Answer:
The numbers are;
x = 100/3, y = 100/3, z = 100/3
Step-by-step explanation:
Given the data in the question;
so let the numbers be; x , y and z
so
x + y + z = 100
now
G(x,y,z) = x + y + z - 100
F(x,y,z) = xyz
Fx = yz, Gx = 1
Fy = xz, Gy = 1
Fz = xy, Gz = 1
Fx = λ × Gx
yz = λ
Similarly, xz = lambda
And xy = lambda
From above clearly, x = y = z
x + y + z = 100
so
3x = 100
x = 100/3
since, x = y = z therefore, each number is equal to 100/3
x = 100/3, y = 100/3, z = 100/3
We want to find 3 positive numbers such that their sum is 100 and the product is maximum.
The maximum product is P = 37,025.93
Let's say that our 3 numbers are:
A, B, and C.
We must have:
A + B + C = 100
The product of these 3 numbers is:
P = A*B*C
For the restriction, we can write:
A = 100 - B - C
Now we can replace that in the product equation to get:
P = (100 - B - C)*B*C
P = 100*B*C - C*B^2 - B*C^2
Now we want to maximize this, to do it, we need to find the zeros of the derivate of the function. This is a two-variable function, but the dependence on C is exactly the same as the dependence on B, so we can find the zero of deriving with respect to one of these only.
dP/dB = 100*C - 2*C*B - C^2 = 0
C*(100 - 2*B - C) = 0
One solution is C = 0, the other is:
C = 100 - 2*B
And from the first restroctopm:
A + B + C = 100
we can get:
C = 100 - A - B
Then:
100 - A - B = 100 - 2*B
Then we get A = B
And if we derive the equation for C instead of B, we will get similar results that will lead to:
A = B = C.
This is what maximizes the product, then we have:
A + B + C = 3*A = 100
A = 100/3 = 33.33
P = (33.33)^3 = 37,025.93
This is the maximum product.
If you want to learn more, you can read:
https://brainly.com/question/11212148
Follow the steps to finish solving the equation -3x+ 18=7x
1. Add 3x to both sides to isolate the variable term
2.Divide both sides by 10
PLEASE HELP WILL GIVE BRAINLYEST AND 20 POINTS
Answer:
9/5=x
Step-by-step explanation:
-3x+ 18=7x
-3x+3x+ 18=7x +3x
18=10x
18/10=10x/10
9/5=x
Answer:
Step-by-step explanation:
- 3x + 18 = 7x
- 3x + 3x + 18 = 7x + 3x ⇔ 18 = 10x
[tex]\frac{18}{10}[/tex] = [tex]\frac{10x}{10}[/tex] ⇔ 1.8 = x
x = 1.8
The perimeter of a rectangle is 212. The length is 16 more than 5 times the width.
Answer: Length is 15 and width is 91
Step-by-step explanation:
If the length is 16 more than 5 times the width, that means:
let's say
x=length
y=width
2x+2y=212
If the length is 16 more times than 5 times the width, that means
y=5x+16
now we can substitute all y's for 5x+16:
2x+(5x+16)2=212
=2x+10x+32=212
=12x+32=212
=12x=180
x=15
If the length is 15, the width is
15*2+2y=212
=30+2y=212
=182/2
y=91
Answer:
width 91 length 15
Step-by-step explanation:
2l+2w=212
l=5w+16
2l+2w=212, l=5w+16
substitute
2(5w+16)+2w=212
12w+32=212
12w=180
w=15
L=5w+16
L=5(15)+16
L=91
4x^10 + 9x^10 what is the sum or difference
Answer:
[tex]13x^1^0[/tex]
Step-by-step explanation:
[tex]4x^1^0+9x^1^0[/tex]
Add similar elements:
[tex]4x^1^0+9x^1^0=13x^1^0[/tex]
List all sets that -1/3 belongs to.
Answer:
dfffffffff
Step-by-step explanation:
xcdsw23456iu76
complete the point-slope equation of the line through (1,0) and (6,-3)
Answer: y- (-3)= -3/5 (x-6)
Step-by-step explanation:
Answer this question please and i will give brainliest
Answer:
false the answer is false
Step-by-step explanation:
Please help i will give brainlest!
Answer:
6×1+9×1/10+4×1/100+7×1/1000
Step-by-step explanation:
Ben’s favorite deli says the average serving time is 12 minutes. Ben notices that the wait time at the deli varies at different times of day, before and after noon. His observations when the wait time is as advertised can be represented by the equation 2|x − 2| − 12 = 0. Solve for the times when the serving time is as advertised, relative to noon. Group of answer choices (THERES ALOT OF ANSWERS BE PREPARED) SELECT ALL THE ANSWER CHOICES.
4pm,
8pm,
9am,
3pm,
noon,
11am,
6pm,
9pm,
7am,
1pm,
2pm,
5pm,
10pm,
10am,
8am,
7pm,
6am,
Answer:
8 pm and 8 am
Step-by-step explanation:
Let us solve the equation
[tex]2|(x-2)|-12=0[/tex]
There is a modulus in the equation this means that one value of the modulus will be positive and the other will be negative
Let us solve for the positive first
[tex]2(x-2)-12=0\\\Rightarrow 2x-4-12=0\\\Rightarrow x=\dfrac{16}{2}\\\Rightarrow x=8[/tex]
Now we add this value with 12 noon
So
[tex]12+8=8\ \text{pm}[/tex]
Let us solve for the negative
[tex]2(-(x-2))-12=0\\\Rightarrow 2(2-x)-12=0\\\Rightarrow 4-2x-12=0\\\Rightarrow x=-\dfrac{8}{2}\\\Rightarrow x=-4[/tex]
So
[tex]12-4=8\ \text{am}[/tex]
The times when the serving time is as advertised is 8 pm and 8 am.
The value of 100 pennies is ___% of the value of a dollar
Answer:
The type of coins =pennies has = 100 pennies.
servant has a total number of 100 coins
The sum of the percentage and pennies = $100
Let us represent the number of nickels as which is _% = 55.4
The number of pennies as y
Step-by-step explanation:
Can someone help me please?
Answer:
the first one and the last three
Step-by-step explanation:
that should be it.
Can someone help? I really don’t understand this at all!
is this pathogroem therom?
What is 40x52 To the 7 power
Answer:
168,439,267,742,187,520,000,000
Step-by-step explanation:
40*52=2080
2080^7=168,439,267,742,187,520,000,000
please please help me!!
Answer:
slope is 4
Step-by-step explanation:
slope of the line is the diference in y /diference in x between any 2 points that belong to the line
slope=(10-2) / (3-1) = 8/2 =4
(I'LL GIVE BRAINLIEST AND EXTRA POINTS IF YOU HELP!!!)
Answer:
24/6048 = 252
Step-by-step explanation:
brainlest plz
and why does she have so many beads
Answer:
she said 24 only goes into 60 once, when in reality it can go in twice
An ice cream factory makes 310 quarts of ice cream in 5 hours. How many quarts can they make per hour?
3x -5y + 2z = -53
x - 7y - 4z = -37
5x+9y+2x = 57
Answer:
answer is 57
Step-by-step explanation:
3x-5y sshsbwisiehdducux sh
I need help I am in 3grade and I need help with it so if you can please help
Answer:
what do you need help with exactly?
Step-by-step explanation:
Answer:
your supposed to ask a question
Step-by-step explanation:
2x^3 + 10x^2 − 4x^2y − 20xy
Factor the entire expression completely. Show the steps of your work.
Answer:
2x ( x + 5 ) ( x − 2 y )
Step-by-step explanation:
1) factor out 2x from the equation
2) factor out x from the equation
3) factor out -2y from the equation
4) factor out x + 5 from the equation
2x ( x + 5 ) ( x − 2 y )
Which number line shows the solution to the inequality 5x + 3> - 17
The time taken by artisans A. B and C to do an
embroidery job is 15 hours, 18 hours, and 15 hours.
respectively. A, B, and C begin working together but
after 3 hours B is put on another job. How long will A
and C take to finish the embroidery job?
Answer:
3 hours 15mins
Step-by-step explanation:
in 1 hours time, A will complete 1/15 of the job, B will complete 1/18 and C 1/15.
After 3 hours, A completed 3/15 (aka 1/5) of the job, B 3/18 (aka 1/6) and C being the same as A.
total job done after 3 hrs is 1/5 + 1/6 + 1/5 which is 17/30 of the job
left: 13/30
in 1 hr, A and C will do 2/15 of the job (4/30)
therefore, no. of hours needed: 13/4 hours = 3.25 hours (3 hours 15mins)
How many 1 6 cup servings are in 3 4 cups of popcorn? (in simplest fraction form)
Answer: 8/17
Step-by-step explanation: 16 ÷ 34 = 8/17
Hope this helps ^_^
Pregnancy length (in days) is a normally distributed random variable with a mean of 266 days and a standard deviation of 16 days. Calculate the z-score for a pregnancy lasting 286 days. Do not round.
Answer:
it=552
Step-by-step explanation:
with rounding it = 550
The value of z-score for a pregnancy lasting 286 days will be;
⇒ z - score = 1.25
What is Standard deviation?Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
Mean = 266 days
Standard deviation = 16 days
Now,
We know that;
⇒ z - score = (X - μ) / σ
Substitute all the values, we get
⇒ z - score = (286 - 266) / 16
⇒ z - score = 20/16
⇒ z - score = 1.25
Thus, The value of z - score = 1.25
Learn more about the standard deviation visit:
https://brainly.com/question/475676
#SPJ5
How many pounds of grapes can I buy for $1.00?
2.09
Here you go! Hope it helps!
There are 19.3 cups of flour in a bag. The chef uses 2.9 cups for making cookies.
Then, he uses 1.2 cups of sugar and 5.1 cups of flour for making banana bread.
How many cups of flour are left?
Answer:
10.1 cups left
Hope this helps!
Can you pls give brainly if this helps
4.497 < 4.387
Is this true?
Answer:
Yes
Step-by-step explanation:
Can someone help me please
===================================================
Work Shown:
For any triangle, the three interior angles always add to 180
(4x-12) + (6x-17) + (2x+5) = 180
(4x+6x+2x) + (-12-17+5) = 180
12x - 24 = 180
12x = 180+24 ..... adding 24 to both sides
12x = 204
x = 204/12 ..... dividing both sides by 12
x = 17
We can use this x value to find the three angles
4x-12 = 4*17-12 = 56
6x-17 = 6*17-17 = 85
2x+5 = 2*17+5 = 39
As a check,
56+85+39 = 180
which confirms we have the right x value.
We see that 56 is the middle angle, so this is the second largest angle.
Sarah has saved 254 pound coins. She puts the pound coins into bags.
There are 20 pound coins in each full bag of coins. Sarah is going to take all her full bags of coins to the bank.
She can only take up to 5 full bags of coins to the bank each day.
Sarah wants to go to the bank on as few days as possible.
On how many days will Sarah need to go to the bank?
Answer:
Step-by-step explanation:
So for the fewest days it would be 3 days. The reason for that is because she has 254 pound coins. And she can inly take 5 bags to the bank a day, all of those 5 bags have 100 pound coins in them. If she take 2 days and get 200 pound coins to the bank. Then on the third day she would only have to bring three bags. So your answer for the fewest days possible is three days!
Hope it helps
The expression 2y + 2.7 is equal to for y = 4.
Answer:
10.7
Step-by-step explanation:
i am not certain but since y is the 4 you will have 2(4) + 2.7 so you get 8+2.7 since you do 2x4 then you add 8 and 2.7 to get 10.7
What is the value of the expression below?
-8+19+8
ОО
O 11
O 19
O 35
Answer:
the answer would be 19.
Step-by-step explanation:
-8+8=0
0+19=19
Answer:
19
Step-by-step explanation:
PLEASE NEED HELP URGENTLY!
Raul tried to find the midpoint between 5 & 3i and 12 + 7i. Check his work below.
Sum=(5+(-3))+(12+7)i
=2+19i
so the midpoint is 1+ 19over2 i
What mistake did Raul make?
AHe subtracted the values instead of adding them.
BHe did not add the corresponding parts of the complex numbers.
CHe found the sum instead of the average because he forgot to divide by two.
DHe added the numbers in the wrong order.
Answer:
B.He did not add the corresponding parts of the complex numbers.
Step-by-step explanation:
A mid point is a point that is of equal distance to two reference points.
Given: Find the midpoint of 5+(-3)i and 12+7i.
These expressions have two parts: the value and complex number parts.
Thus the addition ought to have been;
(5+(-3i)) + (12+7i) = (5 - 3i) + (12 + 7i)
= (5 + 12) + (-3i + 7i)
= 17 + 4i
The midpoint can be determined as:
[tex]\frac{(17 +4i)}{2}[/tex]
Thus it can be observed that Raul did not add the corresponding parts of the complex numbers.
Answer:
bbbbbbbbb
Step-by-step explanation: