cars that dealership A sold is: 98 cars.
The number of trucks that dealership B sold is: 66 trucks.
How to write a system of equations to model this situation?In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of cars sold.Let the variable y represent the number of trucks sold.Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;
x + y = 164.
Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;
2x + 0.5y = 229.
By solving the systems of linear equations simultaneously, we have:
2x + 0.5(164 - x) = 229
1.5x + 82 = 229
x = 98 cars.
For the y-value, we have;
2(98) + 0.5y = 229
0.5y = 229 - 196
y = 33/0.5
y = 66 trucks.
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Calculate the unshaded portion of the figure
Answer:
Approx 8.47 [tex]m^2[/tex]
Step-by-step explanation:
First, find the area of the entire figure. Which can be found by multiplying the two sides of the square by each other= [tex]6*6=36m^2[/tex]
Now, ignore the square and just focus on the pentagon and finding the area of that. The formula for the area of a pentagon is [tex]A=1/2Apothem*Perimeter[/tex]
In order to find the apothem, you can make a mini triangle and use trig (Tangent) to find the height (apothem) of the triangle. Then, you take the side length of the base of the pentagon which is 4 and then you multiply it by the number of sides (5) to get 20. Then, by plugging it into our formula, you use the apothem*10 (divided by 2) and you get the area, and then you just subtract that from 36.
dos aviones de parte de una ciudad a las 8 AM el primer avión quiso regresar a la ciudad 5 horas y el segundo avión regresa casa 3 horas en cuanto tiempo volverán a dentrar a la ciudad
Both planes will reach the city at the same time again at 11 PM.
How to deal with periodic events?Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.
The periods for this problem are given as follows:
5 hours.3 hours.As 5 and 3 are prime numbers, the least common factor is given as follows:
5 x 3 = 15.
15 hours after 8 AM is of 11 PM.
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Plot ΔABC on graph paper with points A(10,4), B(-1,1), and C(4,2). Reflect ΔABC by multiplying the x-coordinates of the vertices by −1. Then use the function (x,y)→(x−5,y+4) to translate the resulting triangle. Name the coordinates of the vertices of the result. Question 4 options:
These are the coordinates of the vertices of the transformed triangle.
Vertex A: (-15, 8)
Vertex B: (-4, 5)
Vertex C: (-9, 6)
To plot ΔABC and perform the given transformations, let's follow the steps:
Plot ΔABC:
Point A(10,4)
Point B(-1,1)
Point C(4,2)
Reflect ΔABC by multiplying the x-coordinates by -1:
Reflecting A: (-10,4)
Reflecting B: (1,1)
Reflecting C: (-4,2)
Translate the reflected triangle using the function (x,y) → (x-5, y+4):
Translating (-10,4): (-10-5, 4+4) = (-15, 8)
Translating (1,1): (1-5, 1+4) = (-4, 5)
Translating (-4,2): (-4-5, 2+4) = (-9, 6)
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Deigo wrote 6^4*8^3=48^7. explain what his mistake was.
The index forms are of different bases and thus cannot be multiplied and their exponents added.
How to determine the valueTo determine Deigo's mistake, we need to know index forms and their rules.
Index forms are defined as mathematical forms that are used in representing numbers or variables that are too large or too small in more convenient forms.
They are also called scientific notation or standard forms.
The rules of index forms are;
Subtract the exponents when like bases are dividedAdd the exponents when like bases are multipliedFrom the information given, we have;
6⁴ × 8³ = 48⁴⁷
They are not of like bases and thus cannot be multiplied
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I NEED YOUR HELP! PLEASE HELP! I WILL MARK YOU BRAINLIEST!!!!!!!!!!Andrea has 533.8 cm 3 of modeling clay. She plans to use 8.4 cm 3 to form a right pentagonal prism. She will also make a second prism that is a dialation of the first prism with a scale factor of 4. Does Andrea have enough modeling clay for both prisms? Determine the amount of clay that andrea has left over or is short.
If the height (h) of the prism is less than or equal to 0.978 cm, then Andrea has enough modeling clay for both prisms. If the height exceeds 0.978 cm, she will be short of modeling clay.
Let's calculate the volumes of both prisms:
Volume of the first prism: V1 = (8.4 cm²) × h
Volume of the second prism: V2 = (16 × 8.4 cm²)×(4h)
= 537.6 cm³ h
We know that Andrea has 533.8 cm³ of modeling clay.
To determine if she has enough clay for both prisms, we need to compare the total volume of the prisms to the amount of clay she has:
Total Volume = V1 + V2 = (8.4 cm²) × h + (537.6 cm³ × h)
Total Volume = (546 cm²) × h
Now we can set up the equation:
Total Volume ≤ Amount of Clay
(546 cm²) × h ≤ 533.8 cm³
Solving for h:
h ≤ 533.8 cm³ / (546 cm²)
h ≤ 0.978 cm
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For the athletic banquet one adult ticket cost $15.00 and one student ticket cost $10.00. One hundred forty tickets were sold for a total of $1600. How many students tickets were sold
Answer:160 students
Step-by-step explanation:
did I do it
(your answer needs to be more than 20 characters long)
Type the correct answer in the box.
Fill in the missing term in the equation.
(1 + 2)(2+1) + blank
= 5(2+i)
A store has 7 bags of sugar in an aisle. Each small bag weighs 4 pounds. each large bag weighs 10 pounds. There are 52 pounds of sugar in the aisle. Write a system of equations for the situation. Be sure to identify what your variables represent.
Answer: 4 small bags, 3 large bags (equations below in explanation)
Step-by-step explanation:
x=number of small bags
y=number of large bags
x+y=7
4x+10y=52
Subtract them after multiplying the first equation by 4.
4x+4y=28
4x+10y=52
-6x=-24
x=4
x+y=7
4+y=7
y=3
A box plot uses a number line from 13 to 33 with tick marks every one-half unit. The box extends from 15 to 30.5 on the number line. A line in the box is at 21.5. The lines outside the box end at 14 and 32. The graph is titled Number of Points, and the line is labeled Points Scored in Basketball. What value does 75% of the data lie above? Find the value. Lower quartile (Q1) = 14 Lower quartile (Q1) = 15 Upper quartile (Q3) = 30.5 Upper quartile (Q3) = 32
Given statement solution is :- The quartile value above which 75% of the data lies is 31.625.
To find the value above which 75% of the data lies, you can determine the third quartile (Q3) of the data set. In this case, the upper quartile (Q3) is given as 30.5.
Since the data is represented on a number line with tick marks every one-half unit, we can divide the range between Q3 and the maximum value (32) into four equal parts. Each part represents 25% of the data.
To find the value that corresponds to 75% of the data lying above, we need to determine the value that is three-fourths of the way between Q3 and the maximum value.
First, calculate the range between Q3 and the maximum value: 32 - 30.5 = 1.5.
Next, divide the range by four to find the size of one-fourth of the range: 1.5 / 4 = 0.375.
Now, multiply the size of one-fourth of the range by three to find the size of three-fourths of the range: 0.375 * 3 = 1.125.
Finally, add the size of three-fourths of the range to Q3 to find the value above which 75% of the data lies: 30.5 + 1.125 = 31.625.
Therefore, the quartile value above which 75% of the data lies is 31.625.
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100 points please help me answer this
The complete table for the function are
- f(1) - 3 = -5
- f(0) - 3 = -5.5
- f(2) - 3 = -7
- f(6) - 3 = undefined
- f(14) - 3 = -1
- f3(0) - 3 = 2
How to complete the missing parts of the table for the function.From the question, we have the following parameters that can be used in our computation:
The function equation and the incomplete table of values
This is given as
g(x) = - f(x) - 3
From the table, the missing values are at all values of x
So, we have
- f(1) - 3 = -2 - 3 = -5
- f(0) - 3 = -2.5 - 3 = -5.5
- f(2) - 3 = -4 - 3 = -7
- f(6) - 3 = undefined
- f(14) - 3 = 2 - 3 = -1
- f3(0) - 3 = 5 - 3 = 2
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A cube has a volume of 216 cubic inches. What is the length of each edge of the cube? A. 9 in. B. 6 in. C. 4 in. D. 3 in.
The length of each edge of the cube = 6 inches, Thus option B is correct.
The volume of a cube = 216 cubic inches,
length of each edge of a cube is an inch
To find the value of a:
The formula for the volume of a cube is [tex]a^{3}[/tex]
The volume of cubic = [tex]a^{3}[/tex]
V = [tex]a^{3}[/tex]
substitute the volume value given in the equation in the above formula
216 = [tex]a^{3}[/tex]
[tex]a = \sqrt[3]{216}[/tex]
[tex]a[/tex] = 6
a = 6inches
Therefore, the length of each edge of the cube is 6 inches.
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) 65 people were asked on the activities they engage in during their free time. The results showed that 23 visit national parks, 26 engage in cycling while 22 engage in swimming. Furthermore 9 engage in swimming and visit national parks, 9 engage in swimming only while 11 visit national parks only. How many engage in
i. Swimming and cycling
Answer:
Step-by-step explanation:
i am working on the assumption that nobody does all three of them
i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.
the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.
so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4
A lawnmower was discounted 32%. The lawnmower sold for $117.81 including sales tax of 5% of the sale price. What was the original price of the mower?
Step-by-step explanation:
We can begin by using the fact that the selling price was 117.81, including a sales tax of 5%. Let x be the original price of the lawnmower.
After the discount of 32%, the selling price is:
0.68x + 0.05(0.68x) = 117.81
Simplifying and solving for x, we get:
0.68x + 0.034x = 117.81
0.714x = 117.81
x = 165
Therefore, the original price of the lawnmower was $165.
Write an expression using the distributed property to dind the product of 7x63
The product of the expression 7 x 63 is 441.
We have,
To find the product of 7 x 63 using the distributive property, we can break down 63 as the sum of its factors, such as 60 and 3:
7 x 63 = 7 x (60 + 3)
Now, we can apply the distributive property by multiplying 7 to each term inside the parentheses:
7 x (60 + 3) = 7 x 60 + 7 x 3
Simplifying further:
7 x 60 + 7 x 3 = 420 + 21
Therefore,
The product of 7 x 63 is 441.
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Classwork Topic: Solve problems 25 May 2023 1. Jessica and Melissa shared 12 pieces of dried pears. Jessica ate = of the dried pears! Melissa ate . How Pieces did they eat in all? What fraction of the dried eat altogether? many pears did they 2. There were is children playing in the park. One third of the children went home. How many children stayed in the park?
Apologies, but your questions seem to have errors and incomplete information.
For the first question about Jessica and Melissa sharing 12 pieces of dried pears, it is unclear how much Jessica ate as the fraction is missing. Similarly, information about how many pears Melissa ate is also missing. To answer the question accurately, I need the missing information.
For the second question about the children playing in the park, you mentioned that one-third of the children returned home, but you didn't provide the total number of children initially in the park. Without that information, I cannot determine how many children stayed in the park.
Please provide complete and accurate information for a precise answer.
A number n minus the sum of the number and eight
The algebraic expression for the sentence in this problem is given as follows:
n - (x + 8).
How to obtain the algebraic expression for the sentence?The sentence in this problem is given as follows:
"A number n minus the sum of the number and eight".
The sum of an unknown number x and eight is given as follows:
x + 8.
The subtraction of the number n by the expression is given as follows:
n - (x + 8).
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Suppose you went to the doctor and the co-pay each visit is 25$, and the price for each round of the shots is $135.
If you went to the doctors 3 times a week for 2 months straight, Can you tell me how much you spent in total for them visit? Also, you only receive the shot 2 times out of the visit.
(visit)1=25 3x25=75 '' 8weeks within 2 months'' =co-pay
8x75=600$
2x8=16
16x135=2,160$ = shots
Trivia Question ?:) on a average how much did she spend each visit ?
Given statement solution is :- On average, she spent approximately $115 per visit.
To calculate the total amount spent on the visits, we need to add up the co-payments and the cost of the shots.
Co-payments:
The co-pay for each visit is $25, and you visited the doctor 3 times a week for 8 weeks within 2 months. So the total co-payment is:
3 visits/week * $25/visit * 8 weeks = $600.
Shots:
You received the shot 2 times out of each visit, and you visited the doctor 3 times a week for 8 weeks within 2 months. So the total cost of the shots is:
2 shots/visit * $135/shot * 8 weeks = $2,160.
Total amount spent:
Co-payments + Shots = $600 + $2,160 = $2,760.
Therefore, the total amount spent for the visits and shots over 2 months is $2,760.
Trivia Answer:
To find out the average amount spent per visit, we can divide the total amount spent by the total number of visits. In this case, the total amount spent is $2,760, and the total number of visits is 3 visits/week * 8 weeks = 24 visits.
Average spent per visit = Total amount spent / Total number of visits
Average spent per visit = $2,760 / 24 visits
Average spent per visit ≈ $115.
Therefore, on average, you spent approximately $115 per visit.
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What is the quantity of goods and services that sellers are willing and able to sell known as?
The quantity of goods and services that sellers are willing and able to sell is known as the quantity supplied.
What is quantity supplied of goods by a seller?Quantity supplied is defined as the amount of goods and services that a supplier is able to produce and sell at a given market price.
The quantity supplied differs from the actual amount of supply as price changes influence how much supply producers actually put on the market.
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Simplify the rational expression
7x/14x^6
The simplified form of the rational expression [tex](7x)/(14x^6)[/tex] is [tex]1/(2x^6).[/tex]
To simplify the rational expression [tex](7x)/(14x^6)[/tex], we can begin by simplifying the numerator and denominator separately.
In the numerator, 7x, we can see that both 7 and x have a common factor of 7. So, we can rewrite the numerator as 7 × x = 7x.
In the denominator, [tex]14x^6[/tex], we can see that both 14 and x^6 have a common factor of [tex]2x^6[/tex].
So, we can rewrite the denominator as
[tex]14 \times x^6 = 2 \times 7 \times x^6 = 2 \times 7x^6.[/tex]
Now, we can simplify the rational expression by canceling out the common factors in the numerator and denominator:
[tex](7x)/(14x^6) = (7x)/(2 \times 7x^6) \\= (7x)/(2 \times 7 \times x^6) \\= (cross(7x))/(2 \times cross(7) \times x^6) \\= 1/(2x^6)[/tex]
Therefore, the simplified form of the rational expression[tex](7x)/(14x^6)[/tex] is [tex]1/(2x^6).[/tex]
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Find the area of the figure below.
Enter the answer as square inches.
Answer:
42
Step-by-step explanation:
Rectangle: A = 6 x 5 = 30
Triangle: A = 1/2(6 x 4) = 12
Area of figure: 30 + 12 = 42
Answer:
area of rectangle+area of triangle= area of figure
6×5 + 1/2×4×6=30+24= 42
or
given figure is a trapezium
so we know are of trapezium= 1/2×sum of parallel sides×height
= 1/2×( 5+9)×6
=42
What is the percentage is the discount of$38 and $95
The percentage discount between $38 and $95 is 150%.
How to compute the percentage discount?We shall follow these steps to estimate the percentage discount between $38 and $95:
First, find the difference between the original price and the discounted price.
Next, divide the result by the original price.
Finally, multiply the result by 100 to present it as a percentage.
Given:
Original price = $95
Discounted price = $38
Difference = $95 - $38 = $57.
Next, Difference / Original price * 100:
($57 / $38) * 100 ≈ 150%
Therefore, the percentage discount between $38 and $95 is 150%.
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What is the balance after three years on a CD with an initial investment of $2,200 and a 2.95% interest rate?
The remaining balance on a CD with a $2,200 initial investment and a 2.95% interest rate after three years would be roughly $2,393.10.
To solve this problemThe compound interest formula is as follows:
Balance = Principal * (Rate/100 + Rate * 1)Time
Where
The initial investment is the principalRate is the period-to-period interest rateThe amount of periods makes up timePrincipal (P) is equal to $2,200.
Rate (R) = 2.95% = 2.95/100 = 0.0295 in decimal form.
Time (T) = 3 years.
The following formula is substituted for the values:
Balance =[tex]$2,200 * (1 + 0.0295)^3.[/tex]
Exponent calculation:
Balance = [tex]$2,200 * (1,0295)^3[/tex]
Calculating the result:
Balance ≈ $2,200 * 1.089135
Balance ≈ $2,393.10
So, the remaining balance on a CD with a $2,200 initial investment and a 2.95% interest rate after three years would be roughly $2,393.10.
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Henry has $21.50 to ride the trolley around San Francisco this week. It will cost him $0.50 every time he rides. Identify the dependent variable and the independent variable in this scenario.
Dependent variable: Total cost of riding the trolley
Independent variable: Number of times Henry rides the trolley.
In this scenario, the dependent variable is the total cost of riding the trolley, and the independent variable is the number of times Henry rides the trolley.
The dependent variable, the total cost of riding the trolley, depends on the independent variable, which is the number of times Henry rides the trolley. As Henry rides the trolley multiple times, the total cost will vary based on the number of rides.
The independent variable, the number of times he rides, determines the value of the dependent variable, the total cost.
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