Answer:
a) The function is: f(x, y) = x + y.
The constraint is: x*y = 196.
Remember that we must write the constraint as:
g(x, y) = x*y - 196 = 0
Then we have:
L(x, y, λ) = f(x, y) + λ*g(x, y)
L(x, y, λ) = x + y + λ*(x*y - 196)
Now, let's compute the partial derivations, those must be zero.
dL/dx = λ*y + 1
dL/dy = λ*x + 1
dL/dλ = (x*y - 196)
Those must be equal to zero, then we have a system of equations:
λ*y + 1 = 0
λ*x + 1 = 0
(x*y - 196) = 0
Let's solve this, in the first equation we can isolate λ to get:
λ = -1/y
Now we can replace this in the second equation and get;
-x/y + 1 = 0
Now let's isolate x.
x = y
Now we can replace this in the last equation, and we will get:
(x*x - 196) = 0
x^2 = 196
x = √196 = 14
then the minimum will be:
x + y = x + x = 14 + 14 = 28.
b) Now we have:
f(x) = x*y
g(x) = x + y - 196
Let's do the same as before:
L(x, y, λ) = f(x, y) + λ*g(x, y)
L(x, y, λ) = x*y + λ*(x + y - 196)
Now let's do the derivations:
dL/dx = y + λ
dL/dy = x + λ
dL/dλ = x + y - 196
Now we have the system of equations:
y + λ = 0
x + λ = 0
x + y - 196 = 0
To solve it, we can isolate lambda in the first equation to get:
λ = -y
Now we can replace this in the second equation:
x - y = 0
Now we can isolate x:
x = y
now we can replace that in the last equation
y + y - 196 = 0
2*y - 196 = 0
2*y = 196
y = 196/2 = 98
The maximum will be:
x*y = y*y = 98*98 = 9,604
Abby took an 8-question multiple-choice quiz. Suppose
that her probability of correctly answering any question is
0.75. What is Abby's probability of correctly answering
exactly 6 questions on the quiz?
O 0.311
0 0.623
O 0.240
0.089
Convert the rate 25 miles per hour to feet per second
Answer:
36.67 feet / second
Step-by-step explanation:We will be using Dimensional Analysis to solve this question
We are given the rate: 25 miles / hour
Converting the Miles to feet:
We know that 1 mile = 5280 feet
So, we can say that [tex]\frac{5280 feet}{1 mile}[/tex] = 1
Multiplying the Given rate by 1:
[tex]\frac{25 miles}{Hour}[/tex] * 1
(multiplying by 1 will not change the actual value of the expression)
[tex]\frac{25 miles}{Hour}[/tex] * [tex]\frac{5280 feet}{1 mile}[/tex] (since 5280 feet/ 1 mile = 1)
here, the 'mile' will cancel out and we will get:
[tex]\frac{25 * 5280 feet }{Hour }[/tex]
[tex]\frac{132000 feet}{Hour}[/tex]
Converting the Hours to Seconds:
We know that 1 hour = 3600 seconds
So, we can say that:
[tex]\frac{1 Hour}{3600 seconds}[/tex] = 1
Multiplying the Rate by 1:
[tex]\frac{132000 feet}{1 Hour} * 1[/tex]
(multiplying by 1 will not change the actual value of the expression)
[tex]\frac{132000 feet}{1 Hour} * \frac{1 Hour}{3600 seconds}[/tex] (since 1 hour / 3600 seconds = 1)
Here, the 'Hour' in the numerator and the denominator will cancel out to make:
[tex]\frac{132000 feet}{3600 seconds}[/tex]
which can be simplified to:
[tex]\frac{36.67 feet}{second}[/tex]
Therefore, 25 mph can also be written as 36.67 feet per second
A country’s daily oil production can be approximated by q(t)=0.013t^2-0.6t+5.27
What is the volume of the figure? Enter the answer in the box.
Answer:
217,600
Step-by-step explanation:
Multiply all the sides
Help! This is due today and I don’t know nothing
Answer:
1.A
2.A
3.B
4.B
Step-by-step explanation:
That the answer
Write the slope-intercept form of the equation of the line described. Through (-5, 2) parallel to y = 4
Solve for x helppp(10 points)
Answer:
x = n - m
Step-by-step explanation:
To solve for x we have to isolate it.
[tex]x^{2} \\[/tex] + [tex]m^{2}[/tex] = [tex]n^{2}[/tex]
First, let's subtract [tex]m^{2}[/tex] from both sides of the equation:
[tex]x^{2} \\[/tex] + [tex]m^{2}[/tex] - [tex]m^{2}[/tex] = [tex]n^{2}[/tex] - [tex]m^{2}[/tex]
Now the equation looks like this: [tex]x^{2} \\[/tex] = [tex]n^{2}[/tex] - [tex]m^{2}[/tex]
Now we have apply a square root to both sides to remove the exponent from the x: [tex]\sqrt{x^2}[/tex] = [tex]\sqrt{n^2 - m^2}[/tex]
The square root and the exponents cancel out on both sides and you're left with: x = n - m
To solve for x the equation is: x = n - m
I hope this helps! :)
A t-shirt printing company charges a one-time setup fee, plus a charge to print each t-shirt. The math club had 75 t-shirts printed for a cost of $424. The science club had 50 t-shirts printed for a cost of $299. What is the cost of having 170 t-shirts printed? *
Answer:
$826.70
Step-by-step explanation:
If 75 t-shirts cost $ 424, it implies that the value of each shirt is $ 5.65 (424/75). Now, in the case of the 50 shirts, the total value is $ 299, with which the value of each unit is $ 5.98.
Thus, we can see that in an increase of 50% of the units (from 50 to 75), the discount is of the order of, as it arises from the following calculation:
5.98 = 100
5.65 = X
((5.65 x 100) / 5.98) = X
94.48 = X
Thus, since 100 - 94.48 is 5.52, the discount made for the 25 shirts is 0.22% each unit (5.52 / 25). Thus, in the case of printing 170 t-shirts, taking into account this tariff system, and taking as a base price that of 50 t-shirts at $ 299, a discount of 0.22% would be made on each of the 120 remaining t-shirts. Thus, 120 t-shirts at $ 717.6 (5.98 x 120) would be added to the initial $ 299, on which a 26.4% discount (0.22 x 120) would be applied, with which the final price would be $ 527.7 (717 x 0.736).
Thus, the total price of the shirts would be $ 826.7 (that is, adding the base price of $ 299 plus the price of the 120 extra shirts of $ 527.7).
Can y’all pls solve this
Answer:
1.
x=2+5x=0+7x=4x+1+37x=x+2+42.
x=2-33x=-2-4x=2x+7-5x=4x+6-7everything is on the image, this is a timed test so it would mean alot if you could help
Answer:
no its not 3 goes to two letter so no
Step-by-step explanation:
In △LMN, S is the centroid. If NP=69 find SP.
Answer:
maybe in the 70s actually
Step-by-step explanation:
Answer:
23
Step-by-step explanation:
The centroid divides each median in a ratio of 2:1.
Please help. It’s not “yes, corresponding angles converse”
Answer:
Yes,Corresponding Angles
Step-by-step explanation:
any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.
Answer:
It is yes,corresponding angles
Step-by-step explanation:
Solve the following equation.
1/3 k + 80 = 1/2 k + 120
Answer:
2; 3; 80; 1; -40; 1; -240 (answered from left to right then the next line)
Step-by-step explanation:
This is a question on fractions and solving algebraic equations. If you wish to venture further into it/understand this topic better, you may want to follow my Instagram account (learntionary), where I post some of my own notes on certain topics and also some tips that may be useful to you :)
Answer:
240
Step-by-step explanation:
k/3+80=k/2+120
K/3-k/2=120-80
3k-2k/6=40
K/6=40
K=240.
So the value of k is 240.
A middle school mathematics teacher except a teaching position that pays 40,000 per year, each year the expected raise is $2000. How much total money with this teacher and teaching middle school math Mathematics over the first 30 years?
9514 1404 393
Answer:
$2,070,000
Step-by-step explanation:
The series of salaries has a first term of $40,000 and a common difference of $2,000. The sum of them is given by the formula ...
Sn = (2a1 +d(n -1))(n/2)
where a1 is the first term of the series, d is the common difference, and n is the number of terms.
In this problem, we have ...
a1 = 40,000; d = 2,000; n = 30
so the sum is ...
S30 = (2(40,000) +2,000(30 -1))(30/2) = (80,000 +58,000)(15)
S30 = 2,070,000
The teacher will earn $2,070,000 over 30 years on this salary schedule.
f (x) = 20 - (1.27)
growth or decay ?
Answer:
Decay...? Read below
Step-by-step explanation:
Assuming you meant to put 20 - (1.27)x, it is decay. As the x increases, the y decreases, making it decay.
Reduce the matrix
[1,2,-1;-1,3,3;0,2,-1]
to echelon form
Answer:
[1, 0, 0; 0, 1, 0; 0, 0, 1]
Step-by-step explanation:
[1, 2, -1; -1, 3, 3; 0, 2, -1]
Row Operation 1: Add 1 times the 1st row to the 2nd row:
[1,2,-1;0,5,2;0,2,-1]
Row Operation 2: Multiply the 2nd row by 1/5:
[1,2,-1;0,1,2/5;0,2,-1]
Row Operation 3: Add -2 times the 2nd row to the 3rd row:
[1,2,-1;0,1,2/5; 0, 0, -9/5]
Row Operation 4: Multiply the 3rd row by -5/9:
[1,2,-1;0,1,2/5; 0, 0, 1]
Row Operation 5: Add -2/5 times the 3rd row to the 2nd row:
[1,2,-1;0,1,0;0,0,1]
Row Operation 6: Add 1 times the 3rd row to the 1st row:
[1,2,0;0,1,0;0,0,1]
Row Operation 7: Add -2 times the 2nd row to the 1st row:
[1,0,0; 0,1,0;0,0,1]
Which expression is equivalent to 3m+1-m?
A-2+m-1+m
B-1+m
C-3m-1
D-3m
Answer:
A
Step-by-step explanation:
Answer:
option (a) is correct.
2 + m - 1 + m is an equivalent expression to the given expression 3m+1-m
Step-by-step explanation:
Given expression 3m+1-m
We have to choose an equivalent expression from given options.
Equivalent expression are those expression that looks different but are same.
Like 4+2 = 6 and 3+ 3 = 6
Both have same value but looks differently.
Like terms are term having same variable with same degree.
Consider the given expression 3m+1-m
Simplify by adding like terms,
3m + 1 - m = (3-1) m + 1
Thus, (3-1) m + 1 = 2m + 1
Also 2m + 1 can be written as m + m + 2 - 1
Thus, option (a) is correct.
find the equation of the line shown
Answer:
y = x + 1
Step-by-step explanation:
find slope (y2-y1)/(x2-x1)
pick 2 points (0,1) and (1,2)
(2-1)/(1-0) = 1/1 = 1
Since (0,1) you know that y intercept is 1
the equation in slope intercept form: y = x + 1
The GCF of 26 39 and 65
(GIVING BRAINLIEST!!)
Solve the equation using equivalent fractions. SHOW YOUR WORK
4/5 + 3/15 - 2/3
Answer:
0.3 or 1/3
Step-by-step explanation:
add 4/5 + 3/15=1
then 1-2/3 = 1/3
Answer: 1/3
[tex]\frac{4}{5}+\frac{3}{15}-\frac{2}{3}\\\\=\frac{4}{5}+\frac{3}{3.5}-\frac{2}{3}\\\\=\frac{4}{5}+\frac{1}{5}-\frac{2}{3}\\\\=1-\frac{2}{3}\\\\=\frac{3}{3}-\frac{2}{3}\\\\=1/3[/tex]
Step-by-step explanation:
FInd the area of the circle
Answer:
A = 12.56 m²
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASGeometry
Area of a Circle: A = πr²d = 2rStep-by-step explanation:
Step 1: Define
d = 4 m
Step 2: Find r
Substitute: 4 = 2rIsolate r: 2 = rRewrite: r = 2 mStep 3: Find Area
Substitute: A = π(2)²Substitute: A = (3.14)(2)²Evaluate: A = (3.14)(4)Multiply: A = 12.56 m²the ratio of horses to chickens on a farm is 9:4. If there are a total of 169 animals, how many chickens are on the farm?
Answer:
52 chickensStep-by-step explanation:
Step one:'
given
we are told that the total number of animals is 169
the ratio of horses to chickens= 9:4
total ratio= 13
Required:
number of chickens
Applying part to all principle, let the number of chickens be x
4/13=x/169
cross multiply
4*169=13*x
divide both sides by 13
x=4*169/13
x=676/13
x=52
There are 52 chickens
Hi. :) if you are a "Blink" what album should i get?
Answer:
Changes
Step-by-step explanation:
#teamtrees #WAP (Water And Plant)
Answer:
♡ let's kill this love! ♡
you should definitely get "the album."
it has a very good rating and its great ☆
stan blackpink for clear skin, have a great day!
-madi/madeline
✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧
Step-by-step explanation:
16. Mario has $15. He spends $6.25 on admission to the ice
skating rink, $2.95 to rent skates, and $1.65 each for 2 hot
chocolates. How much money does he have left?
Answer:
4.15
Step-by-step explanation:
Minus it all
15 minus 6.25 is 8.75
8.75 minus 2.95 equals 5.8
5.8 minus 1.65 equals 4.15
indicate in standard form the equation of the line passing through the given points, in the equation box below. X(0, 6), Y(5, 6)
Answer:
0x + y = 6
Step-by-step explanation:
Equation of the Line
The equation of a line passing through points (x1,y1) and (x2,y2) can be written as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
It can be later converted to any other form of the line. For example, the standard form is:
[tex]Ax + By = C[/tex]
Let's find the equation by using the given points (0,6) (5,6):
[tex]\displaystyle y-6=\frac{6-6}{5-0}(x-0)[/tex]
Operating:
[tex]\displaystyle y-6=\frac{0}{5-0}(x-0)[/tex]
y - 6 = 0
Or, equivalently:
0x + y = 6
This corresponds to a horizontal line
1.682 inches rounded to the nearest whole number is 1 inches?
Answer:
No, it is 2 inches because 6 rounds up.
Hope this helps and have a great day!
And please mark me brainliest if you can :)
Factorise fully the following 2x+8
**Need Help as soon as possible**
Find f(0), f(1), and f(5)
SEE PHOTO for details.
(I will give you POINTS)
Answer:
f(0)=1
f(1)=4
f(5)=-4.5
Step-by-step explanation:
0 and 1 are in the second domain, so you use the second equation
(0+1)^2=1^2=1
(1+1)^2=2^2=4
5 is in the third domain, so you use the third equation
-1/2(5)-2=-2.5-2=-4.5
Omar is about to start his final semester of college, and he doesn't have enough money saved to afford the $750 he needs in books. He's 21, so he's going to open his own credit card to pay for the books, and then not use it again. His plan is to pay $100 per month toward his bill, until it's paid off. Which credit card offer is the best offer for Omar?
2. The mean birth weight of a full term boy born in the US is 7.7 lbs, with standard deviation of 1.1 lbs. A. Find the probability that a boy born full term in the US weighs less than 7 lbs. B. Find the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs.
Answer:
A
The value is [tex]P( X < 7 ) =0.26226[/tex]
B
The value is [tex]P( X < 7 ) = 0.00073[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 7.7 lbs[/tex]
The standard deviation is [tex]\sigma = 1.1 \ lbs[/tex]
The sample size is n = 25
Generally the probability that a boy born full term in the US weighs less than 7 lbs is mathematically represented as
[tex]P( X < 7 ) = P( \frac{X - \mu }{\sigma} < \frac{7 - 7.7 }{1.1 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P( X < 7 ) = P(Z <- 0.6364 )[/tex]
From the z table the area under the normal curve to the left corresponding to -0.6364 is
[tex]P(Z <- 0.6364 ) =0.26226[/tex]
=> [tex]P( X < 7 ) =0.26226[/tex]
Generally the standard error of mean is mathematically represented as
[tex]\sigma_{x} = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{x} = \frac{ 1.1 }{\sqrt{25} }[/tex]
=> [tex]\sigma_{x} = 0.22[/tex]
Generally the probability that the average weight of 25 baby boys born in a particular hospital have an average weight less than 7 lbs is mathematically represented as
[tex]P( \= X < 7 ) = P( \frac{\= X - \mu }{\sigma_{x}} < \frac{7 - 7.7 }{ 0.22 } )[/tex]
=> [tex]P( X < 7 ) = P(Z <- 3.1818 )[/tex]
From the z table the area under the normal curve to the left corresponding to -3.1818 is
=> [tex]P(Z <- 3.1818 ) = 0.00073[/tex]
=> [tex]P( X < 7 ) = 0.00073[/tex]