what is required for a current to flow?

A. Electrons, protons, and an energy source

B. An insulator, battery, and recipient

C. A recipient, a connection, and something made out of rubber

D. An Energy source, a recipient, and a connection

What Is Required For A Current To Flow?A. Electrons, Protons, And An Energy SourceB. An Insulator, Battery,

Answers

Answer 1

Therefore , the solution of the given problem of unitary method comes out to be  enable the current to travel, a connection, such as a wire or conductor, is required.

What is a unitary method?

Utilizing previously well-known variables, this uniform convenience, or all crucial elements from a prior flexible study that followed a particular methodology event can all be used to achieve the goal. It will be possible to contact the entity again if the anticipated assertion outcome actually happens; if it doesn't, both important systems will surely miss the statement.

Here,

D. In order for a current to move, there must be an energy source, a recipient, and a connection.

Current is the movement of charged ions through a conductor, most frequently electrons.

The energy required to transport the charged particles is provided by an energy source, such as a battery or generator.

The current has a route through a recipient, which can be a machine or a circuit.

In order to finish the circuit and enable the current to travel, a connection, such as a wire or conductor, is required.

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Related Questions

Katya is going on a 7-night trip. She is staying in a hotel that costs $129 per night and her airfare is $375. If she budged $2.000 for the trip, how much money will she have left for the trip?

A. $672
B. $686
C.$704
D.$722

Answers

Answer: D. $722

Step-by-step explanation:

$2,000 - $375 (initial airfare cost which will only be once)

= 1,625

7 x 129 = 903 (cost of the 7 nights in a hotel)

1,625 - 903 = 722

$722 left for the trip

Elijah works in a department store selling clothing. He makes a guaranteed salary of $500 per week, but is paid a commission on top of his base salary equal to 30% of his total sales for the week. How much would Elijah make in a week in which he made $775 in sales? How much would Elijah make in a week if he made

x dollars in sales?
Total earnings when selling $775:
Total earnings when selling $x:

Answers

Elijah's total earnings for the week if he made x dollars in sales would be: $500 + 0.3x.

What is sale?

A sale is an event or activity in which goods or services are sold at a reduced or discounted price.

What is discount?

A discount is a reduction in the price of an item or service. It is often offered as a promotion or incentive to encourage customers to buy or use a product or service.

According to given information:

Total sales commission earned by Elijah for selling $775 worth of clothing:

30% of $775 = 0.3 x $775 = $232.50

Therefore, Elijah's total earnings for the week would be:

$500 (guaranteed salary) + $232.50 (commission) = $732.50

For selling x dollars worth of clothing, the commission earned by Elijah would be:

0.3x

Therefore, Elijah's total earnings for the week if he made x dollars in sales would be:

$500 (guaranteed salary) + 0.3x (commission) = $500 + 0.3x

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Simplify to create an equivalent expression.

4
(

11
+
4
n
)

3
(

2
n
+
9
)

Answers

Answer:

Step-by-step explanation:

To simplify this expression, we will distribute the -4 and -3 to the terms inside the parentheses:

-4(-11+4n) - 3(-2n+9)

= 44 - 16n + 6n - 27

= -16n - 17

Therefore, the simplified expression is -16n - 17.

The ratio of new car sales to used car sales at the car lot is 3:5. If the total car sales were $287,400 last month, what was the total of the used car sales?

Answers

Answer:

Therefore, the total used car sales were $179,625.

Step-by-step explanation:

Let's assume that the ratio of new car sales to used car sales is 3x:5x, where x is a constant.

The total car sales were $287,400, which means the sum of the new car sales and used car sales is $287,400:

3x + 5x = 8x

So, the total sales can be expressed as:

8x = $287,400

To find the value of x, we need to divide both sides by 8:

x = $35,925

Now, we can calculate the used car sales by multiplying 5x by the value of x:

Used car sales = 5x * x = 5 * $35,925 = $179,625

Therefore, the total used car sales were $179,625.

A pyramid has a height of 5 inches and a volume of 60 cubic inches. Which of the following figures could be the base for this pyramid?
Select 3 answers that apply.
A a hexagon with an area of 36 square inches
11 a right triangle with one leg 5 inches and the hypotenuse 13 inches
ca circle with radius 4 inches
Da 4-inch by 9-inch rectangle
a 3-inch by 4-inch rectangle
a square with side length 6 inches
E

Answers

The 3 correct answers of the figures that could be the base for the pyramid that has a height of 5 inches and a volume of 60 cubic inches are:

A hexagon with an area of 36 square inches (option A)A 4-inch by 9-inch rectangle (option D)A 3-inch by 4-inch rectangle (option E)

How do we calculate?

The formula to find the base of a pyramid given its height and volume,

Volume of pyramid = (1/3) * Base area * Height

Substituting in the given values, we have:

60 = (1/3) * Base area * 5

Base area = 36 square inches

In conclusion, any figure with a base area of 36 square inches could be the base for this pyramid.

The following figures have a base area of 36 square inches:

A hexagon with an area of 36 square inches A 4-inch by 9-inch rectangle A 3-inch by 4-inch rectangle

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One paperclip has the mass of 1 gram. 1,000 paperclips have a mass of 1 kilogram. How many kilograms are 5,600 paperclips?

Answers

Answer: 5.6 kilograms.

Step-by-step explanation:

We know that 1,000 paperclips have a mass of 1 kilogram.

Therefore, one paperclip has a mass of 1/1000 kilograms, or 0.001 kilograms.

To find out how many kilograms 5,600 paperclips have, we can multiply the mass of one paperclip (0.001 kilograms) by the number of paperclips:

0.001 kilograms/paperclip * 5,600 paperclips = 5.6 kilograms

Therefore, 5,600 paperclips have a mass of 5.6 kilograms.

What is m24 if m25 = (2x)° and m24 = (x +9)°?
4
X
5
m24 =

Answers

The value of angle m<4 is 66 degrees

What are supplementary angles?

The angles on a straight line are supplementary, this means that the angles sum up to 180 degrees.

From the information given, we have that;

m<4 = x + 9 degreesm< 5 = 2x degrees

Equate the angles to 180 degrees

We have;

m<4 + m<5 = 180

Substitute the expression for each of the angles , we have;

x + 9 + 2x = 180

collect the like terms

3x = 180 - 9

subtract the values

3x = 171

Divide by the coefficient

x = 57

But m<4 = 57 + 9 = 66 degrees

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Identify the rate, base, and percent in each statement. Place them in
the correct columns to complete the table.
1) 25 is 25% of 100
2) 15 is 25% of 60
318 is 20% of 90
4) 18 is 30% of 60
5) 20% of 150 is 30
What it is rate?
What it is base?
What it is percentage?

Answers

Answer:

In each statement:

The rate is the percentage or ratio that relates the quantity being described to the base.

The base is the total quantity or amount that the rate is applied to.

The percent is the rate expressed as a percentage, or the part of the base that corresponds to the rate.

What is the answer to x3 y3 z3 k?

Answers

Answer:

The equation x3+y3+z3=k is known as the sum of cubes problem.

Step-by-step explanation:

Pupils in a class were asked how they travel to school. The results were recorded in the table below
Car 13 bus 6 train 5 walk 8
If s pupil in the class was picked at random what is the probability that one of them walked to school as a percentage

Answers

Answer:

1/3

Step-by-step explanation:

if 62 miles is equal to 100 kilometers , what is the ratio of miles to one kilometer

Answers

Answer:

0.62 to 1

Step-by-step explanation:

62/100

Divide the numerator and denominator by 100.

62/100 = 0.62/1

The ratio is 0.62 to 1.

Answer:

Step-by-step explanation:

1 mile is equal to 1.60934 km

1km is equal to 0.621371 mile

The entry fee to East Egg Hunt Event is $7.00. Each ride requires a ticket that cost $2.00. Cassie spent a total of $45.00. How many tickets Cassie Purchase?​

Answers

Answer: 19 tickets

Step-by-step explanation:  $45 - $7 = 38      38 divided by $2 = 19 tickets

circumference is 1884, what is the diameter

Answers

Answer: how many places are you looking for? because it would be around 599.696332...(and more decimal numbers)

you get this from dividing 1884 by 3.14159 (pi)

Just number 9 with work

Answers

The correct answer is (c) Left 5. The transformation is a horizontal shift to the left by 5 units.

What is equation?

An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.

Here,

The given equation is y = 12/(x + 5), which represents a rational function. The parent function for this type of function is y = 1/x, which has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

To transform the parent function represented by y = 1/x into y = 12/(x + 5), we need to apply the following transformations:

Vertical stretch by 12: This means that the y-values of the graph will be multiplied by a factor of 12, causing the graph to become narrower and taller. Horizontal shift left 5 units: This means that the graph will be shifted 5 units to the left, causing the vertical asymptote to move from x = 0 to x = -5.

Therefore, the correct answer is (c) Left 5, since this represents the horizontal shift of 5 units to the left. The other answer choices do not accurately describe the transformation of the parent function into the given equation.

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PLEASE HELP ME

Given the following quadratic functions, complete the following:
1. Identify the zeros.
2. Identify the vertex.
3. Write the quadratic equation in factored form for the function that is graphed.

Answers

The zeros and vertex of each quadratic equation are:

Case 1: y = 4 · (x + 2) · (x - 2), Roots: - 2, 2, Vertex: (0, - 16)

Case 2: y = (1 / 2) · (x + 5) · (x - 3), Roots: - 5, 3, Vertex: (- 1, - 8)

Case 3: y = - 2 · (x + 4) · (x + 2), Roots: - 4, - 2, Vertex: (- 3, 2)

Case 4: y = - 2 · (x + 6) · (x + 2), Roots: - 6, - 2

Vertex: (- 4, 8)

How to analyze quadratic functions and derive their expressions

Graphically speaking, quadratic functions have the form of the parabola. The zeros are the points of parabola that are on the horizontal axis (x-axis) and the vertex is the only point of the parabola. The factor form of the parabola is:

y = C · (x - r₁) · (x - r₂)

Where:

C - Vertex constantr₁, r₂ - Roots

Now we proceed to determine all the features of the quadratic function:

Case 1

Roots: r₁ = - 2, r₂ = 2

Vertex: (h, k) = (0, - 16)

C = y / [(x - r₁) · (x - r₂)]

C = - 16 / [2 · (- 2)]

C = - 16 / (- 4)

C = 4

Factor form: y = 4 · (x + 2) · (x - 2)

Case 2

Roots: r₁ = - 5, r₂ = 3

Vertex: (h, k) = (- 1, - 8)

C = y / [(x - r₁) · (x - r₂)]

C = - 8 / [(- 1 + 5) · (- 1 - 3)]

C = - 8 / [4 · (- 4)]

C = - 8 / (- 16)

C = 1 / 2

Factor form: y = (1 / 2) · (x + 5) · (x - 3)

Case 3

Roots: r₁ = - 4, r₂ = - 2

Vertex: (h, k) = (- 3, 2)

C = y / [(x - r₁) · (x - r₂)]

C = 2 / [(- 3 + 4) · (- 3 + 2)]

C = 2 / [1 · (- 1)]

C = - 2

Factor form: y = - 2 · (x + 4) · (x + 2)

Case 4

Roots: r₁ = - 6, r₂ = - 2

Vertex: (h, k) = (- 4, 8)

C = y / [(x - r₁) · (x - r₂)]

C = 8 / [(- 4 + 6) · (- 4 + 2)]

C = 8 / [2 · (- 2)]

C = 8 / (- 4)

C = - 2

Factor form: y = - 2 · (x + 6) · (x + 2)

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(x^2-4x+3) + (3x^2-3x-5) ASAP PLS

Answers

Answer:

(x - 2)(4x + 1)

3) Given that f(x) = 3x – 5 g(x) = 2x – 6 and h(x) = x + 4
4 2x
Find:- i) f(-3) = ii) g[f(0)] = iii) f[h(2)] =

iv) hᴏf(x) v) h-1(1) =

Answers

The Answer for the given functions are:

i) f(-3) = -14.

ii) g[f(0)] = -16.

iii) f[h(2)] = 13.

iv)  hᴏf(x) = 3x - 1.

v)  h-1(1) = -3.

What is the functiοn nοtatiοn?

Functiοn nοtatiοn is a way οf representing a functiοn using algebraic symbοls. It is a shοrthand way οf expressing a relatiοnship between twο quantities οr variables, where οne variable depends οn the οther.

i) Tο find f(-3), we substitute x = -3 in the expressiοn fοr f(x) and simplify:

f(-3) = 3(-3) - 5 = -9 - 5 = -14

Therefοre, f(-3) = -14.

ii) Tο find g[f(0)], we first evaluate f(0) and then substitute that value intο g(x):

f(0) = 3(0) - 5 = -5

g[f(0)] = g(-5) = 2(-5) - 6 = -10 - 6 = -16

Therefοre, g[f(0)] = -16.

iii) Tο find f[h(2)], we first evaluate h(2) and then substitute that value intο f(x):

h(2) = 2 + 4 = 6

f[h(2)] = f(6) = 3(6) - 5 = 18 - 5 = 13

Therefοre, f[h(2)] = 13.

iv) Tο find hᴏf(x), we substitute f(x) intο the expressiοn fοr h(x) and simplify:

hᴏf(x) = h[f(x)] = f(x) + 4 = (3x - 5) + 4 = 3x - 1

Therefοre, hᴏf(x) = 3x - 1.

v) Tο find h-1(1), we need tο sοlve fοr x in the equatiοn h(x) = 1:

h(x) = x + 4 = 1

Subtracting 4 frοm bοth sides, we get:

x = 1 - 4 = -3

Therefοre, h-1(1) = -3.

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the worlds population hit 8 billion in 2022. suppose the population increases exponentially with doubling time of 60 years. what population can we expect in the year 2100. Answer in billions

Answers

The population in the year 2100 will be approximately 18.8 billion.

Determine exponential equation

The exponential equation to model the world population (in billions) after t years is P(t) = 8(1.011)[tex]^t[/tex], where P(t) is the population in billions and t is the number of years after 2022.

To write this equation, we need to use the information provided in the question. The initial population in 2022 is 8 billion, so this is our starting value. The growth rate is 1.1% per year, which can be written as 1.011 in decimal form.

We can use the formula for exponential growth, P(t) = P0(1 + r[tex])^t[/tex]where P0 is the initial population, r is the growth rate, and t is the number of years.

Substituting the values for [tex]P_0[/tex]and r into the equation, we get:

P(t) = 8(1.011[tex])^t[/tex]

2100-2022=78

This equation can be used to find the population after t years.

For example, to find the population after 5 years, we can substitute t = 78 into the equation and get:

P(5) = 8(1.011[tex])^78[/tex] ≈ 18.8 billion

Therefore, the population in year  2100 will be approximately 18.8 billion.

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Adrian eats 2/3's of a pack of gum each
day. How many packs of gum will he
have eaten after 7 days?

10 points given!!

Answers

4 and 2/3 packs of gum

You are thinking about changing employment. Your goal is to work for three years and then return to university full-time, in pursuit of an advanced degree. A potential employer just offered you an annual salary of R55 000, R60 000, and R65 000 a year for the next three years, respectively. All salary payments will be made as lump sum payments at the end of each year. The offer also includes a starting bonus of R4 500, payable immediately. What is this offer worth to you today, at a discount rate of 8,25%?

Answers

Answer:

55K+60K+65K=184K

100% - 8.25%=91.75%

184000x91.75%=168820

Ans:168K

Answer:

Step-by-step explanation:

To determine the value of the offer today, we need to calculate the present value of all the cash flows using a discount rate of 8.25%.

First, let's calculate the present value of the salary payments.

PV(year 1 salary) = R55 000 / (1 + 0.0825)^1 = R50 760.87

PV(year 2 salary) = R60 000 / (1 + 0.0825)^2 = R51 423.95

PV(year 3 salary) = R65 000 / (1 + 0.0825)^3 = R52 110.69

Next, let's calculate the present value of the starting bonus.

PV(starting bonus) = R4 500 / (1 + 0.0825)^0 = R4 500

Finally, we can add up all the present values to find the total present value of the offer:

PV(total offer) = PV(year 1 salary) + PV(year 2 salary) + PV(year 3 salary) + PV(starting bonus)

PV(total offer) = R50 760.87 + R51 423.95 + R52 110.69 + R4 500

PV(total offer) = R158 795.51

Therefore, the offer is worth R158 795.51 to you today at a discount rate of 8.25%.

To amend a country’s constitution, 7/9 of the 84 states in that country must approve the amendment. If 66 states approve the amendment, will the constitution be amended?

Answers

Answer:

Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.

Step-by-step explanation:

To determine whether the constitution will be amended, we need to compare the number of states that have approved the amendment to the required number of states needed for approval.

The requirement is that 7/9 of the 84 states must approve the amendment. So, we need to calculate 7/9 of 84 to find out how many states need to approve the amendment:

(7/9) x 84 = 66.67

Rounding up, we see that 66.67 is equivalent to 67 states. This means that in order for the amendment to be approved, at least 67 states must approve it.

Since only 66 states approve the amendment, it falls short of the required 7/9 majority. Therefore, the constitution will not be amended.

The maximum number of grams of fat that should be in a diet vary directly as a persons way a person weighing 126 pounds should have no more than 84 g of fat per day. What is the maximum daily intake for personally and 30
ponds

Answers

the maximum daily intake of fat for a person weighing 30 pounds should be no more than 20 grams.

Helppppppppppppppppp

Answers

(5x10)x(3x10) = 1500

if you have 2 bags of candy each with 4 pieces of candy in them you will have 8 because 2x4=8

Answers

Answer:

Step-by-step explanation:

ex  2

        4444

2

 4444

Yes, that's correct I even tried to show you.

The 2 is the bags of candy

4 pieces of candy per bag

equals to 8 in total

need an answer NOW!! id prefer if sin cos and/or tan was used to find the side length, but its okay if you use pythagorean theorem

Answers

The length of the side of the tent is 5.8 feet calculated using the height of the equilateral triangle.

Equilateral triangle:

An equilateral triangle is a type of triangle where all three sides have the same length, and all three angles are equal to 60 degrees.

The formula for the height of an equilateral triangle is given by

                 Height (h)  =  ½(√3a)

Where 'a' is the equal side of the equilateral  

In the given problem we use the height of the triangle to calculate the side of the triangle tenth.

Here we have  

The height of the tent is 5 ft which is the height of the equilateral triangle  

As we know,

Height of equilateral triangle =  ½(√3a)

Let 'a' be the side of the triangle tent

=> 5 ft = ½(√3a)

Multiply by 2 on both sides

=> 5 × 2 = 2(1/2)√3a

=> √3a = 10

=> (1.732) a = 10    [ ∵ √3  1.732 ]  

=> a = 5.8  

Therefore,

The length of the side of the tent is 5.8 feet calculated using the height of the equilateral triangle.

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The volume of a cuboid is 630cm3.
The length is 14cm and the width is 90mm.
Whatt is the height of the cuboid in cm.

Answers

Answer:

Height = 630 / (14 x 0.9) = 47.5 cm

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct option is 1 and 4  of the given inequality  –3(2x – 5) < 5(2 – x)

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x

x < 5

Therefore, options 1 and 4 are correct. The other options do not correctly represent the inequality.

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How many solutions and what is the solution, as an ordered pair?

Answers

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

what is solution ?

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

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if AC = 57, find the measure of AB

Answer choices:
A. 9
B. 30
C. 6
D. 27

Answers

the answer should b c

Circle p has a radius of 8 inches

Answers

The area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.

How to evaluate for the area of the sector.

The area of a sector is calculated by multiplying the fraction of the angle for the sector divided by 360° and πr², where r is the radius.

the angle of the sector = 70°

the radius = 8 ft

hence the area of the sector is calculated as follows:

(70°/360°) × 22/7 × 8 in × 8 in

we simplify by division and multiplication

1/36 × 22 × 64 in²

352 in²/9

39.1111 in²

Therefore, the area of the sector that is the smaller region of the circle is evaluated to be equal to 39.1 in² to the nearest tenth.

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medusa inc. owns 62% of the outstanding voting shares of gorgon inc. common stock and plans to hold the shares indefinitely. which classification or method will medusa use to account for its investment in gorgon? group of answer choices investment in trading securities investment in available for sale securities equity method consolidation method during last nights basketball game the number of points scored by the hornets was triple the number of points scored by the raiders the raiders scored 6 points how many points did the hornets score?291218? in maslow's theory, after physiological needs have been satisfied, the next need level is likely to be: what is the lowest possible frequency of an aliased signal if a 120 khz signal is sampled at 150 khz? which of the following is not a source of monopoly power? multiple choice question. patents economies of scale free entry and exit economies of scope the offeror can withdraw the contract at any time before the offeree's acceptance of the contract is courts have ruled that inmates are entitled to have legal materials and resources available to assist them in filing complaints, which includes: Vincent bought a lot with an area of 105. 7 square meters at 12,500. 00 pesos per square meter. He paid -0. 45 of the amount in cash and the rest 24 equal monthly installments. How many much is his monthly installment? suppose 60% of american adults believe martha stewart is guilty of obstruction of justice and fraud related to insider trading. we will take a random sample of 20 american adults and ask them the question. then the sampling distribution of the sample proportion of people who answer yes to the question is: group of answer choices if the area of a circle is less than $60\pi$ square inches, what is the greatest possible integer value in inches of the radius of the circle? Which of the following characteristics would you expect to find in a member of the bilateral?a) two tissue layers (diploblastic)b) specialized head regionc) coelomd) segmentation Put the following steps of DNA replication in chronological order. 1. Single-stranded binding proteins attach to DNA strands. 2. An RNA primer is created. 3. Primase binds to the origin. 4. DNA polymerase begins to synthesize DNA 5. Hydrogen bonds between base pairs of antiparallel strands are broken. A. 5, 1, 3, 2,4 B. B. 3, 1, 5, 4,2 C. 1,5, 3, 4,2 D. 3, 5, 1, 2,4 Mercury concentrations were measured in freshwater shrimp populations in two different ponds, one polluted with mercury and one unpolluted, with a similar food web in each pond. Which of the following best identifies the scientific question that would guide this investigation?a. How does the food web in a pond affect biomagnification of toxins?b. How much mercury is found in the tissues of shrimp predators in an unpolluted pond?c. How do different species of shrimp excrete mercury from their bodies?d. How much mercury accumulates in the tissues of freshwater shrimp living in a polluted pond? what kind of acting role means that you will not speak and likely not be seen clearly in the final film? group of answer choices background lead featured supporting how did the overcharge computed? how did the concept of beyond reasonable doubt affect the computation of overcharge? g what is the relationship between the wavelength of light, its color, and the energy of its photons? 1.000 g of a weak base was titrated with hcl and gave the above curve. what is the most likely base? what is the ratio of the induced emf in the loop cdbc to the induced emf in the loop cadc; i.e., what is ecdbc ecadc ? when capable of concrete operational thought, children: group of answer choices are limited to intuitive thought. can apply their reasoning to real situations. can reason about abstractions. are likely to be misled by appearances. 4. in exercise 3, you used a $100 gas card that you purchased with a credit card. the credit card gave you a 5% rebate on the purchase. including this rebate, what did you actually pay for each gallon of gasoline in exercise 3?