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Consider the following sequence 4, 8, . . .
a. Assuming the sequence is arithmetic:
i. Write the next four terms
ii. What is the generator?
iii. Write a formula for t(n).
iv. Create a table and graph your sequence.
b. Assuming the sequence is geometric:
i. Write the next four terms
ii. What is the generator?
iii. Write a formula for t(n).
iv. Create a table and graph your sequence
Answers
9514 1404 393
Answer:
a. 12, 16, 20, 24; t(n)=4n
b. 16, 32, 64, 128; t(n)=2·2^n
Step-by-step explanation:
a. The difference of the given terms is 8-4=4, so the arithmetic sequence has a first term of 4 and a common difference of 4. The general term has the formula ...
t(n) = t(1) +d(n -1)
t(n) = 4 +4(n -1) . . . . . with t(1) and d filled in
t(n) = 4n . . . . . . . . . . simplified
This formula can be considered to be the generator of the sequence. For values of n from 3 to 6, the next four terms are ...
t(3) = 12; t(4) =16; t(5) = 20, t(6) = 24
A table and graph are shown in the first attachment.
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b. The ratio of the given terms is 8/4 = 2, so the geometric sequence has a first term of 4 and a common ratio of 2. The general term has the formula ...
t(n) = t(1)·r^(n-1)
t(n) = 4·2^(n-1) . . . . . . . with t(1) and r filled in
t(n) = 2·2^n . . . . . . . . simplified
This formula can be considered to be the generator of the sequence. For values of n from 3 to 6, the next four terms are ...
t(3) = 16; t(4) = 32; t(5) = 64; t(6) = 128
A table and graph are shown in the second attachment.
Related Questions
3/8 + 1/8 + 2/3 - 1/2 =
Answers
Answer: 2/3 (answer in decimal form = 0.6)
Step-by-step explanation: The least common multiple (LCM) of two or more non-zero whole numbers is the smallest whole number that is divisible by each of those numbers. In other words, the LCM is the smallest number that all of the numbers divide into evenly. Then do the rest of the operations.
Amelia and her children went into a grocery store and she bought $10 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. She bought a total of 12 apples and bananas altogether. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Amelia bought.
Answers
Answer:
8 apples
4 bananas
Step-by-step explanation:
8 apples (8$)
4 bananas (4$)
12 total
10 $ total
hope it helps
Multiply.
3 1/2 times 2 2/3
Answers
Answer:
Step-by-step explanation:
What is the product?
(Y^2+3Y+7)(8y^2+y+1
Answers
Answer:
8y⁴+25y³+60y²+10y+7
Step-by-step explanation:
8y⁴+y³+y²+24y³+3y²+3y+56y²+7y+7
8y⁴+25y³+60y²+10y+7
Answer:
8y^4+25y^3+60y^2+10y+7
Step-by-step explanation:
(y^2+3y+7)(8y^2+y+1)
We are going to multiply the first term, y^2, by the whole second part (8y^2+y+1)
8y^4+y^3+y^2
now we multiply the 2nd term, 3y, by the whole second part (8y^2+y+1))
24y^3+3y^2+3y
now we do the same to the last term, 7.
56y^2+7y+7
now we need to add all three of our products together
(8y^4+y^3+y^2)+(24y^3+3y^2+3y)+(56y^2+7y+7)
adding like terms:
8y^4+y^3+24y^3+y^2+3y^2+56y^2+3y+7y+7
we get:
8y^4+25y^3+60y^2+10y+7
The perimeter of a rectangle is represented by the expression 12x-2812x−28. The length of the rectangle is represented by the expression 2x+102x+10. Which expression represents the width of the rectangle?
Answers
Answer:
339,006 that's the answer
a man walks for 45 minutes at a rate of 3 mi/h then jogs for 75 minutes at a rate of 5 mi/h then rests for 30 minutes and finally walks for 90 minutes at a rate of 3 mi/h. Write a piecewise-defined function expressing the distance he traveled as a function of time.
Answers
Answer:
Sorry need points
Step-by-step explanation:
Is 27, 333 divisible by 3? Write the number 27,333 as the product of 3 and another factor.
Answers
Yes, 3 divides 27,333. We have
27,333 = 27,000 + 333
… = 27•1,000 + 333
… = 3•9•1,000 + 3•111
… = 3•(9•1,000 + 111)
… = 3•(9,000 + 111)
… = 3•9,111
e/kaid_274404147475337871026587/assig!
Khan Academy
Percent word problems
Of the 50 U.S. states, 4 have names that start with the letter W.
What percentage of U.S. states have names that start with the letter W?
0
Stuck? Review related articles/videos or use a hint.
Answers
Answer:
Step-by-step explanation:
4/50 = 0.08
0.08(100) = 8%
Hanna and Dien are both getting a raise. Who will earn more
per hour after the raise?
Answers
Step-by-step explanation:
First, you need to calculate how much they will earn per hour by multiplying their raise per hour by there hours and adding it to their earnings divided by the hours worked. Then, whoever's is the highest will be the answer.
Hanna will earn more per hour after the raise, with an hourly rate of $10.75 compared to Dien's hourly rate of $10.60.
What is Division?A division is a process of splitting a specific amount into equal parts.
To find the new earnings per hour for Hanna and Dien
Divide their total earnings after the raise by the total number of hours they worked after the raise.
The raise per hour is already given, so we can simply add it to their old hourly rate.
For Hanna, her new hourly rate would be:
(New earnings) / (Hours worked) = (78 + 8) / 8
= 86 / 8
= $10.75
This means that Hanna will earn $10.75 per hour after the raise.
For Dien, his new hourly rate would be:
(New earnings) / (Hours worked) = (60.60 + 3) / 6
= 63.60 / 6
= $10.60
This means that Dien will earn $10.60 per hour after the raise.
Therefore, Hanna will earn more per hour after the raise, with an hourly rate of $10.75 compared to Dien's hourly rate of $10.60.
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Find the value for x.
Answers
Answer:
x = 21Step-by-step explanation:
5x - 12 = 3x + 30
5x - 3x = 30 + 12
2x = 42
x = 21
---------------------
check
5 * 21 - 12 = 3 * 21 + 30
93 = 93
the answer is good
Issac wanted to make a homemade bubble solution to play with his friends. A bubble recipe he found requires 4 cups of warm water for every 1/2 cup of soap. If he had 2/3 cup of soap how many cups of warm water will he need
A- 1/12
B- 1 1/3
C- 5/13
D- 8
Answers
Answer: 8/3
You first do 4x2 than you would have to divide by 3. 4x2*3
The number of cups of warm water need for 2/3 cup of soap to make solution is [tex]5\frac{1}{3}[/tex]. Therefore, option C is the correct answer.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, a bubble recipe he found requires 4 cups of warm water for every 1/2 cup of soap.
Let the number of cups of warm water need for 2/3 cup of soap be x.
Now, the proportion is
4:1/2 :: x:2/3
1/2 x=4×2/3
x/2=8/3
x=16/3
x= [tex]5\frac{1}{3}[/tex]
Therefore, option C is the correct answer.
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You pay a real estate agent a 4% commission for selling your
house. After paying the commission, you receive $302,900. What
was the actual selling price of the house?
Yes
Answers
Answer:
Step-by-step explanation: 56
A pair of shoes is originally sold for $85. Currently, there is a 15% off sale. How much would the pair of shoes cost after the discount? Group of answer choices
Answers
Answer:
$72.75
Step-by-step explanation:
15% of $85 is $12.75
$85 - $12.75 = $72.25
Which equation represents a line that is parallel to the line 4x-3y=15
1) y = -4/3x - 4
2) y = -3/4x - 2
3) y = 4/3x + 2
4) y = 3/4x - 6
Answers
Answer:
1
Step-by-step explanation:
because... it is
I need help with the question
Answers
Answer:
[tex]A = 25\pi[/tex] or 25 × 3.14 = 78.5m
Step-by-step explanation:
The radius is half of the diameter. So the radius = 5m (10/2)
[tex]A = \pi r^{2}[/tex]
[tex]A = \pi (5^{2} )[/tex]
[tex]A = 25\pi[/tex]
If the legs of each triangular base are 5 cm and 3 cm and the height of the prism is 4 cm, what
are the coordinates of the vertices of the prism?
Answers
The coordinates of the six vertices of the prism are listed below:
[tex](x_{1},y_{1}, z_{1}) = (0, 0, 0)\,[ft][/tex] [tex](x_{2}, y_{2}, z_{2}) = (0, 0, 5)\,[ft][/tex] [tex](x_{3}, y_{3}, z_{3}) = (3, 0, 0)\,[ft][/tex] [tex](x_{4}, y_{4}, z_{4}) = (0, 4, 5)\,[ft][/tex] [tex](x_{5}, y_{5}, z_{5}) = (0, 4, 0)\,[ft][/tex][tex](x_{6}, y_{6}, z_{6}) = (3, 4, 0)\,[ft][/tex]The number of vertices of a prism with a polygonal base ([tex]n[/tex]) is described by the following expression:
[tex]n = 2\cdot s[/tex] (1)
Where [tex]s[/tex] is the number of sides of the base.
If we know that [tex]s = 3[/tex], then the number of vertices of the prism are:
[tex]n = 2\cdot 3[/tex]
[tex]n = 6[/tex]
A prism with triangular base has six vertices, let suppose that the triangle of the base is right-angled. and coincides with a right-hand rectangular coordinate system. Then, we can conclude that the coordinates of the six vertices are the following:
[tex](x_{1},y_{1}, z_{1}) = (0, 0, 0)\,[ft][/tex] [tex](x_{2}, y_{2}, z_{2}) = (0, 0, 5)\,[ft][/tex] [tex](x_{3}, y_{3}, z_{3}) = (3, 0, 0)\,[ft][/tex] [tex](x_{4}, y_{4}, z_{4}) = (0, 4, 5)\,[ft][/tex] [tex](x_{5}, y_{5}, z_{5}) = (0, 4, 0)\,[ft][/tex][tex](x_{6}, y_{6}, z_{6}) = (3, 4, 0)\,[ft][/tex]We kindly invite to check this question on prisms: https://brainly.com/question/8828506
Find The slope of the line represented by the points in the table (use your notes to get the formula it needed).
4.
Number
of Hours
1
2.
3
4
Cost
($)
$17
$29
$41
$53
Answers
Solve the inequalities from parts A and D for the variables b and n, respectively.
Part A:2b<56
Part D:n<56
Answers
Answer:
Part A: b < 28
Part D: n < 56
Step-by-step explanation:
part A: divide each term in and simplify.
Inequality Form: b < 28
part d: this is already solved but can be shown in multiple forms.
Inequality Form: n < 56
Interval Notation: ( -∞ , 56)
Determine the ordinary simple interest on a 90-day loan of Php8000 at 8 ½ % interest rate.
Answers
Answer:
$170
Step-by-step explanation:
Pls help brainlist pls help
Answers
Answer:
The slope of the function represents how much the function rises per amount that it moves horizontally.
Step-by-step explanation:
Help help help math please help help
Answers
Answer:
x=11
Step-by-step explanation:
We know that angles on a straight line equal 180 degrees, so we know that 8x+10+7x+5 = 180.
Simplify
15x+15=180
Solve
Take away 15 from both sides
15x = 165
Divide 165 by 15
x = 11
(8 points) will mark brainliest!! pls help:)
Answers
Answer:
-0.366666666667
Step-by-step explanation:
that's what you get when you divide -22/5 (-4 2/5) by 4/3 (1 1/3)
Answer:
-24/5 is the correct answer.
Steps:
1) -4 x 2/5 = -8/5
2) 1 x 1/3 = 1/3
3) -8/5 : 1/3 = -24/5
Please take a look at the picture
Answers
Answer:
B) -g/-h
Step-by-step explanation:
-g/-h=g/h
Rewrite the fraction.
-(-g/h) = g/h
Hope this helps :)
What is the equation for the line in slope-intercept form?
Enter your answer in the box.
Answers
What is the Bill of Rights?
The first amendment to the Constitution, which is actually a group of ten amendments
The list of laws that people of the United Stated needed to follow
The document that replaced the Constitution
The document that replaced the Articles of Confederation
Answers
Answer:
The first amendment to the Constitution, which is actually a group of ten commandments
Step-by-step explanation:
The first amendment to the Constitution is actually a group of ten amendments called the Bill of Rights. The Bill of Rights guarantees all Americans certain freedoms, such as freedom of religion, freedom of the press, freedom of speech, the right to bear arms, and the right to a fair trial.
2yx= 4 is it a linear function?
Answers
Answer:
No, it is not a linear function, rather a rational function
Step-by-step explanation:
Because the term on the left-hand side contains both x and y, then neither variable varies directly with the other, hence, it's a rational function:
2yx=4
yx=2
y=2/x
Write as a fraction
3÷151
Answers
Answer:
3/151
Step-by-step explanation:
That's the answer
pls help me find the missing angle
Answers
Answer:
b=114
c=43................
An ice cream factory makes 300 quartz of ice cream in 10hr how many quartz can be made in 12 hours
Answers
Answer:
360
Step-by-step explanation:
Answer:
360 quarts
Step-by-step explanation:
300/10=30
30*12=360
What is the surface area of the rectangular prism below?
Answers
Answer:
8*8 *2=64
8*19 *2=304
8*19*2=304
672units is your answer
The surface area of the rectangular prism below is 736 square units
Surface area of rectangular prismThe formula for calculating the surface area of the rectangular prism is expressed as:
A = 2(lw + wh + lh)
Given the following parameters
l = 8
w = 19
h = 8
Substitute
SA = 2(8(19) + 8(19) + 8(8))
SA = 2(152 + 152 +64)
SA = 2(304+ 64)
SA = 2(368)
SA = 736 square units
Hence the surface area of the rectangular prism below is 736 square units
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