Therefore, in about 15 years and 2 months, the senior class will have about 100 students.
What is equation?An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.
Given by the question.
Let P be the initial population of the senior class in the high school, and r be the rate of decrease in population per year (in decimal form).
Then, we can write the following equation to represent the situation:
P[tex](1-r)^{n}[/tex] = 100
We know that the current population of the senior class is 320, so we can substitute these values into the equation:
320[tex](1-0.07)^{n}[/tex] = 100
Simplifying the equation, we get:
[tex]0.93^{n}[/tex] = 0.3125
Taking the natural logarithm of both sides, we get:
n ln (0.93) = ln (0.3125)
Dividing both sides by ln (0.93), we get:
n = ln (0.3125) / ln (0.93)
Using a calculator, we find that n is approximately equal to 15.21 years.
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Explain how to solve the given equation for "x".
X = 2 is the solution of the given equation for "x".
What does a math equation mean?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. For instance, 3x + 5 = 14 is an equation where 3x + 5 and 14 are two expressions separated by the 'equal' sign.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. By solving for x, we discover that x equals 7, which is the value for the variable.
8ˣ = (25)
8ˣ = (5)²
X = 2
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find the area of a quadrilateral ABCD in each case.
The area of the quadrilateral ABCD for this case is of 4 square units.
How to obtain the area of the quadrilateral ABCD?The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.
The lengths for each diagonal of the diamond are given as follows:
Diagonal AC = 2 - 0 = 2.Diagonal BD = 4 - 0 = 4.The product of the diagonal lengths is given as follows:
AC x BD = 2 x 4 = 8 square units.
Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:
0.5 x 8 square units = 4 square units.
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Is this a compound?
First, Gabriel planted the geraniums in a clay pot, and then he placed the pot on a sunny windowsill in his kitchen
A. YES
B. NO
Answer:
yes it is right now you can write it
why does a square root have a plus or minus sign attached to it.
Answer:
To indicate that we want both the positive and the negative square root of a radicand
Answer:
Because a negative number times a negative number has a positive answer
Step-by-step explanation:
a factory was manufacturing products with a defective rate of 7.5%. if a customer purchases 3 of the products , what is the probability of getting at least one that is defective
If a customer purchases 3 of the products, the probability of getting at least one that is defective is 38.59%.
How to determine the probabilityIn order to determine the probability of getting at least one defective product if a customer purchases three products with a defective rate of 7.5%, we can use the concept of complementary probability.
The probability of getting at least one defective product can be calculated as the complement of the probability of getting none defective products.
So, the probability of getting no defective products is:
P(none defective) = (1 - 0.075)³ = 0.6141
Therefore, the probability of getting at least one defective product is:
P(at least one defective) = 1 - P(none defective) = 1 - 0.6141 = 0.3859 or 38.59%
.So, the probability of getting at least one that is defective is 38.59%.
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A wire first bent into the shape of a rectangle with width 5cm and lenth 11 cm.then the wire is unbent and reshaped into a square what is the length kf a side of the square
The length of a side of the square is 8 cm.
What do you mean by perimeter of a rectangle and square?
When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.
The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.
The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.
Calculating the length of a side of the square:
The length of the rectangle is 11 cm and the width is 5 cm.
Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.
Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.
Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:
[tex]32 = 4s[/tex]
[tex]s = 32/4[/tex]
[tex]s = 8[/tex]
Therefore, the length of a side of the square is 8 cm.
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In ABC, D is a point on AB and E is a point
on AC such that DE is parallel to BC. If AE = 3,
EC = x, ED = x + 1, and CB = x + 5, find the
length of EC. [Only an algebraic solution will be
accepted.]
The required value of EC is 5 units.
How to find the value of EC?Since DE is parallel to BC, we can use the property of similar triangles to set up a proportion:
AD/DB = AE/EC
We know that AD + DB = AB = x + 5. Since D is a point on AB, we can express AD and DB in terms of x:
AD = x, DB = x + 5 - x = 5
We also know that AE = 3 and ED = x + 1. Using these values, we can express AD in terms of ED:
AD = ED - AE = (x + 1) - 3 = x - 2
Substituting these values into the proportion, we get:
(x - 2)/5 = 3/EC
Multiplying both sides by 5EC, we get:
x - 2 = 15/EC
Multiplying both sides by EC, we get:
EC(x - 2) = 15
Expanding the left side, we get:
ECx - 2EC = 15
Solving for EC, we get:
EC = 15/(x - 2)
We are given that EC = x, so we can set these expressions equal to each other:
x = 15/(x - 2)
Multiplying both sides by (x - 2), we get:
x(x - 2) = 15
Expanding the left side, we get:
x² - 2x = 15
Bringing all terms to one side, we get:
x² - 2x - 15 = 0
We can factor this quadratic equation:
(x - 5)(x + 3) = 0
Therefore, x = 5 or x = -3. We reject x = -3 since we are given that EC > 0. Thus, the length of EC is: EC = x = 5.
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Find the value of x.
The calculated value of x in the similar triangles is 14 and it is calculated from the ratio 10 : x = 20 : 28
Calculating the value of x in the triangleGiven the triangle
The triangle is a superset of similar triangles
So, we have the following equivalent ratio that can be used to determine teh value of x
The set up of teh ratio is
10 : x = 10 + 10 : 28
Evaluating the like terms, we get
10 : x = 20 : 28
So, we have
x/10 = 28/20
Multiply both sides by 10
x = 14
Hence, the value of x is 14
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Translate the sentence into an equation.
Seven more than the quotient of a number and 4 is equal 5to .
The following equation can be used to represent the sentence:
7 + (x/4) = 5 where x stands for a number.
What is a linear equation?A straight line on a graph is represented by a linear equation. It has a constant slope and y-intercept, one or more variables, typically expressed by x and y. Several different real-world situations can be represented by linear equations, such as estimating the cost of goods based on the quantity purchased or calculating a car's distance traveled based on speed and time. Finding the value of the variable that causes the equation to be true is the first step in solving a linear equation. In mathematics, science, engineering, and economics, linear equations are frequently employed.
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Elouise finds a woodlouse that is 8 mm long. When she views it under the microscope it
appears 12 cm long.
What is the magnification?
Answer:
Step-by-step explanation:
This can be solved by taking X as the magnification
8*x = 12cm *10
x= 120/8
x= 30/2= 15
the magnification = 15 times
Our class is planning to paint a rectangular mural with an area of 60 square feet, it has to be at least 4 feet high but no more than 6 feet the length and width have to be hold numbers list of possible width for the
The possible widths for the rectangular mural are between 10 and 15 feet. We can also list the number of possible widths within this range, which is six. They are 10 feet, 11 feet, 12 feet, 13 feet, 14 feet, and 15 feet.
To determine the possible widths for the rectangular mural with an area of 60 square feet, we can use the formula for the area of a rectangle, which is length multiplied by width. Since the area is given as 60 square feet and the length should be between 4 and 6 feet, we can set up inequality as follows:
4w ≤ 60 ≤ 6w
where w is the width of the mural in feet. Solving this inequality for w, we get:
10 ≤ w ≤ 15
It is important to consider the dimensions carefully to ensure that the mural meets the requirements and fits in the desired space. By having multiple possible widths, the class can select the most suitable one based on the available resources and space.
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Complete question:
Our class is planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list a number of possible widths for our class. Planning to paint a rectangular mural with an area of 60 square feet, it should be at least 4 feet high but not more than 6 feet in length and width, and list the number of possible widths for it.
Line A has a gradient of -5. Line B is perpendicular to line A. a) What are the coordinates of the y-intercept of line B? b) What is the equation of line B? S Give your answer in the form y where m and c are integers or fractions written in their simplest form. mx + c,
The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.
What is equation?An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.
Here,
Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.
a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:
y = (1/5)x + c
0 = (1/5)(0) + c
c = 0
Therefore, the y-intercept of line B is (0,0).
b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.
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Tiana has a new beaded necklace. The necklace has 3 blue beads and 17 white beads. What percentage of the beads on Tiana's necklace are blue?
Therefore, 15% of the beads on Tiana's necklace are blue.
What is percentage?Percentage is a way of expressing a fraction or a proportion out of 100. It is denoted by the symbol "%". For example, if we say that 50% of the students in a class are girls, it means that 50 out of every 100 students are girls.
Percentage can be calculated by dividing the given quantity by the total and multiplying by 100. For example, if there are 20 girls out of a total of 40 students in a class, the percentage of girls in the class can be calculated as follows:
Percentage of girls = (number of girls / total number of students) x 100%
= (20 / 40) x 100%
= 50%
by the question.
Tiana's necklace has a total of 3 + 17 = 20 beads.
To find the percentage of blue beads, we need to divide the number of blue beads by the total number of beads and then multiply by 100 to get the percentage:
percentage of blue beads = (number of blue beads / total number of beads) x 100
percentage of blue beads = (3 / 20) x 100
percentage of blue beads = 15
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Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference
is +∞
Answer:
Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference
is +∞
Step-by-step explanation:
To show that the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞, we can use the formula for the sum of the first n terms of an arithmetic sequence:
Sn = n/2 [2a + (n-1)d]
where a is the first term, d is the common difference, and n is the number of terms in the sequence.
Now, if we let n approach infinity, the sum of the first n terms of the sequence will also approach infinity. This can be seen by looking at the term (n-1)d in the formula, which grows without bound as n becomes larger and larger.
In other words, as we add more and more terms to the sequence, each term gets larger by a fixed amount (the common difference d), and so the sum of the sequence increases without bound. Therefore, the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.
3) One piece of fencing is 71/8 feet long. How long will a fence be that is made up of 9 of these pieces?
Answer:
Step-by-step explanation:
71/8*9 which it 639/8 feet long
Josiah kept track of how many songs of each genre were played in an hour from his MP3 player. The counts are displayed in the table below. He has a total of 1,500 songs on his player. Josiah predicted the number of rock songs on his MP3 player to be 300 songs. Which statements about his solution are true? Select three choices. Josiah’s Music Sample 1 Sample 2 R & B 5 R & B 4 Pop 4 Pop 3 Classical 3 Classical 5 Jazz 2 Jazz 4 Rock 6 Rock 4 Josiah’s work: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction. StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction. 300 = x. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5. He did not multiply the numerator and denominator by the correct number to equal 1,500. His answer will be one-half of what he got because he did not divide 10 by 2 when setting up the proportion. He can only solve the proportion by multiplying the numerator and denominator by a common multiple. He should have multiplied the numerator and denominator by 75, not 30, because 20 times 75 = 1,500
Answer:
The following statements about Josiah's solution are true:
He found the proportion of rock songs to the total number of songs correctly: StartFraction 10 over 20 EndFraction = StartFraction x over 1,500 EndFraction.
He solved the proportion correctly: StartFraction 10 times 30 over 20 times 30 EndFraction = StartFraction x over 1,500 EndFraction.
He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).
Therefore, the statements that are true are:
He found the proportion of rock songs to the total number of songs correctly.
He solved the proportion correctly.
He correctly determined that the number of rock songs on his MP3 player is 300 (x = 300).
change the denominator of the fraction a+3/6-2a to 2(a^2-9)
The answer of the given question based on the changing the denominator of fraction the answer is the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
What is Formula?In mathematics, formula is mathematical expression or equation that describes relationship between two or more variables or quantities. A formula can be used to solve problems or make predictions about particular situation or set of data.
Formulas often involve mathematical symbols and operations, like addition, subtraction, multiplication, division, exponents, and square roots. They may also include variables, which are typically represented by letters, and constants, which are fixed values that do not change.
To change the denominator of the fraction a+3/6-2a to 2(a²-9), we need to factor the denominator of the original fraction and then use algebraic manipulation to rewrite it in the desired form.
First, we can factor the denominator of the original fraction as follows:
6 - 2a = 2(3 - a)
Next, we can rewrite the denominator using the difference of squares formula:
2(a² - 9) = 2(a + 3)(a - 3)
Now, we can use the factored form of the denominator to rewrite the original fraction:
(a + 3)/(6 - 2a) = (a + 3)/(2(3 - a)) = -(a + 3)/(-2(a - 3)) = (3 + a)/(2(a - 3))
Therefore, the fraction a+3/6-2a can be rewritten with a denominator of 2(a²-9) as (3 + a)/(2(a - 3)).
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Who ever helps me, Get 100 points
Step-by-step explanation:
a) Area=144m²
side²= 144
side=12m
b) perimeter=32m
4×side=32
side=32/4
side=8m
two fifths of 60 is what number
Answer:
I hope this helps please rate my answer
Step-by-step explanation:
2/5×60
2×12=24
The random variable x is known to be uniformly distributed between 10 and 20. Show the graph of the probability density function: Compute P(x 15). Compute P(12 =x= 18). St Compute E(x). Compute Var(x).
Compute P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.
Compute P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.
Compute E(x): The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15
Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.
The probability density function is as follows: As the random variable x is uniformly distributed between 10 and 20. Thus, f(x) = 1/(20-10) = 1/10 for 10 ≤ x ≤ 20.Compute P(x ≤ 15):Thus, P(x ≤ 15) = (15-10)/(20-10) = 5/10 = 0.5.Compute P(12 ≤ x ≤ 18):Thus, P(12 ≤ x ≤ 18) = (18-12)/(20-10) = 6/10 = 0.6.Compute E(x):The expected value of x is: E(x) = (a+b)/2 = (10+20)/2 = 15.Compute Var(x):The variance of x is: Var(x) = (b - a)^2/12 = (20 - 10)^2/12 = 100/12 = 8.33.
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URGENT!!!!! Examine the graph of the function What is the initial value of the function?
Enter your answer as a number, like this: 42
The answer of the given question based graph of function on finding the initial value of the function the answer is the initial value of the function is 2.
What is Graph?A graph is visual representation of data that displays relationship between variables. It consists of points or vertices connected by lines or arcs that represent relationships between variables. Graphs can be used to represent various types of data, like numerical, categorical, and ordinal data.
Graph are commonly used in mathematics, science, engineering, and social sciences to help people understand complex data and relationships. Different types of graphs like bar graphs, line graphs, scatter plots, pie charts, and histograms. Graphs are powerful tool for data analysis and visualization, and they can help people identify patterns, trends, and outliers in data.
If the function intersects both the x-axis and y-axis at the point (2,4), then the function can be written in the form:
y = a(x - 2)(x - 4)
where a is some constant.
To find the value of a, we can use the fact that the function passes through the point (0,2). Substituting x = 0 and y = 2 into the equation above, we get:
2 = a(0 - 2)(0 - 4)
2 = 8a
Solving for a, we get:
a = 2/8 = 1/4
Therefore, the function is:
y = (1/4)(x - 2)(x - 4)
To find the initial value of the function, we need to determine the value of the function when x is equal to zero. Substituting x = 0 into the equation above, we get:
y = (1/4)(0 - 2)(0 - 4)
y = (1/4)(8)
y = 2
Therefore, initial value of function is 2.
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what is the probability that the gambler has to play at least n rounds of the game before getting his first win?
The probability that the gambler has to play at least 3 rounds of the game before getting his first win is equal to 3/4.
The probability that the gambler has to play at least n rounds of the game before getting his first win is equal to 1 - (the probability of winning in the first n-1 rounds). To calculate the probability of winning in the first n-1 rounds, use the following formula:
P = (1/2)^(n-1)
Where P is the probability of winning in the first n-1 rounds.
For example, if the gambler has to play at least 3 rounds of the game, the probability of winning in the first 2 rounds is equal to (1/2)^(3-1) = (1/2)^2 = 1/4.
So, the probability that the gambler has to play at least 3 rounds of the game before getting his first win is equal to 1 - (1/4) = 3/4.
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what types of inferences will we make about population parameters? (select all that apply) causation estimation implied testing regression
The types of inferences that will be made about population parameters are causation, estimation, and regression on the basis of relationship.
What are the types of inferences?Causation is the process of showing the cause-and-effect relationship between two variables. In this case, one variable influences the other variable. This type of inference is significant when making decisions because it helps us understand how a change in one variable leads to a change in another variable.
Estimation: In statistical analysis, estimation refers to determining the possible value of an unknown population parameter. It is impossible to calculate the population parameters directly, and hence we use sample statistics to estimate them.
Regression analysis is the statistical technique used to identify the relationship between two variables. It involves estimating the coefficients of the model that best fit the data.
This type of inference helps us predict the value of a dependent variable based on an independent variable.
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104.
Simplify the polynomial by writing each of its term in standard form.
12a^2 · 3ba − 2ab · 3ab^2+11aba
The simplified polynomial, with each term written in standard form, is: 36a^3b - 6a^2b^3 + 11a^2b
How to simplify the polynomialTo simplify the given polynomial, we need to expand and combine like terms.
First, we can distribute the coefficients of the first term:
12a^2 · 3ba = 36a^3b
Next, we can simplify the second term by multiplying the coefficients and adding the exponents:
-2ab · 3ab^2 = -6a^2b^3
Finally, we can combine the like terms:
36a^3b - 6a^2b^3 + 11a^2b
To write each term in standard form, we arrange the terms in decreasing order of exponents of 'a' and 'b':
36a^3b - 6a^2b^3 + 11a^2b
So, the simplified polynomial, with each term written in standard form, is:
36a^3b - 6a^2b^3 + 11a^2b
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Mark wants to buy a new pair of sneakers that cost 215. His aunt gave him 100 for the sneakers. Market also lnow sthat he can esrn 16 for each hour that he works at his aunts store how many full hours must mark work to buy the sneakers
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.
Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,
therefore, we can say that 215 - 100 = 115
therefore, Mark now needs only 115 for him to buy sneakers and now we need to find how many full hours do Mark need to work to buy sneakers:
therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:
115/16 = 7.2
we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:
8 hours.
Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.
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Can someone give me the answer please and the other one
Answer:
58 degrees
Step-by-step explanation:
51+27=58 degrees
second one is 56 degrees
132-76=56 degrees
To celebrate Halloween, Florence's class is making candy necklaces. Florence is helping pass out string from a 50-yard-spool. She gives 30 inches of string to each student. If there are 24 students in her class, how many yards of string will be leftover?
There will be 30 yards of the string that will be leftover.
What are Arithmetic operations?
It is a field of mathematics that deals with the study of numbers and the operations on those numbers that are relevant to all other areas of mathematics. The basic operations included in it are addition, subtraction, multiplication, and division. The term "arithmetic operator" refers to the operator that does the calculation.
Given that,
Total Length of string = 50 yards.
The total number of students = 24.
Total used string = 24 × 30 = 720.
We know that 1 foot = 12 inches,
So, 150 feet = 1800 inches.
Therefore, yards of string leftover = (1800 - 720)/36
= 1080/36
= 30 yards.
Hence, there will be 30 yards of string that will be leftover.
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A) 4 x + 7 = 2 x + 13 ;
b) x – 2 = 10 + 5 x ;
c) – 3 x – 8 = – 7 x – 4 ;
d) 2 t + 5 = 5 t + 12 ;
e) 7 x – 6 = 6 x + 3
f) 15 x = 7 x + 4
For equation a, x = 3
For equation b, x = -11/4.
For equation c, x = 1.
For equation d, x = -7/3.
For equation e, x = 9.
For equation f, x = 1/2.
To solve this equation, we need to isolate the variable x on one side of the equation.
7x - 6 = 6x + 3
Subtracting 6x from both sides:
x - 6 = 3
Adding 6 to both sides:
x = 9
Therefore, the solution to the equation is x = 9.
In the other equations:
a) 4x + 7 = 2x + 13
Subtracting 2x from both sides:
2x + 7 = 13
Subtracting 7 from both sides:
2x = 6
Dividing by 2:
x = 3
Therefore, the solution to the equation is x = 3.
b) x - 2 = 10 + 5x
Subtracting x from both sides:
-2 = 9 + 4x
Subtracting 9 from both sides:
-11 = 4x
Dividing by 4:
x = -11/4
Therefore, the solution to the equation is x = -11/4.
c) -3x - 8 = -7x - 4
Adding 7x to both sides:
4x - 8 = -4
Adding 8 to both sides:
4x = 4
Dividing by 4:
x = 1
Therefore, the solution to the equation is x = 1.
d) 2t + 5 = 5t + 12
Subtracting 2t from both sides:
5 = 3t + 12
Subtracting 12 from both sides:
-7 = 3t
Dividing by 3:
t = -7/3
Therefore, the solution to the equation is t = -7/3.
f) 15x = 7x + 4
Subtracting 7x from both sides:
8x = 4
Dividing by 8:
x = 1/2
Therefore, the solution to the equation is x = 1/2.
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Complete Question:
Find X for each equation.
A) 4 x + 7 = 2 x + 13 ;
b) x – 2 = 10 + 5 x ;
c) – 3 x – 8 = – 7 x – 4 ;
d) 2 t + 5 = 5 t + 12 ;
e) 7 x – 6 = 6 x + 3
f) 15 x = 7 x + 4
find the smallest positive integer $n$ so that \[\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2}
The smallest positive integer n so that,
$$\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix}$$is a column matrix that contains integers,
we can write it as follows. $$\begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix} = \begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix} \frac{1}{n}.$$Since n has to be an integer, we have to find the smallest positive integer n for which the right-hand side is a column matrix containing integers. Since the left-hand side has a factor of 1/n, we can see that the smallest value of n must be a divisor of the denominator of the left-hand side. The denominator of the left-hand side is $\sqrt{2}/2$. If we multiply this by 100, we get 70.710678.
Therefore, the smallest positive integer n that satisfies the equation is the smallest divisor of 70.710678. This is 2, and it gives us the column matrix $$\begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}.$$Therefore, the smallest positive integer n is 2.
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The average mass of six people is 58kg. The lightest person has a body mass of 43kg. What is the average mass of the other 5 people.
Answer: 61 kg
Step-by-step explanation:
To find the average mass of the other 5 people, we need to subtract the mass of the lightest person from the total mass of all six people and then divide by 5 (since we're looking for the average of the other 5 people). Here are the steps:
Find the total mass of all six people:
To find the total mass of all six people, we can multiply the average mass by 6:
Total mass of all six people = 58 kg/person x 6 people = 348 kg
Subtract the mass of the lightest person:
We need to subtract the mass of the lightest person (43 kg) from the total mass of all six people:
Total mass of the other 5 people = Total mass of all six people - Mass of the lightest person
Total mass of the other 5 people = 348 kg - 43 kg = 305 kg
Find the average mass of the other 5 people:
Finally, we divide the total mass of the other 5 people by 5 to find the average mass:
Average mass of the other 5 people = Total mass of the other 5 people / 5
Average mass of the other 5 people = 305 kg / 5 = 61 kg
Therefore, the average mass of the other 5 people is 61 kg.
