Which statement describes the relationship between the
function and its inverse?
O The range of both f(x) and f'(x) is all real numbers.
O. The domain of both f(x) and f'(x) is all real numbers.
O The range of f(x) is y > 0 and the domain off'(x) is
X>0.
O The domain of f(x) is x > 0 and the range of f1(x) is
y>0.
Answer:
The third,
The range of [tex]f(x)[/tex] is [tex]y > 0[/tex] and the domain of [tex]f^{-1} (x)[/tex] is [tex]x>0[/tex]
Step-by-step explanation:
The solution to the function is range of f(x) is y > 0 and the domain of f' ( x ) is x > 0
Define domain and range?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. Once we enter an x value, the function outputs this sequence of values.
The collection of results from a relation or function is known as the range. It is, in other words, the range of potential y values. As ordered pairs of the form (x,y), the y coordinate is provided after the x coordinate. After the input is a list of the output.
Given the data,
Let's write the function as f. ( x )
The function's inverse is now presented as
Function is equal to f'(x), where x and y intercepts are switched.
The range of f(x) is now all the values of y.
And , y > 0
Hence, x > 0 defines the domain of f' (x).
As a result, the domain of f' (x) is x > 0 while the range of f(x) is y > 0.
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Compare the rules of two games. Game A: Two six-sided dice are thrown. The numbers on the dice determine which player gets a point. Player 1 gets a point if the product of the numbers on the dice is even. Player 2 gets a point if the product is odd. Game B: Two six-sided dice are thrown. The numbers on the dice determine which player gets a point. Player 1 gets a point if the sum of the numbers on the dice is even. Player 2 gets a point if the sum is odd. IN Which statement accurately describes whether these games are fair?
Answer:
Neither game A or B is fair
Step-by-step explanation:
statement accurately describes whether these games are fair is neither game A nor game B.
What is probability?Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
For, game A:
Odd x odd= odd,odd x even= eveneven x even = evenNot fair
For game B,
Odd + odd = eveneven + even= evenodd+ even= oddAgain, unfair.
P (odd, odd)= 1/4
P(even, even)=1/4
P(odd, even)=1/2
Hence, none of the game is fair.
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EASY POINTS!!!
Which value for x makes the following number sentence true?
10x - 4x = 36
A. 216
B. 30
C. 6
D. 3
Answer:
C. 6
Step-by-step explanation:
10x - 4x = 36
1. Take away 4x from each side
6x = 36
2. Divide by six
x = 6
A PE Teacher pays a total of $960 for 6 basketballs and 8 volleyballs. The price of 6 basketballs is equivalent to 8 volleyballs. How much does each basketball cost than each volleyball?
solve by assuming question
Answer: solving by forming simple algebra equation
Step-by-step explanation:
8x (x is the cost of 1 volleyball)
6y (y is the cost of 1 basketball)
We know that cost of 8 volleyballs is = cost of 6 basketballs
i.e. 8x = 6y
& total money spent to buy 8 volleyballs and 6 basketballs is $960
so we can write;
8x + 6y = 960
= (6y) + 6y = 960
= 12y = 960
= y or cost of 1 basketball is (960/12) = $80
& if we want to know the value of x (cost of 1 volleyball)
8x = 6y
= 8x = 6(80)
& x = 6(80/8)
= 6 (10) = 60
so the cost of basketball is $80 & 1 volleyball is $60
Hope it helps :)
p.s. that the equation I formed were made as if I was making an assumption & the conditions were kept uniform from the beginning, this is very applicable in day to day scenario; for e.g. when you go out with you friends to eat and have to split the bill - this assumption and division is called algebra - so value this education!
Which expression is the factored form of X^3 2x^2 5x 6?
The factors of the given equation x³ - 2x² - 5x + 6 is (x - 1)(x + 2)(x - 3) with the help of synthetic division.
Let f(x) = x³ - 2x² - 5x + 6
Substitute x = 1
f(1) = (1)³ - 2(1)² - 5(1) + 6
⇒ f(1) = 1 - 2 - 5 + 6
⇒ f(1) = -1 + 1
⇒ f(1) = 0
As x = 1 is the root of the given equation therefore one of the factor of the given equation is (x-1)
Now use long division method, we get (x² - x - 6) as another factor.
⇒ f(x) = (x - 1)(x² - x - 6)
⇒ f(x) = (x - 1)(x² - 3x + 2x - 6)
⇒ f(x) = (x - 1)(x(x-3) + 2(x-3))
⇒ f(x) = (x - 1)(x - 3)(x + 2)
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In SHORT BINGO, a $5\times5$ card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares. Specifically, a card is made by placing 5 numbers from the set $1-10$ in the first column, 5 numbers from $11-20$ in the second column, 4 numbers $21-30$ in the third column (skipping the WILD square in the middle), 5 numbers from $31-40$ in the fourth column and 5 numbers from $41-50$ in the last column. One possible SHORT BINGO card is: To play SHORT BINGO, someone names numbers, chosen at random, and players mark those numbers on their cards. A player wins when he marks 5 in a row, horizontally, vertically, or diagonally. How many distinct possibilities are there for the values in the first row of a SHORT BINGO card
The first row of the SHORT BINGO card contains 5 numbers, one from each of the sets $1-10$, $11-20$, $21-30$, $31-40$, and $41-50$. Since the WILD square is in the middle of the card, it does not affect the possibilities for the first row.
A probability simple definition is what?A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
For the first column, there are 10 possibilities, as it can contain any number from the set $1-10$.
For the second column, there are 10 possibilities, as it can contain any number from the set $11-20$.
For the third column, there are 9 possibilities, as it can contain any number from the set $21-30$ except the one already used.
For the fourth column, there are 10 possibilities, as it can contain any number from the set $31-40$.
For the fifth column, there are 10 possibilities, as it can contain any number from the set $41-50$.
The total number of distinct possibilities for the values in the first row of a SHORT BINGO card is the product of the possibilities for each column, which is:
10 * 10 * 9 * 10 * 10 = 90000.
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35 POINTS Complete the sentence.
Statistics is the result of __________ data.
Answer:
analysis (i got to put a bunch of random stuff here cs the limit)
A number is divided by 9. When
the quotient is multiplied by 6,
the product is 108. What is the
number?
Explain how you found the
answer.
Answer:
The number is 162.
Step-by-step explanation:
Let's let the number =n
So, we can set up an equation.
(n/9) is a number divided by 9.
Its "quotient" (the answer to that expression) is multiplied by 6.
6(n/9)
The product (answer) is 108.
6(n/9) = 108.
Then we can solve.
6(n/9) = 108
(n/9) = 18
n = 162
What is the median of the following 9 numbers: 23, 15, 32, 27, 19, 11, 30, 19, 22?
The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.
What is a median?The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.
The median for odd data will be
Median = [(n + 1) / 2]th
The median for even data will be
Median = {[n / 2 + (n + 2)/ 2] / 2}th
The data is given below.
23, 15, 32, 27, 19, 11, 30, 19, 22
Arrange the data in ascending order. Then we have
11, 15, 19, 19, 22, 23, 27, 30, 32
Then the median of the following 9 numbers is calculated as,
Median = [(9 + 1) / 2]th
Median = (10 / 2)th
Median = 5th
Median = 22
The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.
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I have two fair dice each numbered 1 to 6 I throw both dice and add the two numbers together. What is the probability that the number I get is a multiple of 5 .
Answer:
7 / 36
Step-by-step explanation:
Using the sample space attached,
Required outcome = multiple of 5 from the sun of two rolled dice = 7
Total possible outcomes =(number of faces)² = 6² = 36
Therefore, the probability of obtaining a sum which is a multiple of 5 is :
P(sum which is a multiple of 5) :
Required outcome / Total possible outcomes
= 7 / 36
I NEED HELP PLEASEEE!!!
If the radius is quadrupled, then the area of the new area to the old area will be 4:1
What is quadrupled?You should be aware that the quadrupled of a circle is four times the area of the old one.
In this case the area of the circle is denoted by
Area = πr²
Where r= radius=6 cm
The area of the old circle is 22/7 * 6 * 6
Area of the circle is = 113.1cm²
To this effect, the area of the new circle is 4(area of the old one)
Area = 4*22/7 * 6 * 6
Area = 3167/7
Area is = 452.6
This implies that 4(113.2) =452.6
In conclusion, you will discover that four times the area of the new circle is the old circle
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A company wanted to determine the health care costs of its employees. A sample of 25 employees were interviewed and their medical expenses for the previous year were determined. Later the company discovered that the highest medical expense in the sample was mistakenly recorded as 10 times the actual amount. However, after correcting the error, the corrected amount was still greater than or equal to any other medical expense in the sample. Which of the following sample statistics must have remained the same after the correction was made
After the modification, the maximum amount of medical costs in the sample must have stayed the same.
After the wrongly recorded medical expense was repaired, the adjusted amount remained more than or equal to every other medical expense in the sample. This suggests that the sample statistic linked to the highest value must have remained unchanged after the modification.
The highest value, also known as the maximum or largest value, of the medical expenses in the sample, had to have remained constant. Even though the real quantity was mistakenly recorded as being 10 times its value, the rectified amount still had the highest value in the sample.
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Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
20% tip on a bill of $13.48
The amount of the tip is approximately $
If the length of the American flag is 1.8 yards, find the hight
HELP! THIS IS DUE TODAY, and i will mark brainlest!
Answer:
Last option...
Step-by-step explanation:
Answer:
The very last one
Step-by-step explanation:
x cannot have two outcomes
Create a word problem for 4 x 8 = ?
and solve it using a bar model?
Answer:
Jackie has been assigned to hand out papers to all the students in her class. Each student gets 4 pieces of paper, and there are 8 total students. How many papers total does Jackie need to get?
(I cannot show a picture of a bar model, apologies)
can you please help that will be super kind of u to do that
Answer:
B
Step-by-step explanation:
I think your supposed to just count the dots
Answer:
B. 18
Step-by-step explanation:
The number of observations here means every time they saw how many pennies someone brought in. So you count up the total number of dots from 0-50 on here, and there are 18.
How do I find the indicated value?
Answer:
65ᵗʰ Term of the sequence is 479
50ᵗʰ Term of the sequence is 346
Step-by-step explanation:
1.)Here,
First Term = a₁ = 3
Second Term = a₂ = 10
Third Term = a₃ = 17
Now,
Common Difference (d)
d = a₂ - a₁ = (-7) - (-15) = -7 + 15 = 8
d = a₃ - a₂ = 1 - (-7) = 1 + 7 = 8
Here, Common Difference is same everywhere
Now, For 65ᵗʰ term, n = 65
aₙ = a + (n - 1)d
a₆₅ = (-15) + (65 - 1) × 8
a₆₅ = (-15) + 64 × 8
a₆₅ = (-15) + 512
a₆₅ = 479
Thus, 65ᵗʰ Term of the sequence is 479
2.)Here,
First Term = a₁ = -15
Second Term = a₂ = -7
Third Term = a₃ = 1
Now,
Common Difference (d)
d = a₂ - a₁ = 10 - 3 = 7
d = a₃ - a₂ = 17 - 10 = 7
Here, Common Difference is same everywhere
Now, For 50ᵗʰ term, n = 50
aₙ = a + (n - 1)d
a₅₀ = 3 + (50 - 1) × 7
a₅₀ = 3 + 49 × 7
a₅₀ = 3 + 343
a₅₀ = 346
Thus, 50ᵗʰ Term of the sequence is 346
-TheUnknownScientist
Convert 1.45454... into a ratio of two integers. Enter your answer as a fraction in lowest terms.
Answer:
16/11
Step-by-step explanation:
Let x = 1.45454...
Multiply both sides by 100:
100x = 145.454...
Subtract both sides by x:
100x - x = 145.454... - x
100x - x = 145.454... - 1.45454...
99x = 144
x = 144/99
The term can be simplified in lowest as 16/11. Hence, 1.45454... can be written as the ratio of two integers of 16/11
if there were 125 students in 5 buses what is the ratio of students to buses
Answer:
125:5
Step-by-step explanation:
obvious.
Complete the equation describing how x and y are related -2
The equation of the line found is:
y = 3x + 1.
Since the rate of change is always the same, that is, when x changes by 1, y always changed by the same value, this is a linear equation.
Linear equation:
A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant. The standard form of linear equations in two variables is of the form Ax + By = C. where x and y are variables, A and B are coefficients, and C is a constant.
The equation of a line is given by:
y = mx + b
In which:
m is the slope, that is, by how much y changes when x changes by 1.
b is the y-intercept, which is the value of y when x = 0.
From the table, when x =0 and y =1 , thus b = 1.
When x = and y = 1 . When x =1 and y = 4 , when x = 2 and y =7 , and so on. That is, when x changes by 1, y changes by 3, and the slope is m = 3.
The equation of the line is:
y = 3x + 1.
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please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
[tex]x \approx 86.5[/tex]
Step-by-step explanation:
To solve the given problem, use the following trigonometric ratios,
[tex]sin(\theta) = \frac{opposite}{hypotenuse}\\\\cos(\theta) = \frac{adjacnet}{hypotenuse}\\\\tam(\theta) = \frac{opposite}{adjacent}[/tex]
Each of the sides are named relative to the given angle, therefore, when looking at different angles, the sides will have different names. In this case, one is given the length of the hypotenuse, and one is asked to find the length of the given side. Therefore, it would make the most sense to use the ratio of sine ([tex]sin[/tex]). Substitute in the given values and solve,
[tex]sin(84)=\frac{x}{87}[/tex]
Manipulate the equation so that it is solved for (x),
[tex]x=(87(sin(84))[/tex]
Solve,
[tex]x \approx 86.5[/tex]
Find the value of x such that the data set has the given mean.
100, 122, 103, 113, 109, x; mean 102
Answer:
[tex]mean = \frac{sum}{number} \\ 102 = \frac{(100 + 122 + 103 + 113 + 109 + x)}{6} \\ 612 = 547 + x \\ x = 65[/tex]
Please help I have a learning disability and need help with this.
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
( 3 6) 9 and 3 (6 9)
yes, it uses the Associative Property
yes, it uses the Commutative Property
yes, it uses the Identity Property
no they are not equivalent
Answer:
No, they are not equivalent.
Step-by-step explanation:
The first expression, (3 6) 9, is equal to 9, while the second expression, 3 (6 9), is equal to 3. The two expressions are not equivalent because they do not produce the same result when the operations are carried out. The properties of associativity, commutativity, and identity do not apply to these expressions.
Answer:
no they are not equivalent
Step-by-step explanation:
The two expressions are not equivalent. This is because the distributive property does not apply in this case, as the parentheses on the left side of the expression have precedence over the parentheses on the right side. Therefore, the expression on the left side would be evaluated first, resulting in a different answer than the expression on the right side.
Eliminate the parameter in the equations x = and y = t – 4. How can the rectangular equation be described? cubic linear quartic quadratic
x= t^ 1/3 !!!
edg 2021 cumu review
Answer:
Step-by-step explanation:
If [tex]x = t^{1/3}[/tex], then [tex]t=x^{3}[/tex]
Now, puting [tex]t[/tex] value in the other equation, we have
[tex]y=x^{3} - 4[/tex]
Therefore, is a cubic equation
Rectangular equation be described as the cubic equation. The cubic equation is obtained after rearranging the equation. Option A is correct.
How do we determine the solution to an equation?We do the identical actions on both sides to ensure that the equality of both expressions is maintained.
Solving equations entails determining the values of the variables involved for which the equation is valid.
Given equation;
[tex]\rm x = t^{\frac{1}{3} }\\\\ t=x^3[/tex]
Put the value of t in the equation;
y = t – 4
y=x³-4
The obtained equation is cubic in nature.
Hence,rectangular equation be described as the cubic equation.
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Help ASAP plz need answer
u can download the gauthmath app. i promise it's very helpful :)
Answer:
y=1/4x+5
Step-by-step explanation:
............ ............
The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRYYYYYYYYYYY
The area of the floor in the scale drawing is 60 inches²
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Actual rectangular floor.
Length = 24 feet
Width = 40 feet
Scale rectangular floor.
Length = 6 inches
Width = 40/4 = 10 inches
The area of the scale rectangular floor.
= Length x Width
= 6 x 10
= 60 icnhes²
Thus.,
The area of the floor is 60 inches².
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Peggy completed 5/6 of the math homework and Al completed 4/5 of the homework. Did Peggy or Al complete more hoof the math homework?
Peggy completed more of the math homework than Al
What does division of fractions mean?
A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.
we know that
In order to be able to compare fractions more easily it is recommended that both have the same denominator
Peggy
5/6 x 5 = 25/30
Al
4/5 x 6 = 24/30
Peggy completed more of the math homework
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Finding the slope ?identify the slope
the slope of the given straight line will be -3
What is the slope of line?
Given two line-side coordinates, use the slope formula to determine the slope of the line. The slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1). x1 and y1 are represented by the first point's coordinates. The second points are located at x2, y2, and their locations. Whichever point you choose to classify as the first and which as the second doesn't matter.
We know that formula two find the slope of the line joining two points which is
Slope is = y2-y1/x2-x1
=9-0/0-3
=-3
Hence the slope of the given straight line will be -3
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A 5/44 lottery requires choosing five of the numbers 1 through 44. How many different lottery tickets can you choose
The number of different lottery tickets that can be chosen in a 5/43 lottery is 8,145,060.
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
The number of different lottery tickets that can be chosen in a 5/43 lottery is 8,145,060. This can be calculated using the combination formula, which is:
[tex]nCr = n / (r(n-r))[/tex]
where n is the total number of options (43) and r is the number of choices (5).
so, [tex]43C5 = 43 / (5(43-5)) = 8,145,060.[/tex]
Lottery tickets that can be chosen in a 5/43 lottery is 8,145,060.
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