Answer:
Step-by-step explanation:
Let's assume that the amount invested at 10% is x, and the amount invested at 5% is (60000 - x), since the total investment is $60,000.
The interest earned on the 10% investment after one year would be 0.10x, and the interest earned on the 5% investment after one year would be 0.05(60000 - x).
We are given that the interest earned by the two accounts is equal, so we can set up an equation:
0.10x = 0.05(60000 - x)
Simplifying this equation, we get:
0.10x = 3000 - 0.05x
Adding 0.05x to both sides, we get:
0.15x = 3000
Dividing both sides by 0.15, we get:
x = 20000
Therefore, the amount invested at 10% is $20,000, and the amount invested at 5% is ($60,000 - $20,000) = $40,000.
To check that the interest earned is equal for both investments, we can calculate:
Interest earned on 10% investment = 0.10($20,000) = $2,000
Interest earned on 5% investment = 0.05($40,000) = $2,000
As expected, the interest earned on both investments is equal.
Below is the graph of y=x^2. Translate it to make it the graph of y=(x-2)^2-5.
Using translation the graph of y = (x - 2)² - 5 is the graph of y = x² shifted 2 units to the right and 5 units down.
What is translation?
A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.
To translate the graph of y = x² to y = (x - 2)² - 5, apply the following transformations -
Shift the graph to the right by 2 units.
This means that we replace x with x - 2, which moves the graph 2 units to the right.
Shift the graph down by 5 units.
This means that we subtract 5 from the entire function, which moves the graph 5 units down.
So the transformed function is -
y = (x - 2)² - 5
To see how this transformation changes the graph, compare the original function y = x² to the transformed function y = (x - 2)² - 5.
The vertex of the parabola has moved from the origin (0,0) to the point (2,-5).
Therefore, the graph is shifted using translation.
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Which list orders from least t greatest? -5, 1, 3, -2
A. 1 , -2, 3, -5
B. -2, -5, 1, 3
C. -5, -2, 1, 3
D. 3, 1, -2, -5
PLS HELP ME!!!!!!!!
Please help will get brainliest and 70 coins! <33
The last number in Row 8 is 56.
The number in Row 12 and column 3 is 80.
The row and column that will contain the number 400 is Row 58 Column 1
What does the figure shown in the image represent?The figure shown in the image represents the multiplication table 7.
Each column contains 7 numbers.
Beginning with the first Row and column, 7 numbers are added until the next row. At the end of each row is a multiple of 7.
The last number in Row 8 will be the product of 7 and 8 = 56
The number in Row 12 and Column 3 will be:
7 * 11 + 3 = 80
The row and column that will contain the number 400 will be:
400/7 = 77 remainder 1
Hence, it will be Row 58 Column 1.
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PLEASE HELP NOW!!!!!!!!!!!!! 50pts!!! BRAINLIEST ANSWER!!!!!!
Figure ABCDE has vertices A(−2, 3), B(2, 3), C(5, −2), D(0, −3), and E(−2, −2). Plot the points on your own coordinate grid and connect the points in alphabetical order. Decompose Figure ABCDE into rectangles and triangles.
Part A: How many triangles and rectangles did you make? (1 point)
Part B: Use Figure ABCDE created on your coordinate grid to find the lengths, in units, of Sides AB and AE. (4 points)
Part C: What is the area of Figure ABCDE? Show your work. (5 points)
Part A: You can decompose Figure ABCDE into two triangles and two rectangles. The two triangles are triangle ABC and triangle AED. The two rectangles are rectangle BCD and rectangle AEB.
Part B: The length of Side AB is 4 units and the length of Side AE is 5 units.
Part C: To find the area of Figure ABCDE, we can simply add the areas of the two triangles and two rectangles. The area of triangle ABC is 3 units2, the area of triangle AED is 6 units2, the area of rectangle BCD is 10 units2, and the area of rectangle AEB is 3 units2. Thus, the area of Figure ABCDE is 3 + 6 + 10 + 3 = 22 units2.
Find the value of each variable, help pls??
Answer:
x = 145
Step-by-step explanation:
We are given a polygon that has 7 sides. We can use the formula [tex]S=(n-2) * 180[/tex] which allows us to write an algebraic expression to solve for x where n = number of sides.
[tex]S=(7-2) * 180[/tex]
Evaluate
[tex]S=5*180[/tex]
[tex]S=900[/tex]
Now that we have our number, lets write an algebraic expression that will help us find the value of x.
[tex]x+116+129+120+130+135+125=900[/tex]
Add like terms
[tex]x+755=900[/tex]
Subtract 755 on both sides
[tex]x=145[/tex]
We can check our work by adding all the angle measures together
[tex]145+116+129+120+130+135+125=900[/tex]
Thus we know 145 is the correct answer.
Question content area top
Part 1
The intensity of a sound is given by II0100.1L, where L is the loudness of the sound as measured in decibels and I0 is the minimum intensity detectable by the human ear.
a) Find I, in terms of I0, for the loudness of a small engine, which is decibels.
b) Find I, in terms of I0, for the loudness of a quiet sound, which is decibels.
c) Compare your answers to parts (a) and (b).
d) Find the rate of change dI/dL.
e) Interpret the meaning of dI/dL
Answer:
B
HOPE THIS HELPS
4. If you are comparing a single proportion statistic to the populations parameter, what type of test should you use?
a. Two-proportion z-test
b. one-propotion z-test
c. one sample t-test
d. 2 sample t-test
When two-proportion z-test if you're evaluating the populations parameter against a single proportion statistic.
what is proportionality ?Relationships generally regarded to as symmetrical when they continuously maintain a similar ratio. For instance, the number of trees in a vineyard and the number of apples in a yield of apples depend upon that average number of apples delivered by each tree. A linear relationship among two quantities or variables is described to as being proportional in mathematics. If the initial quantity doubles, the other amount does do so. Once one of the variables is reduced to 1/100th of its previous value, the other decreases as well. If two quantities be proportional, it means that if one grows, the other climbs as well, and their connection is constant at all values. The size and circumference of a sphere are used as an example.
given
To compare a proportion of replies or values in a sample of data to a (hypothesized) proportion in the population .
from which our sample data are obtained, one can use the single proportion (or one-sample) binomial test.
We rarely have access to statistics for a whole population, so this is significant.
when two-proportion z-test if you're evaluating the populations parameter against a single proportion statistic.
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Help Please!!!
That partitions the segments into a ratio of 3 to 2
let's say the segment with A(-5 , -8) and B(10 , 7) gets partitioned by point C
[tex]\textit{internal division of a line segment using ratios} \\\\\\ A(-5,-8)\qquad B(10,7)\qquad \qquad \stackrel{\textit{ratio from A to B}}{3:2} \\\\\\ \cfrac{A\underline{C}}{\underline{C} B} = \cfrac{3}{2}\implies \cfrac{A}{B} = \cfrac{3}{2}\implies 2A=3B\implies 2(-5,-8)=3(10,7)[/tex]
[tex](\stackrel{x}{-10}~~,~~ \stackrel{y}{-16})=(\stackrel{x}{30}~~,~~ \stackrel{y}{21}) \implies C=\underset{\textit{sum of the ratios}}{\left( \cfrac{\stackrel{\textit{sum of x's}}{-10 +30}}{3+2}~~,~~\cfrac{\stackrel{\textit{sum of y's}}{-16 +21}}{3+2} \right)} \\\\\\ C=\left( \cfrac{ 20 }{ 5 }~~,~~\cfrac{ 5}{ 5 } \right)\implies C=(4~~,~~1)[/tex]
Answer:
( 4, 1 )
Step-by-step explanation:
1. Suppose a new tennis ball drops downward from a height of 30 feet onto a paved parking lot and keeps
bouncing up and down, again and again. Rebound height of the ball should be of its drop height. Make
a table and plot the data showing expected heights of the first ten bounces of the tennis ball.
Bounce Number 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10
Rebound Height (in feet) ??
Answer: Let's assume that each time the ball rebounds, it bounces back up to exactly 2/3 of its previous height. We can use this information to create a table and plot the expected rebound heights for the first ten bounces.
Bounce Number Rebound Height (feet)
0 30.0
1 20.0
2 13.3
3 8.9
4 5.9
5 3.9
6 2.6
7 1.7
8 1.1
9 0.7
10 0.5
To plot this data, we can use a scatter plot with the bounce number on the x-axis and the rebound height on the y-axis. The points should be connected by a line to show the trend.
Tennis ball bounce heights
Note that the rebound heights decrease quickly and approach zero, but they never actually reach zero due to the rounding in our calculations.
Step-by-step explanation:
(Please answer both I will give brainlest)
Find the indicated side x. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume b-10 and c-22. Round your answer to one decimal place.)
X=
(Refer to picture )
7.
Find the indicated angle. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a-10, b-6, and c-12. Round your answer to one decimal place.)
0-
Applying the law of sines, the value of c is calculated as: c ≈ 11.8.
What is the law of Sines?The Law of Sines, also known as the Sine Rule, is a theorem in trigonometry that relates the side lengths of a triangle to the sine of its angles.
Specifically, it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is equal for all three sides of the triangle. Mathematically, this can be expressed as:
a / sin A = b / sin B = c / sin C
Where a, b, and c are the lengths of the sides of the triangle, and A, B, and C are the measures of the angles opposite those sides.
Applying the law of sines, we have:
c/sin 105 = 7/sin 35
Cross multiply:
c * sin 35 = 7 * sin 105
c = 7*sin 105/sin 35
c ≈ 11.8
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A polygraph (lie detector) is said to be 90% reliable in the following sense: There is a 90% chance that a person who is telling the truth will pass the polygraph test; and there is a 90% chance that a person telling a lie will fail the polygraph test. (a) Suppose a population consists of 5% liars. A random person takes a poly- graph test, which concludes that they are lying. What is the probability that they are actually lying? (b) Consider the probability that a person is actually lying given that the poly graph says that they are. Using the definition of reliability, how reliable must the polygraph test be in order that this probability is at least 80%?
a. The probability that they are actually lying is 0.3214. b. The polygraph test must be 98.7% in order that this probability is at least 80%.
What is probability tree diagram?It is simpler to construct and see every possible scenario using the tree diagram. Its two main sites are the ends and the branches of the tree. The probability is written on each branch, and the ends hold the final findings. Use tree diagrams to identify when to multiply and when to add.
The probability of lie = 0.5
The probability of truth = 1 - 0.5 = 0.95
The liars that pass polygraph = 0.10
The liars that fail the polygraph is = 0.90
The truth that pass on polygraph = 0.90
The truth that fails on polygraph = 0.10
a. The probability that they are actually lying is:
P (Lying| fair) = P (fair| Lying) P (lying) / P (fair)
= (0.90)(0.05)/ (0.70)(0.05) + (0.10)(0.95)
= 0.3214
b. P (Lying| fair) > 0. 80
= (x)(0.05)/ (x)(0.05) + (1-x)(0.95) > 0.80
x > 0.987
Hence, the polygraph test must be 98.7% in order that this probability is at least 80%.
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six numbers have a median of 9, all of the numbers are even, the range is 8 and the mode is 6
Answer:
Step-by-step explanation:
Let's start by finding the six even numbers. We know that the median is 9, so the middle two numbers in the set must be 9. Since all of the numbers are even, these two numbers must be 8 and 10.
So we have four numbers remaining, and we know that they are even. We also know that the range is 8, which means that the largest number in the set minus the smallest number in the set is 8. Since the largest number is 10, the smallest number must be 2.
So far, we have the following numbers in the set:
2, 8, 9, 9, 10
Now we need to find one more even number to make a set of six. We are given that the mode is 6, which means that one of the numbers in the set must be 6. However, we cannot add 6 to the set because it is odd. Therefore, the other number in the set that is closest to 6 must appear twice in the set, making it the mode. The number closest to 6 is 8, so we can add one more 8 to the set.
The final set of six even numbers that satisfy the given conditions is:
2, 8, 8, 9, 9, 10
The measure of G is 125. What is the measure of the supplement of G
Answer:
55°
Step-by-step explanation:
supplementary angle sum to 180° , then supplement of G is
supplement = 180° - 125° = 55°
Help Please!!!
That partitions the segments into a ratio of 2 to 1
The coordinates of the point on the directed line segment is (- 6, 4).
What is a line segment?A line segment is a subset of a line that has two endpoints.
We know, When a line segment is divides another line segment in the ratio of m : n at (x, y), The coordinate of the intersecting points is,
x = (nx₁ + mx₂)/(m + n) and y = (ny₁ + my₂)/2.
Therefore, The coordinates of the point directed on the line segment is,
x = (1×2 + 2×- 10)/(1 + 2).
x = (2 - 20)/3.
x = - 18/3.
x = - 6.
And,
y = (- 8×1 + 10×2)/(1 + 2).
y = 12/3.
y = 4.
So, The coordinates are (- 6, 4).
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Write an expression that represents the area of just the portrait (white rectangle)
the area of the rectangle will be 1.5w².
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
Area of rectangle is A = a*b
The given length of the rectangle is w
The width will be 1.5w
So the rectangle of the white figure is Area = w*1.5w = 1.5 w²
hence the area of the rectangle will be 1.5w².
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Find the limit lim……..
Answer: 7/13
Step-by-step explanation:
2(x-5)(x-3)/3(x-5)(x-2)
take (x-5) away from both
2x-3/3x-2
2(5)-3/3(5)-2
=7/13
1. we have to buy flat bar length=1ft.that is 2pesos per cm.how much money we need to buy for that flat bar?
Answer:
The first thing you want to d is find out how many centimeters are in 1 foot, because if a flat bar cost 2 pesos per centimeter, and they want 1 foot, then you will multiply how many centimeters in 1 foot, by how much each centimeter cost: 2 pesos:
There are exactly 30.48 centimeters in 1 foot, so you will multiply that by 2:
2 * 30.48 = 60.96
It will cost 60.96, or rounded up to 61 pesos for a 1 foot flat bar.
Step-by-step explanation:
Hope it helps! =D
X=6 y=1/2 what is the equation that represents the inverse variation
Answer:
The equation that represents inverse variation for the given values of x=6 and y=1/2 is y = 3/x.
Step-by-step explanation:
Inverse variation is a type of relationship between two variables, in which the product of the variables is constant. The equation that represents inverse variation is:
y = k/x
where y and x are the variables, and k is the constant of proportionality.
To find the equation that represents inverse variation for the given values of x=6 and y=1/2, we can first substitute these values into the equation:
1/2 = k/6
To solve for k, we can multiply both sides by 6:
k = 6 * (1/2)
k = 3
Now that we know the value of k, we can substitute it back into the equation to get the final equation for the inverse variation:
y = 3/x
Therefore, the equation that represents inverse variation for the given values of x=6 and y=1/2 is y = 3/x.
Jane, Judy and John all love to play carnival in Trinidad & Tobago , but they find it very expensive .Because of the cost,Jane plays every 2 years ,Judy every 3 years and John every 5 years .If they all played in 2009,in which year will they next play together?
Jane, Judy, and John will next play together in 30 years, which is 2009 + 30 = 2039.
What is the least common multiple (LCM)?
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them
To solve this problem, we need to find the least common multiple (LCM) of the numbers 2, 3, and 5. The LCM is the smallest number that is a multiple of all three numbers.
Prime factorizing the numbers, we have:
2 = 2
3 = 3
5 = 5
To find the LCM, we take the highest power of each prime factor that appears in any of the numbers, and multiply them together. Therefore, the LCM of 2, 3, and 5 is:
LCM = [tex]2^1 * 3^1 * 5^1 = 30[/tex]
Hence, Jane, Judy, and John will next play together in 30 years, which is 2009 + 30 = 2039.
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Find the different quotient of f
Answer:
2x + h - 5
Step-by-step explanation:
To find f(x + h) we simply plug (x + h) into the function f(x), anywhere we see an x.
[tex]f(x) = x^{2} -5x+9\\f(x+h) = (x+h)^{2}-5(x+h)+9[/tex]
Now we can plug them into the fraction:
[tex]\frac{((x+h)^{2}-5(x+h)+9)-(x^{2} -5x+9)}{h}[/tex]
Expanding all of the terms, we get:
[tex]\frac{(x^{2} +2hx + h^{2} -5x-5h+9)-(x^{2} -5x+9)}{h}[/tex]
Distributing the negative we get:
[tex]\frac{x^{2} +2hx + h^{2} -5x-5h+9-x^{2} +5x-9}{h}[/tex]
Now we see that [tex]x^{2} -x^{2} ,-5x+5x,[/tex] and [tex]9-9[/tex] all cancel, leaving us with:
[tex]\frac{2hx + h^{2}-5h}{h}[/tex] (Notice the only terms left are those with h in them)
As every term contains an h, we can remove an h from every term, giving us:
2x + h - 5
Please help me!! <3
Find the equation of the circle represented by the given figure.
*Use y as a variable in the equation y + 16 = 0 to help solve for the radius.*
The equation of the circle has the following format:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In which:
[tex](x_0, y_0)[/tex] are the coordinates of the center.r is the radius.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by the equation presented as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
From the figure, you must identify the coordinates of the center, and then replace the given point [tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex] into the equation to solve for the radius r.
Missing InformationThe problem is incomplete, hence the procedure to obtain the equation of the circle was presented.
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PLS Help sooner than later!!
The radius of a certain molecule is about 1.3 angstroms. One angstrom is 0.000001 cm. What is the diameter of this molecule in centimeters?
Answer:
Step-by-step explanation:
radius of a circle is half of the diameter
Diameter :D , Raduis : R
D = 2R
R = 1.4 angstrom
1 angstrom = 0.00000001 cm = 10^-7 cm
R = 1.4 * 10^-7 cm
D = 2.8 * 10^-7 cm
The Diameter is 2.8x10^-7 cm
The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total amount due at time t.
P=$3000, r= 6%, t = 4 years
(Round to the nearest cent as needed.)
The loan's future value A, or the total amount due at time t is equal to $3,720.
How to calculate the simple interest and future value?Mathematically, simple interest can be calculated by using this formula:
S.I = PRT or S.I = A - P
Where:
S.I represents the simple interest.P is the principal or starting amount.R is the interest rate.A is the future value.T represents the time measured in years.Substituting the given parameters into the simple interest formula, we have;
S.I = 3,000 × 6/100 × 5
S.I = 3,000 × 0.06 × 4
S.I = $720.
Next, we would calculate the future value as follows;
Future value, A = S.I + P
Future value, A = $720 + $3,000
Future value, A = $3,720.
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Which data set has two values for the mode?
2, 2, 2, 5, 6, 7, 9, 10
5, 6, 8,10, 11, 11, 15, 18
12, 12, 13, 13, 14, 14, 15, 15
21, 22, 22, 24, 25, 26, 28, 28
The data set: 21, 22, 22, 24, 25, 26, 28, 28 have two values of mode, which are, 22 and 28.
What is meant by the mode of a data set?
The value that appears the most frequently in a data collection when it is unique is known as the mode, and like the median and mean, it can be used to measure central tendency. Yet, occasionally there is either no mode or more than one mode. When every observed value occurs exactly once in a data collection, there is no mode. When the highest frequency was noted for more than one value in a data collection, there are many modes. The mode cannot be utilised in either of these examples to identify the distribution centre. Categorical variables can be summarised using the mode.
a)2, 2, 2, 5, 6, 7, 9, 10
Here most repeated value is only 2.
So the mode is 2.
b) 5, 6, 8,10, 11, 11, 15, 18
Here most repeated value is only 11.
So the mode is 11.
c)12, 12, 13, 13, 14, 14, 15, 15
Here the values 12,13,14 and 15 are repeated twice.
So this has 4 values as mode.
d) 21, 22, 22, 24, 25, 26, 28, 28
Here 22 and 28 are repeated twice.
So this data set has 2 values for the mode.
Therefore the data set: 21, 22, 22, 24, 25, 26, 28, 28 have two value of mode, which are, 22 and 28.
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Answer:
D
Step-by-step explanation:
here is a pic for proof
Determine if this equation is true or false:
Answer:
The equation is false
Step-by-step explanation:
(x+5)^2 = x^2+25
FOIL the left hand side.
(x+5)(x+5)
x^2 +5x+5x+25
x^2 +10x+25
This does not equal x^2+25.
The graph shows the location of all solutions for some linear equation. The coordinates of two of the points are labeled. Which linear equation matches this graph? A) x + y = 6 B) y = 2x + 4 C) 3x + y = 9 D) y = −2(x − 5) − 6
The linear equation for coordinate points (-2,8) and (5,-6) is option B: y = -2x + 4.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
Since there are two points on the graph, use the slope-intercept form of a linear equation to find the equation that matches the graph.
The slope-intercept form is -
y = mx + b
Where m is the slope and b is the y-intercept.
To find the slope, we use the two given points -
m = (y2 - y1) / (x2 - x1)
m = (-6 - 8) / (5 - (-2))
m = -14 / 7 = -2
To find the y-intercept, we can use one of the points and the slope -
y = mx + b
8 = (-2) × (-2) + b
8 = 4 + b
b = 4
So the equation that matches the graph is -
y = -2x + 4
Therefore, the equation is -2x + 4.
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please help me with tgis
The value of x is 11. 18
The value of y is 8. 67
How to determine the valueUsing the Pythagorean theorem, we have that;
x² = y² + z²
Substitute the values, we get;
x² = 10² + 5²
find the squares
x² = 100 + 125
Add the values
x² = 125
Find the square root
x = 11. 18
Using the Pythagorean theorem, we have;
y² = 9² - (√6)²
Find the squares
y² = 81 - 6
substract the values
y² = 75
Make 'y' the subject
y = 8. 67
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A pharmaceutical company claims that its new medication results in side effects for 20% of those people who take it. A sample of 100 consumers of that medication is randomly selected. Find the mean and standard deviation for the number of patients that experience side effects in such groups of 100.
The mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
The number of patients experiencing side effects in a sample of 100 patients as a binomial distribution with n = 100 and p = 0.20.
The mean of a binomial distribution is given by:
μ = np
Substituting n = 100 and p = 0.20, we get:
μ = 100 × 0.20 = 20
Therefore, the mean is 20.
The variance of a binomial distribution is given by:
σ²= np(1 - p)
Substituting n = 100 and p = 0.20, we get:
σ² = 100 × 0.20 × (1 - 0.20) = 16
Therefore, the variance of the number of patients experiencing side effects in a sample of 100 patients is 16.
The standard deviation of a binomial distribution is the square root of its variance:
σ =√Variance
=√16
= 4
Hence, the mean is 20 and standard deviation for the number of patients that experience side effects in such groups of 100 is 4.
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a class has seven girls and four boys if the teacher randomly picks seven students what is the probability that he will pick all girls
Answer:
the probability is that the teacher will most likely pick between 2-4 boys and the rest would be girlso so the probability of it being all girls unless he choosing all girls on pourpose it would be a slim chance. if you need a percentage it would probably be like a 1.25% chance
Step-by-step explanation:
A farmer is planning to create a new gazing field for his horses. He determines that he needs 280 yards of fencing for his new field. The fencing is sold by the foot. How many feet of fencing should the farmer buy? Explain.
Answer:
280 yards * 3 feet/yard = 840 fee
Step-by-step explanation:
since the fencing is sold by the foot, we need to convert the given 280 yards to feet in order to determine how much fencing the farmer should buy.
To convert yards to feet, we multiply the number of yards by 3, since there are 3 feet in 1 yard.
280 yards * 3 feet/yard = 840 feet
Therefore, the farmer needs to buy 840 feet of fencing for his new grazing field.