Answer:
Maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm
Step-by-step explanation:
Surface area of box
[tex]4xy+x^2=120\\\Rightarrow y=\dfrac{120-x^2}{4x}[/tex]
Volume of box is
[tex]V=x^2y\\\Rightarrow V=x^2\times \dfrac{120-x^2}{4x}\\\Rightarrow V=\dfrac{120x-x^3}{4}\\\Rightarrow V=30x-\dfrac{1}{4}x^3[/tex]
Differentiating with respect to [tex]x[/tex]
[tex]\dfrac{dV}{dx}=30-\dfrac{3}{4}x^2[/tex]
Equating with zero
[tex]30-\dfrac{3}{4}x^2=0\\\Rightarrow x^2=\dfrac{30\times 4}{3}\\\Rightarrow x^2=40\\\Rightarrow x=6.32[/tex]
Double derivative of the volume
[tex]\dfrac{d^2V}{dx^2}=-\dfrac{6x}{4}=-\dfrac{6\times 6.32}{4}=-9.48<0[/tex]
So, the volume is maximum at [tex]x=6.32[/tex]
[tex]y=\dfrac{120-x^2}{4x}=\dfrac{120-40}{4\times \sqrt{40}}\\\Rightarrow y=3.16[/tex]
So, the maximum length and breadth of the box is 6.32 cm and the height of the box is 3.16 cm.
Returning to a possible class quiz, Sue believes there will be a quiz and offers 3:2 odds, Torik does not and offers 3:1 odds. The odds Torik is offering are enticing, and you have $200 where you can afford to lose up to $20. Now, one possibility is to bet $20 only with Torik; if there is not a quiz, he wins and keeps your $20. If there is quiz, you win and he owes you $60. But, by hedging, you can bet more without incurring any greater risk. Explain what to do and how much you can earn if there is a quiz.
Answer and explanation:
The hedging strategy is one where an individual is able to hold two opposing positions such that he is able to protect either position from profit or loss as each move in opposite directions. For example in this situation, if Sue wants to hedge her bets here, she would need to place a bet that there will be a quiz and also place a bet that there will be no quiz. In this way she uses up to $40, $20 for no quiz and $20 for a quiz. If for instance it goes in Torik's favour and there is no quiz, Sue loses $20 but also gets that $20 back. If it goes in Sue's favour, then she makes $60
5( 3+7) =
Distributive property solving?
Answer:
50
Step-by-step explanation:
5(3 + 7)
15 + 35 = 50
Dan spends 1/4 of his wages on rent and 2/3 on food. If he makes £264 per week, how much money does he have left?
Answer:
Step-by-step explanation:
¼ + ⅔ = 11/12
1 - 11/12 = 1/12
He has 1/12 of £264 = £22 left
Given the following sequence, how many circles will be in the 6th term?
Answer:
25 i think
Step-by-step explanation:
What are the zeros of the quadratic equation y=5(2x−1)(x+3)?
Explain whether the following statement is true or false. The function notation f-1(x) means 1/f(x)
Answer:
True
Step-by-step explanation:
f-1(x) otherwise known as the inverse of f(x) is the mathematical equivalent as 1/f(x).
Being inverse simply means that it "reverses" the operation that was applied to it with the original function .
For example: suppose f(x) = x+1, then if x = 1, f(1) = 1+1 =2
Now if we do f-1(x) or 1/f(x), then 1/f(1) = 1/1 +1 = 1/2
So, 2/1 is in fact the inverse of 1/2.
Hence, f-1(x) is the same as 1/f(x)
Write the rate as a unit rate:
400 miles in 8 hours
Answer:
50miles/hour
Step-by-step explanation:
400/8 is 50.
The rate as a unit rate of 400 miles in 8 hours is 50 miles.
What is difference between rate and unit rate ?"The process of breaking down the cost to a smaller unit reveals the unit rate of the product. Since rate is a ratio that compares two different units."
Based on the given conditions,
Rate as a unit rate :
= [tex]\frac{400}{8}[/tex]
Cross out the common factor
= 50 miles
Hence, the rate as a unit rate of 400 miles in 8 hours is 50 miles.
Learn more about rate and unit rate here
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Exercise 1.10.4: Mathematical statements into logical statements with nested quantifiers. info About Translate each of the following English statements into logical expressions. The domain is the set of all real numbers. (a) There are two numbers whose ratio is less than 1. (b) The reciprocal of every positive number is also positive. (c) There are two numbers whose sum is equal to their product. (d) The ratio of every two positive numbers is also positive. (e) The reciprocal of every positive number less than one is greater than one. (f) There is no smallest number. (g) Every number other than 0 has a multiplicative inverse. (h) Every number other than 0 has a unique multiplicative inverse.
Answer:
З x,y : ( x/y < 1, y/x < 1 )
Step-by-step explanation:
This is a bit somehow, I really do hope it doesn't confuse you. Here's your solution.
The domain in this question is one with a set of all real numbers. These real numbers needs the logical expressions of the English statements to be expressed with respect to real number. And so we're having
A) З x,y : ( x/y < 1, y/x < 1 )
B) ∀ Y : ( Y > 0 = 1/Y > 0 )
C) з x,y : ( x+y = xy )
D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))
E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )
F) n ( ( з x ∀ y ( x <y ) )
G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))
H) ∀x ( (x≠0) = ( з! y (xy = 1))
What is the slope of line b
You received a special shopper
discount card for your birthday for
10% off any purchase. You decide to
buy a pair of sneakers costing $65
and use your discount card. If sales
tax of 8% is applied after the
discount, what was your final price
for the sneakers?
simplify: (2x^2y^3)3 x (4xy)2
Answer: 48yx^1+2y^3
Step-by-step explanation:
In 2000, the average plane ticket cost $323.85. Now, the average place ticket is $342.98. Determine the change in price of the plane ticket.
Answer:
19.13
Step-by-step explanation:
You take 342.98 and you minus 323.85
Which measurements are equal to 671 decimeters? Check all that apply.
67,100 millimeters
0.671 kilometers
67.1 hectometers
6.71 decameters
6,710 centimeters
Answer:
d and b
Step-by-step explanation:
Answer:
67100 millimeters
Step-by-step explanation:
Write an equation in slope-intercept form for the table.
Answer:
y=4x+3
Step-by-step explanation:
y=mx+c where m is the slope and c is the intercept.
To find m, get two points and plug them into the formula (y2-y1)/(x2-x1):
(0,3) and (2,11)
m=(11-3)/(2-0)
=8/2
=4
y=4x+c
To find c, plug in one of the points, eg. (3,15)
15=4(3)+c
15=12+c
c=3
y=4x+3
You are having a picnic and need to buy paper plates. A store sells
two different brands of paper plates. Brand A costs $.96 for 12 paper
plates, and Brand B costs $1.40 for 20 paper plates. How much
money will you save if you buy 60 of the brand of paper plates with
the lower unit price?
Which table represents the statement "Brian rides a bicycle at a rate of 12 meters per second"? Seconds /meters
Answer:
D
Step-by-step explanation:
The rate of 12 meters per second means that the constant of proportionality (k) or slope = 12.
That is m/s = 12.
The table that has a constant of proportionality that equals 12 is the table that represents the statement given.
The table in option D has a constant of proportionality of 12, since the ratio of m/s for all its given pair of values will give us 12 all through.
Answer:
I think your answer is B
Step-by-step explanation:
Pls need help give the correct answer:))
When reflecting across the x axis, the x value stays the same and the y value becomes the opposite sign.
The new point would be (-8, 12)
Solve the inequality
Answer: Hi there, the answer should be the third option v < -8.
How many solutions can be found for the system of linear equations represented on the graph
A)no solution
B)one solution
C)two solutions
D)infinitely many solutions
Answer:
1. 2/y-1
2. y-2
Step-by-step explanation:
The equation in blue is 2/y-1
The equation in red is y−2
So the answer is one solution
Richard earns,php 32,500.00 a year he spend 16% his salary on rent.how much does richard spend on rent?
Answer:
He would spend $5,200 a year.
Step-by-step explanation:
32,500 x 0.16 = 5,200
Someone help me please!
Solve the equation 1/4t + -6 = -4
Answer:
The answer is t=8
Step-by-step explanation:
simplify both sides or the equation, then isolate the variables
Answer:
t = 8
Step-by-step explanation:
Isolate the variable, t. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, add 6 to both sides of the equation:
1/4t + (-6) = -4
1/4t - 6 = -4
1/4t - 6 (+6) = -4 (+6)
1/4t = -4 + 6
1/4t = 2
Next, multiply 4 to both sides of the equation to isolate the variable, t:
4 * (1/4)t = (2) * 4
t = 2 * 4
t = 8
t = 8 is your answer.
~
I need help please.
Answer:
A. 88.75%
Step-by-step explanation:
Luis bought 8 2/5 pounds of oranges for his soccer team. The team ate 4 5/8 ponds of oranges. About how many oranges are left
Answer:
3.775
Step-by-step explanation:
Answer:
3.775 OR 151/40 OR 3 31/40
Step-By-Step Explanation:
Subtract 8 2/5 by 4 5/8
Given that line AD ll to line EH, find the measure of
Answer:
x=7.5
Step-by-step explanation:
Since AD II EH, ∠CBD=∠BFH (alternate angles)
2x+60=10x
8x=60
x=7.5
Answer:
x = 7.5
each angle measures 75°
Step-by-step explanation:
the two angles are corresponding, meaning they are equal
10x = 2x + 60
8x = 60
x = 7.5
if somone can help.
Answer:
c cause it says length = 5x
I NEED HELP. This id due in 2 hours, i dont get it pls help me. THis is worst 60% of my grade make sure its correct pls and thanks
Answer:
Four pounds of strawberries costs $12: y=3x
Ben reads 5 novels per month: y=5x
Maya puts $4 into her bank account each week: y=4x
Every day a kindergarten class chooses randomly one of the 50 state flags to hang on the wall, without regard to previous choices. We are interested in the flags that are chosen on Monday, Tuesday and Wednesday of next week. 30 Experiments with random outcomes (a) Describe a sample space ± and a probability measure P to model this experiment. (b) What is the probability that the class hangs Wisconsin’s flag on Monday, Michigan’s flag on Tuesday, and California’s flag on Wednesday? (c) What is the probability that Wisconsin’s flag will be hung at least two of the three days?
Answer:
a) [tex]S=50[/tex]
[tex]P(X)=0.02[/tex]
b) [tex]P(W,M,C)=8*10^-^6[/tex]
c) [tex]P(W_2_3)=1.18*10^-^3[/tex]
Step-by-step explanation:
From the question we are told that
Sample space S=50
Sample size n=30
a)Generally the sample space S is
[tex]S=50[/tex]
The probability measure is given as
[tex]P(X)=\frac{1}{50}[/tex]
[tex]P(X)=0.02[/tex]
b)
Generally the probability that the class hangs Wisconsin’s flag on Monday, Michigan’s flag on Tuesday, and California’s flag on Wednesday is mathematically given as
Probability of each one being hanged is
[tex]P(X)=\frac{1}{50}[/tex]
Therefore
[tex]P(W,M,C)=\frac{1}{50} *\frac{1}{50}* \frac{1}{50}[/tex]
[tex]P(W,M,C)=\frac{1}{125000}[/tex]
[tex]P(W,M,C)=8*10^-^6[/tex]
c)Generally the probability that Wisconsin’s flag will be hung at least two of the three days is mathematically given as
Probability of two days hung +Probability of three days hung
Therefore
[tex]P(W_2_3)=^3C_2 (1/50) * (1/50) * (49/50) +^3C_3 (1/50) * (1/50) *(1/50)[/tex]
[tex]P(W_2_3)=148 / 125000[/tex]
[tex]P(W_2_3)=1.18*10^-^3[/tex]
PLEASE PLEASE IM BEGGING HELP ME!! Translate this sentence into an equation.
72 is the product of 4 and Gail's score.
Use the variable g to represent Gail's score.
Answer: Translate this sentence into an equation. The product of Greg's age and 6 is 102. Use the variable g to represent Greg's age.
Ans :-g*6=102
Step-by-step explanation: hope it help
PLEASE MARK Me BRAINLYEST PLEASE!!! PLEASE!!!! I REALLY Need IT PLEASE!
Recall the Spice Girls Emporium example. A list of useful information is given below. n = 36 The sample mean income is $41,100 The population standard deviation is estimated to be $4,500 What if we wanted to change our level of confidence to be 99%? What would our new margin of error be? Your answer should be given as an integer.
Answer: Margin of error = 1932
Step-by-step explanation: Margin of Error is the amount of variation a survey's results have. In other words, it is understood as the measure of variation one can see if the same survey was taken multiple times.
Margin of error is calculated as [tex]z\frac{\sigma}{\sqrt{n}}[/tex]
z is z-score related to the percentage of confidence, in this z = 2.576
σ is population standard deviation
n is how many individuals are there in the sample or population
With a new level of confidence of 99%:
ME = [tex]2.576.\frac{4500}{\sqrt{36}}[/tex]
ME = 2.576(750)
ME = 1932
The new margin of error would be 1932.
Which ordered pair represents the solution to:
2x + 3y = 22
| 3x + 2y = 18
O A. (6,2)
OB. (-8,16)
OC. (8.-16
OD. (-2,6)
O E. (2,6)