For the following exercise determine whether the graph shown represents a geometric sequence.
Answers
Answer:
Graph of a geometric sequence
equal changes in the input cause the output to be successively multiplied by a constant. cause the output to be successively multiplied by a constant (determined by the common ratio). Thus, geometric sequences always graph as points along the graph of an exponential function.
An example of a geometric sequence is given below as
A geometric sequence takes the function given in the formula below
[tex]a_n=ar^{n-1}[/tex]When n=1, An=-3
[tex]\begin{gathered} a_{n}=ar^{n-1} \\ -3=ar^{1-1} \\ -3=a \\ a=-3 \end{gathered}[/tex]When n=2 ,An=-1
[tex]\begin{gathered} a_{n}=ar^{n-1} \\ -1=-3r^{2-1} \\ -1=-3r \\ r=\frac{-1}{-3} \\ r=\frac{1}{3} \end{gathered}[/tex]When n=3,An =1
[tex]\begin{gathered} a_{n}=ar^{n-1} \\ 1=3r^{3-1} \\ \frac{1}{3}=r^2 \\ r^=\sqrt{\frac{1}{3}} \end{gathered}[/tex]We can see that they do not have a constant value of the common ratio (r)
Hence,
The graph DOES NOT represent a geometric sequence
Related Questions
2) The graph represents the cost of a medical treatment, in dollars, as a function of time, d, in decades since 1978.
It is said that the expression 150(1.8225) ଷrepresents the cost of medical treatment sometime after
1978.
a) Which year does it represent?
b) What would be the medical cost in 1998?
c) If this trend continues, what are the medical costs in 2022?
Answers
Since 1978, the graph shows the dollar cost of a medical procedure as a function of time, d. In 1993 year does it represent.
The cost of treatment when d = 1 is $273
Given that,
Since 1978, the graph shows the dollar cost of a medical procedure as a function of time, d.
We have to find in which year does it represent.
Let the equation be
y=150×[tex]e^{at}[/tex]
Where t is the time for year
According to the figure,
y pass (0.5,202.50)
We get,
202.5=150×[tex]e^{0.5a}[/tex]
[tex]e^{0.5a}[/tex]=1.35
Now,
150×(1.35)³=150×[tex](e^{0.5a})^{3}[/tex]
150×(1.35)³=150×[tex]e^{1.5a}[/tex]
1.5 is for 15 years.
1978+15=1993.
Therefore, in 1993 year does it represent.
The graph represents an exponential function:
[tex]$$y=a b^x$$[/tex]
When (x, y)=(0,150), the equation becomes
[tex]$$\begin{aligned}&150=a b^0 \\&a=150\end{aligned}$$[/tex]
When (x, y)=(0.5,202.5), the equation becomes [tex]$202.5=a b^{0.5}$[/tex]
Substitute 150 for a
[tex]$$202.5=150 b^{0.5}$$[/tex]
Divide both sides by 150
[tex]$$1.35=b^{0.5}$$[/tex]
Square both sides
b=1.82
So, the equation of the graph is:
y=150 * 1.82^x
When x=1, we have:
[tex]$$\begin{aligned}&y=150 * 1.82^1 \\&y=273\end{aligned}$$[/tex]
Hence, the cost of treatment when d=1 is [tex]$\$ 273$[/tex].
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Problem: Mickey Mouse has an account balance of $250 and is withdrawing $15 per
week. Minnie Mouse has $100 in her bank account and deposits $10 each week. At what
week will they have the same amount in their accounts? What will that amount be?
What are you trying to find out:
Workspace:
Solution:
Answers
If you’re depositing money to an account, you are adding more money. So, you’ll use addition.
What are you trying to find out: At what week will both Minnie And Mickey Mouse have an equal account balance? How much money will they both have in their account at that week?
So we can find the answer by using the equation, 250 - 15x = 100 + 10x where the variable x represents the amount of weeks.
Workspace:
You can either replace the x with multiple numbers until you get your answer or solve the problem a quicker way.
1. Move all terms containing x to the left
250 - 15x = 100 + 10x
Use inverse operations, so instead of + 10 you’ll - 10. You can only add, subtract, multiply, and divide alike terms.
250 - 15x - 10x = 100
250 - 25x = 100
2. Move all terms that do NOT contain x to the right
To do this you must do inverse operations, so - 250, remember that you can only preform operations on alike terms.
-25x = 100 - 250
-25x = - 150
3. Divide each term by -25
A variable next to a number means multiplication, and division is the opposite of multiplication.
-25x/-25 = -150/-25
Cancel out both -25s on the left but leave the x
x = -150/-25
x = 6
So, at week 6 both will have the same amount of money in their account. We still have to answer the second question, what will the amount be? But, all we have left to do is replace the x with 6, and figure out the rest, which should be easy.
250 - 15(6) = 100 + 10(6)
250 - 90 = 100 + 60
160 = 160
Solution: At week 6, both Mickey and Minnie Mouse will have an equal amount of money in their account, which would be $160.
rectangular paperboard measuring 28 long and 18 wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Answers
Perimeter that remains after the semicircle is removed = 377.77
How to find area of the paperboard ?
Length of paper board = 28
Width of paper board = 18
Now, the area of the board = 28 * 18 = 505
Radius of the semi circle = Half of the width of the paperboard = 9
Area of semicircle is = 1/2πr² = 127.23so the area of paperboard is 505 and semicircle is 127.23 .
TO find area of paper board after the cutting semi circle = 505 - 127.23
= 377.77
The remaining area of rectangle is 377.77
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I am SO confused. Are < and > the signs that have a closed dot on a number line, or do they have an open one? Please help!
Answers
The symbols '>' and '<' have an open dot when displayed on the number line.
Why do the prescribed symbols have an open dot and not a closed dot?
The '>' and '<' symbols have an open dot on the number line because the number that succeeds the symbol is not considered while plotting the range of values that would satisfy any given equation.
Moreover, if a closed dot is put in there, the whole solution becomes incorrect as an unwanted value gets included in the range of values of the domain of the given function.
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please help me and show work
Answers
Answer:
C
Step-by-step explanation:
find the gradient of the 2 points (2,6) &(-3,2)
y2-y1/x2-x1...use the gradient formula
-2-6/-3-2
=-8/-5
=8/5
therefore the line parallel to this line will have the same answer
Therefore C is correct
Answer this easy IXL question please
Answers
Answer:
∠C = 30°
Step-by-step explanation:
Trigonometry:[tex]\sf Tan \ \theta = \dfrac{opposite \ side}{adjacent \ side}[/tex]
[tex]\sf = \dfrac{5\sqrt{41}}{5\sqrt{123}}\\\\=\sqrt{\dfrac{41}{123}}\\\\=\sqrt{\dfrac{1}{3}}\\\\= \dfrac{1}{\sqrt{3}}[/tex]
[tex]\sf C =tan^{-1} \ \dfrac{1}{\sqrt{3}}[/tex]
= 30°
Melissa's average daily balance for the last month was $560. The finance charge was $8.12.
What was the monthly percentage rate? Round to the nearest hundredth of a percent.
Answers
Answer:
1.45%
Step-by-step explanation:
[tex] \frac{8.12}{560} (100) = .0145(100) = 1.45\%[/tex]
Write three numbers that are divisible by 2, 4, 8, and 10
Answers
Answer:
40, 80, 120
Step-by-step explanation:
-they’re common multiples of 2, 4, 8, and 10
The area of the triangle below is 60 in2. What is the perimeter?
Answers
Answer:
P = 63 inches
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 2x - 6 , h = 4 and A = 60 , then
[tex]\frac{1}{2}[/tex] × 4 ×(2x - 6) = 60
2(2x - 6) = 60 ( divide both sides by 2 )
2x - 6 = 30 ( add 6 to both sides )
2x = 36 ( divide both sides by 2 )
x = 18
2x - 6 = 2(18) - 6 = 36 - 6 = 30
perimeter (P) is the sum of the 3 sides , so
P = 18 + 30 + 15 = 63 inches
Find the monthly interest payment in the situation described below. Assume that the monthly interest rate is 1/12 of the annual interest rate. You maintain an average balance of $500 on your credit card, which carries an 18% annual interest rate. WHat is the monthly interest payment?
Answers
Using an average credit card amount of $500 and an annual percentage rate of 18%, the monthly interest payment is $7.5.
It is possible to calculate the monthly interest payment as follows:
I = [tex]\frac{PNR}{100}[/tex]
Given P = 500, N = 1, R = 18%
[tex]I = \frac{500*1*18}{100}[/tex]
[tex]I = \frac{9000}{100}[/tex]
[tex]I = 90[/tex]
Yearly Interest is $[tex]90[/tex]
Monthly interest :
[tex]M.I = \frac{18}{12}[/tex]
[tex]M.I = 1.5%[/tex]
Monthly interest payment = $[tex]500*1.5[/tex]= $[tex]7.5[/tex]
Monthly interest payment:
The percentage of the monthly payment earmarked for paying off the loan charge is referred to as the monthly interest payment.
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Solve for X please help I do not understand !
Answers
Answer:
x=45
Step-by-step explanation:
Which expression is equivalent to k4⋅m9⋅−(k5m4)0?
Answers
Answer: eighty-eight thousand
Step-by-step explanation:
The expression equivalent to [tex]k^4m^9 - (k^5m^4)[/tex] would be; [tex]k^{-1}m^5[/tex]
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.
To find equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.
We need find the expression into an equivalent form [tex]k^4m^9 - (k^5m^4)[/tex]
This expression could also be given by;
[tex]k^4m^9 - (k^5m^4)[/tex]
Now subtract the like terms to get the values then we get;
[tex]k^4m^9 - (k^5m^4)[/tex] = [tex]k^{-1}m^5[/tex]
Hence, the expression equivalent to form [tex]k^4m^9 - (k^5m^4)[/tex] would be; [tex]k^{-1}m^5[/tex]
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(-17.2 x 2.5) x 4 Write your answer as a decimal
Answers
Answer as a decimal is -172.
Given :
= (-17.2 x 2.5) x 4
= (-43) x 4
= -172
Therefore the answer as a decimal is -172.
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Find the area of a square tile which has a width of 3x - 5
Answers
Answer:
[tex]9x^2 - 30x + 25[/tex]
Step-by-step explanation:
To solve for area, multiply the width times the height. In this case, since the shape is a square, the width is the same as the height. So, multiplying 3x - 5 times 3x - 5 should give us the area.
[tex](3x-5)(3x-5)\\(3x)(3x) + (3x)(-5) + (-5)(3x) + (-5)(-5)\\9x^2 - 15x - 15x + 25\\9x^2 - 30x + 25[/tex]
If you don't understand the algebra there, use an area model, and please let me know if you're not sure how to do that. I'll help you out as much as I can! :)
List -2.7, -2.27, -2.3, -0.35 from least to greatest
Answers
A number with a whole number and a fractional component separated by a point is referred to as a decimal.
What is meant decimal places?A number with a whole number and a fractional component separated by a point is referred to as a decimal.
The word Decimus, which means tenth in Latin, is derived from the base word Decem, or 10. As a result, the decimal system, often known as a base-10 system, has 10 as its fundamental unit.
The tenth place is represented by the first digit following the decimal. The hundredth place is represented by the digit that follows the decimal. Up until there are no more digits, the remaining ones keep the place values filled in.
The accepted method for representing both integer and non-integer numbers is the decimal numeral system. It is the expansion of the Hindu-Arabic numeral system to non-integer values. There are various ways to represent numbers in the decimal system referred to as decimal notation.
Therefore, the correct answer is -2.7, -2.3, -2.27, -0.35.
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pls help me is due in 30 min
Answers
1540 / 2200 = 0.7
0.7 x 100 = 70%
Final answer - 70%
write 3/4 in lowest terms
Answers
Answer:
that is the lowest term I think
10. Higher Order Thinking Winston compares the heights of two plants
to see which plant grows more per day. The table shows the height
of Plant 1, in centimeters, over 5 days. The graph shows the height
of Plant 2, in centimeters, over 10 days. Winston says that since
Plant 1 grows 6 cm per day and Plant 2 grows 4 cm per day,
Plant 1 grows more per day.
Plant 1
Days
2
Height (cm) 6
a. Do you agree with Winston? Explain your response.
3 4 5
9 12 15
b. What error might Winston have made?
Answers
Answers to both subparts are shown:
Although Plant 2 clearly grew 2 cm per day as per the graph, Plant 1 still outgrew Plant 2 by 4 cm.Winston's claim that Plant 2 grows 4 cm per day is false, as shown by the graph, which contradicts Winston's claim, and Plant 2 actually grows 2 cm per day.What is a graph?The relationship between lines and points is described by a graph, which is a mathematical representation of a network. A graph is made up of some points and connecting lines. It doesn't matter how long the lines are or where the points are located. A node is a name for each element in a graph.So, (A) The given statement of Winston is partially correct.
In the graph, we can clearly see that Plant 2 grew 2 cm per day, but still, Plant 1 grows more than plant 2 by 4 cm.(B) Error in Winston's statement:
From the above part, we know that the error is Winston's statement that Plant 2 grows 2 cm per day, but according to the graph Plant, 2 grows by 2 cm per day.Therefore, answers to both subparts are shown:
Although Plant 2 clearly grew 2 cm per day as per the graph, Plant 1 still outgrew Plant 2 by 4 cm.Winston's claim that Plant 2 grows 4 cm per day is false, as shown by the graph, which contradicts Winston's claim, and Plant 2 actually grows 2 cm per day.Know more about graphs here:
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Please please please help, due in 10 minutes!!! Anyeny bought 3/4 pound of raspberries for $6. What is the cost of 1&1/4 pounds of raspberries?
Answers
Answer
The cost of 1 and (1/4) pounds of raspberries is $10.
Explanation
Anyeny bought (3/4) pounds of raspberries for $6.
What is the cost of 1 and (1/4) pounds of raspberries.
[tex]1\frac{1}{4}=\text{ }\frac{5}{4}[/tex]
(3/4) pounds = $6
(5/4) pounds = x dollars
Creatin a mathematical relation by cross multiplying
(3/4) × x = (5/4) × 6
[tex]\begin{gathered} \frac{3}{4}\times x=\frac{5}{4}\times6 \\ \frac{3x}{4}=\text{ }\frac{30}{4} \\ \text{Cross multiply} \\ 3x\times4=30\times4 \\ 12x=\text{ 120} \\ \text{Divide both sides by 12} \\ \frac{12x}{12}=\frac{120}{12} \\ x=10 \end{gathered}[/tex]Hence, the cost of 1 and (1/4) pounds of raspberries is $10.
Hope this Helps!!!
-13 = p/7
WILL MARK BRAINLIEST!!
Answers
Answer:
-91
Step-by-step explanation:
-13 x 7
a bicylist started riding at 8:00 am the digram below shows the distance the bicylist had traveled at diffrent times. what was the bicylist average rate of speed in miles per hour
Answers
there is no answer because there is no .Th in what ever you ate trying to talk abput
|x| + 4> 8 .............
Answers
Answer:
x>4, x<-4
Step-by-step explanation:
|x| + 4 > 8
|x| > 4
x>4, x<-4
Select the correct constant rate of change for each table of data.
Answers
The constant rate of change for the tables are:
First table: 10
Second table: 12.
Third table: 1/12.
Last table: 1/10.
How to Find the Constant Rate of Change of a Table?To find the constant rate of change (k) of a table of x and y variables, the formula that can be used is:
k = y/x.
Any pair of values, (x, y), from the given table can be used in finding the constant rate of change between the two given variables in each of the tables.
a. The constant rate of change of the first table = 110/11 = 70/7 = 30/3 = 10.
b. The constant rate of change of the second table = 108/9 = 12.
c. The constant rate of change of the third table = 10/120 = 1/12.
d. Constant rate of change for the last table = 10/100 = 1/10.
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A medical company tested a new drug for possible side effects. The table shows the relative frequency that a study participant experienced the side effect.
Does this data suggest an association between age and experiencing side effects?
Answers
Question
Divide.
16.85÷5
Answers
Answer:3.37
Here hope this helps
3. Solve the following equations.
a. 33.5 ÷ 10 = b. 412 ÷ 10 =
c. 73.6 ÷ 10 = d. 6,132 ÷ 10 =
4. Explain the placement of the decimal point when dividing by a power of 10.
Answers
The corresponding solutions of equations a, b, c and d are 3.35. 41.2, 7.36 and 613.2
How to solve an equation with powers of 10?a. 33.5 ÷ 10 = 3.35
b. 412 ÷ 10 = 41.2
c. 73.6 ÷ 10 = 73.6
d. 6,132 ÷ 10 = 613.2
When a number is divided by powers of 10, the decimal point moves to the left side by the number of places the power has e.g
345 ÷ 10 = 34.5 (It moves one place to the left because the power of 10 is 1 i.e. 10 = 10²)
3456 ÷ 100 = 34.56 (It moves two places to the left because the power of 100 is 2 i.e. 10 = 10²)
Therefore, the solution of a, b, c and d are 3.35. 41.2, 7.36 and 613.2 respectively.
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what is the slope.example answer:m=1
Answers
The slope of the given line 2 / 3
What is a slope ?Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation. The m is the slope of the line. And b is the b in the point that is the y-intercept (0, b). For example, for the equation y = 3x – 7, the slope is 3, and the y-intercept is (0, −7).
The given graph indicates that the two points are :
A( 3 , 0 ) and B (0 , -2 )
Thus the slope can be given by the formula mentioned below :
[tex]\frac{y_{2}- y_{1} }{x_{2}- x_{1} }[/tex]
this means - 2 - 0/ 0 - 3
= - 2/ -3
2 / 3
Thus the slope of the given line 2 /3
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can anybody tell me what 11.8 x 5 is step by step ?
Answers
Step-by-step explanation:
hope this helps!! the explanation is in my working. bring the "4" from the "40" (8 x 5) to the top of "1"
Answer:
59
Step-by-step explanation:
To mutlipy a decimal by a whole number, just multiply it like normal
118 x 5 = 590
11.8 has one decimal place so your answer will have one too
59.0 which is the same as 59
The length of the hypotenuse of a right triangle is 13cm. The length of one leg is 5cm. Find the length of the other leg.
Answers
5^2 = 25
x^2 + 25 = 169
169 - 25 = 144
Square root of 144 = 12
12cm
you have $1 and you are going to buy some pencils and 7 patties let X represent the number of pencils you can buy and let y represent the number of peppermint patties you can buy if pencils cause 0.10 each and Peppermint Patties cost 0.05 each write a linear equation in standard form that represents this situation what does the x intercept represent? what does the Y intercept represent
Answers
Let:
x = Number of pencils you can buy
y = Number of peppermint patties you can buy
a = cost of each pencil
b = cost of each peppermint patty
The standard form of a linear equation is given by:
[tex]\begin{gathered} Ax+By=C \\ \\ \end{gathered}[/tex]So:
[tex]0.1x+0.05y=1[/tex]The graph of this equation is:
The x-intercept represents the maximum number of pencils you can buy
The y-intercept represents the maximum number of peppermint patties you can buy
