True, Regardless of the testing point used we arrive at the same answer for the direction of a phase plane.
We were able to sketch the solution, y(t), in the y-t plane for the single differential equation case and observe actual solutions. Due to the fact that our answers are actually vectors, this would be fairly challenging in this situation.
Here, we're going to plot the points that we represent as the system's solutions as points in the x1x2 plane. Our equilibrium solution will line up with the x1x2 plane's origin, which is also known as the phase plane.
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Jennifer planted a tree that was 0.17 of a meter tall after 10 years the tree was 100 times as tall as when she planted it what is the height of it now
Answer:
Step-by-step explanation:
.17(100)=17
17 meters
Determine whether the Mean Value theorem can be applied to fon the closed interval [a, b]. (Select all that apply.) f(x) = 9 sin x, [0, 1] a. Yes, the Mean Value Theorem can be applied. b. No, f is not continuous on [a, b]. c. No, f is not differentiable on (a, b). d. None of the above.
According to the Mean value theorem conditions. The answer will be (a) that is Mean Value Theorem can be applied.
What is Mean Value Theorem?The Mean Value Theorem says that there exists a point c in the interval (a, b) such that f'(c) equals the function's average rate of change throughout [a , b] if a function f is continuous on the closed interval [a , b] and differentiable on the open interval (a , b).
Why is it called mean value theorem?The name derives from the fact that an average rate of change during an interval may be considered as an average (or mean) of the instantaneous rates of change along the interval thanks to the fundamental theorem of calculus.
[tex]f(x) = 9\sin x[/tex] is continuous on [0,1] since every value for [tex]9\sin x[/tex] exist in that interval.
[tex]f(x) = 9\sin x[/tex] is differentiable on (0,1) since at every point the derivative exist that is [tex]9 \cos x[/tex] is valid in that interval.
The answer is (a) that is Yes, The Mean Value Theorem can be applied.
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Graham graphs the following system of equations to determine its solution.
2x + 4y = 12
2x - y = 2
What is the correct solution?
Please explain step by step to get marked as brainliest!
Answer:
x=2 and y=2
Step-by-step explanation:
2x=12-4y
x=12-4y/2
x=6-2y
substitute equation on in two
2(6-2y)-y=2
12-4y-y=2
12-5y=2
5y=12-2
5y=10
y=10/5
y=2
substitute in the equation 6-2(2)=2
y=2 and x=2
Change the circle equation into standard form then answer the following questions:
of the center?
of the vertices?
Coordinates
Coordinates
How long is the radius?
Domain?
Range?
X²+ y²-14X + 8Y+ 40 = 0
hey can anyone help I pay?
Answer:
The Venn diagram below shows information
about the number of items in sets A and B.[asy]
label("A",(0,75));
label("B",(100,75));
label("C",(50,0));
label("D",(0,45));
label("E",(100,45));
draw(Circle((50,60), 40));
draw(Circle((50,30), 40));
draw(Circle((20,60), 20));
draw(Circle((80,60), 20));
[/asy]To find P(A'|B), we can use the formula:P(A'|B) = P(A' and B) / P(B)We can find P(A' and B) by looking at the Venn diagram. It is the number of items in the intersection of sets A' and B, which is represented by the region labeled "D" in the Venn diagram. This region contains 10 items.To find P(B), we can look at the Venn diagram and add up the number of items in both sets B and the intersection of A and B. This is represented by the regions labeled "D" and "E" in the Venn diagram, and contains a total of 20 items.Plugging these values into the formula above, we get:P(A'|B) = (10 items) / (20 items) = 1/2So, the probability that an item chosen at random belongs to A' given that it belongs to B is 1/2. This fraction is already in its simplest form.
Step-by-step explanation:
name the additive inverse of 5 + i
The additive inverse of 5 + i is (-5) + (-1)
what is additive Inverse?
To get a result equal to 0, add the original number and the additive inverse by simply changing the sign of the integer. On the basis of negation of the original number, the characteristics of additive inverse are listed below. For instance, if x is the starting number, then -x is x's additive inverse.
Given:
5 + I
As, the additive inverse is the opposite sign of the given number.
For example, if the number is -6 and we have to find its additive inverse.
So, the additive inverse will be 6.
Similarly for 5 + i ;
the additive inverse is (-5) + (-1)
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For any positive integer x, let x^R be the integer whose binary representation is the reverse of the binary representation of x. (Assume no leading 0s in the binary representation of x.) Define the function R^+: N rightarrow N where R+(x) = x + x^R. a. Let A_2 = { | R^+ (x) = y}. Show A_2 elementof L. b. Let A_3 = { | R^+ (R^+ (x) = y}. Show A_3 elementof L.
Define the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]
(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y} language A₂ ∈L.
(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y} language A₃ ∈L.
Given that,
For any positive integer x, let [tex]x^{R}[/tex] be the integer with the opposite of x's binary representation in terms of representation. (Assume that x's binary form has no leading 0s.) Specify the function [tex]R^{+}[/tex]: N ⇒ N where R+(x) = x + [tex]x^{R}[/tex]
(a) Let A₂ = {(x,y) | [tex]R^{+}[/tex] (x) = y}. Show A₂ ∈L.
(b) Let A₃ = {(x,y) | [tex]R^{+}[/tex] ([tex]R^{+}[/tex] (x)) = y}. Show A₃ ∈L.
We know that,
Consider the Turing machine M, which computes the inverse of x for every positive inter. The result will also be x if the computation is done using both the integer x and its inverse.
This is because the result of adding a binary number 1 to 0 is always 1. The criterion is that the binary representation of x must not contain 0. In this case, a positive integer x is converted into binary representation.
Only x values with a binary representation of 1 will be accepted by the Turing machine. Even the Turing machine will accept inverse-of-x values with binary representations of 0.
Therefore, It is proved that language A₃ ∈L.
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8. Jim hopes a park will be built within 5 miles of his
house. If a park is built at the coordinates (3, 7),
does that meet Jim's criteria? Explain.
No, he wanted a park developed within 5 miles of his residence, yet this park is 8.30 miles away.
What is coordinate?The horizontal and vertical distances from the two reference axes are used to define the location of a point on a coordinate plane. The x-value and y-value are often denoted as (x,y). To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate.
Here,
let the house be (0,0).
coordinate of park=(3,7)
distance=√3²+7²
=√21+49
=√69
=8.30 miles.
No, He wanted a park to be built within 5 miles of his house while this park is 8.30 miles from his house.
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Notice
-4x plus what results in 5x?
Answer: 9x
Step-by-step explanation:
-4x+y=5x
solve for x
y=9x
7. A five-person committee is to be selected from a group of 12 people. How many
different combinations are possible?
Answer: 792 Combinations
how can you prove that these two triangles are congruent?
suppose an analysis of variance (anova) has determined that there is a difference between means and the following tukey's results are shown. determine which mean is different.
the difference between Group B and Group C (-0.3) is less than the other differences, we can conclude that Group B and Group C are the means that are different.
The ANOVA test has determined that there is a difference between the means, and the Tukey's results can help to determine which mean is different. In this case, Group B (4.0) and Group C (4.3) are significantly different, meaning that one of those means is different from the other groups.
An ANOVA test has been conducted and it has been determined that there is a difference between the means. The Tukey's results can be used to identify which mean is different. In this case, Group B (4.0) and Group C (4.3) are significantly different, meaning that one of those means is different from the means of the other groups (A: 2.2 and D: 4.5). Therefore, Group B and Group C are the means that are different.
Tukey's Test
Group A vs B: 2.2 - 4.0 = -1.8
Group B vs C: 4.0 - 4.3 = -0.3
Group C vs D: 4.3 - 4.5 = -0.2
Since the difference between Group B and Group C (-0.3) is less than the other differences, we can conclude that Group B and Group C are the means that are different.
The complete question is :
suppose an analysis of variance (anova) has determined that there is a difference between means and the following tukey's results are shown. determine which mean is different.
Group A: 2.2
Group B: 4.0
Group C: 4.3
Group D: 4.5
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Milo worked for 5 hours on Monday and 4 hours on Tuesday. he earned $14 per hour. How much money did milo earn on both days combined? show
your work
Answer:
$126
Step-by-step explanation:
Monday: 5HR X $14 = $70
Tuesday: 4HR X $14 = $56
$70+$56=$126
Given f(x) = 3x - 5, find f(X - 2)
This question is about evaluating Functions.
Answers are
f(x- 2) = 3x - 7
f(x - 2) = x -7
f (x - 2) = 3x - 11
f(x - 2) = 3x² - 11x + 10
After evaluating f(x) = 3x - 5, the answer is f(x-2) = 3x - 11
What do you mean by functions?
A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). Expressions of well-known functions can be found in many frequently used mathematical formulas. A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X.
The set X is called the domain of the function and the set Y is called the codomain of the function.
Given function:
f(x) = 3x - 5
For f(x-2) substitute x as (x-2) in given function
f(x-2) = 3(x - 2) - 5 = 3x - 6 - 5 = 3x - 11
therefore, f(x-2) = 3x - 11
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if a is an nxn diagonalizable matrix then each vector in rn can be written as a linear cobination of eigenvectors of a
the given statement if a is an n x n diagonalizable matrix then each vector in R^n can be written as a linear combination of eigenvectors of a is false.
What is Diagonalizable matrix?
If there is an invertible matrix P and a diagonal matrix D such that
P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.
If and only if the algebraic multiplicity of each of A's eigenvalues is equal to the geometric multiplicity of each eigenvalue, then A is diagonalizable. The fact that the geometric sum of the eigenvalues of A is n is an equivalent description.
The given statement is false.
If A is diagonalizable, then A had n distinct eigenvalues. It could have repeated eigenvalues as long as the basis of each eigenspace is equal to the multiplicity of that eigenvalue.
Hence, the given statement is false.
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TRUE OR FALSE in html5, it is only possible to check a form for valid inputs (say within a given range) once the data has been submitted to the server.
The statement that servers that exist within a data center that is publicly accessible on the internet are referred to as on-premises servers is False.
HTML5
HTML5 is a markup language used for structuring and presenting content on the World Wide Web. It is the fifth and final major HTML version that is a World Wide Web Consortium recommendation. The current specification is known as the HTML Living Standard.
On-premises servers
On-premises servers refer to the group of servers that are under the control of a private entity. This is not like the traditional cloud computing method where resources can be leased to third-party service providers.
The use of the term, on-premises refers to the local installation of these resources as against the cloud type where the resource is on the vendor's server and a client can reach the software via their internet browsers.
Hypertext Markup Language revision 5 (HTML5) is markup language for the structure and presentation of World Wide Web contents. HTML5 supports the traditional HTML and XHTML-style syntax and other new features in its markup, New APIs, XHTML and error handling.
The statement that servers that exist within a data center that is publicly accessible on the internet are referred to as on-premises servers is False.
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You bought a car 3 years ago, taking out a $14,000.00 loan at a 5.8% interest rate for 4 years.
Your monthly payments are $327.51.
A. How much will still be owed after making payments for 3 years?
I will still owe ________
after making payments for 3 years.
B. If the car's value is now $7,500.00 then how much equity do you have after making payments for 3
years?
I will have ______ in equity after making payments for 3 years.
Enter the given values.
N: =
0
Number of Compounding Periods
1:%=
0
Annual Interest Rate as a Percent
PV: =
0
Present Value
PMT: = 0
Payment
FV: =
Future Value
P/Y:
Payments per Year
C/Y:
0
12 :
Solve
Solve
12 :
Compounding Periods per Year
PMT: = END Payments are made at the end of the period
Answer:
To answer these questions, we need to first calculate the total number of payments you have made over the past 3 years. We can do this by multiplying the number of payments per year (12) by the number of years (3). This gives us a total of 36 payments.
Next, we can use a financial calculator or spreadsheet program to solve for the remaining balance on your loan after making 36 payments of $327.51 each. In a financial calculator, we can enter the following values:
N: 36
I: 5.8
PV: -14000
PMT: 327.51
FV: 0
Solving for PV gives us a remaining balance of $4,819.56. Therefore, the answer to part A is $4,819.56.
To find your equity in the car, we can subtract the remaining balance on the loan from the value of the car. In this case, your equity would be $7,500.00 - $4,819.56 = $2,680.44. Therefore, the answer to part B is $2,680.44.
Step-by-step explanation:
Brainliest? :>
21. Which relation is a function?
A. (,0), (0, 1), (2, 2)}
B. {(-2,2), (-1, 1), (-2,4)}
C. {(-1,4), (0, 5), (0,4)}
D. {(2, 1), (4,3), (6,5)}
Answer:
The correct answer is D
Step-by-step explanation:
In order for a relation to be a function, every input for x can only have one output. Therefore, D is the correct answer.
Answer:
D
Step-by-step explanation:
A function is a relation where every input has only 1 output.
Inputs are the x's and outputs are the y's.
Answer a is missing an input. You have (,0) The first number is missing.
B is not a function because the input -2 has to outputs 2 and 4.
C is not a function because the input 0 has two outputs 5 and 4
the set of numbers that include all the positive and negative whole numbers and zero; there are integers that are not whole numbers.; is 0 a whole number; are all integers natural numbers; are whole numbers rational numbers; there are whole numbers that are not rational numbers.; the set of whole numbers and their opposites are called; classifying numbers
Absolute Value: The "unsigned" number that corresponds to the (Positive) distance between a number and zero on the number line. [tex]| - 4| = 4 and | 4| = 4;[/tex]
What are real numbers?Positive and negative integers, fractions, rational numbers, including irrational numbers, and negative integers are all examples of real numbers. fictitious numbers, Real numbers are those that fall between the two extremes,
Absolute Value: The "unsigned" number that corresponds to the (Positive) distance between a number and zero on the number line. | - 4| = 4 and | 4| = 4; The collection of positive numbers used to count items is known as the counting numbers, sometimes known as natural numbers. 1, 2, 3, 4, 5, ...; Fractions and decimals are not integers; rather, integers are the set of all whole numbers, along with their opposites (the positive whole numbers, the negative whole numbers, and zero). -3, -2, -1, 0, 1, 2, 3, ...; Irrational Numbers - The collection of all non-terminating, non-repeating decimal numbers; Natural Integers: The collection of positive numbers utilized in object counting (also called counting numbers). 1, 2, 3, 4, 5, ...; Unfavorable Numbers - the range of numbers on the number line that are less than zero and to the left of zero.; Number Line - a horizontal line with points representing different numbers. In a number line with just whole numbers or integers, the dots are uniformly spaced out according to the value of the number they represent.; Opposite - a number that is on the other side of zero and at the same distance from zero as a given integer. For instance, the opposites of 7 and -7 and 9 and 9 are both 7; positive figures - the group of numbers on the number line that are greater than zero and to the right of zero.
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20% of the school are seniors, 30% Juniors, 15% sophomores, and 35% freshman. What is the probability that if I select 10 people, I will get 2 seniors and 8 freshmen?
The probability that if I select 10 people, I will get 2 seniors and 8 freshmen is 0.00000901
How to determine the probability?From the question, we have the following parameters that can be used in our computation:
Seniors = 20%Juniors = 30%Sophomores = 15%Freshman = 35%Also from the question, we have
Number of people selected = 10
To get 2 seniors and 8 freshmen, the probability equation is
Probability = (Seniors)² * (Freshman)⁸
Substitute the known values in the above equation, so, we have the following representation
Probability = (20%)² * (35%)⁸
Evaluate
Probability = 0.0000090075
Approximate
Probability = 0.00000901
Hence, the probability is 0.00000901
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Find the volume of the garden shed
Answer:
47.3 m³
Step-by-step explanation:
The garden shed is made up of a rectangular prism and a pyramid.
Volume of a rectangular prism[tex]\begin{aligned}\textsf{Volume of a rectangular prism}&=\sf width \times length \times height\\&=4 \times 4 \times 2\\&=16 \times 2\\&=32\;\; \sf m^3\end{aligned}[/tex]
Volume of a pyramidFrom inspection of the given diagram, the slant height of the pyramid is 3.5 m.
Calculate the perpendicular height of the pyramid using Pythagoras Theorem:
[tex]\begin{aligned}\implies a^2+b^2&=c^2\\2^2+h^2&=3.5^2\\h^2&=8.25\\h&=\sqrt{8.25}\;\; \sf m\end{aligned}[/tex]
Therefore:
[tex]\begin{aligned}\textsf{Volume of a pyramid}&=\dfrac{\sf length \times width \times height}{3}\\\\&=\dfrac{\sf 4 \times 4 \times \sqrt{8.25}}{3}\\\\& = 15.31883372\;\; \sf m^3\end{aligned}[/tex]
Volume of the garden shed[tex]\begin{aligned}\implies \textsf{Volume of shed}&=\textsf{Volume of rectangular prism}+\textsf{Volume of pyramid}\\&=32+15.31883372\\& = 47.3\;\; \sf m^3\;(nearest\;tenth)\end{aligned}[/tex]
what’s 10.37304 rounded to the nearest hundredth?
Answer:
10.37
Step-by-step explanation:
3 in the thousandths place is lower than 5 therefore you have to turn the thousandths into a 0 and don't change the forenumber
If f(x) = - 3x ^ 2 + x - 9 and g(x) = x ^ 3 + 6x
what is (f + g)(- 4) ?
If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and the value of x is -4, the value of (f + g)(- 4) is -137.
What is function?A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are typically categorized into four categories. Depending on the Element: One function to one function, many functions to one function, onto function, one function to one and onto function, into function A "vertical line test" can be used to identify whether a relation is a function when looking at a graph. If a vertical line can be drawn anywhere on the graph and cross the relation twice, the relationship is not a function.
Here,
(f+g)(x)=f(x)+g(x)
f(-4)=-3*(-4)²-4-9
f(-4)=-61
g(-4)=(-4)³-3*4
g(-4)=-76
(f+g)(-4)=f(-4)+g(-4)
=-61-76
(f+g)(-4)=-137
If the supplied functions are f(x) = - 3x 2 + x - 9 and g(x) = x 3 + 6x and x is -4, the value of (f + g)(- 4) is -137.
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A cafeteria serves lemonade that is made from a powdered drink mix. There is a proportional relationship between the number of scoops of powdered drink mix and the amount of water needed to make it. For every 2 scoops of mix, one half gallon of water is needed, and for every 5 scoops of mix, one and one fourth gallons of water are needed.
Part A: Find the constant of proportionality. Show every step of your work.
Part B: Write an equation that represents the relationship. Show every step of your work.
Part C: Describe how you would graph the relationship. Use complete sentences.
Part D: How many gallons of water are needed for 12 scoops of drink mix?
Answer:
A. 1/4 gal/scoop
B. w = 1/4s
C. line through the origin with slope 1/4; s-, w- axes labeled "scoops" and "gallons"
D. 3 gallons
Step-by-step explanation:
Given 2 scoops of powdered drink mix needs 1/2 gallon of water, you want (A) the constant of proportionality, (B) the equation for the relationship, (C) a description of the graph, (D) gallons for 12 scoops.
Proportional relationshipA proportional relationship between gallons of water (w) and scoops of drink mix (s) can be written as ...
w = ks
where k is the constant of proportionality.
A Proportionality constantSolving the equation for k, we get ...
k = w/s
Using the given values, we find k to be ...
k = (1/2 gal)/(2 scoops) = 1/4 gal/scoop
The constant of proportionality is 1/4 gallon per scoop.
B EquationWe show the equation in part A. Filling in the value of k gives ...
w = 1/4s . . . . . . . where s is number of scoops, and w is gallons of water
C GraphThe attached shows a graph. A line starts at the origin with slope 1/4; s-, w- axes are labeled "scoops" and "gallons". The practical domain is s ≥ 0, so no part of the graph is in the 3rd quadrant.
D 12 scoopsThe equation tells you that 12 scoops will require ...
w = 1/4·12 = 3 . . . . gallons
3 gallons of water are needed for 12 scoops of drink mix.
<95141404393>
find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe−x2/32, [−2, 8]
The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
What is meant by absolute maximum and absolute minimum values?
A function's absolute maximum point is the point at which it can reach its highest value. A similar absolute minimum point is where the function's least possible value is obtained.
Given: [tex]f(x)=xe^{\frac{-x2}{32} }[/tex]
Differentiate the function,
[tex]f'(x)=e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }[/tex]
[tex]e^{\frac{-x^{2} }{32} } -\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=0[/tex]
[tex]\frac{x^{2} }{16} e^{\frac{-x^{2} }{32} }=e^{\frac{-x^{2} }{32} }[/tex]
[tex]\frac{x^{2} }{16} =1[/tex]
[tex]x^{2} =16[/tex]
[tex]x=[/tex] ±[tex]4[/tex]
The interval is given as: [-2,8]
This means that the value of x = -4, is out of the interval.
So, we have the following critical points:
x = (-2, 4, 8)
⇒ f(x) at x = -2
[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-(-2)^{2} }{32} }[/tex]
[tex]f(-2)=-2[/tex] × [tex]e^{\frac{-4}{32} }[/tex]
[tex]f(-2)=-1.765[/tex]
⇒ f(x) at x = 4
[tex]f(4)=4[/tex] × [tex]e^{\frac{-(4)^{2} }{32} }[/tex]
[tex]f(4)=4[/tex] × [tex]e^{\frac{-16}{32} }[/tex]
[tex]f(4)=2.426[/tex]
⇒ f(x) at x = 8
[tex]f(8)=8[/tex] × [tex]e^{\frac{-(8)^{2} }{32} }[/tex]
[tex]f(8)=8[/tex] × [tex]e^{\frac{-64}{32} }[/tex]
[tex]f(8)=1.083[/tex]
Hence, by comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
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sample of 16 students from a large university is taken. The average age in the sample was 22 years with a standard deviation of 6 years. Construct a 95% confidence interval for the average age of the population. Assume the population of student ages
The confidence interval for the average age of the population would be (18.8, 25.2).
What is the confidence interval?
In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter. A confidence interval is computed at a designated confidence level; the 95% confidence level is most common, but other levels, such as 90% or 99%, are sometimes used.
Given that,
Point estimate = sample mean = [tex]\bar x[/tex] =22
sample standard deviation = s = 6
sample size = n = 16
Degrees of freedom = df = n - 1 = 16 - 1 = 15
At 95% confidence level
[tex]\alpha[/tex] = 1 - 95%
[tex]\alpha[/tex] =1 - 0.95 =0.05
[tex]\alpha/2[/tex] = 0.025
[tex]t_{\alpha/2},df[/tex] = t 0.025 , 15 = 2.131
Margin of error = E = [tex]t\alpha/2,df * \frac{s}{\sqrt n}[/tex]
=2.131 * (6 / √16)
Margin of error = E = 3.20
The 95% confidence interval estimate of the population mean is,
= [tex]\bar x \pm E[/tex]
= 22 ± 3.20
= (18.8, 25.2)
Hence, the confidence interval for the average age of the population would be (18.8, 25.2).
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What does the number in the bottom right hand corner of a two-way frequency table represent?; What is a 2 way frequency table?; What are the important parts of a two-way frequency table?
The solutions for all three questions regarding two-way frequency tables are given below.
A two-way frequency table is a method used to visually represent two sets of categorical data. Unlike one-way frequency tables which have only one categorical variable, these have two. The important parts of a two-way frequency table are the topmost rows that have the name of the category. The leftmost column also has the categories listed. The middle columns and rows contain the data (frequency).
The number in the bottom right-hand corner of a two-way frequency is used to denote the total number of data points that are there in the data set given. This is also equal to the sum of the total rows/columns.
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Five subtracted from the product of 6 and a number is at most -25.
The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number be represented as A
Now , the value of A is calculated as
Five subtracted from the product of 6 and a number is at most -25
So , the inequality equation will be
And , substituting the values in the equation , we get
6A - 5 ≤ -25 be equation (1)
Now , adding 5 on both sides of the equation , we get
6A ≤ -25 + 5
6A ≤ -20
Divide by 6 on both sides of the equation , we get
A ≤ -3.33
Therefore , the value of A is -3.33
Hence ,
The value of the number from the equation 6A - 5 ≤ -25 is A = -3.33
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Which of the following are true concerning this diagram? You may assume that the lines are parallel.
The solution is
a) ∠1 ≅ ∠5 by Corresponding Angles
b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles
c) ∠6 ≅ ∠4 by Alternate Interior Angles
d) ∠2 ≅ ∠8 by Alternate Exterior Angles
What are Parallel Lines Cut by Transversal?
Straight, equally spaced lines that never cross each other and are on the same plane are called parallel lines. The angles that are created when any two parallel lines are intersected by a line (referred to as the transversal) have a relationship. Corresponding angles, Alternate Interior Angles, Alternate Exterior Angles, and Consecutive Interior Angles are some of the several pairs of angles that are created at this intersection.
Corresponding angles
When two parallel lines are intersected by a transversal, the corresponding angles have the same relative position
Alternate Interior Angles
Alternate interior angles are formed on the inside of two parallel lines which are intersected by a transversal.
Alternate Exterior Angles
The pairs of angles formed on either side of a transversal that divides two parallel lines are known as alternate exterior angles.
Consecutive Interior Angles
When two parallel lines are cut by a transversal, the pairs of angles formed on the inside of one side of the transversal are called consecutive interior angles or co-interior angles.
Given data ,
From the figure , we can see that
The Corresponding angles are
Angle 1 and Angle 5
Angle 2 and Angle 6
Angle 4 and Angle 8
Angle 3 and Angle 7
The Alternate Interior angles are
Angle 4 and Angle 6
Angle 3 and Angle 5
The Co-Interior angles are
Angle 4 and Angle 5
Angle 3 and Angle 6
The Alternate exterior angles are
Angle 1 and Angle 7
Angle 2 and Angle 8
Hence , the angles from the figure that are true are
a) ∠1 ≅ ∠5 by Corresponding Angles
b) m∠4 + m∠5 = 180° by Co-Interior Angles or same side Interior angles
c) ∠6 ≅ ∠4 by Alternate Interior Angles
d) ∠2 ≅ ∠8 by Alternate Exterior Angles
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Ticket sales for Six Flags White Water totaled $94,520 this summer. Tickets for the water park cost $17 each. How many tickets were sold?
Answer:
5,560
Step-by-step explanation:
Answer:
Step-by-step answer should
be 5560 because if you divide 94,520 by 17 you can use calculator and the answere should be 5,560
