The truth about the end behavior of the graph is
D. As the x-values go to negative infinity, the function's values go to positive infinity.What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of polynomial functionExamining the given graph it can be deduced that end behavior is described as
x ⇒ -∞ f(x) ⇒ ∞
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Answer:
Step-by-step explanation:
The truth about the end behavior of the graph is
D. As the x-values go to negative infinity, the function's values go to positive infinity.
I thought of a 2 digit number. It' a multiple of 9 and the um of it digit i 1/5 of the number itelf. What i my Number?
The 2-digit number that is a multiple of 9 and the sum of it digits is 1/5 of the number itself is 45.
Howto find the 2-digit number?A 2-digit number can be written as:
a*10 + b
Where a and b are single digit numbers.
We know that the number is a multiple of 9, and we also know that:
a + b = (1/5)*(a*10 + b)
We can isolate one of the variables:
a + b = 2a + (1/5)b
b - (1/5)b = 2a - a
(4/5)b = a
So, now we need to find values of b such that:
a is also a whole number.
10a + b is a multiple of 9.
if b = 5 we will get:
(4/5)*5 = a
4 = a
Then the number is 45, which is 5*9, so it is a multiple of 9.
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You and your sister are saving money from your allowances. You have $25 and save $3 each week. Your sister has $40 and saves $2 each week. After how many weeks will you and your sister have the same amount of money
The radius of a circle is 6 centimeters. What is the circle's area?
r=6 cm
Use 3.14 for .
Answer:
A =113.04 cm^2
Step-by-step explanation:
To find the area of a circle, we use the formula:
A = pi r^2
A = (3.14) ( 6)^2
A = 3.14 * 36
A =113.04 cm^2
Can someone PLEASE help me with this? I don’t understand. Show work.
Answers:
A: JPK
B: MPK
C: LPM
D: LPK
The angle that has the measure of 127 degree is angle MPK, and option 2 is the correct answer.
What are vertically opposite angles?The opposing angles created by the junction of two lines are known as vertical angles or vertically opposite angles. A pair of angles that are vertically opposed to one another are always equal. Additionally, a vertical angle and the angle to which it is adjacent are supplementary angles, meaning their sum is 180 degrees.
From the given figure we see that the angle LPJ = 127 degree.
Also, angle LPJ and angle MPK are vertically opposite angles. So, they are equal in measure.
Hence, the angle that has the measure of 127 degree is angle MPK, and option 2 is the correct answer.
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which foods would a nurse encourage for a client with a red blood cell count of 3.2 million cells/cm3? select all that apply.
A nurse would encourage the following foods for a client with a red blood cell count of 3.2 million cells/cm3:
Iron-rich foods (e.g. red meat, poultry, fish, beans, lentils, tofu)Vitamin C-rich foods (e.g. oranges, strawberries, bell peppers, broccoli)Iron is essential for the production of hemoglobin, which is responsible for carrying oxygen in the blood. Vitamin C aids in the absorption of iron from plant-based sources.
A diet high in these nutrients can help maintain or improve red blood cell count. In addition to iron and vitamin C, a balanced diet that includes plenty of fruits and vegetables, lean protein, and whole grains is recommended for overall health.
The nurse may also encourage hydration and physical activity as both are important factors in maintaining healthy blood cells.
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Volume of a rectangular prism calculator is ?
The volume of a rectangular prism is the product of length, width, and height. The length, width, and height are equal for a cube prism.
What is a rectangular prism?
Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom, and four are lateral faces). The prism's faces are all rectangular in shape. There are three sets of identical faces as a result. A rectangular prism is also referred to as a cuboid because of its shape.
The number of face of rectangular prism is 6.
The product of all dimensions of a prism is the volume of the rectangular prism.
Volume= length × width × height
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What is the geometric mean of 16 and 27
Answer:
The answer is 12
Step-by-step explanation:
What Is the Integral of Arctan x And What Are Its Applications?
Integration of tan inverse x yields the antiderivative of arctan, also referred to as the integral of arctan, which is denoted by
[tex]$\int \tan ^{-1} x d x=x \tan ^{-1} x-1 / 2 \ln \left|1+x^2\right|+C[/tex], when the integration constant C is used.
What is meant by Integral of Arctan? The fundamental arctan formula is = tan-1(Perpendicular/Base). The angle formed in this instance by a right-angled triangle's hypotenuse and base is denoted by. Tan x has an integral of ln|cos x| + C. Tan x has an integral of ln|cos x| + C. An angle in a right-angled triangle is tan using the tangent formula. When we know the side opposite to that angle and the adjacent side, we may apply the inverse tangent formula to get the angle. Arctan or tan^-1 are used to denote the inverse of Tangent.The inverse of the tangent function is called the arctangent. ln(|sec(y)|) ln (| sec (y) |) is the integral of tan(y) with regard to y.To learn more about Integral of Arctan, refer to:
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Ramin and Akbar Habil obtained a $98,000 mortgage loan at an annual interet rate of 6. 24%. The loan i for a period of 22 year, and the Habil will pay it in equal monthly payment that include interet. Find the (a) monthly payment , (b) amount paid, and (c) total interet charged
The monthly payment is 611.52, amount paid is 161,441.28 and total interest charges is 63,441.
Find the (a) monthly payment, (b) amount paid, and (c) total interest charged?Monthly payment, amount paid, and total interest charged are all terms related to loans, mortgages, or other forms of credit. Here's what each term means:
Monthly payment: This is the amount of money that you need to pay each month to repay a loan or mortgage over a specified period of time. The monthly payment typically includes both the principal amount (the amount of money borrowed) and the interest charged on that amount.
Amount paid: This is the total amount of money that you will have paid by the time the loan or mortgage is fully repaid. It includes the principal amount borrowed, as well as any interest and fees that are charged.
Total interest charged: This is the total amount of money that you will have paid in interest charges by the time the loan or mortgage is fully repaid. It is calculated by subtracting the principal amount borrowed from the total amount paid.
According to question:
a)98,000/1000×6.24=611.52
Therefore, monthly payment is 611.52.
b)611.52(12×22) =161,441.28
Therefore, amount paid is 161,441.28.
c)161441-98000=63,441
Therefore, total interest charges 63,441
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What is the probability of randomly drawing and immediately eating three red m&ms in a row from a bag that contains 7 red m&ms out of 25 m&ms total
The probability of randomly drawing and immediately eating three red M&Ms in a row from a bag that contains 7 red M&Ms out of 25 M&Ms total is 1/280.
This can be calculated by using the formula for probability, which is n/(N), where n is the number of desired outcomes and N is the total number of outcomes. In this case, n is equal to 7 (the number of red M&Ms) and N is equal to 25 (the total number of M&Ms). Therefore, the probability is 7/25, which simplifies to 1/280.In this case, the probability of drawing three red M&Ms in a row is 3 out of 25, or 3/25.
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2=From Sonnet XIX, by John Milton That murmur, soon replies, "God doth not need Either man’s work or his own gifts; who best Bear his mild yoke, they serve him best. His state Is kingly. Thousands at his bidding speed And post o’er land and ocean without rest: They also serve who only stand and wait. "
The mood of this sestet in Sonnet XIX by John Milton is hopeful.
This quote is from John Milton's Sonnet XIX and speaks about the idea that serving God does not necessarily mean doing physical work for him, but rather bearing his "mild yoke" with devotion.
The line "They also serve who only stand and wait" suggests that waiting for God's will with patience and humility is a form of service in itself. This sonnet explains how a devotee must be. The state of God is described as "kingly" and those who serve him well are said to speed at his bidding, without rest.
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The question for the answer is
That murmur, soon replies, “God doth not need
Either man’s work or his own gifts; who best
Bear his mild yoke, they serve him best. His state
Is kingly. Thousands at his bidding speed
And post o’er land and ocean without rest:
They also serve who only stand and wait.”
What is the mood of this sestet in Sonnet XIX by John Milton?
grim
hopeful
detached
somber
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the data set in ceosal2 contains information on chief executive officers for u.s. corporations. the variable salary is annual compensation, in thousands of dollars, and ceoten is prior number of years as company ceo. find the average salary and the average tenure in the sample. how many ceos are in their first year as ceo (that is, ceoten
After calculation, the average salary is 865.8644 thousands of dollars and average tenure is 7.955 years. Number of CEOs who are in their first year as CEO is equal to 5.
Here are the steps in R Studio to perform the tasks:
(a) Finding the average salary and the average tenure in the sample:
Load the CEOSAL2 data set in R Studio using the read.csv function.
ceos <- read.csv("CEOSAL2.csv")
Calculate the average salary using the mean function:
average_salary <- mean(ceos$salary)
Calculate the average tenure using the mean function:
average_tenure <- mean(ceos$ceoten)
(b) Finding the number of CEOs in their first year as CEO and the longest tenure as CEO:
Use the sum function and a logical test to count the number of CEOs in their first year as CEO:
first_year_ceos <- sum(ceos$ceoten == 0)
Use the max function to find the longest tenure as CEO:
longest_tenure <- max(ceos$ceoten)
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Ramp mut run 12 inche for every 5 inche of rie. What i the required angle of elevation rounded to the nearet 10th
The base of the ramp is 15 inches.
How do you calculate the height of a ramp?Because the ramp is the hypotenuse of a right-angled triangle, the height h, the length of the ramp r, and the angle A are all connected by the equation h = r sin A. Because r is 12 and A is 23, h = 12 sin(23) = 4.689 feet. That is around 4 foot, 8.25 inches.
Ramp runs must have a minimum clear width of 36 inches (measured between handrails where provided). The width of ramps used as a route of escape may also be influenced by applicable life safety rules and criteria for minimum exit widths greater than 36 inches.
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For the purposes of a marketing research, a survey of 1000 women is conducted in a town. The results show that 52 % liked watching comedies, 45% liked watching fantasy movies and 60% liked watching romantic movies. In addition, 25% liked watching comedy and fantasy both, 28% liked watching romantic and fantasy both and 30% liked watching comedy and romantic movies both. 6% liked watching none of these movie genres. Find The number of women who like watching at least two of the given genres
The number of women who like watching at least two of the given genres 1640 women.
Let's call the number of women who liked watching comedies C, the number who liked watching fantasy movies F, and the number who liked watching romantic movies R.
From the information given, we know:
C = 1000 * 52% = 520 women liked watching comedies
F = 1000 * 45% = 450 women liked watching fantasy movies
R = 1000 * 60% = 600 women liked watching romantic movies
We also know that:
25% of women liked watching both comedies and fantasy, so 0.25 * 1000 = 250 women.
28% of women liked watching both romantic and fantasy, so 0.28 * 1000 = 280 women.
30% of women liked watching both comedies and romantic, so 0.30 * 1000 = 300 women.
However, these numbers overlap because some women like all three genres, so we have to subtract the number of women who like all three genres from our total. We don't know the number of women who like all three genres, but we can calculate it by adding up the number of women who liked two genres and subtracting from the total number of women:
Number of women who liked all three genres = (C + F + R - (C & F) - (C & R) - (F & R) + (C & F & R)) = (520 + 450 + 600 - 250 - 300 - 280 + (C & F & R))
Since 6% of women liked watching none of these movie genres, we can subtract this from our total:
C & F & R = 1000 - 6% * 1000 = 940 women
So the number of women who like watching at least two of the given genres = (520 + 450 + 600 - 250 - 300 - 280 + 940) = 1640 women.
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Example
The product of 4 and (3 + x) is equal to 36. What is the value of x?
The equation 4(3 + x) = 36 models this statement.
Think: 4 times what number is 36?
Since 4.9 equals 36, that means (3 + x) equals 9.
Since 3 + x = 9, and 3 + 6 = 9, that means x equals 6.
The sum of twice a number, n, and 14 is 30. Write an equation that models this
statement. Then explain how you might use reasoning to find the value of n.
The equation that models the statement is: 2n + 14 = 30 and the solution is x = 8
How to determine the equation and the solutionFrom the question, we have the following parameters that can be used in our computation:
The sum of twice a number, n, and 14 is 30.
When represented as an equation, we have
2n + 14 = 30
Subtract 14 from both sides
2n = 16
So, we have
n = 8
Hence, the value of n is 8
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a particle moves along the x axis with position function x(t)=t^2-8t-1 on the interval
From t=0 to t=10, the particle moved 17 units in the negative direction.
What is a position function?
You may find out where an object is at a specific time by using the position function, often known as a position equation. For instance, the location function graph shown below illustrates where an automobile will be (in meters) in the first few seconds after starting: the car's position and operation.
Here, we have
Given: a particle moves along the x-axis with position function x(t)=t²-8t-1 on the interval [0,10].
x(t) = t²- 8t-1
Velocity = dx/dt = 2t - 8
v = 2t - 8
0 = 2t - 8
2t = 8
t = 4
x(4) = (4)²-8(4)-1
x(4) = 16 - 32 - 1
x(4) = -17
Hence, from t=0 to t=10, the particle moved 17 units in the negative direction.
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Barium metal was quantitatively precipitated from a 1.52 g sample of BaCl2∙2H2O. The mass of the barium that was collected was 0.844 g. Calculate the experimental mass percent of barium in the sample.
The experimental mass percent of barium in the sample is 55.526.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that the Barium metal was quantitatively precipitated from a 1.52 g sample of BaCl₂∙2H₂O.
The mass of the barium that was collected was 0.844 g.
We need to find the experimental mass percent of barium in the sample.
Let x/100 is the percentage of Barium.
x/100×1.52=0.844
0.0152x=0.844
x=55.526
Hence, the experimental mass percent of barium in the sample is 55.526.
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Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola at (1, 5), and the x-axis.
The area of the region bounded by the parabola is [tex]\frac {5}{12} $[/tex].
Area of the region bounded by y=f(x) and x axis between x=a and x=b is given by [tex]$\int_a^b f(x) d x$[/tex]. The coordinates of all the points mentioned are first calculated and then finally the area of required region OAC is calculated.
The area of the region bounded by the parabola y=[tex]5x^{2}[/tex].
The area that needs to be calculated is the area enclosed by OAC as shown in figure.
From the figure, it is clear that
Area of region OAC=area of region OAB-area of region ABC......(1) let us first calculate the equation of the tangent at(1,5).
⇒[tex]$\frac{d y}{d x}=10 x \Rightarrow \frac{d y}{d x}(1,5)=10$$[/tex]
Equation of tangent is y-5=10(x-1).
This tangent intercepts x axis at [tex]$x=\frac{-5}{10}+1=\frac{1}{2}$[/tex] (Putting y=0 in equation of tangent)
Hence, coordinates of C is (0.5,0) and B is (1,0).
⇒BC=OB−OC⇒BC=1−0.5=0.5
The area of region ABC is [tex]$\frac{1}{2} * B C * A B=\frac{1}{2} * 0.5 * 5=\frac{5}{4}$[/tex]
Now area of region OAB is given by [tex]$\int_0^1 5 x^2 d x \Rightarrow\left[\frac{5}{3} x^3\right]_0^1=\frac{5}{3}$[/tex]
Area of region OAB is thus [tex]$\frac{5}{3}$[/tex]
Now using equation (1) area of region OAC [tex]=\frac{5}{3}-\frac{5}{4}=\frac{5}{12}$[/tex]
The area of region OAC is [tex]\frac {5}{12} $[/tex].
Therefore, the area of the region is [tex]\frac {5}{12} $[/tex].
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Which of the four levels of measurement is most appropriate?
In the four levels of measurement : nominal, interval, ordinal, ratio: "ordinal," is most appropriate for the given for positions of the persons standing in a line
Explain the term levels of measurement?You may find out how accurately variables are recorded using levels of measurement, sometimes known as scales of measurement. A variable in scientific study is something that can have various values throughout your data collection (like height or test scores).Four degrees of measuring exist:
Nominal: The information is only classifiable.Ordinal: The information is classifiable and rankableIntervals: Data can be classified, rated, and spaced evenly between intervals.Ratio: The data is equally distributed, categorized, ranked, and contains a natural zero.Thus, in the four levels of measurement : nominal, interval, ordinal, ratio: "ordinal," is most appropriate.
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The complete question is-
determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for positions of persons in a line (extra?)
ind the work required to project a 4 oz object initially at rest to 170 ft/sec.
In other to get the height of the object after 4 seconds is to substitute 4 into the equation is h= 260 for the given velocity
given the equation:
h = -16t^2 + 129t
we are to find the height of the object after 4 seconds
in other to get the height of the object after 4 seconds is to substitute 4 into the equation.
that means we replace t by 4 in the equation
so,
h = - 16t^2 + 129t
substituting 4 into the equation
h = -16(4)^2 + 129(4)
h = - 16(16) + 516
h = -256 + 516
h =260
complete question
If an object is projected upward with an initial velocity of 129 ft per sec, its height h after t seconds is h = - 1662 + 129t. Find the heightof the object after 4 seconds.The height of the object after 4 seconds is(Simplify your answer.)ft.
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Part of a train timetable is shown.
Preston
Nuneaton
07 29
08 52
Milton Keynes 09 28
08 40
10 28
11 11
1221
1354
14 24
a) Llyr catches the 08 40 train from
Preston. He arrives in
Nuneaton 6 minutes late.
What time does he arrive in
Nuneaton?
1034
b) How long is Llyr's journey from
Preston to Nuneaton?
Give your answer in minutes.
c) Kathy catches the 07 29 train from Preston.
She arrives in Nuneaton on time.
She attends a job interview.
She gets back to Nuneaton station 1 hour and 50 minutes later.
Is she back in time to catch the 10 28 train to Milton Keynes?
You must show your working.
minute
The time that Llyr arrives at Nuneaton, given that it is 6 minutes late, is 10 34.
Llyr's journey from Preston to Nuneaton took 114 minutes.
Kathy would not catch the 10 28 train to Milton Keynes.
How to find the time ?Llyr is meant to arrive in Nuneaton at 10 28 but arrived 6 minutes later which is:
= 10 28 + 6
= 10 34
The time that the trip took is therefore:
= Arrival at Nuneaton - Departure at Llyr
= 10 34 - 08 40
= 1 hour 54 minutes
= 114 minutes
The time that Kathy would get back to the station is:
= Arrival time at Nuneaton + 1 hour 50 minutes
= 08 52 + 1 hour 50
= 10 42
This is too late for the 10 28 train to Milton Keynes.
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I need help finding this answer
The variable is x. Difference = (5 - 4) = 1. Product = 6(5 - 4) = 6. Constant = 5.3
What is variable?A variable in mathematics is an alphabet or phrase that stands in for an unknowable amount, unknowable value, or unknowable number. Particularly in the case of algebraic expressions or algebra, the variables are utilised. As an illustration, the linear equation x+9=4 has the variables x and 9 as constants.
According to the mathematical operation, the variable is a quantity that can change or is not fixed. Typically, in algebra, we use the terms "x" and "y" to express an unknown integer. However, this is not unique, and we are free to employ any alphabet.
The given expression is:
x + 6(5 - 4) + 5.3
The variable is x.
Difference = (5 - 4) = 1
Product = 6(5 - 4) = 6
Constant = 5.3
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Consider the population model DP/dt=0.3(1-P/200) (P/50-1) Pwhere P(t) is the population at time t.a)For what values of P is the population in equilibrium?b)For what values of P is the population increasing?c)For what values of P is the population decreasing?
For the population model DP/dt = 0.3(1-P/200)(P/50-1)P describes how the population changes over time based on the value of P.
a) The population is in equilibrium at P = 0 and P = 200,
b) increasing for values of P between 50 and 200, and
c) decreasing for values of P between 0 and 50 and values of P greater than 200.
The population model
=> DP/dt = 0.3(1-P/200)(P/50-1)P
is a mathematical expression that describes the change in population size over time.
In this model, P(t) represents the population at time t and the rate of change of the population, DP/dt, is a function of P.
The population is in equilibrium when the rate of change is zero, meaning the population is neither growing nor declining. To find the equilibrium population, we set DP/dt = 0 and solve for P. In this case, we have:
=> 0.3(1-P/200)(P/50-1)P = 0
Solving for P, we find two solutions: P = 0 and P = 200. These represent the minimum and maximum populations, respectively.
The population is increasing when the rate of change is positive, meaning the population is growing.
If DP/dt > 0, then the population is increasing, and if DP/dt < 0, then the population is decreasing.
In this case, we have:
=> DP/dt = 0.3(1-P/200)(P/50-1)P
To simplify, we can write:
=> DP/dt = 0.3(P/50-1)(P/200-1)P
=> (P/50-1)(P/200-1) > 0.
This occurs when 50 < P < 200.
Therefore, the population is increasing for values of P between 50 and 200.
The population is decreasing when the rate of change is negative, meaning the population is declining.
If DP/dt > 0, then the population is increasing, and if DP/dt < 0, then the population is decreasing.
In this case, we have:
DP/dt = 0.3(1-P/200)(P/50-1)P
To simplify, we can write:
DP/dt = 0.3(P/50-1)(P/200-1)P
Since the sign of P is positive, the sign of DP/dt is negative for all values of P where
=> (P/50-1)(P/200-1) < 0.
Therefore, the population is decreasing for values of P between 0 and 50 and values of P greater than 200.
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hurry please ! I need help on this !
Answer:104.27
Step-by-step explanation:
rectangle 13 x 5 semi circle 1/2(πx 5 to the second power)
65 39.27
he total number of scarves knitted varies directly with the number of days. Four scarves require 6 days to knit.
Write a direct variation equation to represent this relationship. Express the constant of variation as a decimal.
Answer:
s = 1.5d
where s = number of scarves knitted
d = number of days required to knit s scarves
Step-by-step explanation:
Let s represent the number of scarves knitted in 4 days
The direct variation relationship is s = kd where k = constant of proportionality
So k = s/d
For s = 6, d = 4
So k = 6/4 = 1.5
So the direct variation equation is s = 1.5d
Question 3 Consider the sequence {12,5, -2, -9,-16...) Select all the items that define the sequence (a) Sequence with ao = 12 and an = (-1 - 7 (b) Sequence with ag = 12 and an+1 = 12 – 70- (c) Sequence {an}8 and an = 12-772 (d) Sequence {anand Cha = 54 - 7n SI (b) Question 4 Select all the sequences below that are geometric (a) (2) (b) (210"} (c){2-1} (d) {n} e) {- 1} () {2-1.31-*} (a) (b) Od le) (F) Question 1 Select all items that describe the sequence below (256, 128, 64,32,...} Increasing Decreasing Bounded above O Bounded below O Geometric Question 2 Select all items that describe the sequence below {1, 4, 9, 16, 25,...} Increasing O Decreasing O Bounded above O Bounded below O Geometric Question 3 Which sequence has a faster growth rate? 200n Inn an bir 1 200 (a) 200nInn (b) br 1 200 nd (c) Both sequences have the growth rate (a) Ob O
The sequence {12,5, -2, -9,-16...) can be defined as a sequence with a0 = 12 and aₙ = 19 - 7n.
Also, the sequence {1, 4, 9, 16, 25,...} can be defined as increasing and unbounded.
A sequence is a list of numbers (or elements) that exhibits a particular pattern. For example, Olivia has been offered a job with a monthly salary of $1000 and an annual increment of $500. Can you calculate her monthly salary in the first three years? It will be $1000, $1500, and $2000. Observe that Olivia's salary over a number of years forms a sequence as they follow a pattern where the numbers increase by $500 every time. The order of a sequence can be either in ascending order or in descending order.
1] We are given a sequence: {12,5, -2, -9,-16...)
This sequence is an Arithmetic progression with the first term a = 12 and common difference d = -7.
2] The given sequence is {1, 4, 9, 16, 25,...}
The general term for this sequence is aₙ = n²
This sequence can be defined as increasing and unbounded.
Thus, the sequence {12,5, -2, -9,-16...) can be defined as a sequence with a0 = 12 and aₙ = 19 - 7n.
Also, the sequence {1, 4, 9, 16, 25,...} can be defined as increasing and unbounded.
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Which statement in the proof is not correctly supported?
Statement 3, because this statement is true only by the addition property of equality.
Statement 3, because the transitive property applies only to congruence and equality.
Statement 2, because the sum of the angles needs to be given as 180 to apply the linear pair theorem.
Statement 2, because the linear pair theorem only applies to angles that are complementary.
Question(0)1) The unique solution to the initial value problemy' + y = g(t), y(0)=y0is y(t) = 6e^(-4t) -4t -1 Determine the constant y0 and the function g(t)y0=g(t).
The constant y(t) = (y0-5)e^(-t) + 6e^(-4t) - 4t - 1; g(t) = (y0-4)e^(-t) + 6e^(-4t) - 4t; y0 = g(t).
What is algebra ?
Algebra is a branch of mathematics in which arithmetic operations and other formal manipulations are applied to abstract symbols rather than specific numbers.
Since y(t) = 6e^(-4t) - 4t - 1 is the general solution of the non-homogeneous equation y' + y = g(t), we can write it as:
y(t) = C1e^(-t) + 6e^(-4t) - 4t - 1
Setting t = 0 and using the initial condition y(0) = y0, we get:
y0 = C1 + 6 - 4 * 0 - 1
Solving for C1, we get:
C1 = y0 - 5
So, the general solution of the non-homogeneous equation is:
y(t) = (y0 - 5)e^(-t) + 6e^(-4t) - 4t - 1
Finally, the function g(t) can be found by comparing the general solution of the non-homogeneous equation with the right-hand side of the equation:
g(t) = (y0 - 5)e^(-t) + 6e^(-4t) - 4t - 1 + y = (y0 - 5 + 1)e^(-t) + 6e^(-4t) - 4t
Therefore, g(t) = (y0 - 4)e^(-t) + 6e^(-4t) - 4t.
So, the constant y(t) = (y0-5)e^(-t) + 6e^(-4t) - 4t - 1; g(t) = (y0-4)e^(-t) + 6e^(-4t) - 4t; y0 = g(t).
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the length of jk is 2x - 9 units. the length of rs is -4x 30 units. for what value of x are the segments congruent?
For the segments to be congruent, x should be 13/2.
This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.
Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.
So, to be congruent, JK and RS must be of equal length.
Or in other words, 2x-9 = 30-4x
or 6x= 30 + 9 =39
i.e. 6x = 39.
Dividing both sides by 3, we get
2x=13 , which implies , x =13/2 or 6.5
Thus, for JK and RS to be congruent , x =13/2.
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For the segments to be congruent, x should be 13/2.
This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.
Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.
So, to be congruent, JK and RS must be of equal length.
Or in other words, 2x-9 = 30-4x
or 6x= 30 + 9 =39
i.e. 6x = 39.
Dividing both sides by 3, we get
2x=13 , which implies , x =13/2 or 6.5
Thus, for JK and RS to be congruent , x =13/2.
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A company orders 10 boxed lunches from a deli for $130. Assume each boxed lunch is the same price. If c represents the total cost in dollars and cents of the lunch order for any number, b, of boxed lunches ordered, write a proportional equation for c in terms of b that matches the context.
A proportional equation for 'c' in terms of 'b' that matches the context
is c = 10b.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given, A company orders 10 boxed lunches from a deli for $130.
So, The cost of one box is (130/10) = $3.
Let, c represents the total cost in dollars and cents of the lunch order for any number b.
Therefore, the proportional equation is c = 10b.
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Answer:
Step-by-step explanation:
The answer is C=13b