Using the same pictorial sequence from Growing Dots 1 and Growing Dots 2, but a different beginning point, describe the pattern you see. Assuming the sequence continues in the same way, how many dots are there at 100minutes? Create a table and graph. Write an equation for the number of
dots at tminutes.
Answers
In total there will be 397 dots after 100 minutes.
What do you mean by airthmetic sequences?
Arithmetic sequences are sequences of the form:
a, a+d, a+2d, a+3d, a+4d, …
a is the first term and d is the common difference
series. The n terms of the arithmetic progression are given by
[tex]a_{n}[/tex] = a + (n - 1)d
The number d is called the common difference
Arithmetic progressions differ by d and any terms [tex]a_{n}[/tex] and [tex]a_{n-1}[/tex]
d = [tex]a_{n}-a_{n-1}[/tex] -
According to the given pattern, in the first figure, number of dots is 1 , in the second figure, number of dots become 5 , similarly in the next the count is 9 and 14
So, the sequence become
1,5,9,14......
here first term , a = 1
common difference , d = 5-1 = 4
We need to find the number of dots after 100 minutes
So, here n = 100
We need to find [tex]a_{100}[/tex]
[tex]a_{100}[/tex] = a + (100 - 1) d = 1 + 99(4) = 1 + 396 = 397
Therefore, in total there will be 397 dots after 100 minutes.
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Related Questions
7/2a+4/2a^2 as a fraction
Answers
Answer:
1/2a (4a+7)
Step-by-step explanation:
First You Divide:7/2a+ 2a^2
Rearrange Terms: 2a^2+ 7/2a
Find the Common Factor: 1/2(4a^2+7a)
Rewrite in the Fraction Form: 1/2a (4a+7)
I know this is the right answer because I learned this in 5th grade.
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A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1600 miles, and the sum of their fuel efficiencies was 45 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Answers
If the fuel efficiencies of each of the cars that week is 20 gallons of gas and 25 gallons of gas.
How to find the efficiencies?Let x represent the gallons consumed by car 1
Let y represent gallons consumed by car 2
Formulate an equation:
30x+40y = 1600 equation 1
x+y = 45 equation 2
Substituting equation 2 into equation 1,
30x+40(45-x) = 1600
30x+ 1800-40x = 1600
-10x+1800 = 1600
-10x = -200
Divide both side by -10x
x = -200/-10
x = 20
Substitute value of x into equation 2
x+y = 45
20+y = 45
y = 25
Hence,
Car 1 consumes 20 gallons of gas and Car 2 consumes 25 gallons of gas.
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From their locations in the diagram, what are two possible values for n and m? The letters n and m represent two unknown numbers.
Answers
The possible values for n and m are:
m = √5 and n = 7/5
In this question, we have been given the locations of numbers n and m.
From their locations in the diagram, we need to find the possible values for n and m.
From the location of n we can say that the value of n is a rational number but not an integer.
We know that rational numbers are of the form p/q where p, q are integers with q ≠ 0
And the value of m is an irrational number.
So, the possible value of n am m:
m = √5 and n = 7/5
Therefore, the possible values for n and m are:
m = √5 and n = 7/5
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Add.
−1 4/5 + (−1/4) + (−1/5)
Answers
The required simplified value of the given expression is given as -13/20.
Given that,
An expression is given, −1 4/5 + (−1/4) + (−1/5) we have to determine the sum of the expression.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
here,
= -1 4/5 + (-1/4) + (-1/5)
= -1/5 -1/4 -1/5
= -2/5 -1/4
= -13/20
Thus, the required simplified value of the given expression is given as -13/20.
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Calculating Loan Risk
Cass is reviewing historical data about loans the financial institution gave out to see how credit score was linked to defaulting. In the past, the financial institution gave loans only to those with a credit score of 501 or above.
Answers
Answer:
Loan analysis is an evaluation method that determines if loans are made on feasible terms and if potential borrowers can and are willing to pay back the loan. It checks the eligibility of the potential borrower against the criteria set forth for lending. Loan analysis helps in assessing the skills and financial knowledge of the borrower to ...
What are some points on a graph of the equation y=-1/3x-1
Answers
A few points (co-ordinates) for the given equations are :
(1,-1/2),(-1,1/4),(0,1),,(2,-1/4)
What are the points on the graph called?These points are called Coordinates, where the horizontal line denotes the x-axis and the verticle line is the y-axis.
Each point is identified by both x and y coordinates. A point's x-coordinate is a value that indicates how far the point is from the horizontal or x-axis origin.
According to the given information:y denotes the distance of the point on the vertical line from the origin
x denotes the distance of the point on the horizontal line from the origin
In the given equation y=-1/3x-1
We can substitute x with any integer (i.e any number among the positive or negative numbers)
Putting, x=1 in the given equation we get
y=-1/(3x1)-1
⇒ y=-1/3-1
⇒y=-1/2
Thus the coordinate when x=1 is (1,-1/2)
Similarly by putting x=0, 1, 2, -1 ;we get the following co-ordinates respectively
(0,1), (1,-1/2), (2,-1/4),(-1,1/4)
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Which input value produces the same output value for the two functions on the graph?
f(x) equals negative StartFraction 2 Over 3 EndFraction x plus 1. g(x) equals StartFraction 1 Over 3 EndFraction x minus 2. A coordinate grid with two lines. One line labeled f(x) passes through (negative 3, 3), (0, 1), and point (3, negative 1). The second line is labeled g(x) and passes through (negative 3, negative 3), (0, negative 2), and point (3, negative 1).
x = –3
x = –1
x = 1
x = 3
Answers
An input value that would produce the same output value for the first functions on the graph is 0. Also, an input value that would produce the same output value for the second functions on the graph is 3.
How to determine the correct input value?In this exercise, you are required to determine the input value that would produce the same output value for the two functions on the graph. This ultimately implies that, the two functions would be equated as shown below.
From the information provided above, the two functions include the following:
f(x) = -2/3(x + 1)
g(x) = 1/3(x - 2)
Equating the two equations, we have:
f(x) = g(x)
-2/3(x + 1) = 1/3(x - 2)
-2x/3 -2/3 = x/3 - 2/3
-2x/3 - x/3 = - 2/3 + 2/3
x = 0.
For the second function on the graph, the coordinates are as follows:
f(x) = (-3, 3), (0, 1), (3, -1)
g(x) = (-3, -3), (0, -2), (3, -1)
Therefore, the above function produces the same input value (x) at point 3.
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Answer:
D
Step-by-step explanation:
edge 23
How did you compute sums of dollar amounts that were not whole numbers? For example, how did you compute the sum of $5.89 and $1.45? Use this example to explain your strategy.
Answers
The Sum of dollars in decimal is not a whole number.
Whole numbers are made up of natural numbers plus the number zero. In mathematics, the set of whole numbers is symbolized by the symbol W and is given as W = {0, 1, 2, 3, 4, …}.
To calculate a number of dollars that is not a whole number.
As an example, consider the sum of $5.89 and $1.45:
$5.89 + $1.45
Taking the whole numbers first:
$5 + $1 = $6
Take the sum of the decimals :
$0.89 + $0.45 = $1.34
sum of original whole + sum of decimal whole
$6 + $1 = $7
Remaining decimal: $1.34 - $1 = $0.34
$7 + $0.34 = $7.34
Therefore $7.34 is not a whole number
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I want the answer please please
Answers
because that rate is constantly changing whereas the others are stable for the most part
-10b+3 ≤-37
Compound inequalities
Answers
Great by is reducing by 250% the regular price of a tally set selling it for $225 the regular price of the tally set is
Answers
The regular price of the tally set is $300.
How to calculate the price?From the information Illustrated, Great by is reducing by 250% the regular price of a tally set selling it for $225.
Let the regular price be represented by x.
Therefore, x - (25% × x) = 225
x - 0.25x = 225
0.75x = 225
Divide
x = 225 / 0.75
x = 300
The price is $300.
Note that the above percentage in the question is 25% and not 250%.
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What is the slope of this line
Answers
Answer: Slope is 0
Step-by-step explanation
the graph's points doesn't change its value on the y - values but the x values change by 1 meaning the slope is 0/1 meaning there is no slope
6. Solve for y. 12y - 10 = 14y
02
0 5
O-5
O-2
Answers
Answer:
can you pls clear your questions?
Consider a particle moving along the x-axis where
x(t)
is the position of the particle at time t,
x ′(t)
is its velocity, and
x ″(t)
is its acceleration
Answers
Regarding the velocity and acceleration functions, it is found that:
b) The particle is moving to right on these following intervals: (0,1) U (3,10).
c) The velocity when the acceleration is of zero is: -1 m/s.
When a particle is moving to right?A particle is moving to right when it's velocity is positive.
In this problem, the velocity function is presented as follows:
v(t) = 3t² - 12t + 9.
The velocity function is a concave up quadratic function, which is positive to left of the smaller root and to the right of the larger root.
The roots of the function are given as follows:
v(t) = 3(t² - 4t + 3)
Then:
3(t² - 4t + 3) = 0
t² - 4t + 3 = 0
(t - 1)(t - 3) = 0.
t - 1 = 0 -> t = 1.t - 3 = 0 -> t = 3.Considering the domain of the function, the intervals in which the car is moving right are:
(0,1) U (3,10).
What is the velocity when the acceleration is of zero?The acceleration is given by the following equation:
a(t) = 6t - 12.
It is of zero when:
6t - 12 = 0
6t = 12
t = 12/6
t = 2.
The velocity at this instant is of:
v(2) = 2² - 4(2) + 3 = -1 m/s.
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Please help please and thank you..
Answers
The value of x for the triangle by the mid point theorem is obtained as 5.
What is defined as the mid-point theorem?The line segment of a triangle connecting the midpoint in two the triangle's sides is thought to be parallel to that third side and also half the length of the third side, according to the midpoint theorem. A location that is at, close, or equally far both from ends of a line segment is referred to as the midpoint. To put it another way, the midpoint is indeed the place in a fact where the beginning and the conclusion meet.For the given diagram in the question.
As, the sides of the triangle is divided in equal parts.
By the mid -point theorem-
(1/2)24 = x + 7
12 = x + 7
x = 12 - 7
x = 5
Thus, the value of x for the triangle by the mid point theorem is obtained as 5.
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5. Simplify the complex fraction. a.-2/7
1 1/3
Answers
The simplification of the complex fraction is found as 11/14.
Define complex fraction/mixed fraction?A mixed fraction is a fraction that is created by fusing a fraction with a whole number. An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that. Step 1: Multiply the mixed fraction's denominator by the whole number component.Step 2: Increase the product from Step 1 by the numerator.Step 3: In the numerator/denominator form, write the improper fraction using the total from Step 2.For the given question, the expression is-
-2/7 + 1 1/3
To convert mixed fraction 1 1/3 i improper fraction, multiply 3 with 1 and add 1.
1 1/3 = 1 x 3 + 1 /3
1 1/3 = 4/3 Put in main equation.
-2/7 + 4/3
Simplify the expression.
= -2 x 3 + 4 x 7/ (7 x 4)
= -6 + 28 / 28
= 22/28
Divide both with 2
= 11/14
Thus, the simplification of the complex fraction is found as 11/14.
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The correct question is
Simplify the complex fraction.
-2/7 + 1 1/3
3
8
13
24
53
123
213
Answers
Answer:
321 is the next number that comes in the calculator.
Order the steps to show how to solve the system of equations using substitution.
y=6x+1
7x – 2y= –1
Answers
Answer: The correct answer is x=−1/5 and y=−1/5
Step-by-step explanation:
Solve the System by substitution:
y=6x+1 and 7x−2y=−1
Solve y=6x+1 for y:
y=6x+1
Substitute 6x+1 for y in 7x−2y=−1:
7x−2y=−1
7x−2(6x+1)=−1
−5x−2=−1 (Simplify both sides)
−5x−2+2=−1+2 (Add 2 to both sides)
−5x=1
−5x/−5 = 1/−5 (Divide both sides by -5)
x=−1/5
Substitute −1/5 for x in y=6x+1:
y=6x+1
y=6(−1/5)+1
y=−1/5 (Simplify both sides)
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Write log₂ A as a natural logarithm.
Answers
Answer:
ln A / ln 2
Step-by-step explanation:
Using the change of base rule: ln A / ln 2
The formula is у= 6х - 5 Determine the value of x, if y=7
Answers
Answer:
x=2
Step-by-step explanation:
You can put the equation as 7=6x-5
Move equation
12=6x
Divide
x=2
The quotient is a multiple of 4 the dividend is a multiple of 9 the divisior is a factor of 12 possible solution
Answers
graph: y = |x+2| + 1
Answers
14.4.3 Quiz: Stretching and Compressing Functions
Question 2 of 10
Suppose f(x) = x². What is the graph of g(x)=f(x)?
Answers
If f(x) = x², the graph of g(x) = f(x) is x².
What is a Graph of a function?
The graph of a function f is the set of all points in the plane of the form (x, f(x)).
How to find the graph of a function:
You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.
We are given the function; f(x) = x²
Also, we want to find the graph of g(x) = f(x)
From the above, it means that we put x in place of x for function f(x) to get the function g(x).
so, g(x) = f(x)
g(x) = (x)²
Hence the graph of g(x) = f(x) is x².
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??? brianlest?? help please
math
Answers
Answer:
try to show it step by step
Hope it helps
A bag contains 3 gold marbles, 5 silver marbles, and 26 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
Answers
The expected value if you play this game will be -$0.205.
Let the number of gold, silver, and black marbles be P1, P2, and P3, respectively.
Given, The bag contains,
Number of gold marbles (P1) = 3
Number of silver marbles (P2) = 5
Number of black marbles (P3) = 26
Also given,
The winning value if a gold marble is selected = $3
The winning value if a silver marble is selected = $2
The losing value if a black marble is selected = $1
Probability = Expected value/ Sum of the total number of events
Probability of picking a gold marble,
P1 = 3/ (3+ 5+ 26)
= 3/34.
Probability of picking a silver marble,
P2 = 5/ (3+ 5+ 26)
= 5/34.
Probability of picking a black marble,
P3 = 26/ (3+ 5+ 26)
= 26/34.
The expected value if you play the game will be,
Value = ($3) P1 + ($2) P2 + (-$1) P3
= ($9/34) + ($10/34) - ($26/34)
= - ($7/34)
= -$ 0.205
Thus, you will face a loss of 0.205 cents.
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which is the correct answer ????
Answers
Which of these types of angles have the same measure after being rotated, reflected, or translated in a coordinate plane?
I. Acute Angles
II. Right Angles
III. Obtuse Angles
a
I. II. and III.
b
I. and II. only
c
II. and III. only
d
I. only
Answers
The type of angles have the same measure after being rotated, reflected, or translated in a coordinate plane is a I. II. and III.
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation is basically of two major divisions
Rigid transformationnon rigid transformationNon rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation
In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are
rotationreflectiontranslationSince the transformation types mentioned are all rigid transformation hence all the angles will remain same
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Please help
A T-shirt company can produce and sell x T-shirts per day. The total cost C (in dollars) for producing x T-shirts is
C = 1,780 + 7x,
and the total revenue R (in dollars) is
R = 14x.
Find the profit (in dollars) obtained by selling 275 T-shirts per day.
Answers
Answer:
$145
Step-by-step explanation:
The revenue - the cost is the profit.
14x - (1708 + 7x) Distribute what is in the parentheses by -1
14x -1(1780) -1(7x) Simplify
14x - 1780 -7x Combine like tersm
7x - 1780 Plug in 275 for x
7(275) - 1780
1925 - 1780
145
Lena took out a $9000 loan for 7 months and was charged simple interest. The total interest she paid on the loan was $336.
Answers
The loan given has a rate of 0.53%
Simple InterestSimple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time. In simple interest, the principal amount is always the same, unlike compound interest where we add the interest of previous years principal to calculate the interest of the next year.
The formula of simple interest is given as;
S.I = P(1 + RT)
S.I = Simple interestP = principalR = rateT = timeSubstituting the values into the formula;
(9000 + 336) = 9000(1 + r * 7)
9336 = 9000 + 63000r
Collecting like terms
336 = 63000r
r = 0.0053
r = 0.0053 * 100
r = 0.53%
The rate on the loan is 0.53%
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Select the correct answer from each drop-down menu. Using the image below, select the best answer from each pull-down to complete the statements. The measure of ∠FED is ? °. ∠CBD and ∠ ? are complementary angles. Please help. thank you
Answers
The value of ∠FED is 120° and ∠CBD is complementary to ∠FDE
What are complementary angles?Complementary angles are two angles that sum up to 90°
For example 60° and 30° are complementary.
Either angle is called the complement of the other angle.
∠FED, ∠FDE and ∠DFE are in a triangle.
so,
∠FED + ∠FDE + ∠DFE = 180°
16x - 8 + 2x + 9 + 35 = 180 ( sum of angles in a triangle)
18x +36 = 180
18x = 180 - 36
18x = 144
x = 144/18
x = 8
so ∠FED = 16x - 8
Substitute x = 8 into the equation above we have
16(8) - 8 = 128 - 8 = 120°
∠FDE = 2x + 9
∠FDE = 2(8) + 9 = 25°
∠BED = 6x + 12
∠BED = 6(8) + 12
∠BED = 48 + 12
∠BED = 60°
∠CBD = -2x + 81
∠CBD = -2(8) + 81
∠CBD = 65°
so since ∠CBD = 65° and 90 - 65 = 25°
∠CBD is complementary to ∠FDE
In conclusion, ∠FED is 120° and ∠CBD is complementary to ∠FDE
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