(Q2) Order the sides of ΔDEF from shortest to longest.

The point where the tangent plane to the surface is horizontal will be (1.0899, 1.6595).

To determine the partial derivatives of the function f(x, y) with respect to x and y:

\(fx = 2xy^3 - 4y - 1\\fy = 2x^3y - 4x\)

Now, we can find the gradient of f:

\(grad(f) = < fx, fy > = < 2xy^3 - 4y - 1, 2x^3y - 4x >\)

To determine the point where the tangent plane to the surface is horizontal, the critical points of f where grad(f) = 0:

\(2xy^3 - 4y - 1 = 0\\2x^3y - 4x = 0\)

From the second equation,

\(2x(x^2y - 2) = 0\)

Therefore, either x = 0 or x^2y - 2 = 0 Substituting this into the first equation, we get:

\(2x(2/x^6) - 4(2/x^2) - 1 = 0\\4/x^5 - 8/x - 1 = 0\)

Therefore, the point where the tangent plane to the surface is horizontal  x ≈ 1.0899 and y ≈ 1.6595.

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The consumption bundle that will not be the consumer's choice, given the assumptions of choosing the optimal bundle, is option B) 30 snacks and 12 meals. To determine the optimal consumption bundle, we need to consider the consumer's budget constraint and maximize their utility.

Given that the price of snacks is $4 and the price of meals is $10, and the consumer has $240 remaining on their meal card, we can calculate the maximum number of snacks and meals that can be purchased within the budget constraint.

For option A) 5 snacks and 20 meals, the total cost would be $4 × 5 + $10 × 20 = $200. Since the consumer has $240 remaining, this bundle is feasible.

For option B) 30 snacks and 12 meals, the total cost would be $4 × 30 + $10 × 12 = $240. This bundle is on budget constraint, but it may not be the optimal choice since the consumer could potentially consume more meals for the same cost.

For option C) 20 snacks and 16 meals, the total cost would be $4 × 20 + $10 × 16 = $240. This bundle is also on budget constraint.

Since options A, C, and D are all feasible within the budget constraint, the only bundle that will not be the consumer's choice is option B) 30 snacks and 12 meals. The consumer could achieve a higher level of utility by reallocating some snacks to meals while staying within the budget constraint. Therefore, the correct answer is option B.

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The statement which is true about the end behaviour of the graphed function is; As the x-values go to positive infinity, the function’s values go to positive infinity.

The graph given according to the task content is described to have its first minimum at (-2,0), and then a maximum at; (-0.5, 5) and finally a minimum at; (1.05, -41).

Additionally, since the graph has 3 zeroes as given, it follows that the graph is that of a cubic function which takes the w-form.

Consequently, it can be inferred from the statements above that; As the x-values go to positive infinity, the function’s values go to positive infinity.

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Answer:

A

Step-by-step explanation:

edge 23

Step-by-step explanation:

8). 5 ft² into squared Inches:

=> since 1 ft² = 144 in²

=> 5x144

=> 720 in²

9). 16 000 cm² to m²:

=> since 1 m²= 10 000 cm²

=> 16 000 ÷ 10 000

=> 1.6 m²

10). 90 km/h to m/h

=> since 1000 m= 1 km

=> 90x1000

=> 90 000 m/h

11). 30 m/s to m/min

=> since 60 s= 1 min

=> 30÷60

=> 0.5 m/min

12). 15 rpm into rps

=> since 1 min= 60 s

=> 15x60

=> 900 rps

The lowest is the cash price for other options, you have to pay more for a laptop and refrigerator. Then the suitable method is to save up and pay cash.

The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.

If someone were unable to pay cash right now then the suitable method will be

For laptop:

Rent to own payments will be

$150 each month for 12 months, then the total becomes

⇒ 150 × 12 = $1800

The installment plan will be

$100.83 each month for 12 months, then the total becomes

⇒ 100.83 × 12 = $1209.96

The cash price is $1000. So, the lowest is the cash price for other options you have to pay more.

For refrigerator:

Rent to own payments will be

$140 each month for 12 months, then the total becomes

⇒ 140 × 12 = $1680

The installment plan will be

$80.67 each month for 12 months, then the total becomes

⇒ 80.67 × 12 = $968.04

The cash price is $800. So, the lowest is the cash price for other options you have to pay more.

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Answer:

1.67 gallons

Step-by-step explanation:

Given that:

Original mixture contains 80% detergent and 20% water in a 15 gallon bucket.

New Mixture to contain 60% detergent and 40% water of 5 gallon bucket.

To find:

Volume of Pure water to be added to each 5 gallon bucket to obtain the new mixture.

Solution:

First of all, let us calculate the answer by adding pure water to 15 gallon bucket.

Let the number of gallon of water to be added = \(x\)

New volume = (15+\(x\)) gallons

Now, let us compare the number of gallons of water in the mixture before and after.

\(15\times 20\% + x = (15+x)\times 40\%\\\Rightarrow (3+x)\times 5 = (15+x)\times 2\\\Rightarrow 15+5x=30+2x\\\Rightarrow 3x=15\\\Rightarrow x =5\ gallons\)

Therefore, to a 15 gallon bucket (80% detergent and 20% water)of detergent mixture, if we add 5 gallons of pure water , it will become 60% detergent and 40% water.

To a 5 gallon bucket, the number of gallons of water to be added = \(\frac{5}{3} =\bold{1.67\ gallons}\)

The plane left Bristol airport at 16:55.

This is a problem from time and distance. We can solve this problem by following a few steps.

We have to know the relation between time, speed, and distance. The relation is denoted as,

t = s/v; t is denoted as time interval, v is denoted as velocity or speed in this case and s is denoted as displacement or distance.

We have to find the time. Here velocity is 162 mph and the total distance between  Bristol airport to Leeds Bradford airport is 216 miles.

t = 216 miles/ 162 mph = 1.33 hour = 80 minutes.

Therefore the plane left Bristol airport is, ( 18 hours 15 minutes - 80 minutes) = 16 hour 55 minutes = 16:55

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Answer:

  4 pairs

Step-by-step explanation:

You want the number of pairs of integers (m, n) such that m > n and m² -n² = 96.

The difference of squares is factored as ...

  m² -n² = (m -n)(m +n)

In order for the difference to be 96, these factors must be factors of 96.

The prime factorization of 96 is ...

  96 = 2^5 · 3

The number of divisors of 96 is the product of the exponents of these factors, each increased by 1:

  (5+1)(1+1) = 12

That is, there are 12/2 = 6 factor pairs ab such that a<b. They are ...

   96 = 1·96 = 2·48 = 3·32 = 4·24 = 6·16 = 8·12

The values of m and n relate to the values of 'a' and 'b' by ...

  m = (a+b)/2

  n = (b-a)/2

In order for m and n to be integers, the values of 'a' and 'b' must both have the same parity. That is, they must both be even, or both be odd. This eliminates the factor pairs 1·96 and 3·32, leaving 4 (a, b) pairs, hence 4 (m, n) pairs. Possible ordered pairs are ...

  (m, n) ∈ {(25, 23), (14, 10), (11, 5), (10, 2)} . . . . . 4 pairs

The correct option is option (B) .

Number of rooms in house is an example of discrete Variable.

Discrete Variables:

A variable is something whose value changes.

A discrete variable is a variable whose value can be obtained by counting.

In theory, it should always be possible to count the values of discrete variables.

Each probability is between 0 and 1. The sum of the probabilities is 1..

Examples:

As above discussion about Discrete variable now we check the given options.

a) temperature is a continuous variable not discrete, as it does have fractional value too.

so , option (a) is not an example of discrete Variable.

similarly , length is also a continuous variable not discrete so, option (d) exclded .

size of house may be discrete Variable as it's depends on what accuracy is mentained.

Hence, option (b) , number of rooms in house is an example of discrete Variable.

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Answer:

number of rooms in house

Step-by-step explanation:

I took the test :)

I hope this helps!

Answer:

q = p/6 - 7/6

Step-by-step explanation:

Answer:

An angle is the space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet.

"in any triangle, the longest side is opposite the largest angle"

Step-by-step explanation:

Answer:

an angle is a In-plane geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. An angle is denoted using the symbol. and you can describe an angle by looking for the figure formed by two rays meeting at a common end point.

Step-by-step explanation:

hope this helps you

The mystery number is y = 0.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression. Numbers (constants), operations, variables, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Let's assume the mystery number to be y.

When we multiply it by 1, add 5, and finally subtract by 2 we obtain 3.

Using the statement we obtain the expression,

y × 1 + 5 - 2 = 3

y + 5 - 2 = 3

y + 3 = 3

Subtracting 3 from each side of the equation,

y + 3 - 3 = 3 - 3

y = 0

Hence the mystery number is 0.

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Answer:

9

Step-by-step explanation:

because if she can make 3 in 15minutes then 45 minutes is triple the time so triple the bracelets please give brainliest bye have a good day :D

Answer:

1872

Step-by-step explanation:on edge

Answer:

C) 1,872 square inches

Step-by-step explanation:

Hope this helps!

Brainliest if correct pls??

Answer:

Dimensions Of The Driveway is Length=16 Feet & Width=9 Feet

Step-by-step explanation:

According To Question,We Have Given

Length of Driveway Is 7 feet longer than its Width

Let the Width be X Feet . So Length is (X+7)Feet

Area Of Driveway = 144 sq. Feet

X * (X+7) = 144

\(X^{2}\)+7X=144

\(X^{2}\)+16X-9X-144=0

X(X+16)-9(X+16)=0

X = -16 & +9 (Neglect -16 because Width=X, that Can Never be in Negative)

So X = +9

Now Put this value, We get Width = 9 Feet & Length =16 Feet

Answer:

\(\mathrm{a=-50,\ d=7,\ general\ formula=7(n-1)-50}\)

Step-by-step explanation:

\(\mathrm{Solution,}\\\mathrm{Given,}\\\mathrm{15^{th}\ term(t_{15})=48}\\\mathrm{or,\ a+14d=48.........(1)}\\\mathrm{And\ 40^{th}\ term(t_{40})=223}\\\mathrm{or,\ a+39d=223......(2)}\\\mathrm{n^{th}\ term(t_n)=\ ?}\\\mathrm{Subtracting\ equation(1)\ from\ (2),}\\\mathrm{25d=175}\\\mathrm{or,\ d=7}\\\mathrm{Now,\ a+14d=48\ or,\ a=48-14d=48-14(7)}\\\mathrm{\therefore a=-50}\)

\(\mathrm{t_n=a+(n-1)d}\\\mathrm{or,\ t_n=-50+(n-1)7}\\\mathrm{\therefore general\ formula=7(n-1)-50}\)

Answer:

1. the range is 68

2. the iqr is 37.5

3. the mode is 17

4. the mean is 52

5. the median is 44

6. min=7

q1=17

median=39

q3=55

max=62

iqr=38

7. data set a: q1=2 median=4 q3=5 iqr=3

data set b: q1=1 median=5 q3=7 iqr=6

Step-by-step explanation:

1. in order to find the range you subtract the largest number from the smallest number in this case its 81-13

2. you need to put the numbers from smallest to largest then you find the first quartile and the third quartile in this case it would be q1=(8+12)/2 =10 and q3= (39+56)/2=47.5

then you find the iqr by subtracting q1 from q3 so q3-q1= IQR

3. the mode is the number that shows up the most

4. to find the mean you have to add up all the numbers than divide it by how many numbers there are so all the numbers add up to 260 and you divide that by 5

5. to find the median you need to put the numbers from smallest to largest and the number in the middle is the median

i hope i helped! and for 6 and 7 you just do everything i mentioned above :)

Answer:

$50

Step-by-step explanation:

Given data

We are given that the price is $40

the markup percent is 25%

Hence the price will be

40+25% of 40

=40+ 25/100*40

=40+ 0.25*40

=40+10

=$50

Therefore, the price of the dress is $50

Answer:

(-b-81)/6=a

Step-by-step explanation:

3b−2a-17 = 4a+4b+64

3b-4b-17-64=4a+2a

-b-81=6a

(-b-81)/6=a

Answer:

n=5

Step-by-step explanation:

tan 45 = n/5

n=tan 45 × 5

n = 5

Answer:

No, -4xy^2 and 1/2 x^2y are not like terms.

Step-by-step explanation:

Like terms are terms that have the same variables with the same exponents. In this case, -4xy^2 and 1/2 x^2y do not have the same variables with the same exponents, so they are not like terms.

-4xy^2 has a coefficient of -4, a variable x, and an exponent of y^2. 1/2 x^2y has a coefficient of 1/2, a variable x, and an exponent of x^2y. Since the variables and exponents are not the same, these terms are not like terms.

To combine like terms, you must add or subtract the coefficients of the terms and keep the variables and exponents the same. In this case, you cannot combine -4xy^2 and 1/2 x^2y because they are not like terms.

The equation of the plane through the point (6, 0, 5) and perpendicular to the line x is y = 0.

To find the equation of a plane, we need a point on the plane and a normal vector perpendicular to the plane.
Given the point (6, 0, 5) and the line x, we need to find a vector that is perpendicular to the line x.
Since the line x is a one-dimensional object, any vector with components in the y-z plane will be perpendicular to it.

Let's choose the vector (0, 1, 0) as our normal vector.
Now, we can use the point-normal form of the equation of a plane to find the equation of the plane:
(x - 6, y - 0, z - 5) · (0, 1, 0) = 0
Simplifying, we get:
y = 0
Therefore, the equation of the plane through the point (6, 0, 5) and perpendicular to the line x is y = 0.

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Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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Answer:

(x, y) =(-1, - 1)

Step-by-step explanation:

-Substitute the value of x

-solve the equation

-Substitute the value of y

-check the possible solution

-check solution

-simplify

Answer:

10 girls

Step-by-step explanation:

Because 2/3 of 30 is 20 making the other 10 girls

The nail is 5/6 inches long and each strike of the hammer moves it 1/12 inches into the board.

To determine how many strikes are needed to drive the nail completely into the board you have to divide the size of the nail by the length it moves into the board each strike:

To divide fractions, you have to multiply the dividend (first fraction) by the reciprocal of the divisor (second fraction)

To determine the reciprocal you have to turn the fraction upside down:

Next, multiply both fractions:

To drive the nail completely into the board, Troy has to strike the hammer 10 times.

I believe the answer is 13 ways to make 27 cents using Quarters, dimes, nickels, and pennies.

Step-by-step explanation:

Answer - The answer is B AND C

Pls give brainliest

Answer:

Hello there! Your answer would be C and B.

Step-by-step explanation:

You might know that a Rhombus is a special type of parallelogram whose all sides are equal. The difference between a square and a rhombus is that all angles of a square are right angles, but the angles of a rhombus need not be right angles. So, a rhombus with right angles becomes a square. It is not D because it shows you that it has right angles. A does not have equal sides therefore it is not a rhombus :]

hope this helps! feel free to clarify if unsure