Find the absolute maximum and minimum of the function f(x,y)=x2+y2 subject to the constraint x4+y4=1296. As usual, ignore unneeded answer blanks, and list points in lexicographic order. Absolute minimum value: attained at ( , ), ( , ), ( , ), ( , ). Absolute maximum value: attained at ( , ), ( , ), ( , ), ( , ).

Sofia's net pay for this first pay period is $3,801.15.

In the given question, we have to compute Sofia's net pay for this first pay period.

As we know that;

A person's net income, which differs from their gross income since it takes payroll deductions into account, is how much money they really take home from each paycheck. A person's net salary is the amount they earn after all necessary deductions, such taxes, have been made from their gross remuneration. After all deductions have been made, this is the total amount that is put into the employee's bank account. The amount an employee receives before any payroll deductions, including those for taxes, benefits, and other costs, is known as their gross pay.

So calculation of net pay is given below;

According to the calculation, Sofia's net pay for this first pay period is $3,801.15.

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The length of the rectangular garden is 9 feet.

Let x = length of the rectangular garden in feet

y = width of the rectangular garden in feet

If a client asked Leah to design a rectangular garden with a length that is two feet less than three times the width, then

x = 3y - 2     (equation 1)

If the rectangular garden is to have an area of 33 square feet, then the product of the length and width should be equal to 33 square feet.

A = l x w

33 = xy

Substitute the expression for x and solve for y.

33 = xy

33 = (3y - 2)y

33 = 3y² - 2y

3y² - 2y - 33 = 0

(3y - 11)(y + 3) = 0

3y - 11 = 0     ;     y + 3 = 0

3y = 11     ;     y = -3

y = 11/3

Substitute the value of y and solve for x.

x = 3y - 2     (equation 1)

x = 3(11/3) - 2

x = 9

length of the rectangular garden = 9 feet

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Answer:

SSS: Side-Side-Side
SAS: Side-Angle-Side
ASA: Angle-Side-Angle

AAS: Angle-Angle-Side

Step-by-step explanation:

They are the conditions used to determine whether two triangles are congruent or not.

The required angles are :

corresponding angles:  ∠7=∠5

alternate interior angles: ∠4 = ∠2 and∠3 = ∠1

alternate exterior angles: ∠7 = ∠6

same side interior angles: ∠7 = ∠8

alternate interior angles

alternate exterior angles

same side interior angles

Corresponding angles:

one that hold the same relative position as another angle somewhere in figure.

Alternate interior angles:

Alternate interior angles are the angles formed on the opposite sides of the transversal.

Alternate exterior angles:

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

Same side interior angles:

The theorem states that the same-side interior angles must be supplementary given the lines intersected by the transversal line are parallel.

corresponding angles:

∠7=∠5

alternate interior angles:

∠4 = ∠2

∠3 = ∠1

alternate exterior angles:

∠7 = ∠6

same side interior angles:

∠7 = ∠8

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It will take 20 years for the bank's money to double

What is simple interest ?

The principal of a loan or the initial deposit into a savings account serves as the foundation for simple interest. Simple interest does not compound, therefore the creditor only has to pay interest on the capital sum and the borrower never has to pay interest on the interest that has already accrued.

Simple Interest formula

I = (P*T*R)/100

The given values are

I = 50000

P = 50000

R = 5%

The formula for T will become

T = (I*100)/(P*R)

  = (50000 *100) / (50000 * 5)

  = 5000000 / 250000

T = 20 Years

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Python code for given situations:

1)

areaOfSquare = int(input('Area of the square: '))

if areaOfSquare >= 0:

sideOfSquare = sqrt(areaOfSquare)

print(sideOfSquare)

else:

print("INVALID")

2)

while True:

n=int(input("Enter a number: "))

if(n>=1 and n<=10):

break;

3)

response = str()

while True:

response=input("Enter a number: ")

if (response=='y' or response =='Y' or response=='N' or response=='n'):

break;

In this question we need to write Python code for given situations.

1)

areaOfSquare = int(input('Area of the square: '))

if areaOfSquare >= 0:

sideOfSquare = sqrt(areaOfSquare)

print(sideOfSquare)

else:

print("INVALID")

2)

while True:

n=int(input("Enter a number: "))

if(n>=1 and n<=10):

break;

3)

response = str()

while True:

response=input("Enter a number: ")

if (response=='y' or response =='Y' or response=='N' or response=='n'):

break;

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exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph and if the log term involved in the given function then it is a logarithmic

How do you identify an exponential function from a graph?

Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph

and if the log term involved in the given function then it is a logarithmic

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The trapezoidal rule uses trapezoidal approximations to approximate the definite integral, whereas the midpoint rule uses rectangular regions to do so. By first approximating the original function with piecewise quadratic functions, Simpson's rule approximates the definite integral.

Since

"frac" (1-x) = (1-x)-1 = 1+x2+x3+x4+.... = "sum_n=0" infty" xn "hspace"

5mm for "left | x | 1"

How can a power-based integral be evaluated?

Power Rule for Integrals To apply this rule, simply add one to the exponent.The expression is then divided by the same number.The constant C is added in the final step. Now, we will solve some problems to determine the integrals of polynomials and root functions.

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Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

30-60-90 tri so x=[tex]5\sqrt{3}[/tex]

Answer:

5√3

Step-by-step explanation:

Given a=5 and ∠β=60°,

b = 8.66025 = 5√3

b = √c^2 - a^2

= √10^2 - 5^2

= √75

= 8.66025 = 5√3

Thanks.

The survey is of the population of all the patients present in that particular hospital.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a certain population.

Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers.

Surveys are used to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions.

Surveys might have narrow, focused objectives or they can have broad, more general objectives.

So, in the given situation the survey states that 62.42% of the respondents indicated that the health care providers needed to spend more time with each patient.

So, it is clear that the remaining respondents have the opposite view on this.

So, the respondents will be all the patients present in the local hospital.

Therefore, the survey is of the population of all the patients present in that particular hospital.

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Answer:

The volumes are equal.

Step-by-step explanation:

Areas are numbers. Numbers are not congruent. They may be equal.

Volume of cylinder = (area of base) × height

Volume of prism = (cross-sectional area) × height

Since the cross-sectional area are equal, and the heights are equal, the volumes are equal.

The midpoint of A and B is (Xa , Yb) = (-4,1) and  the midpoint of C and D is (Xc , Yd) = (4 , 6)

What is midpoint?

A(-3,5) and B(-5, -3)

(Xa , Yb) = [(x₁ + x₂ / 2) , (y₁ + y₂ / 2)]

= [(-3 + (-5) / 2) , (5 +(-3) / 2)]

= (-8/2 , 2/2)

(Xa , Yb) = (-4,1)

Hence, the midpoint of A and B is (Xa , Yb) = (-4,1).

C(7,9) and D(1,3)

(Xc , Yd) = [(x₁ + x₂ / 2) , (y₁ + y₂ / 2)]

= [(7+1/2) , (9+3 / 2)]

= ( 8/2 , 12/2)

(Xc , Yd) = (4 , 6)

Hence, the midpoint of C and D is (Xc , Yd) = (4 , 6).

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The length of the rectangular solar panel the electrician is installing is 25m

The length of the panel is calculated from the Area of the panel which is given by the formula

Ares of rectangle = length * width

given units

area = 180 squared meters

width of the section = 7 1/5

From area = length  * width

length  = are / width

length  = 180 / 7 1/5

length = 25 m

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Answer:

25m

Step-by-step explanation:

25m

The binary search tree is better than the sorted link with respect to efficiency and intricacy.

Comparing a sorted linked list to a binary search tree for up to 1000 integer members, the intricacy of the algorithm in the sorted linked list grows over time. It differs depending on where the seeking element is located in sorted links. It requires little time if the searching element is present at the beginning of the linked list. However, in a linked list, the worst-case scenario occurs if the seeking element is present at 1000. Searching for the element in that position takes a long time.

The 1000 elements in a binary search split into two main wings. This type of search varies in difficulty depending on tree height. In the worst situation, if there are about equal numbers of elements on the left and right sides of the wing, searching for an element takes about half as long as searching for it in sorted links. Binary is more effective than Sorted as it uses a binary search algorithm instead of the linear search technique used by linked lists.

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The total number of units of fuel used per mile is f(N) = 12 + 2.2N

What is a linear function?

A straight line on the coordinate plane is represented by a linear function. The formula for a linear function is f(x) = mx + b, where m and b are real values.

Let 'N' represent the number of railcars on the train.

Each railcar on the train adds 2.2 units of fuel per mile and then,

Total consumption for 'N' number of railcars = 2.2N units of fuel per mile.

The fixed amount of fuel consumption = 12 units of fuel per mile.

The expression for fuel consumption per mile is given by:

f(N) = 12 + 2.2N

Hence, the expression for f(N) is 12 + 2.2N.

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The time required by the bacteria to reach 15000 is :

log(2)/log(1.5) = t

Given:

P(t) = P0·bt

P(t) = bacteria population at time t

P0 = starting bacteria population = 10,000

b = growth rate

t = days

we are asked to find out after how many hours will the bacteria population reach 15000 = ?

P(t) = P0·bt

At t = 1 day, P(t=1) = 15,000:

15,000 = 10,000·b1

15,000/10,000 = b

1.5 = b

P(t) = 10,000·1.5t

Population doubles when P(t) = 20,000:

20,000 = 10,000·1.5t

2 = 1.5t

log(2) = log(1.5t)

log(2) = t·log(1.5)    [Log property: log(ab) = b·log(a)]

log(2)/log(1.5) = t

Hence we get the required answer.

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Step-by-step explanation:

reflect it up over the horizontal line y = 7.5

it now covers completely the C triangle.

and then move (translate) it 2 units to the right.

By using Unitary method, it can be calculated that

An object whose mass is 10 kg weighs 90 N

What is unitary method?

Unitary method is the process in which the value of single unit can be calculated from the value of multiple unit and the value of multiple unit can be calculated from the value of single unit. Sometimes Value of single unit can be less than the value of multiple unit. For example - The relation between the cost of a commodity and the quantity of the commodity

Sometimes Value of single unit can be more than the value of multiple unit. For example - The relation between the number of men and the number of days taken by those men to do a certain job.

Here, Unitary method will be used

The weight of an object varies directly with the mass of the object.

An object whose mass is 7 kg weighs 63 N

An object whose mass is 1 kg weighs [tex]\frac{63}{7}[/tex] N

An object whose mass is 1 kg weighs 9 N

An object whose mass is 10 kg weighs [tex]9 \times 10[/tex] = 90 N

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The reason they have to be simplified is that you cannot add radical unless the number under the radical is the same on all of them.

For example:

If you add √8 + √32 without simplifying, the best you could do is an estimate. But if you're required to put your answer in standard radical form this would be an issue.

So, you would have to simplify to combine:

√4√2 + √16√2

2√2 + 4√2

6√2

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Rob earned $70 then he would have $25.

What are ratio and proportion?

A ratio is an ordered pair of numbers a and b, denoted by the symbol a / b, where b does not equal zero. A proportion is an equation that sets two ratios equal to each other. For example, if there is one boy and three girls, the ratio could be written as 1: 3. (for every one boy there are 3 girls) One-quarter are boys, and three-quarters are girls.

If for every $14 he earns $5.

Then on Saturday, he earned $70 so the total amount of money he would have

                         = 5 * 70/14

                         = 5 * 5

                         = $25

Hence, if Rob earned $70 then he would have $25.

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Using Cooking measurements,

The value replacement for 3/4 cup is = 36 teaspoons or 12 tablespoons.

Cooking Measurements :

Calculate and determine the specific amounts of ingredients required using standard measuring equipment.

A measuring spoon, measuring cup, or measuring utensil.

Measuring Spoons come in a variety of sizes and materials. The smallest set of spoons measure smudges, pinches and dashes. Other sets include tsp (tsp) and tsp (tbsp)

we have given 3/4 cup and we want to replace it

Using the cooking measurement chart ,

1 cup = 16 tablespoons or 48 teaspoons

1/2 cup = 8 tablespoons or 24 teaspoons

we have 3/4 cup then

3/4 cup = 1 cup - 1/4 cup

1/4 cup = 4 tablespoons or 12 teaspoons

then , 3/4 cup = 16 tablespoons - 4 tablespoons

= 12 tablespoons or

3/4 cup = 48 teaspoons - 12 teaspoons

= 36 teaspoons

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The total time would be 38,3 seconds moves of arc length of 24.0 cm

The measurement of a circle's boundaries is also known as the circumference or the perimeter of the circle. whereas the circumference of a circle shows the space it occupies. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units such as cm or m are used to measure it.

First we convert cm to meters.

6.00cm= 0.006m

24.0cm= 0.024m

Circumference

2πr = 2(π)(0.006)= 0.0376

The second hand taking 60 sec for one rev, so:

60*0.024/ 0.0376 = 38.3 seconds.

Hence we get the time as 38.3 seconds

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Answer:

165 miles

Step-by-step explanation:

Distance = rate x time

Distance = 55(3)

Distance = 165 miles

Answer:

distance = 165 miles

Step-by-step explanation:

We know that d=rt

Distance = rate * time

distance = 55 miles / hour * 3 hours

distance = 165 miles

The total number of cartons of ice cream that are there in total are 312.

The frozen peas that were packed into each box are 24.

A ratio is an ordered pair of numbers a and b, denoted by a / b, where b does not equal zero. A proportion is an equation that equalizes two ratios.

The ratio formula for any two quantities is a: b a/b. The percentage formula, on the other hand, is written as a:b::c:dab=cda:b::c:dab=cd.

Given,

The cartons of ice cream that fit into each packing box=24

Also given that,

No. of packing boxes=13

Therefore, 24×13=312

The total number of cartons of ice cream that are there in total are 312.

And given that 192 packs of frozen peas were packed into 8 boxes.

So, The number of packs that each box contains are,

192/8=24

The frozen peas that were packed into each box are 24.

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The complete question is:

"24 cartons of ice cream fit into each packing box.

If there are 13 packing boxes, how many cartons of ice cream are there in total?

192 packs of frozen peas were packed into 8 boxes.

How many were packed into each box?"

x is his present age in years

his age 11 years ago is x-11

54 is more than 30 by 14

Subtraction is an arithmetic operation that represents the operation of removing a number from another number. Subtraction is represented by the minus sign,

Other arithemetic operations are addition, multiplication and division.

The mathemetical properties that it follows is Identity Property. ...

Commutative Property and Associative Property.

Let the number by how much 30 is less than 54 be x,

then

30 + x = 54

x = 54 - 30

x = 14

Therefore, 30 is less than 54 by 14

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The correct answer is at the univariate level, descriptive statistics are used for 'data reduction'

By creating the summaries of data samples, descriptive statistics can be used to describe the characteristics of a data set.

It is frequently presented as a summary of data that explains the contents of data. For instance, a census of the population may contain descriptive data on the proportion of men and women in a particular city.

Informational and intended to describe the precise features of a data set, descriptive statistics provide details. The greatest individual batting average for a player, the average number of runs per division, and the number of runs allowed per team are some descriptive statistics that may be used to analyse data from the previous Major League Baseball season.

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The probability is less than 5% is [tex]P(X\geq 3) = 1.16%[/tex]%.

Three or more of the plants in the bundle die before producing any rhubarb.

Given, n = 10 and p = 0.05

The binomial Probability:

[tex]P(x=k)=\left(\begin{array}{ccc}n\\k\\\end{array}\right) p^{k}. (1-p)^{n-k}[/tex]

Putting n = 10 and p = 0.05 in the last equation.

[tex]P(x=k)=\left(\begin{array}{ccc}10\\k\\\end{array}\right) 0.05^{k}. (1-0.05)^{10-k}[/tex]

For k = 0

[tex]P(x=0)=\left(\begin{array}{ccc}10\\0\\\end{array}\right) ((0.05)^{0}).(0.95)^{10-0}=0.5987[/tex]

For k = 1

[tex]P(x=1)=\left(\begin{array}{ccc}10\\1\\\end{array}\right) (0.05)^{1}. (0.95)^{10-1}=0.315[/tex]

For k = 2

[tex]P(x=2)=\left(\begin{array}{ccc}10\\2\\\end{array}\right) (0.05)^{2}. (0.95)^{10-2}=0.0746[/tex]

[tex]P(X\geq 3)=1-P(X=0)-P(X=1)-P(X=2)\\P(X\geq 3)=1-0.5987-0.3151-0.0746\\P(X\geq 3)=0.0116\\[/tex]

[tex]P(X\geq 3)=1.16%[/tex]%

The probability is less than 5% is [tex]P(X\geq 3) = 1.16%[/tex]%.

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The three sides of a triangle that is 5cm, 3cm, and 8cm not of the triangle.

Triangle:

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same

Here we have to find the given three sides of a triangle possible.

The three sides are 5cm, 3cm, and 8cm.

The property of a triangle is that the sum of two sides of a triangle is greater than the third side of a triangle.

The three sides are:

a = 5cm

b = 3cm

c = 8cm

a + b > c

5 + 3> 8

8> 8 which is incorrect

Therefore the three sides in not sides of a triangle.

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