Answer:
Following are the responses to the given question:
Step-by-step explanation:
Given:
[tex]\to f(x,y)=xy\\\\\to 48x^2+3y^2=3456\\\\[/tex]
let [tex]\phi(x,y)=48x^2+3y^2=3456[/tex]
using the lagrange multiplies:
[tex]\bigtriangledown f=\lambda \bigtriangledown \phi\\\\i)\ \ y=96 \lambda x \to \lambda=\frac{y}{96\ x} \\\\ii)\ \ x=6 \lambda y \to \lambda=\frac{y}{6\ y} \\\\iii)\ \ 48x^2+3y^2=3456\\\\[/tex]
From equation (i) and (ii)\\\\
[tex]\to \frac{y}{96x}=\frac{x}{6y}\\\\\to 6y^2=96x^2\\\\\to 3y^2=48x^2\\\\[/tex]
From equation 3:
[tex]48x^2+48x^2=3456\\\\96x^2 3456\\\\x^2=36\\\\x=\pm 6\\\\\therefore 3y^2=48(36)\\\\3y^2=1728\\\\y^2=576\\\\y=\pm24\\\\(x,y)=(\pm 6,\pm 24)\\\\Maximum \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 144 \ \ \ \ at \ \ (6,24) \ \ \ \ \ \ \ and \ \ \ \ \ \ (-6, -24) \\\\Minimum \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -144 \ \ \ \ at \ \ (-6,24) \ \ \ \ \ \ \ and \ \ \ \ \ \ (6,-24)\\\\[/tex]
Attendance has never been a component of the grade for this course. However, over the years I have noticed that 40% of those who attend regularly receive an above average grade (B or better), while only 10% of those who do not attend regularly receive an above average grade. About 70% of the students attend class regularly. One student is randomly selected at the end of the semester. Find the probability that the student did not attend class regularly given that (s)he did not receive an above average grade
Answer:
0.3913 = 39.13% probability that the student did not attend class regularly given that (s)he did not receive an above average grade
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Did not receive an above average grade.
Event B: Did not attend class regularly.
Probability of an student not receiving an above average grade:
100 - 40 = 60% of 70%(attend class regularly).
100 - 10 = 90% of 100 - 70 = 30%(do not attend class regularly).
So
[tex]P(A) = 0.6*0.7 + 0.9*0.3 = 0.69[/tex]
Did not receive an above average grade and did not attend class regularly:
90% of 30%. So
[tex]P(A \cap B) = 0.9*0.3 = 0.27[/tex]
Find the probability that the student did not attend class regularly given that (s)he did not receive an above average grade
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.27}{0.69} = 0.3913[/tex]
0.3913 = 39.13% probability that the student did not attend class regularly given that (s)he did not receive an above average grade
Jon is taking a 625 mile trip, on the first day he drove 183 miles. How many more miles does he need to drive???
Answer:
442
Step-by-step explanation:
624-183= 442 he needs to drive 442 miles more
(1 point) A bucket that weighs 3.6 pounds and a rope of negligible weight are used to draw water from a well that is 78 feet deep. The bucket is filled with 38 pounds of water and is pulled up at a rate of 2.9 feet per second, but water leaks out of a hole in the bucket at a rate of 0.1 pounds per second. Find the work done pulling the bucket to the top of the well. Your answer must include the correct units. (You may enter lbf or lb*ft for ft-lb.)
Answer:
The total work done in pulling the bucket to the top of the well is approximately 3,139.1 ft·lb
Step-by-step explanation:
The given parameters are;
The mass of the bucket, W = 3.6 pounds
The depth of the well, h = 78 feet deep
The mass of water in the bucket = 38 ponds
The rate at which the water is pulled up = 2.9 feet per second
The rate at which water is leaking from the bucket, [tex]\dot m[/tex] = 0.1 pounds per second
We separate and find the work done for lifting the bucket and the water individually, then we add the answers to get the solution to the question as follows;
The work done in lifting bucket empty from the well bottom, [tex]W_b[/tex] = W × h
∴ [tex]W_b[/tex] = 3.6 pounds × 78 feet = 280.8 ft-lb
The work done in lifting bucket empty from the well bottom, [tex]W_b[/tex] = 280.8 ft-lb
The time it takes to lift the bucket from the well bottom to the top, 't', is given as follows;
Time, t = Distance/Velocity
The time it takes to pull the bucket from the well bottom is therefore;
t = 78 ft./(2.9 ft./s) ≈ 26.897
The time it takes to pull the bucket from the well bottom to the top, t ≈ 26.897 s
The mass of water that leaks out from the bucket before it gets to the top, m₂, is therefore;
m₂ = [tex]\dot m[/tex] × t
∴ m₂ = 0.1 lbs/s × 26.897 s = 2.6897
The mass of the water that leaks, m₂ = 2.6897 lbs
The mass of water that gets to the surface m₃ = m - m₂
∴ m₃ = 38 lbs - 2.6897 lbs ≈ 35.3103 lbs
Given that the water leaks at a constant rate the equation representing the mass of the water as it is lifted can b represented by a straight line with slope, 'm' given as follows;
The slope of the linear equation m = (38 lbs - 35.3103 lbs)/(78 ft. - 0 ft.) = 0.03448[tex]\overline 3[/tex] lbs/ft.
Therefore, the equation for the weight of the water 'w' can be expressed as follows;
w = 0.03448[tex]\overline 3[/tex]·y + c
At the top of the well, y = 0 and w = 38
∴ 35.3103 = 0..03448[tex]\overline 3[/tex] × 0 + c
c = 35.3103
∴ w = 0.03448[tex]\overline 3[/tex]·y + 35.3103
The work done in lifting the water through a small distance, dy is given as follows;
(0.03448[tex]\overline 3[/tex]·y + 38) × dy
The work done in lifting the water from the bottom to the top of the well, [tex]W_{water}[/tex], is given as follows;
[tex]W_{water} = \int\limits^{78}_0 {0.03448\overline 3 \cdot y + 35.3103 } \, dy[/tex]
[tex]\therefore W_{water} = \left [ {\dfrac{0.03448\overline 3 \cdot y^2}{2} + 35.3103 \cdot y\right ]^{78}_0[/tex]
[tex]W_{water}[/tex] = (0.034483/2 × 78^2 + 35.3103 × 78) - (0.034483 × 0 + 38 × 0) ≈ 2,859.1
The work done in lifting only the water, [tex]W_{water}[/tex] ≈ 2,859.1 ft-lb
The total work done, in pulling the bucket to the top of the well, W = [tex]W_b[/tex] + [tex]W_{water}[/tex]
∴ W = 2,859.1 ft.·lb + 280.8 ft.·lb ≈ 3,139.1 ft·lb
The total work done, in pulling the bucket to the top of the well, W ≈ 3,139.1 ft·lb.
What is diffusion concentration gradient
Which of the following equations has infinitely many solutions? A. 2x + 5(2x + 6) = 12x + 30 B. 2x + 5 = 2 C. 2(x + 5) + 2 = 6x + 2(x + 2) D. 5x + 2 = 2x + 6
Answer:
A. 2x + 5(2x + 6) = 12x + 30
Step-by-step explanation:
Infinitely many solutions means the two sides of the equation will be equal to each other, so B and D can be eliminated. Distribute for A and C to check
A. 2x + 5(2x + 6) = 12x + 30
2x + 10x + 30 = 12x + 30
12x + 30 = 12x + 30
C. 2(x + 5) + 2 = 6x + 2(x + 2)
2x + 10 + 2 = 6x +2x + 4
2x + 12 = 8x + 4
You only get the same equation for A, therefore A is the correct answer
Aiden researches and finds that 37% of students at his school participate in the after school program. Aiden takes a random sample of 50 students and finds that 27 students participate in the after. Which statement correctly describe the sample ratio?
O The sample ratio is 27%, which is above the population ratio.
O The sample ratio is 27%, which is below the population ratio.
O The sample ratio is 54%, which is above the population ratio.
O The sample ratio is 54%, which is below the population ratio.
Answer:
Divide the number of students who participate in the after school program by the number of students in the sample. Multiply by 100 to find the percentage.
Step-by-step explanation:
Use the random sample to make an inference about the sample and population.
Please help.
You will get brainliest.
Answer:
[tex] 18,432\pi \: {in}^{3} [/tex]
Step-by-step explanation:
Base diameter of cylinder = 48 in
So, base radius (r) = 48/2 = 24 in
Height of oil filled in the can (h) = 32 in
Volume of portion of the can that is filled with oil
[tex] = \pi {r}^{2} h \\ \\ = \pi \times (24)^{2} (32) \\ \\ =18,432\pi \: {in}^{3} [/tex]
The cost table shows the average cost, a(x), of
producing x number of earbuds.
When verifying that a function represented in another
table is the inverse of the given cost function, which
ordered pair can be expected?
2 20
a(x) 52
25 30
67.5 84
O (20, 20)
O (52, 20)
O (20,52)
O (52,52)
Reverse the numbers in the table to get:
(52,20) (67.5,25) and (64,30)
The answer would be (52,20)
The ordered pair can be expected will be (52, 20). Then the correct option is B.
What is the inverse function?Let the function f is given as
y = m(x + a) + c
Then the inverse function of the function f will be given by swapping x with y and y with x.
The cost table shows the average cost, a(x), of producing x number of earbuds. When verifying that a function represented in another table is the inverse of the given cost function.
(2, 20), (a(x), 52), (25, 30), (67.5, 84)
The ordered pair of the inverse function is given as,
(20, 2), (52, a(x)), (30, 25), (84, 67.5)
The ordered pair can be expected will be (52, 20). Then the correct option is B.
More about the inverse function is given below.
https://brainly.com/question/2541698
#SPJ6
If Dede uses 10 cups of yellow paint, how much blue paint should she use to make this
same shade of green?
Answer:
10 cups
Step-by-step explanation:
Answer:
10 cups
Step-by-step explanation:
10 × 2 = 20
20÷2= 10
# Prove
Please help me anyone please help.
No links and random answers please.
Answer:
proved
Step-by-step explanation:
hope it helped!!!
Mae Ling earns a weekly salary of $310 plus a 8.0% commission on sales at a gift shop. How much would she make in a work week if she sold $4,100 worth of merchandise
Answer:
638 in week
Step-by-step explanation:
4100×0,08=328
328+310=638
If the center of a circle is
(-5,8) and a point on the circle is (-5, -4) What is the radius?
Answer:
The radius is 12.
Step-by-step explanation:
You're given the center and a point on the circle. The point and the center both have an x-coordinate of -5, so there is no horizontal distance between them. The distance is only in the vertical direction. The distance from 8 to -4 is 12. Since this is the distance from the center to a point on the circle, this equals the radius.
you need 4/5 of a cup of strawberries for a single pie, how ,many cups are need for 9 pies?
Answer:
7 2/5 cups
Step-by-step explanation:
4 x 9 = 36
36/5 = 7.2
find the missing side of each triangle using the pythagorean theorem
Answer:
x=5
Step-by-step explanation:
The pythagorean theorem stats a^2+b^2=c^2. We are already given the values of the two legs of the triangle so we need to solve for the length of the hypotenuse (the longest part of the triangle). To do so, you put in 3 and 4 as a and b so you get 3^2+4^2=c^2. After squaring both numbers you get 16+9=c^2. Then you add 16 and 9 to get 25=c^2. To get rid of the power of 2, we square root both sides to get rid of the exponent. Since 25 is a perfect square, you get c=5 which means that the x value eqals 5.
Someone come in clutch pls
Answer:
vertical angles is the answer
Jaime earned some money mowing the neighbor's lawn. He spent one-fourth of his money to take his friends to see a movie. Then he spent $7.00 on popcorn and drinks. When he went home, he had $71.00 left. How much did Jaime earn mowing the neighbor's lawn?
A. $13
B. $64
C. $78
D. $104
Which of the following verbal sentences represents the algebraic sentence below?
2x – 5 = -15
what is 27+27 BumblebeeTuna
Answer: 54
Step-by-step explanation:
ay know what 10,000 x 1 is
Answer:
1
Step-by-step explanation:
any thing times 1 is 1
The Reeds are moving across the country. Mr. Reed leaves 4.5 hours before Mrs. Reed. If he averages 40mph and she averages 60mph, how many hours will it take Mrs. Reed to catch up to Mr. Reed?
Mr. Reed DATA:
rate = 40 mph ; time = x 4.5 hrs ; distance = 40x miles
-----
Mrs. Reed DATA:
rate = 60 mph ; time = x hrs ; distance = 60x - 210 miles
------
Equation:
40x = 60x -210
-20x = -210
x = 10.5 hrs
x-3.5 = 7 hrs (Mr. Reed's time)
Do creative people make better teachers? Ten teachers at a large university were given a creativity test (scores range from 0 to 20, with higher scores indicating greater creativity) and were evaluated regarding teaching performance by students and peers (a score of 100 indicates an average performance, and larger scores indicate better performance). The creativity scores and teaching performance scores are given below.
Answer:
The answer is "0.898"
Step-by-step explanation:
Using the command in any cell that is" =CORREL(I5:I14, J5:J14)" throughout the I5:I14 its value is the creativity scores that is the J5:J14 which is the value of the performance of the score, that gets the correlation coefficient that is equal to 0.897886. Hence, the correlation of the coefficient = 0.898
HELP ME PLZ!!!!! ..................................
Step-by-step explanation:
the the number on the top corner is adding zeros so 6.3 / 10/3 the answer is for that 6.30
Justin and Dan ordered a pizza. Justin ate 1/4 and ate 3/8 of the pizza what fraction of the pizza is left? please show how you got the answer.
Answer:
3/8 of the pizza is left
Step-by-step explanation:
say the pizza was cut into 8 slices. Justin at 1/4 of the pizza, we can also put that as 2/8. so now 2 slices are gone. that leaves us with 6 slices. Dan ate 3/8 so now 3 more slices are gone. now we only have 3 left. since we started out with 8 we'll use that as a denominator; 3/8. or look at the image attached
Answer:3/8
Step-by-step explanation:
PLEASE HELP SMART PEOPLE :C
Answer:
C 290 in^2
Step-by-step explanation:
Chase had $236.00 in his savings account. Then he spent 34% or that money on a new skateboard. How much money did Chase spend on his skateboard
Answer:
$80.24
Step-by-step explanation:
what is value of this expression
Answer:
Step-by-step explanation:
= 4 + (-2)/ -3 + 3
= 4 - 2/ -3 + 3
= 2/0 If the denominator is 0, the value is undefined.
Answer:
2/0, which would be undefined.
Step-by-step explanation:
PLEASE HELP ME ON THIS!
the height of a rectangular prism is 8 meters, and the volume is 308 cubic meters. what is the area of the prisms base in square meters?
9514 1404 393
Answer:
38.5 square meters
Step-by-step explanation:
The relevant volume formula is ...
V = Bh . . . . where B is the area of the base, and h is the height
Solving for B, we get ...
B = V/h
B = (308 m³)/(8 m) = 38.5 m²
The area of the prism's base is 38.5 square meters.
girl name are April, may, June, what is the name the mother?
mary is the 4th childs nam,e
PLEASE HELP thank u very much
Martina designed a painting for art class, as shown in the drawing below. Her design contains 4 circles on a square canvas. Each circle has a radius of 6 inches. The circles touch the edges of the canvas and each other, as show below.
The shaded section of Martina's design will be painted black. Which is closest to the area that will be painted black?
Answer:
area of shaded region =(6×4)²-4(π6²)=123.61in²
Answer:
area of shaded region (6x4)²-4(6²)=123.61in²
s
WILL MARK BRAINLEST
Which statement cannot be true of the graph of a proportional relationship?
A It is not linear.
B It is a straight line.
C It includes the origin.
D It shows a constant ratio.
Answer:
A
Hope that helps!
Step-by-step explanation: