the largest rectangular area is actually a square.
so the side would be 400/4 = 100 feet
area of a square is S^2
100^2 = 10,000 square feet
Maximum area is 5625m² when the dimensions are 75m × 75m.
To maximize the area of the rectangular field enclosed by a 300-meter-long fence, let's denote the length of one side as x meters and the other side as y meters.
Since the fence length is 300 meters, the perimeter of the rectangle is 2x + 2y = 300, or x + y = 150.
We want to maximize the area, which is given by A = xy.
To find the maximum, we'll use the constraint equation to express one variable in terms of the other, then substitute into the area formula.
1. From the constraint equation, x = 150 - y.
2. Substitute x into the area formula: A = (150 - y)y.
3. Take the derivative of A with respect to y and set it to zero to find the critical points.
4. Solve for y to find the value that maximizes A.
5. Use this value of y to find the corresponding x.
6. Calculate the maximum area using A = xy.
What are the rules for dividing signed numbers
Final answer:
In dividing signed numbers, the answer's sign depends on the signs of the numbers involved: same signs result in a positive answer, different signs yield a negative answer. Additionally, the final answer should have the same number of significant figures as the number with the fewest significant figures in the problem.
Explanation:
Rules for Dividing Signed Numbers
The rules for dividing signed numbers are similar to the rules for multiplication. When dividing numbers, it is important to consider both the sign of the numbers involved as well as the significant figures in the result. Here are the key rules to remember:
When two positive numbers divide, the answer has a positive sign, e.g., 6 ÷ 2 = 3.When two negative numbers divide, the answer also has a positive sign, e.g., (-6) ÷ (-2) = 3.When the numbers being divided have opposite signs, the answer has a negative sign, e.g., (-6) ÷ 2 = -3 or 6 ÷ (-2) = -3.As for the significant figures, the final answer should have the same number of significant figures as the number with the fewest significant figures before the division. For example, if you are dividing 23 by 448, limit the final reported answer to two significant figures.Remember, when performing calculations, significant figures are important for maintaining accuracy based on the precision of the data you start with.
When asked to factor the trinomial 4x2 + 20x + 25, a student gives the answer (2x - 5)(2x - 5). what is one thing wrong with this answer?
Answer:
The minus signs should be plus signs
The required factor of the given trinomial is (2x+5)(2x + 5).
Given that,
When asked to factor the trinomial 4x² + 20x + 25, a student gives the answer (2x - 5)(2x - 5). the mistakes in the solution is to be justified.
What is the factors?
factors can be defined by splitting the value into multipliable values.
Here,
Given trionomial,
= 4x² + 20x + 25,
= 4x² + 10x + 10x + 25
= 2x(2x + 5) + 5 (2x + 5)
= (2x + 5)(2x + 5)
Thus, the required factor of the given trinomial is (2x+5)(2x + 5).
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An airline claims that the no-show rate for passengers booked on its flights is less than 6%. of 380 randomly selected reservations, 18 were no-shows. assuming that this data is used to test the airline's claim, find the p-value for the test. 0.3508 0.1499 0.1230 0.0746
The p-value in this context represents the probability that the no-show rate is indeed less than 6%, given the collected sample data. It is calculated using a test statistic formula and compared to a chosen significance level to determine whether to reject or not reject the null hypothesis (the airline's claim). The correct p-value can't be identified from the provided options without further details or calculations.
Explanation:To answer your question, we first need to understand the concept of a p-value and how to calculate it. The p-value is calculated in a hypothesis test and it's the probability of getting sample data like ours, or more extreme, if the null hypothesis is true.
The null hypothesis, in this case, would be the claim that the airline's no show rate is less than 6%.The alternative hypothesis would be that the no-show rate is 6% or higher.We know that 18 out of 380 randomly selected reservations were no-shows. So, we can use the test statistic formula to calculate the p-value which represents the probability that the no-show rate is less than 6% if our null hypothesis is true. The options provided here (0.3508, 0.1499, 0.1230, 0.0746) seem to be possible outcomes of that calculation.
Depending on the result of this calculation, we would then determine whether to reject the null hypothesis or not. If the p-value is less than or equal to our significance level (say 0.05 or 5%), then we reject the null hypothesis. Conversely, if the p-value is greater than our significance level, we do not reject the null hypothesis and we can say there is not enough evidence to support the claim.
Unfortunately, without further information or calculations, we can't definitively identify the correct p-value from the options provided in your question.
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the length of a rectangle is 2 inches less than twice its width. If the perimeter of the rectangle is 74 inches, what is the area of the rectangle
The table below shows the fifth roots of different numbers:
Number (x) 32 −32 243 −243
Fifth root of the number (y) 2 −2 3 −3
Part A: Does the table represent y as a function of x? Justify your answer. (5 points)
Part B: The total cost f(x), in dollars, for renting a boat for x hours is shown below:
f(x) = 7x + 5
What is the value of f(5) and what does f(5) represent? (5 points)
The temperature, t, in Burrtown starts at 25°F at midnight, when h = 0. For the next few hours, the temperature drops 3 degrees every hour. Which equation represents the temperature, t, at hour h?
Answer: t= -3h + 25
Step-by-step explanation: this is the correct answer apex approved
The equation represents the temperature, t, at hour h is t = 25 - 3h.
What is an equation?An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
According to the question
The temperature, t, in Burrtown starts at 25°F at midnight, when h = 0.
For the next few hours, the temperature drops 3 degrees every hour.
⇒ t = 25 - 3h
Hence, the equation represents the temperature, t, at hour h is t = 25 - 3h.
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10 points! I will thanks, rate, and give best answer!!
Find the 4th term if the sequend in which a 1 = 2 and a n+1 = -4a n + 2
There are 7 black marbles and 9 white marbles in a bag. what is the probability of drawing 2 black marbles then a white marble without replacement
Find all solutions to the equation. cos x = sin x
1)The square shown has a perimeter of 32 units. The square is rotated about line k.
What shape is created by the rotation and what is the approximate circumference of the base?
Circumference of a circle: C = 2πr
a cone with a base circumference of about 25 units
a cone with a base circumference of about 50 units
a cylinder with a circumference of about 25 units
a cylinder with a circumference of about 50 units
2) The equilateral triangle shown is rotated about line a. Each side of the triangle measures 20 mm.
What shape is created by the rotation and what is the approximate circumference of the base?
Circumference of a circle: C = 2πr
a cylinder with a circumference of about 63 mm
a cylinder with a circumference of about 126 mm
a cone with a base circumference of about 63 mm
a cone with a base circumference of about 126 mm
1) The shape created by rotating a square about a line is a right circular cylinder. The approximate circumference of the base is about 25 units.
2) The shape created by rotating an equilateral triangle about a line is a cone. The approximate circumference of the base is about 63 mm.
How to determine solid formed after rotating a plane shape1) The shape created by rotating a square about a line is a right circular cylinder. The approximate circumference of the base is about 25 units.
Rotating a square about line k creates a right circular cylinder. The base, retaining the square's shape, has a circumference equal to the square's perimeter. With a square perimeter of 32 units
Perimeter of square = 4L
32 = 4L
L = 32/4 = 8 units
Radius of circular base of cylinder = 8/2 = 4 units
Circumference = 2πr
C = 2 * 3.142 * 4 = 25.136 units
The cylinder's base circumference is about 25 units,
2) The shape created by rotating an equilateral triangle about a line is a cone. The approximate circumference of the base is about 63 mm.
Rotating an equilateral triangle about a line creates a cone. The base retains the triangle's shape, and the circumference is equal to the triangle's perimeter.
With each side measuring 20 mm
Radius of cone = 20/2 = 10 mm
Circumference of base = 2πr
C = 2*3.142*10 = 62.884 mm
So,
Circumference of the base is approximately 63 mm
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Complete question
Stacy needed to fill her gas tank for a road trip. if she spent $45.87 and purchased 11 gallons how much did each gallon cost?
You need to stabilize a flagpole by string in a guy-wire from the top of a flagpole to the ground. The pole is 15 feet tall and angle of elevation is 70 degrees. Using trig ratios calculate how much wire is needed
The length of the wire needed is:
15.9625 feet
Step-by-step explanation:We will model this problem with the help of a right angled triangle such that the side opposite to the angle 70 degree is: 15 feet.
Now, we are asked to find the amount of wire used i.e. we are asked to find the hypotenuse of the right angled triangle.
We will use the sine trignometric ratio as follows:
[tex]\sin 70=\dfrac{15}{x}\\\\i.e.\\\\x=\dfrac{15}{\sin 70}\\\\i.e.\\\\x=\dfrac{15}{0.9397}\\\\i.e.\\\\x=15.9625\ feet[/tex]
how many leaves on a tree diagram are needed to represent all possible combinations tossing a coin 3 times
Jessica is baking a cake. the recipe says that she has to mix 96 grams of sugar into the flour. jessica knows that 1 cup of this particular sugar has a mass of 128 grams. she added 1/2 of a cup of sugar into the flour. should jessica add more sugar to make the exact recipe, or did she go over by what amount?
Answer:
she needs to add 32 grams. this is 1/4 cups
Step-by-step explanation:
You made two deposits to your bank account this month. One deposit was $17.92, and the second deposit was $15.33. Your balance at the end of the month is $72.31, and you made no withdrawals. Write and evaluate an expression for your balance at the beginning of the month.
A. $72.31 + ($17.92 – $15.33); $74.90
B. $72.31 – $17.92 – $15.33; $39.06
C. $72.31 + $17.92 + $15.33; $105.56
D. $72.31 – ($17.92 – $15.33); $69.72
To find the beginning balance, subtract total deposits from the end balance: $72.31 - ($17.92 + $15.33) = $39.06.
The correct option is: B. $72.31 - $17.92 - $15.33; $39.06
To find the balance at the beginning of the month, we need to subtract the total amount of deposits from the balance at the end of the month.
Given:
- Balance at the end of the month: $72.31
- First deposit: $17.92
- Second deposit: $15.33
We can use the following expression to find the balance at the beginning of the month:
[tex]\[ \text{Balance at the beginning of the month} = \text{Balance at the end of the month} - (\text{First deposit} + \text{Second deposit}) \][/tex]
Now, let's evaluate this expression to find the correct option.
The expression to find the balance at the beginning of the month is:
[tex]\[ \text{Balance at the beginning of the month} = \$72.31 - (\$17.92 + \$15.33) \][/tex]
[tex]\[ \text{Balance at the beginning of the month} = \$72.31 - \$33.25 \][/tex]
[tex]\[ \text{Balance at the beginning of the month} = \$39.06 \][/tex]
So, the correct option is: B. $72.31 - $17.92 - $15.33; $39.06.
Andrea can clean a house 4 times as fast as Denise. When they work together, Andrea and Denise can clean a large house in 8 hours. How many hours would it take Denise to clean the house by herself?
20
15
40
5
Answer:
8 hours
Step-by-step explanation:
A&D can clean a house in 8 hours together.
Proportionally, Denise works at x. Andrea works at 4x. There is a total of 5x.
Out of the 5x, Denise accounts for x.
x/5x = 1/5 of the work over 8 hours.
1/5 ( Denise's time for cleaning the whole house) = 8 hours.
Multiply both sides by 5:
5(1/5)(Denise's time for cleaning the whole house) = 5*8
Denise's time for cleaning the whole house = 40 hours
I like this method better...
That means in ONE hour, they get 1/8 of the job done.
Let's say Denise takes x hours to clean the house.
In one hour, she would do 1/x of the job (x can't be 0 hours).
Since Andrea does the house 4 times as fast as Denise, who takes x hours to do the job, Andrea takes x/4 hours.
In one hour, Andrea does 4/x of the job.
In one hour the part of the job Andrea does, plus the part of the job Denise does, must total 1/8.
(4/x) + (1/x) = 1/8
5/x = 1/8
Cross multiply:
x = 40
So it would take Denise 40 hours to clean the house by herself. (She's not really that efficient, or the house was REALLY dirty.
Andrea takes x/4 hours or 40/4 = 10 hours to clean the house by herself.
So with a little help from Denise, Andrea decreases her time to clean the house from the 10 hours it would take by herself to 8 hours.
i need help find the volume of this hexagon based pyramid!
please write steps and its ok to have more than one person answering
Use Gauss-Jordan elimination to solve the following system of equations. 3x + 5y = 7 6x − y = −8 A. x = 2, y = 1 B. x = 5, y = 6 C. x = 3, y = −1 D. x = −1, y = 2
Devon is trying to find the unit price on a six pack of drinks on sale for $2.99 his sister says that at that price each drink should cost over $2 is she correct and how do you know if she's not how would Devon's sister find the correct price
I dont understand
Determine the equation of the inverse of y=-4/x+1
The inverse is y=-a/x-b where a = _____ and b = ___
Solve 4 log12 2 + log12 x = log12 96. Choose one answer.. a. x = 88. b. x = 80. c. x = 12. d. x = 6
Answer:
Option (d) is correct.
The solution of x for the given equation [tex]4log_{12}2\:+\:log_{12}x=log_{12}96[/tex] is 6.
Step-by-step explanation:
Given : [tex]4log_{12}2\:+\:log_{12}x=log_{12}96[/tex]
We have to solve for x.
Consider the given equation [tex]4log_{12}2\:+\:log_{12}x=log_{12}96[/tex]
Subtract [tex]4\log _{12}\left(2\right)[/tex] both side, we have,
[tex]4\log _{12}\left(2\right)+\log _{12}\left(x\right)-4\log _{12}\left(2\right)=\log _{12}\left(96\right)-4\log _{12}\left(2\right)[/tex]
Simplify, we have,
[tex]\log _{12}\left(x\right)=\log _{12}\left(96\right)-4\log _{12}\left(2\right)[/tex]
Consider Right side of above,
[tex]\log _{12}\left(96\right)-4\log _{12}\left(2\right)[/tex]
Apply log rule, [tex]\:a\log _c\left(b\right)=\log _c\left(b^a\right)[/tex]
[tex]4\log _{12}\left(2\right)=\log _{12}\left(2^4\right)[/tex]
[tex]=\log _{12}\left(96\right)-\log _{12}\left(2^4\right)[/tex]
Again applying log rule, [tex]\log _c\left(a\right)-\log _c\left(b\right)=\log _c\left(\frac{a}{b}\right)[/tex]
[tex]\log _{12}\left(96\right)-\log _{12}\left(2^4\right)=\log _{12}\left(\frac{96}{2^4}\right)[/tex]
Simplify, we have,
[tex]=\log _{12}\left(6\right)[/tex]
[tex]\log _{12}\left(x\right)=\log _{12}\left(6\right)[/tex]
when log have same base,
[tex]\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\quad \Rightarrow \quad f\left(x\right)=g\left(x\right)[/tex]
Thus, x = 6
Thus, The solution of x for the given equation [tex]4log_{12}2\:+\:log_{12}x=log_{12}96[/tex] is 6.
Answer:
D is the correct answer for the given equation.
A new computer virus can enter the system through an email or through a webpage. there is a 30\% chance of receiving this virus through the email. there is a 40\% chance of receiving it through the webpage. also, the virus enters the system simultaneously through the email and the webpage with probability 0.15. what is the probability that the virus does not enter the system at all?
A polynomial p(x) has a remainder of 4 when divided by (x+1) and a remainder of 7 when divided by (x-2) what will be the remainder when divided by (x+1)(x-2)
In the diagram, PN¯¯¯¯¯ is the perpendicular bisector of AB¯¯¯¯¯ and is also the angle bisector of ∠CPD. If m∠CPD = x, which quantity is equal to sin ∠DPB?
sin x2
sinx2
cosx2
cos x2
Since ∠CPD = x and segment PN is the angle bisector of this angle, therefore segment PN equally divides ∠CPD into two angles. Which means that:
∠CPN = ∠NPD = x / 2
Further, segment PN is also the perpendicular bisector of AB which further means that the intersection formed by PN and AB creates a right angle (90°). Therefore:
∠NPD + ∠DPB = 90°
x/2 + ∠DPB = 90°
∠DPB = 90 – x/2
Therefore:
sin∠DPB = sin(90 – x/2) which is not in the choices
However we know that the relationship of sin and cos is:
sin(π/2 - θ) = cos θ
Where,
π/2 = 90
θ = x/2
Therefore:
sin(90 – x/2) = cos(x/2)
Answer:
cos(x/2)
The quantity which is equal to sin ∠DPB is:
cos(x/2)What is an Angle?This refers to the figure which is formed by two rays with a common endpoint.
Hence, we know that
∠CPN = ∠NPD = x / 2If we segment PN which is the bisector of AB, it would crerate angle 90 and this would give us:
∠NPD + ∠DPB = 90°x/2 + ∠DPB = 90°
∠DPB = 90 – x/2
With this in mind, there is the relation between sin and cos, which would be:
sin(π/2 - θ) = cos θWe are aware that
π/2 = 90θ = x/2Hence,
sin(90 – x/2) = cos(x/2)
=cos(x/2)
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How do I solve this? (Geometry)
A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000?
Using the unitary method, we can estimate that $2000 will be spent on the purchase of 250,000 sheets of paper.
What is unitary method?The unitary method is a technique in mathematics for solving a problem by finding the value of a single unit, I.e.,1,(by dividing) and then finding the necessary value by multiplying the single unit value.A method of solving a problem that involves first determining the value of a single unit, And then multiplying that value to determine the required value.According to the question,
A company can buy packages of 500 sheets of paper for $4. At that rate, how much paper can be bought for $2000?let the number of paper be "X".$4=500$2000= 250,000Hence we can say that Using the unitary method, we can estimate that $2000 will be spent on the purchase of 250,000 sheets of paper.
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A tennis racket normally costs $6060. the tennis racket is on sale for 60 60% off. what is the sale price of the tennis racket?
A kayaker spends a morning paddling on a river. She travels 9 miles upstream and 9 miles downstream in a total of 6 hours. In still water, she can travel at an average speed of 4 miles per hour. What is the average speed of the river's current in miles per hour?
A) 1 mi/h
B) 2 mi/h
C) 3 mi/h
D) 1.5 mi/h
Average speed is the ratio of the total distance traveled to the total time taken. The average speed of the river's current is 2 mi/h.
What is Average speed?Average speed is the ratio of the total distance traveled to the total time taken.
As we know that the total time taken by the boat to travel upstream and downstream is 6 hours. And the distance traveled by Kayaker is 9 miles, each time while going upstream and downstream.
We know that when the boat is traveling upstream the water current will try to resist the boat, therefore, the speed of the boat while going upstream is (4-x), where x is the speed of the boat. Similarly, the speed of the boat when going downstream will be (4+x), as the water stream will try to provide a push to the boat. Therefore, the total time taken by the Kayaker can be written as,
Total Time
= Time taken while going upstream + Time taken while going downstream
[tex]\rm 6 = \dfrac{Distance\ upstream}{Speed\ upstream} + \dfrac{Distance\ Downstream}{Speed\ Downstream}[/tex]
[tex]\rm 6 = \dfrac{9}{(4+x)} + \dfrac{9}{(4-x)}[/tex]
Taking the LCM,
[tex]6 = \dfrac{9(4+x)+9(4-x)}{(4+x)(4-x)}\\\\6\times (4+x)(4-x) = 9(4+x)+9(4-x)\\\\6(16-x^2) = 36+9x+36-9x\\\\96 - 6x^2 = 72\\\\-6x^2 = 72-96\\\\6x^2 = 24\\\\x^2 = 4\\\\x =2[/tex]
Hence, the average speed of the river's current in miles per hour is 2 mi/h.
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James wants to go to a concert with his friends. The tickets to the show cost $10 each. If James buys x tickets at a cost of c dollars, represent c as a function of x.
Answer:
C = f(x)=10x
Step-by-step explanation:
plato answer
What is the solution to 2x-8<12 ?
A. X<2
B. X<8
C. X<10
D. X<40
Answer:
x < 10
Step-by-step explanation: