The sets A and B define a function, while the set C does not.
To determine whether a set defines a function, we need to check if there is one and only one output for each input. In other words, there should not be two different outputs for the same input.
\( A=\{(a, d),(c, d),(e, f),(b, f)\} \)
In this set, there are no repeated inputs, so it does define a function.
\( B=\{(1,3),(2,4),(5,6),(3,4)\} \)
In this set, there are also no repeated inputs, so it does define a function.
\( C=\{(1, a),(2, b),(3, c),(2, a),(4, d),(5, c)\} \)
In this set, there are two different outputs for the input 2 (b and a), so it does not define a function.
Therefore, the sets A and B define a function, while the set C does not.
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Letf(x)=x−21andg(x)=x3+2. Find the following functions. Simplify your answers.f(g(x))=g(f(x))=
The simplified functions of f(g(x)) and g(f(x)) are: f(g(x))=x3 and g(f(x))=x3−6x2+12x−6
To find the function f(g(x)), we need to substitute g(x) into f(x). This means we will replace the x in f(x) with the expression for g(x):
f(g(x))=f(x3+2)=(x3+2)−2
Simplifying this expression gives us:
f(g(x))=x3
Similarly, to find the function g(f(x)), we need to substitute f(x) into g(x):
g(f(x))=g(x−2)=(x−2)3+2
Simplifying this expression gives us:
g(f(x))=x3−6x2+12x−6
Therefore, the functions f(g(x)) and g(f(x)) are:
f(g(x))=x3
g(f(x))=x3−6x2+12x−6
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simplify all the exponets
The simplified form of the given expression by the laws of indices is; x^(-3/10).
What is the simplified form of the expression?As evident in the task content; the given expression is;
1 / ⁵√√x³
Therefore, we have that;
By the laws of indices we have that;
= 1 / ⁵√x^(3/2)
= 1 / x^(3/10)
On this note, the simplified form of the expression as required is; x^(-3/10).
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For each of the following, find the formula for an exponential
function that passes through the two points given.
a. (-2, 3/4) and (2,12)
f(x)=?
b. (-3,6) and (3,2)
g(x)=?
The formula for the exponential function that passes through the given points is (a) 3(2ˣ) and (b) g(x) = (2(3)^(1/2))((1/3)^(x/6)).
To find the formula for an exponential function that passes through two points, we can use the formula:
f(x) = abˣ
where a and b are constants. We can use the two points to create a system of equations and solve for the constants.
For part a:
3/4 = ab⁻²
12 = ab²
Dividing the second equation by the first equation gives us:
16 = b⁴
Taking the fourth root of both sides gives us:
b = 2
Plugging this value back into the first equation gives us:
3/4 = a2⁻²
3/4 = a(1/4)
a = 3
So the formula for the exponential function is:
f(x) = 3(2ˣ)
For part b:
6 = ab⁻³
2 = ab³
Dividing the second equation by the first equation gives us:
1/3 = b⁶
Taking the sixth root of both sides gives us:
b = (1/3)^(1/6)
Plugging this value back into the first equation gives us:
6 = a(1/3)^(-1/2)
6 = a(3)^(1/2)
a = 6 / (3)^(1/2)
a = 2(3)^(1/2)
So the formula for the exponential function is:
g(x) = (2(3)^(1/2))((1/3)^(x/6))
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At the movie theatre, child admission is $5.30 and adult admission is $8.70. On Saturday, 163 tickets were sold for a total sales of $1169.90. How many child tickets were sold that day?
The number of child tickets were sold that day are 73.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that;
Cost of child admission= $5.30
Cost of adult admission= $8.70
Now,
Let's assume that "c" represents the number of child tickets sold, and "a" represents the number of adult tickets sold. We can create two equations based on the given information:
c + a = 163 (equation 1: the total number of tickets sold)
5.30c + 8.70a = 1169.90 (equation 2: the total sales)
We can use equation 1 to solve for "a" in terms of "c":
a = 163 - c
Substituting this expression for "a" into equation 2, we get:
5.30c + 8.70(163 - c) = 1169.90
Simplifying and solving for "c", we get:
5.30c + 1418.10 - 8.70c = 1169.90
-3.4c = -248.20
c = 73
Therefore, by algebra the answer will be 73.
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Chase starts an IRA (Individual Retirement Account) at the age of 26 to save for retirement. He deposits $400 each month. Upon retirement at the age of 65 his retirement savings is $838,879.58, Determine the amount of money Chase deposited over the length of the investment and how much he made in interest upon retirement Formulas
The total number of months he made deposits and multiply that by the monthly deposit amount.
Chase started an IRA at the age of 26 and deposited $400 each month until he retired at the age of 65. To determine the amount of money Chase deposited over the length of the investment, we need to calculate the total number of months he made deposits and multiply that by the monthly deposit amount.
Number of months = (Retirement age - Starting age) * 12
Number of months = (65 - 26) * 12
Number of months = 468
Total deposits = Number of months * Monthly deposit amount
Total deposits = 468 * 400
Total deposits = $187,200
To determine how much Chase made in interest upon retirement, we need to subtract the total deposits from the retirement savings.
Interest = Retirement savings - Total deposits
Interest = $838,879.58 - $187,200
Interest = $651,679.58
Therefore, Chase deposited a total of $187,200 over the length of the investment and made $651,679.58 in interest upon retirement.
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a) Bishwant is 5 feet 6 inch tall. Find his height in inch, centimeter and meter
Can someone help me on this please:)
The solution to the equation (-3/4)(-16 + 8x) by applying the distributive property is 12 - 6x
How to solve an equation?An equation is an expression containing numbers and variables linked together by mathematical operations such as addition, subtraction, division, multiplication and exponents.
The distributive property states that for three variables a, b and c, the following rule apply:
a(b + c) = ab + ac
Given that:
(-3/4)(-16 + 8x)
Applying the distributive property:
= (-3/4)(-16) + (-3/4)(8x)
= 12 - 6x
The solution is 12 - 6x
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PLEASE HELP! 10 POINTS! ITS URGENT! NO EXPLANATION NEEDED!
Answer:its 80 i did the same problem
Step-by-step explanation:
Which situation could be described by the expression f + 1/2
Use the / as a fraction bar
A. Lela walked f miles yesterday, and mile today.
B. Lela walked f miles yesterday, and miles fewer today.
C. Lela walked mile yesterday, and f miles fewer today.
D. Lela walked mile yesterday, and f times as far today.
B. Lela walked f miles yesterday, and miles fewer today.
What is expression?
One or more variables or numbers are combined with one additional action to form an expression.
The situation that could be described by the expression f + 1/2 is:
B. Lela walked f miles yesterday, and miles fewer today.
The expression f + 1/2 represents the total distance that Lela walked over two days, where "f" represents the distance she walked yesterday, and "1/2" represents the distance she walked today.
Option B describes the situation where Lela walked "f" miles yesterday and "1/2" times fewer miles today (or, equivalently, "1/2" times the distance she walked yesterday).
Therefore, the expression f + 1/2 is a valid way to describe this situation.
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Every day Ms.Twinkle walks around a park near her house. The park is the shape of a rectangle 2 mi long and 1 3/10 mi wide. How far does she walk.
Ms. Twinkle walks a total of 6.6 miles around the park.
What is perimeter ?
Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape.
To find how far Ms. Twinkle walks, we need to find the perimeter of the rectangle-shaped park, which is the sum of the lengths of all its sides.
The length of the park is 2 miles and the width is 1 3/10 miles. We can write the width as a mixed number of 1 + 3/10 = 13/10 miles.
Therefore, the perimeter of the park is:
Perimeter = 2(length + width)
Perimeter = 2(2 + 13/10)
Perimeter = 2(20/10 + 13/10)
Perimeter = 2(33/10)
Perimeter = 66/10
Perimeter = 6.6 miles
Therefore, Ms. Twinkle walks a total of 6.6 miles around the park.
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Find the zeros of the function and state the multiplicities. c(x)=6x^(3)+3x^(2)-3x
The zeros of the function c(x) = 6x^3 + 3x^2 - 3x are x = 0, 1/2, and -1, all with a multiplicity of 1.
To find the zeros of the function c(x) = 6x^3 + 3x^2 - 3x, we need to factor the equation and set it equal to zero.
First, we can factor out a common factor of 3x from all of the terms:
c(x) = 3x(2x^2 + x - 1)
Next, we can use the quadratic formula to find the zeros of the remaining quadratic equation:
2x^2 + x - 1 = 0
x = (-1 ± √(1^2 - 4(2)(-1)))/(2(2))
x = (-1 ± √(1 + 8))/4
x = (-1 ± √9)/4
x = (-1 ± 3)/4
So, the two zeros of the quadratic equation are:
x = (-1 + 3)/4 = 1/2
x = (-1 - 3)/4 = -1
Finally, we can combine the zero from the factored term with the zeros from the quadratic equation to find all of the zeros of the function:
x = 0, 1/2, -1
The multiplicities of these zeros are:
x = 0 has a multiplicity of 1
x = 1/2 has a multiplicity of 1
x = -1 has a multiplicity of 1
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Mengxi has $10 000 to invest. She invests part in a term deposit paying 5% /year, and the remainder in Canada Savings Bonds paying 3. 5% /year. At the end of the year, she has earned simple interest of $413. How much did she invest at each rate? (Algebra)
Mengxi invested $4,200 in the term deposit paying 5% /year and $5,800 in Canada Savings Bonds paying 3.5% /year. The total interest earned is $413.
Let's assume that Mengxi invests x dollars in the term deposit paying 5% /year, and the remaining (10000 - x) dollars in Canada Savings Bonds paying 3.5% /year.
At the end of the year, Mengxi earns a total of $413 in simple interest. The interest earned from the investment in the term deposit is calculated as 0.05x, while the interest earned from the investment in Canada Savings Bonds is 0.035(10000 - x).
Thus, we can write the following equation to represent the total interest earned:
0.05x + 0.035(10000 - x) = 413
Simplifying the equation, we get:
0.015x + 350 = 413
0.015x = 63
x = 4200
Therefore, Mengxi invested $4,200 in the term deposit paying 5% /year, and $5,800 (10000 - 4200) in Canada Savings Bonds paying 3.5% /year.
To check the answer, we can calculate the interest earned from each investment and add them up:
0.05(4200) + 0.035(5800) = 210 + 203 = 413
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speed=_______÷_______
Answer:
i need more details i cant answer.
find the measure of rhf
Answer:
<RHF = 68°
Step-by-step explanation:
<RHG and <FHY are vertical opposite angle which mean they equal to each other.
<RHG = <FHY
(6m+88) = (7m+84)
88 - 84 = 7m - 6m
4 = m
Plug m=4 into the <RHG to solve for the measurement.
<RHG = 6m+88
<RHG = 6*4+88
<RHG = 24+88
<RHG = 112°
<RHG and <RHF are supplementary angle which mean they both linear adding up to 180°
<RHF + <RHG = 180°
<RHF + 112° = 180°
<RHF = 68°
Logan invested $3,800 in an account paying an interest rate of 5% compounded
continuously. Qasim invested $3,800 in an account paying an interest rate of 6%
compounded annually. To the nearest hundredth of a year, how much longer would
it take for Logan's money to double than for Qasim's money to double?
Answer:
Step-by-step explanation:
The formula to calculate the doubling time for continuously compounded interest is:
t = ln(2) / (r * ln(1 + (r/n)))
where t is the time in years, r is the annual interest rate as a decimal, and n is the number of times the interest is compounded per year (which is infinity for continuous compounding).
For Logan's investment, we have:
r = 0.05
n = infinity
t1 = ln(2) / (0.05 * ln(1 + (0.05/infinity)))
t1 ≈ 13.86 years
For Qasim's investment, we have:
r = 0.06
n = 1
t2 = ln(2) / (0.06 * ln(1 + (0.06/1)))
t2 ≈ 11.55 years
To find the difference in the time it takes for their investments to double, we can subtract t2 from t1:
t1 - t2 ≈ 13.86 - 11.55 ≈ 2.31
So it would take Logan's money approximately 2.31 years longer to double than Qasim's money, to the nearest hundredth of a year.
Landon just got hired for a new job and will make \$30,000$30,000 in his first year. Landon was told that he can expect to get raises of \$3,000$3,000 every year going forward. How much money in salary would Landon make in his 23rd year working at this job?
Landon would make a salary of $96,000 in his 23rd year working at this job.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
If Landon starts with a salary of $30,000 and gets a raise of $3,000 every year going forward, then his salary in the 23rd year can be calculated as follows:
Salary in 2nd year = $30,000 + $3,000 = $33,000
Salary in 3rd year = $33,000 + $3,000 = $36,000
Salary in 4th year = $36,000 + $3,000 = $39,000
and so on...
So, we can see that Landon's salary increases by $3,000 every year.
His salary in the 23rd year would be:
Salary in 23rd year = $30,000 + ($3,000 x 22) = $30,000 + $66,000 = $96,000
Therefore, Landon would make a salary of $96,000 in his 23rd year working at this job.
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of a The cumulative distribution function handon variable X is given by Ex (x) = 0 X 4 for xco for 8 OcXL4 for x7,4 1 Find. a) The pdf of a b) P(X=-1) c) PC z cx
a)f(x) = { 0, if x < 0 \\ 4x, if 0 ≤ x < 4 \\ 0, if x ≥ 4 }
b)P(X=-1) = 0
c)P(X ≤ 3) = 4 * 3 = 12
a) The pdf (probability density function) of the variable X is given by
f(x) =
{
0, if x < 0 \\
4x, if 0 ≤ x < 4 \\
0, if x ≥ 4
}
b) P(X=-1) = 0, since x < 0
c) P(X ≤ 3) = 4 * 3 = 12
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Can someone help pls?!
Simplify arctan4/7 + arctan7/4
(round to the nearest degree).
a. 45°
b. 90°
c. 0°
arctan(4/7) + arctan(7/4) is 90 degrees
What is Trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the functions that describe those relationships. It has applications in fields such as engineering, physics, astronomy, and navigation.
We can use the following trigonometric identity to simplify the expression:
arctan(x) + arctan(1/x) = pi/2
where x is a positive number.
In this case, we can set x = 4/7, which is a positive number, and apply the identity to get:
arctan(4/7) + arctan(7/4) = pi/2
Therefore, the sum of the two arctan terms simplifies to pi/2.
So, the simplified expression is:
arctan(4/7) + arctan(7/4) = 90 degrees (rounded to the nearest degree).
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Please answer number 10, make sure to answer both parts. Thank you.
The volume is 3x³ + 16x² + 3x - 10, while when the height is reduced by 50%, the new volume is (1/2)(3x³ + 16x² + 3x - 10)
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical operations like exponents, addition, subtraction, multiplication and division.
The volume of the triangular prism is:
Volume = area of base * height
Substituting:
Base area = (1/2) * (2x + 2) * (x + 5) = x² + 6x + 5; height = 3x - 2
Volume = area of base * height = (x² + 6x + 5)(3x - 2)
Volume = 3x³ + 18x² + 15x - 2x² - 12x - 10 = 3x³ + 16x² + 3x - 10
The volume is 3x³ + 16x² + 3x - 10
If the height is reduced by 50%, new height = (1/2)(3x - 2)
Volume = area of base * height = (x² + 6x + 5) * (1/2)(3x - 2)
Volume = (1/2)(3x³ + 16x² + 3x - 10)
The new volume is (1/2)(3x³ + 16x² + 3x - 10)
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A of a point about a fixed point is a composite of two reflections of the point across intersecting lines. The point of intersection of the lines is the
The point of intersection of the two lines is the fixed point or center of the point reflection.
A point reflection is a geometric transformation that maps a point across a fixed point called the center of reflection. The transformation involves reflecting the point across two intersecting lines that pass through the center of reflection. The point reflection can be thought of as a composite of two reflections, one across each line of reflection. The result is a mirror image of the original point that is equidistant from the center of reflection. The concept of point reflection is used in geometry to construct symmetrical figures and in crystallography to describe the symmetry of crystals.
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Tell whether each equation is true for no real number, some real
number(s), or all real numbers. (a) x · 1 = x
The equation x · 1 = x is true for all real numbers. This is because any number multiplied by 1 is equal to itself.
For example, if x = 2, then 2 · 1 = 2. If x = 5, then 5 · 1 = 5. This is true for any value of x, so the equation is true for all real numbers.
In mathematical terms, 1 is known as the multiplicative identity because it does not change the value of a number when it is multiplied by it. Therefore, the equation x · 1 = x is always true for any real number x.
In conclusion, the equation x · 1 = x is true for all real numbers.
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USING R STUDIO( only answer number 2)
HOW DO I INPUT THIS, EXACT COMMANDS
PLEASE
2) Now, we'll use the means and standard deviations we've found to predict what proportion of people should different heights if the height variables follow a normal distribution. This will involve finding Z-scores and then using the pnorm command. See these notes on doing calculations with the normal distribution.
Task. Assuming that height follows a normal distribution with the mean and standard deviation you found in the previous exercise, find the Z-scores for heights 6'4", 5'8", and 5'2". Then, answer the following questions:
• What percentile is the height 5'2"?
• What portion of people are taller than 6'4"?
• What portion of people are between 5'2" and 5'8"?
that question above is based on the question/data below which is answered
Now, let's find the means and standard deviations
of height and weight
Task. Store the mean and standard deviation of
the height and weight variables under the
names height.xbar, weight.xbar, height.s
and weight.s (recall that & and s are the
mathematical symbols used most commonly for a
sample mean and a sample standard deviation).
Also, output the means and standard deviation.
Recall that mean and sd are the commands to find
the mean and standard deviation of a variable.
When I say to store these values under the
names height.bar, weight.bar, height.s
and weight.s, I mean to write a command like
height.xbar
<- mean(...)
This won't output the mean, but it will save it
as height.sbar, and then in future problems you
can write height.bar rather than copying and
pasting the actual number. To output the mean, you
can issue a command consisting of just the variable
name on a line by itself, like this:
height.xbar
## 111 67.145
ANSWER TO THIS IS "mean(cdc$weight) and height.xbar <- mean(cdc$weight)
To input the given commands and find the Z-scores for the different heights, you will need to use the following steps:
1. Convert the heights from feet and inches to inches. For example, 6'4" would be 76 inches, 5'8" would be 68 inches, and 5'2" would be 62 inches.
2. Use the formula Z = (X - mean) / standard deviation to find the Z-scores for each height. For example, for the height of 6'4", you would use the formula Z = (76 - height.xbar) / height.s.
3. Use the pnorm command to find the percentiles for each Z-score. For example, for the Z-score of the height 6'4", you would use the command pnorm(Z).
4. Use the pnorm command with the lower.tail = FALSE argument to find the portion of people taller than a given height. For example, for the height of 6'4", you would use the command pnorm(Z, lower.tail = FALSE).
5. Use the pnorm command with the lower and upper limits to find the portion of people between two heights. For example, for the heights of 5'2" and 5'8", you would use the command pnorm(upper limit) - pnorm(lower limit).
Using these steps, you can input the given commands and find the Z-scores and percentiles for the different heights. Remember to use the variable names height.xbar and height.s for the mean and standard deviation of the height variable, and to use the number, variable, and height terms in your answer.
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Mr. Silverstone invested some money in 3 different investment products. The investment was as follows: a. The interest rate of the annuity was 2%. b. The interest rate of the annuity was 4%. c. The interest rate of the bond was 5%. d. The interest earned from all three investments together was $950. Which linear equation shows interest earned from each investment if the total was $950? a.) a + b + c = 950 b.) 0.04a + 0.06b + 0.05c = 9.50 c.) 0.04a + 0.06b + 0.05c = 950 d.) 4a + 6b + 5c = 950
The linear equation that shows the interest earned from each investment is (d): "4a + 6b + 5c = 950"
What is investment?Investment refers to the act of allocating money or other resources to an asset or venture with the expectation of generating a profit or some other form of return over a period of time. The primary goal of investing is to use the available resources to generate a return that is greater than the initial investment, thus growing wealth over time.
What is linear equation?A linear equation is an algebraic equation in which the highest power of the variable is one. In other words, a linear equation is a polynomial of degree one. It represents a straight line when plotted on a graph. The general form of a linear equation with one variable, x, is:
ax + b = 0
In the given question,
Let's assume that Mr. Silverstone invested a dollars in the first annuity with an interest rate of 2%, b dollars in the second annuity with an interest rate of 4%, and c dollars in the bond with an interest rate of 5%. The interest earned from each investment can be calculated as follows:
Interest earned from the first annuity = 0.02a
Interest earned from the second annuity = 0.04b
Interest earned from the bond = 0.05c
The total interest earned from all three investments together is given as $950. Therefore, we can write the equation:
0.02a + 0.04b + 0.05c = 950
This is the same as option (c) given in the question: "0.04a + 0.06b + 0.05c = 950". However, option (c) has some errors in the coefficients, as the interest rates for the annuities were given as 2% and 4%, not 4% and 6%.
Therefore, the linear equation that shows the interest earned from each investment if the total was $950 is:
0.02a + 0.04b + 0.05c = 950
This can also be simplified as:
2a + 4b + 5c = 95000 (by multiplying both sides by 100 to remove the decimals)
So, the correct option is (d): "4a + 6b + 5c = 950".
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y = -15 x -5
11 x + y = -17
I need help with this.
Answer:
system of equation:
(x,y)
(3,-50)
Step-by-step explanation:
equation solving
A family goes to a restraint when the bill comes this is printed at the bottom of it how much was the price of the meal? Explain your reasoning
Using the gratuity percentages, we found that the amount of meal is $32.6 and the amount to be paid is $41.89
What is meant by percentage?
A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.
Given,
Gratuity guide :
15% would be $4.89
18% would be $5.87
20% would be $6.52
1) The tip percentages are given above.
If the cost of the meal is x.
15% of x = 4.89
18% of x = 5.87
0.15x = 4.89
x = 32.6
0.18x = 5.87
x = 32.6
So the cost of the meal is $32.6.
2)The family choose a 20% tip.
The tax percentage is 8.5% of 32.6.
Tip = 6.52 ( from gratuity guide)
Tax = 8.5 % of 32.6
= 0.085 * 32.6 = $2.77
Total amount to be paid = 32.6 + 6.52 + 2.77 = $41.89
Therefore using the gratuity percentages, we found that the amount of meal is $32.6 and the amount to be paid is $41.89.
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The angles in a triangle are in a 1:2:3 ratio
show that the triangle is right angled
The triangle with measure of the angle is 30°, 60°, and 90° proves that it is right angled triangle.
Let us consider 'x' be the measure of the angles in a triangle.
Ratio of the angles in a triangle is 1 : 2 : 3
Measure of angle 1 = 1x
Measure of angle 2 = 2x
Measure of angle 3 = 3x
Sum of all the interior angles in a triangle = 180°
Substitute the value of the measure of the angles we get,
⇒ 1x + 2x + 3x = 180°
⇒ 6x = 180°
⇒ x = 180° / 6
⇒ x = 30°
Measure of angle 1 = 30°
Measure of angle 2 = 2× 30°
= 60°
Measure of angle 3 = 3× 30°
= 90°
Therefore, as measure of one of the interior angle is 90 degree this implies it is a right angled triangle.
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The width of a rectangle is 4 units less than the length. The area of the rectangle is 21 square units. What is the length, in units, of the rectangle?
Answer:
Let's call the length of the rectangle "L" and the width "W".
From the problem, we know that:
W = L - 4
And
Area = Length x Width
Substituting the first equation into the second equation, we get:
Area = L x (L - 4)
We also know that the area is 21 square units, so we can set up the following equation:
21 = L x (L - 4)
Expanding the right side of the equation:
21 = L^2 - 4L
Rearranging the terms:
L^2 - 4L - 21 = 0
Now we can solve for L using the quadratic formula:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
Where a = 1, b = -4, and c = -21
L = (-(-4) ± sqrt((-4)^2 - 4(1)(-21))) / 2(1)
L = (4 ± sqrt(100)) / 2
L = (4 ± 10) / 2
L = 7 or L = -3
Since the length cannot be negative, we choose L = 7.
Therefore, the length of the rectangle is 7 units.
Given :. f(X)=2/x²+1
Determine f(x-¹)-x²f(-1)
The given function evaluates to [tex]\frac{x^2(1-x)}{x^2 + 1}[/tex].
What is a Function?A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.
As per the given data:
The function is [tex]f(x) = \frac{2}{x^2 + 1}[/tex]
To determine the function: [tex]f(\frac{1}{x}) - x^2f(-1)[/tex]
Substituting (1/x) and (-1) respectively:
[tex]= \frac{2}{\frac{1}{x}^2 + 1} - x^2\frac{2}{(-1)^2 + 1}[/tex]
[tex]= \frac{2x^2}{x^2 + 1} - x^2\frac{2}{2}[/tex]
[tex]= \frac{2x^2}{x^2 + 1} - x^2[/tex]
Taking the LCM:
[tex]= \frac{2x^2 - x^3 - x^2}{x^2 + 1}[/tex]
[tex]= \frac{x^2 - x^3}{x^2 + 1}\\= \frac{x^2(1-x)}{x^2 + 1}[/tex]
Hence, the given function evaluates to [tex]\frac{x^2(1-x)}{x^2 + 1}[/tex]
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Mark Twain was the pen name of Samuel Clemens, who spent several years as a steamboat pilot. He chose the name because the leadsman on a steamboat would call out "mark twain" to indicate that the water depth was 12 feet and safe for the boat to pass. Convert this depth to fathoms.
The depth of water is fount to be 2.0 fathom when its was 12 feet.
Explain about the unit conversion?The same attribute is expressed using a unit conversion, but in a different measurement system. For illustration, time can be defined in minutes rather than hours, and distance can be specified in kilometres, feet, or a different measurement unit though rather than miles.Given:
Samuel Clemens, who worked as a steamboat pilot for several years, wrote under the pseudonym Mark Twain. He chose the name because a steamboat's leadsman would yell "mark twain" when the water was 12 feet deep and it was safe is for boat to pass.Conversion unit:
1 foot = 0.167 fathom
Then,
12 feet = 0.167*12 fathom
12 feet = 2.004 fathom
12 feet = 2.0 fathom
Thus, the depth of the water is fount to be 2.0 fathom when its was 12 feet.
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Lucky Duck
What is the probability you will choose each duck described below?
Write the answer as a fraction in lowest terms and place it in the appropriate
box (certain, likely, unlikely, impossible).
The ducks are
numbered from one
through twelve!
Even Unlikely Impossible
The answer response are:
A duck with wings: Likely Duck number 7: Unlikely A duck with a number greater than 3: Certain Duck number 15: Impossible A duck with a number greater than 10: Unlikely A duck with a number: Certain Duck number 4: Likely A duck with sunglasses: Impossible A duck with a hat: Unlikely An even-numbered duck: LikelyHow do you explain the probability?A duck with wings: Likely
There is a high likelihood that all the ducks have wings since it is a natural characteristic of ducks.Duck number 7: Unlikely
There are 12 ducks in total, and only one of them is duck number 7, so the probability of choosing duck number 7 is 1/12, which is unlikely.A duck with a number greater than 3: Certain
There are 9 ducks with numbers greater than 3 (4, 5, 6, 7, 8, 9, 10, 11, 12), so it is certain that you will choose a duck with a number greater than 3.Duck number 15: Impossible
There are only 12 ducks, and none of them are numbered 15, so it is impossible to choose duck number 15.A duck with a number greater than 10: Unlikely
Only two ducks have numbers greater than 10 (11, 12), so the probability of choosing a duck with a number greater than 10 is 2/12 or 1/6, which is unlikely.A duck with a number: Certain
All ducks have numbers from 1 to 12, so it is certain that you will choose a duck with a number.Duck number 4: Unlikely
There is only one duck numbered 4, so the probability of choosing duck number 4 is 1/12, which is unlikely.A duck with sunglasses: Impossible
There is no information given that any of the ducks have sunglasses, so it is impossible to choose a duck with sunglasses.A duck with a hat: Unlikely
There is no information given that any of the ducks have hats, so the probability of choosing a duck with a hat is unlikely.Lastly, An even-numbered duck: Likely
There are six even-numbered ducks (2, 4, 6, 8, 10, 12), so the probability of choosing an even-numbered duck is 6/12 or 1/2, which is likely.Learn more about probability here:
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See transcribed text below
Date:
Period:
What is the probability you will choose each duck described below? Write the answer as a fraction in lowest terms and place it in the appropriate box (certain, likely, unlikely, impossible).
33
1. A duck with wings
2. duck number 7
3. a duck with a number greater than 3
4. duck number 15
5. a duck with a number greater than 10
6. a duck with a number
7. duck number 4
8. a duck with sunglasses
9. a duck with a hat
10. an even-numbered duck
The ducks are numbered From one through twelve!
Kibb
Certain
Likely
Even
Unlikely Impossible
ว