The perimeter of a rectangle is 40 inches. Find the length and width if the length is an integer and the width is 2 times the next consecutive integer. Length = Width =

The amount of milk remaining after the milk is sold to the customer and hotel is 18 liters.

Given is that a milkman had 31 liters of milk in the can. He sold 11 liters to a customer and 2 liters to a hotel.

Assume that the remaining milk in the container is denoted by [x]. Then, we can write -

[x] = Total milk - {milk sold to customer + milk sold to can}

[x] = 31 - {11 + 2}

[x] = 31 - 13

[x] = 18

Therefore, the amount of milk remaining in the can is 18 liters.

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By using the concept of maxima of a function, it can be calculated that-

He must spent $8000 to maximize sales

Maximum sales is 1548000 units

What is maxima of a function?

Maxima of a function gives the maximum value of the function within a given domain or within an interval.

Here,

S(x) = [tex]-2x^3 + 12x^2 + 192x + 268[/tex]

S'(x) = [tex]-6x^2+24x+192[/tex]

S'(x) = 0

[tex]-6x^2+24x+192=0\\-6(x^2-4x-32)=0\\x^2-4x-32=0\\x^2-8x+4x-32=0\\x(x-8)+4(x-8)=0\\(x-8)(x+4) = 0\\[/tex]

x - 8 = 0 or x + 4 = 0

x = 8 or x = -4

But x = -4 is not possible

So he must spent $8000 to maximize sales

S''(x) = -12x + 24

S''(8) = -12(8) + 24 = -72<0

Hence sales is maximum

Maximum sales = S(8) = [tex]-2(8)^3+12(8)^2+192(8)+268[/tex]

                                     = 1548

Maximum sales is 1548000 units

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An equation whose solution is the number of months, m, it takes for the account balance to reach $2000 would be the initial balance minus the monthly rent times the number of months equals $2000.

$4800-$400m=$2000

Given:

initial balance : $4800

removed from the account each month for rent : $400

Since the account starts with $4,800 and decreases by $400 each month, there will be 4800−400m dollars left in the account after m months have passed.

The question asks us to set up an equation representing the number of months that pass before this quantity equals 2,000, and so the desired equation is

4800−400m=2000.

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The Area of given figure is 48.28 unit² (Approx.)

Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, etc.

When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.

We are Given Length of parallel lines are 13 , 6 respectively

Diameter of semi-circle = 6

Height of parallelogram = 8

Area of given figure

Radius of semi-circle = Diameter of semi-circle / 2

Radius of semi-circle = 6 / 2

Radius of semi-circle = 3

Area of given figure = [1/2][Sum of parallel line][Height] + [πr² / 2]

Area of given figure = [1/2][13 + 6][8] + [(3.14)(3)² / 2]

Area of given figure = 42 + 6.28

Area of given figure = 48.28 unit² (Approx.)

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Using percentage error, the error factor is ± 2.15 inches and the smallest size is 40.85 inches and largest size is 45.15 inches.

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage. In other words, the percent error is the relative error multiplied by 100.

The formula of percentage error is given as

P.E = [(actual value - estimated value) / actual value] × 100

Since we know the percentage error and actual value, we can find the difference or actual error by;

5 / 100 = x / 43

0.05 = x / 43

x = 2.15

The increase of decrease in size is by a factor of ± 2.15

The smallest size = 43 - 2.15 = 40.85 in

The largest size = 43 + 2.15 =  45.15 in

The smallest and largest size are 45.15 and 40.85 inches respectively

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The compositions of the functions are given as follows:

The domain and the range of the functions are given as follows:

The representation of the composite function is that the output of the inner function works as the input to the outer function, as follows:

(f ∘ g)(x) = f(g(x)).

Hence, at x = 0, the composite function is given as follows:

(f ∘ g)(0) = f(g(0)) = f(1) = 0.

At x = 1, the composite function is given as follows:

(g ∘ f)(0) = g(f(0)) = g(1) = -2.

The definitions of the domain and of the range of a function are given as follows:

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The equation that represents the graph that gives the number of servings, y, in x pints of frozen yogurt is: y = 3x.

A proportional relationship graph is a straight line graph that passes through the point of origin, (0, 0), which has an equation that can be expressed in the slope-intercept form as y = kx.

"k" is the constant of proportionality, which is the ratio of y to x. k = y/x.

Given the graph above, we need to find the constant of proportionality, k. To do this, use the coordinates of one point on the graph, say (1, 3):

Constant of proportionality, k = y/x = 3/1

k = 3

To write the equation that gives the number of servings, y, in x pints of frozen yogurt, substitute k = 3 into y = kx:

y = 3x

The equation is: y = 3x.

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2018 depreciation (year 3) deduction for the machine is $6000 when ABC Corp spent $31,250 on a production machine on January 1, 2019.

Given that,

ABC Corp spent $31,250 on a production machine on January 1, 2019. The corporation is depreciating the equipment using the MACRS accelerated depreciation tables for 5-year property, half-year convention, and has chosen not to exercise Section 179 expensing or to claim bonus depreciation in 2019.

We have to find what is the machine's Year 3 depreciation deduction for 2021.

We know that,

Computation of 2018 depreciation (year 3) deduction for the machine using MACRS accelerated depreciation table for 5 year property.

Name of the asset is production machine

Basis of machine is $31,250

MACRS Percentage from MACRS Percentage Table A-1 by IRS Publication 946 for 5 year property using half year convention for 3rd year is 19.20%

2018 depreciation (year 3) deduction for the machine  is

$31,250×19.20%=$6,000

Therefore, 2018 depreciation (year 3) deduction for the machine is $6000 when ABC Corp spent $31,250 on a production machine on January 1, 2019.

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Answer:

Below

Step-by-step explanation:

edited:  FOR QIII   (I didn't see that part)

Remember for a right triangle  S-O-H-C-A-H-T-O-A

   Tan is OPPOSITE LEG / ADJACENT LEG

   make the right triangle with legs 3 and 4  ( in quadrant III)

      then the hypotenuse is 5

         sin = opp/ hyp =  - 3/5

            cos = -  4/5

                csc = 1/sin = - 5/3

                   sec = 1/cos = - 5/4

                       cot = 1/tan = 3/4

Part (a)

The compound interest formula is

A = P*(1+r/n)^(n*t)

where,

For option 1, we have these values:

Plug them into the formula to get:

A = P*(1+r/n)^(n*t)

A = 4000*(1+0.018/4)^(4*3)

A = 4221.4270078004

A = 4221.43

The account balance after three years is $4221.43

Then subtract off the deposit to find the interest made.

i = A - P

i = 4221.43 - 4000

i = 221.43

Answer: Option 1 pays $221.43 in interest.

====================================================

Part (b)

If n heads to infinity, then the compound interest formula is replaced with the continuously compounded interest formula.

That formula is

A = P*e^(r*t)

where the new item 'e' is a special constant.

e = 2.718...

It's similar to how pi = 3.14...

Most calculators have an "e" button, so it's best to let the calculator handle the decimal digits of "e".

For option 2, we have:

So,

A = P*e^(r*t)

A = 4000*e^(0.015*3)

A = 4184.11143963493

A = 4184.11

and,

i = A - P

i = 4184.11 - 4000

i = 184.11

Answer: Option 2 pays $184.11 in interest.

Option 1 is the better choice.

Answer:

$7.25.

Step-by-step explanation:

To find the cost of Wilson's bus ticket, we first need to determine how many additional miles he traveled beyond the first 10 miles. Since the ticket price was $0.50 per 1/2 mile, we can divide the number of additional miles by 0.5 to find the number of additional 1/2 miles. For example, if Wilson traveled 12 miles, he would have traveled 2 miles beyond the first 10 miles. Dividing 2 by 0.5, we get 4, so he would have traveled an additional 4 1/2 miles.

Once we know the number of additional 1/2 miles, we can multiply that number by the ticket price per 1/2 mile to find the cost of the additional portion of the ticket. For example, if the ticket price was $0.50 per 1/2 mile and Wilson traveled an additional 4 1/2 miles, the cost of the additional portion of the ticket would be 4.5 * $0.50 = $2.25.

Finally, we can add the cost of the initial portion of the ticket, which was $5.00 for the first 10 miles, to the cost of the additional portion to find the total cost of the ticket. For example, if the initial portion of the ticket was $5.00 and the additional portion was $2.25, the total cost of the ticket would be $5.00 + $2.25 = $7.25.

In conclusion, to find the cost of Wilson's bus ticket, we need to divide the number of additional miles he traveled beyond the first 10 miles by 0.5 to find the number of additional 1/2 miles, multiply that number by the ticket price per 1/2 mile to find the cost of the additional portion of the ticket, and then add that amount to the cost of the initial portion of the ticket to find the total cost.

Answer:$11.00

Explanation:22-2=20

20÷5=4

4÷2=2

2×$5.00=$10

additional 2 miles

2×$0.50=$1

so

$10+$1=$11.00

The value of x in the parallel lines is 102 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angle, linear angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the value of x using the angle relationships.

Alternate exterior angles are the pair of angles on the outer side of the two parallel lines but on the opposite side of the transversal.

Therefore,

x = 102 degrees(alternate exterior angles)

Alternate exterior angles are congruent.

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The amount of paycheck of Salesperson 1 and Salesperson 2 is $770 and $905 respectively.

What is Percentage?

The percentage is one of the most used methods to portray statistics. Percentage simply means "per hundred," and the sign for percentage is%. One percent (or 1%) is one hundredth of a total or whole number and is computed by dividing the whole or entire number by 100.

Solution:

Given: Paycheck of Salesperson 1 = 85% of Salesperson 2

Let, Paycheck of Salesperson 2 = x

So, paycheck of Salesperson 1 = 85/100 x

According to the question,

85/100 x + x = 1675

185/100x = 1675

x = 167500 / 185

x = 905.4$ = 905$

Salesperson 1 = 770$

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Answer: the length of the garden is 35 meters

Step-by-step explanation:

The formula for perimeter is 2W+2L=perimeter

With the given information you can plug in the values and use them to solve for the length, L.

W=20 and p=110 so now plug them in and solve for L

2(20)+2L=110      multiply the 20 by 2

40+2L=110      subtract 40 from both sides

2L=70    divide both sides by 2

L= 35 meters

You can check to see if you got the right answer by plugging the L in and find p.

2(20)+2(35)=40+70=110 by getting 110 it means it is the correct value for L

The metrics of dispersion are mean deviation and range. While quartile deviation is a measure of dispersion, quartiles themselves are not.

25% from the lowest to the highest number in the first quartile. 25.1% to 50% in the second quartile (till median) Three-quarter range: 51% to 75% (above the median) 25% of the highest values are in the fourth quartile.

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3). As the second quartile, the median is used (Q2). The distance between the upper and lower quartiles is known as the interquartile range.

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Answer:

x= 12

Step-by-step explanation:

Y[tex]\alpha[/tex] X

Let the constant be k

For the proportionality sign to be gone,a constant has to be introduced.

Since y varies directly,the constant ( k) will multiply x

Y= kx

Substitute for x=6 and y=36 to find k

36=6x

x = 36/6 = 6

To find the value of x,substitute for k = 6 and y = 72

72= 6x

x = 72/6

x=12

Answer:

here's how you will do it hope it helps you-

Answer:

Split the variable by dividing each side by the factors that do not contain the variable.

Dạng chính xác:

x

=

−

3

13

Dạng thập phân:

x

=

−

0.

¯¯¯¯¯¯¯¯¯¯¯¯

230769

Answer:

Step-by-step explanation:

10(a)+5(c)=310

a= number of adult

c= number children

The reason for the similarity of the triangles FGH and JHK is given as follows:

HL.

The similarity theorems are listed as follows:

The similarities between the triangles FGH and JHK are given as follows:

As they are right triangles, the remaining side should also be equal, according to the trigonometric ratios, hence the theorem is the SSS theorem, also called HL theorem.

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Answer:20[tex]m^{2}[/tex]

Step-by-step explanation:

The formula to find the area of a triangle is [tex]\frac{1}{2}[/tex]bh.

b is the base value

h is the value of the height.

1/2b is 5 and 5 times 4 is 20 :)

Answer:

Area: 200.96

Circumference: 50.24

Step-by-step explanation:

Area: π* r²

Circumference: 2* π*r

Graphing these equations can help find the solution to the system by unique solution, no solution and infinite number of solution.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Given

Graphing these equations can help find the solution to the system by,

There are three possible outcomes when two equations with two variables are considered in a two-dimensional plane.

1.Unique solution: A point will be where the graphs of the two lines connect.

The One equation's coefficient of variation and constant will not be proportionate to another equation's coefficient of variation and constant.

2. No Solution: The two lines run parallel to one another.

While constants are not proportional, the coefficient of variables of one equation will be related to the coefficient of variables of another equation.

3, Infinite number of Solution: The two lines will coincide.

One equation's coefficient of variation and constant will be proportional to another equation's coefficient of variation and constant.

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Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The algebraic expression for the statement, "16 more than the product of 43y", is : 43y + y.

An algebraic expression can be described as an expression that consists of terms and algebraic operations.

The terms could be variables and constants, while the algebraic operations could be addition, subtraction, multiplication, or division.

For example,  3x² − 2xy + 5 is an algebraic expression that consists of three terms.

To write an algebraic expression for the statement given above, we have the following:

The variable that represents the unknown number is y.

Product means multiplication.

The product of 43 and a is: 43 × y = 43y.

Therefore, "16 more than the product of 43y" would be translated as: 43y + y.

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Answer:

-3

Step-by-step explanation

x^3+(5x+y)2

-1^3=-1

-1 x -1 x -1 = -1

(5x+y)2

(5(-1)+(4)2

(-5+(4))2

(-1)2 = -2

Bring -1 down from -1^3

-1-2=-3

You answer is -3

Answer:

Step-by-step explanation:

(19/3)+(7/2)

(11/2)+(13/3)

=> 6.33 + 3.5   /   5.5 + 4.33  = 1

Answer:

the correct answer is 3

hope it is right

The answer to the expression is 3

When two lines intersect with each other then point of intersection formed by two intersecting lines create V in an absolute value graph is known as Vertex.

As given in the question,

Given : Two lines intersect with each other .

Therefore, point of intersection of two lines created V shape on the graph is called vertex.

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