The value of f is 0.02.
What is an expression ?Expression is a formation of numbers and variables with mathematical operations.
According to the given question we have to solve for f or we can say we have to find the value of f for the given expression which is
2+1.25f=10−2.75f (lets multiply each term by 100 to remove
decimals )
∴ 200 + 125f = 1000 - 275f
125f + 275f = 1000 - 200
400f = 800
f = 800/400
f = 2.
As we have multiplied by 100 we have to divide by 100 we obtain the exact result.
So, 2/100 is = 0.02
f = 0.02.
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need help with this plz help me
Find the perimeter of 6 regular octagons linked together side by side,if one side is 4.5 inches.
On a recent business trip, a salesman traveled 52 miles the first hour, 64 miles the second hour and 49 miles the third hour.
How many miles did he average per hour?
Answer: He traveled 54.28 miles per hour as an average.
Step-by-step explanation:
Since we have given that
Number of miles traveled in first hour = 52 miles
Number of miles traveled in second hour = 64 miles
Number of miles traveled in third hour = 49 miles
Average per hour is given by
[tex]=\dfrac{3}{\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}}\\\\\\=\dfrac{3}{\dfrac{1}{52}+\dfrac{1}{64}+\dfrac{1}{49}}\\\\\\=\dfrac{3}{\dfrac{784+637+832}{40768}}\\\\\\=\dfrac{3}{\dfrac{2253}{40768}}\\\\\\=\dfrac{40768\times 3}{2253}\\\\\\=\dfrac{122304}{2253}\\\\\=54.28\ miles/hr[/tex]
Hence, he traveled 54.28 miles per hour as an average.
the sum of two consecutive numbers is 73. what are the numbers?
Describe the graph of the basic rational function, f(x)=1/x. Talk about its domain and range and compare the function to other ones, i.e. linear or quadratic or exponential.
Final answer:
The graph of f(x) = 1/x is a hyperbola with vertical and horizontal asymptotes at x = 0 and y = 0, respectively. The domain is all real numbers except 0, and the range is the same. Unlike linear, quadratic, or exponential functions, the hyperbolic shape of 1/x presents its unique characteristics needing careful domain consideration.
Explanation:
The graph of the basic rational function f(x) = 1/x is characterized by two distinct branches, one in the first quadrant (where x and y are both positive) and the other in the third quadrant (where x and y are both negative). This function is a hyperbola, and as the value of x approaches zero from either the positive or negative side, the value of f(x) increases without bound, referred to as a vertical asymptote at x = 0. Additionally, as the value of x becomes very large or very small (approaching positive or negative infinity), the value of f(x) approaches zero, creating a horizontal asymptote at y = 0. Importantly, this function is undefined at x = 0, so the domain is all real numbers except 0, (domain: ℝ \ {0}). The function takes on all real number values for the output, so the range is also all real numbers except 0 (range: ℝ \ {0}).
Comparing to other types of functions, unlike linear functions like f(x) = 7x which produces a straight line or quadratic functions such as f(x) = 2x² which graphs as a parabola, the rational function f(x) = 1/x leads to a non-linear graph with two separate branches. Exponential functions like f(x) = eⁿ¹, however, grow or decline at an increasing rate, which is a different behavior compared to the hyperbolic decline or rise of a rational function. It's vital to note that as with the function |√x|, there are points along the graph of 1/x where the function is not defined, highlighting the importance of considering the domain in function analysis.
The function 1/x² also represents a rational function but with a different characteristic as it exhibits positive blowup on both sides. This means that as x approaches zero, whether from the positive or negative side, the function tends to positive infinity, a behavior different from the reciprocal function 1/x.
Which expression is modeled by this arrangement of tiles?
A.-40/10
B.40/(-10)
C.40/10
D.40/40
ASAP
Put a check by all the factors of 15
answers : 1, 2, 3, 4, 5, 10, 15.
please answer ASAP
A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile. 1)A deer is 10 miles per hour faster than a bison. 2)A bison is 10 miles per hour faster than a deer. 3)A deer is 0.66 miles per hour faster than a bison. 4)A bison is 0.66 miles per hour faster than a deer.
how many 5/16 are in 1 7/8
To determine how many 5/16 are in 1 7/8, you convert 1 7/8 to an improper fraction, 15/8, and then divide it by 5/16, which yields 6.
Explanation:To find out how many 5/16 are in 1 7/8, you first need to convert 1 7/8 to a improper fraction. Since 1 is equal to 8/8, adding 7/8 gives us 15/8. Now, to find how many 5/16 are in 15/8, you can divide 15/8 by 5/16. To do this, you multiply 15/8 by the reciprocal of 5/16, which is 16/5.
15/8 × 16/5 = (15×16)/(8×5) = 240/40. This simplifies to 6, meaning there are 6 segments of 5/16 in 1 7/8.
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At one basketball game there were 1207 people. At the next game they were 958 people how many people were at two games?
Suppose another sample of 41 students is to be randomly selected from this population. find the probability that the mean of this sample is greater than 110.
How many five digit zip codes are possible if digits cannot be repeated?
1st digit - 0-9 = 10 numbers
2nd digit = 9 numbers
3rd digit = 8 numbers
4th digit = 7 numbers
5th digit = 6 numbers
10 * 9 * 8 * 7 * 6 = 30,240 zip codes
Select all statements below which are true for all invertible n×nn×n matrices aa and bb
a. (ab)−1=a−1b−1(ab)−1=a−1b−1
b. aba−1=baba−1=b
c. (in+a)(in+a−1)=2in+a+a−1(in+a)(in+a−1)=2in+a+a−1
d. a2b7a2b7 is invertible
e. a+ba+b is invertible f. (a+b)(a−b)=a2−b2(a+b)(a−b)=a2−b2
Answer:
The statements that are correct are:
c) [tex](in+a)(in+a^{-1})=2in+a+a^{-1}[/tex]
d) [tex]a^2b^7[/tex] is invertible.
e) [tex]a+b[/tex] is invertible.
Step-by-step explanation:
We are given that:
a and b are invertible n×n matrices.
We have to tell which of the following statements are true.
a)
[tex](ab)^{-1}=a^{-1}b^{-1}[/tex]
This statement is false.
Since:
[tex](ab)^{-1}=b^{-1}a^{-1}[/tex] and it may not be equal to the term [tex]a^{-1}b^{-1}[/tex]
b)
[tex]aba{-1}=b[/tex]
This expression could also be written as:
[tex]ab=ba[/tex]
Since on Post multiplying by a on both the sides.
But here we don't know whether the matrices are commutative or not.
Hence, the statement is false.
c)
[tex](in+a)(in+a^{-1})=2in+a+a^{-1}[/tex]
This statement is true.
since,
[tex](in+a)(in+a^{-1})=in(in+a^{-1})+a(in+a^{-1})\\\\=in^2+in.a^{-1}+a.in+aa^{-1}\\\\=in+a^{-1}+a+in\\\\=in+a^{-1}+a[/tex]
where in denote the identity matrix.
and we know that:
[tex]in^2=in[/tex]
d)
[tex]a^2b^7[/tex] is invertible.
This statement is true.
Since we know that prodct of invertible matrices is also invertible.
As [tex]a[/tex] is invertible so is [tex]a^2[/tex].
Also [tex]b[/tex] is invertible so is [tex]b^7[/tex].
Hence Product of [tex]a^2[/tex] and [tex]b^7[/tex] is also invertible.
i.e. [tex]a^2b^7[/tex] is invertible.
e)
[tex]a+b[/tex] is invertible.
This statement is true as sum of two invertible matrices is invertible.
f)
[tex](a+b).(a-b)=a^2-b^2[/tex]
This statement is false.
Since,
[tex](a+b).(a-b)=a(a-b)+b(a-b)\\\\=a.a-a.b+b.a-b.b\\\\=a^2-ab+ba-b^2[/tex]
Now as we are not given that:
[tex]ab=ba[/tex]
Hence, we could not say that:
[tex](a+b).(a-b)=a^2-b^2[/tex]
The correct statements which are true for all invertible [tex]\left({n\times n}\right)\cdot\left({n\times n}\right)[/tex] are:
(c). [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex]
(d). [tex]{a^2}{b^7}[/tex] is invertible.
(e). [tex]a+b[/tex] is invertible.
Further Explanation:
Given:
The matrix [tex]a[/tex] and [tex]b[/tex] are invertible [tex]\left({n\times n}\right)[/tex] matrices.
Calculation:
(a)
The statement is [tex]{\left({ab}\right)^{-1}}={a^{-1}}{b^{-1}}[/tex] false.
[tex]\begin{aligned}{\left({ab}\right)^{-1}}&={a^{-1}}{b^{-1}}\\\left({ab}\right){\left({ab}\right)^{-1}}&=\left({ab}\right){a^{-1}}{b^{-1}}\\I&\ne ab{a^{-1}}{b^{-1}}\\\end{aligned}[/tex]
The statement is [tex]{\left({ab}\right)^{-1}}={a^{-1}}{b^{-1}}[/tex] false.
(b)
The statement is [tex]ab{a^{-1}}=b[/tex].
Now multiply by a both the side.
[tex]\begin{aligned}ab{a^{-1}}a&=ba\\ab&\ne ba\\\end{aligned}[/tex]
The statement is [tex]ab{a^{-1}}=b[/tex] is false.
(c)
The statement is [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex].
Solve the above equation to check whether it is invertible.
[tex]\begin{aligned}\left({in+a}\right)\left({in+{a^{-1}}}\right)&=in\left({in+{a^{-1}}}\right)+a\left({in+{a^{-1}}}\right)\\&=i{n^2}+in\cdot{a^{-1}}+a\cdot in+a{a^{-1}}\\&=in+{a^{-1}}+a+in\\&=in+{a^{-1}}+a\\\end{aligned}[/tex]
The statement is true.
(d)
The statement is [tex]{a^2}{b^7}[/tex].
The product of invertible matrices is always invertible.
As [tex]a[/tex] is invertible so [tex]{a^2}[/tex] is also invertible.
As [tex]b[/tex] is invertible so [tex]{b^7}[/tex] is also invertible.
Hence, the product of [tex]{a^2}[/tex] and [tex]{b^7}[/tex] is also invertible.
The statement is true.
(e)
The statement [tex]a+b[/tex] is true as [tex]a+b[/tex] is always invertible.
(f)
The statement is [tex]\left({a+b}\right)\cdot\left({a-b}\right)={a^2}-{b^2}[/tex].
Solve the equation to check the inevitability.
[tex]\left({a+b}\right)\times\left({a-b}\right)={a^2}-ab+ba-{b^2}[/tex]
The statement is not true as [tex]ab=ba[/tex].
Hence, the correct statements which are true for all invertible [tex]\left({n\times n}\right)\cdot\left({n\times n}\right)[/tex] are:
(c). [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex]
(d). [tex]{a^2}{b^7}[/tex] is invertible.
(e). [tex]a+b[/tex] is invertible.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: Invertible, matrices, matrix, statement, function, true, determinants, elements, inverse.
The gasoline tank of a minivan holds 18 gallons. How many quarts can the tank hold?
To convert 18 gallons to quarts, multiply by the conversion factor of 4 quarts per gallon, giving a result of 72 quarts.
The gasoline tank of a minivan holds 18 gallons. To determine how many quarts it can hold, we need to use the conversion factor that 1 gallon is equivalent to 4 quarts. Since we are converting from a larger unit to a smaller unit, we will multiply the number of gallons by 4.
18 gallons x 4 quarts/gallon = 72 quarts
Therefore, the minivan's gasoline tank can hold 72 quarts of gasoline.
A swimming pool is being filled ata rate of 15 pints per minute. How many gallons per hour is this
1 gallon = 8 pints
15/8 = 1.875 gallons per minute
60 minutes per hour
1.875 * 60 = 112.5 gallons per hour
Jeremy Spent 1/4hours on homework after school another 1/2 after she got home and a final 1/3 hour after dinner. Did she spend more or less than one hour on homework and all? Explain.
Line segment CD is shown on a coordinate grid:
A coordinate plane is shown. Line segment CD has endpoints 1 comma 2 and 1 comma negative 1.
The line segment is rotated 90 degrees counterclockwise about the origin to form C'D'. Which statement describes C'D'?
A) C'D' and CD are equal in length.
B) C'D' is parallel to CD.
C) C'D' is half the length of CD.
D) C'D' is greater than twice the length of CD.
How many solutions does the following equation have?
|3x + 12| = 18 (5 points)
No solution
One solution
Two solutions
Infinitely many solutions
A total of 428 tickets sold for the school play. They were either adults tickets or student tickets. The number of students tickets sold was three times the number of adult tickets sold. How many adults tickets were sold.
107 adult tickets were sold for the school play.
Explanation:Let's denote the number of adult tickets sold as x. According to the given information, the number of student tickets sold is three times the number of adult tickets sold. So, the number of student tickets sold would be 3x. The total number of tickets sold is 428, so we can set up the equation:
x + 3x = 428
Combining like terms, we have:
4x = 428
Dividing both sides of the equation by 4, we find:
x = 107
Therefore, 107 adult tickets were sold.
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Is the symbol μμ used for the population mean or sample mean?
choices are.....
population mean
sample mean
The symbol μ is used for population mean, while x is used for sample mean in statistics.
Explanation:The symbol μ (pronounced "mew") is used to represent the population mean.
The population mean is a parameter that represents the average value of a variable in the entire population.
On the other hand, the symbol x is used to represent the sample mean, which is the average value calculated from a subset of the population called a sample.
The symbol μ (pronounced "mew") is used to represent the population mean.
It denotes the mean of all values within an entire population, which is a parameter of that population.
To illustrate why μ represents the population mean, consider a dataset: 1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 4.
If this were to represent an entire population, we would calculate the mean and then denote it with μ.
Which inequality models this problem?
Esin started a T-shirt-printing business. She spent $2500 to purchase supplies to get started and she uses about $4.50 worth of supplies per T-shirt printed. Esin charges $25 for each T-shirt. Let s represent the number of T-shirts.
What is the minimum number of T-shirts Esin will need to sell to make a profit?
25s<2500+4.5s
{$7.04,$7.04,$7.05,$11.99,$12.50,$12.99,$9.98,$9.99,$8.51,$11.95}
What is the mode?
What is the median?
What is the mean?
What is the IQR?
The mode of the given data set is $7.04, the median is $9.99, the mean is $9.634, and the IQR is $3.48.
Explanation:The mode of the given set is $7.04, as it occurs the most number of times.
The median is $9.99, which is the middle value when the data is arranged in ascending order.
The mean can be calculated by finding the sum of all the values and dividing it by the total number of values. In this case, the mean is $9.634.
The IQR (Interquartile range) is the difference between the third quartile and the first quartile. To find the IQR, we need to first calculate the quartiles. First, we arrange the data in ascending order: $7.04, $7.04, $7.05, $8.51, $9.98, $9.99, $11.95, $11.99, $12.50, $12.99. The first quartile is the average of the 3rd and 4th values, which is $8.51. The third quartile is the average of the 8th and 9th values, which is $11.99. Therefore, the IQR is $11.99 - $8.51 = $3.48.
Your great aunt sally loans you $5000 for three years and asks that you repay it with annually compounding interest at the rate of 8% per year. how much do you repay her after three years?
Plz help it’s du in like 1 hour
How do transformations affect the logarithmic graph?
Which expression shows the result of applying the distributive property to 12(5y+4) ?
A. 17y + 16
B. 5y + 48
C. 60y + 48
D. 60y + 4
Determine the quadrant when the terminal side of the angle lies according to the following conditions: sin (t) > 0, cos (t) < 0.
What is the inverse of the statement? A number that has exactly two distinct factors is prime.
Answer:
The inverse statement is
"A number that does not has exactly two distinct factors is not prime"
Step-by-step explanation:
Given a statement we have to tell the inverse of that statement.
The given statement is
"A number that has exactly two distinct factors is prime".
We have to write the inverse of the above statement.
The inverse of the statement is
"A number that does not has exactly two distinct factors is not prime"
Prove that for any positive integer n a field f can have at most a finite number of elements of multiplicative order at most n
how do you write 2.22 in expanded form
Answer:
[tex]2 + \frac{2}{10}+\frac{2}{100}[/tex]
Step-by-step explanation:
In the expanded form we write a number as the sum of all place value of its digits from left to right,
Here, the given number,
2.22
By the place value chart,
Place value of first digit = 2 ( ones )
Place value of the first digit after decimal = [tex]\frac{2}{10}[/tex] ( tenth )
Place value of the second digit after decimal = [tex]\frac{2}{100}[/tex] ( hundredth )
[tex]\implies 2.22 = 2 + \frac{2}{10}+\frac{2}{100}[/tex]