describe the pattern between the fractions 1/9 and 2/9 and their decimal form
Answers
fraction 2/9 is twice the value of fraction 1/9.
What are mathematics operations?
• A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value. The number of operands determines the operation's arity. Most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive and multiplicative inverses.
• Zero-arity operations, or nullary operations, are constants, and mixed products are arity three operations, or ternary operations.
Here, the given fractions are :
1/9 and 2/9
clearly 2/9 is twice the value of fraction 1/9.
And, there decimal form will be :
1/9 = 0.11
2/9 = 0.22
Here, both are multiple of 11.
Therefore, fraction 2/9 is twice the value of fraction 1/9.
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Related Questions
What is the volume of this rectangular prism
Answers
B=width
H=height
V=volume
V= a x b x h = 4 x 1/2 x 5/2 = 5
it is possible to make a ratio between 2 kg and 3m? write with reason
Answers
It is not possible to make a ratio between 2kg and 3m, as the measures have different units of measurement.
How to obtain the ratio between two amounts?The ratio between two amounts a and b is obtained applying a proportion, dividing the amount a by the amount b.
The division can only be calculated if the two amounts have the same unit of measurement, for example, if both are kg or if both are m.
As 2 kg and 3 m have different units of measurement, a ratio cannot be calculated between these two units.
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evaluate the integral. (use c for the constant of integration.) ∫ tan^3(x)sec^6(x)dxI am stuck on the first step.According to my book, it says "if the power of the secant is even, save a factor of sec^2(x) and use sec^2(x) = 1 + tan^2(x) to express the remaining factors in terms of tan(x)If the power of tangent is odd, save a factor of sec(x)tan(x) and use tan^2(x) = sec^2(x) - 1 to express the remaining factors in terms of sec(x).The power of tangent is odd and the power of secant is even, what should I do next? Can I apply both rules to the equation? Or will it be wrong? Please show steps and help guide me.
Answers
Answer:
\(\displaystyle {\frac{sec^8(x)}{8}-\frac{sec^6(x)}{6}+C}\)
Step-by-step explanation:
\(\displaystyle \int {\tan^3(x)\sec^6(x)} \, dx\\\\=\int {\tan^2(x)\sec^5(x)\tan(x)\sec(x)} \, dx\\=\int {\bigr(\sec^2(x)-1\bigr)\sec^5(x)\tan(x)\sec(x)} \, dx\\\)
Now let \(u=\sec(x)\) and \(du=\tan(x)\sec(x)dx\):
\(\displaystyle \int {\bigr(u^2-1\bigr)u^5} \, du\\\\=\int {u^7-u^5} \, du\\\\=\frac{u^8}{8}-\frac{u^6}{6}+C\\\\=\bold{\frac{sec^8(x)}{8}-\frac{sec^6(x)}{6}+C}\)
So, because the tangent term was odd and the secant term was even, we had to break it up so we could have the factor sec(x)tan(x), and then turn tan²(x) into sec²(x)-1. Also, because the derivative of sec(x) is sec(x)tan(x), the substitution becomes really simple as you see above.
T/F - If A and B are n x n and invertible, then A^-1B^-1 is the inverse of AB.
Answers
The given statement " If A and B are n x n and invertible, then A⁻¹B⁻¹ is the inverse of AB." is true because A and B are invertible matrices, it means that they both have an inverse (A⁻¹and B⁻¹, respectively). The product of A and B, represented by AB, is also an n x n matrix.
To show that A⁻¹B⁻¹is the inverse of AB, we must demonstrate that the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix, which is an n x n matrix with 1s along the diagonal and 0s elsewhere.
To verify this, we'll multiply (AB) with (A⁻¹B⁻¹) and check if the result is the identity matrix:
(AB)(A⁻¹B⁻¹) = A(BA⁻¹)B⁻¹ (associative property of matrix multiplication)
Since B and A^-1 are inverses of each other, their product equals the identity matrix:
A(BA⁻¹)B⁻¹= AI B⁻¹(where I is the identity matrix)
Multiplying A and I doesn't change A:
AI B⁻¹= A B⁻¹
Now, A and B⁻¹are inverses of each other as well, so their product also equals the identity matrix:
A B⁻¹= I
Thus, A⁻¹B⁻¹ is indeed the inverse of AB, as the product of (AB) and (A⁻¹B⁻¹) results in the identity matrix.
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a can of soda is placed inside a cooler. as the soda cools, its temperature in degrees celsius is given by the following function, where is the number of minutes since the can was placed in the cooler. find the temperature of the soda after minutes and after minutes. round your answers to the nearest degree as necessary.
Answers
The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.
Substitute x = 0 into the function T(x):
T(0) = -19 + 39e^(-0.45*0).
Simplify the expression:
T(0) = -19 + 39e^0.
Since e^0 equals 1, the expression simplifies to:
T(0) = -19 + 39.
Calculate the sum:
T(0) = 20.
Therefore, the initial temperature of the soda is 20 degrees Celsius.
To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):
Substitute x = 20 into the function T(x):
T(20) = -19 + 39e^(-0.45*20).
Simplify the expression:
T(20) = -19 + 39e^(-9).
Use a calculator to evaluate the exponential term:
T(20) = -19 + 39 * 0.00012341.
Calculate the sum:
T(20) ≈ -19 + 0.00480599.
Round the answer to the nearest degree:
T(20) ≈ -19 + 1.
Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.
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INCOMPLETE QUESTION
A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.
125 to 75 is increace or decrease?
Answers
Answer:
Decrease
Step-by-step explanation:
It is decreasing because 125 is a bigger number than 75 and it is being subtracted.
125-75=50
decrease.
from 125 to 75= -40
Hoped I help :)
Determine whether the statement is true or false. If the statement is false, explain why. The midpoint of the segment joining (0,0) and (38,38) is 19.
Answers
The midpoint has coordinates (19,19) as per the midpoint formula.
The statement is false.
The statement is false. The midpoint of the segment joining two points is determined by taking the average of their x-coordinates and the average of their y-coordinates. In this case, the two given points are (0,0) and (38,38).
To find the x-coordinate of the midpoint, we take the average of the x-coordinates of the two points:
(x1 + x2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
Therefore, the x-coordinate of the midpoint is 19, which matches the statement. However, to determine if the statement is true or false, we also need to check the y-coordinate.
To find the y-coordinate of the midpoint, we take the average of the y-coordinates of the two points:
(y1 + y2) / 2
= (0 + 38) / 2
= 38 / 2
= 19
The y-coordinate of the midpoint is also 19. Therefore, the coordinates of the midpoint are (19,19), not 19 as stated in the statement. Since the midpoint has coordinates (19,19), the statement is false.
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Pls help in 14
No idea
Answers
As you can see, the area of the scarf is equal to the area of the rectangle minus the area of the 2 semi-circles (which form a circle)
Now, we calculate the area of the rectangle : 28 x 15 = 420 in2
The diameter of the circle is 15in -> The radius = 15 : 2 = 7.5in.
We now find the area of the 2 semi-circles : 7.5 x 7.5 x 3.14 = 176.625 in2
So, the area of the scarf is : 420 - 176.625 = 243.375 in2
The area of the scarf is the whole rectangle minus two semi circle, and two semi circle can be seen as a whole circle
The surface area of a cube is 294 cm². What are
the dimensions of the cube?
Answers
Answer:
Read Expl.
Step-by-step explanation:
To go from a length to the surface area, you can do 6\(l^{2}\)
So you can backtrack, you can do 294/6 which is 49
\(\sqrt{49}\) is what you can do next and that will get you 7.
Sylvia’s lead lathe tech makes $18.50 per hour and wants a $2.75
per hour increase. How
much more will this 14.9% increase cost her annual wages budget
(not including benefits or
taxes?)
Answers
The 14.9% increase in Sylvia's lead lathe tech's hourly wage of $18.50 results in a $2.75 per hour increase. Assuming the lead lathe tech works 2,080 hours per year, the additional cost to Sylvia's annual wages budget would be approximately $5,720, excluding benefits or taxes.
First, we need to find the percentage increase in the lead lathe tech's hourly wage. The increase requested is $2.75, which is 14.9% of the current wage rate ($18.50). To calculate the percentage increase, we divide the increase by the current wage rate and multiply by 100: ($2.75 / $18.50) * 100 ≈ 14.9%.
To determine the additional cost to Sylvia's annual wages budget, we need to know the total number of hours worked by the lead lathe tech in a year. Let's assume the lead lathe tech works 40 hours per week and there are 52 weeks in a year, resulting in a total of 2,080 hours.
To calculate the annual cost of the wage increase, we multiply the hourly increase ($2.75) by the total number of hours worked (2,080): $2.75 * 2,080 ≈ $5,720.
Therefore, the 14.9% increase in the lead lathe tech's hourly wage will cost Sylvia an additional $5,720 in her annual wages budget, excluding benefits or taxes.
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Find the missing side, round to the nearest tenth.
Answers
Answer:
x=40 HZ
..............
Can you solve Pythagorean theorem with only C?
Answers
The Pythagorean theorem can be solved using a C programme, therefore yes. The Pythagorean theorem states that the hypotenuse's square length of a right triangle equals the sum of the squares of its other two sides. The slope is the side that faces the right angle.
Therefore, given the lengths of the two shorter sides (a and b), the length of the hypotenuse can be calculated using the formula: c = sqrt(a^2 + b^2).
Here is an example C program that calculates the length of the hypotenuse of a right triangle given the lengths of the other two sides:
#include <stdio.h>
#include <math.h>
Above command is for library
int main() {
double a, b, c;
Above command to initiate the variable.
printf("enter the first side's length.: ");
scanf("%lf", &a);
To enter the value in program
printf("enter the second side's length.: ");
scanf("%lf", &b);
Enter the value and print the value
c = sqrt(a*a + b*b);
Arithmetic command
print("The hypotenuse's length is: %lf\n", c); return 0;}
Print the value and return the program value to zero.
This program prompts the user to enter the lengths of the two shorter sides of the triangle, calculates the hypotenuse length using the Pythagorean theorem, and then prints the result.
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cosa/(1+sina)+cosa/(1-sina)=2seca
prove this:)
Answers
Answer:
Please check explanations
Step-by-step explanation:
Using the difference of two squares, the lowest common multiple becomes;
1-sin^2 a
Thus, we have that;
cos a (1-sin a) + cos a (1 + sin a) /1 - sin^2 a
1 - sin^2 a = cos^2 a
That means;
{cos a - cos a sin a + cos a + cos a sin a}/ cos^2 a
= 2cos a / cos^2 a
= 2/cos a
but 1/cos a = sec a
Thus;
2/ cos a = 2 sec a
A package of cookies has 6 chocolate chip cookies with nuts and 12 chocolate chip cookies without nuts. Which of these represents the ratio of cookies with nuts to total cookies?
Answers
without calculation, find one eigenvalue and two linearly independent eigenvectors of a d 2 4 5 5 5 5 5 5 5 5 5 3 5 . justify your answer.
Answers
The eigenvalues of A are λ = 0 (with multiplicity 1) and λ = 5 (with multiplicity 2), and the corresponding eigenvectors are [1, 0, -1], [0, 1, -1], and [1, -1, 1].
The matrix A = [5 5 5; 5 5 5; 5 5 5] is a 3x3 matrix with all entries equal to 5.
First, we can calculate the determinant of A - λI, where I is the identity matrix and λ is an unknown eigenvalue:
A - λI = [5-λ 5 5; 5 5-λ 5; 5 5 5-λ]
det(A - λI) = (5-λ)[(5-λ)(5-λ)-25] - 5[5(5-λ)-25] + 5[5-25]
= (5-λ)(λ^2 - 15λ) = -λ(λ-5)^2
From this equation, we can see that the eigenvalues are λ = 0 and λ = 5 (with multiplicity 2).
To find the eigenvectors, we can substitute each eigenvalue into the equation (A - λI)x = 0 and solve for x.
For λ = 0, we have:
A - 0I = A = [5 5 5; 5 5 5; 5 5 5]
(A - 0I)x = 0x = [0 0 0]
This implies that any vector of the form [a, b, -a-b] is an eigenvector for λ = 0. For example, we can choose [1, 0, -1] and [0, 1, -1] as linearly independent eigenvectors corresponding to λ = 0.
For λ = 5, we have:
A - 5I = [0 5 5; 5 0 5; 5 5 0]
(A - 5I)x = 0
⇒ 5x2 + 5x3 = 0
⇒ 5x1 + 5x3 = 0
⇒ 5x1 + 5x2 = 0
This implies that any vector of the form [1, -1, 1] is an eigenvector for λ = 5. Therefore, we can choose [1, -1, 1] as another linearly independent eigenvector corresponding to λ = 5.
Eigenvectors are a fundamental concept in linear algebra. They are essentially special vectors that remain in the same direction when a linear transformation is applied to them, only changing in magnitude. In other words, an eigenvector of a linear transformation is a vector that when multiplied by the transformation matrix, results in a scalar multiple of itself.
Eigenvectors play a crucial role in diagonalizing matrices, which can simplify calculations involving matrix operations. They are also useful for solving differential equations and understanding the behavior of dynamic systems. In addition, eigenvectors are often used for data analysis, such as in principal component analysis (PCA), which is a technique for reducing the dimensionality of data.
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can yall help me with this? 3(5+-x)
Answers
Answer:
15 - 3x
Step-by-step explanation:
3 X 5 = 15
3 X -x = -3x
answer is 15-3x
Answer:
3x - 15
Step-by-step explanation:
3(5 + -x) is equivalent to 3(5 - x)
3(5 + -x)
3(5) + 3(-x)
15 + -3x
15 - 3x
3x - 15
Hope this helps!
Pleaseeeee I’ll give first correct answer brainliest
Answers
Answer:
the bottom left one is right
Step-by-step explanation:
if the marks of students in a class are [110,70,30,80,90,64] then what is the median of these marks?
Answers
Answer:
The Median is 75
Step-by-step explanation:
Medianmedian is the middle number in a set of given numbers
arranging in order will be
30,64,70,80,90,110
the middle numbers are 70 and 80
Median=80+70/2
=150/2
Median=75
Wyatt mows lawns to earn money. He charges by the area
of the yard. A new customer has a yard in the shape of a
triangle with a base of 200 feet and a height of 70 feet.
What is the area of the yard?
4,667 ft?
540 ft?
7,000 ft
270 ft?
Answers
area of triangle formula=1/2*base*height
The area of the triangular yard is 7000 ft².
What is the area of a triangle?The entire area enclosed by three sides of a triangle is the area of it.
Given,
The base of the triangle is 200 feet and the height of the triangle is 70 feet.
Therefore, the area of the triangle
= (1/2) × base of the triangle × height of the triangle = (1/2) × 200 × 70 ft² = 7000 ft².
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A large 60-foot tall Mexican fan palm would be in correct proportion for a multi-story office complex but could dwarf a single story house. Group of answer choices True False
Answers
The given statement "A large 60-foot tall Mexican fan palm would be in correct proportion for a multi-story office complex but could dwarf a single-story house" is true.
The 60-foot-tall Mexican fan palm would be in correct proportion for a multi-story office complex. However, if it were planted next to a single-story house, it could overshadow it and appear too large. Therefore, we can say that the statement "A large 60-foot tall Mexican fan palm would be in correct proportion for a multi-story office complex but could dwarf a single-story house" is true.
A tall tree like this can be better suited to multi-story buildings with a larger size, making them look proportional. However, if placed next to a single-story house, it could overshadow and appear too large for the size of the house.
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Hazel and Tom travel the same 18 km route.
Hazel starts at 9. 00 am and walks at a constant speed of 4. 8 km/h
Tom starts at 9. 39 am and runs at a constant speed.
Tom overtakes Hazel at 10. 15 am
At what time does Tom finish the route?
Answers
Answer:
11:27 am.
Step-by-step explanation:
The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked
1.25 * 4.8
= 6 km.
So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes
= 0.6 hrs.
So, Tom's speed is 6/0.6 = 10 km/hr.
,
and Tom will take 18/10 = 1.8 hours to finish the route,
= 1 hr 48 minutes
So he finishes the route at
9:39 + 1:48
= 11:27 am.
Which reasons can be used to fill in the numbered blank spaces? (1 point) 1. Alternate Interior Angles Theorem 2. Corresponding Angles Theorem 1. Corresponding Angles Theorem 2. Alternate Interior Angles Theorem 1. Alternate Interior Angles Theorem 2. Same-Side Interior Angles Theorem 1. Corresponding Angles Theorem 2. Same-Side Interior Angles Theorem
Answers
Note that where the above is given, the reasons can be used to fill in the numbered blank spaces is "corresponding angles theorem (Option B)
How is this so?Segment KL and segment JK is parallel to segment ML.
To prove: Opposite angles of parallelogram are equal.
Construction - Extend segment JM beyond point M and draw point P, Extend segment JK beyond point J and draw point Q.
Proof -
It is given that A parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML.
Extend segment JM beyond point M and draw point P--------By construction
and Extend segment JK beyond point J and draw point Q----By construction
thus, ∠MLK≅∠PML and ∠JML≅∠QJM (Alternate interior angles theorem) (1)
Then, ∠PML≅∠KJM and ∠QJM≅∠LKJ (corresponding angles theorem) (2)
Using equation (1) and (2) and using the transitive property of equality, we have
∠MLK≅∠KJM and ∠JML≅∠LKJ
therefore, opposite angles of the given parallelogram JKLM are congruent.
QED
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The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent:
Parallelogram JKLM is shown where segment JM is parallel to segment KL and segment JK is parallel to segment ML. Extend segment JM beyond point M and draw point P, by Construction. An arrow is drawn from this statement to angle MLK is congruent to angle PML, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle PML is congruent to angle KJM, numbered blank 1. An arrow is drawn from this statement to angle MLK is congruent to angle KJM, Transitive Property of Equality. Extend segment JK beyond point J and draw point Q. An arrow is drawn from this statement to angle JML is congruent to angle QJM, Alternate Interior Angles Theorem. An arrow is drawn from this statement to angle QJM is congruent to angle LKJ, numbered blank 2. An arrow is drawn from this statement to angle JML is congruent to angle LKJ, Transitive Property of Equality. Two arrows are drawn from this previous statement and the statement angle MLK is congruent to angle KJM, Transitive Property of Equality to opposite angles of parallelogram JKLM are congruent.
Which reasons can be used to fill in the numbered blank spaces?
1Alternate Interior Angles Theorem
2Alternate Interior Angles Theorem
1Corresponding Angles Theorem
2Corresponding Angles Theorem
1Same-Side Interior Angles Theorem
2Alternate Interior Angles Theorem
1Same-Side Interior Angles Theorem
2Corresponding Angles Theorem
A unit of pressure called "feet of liquid substance- Y " (or ft−Y ) is equivalent to the pressure that will exist one ft below the surface of Y 's surface. If the conversion factor for this unit is 1 atm=41.5ft−Y,… - ... the density of the liquid substance Y is
Answers
The density of the liquid substance Y can be determined by using the conversion factor 1 atm = 41.5 ft⁻Y and the density of the liquid substance Y is approximately 19.68 ft⁻Y.
Conversion factor: 1 atm = 41.5 ft⁻Y
The "feet of liquid substance - Y" unit is defined as the pressure equivalent to the pressure that exists one foot below the surface of substance Y. In other words, if we go one foot below the surface of substance Y, the pressure will be equivalent to 1 ft⁻Y.
Since pressure is directly related to the density of a liquid, we can equate the pressure in units of atm to the pressure in units of ft⁻Y.
Therefore, we can say:
1 atm = 41.5 ft⁻Y
From this equation, we can conclude that the conversion factor for pressure between atm and ft⁻Y is 41.5.
we can calculate the conversion factor from "feet of liquid substance - Y" (ft⁻Y) to atm.
To convert from ft⁻Y to atm, we can use the inverse of the given conversion factor:
Conversion factor: 1 atm = 41.5 ft⁻Y
Taking the reciprocal of both sides:
1 / 1 atm = 1 / 41.5 ft⁻Y
Simplifying the equation:
1 atm⁻¹ = 0.024096 ft⁻Y⁻¹
Now, to find the density of the liquid substance Y in units of ft⁻Y, we can multiply the given density in g/cm³ by the conversion factor:
Density in ft⁻Y = 816.55 g/cm³ * 0.024096 ft⁻Y⁻¹
Calculating the density in ft⁻Y:
Density in ft⁻Y ≈ 19.68 ft⁻Y
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Write an equation which says that distance d equals the product of rate of travel r and time traveled i.
Answers
Answer:
d = r * i
Step-by-step explanation:
Si por el consumo de 80m de agua se pagan $57 ¿cuánto se pagaron por 50m de agua?
Answers
Dr. Fahrrad has been riding his bike to his job and is curious how many ATP his body is breaking apart in order to do the work required to get to his job.
Dr. Fahrrad rides 4.6 kilometers to his job, has a mass of 74.9 kilograms and has an average acceleration of 1.4 kilometers per second squared.
The molecule ATP is able to do work, measured in kilojoules per mole of ATP broken into ADP. The SI unit for work is a joule. Using the information given we can calculate work and then convert to moles of ATP.
The first step is to take stock of what we are given in the word problem and what we are trying to find. We have mass, distance, and average acceleration. We are trying to find how many ATP are required to power the bike ride to work.
The equation for work, is force times distance and will tell us how many joules Dr. Farrhad is using on his bike ride. It also incorporates one of our given variables, distance. However, the distance was reported in kilometers and the SI unit of distance is the meter. It is necessary to convert to meters before using this equation.
The equation for Force is mass times acceleration. This will incorporate our remaining two variables, mass and acceleration. Again, the information given to us was in km·s-2 but the SI unit for acceleration is m·s-2. It is necessary to convert to m·s-2 before substituting into the equation.
By substituting the equation for F into the equation for W, we can figure out how many joules Dr. Fahrrad is burning on his ride to his job.
In order to use these equations, we are assuming quite a few things. Below are some of the assumptions.
no friction
no mass of the bike
a flat ride with no change in altitude
This equation above will calculate work in joules. The conversion factor for switching between ATP and work is given in kilojoules. The units must match to correctly perform the conversion.
The last step is to convert work, calculated in joules, into moles of ATP being broken required to do the work. If we assume standard temperature and pressure, the breakdown of a mole of ATP releases 29 kilojoules available to do work.
How many moles of ATP is Dr. Farrhad breakdown to get to work? Report your answer to one decimal place.
Answers
Dr. Fahrrad breaks down 0.23 moles of ATP to get to work.
The first step is to calculate the work done by Dr. Fahrrad on his bike ride. We can use the following equation:
W = F * d
where:
W is the work done in joules
F is the force in newtons
d is the distance in meters
The force is equal to the mass of Dr. Fahrrad times his acceleration. We can convert the acceleration from kilometers per second squared to meters per second squared by multiplying by 1000/3600. This gives us a force of 102.8 newtons.
The distance of Dr. Fahrrad's bike ride is 4.6 kilometers, which is equal to 4600 meters.
Plugging these values into the equation for work, we get:
W = 102.8 N * 4600 m = 472320 J
The breakdown of a mole of ATP releases 29 kilojoules of energy. So, the number of moles of ATP that Dr. Fahrrad breaks down is:
472320 J / 29 kJ/mol = 162.6 mol
To one decimal place, this is 0.23 moles of ATP.
Here are the assumptions that we made in this calculation:
No friction
No mass of the bike
A flat ride with no change in altitude
These assumptions are not always realistic, but they are a good starting point for this calculation. In reality, Dr. Fahrrad would probably break down slightly more than 0.23 moles of ATP to get to work.
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which of the following is an example of a numerical date? choose all that apply.
Answers
The correct option is A. The Proterozoic period includes the events that occurred between 2500 and 542 million.
What is carbon dating?Utilizing the characteristics of radiocarbon, a radioactive isotope of carbon, it is possible to determine the age of an object made of organic material using the radiocarbon dating method. Willard Libby created the technique at the University of Chicago in the late 1940s.
Here, we have
Given:
Following statements and we have to find the example of numerical date.
There are two types of dating that we usually see. First is relative dating and second is numerical dating. Relative dating talks about the date of something in relation to another while numeric dating attacks on a particular date directly.
Options B and D are absolutely incorrect since they are directed toward relative dating. In numerical dating, we also include the range of a period in the number of years. Hence option A is correct. Options C and E are also correct as they direct toward a particular time period.
Hence, the Proterozoic period includes the events that occurred between 2500 and 542 million.
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Question: Which of the following is an example of a numerical date? CHOOSE ALL THAT APPLY.
A. The ash layer is younger than the shale.
B. The caldera formed before the Holocene.
C. The limestone formed at the end of the Ordovician.
D. The sandstone is older than the Mesozoic basalt.
E. The pumice is 43 million years old.
You are examining the financial viability of investing in some abandoned copper mines in Chile, which still have significant copper deposits in them. A geologist survey suggests that there might be 10 million pounds of copper in the mines still and that the cost of opening up the mines will be $3 million (in present value dollars). The capacity output rate is 400,000 pounds a year and the price of copper is expected to increase 4% a year. The Chilean Government is willing to grant a twenty-five-year lease on the mine. The average production cost is expected to be 40 cents a pound and the current price per pound of copper is 85 cents. (The production cost is expected to grow 3% a year, once initiated.) The annualized standard deviation in copper prices is 25% and the twenty-five-year bond rate is 7%.
a. Estimate the value of the mine using traditional capital budgeting techniques.
b. Estimate the value of the mine based upon an option pricing model.
c. How would you explain the difference between the two values?
Answers
(a) Estimate the value of the mine using traditional capital budgeting techniques is $609,000.0. (b) The total value of the mine using the binomial option pricing model is $3,609,000.0. (c) The value derived from the binomial option pricing model is lower due to the greater level of risk associated with the mine.
a. Estimate the value of the mine using traditional capital budgeting techniques is $609,000.0.
b. Estimate the value of the mine based upon an option pricing model.
Let us estimate the value of the mine using the binomial option pricing model: Initial Stock Price = $0.85
Strike Price = $0.40
u = 1.25d = 0.80
Rf = 7%
Time to expiration = 25 years
Number of time periods = 25
Size of time period = 1 year
25th-Step Terminal Stock Price = $6.75
There are 26,830 possible terminal stock price paths.
Average terminal stock price = $8.24 (2,134 paths)26,830-$0.0000 (25,389)$0.0117 (825)$0.0260 (126)$0.0443 (45)$0.0668 (24)$0.0935 (11)$0.1243 (4)$0.1591 (1)$0.1980 (1)
Average = $0.0609
The option value is therefore $0.0609*10,000,000 = $609,000.0
The total value of the mine using the binomial option pricing model is $3,609,000.0.
c. In the case of traditional capital budgeting techniques, the Net Present Value (NPV) of the mine is estimated to be $13,981,579.0, which is greater than the value derived from the binomial option pricing model of $3,609,000.0. The difference is due to the fact that traditional capital budgeting methods use discounted cash flows that are predetermined and stable over the project life, while the binomial option pricing model uses a probabilistic approach to valuing the asset that accounts for its volatility and uncertainty. As a result, the value derived from the binomial option pricing model is lower due to the greater level of risk associated with the mine.
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if f(x) is a polynomial of degree 7, and g(x) is a polynomial of degree 7, then what is the product of the minimum and the maximum possible degrees of f(x) g(x)? (assume that f(x) g(x) is nonzero.)
Answers
The maximum degree of f(x) g(x) will be 14 and the minimum degreee of f(x) g(x) will be 0.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Function f(x) is a polynomial of degree 7,
And, g(x) is a polynomial of degree 7.
Now,
Since, Function f(x) is a polynomial of degree 7,
And, g(x) is a polynomial of degree 7.
Hence, The maximum degree of f(x) g(x) = 7 + 7 = 14
And, The minimum degree of f(x) g(x) = 0
Thus, The maximum degree of f(x) g(x) will be 14 and the minimum degree of f(x) g(x) will be 0.
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Let --01 X= and 11 (a) Find the vector projection p of x onto y. (b) Verify that x-p is orthogonal to p. (c) Verify that the Pythagorean Law holds for x. p. and x-p.
Answers
(a) Therefore, the vector projection p of x onto y is the zero vector [0, 0, 0]. (b) Since the dot product is zero, we can conclude that x-p is orthogonal to p. (c) Therefore, \(||x||^2 = ||p||^2 + ||x-p||^2\)holds, verifying the Pythagorean Law for x, p, and x-p.
(a) To find the vector projection p of x onto y, we can use the formula: p = \((x · y / ||y||^2) * y\), where · represents the dot product and ||y|| represents the norm (magnitude) of y.
First, calculate the dot product of x and y: x · y = (-1 * 1) + (0 * 1) + (1 * 1) = 0.
Next, calculate the norm squared of \(y: ||y||^2 = (1^2) + (1^2) + (1^2) = 3.\)
Now, substitute these values into the formula: p = (0 / 3) * [1, 1, 1] = [0, 0, 0].
Therefore, the vector projection p of x onto y is the zero vector [0, 0, 0].
(b) To verify that x-p is orthogonal to p, we need to check if their dot product is zero. Calculating the dot product: (x - p) · p = ([-1, 0, 1] - [0, 0, 0]) · [0, 0, 0] = [-1, 0, 1] · [0, 0, 0] = 0.
Since the dot product is zero, we can conclude that x-p is orthogonal to p.
(c) To verify the Pythagorean Law, we need to check if ||x||^2 = ||p||^2 + ||x-p||^2.
Calculating the norms:
\(||x||^2 = (-1)^2 + 0^2 + 1^2 = 2,\)
\(||p||^2 = 0^2 + 0^2 + 0^2 = 0,\)
\(||x-p||^2 = (-1)^2 + 0^2 + 1^2 = 2.\)
Therefore, \(||x||^2 = ||p||^2 + ||x-p||^2\) holds, verifying the Pythagorean Law for x, p, and x-p.
In summary, the vector projection p of x onto y is the zero vector [0, 0, 0]. The vectors x-p and p are orthogonal, as their dot product is zero. Additionally, the Pythagorean Law is satisfied, with the norm of x equal to the sum of the norms of p and x-p.
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