Find the sum of the first 9 terms
of the geometric sequence: 0.5, 1, 2,-..
Answer:
S₉ = 255.5
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 0.5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{1}{0.5}[/tex] = 2 , then
S₉ = [tex]\frac{0.5(2^{9}-1) }{2-1}[/tex]
= [tex]\frac{0.5(512-1)}{1}[/tex]
= 0.5(511)
= 255.5
PLEASE HELP ME !!???! I DONT GET IT
Answer:
see explanation
Step-by-step explanation:
the perimeter (P) is the sum of the 3 sides of the triangle, then
P = 31 + 19.5 + 16.2 = 66.7 units
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 16.2 and h = 13 , then
A = [tex]\frac{1}{2}[/tex] × 16.2 × 13 = 8.1 × 13 = 105.3 units²
heyyy please help me here
Answer:
The correct answer is 111.
Step-by-step explanation:
Each time, the number increases by the number it increased by before, plus 2.
The full sequence would be:
3, 9, 17, 27 , 39, 53, 69, 89, 111.
Hope this helps:) Goodluck!
Which is the graph of the function f(x) = -√x
what does x equal when 6600/80 = x
Answer: 82.5
Step-by-step explanation: 6600 divided by 80 is 82.5
Answer:
82.5
Step-by-step explanation:
A marine biologist compared two large pools that could be used for a new dolphin training arena. Pool A held 2 x 1010 gallons, and pool B held 2 x 108 gallons. How many times more gallons will the larger pool hold than the smaller pool?
4
20
100
200
Answer:
20
Step-by-step explanation:
a bucket is 12cm in diameter at the top , 8cm in diameter at the bottom and 4cm deep.calculate uts volume in cm cubein terms of pi
Answer:
that is 12x8x4= 384
that should be the final answer
HELPPP PLEASEEEEE
Tyrion creates a set of nesting shapes as a toy set for his baby nephew. The outer figure is a
cube with an edge length of 20 centimeters. The middle figure is a square pyramid with an
identical square base and the same height as the cube. The innermost figure is a cone with a
diameter and height equal to the edge of the cube. Calculate the difference of volumes
between cube and cone. Round your answers to the nearest whole cubic centimeter.
Answer:
5906
Step-by-step explanation:
The difference in volumes between cube and cone is 5190.52 cubic units.
How to find the volume of a cube?Suppose that:
The side length of the considered cube is L units.
Then, we get:
The volume of that cube = L³ cubic units.
The outer figure is a cube with an edge length of 20 centimeters.
The volume of that cube = L³ cubic units.
= 8000 cubic units.
The volume of that cone
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
The height is 20 cm and the radius will be
[tex]D = 20\sqrt{2} \\ = 28.2\\\\r = D/2\\ = 14.1[/tex]
volume of that cone
[tex]V = \dfrac{1}{3} \pi r^3 h \: \rm unit^3[/tex]
= [tex]V = \dfrac{1}{3} (3.14) (14.1)^3 (20) \: \rm unit^3[/tex]
= 59190.52 cubic units
Therefore, the difference in volumes bbetween cube and cone is 5190.52 cubic units.
Learn more about the volume of a cube here:
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Find the range and interquartile range of the data.
2, 4, 8 , 3, 2
Answer:
IQR = 4
Step-by-step explanation:
Q3 = 6
Q1= 2
6-2=4
A softball has a volume of about 29 cubic inches. Find the radius of the softball. Round your answer to the nearest tenth.
The radius of the softball is about _ inches.
The geometry of the softball is a sphere. Then the radius of the softball will be 1.91 inches.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
A softball has a volume of about 29 cubic inches.
Then the radius of the softball will be
The geometry of the softball is a sphere.
Then the volume of the sphere is given as
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
where r is the radius of the softball.
Then we have
[tex]\rm r^3 = \dfrac{3V}{ 4 \pi}\\\\r^3 = \dfrac{3 \times 29}{4 \times \pi}\\\\r^3 = \dfrac{87}{12.5664}\\\\r^3 = 6.9232\\\\r \ \ = \sqrt[3]{6.9232}\\\\r \ \ = 1.9059 \approx 1.91 \ in.[/tex]
More about the geometry link is given below.
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A quantity of bacteria doubles every hour. If you start with 100 bacteria cells, the number of cells you will have at any time can be found by the formula c = 100(2)x. How many hours will it take to have 1,000,000 bacteria? Round to the nearest whole number.
Answer:
10,000 hours
Step-by-step explanation:
10,000 x 100 = 1,000,000
Hope this helps!
here it is could you help me.
Answer:
7. D.58
Because 90-32=58 (that cube on the edge means 90degree)
8. A.45
Because 180-135=45
9. C. Because angles are equal
10. C. 95
180-85=95
What is an equation of the line that passes through the point (-4,-6) and is
parallel to the line 33 – y = 6?
Hey there!
33 - y = 6
33 - 1y = 6
-1y + 33 = 6
-y + 33 = 6
SUBTRACT 33 to BOTH SIDES
-y + 33 - 33 = 6 - 33
SIMPLIFY IT!
-y =6 - 33
-y = 6 - 33
-1y = -27
DIVIDE -1 to BOTH SIDES
-1y/-1 = -27/-1
SIMPLIFY IT!
y = -27/-1
y = 27
Therefore, your answer is: y = 27
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
I guess question is wrong :
What is an equation of the line that passes through the point (-4,-6) and is parallel to the line 33 x– y = 6?
3x - y = 6
[tex]m = \frac{ - a}{b} [/tex]
[tex]m = \frac{ - 3}{ - 1} [/tex]
[tex]m = 1[/tex]
Lines are parallel :
m1 = m2
[tex]x - x1 = m(y - y1)[/tex]
[tex]x + 4= 1(y + 6)[/tex]
[tex]x + 4= y + 6[/tex]
[tex]x - y= 6 - 4[/tex]
[tex]x - y - 2 = 0[/tex]
What is the value of 6 n=2 (n-1)!/2
Answer: d- 76.5
Step-by-step explanation:
HELP ASAP PLSSSSS
(picture of graph is below)
Below are the data collected from two random samples of 500 American adults on the number of hours they spend doing leisure and sports activities per day (rounded to the nearest hour):
Number of hours spent doing leisure and sports activities per day 1 2 3 4 5
Sample A: Number of adults 70 90 135 140 65
Sample B: Number of adults 80 80 130 135 75
Dan concludes that adults spend a mean of 3 hours each day doing leisure and sports activities. Bret thinks the mean is 4 hours. Who is correct—Dan or Bret? Explain your answer in two or three sentences. Make sure to use facts to support your answer.
Answer:
Dan is correct
Step-by-step explanation:
Mean = the sum of all data values divided by the total number of data values
Number of adults in Sample A:
= 70 + 90 + 135 + 140 + 65 = 500
Mean of Sample A:
= [ (1 × 70) + (2 × 90) + (3 × 135) + (4 × 140) + (5 × 65) ] ÷ 500
= 1540 ÷ 500
= 3.08
Number of adults in Sample B:
= 80 + 80 + 130 + 135 + 75 = 500
Mean of Sample A:
= [ (1 × 80) + (2 × 80) + (3 × 130) + (4 × 135) + (5 × 75) ] ÷ 500
= 1545 ÷ 500
= 3.09
Mean of the two samples:
= (3.08 + 3.09) ÷ 2
= 3.085 hours
= 3 hours (nearest hour)
The mean of Sample A is 3.08 hours and the mean of Sample B is 3.09 hours, so the mean of the entire sample is 3.085 hours. If we round this to the nearest hour, then the mean is 3 hours. Therefore, Dan is correct in concluding that the adults spend a mean of 3 hours each day doing leisure and sports activities.
Three less than the quotient of a number and 4 is 18. What is the number? Let n be the unknown number.
Answer:
n = 84
Step-by-step explanation:
18 + 3 = 21, so that means the quotient of the number and 4 is 21.
21 * 4 = 84
CHECK:
84 / 4 = 21
21 - 3 = 18
Four girls and six boys are in a Spanish club. Three of the people will be chosen at random to represent the group in a photograph.What is the probability that one girl and two boys will be chosen
Answer:
18/125
Step-by-step explanation:
4 add 6 is 10
4/10 chance for a girl
6/10 chance for a boy
2 boys and a girl is 4/10, 6/10, 6/10
4/10 multiplied by 6/10 multiplied by 6/10 is:
144/1000
This can be simplified to 72/500
This can be simplified to 36/250
This can be simplified to 18/125
What is the coefficient of the x2-term of the algebraic expression 2 x 4 + x squared minus x + 7?
-1
1
0
2
Answer:
1
Step-by-step explanation:
If x doesnt have a number in front of it the coefficient is 1. x^2 + 3x + 7 = 1x^2 + 3x + 7 /// same thing
Answer:
i believe its B. 1
Step-by-step explanation:
The points P (22, 15), Q (−13, c) and R (k, 24) all lie on a circle, centre (2, 0). Find the radius of the circle and the possible values of the constants c and k.
Answer:
r = 25c = 20k = 9 or k = -5Step-by-step explanation:
Circle of center A(2, 0) and radius r.
P (22, 15), Q(−13, c) and R (k, 24) all lie on a circle,
[tex]r=AP=\sqrt{\left( 22-2\right)^{2} +\left( 15-0\right)^{2} }[/tex]
[tex]=25[/tex]
Q(−13, c) lies on the circle then ,
[tex]AQ=r\Longrightarrow AQ^{2}=r^{2}\Longrightarrow (-13-2)^{2}+(c-0)^2=25^2=625[/tex]
[tex]\Longrightarrow 225+c^{2}=625[/tex]
[tex]\Longrightarrow c=20[/tex]
R (k, 24) lies on the circle then ,
[tex]AR=r\Longrightarrow AR^{2}=r^{2}\Longrightarrow (k-2)^{2}+(24-0)^2=25^2=625[/tex]
[tex]\Longrightarrow (k-2)^{2}+576=625[/tex]
[tex]\Longrightarrow (k-2)^{2}=49[/tex]
[tex]\Longrightarrow k-2=7\ \ or \ \ k-2=-7[/tex]
[tex]\Longrightarrow k=9\ \ or \ \ k=-5[/tex]
Amanda created a table to help her represent the sample space of spinning a spinner and flipping a coin.
Result of spin
Result of coin toss Red Green Yellow Blue
Heads Red, heads Green, heads Yellow, heads Blue, heads
Tails Red, tails Green, tails Yellow, tails Blue tails
What is the probability that the result of the spin is blue and the coin lands heads up?
two over eight
three over eight
one over eight
four over eight
Answer:
[tex]\sf \dfrac{1}{8}[/tex]
Step-by-step explanation:
Spinner choices: Red, Green, Yellow, Blue
Coin choices: Heads, Tails
[tex]\large\begin{array}{| c | c | c | c | c |}\cline{1-5} & \sf Red & \sf Green & \sf Yellow & \sf Blue\\\cline{1-5} \sf Heads & RH & GH &YH & BH \\\cline{1-5} \sf Tails &RT & GT& YT& BT\\\cline{1-5}\end{array}[/tex]
[tex]\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}[/tex]
[tex]\implies \sf P(blue)=\dfrac{1}{4}[/tex]
[tex]\implies \sf P(heads)=\dfrac{1}{2}[/tex]
[tex]\implies \sf P(blue)\:and\:P(heads)=\dfrac{1}{4} \times \dfrac{1}{2}=\dfrac{1}{8}[/tex]
PLEASE ANSWER AS FAST as u can
Answer:
5.4 cm
Step-by-step explanation:
[tex] c =\pi d[/tex][tex] \implies 17 =\pi d[/tex][tex] \implies \frac{17}{\pi} =d[/tex][tex] \implies \frac{17}{3.14} =d[/tex][tex] \implies 5.41401274 =d[/tex][tex] \implies d\approx 5.4\: cm[/tex]Hope it helps you in your learning process
Find the base and height of this parallelogram.
Divide the parallelogram into two triangles, assume that our e diagonal is the "base" for both new triangles. What's the height of that triangle? Use the sine function. It's (f/2) * sin (angle)! The area of the triangle is equal to our "base" e times height: e * (f/2) * sin (angle)
The base is 12 feet long, the height is 17 feet long.
How To Solve: https://brainly.com/question/544471
Credit to: naǫ
Simplify the expression. Write your answer as a power.
Answer:
2/3 to the power 8
Step-by-step explanation:
Power : 2 + 6 = 8
me podrían ayudar con esto?
Answer:
0
Step-by-step explanation:
This would be basically be zero/0 because anything times 0 is just nothing.
In many cases, lenders allow homeowners to include their homeowners insurance premium with their monthly mortgage payment. tim’s home is worth $279,500. if his homeowners insurance premium is $0.33 per $100, how much is added to his monthly mortgage payment for insurance? a. $7.69 b. $76.86 c. $92.35 d. $922.35 please select the best answer from the choices provided a b c d
The amount that is added to his monthly mortgage payment for insurance is b. $76.86.
What is a Mortgage?This refers to the amount of money that is paid for the downpayment for a piece of property.
Given that the worth of the home is $279,000
premium is $0.33 per $100.
1 month premium on $1 is $0.0275/100
Now, one month's premium is calculated as:
$0.0275/100 * 279,000
=$76.86
Read more about mortgages here:
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A quantity with an initial value of 620 grows continuously at a rate of 0.3% per second. What is the value of the quantity after 0.5 minutes, to the nearest hundredth?
Answer:
678.39
Step-by-step explanation:
For this we should probably use the formula A = Pe^rt. The question says that the value grow "continuously" which is our hint that we should use A = Pe^rt rather than A = P(1 +r/n)^nt. Our P = 620 as it is our initial value. e is a constant approx = 2.718. r is our rate, so 0.3% = 0.003, and our t will be in seconds. We need to figure out how many seconds are in .5 minutes, so 30, and that means our t will = 30. Let's plug these in. 620e^(0.003 * 30) = A. This will give us our answer which when rounded to the hundredths = 678.39.
Hope this is helpful.
Can you answer this for me ty :)
Find the Volume of the Sphere if:
r=10 and pi= 3.1416
Answer:
4188.79
Step-by-step explanation:
formula- [tex]\frac{4}{3}[/tex] × [tex]\pi[/tex] × [tex]r^{3}[/tex]
r= radius
Help with this volume problem? (please include how you got the answer) will give brainlyest
Answer:
35.28 m
Step-by-step explanation:
Formula for volume of pyramid:
[tex]V=b^2\frac{h}{3}[/tex]
Therefore since,
base - 4.2 m
height - 6 m
Then,
[tex]V=4.2^2\frac{6}{3}[/tex]
[tex]V=35.28m[/tex]
Kavinsky
anyone knows the answer?!
Answer:
p = -6.32, 6.32
Step-by-step explanation:
[tex]3 {p}^{2} - 120 = 0[/tex]
[tex] {p}^{2} - 40 = 0[/tex]
[tex] {p}^{2} = 40[/tex]
p = -2√10, 2√10
p= -6.32, 6.32