please solve
Use the Lagrange multiplier method to find the maximum of the function f(x, y) = 3x + 4y subject to the constraint x? +7y? =1.

Answer:

D. y=-1/4x+3​

Answer:

A. 13.5

Step-by-step explanation:

60 ft. = 3 in.

20 ft. = 1 in.

270/20 = 13.5

Answer:

Answer: C. 32 cm

Step-by-step explanation:

Triangle Inequality Theorem

Let y and z be two of the side lengths of a triangle. The length of the third side x cannot be any number. It must satisfy all the following restrictions:

x + y > z

x + z > y

y + z > x

Combining the above inequalities, and provided y>z, the third size must satisfy:

y - z < x < y + z

We know the triangle has two congruent angles, which means the triangle is isosceles, i.e., it has two congruent sides.

We are given two side lengths of 16 cm and 32 cm. The third side must have a length of 16 cm or 32 cm for the triangle to be isosceles.

If the third side had a length of 16 cm then the lengths would be 16-16-32. But that combination cannot form a triangle because of the condition stated above.

If y=16, z=16, and x=32 (the worst possible combination), then the inequality

0 < x < 32

wouldn't be satisfied, thus the third side cannot have a length of 16 cm and it must have a length of 32 cm

Answer: C. 32 cm

We want to find the length of the missing leg of the given triangle. We will see that the correct options are C and D.

Two angles are congruent if these have the same measure.

Then if the triangle has two congruent angles it means that the triangle must be an isosceles triangle.

We know that one side measures 16cm and the other side measures 32 cm, and this is an isosceles triangle, so it must have two equal sides.

Then the possible measures of the missing side are either 16cm or 32 cm.

So the correct options are C and D.

If you want to learn more about triangles you can read:

https://brainly.com/question/14285697

Answer:

The height of the cuboid = 5 cm

Step-by-step explanation:

Explanation:-

Given that the volume of the cuboid = 40 cm³

Given that length of the cuboid (l) = 2 cm

Given that the width of the cuboid (w) = 4 cm

The volume of the cuboid is determined by

\(V = length X width X height\)

40 = 2× 4× h

h = 5

The height of the cuboid = 5 cm

The estimated total time for all five pools is approximately 13.85 hours.

To estimate the time required to install the fifth pool using the learning curve, we can use the formula:

Time for nth unit = Time for first unit * (n^b)

Where:

Time for nth unit is the estimated time to install the nth pool

Time for first unit is the estimated time to build the first pool (30 hours)

n is the number of units (in this case, n = 5 for the fifth pool)

b is the learning curve exponent (85% learning rate corresponds to b = log(0.85) / log(2))

Let's calculate the estimated time for the fifth pool:

b = log(0.85) / log(2) ≈ -0.157

Time for fifth pool = Time for first pool * (5^b)

Time for fifth pool = 30 * (5^(-0.157))

Calculating this, we find:

Time for fifth pool ≈ 30 * 0.6764 ≈ 20.29 hours

Therefore, the estimated time required to install the fifth pool is approximately 20.29 hours.

To calculate the total time for all five pools, we need to sum the time required for each pool from the first to the fifth. Since the learning curve assumes decreasing time with increasing units, we can use a summation formula:

Total time for all units = Time for first unit * ((1 - (n^b)) / (1 - b))

Using this formula, let's calculate the total time for all five pools:

Total time for all five pools = Time for first pool * ((1 - (5^b)) / (1 - b))

Total time for all five pools = 30 * ((1 - (5^(-0.157))) / (1 - (-0.157)))

Calculating this, we find:

Total time for all five pools ≈ 30 * 0.4615 ≈ 13.85 hours

Therefore, the estimated total time for all five pools is approximately 13.85 hours.

Learn more about  time from

https://brainly.com/question/30132266

#SPJ11

Answer:  SR = 42

Step-by-step explanation:

8x-6 = 36  + x

subtract x

8x - x - 6 =  36 + x - x

(Note +x -x = 0, same goes to any number or variable.)

7x - 6 =  36

add 6

7x  - 6 + 6 = 36 + 6

7x = 42

7x/7 = 42/7

x = 6

So far we found x, so now we would put x in SR which is 8x - 6

SR = 8x - 6

SR = 8(6)  - 6

SR = 48  - 6

SR =  42.

Therefore SR is 42.

Answer:

-2(6x-y)

-2(6×-3-4)

-2(-18-4)

-2(-22)

44

hope this helps you

Answer:

It is negative 44(:

Step-by-step explanation: I just got it right

Answer:

Option (1)

Step-by-step explanation:

Lines X and Y are intersecting at a point.

Two pairs of vertical angles have been formed at the point of intersection.

1). ∠1 and ∠3

2). ∠2 and ∠4

It's given that m(∠1) = m∠3 = 55° [Since pair of vertical angles are equal in measure]

If line Y is rotated 5° clockwise about the point of intersection of both the lines,

∠1 and ∠3 both will increase by 5°.

Therefore, measure of angles 1 and angle 3 will become (55° + 5° = 60°).

Option (1) will be the answer.

The new measure of angle 3 is 60 degrees

When a point or line is rotated, it must be rotated about a point of rotation

The angle measure is given as:

\(\angle 1 = 55^o\)

By vertical angle theorem, we have:

\(\angle 3 = \angle 1\)

So, the angle measure becomes

\(\angle 3 = 55^o\)

The angle of rotation is given as: 5 degrees.

So, the new measure of angle 3 is:

\(\angle 3 = 55^o + 5^o\)

\(\angle 3 = 60^o\)

Hence, the new measure of angle 3 is 60 degrees

Read more about rotation at:

https://brainly.com/question/2283733

Answer:

6

Step-by-step explanation:

Because 3 plus 3 is 6

Answer:

#1 (4b + 6a) #2  150y

Step-by-step explanation:

#1 :area of right triangle: ab/2

4x2/2 = 4b

area of rectangle: length x width

2 x 3 = 6a

#2:

5y + 2.5y = 7.5y x 2 = 15y

so the top and bottom are both 15 y

the sides are each 5y so thats 10 y

15x10= 150y

Answer: 14,358 cubic feet

Step-by-step explanation:

Volume of hemisphere = 0.5 x volume of sphere

Volume of hemisphere = 0.5 x 4/3 pi r^3

Volume of hemisphere = 0.5 x 4/3 pi 19^3

Volume of hemisphere = 0.5 x 4/3 pi 6859

Volume of hemisphere ≅ 14,358 cubic feet

The relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.

What is frequency ?

Frequency refers to the number of times that an event or value occurs within a specific period or dataset. It is a measure of how often a particular value or category appears in a set of data. The frequency can be expressed as an absolute count or as a proportion or percentage relative to the total number of observations in the dataset. Frequency is often used in statistical analysis to describe the distribution of data and to calculate various measures of central tendency and variability.

The relative frequency of a student being a tenth grader that gets their news from the internet is given by:

(number of tenth graders who get their news from the internet) / (total number of students)

So, the relative frequency for tenth graders is

34/175 = 0.194

Rounding to the nearest hundredth gives 0.19.

Therefore, the relative frequency of a student being a tenth grader that gets their news from the internet is 0.79.

To know more about frequency visit :

https://brainly.com/question/254161

#SPJ1

Answer:

No, The line x = 3 is not parallel to the line y = 1/3

Step-by-step explanation:

Here's What the graph looks like on Demos graphing calculator.

High Hopes^^

Barry-

The value of df for a test with four categories and a sample of any size is 3.

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as (number of categories - 1) since one category can be determined from the frequencies of the other categories.

In this case, there are four categories, so the degrees of freedom would be (4 - 1) = 3.

Know more about degrees of freedom here:

https://brainly.com/question/31424137

#SPJ11

Answer:

Step-by-step explanation:

bowling balls without holes = 77  and 35%

find: how many bowling balls in the store?

let x be the total

its a ratio and proportion:

 77   =     x      

 35        100

cross multiply:

35 (x) = 77 (100)

x = 7700 / 35

x = 220   ------>> total number of balls in the store

77 bowling balls without holes are available in a store that sells bowling supplies. 220 bowling balls will be available in the store if 35% of the balls do not have holes.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

Given that, there are 77 bowling balls in the bowling alley that don't have holes drilled in them. 35 percent of bowling balls are black holes.

Bowling balls without holes = 77  and 35%

let x be the total its a ratio and proportion:

77/35 = x/100

35 (x) = 77 (100)

x = 7700 / 35

x = 220  

Thus, 77 bowling balls without holes are available in a store that sells bowling supplies. 220 bowling balls will be available in the store if 35% of the balls do not have holes.

Learn more about the ratio here:

brainly.com/question/13419413

#SPJ2

Answer:

  (c)  Almond bark costs $0.60 more per ounce than peanut brittle

Step-by-step explanation:

You want to know the difference in cost per ounce based on a graph of cost for Peanut Brittle, and a table of cost for Almond Bark. Both representations show the cost for 10 ounces: $10 for Peanut Brittle, and $16 for Almond Bark.

The cost per ounce is the cost divided by the corresponding weight in ounces. For the two candies, the costs are ...

The $1.60 cost per ounce for Almond Bark is higher than the $1.00 cost per ounce for Peanut Brittle by ...

  $1.60 -1.00 = $0.60

Almond Bark costs $0.60 more per ounce than Peanut Brittle.

The difference in the cost of the candies, using a proportional relationship, is given by the following option:

Peanut brittle costs $0.60 more per ounce than almond bark.

A direct proportional relationship is defined when the output variable y is calculated with the multiplication of the input variable x and the constant of proportionality r as follows:

y = rx.

In the context of this problem, the variables are defined as follows:

For Peanut Brittle, the cost per ounce is given as follows:

r = 10/10 = $1.

For Almond Bark, the cost per ounce is given as follows:

r = 8/5 = $1.6.

The difference of these costs is given as follows:

1.6 - 1 = $0.6.

Hence the correct option is given as follows:

Peanut brittle costs $0.60 more per ounce than almond bark.

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

Answer: GH = 12

Step-by-step explanation:

Don't panic! Remember that a perpendicular bisector divides a segment equally in half. (If you're writing a proof, cite the "Definition of a perpendicular bisector)

It breaks down to: GH = HI

HI = 12

By the transitive property of segment congruence: GH = 12

Good luck!

Answer:

im sorry but i really cant see the image

Step-by-step explanation:

Answer:

-49

Step-by-step explanation:

– 49 (18 – 17)

– 49 (1)

– 49

If this was helpful, please mark brainliest. Have a beautiful day!

Answer:

Look for 75% of 1 1/2, I got 1.125 or 1 1/8

Step-by-step explanation:

There are 2 ways to solve this system: by elimination or by graphing. I will solve it by elimination. First will solve for x.

\(2x - 2y = 6\\3x + 2y = 9\\\\5x = 15\\\\x = 3\\\)

Now we will solve for y using what we got for x.

\(2(3) - 2y = 6\\\\6 - 2y = 6\\\\-2y = 0\\\\y = 0\)

Solution:

A: \((0, 3)\)

x=3.07 metre / 3m ( neglecting the decimal)

Answer:x=3.07

Step-by-step explanation:

4 square root 2=(4×2)(2 4-3)÷ 2 square root 2

Answer =3

3.07

After applying the substitution u = 4x + π to the integral ∫π0 sin(4x + π)dx,  the new limits of integration are from u = π to u = 5π. To determine this, we need to use the original limits.

To find the new limits of integration, we need to substitute the original limits into the equation u = 4x + π and solve for the corresponding values of u.

For the lower limit of integration, x = 0, we substitute into the equation:

u = 4(0) + π

u = π

For the upper limit of integration, x = π, we substitute into the equation:

u = 4(π) + π

u = 5π

Therefore, after applying the substitution, the new limits of integration for the integral ∫π0 sin(4x + π)dx are from u = π to u = 5π.

Learn more about integration here:

https://brainly.com/question/31744185

#SPJ11

The p-value of the given hypothesis is; 0.9999

The formula for the z-score of proportions is;

z = (p^ - p)/√(p(1 - p)/n)

where;

p^ is sample proportion

p is population proportion

n is sample size

We are given;

p^ = 15% = 0.15

p = 20% = 0.2

n = 5000

Thus;

z = (0.15 - 0.2)/√(0.2(1 - 0.2)/5000)

z = -8.8388

From p-value from z-score calculator, we have;

P(Z < -8.8388) = 1 - 0.0001 = 0.9999

Read more about p-value at; https://brainly.com/question/4621112

#SPJ1

Answer:  80%

Step-by-step explanation:

hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.

Odd number integers = 2k + 1, where k is integer

Even number integer = 2k

Odd integer + even integer

 = 2k + 1 + 2k

= 4k + 1

 = 2(2k) + 1

Let 2k = t, where t is integer

  = 2t + 1

 = Odd integer by definition

If number is 2t + 1 where t belongs to integer, then it is odd integer.

Hence proved.

The question is incomplete. The complete question is :

Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd

learn more about of odd number here

https://brainly.com/question/21330408

#SPJ4

An infinite geometric series is one in which each term is equal to the preceding term multiplied by a fixed non-zero number, known as the common ratio.

The first term is called a1, and the common ratio is represented by r.In this particular question, we are required to find the value of a1 and r for an infinite geometric series. The partial sum S2 will also need to be found.For a geometric sequence that is infinite, the formula for the partial sum, Sn, is:Sn = a1 / (1-r), where a1 is the first term and r is the common ratio.To solve for a1, it is necessary to know two other variables: the common ratio r and the value of the first term a1. S2 is the sum of the first two terms, so: S2 = a1 + arTo find S2, we must first determine a1 and r. a1 is the first term in the sequence, and r is the common ratio. We can obtain both a1 and r by dividing the second term by the first term.The formula is:r = (ar/a1) = a2/a1 Substitute the value of r and a1 into the formula for S2 to obtain the result: S2 = a1 + ar = a1 + a1r = a1(1+r) Therefore, the value of a1 is a constant number that will appear in the series, and the common ratio, r, will be multiplied by this number to obtain the next value in the series.

So, a1 is the first term, and r is the common ratio of the infinite geometric series. S2, the sum of the first two terms, is found by using the formula S2 = a1 + ar where a1 is the first term and r is the common ratio.

To know more about Geometric series visit-

https://brainly.com/question/30264021

#SPJ11

Chocolate = 18%

Vanilla = 25%

Strawberry = 12%

Mint Chip = 10%

Other = 35%

The explanation for me getting these exact percentages is because of the formulas given for calculating the percentages from specific numbers and real world problems like this. When you are trying to find the calculation precentages of these types of questions, you divide the number by the total surveyed and multiple by 100.

Example:

125 / 500 = 0.25

0.25 x 100 = 25%

So, this is also how I got the other numbers, just change the "125" to the other numbers.

The experimental probability of each outcome in the sample space are:

P(chocolate) = 18%, P(strawberry) = 12%, P(vanilla ) = 25%, P(mint chip) = 10% and P(other) = 35%

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Flavor               Number of people

chocolate                  90

strawberry                 60

vanilla                        125

mint chip                    50

other                          175

So, the Experimental probability are:

P(chocolate)= 90/ 500 x 100 = 18%

P(strawberry) = 60/ 500 x 100 = 12%

P(vanilla ) = 125/ 500 x 100 = 25%

P(mint chip) = 50/ 500 x 100 = 10%

P(other) = 175/ 500 x 100 = 35%

Learn more about Probability here:

brainly.com/question/30034780

#SPJ2

The solution set of the inequality x-15≤6/9 is  x≤47/3.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is x-15≤6/9

x minus fifteen lesser than or equal to six by nine.

x is the variable and minus is the operator,

x-15≤6/9

On the right side the numerator and denominator is divided by 3

x-15≤2/3

Add 15 on both sides

x≤2/3+15

x less than or equal to two by three plus fifteen.

x≤2+3(15)/3

When three is multiplied with fifteen we get 45.

x≤45+2/3

So when forty five and two are added we get 47.

x≤47/3

Hence, the solution set of the inequality x-15≤6/9 is  x≤47/3.

To learn more on Inequality click:

https://brainly.com/question/28823603

#SPJ9

Complete quesstion,

Find the solution set of the  inequality x-15≤6/9

Answer:

volume = 960π m³ ; surface area = 368π m²

Step-by-step explanation:

base area = 8²π = 64π m²

base perimeter = 8 x 2 x π = 16π m

lateral area = 16π x 15 = 240π m²

surface area = 2 x 64π + 240π = 128π + 240π = 368π m²

Volume = 64π x 15 = 960π m³

Answers: Equation: 52 = 7x

Octaves: x = 7.43

Explanation:

Let's call x the number of octaves in a piano

Then, every octave has 7 white keys. It means that the number of keys in a piano can be calculated as 7 times x or 7 times the number of octaves:

Number of keys = 7x

Then, the number of keys, in this case, is equal to 52, so we can replace the number of keys by 52 and get:

52 = 7x

Now, we can solve for x, dividing both sides by 7 as:

52/7 = 7x/7

7.43 = x

Therefore, the piano has 7.43 octaves