The mass of one molecule of methane is 2.658 × [tex] {10}^{-23} [/tex] and number of molecules of methane is 3.76.
Mass of one molecule of methane = mass of one carbon atom + 4×mass of one hydrogen atom
Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 4 × 1.67 × [tex] {10}^{-24} [/tex]
Performing multiplication first
Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 4 × 6 68 × [tex] {10}^{-24} [/tex]
Equating the exponents
Mass of methane = 1.99 × [tex] {10}^{-23} [/tex] + 0.668 × [tex] {10}^{-23} [/tex]
Performing addition
Mass of methane = 2.658 × [tex] {10}^{-23} [/tex]
Now, 2.658 × [tex] {10}^{-23} [/tex] is the weight of molecules number = 1
1 gram will have number of molecules = 1/ 2.658 × [tex] {10}^{-23} [/tex]
Number of molecules = 3.76
Thus, mass is 2.658 × [tex] {10}^{-23} [/tex] and 3.76 molecules are there.
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Suppose an exxon corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 4. 25%, how much is the bond worth today?.
The present value of the bond is $3,345.90. This is calculated by taking the future value of the bond ($4,500) and dividing it by the present value factor for 4.25% for 10 years (1.427).
PV = FV / (1 + r)n
PV = $4,500 / (1 + 0.0425)10
PV = $4,500 / 1.427
PV = $3,345.90
The present value of an asset is the value of the asset today, taking into account the time value of money and the interest rate of the investment. In this example, the Exxon Corporation bond will pay $4,500 ten years from now, and the going interest rate on safe 10-year bonds is 4.25%. To calculate the present value of the bond today, we use the present value formula, which is the future value of the bond divided by the present value factor for the given interest rate and number of years. In this case, the present value factor is 1.427, and the present value of the bond is $3,345.90. This means that the bond is worth $3,345.90 today, taking into account the time value of money and the given interest rate.
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Find the measure of the base angle in an isosceles triangle that has a base length of 6 and a leg length of 5. Round your answer to the nearest whole degree.
The base angle for the isosceles triangle is 53°.
What is an isosceles triangle?Any triangle with two sides that have the same length is said to be an isosceles triangle. If the two sides of a triangle are congruent, then the angle across from them must likewise be, according to the theorem that explains the isosceles triangle. As a result, the two angles of an isosceles triangle that are on opposite sides with equal numbers are equal in size.
Given base length = 6 and leg length = 5
draw a perpendicular to the base that divides the base into equal parts,
as shown in the image attached
let the base angle be Ф,
and using a cosine formula for the base angle
cosФ = base/hypotenuse
from construction base = 3 and hypotenuse = 5
cosФ = 3/5
Ф = cos⁻¹(3/5)
Ф = 53.13°
Ф = 53° (approx)
Hence the base angle is 53°
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A front-end loader is to load trucks with granular material that has a swell factor of 15%. If the loader has a heaped capacity of 10 cu. Yd. , calculate the total cycle time for the loader if it can move 55 cu. Yd. Of in-bank material in 1 hr. With an efficiency of 48 min. /hr
A front-end loader to load trucks with granular material that has a swell factor of 15%. If the loader has a heaped capacity of 10 cu. Yd. the total cycle time for the loader, if it can move 55 cu, is 16.2 hours( 55 cu. Yd. / 10 cu. Yd. (heaped capacity) * 15% (swell factor) * 48 min. /hr)
The total cycle time for a front-end loader to load trucks with granular material with a swell factor of 15% can be calculated by taking the total amount of in-bank material to be loaded and dividing it by the heaped capacity of the loader. This will give us the total number of cycles the loader must complete. Once we have this number, we must multiply it by the swell factor. This gives us the total number of heaped cycles the loader will have to complete.
Finally, we must multiply the total number of heaped cycles by the efficiency of the loader. Efficiency is the amount of time it takes for the loader to complete one heaped cycle. In this case, the total cycle time for the loader to load is 55 cu. Yd. Of in-bank material with a swell factor of 15% and a heaped capacity of 10 cu. Yd. Is 16.2 hours, assuming the loader has an efficiency of 48 min. /hr.
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if micheal's pool hold 21,000 gallons of water and it is 90 percent full, how many gallons of water are there?
The number of gallons of water that Michael's pool holds for the given condition will be 18,900 gallons.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
If Michael's pool holds 21,000 gallons of water and it is 90 percent full.
The number of gallons of water that Michael's pool holds will be given as,
⇒ 90% of 21,000
⇒ 0.90 x 21,000
⇒ 18,900 gallons
The number of gallons of water that Michael's pool holds for the given condition will be 18,900 gallons.
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Question 3(Multiple Choice Worth 2 points)
(Slope LC)
What is the slope of the linear relationship?
A graph of a linear function that decreases from left to right passing through the points 1 comma 0 and 3 comma negative 3.
negative three halves
three halves
negative two thirds
two thirds
Answer:
(a) negative three halves (-3/2)
Step-by-step explanation:
You want the slope of the line through points (1, 0) and (3, -3).
Slope formulaThe slope can be found using the formula ...
m = (y2 -y1)/(x2 -x1)
m = (-3 -0)/(3 -1) = -3/2
(a) The slope of the line is -3/2.
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explain how the probability associated with the roll of each individual die in the pair explains the higher variability in the total outcome of the roll of each pair. how do the concepts of permutations and combinations apply to this example? discuss how the notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls.
The probability of each individual dying in the pair explains the higher variability in the total outcome of the roll of each pair because there are more possible combinations of outcomes.
The concepts of permutations and combinations apply to this example by showing the different ways the dice can be rolled to achieve a specific total outcome. Each die in a pair of dice has a probability of 1/6 of rolling any number between 1 and 6.
When rolling two dice, there are 36 different possible outcomes (6x6) and each one has a different probability of happening. This is where the concepts of permutations and combinations apply, as each possible combination of dice rolls will result in a different total outcome.
The notion of degree of freedom can be used to illustrate the accumulating results of a set of dice rolls by showing how the total outcome is affected by the roll of each individual die.
For example, if the first die rolls a 4, the second die has 5 degrees of freedom as it can roll any number between 1 and 6 (except for 4) and still achieve a total outcome of 9. As the number of dice being rolled increases, the degree of freedom decreases, making the probability of rolling a specific total outcome less likely.
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What is inverse of inverse log?.
The inverse of a logarithmic function is an
The inverse of the inverse logarithmic function is simply the exponential function.
The inverse logarithmic function (also known as the logarithm or log) takes as input a number x and returns the power to which a fixed number (usually 10 or e) must be raised to produce x. The inverse of the logarithmic function is the exponential function, which takes as input a power and returns the number that would result from raising a fixed number to that power. In other words, if log_b(x) = y, then b^y = x, where b is the fixed number.
In other words, the exponential function is the inverse of the inverse logarithmic function.
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Does a square root graph have an inverse?.
A square root function is the inverse of a quadratic function. If a function f is the inverse of another function f1, then f is the inverse of f1.
The order of positive integers is preserved by the square function: greater numbers have larger squares. The square, then, is a monotonic function on the range [0, +]. Since negative integers have squares that are proportional to their absolute values, the square on [(,0] is a monotonically declining function.
The horizontal line test determines whether or not f has an inverse if any horizontal line crosses its graph more than once.
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How do you find the area of a 45 45 90 triangle with only the hypotenuse?.
The area of a 45-45-90 triangle, with a hypotenuse of 8mm in length is [tex]4mm^{2}[/tex]
This is a 45-45-90 triangle the base of the triangle and the height of the triangle are equal. So we simply need to find the values of the two sides and plug them into the formula.
[tex]a^{2} +b^{2} = 8^{2}[/tex]
[tex]a=b[/tex]
[tex]a^{4} =16[/tex]
[tex]a^{2} =8[/tex]
[tex]a=\sqrt{8}[/tex]
[tex]Area = 1/2 *base.height[/tex]
[tex]area=1/2*\sqrt{8} .\sqrt{8}[/tex]
[tex]Area= 4mm^{2}[/tex]
A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.
In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.
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Complete Question:
What is the area of a 45-45-90 triangle, with a hypotenuse of 8mm in length?
Sohan the toy shop on the two tricycles at the same price each one was sold for 2200 on the one he made a profit of 10% and on the other he lost 12% what was the cost of each of the cycle
Please answer the question... I need the answer
Answer:
Step-by-step explanation:
cp of first tricycle=100/(P%+100)*sp
cp=100/10+100*2200
=100/110*2200
CP=Rs 2000
Cp of second tricycle=100/(100-L%)*SP
=100/100-12*2200
100/88*2200
CP=2500
Thanks for the question
I need help fast please!!
f(-2) = 3 (value on y axis)
if f(x) = -1, x = 0 (when y = -1)
What does it mean when you substitute a value into an equation and the result is a true statement?.
When you substitute a value into an equation and the result is a true statement it means solution to an equation is a value of a variable.
The substitution method is a quick and easy way to algebraically solve a set of linear equations and determine the variables' solutions. According to what the name implies, this method entails determining the value of the x-variable in terms of the y-variable from the first equation and then substituting or replacing the value of the x-variable in the second equation.
We can solve and determine the value of the y-variable in this method. Finally, we may use any of the above equations to obtain x by substituting the value of y. This procedure can also be switched around so that we first solve for x before solving for y.
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Mi White i renting a van for one week in a few additional day D. He doe not have to pay a per mile fee. Evaluate the expreion 440130 D to find how much he will pay for the nine day rental
For the nine-day rental, the expression for the same sum will be charged as $1,610
The formula combines numerical elements and operations symbolised by the signs for addition, subtraction, multiplication, and division.
Expression are the Mathematical symbols can be used to represent variables, operations, functions, brackets, punctuation, and grouping in addition to numbers (constants). The operation order and other characteristics of the logical syntax can also be indicated by them.
Given that Mr. White will be leasing an enormous vehicle for a week plus a few more days, He is not required to pay a per-mile charge. The formula is 440 + 130d.
The sum will be computed as follows by the expression:
A = 440 + 130d
A = 440 + ( 130 x 9 ) ( 130 x 9 )
A = 440+ 1170
A = 1,610
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Evaluate −xyz
if x= −2/3
, y= 0.6
, and z= 1 7/8
Write your answer as a fraction in simplest form.
Answer:
17/20
Step-by-step explanation:
_(_2/3)*6/10*17/8
2/3×6/10×17/8
=17/20
bag a has 2 yellow marbles,2 red marbles,and 3 blue marbles picking from bag a is certain,likely,unlikely,impossible
Picking a green marble from bag A is D. impossible.
What is an impossible probability ?The probability of an impossible occurrence is the likelihood that an event won't occur at all and won't have any chance of happening in the future. As a result, the likelihood of such an event is always zero. An impossible event is one that doesn't take place. There is no chance that it may occur. Therefore, there is no chance of that happening.
There are no green marbles in Bag A which means that it is not possible to pick a green marble from Bag A. The probability of picking a green marble is 0 and the likelihood is impossible.
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The full question is:
Bag a has 2 yellow marbles,2 red marbles, and 3 blue marbles picking a green marble from bag a is certain,likely,unlikely,impossible
Write 256 as a product of primes.
Use index notation when giving your answer.
The number 256 can be written as products of its prime numbers in index notation as 256 = 2⁸
What is prime factorizationPrime factorization is a way of expressing a number as a product of its prime factors. A prime number is a number that has exactly two factors, which includes 1 and the number.
The first five prime numbers are 2, 3, 5, and 7. We shall divide the number 256 with prime numbers that are factors beginning with 2;
256/2 = 128
128/2 = 64
64/2 = 32
32/2 = 16
16/2 = 8
8/2 = 4
4/2 = 2
2/2 =1
so; 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Therefore, the number 256 expressed as product of its prime factors in index notation is written as 256 = 2⁸
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Geometry
A drawer contains 12 white socks and 8 black socks. You randomly choose 1 sock and do not replace it. Then you randomly choose another sock.
a. What is the probability of selecting a white sock first and then a black sock?
b. What is the probability of selecting two white socks?
c. What is the probability of selecting two black socks?
12 white socks, 8 black socks, 20 total socks:
a.
[tex]\dfrac{12}{20}\cdot\dfrac{8}{19}\approx 0.252631578947\approx 25.3\%[/tex]
b.
[tex]\dfrac{12}{20}\cdot\dfrac{11}{19}\approx 0.347368421053\approx 34.7\%[/tex]
c.
[tex]\dfrac{8}{20}\cdot\dfrac{7}{19}\approx 0.147368421053 \approx 14.7\%[/tex]
Kate's food budget for the month is R700. The first week she spent R189,75, the second week she spent R203,20 and the third week she spent R146,95. How much does she have left for the last week?
Answer: R160.10
Step-by-step explanation:
R700-R189.75=R510.25
R510.25-R203.20=R307.05
R307.05-R146.95=R160.10
i need help with finishing this ASAP
Answer: Look at the image below.
Step-by-step explanation: I traced it out and did the math for you.
Hope this helps! :)
which equation represents the graph below?
Answer:
linear equation represents the graph below
What is a partial sum example?.
A partial sum is basically a addition of series and adding number upto a partial value.
For example,
635 + 312 is calculated by adding 600 + 300 = 900, 30 + 10 = 40 and 5 + 2 = 7.
These partial sums are then added as 900 + 40 + 7 = 947
A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit.
A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums.
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total.
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- You have a total of 10 coins consisting of nickels and dimes in your
pocket. The value of the coins is $0.70. Write and solve a system of linear
equations to find the numbers of nickels and dimes in your pocket.
Answer:The value of the coins is $0.70. Write and solve a system of linear equations to find the numbers of nickels and dimes in your pocket. There are 6 nickels and 4 dimes.
Step-by-step explanation:
hi may you help if you can thanks
Answer: A 4 91/100
Step-by-step explanation: its 491/100 because the 100 is 1 and 4 is the number 4 and 91/100 is .91
What is the y-intercept of the graph with the equation 2x 3y − 6?.
The y-intercept of line 2x - 3y = -6 is (0,2).
The y-intercept of a line is the point where the line intersects the y-axis. It can be found by setting x to 0 and solving for y. In this case, we have the equation 2x - 3y = -6.
By setting x to 0, we get:
2(0) - 3y = -6
Which simplifies to: -3y = -6
And finally, by dividing both sides by -3, we get the value of y: y = 2
It means the line will intersect the y-axis at point (0,2) which means
when x =0 the line will be at y = 2.
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At Chocolatier Incorporated, there are two factors that determine the cost of health
care. If an employee makes less than $65,000 per year, he pays
$52 per month for
individual coverage and $98 per month for family coverage. If an employee makes at
least $65,000 per year, individual coverage is $67 per month and family coverage is
$122 per month.
a) Graham makes $62,800 per year. He has individual health care. His yearly contribution
is 10% of the total cost. How much does his employer contribute?
b) Claudia s annual salary is $75,400. She has family health care. Her employer
contributes $1,052 per month toward her total coverage cost. What percent does
Claudia contribute toward the total coverage? Round to the nearest tenth of a percent.
a) Graham's employer contributes $561.60 per year towards his coverage.
b) Claudia contributes 28.2% towards the total coverage cost.
What is percentage?
Percentage is a way of expressing a number as a fraction of 100. It is typically represented by the symbol "%", and is often used to express a change or a part of a whole.
a) Graham makes $62,800 per year, which is less than $65,000, so he pays $52 per month for individual coverage. His yearly contribution is 10% of the total cost, so his employer contributes 90% of the total cost. To find the total cost, we can multiply the monthly cost by 12: $52/month * 12 months/year = $624/year. So Graham's employer contributes $624 * 90% = $561.60 per year towards his coverage.
b) Claudia's annual salary is $75,400, which is at least $65,000, so she pays $122 per month for family coverage. Her employer contributes $1,052 per month towards her total coverage cost. To find the total cost, we can multiply the monthly cost by 12: $122/month * 12 months/year = $1,464/year. To find the percentage Claudia contributes, we divide her contribution by the total cost and multiply by 100: $1,464-$1,052 / $1,464 * 100 = 28.2%. So Claudia contributes 28.2% towards the total coverage cost.
Hence,
a) Graham's employer contributes $561.60 per year towards his coverage.
b) Claudia contributes 28.2% towards the total coverage cost.
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What is an equivalence class example?.
An example of equivalence class is the equivalence relation Congruence Modulo n. Here, two integers say "a" and "b" are equivalent if they results same remainder after dividing by n.
Equivalence classes are constructed such that elements a and b belong to the same equivalence class if and only if a and b are equivalent. Formally, the set S and the equivalence relation ~ on S, the equivalence class of the element a in S is the set [a] = { x Ε X | and ~ x} = S / ~. Example 1 : If X is the set of all pens and ~ is the "has the same color as" equivalence relation, then one particular equivalence class consists of all black pens.
Example 2: A well-known example is itthe equivalence relation Congruence Modulo n . Two integers "a" and "b" are equivalent if they have the same remainder after division by n. For example, consider the congruence relation modulo 2 on the set of integers,
R ≈ { (a,b) | a ≡ b mod 2}
The possible remainders for n = 2 are 0 and 1. An equivalence class consists of those integers that have the same remainder. Hence, there are 4 equivalence classes in this example:
[0] = { ...........,-8,-6,-4,-2,0,2,4,6,8,......}
[1] = {..........-7, -5, -3,1,3,5,7,........}
Similarly, one can show that the relation of congruence modulo n has (n -1) equivalence classes, [0], [1], ...., [ n - 1].
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J.5 Unit rates
2NB
You have prizes to reveal!
Go to your game board.
Finn ran a total of 6 miles over the course of 2 track practices. How many miles would Finn have run after 6 track practices? Solve using unit rates.
miles
Finn would run 18 miles after 6 track practices.
What are the total miles?Generally, A unit rate is a ratio of two measurements with a denominator of 1. To find the number of miles Finn would run after 6 track practices, we can use the unit rate of miles per practice to multiply by the number of practices.
Unit rate: 6 miles / 2 practices = 3 miles per practice
To find the total number of miles Finn would run after 6 practices, we can multiply the unit rate of 3 miles per practice by the number of practices, 6.
Total miles: 3 miles/practice * 6 practices = 18 miles
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If f(x) = g(x) = 2x² - 4x + 4 and f(x) = 3x² - 2x + 1, what is
g(x)?
g(x) must be equal to f(x).
What is equivalent function?An equivalent function is a mathematical expression that produces the same result as another expression. It is a function that is mathematically equivalent to a given function, meaning that its graph is the same as that of the given function. Equivalent functions are useful in problem solving as they can be used to simplify a problem or to show a relationship between two functions.
g(x) = 3x² - 2x + 1. This means that f(x) and g(x) are equivalent functions, and thus have the same output for any given input. This means that when x is plugged in to both equations, the resulting output will be the same. Therefore, g(x) must be equal to f(x).
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Find the equation of the line joining the points A (1,2) and 8(-1,8)
First, you need to find the slope between the two points:
[tex]\begin{aligned}\dfrac{8-2}{-1-1} & = \dfrac{6}{-2}\\[0.5em]&=-3\endaligned}[/tex]
Now, you use one of the points to find the equation.
You can use point-slope form:
y - 1 = -3 (x-2)
Or you can use slope-intercept form:
y = -3x + 5
Note:
You can find the slope-intercept form by taking y = mx + b and substituting in the slope and a point and solving for b:
2 = -3 (1) + b
In 1992, Jason bought a gallon of gas for $1.20. Yesterday, he bought a gallon of gas for $2.17. What is the percentage increase of the price of a gallon of gas from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.
The percentage increase in the price of a gallon of gas is 80.84 %.
Given,
Jason bought a gallon of gas in 1992 = $1.20
He bought a gallon of gas yesterday = $2.17
Using the formula for the percentage increase in the price,
= ( New Price - Old Price) / Old Price × 100
= ( 2.17 - 1.20) / 1.20 × 100
= 80.84%
Therefore, the percentage increase in the price of a gallon of gas from 1992 to yesterday is 80.84 %.
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