What are the first five terms in the
recursive sequence defined by the
following?
Answers
The first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}
Recursive functionGiven the nth term of a recursive expression shown below
an =an-1 - 1.4
where
an-1 is the preceding term
a1 is the first term
an is the nth term
an-1 is
Given the following
a1 = 0
For the second term a2
a2 = 0 - 1.4
a2 = -1.4
For the third term a3
a3 = -1.4 - 1.4
a3 = -2.8
For the fourth term a4
a4 = -2.8 - 1.4
a4 = -4.2
For the fifth term a2
a5 = -4.2 - 1.4
a5 = -5.6
Hence the first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}
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Related Questions
Year: %Households:
1999 12.3
2000 18.2
2001 24.4
2002 25.7
2003 27.9
Estimate the instantaneous rate of change in percent of households that played games over the internet in the year 2000. Use the method of averaging a preceding and following interval AND the method of choosing a surrounding interval.
Answers
Based on the table showing the percentage of households playing games over the net, the average rate of change from 1999 to 2003 is 3.9% per year.
What is average rate of change?This can be found as:
= (27.9 - 12.3) / 4 years
= 3.9% per year
In 2000, the instantaneous rate of change would be:
= (Rate in 2001 - Rate in 1999) / difference in years
= (24.4 - 12.3) / (2001 - 1999)
= 6.05%
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Which graph shows the system
x²+y=2
x²+y²=9?
Answers
Annel sells a phone which costs $180 and earns $9 commission. If he sells $640 worth of phones the following days, how much will he earn in commission?
Answers
The percentage of the cost of the phones Annel earns in commission is 5%. If he sells $640 worth, the amount he earns as percentage will be $32.
How can the amount Annel earns be found?The amount in commission Annel earns when he sells the phone worth $180 = $9
The percentage of the amount sold, Annel earns as commission is therefore;
[tex] \frac{9}{180} \times 100 = 5\%[/tex]
The amount earned as commission if he sells $640 worth of phones is found as follows;
Amount earned = 5% × 640 = 32
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The length of each edge of a cube is decreased by $40\%$. By what percent does the volume of the cube decrease
Answers
what is the rule for the following sequence:
-1; -4; -9; -16; -25
Answers
Answer:
It´s an exponential rule. where one of the factors is negative
Step-by-step explanation:
1 * -1 = -1
2 * -2 = -4
3 * -3 = -9
4 * -4 = -16
5 * -5 = -25
The center of circle q has coordinates (-2, 1). if circle q passes through r (6, 7), what is the length of its diameter?
Answers
There are multiple strategies we can use to find the diameter of a circle. For this question, we must calculate the length of the radius first and multiply by 2 to find the diameter.
Solving the QuestionWe're given the centre and a point on the circumference: [tex](-2,1),(6,7)[/tex].
Find the distance between them using the distance equation:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Plug in the given points:
[tex]d=\sqrt{(-2-x_1)^2+(1-y_1)^2}\\d=\sqrt{(-2-6)^2+(1-7)^2}\\d=\sqrt{(-8)^2+(-6)^2}\\d=\sqrt{64+36}\\d=\sqrt{100}\\d=10[/tex]
Therefore, the radius of the circle is 10 units.
Multiply the radius by 2 to find the length of the diameter:
10 × 2
= 20
Therefore, the length of the diameter is 20 units.
Answer20 units
Hank runs a successful hot dog stand right across from the arch at the University of Georgia in downtown Athens. Hank has to order his hot dogs, buns, mustard, relish, and all other condiments in bulk, as well as pay taxes, licensing fees, and other small business expenses. Therefore, Hank has a relatively large “sunk” cost associated with his business – it averages out to $950 per week just to keep the cart open. The cost of producing hot dogs is given by C(h) = 950 + .45(h). Where h is the number of hot dogs and C(h) is the cost. If he sold 100 hotdogs at $10.25 each, how much profit would he make for the week?
Answers
The profit he would make in one week is $30.
What is Hank's profit?Profit is the total revenue less total cost.
Total revenue = price of one hot dog x number of hotdogs sold
$10.25 x 100 = $1025
Total cost = 950 +( 0.45 x 100)
950 + 45 = 995
Profit = 1025 - 995 = $30
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If the measure of angle ø is 3pie/4, which statements are true?
The measure of the reference angle is 45°.
cos (0) = √2
sin (0) = √2
The measure of the reference angle is 60°.
The measure of the reference angle is 30°.
tan (0) = 1
Answers
Find 3π/4 in degrees
(3(180))/43(45)135°Referance angle
π-3π/4180-13545° or π/4Option A
TanØ=sinØ/cosØ=√2/√2=1Answer:
The measure of the reference angle is 45°.
[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
Reference Angle: The smallest possible angle made by the terminal side of the given angle and the x-axis. The reference angle is always between 0° and 90° (0 and π/2 radians).
To convert radians to degrees, multiply by 180/π:
[tex]\implies \sf \theta=\dfrac{3\pi}{4} \cdot \dfrac{180}{\pi}=135^{\circ}[/tex]
Positive angles are drawn in a counterclockwise direction from the x-axis.
(See attached for diagram of the angle θ and its reference angle).
Angles on a straight line sum to 180°.
Therefore, to calculate the reference angle, subtract the measure of the angle from 180°:
[tex]\implies \sf Reference\:angle=180^{\circ}-135^{\circ}=45^{\circ}[/tex]
The angle 135° lies between 90° and 180° and so is in Quadrant II.
Therefore, the exact trigonometric ratios for 135° are:
[tex]\sin 135^{\circ}=\dfrac{1}{\sqrt{2}} \textsf{ or }\dfrac{\sqrt{2}}{2}\\\\ \textsf{(Since sine function is positive in the Quadrant II)}[/tex]
[tex]\cos 135^{\circ}=-\dfrac{1}{\sqrt{2}} \textsf{ or }-\dfrac{\sqrt{2}}{2}\\\\\textsf{(Since cosine function is negative in the Quadrant II)}[/tex]
[tex]\tan135^{\circ}=-1\\\\\textsf{(Since tangent function is negative in the Quadrant II)}[/tex]
Therefore, the true statements are:
The measure of the reference angle is 45°.
[tex]\sin(\theta)=\dfrac{\sqrt{2}}{2}[/tex]
David has kept track of his family’s grocery bills for the past 10 weeks, as shown in the table.
Week 1 2 3 4 5 6 7 8 9 10
Bill ($) 92 106 129 115 100 84 110 156 98 87
Would you choose to use a histogram, a circle graph, or a line graph to display the data? Explain your choice. Then make a display.
Answers
The data should be displayed using a line graph, as shown in the attached figure.
Definition of a Line Graph
In a line graph, also known as a line plot or a line chart, each data point is connected by its own line. A line graph displays numerical values across a chosen time span.
Why is a line graph the best choice in this situation?
A line graph would be the best option for showing the data for David's family's grocery spending over the previous 10 weeks because it would show us the trend in the data. This graph tells us of how we can recognize instances where there were significant expenses by analyzing the trend from the line graph.
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Six numbers from a list of nine integers are $7$, $8$, $3$, $5$, $9$, and $5$. What is the largest possible value of the median of all nine numbers in this list
Answers
8 is the largest possible value of the median of all nine numbers in this list.
Lets simplify it,
⇒ The given six numbers are 7,8,3,5,9 and 5.
⇒ Arrange the six numbers in order 3,5,5,7,8,9.
⇒ We have three more numbers to insert into the list, and the median will be the highest 5(and 5 lowest) number on the list. If the three numbers are greater than 9, the median will be the highest it can possible be.
∴ The median is the 5th item of data which is 8.
∴ Median=8
Hence 8 is the largest possible value of the median of all nine numbers in this list.
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find the volume of these rctangular prisms l=11.5cm w=2.5mm h=6cm
step by step pls
Answers
Answer:
172.5cm^3
Step-by-step explanation:
* = multiply or times
volume = length*width*height
Plug in the numbers: 11.5*2.5*6 = 172.5cm^3
what is the distance between the points (23,-33) and (4,9) if necessary round your answer to two decimal places
Answers
The distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
What is the distance between the points (23,-33) and (4,9)?The distance between two points on a graph can be determined using the equation;
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
Given that;
x₁ = 23x₂ = 4y₁ = -33y₂ = 9We substitute our values into the equation above.
D = √[ ( x₂ - x₁ )² + ( y₂ - y₁ )² ]
D = √[ ( 4 - 23 )² + ( 9 - (-33) )² ]
D = √[ ( -19 )² + ( 42 )² ]
D = √[ 361 + 1764 ]
D = √[ 2125 ]
D = 46.10
Therefore, the distance between the points (23,-33) and (4,9) rounded to two decimal places is 46.10.
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Total area=
Help me please thanks so much
Answers
Answer:
1954
Step-by-step explanation:
11*7*50
In a survey of 1002 people, 701 (which is 70%) said that they voted in the most recent presidentia l election (based on data from ICR Research Group). The margin of error for the survey was 3 percentage points. However, actual voting records show that only 61% of all eligible voters actually did vote. Does this necessarily imply
Answers
Based on the percentage of people who actually voted and the margin of error, the data implies that people lied when responding to the survey.
What is the evidence that people lied?The evidence that people lied about voting would bet be shown by the confidence interval. If the confidence interval of the survey does not have the actual percentage of people who voted in it, then people lied.
The confidence interval is:
= Average ± Margin of error
Solving:
= 70% + 3%
= 73%
= 70% - 3%
= 67%
Confidence interval is:
67% - 73%
The actual percentage of 61% who voted is not in this interval which means that some people lied about voting in the survey.
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A square has side lengths of 9, which of the following is a correct formula for finding the area of a square
Answers
Answer:
9 x 9 = 81
Step-by-step explanation:
area = width x height
Since it's a square, width = height
Explain or show how to determine if the following coordinates are a solution to the following system of linear inequalities. y<4x+8 y>x-6
Answers
The inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the inequalities y < 4x + 8 and y > x - 6, the solution to the inequalities is the darker region shown in the graph.
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Someone please help me
The top number is 18
Answers
Answer:
x = 24
Step-by-step explanation:
Since this is a right angle, we can use the Pythagorean Theorem to find x. In the formula, a^2 + b^2 = c^2, variables a and b represent the lengths of the legs, and variable c represents the length of the hypotenuse.
a^2 + b^2 = c^2
18^2 + x^2 = 30^2
324 + x^2 = 900
x^2 = 576
x = 24
A 2-column table with 6 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2. The second column is labeled f of x with entries 18, 3, 0, 3, 6, 3.
Using only the values given in the table for the function f(x) = –x3 + 4x + 3, what is the largest interval of x-values where the function is increasing?
(
,
)
Answers
The largest interval of x-values where the function is increasing is (-1, 1)
How to determine the largest increasing interval?The table of values is added as an attachment
From the table, the function f(x) decreases from x = -3 to x = -1 and x = 1 and x = 2
So, we make use of the intervals
x = -1, 0 and 1
From the table,
From x = -1 to 0, the change is 3
From x = 0 to 1, the change is 3
From x = -1 to 1, the change is 6
Using the above highlights, the largest increasing interval is (-1, 1)
Hence, the largest interval of x-values where the function is increasing is (-1, 1)
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A British pound cost $2.00 in U.S. dollars in 2008, but $1.27 in U.S. dollars in 2017. a)Was the pound weaker or stronger against the dollar
Answers
The pound was stronger in 2008 against the dollar than in 2017.
The Pound to greenback rate reached a high of $2.649 on the sixth Mar 1972. That remains the most powerful the Pound has been towards USD because it freely floated in 1971.
One might count on that the strongest economies might have the most powerful international currencies; but, that is not always the case. It turns out that lengthy-term movements in forex costs are extra essential than alternate quotes, that's why the British pound is worth extra than the U.S. dollar.
What topics is how the price of that forex adjustments over the years relative to different currencies. Historically, for over 20 years one U.S. dollar has been really worth less than one British pound. As of July 31, 2020, the greenback is sitting around 1.32 to at least one pound. 2 this is down from 1.68 in may additionally 2014 and 1. forty in March 2018.
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a data set has 8 numbers and 2 is the highest number what is the lowest?
Answers
The lowest number in the data set is -5.
How to illustrate the information?Let the data sets be consecutive numbers that has a highest number of 2.
Consecutive numbers mean that the.numvers follow each other. This will be:
-5, -6, -7, -8, -9, 0, 1, 2
Based on the numbers illustrated above, the lowest number is -5.
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You are deciding a social hall that will seat no more than 1600 people. You want at least 500 seats to be priced at $20 each, and at least 800 seats to be priced at $30 each. Those investing in the social hall would also like to bring in at least $2800 in revenue from the ticket sales. Let X represent the number of $20 seats, and let Y represent the number of $30 seats. Which system of inequalities represents this situation?
x ≥ 0
y ≥ 0
x + y ≥ 1600
20x + 30y ≤ 2800
x ≥ 500
y ≥ 800
x + y ≤ 1600
20x + 30y ≥ 2800
x ≥ 800
y ≥ 500
x + y ≤ 1600
20x + 30y ≤ 2800
x ≥ 500
y ≥ 800
x + y ≤ 1600
20x + 30y ≤ 2800
Answers
Answer: Option B
Just trust me that its right.
Mr. Mendez awards extra credit on quizzes to his students with quiz grades that exceed the class mean. Given that 107 students take the same quiz, what is the largest number of students who can be awarded extra credit
Answers
Answer:
106
Step-by-step explanation:
If 1 student gets a 1, and 106 get a 100, then the mean will be 99.99, and 106 students will get the extra credit.
Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6,-9)? OA X=-9 OB. Oc y=-9 D. y=-4
Answers
Hope it helps : )
Twenty-one is 25% of what number?
A. 5.25
B. 84
C. 10.5
D. 63
Answers
Answer: 84
Step-by-step explanation:
When substituting this question into an algebraic equation you can write it as:
21=.25x
(x clearly represents the number you are trying to find)
When you divide both sides by .25 to isolate x you get x=84
Two cans each hold 750ml by how many ml is their total volume less than 1.8 liters
Answers
If two cans hold 750ml ,then their voLume is 0.3 liters less than 1.8 liters.
Given volume of two cans being 750 ml each.
We are required to calculate the quantity in liters of how much the volume of two cans less than 1.8 liters.
Volume is the quantity of substance a container can hold in its capacity.
So volume of cone means quantity of liquid cone can hold if fully filled.
Volume of first cone=750 ml
Volume of second cone=750 ml
Total volume=750+750
=1500 ml
1 liter= 1000 ml
so 1500 ml will be equal to 1500/1000
=1.5 liter
We are required to do comparison with 1.8 liters.
Difference =1.8-1.5
=0.3 liters.
Hence two cans have 0.3 liters less than 1.8 liters.
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Find the product -2/9(-5/3) I-Ready math
Answers
The product of the given fractions, -2/9(-5/3), is: 10/27.
How to Find the Product of Two Fractions?Given the fractions, -2/9(-5/3), recall that minus multiplied by minus equals plus.
So therefore, the product of the two fractions would be a positive number. Thus:
-2/9(-5/3) = (-2 × -5)/(9 × 3)
-2/9(-5/3) = 10/27
Therefore, the product is: 10/27.
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. If sin(x + y)=sin x.cos y+cos x.sin y, then find the value of sin 75 degrees
Answers
Answer:
[tex]\sf \dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]
Step-by-step explanation:
Trigonometry:75 = 45 + 30
Sin (x + y) = Sin x *Cos y + Cos x * Sin y
Sin (45 + 30) = Sin 45 * Cos 30 + Cos 45 * Sin 30
[tex]\sf =\dfrac{1}{\sqrt{2}}*\dfrac{\sqrt{3}}{2}+\dfrac{1}{\sqrt{2}}* \dfrac{1}{2}\\\\\\=\dfrac{\sqrt{3}}{2\sqrt{2}}+\dfrac{1}{2\sqrt{2}}\\\\\\=\dfrac{\sqrt{3}*\sqrt{2}}{2*\sqrt{2}*\sqrt{2}}+\dfrac{1*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}\\\\\\=\dfrac{\sqrt{6}}{2*2}+\dfrac{\sqrt{2}}{2*2}\\\\\\=\dfrac{\sqrt{6}+\sqrt{2}}{4}[/tex]
HELP HELP HELP
HELP HELP HELP
HELP HELP HELP
(DIVISION) NO SYNTHETIC DIVISION NOR FACTORING
STEP BY STEP
Answers
Answer:
[tex]2x - 3 + \frac{1}{x-1}[/tex]
Step-by-step explanation:
Attachment :)
We use long division
suppose sin(A) = 1/4. use the trig identity sin^2(A)+cos^2(A)=1 to find cos(A) in quadrant II. around to ten-thousandth.
a. 0.1397
b. 0.4630
c. -0.8572
d. -0.9682
Answers
In quadrant II, [tex]\cos(A)[/tex] will be negative. So
[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = -\sqrt{1 - \sin^2(A)} = -\dfrac{\sqrt{15}}4 \approx \boxed{-0.9682}[/tex]
The requried, rounded to four decimal places, cos(A) is approximately -0.9682. The correct answer is option d. -0.9682.
To find cos(A) in quadrant II, we can use the given information and the trigonometric identity [tex]sin^2(A) + cos^2(A) = 1[/tex].
Given [tex]sin(A) = 1/4[/tex], we can find [tex]cos(A)[/tex] as follows:
[tex]sin^2(A) + cos^2(A) = 1[/tex]
[tex](1/4)^2 + cos^2(A) = 1[/tex]
[tex]1/16 + cos^2(A) = 1[/tex]
Now, let's solve for [tex]cos^2(A)[/tex]:
[tex]cos^2(A) = 1 - 1/16[/tex]
[tex]cos^2(A) = 16/16 - 1/16[/tex]
[tex]cos^2(A) = 15/16[/tex]
Next, find the value of [tex]cos(A)[/tex] by taking the square root:
[tex]cos(A) = \pm \sqrt{(15/16)[/tex]
Since we are in quadrant II, where cosine is negative, we take the negative value:
[tex]cos(A) \approx -\sqrt{(15/16)[/tex]
Now, calculate the approximate value of cos(A):
[tex]cos(A) \approx -0.9682[/tex]
Rounded to four decimal places, cos(A) is approximately -0.9682. The correct answer is option d. -0.9682.
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Mr. Omwoyo, the principal of Maili Mbili Secondary would wish to cover the floor of the new administration block using square tiles. The floor is a rectangle of sides 12.8m by 8.4m. Find the area of the largest tiles in cm² which can be used to fit exactly without cutting.
Answers
Answer:
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