Answer:
The sum of terms 12 the geometric sequence 1,3,9... = 265720
Step-by-step explanation:
Formula:-
Sₙ = a₁(1 - rⁿ)/(1 - r)
Where Sₙ - sum of n terms in the GP
a - First term of GP
r - Common ratio
n - Number
It is given the geometric sequence 1,3,9....
To find the sum of 12 terms
Here a = 1, r = 3 and n = 12
Sₙ = a₁(1 - rⁿ)/(1 - r) = 1(1 - 3¹²)/(1- 3) = 265720
Answer:
The sum of the 12 terms = 265720
Step-by-step explanation:
* Lets study the geometric sequence rule
- If a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , .........................
∴ an = a[(r)^(n-1)]
- Where a is the first term and r is the common ratio and
n is the position of the term in the sequence
- The rule of the sum of some terms is Sn = [a(1 - r^n)]/(1 - r)
- Where n is the number of terms we want to add
* Lets check our terms in the sequence
- The terms are 1 , 3 , 9 , ..........
- To find the common ratio divide the 2nd term by 1st term
∵ the second term is 3 and the first term is 1
∴ 3/1 = 3
∴ The common ratio is 3
∵ n = 12 and a = 1
* Lets substitute the values of a , r , n in the rule of the sum to
find the sum of the 12 terms
∴ S12 = [1(1 - 3^12)]/(1 - 3) = (1 - 3^12)/-2 = 265720
* The sum of the 12 terms = 265720
what is the measure of angle F in degrees and please explain step by step
At the beginning of January, Kesia Records paid $148,950 to acquire the exclusive rights to a new album. It costs them $1.13 to print a copy of this album, which they can sell for $9.75. The following chart shows the sales of that record, along with the overhead expenses of running a record studio, not counting production costs. Month Albums Sold Expenses Jan. 5,486 $27,714 Feb. 8,191 $21,689 Mar. 4,796 $25,195 Apr. 7,490 $28,766 May 6,272 $24,604 Jun. 5,131 $29,040 In whch month did Kesia Records first break even? a. January b. March c. April d. May
Answer:
d. May
Step-by-step explanation:
To find when Kesia records got to break even, we first need to find how much they made total per month.
Now we need to first find how much they made on January.
The production cost of January will be:
Production cost = 5486 x 1.13
Production cost = $6199.18
Now that we know the production cost, we need to solve first for the total revenue.
Total Sales Revenue = 5486 x 9.75
Total Sales Revenue = $53488.50
Now that we have both the revenue and the production cost, we need can find how much profit by:
Profit = Total Sales Revenue - Production cost - Overhead
Profit = 53488.50 - 6199.18 - 27714
Profit = $19575.32
So they made a profit of $19575.32 by the end of January.
Now we move on to the other months.
Production cost = 8191 x 1.13
Production cost = $9255.83
Total Sales Revenue = 8191 x 9.75
Total Sales Revenue = $79862.25
Profit = 79862.25 - 9255.83 - 21689
Profit = $48917.42
Now that we have the profit for 2 months, we simply add them together.
Current Value = 19575.32 + 48917.42
Current Value = 68492.74
By doing the same process with the rest of the months, we get:
Refer to Image.
We can see in the image that by May they reach a total profit of $149897.77.
Since Kesia records paid $148950, the company got to break even at the month of May.
Answer:
d
Step-by-step explanation:
on the subway eight out of 11 people are carrying a briefcase based on this information if there are 700 people on the subway then about how many do not have a briefcase
509 people.
[tex]700 \div 11 = 63.6363[/tex]
[tex]8 \times 63.6363 = 509.094[/tex]
you can't have 0.094 of someone so we round the answer off the 509.
Two points on a line are chosen to find the slope. The rise is 8 and the run is 12. What is the slope of the line?
Answer:
[tex]\large\boxed{The\ slope\ m=\dfrac{2}{3}}[/tex]
Step-by-step explanation:
[tex]\text{The slope}\ m=\dfrac{rise}{run}\\\\\text{We have}\ riese=8\ \text{and}\ run=12.\ \text{Substitute:}\\\\m=\dfrac{8}{12}=\dfrac{8:4}{12:4}=\dfrac{2}{3}[/tex]
Answer:
The Slope is [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Slope is calculated by the formula [tex]m=\frac{rise}{run} \\[/tex]
Here the rise = 8 ad the run = 12. So the slope can be calculated as
[tex]m = \frac{rise}{run} = \frac{8}{12} = \frac{2}{3}\\[/tex]
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a direct variation includes the points (4,20) and (1,n). find n
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf (\stackrel{x}{4},\stackrel{y}{20})\qquad \textit{we know that } \begin{cases} x=4\\ y=20 \end{cases}\implies 20=k4\implies \cfrac{20}{4}=k \\\\\\ 5=k~\hspace{10em} therefore\qquad \boxed{y=5x} \\\\\\ (\stackrel{x}{1},\stackrel{y}{n})~~\textit{when x = 1, what is \underline{y}?}\qquad y=5(1)\implies \stackrel{n}{y}=5[/tex]
I reallly neeeeeeed help so anybody??
Answer:
D
Step-by-step explanation:
Since the ordered pairs are linear then the slope m between corresponding points will be equal.
To calculate m use the slope formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (6, 7) and (x₂, y₂ ) = (2, 5)
m = [tex]\frac{5-7}{2-6}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]
Repeat with (x₁, y₁ ) = (6, 7) and (x₂, y₂ ) = (k, 11)
m = [tex]\frac{11-7}{k-6}[/tex] = [tex]\frac{1}{2}[/tex], that is
[tex]\frac{4}{k-6}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )
k - 6 = 8 ( add 6 to both sides )
k = 14 → D
I need the answer to number 4
Answer: 6.3
Step-by-step explanation
I did this today and it's easy but you have to show a lot of work well I did but you don't have to you can just circle it in
Which point has the coordinates (-3 1/2,2)
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷The answer is point X.
Explanation: If you can see the graph, You can see that there are two points that are on the left, which is negative for the first number. Then, the second number, the Y position, which is 2, goes up, not down. So the right one is point X.
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
DOGE
The point X has the given coordinates (-3 1/2, 2).
How do we read a graph in the Coordinate (x-y) plane?A point on the graph can be read as a point (x, y) where y is the perpendicular distance of the point from the x-axis and x is the perpendicular distance of the point from the y-axis.
If the point is left to the y-axis, we take the distance negative.
If the point is below the x-axis, we take the distance negative.
How do we solve the given question?We are asked which point in the graph represents the point (- 3 1/2, 2).
To answer the question, we will analyze all the points to determine their coordinates.
Point W:
The perpendicular distance from the y-axis (x) = 2 units.
The perpendicular distance from the x-axis (y) = 3 1/2 units.
∴ The point W is (2, 3 1/2).
Point X:
The perpendicular distance from the y-axis (x) = 3 1/2 units.
The perpendicular distance from the x-axis (y) = 2 units.
∵ The perpendicular distance from the y-axis (x) is on the left side of the y-axis, we take x = 3 1/2 as negative, that is, x = -3 1/2.
∴ The point X is (-3 1/2, 2).
Point Y:
The perpendicular distance from the y-axis (x) = 2 units.
The perpendicular distance from the x-axis (y) = 3 units.
∵ The perpendicular distance from the y-axis (x) is on the left side of the y-axis, we take x = 2 as negative, that is, x = -2.
∵ The perpendicular distance from the x-axis (y) is below the x-axis, we take y = 3 as negative, that is, y = -3.
∴ The point Y is (-2, -3).
Point Z:
The perpendicular distance from the y-axis (x) = 2 units.
The perpendicular distance from the x-axis (y) = 3 units.
∵ The perpendicular distance from the x-axis (y) is below the x-axis, we take y = 3 as negative, that is, y = -3.
∴ The point Z is (2, -3).
∴ We can say that point X has the given coordinates (-3 1/2, 2).
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indicate in standard form the equation of the line passing through the given points (6,2) m=-1/2
Answer:
x + 2y = 10Step-by-step explanation:
The standard form of an equation of a line:
[tex]Ax+By=C[/tex]
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the point (6, 2) and the slope m = -1/2. Substitute:
[tex]y-2=-\dfrac{1}{2}(x-6)[/tex]
Convert to the standard form:
[tex]y-2=-\dfrac{1}{2}(x-6)[/tex] multiply both sides by 2
[tex]2y-4=-(x-6)[/tex]
[tex]2y-4=-x+6[/tex] add 4 to both sides
[tex]2y=-x+10[/tex] add x to both sides
[tex]x+2y=10[/tex]
You want to take a trip to New Zealand.
Your friend does some research and tells you the range of the prices for flights is $651.
Which of the following could be the prices for flights that your friend found?
$890, $1340, $1441, $1210
$930, $1620, $1245, $1581
$942, $1593, $1220, $980
$1260, $925, $1676, $1095
Answer: The correct answer is the third choice.
Step-by-step explanation: In order to solve this problem you need to calculate the range of each of the options presented. In order to do this you need to calculate the difference between the highest number and the lowest number. In the third option the lowest number is $942 and the highest number is $1,593. $1,593 - $942 = $651.
The prices my friend found are $942, $1593, $1220, $980.
What is range?Range is the difference between the highest and lowest values of a set of observations. Range is a measure of variation.
Range = highest value - lowest value
Which could be the set of prices?In order to determine the prices found, we have to determine the range of each option.
Option A: $1441 - $890 = $551Option B: $1581 - $930 = $690Option C: $1593 - $942 = $651Option D: $1676 - $925 = $751To learn more about range, please check: https://brainly.com/question/23748991
A canoe can go 24 KM downstream in three hours. The return trip takes four hours. What is the speed of the current?
Answer:
The speed of the current 1 km/hr
Step-by-step explanation:
It is given that,
A canoe can go 24 KM downstream in three hours. The return trip takes four hours.
Points to remember
Let speed of canoe in still water = x km/hr
Speed of stream or current = y km/hr
Downstream speed with stream speed = x + y
Upstream speed against stream speed = x - y
To find the speed of current
From the given information we can write,
Downstream speed = x + y = 24/3 = 8 km/hr
upstream speed =x - y = 24/4 = 6 km/hr
y = [(x + y) - (x -y)]/2 = (8 - 6)/2 = 1
Therefore the speed of the current = 1 km/hr
what is Convert 32º 15’ 45” to decimal
Answer:
N\77777
Step-by-step explanation:
Answer:
N\77777
Step-by-step explanation:
simplify (-5xsquared-3x-7)+(-2x to the third +6xsquared -8)
Answer:
[tex]\large\boxed{(-5x^2-3x-7)+(-2x^3+6x^2-8)=-2x^3+x^2-3x-15}[/tex]
Step-by-step explanation:
[tex](-5x^2-3x-7)+(-2x^3+6x^2-8)\\\\=-5x^2-3x-7-2x^3+6x^2-8\qquad\text{combine like terms}\\\\=-2x^3+(-5x^2+6x^2)-3x+(-7-8)\\\\=-2x^3+x^2-3x-15[/tex]
3x - x + 3 + x - 5 - x = x + 10
Answer:
x=12
Step-by-step explanation:
Let's solve your equation step-by-step.
3x−x+3+x−5−x=x+10
Step 1: Simplify both sides of the equation.
3x−x+3+x−5−x=x+10
3x+−x+3+x+−5+−x=x+10
(3x+−x+x+−x)+(3+−5)=x+10(Combine Like Terms)
2x+−2=x+10
2x−2=x+10
Step 2: Subtract x from both sides.
2x−2−x=x+10−x
x−2=10
Step 3: Add 2 to both sides.
x−2+2=10+2
x=12
Answer:
x= 12
Step-by-step explanation:
Cancel xx on both sides.
3x-x+3-5-x=103x−x+3−5−x=10
3x-x+3-5-x3x−x+3−5−x to x-2x−2.
x-2=10x−2=10
3 Add 22 to both sides.
x=10+2x=10+2
10+210+2 to 1212.
x=12x=12
Please help in this question
Answer:
3
Step-by-step explanation:
first turn 9 and 3/4 and make it inproper fraction wich is 27/4
then divide them
Answer:
a
Step-by-step explanation:
2 3/4 x 6 2/3 what would be the answer
Answer:
do the work
Step-by-step explanation:
convert the 2 fractions
then multiply vetically
Answer:
18 1/3
Step-by-step explanation:
Multiply the two fractions together
Plz help !! Me with it
Answer:
x=31
Step-by-step explanation:
4+ sqrt (x+5) = 10
Subtract 4 from each side
4 -4+ sqrt (x+5) = 10-4
sqrt(x+5) = 6
Square each side
(sqrt(x+5))^2 = 6^2
x+5 = 36
Subtract 5 from each side
x+5-5 = 36-5
x = 31
Answer: b. 31
Step-by-step explanation:
[tex]4+\sqrt{x+5}=10\\\\\sqrt{x+5}=6\\\\(\sqrt{x+5})^2=(6)^2\\\\x+5=36\\\\x=31\\\\\\Check:\\4+\sqrt{(31)+5}=10\\\\4+\sqrt{36}=10\\\\4+6=10\ \checkmark[/tex]
What is the approximate area of the shaded region
ANSWER
The correct answer is
21.5 square centimeters
EXPLANATION
The shaded area is the area of the square minus the area of the Circle.
Area of shaded region
[tex] = {l}^{2} - \pi \: {r}^{2} [/tex]
From the diagram,
[tex]l = 10cm[/tex]
and
[tex]r = \frac{l}{2} = \frac{10}{2} = 5cm[/tex]
This implies that,
Area of shaded region
[tex] = {10}^{2} - \pi \times {5}^{2} [/tex]
[tex] = 100 -25 \pi [/tex]
[tex] \approx21.5 {cm}^{2} [/tex]
The answer would be 21.5 square centimeters. Hope this helps!
Tabitha received $2,200 from her aunt as a birthday gift. She decided to put the money in an account to save for college. The account has a fixed interest rate of 7.8%, compounded semi-annually. How much money will be in the account after five years?
3225.36
Step-by-step explanation:
In triangle DEF the measure of angle DFE is 12.4 degrees and the measure of angle DEF is 92.1 degrees what is the measure of angle EDF in degrees
The sum of the angle of the triangle is 180 degrees. Then the measure of angle ∠D is 75.5°.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
Given
In triangle DEF, the measure of angle ∠F is 12.4° and the measure of angle ∠E is 92.1°.
Then the measure of angle ∠D will be.
We know that the sum of the angle of the triangle is 180 degrees. Then
∠D + ∠E + ∠F = 180°
∠D + 92.1° + 12.4° = 180°
On simplifying, we have
∠D = 180 - 92.1 - 12.4
∠D = 75.5°
Thus, the measure of angle ∠D is 75.5°.
More about the triangle link is given below.
https://brainly.com/question/25813512
Final answer:
The measure of angle EDF in triangle DEF, given the measures of angles DFE and DEF, is 75.5 degrees, found by subtracting the sum of the known angles from 180 degrees.
Explanation:
To find the measure of angle EDF in triangle DEF where the measure of angle DFE is 12.4 degrees and the measure of angle DEF is 92.1 degrees, we can use the fact that the sum of the internal angles in any triangle is always 180 degrees. By subtracting the measures of angles DFE and DEF from 180 degrees, we can find the remaining angle's measure.
Angle EDF = 180 degrees - (Angle DFE + Angle DEF) = 180 - (12.4 + 92.1) degrees = 180 - 104.5 degrees = 75.5 degrees.
You choose a movie disk at random from a case containing 8 comedy discs, 5 science fiction discs, and 7 adventure discs. The disc is not a comedy.
Answer:
i think it is adventure
Step-by-step explanation:
your welcome
Find f(–2) for f(x) = 3 • 2x
Answer: f(-2)= -12
Step-by-step explanation:
f(-2)= 3*2(-2)
f(-2)= 3*(-4)
f(-2)= -12
They wrong the real answer here is 3/4
i need help with all the problems shown before 6:00am tomorrow morning
If a circle has a diameter of 16 feet which expression gives its area in square feet
Answer: [tex] (8)^2\pi\ feet^2[/tex]
or
[tex]64\pi \ feet ^2[/tex]
Step-by-step explanation:
We are given that the diameter of a circle = 16 feet
Then the radius of the circle = [tex]r=\dfrac{d}{2}=\dfrac{16}{2}=\ 8 feet[/tex]
Also, the area of a circle is given by :_
[tex]A=\pi r^2[/tex] , where r is radius of the circle .
For r = 8 feet
The area of the circle = [tex]\pi (8)^2=\pi (64)=64\pi \ feet ^2[/tex]
Hence, the expression that gives its area in square feet =
[tex] (8)^2\pi \ feet^2[/tex]
or
[tex]64\pi \ feet ^2[/tex]
what is the valume of that?
Answer:
960 in^3
Step-by-step explanation:
Multiply the base by the height
Base: (12*8)/2=48
Height: 20
The volume of a triangular prism is the area of the base multiplied by the height.
Let's first identify our values:
20 in = height of prism
12 in = base of triangle
8 in = height of triangle
First, we need to calculate the area of the triangle. To calculate the area of the triangle, we multiply the base of the triangle by the height of the triangle. In this case, the base is 12 and the height is 8 so 12 × 8 = 96 and then we divide 96 by 2 and we will get a quotient of 48.
Finally, we will multiply the area of the triangle which is 48 by 20.
48 × 20 = 960[tex]in^{2}[/tex].
the town library is raising money by selling old books for $2 each which equation can be used to find the amount of money raised if number of books sold is no let x represent the number of books sold and y represent the number of dollars raised
Answer:
(6550)
Step-by-step explanation:
You can put this solution on YOUR website!
Call the number of hardcover and paperback books, h and p.
Thus
h + p = 8 and the value equation is
4h + 2p = 26
Now multiply the top one by four and subtract from the second one...we get
4h + 2p = 26
-(4h + 4p = 32)
----------------
-2p = -6
p = 3 so that
h = 5 x + y = 8, (1)
4x + 2y = 26, (2)
where x and y are the numbers of hardcover and softcover books respectively.
To solve, multiply the equation (1) by 2 (both sides) and then distract it from the equation (2). You will get
4x - 2x = 26 - 16, or
2x = 10, or x = 5 - the number of hardcover books purchased.
Then from the equation (1) you get y = 3.
Check. 4*x + 2*3 = 4*5 + 2*3 = 26. OK.
Answer:
y=2x
Step-by-step explanation:
Attached, is a picture with all the work!
Stephen takes a walk around the block. The rectangular block is 80m long and 115m wise. How far does Stephen walk? whoever answer I give them brainliest
Answer:
Option A. [tex]390\ m[/tex]
Step-by-step explanation:
we know that
To find how far Stephen walk, calculate the perimeter of the block
Remember that
The perimeter of rectangle (block) is equal to
[tex]P=2(L+W)[/tex]
we have
[tex]L=80\ m[/tex]
[tex]W=115\ m[/tex]
substitute the values
[tex]P=2(80+115)=390\ m[/tex]
HELP ASAP!!! What is the value of x?
Enter your answer in the box.
x =
Answer:
8
Step-by-step explanation:
Pythagoras theorem states a²+b²=c²
In this example c² is given to us (10) and a² is given to us (6)
To work out x we have to √10²-6² which is 8
what is the spread of the middle 50% of the data called
the spread of the middle data is called the interquartile range and the left and right twenty five percent data are both called the twenty five percent quartiles
HOPE THIS HELPS
The Interquartile Range (IQR) is the spread of the middle 50% of data. It is found by subtracting the first quartile (Q1) from the third quartile (Q3). A larger IQR indicates more variability within the dataset.
Explanation:Interquartile Range (IQR)
The spread of the middle 50% of data in a dataset is known as the Interquartile Range (IQR). It is a measure of statistical dispersion and part of the five-number summary commonly used in descriptive statistics. To calculate it, you subtract the first quartile value (Q1) from the third quartile value (Q3). This range covers the middle 50 percent of the data, indicating where the bulk of the values fall and providing a sense of variability. An example based on given data can illustrate where Q1 is at 64.5 and Q3 is at 70, thus the IQR is 70 - 64.5 = 5.5. A larger IQR indicates more variability within the middle portion of the dataset. It is used alongside other descriptive statistics like the median, range, and standard deviation to provide a comprehensive understanding of the data's distribution.
Here is a picture of a cube, and the net of this cube.
What is the surface area of this cube?
Enter your answer in the box.
ft²
A cube and a net of the cube are shown. The edge length of the cube is labeled 16 feet. The net consists of 4 squares connected vertically, and 1 square is attached to the right of the third square and 1 square is attached to the left of the second square. One square in the net is labeled with a side labeled 16 feet.
Answer:
96 ft²
Step-by-step explanation:
in a cube all sides are congruent so you take one measurement and multiply it by the number of sides, so you do 16 × 6 equals 96.
Answer:
Step-by-step explanation: other people said...
96ft but the real answer is...
1536 like is this helped