2. Fiona is studying how income taxes impact various families and their finances. She creates a table with various amounts of taxes owed and estimates
that this represents 9% of each family's gross income.
Solve for the gross income for each family based off of their taxes owed.
The equation is Gross Income = Taxes Owed / 0.09.
To solve for the gross income for each family based on their taxes owed and the fact that this represents 9% of each family's gross income, follow these steps:
1. Write the equation: Taxes Owed = 0.09 * Gross Income
2. Rearrange the equation to solve for Gross Income: Gross Income = Taxes Owed / 0.09
3. Substitute the Taxes Owed value for each family into the equation and calculate their Gross Income.
For each family, input their taxes owed into the equation and you will find their gross income. Remember, the equation is Gross Income = Taxes Owed / 0.09.
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A small private airplane traveled 140 miles in the same amount of time it took a helicopter to travel 95 miles. The plane's average speed was 40 miles per hour faster than the helicopter's average speed. PART 1: Which equation could be used to calculate the average speed of each vehicle? A. 140 95 B. 95 x + 40 Y Y + 40 C. 140x = 95x + 40 D. 40. 235â
The equation that could be used to calculate the average speed of each vehicle is C. 140x = 95x + 40, where x represents the average speed of the helicopter in miles per hour and 140x represents the distance traveled by the small private airplane.
The equation that can be used to calculate the average speed of each vehicle is:
C. 140x = 95x + 40
Let's break it down:
'x' represents the average speed of the helicopter in miles per hour.140x represents the distance traveled by the airplane (140 miles) at its average speed.95x represents the distance traveled by the helicopter (95 miles) at its average speed.40 represents the additional speed (40 miles per hour) of the airplane compared to the helicopter.Since the time taken by both vehicles is the same, the distances covered by each vehicle can be equated, giving us the equation 140x = 95x + 40.
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27. the value of a certain car can be modeled by the function
y = 18000(0.76)', where t is time in years. will the value of the function ever be 0?
The function given is y = 18000(0.76)^t, where y represents the value of the car and t represents the time in years.
This is an exponential decay function, meaning that the value of the car decreases over time. To determine if the value of the function will ever be 0, we would need to find if there exists a time t when y = 0. Let's analyze the function:
0 = 18000(0.76)^t
In an exponential decay function, the base (0.76 in this case) is between 0 and 1, so as time (t) increases, (0.76)^t will approach 0, but it will never actually reach 0. Thus, the value of the car will keep decreasing over time but will never be exactly 0.
In summary, the value of the function, which represents the car's value, will never be 0, but it will get infinitely close to 0 as time progresses. This is a characteristic of exponential decay functions, where the value never reaches 0 but approaches it as time goes on.
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5. A 40-kg ornamental star is suspended by two chains fastened to
horizontal beams at different heights with angles as shown.
Determine the tension in each chain.
The diagram is shown below; I also know we have to split up the triangles to make two right angle triangles but I’m not sure where to go from there
Answer:We can start by resolving the forces acting on the ornamental star in the vertical direction and in the horizontal direction. Since the star is stationary, these forces must balance each other out.
Let's call the tension in the higher chain T1 and the tension in the lower chain T2. We can use trigonometry to find the vertical and horizontal components of each tension force.
For T1:
The vertical component is T1cos(40°) and the horizontal component is T1sin(40°).
For T2:
The vertical component is T2cos(30°) and the horizontal component is T2sin(30°).
Now, resolving the forces in the vertical direction, we have:
T1cos(40°) + T2cos(30°) - mg = 0
where m is the mass of the star and g is the acceleration due to gravity.
Substituting the values:
T1cos(40°) + T2cos(30°) - (40 kg)(9.81 m/s^2) = 0
T1cos(40°) + T2cos(30°) = 392.4 N
Next, resolving the forces in the horizontal direction, we have:
T1sin(40°) = T2sin(30°)
Now we have two equations with two unknowns:
T1cos(40°) + T2cos(30°) = 392.4 N
T1sin(40°) = T2sin(30°)
Solving these equations simultaneously, we get:
T1 = 266.4 N
T2 = 205.1 N
Therefore, the tension in the higher chain (T1) is 266.4 N and the tension in the lower chain (T2) is 205.1 N.
Step-by-step explanation:
(5 points) The total revenue (in dollars) and total cost (in dollars) for the production and sale of x TV's are given as R(x) = 190x – 0.4x^2 and C(x) = 3560 + 20x. Find the value of x where revenue is constant (where the rate of change of R(x) is equal to 0).
The revenue function is constant when x = ______
The rate of change of the revenue function R(x) is given by its derivative R'(x) = 190 - 0.8x. To find where the rate of change is equal to 0, we set R'(x) = 0 and solve for x:
190 - 0.8x = 0
0.8x = 190
x = 237.5
Therefore, the revenue function is constant when x = 237.5.
To find the value of x where revenue is constant, we need to find the point where the rate of change of the revenue function R(x) is equal to 0. This can be achieved by finding the derivative of R(x) with respect to x, and then setting it equal to 0.
R(x) = 190x - 0.4x^2
The derivative of R(x) with respect to x is:
R'(x) = dR(x)/dx = 190 - 0.8x
Now, set R'(x) equal to 0 and solve for x:
0 = 190 - 0.8x
0.8x = 190
x = 190 / 0.8
x = 237.5
The revenue function is constant when x = 237.5.
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Question 1(Multiple Choice Worth 2 points)
(Circle Graphs MC)
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 3(Multiple Choice Worth 2 points)
(Comparing Data LC)
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?
Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed
Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 11, 35, 39, 40, 42, 42, 45, 49, 49, 51, 51, 52, 53, 53, 54, 56, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 49 is the most accurate to use to show that they need more money.
The range of 49 is the most accurate to use to show that they have plenty of money.
The IQR of 13 is the most accurate to use, since the data is skewed.
Question 5(Multiple Choice Worth 2 points)
(Making Predictions MC)
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6(Multiple Choice Worth 2 points)
(Creating Graphical Representations LC)
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Answer:
Step-by-step explanation:
Car are the preferred transportation for 168 residents.Together, Walk and Streetcar are the preferred transportation for 55 residents.Bus is the preferred transportation for 45 residents.Bicycle is the preferred transportation for 50 residents.Question 2(Multiple Choice Worth 2 points)(Appropriate Measures MC)The box plot represents the number of tickets sold for a school dance.A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the numb
For a certain company , the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0. 5x^2.
a) set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces (hint: it is a quadratic polynomial)
b) find two values of x that will create a profit of $300
c) is it possible for the company to make a profit of $15,000
Answer:
Step-by-step explanation:
a) Profit = Revenue - Cost = (90x - 0.5x²) - (50x + 300)
= -0.5x² + 90x - 50x - 300
= -0.5x² + 40x - 300
b) -0.5x² + 40x - 300 = 300
-0.5x² + 40x - 600 = 0
use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -600):
x = 20, 60
c) -0.5x² + 40x - 300 = 15000
-0.5x² + 40x - 15300 = 0
use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -15300):
x = 40±10√290i
Not possible to make a profit of $15,000
Question 6 < > Evaluate the integral: fa®V1+362'de : 1+ +C
To solve this integral, we'll use a trigonometric substitution. Let x = (1/6)tan(θ), which implies dx = (1/6)sec^2(θ)dθ.
Now, we can rewrite the integral as:
∫√(1 + 36(1/6tan(θ))^2) (1/6)sec^2(θ)dθ
Simplify the expression inside the square root:
∫√(1 + 6^2tan^2(θ)) (1/6)sec^2(θ)dθ
Now, recall the trigonometric identity: 1 + tan^2(θ) = sec^2(θ). Using this identity, we have:
∫√(sec^2(θ)) (1/6)sec^2(θ)dθ
Simplify and integrate:
(1/6)∫sec^3(θ)dθ
Unfortunately, the integral of sec^3(θ) is non-elementary, so we cannot find a closed-form expression for it. However, you can look up the techniques used to evaluate this integral, such as integration by parts or reduction formulas, if you need a more detailed solution.
Remember to convert the result back to the original variable x using the substitution x = (1/6)tan(θ), and don't forget to add the constant of integration, C, at the end.
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A survey found that the relationship between the years of education a person has and that person's yearly income in his or her first job after completing schooling can be modeled by the equation y = 1200 x + 7000, where x is the number of years of education and y is the yearly income. According to the model, how much does 1 year of education add to a person's yearly income?
According to the model, each additional year of education adds $1200 to a person's yearly income in their first job after completing schooling.
We're given the equation y = 1200x + 7000, where x represents the number of years of education, and y represents the yearly income.
To find how much 1 year of education adds to a person's yearly income, we need to look at the coefficient of the variable x, which is 1200.
So according to the model, 1 year of education adds $1,200 to a person's yearly income.
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identify the pattern, then write the next three terms in this sequence. 12. 83, 75, 67, 59
Answer:
The pattern is you are subtracting by 8. The subsequent three terms are 51, 43, and 35.
Step-by-step explanation:
First, you can subtract the first value from the second to find the common difference. Then you continue on this pattern. Simple!
Mrs. Ross is a librarian at Westside Library. In examining a random sample of the library's book collection, she found the following. 902 books had no damage, 80 books had minor damage, and 43 books had major damage. Based on this sample, how many of the 30,000 books in the collection should Mrs. Ross expect to have no damage? Round your answer to the nearest whole number. Do not round any intermediate calculations. Books 5 ? X
There would be 26,790 books. of the 30,000 books in the collection should Mrs. Ross expect to have no damage
Out of the random sample, 902 books had no damage. To estimate the number of books with no damage in the entire collection of 30,000 books, we can use the proportion of books in the sample that had no damage.
The proportion of books in the sample with no damage is:
902 / (902 + 80 + 43) = 0.893
Therefore, we can expect approximately:
30,000 x 0.893 = 26,790
books in the collection to have no damage. Rounded to the nearest whole number, the answer is:
26,790 books.
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Select two trigonometric functions that are equivalent to the ratio x/y.
Sine and cosine are both equivalent to x/y, depending on the angle of the point on the circle.
To find two trigonometric functions equivalent to the ratio x/y, we can use the unit circle. Let's assume that x and y are the coordinates of a point on the circle, where x represents the horizontal displacement, and y represents the vertical displacement.
From this, we can find that the sine of the angle that x and y make with the x-axis is y, and the cosine of that angle is x. Therefore, the two trigonometric functions equivalent to the ratio x/y are sine and cosine.
We can write this as sin(angle) = y/y and cos(angle) = x/y. It's important to note that the value of the angle depends on the position of the point on the unit circle.
So, sine and cosine are both equivalent to x/y, depending on the angle of the point on the circle.
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I need to find the 2 answers
Answer:
28 degrees and 62 degrees
Step-by-step explanation:
Set up your equation like this:
x+(x-34)=90
2x-34=90
2x=56
x=28
28+34=62
So the smaller angle is 28 degrees and the larger angle is 62 degrees.
Hope this helps!! :D
Please help and show work pls
noah and emma are standing on opposite sides of a 43.3 ft tree looking up at noah’s cat, which is perched at the very top. they are separated by a horizontal distance of 100 ft. the distance from emma to the cat is 50 ft and her angle of elevation to see the cat is 60°. the distance from noah to the cat is 86.6 ft and his angle of elevation to see the cat is 30°.
(a) identify three different trigonometric ratios that could have been used to find the distance x between emma and the base of the tree. for each trigonometric ratio, determine the distance. round to the nearest whole number.
(b) use the pythagorean theorem to find the distance x between emma and the base of the tree. round to the nearest whole number.
(a) The three different trigonometric ratios that could have been used to find the distance x between Emma and the base of the tree are sin(60°) = 43.3/50, cos(60°) = x / 50, and tan(60°) = 43.3 / x. The distance is 25 ft.
(b) Using the Pythagorean theorem, the distance x between Emma and the base of the tree is 25 ft.
(a) We can use sine, cosine, and tangent trigonometric ratios to find the distance x between Emma and the base of the tree.
1. Sine:
sin(60°) = opposite/hypotenuse = (tree height) / 50
tree height = 50 * sin(60°) = 43.3 ft (since it's given that the tree is 43.3 ft tall)
2. Cosine:
cos(60°) = adjacent/hypotenuse = x / 50
x = 50 * cos(60°) = 25 ft
3. Tangent:
tan(60°) = opposite/adjacent = (tree height) / x
x = (tree height) / tan(60°) = 43.3 / tan(60°) ≈ 25 ft
(b) To find the distance x between Emma and the base of the tree using the Pythagorean theorem, we can consider the triangle formed by Emma, the base of the tree, and the top of the tree.
Let's call the distance from the base of the tree to the top of the tree (tree height) y.
Emma's distance to the cat (50 ft) is the hypotenuse, the distance x is one leg, and the tree height y (43.3 ft) is the other leg of the right triangle.
Using the Pythagorean theorem: x² + y² = hypotenuse²
x² + 43.3² = 50²
x² + 1874.89 = 2500
x² = 625.11
x ≈ 25 ft
So, the distance between Emma and the base of the tree is approximately 25 ft.
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EASY POINTS!!
i need someone to write three sentences that explains how i got the answer i have the equation already but dont know how to do it THANKS SO MUCH.
An amusement park has discovered that the brace that provides stability to the Ferris wheel has been damaged and needs work. The arc length of the steel reinforcement that must be replaced is between the two seats shown below. The sector area is 28.25 ft2 and the radius is 12 feet. What is the length of steel that must be replaced (Arc Length)? Describe the steps you used to find your answer and show all work. Round θ to the nearest tenth.
my "work":
Area of Sector = 28.25 ft² & Radius = 12 feet
Area of sector = ∅/360 × π × r²
Put the values,
28.25 = ∅/360 × π × 12²
∅ = (28.25 × 360) / π×12²
∅ = 22.47 ≈ 22.5
length of arc =∅/360 × 2 × π × r
L = 22.5/360 × 2 × π × 12
L = 4.71 Feet
We used the given sector area formula, 28.25 = ∅/360 × π × 12², to find the central angle (∅) by rearranging the equation
The Explanation of your solutionFirst, we used the given sector area formula, 28.25 = ∅/360 × π × 12², to find the central angle (∅) by rearranging the equation and solving for ∅, which resulted in ∅ ≈ 22.5 degrees.
Next, we applied the arc length formula, L = ∅/360 × 2 × π × r, and plugged in the values we had, including the calculated ∅ and the given radius (12 feet).
Finally, we calculated the arc length (L) to be approximately 4.71 feet, which is the length of steel that must be replaced.
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Nathan ordered 1 cheeseburger amd 1 bag of chips for 3. 75 jack ordered 2 cheeseburgers and 3 bags of chips for 8. 25
The cost of a bag of chips is $0.75 and the cost of a cheeseburger is $3.
What is equation?The definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
let the cost of a cheesburger be x.
let the cost of a bag of chips be y
therefore, it is given that x + y = 3.75 ...........(i)
it is also given that 2x + 3y = 8.25 ............(ii)
multiplying the equation in( i) by 2 we get 2x + 2y = 7.50 ......(iii)
subtracting the equation in iii) from the equation in ii) we get y = $0.75
Therefore ,the cost of a bag of chips is $0.75
Substituting the value of y found in (ii) we get x = 3.
therefore ,the cost of a cheeseburger is $3.
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The complete question is ,
Nathan ordered 1 cheeseburger and 1 bag of chips for 3. 75 jack ordered 2 cheeseburgers and 3 bags of chips for 8. 25.find the value of one cheeseburger and one bag?
Jan and Jackie check out the same number of library books. Jan turns in 4 books after 3 weeks. Jackie returns 2 books that week and 4 books later. Write algebraic expressions to represent the books Jan and Jackie have left
The algebraic expressions representing the books Jan and Jackie have left are J - 4 and J - 2 - 4, respectively, where J is the initial number of books checked out by both.
Let's use "J" to represent the number of books Jan and Jackie checked out from the library. After 3 weeks, Jan turned in 4 books, so she has J - 4 books left.
Jackie returned 2 books after the first week, so she has J - 2 books left. When she returned 4 more books later, she had J - 2 - 4 = J - 6 books left. Therefore, the algebraic expressions for the number of books Jan and Jackie have left are
Jan: J - 4
Jackie: J - 6
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Here is the information about 30 students in a class
18 of the students do not walk to school
Three quarters of the students who walk to school are boys
There are 6 more girls than boys who do not walk to school
Use the information to fill in the missing numbers in this table
Number who walk to school Number who do not walk to school Total
Number of Boys
Number of Girls
Total 12 18 30
Answer:
Step-by-step explanation:
18 students don't walk to school
6 boys, 12 girls
12 students walk to school (30-18)
3/4 of students who walk to school are boys = 9 boys, 3 girls
Alex can stack exactly 16 cookies, each with a diameter of 5 cm inside a cylindrical container with the same diameter and a volume of 100% cm³. What is
the surface area of the container? Round your answer to the nearest square centimeter.
Answer:
Read
Step-by-step explanation:
If Alex can stack exactly 16 cookies with a diameter of 5 cm inside a cylindrical container with the same diameter, then the height of the cylinder will be equal to the height of 16 cookies stacked on top of each other, which is 16 multiplied by the height of one cookie.
The diameter of each cookie is 5 cm, so the radius is 2.5 cm. The volume of each cookie is πr²h, where r is the radius and h is the height, so the volume of one cookie is:
V1 = π(2.5 cm)²h
The volume of 16 cookies will be:
V16 = 16π(2.5 cm)²h
Since the volume of the cylindrical container is 100% cm³, we have:
V16 = Vcyl
where Vcyl is the volume of the cylindrical container. Therefore:
16π(2.5 cm)²h = Vcyl
The height of 16 cookies stacked on top of each other is 16 times the height of one cookie, so:
h = 16(1 cm) = 16 cm
Substituting this value into the equation above and solving for the radius, we get:
r = √(Vcyl / (16πh)) = √(100 cm³ / (16π(16 cm))) ≈ 1.03 cm
The surface area of the cylindrical container is given by the formula:
A = 2πr² + 2πrh
Substituting the values we found for r and h, we get:
A = 2π(1.03 cm)² + 2π(1.03 cm)(16 cm) ≈ 142 cm²
Therefore, the surface area of the container is approximately 142 square centimeters. Rounded to the nearest square centimeter, the answer is 142 square centimeters.
The surface area of the given cylindrical container is 290 cm².
What is the volume of a cylinder?The volume of a cylinder is given by the formula:
V = πr²h
where r is the radius of the cylinder and h is its height.
We know that the volume of the cylindrical container is 100π cm³ and that it has the same diameter as the cookies, which is 5 cm.
Since the diameter of the container is 5 cm, its radius is 2.5 cm.
We can rearrange the formula for volume to solve for
h = V/πr²
h = 100π/π(2.5)²
h = 16
So, the height of the container is 16 cm.
To find the surface area of the container, we can use the formula:
A = 2πrh + 2πr²
where r is the radius of the container and h is its height.
Substituting the values we have, we get:
A = 2π(2.5)(16)+2π(2.5)²
A = 92.5π
A ≈ 290.45
Rounding to the nearest square centimeter,
A = 290
Thus, the surface area of the container is 290 cm².
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Two weeks ago i bought 20 cupcakes last week I bought 13 help me continue the pattern
Answer:
If the pattern is to continue, the next value would be a decrease of 7 from the previous value because 20-13=7. Therefore, the value for this week would be:
13 - 7 = 6
So, if you were to continue the pattern, you would have bought 6 cupcakes this week.
Consider a population that grows according to the recursive rule Pn=Pn−1+50
, with initial population P0=30
To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.
We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.
Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30
Now let's find the population at any term n, using the recursive rule:
Step 1: Determine the base case, which is the initial population.
P₀ = 30
Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180
Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.
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Find the volume of this cone.
Round to the nearest tenth.
10ft
6ft
To find the volume of a cone, we use the formula:
[tex]V = (1/3)\pi r^2h[/tex]
where V is the volume, r is the radius of the circular base, h is the height of the cone, and [tex]\pi[/tex] is approximately 3.14159.
In this problem, the height of the cone is given as 10 ft and the radius of the circular base is given as 6 ft.
First, we need to find the slant height of the cone. We can use the Pythagorean theorem:
[tex]l = \sqrt{(r^2 + h^2)[/tex]
[tex]l = \sqrt{(6^2 + 10^2)[/tex]
[tex]l = \sqrt{\\(36 + 100)[/tex]
[tex]l = \sqrt{136[/tex]
[tex]l = 11.66 ft[/tex]
Now we can substitute the values into the formula for the volume:
[tex]V = (1/3)\pi r^2h[/tex]
[tex]V = (1/3)\pi (6^2)(10)[/tex]
[tex]V = 120\pi /3[/tex]
[tex]V = 40\pi[/tex]
[tex]V= 125.6 cubic feet[/tex]
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Find the indicated coefficients of the power series solution about x = O of the differential equation (x2 – x + 1)y' – y + 8y = 0, y(0) = 0, y(0) = 4 y = 4x+ 2 x²+ -4 23+ -44/9 24+ 1/6 5 + (326)
The indicated coefficients are:
[tex]c_2 = -(-2) = 2[/tex]
[tex]c_4 = 5/2[/tex]
[tex]c_5 = -22[/tex]
How to find the power series solution of the differential equation?To find the power series solution of the differential equation about x = 0, we assume that the solution has the form:
y(x) = ∑(n=0 to infinity) [tex]c_n x^n[/tex]
where [tex]c_n[/tex] are the coefficients of the power series.
Differentiating y(x), we get:
y'(x) = ∑(n=1 to infinity) [tex]n c_n x^{(n-1)}[/tex]
Next, we substitute y(x) and y'(x) into the differential equation:
([tex]x^2[/tex] - x + 1)y' - y + 8y = 0
([tex]x^2[/tex] - x + 1) ∑(n=1 to infinity)[tex]n c_n x^{(n-1)}[/tex] - ∑(n=0 to infinity)[tex]c_n x^n[/tex] + 8∑(n=0 to infinity)[tex]c_n x^n[/tex] = 0
Simplifying this expression and grouping the terms with the same power of x, we get:
∑(n=1 to infinity) [tex]n c_n x^n (x^2 - x + 1)[/tex]+ ∑(n=0 to infinity) [tex](8c_n - c_{(n+1)}) x^n[/tex] = 0
Since this equation holds for all values of x, we must have:
[tex]n c_n (n+1) - (n+2) c_(n+2) + 8c_n - c_(n+1) = 0[/tex]
for all n ≥ 0, where we have set [tex]c_{(-1){ = 0[/tex]and [tex]c_{(-2)}[/tex]= 0.
Using the initial conditions y(0) = 0 and y'(0) = 4, we have:
[tex]c_0 = 0[/tex]
[tex]c_1 = y'(0) = 4[/tex]
Substituting these values into the recurrence relation, we can recursively find the coefficients of the power series solution:
[tex]n = 0: 0 c_0 - 2 c_2 + 8 c_0 - c_1 = 0 = > c_2 = (4-8c_0+c_1)/(-2) = -2[/tex]
[tex]n = 1: 1 c_1 - 3 c_3 + 8 c_1 - c_2 = 0 = > c_3 = (9c_1-c_2)/3 = 6[/tex]
[tex]n = 2: 2 c_2 - 4 c_4 + 8 c_2 - c_3 = 0 = > c_4 = (10c_2-c_3)/(-4) = 5/2[/tex]
[tex]n = 3: 3 c_3 - 5 c_5 + 8 c_3 - c_4 = 0 = > c_5 = (11c_3-c_4)/5 = -22/15[/tex]
[tex]n = 4: 4 c_4 - 6 c_6 + 8 c_4 - c_5 = 0 = > c_6 = (9c_4-c_5)/(-6) = -64/45[/tex]
Hence, the power series solution of the differential equation about x=0 is:
[tex]y(x) = 4x + 2x^2 - 4x^3 + 23x^4 - 44/9 x^5 + 24/5 x^6 - 326/315 x^7 + ...[/tex]
Therefore, the indicated coefficients are:
[tex]c_2 = -(-2) = 2[/tex]
[tex]c_4 = 5/2[/tex]
[tex]c_5 = -22[/tex]
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Four drivers recorded the distance they drove each day for a week. Which driver's data set has a mode that is greater than the mean or median AND a median with the lowest value of the three measures?
a
Kadisha: 8, 17, 23, 16, 17, 18, 125
b
Cole: 14, 26, 34, 22, 47, 22, 45
c
Fabian: 7, 12, 11, 23, 13, 23, 30
d
Ling: 52, 36, 41, 31, 31, 37, 59
Driver's data set that has a mode that is greater than the mean or median is Fabian and a median with the lowest value of the three measures is Kadisha.
Data of Fabian: 7, 12, 11, 23, 13, 23, 30
Mean = sum of all observation / total no. of observation
Mean = (7+ 12+ 11+ 23+ 13+ 23+ 30) / 7
Mean = 17
Mode = most repeating observation
Mode = 23
For median we have to write observation in ascending order
7,11,12,13,23,23,30
Median = (N+1)/2
Where N = No. of observation
Median = (7+1)/2
Median = 4th observation
Median = 13
Here mode that is greater than the mean or median.
similarly for,
Kadisha: 8, 17, 23, 16, 17, 18, 125
Mean = 32
Median = 17
Mode = 17
Here median with the lowest value of the three measures.
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Polina is designing a new sandbox for her local playground. Polina knows she needs `1894` cubic inches of sand to fill the sandbox up `10` inches. If Polina wanted to fill the sandbox up `3` more inches to the top, how much more sand would she need?
Answer:
568.2 in
Step-by-step explanation:
To find this we first have to divide 1894/10 then we get 189.4 which we multiply by 3 to find how much more sand we need.
Please help me thank you
Find the area and perimeter of the parallelogram. Round to the nearest tenth if necessary.
Area = 156
Perimeter = 71.8
Area = 288
Perimeter = 71.8
Area = 156
Perimeter = 65.2
Area = 288
Perimeter = 65.2
Step-by-step explanation:
area= base*height (8+10)*16=288
perimeter=2L+2B
to find L we will use Pythagorean theorem(check attachment for the solving to find L)
L=17.8
perimeter= 2(17.8)+2(18)
=71.77
=71.8
A student lifts a 12 n textbook 1. 5 and carries the book 5 m across the room in 7s
The student does 18 J of work on the textbook. Their power output is 0.0228 W. Work is calculated by multiplying force and displacement, while power is the rate at which work is done and is calculated by dividing work by time.
To calculate the work done by the student on the textbook, we use the formula
work = force x distance x cos(theta)
where force is the weight of the textbook, distance is the height it is lifted, and theta is the angle between the force and distance vectors, which is 0 degrees since the force is acting vertically upward and the distance is upward as well. Thus, we have
work = 12 N x 1.5 m x cos(0) = 18 J
To calculate the power output of the student, we use the formula:
power = work / time
where work is the work done by the student on the textbook, and time is the total time it took to lift and carry the book. Thus, we have:
time = 1.5 s + 7 s = 8.5 s
power = 18 J / 8.5 s = 2.12 W
Therefore, the student did 18 J of work on the textbook, and had a power output of 2.12 W.
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--The given question is incomplete, the complete question is given
" a student lifts a 12 N textbook 1.5 m in 1.5 s and carries the books 5 m across the room in 7 s. how much work does the student do on the textbook? and what is the power output of the student."--
The window in sandra's dining room is in the shape of a semi circle. the diameter of the window is 16 inches. how many square inches is the window.use 3.14 for π. round to the nearest tenth
The area of the semi-circular window in Sandra's dining room by rounding to nearest tenth is approximately 100.5 square inches.
To find the area of a semi-circle, we need to first calculate the area of a full circle and then divide it by 2. The formula for the area of a circle is
A = π * r², where A is the area and r is the radius.
Find the radius of the semi-circle: Since the diameter is 16 inches, the radius is half of that, which is 8 inchesCalculate the area of a full circle using the formula A = π * r². Substitute the values of π and r,Rounding to the nearest tenth, the area of the window in the shape of semi-circle in Sandra's dining room is approximately 100.5 square inches.
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You and a group of friends want to know how many students in your school prefer rap music. There are 440 students in your school. Each person in the group randomly surveys 20 students. The table shows the results.
A. Use each sample to make and estimate for the number of students in your school who prefer rap music
B. Describe the center and variation of the estimates
The survey results show that the estimates for the number of students in the school who prefer rap music range from 110 to 154. The center of the estimates is around 121, with a variation of about 66.
To estimate the number of students who prefer rap music, multiply the proportion who prefer rap in each sample by the total number of students in the school (440)
Sample 1: 0.25 x 440 = 110
Sample 2: 0.20 x 440 = 88
Sample 3: 0.30 x 440 = 132
Sample 4: 0.35 x 440 = 154
The center of the estimates is the average of the four estimates: (110 + 88 + 132 + 154) / 4 = 121. Variability can be described using the range (154 - 88 = 66) or the standard deviation of the estimates, which requires additional calculations.
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Juanita keeps 25% of the monthly sales from her ice cream shop as a profit. If the shop makes an average of $750 in sales this month, how much money will Juanita keep as profit this month?
Juanita will keep $187.50 as profit from her ice cream shop's sales this month.
Juanita will keep 25% of the monthly sales as profit, which is equivalent to $750 x 0.25 = $187.50. This means that out of the total monthly sales of $750, Juanita will keep $187.50 as her profit, while the remaining $562.50 will go towards the expenses of running the ice cream shop.
Profit is the amount of money that a business earns after deducting all its expenses. It is the excess revenue that remains after all the costs of doing business have been taken into account. Profit is essential for businesses as it helps them to sustain their operations, invest in growth opportunities, and generate returns for their owners or shareholders.
In Juanita's case, her profit is 25% of the monthly sales, which is a significant amount that can help her to keep her ice cream shop running smoothly. By keeping a portion of the sales as profit, Juanita can use the money to pay for her expenses, such as rent, utilities, and supplies, while still having enough left over to reinvest in her business or save for her personal use.
Overall, understanding the concept of profit is crucial for entrepreneurs and business owners to ensure that they can generate enough revenue to cover their expenses and make a profit that will help them to grow and succeed in the long run.
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