What is the correct formula to find the sum of the finite geometric series below?
[tex]\displaystyle 2 + \frac{2}{3} + \frac{2}{9} + \ ... \ + \frac{2}{3^6}[/tex]
We are given the Geometric Series:
[tex]2 + \frac{2}{3} + \frac{2}{9} + \frac{2}{27} + \frac{2}{81} + \frac{2}{243} + \frac{2}{729}[/tex]
which can be rewritten as:
[tex]2 + \frac{2}{3} + \frac{2}{3^{2} } + \frac{2}{3^{3}} + \frac{2}{3^{4}} + \frac{2}{3^{5}} + \frac{2}{3^{6}}[/tex]
here, we can see that every term is (1/3) times the last term
Hence, we can say that the common ratio of this Geometric Series is 1/3
Finding the Sum:
We know that the sum of a Geometric Series is:
[tex]S_{n} = \frac{a(r^{n}-1)}{r-1}[/tex]
(where r is the common ratio, a is the first term, and n is the number of terms)
another look at the given Geometric Series tells us that the first term is 2 and the number of terms is 7
plugging these values in the formula, we get:
[tex]S_{n} = \frac{2((1/3)^{7}-1)}{(1/3)-1}[/tex]
[tex]S_{n} = \frac{-1.99}{-0.67}[/tex]
Sₙ = 2.97
Step-by-step explanation:
[tex] \tt2 + \frac{2}{3} + \frac{2}{ {3}^{2} } + \frac{2}{ {3}^{3} } + \frac{2}{ {3}^{4} } + \frac{2}{ {3}^{5} } + \frac{2}{ {3}^{6} } [/tex]
r = [tex]\tt{a_2 \div a_1}[/tex]
r = [tex]\tt{\frac{2}{3} \div 2}[/tex]
r = [tex]\tt{\bold{\frac{1}{3}}}[/tex]
Soo :
[tex] \sf s_n = \frac{a( {r}^{n} - 1) }{r - 1} [/tex]
[tex] \sf s_7 = \frac{2(( \frac{1}{3} ) {}^{7 - 1} - 1) }{( \frac{1}{3} - 1) } [/tex]
[tex] \sf s_7 \approx \bold{ \underline{2.97}}[/tex]
a company makes carboard cylindrical boxes with a diameter of 10 inches and a height of 8 inches.how many square inches of carboard are needed for each box? Use 3.14 for pi.
Answer:
408.2sq inches
Step-by-step explanation:
Area of the cylindrical box = 2πr(r+h)
r is the radius = diameter/2
r = 10/2 = 5in
h is the height = 8in
Substitute
Area of the cylindrical box = 2(3.14)(5)(5+8)
Area of the cylindrical box = 2 * 3.14 * 5 * 13
Area of the cylindrical box = 408.2sq inches
Find the area of irregular shapes
So far, we have found area for rectangles, triangles, trapezoids, and circles. An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas. But some irregular figures are made up of two or more standard geometric shapes. To find the area of one of these irregular figures, we can split it into figures whose formulas we know and then add the areas of the figures.
Peter was given 40 words to spell to qualify for a prize. He must spell at least 90% of those words correctly. At least how many words should he have to spell correctly to get the prize?
Answer:
He should have to spell at least 36 of these words correctly.
Step-by-step explanation:
40 words.
He must spell at least 90% of those words correctly.
At least how many words should he have to spell correctly to get the prize?
90% of 40. So
0.9*40 = 4*9 = 36
He should have to spell at least 36 of these words correctly.
Describe the relationship between the area of a circle and its circumstances
Answer:
[tex]A = \frac{r}{2}C[/tex]
Step-by-step explanation:
Given
Shape: Circle
Required
The area and the circumference (relationship)
This implies that, we write an expression that relates the area and the circumference.
Circumference is calculated as:
[tex]C = 2\pi r[/tex]
Area is calculated as:
[tex]A = \pi r^2[/tex]
The area can be rewritten as:
[tex]A = \frac{2\pi r^2}{2}[/tex]
Further rewrite as:
[tex]A = \frac{r}{2}*2\pi r[/tex]
Recall that:[tex]C = 2\pi r[/tex]
So, the expression becomes
[tex]A = \frac{r}{2}*C[/tex]
[tex]A = \frac{r}{2}C[/tex]
Will give brainless
This is due tomorrow at 12pm
Answer:
The most common rock-forming minerals are quartz, feldspar, mica, pyroxene, amphibole, and olivine. The most reliable way to identify a mineral is by using a combination of several tests. A crystal is a solid in which the atoms are arranged in repeating patterns.
find the measure of arc URT
Hello!
This question is about relating vertical angles and their arc lengths.
Vertical angles have equal angle measures, meaning that they will also have the same arc measure.
We know that arc QR and arc UT have equal angle measures because they are formed with vertical angles.
That means since we know the measure of the other two arcs, which will both be 125 since they are formed with vertical angles, we can solve for the two unknown arc lengths.
A circle is 360 degrees, meaning that we can make the following equation,
[tex]360=QR+UT+125+125[/tex]
[tex]QR+UT+250=360[/tex]
[tex]QR+UT=110[/tex]
Since QR = UT
[tex]QR/UT=55[/tex]
Now, we can solve for arc URT using all the arc measures we have.
[tex]URT=125+55+125[/tex]
[tex]URT=305[/tex]
Hope this helps!
The points (3,h) and (10,1) fall on a line with a slope of
4/7 What is the value of h?
Answer:
h = -3Step-by-step explanation:
Use slope formula:
(1 - h)/(10 - 3) = 4/7(1 - h) / 7 = 4/71 - h = 4h = 1 - 4h = -3Answer:
The answer is h = -3
Step-by-step explanation:
(1 - h)/(10 - 3) = 4/7
(1 - h) / 7 = 4/7
1 - h = 4
h = 1 - 4
h = -3
Solve and check each equation below . show all work . 24=g+14. f-9=12
Answer:
g = 10
f = 21
Step-by-step explanation:
Given equations:
24 = g + 14
f - 9 = 12
24 = g + 14
Subtract 14 from both sides
24 - 14 = g + 14 - 14
10 = g
g = 10
Check:
24 = g + 14
24 = 10 + 14
24 = 24
f - 9 = 12
Add 9 to both sides
f - 9 + 9 = 12 + 9
f = 21
Check:
f - 9 = 12
21 - 9 = 12
Which graph represents a function with an initial value of 1/2?
Answer:
The initial value is the value of the y-coordinate when the x-coordinate is equal to 0. That is the same to say the value at which the graph intercepts the y-axis. So, you just have to pick the graph whose line intercepts the y-axis at 1/2.
When Ricardo was 9 years old, he was 56 inches tall. By age 12, he had increased his
height by 12%. How tall is he now?
Answer:
He is 62.72 inches tall now
Step-by-step explanation:
the twelve over 100 is the percentage, he increased by 12 percent. and the x over 56 is the new value (x) over the old value. We get 6.72 so we add that to 56 to get 62.72.
A 3 ounces b 4 ounces c 12 ounces or D 15 ounces helps plsss
Answer:
D 15
Step-by-step explanation:
[tex]\frac{5}{20}[/tex]=[tex]\frac{x}{60}[/tex]
Convert 65 degress celsius to degress farenheit.
If necessary, round your answer to the nearest tenth of a degree
Here are the formulas :
C=5/9 ( f-32)
F= 9/5 C+32
Answer: 150 degrees
Step-by-step explanation:
Answer:
149°F
Step-by-step explanation:
The Celsius measure is 65° . We know the relation between Celsius and Farenheight as ,
⇒ C/5 = F-32/89
⇒ 65/5 = F-32/9
⇒ 13 = F-32 / 9
⇒ F - 32 = 13 × 9
⇒ F = 117 + 32
⇒ F = 149 °F
Hence the Faeenheight measure is 149°F .Elizabeth made a scale drawling of a city of Colorado. The scale of the drawling is 1inch=4 yards.an open space is 17 inches in the drawling. How wide is the actual open space.
Answer:
B
Step-by-step explanation:
Jrkrkr
Please help I’m unsure of what the answer is
F178 * 34 = 6052, then 60.52 = 17.8 is equal to
Answer:
sin ( 330 ) − 4 cot( − 45 ) csc ( 60 )
Step-by-step explanation:
is 0.70 equal to 7/10
yes the fraction of .70 is 7/10
Answer:
Yes
Step-by-step explanation:
0.70 = 7/10
Find 3 consecutive even integers such that 5 times the second is 82 more than the first .
find the measure of the angle theta
Answer:
A. 57.8°
Step-by-step explanation:
Reference angle = θ
Length of hypotenuse = 15
Length of adjacent side = 8
Recall, SOHCAHTOA.
Thus, apply CAH to find θ.
Cos θ = Adj/Hyp
Cos θ = 8/15
θ = Cos^{-1}(8/15)
θ = 57.7690474° = 57.8°
Write the polynomial in factored form as a product of linear factors:
p(a) = a^3 + 3a^2+ 9a + 27
zeros of polynomial.
Answer:
Step-by-step explanation:
p(A) = a^3 + 3a^2 + 9a + 27
put brackets around the 1st and second terms and another set around the 3rd and 4th
P(a)= (a^3 + 3a^2) + (9a + 27)
Using the distributive property, pull out the common factor for each of the 2 terms that contain the brackets.
P(a) = a^2 ( a + 3) + 9(a + 3)
Let a + 3 = x
P(a) = a^2x + 9x
Put brackets around these 2 terms
P(a)= x(a^2 + 9)
Substitute a + 3 for x
P(a) = (a + 3) ( a^2 + 9)
roy is 30 miles from dallas ready to leave for pecos
Answer:
It represents the 270 miles that Roy and Travis must travel in 4 hours in order to meet somewhere along the highway.
Step-by-step explanation:
From the information given, the point of interception (4, 270) represent the number of distance, 270 miles, that both Roy and Travis must travel in 4 hours in order to meet along the highway where Roy will give Travis the key to a treasure chest to Roy.
The point intersection (4, 270) represents the time and distance Roy and Travis met
The graph above are linear graph.
Linear graphLinear graph are straight line graph.
Therefore,
d represents a distance in miles from Dallas
h represents the hours travelled
Roy is leaving for Pecos while Travis is in Pecos ready to leave for Dallas.
Therefore, the point intersection (4, 270) represents the time and distance Roy and Travis met.
learn more on linear graph here:https://brainly.com/question/1328896
PLEASE HELP
The Miller family spent a total of $317.05 hosting a party for their grandparents' 50th wedding anniversary. They spent $48.55 on decorations and $8.95 per person on food.
Which equation could be used to find the number of people (x) at the anniversary party?
A.
48.55 + 8.95x = 317.05
B.
48.55x + 8.95 = 317.05
C.
48.55x − 8.95 = 317.05
D.
48.55 − 8.95x = 317.05
!!!!!!! PLEASE HELP!!!!!
Answer:
You have to do 7x+2+6x+9 Which is 13x+11.
Step-by-step explanation:
f(x) = 6X-8
g(x) = -3x+2
Find 3f(x)+2g(x).
What is this answer
Answer:
12x-20
Step-by-step explanation:
f(x)=6x-8
3f(x)=3(6x-8)
3f(x)=18x-24
g(x)=-3x+2
2g(x)= -6x+4
3f(x)+3g(x)=(18x-24)+(-6x+4)
=18x-24-6x+4
=12x-20
Many professional sports are arguing that they need a new stadium to be competitive, as newer stadiums can bring in more fan revenue which can in turn allow teams to buy more expensive players. Some major league baseball teams have built new stadiums in the past decade. Consider the attendance (in millions) in the last year of the old stadium and the first year of the new stadium. Using a sample of 5 randomly selected teams, researchers would like to determine if there is any evidence that attendance levels differ between using old vs new stadiums. The data for these five teams are shown below:
Team Attendance (in millions)
Old Stadium New Stadium
Cincinnati Reds 1.9 2.4
New York Yankees 4.3 3.7
Philadelphia Phillies 2.3 3.3
Seattle Mariners 2.7 2.9
Washington Nationals 1.9 2.3
Required:
a. Calculate the test statistic appropriate to the correct statistical method.
b. Suppose all assumptions were satisfied for valid inference, and the researcher found a statistically significant lower average attendance in the new stadium compared to the old stadium. (This does not mean that this data support this conclusion - this is just hypothetical.) Does this mean that the new stadium caused attendance to decrease? Why or why not?
Answer:
Test statistic = 1.1508
Step-by-step explanation:
Given the data provided
We have to make a table and find d and d²
From the calculations I did in the attachment
n = 5
d² = 1.81
d = 1.5
The t test statistic = 1.5/1.3038 = 1.1505
B. No the new stadium may not have caused the attendance t decrease in this case. Other factors could be responsible for the low attendance.
What would be 12.67 rounded to the nearest tenth.
Answer:
12.7
Step-by-step explanation:
Remember this rule when rounding 5 and below let it go (ex. 12.32 = 12.3) 6 and above give it a shove (ex. 12.47 = 12.5).
Emily bought 48 yards of fabric to make curtains. What is that length in inches?
Answer:1 yard = 36 inches
48 X 36 = 1728 inches
Convert 1.375 to decimal fraction؟
Step-by-step explanation:
11/8 if I'm not wrong
...
Answer:
fgiigdyh
Step-by-step explanation:
PLEASE HELP I WILL GIVE BRAINLIEST
9514 1404 393
Answer:
(C) angles A and B and those corresponding
Step-by-step explanation:
If sides are used to show similarity, at least two sides from each triangle are required. If only two sides are used, then the angle between them must also be shown to be congruent.
A -- has 2 sides, but no angles; (SS) not sufficient
B -- has 2 sides but not the angle between; (SSA) not sufficient
C -- has 2 angles; (AA) sufficient
D -- effectively, one angle; (A) not sufficient
Histogram help fast! Which of the following is a histogram?( look at the photo)
Answer:
B.Step-by-step explanation:
First, we can eliminate answer A. As you should know, answer A is a pie chart as it is a circle and cut into many slices.
Now both answer B and C look similar. They are both a bar graph. So we will come back and look at these later.
Answer D is about math test scores. I have forgotten the name of this graph but I can assure you this is incorrect.
So we are left with B and C. They both are bar graphs, right? Well sort of. Although they look identical, answer B is a histogram. If you look at graph B, you will notice it says age. This shows that there is time between each subject or event. Graph C is a personal question. What kind of pet you have is not directly related to something over time
Therefor the answer has to be B.