The maximum dimensions is a square of sides 36 ft by 36 ft;
The maximum area is 1,296 ft^2
Here, we want to know the diemensions of the largest area the farmer can enclose within the perimeter
Mathematically, the greatest dimension that can maximize the area of the plot is the shape being a square
In other words, we need the diemnsions of both sides to be equal so as to get the area
If the dimensions are equal, we can say the length and width are represented by x
The length is thus as follows;
[tex]\begin{gathered} 4\text{ }\times\text{ x = 144} \\ 4x\text{ = 144} \\ \text{ x = 144/4} \\ x\text{ = 36 ft} \end{gathered}[/tex]The greatest possible or the maximum area is thus;
[tex]36\times36=1,296ft^2[/tex]Construct a box-and-whisker plot for the given data.
The test scores of 40 students are listed below.
25 35 43 44 47 48 54 55 56 57
59 62 63 65 66 68 69 69 71 72
72 73 74 76 77 77 78 79 80 81
81 82 83 85 89 92 93 94 97 98
By median , test scores of 40 students are listed below. So five number summary is 25, 58,72,81,98
What are median in math?
The middle number is obtained by sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.First we need to sort the data from Smallest to largest data value which is allready sorted
n = 40
Five number summary can be calculated as
Minimum = 25
Q1 can be calculated as
Lower Half of 40 values is 20, so median of 20 values will give us 25th percentile so Median = (20+1)/2 = 10.5th here 10th value is 57 and 11th value is 59 so Q1 = (57+59)/2 = 58
Median = (n+1)/2 = (40+1)/2 = 20.5th value and 20th and 21st value is 72 so median = (72+72)/2 = 72
Upper 20 values after median will provide us Q3 or 75th percentile which can be calculated as 20+(20+1)/2 = 30.5th value so 30th value is 81 and 31st value is also 81. So Q3 = (81+81)/2 = 81
Max = 98
So five number summary is 25, 58,72,81,98
And correct boxplot for this data is A. Boxplot A is correct which shows correct five number summary.
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I NEED HELP ASAP ILL PAY YOU
The translation T₁: (x,y) → (x+7, y - 5) is applied to rectangle JKLM.
Next, the translation T₂: (x,y) → (x − 1, y +9) is applied to the rectangle.
What is the image of L(-9, -9) after the two translations are applied?
-
write the sum in sigma notation [tex]\frac{1}{3} +\frac{1}{15} +\frac{1}{35} +\frac{1}{63}[/tex]
Sum in the sigma notation of the given series is equal to
∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.
As given in the question,
Given series :
(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)
Simplify the given series
= [1/ (1 ×3)] + [1/ (3 ×5)] + [1/ (5 ×7)] + [1/ (7×9)]
1, 3, 5, 7 can be expressed as ( 2n + 1) , where n = 0, 1, 2, 3
3, 5, 7, 9 can be expressed as ( 2n + 3) , where n = 0, 1, 2, 3
Express the given series as a sum in the sigma notation form
(1 /3) + ( 1/ 15) + ( 1/ 35) + ( 1/ 63)
=∑ [ 1/ (2n +1) (2n + 3) ] where n = 0,1,2,3
Therefore, sum in the sigma notation of the given series is equal to
∑[1 /(2n +1)(2n + 3)] , n =0,1,2,3.
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Look at the diagram below that shows angle CAB ~ angle CED.
Which statement is TRUE?
A) D= 78 & E= 78
B) DCE= 24 & E= 77
C) D= 79 & E= 77
D) D= 77 & E= 79
The following statement is true about the triangles (d) D = 77 and E = 79
What is dilation?Dilation involves enlarging or reducing the side length of a shape to create another shape by a constant scale factor,
Where the scale factor does not equal to one.
How to determine the true statements in the figure?From the attached image, we understand that there are two shapes
The shapes are triangles
One triangle is the scaled factor of the other
So, the triangles are similar shapes
As a general rule, the following are the properties of a scaled copy of another figure
If the scale factor is greater than 1, the side lengths would be greater than the original figureIf the scale factor is less than 1, the side lengths would be less than the original figureThe corresponding angles of both figures are the sameUsing the above as a guide, we have the following
D =B = 77 -- by corresponding angles
Also, we have
E = A = 180 - 77 - 24 -- by corresponding angles
E = A = 79
Hence, the true statement is (d) D = 77 and E = 79
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I need help with this this is my homework online
Given the exponential model
[tex]y=125000(0.95)^x[/tex]We can find the solution to the given question below.
hEe model says that between the year 2000 and 2001 the population of the boars decreased by 5%. The year 2000 indicates the starting point of the model.
[tex]\begin{gathered} Therfore,x=0 \\ y=125000(0.95)^0 \\ y=125000 \end{gathered}[/tex]Answer: 125000
Use the definition of a derivative to determine whether f(x) = 8x^2 is differentiable at x=0
The definition is option B No, it is not differentiable at x = 0.
Given,
The function, f(x) = 8x²
We have to find that the function is differentiable at x = 0.
So, lets check:
f(x) = 8x²
x = 0
f'(0) = [tex]\lim_{h\to \ 0}[/tex] [tex]\frac{f(0+h)-f(0)}{h}[/tex]
f(0 + h) = 8(0 + h)² = 8 (0 + 0 + h²) = 8h²
f(0) = 8 × 0² = 0
f(0 + h) - f(0) = 8h² - 0 = 8h²
f'(0) = [tex]\lim_{h \to \ 0}[/tex] 8h²/h = 8h = 8 × 0 = 0
That is, the function f(x) = 8x² is not differentiable at x = 0
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Find the first three terms of the sequence defined below, where n represents the position of a term in the sequence. Start with n = 1.an = 3n − 8
Solution:
To find the first three terms of the sequence defined as
This implies that we solve for
[tex]a_n[/tex]for n equals 1, 2, and 3.
Thus,
first term: n=1
[tex]\begin{gathered} a_1=3(1)-8 \\ \Rightarrow a_1=-5 \end{gathered}[/tex]second term: n =2
[tex]\begin{gathered} a_2=3(2)-8 \\ \Rightarrow a_2=-2 \end{gathered}[/tex]third term: n = 3
[tex]\begin{gathered} a_3=3(3)-8 \\ \Rightarrow a_3=1 \end{gathered}[/tex]Hence, the first three terms of the sequence are
[tex]-5,\text{ -2, 1}[/tex]1. Tim wants air conditioning in his room. The air conditioner costs $40. Each day the
electricity costs $1. Write an expression that can be used to find the cost to run the air
conditioner for d days.
Answer:
the answer/expression you require is 40 - 1 = 1 day x - 1 = day 2 (repeat day 2 forever
Step-by-step explanation:
i say this because - 40 for the air conditioner and if it’s - 1 for electricity a day then unless your buying an air conditioner every day i don’t think you,l be repeating day 1 every day
:D
Given the initial inequality 2 > -4, identify whether the operation preserves the inequality symbol or reverses the inequalitysymbol.Add -2 to both sides.
ANSWER:
Preserves the inequality
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]2>-4[/tex]We add -2 on both sides and we have
[tex]\begin{gathered} 2-2>-4-2 \\ 0>-6 \end{gathered}[/tex]This is true, therefore the equality symbol remains the same
A group of friends traveled at a constant rate. They traveled 2/5 of a mile in 1/4 of an hour.Which of the following statements are true about this unit rate? Select all that apply.A divide 2/5 by 1/4 to find the unit rate per hour B The average speed will be less than 1 mile per hour because the group travels less than a fourth of a mile in1/4 of an hour C The group traveled at an average speed of 1 3/5 miles per hour.D The average speed will be greater than 1 mile per hour because the group travels more than a fourth of a mile in1/4 of an hour .E The group traveled at an average speed of 2 1/4 of a miles per hour.
The distance traveled, d = 2/5 miles = 0.4 miles.
The time taken to travel 0.4miles is given as, t = 1/4 hr = 0.25 hr.
Thus, the average speed, s = distance traveled divided by time taken.
i.e.
[tex]\begin{gathered} \text{average speed = }\frac{distance\text{ traveled}}{\text{time taken}}\text{ = }\frac{0.4}{0.25}\text{ } \\ \text{average sp}eed\text{ = 1.6 miles/hr} \end{gathered}[/tex]we can now go through the options and see the correct answers:
option A is correct because unit rate per hour is the same thing as average speed
option B is wrong because average speed is greater than 1mile/hr from our calculation above
option C is wrong because 13/5 gives us 2.6 miles/hr
option D is correct because the average speed is indeed greater than 1
option E is wrong because average speed is 1.6 miles/hr not 2 1/4 miles/hr
Thus, the answers are:
Option A and Option D
6-Mr. Lofters has 7/8 of a gallon of blue paint. He needs to distribute the blue paint out equally to his students. If Mr. Lofters pours 1/16 of a gallon of blue paint into each cup, how many cups of blue paint can he get? IMAGINE WHAT IS HAPPENING IN THE PROBLEM. WHAT OPERATION WILL BE INVOLVED? WHICH NUMBER WILL GO FIRST? LOOK FOR KEYWORDS. DO YOU REMEMBER THE FISH SONG?? YOU'LL REALLY FLIP IF YOU DON'T GET THIS ONE RIGHT.
We need to distribute 7/8 of a gallon into cups of 1/16 of a gallon. It means that to know the number of cups, we need to divide 7/8 into 1/16.
So, let's remember how to make a division between two fractions:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Then, the division of 7/8 into 1/16 is equal to:
[tex]\frac{\frac{7}{8}}{\frac{1}{16}}=\frac{7\cdot16}{8\cdot1}=\frac{112}{8}=14[/tex]Therefore, he gets 14 cups of blue paint.
Answer: 14 cups
Use the long division method to find the result when 8x^3-18x^2+24x+3 is divided by 4x-1. If there is a remainder, express the result in the form q(x)+r(x)/b(x).
Answer:
2x^2 -4x +5 +8/(4x -1)
Step-by-step explanation:
You want to divide 8x^3-18x^2+24x+3 by 4x-1 using polynomial long division.
Polynomial long divisionPolynomial long division is similar to numerical long division, except that the quotient term is always the ratio of the leading dividend term to the leading divisor term.
As with numerical long division, the dividend at each step is reduced by the product of the quotient term and the divisor.
When the dividend is of lower degree than the divisor, the division is finished. That dividend is the remainder.
The attachment shows the division in detail. Your result is ...
q(x) +r(x)/b(x) = (2x^2-4x+5) +(8)/(4x-1)
Jessica bought 3/5 of a pound of organic raspberries for $9 what is the cost of 1 1/3 pounds of raspberries
Using simple multiplication, the cost of 1 1/3 pounds of raspberries equals 12 pounds.
What is multiplication?Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.
Given,
Cost of 3/5 pounds of raspberries = $9
Cost of 1 pound of raspberries = 9 × 5/3
Cost of 1 pound of raspberries = 15 pounds
Cost of 1 1/3 pounds of raspberries = 4/3 × 15
= 12 pounds
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Provide the correct reason for the statement in line 3. (please help)
Answer:
c) subtraction property of =
Step-by-step explanation:
step 3 show the movement of +15 moving to the other side of the = by subtracting 15 on each side, leaving you with 3x-16
Need help thanks. Due today
Answer:
The answer would be D(x/y)= -(11/8) / -(11/4)
Step-by-step explanation:
3) Recall problem 48 from your notes: Half an hour after leaving her house, Leah was 25 miles from
home. Leah then merged onto the freeway, and was able to travel at a constant speed for the next
several hours. Four hours after leaving her house, she was 280 miles from home.
a.
Find the model, m(t) that gives Leah's distance from home d in terms of the number of hours
she has been on the freeway, t.
b.
Suppose that Rachel lives 5 miles away from the same freeway entrance that Leah took. Rachel
leaves her house, and 10 minutes later is on the freeway. After 3.7 hours, Rachel is also 280 miles
away from her home.
i. What is Rachel's average speed on the freeway?
ii. Suppose that Rachel travels at a constant speed once she gets on the freeway. Write a
function k = f(t) that describes the number of miles she is from home, k, in terms of
the number of hours since she left home, t.
c. Assuming they are both traveling at a constant rate, who is driving faster? Give two different
answers to how you can see this
i. intuitively from the information provided.
ii. Algebraically from how you defined the functions.
Answer:
What is the role of ethnocentrism in defining the concept of “progress”
Step-by-step explanation:
Please help I’ll mark you as brainliest if correct!!
Answer:
A. 463-139=324
B. 14,527-7609=6918
Step-by-step explanation:
there ya go! hope it helps you out some!
let me know if it is correct
The calculation for y=0y=0 corresponds to the
point where the graph crosses the________-axis. This is the point (______)
The calculation for y=0 corresponds to the point where the graph crosses the x-axis . This is the point (x,0) .
In the question ,
it is given that y=0 ,
When y=0 in a point (x,y) means , that point lies on the x -axis , and it is called as the x intercept .
X intercept is defined as the point where the graph of a line crosses the x-axis .
the point on the x-axis will be (x,0) ,
So , the graph will cross the x-axis when y=0 , and that point will be (x,0).
and the value of x will be called as the x intercept of the graph .
Therefore , the calculation for y=0 corresponds to the point where the graph crosses the x-axis . This is the point (x,0) .
The given question is incomplete , the complete question is
The calculation for y=0 corresponds to the point where the graph crosses the________-axis. This is the point (______) .
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Find the perimeter of ABO. A) 90 u B) 60 u C) 75 u D) 55 u E) 80 u
Answer:
Step-by-step explanation:
is the base of the triangle 30?
Translate the sentence into an equation.
Eight less than the product of 4 and a number is 9
Use the variable w for the unknown number
Answer:
8-(w x4)=6
Step-by-step explanation:
all you have to do is just follow the words and plug the number in
Victor received an 8-year subsidized student loan of $24,000 at an annual interest rate of 4.55%. If victor qualifies for an income-adjusted repayment plan of $500 per month, how long (in months) will it take him to repay the loan?
Time taken by Victor to repay the subsidized student loan of $24,000 at an annual interest rate of 4.55% is equal to 59 months.
As given in the question,
Principal = $24000 (given)
Rate of interest = 4.55% (given)
Time duration of subsidized loan = 8 years (given)
Repayment (equated monthly instalment) rate = $500 per month
To find: time for Victor to repay loan
We know that Principal + Simple Interest = Amount
Let t be the expected time duration for repayment of the subsidized student loan for Victor
24000+[tex]\frac{(24000).(4.55).t}{100}[/tex] = 500x12t (Simple Interest = Principal x Rate x Time)/100
=> 24000 + 1092t = 6000t
=> 4908t = 24000
=> t = 4.89 years ≈ 59 months
Therefore, it will take 59 months for Victor to repay the subsidized student loan of $24,000 at an annual interest rate of 4.55%.
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Jane, Alan, and Ravi sent a total of 146 text messages over their cell phones during the weekend. Ravi sent 8 fewer
messages than Jane. Alan sent 4 times as many messages as Ravi. How many messages did they each send?
Jane, Alan, and Ravi sent a total of 146 text messages over their cell phones during weekend, Ravi sent 8 fewer messages than Jane. Alan sent 4 times as many messages as Ravi. So as per question data,
Jane sent= 31 messages
Ravi sent= x-8= 31-8 = 23 messages
Alan sent= 4(x-8) = 92 messages
What operations are used here?The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.
The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.
PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.
Let, Jane sent x number of messages
Then, Ravi sent x-8 number of messages
and, Alan sent 4(x-8) number of messages
Total number of messages by them = 146
now,
x+(x-8)+4(x-8)=146
6x-40=146
x=31
so, Jane sent= 31 messages
Ravi sent= x-8= 31-8 = 23
Alan sent= 4(x-8) = 92
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lve the inequalityr divided by negative 3.2 is greater than or equal to 7.6 for r.
r ≥ −24.32
r ≤ −24.32
r ≥ 2.375
r ≤ −2.375
The solution for r of the inequality as described in the task content; r divided by negative 3.2 is greater than or equal to 7.6 is; r ≤ −24.32.
What is the solution for r of the inequality given?It follows from the task content that the inequality given is required to be solved for r.
Since the given inequality according to the task content is;
( r / -3.2 ) ≥ 7.6
Then, by multiplying both sides of the inequality given by; -3.2 in which case the inequality sign is reversed, we have;
r ≤ ( -3.2 × 7.6)
r ≤ -24.32.
Therefore, the solution of the inequality for the variable, r as required is; r ≤ −24.32.
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hey can someone help me with this problem? please I’m really stuck :/
Answer:13x+150<400
Step-by-step explanation:
13(19)+150<400
247+150<400
397<400
Answer:
I think is c but I'm not sure
A package of 5 pairs of insulated gloves costs $28.955. What is the unit price of the pairs of gloves ?
If a package of 5 pairs of insulated gloves costs $28.955,then the unit price of the pairs of gloves is $5.791
A package of 5 pairs of insulated gloves costs $28.955
The price of 5 pairs of insulated gloves = $28.955
Here we have to use the unitary method
The price of 1 pair of insulated gloves = The price of 5 pairs of insulated gloves / 5
Substitute the values in the equation and divide it
The price of 1 pair of insulated gloves = 28.955/5
= $5.791
Hence, if a package of 5 pairs of insulated gloves costs $28.955,then the unit price of the pairs of gloves is $5.791
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Study Island Math Help Worth 40 PTS
Answer:
B
Step-by-step explanation:
using the rules of exponents
• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
given
[tex]5^{8}[/tex] × [tex](5^{12}) ^{-4}[/tex]
= [tex]5^{8}[/tex] × [tex]5^{(12(-4))}[/tex]
= [tex]5^{8}[/tex] × [tex]5^{-48}[/tex]
= [tex]5^{(8-48)}[/tex]
= [tex]5^{-40}[/tex]
= [tex]\frac{1}{5^{40} }[/tex]
I want to place an order of 253,625 books. How can I estimate the number to make sure it’s enough books
The estimate where the number of books is enough is 254,000
What is the estimation of a number?The estimation of numbers is the approximation of the said number.
This means that the estimation of a number is close to the said number, but it has a slight different value
How to estimate the number of books?The number of books is given as
Number of books = 253,625
From the question, we understand that:
You want to make sure that the number of books is enough
This means that we estimate the number of books to a number greater than 253,625
A good way to do this is to approximate to the nearest thousand
When the number is approximated to the nearest thousand, we have
Estimate = 254,000
Hence, the estimate is 254,000
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Please help me get the anwser im not sure if im right.
we have the expression
[tex]2(y-z)(r-s)[/tex]Applying distributive property
[tex]\begin{gathered} 2(y-z)(r-s) \\ 2(yr-ys-zr+zs) \\ 2yr-2ys-2zr+2zs \\ \end{gathered}[/tex]therefore
There are 4 terms
The answer is option BSuppose you have a $60000 loan with an annual percentage rate of 8% for 25 years? Requires monthly payment?
The required monthly payment is $ 180,000
How to calculate SI?Simple interest is the cost of borrowing money that does not take compounding into consideration. In other words, just the principal is affected by simple interest. Simple interest is calculated by multiplying the principal by the time, interest rate, and time period. "Simple Interest = Principal x Interest Rate x Time" is the written formula.
Given: Principal= $60000
Rate= 8% and time= 25 years
To calculate the monthly payment use the formula:
Simple interest=PRT/100
= 60,000×8×25/100
=120,000
And total amount accrued will be $180,000.
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Answer this question find angle a,b,c,d,e,f
We can determine the values of the angles as follows:
*By opposite by angle we will have that angle f is equal to:
[tex]f=180-44-78\Rightarrow f=58[/tex]angle f has a measurement of 58°.
*By supplementary angles we will have that angle e is equal to:
[tex]e=90-64\Rightarrow e=26[/tex]angle e has a measurement of 26°.
*As is indicated (Two lines have the same markings indicating they are parallel) we will have that the measurement of angle b is 78°.
*By complementary angles, the measurement of angle a is:
[tex]a=180-78\Rightarrow a=102[/tex]angle a has a measurement of 102°.
*We will have by alternate exterior angles that c has a measurement of 58°.
*By supplementary angles, we will have that the measurement of angle d equals:
[tex]d=180-58\Rightarrow d=122[/tex]angle d has a measurement of 122°.