This means that there is a 50% chance that the outcome of a trial will be 17.
The given table represents the frequency distribution of a discrete random variable X, which has four possible outcomes: 15, 16, 17, and 18. The frequency of each outcome indicates the number of times that outcome occurs in 16 trials.
To calculate the probability of a specific outcome, we divide its frequency by the total number of trials. In this case, we want to find P(X=17), which is the probability that the outcome of a trial is 17. From the table, we see that the frequency of X=17 is 8, which means that 17 occurred 8 times out of 16 trials. Therefore,
P(X=17) = frequency of X=17 / total number of trials = 8 / 16 = 0.5
This means that there is a 50% chance that the outcome of a trial will be 17.
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Full Question: The Following Table Is Based On 16 Trials. X 15 16 17 18 Frequency 2 4 8 2 Based On The Table, What Is P(X=17)? Leave Your Answer In Decimal Form To Three Places.
The following table is based on 16 trials.
x 15 16 17 18
frequency 2 4 8 2
Based on the table, what is P(x=17)?
Leave your answer in decimal form to three places.
Find the volume of the solid enclosed by the paraboloids z = 4 (x² + y²) and z = 50 – 4 (x2 + y²).
The volume of the solid enclosed by the paraboloids z = 4 (x² + y²) and z = 50 – 4 (x² + y²) is approximately 164.93 cubic units.
To find the volume of the solid enclosed by the two paraboloids, we need to first find the intersection of the two surfaces. Setting the equations of the paraboloids equal to each other, we get:
4(x² + y²) = 50 - 4(x² + y²)
Simplifying this equation, we get:
8x² + 8y² = 50
Dividing by 8, we get:
x² + y² = 6.25
This equation represents a circle of radius 2.5 centered at the origin in the xy-plane.
To find the volume of the solid, we can use a double integral in cylindrical coordinates:
V = ∫∫R (50 - 4r²) - 4r² r dr dθ
where R is the region enclosed by the circle x² + y² = 6.25.
Evaluating the integral, we get:
V = ∫0^2π ∫0^2.5 (50 - 8r²) r dr dθ
= 2π [25r² - (4/3)r^4]0^2.5
= 2π [156.25/3]
≈ 164.93 cubic units
Therefore, the volume of the solid enclosed by the paraboloids z = 4 (x² + y²) and z = 50 – 4 (x² + y²) is approximately 164.93 cubic units.
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why zero is neither positive or negative probe with scientific ?
Answer: As the Integers being positive or negative depends on the 0 As it is reference present on the centre of the number line
Numbers on the left side are negative while that on right side being positive
Step-by-step explanation:
I need this by the end of the day may someone help me only have 13 points left
There are different ways a person can make up a story about a word problem. The square root of 81 - 7 is 2. Hence the story is given below.
What is the story of the word problem?The hypothetical story goes like this: Mia was trying to figure out the length of the missing side of a square garden bed. She knew that the total area of the garden bed was 81 square feet. She also knew that she had already planted in a section of the garden bed that was 7 feet wide.
So, what will be the length of the missing side of the garden bed if Mia wants to make sure it is completely filled with soil. In order to solve this problem, Mia used the equation: the square root of 81-7=2. She plugged in the values she knew and solved for the missing side length. Therefore, The solution will be:= ✓81 - 7= 9 - 7= 2
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A story for the word problem is that what will be the length of the missing side of a square garden when the total area is 81 feet² and the width was 7 feet wide?
How to explain the square rootFrom the information, we are seeking a story problem that has the equation had the square root of 81 - 7 = 2.
This will be written as story for the word problem is that what will be the length of the missing side of a square garden when the total area is 81 feet ² and the width was 7 feet wide?
The length will be calculated thus :
= √ 81 - 7
= 9 - 7
= 2
The length of the missing side is 2 feet.
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Christy went jogging on saturday. the table shows how far she had jogged after various times.
distance (miles) 10
15
20
time (hours)
2
3
4.
christy subtracted to find her jogging rate for each time period and said that her rate
increased each hour, from 8 to 12 to 16 miles per hour. is christy correct? explain why or
why not.
She is incorrect when she said that her rate increased each hour from 8 to 12 to 16 miles per hour. Her jogging rate was actually a steady 5 miles per hour.
You asked if Christy is correct when she said that her rate increased each hour, from 8 to 12 to 16 miles per hour. Let's analyze the data given in the table and see if she's right.
The table shows the distance Christy jogged and the corresponding time:
- 10 miles in 2 hours
- 15 miles in 3 hours
- 20 miles in 4 hours
To find her jogging rate for each time period, we need to divide the distance by the time.
1. For the first 2 hours:
Jogging rate = distance / time = 10 miles / 2 hours = 5 miles per hour
2. For the first 3 hours:
Jogging rate = distance / time = 15 miles / 3 hours = 5 miles per hour
3. For the first 4 hours:
Jogging rate = distance / time = 20 miles / 4 hours = 5 miles per hour
Christy's jogging rate remained constant at 5 miles per hour throughout her run. Therefore, she is incorrect when she said that her rate increased each hour from 8 to 12 to 16 miles per hour. Her jogging rate was actually a steady 5 miles per hour.
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Many artists incorporate geometry shapes into their art. an artist wants to make a sculpture shaped like a cone with a height of 4.2 inches and a radius of 2.5 inches.the artist needs to know the volume of the sculpture to purchase the correct amount of materials
part a. which equation shows the art is used to calculate the volume of a cone with the given measurements
part b. what is the volume,in cubic inches,of the cone? use 3.14 for pie and round your answer to the nearest tenth
The volume of the cone is approximately 26.1 cubic inches.
What is the equation used to calculate the volume of a cone with a radius of 2.5 inches and a height of 4.2 inches?The formula used to calculate the volume of a cone is:
V = (1/3) × π ×[tex]r^2[/tex] × h
where V is the volume of the cone, r is the radius of the base of the cone, h is the height of the cone, and π is a mathematical constant that is approximately equal to 3.14.
Part b. Plugging in the given values, we get:
V = (1/3) × 3.14 ×[tex]2.5^2[/tex]× 4.2
V = (1/3) × 3.14 × 6.25 × 4.2
V = 26.125 cubic inches (rounded to the nearest tenth)
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The circumstances if the base of the cone is 12π cm. If the volume of the cone is 96π, what is the height
24 cm is the height of cone .
What is known as a cone?
A cone is a three-dimensional geometric object with a smooth transition from a flat, generally circular base to the apex, also known as the vertex.
A cone is a three-dimensional geometric structure with a smooth transition from a flat base—often but not always circular—to the point at the top, also known as the apex or vertex. Cone. a right circular cone having the following measurements: height, slant height, angle, base radius, and height.
V=1/3hπr²
V = 1/3 * h * 12π
96π = 1/3 * h * 12π
96π * 3/12π = h
8 * 3 = h
h = 24 cm
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help!!
this is due by today, if anyone could help i would really appreciate help
the question is: what is the area of the shaded portion?
Diversifying Your Savings Portfolio 1.2
You saved $30,000.00 and want to diversify your monies. You invest 40% in a
Treasury bond for 3 years at 5.35% APR compounded annually You place 10% in a CD
at 4.75% APR for 3 years compounded annually 30% you invest in a stock plan and
the remainder is in a savings account at 3.90% APR compounded annually. The stock
plan increases 9% the first year, decreases in value by 5% the second year, and
increases by 7% the thind year.
1. What are the balances for each type of investment a
year?
2. What is your total gain from all of the investments combined?
of the thind
3. If you had invested 40% in stock and 30% in Treasury bonds, would you have
more or less of a gain after the three years?
Be sure to include in your response:
Detailed calculations for each type of investment.
Answers to the original questions.
Answer:
ChatGPT
To find the balances for each type of investment after one year, we can use the formula for compound interest:
Treasury bond: A = P(1 + r/n)^(nt)
A = 0.4(30000)(1 + 0.0535/1)^(1*1) = $12,912.00
CD: A = P(1 + r/n)^(nt)
A = 0.1(30000)(1 + 0.0475/1)^(1*1) = $10,316.25
Stock plan: After the first year, 30% is still in the savings account. The other 70% is in the stock plan, which increased by 9%, so the new value is:
0.7(30000)(1 + 0.09) = $23,940.00
Savings account: A = P(1 + r/n)^(nt)
A = 0.2(30000)(1 + 0.039/1)^(1*1) = $6,351.00
To find the total gain from all of the investments combined, we need to add up the gains from each investment:
Treasury bond: $12,912.00 - $12,000.00 = $912.00 gain
CD: $10,316.25 - $9,000.00 = $1,316.25 gain
Stock plan: After the second year, the stock plan decreased in value by 5%, so the new value is:
0.7($23,940.00)(1 - 0.05) = $19,149.00
After the third year, the stock plan increased by 7%, so the final value is:
0.7($19,149.00)(1 + 0.07) = $20,129.57
The gain from the stock plan is:
$20,129.57 - $21,000.00 = -$870.43 loss (since the stock plan decreased in value overall)
Savings account: $6,351.00 - $6,000.00 = $351.00 gain
Total gain = $912.00 + $1,316.25 - $870.43 + $351.00 = $708.82
If you had invested 40% in stock and 30% in Treasury bonds, the calculations would be:
Treasury bond: A = P(1 + r/n)^(nt)
A = 0.3(30000)(1 + 0.0535/1)^(1*3) = $12,853.81
Stock plan: After the first year, 40% is still in the savings account. The other 60% is in the stock plan, which increased by 9%, so the new value is:
0.6(30000)(1 + 0.09) = $16,200.00
After the second year, the stock plan decreased in value by 5%, so the new value is:
0.6($16,200.00)(1 - 0.05) = $15,390.00
After the third year, the stock plan increased by 7%, so the final value is:
0.6($15,390.00)(1 + 0.07) = $16,019.16
Total gain = ($12,853.81 - $12,000.00) + (-$981.84) + ($1,019.16) = $890.13
Therefore, investing 40% in stock and 30% in Treasury bonds
). Brooklane Ltd. Has recently appointed a new CEO of the company. The CEO has several new ideas for the organisation. One idea, which he wants to explore is the elimination of annual budgets. You are working as a management team member in this company and CEO has asked you to write a report which investigates this idea.
Question
a) Write a report for the CEO setting out the advantages and limitations of an annual budgeting system. Use academic sources to support your answer.
Part (two). The following information relates to the wards in the cardiology department of Good Health Hospital for one accounting period
Wards 1 ,2 ,3
Number of Beds 12 ,10,20
Total number of Patients 48,32, 108
Total ward staff (excluding consultants) 8, 8 ,12
Ward staff – full-time equivalent 5 ,4 ,6
Variable operating costs for period £58,000, £66,000, £98,000
Operating fixed costs £85,000 ,£67,000, £88,000
General overhead costs £40,000, £40,000, £40,000
General overhead costs are made up of recharges from support services. The total cost of £120,000 is split equally between the three wards. The hospital manager is concerned about the high costs of running the three heart-care wards. She has asked you to investigate their performance.
Question
b) Write a report which investigates the costs of operating the three hospital wards. Your report should include appropriate measures of performance for each ward and you should draw conclusions from the costs. Calculate necessary calculations to support your conclusions.
[Hint: Calculations include: Patient (turnover) per bed, FTE Staff per bed & per patients, Variable Cost per bed & per patient and Fixed cost per bed & per patient. ]
a The purpose of this report is to investigate the advantages and limitations of the annual budgeting system to determine whether the elimination of the system is a good idea.
b Report on the Advantages and Limitations of an Annual Budgeting System This report investigates the advantages and limitations of an annual budgeting system. The purpose is to assess the feasibility of eliminating the annual budgeting system at Brooklane Ltd. By analyzing academic sources, we can gain insights into the potential benefits and drawbacks of such a decision.
Advantages of an Annual Budgeting SystemThe annual budgeting system has several advantages. Firstly, it allows organizations to set financial goals and targets for the coming year. This helps organizations to allocate resources and prioritize their spending to achieve their goals.
Limitations of an Annual Budgeting System is that despite its advantages, the annual budgeting system also has limitations. Firstly, it can be time-consuming and costly to prepare, especially for larger organizations. This can divert resources from other important areas of the organization.
In conclusion, the annual budgeting system has both advantages and limitations.
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V=-x2+14x -24 I need to find the range domain and graph?
5.
Sarah deposited $800 in an account that earns
2% interest compounded annually. Claire deposited
$800 in an account that earns 2% simple interest.
How much will each girl have in their account at the
end of 8 years if they do not make any deposits or
withdrawals?
Answer:
Sarah will have $937.28 and Claire will have $928.
Step-by-step explanation:
All my work is provided in the screenshots that are attached to my answer! Drop questions in the comments and I'll try to respond if I remember/see them lol.
Have a great day!
How many numbers from 2 through 100 can be expressed as p², where p is a prime number?
F. 4
G. 5
H. 7
J. 8
K. 9
Use the image to determine the direction and angle of rotation.
Graph of triangle ABC in quadrant 1 with point A at 1 comma 3. A second polygon A prime B prime C prime in quadrant 4 with point A prime at 3 comma negative 1.
90° clockwise rotation
180° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
The rotation used in this problem is given as follows:
90º clockwise rotation.
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)A vertex and it's equivalent is given as follows:
A(1,3) and A'(3, -1).
Hence the rule is:
(x,y) -> (y, -x).
Which is the rule for a 90° clockwise rotation = 270º counterclockwise rotation.
Missing InformationThe image is presented at the end of the answer.
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Answer:
90° clockwise rotation
Step-by-step explanation:
I did the exam and got it correct
In a circle with radius 6 and angle intercepts an arc of length 3pi find the angle in radians in simplest form
In a circle with radius 6 and angle intercepts an arc of length 3π , the angle in radians in simplest form is π/2.
In a circle, the length of an arc is proportional to the angle that it intercepts. The ratio of the arc length to the circumference of the circle is equal to the ratio of the angle in radians to 2π. Thus, we can write:
(arc length) / (circumference) = (angle) / (2π)
In this problem, we are given that the circle has a radius of 6 and that the arc length is 3π. We can use the formula for the circumference of a circle, which is C = 2πr, to find the circumference of this circle:
C = 2πr = 2π(6) = 12π
Now we can use the formula above to find the angle in radians:
(3π) / (12π) = (angle) / (2π)
Simplifying this equation, we get:
angle = (3π * 2π) / 12π = 1/2 * π
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What is the explicit equation for the nth term of the arithmetic sequence 6.3, 3.6, 0.9, –1.8, –4.5, …? an = 6.3 – 2.7n an = 6.3 – 2.7(n – 1) an = 6.3 + 2.7n an = 6.3 + 2.7(n + 1)
The explicit equation for the nth term of the arithmetic sequence is an = 9 - 2.7n.
What is the implicit equation?
An implicit equation is an equation in which the variables are not explicitly expressed in terms of each other. In other words, the equation does not give a direct formula for one of the variables in terms of the other(s), but rather relates the variables through some function or equation.
What is the explicit equation?
An explicit equation is an equation in which one variable is expressed directly in terms of the other(s). In other words, the equation gives a formula for one of the variables in terms of the other(s).
According to the given information:
the first term of the sequence is a1 = 6.3, and the common difference between consecutive terms is d = -2.7 (since we subtract 2.7 from each term to get to the next term). Therefore, the explicit equation for the nth term of the sequence is:
an = 6.3 + (n - 1)(-2.7)
Simplifying this expression, we get:
an = 6.3 - 2.7n + 2.7
an = 9 - 2.7n
So the correct equation for the nth term of the arithmetic sequence 6.3, 3.6, 0.9, -1.8, -4.5, ... is:
an = 9 - 2.7n
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Need help please answer
what is the unit rate of y=8x
The unit rate of the linear equation y = 8x is 8.
What is the unit rate of a linear equation?A linear equation of a function illustrates the straight line on a coordinate plane. It can be expressed in a slope intercept form y = mx + b, where:
m = slopeb = y-interceptThe slope shows steep the gradient is and it is the change in the rise over the run. For a unit rate which is usually the ratio between two different quantities. We can say in the linear equation, the unit rate represents the slope of the function.
Given that:
y = 8x
To find the unit rate(slope) which is the change in the y-axis(rise) over the change in the x-axis(run) by using slope-intercept form. Then, we can conclude that the unit rate is 8.
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The carbon monoxide wel wat is predicted to be 0.02.2+1 arts permitin), where is the population in thousands In was the population of the oty i predicted to be ) - 12 those perle Therefore, it was the one will be D) - 02/12 - 02.10 Find that which in de will be increasing in 2 years.
I apologize, but I am having trouble understanding your question. Can you please provide more context and clarity? Specifically, what do you mean by "carbon monoxide wel wat" and "arts permitin"? Additionally, what city or population are you referring to? Once I have a better understanding of your question, I will do my best to provide a helpful response.
Hi! It seems like the question is asking about the prediction of carbon monoxide levels in relation to population growth. Unfortunately, the text is a bit unclear, so I'll try my best to answer based on the provided information.
The given equation for carbon monoxide levels (CO) is: CO = 0.02(2 + P), where P is the population in thousands. To find the predicted increase in CO levels after 2 years, you would need to know the population growth rate or the population for those years. Please provide more information or clarify the question, and I'll be happy to help further
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Enter the value of c when the expression 21. 2x + c is equivalent of to 5. 3(4x - 2. 6).
The value of c is 21.8.
We can solve for c by simplifying the expression on the right side of the equation and equating it to the expression on the left side.
Starting with the right side, we distribute the 3 across the parentheses:
5 * 3 * (4x - 2.6) = 60x - 13
Now, we can set this equal to the expression on the left and solve for c:
21.2x + c = 60x - 13
c = 60x - 13 - 21.2x
c = 38.8x - 13
However, we are asked to find the value of c, not in terms of x. Since we were not given a specific value for x, we cannot solve for c exactly. Therefore, we can only express the value of c in terms of x, which is c = 38.8x - 13.
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A population of insects increases at a rate of 280 +64 +0.9t^2 insects per day Find the Insect population after 5 days, assuming that there are consects att Round your arwer to the ne
Since we need to round our answer to the nearest whole number, the insect population after 5 days will be approximately 367 insects.
Given the rate at which the insect population increases, we can determine the population after 5 days using the given formula: 280 + 64 + 0.9t^2 insects per day.
First, we need to substitute t with the number of days, which is 5:
280 + 64 + 0.9(5)^2
Now, calculate the value of the equation:
280 + 64 + 0.9(25) = 280 + 64 + 22.5 = 366.5
OR,
The population of insects after 5 days can be found by plugging in t = 5 into the given equation:
Population = 280 + 64 + 0.9(5)^2
Population = 280 + 64 + 22.5
Population = 366.5
Rounding to the nearest insect, the population after 5 days is 367 insects.
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Tell which property the statement illustrates.
(x + 2) + 5 = x + (2 + 5)
The given statement:
(x + 2) + 5 = x + (2 + 5)
illustrates the associative property of addition.
There are three properties of addition : Associative, commutative and identity.
The associative property of addition states that : (a+b)+c = a + (b+c)
The commutative property of addition states that : a + b = b + a
The identity property of addition states that : a + 0 = a.
Therefore, the statement is illustrating the associative property of addition.
The diagonal of a table top is 40 inches and the width is 21 inches. What is the area of the table? Round to the nearest inch.
The area of the table is approximately 651 square inches.
What is Area ?
Area is a measure of the size of a two-dimensional shape or surface, such as a rectangle, circle, or triangle. It is expressed in square units, such as square inches, square feet, or square meters.
Let's use the Pythagorean theorem to find the length of the table top:
Substituting the given values, we get:
40*40 = [tex]length^{2}[/tex] + 21*21
Simplifying and solving for length, we get:
[tex]length^{2}[/tex]= 1600 - 441
[tex]length^{2}[/tex] = 961
length = 31 inches (rounded to the nearest inch)
Now that we know the length and width of the table, we can find the area by multiplying them together:
area = length x width
area = 31 x 21
area = 651 square inches (rounded to the nearest inch)
Therefore, the area of the table is approximately 651 square inches.
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Mrs. Booth is trying to building a pool with the following dimensions:
4x^2 +15
8x^2 + 10
8x^2
The following polynomial represents the perimeter of the pool, ax^2 + bx + c. Find the values of a, b, and c that represent
the perimeter of the perimeter of the pool
The values of a, b, and c that represent the perimeter of the pool are a = 80, b = 0, and c = 100.
Step 1: Add the three dimensions together to find the total length of one side of the perimeter:
(4x^2 + 15) + (8x^2 + 10) + (8x^2) = 20x^2 + 25
Step 2: Since the perimeter has 4 equal sides (it's a rectangle), multiply the total length of one side by 4:
Perimeter = 4(20x^2 + 25) = 80x^2 + 100
Now, compare the perimeter polynomial with the general form ax^2 + bx + c:
80x^2 + 100 = ax^2 + bx + c
From this comparison, you can see that:
a = 80
b = 0 (since there is no term with x)
c = 100
So, the values of a, b, and c that represent the perimeter of the pool are a = 80, b = 0, and c = 100.
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Abd and dbc are linear pairs, and abd and evc are vertical angles. if mabd = 5(2x + 1), mdbc= 3x + 6, and mebc = y+135/2, select all statements that are true
The following statements are true:
mabd + mdbc = 180 degrees
mabd = mevc
What are the true statements given that abd and dbc are linear pairs, abd and evc are vertical angles, and the measures are given?According to the definition of linear pairs, the two angles add up to 180 degrees. Therefore, mabd + mdbc = 180 degrees.
According to the definition of vertical angles, they have the same measure. Therefore, mabd = mevc.
Since abd and evc are vertical angles, and mabd = mevc, then mabd = mebc. Therefore, we can substitute mabd in the equation mebc = y+135/2 to get 5(2x + 1) = y+135/2.
We can solve for y to get y = 10x + 260.
Now we can substitute this value of y into the equation mebc = y+135/2 to get mebc = 10x + 347.5.
Therefore, none of the statements in the question that mention mebc are necessarily true or false, since we don't have enough information about the value of x to determine its measure.
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For each problem, determine what will happen to the first factor?
10 x 1/2
15 x 7/2
When multiplying a whole number with a fraction, the first factor will be reduced to a fraction or a decimal, depending on the problem.
In both of the given problems, we are multiplying a whole number with a fraction. When we multiply a whole number with a fraction, we can simply multiply the whole number with the numerator of the fraction and keep the denominator as it is. So, in the first problem, we have 10 multiplied by 1/2. Multiplying 10 with 1 gives us 10, and then we divide it by 2, which gives us 5. Therefore, the first factor, which is 10, will be reduced to 5 in this problem.
In the second problem, we have 15 multiplied by 7/2. Multiplying 15 with 7 gives us 105, and then we divide it by 2, which gives us 52.5. Therefore, the first factor, which is 15, will be reduced to 52.5 in this problem.
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The ceiling of Stacy's living room is a square that is 25 ft long on each side. Stacy knows the diagonal of the ceiling from corner to corner must be longer than 25 ft, but she doesn't know how long it is.
Solve for the length of the diagonal of Stacy's ceiling in two ways:
(a) Using the Pythagorean Theorem.
(b) Using trigonometry
The length of the diagonal of Stacy's ceiling using the Pythagorean Theorem and trigonometry is 35.36 ft.
(a) Using the Pythagorean Theorem:
Since the ceiling is a square, we can treat it as two right triangles. Let's call the length of the diagonal 'd'. Now, we can apply the Pythagorean Theorem (a² + b² = c²) to one of the right triangles:
a² + b² = d²
25² + 25² = d²
625 + 625 = d²
1250 = d²
Now, take the square root of both sides:
√1250 = d
d ≈ 35.36 ft
(b) Using trigonometry:
In one of the right triangles, the angle between the two sides of the square (25 ft each) is 45 degrees. We can use the tangent function (tan) to relate the angle to the side lengths:
tan(45) = opposite side / adjacent side
tan(45) = 25 / 25
Since tan(45) = 1, we have 1 = 1, which confirms the angle is 45 degrees. Now, we can use the sine or cosine function to find the diagonal:
sin(45) = opposite side / hypotenuse
sin(45) = 25 / d
OR
cos(45) = adjacent side / hypotenuse
cos(45) = 25 / d
Both functions give us the same result since the angles are 45 degrees. Solving for 'd':
d = 25 / sin(45)
d ≈ 35.36 ft
So, the length of the diagonal of Stacy's ceiling is approximately 35.36 ft using both methods.
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Which table has a constant of proportionality between
�
yy and
�
xx of
12
1212?
Choose 1 answer:
Choose 1 answer:
(Choice A)
�
xx
�
yy
1
2
2
1
start fraction, 1, divided by, 2, end fraction
6
66
2
22
24
2424
10
1010
120
120120
A
�
xx
�
yy
1
2
2
1
start fraction, 1, divided by, 2, end fraction
6
66
2
22
24
2424
10
1010
120
120120
(Choice B)
�
xx
�
yy
1
4
4
1
start fraction, 1, divided by, 4, end fraction
3
33
3
33
60
6060
12
1212
144
144144
B
�
xx
�
yy
1
4
4
1
start fraction, 1, divided by, 4, end fraction
3
33
3
33
60
6060
12
1212
144
144144
(Choice C)
�
xx
�
yy
1
3
3
1
start fraction, 1, divided by, 3, end fraction
4
44
6
66
78
7878
9
99
117
117117
C
�
xx
�
yy
1
3
3
1
start fraction, 1, divided by, 3, end fraction
4
44
6
66
78
7878
9
99
117
117117
The table that have a constant of proportionality between y and x of 12 is the first table
What is the table that have a constant of proportionality between y and x of 12?From the question, we have the following parameters that can be used in our computation:
The table of values
From the first table of values, we have the following readings
(x, y) = (1/2, 6), (2, 24) and (10, 120)
Using the above as a guide, we have the following:
The constant of proportionality between y and x in the graph is
k = y/x
Substitute the known values in the above equation, so, we have the following representation
k = 6/(1/2) = 24/2 = 120/10
Evaluate
k = 12 = 12 = 12
Hence, the constant of proportionality between y and x in the first table is 12
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Complete question
Which table has a constant of proportionality between y and x of 12?
x 1/2 2 10
y 6 24 120
x 1/4 3 12
y 3 60 144
x 1/3 6 9
y 4 78 117
Dan's small business earned about $85,000 this year. Based on data from similar businesses, Dan expects his annual earnings to increase by 12% each year. Write an exponential equation in the form y=a(b)x that can model Dan's annual earnings, y, in x years. Use whole numbers, decimals, or simplified fractions for the values of a and b. y = _____ To the nearest hundred dollars, how much is Dan's small business predicted to earn in 5 years?
The equation would be written as: y = $85,000(1 + 0.12/1)^5
Then the predicted earning would be y = $132,559
How to solve for the earningy=a(b)x
where y = income
a = $85,000
b = (1 + r = percent increase)
then x = time period = 5 years
When we put in the values we would have y = $85,000(1 + 0.12/1) ^5
The exponential function of the form y = a(b)^x is: y = $85,000(1 + 0.12/1) ^5
When we solve the above, we would have the income = y = $132,559
Therefore the predicted earnings that Dans small business would have in a period of five years is equal to $132,559
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An architect draws a blueprint of the newly modeled family room she is designing for her basement. The scale she uses is 1 inch = 2.5 feet. If the length of the family room is 8 inches, and the width of the family room is 4 inches, what are the actual dimensions of the family room?
Answer:20 feet by 10 feet
Step-by-step explanation:
an airplane is 58 m long. a scale model of the plane is 40.6 cm long.
determine the scale factor used to create the model as a decimal rounded
to the nearest thousandth
If a scale model of the plane is 40.6 cm long, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.
To determine the scale factor used to create the model, we need to divide the length of the actual airplane by the length of the model airplane:
58 m / 40.6 cm
To perform this calculation, we need to convert the units so that they match. We can convert 58 m to cm by multiplying by 100:
58 m = 58 × 100 cm = 5800 cm
Now we can divide:
5800 cm / 40.6 cm = 142.857...
Rounding to the nearest thousandth, we get:
142.857... ≈ 142.857
Therefore, the scale factor used to create the model is approximately 1:142.857 or 0.007 rounded to the nearest thousandth.
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