The possible lengths of the tree lot are 25 + 5√5 yards and 25 - 5√5 yards.
Let's denote the length of the rectangular tree lot as "l" and the width as "w".
We know that the perimeter of a rectangle is given by the formula:
Perimeter = 2(l + w)
Given that the perimeter of the tree lot must be 100 yards, we can write the equation as:
2(l + w) = 100
Next, we know that the area of a rectangle is given by the formula:
Area = l × w
Given that the area of the tree lot must be at least 500 square yards, we can write the inequality as:
l × w ≥ 500
Now, let's solve the equations simultaneously to find the possible lengths of the tree lot.
Perimeter equation:
2(l + w) = 100
l + w = 50
w = 50 - l
Area inequality:
l × w ≥ 500
Substituting the value of w from the perimeter equation into the area inequality, we have:
l × (50 - l) ≥ 500
50l - l^2 ≥ 500
l^2 - 50l + 500 ≥ 0
Now, we need to find the values of l that satisfy the inequality. Since the coefficient of the squared term is positive, the graph of this quadratic opens upward. This means that the values of l that satisfy the inequality will be either the entire range of possible values or a portion of it.
To find the possible lengths, we can either factor the quadratic or use the quadratic formula. Let's use the quadratic formula:
l = (-(-50) ± √((-50)^2 - 4(1)(500))) / (2(1))
l = (50 ± √(2500 - 2000)) / 2
l = (50 ± √500) / 2
l = (50 ± 10√5) / 2
l = 25 ± 5√5
Therefore, the possible lengths of the tree lot are 25 + 5√5 yards and 25 - 5√5 yards.
In summary, the possible lengths of the rectangular tree lot are 25 + 5√5 yards and 25 - 5√5 yards, respectively.
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Name the quadrant in which angle 0
must lie for the following to be true.
cos > 0 and
tan 0 <0
Enter a, b, c, d, or e.
a. l
b. ll
c. III
d. IV
e. All of the above.
Answer:
D is the correct answer
Step-by-step explanation:
Acellus
To solve the quadratic equation 3(x−7)2=27 , Diego and Mai wrote the following: Diego 3(x−7)2=27 (x−7)2=9 x2−72=92 x2−49=81 x2=130 x=130−−−√ and x=−130−−−√ Mai 3(x−7)2=27 (x−7)2=9 x−7=9 x=16 Identify the mistake(s) each student made. Solve the equation and show your reasoning.
Given statement solution is :- The correct solutions to the quadratic equation [tex]3(x-7)^2 = 27[/tex] are x = 10 and x = 4.
Diego made an error in the step where he simplified [tex](x-7)^2 = 9 to x^2[/tex] - 72 = 9. The correct expansion of [tex](x-7)^2 is x^2 - 14x + 49[/tex], not [tex]x^2 - 72.[/tex]Therefore, his subsequent steps and solution are incorrect.
Mai made an error in the step where she simplified [tex](x-7)^2 = 9[/tex] to x - 7 = 9. The square root of 9 is ±3, so the correct equation should be x - 7 = ±3, not x - 7 = 9. Therefore, her solution is incorrect.
To solve the equation correctly, we start with the equation [tex]3(x-7)^2 = 27.[/tex]
Dividing both sides by 3, we have:
[tex](x-7)^2 = 9[/tex]
Taking the square root of both sides, we get:
x - 7 = ±3
Now, we need to solve for x by adding 7 to both sides:
x = 7 ± 3
This gives us two possible solutions:
x = 7 + 3 = 10
x = 7 - 3 = 4
So, the correct solutions to the quadratic equation [tex]3(x-7)^2 = 27[/tex] are x = 10 and x = 4.
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There are 7 teachers going to the museum. There are 8 times as many students going as teachers. They will need 1 van for every 6 people.
The sentence with proper subject-verb agreement is the student as well as the teacher want to go to the museum. In this sentence, the subject is what we call a compound subject, meaning that the verb refers and agrees with more than just one singular word.
The compound subject is "student" and "teacher" and they are connected by "as well as", which functions as a coordinating conjunction would. That's why the verb should conjugate in its plural form.
Option A is incorrect because the structure inside parentheses is not related to the verb and does not influence its conjugation. Options C and D have a verb in the singular form for a compound subject - that would demand a plural conjugation.
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A 3-quart jug of water costs $3.48. What is the price per cup?
The calculated value of the price per cup is $1.16
How to calculate the price per cup?From the question, we have the following parameters that can be used in our computation:
A 3-quart jug of water costs $3.48
The price per cup is calculated as
Unit rate = Total cost/Size of the cup
Substitute the known values in the above equation, so, we have the following representation
Unit rate = 3.48/3
Evaluate
Unit rate = 1.16
Hence, the price per cup is $1.16
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e-Test Active
2
3
=+
4
Of(x) = -3x+4
Of(x) = -x +
Of(v)=-3y+4
5
6
7
8
10
TIME REI
Consider the function represented by 9x+3y=12 with x as the independent variable. How can this function be
written using function notation?
42-
The function notation of 9x + 3y = 12 is given as follows:
f(x) = 4 - 3x.
How to write the function notation?The function in the context of this problem is given as follows:
9x + 3y = 12.
The format for the function notation is given as follows:
Hence we must isolate the variable y, as follows:
3y = 12 - 9x
y = 4 - 3x (each term of the expression is divided by 3).
f(x) = 4 - 3x.
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Use the data set below to answer the following questions. 20 26 28 25 28 18 23 15 17 26 29 24 29 29 17 15 17 20 30 29 16 21 22 28 19
Approximately what percent of the data are greater than 28?
Approximately what percent of the data are less than 23?
Approximately what percent of data are greater than 17.5?
Approximately what percent of data are between 17.5 and 28?
Approximately 37.5% of the data are greater than 28, 33.3% of the data are less than 23, 91.7% of the data are greater than 17.5, and 62.5% of the data are between 17.5 and 28.
To answer the questions, we can analyze the given data set.
First, let's count the number of data points that satisfy each condition:
Greater than 28:
There are 9 data points greater than 28 (29, 29, 29, 30, 29, 29, 28, 28, 28).
Less than 23:
There are 8 data points less than 23 (20, 18, 15, 17, 17, 15, 17, 19).
Greater than 17.5:
There are 22 data points greater than 17.5.
Between 17.5 and 28:
There are 15 data points between 17.5 and 28.
Now, let's calculate the approximate percentage for each condition:
Percent greater than 28:
The total number of data points is 24. Approximately, 9 out of 24 data points are greater than 28.
Percentage =[tex](9 / 24) \times 100 = 37.5[/tex]%.
Percent less than 23:
Approximately, 8 out of 24 data points are less than 23.
Percentage = [tex](8 / 24) \times 100 = 33.3[/tex]%.
Percent greater than 17.5:
Approximately, 22 out of 24 data points are greater than 17.5.
Percentage = [tex](22 / 24) \times 100 = 91.7[/tex]%.
Percent between 17.5 and 28:
Approximately, 15 out of 24 data points are between 17.5 and 28.
Percentage = [tex](15 / 24) \times 100 = 62.5[/tex]%.
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enter the number that belongs in the green box 4 29 10
Answer:
Set your calculator to degree mode.
x^2 = 4^2 + 10^2 - 2(4)(10)(cos 29°)
x^2 = 46.0304
x = 6.78
The number that belongs in the green box is 6.78.
The class had 7 tests, on which he scored 85, 93, 78, 90, 88, 97, and 88.
What is the mean?
what is the probability that either event will occur? ASAP
The probability that either event will occur is 0.67
What is the probability that either event will occur?From the question, we have the following parameters that can be used in our computation:
Event A = 3
Event B = 1
Other Events = 2
Using the above as a guide, we have the following:
Total = A + B + C
So, we have
Total = 3 + 1 + 2
Evaluate
Total = 6
So, we have
P(A) = 3/6
P(B) = 1/6
For either events, we have
P(A or B) = 3/6 + 1/6 = 0.67
Hence, the probability that either event will occur is 0.67
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Pls help
This other expression is equal to
A merchant has 1500 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is
Answer:
900 kg
Step-by-step explanation:
Let's assume the cost price (C.P.) of sugar is Rs. x per kg.
The total quantity of sugar is 1500 kg.
Let the quantity of sugar sold at 8% profit be represented by y kg.
The quantity of sugar sold at 18% profit would then be (1500 - y) kg.
Using the rule of alligation, we can set up the following proportion:
(8% profit) y kg
-------------- = ------
(18% profit) (1500 - y) kg
Simplifying the proportions, we find that the difference in percentages is 4% (18% - 14% = 4%) and 6% (14% - 8% = 6%).
The ratio of these differences is 2:3.
This means that for every 2 kg of sugar sold at 8% profit, 3 kg of sugar is sold at 18% profit.
Since y represents the quantity sold at 8% profit (2 kg), we can calculate the quantity sold at 18% profit (3 kg) as follows:
(2 kg) * (3/2) = 3 kg
Therefore, the quantity sold at 18% profit is 900 kg.
11. Which one of the following is unique? b. mode a. Mean c. Median d. A and B
Among the mean, mode, and median, the unique one is the b. mode.
What is the mode?The mode is the data value that occurs many times more than other data values.
Unlike the mean that shows the average value of all the data values, the mode occurs more. While we compute the mean by dividing the total data value by the number of data items, the mode is not computed but found as the most frequent data value.
Similarly, the median can be computed when two values occur as the middle values.
Thus, among the three measures of central tendency, the mean, the median, and the mode, the mode is the most unique since it is not computed.
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HELLLLPPPPP!!!!!!!!!!!! AHHHHHHHHHHH!!!!!!!
kenji is raising baby kittens. their weights after three weeks are 12 ounces, 14 ounces, 15 ounces, 15, ounces and 14 ounces, what is the mean weight of the kittens????
Answer: 14 ounces
Step-by-step explanation:
To find the mean, we add up all the values and divide by the number of values.
[tex]\displaystyle \frac{12+14+15+15+14}{5} =\frac{70}{5} =14\;ounces[/tex]
What is the circumference of the circle if the radius is 10 cm?
The circumference of the circle is 62.8cm.
The Circumference of the circle is given by the formula,
Circumference = 2*[tex]\pi[/tex]*r cm.........equation 1
Given, r = 10cm
On substituting the radius value in equation 1
Circumference = 2*[tex]\pi[/tex]*10
Circumference = 62.8 cm
Therefore, the circumference of the circle is 62.8cm.
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What is (fg)(x)?
f(x)=2x
g(x)=2x2+3x
Write your answer as a polynomial or a rational function in simplest form
Given statement Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.
To find (fg)(x), we need to first find the product of f(x) and g(x) and simplify the expression.
f(x) = 2x
g(x) = [tex]2x^2[/tex] + 3x
To find (fg)(x), we substitute g(x) into f(x):
(fg)(x) = f(g(x)) = f([tex]2x^2[/tex] + 3x)
Now we substitute f(x) = 2x into the expression above:
(fg)(x) = 2([tex]2x^2[/tex] + 3x)
Distribute the 2:
(fg)(x) = [tex]4x^2[/tex] + 6x
So, (fg)(x) = [tex]4x^2[/tex] + 6x.
Function Multiplication Simplified solution is :- (fg)(x) = [tex]4x^2[/tex] + 6x.
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What means killogram?
Answer:
1,000 grams
noun. a unit of mass equal to 1,000 grams: the basic unit of mass in the International System of Units (SI). Up until 2019 the kilogram was defined as equal to the mass of an international prototype, a platinum-iridium cylinder kept in Sèvres, France.
Simplify the rational expression
7x/14x^6
The simplified form of the rational expression is 1/(2[tex]x^5[/tex]).
To simplify the rational expression (7x)/(14[tex]x^6[/tex]), we can reduce the numerator and denominator by their greatest common factor.
In this case, the greatest common factor is 7x.
Dividing both the numerator and denominator by 7x, we get:
(7x)/(14[tex]x^6[/tex]) = (7x)/(7x × 2[tex]x^5[/tex])
Canceling out the common factor of 7x, we have:
= 1/(2[tex]x^5[/tex])
Therefore, the simplified form of the rational expression is 1/(2[tex]x^5[/tex]).
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Find the exact value of cos (-n/12)
The exact value of cos(-n/12) is equal to cos(n/12).
The cosine function (or cos function) in a triangle is the ratio of the adjacent side to that of the hypotenuse.
The value of cosine function is periodic with a period of 2π. Therefore, we can use the property cos(x) = cos(x + 2πk) for any integer value of k.
In this case, we have cos(-n/12). To find the exact value, we can use the fact that cos(x) = cos(-x) for any angle x. Therefore, we can rewrite cos(-n/12) as cos(n/12).
So, the exact value of cos(-n/12) is equal to cos(n/12).
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George and Manuel had a roofing business George as owner of the materials received $3 for every $2 manual received on a job that paid $750 what amount did each receive
Manuel received $187.50, and George received $562.50 for the job.
Let's break down the information provided:
The job paid a total of $750.
George received $3 for every $2 that Manuel received.
To determine the amounts George and Manuel received, we can set up a ratio based on their earnings.
Let's assume Manuel's earnings as the base amount:
George's earnings : Manuel's earnings = $3 : $2
We can set up the following equation to solve for Manuel's earnings:
(Manuel's earnings / Manuel's earnings) = ($2 / $2)
Since the ratio is equivalent, we can say:
George's earnings / Manuel's earnings = $3 / $2
To find the amount each person received, we'll assign a variable to Manuel's earnings. Let's call it "x."
Therefore, George's earnings can be represented as "3x."
According to the given information, their total earnings should sum up to $750:
x + 3x = $750
Combining like terms, we have:
4x = $750
To solve for x, we divide both sides by 4:
x = $750 / 4
x = $187.50
Now, we can determine the amounts each person received:
Manuel's earnings = x = $187.50
George's earnings = 3x = 3 * $187.50 = $562.50
Therefore, Manuel received $187.50, and George received $562.50 for the job.
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Graph the image of this quadrilateral after a dilation with a scale factor of 2 centered at the origin. Use the polygon tool to graph the quadrilateral.
The new coordinates of the quadrilateral ABCD after the dilation is:
A' = (-6, 6)
B' = (-8, -4)
C' = (4, -8)
D' = (0, 0)
We have,
To find the coordinates of the new quadrilateral after a dilation with a scale factor of 2 centered at the origin, we multiply the x and y coordinates of each point by the scale factor.
Given the original coordinates of the quadrilateral ABCD:
A = (-3, 3)
B = (-4, -2)
C = (2, -4)
D = (0, 0)
To dilate the coordinates with a scale factor of 2, we multiply each coordinate by 2:
A' = 2 x (-3, 3) = (-6, 6)
B' = 2 x (-4, -2) = (-8, -4)
C' = 2 x (2, -4) = (4, -8)
D' = 2 x (0, 0) = (0, 0)
Thus,
The new coordinates of the quadrilateral ABCD after the dilation is:
A' = (-6, 6)
B' = (-8, -4)
C' = (4, -8)
D' = (0, 0)
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The room is 20 feet by 25 feet. The walls are 8 feet tall. You will be painting all 4
walls, but not the ceiling.
The paint costs $13.98 per gallon and covers 400 square feet per gallon.
1. What are the dimensions of the 4 walls?
2. What is the total area to be covered? Show your computations here.
3. How many gallons of paint will you need? (remember each gallon covers 400 sq ft)
1) The dimensions of the 4 walls are:
Two walls are 20 feet long and 8 feet tall.
Two walls are 25 feet long and 8 feet tall.
2) Total area to be covered:
= 720 square feet.
3) You will need 1.8 gallons of paint to cover all four walls of the room.
Now, The dimensions of the 4 walls are:
Two walls are 20 feet long and 8 feet tall.
Two walls are 25 feet long and 8 feet tall.
And, The total area to be covered is:
For the two 20 feet long walls:
A = 20 feet x 8 feet
A = 160 square feet each.
And, For the two 25 feet long walls:
A = 25 feet x 8 feet
A = 200 square feet each.
Hence, Total area to be covered:
= (160 + 160 + 200 + 200) square feet
= 720 square feet.
For the number of gallons of paint needed, divide the total area to be covered by the area covered by one gallon of paint:
Number of gallons of paint needed = Total area to be covered / Area covered by one gallon of paint
Number of gallons of paint needed = 720 square feet / 400 square feet per gallon
Number of gallons of paint needed = 1.8 gallons
Therefore, you will need 1.8 gallons of paint to cover all four walls of the room.
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pls help me with this
The term 9b represents the cost to rent a bike.
We have,
Rentals
Bike $9/h
Electric scooter $10/h
Kayak $18/h
Canoe $20/h
Paddleboard $22/h
Helmet Add $6
Here, the term 9b represents the cost to rent a bike.
In the provided rental options, the cost of renting a bike is $9 per hour.
The term "9b" indicates that the cost is calculated by multiplying the hourly rate of $9 with the number of hours (b) the bike is rented for.
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Acylinder has a volume of 400 cubic feet. If the height of the cylinder is 25 feet, what is the radius of the cylinder? Use 3.14 for me and round to the nearest hundredth
adius hype your answer...
1
The radius of the cylinder is 2.25 feet.
To find the radius of the cylinder, we can use the formula for the volume of a cylinder:
V = πr²h
Given that the volume V is 400 cubic feet and the height h is 25 feet, we can substitute these values into the formula and solve for the radius r.
400 = 3.14 r² x 25
Dividing both sides of the equation by (3.14 * 25) to isolate r^2, we have:
r² = 400 / (3.14 x 25)
r² ≈ 5.08
Taking the square root of both sides to solve for r, we get:
r ≈ √5.08
r ≈ 2.25
Therefore, the radius of the cylinder is 2.25 feet.
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A cheetah's speed was timed over a 50-yard distance. The cheetah was clocked running 60 miles per hour. Write an equation to represent this situation. (If your answering please show how you solved this)
The equation that represents this situation is:
⇒ 60t = 0.0284091
where t is the time in minutes.
We have to given that,
The speed of the cheetah is 60 miles per hour
The distance timed was 50 yards
Now, We have to convert the distance to miles, because the speed is in miles per hour.
Since, 1 yard = 0.000568182 miles
Hence, 50 yards = 50 x 0.000568182 miles
50 yards = 0.0284091 miles
Now we can use the formula:
distance = speed x time
We know that,
The distance is 0.0284091 miles, and the speed is 60 miles per hour.
Hence, the time it took the cheetah to run the 50-yard distance.
So, the speed from miles per hour to miles per minute, since we want the time in minutes:
60 miles per hour = 1 mile per minute
Now we can plug in the values we know:
0.0284091 miles = (1 mile per minute) x time
Solving for time:
time = 0.0284091 / 1
time = 0.0284091 minutes
time = 0.0284091 minutes x 60 seconds per minute
time = 1.704546 seconds
Thus, the equation that represents this situation is:
⇒ 60t = 0.0284091
where t is the time in minutes.
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Need help with this equation 8x²+10x-3
Answer:
Step-by-step explanation:
You have to use the quadratic formula
x = -b +/- [tex]\sqrt{(b^{2} -4ac)/2a[/tex]
and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2
you usually have to reject an answer but since there is no equal sign in the question, you should be fine
What are the minimum and maximum values of the function?
Learning Page
Computing expected value in a game of chance
QUESTION
Scott is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random.
This game is this: Scott spins the spinner once. He wins $1 if the spinner stops on the number 1, $3 if the spinner stops on the number 2, $5 if the spinner
stops on the number 3, and $7 if the spinner stops on the number 4. He loses $1.25 if the spinner stops on 5 or 6.
(a) Find the expected value of playing the game.
dollars
(b) What can Scott expect in the long run, after playing the game many times?
Scott can expect to gain money.
He can expect to win dollars per spin.
Start
Scott can expect to lose money.
He can expect to lose dollars per spin.
Scott can expect to break even (neither gain nor lose money).
00 EXPLANATION
0 0/5
Answer:$0.25
Step-by-step explanation:
To find the expected value of playing the game, we need to multiply the payoff for each possible outcome by its probability and then add up all the values.
Let's first find the probabilities of each outcome:
- Probability of spinning1:1/6
- Probability of spinning2:1/6
- Probability of spinning3:1/6
- Probability of spinning4:1/6
- Probability of spinning5 or6:2/6( or1/3)
Now let's calculate the expected value:
Expected value=(1/6*$1)+(1/6*$3)+(1/6*$5)+(1/6*$7)+(1/3*-$1.25)
Expected value=$0.25
So the expected value of playing the game is$0.25 per spin.
In the long run, Scott can expect to gain money since the expected value is positive. However, this doesn't guarantee that he will actually win money every time he plays the game, as there is still a certain degree of randomness involved in each spin.
What is the sum of 104, 25, -11 to come of it
Answer:
118
Step-by-step explanation:
104+25+(-11)
129-11
118
Therefore, our answer is 118
Joshua and Milap were having a contest flying
planes. Joshua's plane flew 125 feet. Milap's
plane flew 12 feet less than twice as far as
Joshua's. How far did Milap's plane fly?
A 137 feet
B 238 feet
C 250 feet
D 262 feet
Answer Question 11 please
Answer:
increasing exponential function.
Step-by-step explanation:
We can see from the table that the function is not increasing by the same amount as it goes up by 1 in x, so it is not linear.
It must be exponential.
It is increasing at it increases in x, so it is an increasing exponential function.