a) for initial value 4 function oscillate between 4 and -2
b) for a initial value of 2 function oscillate between 2 and 0
c) for a initial value of 1 function value is constant = 1
What is a function?A function is a relationship between a set of inputs that each have one output. A function, in simple terms, is a relationship between inputs, with each input corresponding to exactly one output. Each function has a domain as well as a co-domain or range. The general notation for a function is f(x), where x is the input. A function is generally represented as y = f. (x).
In math, there are various types of functions. Among the most important types are:
Injective function: When there is a mapping for a range for each domain between two sets.Surjective functions, also known as Onto functions, are used when there are multiple elements mapped from domain to range.A polynomial function is a function made up of polynomials.Inverse Functions: A function that has the ability to invert another function.f(x) = 1/2.x + 1
f(4) = 1/2*4+1=3
f(4) = 1/2*3+1=2.5
f(4) = 1/2*2.5+1=2.25
f(4) = 1/2*2.25 + 1 = 2.125
f(4) = 1/2*2.125+1 = 2.0625
f(4) = 1/2*2.0625 + 1 = 2.0123
As the iteration increases function value converges to 2
You can write a simple MATLAB program to check it
matlab code:
clc;
clear all;
close all;
syms x;
f=-x+2;
y(1)=4;
g(1)=2;
h(1)=1;
for n=1:20
y(n+1)=subs(f,x,y(n));
g(n+1)=subs(f,x,g(n));
h(n+1)=subs(f,x,h(n));
end
t=[y',g',h'];
output :
t =
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
-2 0 1
4 2 1
a) for initial value 4 function oscillate between 4 and -2
b) for a initial value of 2 function oscillate between 2 and 0
c) for a initial value of 1 function value is constant = 1
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Derrick would like to explore his area. He estimates that his walking speed is 3.5 mph in the difficult terrain he has been given. If Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, how far can he explore and still make it back by sunset?
If Derrick leaves at around 12 pm, and the sun sets at 4:45 pm, the distance he can explore and still make it back by sunset is : 1.24 miles.
How to find the distance?In order to find how far Derrick can explore, we need to know how much time he has before sunset.
If the sun sets at 4:45 pm, and he leaves at 12 pm, we can find the amount of time he has by subtracting 12 pm from 4:45 pm.
4:45pm - 12:00pm
= 4:45pm
We can convert the hours and minutes to minutes only.
4 hours × 60 minutes/hour + 45 minutes
= 260 minutes
Since Derrick's walking speed is 3.5 mph, let convert this to minutes per mile by using the conversion factor 1 hour = 60 minutes.
Now let find the distance Derrick can travel
Distance = 260 minutes / 3.5 mph × 60 minutes/hour
Distance = 260 minutes / 210 minutes/mile
Distance = 1.24 miles
Therefore Derrick can explore 1.24 miles before sunset.
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You have 2 different savings accounts. For Account A, the simple interest earned after 18 months is $8.10. For Account B, the simple interest earned after 18 months is $16.50. If the interest rate is 3.6% for Account A and 2.2% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
The required principal in accounts A and B are $150 and $500 respectively, while the interest earned by account B is greater than the interest earned by account A.
What is simple interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan.
SI = Principal [rate×time]
Here,
For Account A,
SI = Principal [rate×time]
8.10 = P [0.036 × 18 / 12]
P = $150
Similarly
For Account B,
P = $500
Now,
for an account, A interest earned in the first month is given as,
SI = 150 × 0.036 × 1 / 12
SI = $0.45
Similarly,
for account B interest earned in the first month is given as,
SI = $0.92
Thus, the required principal in accounts A and B are $150 and $500 respectively, while the interest earned by account B is greater than the interest earned by account A.
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Researches are conducting a study to determine the effect of caffeine on memory among Americans. A sample of 100 individuals is given a list of 20 words to look at and remember over the course of 24 hours. Which of the following uses correct notation?
a. n = 100 b. N = 100 c. n = 20 d. N = 20
The correct notation for the sample size in this research study is "n = 100."
A sample is a portion of the population that is selected to represent the entire population.
In this study, the sample size of 100 individuals is a representation of the entire population of Americans, and the researchers are using this sample to gather information about the effect of caffeine on memory.
The notation "n" and "N" are commonly used in statistics to refer to sample size and population size, respectively. In this research study, the sample size is 100 individuals, so the correct notation is "n = 100."
In this case, the sample size of 100 individuals is considered a small to medium sample size.
Therefore, option (a) is correct.
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Triangle XYZ is a right triangle with ZQ¯¯¯¯¯⊥XY¯¯¯¯¯¯ . A right triangle with vertices labeled X, Y, and Z. Side Y Z is the base. Angle Z is marked as a right angle. Side X Y contains a midpoint labeled Q. A line segment is drawn through vertex Z to the point Q that bisects angle X Z Y into two parts. Angle X Q Z is marked as a right angle. Side Z X is labeled as a. Side Y Z is labeled as b. Side X Y is labeled as c. Segment X Q is labeled as f. Segment Q Y is labeled as e. Segment Q Z is labeled as d. Drag and drop a correct answer into each box to complete the proof of the Pythagorean theorem. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. By the angle-angle similarity postulate, △YXZ∼△YZQ and △YXZ∼△ZXQ. Since similar triangles have Response area sides, ac=fa and bc=eb . Solving the equation for a² and b² gives a2=cf and b2= Response area. Adding these together gives a2+b2=cf+ce. Factoring out the common segment gives a2+b2=c(f+e). Using Response area gives a2+b2=c(c), which simplifies to a2+b2=c2 .
The answers are proportional , ce, segment addition postulate if the Triangle XYZ is a right triangle with ZQ XY.
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
Given,
Triangle XYZ is a right triangle with ZQ XY.
proportional
ce
segment addition postulate
You want the words that finish the proof of the Pythagorean theorem.
Similar triangles
The proof makes use of the fact that the right triangles in the figure are all similar, and the fact that similar triangles have proportional sides.
The proportion b/c = e/b can be rearranged to b² = ce.
Then the segment addition theorem is invoked to let you use the fact that f+e = c.
Therefore, The answers are proportional , ce, segment addition postulate if the Triangle XYZ is a right triangle with ZQ XY.
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The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
The graph that shows the relationship would be C. graph of a line passing through the points negative 2 comma 4 and 0 comma 0
How to find the graph ?To find the graph, first find the slope of the line using the points from the table, ( - 1, 2 ) and ( 1, - 2).
The slope is:
= ( Y2 - Y1) / ( X 2 - X 1 )
= ( - 2 - 2 ) / ( 1 - ( - 1 ))
= - 2
This means that if a point on the graph has the x value of - 2, the y value would be:
= x - value x slope
= - 2 x - 2
= 4
The point would therefore be ( -2, 2 ) which makes option C correct.
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Task 4
misc. 7%
gifts &
entertainment
12%
clothes 5%
savings
10%
debt 5%
housing 30%
Spending Guidelines
(% of net incomes)
food 20%
transportation
11%
Lily makes a net annual income of
$52,500 and has saved enough
money for a 20% down payment on
a $230,000 house. She estimates her
mortgage will be $1,200 per month.
Can she afford this mortgage?
1: What is Lily's net monthly income?
2: How much is her down payment?
3: Not considering the down payment, is a
$1,200 monthly mortgage payment within
the Spending Guideline for housing?
According to the problem Lily's net monthly income is $4,375.
What is net monthly income?Net monthly income is the total amount of money an individual earns each month after deducting any taxes, insurance, or other expenses from the total gross income. It is the amount of money a person has available to pay bills, save, or use for other purposes. Net monthly income is often referred to as take-home income, since it is the money an individual actually has after taxes and other deductions.
1: Lily's net monthly income is $4,375.
2: Lily's down payment is $46,000 (20% of $230,000).
3: Yes, a $1,200 monthly mortgage payment is within Lily's Spending Guideline for housing. The guideline recommends spending no more than 30% of net income on housing. In this case, 30% of $4,375 is $1,312.50, so $1,200 is within the guideline.
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Using Mathematical operations, Her monthly income is 4375. As 1200 < 4375, she can manage monthly mortgage payment within the Spending Guideline for housing.
Arithmetic operations are the foundation of mathematics. Addition, subtraction, multiplication, and division are the fundamental operations that can be carried out on relations.
We hardly never go a day without using them. Every day, we perform mathematical operations to determine total revenue and expenses for businesses, make monthly or annual budgets, calculate distances, and more.
For instance, we use them to figure out how many questions there were altogether on our assignment, how much time and money we spent, how many chocolates we consumed, how many points we obtained overall for all of our subjects, etc.
Given,
Lily makes a net annual income of $52,500,
Her monthly income will be = 4375
20% down payment on a $230,000 house = 0.20 × 230000 = 46,000
Her down payment = 46,000
her mortgage will be $1,200 per month.
As 1200 < 4375, she can manage monthly mortgage payment within
the Spending Guideline for housing.
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Find STV
A. 39
B. 40
C. 45
D. 35
Answer:
D. 35°.
Step-by-step explanation:
1. additional building is performed and provided in the attachment;
2. m∠SUV=55/2x=27.5x;
3. m∠TUS=180-m∠SUV=180-27.5x;
4. m∠SUC=0.5(180°-95°)=42.5°, then m∠SUC=m∠CSU=42.5°;
5. m∠UST=90-m∠CSU=90-42.5=47.5°;
6. in ΔSTU: m∠UST+m∠TUS+m∠STU=180°, then
47.5°+180°-27.5x+10x+5°=180, ⇒ x=3;
7. finally, if x=3, then m∠STU=m∠STV=3*10+5=35°.
The following table gives wages and profits for a Robert's Manufacturing.
Year 1998 2000 2002 2004
Wages in Millions 4 6 8.7 14.7
% increase in wages 25 50 45 69
Profits in Millions 1 1.4 2.3 4.3
% increase in profits 20 40 64 87
The information given in the table is displayed in the two graphs below.
It is time for the boss, David, to complete the annual employee reviews. David wants to use the information above to show to the employees requesting a pay raise. Which graph should David use to limit the amount of pay raises?
A.
Either graph will do since they are based off of the same information.
B.
Based on the employee evaluations, everyone should get a raise this year.
C.
Graph (w)
D.
Graph (z)
Answer:
year 1998
Step-by-step explanation:
The table of values forms a quadratic function F(x)
The equation that represents f(x) is f(x) = x²-2x-8.
What is the equation that represents f(x)?This equation is a parabola in the form of y = ax² + bx + c, where a, b, and c are constants.The value of a is 1, b is -2, and c is -8.The domain of this equation is all real numbers and the range is all real numbers greater than or equal to -8.The parabola of this equation is a "U" shape that opens upwards.The vertex is located at (x,y) = (1, -8) and the axis of symmetry is the line x = 1.The y-intercept is -8, which can be seen in the table of values.As x increases, the parabola will move up, and as x decreases, the parabola will move down.The graph of this equation is symmetrical around the y-axis.The equation that represents f(x) is d. f(x) = x²-2x-8. This is a quadratic function, which is a type of polynomial equation with one variable (in this case, x). A quadratic equation is defined as an equation of the form ax² + bx + c = 0, where a, b, and c are constants and a is not equal to 0.To find the equation that represents f(x), we can use the values given in the table and solve for the constants a, b, and c. For example, when x = 0, f(x) = -8, so we can set -8 = c. When x = 1, f(x) = -2, so we can set -2 = -a + b. Finally, when x = 2, f(x) = 6, so we can set 6 = 4a - 2b.We can then use these three equations to solve for the constants a, b, and c, and find that a = 1, b = -2, and c = -8. This gives us the equation f(x) = x² - 2x - 8, which represents the given table of values.To learn more about quadratic function refer to:
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Match each system on the left with all words that describe the system on the right Choices on the right can be used more than onceinconsistentconsistent independent dependenty = 2x + 3 x+y = -3 3y = 9x – 62y - 6x = 4 y = - 1/2x + 2 x+ 2y = 4
By rewriting the 3 given systems, we will see that:
1) Independent and consistent.
2) Independent and inconsistent.
3) Dependent.
Let's analyze each system.
Let's look at the first one, we can rewrite it as:
y = 2x + 3
y = -x - 3
So, the slopes are different, meaning that we have one solution, so this system is consistent and independent.
Now let's look at the second system, we can rewrite it as:
y = 3x - 2
y = 3x + 2
Here both lines have the same slope, so the lines never do intersect, meaning that the system is inconsistent and independent.
For the final system, we have:
y = (-1/2)*x + 2
y = (-1/2)*x + 2
So, we have two equal lines, so this system is dependent.
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Any help please, thanks
The answer should be
B, The price of each cup of lemonade is $0.25, less at Florence's Lemonade Stand.
If I'm right Your Welcome, I'm glad I can help.
I'm just finishing the challenge answer 5 math questions.
So hope I helped. Your Welcome.
2. A colony of bacteria has an initial population of 5,000. After applying a test serum to the bacteria, the population decreases 7% each day. Which equation rep change in bacteria population?
If a colony of bacteria has an initial population of 5,000. After applying a test serum to the bacteria, the population decreases 7% each day. The equation that represent change in bacteria population is: P(t) = 5000(1-0.07)^t.
How to find the equation that represent change in population?The equation for the change in bacteria population over time can be represented as:
P(t) = P0(1-r)^t
Where:
P(t) = population at time t (in days)
P0 = initial population = 5,000
r = rate of change = -0.07 for a 7% decrease per day
t = number of days
So, the equation is:
P(t) = 5000(1-0.07)^t
Therefore the equation that represent change in bacteria population is: P(t) = 5000(1-0.07)^t.
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scouting troops in Sullivan County are putting on a crab feed to raise money for camp. They offer a complete crab dinner as well as a vegetarian option. One troop member sold tickets for 36 crab meals and 16 vegetarian meals, with total receipts of $1,632. Another sold tickets for 21 crab meals and 28 vegetarian meals, bringing in a total of $1,344. How much do the two types of tickets cost?
The two types of tickets cost $36 and $21.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Let x = cost of a crab meal
and, y = cost of a vegetarian meal
So, the system of equations
36x + 16y = 1632.......(1)
21x + 28y = 1344 ...........(2)
Solving equation (1) and (2) we get
36x + 16 ( 1344 - 21x) / 28 = 1632
36x + 768 - 12x = 1632
24x = 864
x= 36
and, y = 1344 - 21(36) / 28
y = 21
Hence, tickets cost are $36 and $21.
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Prove whether each argument is valid or invalid. First find the form of the argument by defining predicates and expressing the hypotheses and the conclusion using the predicates. If the argument is valid, then use the rules of inference to prove that the form is valid. If the argument is invalid, give values for the predicates you defined for a small domain that demonstrate the argument is invalid.
The domain for each problem is the set of students in a class.
(c)Every student who missed class got a detention.
Penelope is a student in the class.
Penelope got a detention.
Penelope missed class.
(e)Every student who missed class or got a detention did not get an A.
Penelope is a student in the class.
Penelope got an A.
Penelope did not get a detention.
(c) The argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) The argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
(c) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", and "D(x)" be the predicate "x got a detention".
Hypotheses: M(Penelope), D(Penelope)
Conclusion: M(Penelope)
Using modus ponens, which states that if P implies Q and P is true, then Q must be true, we can conclude that M(Penelope) is true:
From M(Penelope) and "Every student who missed class got a detention", we have D(Penelope)
From D(Penelope), we have M(Penelope)
So, the argument is valid, and we can conclude that Penelope missed class because she got a detention.
(e) To prove this argument's validity, we need to define the predicates and express the hypotheses and conclusion using them:
Let "M(x)" be the predicate "x missed class", "D(x)" be the predicate "x got a detention", and "A(x)" be the predicate "x got an A".
Hypotheses: A(Penelope), ~D(Penelope)
Conclusion: ~M(Penelope)
Using modus tollens, which states that if P implies Q and Q is false, then P must be false,
we can conclude that M(Penelope) is false:
From A(Penelope) and "Every student who missed class or got a detention did not get an A",
we have ~M(Penelope) & ~D(Penelope)
From ~D(Penelope), we have ~M(Penelope)
So, the argument is valid, and we can conclude that Penelope did not miss class because she got an A and did not get a detention.
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A study shows that 80% of the population of a city have brown eyes and 20% do not. The study also shows that 20% of the people who do not have brown eyes do not have brown hair, while 90% of the people who have brown eyes have brown hair. A relative frequency table was constructed for this data. What is the largest marginal relative frequency and its interpretation?
0.90; Individuals with brown hair
0.88; Individuals with brown hair
0.80; Individuals with brown eyes
0.72; Individuals with brown eyes
The largest marginal relative frequency and its interpretation is
0.80; Individuals with brown eyes.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.
Given, 80% of the population of a city have brown eyes and 20% do not,
let B for brown eyes and B' for nonbrown eyes
p(B) = 0.80
p(B') = 0.20
The study also shows that 20% of the people who do not have brown eyes do not have brown hair, while 90% of the people who have brown eyes have brown hair,
here H for brown hair and H' for non-brown hairs
p(H given B) = 0.90
p(H given B') = 0.20
using bays theorem for calculation,
p(H ∩ B) = p(H given B) x p(B)
p(H ∩ B) = 0.90 x 0.80
p(H ∩ B) = 0.72
p(H' ∩ B) = p(B) - p(H ∩ B)
p(H' ∩ B) = 080 - 0.72
p(H' ∩ B) = 0.08
p(H ∩ B') = p(H given B') x p(B')
p(H ∩ B') = 0.20 x 0.20
p(H ∩ B') = 0.04
p(H' ∩ B') = p(B') - p(H ∩ B')
p(H' ∩ B') = 0.20 - 0.40
p(H' ∩ B') = 0.16
Hair/eyes Brown other total
Brown 0.72 0.04 0.76
other 0.08 0.16 0.24
total 0.80 0.20 1
so 0.80 is the highest which is for brown eyes.
Hence option C is correct.
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Please help me with this question.
The solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.Given is the initial value problem -
y''' + 10y'' + 25y' = 0
We can write the -
[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]
The given differential equation can be solved and written as -
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)
Therefore, the solution of the given differential initial value problem is
y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).
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A local grocery delivery time has a uniform distribution over 0 to 60 minutes. What is the probability that the grocery delivery time is more than 15 minutes on a given day? Answer
The probability that the grocery delivery time is more than 15 minutes on a given day is P ( x > 15 ) = 0.75
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability that the grocery delivery time is more than 15 minutes on a given day be P
Now , the equation will be
The density function is f ( x ) = 1 / ( b - a )
And , the uniform distribution is over 0 to 60 minutes
So , a = 0
b = 60
Substituting the values in the equation , we get
f ( x ) = 1 / ( 60 - 0 )
f ( x ) = 1/60
f ( x ) = 0.01667
Now , the probability P = P ( x > 15 ) , where the termination point is 60 minutes
So , P ( x > 15 ) = ( 60 - 15 ) f ( x )
P ( x > 15 ) = 45 x 0.01667
P ( x > 15 ) = 0.75
Hence , the probability is 0.75
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Please help me with the following question.
The Probability that an incoming lot contain 36% of imperfect cloths will be acceptable is 0.00957
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1,
Given that Cappelli Inc. designs and manufactures women's apparel using material from various mills.
Their acceptance sampling plan states that 10 two inch squares of the incoming material must be carefully checked. If 3 or less squares reveal imperfections, the lot is accepted
Here no of defects in the 10 checked is Binomial because each trial is independent and there are only two outcomes.
X = no of defects is Bin (10, 0.36)
The probability that an incoming lot from Blufton Mills that contains 36 percent imperfect cloth will be accepted
P (X ≤ 3) = 0.00957.
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EASY POINTS!
The subtotal of items in your online shopping cart, before sales tax, is $210. After sales tax is applied, the total becomes $219.66. What is the sales tax percentage?
4.4%
95.4%
7.2%
4.6%
Answer:
4.6%
Step-by-step explanation:
Correct me if I'm wrong
219.66-210=9.66
210x4.6%=9.66
Answer: 4.6%
Step-by-step explanation:
I just took the test :)
Find BDC
A. 75
B. 79
C. 43
D. 41
Answer:
B. 79.
Step-by-step explanation:
1. to connect two points C and T with line;
2. m∠ACT=(63/2)° and m∠BTC=(95/2)°, then
3. in ΔCDT m∠CDT=180-(m∠ACT+m∠BTC)=101°;
4. finally, m∠BDC=180-101=79°.
for more details find the attachment.
In the equation y = 2x + 3 , what is the output if the input is 6?
Answer:
[tex]x=\frac{y-3}{2\\}[/tex]
Step-by-step explanation:
Swap sides so that all variable terms are on the left-hand side. Subtract 3 from both sides. Divide both sides by 2. Dividing by 2 undoes the multiplication by 2.
Select the correct answer. Which value is not part of the five-number summary needed for a box plot of this data? { 5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19} A. 1 B. 5 C. 9 D. 11
Answer:
Step-by-step explanation:nnbjnj
Answer:
Order the row {5, 6, 1, 27, 2, 7, 12, 15, 9, 18, 19} from the smallest number to the biggest number:
{1, 2, 5, 6, 7, 9, 12, 15, 18, 19, 27}.
The minimum is 1, the maximum is - 27.
The median is the middle number in this row - 9.
The median of left part {1, 2, 5, 6, 7} is 5 and the median of the right part {12, 15, 18, 19, 27} is 18.
From the option A-D only number 11 is absent (numbers 1, 5 and 9 are part of the five-number summary).
Answer: correct choice is D.
Step-by-step explanation:
Question 1(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A gymnast joined a yoga studio to improve his flexibility and balance. He pays a monthly fee and a fee per class he attends. The equation y = 10 + 20x represents the amount the gymnast pays for his membership to the yoga studio per month for a certain number of classes.
Which graph represents this situation?
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 20 through the point 1 comma 10
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point 1 comma 30
graph with the x axis labeled number of classes and the y axis labeled monthly amount in dollars and a line going from the point 0 comma 10 through the point one half comma zero
Question 2(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
Question 3(Multiple Choice Worth 2 points)
(Graphing Linear Equations LC)
The table represents a linear relationship.
x −1 0 1 2
y 2 0 −2 −4
Which of the following graphs shows this relationship?
graph of a line passing through the points negative 2 comma negative 4 and 0 comma 0
graph of a line passing through the points negative 2 comma negative 1 and 0 comma 0
graph of a line passing through the points negative 2 comma 4 and 0 comma 0
graph of a line passing through the points negative 2 comma 1 and 0 comma 0
Question 4(Multiple Choice Worth 2 points)
(Graphing Linear Equations LC)
Which of the following graphs has a slope of negative three halves and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1
Question 5(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
A middle school club is planning a homecoming dance to raise money for the school. Decorations for the dance cost $100, and the club is charging $10 per student that attends.
Which graph describes the relationship between the amount of money raised and the number of students who attend the dance?
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma negative 100 through the point 2 comma negative 120
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 80
graph with the x axis labeled number of students and the y axis labeled amount of money raised and a line going from the point 0 comma 100 through the point 2 comma 120
Question 6(Multiple Choice Worth 2 points)
(Graphing Linear Equations MC)
Which graph represents the equation y equals one half times x minus 1?
graph of a line passing through the points negative 2 comma negative 2 and 0 comma negative 1
graph of a line passing through the points negative 2 comma 0 and 0 comma 1
graph of a line passing through the points negative 2 comma negative 3 and 0 comma negative 2
graph of a line passing through the points negative 4 comma 0 and 0 comma 2
Step-by-step explanation:
and a line going from the point 0 comma 100 )
Which graph represents the equation
graph of a line passing through the points negative
Using the slope from the previous problem, find the equation of the line passing through the points (-2,1) and (2,-11) the previous is -3
The equation of the line passing through the points (-2,1) and (2,-11) the previous is -3 is -3x - 4.
What do you mean by slope?It is also commonly represented by the variable "m" in the equation of a line: y = mx + b. A positive slope indicates that the line rises as x increases, a negative slope indicates that the line falls as x increases, and a slope of zero indicates that the line is horizontal.
The equation of the line with slope -3 and passing through the point (-2,1) can be found using point-slope form of a line:
y - 1 = -3 (x + 2)
y = -3x - 5 + 1
y = -3x - 4
The equation of the line passing through the points (-2,1) and (2,-11) is y = -3x - 4.
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What is (f - g)(x)?
f(x) = 5x + 5
g(x) = x² + 9x
The evaluation of (f - g)(x) of the functions gives -x² - 4x + 5
How to evaluate (f - g)(x) of the function?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
We have the functions, f(x) = 5x + 5 and g(x) = x² + 9x.
In order to find (f - g)(x), we will subtract g(x) = x² + 9x from f(x) = 5x + 5. That is:
(f - g)(x) = (5x + 5) - (x² + 9x)
(f - g)(x) = 5x + 5 - x² - 9x
(f - g)(x) = -x² - 4x + 5
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Housing prices in a small town are normally distributed with a mean of $174,000 and a standard deviation of $9,000. Use the empirical rule to complete the following statement. Approximately 95% of housing prices are between a low price of Ex: 5000 and a high price of $ SA
Ally is planning on saving money for a new computer. She currently has $100 in her bank account. She plans on saving an additional $25 each month. a.) Write a linear equation to model how much Ally saves for a computer each month. b.) What will her savings be after 6 months? c.) Ally decides that she will need $1200 to purchase the computer she wants. How many months will it take her to reach this goal?
The linear equation that models how much Ally saves for a computer each month is y = 25x + 100, where x is the number of months that have passed, and y is the total amount saved. After 6 months, her savings will be $250. It will take her 44 months to have $1200 to purchase the computer.
An equation is a mathematical statement that shows that two expressions are equal. Equations use an equals sign (=) to show that the values of the expressions on either side of the sign are equal. It can include variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division
Let x = the number of months
y = total amount she saves
If she currently has $100 in her bank account and she plans on saving an additional $25 each month, then the linear equation to model how much she saves is:
y = $25x + $100
y = 25x + 100
After 6 months, the equation becomes:
y = 25(6) + 100 = 150 + 100 = $250
So after 6 months, Ally will have saved $250.
To find the number of months it will take to reach the goal of $1200, we can rearrange the equation and solve for x:
$1200 = 25x + 100
$1100 = 25x
x = 44
It will take 44 months, or approximately 3 years and 8 months, for Ally to reach her savings goal of $1200.
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The diagonals of rectangle QRST intersect at P. Given that
m/PTS= 34° and
QS=10, find mSRT.
Note that since the diagonals of rectangle QRST intersect at P and m∠PTS = 34°, thus, m∠SRT is 56°.
What are the properties of a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. Rectangles have the following fundamental properties: A rectangle is a quadrilateral.
The two opposite sides are parallel and equal.Each inside angle measures 90 degrees.The total of all internal angles is 360 degrees.The diagonals cut each other in half.The diagonals are both the same length.With regard to the above problem:
Since ∠QRS = 90° (based on the qualities of a rectangle) ; and
∠QRT ≅ ∠RTS = 34° (based on the rule of alternate angles,
Thus, m∠SRT = 90° - 34°
∠SRT = 56°
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Full Question:
The diagonals of the rectangle QRST intersect at P. Given that
m∠PTS= 34° and QS=10, find m∠SRT.
See attached image.
[tex]\int tanx dx\\[/tex]
The value of the integrand is -ln | cos(x) | + C
How to evaluate the integrandFrom the question, we have the following parameters that can be used in our computation:
Integral of tan(x) w.r.t x
The antiderivative (indefinite integral) of the tangent function, tan(x), with respect to x cannot be expressed in terms of elementary functions
However, it can be expressed in terms of special functions, such as the hyperbolic tangent and the dilogarithm.
One possible representation of the antiderivative of tan(x) is:
∫tan(x) dx = -ln | cos(x) | + C
where C is an arbitrary constant of integration.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
Answer:
Step-by-step explanation:
The two correct representations of the inequality -3(2x - 5) < 5(2 - x) are:
-6x + 15 < 10 - 5x
6x - 15 > 5x - 10
