Step-by-step explanation:
We use the symbol f − 1 to denote an inverse function. For example, if f (x) and g (x) are inverses of each other, then we can symbolically represent this statement as:
g(x) = f − 1(x) or f(x) = g−1(x)
One thing to note about the inverse function is that the inverse of a function is not the same as its reciprocal, i.e., f – 1 (x) ≠ 1/ f(x). This article will discuss how to find the inverse of a function.
Since not all functions have an inverse, it is therefore important to check whether a function has an inverse before embarking on determining its inverse.
We check whether or not a function has an inverse in order to avoid wasting time trying to find something that does not exist.
What is the other number to this math equation?
Answer:
You need to ask yourself what times 20 gives you 600. Then ask yourself what times 20 gives you 160. Then that will give you your answer.
Step-by-step explanation:
The graph below does not represent a function. Explain why.
Notice how points T and Z are vertically aligned, or vertically lined up. This is where the graph fails the vertical line test.
The input x = 2 leads to the outputs y = 3 and y = 5 (which are the y coordinates of points Z and T in that order).
A function is only possible when any given input leads to exactly one output only. It would be like saying "the conversion function from Celsius to Fahrenheit has 0 degrees C convert to both 32 degrees F and 50 degrees F at the same time". But such a statement makes no sense and it's not useful. So this is one example of why having one output makes sense for a function.
In short, we need one output for any given input. But the input x = 2 leads to more than one output. That's why we don't have a function.
circle o has diameter ab and chord ac. calculate the measure of cab id bc = 62⁰
Answer:
sin62 =0.883Step-by-step explanation:
0.883=1/0.836=1.133
The measure of ∠CAB is 31⁰.
Given that,
Circle O has diameter AB and chord AC.
We have to determine,
The measure of ∠CAB if BC is 62⁰.
According to the question,
The measurement of the required angle by using circle properties following all the steps given below.
The measure of the BC is 62 degrees.
If the circle has diameter AB and chord AC,
Then,
By the property of the circle,
[tex]\rm m\angle CAB = \dfrac{1}{2} \times BC \\[/tex]
Substitute the value of the BC in the equation,
[tex]m\angle CAB = \dfrac{1}{2} \times BC \\\\ m\angle CAB = \dfrac{1}{2} \times 62 \\\\ m\angle CAB = 31 \ degree \\\\[/tex]
Hence, The measure of ∠CAB is 31⁰.
For more details refer to the link given below.
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Q22. Solve the equation x – 25 = 25 and state which axiom do you use here.
Answer:
x=50
Step-by-step explanation:
The solution to the equation x – 25 = 25 is x = 50. The axiom used to solve the equation is the addition property of equality.
To solve the equation x - 25 = 25, we want to isolate the variable x to find its value.
Adding 25 to both sides of the equation, we get:
x - 25 + 25 = 25 + 25
Simplifying, we have:
x = 50
Therefore, the solution to the equation is x = 50.
In this case, the axiom used to solve the equation is the addition property of equality. According to this axiom, if two expressions are equal, adding the same value to both sides of the equation preserves the equality.
In the given equation, we add 25 to both sides of the equation to maintain equality and obtain the solution x = 50. The addition property of equality allows us to perform this operation and determine the value of x.
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Tích các nghiệm của phương trình Log(x-1)²=2 là
Answer:
-99
Step-by-step explanation:
Log(x-1)²=2
Log(x-1)²=Log(100)
(x-1)²=100
x-1=10 and x-1=-10
x₁=11 and x₂=-9
x₁ × x₂ = 11 × (-9) = -99
rewrite x+2y=-4 in slope intercept
Answer:
y= - 1/2 x-2 ( SEE IMAGE BELOW)
Step-by-step explanation:
FYI you can use the app photo math, you just take a pic of the problem and it gives you the answer and explains the steps and it is free.
Answer:
How do you write
x+2y=4
into slope intercept form?
Answer is:
y=−12x+2
Step-by-step explanation:
Slope intercept form can be represented as
y=mx+b
To get an equation into this form, we should try to get y all alone.
So then from x+2y=4
first, we can subtract x from both sidesand get 2y=−x+4
then, we can divide both sides by 2 to get it in slope intercept form
y=−12x+2
I think is like this. Hope it helps>3
27. A 35 foot long tube is cut into two pieces with ratio 4:5 Find the length of the shorter piece.
a) 9 feet
b) 16 feet
c) 12 feet
d) 20 feet
The length of the shorter piece is 15.55 feet.
Concept:Firstly, we will assume the ratio in which this tube is cut.Then, we will substitute the ratio and solve for the lengths of the two pieces.How to solve the given question?As the tube is cut into a ratio of 4:5, Let the length of the shorter piece be 4k and the longer piece be 5k.Total length of tube = 35 feetThus, the length of the shorter piece is 15.55 feet.
As none of the options matches the answer, all options are incorrect.
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Researchers believe that 24.5% of the adults in the United States are obese. A Gallup poll examined the rate of obesity in America with a survey 86,664 randomly sampled U.S. adults. Of the adults surveyed, 23,053 said that they were obese. Is this enough evidence to state that more than 24.5% of all adults in the U.S. are obese
Answer:
The p-value of the test is 0 < 0.05(standard significance level), which means that this is enough evidence to state that more than 24.5% of all adults in the U.S. are obese
Step-by-step explanation:
Researchers believe that 24.5% of the adults in the United States are obese. Test if there is enough evidence to state that more than 24.5% of all adults in the U.S. are obese.
At the null hypothesis, we test if the proportion is of 24.5% or less, that is:
[tex]H_0: p \leq 0.245[/tex]
At the alternative hypothesis, we test if this proportion is greater than 24.5%, that is:
[tex]H_1: p > 0.245[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.245 is tested at the null hypothesis:
This means that [tex]\mu = 0.245, \sigma = \sqrt{0.245*0.755}[/tex]
Survey 86,664 randomly sampled U.S. adults. Of the adults surveyed, 23,053 said that they were obese.
This means that [tex]n = 86664, X = \frac{23053}{86664} = 0.266[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.266 - 0.245}{\frac{\sqrt{0.245*0.755}}{\sqrt{86664}}}[/tex]
[tex]z = 14.37[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a sample proportion of 0.266 or higher, which is 1 subtracted by the p-value of z = 14.37.
The p-value of z = 14.37 is 1.
1 - 1 = 0
The p-value of the test is 0 < 0.05(standard significance level), which means that this is enough evidence to state that more than 24.5% of all adults in the U.S. are obese
The table shows the displacement-time data for a ship relative to a shore.
t(hours) 2.95 3.15 3.75 3.95 3.99 4.00
s(0 (miles) 14.95 17.61 27.23 31.01 31.80 32.00
Estimate the instantaneous velocity of the ship at t = 4 hours.
A.
20.00 mi./h.
B.
20.15 mi./h.
C.
20.25 mi./h.
OD.
20.50 mi./h.
Answer:
Step-by-step explanation:
need help asap plz!!!!!
Answer:
Step-by-step explanation:
In the simplest way, the domain of a function is basically all of the possible values of the input variable or x-axis in a graph. While the range of a function would be all of the real possible outputs that the function can create. In a graph this would be all of the possible values for the y-axis. For example, in the following function...
y = 4x + 3
The domain of this function would be any and all values for x, while the range of the function would be any and all values that the function can output for y.
The hardware store where you work charge 80 cents including tax, for a pound of nails. A customer purchases 5 3/4 pound of nails. How much should you charge the customer for nails?
Answer:
$4.60
Step-by-step explanation:
1 lb ---> 80 cents
5 3/4 lb ---> 5 3/4 * 80 cents
[tex] 5 \dfrac{3}{4} \times 80 = [/tex]
[tex] = \dfrac{23}{4} \times \dfrac{80}{1} [/tex]
[tex] = \dfrac{23 \times 80}{4 \times 1} [/tex]
[tex] = \dfrac{1840}{4} [/tex]
[tex] = 460 [/tex]
460 cents = $4.60
G.1.- Una Recta contiene los puntos (-3,7)
y (9,-5) Calcule la ecuación de la recta en la
FORma y=mxtb. Explicar los pasos
Given:
A line passes through the points (-3,7) and (9,-5).
To find:
The equation of the line in the form of [tex]y=mx+b[/tex].
Solution:
If a line passes through two points, then the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
A line passes through the points (-3,7) and (9,-5). So, the equation of the given line is:
[tex]y-7=\dfrac{-5-7}{9-(-3)}(x-(-3))[/tex]
[tex]y-7=\dfrac{-5-7}{9+3}(x+3)[/tex]
[tex]y-7=\dfrac{-12}{12}(x+3)[/tex]
[tex]y-7=-1(x+3)[/tex]
On further simplification, we get
[tex]y-7=-x-3[/tex]
[tex]y-7+7=-x-3+7[/tex]
[tex]y=-x+4[/tex]
Therefore, the equation of the required line is [tex]y=-x+4[/tex].
Starting at a train station, Train A goes toward its destination to the right by 600
miles, and Train B goes to the left by 500 miles. Which of the following signed
numbers best represents Train A's direction and distance toward its destination?
A.-600
B.-500
C.500
D.600
9514 1404 393
Answer:
D. 600
Step-by-step explanation:
On a number line, positive numbers increase to the right. 600 to the right would be considered to be +600, choice D.
Somebody help me with this
Answer:
3x4 +x3+ 15x2+30x-14
Step-by-step explanation:
What is the line of symmetry for the parabola whose equation is y = -x2 + x + 3?
x = -1
x = -1/2
x = 1/2
Answer:
[tex]x = \frac{1}{2}[/tex]
Step-by-step explanation:
Given
[tex]y = -x^2 + x + 3[/tex]
Required
The line of symmetry
This is calculated using:
[tex]x= -\frac{b}{2a}[/tex]
Where:
[tex]y = ax^2 + bx + c[/tex]
So, by comparison:
[tex]a = -1[/tex] [tex]b = 1[/tex] [tex]c = 3[/tex]
So, we have:
[tex]x = -\frac{1}{2 * -1}[/tex]
[tex]x = -\frac{1}{-2}[/tex]
[tex]x = \frac{1}{2}[/tex]
1/2 is correct, the formula to use is x= - b/2a :)
PLEASE HELP W THIS I WILL Give YOU THE BRAINLIEST PLEASE ! - What does it mean to have a skewed distribution? What causes a skew in statistical terms? And how does one deal with skewed data when conducting research? Are there specific types of
research questions and types of data where one would expect the data to be skewed?
Answer:
Explained below
Step-by-step explanation:
A) A skewed distribution in a dataset is when the median is not equal to the mean in such a manner that the bell curve is tilted to the left or right.
B) If in a data set, if there are outliers which are extremely large or extremely small in comparison to other values in that same dataset, then we can say that such a curve will be pulled towards the outlier and thus the distribution is skewed.
Also, if the curve is inclined to the left, it means there are few extreme values to the left and it is negatively skewed.
Similarly, if the curve is inclined to the right, it means there are few extreme values to the right and is positively skewed.
C) Example of a research question is;
If in a developed country where the poverty level is about 0%, if we collect the data of income of the households, we will discover majority of people with average income and very few people with extreme high levels of income. This condition means the data is positively skewed.
What is the value ofWhat is the value of the missing angle?
A
20
B
90
C
120
D
100 the missing angle? A 20 B 90 C 120 D 100
Answer:
The missing angle is 120
Step-by-step explanation:
Given
See attachment
Required
The missing angle (?)
Let the missing angle be x
So:
[tex]x + 60 = 180[/tex] --- angle on a straight line
Collect like terms
[tex]x = 180-60[/tex]
[tex]x = 120[/tex]
1
2
3
VX
Which is a unit rate?
4 dollars
3 cans
5 students
2 teachers
6 hours 1 book
O 3 mies 2 days
Answer:
6 hours to 1 book
Step-by-step explanation:
Which is a unit rate?
4 dollars to 3 cans
5 students to 2 teachers
6 hours to 1 book
3 miles to 2 days
A unit rate is a rate of a number to 1. The second number must be 1. The only unit rate is 6 hours to 1 book.
Answer: 6 hours to 1 book
2 times the difference between 49.5 and 37.5
Answer:
24
Step-by-step explanation:
diff is 12
12x2 is 24
Một đề thi trắc nghiệm có 10 câu, mỗi câu có 4 phương án trả lời và chỉ có một đáp án đúng. Một sinh viên trả lời một cách ngẫu nhiên, xác suất để sinh viên được 5 điểm là
Câu trả lời:
0,0584
Giải thích từng bước:
Câu hỏi đưa ra đáp ứng điều kiện cần thiết cho phân phối xác suất nhị thức:
Số câu hỏi, số lần thử, n = 10
Xác suất, p = 1 / số lựa chọn = 1/4 = 0,25
q = 1 - p = 1 - 0,25 = 0,75
Tính xác suất để sinh viên đó được 5 điểm, x = 5;
Gợi lại:
P (x = x) = nCx * p ^ x * q ^ (n-x)
P (x = 5) = 10C5 * 0,25 ^ 5 * 0,75 ^ 5
P (x = 5) = 252 * 0,25 ^ 5 * 0,75 ^ 5
P (x = 5) = 0,0584
Khanacademy Unit:Sequences
What does g(2)=?
Answer:
g(2) = -42
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationAlgebra II
SequencesStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \left \{ {{g(1) = 50} \atop {g(n) = 8 - g(n - 1)}} \right.[/tex]
Step 2: Evaluate
Substitute in x [Function g(n)]: g(2) = 8 - g(2 - 1)(Parenthesis) Subtract: g(2) = 8 - g(1)Substitute in function value: g(2) = 8 - 50Subtract: g(2) = -42Consider the frequency distribution below, which has single values as classes: Value Frequency 10 11 12 13 14 15 16 17 18 19 20 21 1 3 7 18 10 4 2 7 16 10 6 2 Construct a new frequency distribution for this data with 4 classes.
The original table (attached to this response) shows single values as classes.
To construct a new frequency distribution for this data with 4 classes, follow these steps:
i. Starting from the least value (which is 10) create groups each of 4 values. For example, the first group will contain 10, 11, 12 and 13. Therefore, we have a class of 10 - 13.
The second group will contain 14, 15, 16 and 17. Therefore, we have a class of 14 - 17
The third group will contain 18, 19, 20 and 21. Therefore, we have a class of 18 - 21
ii. Get the frequency of these classes, we add the frequencies of the members of the class.
For example,
Class 10 - 13 will have a frequency of (1 + 3 + 7 + 18) = 29
Class 14 - 17 will have a frequency of (10 + 4 + 2 + 7) = 23
Class 18 - 21 will have a frequency of (16 + 10 + 6 + 2) = 34
The new table has been attached to this response.
What the cubic inches…
Step-by-step explanation:
The radius r is 5 in (r = D/2). so the volume V of the beach ball is
[tex]V= \dfrac{4 \pi}{3}r^3 = \dfrac{4 \pi}{3}(5\:\text{in})^3[/tex]
[tex]\:\:\:\:\:= 523.6\:\text{in}^3[/tex]
What is the distance between [(3 + 4i) + (2 - 3i)] and (9 - 2i)?
Answer:
5
Step-by-step explanation:
(3 + 4i) + (2 - 3i) = 3 + 4i + 2 - 3i = 5 + i
distance between (5 + i) and (9 - 2i) is the difference between them. and difference means subtraction.
(9 - 2i) - (5 + i) = 9 - 2i - 5 - i = 4 - 3i
and since we are looking for a distance, we are looking for the absolute value of that subtraction.
after all, we could have done the subtraction also in the other direction
(5 + i) - (9 - 2i) = -4 + 3i
and this must be the same distance.
|(-4 + 3i)| = |(4 - 3i)|
and that is done by calculating the distance of any of these 2 points from (0,0) on the coordinate grid of complex numbers.
|(a +bi)| = sqrt(a² + b²)
in our case here
distance = sqrt(4² + (-3)²) = sqrt(16 + 9) = sqrt(25) = 5
as you can easily see, this is (as expected) the same for the result of the subtraction in the other direction :
sqrt((-4)² + 3²) = sqrt(16+9) = sqrt(25) = 5
The distance between major cracks in a highway follows an exponential distribution with a mean of 5 miles. (a) What is the probability that there are no major cracks in a 10-mile stretch of the highway
Answer:
[tex]P(Y=0) = 0.1353[/tex]
Step-by-step explanation:
From the question we are told that:
Exponential distribution mean [tex]\=x = 5 miles[/tex]
Distance [tex]d=10miles[/tex]
Generally the equation for Exponential distribution is mathematically given by
[tex]\lambda=\frac{1}{E(X)}[/tex]
[tex]\lambda=\frac{1}{5}[/tex]
Therefore
Possion Y
[tex]10\lambda=10*(1/5)[/tex]
[tex]10\lambda=2[/tex]
Generally the equation for The probability that there are no major cracks in a 10 mile stretch of the highway is mathematically given by
[tex]P(Y=0) = \frac{e-2 (2)0}{0!}[/tex]
[tex]P(Y=0) = e-2[/tex]
[tex]P(Y=0) = 0.1353[/tex]
Please look below and answer (No links) please explain. I will give brainiest
Answer:
The slope is 1/2 because for every y value that it goes down, the x value goes down by 2. The y-intercept is 4 because when x is 0, y is equal to 4.
The mapping shows a relationship between input and output values.
Answer:
where is the photo
Step-by-step explanation:
PLEASE HELP ASAP!!
Q: Use the graph of f below. Assume the entire function is graphed below. Find where f(x)<0.
(graph and answers pictured.)
Answer:
Option (4)
Step-by-step explanation:
From the graph attached,
We have to find the interval in which the function is less than zero or negative.
Value of the function are along the y-axis and negative value of the function means negative side of the y-axis.
In the graph, function is below the x-axis in the interval x > 4 and x = 6 only.
Therefore, in the interval (4, 6] function f(x) < 0.
Option (4) is the correct option.
pls help! show your work!
(3sqrt4)/(3sqrt5)
Answer:
3sqaure root 100/5
Step-by-step explanation:
It would look like this picture Below
Enlarge the triangle by scale factor -1/3 with centre (-1,2)
PLEASE CAN SOMEONE HELP?????????????/
The coordinates of the image after a dilation by scale factor -1/3 with center (-1, 2) are (0, 2), (0, 4), and (-1, 4).
What is dilation?In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape.
Next, we would have to dilate the coordinates of the pre-image by using a scale factor of -1/3 centered at the point (-1, 2) by using this mathematical expression:
(x, y) → (k(x - a) + a, k(y - b) + b)
For coordinate A, we have;
Coordinate A = (-4, 2) → (-1/3(-4 - (-1)) + (-1), -1/3(2 - 2) + 2)
Coordinate A = (-4, 2) → (-1/3(-4 + 1) - 1, -1/3(2 - 2) + 2)
Coordinate A' = (1, 1) → (0, 2)
For coordinate B, we have;
Coordinate B = (-4, -4) → (-1/3(-4 - (-1)) + (-1), -1/3(-4 - 2) + 2)
Coordinate B = (-4, -4) → (-1/3(-4 + 1) - 1, -1/3(-4 - 2) + 2)
Coordinate B' = (1, 1) → (0, 4)
For coordinate C, we have;
Coordinate C = (-1, -4) → (-1/3(-1 - (-1)) + (-1), -1/3(-4 - 2) + 2)
Coordinate C = (-1, -4) → (-1/3(-1 + 1) - 1, -1/3(-4 - 2) + 2)
Coordinate C' = (1, 1) → (-1, 4).
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