The formula that describes the sequence given i.e. [tex]\frac{-2}{3}[/tex],-4,-24,-144 (geometric sequence) is [tex](\frac{-2}{3} )(6)^{n-1}[/tex]
Geometric progression:
A geometric progression or a geometric sequence is a series, in which each word is varied by another by a common ratio. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence. It is symbolized by:
A, AR,[tex]AR^{2}[/tex],[tex]AR^{3}[/tex]...
Where A is the first term of the geometric sequence and R is the common ratio of the geometric sequence.
The general term of geometric sequence i.e. nth term =[tex]AR^{n-1}[/tex]
Given that A= [tex]\frac{-2}{3}[/tex] and R=6
As a result the general term of geometric sequence i.e. nth term =[tex](\frac{-2}{3} )(6)^{n-1}[/tex]
Therefore,The formula that describes the geometric sequence given i.e. [tex]\frac{-2}{3}[/tex],-4,-24,-144 is [tex](\frac{-2}{3} )(6)^{n-1}[/tex]
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Ms. Francis is planning a birthday party for her daughter. There will be 22 children at the party, and in order to seat them all she needs to rent square card tables. Only 1 child can sit at each side of a card table.
Ms. Francis wants to arrange the tables in a rectangular shape so they look like one large table. The room is large enough that
the rectangle can be made with more than one row of tables.
Part A: How many different arrangements can Ms. Francis make to seat all 22 children?
Part B: What is the smallest number of tables that Ms. Francis needs to rent?
DIRECTIONS: To solve the problem, apply the steps of the Mathematical Problem-Solving Routine.
Understand
1. Try to visualize the situation. Consider drawing a diagram
2. State the problem in your own words.
3. What is the important information in the problem?
Plan
4. What strategy will you use to solve the problem? Why?
Predict an answer.
Answers to both the subparts are:
(A) Ms. Francis would have to rent 6 tables in order for everyone to have their own side.(B) She could have all of the children sitting at their tables, each with their own side, but the sixth table would only have two other children.What are mathematical operations?An operation is a function in mathematics that takes zero or more input values (also known as "operands" or "arguments") and produces a well-defined output value. The arity of the operation is determined by the number of operands.Binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse, are the most commonly studied. A constant is an operation of arity zero, also known as a nullary operation. The mixed product is an example of a 3rd order operation, also known as a ternary operation.So, there will be 22 children at the party and each table will have 1 child sitting on each side.
This means that at 1 table there will be sitting 4 children.(A) Ms Francis would have to rent 6 tables in order for everyone to have their own side.
Then,
4 × 6 = 24
(B) She could have all of the children sitting at their tables, each with their own side, but the sixth table would only have two other children.
Therefore, the answers to both the subparts are:
(A) Ms. Francis would have to rent 6 tables in order for everyone to have their own side.(B) She could have all of the children sitting at their tables, each with their own side, but the sixth table would only have two other children.Know more about mathematical operations here:
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A rose bush grows at a rate of 1.5 inches per week about how tall will the rose bush be after 40 weeks will it be reasonable why and why not explain pls ASAP
The rose bush will be 60 inches tall after 40 weeks
Calculating heightFrom the question, we are to calculate how tall the rose bush would have grown in 40 weeks
From the given information,
"A rose bush grows at a rate of 1.5 inches per week"
To calculate how tall the rose bush would have grown in 40 weeks, we will multiply the rate at which the bush grows by 40
That is,
1.5 × 40
= 60 inches
Hence, the rose bush will be 60 inches tall after 40 weeks
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X And y values shown x
X. Y
2. 6
5. 15
8. 24
The constant of variation is 3.
How to illustrate the information?It should be noted that in the information, we are given the values of both x and y.
When x is 2, y is 6. When x is 5, y is 15. Finally when x is 8, y is 24.
The constant is given as 6/2 or 15/5 or 24/8. This will give 3.
Therefore, the constant of variation is 3.
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X And y values shown x
X. Y
2. 6
5. 15
8. 24
What is the constant of variation?
Which of the following pairs consists of equivalent fractions?
Answer:
I think it's the last answer
Two shops rent canoes for a rental fee plus a fee per hour. The table shows the total cost (in dollars) for x hours at Shop B is represented by the equation y=4x+6. Which shop charges less per hour? How many hours must a canoe be rented for the total costs to be the same? (PLEASE SHOW WORK)
Using linear functions, it is found that:
Shop A charges less per hour.The canoe must be rented for 3 hours for the costs to be the same.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For Shop A, we have a linear function that:
Has a rate of change of $3, hence m = 3.The intercept is b = y(0) = 12 - 3 = 9.Hence the functions are given by:
A(x) = 3x + 9.B(x) = 4x + 6.Due to the lower slope, shop A charges less per hour. The costs will be the same when:
A(x) = B(x)
3x + 9 = 4x + 6
x = 3.
The canoe must be rented for 3 hours for the costs to be the same.
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What does 5 less than 3 times mean? I need help badly it’s due tomorrow for Algebra 1.
HERES THE FULL QUESTION: The width of a rectangle is five less than three times the length of the rectangle if the perimeter of the rectangle is 70 inches what are the dimensions of the rectangle?
The dimensions of the rectangle are 10 inches by 25 inches
How to the dimensions of the rectangle?The given parameters are
Width = five less than three times the lengthThe perimeter of the rectangle = 70The above parameters mean
w = 3l - 5
P = 70
The perimeter of the rectangle is
P =2(l + w)
So, we have
2(l + 3l - 5) = 70
Divide by 2
l + 3l - 5 = 35
Evaluate the like terms
4l = 40
Divide by 4
l = 10
Substitute l = 10 in w = 3l - 5
w = 3 * 10 - 5
w = 25
Hence, the dimensions of the rectangle are 10 inches by 25 inches
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Find the distance between the points J(-8, 0) and K(1, 4). Answer in simplest exact form.
What’s the exact distance?
Answer:
distance = [tex]\bf \sqrt{97}[/tex] units
Step-by-step explanation:
To find the distance between two points given their coordinates, we can use the following formula:
[tex]\boxed{\mathrm{distance} = \sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}}[/tex],
where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are coordinates of the two points.
The two points we are given are:
• J(-8, 0)
• K(1, 4).
Using these coordinates and the formula above, we can calculate the distance between the points:
distance = [tex]\sqrt{(-8 - 1)^2 + (0 - 4)^2}[/tex]
= [tex]\sqrt{(-9)^2 + (-4)^2}[/tex]
= [tex]\sqrt{81 + 16}[/tex]
= [tex]\bf \sqrt{97}[/tex]
Therefore, the distance between J and K is [tex]\bf \sqrt{97}[/tex] units.
name the property illustrated by each statement of if t-13=52, then 52=t-13
The property illustrated by each statement of if t-13=52, then 52=t-13 is commutative
t-13=52, then 52=t-13
The property illustrated to each statement is commutative because it shows that for some value of t both statements are equal.
In mathematics, a binary operation is commutative if changing the order of the operands does now not alternate the result. it's far a essential belongings of many binary operations, and lots of mathematical proofs rely on it. most acquainted as the call of the assets that says something like "3 + four = 4 + 3" or "2 × 5 = 5 × 2",
the property also can be utilized in greater superior settings. The name is wanted because there are operations, which includes department and subtraction, that do not have it (for example, "3 − five ≠ 5 − 3");
such operations are not commutative, and so are called noncommutative operations.
The idea that easy operations, along with the multiplication and addition of numbers, are commutative become for many years implicitly assumed.
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cost to rent a pavilion is $50 plus $15 for each hour of use.
e a rule for the cost of renting a park pavilion. Write ordered
= to represent the cost of renting a pavilion for 3, 4, 5, and 6 hours.
Answer:
the cost of renting the pavilion for 8 hours = $130
Step-by-step explanation:
$50 plus $10 per hour
so 8 hour = 10 * 8 = $80
$50 + $80 = $130
help with this please.
Using integrals, it is found that the cumulative distribution function(cdf) at x = 2.27 is given by:
P(X ≤ 2.27) = 0.897.
How to find the cumulative distribution function of a distribution?The cumulative distribution function of a distribution given by f(x) at a value of x = x* is given by the following integral:
[tex]\int_{-\infty}^{x^{\ast}} f(x) dx[/tex]
For this problem, the distribution is given by:
[tex]f(x) = e^{-x}, x > 0[/tex]
Hence, at x = 2.27, the cdf is given by:
[tex]\int_{0}^{2.27} e^{-x} dx[/tex]
The infinity was replaced by 0 because the lower bound of the definition of the distribution is of 0. Hence:
[tex]\int_{0}^{2.27} e^{-x} dx = -e^{-x}|_{x = 0}^{x = 2.27}[/tex]
Applying the Fundamental Theorem of Calculus:
P(X ≤ 2.27) = -e^(-2.27) + e^0 = -e^(-2.27) + 1 = 0.897.
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organic hotdogs are $2.00 each at the grocery store.At the major league baseball game, an organic hot dog costs $6.50. How much does the baseball field mark up its organic hot dogs?
Answer:$4.50, or a 325% markup
Step-by-step explanation:
yes?
The post office will only accept packages for which the length plus the "girth" (distance around) is no more than 108 inches. Thus, we must have L+2(x+y)<=108.
What is the greatest acceptable length for a package that has a square base measuring 9 inches by 9 inches?
answer
6 in. wide, 8 in. deep and 5 feet long.
Nina wants to download games for her video game console. Older games cost 150 points and new releases cost 600 points. Nina has 6000 points to use. The equation 150a+600b=6000, where a is the number of older games and b is the number of new releases, models the situation. How many older games can she download if she downloads one new game? four new games?
Considering the definition of an equation and the way to solve it, Nina can download 36 older games and 24 older games if she downloads one and four new games respectively.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it and the equality is true. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseIn this case, Nina wants to download games for her video game console. Older games cost 150 points and new releases cost 600 points. Nina has 6000 points to use.
The equation 150a+600b=6000, where a is the number of older games and b is the number of new releases models the situation.
If Nina downloads one new game, that means that the value of the variable "b" is 1. Substituting in the equation that models the previously mentioned situation, and solving, you obtain:
150a+600×1=6000
150a + 600=6000
150a= 6000 - 600
150a= 5400
a= 5400÷150
a= 36
If Nina downloads four new game, that means that the value of the variable "b" is 4. Substituting in the equation that models the previously mentioned situation, and solving, you obtain:
150a+600×4=6000
150a + 2400=6000
150a= 6000 - 2400
150a= 3600
a= 3600÷150
a= 24
Finally, Nina can download 36 older games and 24 older games if she downloads one and four new games respectively.
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How many full cases and additional items are needed to fulfill the order of 60 items ordered and 14 items per case
Answer:
Step-by-step explanation:
Answer:
there are many case and additional
items are needed to fulfill to order
of60items ordered
Step-by-step explanation:
18
26
52
44
Mandy is working at the zoo. She must record the ages of the tortoises There are 9 tortoises.
Their ages are 29, 2, 12, 26, 18, 34, 54, 44, and 18.
What is the mean age of the tortoises? You may use a calculator. Round to the nearest whole
number.
3) Read the following and answer the question
Answer:
26 is the approximate mean
Find a possible formula for the exponential function graphed below.
Check the picture below.
[tex]{\LARGE \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \textit{we know that} \begin{cases} x=0\\ y=40 \end{cases}\implies 40=ab^0\implies 40=a(1)\implies 40=a \\ ~\hfill \underline{y = 40b^x} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{we also know that} \begin{cases} x=3\\ y= 15 \end{cases}\implies 15 = 40b^3\implies \cfrac{15}{40}=b^3\implies \cfrac{3}{8}=b^3 \\\\\\ \sqrt[3]{\cfrac{3}{8}}=b\implies \cfrac{\sqrt[3]{3}}{\sqrt[3]{8}}=b\implies \cfrac{\sqrt[3]{3}}{2}=b~\hfill \underline{y = 40\left( \frac{\sqrt[3]{3}}{2} \right)^x}[/tex]
what are the next 2 numbers in 0.006 0.6 6 ___ ____ ??
Answer:
60 and 600
Step-by-step explanation:
im guessing..
What is the value of 12(a • b + a2) + 6 if a = 3 and b = −4?
A: −30
B: −42
C: −54
D: 330
Answer: -30 ==> A
Step-by-step explanation:
a = 3 and b = −4
12(a • b + a2) + 6=
12(a • b + a^2) + 6=
12(3 • (-4) + 3^2) + 6=
12(-12 + 9) + 6=
12(-3)+6=
-36+6=
-(36-6)=-30 ==> A
Answer:
a) -30
Step-by-step explanation:
Given that,
→ a = 3
→ b = -4
Let's solve the problem,
→ 12(a × b + a²) + 6
→ 12(3 × -4 + (3)²) + 6
→ 12(-12 + 9) + 6
→ 12 × -3 + 6
→ -36 + 6 = -30
Hence, the answer is -30.
Determine if the sentence is true. Select all that apply. □ 2 + 5 = 19 − 12 □ -.+ /. = 2 − 1 − 1 □ 5 − 4 − 3 − 2 − 1 = 30 − 34 − 1 □ 2 � + 8 = 2� − 8 □ 2 x + 5 − 4x = 3 x − 2 − 5x + 16
The equations that are true are:
2 + 5 = 19 - 12
5 - 4 - 3 - 2 - 1 = 30 - 34 - 1
Which sentences are true?Here we have some equations, the equations are only true if we have the exact same number in both sides of the equation.
The first one is:
2 + 5 = 19 - 12
If we simplify both sides we get:
2 + 5 = 7
19 - 12 = 7
Then the equation becomes:
2 + 5 = 19 - 12
7 = 7
This is true.
The next equation is:
5 - 4 - 3 - 2 - 1 = 30 - 34 - 1
If we simplify both sides we get:
5 - (4 + 3 + 2 + 1) = 30 - 35
5 - 10 = 30 - 35
-5 = -5
This is true.
The last equation is:
2x + 5 - 4x = 3x - 2 - 5x + 16
Here we have a variable, so we need to solve this for x.
2x -4x + 5 = 3x - 5x + 16 - 2
-2x + 5 = -2x + 14
-2x + 5 + 2x = 14
5 = 14
This equation is false, because 5 is different than 14.
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Your friend swims on the school team.
In his first four races, his times are 24.7, 23.5, 25.6, and 27.2 seconds
You need a value less than 23.5 or greater than 27.2.
Given the time in his first four races is: 24.7 , 23.5 , 25.6 , 27.2 seconds.
To find the time for her race which would make a higher difference, we need to make use of range.
The range formula is frequently employed in statistics to ascertain the range provided in a specific data set. The formula finds the difference between the lowest and highest value, which aids in locating the set's center. In distribution, a wide range denotes increased variability while a narrow range denotes lower variability. The mean, median, and mode are among the additional statistical concepts included in the range formula.
The range is the difference between the highest and lowest value. In this case, the highest and the lowest numbers are 27.2 and 23.5 seconds.
To make a larger range, we simply need to pick a number smaller than 23.5 or larger than 27.2. This will produce a larger difference (or range).
Hence we acquired the desired result.
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Your question is incomplete. Please find the missing content here.
Your friend swims on the school team.
In his first four races, his times are 24.7, 23.5, 25.6, and 27.2 seconds. Which time listed for her next race would make the range larger?
In the past month, Deandre rented 1 video game and 7 DVDs. The rental price for the video game was $3.20. The rental price for each DVD was $4.90. What Is
the total amount that Deandre spent on video game and DVD rentals in the past month?
Answer:
Deandre spent $36.50 on video games and DVD rentals in the past month.
Step-by-step explanation:
values
video game = $3.20
DVD = $4.90
let video games be represented with the variable v
dvd represented by the variable d
make an equation
7d + 1v = ?
plug in values
7(4.90) + 1(3.20) = ?
7 x 4.90 = 34.3
1 x 3.20 = 3.20
34.3 + 3.20 = 36.50
thus 7d + 1v = $36.50
8.
-2|3x+1|=-10
hsiaodkmakakcmd help
Answer: x=-2, 4/3
Step-by-step explanation:
-2|3x+1|=-10
-2|3x+1| / (-2) = -10/(-2)
-2|3x+1| / (-2) = 5
|3x+1|=5
3x+1=5
3x=4
x=4/3
3x+1=-5
3x=-6
x=-2
x=-2, 4/3
-5x-20+8+16x simplify please show steps
Answer:-12+16x
Step-by-step explanation:
-5x-20+8+16x
-5x-12+16x
-12+16x
Answer: 11x-12
Step-by-step explanation:
(-5x)-(20)+(8)+(16x)It would be easier to rearrange this equation by degree (ie ax^2, ax^1, a)
(16x)-(5x)-(20)+(8)You cannot subtract ax^1 by a, but you can subtract ax^1 by ax^1 (16x-5x)
16x-5x= 11xWe can also subtract a by a (-20+8)
-20+8= -12Remember your positive and negative signs
Answer: 11x-12In a video game, players start with a score of 100 points.
They earn 8 points for each gold coin and 25 points for
each gem they find. Mario finds 3 gold coins and 2 gems.
Write and evaluate an algebraic expression to find Marios
score. Use c for the number of gold coins found and g for
the number of gems found. Show your work.
SOLUTION
Mario's score in the video game is 174.
What is Mario's score?
Mario's score is a function of the number of points started with, the point per coin, the point per gem , number of gem and coins found. The mathematical operations that would be used are addition and multiplication.
Addition is the process of determining the sum of two or more numbers. Multiplication is the process of determining the product of two or more numbers.
Mario's score = beginning point + (number of gold coins x score per gold coin) + (number of gems x score per gem)
Mario's score = 100 + 3c + 2g
Mario's score = 100 + (3 x 8) + (2 x 25)
Mario's score = 100 + 24 + 50 = 174
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convert 7 yards per minute to feet per second
(3 feet=1 yard)
Answer:
0.35 feet per second
Step-by-step explanation:
To start, there's 3 feet in 1 yard.
So, we have to convert the 7 yards per minute to feet.
7 x 3 = 21
Then, we have to convert 21 feet per minute to X amount of feet per second.
To note, there are 60 seconds in a single minute
Therefore, you have to divide 21 by 60 to find the amount of feet in one second.
21 / 60 = 0.35
The answer is 0.35 feet per second
Calculate marginal opportunity costs using graph showing oranges and cherries
To calculate marginal cost ; we use "subtract the quantity change from the overall cost change."
The potential cost of increasing orange output from 50 to 80 units was (250 – 200) = 50 cherries.
The potential cost of increasing cherry production from 100 to 200 units was (86-80) = 6 oranges.
Opportunity cost for an orange right now is,
equals 1.67 cherries.
Opportunity cost is therefore 3.34 cherries for two oranges.
One cherry's opportunity cost is,
0.06 orange units
1.8 oranges are the opportunity cost of 30 cherries.
Conclusion
a. Cherry 50
b. Oranges, six
c. Cherry 3.34
d. Oranges, 1.8
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Which of the following represents the range of the graph of F(x) below?
A. x<2
B. All real numbers
C. y ≤ 2
-6
D. x≤2
FOX
6
(0, 2)
5
[tex]y \leqslant 2[/tex]
How to Write 209.105 in expanded form
Answer:
209.106 = (2 x 100) + (0 x 10) + (9 x 1) + (1/10) + (0/100) + (6/1000)
Answer: 200 + 9 + 0.1 + 0.005
Step-by-step explanation: For expanded form you need to break up the number into its individual parts. You have 2 hundreds, 9 ones, 1 tenths, and 5 thousandths.
This diagram shows a pre-image △ABC and its image, △A′′B′′C′′ , after a series of transformations.
Select from the drop-down menus to correctly complete the statements.
△ABC is
1. reflected across the y-axis.
2. rotated 90 degrees counterclockwise about the origin.
3. translated 4 units right
to become △A′B′C′. Then △A′B′C′ is
1. reflected across the x-axis.
2. reflected across the line y = x
3. rotated 90 degrees counterclockwise about the origin
to become △A′′B′′C′′ . Because the transformations are
1. both rigid
2.not both rigid,
The pre-image and image are
1. congruent
2. not congruent
Using translation concepts, we have that:
△ABC is 3. translated 4 units right to become △A′B′C′. Then, △A′B′C′ is 3. rotated 90 degrees counterclockwise about the origin to become △A′′B′′C′′ .Because the transformations are both rigid, the pre-image and the image are congruent.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
On the translation of △ABC to △A′B′C′, the rule applied to the vertices is:
(x,y) -> (x + 4, y).
Hence it was translated 4 units right.
On the translation of △A′B′C′ to △A′′B′′C′', the rule is given by:
(x,y) -> (-y,x).
Hence it was rotated 90 degrees counterclockwise about the origin.
The triangle keeps the same size after the translations, hence:
Because the transformations are both rigid, the pre-image and the image are congruent.
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Distribute 10(3x+8x^2)
Answer:
Evaluate
30x + 160xn
Step-by-step explanation:
Answer:
Solution :
30x + 80x^2
Step-by-step explanation:
1) Distribute the outer term into the first by multiplying the numerical values and then the terms
2) Repeat for the second one.