Answer: 1.68
Step-by-step explanation: Okay, to find this we need to use this formula:
Amount = Part percent * whole number / 100
So, now let's plug in the numbers:
Amount = 14 * 12 / 100
= 168/100
= 1.68
Therefore the amount of gold in the rock is 1.68 oz out of the 12 ounces.
I hope this helped!
Answer: 1.68
Step-by-step explanation: So, if we want to find how much gold is in the rock, it's a good idea to set up a proportion. So, it would be like this:
[tex]\frac{14}{100} = \frac{?}{12}[/tex]
Now, we would cross-multiply the 12 and the 14, which is 168, and then divide it by 100. That can be found by moving the decimal 2 places left of 168.00. So, that would be 1.68. Therefore, there are 1.68 ounces of gold in the rock. I hope this helped!
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.x=1+(y−2)2,x=2
The volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is 16π/3.
What is the bounded region?
A territory is said to be bounded if it has a boundary or other restrictions applied to it. In other words, a bounded shape is limited by a set of measurements or characteristics and cannot be an indefinitely huge area.
Here, we have
Given: x = 1+(y−2)², x=2
We have to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.
Rotating with the cylinder method about the x-axis means it must be a dy integral. The given parabola equation is already solved for x. Find the intersections:
2 = 1 + (y−2)²
0 = (y -1)(y-3)
y = 1, 3
We will integrate from
y = 1 to 3
The radius of each cylinder will be r=y and the height will be (greater minus lesser, i.e. right minus left).
h = 2 - (1 + (y-2)²)
h = 1 - y² + 4y -4
h = - y² + 4y - 3
Volume = [tex]\int\limits^a_b {2πrh} \, dy[/tex]
= 2π∫₁³ y.( - y² + 4y - 3)dy
= 16π/3
Hence, the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis is 16π/3.
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An unbiased statistic is a statistic whose mean value is ____ the population characteristic estimated
equal to the population characteristic mean that it is estimating. It is not affected by any outside biases, making it a reliable and accurate measure.
An unbiased statistic is a statistic which is not affected by any outside biases. This means that the value of the statistic is equal to the population characteristic that it is estimating. For example, the mean of a sample is an unbiased estimate of the population mean. Unbiased statistics provide reliable and accurate measures, as they are not affected by any external influences. This makes them a valuable tool for researchers, as they can use them to accurately represent the population that they are studying. Unbiased statistics are essential for drawing valid conclusions from statistical data.
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Select the correct answer from the drop-down menu.
June collected data showing the monthly expenses of some girls at her school. She wants to know the difference between the highest monthly expenses and the lowest monthly expenses.
To do that, she has to find the ________
To find the difference between the highest monthly expenses and the lowest monthly expenses, June has to find the range of the data.
The value of a baseball card in dollars has been found to be 0.35y + 0.15, where y is the number of years since it was released. By how much is the baseball card's value increasing per year?
35%
0.15%
.35%
15%
The value of baseball cards is increasing by 35% per year.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 9 is an equation.
We have,
The value of a baseball card in dollars is given by,
0.35y + 0.15
Where y is the number of years since it was released.
This means,
The value of the baseball card is 0.15.
There is a yearly increase of 35%.
35% = 35/100 = 0.35
Thus,
The value of baseball card is increasing at 35% per year
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the admission fee at a small fair is $1.50 per child and $4.00 per adult. on a certain day, 2200 people enter the fair and $5050 is collected. how many children and how many adults attended?
Answer: 1,500+7=2,200 Y=700 2.
Anya gathered a random sample of bags of potato chips from a popular company. She calculated data on different variables. For one data that she collected, she constructed a circle graph. Which of the following variables did she use?
Price of bag of potato chips
Number of chips in the bag of potato chips
Weight of bag of potato chips
Flavor of the bag will be shown in circle graph because different bag has different flavor
given that
A chord diagram's intersection graph is referred to as a circle graph in graph theory. In other words, it is an undirected graph whose vertices can be connected by a finite system of circular chords, with two vertices being connected only when their corresponding chords cross.
Anya selected a smattering of bags of potato chips from a well-known manufacturer.
She computed data on several variables.
She created a circle graph for one of the data sets she collected.
We now need to determine which variables she used in the circle graph.
The average of all the potatoes will be displayed in a circular graph.
Because the price of a bag of potatoes is the same for everyone, it won't be displayed.
Since there are the same number of chips in every bag, the number of chips in the potato chip bag will not be displayed.
Since the weight of each bag of potato chips is the same, it will not be displayed.
Since each bag has a distinct flavor, the circle graph will display the bag's flavor.
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1 week is 5 miles 2 weeks is 6 miles 3 weeks is 7 miles 4 weeks is 8 miles write an equation while w is weeks and m is miles m=w...
Answer: w=m+4
Step-by-step explanation: Every week there are 4 more miles than the number of weeks. Ex. 1 week / 5 miles 5-1=4.
For each of the following expression, write the shape of the resulting tensor. Use commas to separate thedimensions. For example, if the resulting tensor is a 2 by 3 matrix then write 2,3. If the expression is invalid,write None.ones (100) + ones (100)ones (100,1)+ ones (100,1)ones (100,1)+ones (1,100)ones (2,3) + 1
The result of this addition is a single tensor with 100 elements, which has the shape 100. Therefore, the shape of the resulting tensor is 100.
The expression is ones(100) + ones(100). This expression is valid, and the shape of the resulting tensor is a 100-dimensional vector.
We can calculate this by starting with the shape of each of the tensors. The first tensor, ones(100), is a 1-dimensional tensor with 100 elements. The second tensor, ones(100), is also a 1-dimensional tensor with 100 elements.
When we add these two tensors together, we are combining the elements of each tensor into a single tensor. In this case, we are combining the 100 elements from the first tensor with the 100 elements from the second tensor, resulting in a single tensor with 100 elements.
The result of this addition is a single tensor with 100 elements, which has the shape 100. Therefore, the shape of the resulting tensor is 100.
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what is the slope of the line through the points (-2,6) and (-4,9) ?
Answer:
= (-3)/2
Step-by-step explanation:
Compute the slope of the line through the following points:
p_1 = (-2, 6) and p_2 = (-4, 9)
The slope of the line through (x_1, y_1) and (x_2, y_2) is:
(y_2 - y_1)/(x_2 - x_1)
Substitute (x_1, y_1) = (-2, 6) and (x_2, y_2) = (-4, 9):
= (9 - 6)/(-4 - -2)
9 - 6 = 3:
= 3/(-4 - -2)
-(-2) = 2:
= 3/(-4 + 2)
-4 + 2 = -2:
= 3/(-2)
Multiply numerator and denominator of 3/(-2) by -1:
Answer: = (-3)/2
When looking for the domain of a graph, which values are you looking for?
x-values
y-values
Every one of a method's x-values, or entries, make up the domain, and all of a substring y-values, or outputs, make up the range. The domain of a vertex is every value in the structure, from left to right. The graph's range includes all integers from lower to higher.
Let x and y be functions of time t such that the sum of x and twice y is constant. Which of the following equations describes the relationship between the rate of change of with respect to time and the rate of
change of with respect to time?
A) dx/dt=2dy/dt
B) dx/dt=-2dy/dt
C) 2dx/dt+dy/dt=0
D) dx/dt + 2dy/dt=K, where K is a function of t
B) dx/dt=-2dy/dt is the relation of the rate of change for the conditon given in the question.
what is rate of change?Rate of change is a measure of how quickly a variable is changing. It is often represented by the symbol "d/dt" or "∆y/∆x" and is calculated by finding the ratio of the change in one variable to the change in another variable.
Given :
x + 2y =k
where k is a constant
differentiating above equation with respect to time we get
=> dx/dt + 2dy/dt =dk/dt
=> dx/dt + 2dy/dt =0
=> dx/dt = -2dy/dt
so Option B) dx/dt=-2dy/dt is correct option for the above problem
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Lower limit= Q₁-1.5xIQR Upper limit= Q3 +1.5xIQR IQR = Q3 - Q₁
The manager of a local fast-food chain wants to improve the service provided to customers who use the drive-up
window. As a first step in this process, the manager records how long it takes from the time the customer first
enters the drive-in window until they are served their food at the final window. Below are the times (in minutes) fo
the 30 customers (in order):
2 2 3 4 4 6 8 9 10 10 10 10 10 11 11
13 13 13 13 14 14 14 15 18 18 20 20 23 37 41
(a) Calculate the median.
(b) Calculate the first and third quartile.
QI=
Q3=
(c) Calculate the interquartile range.
IQR=
Lower=
(d) Calculate the lower and upper limits.
Upper=
The median is the middle value of a data set, the first quartile (Q1) is the median of the lower half of the data set, while the third quartile is the upper half. The interquartile range (IQR) is the difference between the first and third quartiles.
What is an interquartile range?The interquartile range (IQR) is a measure of variability defined as the difference between a data set's 75th percentile (Q3) and 25th percentile (Q1). It is often referred to as the midspread or the middle 50% of a data set. The interquartile range (IQR) is a measure of the dispersion of the middle 50% of values in a data set that is commonly used in descriptive statistics.
In the given question, the median is the data set's midway value. The data must first be organized in ascending or descending order before the median can be calculated. Because the data set is already in order in this example, the median may be computed simply locating the data set's middle value. The supplied data set's median is 10 minutes.
The first quartile (Q1) is the median of the data set's bottom half. To compute Q1, first organize the data in ascending or descending order. The lower part of the data set has values ranging from 2 to 11. This subset's median time is 6.5 minutes, which is in the top quartile.
The third quartile (Q3) is the median of the data set's upper half. To compute Q3, first organize the data in ascending or descending order. The upper part of the data set has values ranging from 13 to 41. This subset's median is 14.5 minutes, which is in the third percentile.
The difference between the first and third quartiles is defined as the interquartile range (IQR). The data must first be organized in ascending or descending order before the IQR can be calculated. The supplied data set's IQR is 14.5 - 6.5 = 8 minutes.
The first quartile minus 1.5 times the interquartile range is the lower limit. The data must first be organized in ascending or descending order before the lower limit can be calculated. The supplied data set has a lower limit of Q1 - 1.5 x IQR = 6.5 - (1.5 x 8) = -5.5 minutes.
The third quartile plus 1.5 times the interquartile range is the top limit. The data must first be organized in ascending or descending order before the upper limit can be calculated. The presented data set has an upper limit of Q3 + 1.5 x IQR = 14.5 + (1.5 x 8) = 23.5 minutes.
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b. Mai says that the tiles have the same area as one-foot by one-foot tiles. Do you
agree with Mai? Explain or show your reasoning.
Answer:
yes most are 12x12 inch tiles so yes
Step-by-step explanation:
In trapezoid ABCD we have AB parallel to DC, E as the midpoint of BC, and F as the midpoint of DA. The area of ABEF is twice the area of FECD. What is AB/DC ?
(A) 2
(B) 3
(C) 5
(D) 6
(E) 8
In trapezoid ABCD we have AB parallel to DC, E as the midpoint of BC
AB/DC = 5
given that
In American and Canadian English, a quadrilateral having at least one pair of parallel sides is referred to as a trapezoid (/traepzd/). It is referred to as a trapezium in British and other varieties of English (/trpizim/).
In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides. If the remaining two sides are parallel, they are referred to as the legs (or lateral sides); if not, the trapezoid is a parallelogram, and there are two pairs of bases. A scalene trapezoid is one that lacks equal-sized sides.
In trapezoid ABCD we have AB parallel to DC
E as the midpoint of BC
F as the midpoint of DA.
The area of ABEF is twice the area of FECD.
AB+EF/2 = 2(DC+EF/2)
AB+EF/2 = DC+EF
AB+EF = 2DC+2EF
EF is the midline between AB and DC
AB + (AB+DC/2) = 2DC+2(AB+DC/2)
[tex]\frac{3}{2}[/tex]AB +DC/2 = 2DC +AB + DC
[tex]\frac{3}{2}[/tex]AB +DC/2 = 3DC+AB
[tex]\frac{3}{2}[/tex]AB - AB = 3DC - DC/2
AB/2 = 5DC/2
AB = 5DC
AB/DC = 5
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Vanessa is buying a house next year. She applies for a $300,000 loan to be paid in 30 years. Her credit score is 550 Using the table, how much bigger will her monthly payment be than if her score were 850?O $745O $42O $258O $97
$745 is bigger will her monthly payment of credit score.
How does a credit score operate and what is it?
A consumer's creditworthiness is indicated by a credit score, which ranges from 300 to 850. The better a borrower seems to potential lenders, the higher their score.
A credit score is based on a person's credit history, which includes the number of open accounts, total amounts owed, payment history, and other elements.
We are given a table in which we are specified different monthly payments for different credit scores for a $300,000 loan.
Monthly payment if her credit score is 550 = $2,487
Monthly payment if her credit score is 850 = $1,742
Her monthly payment will be bigger by = Monthly payment if her credit score is 550 - Monthly payment if her credit score is 850 = $2,487 - $1,742 = $745
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How do you find all six trigonometric function of θ if the point (-5,12) is on the terminal side of θ?
The six trigonometric functions of an angle θ in a right triangle are sine (sin θ), cosine (cos θ), tangent (tan θ), cotangent (cot θ), secant (sec θ) and cosecant (csc θ).
To find these functions for a given angle θ, we need to know the length of the sides of a right triangle with angle θ.
Given that the point (-5,12) is on the terminal side of θ, we can apply the Pythagorean Theorem to find the length of the sides of the triangle. The Pythagorean Theorem states that a² + b² = c² where a and b represent the lengths of the sides of the triangle and c is the length of the hypotenuse. Using the point (-5,12), we can solve for c, which is 13.
Therefore, the sides of the triangle have lengths 5, 12, and 13. We can now use these lengths to calculate the trigonometric functions of θ.
sin θ = 12/13
cos θ = 5/13
tan θ = 12/5
cot θ = 5/12
sec θ = 13/5
csc θ = 13/12
Therefore, the six trigonometric functions of θ are sin θ = 12/13, cos θ = 5/13, tan θ = 12/5, cot θ = 5/12, sec θ = 13/5 and csc θ = 13/12.
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Find the future value of a simple interest loan of $15,500 at 6.2% interest for 11 months
$
The amount with simple interest is A = $ 16,380.92
What is Simple Interest?Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as I
Now , the amount with simple interest = A
And , the principal P = $ 15,500
The rate of interest R = 6.2 %
The number of months n = 11 months
So , the number of years T = 11/12 years
Simple Interest I = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
Simple Interest I = ( 15,500 x 6.2 x ( 11/12 ) ) / 100
On simplifying the equation , we get
Simple Interest I = $ 16,380.916987
Simple Interest I = $ 16,380.92
Hence , the future value if $ 16,380.92
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Sarah and Thomas each roll a die. Whoever rolls the higher number wins; if they both roll the same number, neither wins. a.What is the probability that Thomas wins?
b.If Sarah rolls a 3, what is the probability that she wins?
c.If Sarah rolls a 3, what is the probability that Thomas wins?
d.If Sarah wins, what is the probability that Thomas rolled a 3
e.If Sarah wins, what is the probability that Sarah rolled a 3?
Rolls the higher number wins; if they both roll the same number, neither wins.
The answer is-
a)They both start the game with an equal chance of winning, therefore 1/2
b) If she rolls a 3, Thomas must roll a 1 or 2 for her to win, making her chance of winning 1/3.
c) Thomas has a 50% chance of winning if she rolls a three because he has to roll a 4,5 or 6 to do so.
d) In order for Sarah to win, she had to roll a 2, 3, 4, or 6. If Thomas had rolled a 1, 2, 3, 4, or 5, he would have lost. Thus, there is a 1/5 chance that he will roll a 3.
e) If Sarah wins she must have rolled a 2,3,4,5 or 6. So the probability that she rolls a three is also 1/5.
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the present age of Neha is 4 times the age of her son 4 years ago .if her son is 14 years old, find the present age of Neha.
Answer: 4*4= 16
Step-by-step explanation:
if Neha is 4 years older than her son, so she will be sixteen.
he triangles on the grid below represent a translation. On a coordinate plane, triangle A B C is shifted 5 units to the right and 3 units up to form triangle A prime B prime C prime. To form the image, the pre-image moved five units right and three units up. two units right and three units up. five units left and three units down. two units left and three units down.
To form the image, the pre-image should move five units right and three units up.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, The triangles on the grid below represent a translation.
On a coordinate plane, triangle A B C is shifted 5 units to the right and 3 units up to form triangle A prime B prime C prime.
In geometry, figures in a plane can be transformed in a variety of ways, including shifts and scaling, to produce new shapes. The new (transformed) shapes are called images and the original, unaltered shapes are called preimages.
Therefore, The pre-image should travel five units right and three units up to form the image.
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Given an integer N where 1 ≤ N ≤ 105, the task is to find the number of positive integers less than or equal to N that have an odd number of digits without leading zeros.
if N < 10 then the count of numbers will be N , if N / 10 < 10 then 9 , if
N / 100 < 10 then 9 + N – 99 , if N / 1000 < 10 then 9 + 900 , if N / 10000 < 10 then 909 + N – 9999.
in all other case 90909.
what is leading zeros?
Leading zeros are zeros that appear at the beginning of a number or numerical value. These zeros are used to align digits or to indicate the number of digits in a number, but do not affect the value of the number itself. For example, 007 and 7 are the same number but the leading zeros indicate that there are 3 digits in the number.
The above contions specifies the count of number having odd number of digits and without leading zeros.
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each side of a regular septagon has length 5 inches find the area of the region between the sptagon and its circumscribing circle?
The area of the region is equal to the area of the septagon minus the area of the circumscribing circle. The area of the septagon = 7 x (5^2 x (1 + sqrt(3))/4). The area of the circumscribing circle = pi x (5^2/2).
The area of the region between the septagon and its circumscribing circle can be found by subtracting the area of the circumscribing circle from the area of the septagon. The side length of the septagon is 5 inches. The area of the septagon can be calculated using the formula A = 7 x (5^2 x (1 + sqrt(3))/4). This is equal to 58.82 inches squared. The area of the circumscribing circle can be calculated using the formula A = pi x (5^2/2). This is equal to 78.54 inches squared. Therefore, the area of the region between the septagon and its circumscribing circle is 58.82 inches squared minus 78.54 inches squared, which is equal to 19.72 inches squared.
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What fraction of 350 gallons is 135 litres
Answer:
10.19%
Step-by-step explanation:
1 gallon = 3.785 liters
350 gallons = 350 × 3.785 liters = 1324.75 liters
percent = part/whole × 100%
percent = 135 liters / 1324.75 liters × 100%
percent = 10.19%
a and b are friends. a's father d is twice as old as a and b is twice as old as his sister c. the age of d and c differ by 40 years. write a linear equation representing the given situation, assuming the ages of a and b as x and y years respectively.
The A's age is 26 years and B's age is 24 years
What is meant by linear equation? A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Ax+By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x+3y=5. Finding both intercepts of an equation in this format is rather simple (x and y).Let the ages of A and B be x and y years respectively. Then, [tex]$x-y=\pm 2[/tex]Given
D's age [tex]$=2 x$[/tex]years and, C's age[tex]$=\frac{y}{2}$[/tex] years.
Clearly, D is older than C
[tex]$2 \mathrm{x}-\frac{\mathrm{y}}{2}=40 \Rightarrow 4 \mathrm{x}-\mathrm{y}=80$[/tex]
Thus, we have the following two systems of linear equations[tex]$x-y=2$[/tex].(i)
and, [tex]$4 x-y=80$[/tex](ii)
or
[tex]$x-y=-2$[/tex] (iii)
and, [tex]$4 x-y=80$[/tex]..(iv)
Subtracting equation (i) from equation (ii), we get [tex]$3 \mathrm{x}=78 \Rightarrow \mathrm{x}=26$[/tex]Putting [tex]$\mathrm{x}=26$[/tex] in equation (i), we get [tex]$\mathrm{y}=24$[/tex]or
Subtracting equation (iv) from equation (iii), we get [tex]$-3 \mathrm{x}=-82 \Rightarrow \mathrm{x}=\frac{82}{3}=27 \frac{1}{3}$[/tex]
Putting [tex]$\mathrm{x}=\frac{82}{3}$[/tex]in equation (iii), we get
[tex]$\mathrm{y}=\frac{82}{3}+2=\frac{88}{3}=29 \frac{1}{3}$[/tex]
Hence, A's age =26 years and B's age =24 years or
A's age =[tex]27 \frac{1}{3}$[/tex] years and B's age[tex]$=29 \frac{1}{3}$[/tex] years.
The complete question is,
A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B.
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Ana is 2 years older than Wanda. let w represent Wanda's age.
The expression that represents Ana's age is 2 + w.
What is an expression?A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression:
Expression: (Number/Variable, Math Operator, Math Operator)
Given:
let w represent Wanda's age.
let a represent Ana's age.
Also given Ana is 2 years older then Wanda
Ana's age can be calculated as Wanda's age plus 2
Hence the expression which represents Ana's age is given below
Ana's age = 2 + Wanda's age
a = 2 + w
Hence Ana's age is 2 + w.
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How do I check
89,235
-66,456
______
22,779
A group of students are standing in a circle. Each student faces someone across the circle. If student 2 faces student 9, how many students are in the circle?
Becuse there must be the same number of students in both halfs of the circle, we will see that there are 15 students on the circle.
How many students are there?We know that each student faces someone across the circle. If student 2 faces student 9.
Between student 2 and 9 there are:
9 - 2 = 7 students.
So we will have 7 students in both sides of the line formed between students 2 and 9.
And we know that student 1 is on the right side of student 2, so that is one of the seven students, and the other six ones are numbers larger than 9,
Then the total number of students is given by the addition:
9 + 6 = 15
There are 15 students in the circle.
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Bronx 2 Middle School took their fifth grade scholars on a field trip to the Math Museum. General admission tickets to the Math Museum costs $16 for adults and $9 for children. In total, Bx2MS spent a total of $776 on tickets. If eight adults attended this field trip, how many children attended?
The number of the children that attended is 72.
How many children attended?We have to note that we have to put the sentence that we have been given into an equation so that we can be able to answer the question that we have been given here.
We are told that; General admission tickets to the Math Museum costs $16 for adults and $9 for children. In total, Bx2MS spent a total of $776 on tickets. The adults that attended were eight in number. Let the number of the children be X
16(8) + 9X = 776
128 + 9X = 776
776 - 128 = 9X
X = 72
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1. Which are you trying to show is true in Step 3 of a proof by mathematical induction for the statement "For all the positive integers, n³ + 2n is divisible by 3"?
On³+2n=k³ +2k is divisible by 3
O (k+1)³ +2(k+1) is divisible by 3
On³ +2n is divisible by 3
Ok³+2k is divisible by 3
n³ +2n is divisible by 3 is the statement that we want to prove and A) n³+2n=k³ +2k is divisible by 3 is not a valid statement.
Option (A) is correct.
What is mathematical induction?
Mathematical induction is a method of proof used to establish the truth of a statement for all positive integers (or natural numbers).
In step 3 of a proof by mathematical induction, you are trying to show that if the statement is true for some positive integer k, then it is also true for the next positive integer (k+1). So you would be trying to show that:
B) (k+1)³ +2(k+1) is divisible by 3
is true, assuming that
D) k³+2k is divisible by 3
is true.
In other words, you are trying to show that if the statement is true for some positive integer k, then it is also true for the next positive integer (k+1).
Hence, n³ +2n is divisible by 3 is the statement that we want to prove and A) n³+2n=k³ +2k is divisible by 3 is not a valid statement.
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 solve the following equation for g:
m+n^2 = g5M
The solution of the equation for g is (m+n^2)/5M. The solution has been obtained by solving the given equation for g.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal and joined by the equals sign "=". The two expressions need not be completely of variables i.e. one expression may contain variable and the other may not contain a variable.
We are given g: m+n^2 = g.5M
⇒m+n^2 = g.5M
⇒m+n^2 = 5gM
⇒5gM = m+n^2
⇒5gM/5M = (m+n^2)/5M .... (Dividing both sides by 5M)
⇒g = (m+n^2)/5M
Hence, the solution of the equation for g is (m+n^2)/5M.
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