Answer:
a. x= 9
b. 70
c. 110
d. 70
e. 110
Step-by-step explanation:
a.
congruent angles have the same measure. 1 and 3 are congruent and 2 and 4 are congruent
2(12x+2)+2(7x+7)=360
divide both sides by 2
12x+2+7x+7=180
combine like terms
2+7=9
12x+7x=19x
19x+9=180
subtract both sides by 9
19x=171
divide both sides by 19
x=9
7x+7,
7*9+7
63+7 = 70
1 is 70, 3 is 70
12x+2, x=9
108+2 = 110
2 and 4 is 110
Answer:
Step-by-step explanation:
Angles 1 and 2 are supplementary (their sum is 180 degrees)
7x + 7 + 12x + 2 = 180
19x= 171
x = 9
m 1 = 7 * 9 + 7 = 70 degrees
m 2 = 12 * 9 + 2 = 108 + 2 = 110 degrees
m 3 = angle 1 and angle 3 are vertical, so they have the same measure: 70 degrees.
m 4 = angle 2 and angle 4 have the same measure: 110 degrees
• The Adult Pool Area has a total area of 15,000 square feet. The Adult Pool Area consists of a rectangular swimming pool and a concrete walkway of even width surrounding all four sides of the pool. The swimming pool is 130 ft. by 80 ft.
Hint: First draw a picture of the pool and the walkway surrounding it on all four sides and label the walkway of even width, x.
• Now label your picture with an expression for the total length, including the walkway. Then label your picture with an expression for the total width, including the walkway.
Hint: How many sections of the walkway are added to the length? What about the width?
• Using the expressions for total length and width, find an expression for the total area of the rectangular pool and walkway. In order to solve for x, you will need to set the expression for an area equal to 15,000square feet. Now use your factoring skills to solve.
Answer:
crested to undermine this doctrine by requiring rscial integration
Step-by-step explanation:
someone please help.
Answer: This is what I think the answers are....
Hopefully this helps
Step-by-step explanation:
Dose every positive real number
also have both a positive and negative cube root?
Answer:
Any real number will have only one real cube root. Hence the technicalities associated with the principal root do not apply.
Step-by-step explanation:
The area of a square is 108 ft^2, what is the length of one side?
Answer: 10.3923
Step-by-step explanation: yes
What are the domain and range of the function? f(x)=−4x√x
Answer:
Domain x ≥ 0 Range y ≤ 0
Step-by-step explanation:
Answer:
\(Domain = \{x\,|\,x\geq 0\}\)
\(Range=\{\,y\,|\,y\leq 0\}\)
Step-by-step explanation:
Notice that the Range of the function (x-values for which the function exists) is limited by the possible values of x inside the square root. For \(\sqrt{x}\) to exist, x must be larger than or equal to zero (\(x\geq 0\))
So this gives us the description for building the Domain (what is called "set builder notation":
\(Domain = \{x\,|\,x\geq 0\}\)
Now for the Range, let's look into all the possible values that these \(x\geq 0\) values of x can render:
\(x\geq 0\\\sqrt{x} \geq 0\\x\,\sqrt{x} \geq 0\)
but now, if we multiply both sides of the inequality by "-4", the direction of the inequality changes rendering;
\(-4\,x\,\sqrt{x} \leq 0\)
Since these are the possible values of the "y-coordinate", then we right the Range in set builder notation as:
\(Range=\{\,y\,|\,y\leq 0\}\)
Which statements are true? Select three options
There are exactly two planes that contain points A,
B, and F
There is exactly one plane that contains points E, F,
and B
The line that can be drawn through points C and G
would lie in plane x,
The line that can be drawn through points E and F
would lie in planer
The only points that can lie on plane Yare points E
and F. my guy I literally have 5 days before graduation cmon man
Answer:
1. There is exactly one plane that contains points E,F, and B (2nd option)
2. The line that can be drawn through points C and G
would lie in plane x. (3rd option)
3. The line that can be drawn through points E and F
would lie in plane y. (4th option)
Step-by-step explanation:
The line that can be drawn through points C and G would lie in X-plane and the point E and F would lie in Y-plane. Then the correct options are C, D, and E.
What is a plane?A plane is a straight surface, with multiple surfaces that never end in maths.
The points C, D, and G lie in X-plane.
And the points E and F lie in Y-plane.
From the diagram, the conclusion points are given below.
The line that can be drawn through points C and G would lie in X-plane.The line that can be drawn through points E and F would lie in Y-planer.The only points that can lie on plane Y are points E and F.Then the correct options are C, D, and E.
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Which statement best describes La Trishas work
Answer:
Option A that is best describes the given scenario is option A that is “LaTricia is not correct. The word product does mean to multiply, but 12 should be the product and 3 should be one of the factors.”
Step-by-step explanation:
Given that LaTricia wrote a sentence as an equation. Given sentence is “Twelve is the product of three and a number”
Expression written by LaTricia =
Lets first concentrate on sentence and we will create our expression based on sentence and check it against the expression created by LaTricia. Let the number represented by variable w.
So product of 3 and the number will be represented by
And as Twelve is the product of three and a number
That is three is one of the factor and result product is 12. Hence option A that is best describes the given scenario is option A that is “LaTricia is not correct. The word product does mean to multiply, but 12 should be the product and 3 should be one of the factors.”
Complete this item. Identify 1 and 2. Select all that apply of the following terms: acute , right , obtuse , adjacent , vertical , complementary , supplementary. obtuse adjacent vertical supplementary acute right complementary
∠1 and ∠2 are right angles because the measure of both angles is 90 and supplementary angles because the sum of both angles is 180°.
What is the triangle?Triangle is a polygon that has three sides and three angles and the sum of the angle of the triangle is 180 degrees.
The figure is attached in the picture, please refer to the attached picture.
Given that:
An Angle in the figure is a right angle.
Its measure = 90°
So,∠2 = 90° ( vertically opposite angles are equal )
∠1 + ∠2 = 180° ( Linear Pair )
∠1 = 180 - 90
∠1 = 90°
∠1 = ∠2 = 90°
So, ∠1 and ∠2 are right angles because measure of both angles is 90°.
Adjacent angles because both a common arm and a common vertex.
Thus, ∠1 and ∠2 are right angles because the measure of both angles is 90 and supplementary angles because the sum of both angles is 180°.
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Encuentre el valor de x en la siguiente ecuación 6x = 4x + 6
Answer:
\(6x = 4x + 6 \\ 6x - 4x = 6 \\ 2x = 6 \\ x = \frac{6}{2} \\ \boxed{x = 3}\)
Answer:
x = 3
Step-by-step explanation:
In pic
(Credits: Symbolab)
(Hope this helps can I pls have brainlist (crown)☺️)
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.y = 6/7 x2, y = 13/7 − x2; about the x-axis
The volume (V) of the solid obtained by rotating the region bounded by the curve y = (6/7)x^2 about the x-axis is V = π[((9/245)b^5) - ((9/245)a^5)].
the volume (V) of the solid obtained by rotating the region bounded by the curve y = (6/7)x^2 about the x-axis is (2/3)π[(13/7) * sqrt(13/7)] cubic units.
To find the volume (V) of the solid obtained by rotating the region bounded by the curve y = (6/7)x^2 about the x-axis, we can use the disk method. Here's a step-by-step explanation:
1. Identify the function: y = (6/7)x^2
2. Determine the limits of integration: Since we are not given specific bounds, let's assume the region is defined between x=a and x=b.
3. Set up the integral for the disk method: V = π∫[f(x)]^2 dx, where f(x) = (6/7)x^2.
4. Substitute the function and limits into the integral: V = π∫[a to b] [(6/7)x^2]^2 dx
5. Simplify the integral: V = π∫[a to b] (36/49)x^4 dx
6. Integrate to x: V = π[(9/245)x^5]∣[a to b]
7. Evaluate the definite integral: V = π[((9/245)b^5) - ((9/245)a^5)] So, the volume (V) of the solid obtained by rotating the region bounded by the curve y = (6/7)x^2 about the x-axis is V = π[((9/245)b^5) - ((9/245)a^5)].
To find the volume V of the solid obtained by rotating the region bounded by the curve y = 13/7 − x2 about the x-axis. Let us consider a region bounded by the curve y = 13/7 − x2 and the x-axis.Let us rotate this region about the x-axis to obtain a solid with a volume.The region bounded by the curve y = 13/7 − x2 and the x-axis is shown below:We need to integrate to find the volume V of the solid obtained by rotating the region bounded by the curve y = 13/7 − x2 about the x-axis. The volume of the solid is given by: V = ∫(π.y2)dx, where y = 13/7 − x2Integrating V, we get: V = π ∫ (13/7 − x2)2 dx Let us evaluate the integralπ ∫ (13/7 − x2)2 dx= π [(13/7) * x - (1/3) * x3] limits from -sqrt(13/7) to +sqrt(13/7))= π [(13/7) * sqrt(13/7) - (1/3) * (13/7)3/2] - π [-(13/7) * sqrt(13/7) - (1/3) * (13/7)3/2]= (2/3)π[(13/7) * sqrt(13/7)] cubic unitsTherefore, the volume of the solid is (2/3)π[(13/7) * sqrt(13/7)] cubic units.
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in a class of 23 students, 7 have brothers and 5 have sisters. There are 2 students who have a brother and a sister. what is the probability that a student who has a brother also has a sister?
The probability that a student who has a brother also has a sister is 2/7 or approximately 0.2857.
To find the probability that a student who has a brother also has a sister, we need to use the concept of conditional probability.
Let's first find the probability of a student having both a brother and a sister. According to the problem, there are 2 students who have both a brother and a sister. Therefore, the probability of a student having both a brother and a sister is:
P(Brother and Sister) = 2/23
Now, let's find the probability of a student having a brother:
P(Brother) = 7/23
Using the formula for conditional probability, we can find the probability that a student who has a brother also has a sister:
P(Sister|Brother) = P(Brother and Sister) / P(Brother)
Substituting the values we found, we get:
P(Sister|Brother) = (2/23) / (7/23) = 2/7
This means that if we randomly select a student who has a brother, the probability that they also have a sister is about 0.2857.
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please awnser quqestion almost done asking questions
Answer:
12 feet
Step-by-step explanation:
Use the Pythagorean Theorem.
5² + x² = 13²
25 + x² = 169
169 - 25 = 144
√144 = 12
12 feet
Of the 300 students at Central Middle School, 20% are on the honor roll.
How many students are NOT on the honor roll?
How many isoceles triangles are there if each of its sides have an integral length and it's perimeter is 144
Answer:
\( \sf \: 34 \: isosceles \: triangle \: - - - - - - - - - - - - - - - - - - - - - - - - \)
Step-by-step explanation:
\(b = 144 - 2a < 2a \)
So, that
\(a > 36\)
and 2a < 144 so that
\(a < 72\)
since a = b implies a = 48
{37,38,39.......71}/{48}
There are 71-37 = 34 isosceles triangle
the scale on a map is stated as 1: 100 000 on the map jennifer estimates that the distance to her destination is 8cm is shes correct in her estimate ,how many kilometers are there to her destination
By using unitary method it is obtained that Jennifer is at a distance of 8 km to her destination
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 is used
The scale on a map is stated as 1: 100 000
So 1 cm on the map is equivalent to 100000 cm on the ground
8 cm on the map is equivalent to 100000 \(\times\) 8 cm on the ground
8 cm on the map is equivalent to 800000 cm on the ground
8 cm on the map is equivalent to \(\frac{800000}{1000 \times 100}\) km on the ground
8 cm on the map is equivalent to 8 km on the ground
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what impact does multicollinearity have on the p-values on the slopes in a regression model?
It is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques.
Multicollinearity is a statistical phenomenon where two or more independent variables in a regression model are highly correlated with each other. This can cause problems in the regression model as it becomes difficult to distinguish the individual effects of the independent variables on the dependent variable.
When multicollinearity is present in a regression model, the p-values of the slopes of the independent variables are affected. The p-value measures the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. The null hypothesis in a regression model is that the slope of the independent variable is zero, meaning that there is no relationship between the independent variable and the dependent variable.
Multicollinearity can cause the standard errors of the slopes to increase, leading to inflated p-values. In other words, the significance of the relationship between the independent variable and the dependent variable may be underestimated. This is because the highly correlated independent variables are both trying to explain the same variation in the dependent variable, leading to an unreliable estimate of the effect of each independent variable on the dependent variable.
Therefore, it is important to check for multicollinearity in a regression model and take steps to reduce it, such as removing one of the highly correlated independent variables or using regularization techniques. This can help to ensure that the regression model produces reliable estimates of the effects of the independent variables on the dependent variable.
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The function f(x) = three-fourths(10)–x is reflected across the x-axis to create the function g(x). which ordered pair is on g(x)?
The ordered pair that is on g(x) is (2, -3/400)
determine the ordered pair:
The function is given as:
f(x)=3/4(10)∧-x
The rule of reflection across the x-axis is:
g(x) = -f(x)
So, we have:
g(x) = -3/4(10)∧-x
Set x = 2.
So, we have:
g(2) = -3/4(10)∧-2
Evaluate the exponent
g(2) = -3/4 * 1/100
Evaluate the product
g(2) = -3/400
This means that:
(x, y) = (2, -3/400)
Hence, the ordered pair that is on g(x) is (2, -3/400)
Ordered pairs are pairs of two numbers (or variables) that are enclosed in parentheses and separated by commas. For example, (1, 2) is an ordered pair. Coordinate geometry represents points, and set theory represents elements of relations / Cartesian products.
Ordered pairs are pairs of numbers in a particular order. For example, (1, 2) and (-4, 12) are ordered pairs. The order of the two numbers is important. (1, 2) is not equivalent to (2, 1)-(1, 2) ≠ (2, 1).
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A branch of a certain bank has six ATMs. Let X represent the number of machines in use at a particular time of day. The cdf of X is as follows:
F(x) =
0 x < 0
0.06 0 ≤ x < 1
0.16 1 ≤ x < 2
0.33 2 ≤ x < 3
0.69 3 ≤ x < 4
0.92 4 ≤ x < 5
0.99 5 ≤ x < 6
1 6 ≤ x
Calculate the following probabilities directly from the cdf
(a) p(2), that is, P(X = 2) (b) P(X > 3) (c)P(2 ≤ X ≤ 5) (d)P(2 < X < 5)
(a) p(2), that is, P(X = 2)The cdf is given by: F(x) = 0 x < 00.06 0 ≤ x < 10.16 1 ≤ x < 20.33 2 ≤ x < 30.69 3 ≤ x < 40.92 4 ≤ x < 50.99 5 ≤ x < 61 6 ≤ x
The probability mass function p(x) can be derived from the cdf by taking differences:
p(x) = F(x) − F(x-1)Thus the probability mass function p(x) is as follows: p(x) = 0.06 x = 10.1 x = 20.17 x = 30.36 x = 40.23 x = 50.07 x = 60.01 x = 6The probability P(X = 2) can be found as follows: P(X = 2) = p(2) = 0.17(b) P(X > 3)The probability can be found as follows: P(X > 3) = P(4 ≤ X) = 1 - P(X < 4) = 1 - F(3) = 1 - 0.33 = 0.67(c) P(2 ≤ X ≤ 5)The probability can be found as follows: P(2 ≤ X ≤ 5) = F(5) - F(1) = 0.99 - 0.1 = 0.89(d) P(2 < X < 5)
The probability can be found as follows: P(2 < X < 5) = F(4) - F(2) = 0.92 - 0.17 = 0.75.
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What is the mathematical term for raising a number to the power of 2?
The mathematical term for raising a number to the power of 2 is called squaring.
When we square a number, we multiply it by itself. For example, if we square the number 4, we get 16 because 4 multiplied by 4 is 16.
We can represent squaring using the exponent notation. The number being squared is the base, and the power, which is always 2, indicates how many times the base is being multiplied by itself. So, 4 squared can be represented as \(4^{2}\).
Squaring is a fundamental operation in mathematics and has many applications in different fields, including physics, engineering, and finance. It is commonly used in geometry to calculate the area of a square or rectangle. For instance, if we have a square with a side length of 5 units, we can find its area by squaring the side length: A = \(5^{2}\) = 25 square units.
Squaring is also used in statistics to calculate the variance of a data set. The variance measures the spread of the data from the mean, and it is calculated by squaring the difference between each data point and the mean, summing up these squares, and dividing by the number of data points.
In conclusion, squaring is the mathematical term used to describe the operation of raising a number to the power of 2.
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A teacher uses 56 pencils and 80 pieces of paper to make student supply kits for each student in her small group.
• Each student supply kit has an equal number of pencils.
• Each student supply kit has an equal number of pieces of paper.
• The teacher makes the greatest number of student supply kits possible
• No extra pencils or pieces of paper remain after all the supply kits are made.
What are the maximum number of supply kits that can be made and how many pencils and pieces of papers will go in each supply kit?
Answer:
All you have to do is multiply 56x80 and then you get the right answer which is 4480
Solve the following Equations. Some questions will have negative,fractioms or decimal answers
5+2x=65
Answer:
Step-by-step explanation:
5 + 2x = 65
5 + 2x -5 = 65 - 5
2x = 60
\(\frac{2x}{2}\) = \(\frac{60}{2}\)
x = 30
What is the equation of the graphed line written in standard form?
2x + 3y = -6
2x + 3y = 6
y=-2/3x-2
y= 2/3x-2
Answer:
What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.
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In march 2015, the public policy institute of california (ppic) surveyed 7525 likely voters living in california. Ppic researchers find that 68 out of 200 central valley residents approve of the california legislature and that 156 out of 300 bay area residents approve of the california legislature. Ppic is interested in the difference between the proportion of central valley and bay area residents who approve of the california legislature. Ppic researchers calculate that the standard error for the proportion of central valley residents who approve of the california legislature minus bay area residents who approve of the california legislature is about 0. 44. Find the 95% confidence interval to estimate the difference between the proportion of central valley and bay area residents who approve of the california legislature. Responses
The null hypothesis get rejected comparing the 95% confidence interval to the proportion of the given central valley residents and bay area residents .
As given in the question,
Total number of voters in California = 7525
x₁ = Number of voters of central valley residents approved California legislature
= 68
n₁ = Total number of voters of central valley residents
= 200
x₂ = Number of voters of bay area residents approved California legislature
= 156
n₂= Total number of voters of bay area residents
= 300
p₁ = proportion of voters of central valley
p₂= proportion of voters of bay area
p₁ = x₁/ n₁
= 68/200
= 0.34
p₂ = x₂/n₂
= 156/300
= 0.52
Standard error = √p₁(1 -p₁) / n₁ + p₂( 1- p₂)/n₂
= √0.34(1-0.34) / 200 + 0.52(1-0.52)/ 300
= √0.001122 + 0.000832
= 0.044
\(p_{w}\) = (68 + 156 )/ (200 + 300)
= 0.448
\(q_{w} = 1- p_{w}\)
= 1 - 0.448
= 0.552
null hypothesis p₁ - p₂ = 0
z = ( 0.52 - 0.34 ) - 0/ √(0.448)(0.552)( 1/200 + 1/300)
= 4
Tabular value for confidence interval 95% = 1.96
4 > 1.96
We reject the null hypothesis.
Therefore, the difference of proportion of central valley residents and the bay area residents rejection of null hypothesis as per given 95% confidence interval.
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A skier can purchase a daily or season pass.
The daily pass costs $48 per day and included
the price of ski rentals. The season pass costs
$190 plus a daily fee of $10 to rent the skis.
How many days would a skier have to go skiing
in order for both options to cost the same?
A.
5 days
C. 240 days
D. 10 days
B.
3 days
We know that the skier would have to go skiing for 5 days in order for both options to cost the same.
To find out how many days a skier would have to go skiing for both options to cost the same, we need to set up an equation. Let's use "d" to represent the number of days the skier goes skiing.
For the daily pass option:
Total cost = $48 x d
For the season pass option:
Total cost = $190 + ($10 x d)
Now we can set up the equation:
$48 x d = $190 + ($10 x d)
Simplifying this equation, we get:
$38 x d = $190
Solving for "d", we get:
d = 5
Therefore, the skier would have to go skiing for 5 days in order for both options to cost the same.
So the answer is A. 5 days.
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Vince borrows $900 to buy a couch. He will pay off the loan by paying 1.5% simple interest for 2 years. Vince incorrectly calculates the amount he will pay back using the expression below. 900 + 900(1.015 • 2) What is the correct amount Vince will pay back altogether? Explain the error in Vince's expression. A. 00:00 $903; Vince should have subtracted the first 900 from the amount he will pay. B. 00:00 $913.50; Vince multiplied by the wrong number of years. C. 00:00 $927; Vince wrote the wrong number to represent the interest rate. D. 00:00 $1,813.50; Vince forgot to add the initial $900 to the amount he will pay.
Answer: C. 00:00 $927; Vince wrote the wrong number to represent the interest rate.
Step-by-step explanation:
Given that:
Amount borrowed (p) = 900
Simple interest (r) = 1.5% = 0.015
Time (t) = 2 years
Amount he'll pay back (A) :
A = P(1 + rt)
A = 900(1 + 0.015(2))
A = 900(1 + 0.03)
A = 900(1.03)
A = $927
25,000 participants meet for a charity walk 10,190 are ages 35 and up how many are younger
From the 25,000 participants,
\(25000-10190=14810\)14,810 are less than 35 years old.
What is the size of angle p ?
Answer:
55˚
Step-by-step explanation:
1. ∡135˚ = 180-135=45˚
2. p=180-80-45
3. p=55˚
solve for x Assume that lines which appear tangent
Answer:rr
yurrrrrrrrr yesyes ye s
Step-by-step explanation:
Which turtle has the fastest speed?
The speed of a turtle can be found by
distance by time.
is the fastest turtle.
The speed of the fastest turtle is
centimeters per minute.
Answer:
dividing is how you get the answer to the distance and the turtles was faster then the two others
Step-by-step explanation:
hope this helps
Answer:
its d b and d
Step-by-step explanation:
someone help asap please
The gradient of this straight line through the points is 0.16.
The gradient of this lines simply means that it would require one (1) unit to use £0.16 worth of electricity.
How to calculate the gradient of a line?Mathematically, the gradient of a straight line can be calculated by using this formula;
Gradient, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Gradient, m = (y₂ - y₁)/(x₂ - x₁)
From the information provided through this graph, we have the following data points:
Points on x-axis = (30, 100).
Points on y-axis = (4, 15).
Substituting the given points into the formula, we have the following;
Gradient, m = (15 - 4)/(100 - 30)
Gradient, m = 11/70
Gradient, m = 0.16
This ultimately implies that, £0.16 worth of electricity would require one (1) units to be used by David.
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