copy the given expression on your answer sheet
Find the sum of the first 6 terms of the following sequence. Round to the nearest
hundredth if necessary.
324,
54,
9….
Answer:
388.79 (nearest hundredth)
Step-by-step explanation:
Given sequence: 324, 54, 9, ...
Therefore:
[tex]a_1=324[/tex]
[tex]r=\textsf{common ratio}=\dfrac{54}{324}=\dfrac16[/tex]
Sum of a finite geometric series:
[tex]S_n=\dfrac{a_1-a_1r^n}{1-r}[/tex]
Sum of the first 6 terms → n= 6:
[tex]\begin{aligned}S_6 & =\dfrac{324-324(\frac16)^6}{1-\frac16}\\ & =\dfrac{324-\frac{1}{144}}{1-\frac16}\\ & =\dfrac{9331}{24}\\ & = 388.79\:\textsf{(nearest hundredth)}\end{aligned}[/tex]
So
[tex]\\ \rm\Rrightarrow S_n=\dfrac{a-ar^n}{1-r}[/tex]
[tex]\\ \rm\Rrightarrow S_6=\dfrac{324-324(1/6)^6}{1-1/6}[/tex]
[tex]\\ \rm\Rrightarrow S_6=\dfrac{324-\dfrac{1}{12^2}}{\dfrac{5}{6}}[/tex]
[tex]\\ \rm\Rrightarrow S_6=\dfrac{9331}{24}=388.79[/tex]
Please help me out if appreciate it :)
Answer:
51
Step-by-step explanation:
they are congruent so they are equal to eachotjer
A certain gas has a volume of 10 liters at a temperature of 404 kelvins (k) and a pressure of 36 pascals (pa). if the temperature is raised to 450 k and the pressure is raised to 40 pa, what is its volume? to the nearest liter, the volume is liters.
The final volume of the ideal gas is 10.02 liters.
Given Initial volume V₁=10 liters
Initial temperature T₁=404K
Initial pressure P₁ = 36 pascals
Final volume = V₂
Final temperature T₂ = 450K
Final pressure P₂ =40 pascals
What is the ideal gas equation?The ideal gas equation with usual notations is given by:
[tex]\frac{P_1V_1}{T_1} =\frac{P_2V_2}{T_2}[/tex]
So, [tex]\frac{36*10}{404} =\frac{40*V_2}{450}[/tex]
[tex]V_2=[/tex]10.02 liters
Hence, the final volume of the ideal gas is 10.02 liters.
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Answer:
10 liters
Step-by-step explanation:
Find the volume of the cone.
Use 3.14 for π. Round your answer to the nearest tenth if needed. Do not enter units.
Step-by-step explanation:
Volume of a cone = 1/3 x π x r^2 x h
= 1/3 x 3.14 x (8)^2 x (18)
= 1/3 x 3.14 x 64 x 18
= 1/3 x 3.14 x 1,152
= 1/3 x 3.14 x 1,152
= 1,205.76
= 1,205.8 m^3
*Note*: Alter the pi according to the question always.
⚠️⚠️⚠️HELP PLS I NEED HELP ⚠️⚠️⚠️
Answer:
8 , 6 , 12
Step-by-step explanation:
A right angle forms a square corner, like the shown below. Draw two angles that are open less than the right angle. Solve this Problem any way you choose
Answer:
Any angle less than 90 degrees.
Step-by-step explanation:
90 degrees is a right angle. Anything less than that, or less open, would be an acute angle. Anything wider than 90 degrees is an obtuse angle.
chocolate milk cow answer
Answer:
what?
Step-by-step explanation:
Answer:
Please tell me what this means.
The profits in hundreds of dollars, p(c), that a company can make from a product is modeled by a function of the price, c, they charge for the product: p(c) = –20c2 320c 5,120. what is the maximum profit the company can make from the product? $540,000 $640,000 $800,000 $896,000
Answer:
640,000
Step-by-step explanation:
took test
Answer:
B
Step-by-step explanation:
Edge 2022
Determine if the two functions f and g are inverses of each other algebraically. If not, why not? f(x)= 9x+12; g(x)= x-12/9
Answer:
They are not
Step-by-step explanation:
Check the attached photo out
210 divided by 30 please give step my step explanation
Question 2*
10 poir
2
A bacterium has a radius of 3. 6 x 10-9 meters. What is the radius of this bacterium in
standard notation?
F 0. 0000000036 meters
G 0. 0000036 meters
H 0. 000000000036 meters
J 0. 000000036 meters
F) Option F
G) Option G
H) Option H
О
J) Option J
URGENT 10 POINTS
Common ratio of -1,1,4,8,…
Step-by-step explanation:
-1,1,4,81-2,2-1,6-2,10-2=-1,1,4,8 is my answerJohn has 7 mice in his lab. He knows a mouse population doubles every month. When can he expect to have 2,625 mice? Please explain.
Answer:
31 years and 3 months or non
Step-by-step explanation:
the first thought that comes into my mind is
1 month=7 mice
n month= 7×n=2625 mice
n= 2625÷7=375
so it takes him to 375 months = 31 year and 3 months
but putting on a 2nd thought, I noticed that mice and mouse is different species. so there aren't exact answer
Please helpppp meee outttt
Answer:
Measure of <z would 125 degrees
Step-by-step explanation:
Courtney is playing miniature golf. What is the area of the composite figure.
Dominic is buying candy by the pound for a party. For every 1010 pounds of candy he buys, he pays \$ 12$12. What is the cost, per pound, for the candy?
© An object has a mass of 420 kg and a volume of 7 m3.
Find the density of the object in kg/m3.
Answer:
See below
Step-by-step explanation:
you want kg/m^3 so just divide
420 kg / 7 m^3 = 60 kg/m^3
What is the z-score with a confidence level of 95% when finding the margin of error for the mean of a normally distributed population from a sample? 0.99 1.65 1.96 2.58
The value of z-score with a confidence level of 95% in finding margin of error for the mean of a normally distributed population from a sample is 1.96.
What is normally distributed data?Normally distributed data is the distribution of probability which is symmetric about the mean.
The mean of the data is the average value of the given data.The standard deviation of the data is the half of the difference of the highest value and mean of the data set.The confidence level is 95% when finding the margin of error for the mean of a normally distributed population from a sample.
The critical z score value for the confidence level of 95% is 1.96 and +1.96 standard deviation.
Thus, the value of z-score with a confidence level of 95% in finding margin of error for the mean of a normally distributed population from a sample is 1.96.
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Answer:
1.96
Step-by-step explanation:
its 1.96 or c on edge 2020
A store sells apples and oranges. Apples cost 2. 0
Answer:
An apple costs $2? lol thats crazy
please help me with this
Answer:
[tex]183 ft^{2}[/tex]
Step-by-step explanation:
SA = bh + 2ls + lb
b = 6
h = 5
l = 9
s = 5.5
SA= (6 x 5) + 2(9 x 5.5) + (9 x 6)
SA = 30 + 2 x 49.5 + 54
SA = 30 + 99 + 54
SA = 183
Mr Collins invested some money that will double in value every 12 years. If he invested $5,000 on the day of his daughter’s birth, how much will the investment be worth on his daughter’s 60th birthday?
A $160,000. B $300,000. C $80,000. D $320,000
Which expression is equal to (12^4)^-2
A. 12^-8
B. 12^-6
C. 12^8
D. 12^6
Answer:
Hi I believe the answer is A I hope this helps.
Step-by-step explanation:
4x-2=-8
12^-8
Answer:
A. 12⁻⁸
Step-by-step explanation:
When an exponent is applied to a number which already contains an exponent, they should be multiplied.
(12⁴)⁻²12⁻⁸The answer is A.
For which division problems should you write the first digit of the quotient in the hundreds place? Choose all that apply. A. 734 ÷ 6 B. 803 ÷ 10 C. 1,090 ÷ 19 D. 5,280 ÷ 48 E. 9,765 ÷ 26
Step-by-step explanation then the answer:
Hey there, I think this question may be a circle all. So the questions with the answer (quotient) being in the hundreds place would be A, D, and E. Those all have quotients in the hundreds place.
Rewrite the equation in exponential form, and show how you got there:
Answer: [tex]13^0=1[/tex]
Step-by-step explanation:
Logarithms are in the format [tex]log_{b} a=c[/tex] while exponential form is in the format [tex]b^c=a[/tex]
So we can transfer a,b, and c from the log form to the exponential form
[tex]log_{13} 1=0\\\\13^0=1[/tex]
What is the slope of a line parallel to a line whose slope is -5/2?
A) -5/2
B) -2/5
C) 2/5
D) 5/2
Answer:
A) -5/2
Step-by-step explanation:
Parallel lines have same slope.
Help please it's due today. Also please leave an explanation too ty!
A square with sides 6 in is inscribed in a circle. The circumference of this circle is...
A. C = 6 * pi
B. C = 6 * square root of 2 * pi
C. C = 6 * square root of 3 * pi
D. C = 9 * pi
E. C = 36 * pi
Answer:
B. 6π[tex]\sqrt{2}[/tex]
Step-by-step explanation:
If you look at the help image I attached, what we are given is in RED and what we solve is in BLUE.
First, draw a diagonal in the square. Its length is the diameter, but we don't know the exact value. Since two right triangles have been created, we use Pythagorean Therom to solve for the hypotenuse/diameter:
[tex]a^2+b^2=c^2\\6^2+6^2=c^2[/tex]
[tex]\sqrt{36+36} =c[/tex]
[tex]6\sqrt{2}=c[/tex]
If diameter = [tex]6\sqrt{2}[/tex], then radius is [tex]\frac{6\sqrt{2}}{2}[/tex] or [tex]3\sqrt{2}[/tex]
Circumference = 2πr
2π ([tex]3\sqrt{2}[/tex])
6π[tex]\sqrt{2}[/tex]
I hope this helps!
Susan went to a store and bought 3 items. each item cost the same. she spent 12 . how much did each item cost?
Answer:
4 dollars
Step-by-step explanation:
12 divided by 3 is 4
Which values of c will cause the quadratic equation –x2 3x c = 0 to have no real number solutions? check all that apply.
The given quadratic equation will not have any real solution for c<-9/4.
The given quadratic equation is:
[tex]-x^{2} +3x+c=0[/tex]
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation with a≠0.
In order to have no real solution, the discriminant of a quadratic equation will be less than zero.
[tex]D < 0[/tex]
[tex]3^{2} -4(-1)(c) < 0[/tex]
[tex]9+4c < 0[/tex]
[tex]c < -\frac{9}{4}[/tex]
For [tex]c < -\frac{9}{4}[/tex] the given quadratic equation will have no real solutions.
Hence, the given quadratic equation will not have any real solution for c<-9/4.
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The local amusement park is a popular fleld trip destination. This year the senior class at the High
School planned their senior class trip there. The school had to take 24 total vehides between vans
Vand buses. There are 752 total students in the senior class. Each van holds 8 students and each
bus can hold 43 students. How many vans and buses did they have to take?
Answer:
8 vans16 busesStep-by-step explanation:
The given relations can be written as two equations in two unknowns. These can be solved by any of the ususal methods.
__
SetupLet v and b represent the numbers of vans and buses used, respectively.
v + b = 24 . . . . . 24 vehicles were taken
8v +43b = 752 . . . . 752 students were transported
__
SolutionPerhaps the easiest solution is that afforded by a graphing calculator. It shows the solution to be ...
v = 8 . . . . vans required
b = 16 . . . . buses required
__
You can eliminate the v variable by subtracting 8 times the first equation from the second.
(8v +43b) -8(v +b) = (752) -8(24)
35b = 560 . . . . . simplify
b = 16 . . . . . . divide by 35
v = 24 -16 = 8 . . . . . find v from the first equation
They had to take 8 vans and 16 buses.
A bouncy ball is dropped from a height of 16ft and always rebounds of the distance of the previous fall.
What distance does it rebound the 5th time?
What is the total distance the ball has travelled after this time?
Draw a picture to represent the bouncing ball.
The bouncy ball follows a geometric sequence or pattern
The distance of rebound the 5th time is 0.015625 ftThe total distance the ball has travelled after this time is 5.328125 feetThe distance of rebound the 5th timeThe given parameters are:
Initial height, a = 16 ftRebound rate = 0.25The distance at rebound n is represented as:
Hn = a * r^n
At the 5th time, we have:
H5 = 16 * 0.25^5
Evaluate
H5 = 0.015625
Hence, the distance of rebound the 5th time is 0.015625 ft
The total distance travelledTo do this, we calculate H1 to H5
So, we have:
H1 = 16 * 0.25^1 = 4
H2 = 16 * 0.25^2 = 1
H3 = 16 * 0.25^3 = 0.25
H4 = 16 * 0.25^4 = 0.0625
H5 = 0.015625
Add this distances
Total = 4 + 1 + 0.25 + 0.0625 + 0.015625
Total = 5.328125
Hence, the total distance the ball has travelled after this time is 5.328125
See attachment for the picture
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