The explicit formula for a geometric sequence is [tex]a_{n}[/tex] =[tex]a_{1}^{r-1}[/tex]
The sequence is:
1, 2, 4, 8..........
The formula for a geometric sequence,
[tex]a_{n}[/tex] = [tex]a_{1}^{r - 1} }[/tex]
a, ar, [tex]ar^{2}[/tex], [tex]ar^{3}[/tex]
r = common ratio
n = number of sequences in a series.
Let us understand by the sequence,
Here r = 2 , a = 1
Therefore by putting these values in the equation we get,
[tex]a_{n}[/tex] = [tex]a_{1}r^{n-1} }[/tex]
= a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex], ........
1, 2, 4, 8 .........
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Tyrone says it is not possible to show that Δ A D E ≅ Δ A C B . Lorenzo disagrees, explaining that since ∠A D E ≅ ∠A C B , and ∠ A ≅ ∠ A by the Reflexive Property, ΔA D E ≅ ΔA C B . Is either of them correct? Explain.
We can conclude that ΔADE ≅ ΔACB under AA condition.
What exactly does the term "triangle congruency" mean?When the three corresponding sides and angles of two triangles are the same size, they are said to be congruent.These triangles can be moved, rotated, flipped, and turned to appear identical.If they are moved, they will coincide.When two triangles satisfy the five congruence conditions, congruence exists.They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).So,
To prove that: ΔADE ≅ ΔACB
∠A ≅ ∠A = Given∠ADE ≅ ∠ACB = Given∠AED ≅ ∠ABC = AA condition proves that triangles are congruent, so these 2 angles will also be identical.Therefore, ΔADE ≅ ΔACB under AA condition.
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Mayumi rides her bike around a park . each lap around the park is two/ three . mayumi rides of total of three. how many laps around the park mayumi ride ? write your answer as a whole number of laps plus a fraction of a lap you can use the model to help.
Two expression with equal sign in between is equation. If Mayumi rides her bike around a park . each lap around the park is two/ three . Mayumi rides of total of three. Then 4 1/2 laps around the park mayumi ride.
What is Equation?
Two expression with equal sign in between is called as Equation.
Mayumi rides her bike around a park . each lap around the park is two/ three . mayumi rides of total of three. The number of laps around the park mayumi ride be x.
We convert this given data as a expression as given
2x/3=3
Apply cross multiplication.
2x=9
x=9/2,
We need to write answer as a whole number of laps plus a fraction of a lap.
x=4 1/2
Therefore 4 1/2 laps around the park mayumi ride.
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Answer: Mayumi Rides 4 whole laps, plus 1/2 of a lap.
Step-by-step explanation:
Find the 10 th term of each geometric sequence. a₉ = -1/3, r= 1/2
The 10th term of the geometric sequence is -1/6.
Let the following be a geometric sequence:
a(1), a(2), a(3), a(4), a(5), ....
Then we have:
a(2) = a(1) . r
a(3) = a(2) . r
Continue the process, we have
a(n) = a(n-1) . r
Where:
a(n) = nth term
a(n-1) = (n-1)th term
r = ratio
In the given problem, a(9) = -1/3, r = 1/2
Plug these into the above formula:
a(10) = a(9) . r
= (-1/3) . 1/2 = -1/6
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Determine a base area and height for each shape
You have to show the picture of what your talking about. Please do so if you want someone to answer your question.
13. What is the mean of the data set in the box below? −8, −6, −2, 0, −6, −8, 4, −7, −8, 1 A. −8 C. −6 B. −7 D. −4
Answer: D. -4
Step-by-step explanation:
-8 + -6 + -2 + 0 + -6 + -8 + 4 + -7 + -8 + 1= - 40
-40 divided by 10= -4
(You're dividing by 10 because there are 10 numbers that you added up)
The mean is -4.
Find the arithmetic mean a n of the given terms. a n₋₁ = r, a n₊₁=s
The arithmetic mean a n of the given terms a n₋₁ = r, a n₊₁=s is
[tex]a_{n}[/tex] = [tex](a_{n+1} - a_{n-1})/2[/tex].
What is arithmetic mean?a n₋₁ = r, a n₊₁=s is
[tex]a_{n}[/tex] = [tex](a_{n+1} - a_{n-1})/2[/tex]
The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.
The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).
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Caroline is the youngest of four siblings whose ages are consecutive odd integers. If the sum of their ages is 9696, find Caroline's age.
Answer:
2421 or 21
Step-by-step explanation:
Hello!
Consecutive odd integers are set of odd integers that come right after each other.
Let "C" be Caroline's age. Caroline's next older sibling would be C + 2, as odd integers come to every two numbers, and the next would be C + 4, and finally C + 6.
If we add up all the expressions, we should get 9696.
Solve for CC + C + 2 + C + 4 + C + 6 = 96964C + 12 = 96964C = 9684C = 2421The solution to this question does not seem reasonable. I assume that the correct sum of the age should be 96, given 9696.
If this is the case, then Caroline's age would be 21, using the same general logic.
A women's coat comes in sizes 4,6,8 , or 10 in black, brown, ivory, and cinnamon. How many different coats could be selected?
As women's coat comes in sizes 4,6,8 , or 10 in black, brown, ivory, and cinnamon , possibility of selection of different coats is equal to 16.
As given in the question,
Availability of size number in women's coat = 4, 6, 8, or 10
⇒N(S) =4
Availability of color in women's coat = black, brown, ivory, and cinnamon
⇒ N(C) =4
Possibility of selection of different women's coats = N(S) × N (C)
=4 × 4
=16
Therefore, the possibility of selection of different coats is equal to 16 as per the availability of women's coat sizes and colors.
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i think i know the answer but i still need help…
The solutions for 'u' are u ≤ -5 and u ≤ 1
How to solve the inequality
Given the inequalities;
-3u ≤ 15 2u - 1 ≤ 1Let's solve for u in the expression
-3u ≤ 15
Make 'u' the subject
-3u/3 ≤ 15/ -3
u ≤ -5
Let's solve for 'u' in the expression
2u - 1 ≤ 1
collect like terms
2u ≤ 1 + 1
Add like terms
2u ≤ 2
Make 'u' the subject
u ≤ 2/ 2
u ≤ 1
Thus, the solutions for 'u' are u ≤ -5 and u ≤ 1
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6 Sasha thinks of a number.
She adds 1 to her number then multiplies the result by 5.
a Use a mapping to write this as a function.
The answer Sasha gets is 11.
b Use inverse functions to work out the number Sasha thought of in the beginning.
Show all your working.
If the sum of 12 numbers is 480 then what is their mean? (a) 20 (b)40 (c) 30 (d)24
Answer:
A
Step-by-step explanation:
40 x 12 = 480
A number line can represent positions that are north and south of a truck stop on a highway
Positive positions are north of the truck stop and negative positions are south of the truck stop. What is the value, in miles, of each position on a number line?
1. The truck stop ______
2. 5 miles north of the truck stop _____
3. 3.5 mlles south of the truck stop ____
WILL GIVE BRAINLIEST, TYYY !
Using integer numbers, the values of the positions in this problem are given as follows:
1. 0.
2. 5.
3. -3.5.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
In the context of each problem, integer numbers may have different representations, and for this problem, we have that:
The truck stop is the origin, that is, position zero.Positions north of the truck stop will be represented by positive values.Positions south of the truck stop will be represented by negative values.Hence:
5 miles north is represented by the integer 5.3.5 miles south is represented by the integer -3.5.Hence the values of the positions in this problem are given as follows:
1. 0.
2. 5.
3. -3.5.
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Solve each system by elimination.
4x+2y = 4 , 6x + 2y = 8
By elimination, the solution of the system of equations, 4x + 2y = 4 and 6x + 2y = 8, is (2 , -2).
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
Subtracting the two equations will eliminate the variable y.
6x + 2y = 8 (equation 2)
4x + 2y = 4 (equation 1)
2x + 0y = 4
x = 2
Substitute the value of x to any of the two equations and solve for y.
6x + 2y = 8 (equation 2)
6(2) +2y = 8
2y = 8 - 12
2y = -4
y = -2
Hence, the solution of the system of equations is (2 , -2).
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Complete the statement.
7-(-4) is
direction.
units from 7 in the
7-(-4) is 4 units from 7 in the negative direction.
The number line keeps going both ways. You can include 6, 7, and so on, all the way up to the hundreds, thousands, and beyond, because the set of natural numbers only extends to the right.
A number line is a diagram that shows numerical values along a straight line that can be drawn either horizontally or vertically. It's simple for us to compare and compute basic arithmetic operations on numbers when they are written down on a number line. A number line's origin is typically thought to be zero (zero). There are only positive numbers to the right of zero and only negative numbers to the left of zero.
therefore,
7 - (-4)
= 7 + 4
= 11
when we simplify the expression we get the answer as 11 units
the result is that 11 units is 4 units away from 7 in a negative direction.
Hence we get the complete sentence.
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Which set of numbers are irrational number
Answer:
numbers like 9.58596638927, pi, square root of 2, or square root of 11
Determine whether each list is a sequence or a series and finite or infinite. 5+10+ . . . . . . +25
The given list is a finite series.
There are two parts to our question.
In the first part of the question, we are asked whether the given list of numbers is a sequence or a series.
To answer this part, we should be familiar with what the concept of sequence and series.
A sequence is a plain list of numbers.
A series is a sum of numbers in the list.
The given list looks something like this,
5+10+ . . . . . . +25
So, considering the given definitions of both sequence and series we can clearly tell it is a series.
Now up to the second part of the question, is the given series finite or infinite?
We know this is finite because it has a start of 5 and an end of 25. There's an ellipsis in the middle, but it has a beginning and an end, so this will be the right answer.
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Solve the equation. Check your solution.
8.32=4.1z+10.5
Pls help.
Answer:
z = -0.5317073
Step-by-step explanation:
Get variable on left and all constants on right
-4.1z = 10.5 - 8.32
-4.1z = 2.18
Divide both sides by -4.1
z = -0.5317073
To check:
8.32 = 4.1(-0.5317073) + 10.5
Simplify 5x√3x − 2x√3x − x√3x
Answer:
2√3 х^2 this solution
Step-by-step explanation:
I checked everything is correct
The box plot represents the distribution of the number of children in 30 different families. After further examination, the value of 12 is removed for having been recorded in error. The box plot represents the distribution of the same data set, but with the maximum, 12, removed. The median is 2 children for both plots. Explain why the median remains the same when 12 was removed from the data set.
It should be noted that the median remains the same because removing an extreme value from a data set will not have much effect on the median.
What is Box plot definition?Statistical data based on the minimum, first quartile, median, third quartile, and maximum are shown graphically in a box plot. The box plot represents the number of kids in 30 distinct households in accordance with the families, and the value of 12 is subtracted for inaccuracy.
Therefore, if there are two kids in the median for both plots when 12 was eliminated from the data set, it remained unchanged.
In conclusion, the median remains the same because removing an extreme value from a data set will not have much effect on the median.
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Find a*b
a = 4i + 8j
b = -2i + 3j
PLEASE HELP ASAP!!! 15 POINTS!!
Use the sentence to answer the question.
The mechanic said the car needed some brake things replaced.
Which words can replace the imprecise phrase some brake things with domain-specific language?
A. things that stop the car
B: some parts that wore out
C. the wheel cylinders
D. some important parts
Answer:
the wheel cylinders
Step-by-step explanation:
brainliest?
Answer:
the answer is c, the wheel cylinders
3/7 divided by 11/21 = 3/7 x
The solution to the given equation 3/7 divided by 11/21 = (3/7)x is x = 21/11.
What is the solution to the given equation?Given the equation in the question;
3/7 divided by 11/21 = 3/7 x
3/7 ÷ 11/21 = (3/7)x
To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.
3/7 ÷ 11/21 = (3/7)x
3/7 × 21/11 = (3/7)x
( 3 × 21 )/( 7 × 11 ) = (3/7)x
63/77 = (3/7)x
Remove the parenthesis
63/77 = (3/7) × x/1
63/77 = ( 3 × x )/( 7 × 1)
63/77 = 3x/7
Cross multiply
63 × 7 = 3x × 77
441 = 231x
231x = 441
Divide both sided by 231
231x/231 = 441/231
x = 441/231
x = 21/11
The solution to the given equation 3/7 divided by 11/21 = (3/7)x is x = 21/11.
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The table shows information about the
faces, edges and vertices for some
pyramids.
Shape of Faces Edges Vertices
base
Triangle 4
Square 5
Pentagon 6
Hexagon
7
6
8
10
12
Formula:
Write a formula that connects the
number of sides of the base, S,
with the number of faces, F.
Hence, work out the number of faces a
pyramid with a 20-sided base has.
4
5
6
7
Faces:
Formula:
E = 2S is the equation that links the base's S number of sides to its F number of faces.
E = 2S
S is the number of sides on a base.
E equals the number of edges.
Triangle (1)
3 and S are the base side counts.
edges equal 6, hence the answer is E.
E = 2S
Table 2
Base has four sides, hence the response is S.
edge count = E (8 edges)
E = 2E
3rd Pentagon
S is equal to the five sides of the base.
The letter E is equivalent to 10 edges.
S = 2E
4) A hexagon
S is equal to the six sides of the base.
Edge count: 12 equals E.
E = 2S
Thus, it is shown that E = 2S.
The 30 sides of the pyramid foundation.
The answer is S since the base has 20 sides.
The number of edges is E = 2S = 20 x 2 = 40 edges.
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Find the distance between each pair of points.
A(14,-3), B(9,-9)
Answer: (24, -12)
because 14 + 9 is 24 ob. and -3 + -9 will be 3+9 with the - so it's -12
How to draw 2 number lines that show 0.200 and 1/5 are equivalent
We create a number line with a range from 0 to 1.0 and divide it into 5 equal segments to demonstrate the equality between 0.200 and 1/5.
What is a Number Line?The visual representation of numbers on a straight line, either horizontally or vertically, is known as a number line. When numbers are written down on a number line, it is straightforward for humans to compare them and perform basic arithmetic operations on them. One might assume that a number line starts at zero (0). There are only negative numbers to the left of zero and only positive numbers to the right of zero. In other words, as we move to the right on a number line, the value of the numbers increases. This shows that the numbers on the right are more numerous than those on the left.
We create a number line with a range from 0 to 1.0 and divide it into 5 equal segments to demonstrate the equality between 0.200 and 1/5.This line will include points at 0.2, 0.4, 0.6, 0.8, and 1.0.Next, we create a second number line that has five equally spaced segments and ranges from 0 to 5/5.This line will have the following points: 1, 2, 3, 5, 4, and 5/5.These values of 0.200 and 1/5 will be equivalent, as demonstrated by the equal segments.To know more about the number line, visit:
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Write an equation of the line through each pair of points in slope-intercept form.
(0,5) and (3,3)
The equation of line is y = (-2/3)x + 5
Given the points:
(x₁, y₁) = (0, 5)
(x₂, y₂) = ( 3, 3)
The slope-intercept form:
y = mx + b
Where, m is the slope and b is the y-intercept, that is (0, b)
The formula for slope:
m = (y₂ – y₁) / (x₂ – x₁)
We have given
x₁ = 0
x₂ = 3
y₁ = 5
y₂ =3
So,
m = (3 – 5) / (3 – 0) = -2/3
here, we have b = 5
Therefore we have the equation of the line as:
y = mx + b
That is the equation of line is y = (-2/3)x + 5
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You find 400 mg of a substance that has a half-life of 20 days. What is it's daily rate of decay? Round answers to four decimal places.
The daily rate of decay is approximately equal to 0.0347 days⁻¹.
What is the rate of decay of a substance?
According to the statement, we find that a substance is under a decay process, whose differential equation is introduced below:
dm(t) / dt = - k · m(t) (1)
Where:
m(t) - Current mass of a substance, in miligrams.k - Rate of decay, in 1 / day.The half-life of the substance is the time needed for a substance to decrease its mass by half. The rate of decay can be found in terms of half-life:
k = (㏑ 2) / t' (2)
Then, the daily rate of decay of the substance is:
k = (㏑ 2) / (20 days)
k ≈ 0.0347 day⁻¹
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Please help!! Use the vertical line test to determine if each graph shows a relation that is a function.
larry has 4 packages of cards the first box has 17 cards the second one has 21 the third one has 22 the fourth one has 16 useing front end estimateion what is the best estimateion for the total number of baseball cards she has?
If larry has 4 packages of cards the first box has 17 cards the second one has 21 the third one has 22 the fourth one has 16 using front end estimation the best estimation for the total number of baseball cards she has is: 80 cards.
Estimation for the total numberNumber of cards in each of the boxes
First box =17 cards
Second one box=21 cards
Third one box =22 cards
Fourth one box=16 cards
Now let find the best best estimation for the total number of baseball cards:
Total number of baseball cards=17+21+22+16
Total number of baseball cards=20+20+20+20 (rounded to the nearest tens)
Total number of baseball cards=80 cards
Therefore If larry has 4 packages of cards the first box has 17 cards the second one has 21 the third one has 22 the fourth one has 16 using front end estimation the best estimation for the total number of baseball cards she has is: 80 cards.
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Why are there 12 signs of the zodiac. how many people must be present for there to be at least a 50hance that two or more of them?
The answer to the given problem is 5
Probability is the degree to which an occurrence is likely to take place, as determined by the proportion of favorable examples to the total number of instances for which it is probable to have occurred.
Let's assume
1 - P(no one has the same sign) >= 0.5
P(two or more people have the same sign) = 1 - P(no one has the same sign)
= 1 - (12 / (12-n)) / 12^n
1-0.5=0.5 >= P (no one has the same sign) = 12/(12^n x (12-n))
0.5 >= 12 /(12^n x (12-n))
Solve for n.
n = 5
Hence the answer is 5
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