In the above word problem,
a) Peiling has more money than Malcolm.b) They (both Peiling and Malcom) have a total of M2 + P2 = 12 + 3 = 15 $2-notes altogether.What is the explanation for the above solution?
Let's denote the number of $50 notes that Malcolm and Peiling have as M50 and P50 respectively. Similarly, we'll denote the number of $10 notes as M10 and P10 and the number of $2 notes as M2 and P2.
From the problem statement we have the following information:
1. The total number of notes they have is the same: M50 + M10 + M2 = P50 + P10 + P2
2. The number of $2-notes Peiling has is 1/4 of the number of $2-notes Malcolm has: P2 = (1/4)M2
3. The number of $10-notes Peiling has is twice the number of $10-notes Malcolm has: P10 = 2M10
4. Peiling has 8 more $50-notes than Malcolm: P50 = M50 + 8
5. The total number of $2 and $10-notes they have is 42: M10 + M2 + P10 + P2 = 42
Substituting equations (2), (3) and (4) into equation (1) we get:
M50 + M10 + M2 = (M50+8) + 2M10 +(1/4)M2
Solving for M50 we get:
M50 = 8 + 2M10 - (3/4)M2
Substituting equations (2), (3), and (4) into equation (5) we get:
M10 + M2 + 2M10 + (1/4)M2 = 42
Solving for M10 we get:
M10 = 14 - (1/12)M2
Substituting this value of M10 into the equation for M50 we get:
M50 = 8 + 28 - M2/6 - (3/4)M2
Solving for M50 we get:
M50 = 36 - (11/6)M2
Since the number of notes must be a positive integer, the smallest possible value for M50 is when M2=6. This gives us a value of M50=35.
Substituting these values back into the equations for P50, P10 and P2 we find that Peiling has P50=43 $50 notes, P10=28 $10 notes and P2=1.5 $2 notes. However, since the number of notes must be a positive integer, this solution is not valid.
The next smallest possible value for M50 is when M2=12. This gives us a value of M50=34. Substituting these values back into the equations for P50, P10 and P2 we find that Peiling has P50=42 $50 notes, P10=28 $10 notes and P2=3 $2 notes.
Now we can calculate the total amount of money each person has:
Malcolm: 34 * 50 + 14 * 10 + 12 * 2 = $1,864
Peiling: 42 * 50 + 28 * 10 + 3 * 2 = $2,386
So to answer part (a) of the question: Peiling has more money than Malcolm.
To answer part (b) of the question: They have a total of M2 + P2 = 12 + 3 = 15 $2-notes altogether.
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Point B (8, -3) has been transformed. After a reflection over the x-axis, what is the coordinate of point B’?
The coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.
What is Reflection in geometry?A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.
When a point is reflected over the x-axis, its y-coordinate changes sign while its x-coordinate remains the same.
Therefore, to find the coordinates of point B' after reflecting point B over the x-axis, we simply need to change the sign of the y-coordinate of point B.
Starting with point B at (8, -3), reflecting over the x-axis changes the sign of the y-coordinate, so the new point B' is at:
B' = (8, 3)
Therefore, the coordinate of point B' is (8, 3) after reflecting point B (8, -3) over the x-axis.
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need help
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
Rounding to the nearest 50 dollars, we get:
value = $12,550.
What is annual rate of change?The annual rate of change refers to the percentage change in a quantity over a period of one year. It is commonly used to express the growth or decline of economic indicators, such as GDP, inflation, or employment, as well as the performance of financial assets, such as stocks or bonds. To calculate the annual rate of change, you need to take the difference between the initial and final values of the quantity, divide it by the initial value, and multiply the result by 100 to express it as a percentage. For example, if a company's revenue was $1 million in 2021 and $1.2 million in 2022, the annual rate of change in revenue would be (1.2-1)/1 * 100 = 20%.
A) The car depreciated from $44,000 in 1992 to $15,000 in 2006, a period of 14 years.
The annual rate of change can be found using the formula:
[tex]r = (V2/V1)^{(1/n)} - 1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years.
Substituting the given values, we get:
[tex]r = ($15,000/$44,000)^{(1/14)} - 1[/tex]
[tex]r = 0.0576[/tex]
So, the annual rate of change (or depreciation) is 0.0576.
B) To express this rate as a percentage, we can multiply it by 100 and add a percent sign:
[tex]r = 0.0576 x 100%[/tex]
[tex]r = 5.76%[/tex]
So, the car depreciated at an annual rate of 5.76%.
C) If we assume that the car value continues to drop by the same percentage, we can use the formula for exponential decay:
[tex]V = V0*(1-r)^t[/tex]
where V0 is the initial value, r is the rate of change, and t is the time elapsed.
Substituting the given values, we get:
[tex]V = $15,000*(1-0.0576)^3[/tex]
[tex]V = $12,527.31[/tex]
Rounding to the nearest 50 dollars, we get:
[tex]value=12,550[/tex]
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add [-6 -22] + [-3 2 1]
Answer:
-349
Step-by-step explanation:
1)[-6-22]+[-321]
2)(-28)-321
3)-349
Please help brainlesst and pints
The ball will reach its maximum height after 3.5 seconds.
What is projectile motion?
Projectile motion is the motion of an object that is launched into the air and then moves along a curved path under the influence of gravity.
In projectile motion, the object follows a parabolic trajectory, which is a curve described by a quadratic function. The path of the object depends on the initial velocity, angle of projection, and acceleration due to gravity.
The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately.
The height function of the ball thrown The key characteristics of projectile motion are that the object moves in two dimensions, typically horizontally and vertically, and that the motion in each dimension is independent of the other. This means that the horizontal and vertical components of motion can be analyzed separately. is given by h(t) = 112t - 16t^2, where t is the time in seconds and h(t) is the height of the ball at time t.
To find the maximum height, we need to find the vertex of the parabolic function h(t). The vertex of a parabola given by the equation y = ax^2 + bx + c is located at x = -b/2a.
In the case of our height function h(t) = -16t^2 + 112t, the coefficient of the squared term is -16, and the coefficient of the linear term is 112. Therefore, the time at which the ball reaches its maximum height is given by:
t = -b/2a = -112/(2*(-16)) = 3.5
So, the ball will reach its maximum height after 3.5 seconds.
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Question Catherine randomly selects 10 books off of her bookshelf. She records the number of pages in the books in the table below. Use a calculator to create a histogram of the data, and then interpret the plot. Set Xmin to 100, Xmax to 250, and Xscl to 25. Number of Pages 227 142 165 180 145 162 121 195 160 174
1. Data is approx bell-shaped and symmetric
2. Median is between 150 to 175
What is a Histogram?A histogram is a graphical representation of a frequency distribution of a set of continuous data. It is used to display the shape of the data and to show how frequently certain values occur within a given range or interval.
In a histogram, the x-axis represents the range or interval of the data, and the y-axis represents the frequency of occurrence of values within each interval.
The data is divided into a set of bins or intervals, and the height of each bar on the histogram represents the number of data points that fall within that particular bin. The bars of the histogram are typically drawn adjacent to each other, with no gaps between them, to emphasize the continuity of the data.
Therefore, from the histogram used to represent the given data, it can be seen that the data is symmetric and also the median has the values between 150 to 175
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Which of the following is not a perfect square trinomial?
Group of answer choices
A. x^2+16x+64
B. x^2+7x+49
C. x^2+10x+25
D. 4x^2+16x+16
Answer:
B
Step-by-step explanation:
[tex]x^{2} +7x+49[/tex] is a prime equation.
There was a plate of 2
mint brownies, 2 chocolate
brownies and 5 chocolate
brownies with nuts. What
is the probability that
Gavin will randomly take a
brownie with nuts,
put it back, and grab one
without nuts?
Answer:
20/81
Step-by-step explanation:
The total number of brownies is 2 + 2 + 5 = 9. The probability of Gavin taking a brownie with nuts on the first pick is 5/9. After putting it back, the total number of brownies is still 9, but the number of brownies with nuts is now 4. Therefore, the probability of Gavin taking a brownie without nuts on the second pick is 4/9. The probability of both events happening together is the product of the individual probabilities: (5/9) x (4/9) = 20/81. Therefore, the probability that Gavin will randomly take a brownie with nuts, put it back, and grab one without nuts is 20/81.
Answer:
if you add the whole amount, then 2+2+5 is 9. then divide by 4 (the number without nuts) 4/9 is 44 percent
Step-by-step explanation:
Find an angle in each quadrant with a common reference angle with 165°, from 0°≤θ<360°
Answer:
Here are the angles in each quadrant with a common reference angle of 165°:
First quadrant: angle is 15° (subtract 165° from 180°)
Second quadrant: angle is 195° (subtract 165° from 180° and add the result to 180°)
Third quadrant: angle is 195° (subtract 165° from 180° and then subtract the result from 180°)
Fourth quadrant: angle is 195° (subtract 165° from 360°)
2 PART QUESTION PLS HELP Harris has a spinner that is divided into three equal sections numbered 1 to 3, and a second spinner that is divided into five equal sections numbered 4 to 8. He spins each spinner and records the sum of the spins. Harris repeats this experiment 500 times.
Part A
Which equation can be solved to predict the number of times Harris will spin a sum less than 10?
A) 3/500 = x/15
B) 12/500 = x/15
C) 12/15 = x/500
D) 3/15 = x/500
QUESTION 2
Part B
How many times should Harris expect to spin a sum that is 10
or greater?
_______
The equation that can be solved to predict the number of times Harris will spin a sum less than 10 is B) 12/500 = x/15
Harris should expect to spin a sum of 10 or greater 240 times.
How to explain the equationIt should be noted that to predict the number of times Harris will spin a sum less than 10, we need to find the probability of getting a sum less than 10 and multiply it by the total number of experiments (500).
The possible sums that can be obtained are: 5, 6, 7, 8, 9, 10, 11, and 12. The probability of getting a sum less than 10 is the sum of the probabilities of getting each of these outcomes, which is:
P(sum less than 10) = P(1 and 4, 1 and 5, 2 and 4, 2 and 5, 3 and 4, 3 and 5)
= 6/15 * 2/5
= 4/25
Multiplying this probability by the total number of experiments (500), we get:
Number of times Harris will spin a sum less than 10 = (4/25) * 500 = 80
Therefore, the correct equation to predict the number of times Harris will spin a sum less than 10 is: 12/500 = x/15
Part B: Based on the information, the possible outcomes that give a sum of 10 or greater are: 10, 11, and 12. The probability of getting a sum of 10 or greater is the sum of the probabilities of getting each of these outcomes, which is:
P(sum of 10 or greater) = P(1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5, 6 and 4, 7 and 3, 8 and 2, 9 and 1, 8 and 3, 7 and 4, 6 and 5)
= 12/15 * 3/5
= 36/75
= 12/25
Multiplying this probability by the total number of experiments (500), we get:
Number of times Harris should expect to spin a sum of 10 or greater = (12/25) * 500 = 240
Therefore, Harris should expect to spin a sum of 10 or greater 240 times.
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What generalization can you make about the equations?
A whole number by a unit fraction is the same as
About the equation [tex]7 * 3 = 21[/tex], the generalization we can make is that dividing a whole number by a unit fraction is the same as multiplying a whole number by the denominator of the unit fraction.
What is considered as generalization in mathematics?We use generalizations to describe the pattern they see in the relationship of a specific group of numbers. It's a pattern that holds true every time.
In mathematics, generalization can be defined as a statement that is true for an entire class of objects, the process by which we obtain a general statement, or the method by which knowledge is transferred from one setting to another.
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30*8000(5-)1800=?
1500(800-)15000*18000=?
Answer:
1) 2160000000
2) 3.24 * 10^14
Step-by-step explanation:
30*8000(5-)1800
240000 * 5 * 1800
1200000 * 1800
2160000000
1500(800-)15000*18000
1200000 * 15000 * 18000
18000000000 * 18000
3.24 * 10^14
(24x3−2x2−8x+30)÷(x−2)
We can long divide (24x^3 - 2x^2 - 8x + 30) by (x - 2) as follows:
24x^2 + 46x + 86
_______________________
x - 2 | 24x^3 - 2x^2 - 8x + 30
-(24x^3 - 48x^2)
_______________
46x^2 - 8x
46x^2 - 92x
___________
84x + 30
84x - 168
________
198
Therefore, (24x^3 - 2x^2 - 8x + 30) ÷ (x - 2) = 24x^2 + 46x + 86 with a remainder of 198/(x - 2).
Answer:
the quotient is 24x² + 46x + 86 and the remainder is 198. Thus, we can write:
(24x³ - 2x² - 8x + 30) ÷ (x - 2) = 24x² + 46x + 86 + 198/(x - 2)
Step-by-step explanation:
We can perform polynomial long division to divide (24x³ - 2x² - 8x + 30) by (x - 2).
24x² + 46x + 86
----------------------
x - 2 | 24x³ - 2x² - 8x + 30
- (24x³ - 48x²)
------------------
46x² - 8x
- (46x² - 92x)
--------------
84x + 30
- (84x - 168)
--------------
198
Therefore, the quotient is 24x² + 46x + 86 and the remainder is 198. Thus, we can write:
(24x³ - 2x² - 8x + 30) ÷ (x - 2) = 24x² + 46x + 86 + 198/(x - 2)
How do I make x the subject of y=ax^2 + b
Answer:
Step-by-step explanation:
To make x the subject of y = ax^2 + b, we can use the following steps:
1.Subtract b from both sides to isolate the term with x^2:
y - b = ax^2
2.Divide both sides by a to isolate x^2:
(y - b) / a = x^2
3.Take the square root of both sides to solve for x:
x = ± sqrt((y - b) / a))
Therefore, the expression for x as a subject of y = ax^2 + b is:
x = ± sqrt((y - b) / a))
I think you need to make an equation. Help Me!
Answer: h = 7
Step-by-step explanation:
63 = 1/2 * 18 * h
63 = 9 * h
63 = 9h
*Divide 9 on both sides.
7 = h
(5 1/2, - 7 1/2) and (5 1/2, - 1 1/2)
Answer:
Step-by-step explanation:
1) -2
2) 0
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Jessica works in a cake shop . Each cake is cut into 6 slices.
On Saturday 20 slices of chocolate cake were sold 25 slices of lemon cake were sold and 17 slices of carrot cake were sold .
Answer:
What is the question?
Step-by-step explanation:
N/A
Solve 2x^2+8x-3 by completing the square
A(r(t))=\pi(0.25+2t+4t^2)
Explanation:
To write a composite function, we apply one function to another given function. In this case, we want to find area in terms of time; this means that the function A(r) gets applied to the function r(t).
In order to do this, we replace r with r(t). We already know that r(t)=0.5+2t; this means we replace r with 0.5+2t:
A(r(t))=π(0.5+2t)²
To simplify this, we simplify the squared term:
A(r(t)) = π(0.5+2t)(0.5+2t)
A(r(t)) = π(0.5*0.5+0.5*2t+2t*0.5+2t*2t)
A(r(t)) = π(0.25+t+t+4t²)
A(r(t)) = π(0.25+2t+4t²)
Answer:
So the composite function that gives the area of a circle in terms of time is:
A(r(t)) = π(0.25+2t+4t²)
Find the total surface area of this cylinder. Give your answer to 1 decimal place. 18 cm Feedback 24 cm
In light of this, the cylinder's total surface area falls between approximately 1017.9 cm²and 1357.2 cm².
Define the cylinder's entire surface area.A cylinder's total surface area is equal to the sum of all of its faces' surface areas. The cylinder's total surface area—the sum of its curved and circular areas—has a radius of "r" and a height of "h." The entire surface area of the cylinder is calculated as follows:
Define cylinder:Total Surface Area of Cylinder = 2r (h + r) square units.
The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. It is seen as a prism since its base is a circular. It is frequently used as a container and can either be solid or hollow 13.
The following formula can be used to get a cylinder's total surface area:
A = 2πr² + 2πrh
where r is the cylinder's base's radius, h is the cylinder's height, and is a mathematical constant roughly equal to 3.14159.
Yet, we can locate a variety of potential surface areas using the provided information. With the assumption that the radius is equal to the feedback's half (9 cm), we can
after which, we can determine the surface area as follows:
A = 2π(9)² + 2π(9)(18) (18)
A= 2π(81) + 2π(2916)
A ≈ 1017.9 cm²
The surface area can be calculated as follows if we assume that the radius is equal to two-thirds of the feedback (i.e., r = 12 cm):
A = 2π(12)² + 2π(12)(18) (18)
A ≈ 1357.2 cm²
Complete question is given below:
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I need help with this question
The revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016. 2. The revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.
What is fraction and percentage?A factor is a number that represents how two quantities are related to one another. It is frequently used to indicate how much one amount exceeds or falls short of another. For instance, if a business's revenue. On the other hand, a percentage is a technique to represent a portion or ratio of something as a fraction of 100. For instance, if a company made money.
The given revenue for the two years is $138200 and $164900.
The factor of the two revenue is:
factor = 164900 / 138200 = 1.193
Hence, the revenue for Jessicas Cafe in 2017 was 1.193 times larger than the revenue in 2016.
percentage = (164900 / 138200) * 100% = 119.3%
Therefore, the revenue for Jessicas Cafe in 2017 represented 119.3% of the revenue in 2016.
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find the perimeter of the following figures. 21 cm- b. 35 cm 35 cm 35 cm C. 6.75 cm 2.25 cm
Answer:
a. To find the perimeter of the first figure, we need to add up the lengths of all four sides. If the sides are equal, we can simply multiply the length of one side by 4. Therefore, the perimeter of a square with sides of 21 cm is:
Perimeter = 4 x side
Perimeter = 4 x 21 cm
Perimeter = 84 cm
b. To find the perimeter of the second figure, we need to add up the lengths of all three sides. Since all three sides are equal, we can simply multiply the length of one side by 3. Therefore, the perimeter of an equilateral triangle with sides of 35 cm is:
Perimeter = 3 x side
Perimeter = 3 x 35 cm
Perimeter = 105 cm
c. To find the perimeter of the third figure, we need to add up the lengths of all four sides. Therefore, the perimeter of a rectangle with sides of 6.75 cm and 2.25 cm is:
Perimeter = 2 x (length + width)
Perimeter = 2 x (6.75 cm + 2.25 cm)
Perimeter = 2 x 9 cm
Perimeter = 18 cm
Step-by-step explanation:
a. To find the perimeter of the first figure (a square with sides of 21 cm), we need to add up the lengths of all four sides. Since all four sides are equal, we can simply multiply the length of one side by 4. Therefore:
Perimeter = 4 x side
Perimeter = 4 x 21 cm
Perimeter = 84 cm
So the perimeter of the square is 84 cm.
b. To find the perimeter of the second figure (an equilateral triangle with sides of 35 cm), we need to add up the lengths of all three sides. Since all three sides are equal, we can simply multiply the length of one side by 3. Therefore:
Perimeter = 3 x side
Perimeter = 3 x 35 cm
Perimeter = 105 cm
So the perimeter of the equilateral triangle is 105 cm.
c. To find the perimeter of the third figure (a rectangle with sides of 6.75 cm and 2.25 cm), we need to add up the lengths of all four sides. Therefore:
Perimeter = 2 x (length + width)
Perimeter = 2 x (6.75 cm + 2.25 cm)
Perimeter = 2 x 9 cm
Perimeter = 18 cm
So the perimeter of the rectangle is 18 cm.
if x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.
If x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3. the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.
How to find the inverse function?To find the inverse function of f(x) = 5x - 3, we need to follow these steps:
Step 1: Replace f(x) with y:
y = 5x - 3
Step 2: Solve for x in terms of y:
y = 5x - 3
y + 3 = 5x
x = (y + 3)/5
Step 3: Replace x with f^(-1)(x) and y with x:
f^(-1)(x) = (x + 3)/5
Step 4: Check if the inverse function is valid by verifying if f(f^(-1)(x)) = x and f^(-1)(f(x)) = x:
f(f^(-1)(x)) = f((x+3)/5) = 5((x+3)/5) - 3 = x + 2
f^(-1)(f(x)) = f^(-1)(5x - 3) = (5x - 3 + 3)/5 = x/5
Since f(f^(-1)(x)) = x + 2 and f^(-1)(f(x)) = x/5, the inverse function is valid.
Therefore, the inverse function of f(x) = 5x - 3 is f^(-1)(x) = (x + 3)/5.
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The complete question is:
if x is multiplied by 5 and then 3 is subtracted, then the function is f(x)=5x-3.
What are the step to find the inverse to this function?
Lyla goes out to dinner with her freinds where the subtotal is $23.89. A 7% tax and 18% tip is added to the subtotal. How much did she pay in total?
Lyla pays $ 24.14 in total.
What is the total amount?
To add two or more numbers and determine the final total, use the sum. A series of any form of numbers, known as addends or summands, is added; the outcome is their sum or total.
Here, we have
Given: Lyla goes out to dinner with her friends where the subtotal is $23.89. A 7% tax and 18% tip are added to the subtotal.
we have to find out how much did she pay in total.
= $23.89 + 7% + 18%
= $23.89 + 7/100 + 18/100
= $23.89 + 0.07 + 0.18
= $ 24.14
Hence, Lyla pays $ 24.14 in total.
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Karen needs to find a courier to deliver a package the first courier charges a fee of $20 plus $2 per pound the second charges $12 plus $3 per pound karen determines that given her packages weight the two courier services are equivalent in terms of cost. how much will it cost? what is the weight?
Answer:
Step-by-step explanation:
Let's call the weight of Karen's package "w" in pounds.
For the first courier, the cost is given by:
Cost = 20 + 2w
For the second courier, the cost is given by:
Cost = 12 + 3w
We know that these costs are equivalent, so we can set them equal to each other:
20 + 2w = 12 + 3w
Simplifying this equation, we get:
8 = w
So the weight of Karen's package is 8 pounds.
To find the cost, we can plug this weight into either of the equations above:
For the first courier:
Cost = 20 + 2(8) = 36
For the second courier:
Cost = 12 + 3(8) = 36
So it will cost Karen $36 to deliver her package, and the weight of the package is 8 pounds.
A triangular piece of land has base 2 meter and height 10meter. if the land is 15 dolar per square meter what is its value
Answer:
150.00
Step-by-step explanation:
a = 1/2bh
a = 1/2(2)(10)
a = 10 [tex]m^{2}[/tex]
10x15 = 150
Helping in the name of Jesus.
The graphs show the same data. Why do they have different appearances?
Hence, they are different because they drawn from the different scales values.
What is the data?Data in math is a collection of facts and figures that can be in any form—numerical or non-numerical.
Numerical data is the one you can calculate, and it is always collected in number form, such as scores of students in class, wages of workers in an organization or height of players on a football team, etc.
As per the given graphs they are different because they drawn with the help of different scales.
Hence, they are different because they drawn from the different scales values.
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Triangle QRS is shown below. Use the information given to determine the measure of ∠ R.
Angel Q= 38.2
Angel S= 52.7
Angel R=??
I’m so confused please help!
Answer: r=89.1
Step-by-step explanation: It has been given that,
PQ=PR
So, it is an isosceles triangle, hence ∠Q=∠R. let it be x
Now, we know that the sum of the angles of a triangle = is 180
∘
.
So,
∠P+∠Q+∠R=180
38.2+52.7+x=180
90.9+x=180
taking 90.9 in RHS it becomes -, so
x=180-90.9
x=89.1
Solving a System of Linear Equations - Applications - Item 35812
A sandwich shop only sells sandwiches and homemade soup.
The table shows the number of sandwiches and bowls of soup purchased in the past
2 hours.
The total earnings for hours 1 and 2 are given.
Each sandwich costs the same price, and each bowl of soup costs the same price.
The system of equations can be used to represent the situation.
Use the drop-down menus to complete each statement.
the answer is in the attachment below:
A rancher wants to fence an area of 1,500 square yards in a rectangular field that borders a straight river, and then divide it in half with a fence perpendicular to the river. He needs no fence along the river. The dividing fence costs half as much as the surrounding fence. How can he do this so that the cost of the fence is minimized?
The cost of the fence for a rectangular field of 1,500 square yards will be 150k√50 dollars.
Let the length of the rectangular field be L and the width be W. Since the area of the field is 1,500 square yards, we have:
L × W = 1,500
P = 2L + W
C = kP + (1/2)k(L/2)
C = (2k)L + (k/2)W
W = 1500/L
Substituting this into the expression for C, we get:
C = (2k)L + (k/2)(1500/L)
dC/dL = 2k - (k/2)(1500/[tex]L^2[/tex]) = 0
Solving for L, we get:
L = 30√50 yards
Substituting this back into the equation for W, we get:
W = 50/√50 yards
Therefore, the dimensions of the rectangular field that minimize the cost of the fence are L = 30√50 yards and W = 50/√50 yards.
P = 2L + W = 60√50 + 50/√50 yards
C = (2k)L + (k/2)(1500/L) = 90k√50 dollars
k/2 = k/2
Substituting this into the expression for C, we get:
C = 150k√50 dollars
Therefore, to minimize the cost of the fence, the rancher should build a rectangular field with dimensions of L = 30√50 yards and W = 50/√50 yards, and the total cost of the fence will be 150k√50 dollars.
To learn more about rectangular field please click on below link
https://brainly.com/question/17092951
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Nikki invested $1000 at 2% interested compound daily how long will it be until the balance reaches $5000 round to the nearest whole number
now, we could use the compound interest equation using a compounding period of 365 for a year with 365 days, so a daily compounding, OR we can just use the continuously compounding equation, which is equivalent.
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 5000\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=years \end{cases} \\\\\\ 5000 = 1000e^{0.02\cdot t} \implies \cfrac{5000}{1000}=e^{0.02t}\implies 5=e^{0.02t} \\\\\\ \log_e(5)=\log_e(e^{0.02t})\implies \log_e(5)=0.02t\implies \ln(5)=0.02t \\\\\\ \cfrac{\ln(5)}{0.02}=t\implies \boxed{80\approx t}[/tex]