The value of the sum of squares due to regression (ssr) if the total sum of squares (sst) is 22.21 and the sum of squares due to error (sse) is 6.89 will be 15.32.
To find the Sum of Squares due to Regression (SSR), we use the formula:
SST = SSR + SSE
Rearranging the equation to obtain SSR, we get:
SSR = SST - SSE
[tex]$\begin{aligned}SSR&= SST - SSE \\&= 22.21 - 6.89 \\&= 15.32\end{aligned}$[/tex]
Therefore, the value of the Sum of Squares due to Regression (SSR) is 15.32, given the Total Sum of Squares (SST) is 22.21 and the Sum of Squares due to Error (SSE) is 6.89.
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f a barometer were built using water instead of Hg, how high would the column of water be if the pressure were 1 atm, knowing that the density of water is 13.6 times lower than that of mercury?
The height of the water column would be 1033.6 cm if the pressure were 1 atm.
SOLUTION:
If a barometer were built using water instead of mercury, and the pressure were 1 atm, the height of the water column would be:
1. First, find the height of the mercury column at 1 atm. The standard height is 760 mm (or 76 cm) for mercury.
2. Since the density of water is 13.6 times lower than that of mercury, the water column needs to be 13.6 times higher than the mercury column to exert the same pressure.
3. Multiply the height of the mercury column (76 cm) by 13.6:
76 cm x 13.6 = 1033.6 cm.
So, the height of the water column would be 1033.6 cm if the pressure were 1 atm.
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Complete the table
Original Price
Percent of Discount
15%
Sale Price
$146.54
The final result for the money is [tex]172.40[/tex] after you multiply it by a percent.
What does a maths percent mean?In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage.
What does the word "percentage" actually mean?Rather than being stated as a fraction, a percent is a piece of an entire thing expressed as just a number between zero and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the total by its entirety and multiply the result by 100 to get the percentage.
[tex]w-[0.15]=146.54[/tex]
so [tex]w-85p=146.54[/tex]
[tex]146.54[/tex] divided by [tex]80=1.724[/tex] so when you make it a percent it turns it into [tex]172.40[/tex] which is the final answer for the money.
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ASAP
Out of 18 students who study French, German, or both, 13 study French, 5 study only German
and 6 study both.
Draw a Venn diagram below to show the two sets.
Answer:
In this diagram, "F" represents the set of students who study French, "G" represents the set of students who study German, "F∩G" represents the set of students who study both French and German, "G∩F" represents the same set but the order of the labels has been reversed to emphasize that this is the same set, and the numbers inside the diagram indicate how many students belong to each set.
Based on the given information, 13 students study French, 5 study only German (i.e., not French), and 6 study both French and German. Therefore, the number of students who study French only is 13 - 6 = 7.
Step-by-step explanation:
To arrive at the number of students who study French only, we subtract the number of students who study both French and German (6) from the total number of students who study French (13), which gives us 7. This means that there are 7 students who study French but do not study German.
calculate breakeven w/ hidden costs, and no sponsorship number of tickets needed to break even for a run 315 323 331 ticket receipts needed to break even $7,592 $7,784 $7,977 average number of tickets needed to break even per show 79 65 56 break-even occupancy 88% 72% 62%
As per the given average, the solution of the breakeven w/ hidden costs is 62% higher.
Let's assume that the costs associated with running a 315-ticket run are $7,592. This means that on average, each ticket needs to sell for $24.10 (($7,592/315) = $24.10) to break even.
Similarly, if we consider the other two runs, we can calculate the average number of tickets needed to break even per show as follows:
For the 323-ticket run, the average number of tickets needed to break even per show is 65. (($7,784/323) = $24.10)
For the 331-ticket run, the average number of tickets needed to break even per show is 56. (($7,977/331) = $24.10)
Furthermore, we can calculate the break-even occupancy percentage for each run, which is the percentage of tickets that need to be sold to break even. The break-even occupancy for each run is as follows:
For the 331-ticket run,
=> 56/331 = 0.17 or 17%,
=> 1-0.17 = 0.83 or 83%,
=> 0.83/0.17 = 4.88,
=> 4.88 x 100% = 488%,
=> 488% x 0.62 = 303%,
=> 303%/4.88 = 62%
Hence the break-even occupancy is 62%.
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I need help with dis math
an apple falls from a tree 100 km to the ground. if the acceleration due to gravity is 9,8 m/s² and the mass of the apple is 0,2 gram. what is the potential energy of the apple?
Answer: 196 Joules (J)
Step-by-step explanation:
To calculate the potential energy of the apple, we can use the formula:
Potential Energy = Mass x Gravity x Height
First, let's convert the height from kilometers to meters:
100 km = 100,000 meters
Now, let's convert the mass of the apple from grams to kilograms:
0.2 gram = 0.0002 kilograms
Using these values, we can calculate the potential energy:
Potential Energy = 0.0002 kg x 9.8 m/s^2 x 100,000 m
Potential Energy = 196 Joules (J)
Therefore, the potential energy of the apple is 196 Joules (J).
Convert 330 litres per hour into millimeters per minute
330 litres per hour = 5489.64 millimeter³ per minute.
Given that330 litres per hour needs to be converted into millimeters per minute.
Conversion factor: 1 litre =1000 cubic centimeter 1 cubic centimeter =1 millimeter³
∴ 1 litre=1000 millimeter³
∴ 1 litre per hour=1000 millimeter³ per hour
Also, 1 hour = 60 minutes
∴ 1 hour = 60 × 60 seconds = 3600 seconds
∴ 1 second = 1/3600 hours=0.0002778 hours
Thus, 1 litre per hour =1000/3600 millimeter³ per second =0.2778 millimeter³ per second
Therefore, 330 litres per hour = 330 × 0.2778 millimeter³ per second=91.494 millimeter³ per second
Also, 1 minute =60 seconds
∴ 1 minute = 60 × 60 seconds=3600 seconds
∴ 1 second = 1/60 minutes=0.01667 minutes
Thus, 91.494 millimeter³ per second = 91.494/0.01667 millimeter³ per minute = 5489.64 millimeter³ per minute
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The volume of a right cone is 2016
�
π units
3
3
. If its diameter measures 24 units, find its height.
The height of the cone is 13.38 units
What is volume of a cone?A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.
The volume of a cone = 1/3 πr²h
volume = 2016 units³
r = d/2 = 24/2 = 12 units
2016 = 1/3 × 3.14 × 12² h
6048 = 452.16h
h = 6048/452.16
h = 13.38units
therefore the height of the cone is 13.38 units
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MODELING REAL LIFE You deposit $5000 in an account earning 7. 5% simple interest per year. How long will it take for the balance of the account to be $6500?
We use the formula I = Prt where I is the interest earned, P is the principal, r is the interest rate per year, and t is the time in years. Substituting the values, we find that it will take 4 years for a $5000 balance to reach $6500 with a 7.5% simple interest rate.
To solve this problem, we can use the formula for simple interest:
I = Prt
Where I is the interest earned, P is the principal (initial amount), r is the interest rate per year (as a decimal), and t is the time in years.
In this case, we know that the principal is $5000, the interest rate is 7.5% or 0.075, and we want to find the time required for the balance to reach $6500.
Substituting these values into the formula, we get:
I = $6500 - $5000 = $1500
P = $5000
r = 0.075
t = ?
Solving for t, we get:
$1500 = $5000 * 0.075 * t
t = $1500 / ($5000 * 0.075)
t = 4
Therefore, it will take 4 years for the balance of the account to be $6500 with a 7.5% simple interest rate.
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Let x represent the height of first graders in a class. This would be considered what type of variable:NonsensicalLaggingContinuousDiscrete
The height of first graders in a class, represented by x, would be considered a Continuous variable. Continuous variables can take on any value within a specified range and are often used to measure physical attributes, such as height.
Let x represent the height of first graders in a class. Discrete variables are those that can be measured using whole numbers, such as the number of people in a room, the number of items on a grocery list, or the number of pages in a book. Continuous variables, on the other hand, are those that can take on any value, such as height, weight, and time.Continuous variables are those that can take on any value between two points on a measurement scale. For example, the height of first graders in a class can be measured in inches or centimeters and can take on any value between the smallest and largest heights in the class.
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What is the mean of this data set?
A line plot titled Height of Lilies. The bottom of the line plot is labeled height in inches. There is a number line showing whole numbers from 18 to 24. The line plot has one mark above the 18. There is one mark above 19. There are two marks above 20. There are two marks above 21. There are three marks above 22. There are zero marks above 23. There is one mark above 24.
20
20.9
21
22.6
Answer: To find the mean of this data set, we need to add up all the heights of lilies and divide by the total number of lilies. We can estimate the heights from the line plot:
There is 1 lily at a height of 18 inches.
There is 1 lily at a height of 19 inches.
There are 2 lilies at a height of 20 inches.
There are 2 lilies at a height of 21 inches.
There are 3 lilies at a height of 22 inches.
There are 0 lilies at a height of 23 inches.
There is 1 lily at a height of 24 inches.
To calculate the mean, we need to multiply each height by the number of lilies at that height, then add up these products, and divide by the total number of lilies:
(1 x 18) + (1 x 19) + (2 x 20) + (2 x 21) + (3 x 22) + (0 x 23) + (1 x 24)
markdown
Copy code
10
= (18 + 19 + 40 + 42 + 66 + 0 + 24) / 10
= 209 / 10
= 20.9
Therefore, the mean height of lilies in this data set is 20.9 inches. The answer is (B) 20.9.
Step-by-step explanation:
ccording to this statement, government is held accountable by the - a king b church c laws d citizens next pageback
According to the given statement, the government is held accountable by the citizens. Citizens are the ones who elect the government and, thus, have the power to hold it accountable. This is a fundamental principle of democracy that ensures that those in power are serving the people's interests.In a democratic society, the government is accountable to the people.
This means that citizens have the right to hold elected officials accountable for their actions. This is achieved through various means such as free and fair elections, the rule of law, and the right to free speech and expression.Government officials are elected to serve the people and carry out their wishes. This means that they must be transparent and open to criticism. They must be willing to listen to citizens' concerns and take action to address them. This is why democratic societies have mechanisms in place to ensure that citizens can hold their government accountable, such as a free press and independent judiciary.In conclusion, citizens are the ones who hold the government accountable in a democratic society. They have the power to elect officials and the right to criticize them if they are not serving their interests. This ensures that those in power are always acting in the best interests of the people.
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. Calculate the slope of the line that passes through (3, 2) and (-7, 4).
Answer:
-0.2
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}[/tex]
^This here is how I calculated the slope^
Y2=4
Y1= 2
4-2= 2
X2=-7
x1=3
-7-3=-10
2/-10
or -2/10
The number of minutes m you spend in line is 5 times the number of people p in line. Identify the independent and dependent variables. Then write and graph a function that describes the relationship between p and m.
Answer:The number of minutes m you spend in line is 5 times the number of people p in line. Identify the independent and dependent variables. Then write and graph a function that describes the relationship between p and m.
Step-by-step explanation:
Complete the story problem so that it can be represented by the equation, and then solve. Aldo and Leola help their teacher, Ms. Krebs, put books on the bookshelves in her classroom. There are 2 times as many nonfiction books as fiction books. There are fiction books. They put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Then, they put any remaining books on Ms. Krebs's desk. Aldo and Leola put books on each bookshelf. They put books on Ms. Krebs's desk
Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.
To represent the problem as an equation, we first need to define some variables. Let's let "f" represent the number of fiction books, and "n" represent the number of nonfiction books. We know from the problem that there are 2 times as many nonfiction books as fiction books, so we can write:
n = 2f
We also know that they put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Let's call this number "s". We can then write an equation for the total number of books that can fit on the bookshelves:
7s = f + n
Since n = 2f, we can substitute 2f for n in the equation:
7s = f + 2f
Simplifying, we get:
7s = 3f
Finally, we know that any remaining books are put on Ms. Krebs's desk. Let's call this number "r". We can write an equation for the total number of books:
f + n = 7s + r
Substituting 2f for n, we get:
f + 2f = 7s + r
Simplifying, we get:
3f = 7s + r
Now we can solve for "f":
3f = 7s + r
f = (7s + r) / 3
We don't have enough information to solve for "s" or "r", but we can use this equation to find the number of fiction books. For example, if we know that there are a total of 70 books, we can write:
f + n = 70
f + 2f = 70
3f = 70
f = 23.33
Since we can't have a fractional number of books, we would round down to the nearest whole number and get:
f = 23
We could then use the equation f = (7s + r) / 3 to find the number of books on each shelf, assuming there are no books left over:
23 = (7s + 0) / 3
69 = 7s
s = 9.86
Since we can't have a fractional number of books on a shelf, we would round down to the nearest whole number and get:
s = 9
So Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.
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Pease help!!
Question below!
Answer: Line PQ is parallel to line LM
Step-by-step explanation:
We can check if they are of equal distance apart by checking if the ratios of the given lines are equal...in other words we must check if LP/PN=MQ/QN
We know that triangle PNQ is inscribed inside triangle LNM
Using the information we have we see that side LP is 18 units, PN is 16 units, MQ is 27, and QN is 24. With this information we can write out LP/PN=MQ/QN and see if it's true.
LP= 18, PN= 16, 18/16= 1.125
MQ= 27, QN=24, 27/24= 1.125
therefore, LP/PN=MQ/QN is true. Making line PQ and line LM parallel.
Find the measure of x.
29°
X
3.7
x = [?]
X
Round to the nearest hundredth.
Answer:
x ≈ 3.24
Step-by-step explanation:
using the cosine ratio in the right triangle
cos29° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3.7}[/tex] ( multiply both sides by 3.7 )
3.7 × cos29° = x , then
x ≈ 3.24 ( to the nearest hundredth )
A rectangle has an area of 717. 8m2. One of the sides is 7. 4m in length. Work out the perimeter of the rectangle
The perimeter of the rectangle is approximately 208.9 meters.
To find the perimeter of the rectangle, we need to know the length of the other side.
Let's use the formula for the area of a rectangle:
area = length x width
We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:
length = area / width
length = 717.8 / 7.4
length ≈ 97.05 m
Now we have both the length and width of the rectangle, so we can find the perimeter:
perimeter = 2 x (length + width)
perimeter = 2 x (97.05 + 7.4)
perimeter = 2 x 104.45
perimeter = 208.9 m
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Let triangle ABC be similar to DEF. Find the missing side EF.
The length of the side EF is equal to 18 units since the triangle DEF and triangle ABC are similar and DEF is bigger than ABC in the margin of 3 times.
Given, two triangles ABC and DEF.
The length of AB = 8 units
The length of its concurrent side DE = 24 units
Also given that the length of BC = 6 units
Here we can see that:
As both triangles are similar, their corresponding sides are in proportion.
This means that:
[tex]\frac{BC}{EF} = \frac{AE}{DE} =\frac{AC}{DF}[/tex]
Length of AB * 3 = Length of DE
Now the length of the side EF will be 3 times more than the side BC.
Length of EF = Length of BC * 3
Length of EF = 6 * 3
Length of EF = 18 units.
Therefore, the length of the side EF is equal to 18 units.
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2. for each of the following variables, tell me level of measurement and what statistic you would use to quantify central tendency and variability. a. body weight in pounds b. number of cigarettes smoked in a day c. ethnicity d. birth order (i.e., first born, second born, etc.)
In the following question, among the conditions given, the option- a,b and c stand the same ie- The level of measurement is a ratio. The statistic used for the central tendency is the mean or median, whereas d. birth, "is ordinal."
1. Body weight in pounds: The level of measurement is a ratio. The statistic used for the central tendency is mean or median, while for variability, standard deviation or variance can be used.
2. Number of cigarettes smoked in a day: The level of measurement is a ratio. The statistic used for the central tendency is mean or median, while for variability, standard deviation or variance can be used.
3. Ethnicity: The level of measurement is nominal. The statistic used for the central tendency is the mode, while for variability, there is no appropriate statistic.
4. Birth order: The level of measurement is ordinal. The statistic used for the central tendency is median or mode, while for variability, range or interquartile range can be used.
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4. Which of the following is the square of a binomial?
A. r² - 2rs +s²
B. c² + d²
C. 16x² - 25y²
D. d² - de + e²
The correct answer is (A) r² - 2rs +s² which is a square of a Binomial.
What exactly are binomials?
In algebra, a binomial is a polynomial which consists of two terms. The terms may be separated by a plus or minus sign. The general form of a binomial is:
ax + b
where "a" and "b" are constants and "x" is the variable. A binomial can be added, subtracted, multiplied, and divided using algebraic operations. Binomials are commonly used in algebra to represent and solve problems involving two quantities or variables.
Now,
The correct answer is (A) r² - 2rs +s².
This is a perfect square trinomial, which can be written as (r - s)².
Option (B) c² + d² is not a binomial, it is the sum of two squares.
Option (C) 16x² - 25y² is a difference of two squares, which can be written as (4x + 5y)(4x - 5y).
Option (D) d² - de + e² is also a perfect square trinomial, but it cannot be written as the square of a binomial.
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Consider the initial value problem
y^{\,\prime\prime} + 25 y = e^{-t}, \ \ \ y(0) = y_0, \ \ \ y^{\,\prime}(0) = y_0^{\prime}.
Suppose we know thaty(t) \to 0ast \to \infty. Determine the solution and the initial conditions.
y(t) =______________
y(0) =_____________
y^{\,\prime}(0) =
Thus, the solution to the initial value problem is:[tex]y(t) = - y'(t) + \frac{5}{2} (-\frac{1}{5} (y''(0) - 20)) e^{2t} + 3 e^{2t}[/tex]
In this case, the student is asking about an initial value problem with a given differential equation. The differential equation is:[tex]y(t) = y'(t) - 2y(0) + 5[/tex]The initial condition is:y'(0) = 4To solve this initial value problem, we can use the method of integrating factors. First, we need to find the integrating factor. The integrating factor is given by:[tex]e^{∫ -2 dt} = e^{-2t}[/tex]
Now we can multiply both sides of the differential equation by the integrating factor to get:
[tex]e^{-2t} y(t) = e^{-2t} y'(t) + 5e^{-2t} y(0)[/tex]
We can now integrate both sides of this equation with respect to t to get:[tex]e^{-2t} y(t) = - e^{-2t} y'(t) + \frac{5}{-2} e^{-2t} y(0) + C[/tex]where C is the constant of integration.
To find C, we can use the initial condition:y'(0) = 4Substituting this into the equation above gives:C = 3Now we can solve for y(t) by multiplying both sides of the equation by[tex] e^{2t}:y(t) = - y'(t) + \frac{5}{2} y(0) e^{2t} + 3 e^{2t}[/tex]
Finally, we can use the initial condition y'(0) = 4 to solve for the value of[tex] y(0):y'(0) = - y''(0) + 5y(0) + 6y'(0) = - y''(0) + 5y(0) + 24[/tex]
Since y'(0) = 4, we have:[tex]4 = - y''(0) + 5y(0) + 24[/tex]Solving for y(0), we get:[tex]y(0) = -\frac{1}{5} (y''(0) - 20)[/tex]
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Write ^4√11^5 without radicals.
Answer: ^4√11^5 = 11^(5/4)
Step-by-step explanation: When we apply a radical, we are asking what number, when raised to a certain power, gives us the number under the radical. For example, ^4√16 is asking what number, when raised to the fourth power, gives us 16. The answer is 2, since 2^4 = 16.
So, ^4√11^5 is asking what number, when raised to the fourth power, gives us 11^5. We can simplify this expression using the exponent laws:
^4√11^5 = (11^5)^(1/4) = 11^(5/4)
Therefore, the simplified expression for ^4√11^5 is 11^(5/4). This expression does not have any radicals, making it easier to work with and manipulate.
Hope this helps, and have a great day!
the concentration of a drug in a patient's bloodstream is monitored over 10-minute intervals for two hours. t (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 c (mg) 0 2 17 37 55 72 89 103 111 113 113 103 68 a.) how fast is the concentration of the drug changing at 50 minutes? 1.7 mg/min b.) how fast is the concentration of the drug changing at 85 minutes? 1 mg/min c.) is the drug's concentration increasing or decreasing at 115 minutes? decreasing
a) The rate of change of the drug's concentration at 50 minutes is 1.7 mg/min.
b) The rate of change of the drug's concentration at 85 minutes is 0.2 mg/min.
c) The drug's concentration is decreasing at 115 minutes.
a) The central difference approach can be used to calculate the rate of medication change after 50 minutes.
f'(x) = (f(x+h) - f(x-h))/2 × h ....(1)
As per the question, we have h = 10 and x = 50
Substitute the values of h = 10 and x = 50 in (1),
f'(40) = (f(50+10) - f(50-10))/2 × 10
f'(40) = (89-55)/20
f'(40) = 1.7 mg/min
b) For the rate of change of concentration at 85 minutes:
Here, f(80) = 111 mg and f(90) = 113.
The concentration at 90 minutes is 113 mg.
Rate of change = (f(90) - f(80)) / h
= (113 - 111) /10
= 2 / 10
= 0.2 mg/min
c) Since the concentration at 120 minutes (68 mg) is lower than the concentration at 110 minutes (103 mg), the drug's concentration is decreasing.
Therefore, the drug's concentration is decreasing at 115 minutes.
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I need help with this math assignment, specifically #3
The solution to the system of equations are (-4, 5), (2, 7), (3, -1), no solution, (-5, 8) and (7, -3)
How to solve system of equation by substitution method?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Question 1 and 2
See attachment for the graphs, where we have the solutions to be
System 1: (-4, 5)
System 2: (2, 7)
Question 3 and 4
Here, we solve the system of equation by substitution method.
So, we have
2x - 7y = 13
3x + y = 8
Make y the subject in (2)
y = -3x + 8
Let's substitute the value of y in equation (i)
2x - 7(-3x + 8) = 13
2x + 21x - 56 = 13
23x = 13 + 56
23x = 69
Divide both sides by 23
x = 69 / 23
x = 3
Let's find y
y = -3(3) + 8
y = -9 + 8
y = -1
For system (4), we have
x - 3y = 2
2x - 6y = 6
So, we have
x = 2 + 3y
By substitution, we have
2(2 + 3y) - 6y = 6
4 + 6y - 6y = 6
4 = 6
The system has no solution
Question 5 and 6
Here, we have
x + y = 3
x - 3y = -29
By eliminating x, we have
4y = 32
So, we have
y = 8
This means that
x + 8 = 3
x = -5
So, the solution is (-5, 8)
For system 6, we have
3y = 26 - 5x
6x + 7y = 21
So, we have
5x + 3y = 26
6x + 7y = 21
This gives
30x + 18y = 156
30x + 35y = 105
By elimination, we have
17y = -51
y = -3
This means that
6x + 7(-3) = 21
6x = 42
So, we have
x = 7
So, the solution is (7, -3)
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13. The area of the kite is 30 m². What is the value
of x? Explain.
4m
xm
6 m
xm
14.
Answer:
answer is 3
Step-by-step explanation:
help please!! i have no clue how to do this without the answer to DC
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Corey spies a bald eagle in a tall tree. He was able to measure the angle of elevation to the bird from where he stands at 62°. The leaves on the tree make it difficult for Corey to watch the bird, so he moves 10 feet further away from the tree to get a better view. Now his angle of elevation is 56°.
What is the height of the tree? Round your answer to the nearest foot.
pls help
The height of the tree is approximately 76 feet.
What is the angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
We can use tangent to set up the following two equations based on the given angles of elevation:
tan(62°) = h/x
tan(56°) = h/(x+10)
We can rearrange the first equation to solve for "h":
h = x * tan(62°)
tan(56°) = (x * tan(62°)) / (x+10)
We can solve for "x" by multiplying both sides by (x+10) and rearranging:
x = 10 * (tan(62°) - tan(56°)))
Now we can substitute this value for "x" into either of the two equations we set up earlier to find the height of the tree "h". Using the first equation, we get:
h = x * tan(62°) ≈ 76 feet
Therefore, the height of the tree is approximately 76 feet.
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How much plastic wrap will be needed to completly cover and ice cream cone with the slant height of 4. 25 inches and a diameter of 2 inches
The amount of plastic wrap required to cover the entire cone will be 16.575 square inches.
To calculate how much plastic wrap is required to completely cover an ice cream cone with a slant height of 4.25 inches and a diameter of 2 inches, we must use the surface area of the cone.
Here, the ice cream cone can be visualized as a cone-shaped object with an added circular base.
We must use the following formula to calculate the surface area:
Surface area = πr2 + πrl
Where r is the radius and l is the slant height of the cone.
As we know the diameter of the ice cream cone is 2 inches, and its radius can be calculated by dividing it by
2.r = d/2 = 2/2 = 1 inch.
Substitute the values of r and l in the formula, and then calculate the surface area of the cone.
π = 3.14r = 1 inchl = 4.25 inches
Surface area = πr2 + πrl
= 3.14 × 1² + 3.14 × 1 × 4.25
= 3.14 + 13.435
= 16.575 square inches
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if you deposit $4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, how much money will you have in the account in 20 years ? how much will you have if you make deposits for 40 years ?
If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.
Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.
The formula to calculate the future value of an annuity due is:
[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]
Where,
FV = Future Value
PMT = Payment (amount) each period
r = Interest Rate per period
n = Number of periods
To find the future value of an annuity due for 20 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]
To find the future value of an annuity due for 40 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]
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