Hello, would be very nice if someone could help me ! :)
A finite geometric series is the sum of a sequence of numbers. Take the sequence
1, 2, 4, 8, ..., for example. Notice that each number is twice the value of the
previous number. So, a number in the sequence can be represented by the
function f(n) = 2^n-1. One way to write the sum of the sequence through the 5th
number in the sequence is ∑^5 n-1 2^n-1.
This equation can also be written as S5 = 2^0+2^1+ 2^2+ 2^3+ 2^4. If we multiply this equation by 2. the equation becomes 2(S5) = 2^1+ 2^2+ 2^3+ 2^4+ 2^5
What happens if you subtract the two equations and solve for S5? Can you use this information to come up with a way to find any geometric series Sn in the
form ∑^a n-1 b^n-1 ?
Answer:
Step-by-step explanation:
2S₅ - S₅ = 2⁵ - 2⁰
S₅ = 2⁵ - 1
Sₙ = (bᵃ - 1) / (b - 1)
Summer Earnings
Hours worked Earnings in dollars
3
4
48
6
72
10
120
20
240
Which statements are true about the data in this table? Select all that apply.
The rate of change for the data is $12 per hour. $12 is also the constant of proportionality
If you graph the data, it would pass through the origin (0,0)
The data represent a direct variation and can be modeled by the function rule y = 12.
The data indicate a rate that is not constant
The rate of change for the data is $24 per hour. The data representa direct variation and can be modeled by the function ruley-242
The table is an illustration of a proportional relationship. and can be modeled by the function rule y = 12x
The entries of the table is given as:
Hours Earnings
4 48
6 72
10 120
20 240
Start by calculating the rate (m) of the function
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
So, we have:
[tex]m = \frac{72 - 48}{6-4}[/tex]
[tex]m = \frac{24}{2}[/tex]
[tex]m = 12[/tex]
The equation of the table is then calculated as:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = 12(x - 4) + 48[/tex]
[tex]y = 12x - 48 + 48[/tex]
[tex]y = 12x[/tex]
[tex]y = 12x[/tex] means that, the following statements are true:
The rate of change for the data is $12 per hour. $12 is also the constant of proportionalityIf you graph the data, it would pass through the origin (0,0) The data represent a direct variation and can be modeled by the function rule y = 12xRead more about proportional equations at:
https://brainly.com/question/14108707
What is the value of
8x2 + 3x when x = 4?
Answer:
28
Step-by-step explanation:
8*2=16
3*4=12
Then you add 16+12
hopefully it helps
Answer:
76
Step-by-step explanation:
plug in 4 in the equation:
8(4)2 + 3(4) = 76
Please help I'll mark brainliest
A cook came across two cups and one saucer in a kitchen cupboard.
Bored for something to do, she weighed each item.
Altogether, the three items came to 12 ounces.
The larger cup with the saucer weighed exactly double of the smaller cup.
The smaller cup with the saucer weighed exactly the same as the larger cup.
What did each item weigh?
Answer: saucer 3 ounces smaller cup 3 ounces larger cup 6 ounces
Step-by-step explanation:
LAST ATTEMPT MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)
Answer:
There ya go
Step-by-step explanation:
6(25-8w)+20w for w=2
150−28w
i think i dont know
Help, im incredibly confused
[tex]f[/tex](x) = 0.20x + 35 : 29.5
Roy used 1/4 of his money on 3 pens and 6 notebooks. The cost of each pen is 3 times the cost of each notebook. He bought some more pens with 2/3 of his remaining money. How many pens did Roy buy altogether?
=========================================================
Explanation:
Roy spends 1/4 of his money on 3 pens and 6 notebooks. That means 3/4 of it is leftover.
2/3 of 3/4 = (2/3)*(3/4) = 1/2 of his money is spent on buying some unknown number of additional pens. We'll come back to this later.
---------------
In terms of cost,
1 pen = 3 notebooks
which is another way of saying 1 pen is the same price as 3 notebooks.
Multiply both sides by 2 to get
2 pens = 6 notebooks
Therefore, saying "3 pens + 6 notebooks" is the same as "3 pens + 2 pens = 5 pens" when just thinking about costs.
---------------
In short, Roy buying 3 pens and 6 notebooks is the same as him buying 5 pens. He spends 1/4 = 25% of his money on getting these 5 pens.
Multiply those two values by 2 to find that 50% = 1/2 of his money would allow him to get 10 pens.
--------------
Recall that at the end of the first section, we concluded that Roy spent 1/2 of his money on buying those unknown additional number of pens. Then the previous section mentioned that 1/2 of his money gets him 10 pens. Therefore, he must have bought 10 additional pens on top of the original 3 mentioned in the instructions.
Overall, he purchased 3+10 = 13 pens
Answer:
13 pens
Step-by-step explanation:
If a pen costs 3 times the cost of a notebook, then the cost of 3 notebooks will equal the cost of a pen. The 6 notebooks that Roy bought are equivalent in cost to 2 pens, so 1/4 of Roy's money is the cost of 3+2 = 5 pens.
After the first purchase, Roy has (1 -1/4) = 3/4 of his money remaining. If he spends 2/3 of that on more pens, he will have spent ...
(2/3)(3/4) = 2/4
of his money on more pens. We've already seen that 1/4 of his money buys 5 pens, so 2/4 will buy 10 more pens.
Roy bought 3 +10 = 13 pens altogether.
50, 60, 72, ...
Find the 8th term.
c. A square that is 8 inches on a side is placed inside a rectangle that has a length of 24 inches and a width of 20 inches. What is the area of the region inside the rectangle that surrounds the square?
Area = length x width
Area of square = 8 x 8 = 64 square inches
Area of rectangle = 24 x 20 = 480 square inches
Area of rectangle surrounding the square = 480 - 64 = 416 square inches
Answer: 416 square inches
What is 40÷1/2 please help me
Answer: Pretty sure it's 80
Step-by-step explanation:
Please look for the question in the picture.
Answer: The blue dot's value on the number line is 1.
Step-by-step explanation: Each two-skip interval from -7 to -3 is a skip of 4. Therefore, -3 skipped two times is -3 + 4, which equals 1, therefore the blue dot's value on the number line is 1.
You flip a coin 8 times and get tails 6 times. Based on this experiment, what is the probability of flipping a coin and getting heads?
Answer:
1/4
Step-by-step explanation:
If you get 6 tails, then that means you got 2 heads. 8-6=2.
probability= 2/8=1/4 based on this experiment.
Omar needs at least $8 to buy lunch. Which number line represents this scenario?
Answer:
I'd say none, as we're missing something in this problem. Make sure you've included everything to solve this problem. Thanks.
If angle 1 is 110°, what would the other angle measures have to be in order for m || n andq || p?
Angle 2 = °
Angle 3 = °
Angle 4 = °
Answer:
8
Step-by-step explanation:
Answer:
ANGLE2=110° ANGLE3=70° ANGLE4=70°
The two triangles are similar. Find the values of the unknown variables
Answer:
x = 84 y = 59°
Step-by-step explanation:
x = (40/30)×63
x = 84
∆ABC = ∆PQR
so y = 59°
Answer:
1.) 47
2.) 28
Step-by-step explanation:
you just had to use the sin equation for both
Th stalest tree in the world is a red wood in red wood national and state parks .it is 379feet tall .how many yards is this
Answer:
126 1/3 yards
Step-by-step explanation:
1 foot = 1/3 yard
379 feet = 379/3 yard= 126 1/3 yards
PLEASE HELP ME WITH GEOMETRY
Answer:
The answer is A.
Step-by-step explanation:
It is A because both sides match up except for the last pair, where they are the same. Hope this helped!
Which expression is undefined?
Answer:
D: [tex]\frac{3}{(6-6)}[/tex]
Step-by-step explanation:
Option A equates to [tex]-\frac{0}{2}=0[/tex]
Option B equates to [tex]\frac{(-4+0)}{8}=\frac{-4}{8}=-\frac{1}{2}[/tex]
Option C equates to [tex]0\div11 =0[/tex]
Option D equates to [tex]\frac{3}{(6-6)}=\frac{3}{0}[/tex] which cannot be defined as division by 0 is impossible
f(x)=x^2. what is g(x)?
Write five demicals that round to 0.96?
Answer:
0.964
0.959
0.961
0.958
0.963
Step-by-step explanation:
Anything below 5 can be rounded down, anything above 5 can be rounded up.
You can have a decimal after 0.96 to be less than 5, or a decimal after 0.95 to be greater than 5.
Here's some I picked:
0.964
0.959
0.961
0.958
0.963
What does it mean to be an independent student? A. You must pick your own study topics and research them. B. You can set your own deadlines, within a fixed time frame. C. You are responsible for your own study schedule and organization. D. You are expected to work without extra help from a teacher or tutor.
Answer:
C
Step-by-step explanation
It makes the most sense
Answer:
check online for more information
i need help plz
thanks
The perimeter of a rectangular floor is 240 feet. Find the dimensions of the floor if the length is three times the width
The floor has a length of feet and a width of feet.
Answer:
length: 90 ft
width: 30 ft
Step-by-step explanation:
The sum of length and width is half the perimeter, so is 120 ft. The length is 3/(3+1) = 3/4 of the sum, so is (3/4)(120 ft) = 90 ft. The width is 120 ft -90 ft = 30 ft.
The floor has a length of 90 feet and a width of 30 feet.
Which story represents the equation six-sevenths times one-fourth?
A: Victoria drinks six-sevenths of a cup of milk. She drinks one-fourth of a cup more milk. How much milk did she drink in all?
B: Mike walked one-fourth mile and then he took the bus for six-sevenths miles to school. How many miles did he travel in total?
C: Victoria has six-sevenths of a pizza. She ate one-fourth of it for dinner. How much pizza did Victoria eat for dinner?
D: Mike has six-sevenths of a pie. He gives one-fourth to his brother. How much pie does he have left?
Answer:
C I think.
Step-by-step explanation:
I don't know for sure, but A, B and D all talk about adding or subtracting the answers together, while C tells us to find the fraction of a fraction so I'm pretty sure you multiply. Hope this helps!
Which numbered choice shows a set of numbers whose product is -20 and whose sum is +1?
Casey bought 9 tickets to a concert. The total charge was $104, including a $5 service charge. Write an equation you can use to solve to find c, the cost of one ticket.
Answer:
104-5/9
Step-by-step explanation:
just divided ND SUBTRACT
what does 5/6+1/3 equal
Answer:
5/6 + 1/3 = 7/6
Step-by-step explanation:
The area of a square is s2, where s is the side length of the square. Jack has a square-shaped flower garden in his yard. Each side of the garden is 8 feet. What is the area of the flower garden?
Answer:
64 square feet
Step-by-step explanation:
A = s² = 8² = 8*8 = 64
Use the fundamental identities to
Find tan s if sin s=3/4 and s is in quadrant 2
Answer:
Cosine Formula
Thus, the cosine of angle α in a right triangle is equal to the adjacent side's length divided by the hypotenuse. To solve cos, simply enter the length of the adjacent and hypotenuse and solve.