Length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
What is Area of Rectangle?The area of Rectangle is length times of width
Given that, a rancher has 200 feet of fencing to enclose two adjacent rectangular corrals of the same dimensions.
Here, the dimensions of the rectangles are the same.
The width of the two rectangles is W=2W+2W=4W
The length of the two rectangles is L=L+L+L=3L
Because the adjacent side has a common length.
3L+4W=200
3L=200-4W
Divide both sides by 3
L=(200-4W)/3
Let us form an equation using the area of rectangle formula:
A=2LW
=2(200-4W)/3.W
A=400-8W²/3
Let us differentiate to get the area to be maximized dA/dW=0
1/3×(400-8W²)=0
1/3(400-16W)=0
400-16W=0
400=16W
Divide both sides by 16
W=25
The width is 25 feet.
Substitute W value in equation to get L value:
L=200-4×25/3
=200-100/3
=100/3
=33.33
The length is 33.33 feet.
Now let us find the maximum area
A=2LW
=2×33.33×25
=1666.66
Hence, length is 33.33 feet and width is 25 feet are dimensions should
be used so that the enclosed area will be a maximum.
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Question
What is the slope of the line on the graph?
-2
Enter your answer in the box.
Answer:
Step-by-step explanation:
Used (0,0) and (-2,4)
(4-0)/(-2-0)= m
m= 4/-2 = -2
NO LINKS!! Fredrico's Bank will you decide how often your interest will be computed, but with certain restrictions. Read the following options. What is the best deal after one year? Justify your answer.
Compounded quarterly; annual interest rate is 7.875%
========================================================
Explanation:
Let's say we are depositing P = 100 dollars, and we leave it in the account for a timespan of t = 1 year.
This will apply for options A through E.
-------------------
If we go with option A, then we would have n = 1 and r = 0.08
Use the compound interest formula to get the following:
A = P*(1+r/n)^(n*t)
A = 100*(1+0.08/1)^(1*1)
A = 108
We'll have $108 dollars in the account at the end of 1 year if we go with option A. The amount of interest only is A-P = 108-100 = 8 dollars.
-------------------
For option B, we have: n = 4 and r = 0.07875
A = P*(1+r/n)^(n*t)
A = 100*(1+0.07875/4)^(4*1)
A = 108.110625948487
A = 108.11
So far option B is slightly better since you've earned an extra $0.11, aka 11 cents.
-------------------
For option C, we have: n = 4 and r = 0.07875
A = P*(1+r/n)^(n*t)
A = 100*(1+0.0775/12)^(12*1)
A = 108.031299777277
A = 108.03
This amount is less compared to the $108.11 with option B. Therefore, option B is still the best so far.
-------------------
For option D, we have: n = 52 and r = 0.07625
A = P*(1+r/n)^(n*t)
A = 100*(1+0.07625/52)^(52*1)
A = 107.917207523206
A = 107.92
This is worse compared to option C.
Option B is still the best so far.
-------------------
For option E, we have: n = 365 and r = 0.075
A = P*(1+r/n)^(n*t)
A = 100*(1+0.075/365)^(365*1)
A = 107.787584644
A = 107.79
---------------------
Here's a table comparing the balance after 1 year for options A through E. Those balances all have a starting point of $100 as the deposit.
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Option} & \text{Balance after 1 year}\\\cline{1-2}A & \$108\\\cline{1-2}\boldsymbol{B} & \boldsymbol{\$108.11}\\\cline{1-2}C & \$108.03\\\cline{1-2}D & \$107.92\\\cline{1-2}E & \$107.79\\\cline{1-2}\end{array}[/tex]
Option B is the best choice earning the most ($108.11) if you deposit $100.
There's nothing special about the $100, so feel free to change it to something else to try other starting deposits. You'll find that option B will still provide the highest return.
Answer:
B
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedUse the Compound Interest Formula with the given values for each option to calculate a final equation where A equals a multiple of P.
The option with the greatest coefficient of P is the account which yields the highest interest after one year, and is therefore the best deal.
Option AGiven:
r = 8% = 0.08n = 1 (annually)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.08}{1}\right)^1[/tex]
[tex]\implies \sf A=1.08P[/tex]
Option BGiven:
r = 7.875% = 0.07875n = 4 (quarterly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.07875}{4}\right)^{4 \cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.0196875)^4[/tex]
[tex]\implies \sf A=1.081106259P[/tex]
Option CGiven:
r = 7.75% = 0.0775n = 12 (monthly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.0775}{12}\right)^{12\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.006458333\right)^{12}[/tex]
[tex]\implies \sf A=1.080312998P[/tex]
Option DGiven:
r = 7.625% = 0.07625n = 52 (weekly)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.0765}{52}\right)^{52\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.001471154\right)^{52}[/tex]
[tex]\implies \sf A=1.079441506P[/tex]
Option EGiven:
r = 7.5% = 0.075n = 365 (daily)t = 1 yearSubstitute the given values into the formula:
[tex]\implies \sf A=P\left(1+\dfrac{0.075}{365}\right)^{365\cdot 1}[/tex]
[tex]\implies \sf A=P\left(1.000205479\right)^{365}[/tex]
[tex]\implies \sf A=1.077875846P[/tex]
Summary[tex]\begin{array}{|c|l|}\cline{1-2} \sf Answer\;Option & \sf Coefficient\;of\;P\\\cline{1-2} A & 1.08\\\cline{1-2} B & 1.081106259\\\cline{1-2} C & 1.080312998\\\cline{1-2} D & 1.079441506\\\cline{1-2} E & 1.077875846\\\cline{1-2} \end{array}[/tex]
Therefore, the option with the greatest coefficient of P and therefore the best deal is option B.
find two integers whose sum 14 is and product is 45
Answer:
3 and 9
Step-by-step explanation:
The factors of 45 are 1, 3, 5, 9, 15, 4.
3x9=45
3+9=14
Help please i need to find what mHJ is
Answer: 72 for HJ.
Step-by-step explanation:
Simplify 3(2x + 5)
A. 6× + 30
B. 6× + 5
C. 6× + 15
Answer:
C. 6x + 15
Step-by-step explanation:
1. Distribute
3(2x + 5)
6x + 15
(We get this answer by multiplying the number outside the parentheses, which is 3, by the numbers in the parentheses. As in, 3 x 2x = 6x. And 3 x 5 = 15. So, we get 6x + 15).
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The human heart circulates from 770,000 to 1,600,000 gallons of blood through a person's body every year. Write a compound inequality to represent the number of gallons of blood that the heart circulates through the body in one day. x
The amount of blood that the human heart circulates every year is represented by the following compound inequality: 770,000 < x < 1,600,000, where x is in gallons of blood.
What is the compound inequality relative to the case?
Herein we must determine the compound inequality, that is, a simultaneous inequality of the form a < x < b, where a and b are the limits of the inequality. According to the statement, the human heart circulates every year at least 770,000 gallons of blood and at most 1,600,000 gallons of blood. Then, the compound inequality that represents the situation is:
770,000 < x < 1,600,000, where x is in gallons of blood.
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49. $10,000 is invested at an APR of 4% for 10
years.
50. $10,000 is invested at an APR of 5% for 20 years.
51. $15,000 is invested at an APR of 3.2% for 25 years.
52. $3000 is invested at an APR of 4% for 12 years.
53. $5000 is invested at an APR of 3.1% for 12 years.
54. $40,000 is invested at an APR of 8.5% for 30 years.
The total amount, if $10,000 is invested at an APR of 4% for 10 years is $14000.
What is interest?When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.
Given:
$10,000 is invested at an APR of 4% for 10 years.
Calculate the total amount at the end as shown below:
[tex]A = p + p\times r\times t / 100[/tex]
A = 10000 + 10000 × 4 × 10 / 100
A = 10000 + 4000
A = 14000
Similarly, solve all the questions using this formula.
Therefore, the total amount, if $10,000 is invested at an APR of 4% for 10 years is $14000.
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The complete question is:
$10,000 is invested at an APR of 4% for 10 years. Find the total amount after 10 years.
what is the 5/6 of 24?
Answer: 20
Step-by-step explanation:
Use 1 as the denominator to convert any number to a fraction:
24/1
The fraction 5/6 and our new fraction, 24/1, are now side by side, and we can multiply those two fractions to find the answer now that we have converted 24 into a fraction.
Multiply the numerators and denominators after converting the entire number to a fraction.
5*24/6*1 = 120/6
In this instance, it is possible to further simplify our new fraction. To do that, we must determine the two numbers' highest common factor.
So. GCF is 6.
We can now divide both the new numerator and the denominator by 6 to simplify this fraction down to its lowest terms.
120/6 = 20.
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Answer:
20
Step-by-step explanation:
what is the 5/6 of 24?
we can solve by multiplying 5/6 by 24
5/6 × 24 =
20
What are the solutions for the system of equations???
Answer:
(0, 1) and (-3, -2)
Step-by-step explanation:
The solutions are the points of intersection of the two graphs.
We can read the points off the graph.
Answer: (0, 1) and (-3, -2)
Solve for a. √a-b+c=3 A. a=3+√b-√c B. a=9+b-c C.a=9+√b-√c D. a=3+b-c
Answer:
a=9+b−c
Step-by-step explanation:
76°
59°
What does m/1 =?
Answer:
45º
Step-by-step explanation:
[(1 1/4 - 3/4) · (- 2/3) ³] ÷ (-4)
What is the value of the expression
Answer:
Step-by-step explanation:
1 1/4-3/4=5/4-3/4=(5-3)/4=2/4=1/2
(-2/3)3=-8/27
The ratio x:y is equal to is 2 : 5, and y is 80% of z. Write an equation to represent the proportional relationship between x and z.
Answer:
z = 3.125 * x
Step-by-step explanation:
since y is 80 percent of z, we can represent it in the form of a ratio as 80:100.
Simplify it down: 80:100 = 8:10 = 4:5
therefore x:y = 2:5
and y:z = 4:5
"y" is common in both of these ratios. Therefore we now have to make the value of Y same in both of the ratios. Therefore we find the least common multiple of both the y values which is 5 and 4. It is 20.
Now we make the value of y in both the ratios 20. So we need to multiply 5 in 2:5 by 4. Since we multiplied one of the values by 4 we have to multiply the other one as well (2*4). Now our new ratio for x:y is 8:20. Do the same for the other ratio. the other ratio is 4:5. the y value here is 4. 4 needs to be multiplied by 5 to become 20. Therefore multiply 4 by 5 and multiply 5 by 4. our new ratio for y:z is 20:25
As you can see both the y values are similar now.
x:y = 8:20
y:x = 20:25
therefore we can now write x:y:z as 8:20:25
that also means that x:z is now 8:25.
Now we know that when x is 8 z is 25. in this case. 8 and 25 are directly proportional.
therefore we can write an equation as
25 = k*8
k = 25/8
k = 3.125
therefore z = 3.125 * x
Vaughn is making 24 candy bags to sell at the school fundraiser. The bags of candy at the store contain 18 pieces of candy each and sell for $3.20 a bag. Vaugh will repackage this candy to include 15 pieces of candy in each bag. How much profit, not including the money he spent on the candy, will Vaugh make if he charges $3.80 per bag.
The profit that Vaughn would make if he charges $3.80 per bag is $27.20.
What is the profit?The first step is to determine the total pieces of candy that Vaughn plans to sell.
Total pieces of candy = number of pieces in each bag x total number of bags
Total pieces of candy = 24 x 15 = 360
The second step is to determine the total number of bags he has to buy.
Number of bags he is going to buy = total pieces of candy he is going to sell / number of pieces in each bag
Number of bags he is going to buy = 360 / 18 = 20 bags
The third step is to determine the total cost of buying 20 bags
Total cost = number of bags he is going to buy x cost per bag
Total cost = 20 x $3.20
Total cost = $64
The next step is to determine the total revenue from making 24 bags.
Total revenue = price per bag x total number of bags
Total revenue = $3.80 x 24
Total revenue = $91.20
Profit = revenue - cost
$91.20 - $64 = $27.20
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A jar holds 20 cookies, 13 are chocolate-chip cookies, and 7 are brussel-spout-with-turnip-chips cookies. You pick 4 cookies at random. What is the probability that you get exactly 2 of the brussel-spout-with-turnip-chips cookies?
The probability that exactly 2 of the brussel-spout-with-turnip-chips cookies is picked at random is 0.05 approximately to two decimal place.
Probability of an eventTo calculate the probability of an event, we identify an event of the required outcome result and the total number of results or possible outcomes that can occur, and thus divide the number of required outcomes by the total number of possible outcomes.
The total possible outcomes = 20
probability of picking a chocolate-chip cookies = 13/20
probability of picking brussel-spout-with-turnip-chips cookies = 7/20
probability of getting exactly 2 brussel-spout-with-turnip-chips cookies when 4 cookies are picked at random considering the they are not replaced after each pick is calculated as follows;
(13/20) × (13/20) × (7/20) × (7/20)
8281/160000
0.0518.
Hence, from our calculations by simplification the probability of getting exactly 2 brussel-spout-with-turnip-chips cookies when 4 cookies are picked at random is 0.05 approximately to two decimal place.
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Determine which integer in the solution set will make the equation true. 4p + 12 = 16 S: {−1, 1, 3, 4} −1 1 3 4
Answer: The correct integer is 2.
Step-by-step explanation:
4s − 14 = −6
4(2) − 14 = −6
8 - 14 = -6
-6 = -6 .np it was tough but here! brainliest pls ?
how much would it cost to replace all the windows on all the buildings in the united states?
It takes a word processor 39 minutes to word process and spell check 6 pages. Find how long it takes her to word
process and spell check 28 pages.
I need the answer
Answer:6/39=2/13
Step-by-step explanation:the spell check need 2/13 like 1.5sec to check one words
Classify each number below as an integer or not
Answer:
42 is an integer
92.96 is not an integer
-529.79 is not an integer
-12/4 is an integer
-19/15 is not an integer
what was the blackbird doing in the school library\?
kay learned that the average snail moves about .013 meters per second . How many centimeters per second does a snail move?
Answer: 1.3 centimeters
Step-by-step explanation:
.013 x 100 = 1.3
Find log0.81 rounded to the nearest tenth.
The value of the logarithm of 0.81 for logarithm properties is equal to - 0.1.
How to determine the value of a logarithm
Herein we must use logarithm properties to simplify a given logarithm and solve the resulting expression. The properties to be used in this question are described below:
㏒ (a / b) = ㏒ a - ㏒ b
㏒ aᵇ = b · ㏒ a
First, write the logarithmic equation:
㏒ 0.81
㏒ 81 / 100
Second, use the logarithmic property for a division:
㏒ 81 - ㏒ 100
Third, use the logarithmic property for a power:
㏒ 3⁴ - ㏒ 10²
4 · ㏒ 3 - 2 · ㏒ 10
4 · ㏒ 3 - 2
4 · 0.477 - 2
- 0.092
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There are 4 jars with 24.44 ounces of sauce in EACH it takes 3.5 ounces of sauce to make a pizza how many WHOLE pizzas can be made?
Answer: 27 pizzas
Step-by-step explanation:
Total ounces available = 4 jars x 24.44 ounces/jar = 97.76 ounces
(97.76 ounces) x (1 pizza/3.5 ounces) = 27.93 pizzas
You can make 27 whole pizzas (the 28th pizza will be short on the sauce)
Use partial quotients to divide 198➗9 show the work
Answer:
22
Step-by-step explanation:
Who would win the race, (Camila or gabriela) Please help, on edge of failing ngl. !!
Answer:
Camilla will win.
Step-by-step explanation:
Camilla's rate = 12
Gabriella's rate = 10
What is the ratio of shaded to unshaded squares in the grid below?
Group of answer choices
3/5
5/8
1/3
Answer:
1/3
Step-by-step explanation:
shaded is 10 and unshaded is 15
so the answer is 1/3 because
5 can be multiplied both sides
5 times 3 is 15
5 times 1 is 5
So both sides can be multiplied by 5
Answer: alt account
Step-by-step explanation:
are 25/150, 28/154, or 27 62 equivalent to each other?
The fractions 25/150, 28/154, or 27/62 aren't equivalent.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In order to know if they're equivalent fractions, we can convert them to percentage. This will be:
25/150 × 100 = 16.7%
28/154 × 100 = 18.2%
27/62 × 100 = 43.5%
In this case they're not equivalent.
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Gabriel is 10 years younger than mikhail. The sum of their ages is 88. What is mikhail's age
Answer:
Mikhail is 49 years old.
Step-by-step explanation:
39+49=88
16 divide 1 2 The one and two is a fraction together
Answer:
It's 32.
Step-by-step explanation:
Multiply 16 x 2 = 32.
I hope this helps.
Course Grade You were 6 points shy of a B in yo
394. How many points were possible in the course?
mathematics course. Your point total for the course was
(Assume that you needed 80% of the course total for a B.)
The point total possible for the given course is equal to 500.
What is a Percent?
A ratio whose second term is 100 is known as a percent. Parts per hundred are used in percentages. The mathematical representation of percent is %.The percent formula is given as, [tex]x=p \times b[/tex], where b is the base number, x is the number being compared to b, and p is the percent in decimal form.In the question, it is given that you were 6 points shy of a B and the current total points you have is 394.
So, the total number of points you require for a B is calculated as,
[tex]394+6=400[/tex]
So, the value of x is 400.
It is given that you need 80% of the course total for a B.
[tex]\implies p=\frac{80}{100}\\ \implies p=0.8[/tex]
Here, we have to find the base number (b).
We have, x = 80% of b
[tex]\implies x=0.8 \times b\\\implies 400= 0.8 \times b\\\implies x=\frac{400}{0.8}[/tex]
Simplifying, we get
[tex]x=500[/tex]
Therefore, 500 points were possible in the course.
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