A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 75 pounds. There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system

The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]

[tex]q_1=-4 \mathrm{nC} \text { at }(0.6,0.8)[/tex]

[tex]$q_2=6 \mathrm{nC}$[/tex] at (0.6,0)

[tex]$r_1=$[/tex]Distance of [tex]$q_1$[/tex] from origin[tex]$=\sqrt{0.6^2+0.8^2}$[/tex]

[tex]$r_2=$[/tex] Distance of [tex]$q_2$[/tex] from origin [tex]$=0.6$[/tex]

[tex]$\mathrm{k}=$[/tex] Coulomb constant[tex]$=9[/tex]times [tex]10^9 \mathrm{Nm}^2 / \mathrm{C}^2$[/tex]

Electric field is given by

[tex]&E_1=\frac{k q_1}{r_1^2} \\[/tex]

[tex]&\Rightarrow E_1=\frac{9 \times 10^9 \times 4 \times 10^{-9}}{\sqrt{0.6^2+0.8^2}} \\[/tex]

[tex]&\Rightarrow E_1=36 \mathrm{~N} / \mathrm{C}[/tex]

[tex]&\theta=\tan ^{-1} \frac{0.8}{0.6} \\[/tex]

[tex]&\Rightarrow \theta=53.13^{\circ} \\[/tex]

[tex]&E_1=36 \cos 53.13^{\circ} \hat{i}+36 \sin 53.13^{\circ} \hat{j} \\[/tex]

[tex]&\Rightarrow E_1=21.6 \hat{i}+28.8 \hat{j}[/tex]

[tex]&E_2=\frac{k q_2}{r_2^2} \\[/tex]

[tex]&\Rightarrow E_2=\frac{9 \times 10^9 \times 6 \times 10^{-9}}{0.6^2} \\[/tex]

[tex]&\Rightarrow E_2=150 \mathrm{~N} / \mathrm{C}[/tex]

The charge [tex]$q_2$[/tex] is on the [tex]$\mathrm{x}$[/tex] axis itself and it is pointing towards the origin (left side) so the sign will be negative

[tex]E_2=-150 \hat{i}[/tex]

Resultant electric field

[tex]&E=E_1+E_2 \\[/tex]

[tex]&\Rightarrow E=21.6 \hat{i}+28.8 \hat{j}+(-150 \hat{i}) \\[/tex]

[tex]&\Rightarrow E=-128.4 \hat{i}+28.8 \hat{j}[/tex]

Magnitude of electric field is given by

[tex]&|E|=\sqrt{(-128.4)^2+28.8^2} \\[/tex]

[tex]&\Rightarrow|E|=121.6 \mathrm{~N} / \mathrm{C}[/tex]

Magnitude of the net electric field is [tex]$121.6 \mathrm{~N} / \mathrm{C}$[/tex]

Direction is given by

[tex]\theta=\tan ^{-1} \frac{128.4}{28.8}=77.36^{\circ}[/tex]

From the -x axis

[tex](90+77.36)^{\circ}=167.36^{\circ}[/tex]

The direction of the net magnetic field is [tex]$167.36^{\circ}$[/tex]

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Using the probability concept, it is found that 60% of the swim team are sophomores.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

The sum of the probabilities of all outcomes of an event is of 1, hence:

P(freshman) + P(sophomore) = 1.

The probability that a sophomore is elected is $3/2$ times the probability that a freshman is elected, hence:

x + 3/2x = 1.

5/2x = 1

5x = 2

x = 0.4.

Thus:

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The cardinality of the cartesian product of A and B is 18.

Cartesian Product of two sets A and B is defined as the set of all ordered pairs (a,b) where a∈A & b∈B.

Cardinality of a set is defined as the number of elements in that particular set.

For example,  for a set A={2,6,4} , the cardinality is 3.

Given set A= { x | x is a prime number less than 7}

A={2,3,5}

set B =  { y | y is perfect square of an integer and y is less than 29}

B={0,1,4,9,16,25}

The cartesian product of A and B denoted by AxB will be

AxB={(2,0),(2,1),(2,4),(2,9),(2,16),(2,25),(3,0),(3,1),(3,4),(3,9),(3,16),(3,25),(5,0),(5,1),(5,4),(5,9),(5,16),(5,25)}

The number of elements in AxB is 18.

Therefore , the cardinality of the cartesian product of A and B is 18.

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(-1/5, 37/70) are the coordinates of a point 7/10 of the way between A and B.

Let P be the point 7/10 of the way from A to B. This implies that it partitions P in the 7:10 ratio (AP/PB = 7/10).

Should use section formula to find the coordinates, which is given as:

x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Where,

(x₁, y₁) = A(-4, -7)

(x₂, y₂) = B(11, 5)

m = 7 and n = 10.

Put the values to obtain the x and y coordinates of point P.

y = (7×5 + 10(-7))/(7 +10)

On solving;

y = -1/2

Solve for x coordinates;

x = (7(11) + 10(-4))/(7 +10)

on solving;

x = 37/70

Therefore, the coordinates of a point 7/10 a way from A and B is (-1/5, 37/70).

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Answer:

2

-

2 - 4 ^ 5

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

As a reminder, an arithmetic sequence or arithmetic progression (AP) is a progression in which the difference (called the tolerance) between two consecutive terms in the progression is constant.

Therefore, the expression for the nth term is

an = a₁ + (n − 1) d

and in general

an = am + (n - m) d.

where d is the difference.

For an arithmetic series with initial term a₁ and difference between terms of d

an = a₁ + (n − 1) d

We are told

d = -2 and

S8 = 240

So,

a1 = 240 = a1 + ( 30 - 1) * ( -2 ) = a1 - 58

a1 = 240+58 =298

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Considering the condition for a relation to be a function, we have that:

A graph represents a function if each value of the input is mapped to only one value of the output.

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.

Hence:

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Answer:

$14 for 50 copies.

Step-by-step explanation:

Given that,

→ C(x) = 10.00 + 0.08x

Then the cost for 50 copies will be,

→ C(50) = 10.00 + (0.08 × 50)

→ C(50) = 10.00 + 4

→ [ C(50) = $14 ]

Hence, the total cost of $14.

The left over fabric area is; 0.03 m²

Now, if the radius of a circle is r, then the diameter is;

d = 2r

Now, there are 16 identical circles to be cut from a square sheet of fabric whose sides are 0.4 m long.

Thus, the height of the square will be the diameter of four circles.

Height of square = 4(2r) = 8r

Thus;

8r = 0.4

r = 0.4/8

r = 1/20 m

Left over fabric area = (0.4 * 0.4) - (π × (1/20)²)

Left over fabric area = 0.03 m²

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The speed John will be 47 miles per hour. Then the time to travel 376 miles will be 8 hours.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

John drove 235 miles in 5 hours. Then the speed of the John will be

Speed = 235 / 5

Speed = 47 miles per hour

If he continued at that same rate. Then the time to travel 376 miles will be given as,

47 = 376 / Time

Time = 376 / 47

Time = 8 hours

The speed John will be 47 miles per hour. Then the time to travel 376 miles will be 8 hours.

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Answer:8

Step-by-step explanation:

It should be noted that the seat number is C

Jean received seat number 108.

It should be noted that from the information, The seat numbers were either 53, 64, 108, or 216. Candice received the only seat number with a factor of 16. This is 64.

Bill received the seat number that is the greatest multiple of 8 from the group of seats. This is 216.

Rose received the.only seat number that is a prime number. This is 53

Therefore, the remaining number is 108.

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Answer:

15

Step-by-step explanation:

Purdue : IU

   12      :  5

   36     :  x

cross multiply

36*5 = 12x

180 = 12x

180/12 = x

x = 15

Answer:

36/12= 3 so 5*3 would give you 15

The cube of 2.4 is 13.824

A cube can be described as when a number is multiplied three times. This means a product of the same number three times

From the question we are asked to calculate the cube of 2.4

(2.4)³

= 2.4 × 2.4 × 2.4

= 13.824

Hence the cube of 2.4 is 13.824

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Answer:

4

Step-by-step explanation:

[tex]\mathrm{-9 = 9, -5 = 5,\:because\:they\:are\:in\:absolute\:value}\\9 - 5 = 4[/tex]

Answer:

-4

Step-by-step explanation:

−9 − (−5)

Multiply

−1 by −5.

−9 + 5

Add

−9 and 5.

you get...

−4

Answer: Non-rectangular Parallelogram

The opposite sides are parallel, but the figure is not a rectangle. It's also not a square either since those figures have an axis of symmetry.

Answer:

103

Step-by-step explanation:

61+42 = 103

Rani will use 3/2 cups of white rice for 3 cups of milk.

"It is a method in which we obtain the value of a single unit by subtracting the value of multiple units and thus the value of multiple units by subtracting the value of a single unit."

Now, for the given question;

1 cup of white rice is required for every 2 cups of milk by Rani.

Thus,

2 cups of milk ------> 1 cup of white rice.

So, using unitary method. Divide both side by 2.

1 cups of milk ------> 1/2 cup of white rice.

Now, calculate for the 3 cups of milk.

multiplying both side by 3.

3 cups of milk ------> 3/2 cup of white rice.

Therefore, the 3/2 cups of white rice required for the 3 cups of milk.

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Answer:

11 1/4 + 3 1/2

45/4 + 7/2

(45+14)/4

59/4

14 3/4

Answer:

f(-1) = |-1+4| - 5 = -2

f(0) = |0+4| -5 = -1

f(2) = |2+4| -5 = 1

Answer:

√

30

Step-by-step explanation: Simply multiply

√

2

and

√

15

=

√

30

[Caution: If it were -2 and -15, this type of multiplication would not be correct.]

A new apple orchard is being planted by Aaron's uncle. They plant 12 trees after picking up a truckload of them. They still need to plant 40 trees the following day.

The letter (N) is the symbol used to represent natural numbers. Natural numbers are also known as counting numbers, and they begin with the number 1 and continue to infinity (never ending), which is represented by three dots (...)

900n - 9[tex]n^2[/tex] = A(n) = n(900 - 9n)

For the highest A(n), A'(n) = 0, A'(n) = 900 - 18n = 0, 18n = 900, and n = 900/18 = 50.

50 trees should be planted per acre to produce the most apples possible

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Answer:

944cm²

Step-by-step explanation:

Area = Area of parallelogram + Area of trapezoid

Area of parallelogram= l× b= 16×26= 416cm²

Area of trapezoid= h/2(a+b)

where a=26cm, b=40cm, h=16cm

Area of trapezoid= 16/2(26+40)=8(66)=528cm²

Area= 416+528=944cm²

Answer:

x = 4

Step-by-step explanation:

4x + 2(x + 6) = 36

4x + 2x + 12 = 36

6x  = 36 - 12

6x = 24

x = 24

      6

x = 4

Answer:

∠ NST = 59°

Step-by-step explanation:

∠ NST and ∠ LSN form a right angle , that is

∠ NST + ∠ LSN = 90

3x - 1 + 2x - 9 = 90

5x - 10 = 90 ( add 10 to both sides )

5x = 100 ( divide both sides by 5 )

x = 20

Then

∠ NST = 3x - 1 = 3(20) - 1 = 60 - 1 = 59°

Here are the examples of functions in real life.

1. ATM

If you want to withdraw money from your account, the amount of money dispensed by the machine is the amount you request{input}.As a result, the amount requested is a function of the amount distributed{output}. The machine will never give you more or less than what you asked for.

2.Places you can drive with Two Gallons of Fuel

If you still have two gallons of gas in your car's tank, you can visit several locations before running out of gas. As a result, there could be several answers to this question. In this case, the input is two gallons of fuel, and the output is a list of places you can visit with that amount of fuel.

3. Number of Sodas in a Vending Machine

The number of sodas you get from a vending machine is determined by the amount of money you put into it. If you put the same amount in twice and choose the same soda, you will get the same number of cans as you did the first time. In this case, the number is determined by the amount fed into the machine.

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Answer:

B.

Step-by-step explanation:

B is not a function because it has a duplicate x value. Any function that has the same x value makes it automatically not a function.

Answer:

6 zebras

Step-by-step explanation: