how to find domain and range of math function?
The domain are all of the x-values that are located on the x-axis of a cartesian coordinate while the range all of the y-values that are located on the y-axis of a cartesian coordinate.
What is a domain?In Mathematics, a domain is the set of all real numbers for which a particular function is defined.
In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
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Find the supplemet of x
Answer:
the answer is 180 degrees
pls mark me as the brainliest
Write an essay about your learning on how you solve problems involving integers. (5 points). Take a photo of your answer. (To the Online Teacher please provide a link for submission of output).
Answer:
to use integers for certain problems and equation on math, i can also use it for future use in life in case i need it, Its very helpful to learn since it isnt that complicated nor hard, its just a good skill to keep in mind as a student.
How many hours of flight training must be contained in each Part 141 approved commercial pilot certification course for a helicopter rating
The specific number of hours of flight training required for a commercial pilot certification course for a helicopter rating may vary depending on the regulations of the aviation authority in the relevant jurisdiction.
Therefore, a definitive answer cannot be provided without knowing the specific regulations governing the commercial pilot certification course.
Commercial pilot certification courses for a helicopter rating are regulated by aviation authorities such as the Federal Aviation Administration (FAA) in the United States. These authorities establish the minimum requirements and standards for pilot training programs, including the number of hours of flight training.
The FAA's regulations for helicopter pilot certification under Part 141 of the Federal Aviation Regulations (FARs) outline the minimum flight training requirements. However, the specific number of hours required can vary based on factors such as the type of helicopter, the complexity of the training program, and any additional requirements set by the training institution.
To determine the exact number of flight training hours required for a Part 141 approved commercial pilot certification course for a helicopter rating, it is necessary to refer to the regulations of the specific aviation authority and consult the approved training program or contact a reputable flight training institution for accurate and up-to-date information.
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prove that 21 divides 4n+1 + 52n−1 whenever n is a positive integer.
We have proven that 21 divides 4n+1 + 52n−1 whenever n is a positive integer.
To prove that 21 divides 4n+1 + 52n−1 whenever n is a positive integer, we need to show that the expression 4n+1 + 52n−1 is divisible by 21, or in other words, that there exists an integer k such that:
4n+1 + 52n−1 = 21k
To do this, we can use mathematical induction.
Base case:
When n = 1, we have:
4(1) + 5(1) - 1 = 8
8 is not divisible by 21, but we can verify that it is true for n = 2:
Inductive step:
Assume that the statement is true for some positive integer k, that is:
4k+1 + 52k−1 = 21m
where m is some integer.
We need to show that the statement is also true for k + 1, that is:
4(k+1)+1 + 52(k+1)−1 = 21p
where p is some integer.
Starting with the left-hand side of the equation:
4(k+1)+1 + 52(k+1)−1
= 4k+5 + 52k+3 (using algebraic manipulation)
= 4k+1 + 4(4)k+4 + 5(52)k+1 + 5(52)−1
= (4k+1 + 52k−1) + 4(16k+1) + 5(52)k
Since we assumed that 4k+1 + 52k−1 is divisible by 21, we can substitute 21m for this term:
(4k+1 + 52k−1) + 4(16k+1) + 5(52)k = 21m + 4(16k+1) + 5(52)k
Simplifying further:
21m + 4(16k+1) + 5(52)k = 21(m + 16k + 5k) + 4
Since 21(m + 16k + 5k) is divisible by 21, we have shown that 4(k+1)+1 + 52(k+1)−1 is also divisible by 21. Therefore, by mathematical induction, the statement is true for all positive integers n.
Therefore, we have proven that 21 divides 4n+1 + 52n−1 whenever n is a positive integer.
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Given points P(0, -2) and Q(5,3), find PQ and the coordinates of the midpoint of PQ-
Answer:
The midpoint is
\(( \frac{5}{2} , \: \frac{1}{2} )\)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
\(M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} )\)where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
P(0, -2) and Q(5,3)
The midpoint is
\(M = ( \frac{0 + 5}{2} , \: \frac{ - 2 + 3}{2} ) \\ \)We have the final answer as
\(( \frac{5}{2} , \: \frac{1}{2} )\)Hope this helps you
an article which cost money 150 was sold at a loss of 5%.what was the selling price?
Answer:
142.5
Step-by-step explanation:
150/x=100/95
95*150/100=
142.5
solve for p -5(p + 3/5) = -4
Answer:
P = 0.2
Step-by-step explanation:
If you have any questions about the way I solved it, don't hesitate to ask =)
Answer:Solution for -5(p+3/5)=-4 equation:
-5(p+3/5)=-4
We move all terms to the left:
-5(p+3/5)-(-4)=0
We add all the numbers together, and all the variables
-5(+p+3/5)-(-4)=0
We add all the numbers together, and all the variables
-5(+p+3/5)+4=0
We multiply parentheses
-5p+4-3/5*5=0
We multiply all the terms by the denominator
-5p*5*5-3+4*5*5=0
We add all the numbers together, and all the variables
-5p*5*5+97=0
Wy multiply elements
-125p*5+97=0
Wy multiply elements
-625p+97=0
We move all terms containing p to the left, all other terms to the right
-625p=-97
p=-97/-625
p=97/625
Step-by-step explanation:
HELPPPP!!! Question 2!!!
WILL GIVE BRAINLYIST!
The coordinates of K' after the reflection over the line y = -7 are given as follows:
K'(-4, -8).
How to obtain the coordinates of K'?The original coordinates of K are given as follows:
K(-4, -6).
The reflection line for this problem is given as follows:
y = -7.
The line of reflection is an horizontal line, meaning that:
the x-coordinate remains constant.the y-coordinate moves on the opposite direction.y = -6 is one unit above the reflection line y = -7, hence one unit below is given as follows:
y = -7 - 1
y = -8.
Hence the coordinates of K' after the reflection over the line y = -7 are given as follows:
K'(-4, -8).
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Consider the function y = 4x + 5 between the limits of z = 1 and 2 = 5. a) Find the arclength L of this curve: L= Round your answer to 3 significant figures. b) Find the area of the surface of revolution, A, that is obtained when the curve is rotated by 2 radians about the a-axis. Do not include the surface areas of the disks that are formed at z = 1 and a = 5. A Round your answer to 3 significant figures.
Answer: 84π √(17) (rounded to 3 significant figures)
a) To find the arc length of the given curve we need to first evaluate the derivative of y w.r.t. x:dy/dx = 4. The arclength of the curve is given by L = ∫√(1+(dy/dx)^2) dx The value of dy/dx is already given and hence we can substitute the value and integrate .L = ∫√(1+(4)^2) dx = ∫√(17) dx Between the limits z = 1 and 2, x varies from 9 to 13. We need to substitute these values in the integral. L = ∫√(17) dx = √(17) * [x]9^13= √(17) * [13 - 9]= 4 √(17)Answer: 4√17 (rounded to 3 significant figures)
b) The area of the surface of revolution, A, that is obtained when the curve is rotated by 2 radians about the a-axis is given by:A = ∫2π * y √(1+(dy/dx)^2) dx We know that dy/dx = 4 and the value of y is given by 4x+5.A = ∫2π * (4x+5) √(1+(4)^2) dx= ∫2π * (4x+5) √(17) dx Between the limits z = 1 and 2, x varies from 9 to 13. We need to substitute these values in the integral. A = ∫2π * (4x+5) √(17) dx = 2π * √(17) * ∫(4x+5) dx= 2π * √(17) * [2x^2/2 + 5x]9^13= 2π * √(17) * [(26 + 60) - (18 + 20)]= 84π √(17)
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g(x)= -16x2 + 64x + 80 where x is the number of seconds after the rocket is launched. The function can also be written in factored form as g(x) = -16 (x + 1)(x - 5). What is the y-intercept of the function? What does it represent?
Answer:
y=80
Step-by-step explanation:
when solve y-intercept let x=0
y= -16(0)2+64(0)+80
y=0+0+80
y=80
(0;80)
Simplify −2r(−16r + 3r − 18). −26r2 − 36r 26r2 + 36 26r2 + 36r −26r2 + 36r
Answer:
26r^2 + 36r.
Step-by-step explanation:
I need help ASAP!! The answer is 76 degrees. I have no idea how they got the answer.
The required measure of arc BD is 76°.
A figure of a circle is shown,
Where mCB is 136° and subtended by points C and D at B is 74°.
The measure of the arc CD is given as,
= 2 * 74
= 148
Now, BD is given as,
mBD + mCD + mCB = 360
mBD + 148 + 136 = 360
mBD = 76
Thus, the required measure of arc BD is 76°.
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a factory manufacturing tennis balls determines that the probability that a single can of three balls will contain at least one defective ball is 0.025. what is the probability that a case of 48 cans will contain at least two cans with a defective ball?
There is about a 33.7% probability that a case of 48 cans will contain at least two cans with a defective ball.
To solve this problem, we can use the binomial distribution. Let's define "success" as getting a can with no defective ball and "failure" as getting a can with at least one defective ball.
The probability of success in one can is:
P(success) = 1 - P(failure) = 1 - 0.025 = 0.975
The probability of failure in one can is:
P(failure) = 0.025
Now, let's define X as the number of cans in a case of 48 that have at least one defective ball. We want to find the probability that X is greater than or equal to 2.
We can use the binomial distribution formula to calculate this probability:
P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)
P(X = 0) = (0.975)^48 ≈ 0.223
P(X = 1) = 48C1 (0.975)^47 (0.025)^1 ≈ 0.44
where 48C1 is the number of ways to choose one can out of 48.
Therefore, the probability that a case of 48 cans will contain at least two cans with a defective ball is:
P(X ≥ 2) ≈ 1 - 0.223 - 0.44 ≈ 0.337
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How many 1 1/2 -liter bottles of water does it take to fill a 16-liter jug?
The side length of the cube is 5 cm. Find the volume of the cube.
Answer:
125 cm³
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Volume of a Cube Formula: V = a³
a is a side lengthStep-by-step explanation:
Step 1: Define
Identify variables
a = 5 cm
Step 2: Find Volume
Substitute in variables [Volume of a Cube Formula]: V = (5 cm)³Evaluate exponents: V = 125 cm³Answer:
\(\huge\boxed{V=125cm^3}\)
Step-by-step explanation:
The formula of a volume of a cube with edge \(a\):
\(V=a^3\)
We have \(a=5cm\).
Therefore the volume is:
\(V=(5cm)^3=5cm\cdot5cm\cdot5cm=125cm^3\)
On Monday, Jayla raised $30 and Carlos raised $50.
After that, Jayla raised $12 per day and Carlos
raised $7 per day. After how many days will they
have raised the same amount?
They will raise the same amount after days.
Answer:
84 days
Step-by-step explanation:
You would use the LCM to solve this.
12 and 7 don't share any common factors other than 1,
so you would multiply 12 x 7, which gets you 84.
After 84 days they would have raised the same amount.
what feature(s) about a relationship can be observed from examining a scatterplot of two quantitative variables x and y?
By examining a scatterplot, you can gain valuable insights into the relationship between the two quantitative variables x and y, such as direction, strength, form, and outliers.
From examining a scatterplot of two quantitative variables x and y, you can observe the following features about the relationship between the variables:
1. Direction: You can determine whether the relationship between the variables is positive (both variables tend to increase or decrease together) or negative (one variable tends to increase while the other tends to decrease).
2. Strength: You can assess the strength of the relationship by observing how closely the data points are clustered around an imaginary line (e.g., a straight or curved line). A strong relationship has points closely clustered, while a weak relationship has points more scattered.
3. Form: You can identify the form of the relationship, such as linear (points form a straight line) or nonlinear (points form a curve).
4. Outliers: You can detect any outliers, which are data points that do not follow the general pattern of the relationship between the variables.
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Find a vector function r(t), that represents the curve of intersection of the two surfaces. the cylinder x2 y2=36 and the surface z=4xy
Given:
\(\begin{aligned}&x^2+y^2=16 \\&z=x y\end{aligned}\)
Express 16 as \(4^{2}\): \(x^2+y^2=16\)
\(x^2+y^2=4^2\\x^2+y^2=4^2 \times 1\)
Trignometry,
\(\cos ^2(t)+\sin ^2(t)=1\)
Now, substitute \(\cos ^2(t)+\sin ^2(t)\) for 1:
\(\begin{aligned}&x^2+y^2=4^2 \times 1 \\&x^2+y^2=4^2 \times\left[\cos ^2(t)+\sin ^2(t)\right]\end{aligned}\\x^2+y^2=4^2 \times \cos ^2(t)+4^2 \times \sin ^2(t)\)
Law of indicates:
\(\begin{aligned}&x^2+y^2=[4 \times \cos (t)]^2+[4 \times \sin (t)]^2 \\&x^2+y^2=[4 \cos (t)]^2+[4 \sin (t)]^2\end{aligned}\\x^2=[4 \cos (t)]^2 \text { and } y^2=[4 \sin (t)]^2\)
Taking positive square roots as follows:
\(x=4 \cos (t), y=4 \sin (t)\)
Recall that, z = xy.
Now, we have:
\(\begin{aligned}&z=4 \cos (t) \times 4 \sin (t) \\&z=16 \cos (t) \cdot \sin (t)\end{aligned}\)
Now, substitute the values:
\(r(t)=x_t i+y_t j+z_t k\)
So, the vector r(t) is: \(r(t)=(4 \cos (t)) i+(4 \sin (t)) i+(16 \cos (t) \cdot \sin (t)) i\)
Therefore, the vector function r(t) is written as: \(r(t)=x_t i+y_t j+z_t k\)
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Which point is an x-intercept of the quadratic function
f(x) = (x – 8)(x + 9)?
-------------------------------------------------------------------------------------------------------------
Answer: \(\textsf{(8, 0) and (-9, 0)}\)
-------------------------------------------------------------------------------------------------------------
Given: \(\textsf{f(x) = (x - 8)(x + 9)}\)
Find: \(\textsf{Determine the x-intecept}\)
Solution: In order to find the x-intercept we need to set the y-value to 0 which means that we are looking for the points that cross the x-axis. Then we just solve for x and we get the x-intercepts.
Set y to 0
\(\textsf{f(x) = (x - 8)(x + 9)}\)\(\textsf{0 = (x - 8)(x + 9)}\)Determine the first x-intercept
\(\textsf{x - 8 + 8 = 0 + 8}\)\(\textsf{x = 0 + 8}\)\(\textsf{x = 8}\)Determine the second x-intercept
\(\textsf{x + 9 - 9 = 0 - 9}\)\(\textsf{x = 0 - 9}\)\(\textsf{x = - 9}\)There are two x-intercepts of the quadratic function that was provided which are (8, 0) and (-9, 0).
A random sample of 150 teachers in an inner-city school district found that 72% of them had volunteered time to a local charitable cause within the past 12 months. What is the standard error of the sample proportion?
a. 0.037
B. 0.057
C. 0.069
D. 0.016
The given information is as follows:A random sample of 150 teachers in an inner-city school district found that 72% of them had volunteered time to a local charitable cause within the past 12 months.
The formula for calculating the standard error of sample proportion is given as:$$Standard\(\ error=\frac{\sqrt{pq}}{n}$$\)where:p = proportion of success in the sampleq = proportion of failure in the samplen = sample sizeGiven:Sample proportion, p = 72% or 0.72Sample size, n = 150
The proportion of failure in the sample can be calculated as:q = 1 - p= 1 - 0.72= 0.28Substituting the known values in the above formula, we get:\($$Standard \ error=\frac{\sqrt{pq}}{n}$$$$=\frac{\sqrt{0.72(0.28)}}{150}$$$$=0.0372$$\)Rounding off to the nearest thousandth, we get the standard error of sample proportion as 0.037
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Solve pls brainliest
Answer:
A, B, D, E
Step-by-step explanation:
2^4 / 2^5 = 2^-1 or 16/32 = 1/2
A. Option A is correct
B. Option B is also correct because 16/32 simplifies by 16 = 1/2, so option B is correct!
D. 2^-1 = 0.5, and we see that 16/32 = 1/2 = 0.5, so option D is correct!
E. 2^4 x 2^-5 = 2^-1, so this option is also correct!
If you can, please give me a Brainliest; thank you, and Happy New Year!
\(\huge\text{Hey there!}\)
\(\mathsf{\dfrac{2^4}{2^5}}\)
\(\mathsf{= \dfrac{2\times2\times2\times2}{2\times2\times2\times2\times2}}\)
\(\mathsf{= \dfrac{4\times4}{4\times4\times2}}\)
\(\mathsf{= \dfrac{16}{16\times2}}\)
\(\mathsf{= \dfrac{16}{32}}\)
\(\mathsf{= \dfrac{16\div16}{32\div16}}\)
\(\mathsf{= \dfrac{1}{2}}\)
\(\mathsf{= 2^{-1}}\)
\(\mathsf{=2^4\times2^{-5}}\)
\(\huge\text{Therefore, your answers should be:}\)
\(\huge\boxed{\mathsf{Option\ A.\ \dfrac{16}{32}}}\huge\checkmark\)
\(\huge\boxed{\mathsf{Option\ B. \ \dfrac{1}{2}}}\huge\checkmark\)
\(\huge\boxed{\mathsf{Option\ D. \ 2^{-1}}}}}\huge\checkmark\)
\(\huge\boxed{\mathsf{Option\ E. \ 2^4\times2^{-5}}}\huge\checkmark\)
\(\huge\text{Good luck on your assignment \& enjoy your day!}\)
If the following line is run in bash, what is the value of each parameter below?
$$
\$ \#
$$
$\$$
$\$ 0$
$$
\$ 2
$$
\($\$$\): Represents the process ID (PID) of the current shell. \($\$0$\): Refers to the name or path of the shell itself. \($\$2$\): Does not have a value as no command-line arguments are passed in the given line.
When the line "$\$$ \#" is run in Bash, the values of the parameters are as follows:
- $\$$: This parameter represents the process ID (PID) of the current shell. It is a unique identifier for the running shell process.
- $\$0$: This parameter represents the name or the path of the script or command that is being executed. In this case, since only the "$\$$ \#" line is run, $\$0$ would refer to the name or path of the shell itself.
- $\$2$: This parameter refers to the value of the second command-line argument passed to the script or command being executed. However, in the given line "$\$$ \#", there are no command-line arguments passed, so $\$2$ would not have any value.
To summarize:
- $\$$: Represents the process ID (PID) of the current shell.
- $\$0$: Refers to the name or path of the shell itself.
- $\$2$: Does not have a value as no command-line arguments are passed in the given line.
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the triangles below congruent! work out the value of z
Answer:
18
Step-by-step explanation:
if you rotate the shape and if the shapes are the same the answer is 18
20 points, I give out 20 points per question and I ask a lot of question
a binomial distribution has a 60% rate of success. there are 18 trials. what is the probablility that there will be at least 12 successes
The probability that there will be at least 12 successes in the total 18 trials with 60% rate of success is ¹⁸C₁₂(0.6)¹²(0.4)⁶+¹⁸C₁₃(0.6)¹³(0.4)⁵+¹⁸C₁₄(0.6)¹⁴(0.4)⁴+ ¹⁸C₁₅(0.6)¹⁵(0.4)³ +¹⁸C₁₆(0.6)¹⁶(0.4)²+ ¹⁸C₁₇(0.6)¹⁷(0.4)¹+ ¹⁸C₁₈(0.6)¹⁸(0.4)⁰
Binomial Probability distribution, In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments.
We have given that :
Rate of sucess (p) = 60% = 0.6
Rate of failure (q) = 1 - 0.6 = 0.4
Number of trials (n) = 18
We want to find P(there will be at least 12 sucess)
Use binomial distribution to find given mentioned probability.
X ~ Bin( 18, 0.6)
P (X= x ) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾
Let, X= Number of success among 18
So that it suitable for binomial distribution with parameters are n and p.
P(there will be atleast 12 success)
= P(X>= 12)
18
= ∑ ⁿCₓ (p)ˣ(q)⁽ⁿ⁻ˣ⁾ =
x = 12
¹⁸C₁₂(0.6)¹²(0.4)⁶+¹⁸C₁₃(0.6)¹³(0.4)⁵+¹⁸C₁₄(0.6)¹⁴(0.4)⁴+ ¹⁸C₁₅(0.6)¹⁵(0.4)³ +¹⁸C₁₆(0.6)¹⁶(0.4)²+ ¹⁸C₁₇(0.6)¹⁷(0.4)¹+ ¹⁸C₁₈(0.6)¹⁸(0.4)⁰
= say x
Hence, the required probability is x
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estimate the crowd at a parade where people are standing 8ft deep along one side of a 2 mile stretch road.use guide linr if one person per 2.5 square feet
The size of the crowd is 16,896 standing along a 1 mile section of a parade route that is 8 feet deep on both sides of the street.
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.
Given that the size of a crowd standing along a 1-mile section of the parade route that is 8 feet deep on both sides of the street assumes that each person occupies 2.5 square feet.
Since 1 mile is equal to 5280 feet thus,
⇒ 5280 × 8
⇒ 42,240
If one person per 2.5 square feet
Divide this by the amount of space a person occupies
⇒ 42240/2.5
⇒ 16,896
Hence, the size of the crowd is 16,896 standing along a 1-mile section of a parade route that is 8 feet deep on both sides of the street.
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PLEASEE HELP!!! PLEASE
Answer:
B D E
Step-by-step explanation:
Step-by-step explanation:
56 cuz it divides by both 7 and 8
Express
(
2
2
+
2
2
i
)
2
(
2
2
+
2
2
i)
2
in simplest
a
+
b
i
a+bi form.
Answer:
Step-by-step explanation:
Given that
a
= 9.9 cm and
b
= 3.2 cm, work out the perimeter of the triangle.
Give your answer rounded to 1 DP
Answer:
15.8
Step-by-step explanation:
First off, I think you mean area. You can't find the perimeter of a triangle with only two sides listed, neither can you find that side unless you have the perimeter.
1. Area of the triangle formula is axb/2= (9.9x3.2)/2, which when put in a calculator is 15.84.
2. Rounded to 1DP makes it 15.8