(a) To prove that G has neither self-loops nor anti-parallel edges, we will assume the contrary and show that it leads to a contradiction.
Assume there exists a vertex v in G that has a self-loop, meaning there is an edge (v, v) in G. Since every vertex in G is either a source, a sink, or both, this self-loop implies that v is both a source and a sink. However, this contradicts the assumption that every vertex in G is either a source or a sink, but not both. Therefore, G cannot have self-loops.
Now, assume there exist two vertices u and v in G such that there are anti-parallel edges between them, i.e., both (u, v) and (v, u) are edges in G. Since every vertex in G is either a source, a sink, or both, this implies that u is a source and a sink, and v is also a source and a sink. Again, this contradicts the assumption that every vertex in G is either a source or a sink, but not both. Therefore, G cannot have anti-parallel edges.
Hence, we have proved that G has neither self-loops nor anti-parallel edges.
(b) Let's consider the undirected graph Gu obtained by erasing the direction on the edges of G. We need to prove that Gu has a chromatic number of 1 or 2.
Since every vertex in G is either a source, a sink, or both, it implies that every vertex in Gu has either outgoing edges only, incoming edges only, or both incoming and outgoing edges. Therefore, in Gu, a vertex can be colored with one color if it has either all incoming or all outgoing edges, and with a second color if it has both incoming and outgoing edges.
If Gu has a vertex with all incoming or all outgoing edges, it can be colored with one color. Otherwise, if Gu has a vertex with both incoming and outgoing edges, it can be colored with a second color. This proves that the chromatic number of Gu is either 1 or 2.
Therefore, we have proved that the undirected graph Gu obtained from G has a chromatic number of 1 or 2.
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The product of three different positive integers is 8 what is the sum of these integers
Answer:
(4)(2)(1)=
4+2+1=
explanation:
Your Overall grade is calculated by adding 35% of your Minor grade to 65% *
of your Major grade. If your Minor grade is 84 and your Major grade is 61,
what would your overall grade be (rounded to the nearest percentage)?
A. 62
B. 67
C. 65
D. 80
E. 69
Answer:
69%
Step-by-step explanation:
Overall grade = 0.35*minor grade + 0.65*major grade
major grade: 0.65*61 = 39.65
minor grade: 0.35*84 = 29.4
total: 39.65+29.4 = 69.05
Rounded = 69%
A marble has a mass of 5 grams. juan has 17 marbles in his bag.
what is the total mass of the marbles?
o a. 22 grams
o b. 55 grams
o c. 57 grams
o d. 85 grams
Answer:
85 grams
Step-by-step explanation:
Marble: 5 g/marble
17 marbles in a bag: (17 marbles)*(5 g/marble) = 85 grams/bag of 17 marbles
An aerospace company has submitted bids on two separate federal government defense contracts. The company president believes that there is a 45% probability of winning the first contract. If they win the first contract, the probability of winning the second is 73%. However, if they lose the first contract, the president thinks that the probability of winning the second contract decreases to 46%. A. What is the probability that they win both contracts
The probability that they win both contracts is 33% if there is a 45% probability of winning the first contract and the probability of winning the second contract after winning the first contract.
What is probability?Probability is the rate of successful outcomes to the total outcomes of an event.
P(E) = n(E)/n(S)
Where E -event, n(E) - successful/favorable outcomes of event E, and n(S) - total outcomes of the event.
Calculation:It is given that,
An aerospace company has submitted bids on two separate federal government defense contracts.
The probability of winning the first contract is - 45%
The probability of winning the second contract if they win the first contract is - 73%
The probability of winning the second contract if they lose the first contact is - 45%
So, the probability that they win both contracts is
= (probability of winning the first contract) × (probability of winning the second contract)
= 0.45 × 0.73
= 0.3285 ≅ 0.33
⇒ 33%
Therefore, the probability that they win both contracts is 33%.
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An artist charges a $50 supply fee, plus $35 per hour for classes. write an equation to represent the total cost, c, based on the number of hours, h, of the lesson. what will be the total cost if you take a 5 hour art lesson?
The total cost in 5 hours is $225
Given that the charges of a supply fee of an artist is $50
The charges per hour classes is $35
The total cost is expressed by c
The number of hours expressed by h
We need to calculate the total cost in 5 hour lesson
As per the given statement ,
C= 50 +35h
Where h is the number of hours
h = 5 hours
C = 50 + 35h
C = 50 + 35(5)
C = 50 +175
C = $225
The total cost in 5 hours is $225
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Find the volume of the cone.
either enter an exact answer in terms of it or use 3.14 for i and round your final answer to the nearest
hundredth.
The volume of the cone of radius 5 units and height 3 units is 78 cubic units.
Given radius of cone 5 units and height of cone be 3 units.
We are required to find the volume of cone.
Volume is the amount of substance that a container can hold in its capacity.
Formula of cone is 1/3 *π[tex]r^{2} h[/tex] in which r is radius and h is height of cone.
We have to just put the values in formula.
Volume=1/3 *π[tex]5^{2} 3[/tex]
=25*3π/3
=75π/3
=25π
Put π=3.14 as said in the question.
=25*3.14
=78.5 cubic units.
After rounding we will get 78.
Hence the volume of cone whose radius is 5 units and height is 3 units is to be 78 cubic units.
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Question is incomplete as it should include the figure.
30 A club of 12 people would like to choose people for the offices of president, a vice president, and a secretary. How many different ways are there to select the officers so that only one person holds each office?
1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary. This can be obtained by using the formula of permutation.
How many different ways are there to select the officers so that only one person holds each office?Total number of people in the club = 12
total number of positions = (president, vice president, secretary) = 3
From 12 people 3 people are taken at a time.
That is, using the formula for permutation we get,
ⁿPₓ = [tex]\frac{n!}{(n-x)!}[/tex]
Here n = 12 and x = 3
P(12,3)= 12!/(12-3)! =12!/9! = 10×11×12 = 1320
Hence 1320 different ways are there to select the officers so that only one person holds each office given that the club has 12 people who would like to choose people for the offices of president, a vice president, and a secretary.
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What is 3/4 divided 1/6
Answer:
Fraction form: 9/2
Mixed number form: 4 1/2
Decimal form: 4.5
Step-by-step explanation:
To divide the two number, follow these steps.
3/4÷1/6
3/4×6/1=18/4
Reduce.
18/4=9/2 or 4 1/2
Hope this helps!
Answer:
[tex]\dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]
Step-by-step explanation:
[tex] \dfrac{3}{4} \div \dfrac{1}{6} = [/tex]
To divide a fraction by a fraction, rewrite the first fraction and multiply it by the reciprocal of the second fraction. To get the reciprocal of a fraction, flip it. The reciprocal of 1/6 is 6/1.
[tex] = \dfrac{3}{4} \times \dfrac{6}{1} [/tex]
[tex] = \dfrac{3 \times 6}{4 \times 1} [/tex]
[tex] = \dfrac{18}{4} [/tex]
[tex]= \dfrac{9}{2} = 4 \dfrac{1}{2}[/tex]
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between and . Assume that a confidence interval estimate of the population mean annual starting salary is desired. a. What is the planning value for the population standard deviation
The planning value for the population standard deviation is 4330.
Given the confidence interval 20000 and 35000.
We have to find the planning value of standard deviation.
Standard deviation is measuring dispersion of data. Uniform probability distribution has two bounds a and b. The standard deviation is given by :
s=[tex]\sqrt{(b-a)^{2}/12 }[/tex].
Annual starting salaries for college graduates be between 20000 and 35000.
It is uniform in the interval so, a=20000, b=35000.
Now we have to just put the values of a and b in the above formula to get the value of standard deviation.
s=[tex]\sqrt{(35000-20000)^{2} /12}[/tex]
=[tex]\sqrt{(15000)^{2} /12}[/tex]
=[tex]\sqrt{225000000/12}[/tex]
=[tex]\sqrt{18750000}[/tex]
=4330
Hence the planning values for the population standard deviation is 4330.
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Question is incomplete as it should includes the confidence interval of $20000 and $35000.
Oksana wrote the equation below on the whiteboard. 6 b 6 = 48 what is the value of b? 4 7 8 9
The correct answer is 7.
What is linear equation ?A linear equation only has one or two variables. In a linear equation, no variable can be multiplied by a value greater than one or used as the denominator of a fraction. When you find the values that collectively make a linear equation true and plot those values on a coordinate grid, all the points fall on the same line.
I am aware that this query's equation is,
6b + 6 = 48
subtract 6 from both side in the equation.
6b + 6 - 6 = 48- 6
6b = 42
now, divide by 6 from both side in the equation.
6b/6 = 42/6
b = 7.
Therefore, the correct answer is 7.
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I understand this is the question.
Oksana wrote the equation below on the whiteboard.
6 b + 6 = 48
What is the value of b?
(a)4
(b)7
(c)8
(d)9
If a rectangular cross-section with coordinates at (1, 1), (1, 4), (3, 4) and (3, 1) is rotated about the line y = 1, what will be the resulting three-dimensional object? cone cylinder sphere pyramid
Answer:
Step-by-step explanation:
Comment
The first thing you ought to notice is that the original shape is a rectangle, with 2 of the y coordinates of the 4 points of 1. What that statement means is that two of the points (1,1) and (3,1) both sit on the line y = 1. they don't move. The other two points do move and they form a circular shape. So what you are going to get is a cylinder.
Answer: cylinder
Answer: 345
Step-by-step explanation: the alls
Pls answer fast first to answer correct is the gets brainliest
Answer:
The answer is the first option; 6^1/12
Step-by-step explanation:
We can simplify the question by using the radical rule to rewrite it as
6^1/3 ÷ 6^1/4
Then we use exponent rule which states that when we are dividing exponents of the same base, we have to subtract them. We see that the exponents are 1/3 and 1/4. So we use basic fractional division, here's the subtraction:
= 1/3 - 1/4
= 4/3 - 3/4 (we criss-crossed)
= 1/12 (we subtracted the denominators and multiplied the denominators)
Now that we have subtracted the exponents, we can write the answer as 6^1/12
Answer:
Option #1: [tex]6\frac{1}{2}[/tex]
Step-by-step explanation:
#1: Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] and [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]:
[tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}} * \frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex]
#2: Combine and simplify the denominator:
- Multiply [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] by [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] = [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6} \sqrt[4]{6}^3}[/tex]
- Raise [tex]\sqrt[4]{6}[/tex] to the power of 1
- Use the power rule [tex]a^{m} a^{n} =a^{m+n}[/tex] to combine exponents: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^{3} }{\sqrt[4]{6}^{1+3}}[/tex]
- Add 1 and 3
- Rewrite [tex]\sqrt[4]{6}^4[/tex] as 6: [tex]\frac{\sqrt[3]{6} \sqrt[4]{6}^3}{6}[/tex]
#3: Simplify the numerator:
- Rewrite the expression using the least common index of 12: [tex]\frac{\sqrt[12]{6^4} \sqrt[12]{216^3}}{6}[/tex]
- Combine using the product rule for radicals: [tex]\frac{\sqrt[3]{6^4 *216^3}}{6}[/tex]
- Rewrite 216 as [tex]6^3[/tex]: [tex]\frac{\sqrt[3]{6^{4}*(6^{3})^{3}}}{6}[/tex]
- Multiply the exponents in [tex](6^{3})^3[/tex]: [tex]\frac{\sqrt[12]{6^{4}*6^{9}}}{6}[/tex]
- Use the power rule [tex]a^{m}a^{n}=a^{m+n}[/tex] to combine exponents and add [tex]4+9[/tex]:
[tex]\frac{\sqrt[12]{6^{13}}}{6}[/tex]
- Raise 6 to the power of 16: [tex]\frac{\sqrt[12]{13060694016}}{6}[/tex]
- Rewrite 13060694016 as [tex]6^{12}*6[/tex]: [tex]\frac{\sqrt[12]{6^{12}*6}}{6}[/tex]
- Pull terms out from under the radical: [tex]\frac{6\sqrt[12]{6}}{6}[/tex]
#4: Cancel the common factor of 6:
[tex]\frac{\sqrt[12]{6}}{6}=6\frac{1}{2}[/tex]
The correct simplified answer for [tex]\frac{\sqrt[3]{6}}{\sqrt[4]{6}}[/tex] is Option #1: [tex]6\frac{1}{2}[/tex].
Ethan donated 20% of his savings for charity. if the amount he donated was $920, then find his savings.
Total Saving of Ethan is = $4600
Saving after donating 20% = $4600-$920
=$3680
What is Percentage ?
As a fraction of 100, a percentage is a number or ratio. Although the abbreviations "pct.", and occasionally "pc" are also used, the percent sign ("percent") is frequently used to indicate it. A % has no dimensions and no associated unit of measurement.
How to calculate percentage?
Calculating a percentage involves dividing an item by its sum and multiplying the result by 100. The formula for percentage calculation is (value/total value)100%
Solution :
Let the Saving be 100%
Donated salary 20% = $920
finding 80% of the saving
Formula for percentage:
[tex]\frac{value}{total value} *100[/tex]
=[tex]\frac{20}{100} *920[/tex]
= [tex]5*920[/tex]
= [tex]4600[/tex]
Then the Total saving =$4600
The Total saving after donating 20% = $3680
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A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 5 ftys along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole
25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path. This can be obtained by considering this as a right angled triangle.
How fast is the tip of his shadow moving?Let x be the length between man and the pole, y be the distance between the tip of the shadow and the pole.
Then y - x will be the length between the man and the tip of the shadow.
Since two triangles are similar, we can write
[tex]\frac{y-x}{y} =\frac{6}{15}[/tex]
⇒15(y-x) = 6y
15 y - 15 x = 6y
9y = 15x
y = 15/9 x
y = 5/3 x
Differentiate both sides
dy/dt = 5/3 dx/dt
dy/dt is the speed of the tip of the shadow, dx/dt is the speed of the man.
Given that dx/dt = 5 ft/s
Thus dy/dt = (5/3)×5 ft/s
dy/dt = 25/3 ft/s
Hence 25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path.
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I feel like my answers are wrong someone please help
Using translation concepts, the equations are given as follows:
a) [tex]y = \sqrt{16 - 4x^2}[/tex]
b) [tex]y = 3\sqrt{16 - x^2}[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is:
[tex]y = \sqrt{16 - x^2}[/tex]
In item a, when it is horizontally compressed by a factor of 2, it means that x -> 2x, hence:
[tex]y = \sqrt{16 - (2x)^2} = \sqrt{16 - 4x^2}[/tex]
In item b, the transformations are given as follows:
Vertical expansion by a factor of 3, hence y -> 3y.Reflected in the y-axis, hence x -> -x.Then:
[tex]y = 3\sqrt{16 -(-x)^2} = 3\sqrt{16 - x^2}[/tex]
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what is the length of side AB of the triangle?
BC is 3 across & CA is 3 up, but this creates a right-angle triangle. So, Pythagoras Theorem is used to find AB
AB = root 3^2 + 3^2
AB = 3 root 2
or 4.242640687
Thus, AB is 4.24 to 2d.p
(root means square root)
Hope this helps!
A combination lock uses three integers in the combination, and the dial is numbered with the integers 0, 1, 2 and 3. If adjacent numbers in the combination cannot be the same, how many possible combinations are there
There can be 36 combinations.
How to find the total number of combinations?The total number of combinations of the dial can be found by using permutations without any number repeating.
There are four integers on the dial. They are 0, 1, 2, and 3.
It is also given that the numbers shouldn't repeat on the adjacent dial.
Therefore, we can say that there are 4 possible numbers on the first.
Similarly, on the second dial, only 3 numbers are possible since no two adjacent dials can have the same.
This is also the case for the third dial. It can also have 3 possible numbers.
Therefore, the total number of combinations is given by 4*3*3 = 36 combinations.
Therefore, we have found that there can be 36 combinations.
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Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents lolas purchase
The graph that represents Lola's Purchase is as shown in the attached file.
How to interpret Inequality Graph?Lola bought x pencils that cost $0.25 and Y erasers that cost $0.50.
Total expenditure is less than $3.
Representing expense in the equation form gives us;
Expense on pencils + expense on erasers < 3
Thus;
0.25X + 0.50Y < 3
Dividing through by 0.25, we have;
X + 2Y < 12
This inequality when graphed, line will be plotted in dots and area below the line will be in the shaded form.
From the standard equation of line in slope intercept form, we can deduce that; Slope of this line is = (-1/2)
The correct graph is attached below.
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The ratio of girls to boys at a party is 5:4. if there are 20 girls in the class, how many boys are there.
Answer:
16 boys
==========================
Let the number of boys be b and girls be g.
The ratio is:
g/b = 5/4And the number of girls is:
g = 20Substitute the number into ratio and find the value of b:
20/b = 5/4b = 20*4/5b = 16A distribution in which two nonadjacent values occur more frequently than any other values in a set of data is called a(n):______distribution.
In Bimodal Distribution two nonadjacent values occur more frequently than any other values in a set of data.
According to the statement
we have to tell about the that type of distribution in which two nonadjacent values occur more frequently than any other values in a set of data
A bimodal distribution has two peaks. In the context of a continuous probability distribution, modes are peaks in the distribution.
and from this definition we have clear that the in this distribution the values are repeated.
it shows the probability distribution with two peaks in the graphical mode.
Bimodal distribution show repeated value.
it is used in many types of data representation because of two peaks graphical representation than the simple graph.
it is the easiest method than the others distributions.
So, In Bimodal Distribution two nonadjacent values occur more frequently than any other values in a set of data.
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Which statement is true regarding the graphed functions?
141x
12-
10-
g(x)
8-
3)
6
fin
2+
7-6-5-4-3-2-12 1 2 3 4 5 6
-4
-6
-8+
ܘ
-10+
-12+
-14
f(x)
个x
X
The true statement regarding the graphed function is that f(-2) = g(-2).
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Given is a graphed function.
The graph contains two functions f(x) and g(x).
From the graph, it is clear that,
The two graphs intersect at a certain point, where the both functions passes through.
The intersecting point is (-2, 4).
This point can be written as (-2, f(-2)) and (-2, g(-2)).
This implies that,
f(-2) = g(-2)
Hence the true statement is f(-2) = g(-2).
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Your question is incomplete. The complete question is as given below.
A community pool that is shaped like a regular pentagon needs a new cover for the winter months. the radius of the pool is 20.10 ft. the pool is 23.62 ft on each side. to the nearest square foot, what is the area of the pool that needs to be covered?
The area of the pool that needs to be covered is 960.42 square feet.
What is Pythagoras theorem give example?To determine the undiscovered side of a right-angled triangle, utilize the Pythagoras theorem. The hypotenuse (third side) of a right-angled triangle, for instance, can be determined using the formula c2 = a2 + b2, where 'c' stands for the hypotenuse and 'a' and 'b' are the two legs.According to the question:
We have been given that a community pool that is shaped like a regular pentagon needs a new cover for the winter months.To find the area of community pool we will use area of pentagon formula.[tex]Area of pentagon=\frac{1}{2} a * p$[/tex] , where, a represents the apothem or perpendicular distance from the center of the pentagon and p represents perimeter of pentagon.Let us find the perimeter of our given pentagon by multiplying each side length by 5.
[tex]Perimeter of community pool $=5 \times 23.62\\Perimeter of community pool $=118.1$[/tex]
Now let us find apothem of our pentagon by using Pythagoras theorem.
[tex]a^{2}=20.10^{2}-11.81^{2}\\$a^{2}=404.01-139.4761\\$a^{2}=264.5339\\$a=\sqrt{264.5339}\\$a=16.2645$[/tex]
Upon substituting our given values in above formula we will get,
[tex]Area of community pool =\frac{1}{2} \times 16.2645 \times 118.1\\Area of community pool $=8.13224907 \times 118.1\\Area of community pool $=960.418615627971 \approx 960.42$[/tex]
Therefore, the area of the pool that needs to be covered is 960.42 square feet.
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Answer: B). 960 ft2
Step-by-step explanation:
What is the recursive formula for this geometric sequence?
4, -12, 36, -108, ...
Answer: C.
Step-by-step explanation:
The first number is a positive 4, which is your a1. Then the geometric sequence goes to a negative implying that it is multiplied by a negative. So the a1 = 4 and it is being multiplied by a negative 3.
Answer: C
[tex]\left \{ {{a_{1}=4 } \atop {a_{n}=a_{n-1}*(-3) }} \right.[/tex]
Step-by-step explanation:
The starting amount (a1) = 4
The rate is -3 because 4 * -3 = 12 and -12 and -12 * -3 = 36 etc.
how many hours will it take a plane to go 3 008 miles
Based on the speed of the plane, the number of hours it will take to fly 3,008 miles is 5.47 hours.
How long will the plane take to travel 3,008 miles?The speed of the plane is given as 550 miles per hour
In order to reach 3,008 miles, the plane should travel for:
= Distance / Speed
= 3,008 / 550
= 5.47 hours
Rest of the question is:
how many hours will it take a plane to go 3 008 miles if it travels at 550 mph
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Balu had a collection of coins. 1/2 of the coins are from asian countries, 1/3 of them from european countries, 36 are from america, how many asian coins are there
The total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.
Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.
We assume the total coins with Balu to be x.
The fraction of coins from Asian countries = 1/2.
Thus, the number of coins from the Asian countries = 1/2 of x = x/2.
The fraction of coins from European countries = 1/3.
Thus, the number of coins from the European countries = 1/3 of x = x/3.
The number of coins from America = 36.
Thus, the total number of coins = x/2 + x/3 + 36.
But, we assumed that the total number of coins is x.
Thus, we get a linear equation in one variable as follows:
x = x/2 + x/3 + 36.
We solve this equation as follows:
x = x/2 + x/3 + 36,
or, x - x/2 - x/3 = 36,
or, (6x - 3x - 2x)/6 = 36,
or, x/6 = 36,
or, x = 36*6 = 216.
Thus, the total number of coins Balu had in his collection was 216 coins, computed using the linear equation in one variable, x = x/2 + x/3 + 36.
Asian coins were 1/2 a fraction of this, that is, (1/2)*216 = 108 coins.
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ALL U NEED TO TO IS IDENTIFY THE PROPERTYS OF EACH PROBLEM. PLS
20 points
please help me i am in a rush
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "percentages and numbers." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Can someone please help me with this
Answer:
y = 0.5x
Step-by-step explanation:
y = rx
4.5/9 = 0.5
7/14 = 0.5
15/30 = 0.5
y = 0.5x
You are performing an experiment in your lab. to compare with other experiments your results must be in moles. during your final step you burn a strip of magnesium (mg), which results in 187 grams of magnesium oxide (mgo). how should you enter your results?
4.6 moles in 187 grams of magnesium oxide (mgo).
What is mole explain with example?One mole is defined as the amount of substance containing as many elementary entities (atoms, molecules, ions, electrons, radicals, etc.) as there are atoms in 12 grams of carbon - 12(6. 023×1023). The mass of one mole of a substance equals to its relative molecular mass expressed in grams.The relative formula mass of a compound is calculated by adding together the relative atomic mass values for all the atoms in its formula. Moles are units used to measure substance amount. Chemistry (Single Science) Atomic structure.
To solve ,
number of moles is equals to the mass in grams divided by RFM
RFM=16+24.3=40.3
=187/40.3
=4.6 moles of MgO
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Which of the following exponential functions is represented by the graph?
OA)
A) f(x) = -2x
B) f(x) = 2x
C) f(x) = (¹/2)-x
OD) f(x) = (¹/2)*
Answer:
D) f(x) = (1/2)^x
Step-by-step explanation:
at least that is what I think answer D is supposed to be.
I guess the other answer options are actually
A) f(x) = -2^x
B) f(x) = 2^x
C) f(x) = (1/2)^-x
let's look at the most interesting point here : (1, 1/2).
when x=1, then y = 1/2
A fails. because for x = 1 we get y = -2.
B fails. because for x = 1 we get y = 2.
C fails. because for x = 1 we get (1/2)^-1
and that is 1 / 1/2 = 2
so, the only function giving us (1, 1/2) is D, as
(1/2)¹ = 1/2