A geometric series is the sum of an unlimited number. The common ratio of the geometric sequence is 3.
What is geometrical series?A geometric series is the sum of an unlimited number of terms with a fixed ratio between them.
Given the value of a₁ is 10, while the value of a₅ is 810, therefore, the common ratio can be written as,
[tex]\dfrac{a_5}{a_4} \times \dfrac{a_4}{a_3} \times \dfrac{a_3}{a_2}\times \dfrac{a_2}{a_1} = r \times r \times r \times r\\\\\\\dfrac{a_5}{a_1} = r^4\\\\\\dfrac{810}{10} = r^4\\\\\sqrt[4]{81} = r\\\\r = 3[/tex]
Hence, the common ratio of the geometric sequence is 3.
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You are asked to create a 5 LETTER password, how many different passwords can you create if.
a) All letters are capitals and repetition is allowed
b) All letters can be either capitals or lower case, but repetition is
not allowed.
Detailed explanations are most welcome.
We will see that the number of different combinations for each case are:
a) 11,881,376b) 311,875,200How many passwords can we make?
We have 5 selections for each password, we need to find the number of options for each one of these selections.
a) Here we can use only capitals an we can repeat, so for each selection (each letter), we have 26 options.
The total number of combinations will be equal to the product between the numbers of options:
C = 26*26*26*26*26 = 11,881,376
b)Now we can use either capitals or lower case, but we can't repeat. (Here I assume that A is different than a, so we can't use A two times, but we could use A and a).
Then we have 26*2 = 52 options.
For the first letter, we have 52 options.
For the second letter, we have 51 options (because one letter was already used).
For the third letter, we have 50 options, and so on.
The total number of combinations will be:
C = 52*51*50*49*48 = 311,875,200
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Simplify Each Radical Expression. Leave in radical form. (Do not use decimals.)
√(7) + √(28) – √(700)
[tex]\sqrt 7 +\sqrt{28} - \sqrt{700}\\\\\\=\sqrt 7 +\sqrt{4 \times 7} - \sqrt{100 \times 7}\\\\\\=\sqrt 7 + 2\sqrt 7 - 10\sqrt 7\\\\\\=-7\sqrt 7[/tex]
A gas station is 9 miles away. How far is the gas station in kilometers? Use the following conversion: 1 mile is 1.6 kilometers.
1 mile = 1.6 kilometers
Multiply total miles by 1.6
9 miles x 1.6 = 14.4 kilometers
Answer: 14.4 kilometers
Answer:
14.4 kilometres
Step-by-step explanation:
Given that,
→ 1 mile = 1.6 kilometres
By using this information 9 miles will be,
→ 9 miles × 1.6 km
→ [ 14.4 km ]
Thus, the gas station is 14.4 km away.
Express 0.246666…… as a rational number
What is the measure of central angle COB?
What is the measure circumscribed angle A>
m<COB
2(30°)60°Our answer is 60°
<A+60=180<A=120°9x^7-36x^4+45x^6=
Please help
Answer:
9x^4 [ x^3 + 5x^2 - 2 ]
Step-by-step explanation:
9x^7 - 36x^4 + 45x^6
=9x^7 + 45x^6 - 36x^4
=9x^4 [ x^3 + 5x^2 - 2 ]
//
I hope this is the answer that you are looking for
Kasey wants to wrap light strips completely around her circle shaped mirror. She
measured the radius of the mirror at 2 ft. Lights strips at her local store are sold by
the foot. What is the minimum length of lights that Kasey can buy to make sure
there are lights all the way around her mirror?
ratio tables you need 3 sticks of butter for every 24 giant cookies cookie you make
fill out the table
Answer:
Sticks of butter: 2 Number of cookies: 40
Step-by-step explanation:
the ratio begins with 3:24. if you were to divide 3 by 24 it could be 1:8 **2**x 8 =16 so sticks of butter would be 2. 5x8=40.
f(x) = x². What is g(x)?
A. g(x) = -x² – 3
B. g(x) = -3x²
C. g(x) = x² - 3
D. g(x) = -x²
Answer:
A
Step-by-step explanation:
because g(x) is the opposite of f(x) minus three steps
Find the area of the parallelogram please.
Answer: 76.8 mi²
Step-by-step explanation:
The area of a parallelogram can be found be multiplying the base times the height.
A = B * H
A = 9.6 * 8
A = 76.8 mi²
Confused as to why this works? We use the same formula that we do for a rectangle because the "extra triangle" on the left can be moved to fill the empty space on the right. This then gives us a normal rectangle, which allows us to solve for the area
In this question we are provided with the base and height of a parallelogram and we are asked to calculate the area of the parallelogram using the formula.
It is given that the base is 9.6 mi and height is 8 mi.
We know,
[tex] \small\boxed{ \sf {Area_{(parallelogram)} = B × H}}[/tex]
Where,
B stand for BaseH stand for HeightSubstituting the values we get
[tex] \small\sf{ Area_{(parallelogram)} = (9.6 × 8) mi} = 76.8 {mi}^{2} [/tex]
Hence the area of the parallelogram is 76.8 mi².
Francie tried to shade all the multiples of 8 on the hundred chart.
1
2 3
4 5
6
7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
What mistake did Francie make?
The multiples of 8 from 1 to 100 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and 96.
How to calculate the multiples of the number 8?To calculate the multiples of 8 we must multiply 8 by any number and the result will be a multiple of 8.
To identify the multiples of 8 that are between the number 1 and 100, we must multiply the number 8 by the number sequence 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 .
So we will know properly are the multiples of 8 that are between 1 and 100 as shown below:
8 × 1 = 88 × 2 = 168 × 3 = 248 × 4 = 328 × 5 = 408 × 6 = 488 × 7 = 568 × 8 = 648 × 9 = 728 × 10 = 808 × 11 = 888 × 12 = 96Learn more about multiplication in: https://brainly.com/question/23536361
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How much money would Henry have initially borrowed if he accumulated $760 in interest after 2 years at an annual rate of 3.2%
Answer:
380
Step-by-step explanation:
760 divide 2= 380
An ice cream cone has a diameter of 12.8 cm and a slant height of 9 cm. Find the lateral surface area of the cone. Use 3.14 for π. Round your answer to the nearest tenth.
Answer:
about 181 or 180.96
Step-by-step explanation:
π·6.4·6.332+6.42≈180.9555
Find the volume of the cone shown as a decimal rounded to the nearest tenth. 22m 12m
Answer:
829.4 m³
Step-by-step explanation:
Volume of cone:
diameter = 12 m
r = 12 ÷ 2 = 6 m
h = 22 m
[tex]\sf \boxed{Volume \ of \ cone =\dfrac{1}{3} \pi r^2h}[/tex]
[tex]= \dfrac{1}{3}*\dfrac{22}{7}*6*6*22\\\\=\dfrac{22}{7}*2*6*22\\\\=\dfrac{5808}{7}\\\\= 829.4 \ m^3[/tex]
Could someone help me please. I need it fast
Answer:
10.7 cm
Step-by-step explanation:
V = (4/3)πr³
5128.8467 = (4/3)(3.14)r³
1225.043 = r³
r = 10.7
i need help on part c !!!
The volume of a cone with diameter d (and hence radius d/2) and height h is
[tex]V_{\rm cone} = \dfrac\pi3 \left(\dfrac d2\right)^2 h[/tex]
so each scoop holds
[tex]V = \dfrac\pi3 \left(\dfrac{1\,\rm in}2\right)^2 \left(2\,\mathrm{in}\right) = \dfrac\pi6 \, \mathrm{in}^3[/tex]
of coffee.
The volume of a cylinder with base diameter d and height h is
[tex]V_{\rm cylinder} = \pi\left(\dfrac d2\right)^2 h[/tex]
so the coffee can contains
[tex]W = \pi \left(\dfrac{6 \, \rm in}2\right)^2 \left(6\dfrac14 \, \mathrm{in}\right) = 2025\pi \,\mathrm{in}^3[/tex]
of coffee.
One full scoop then uses up [tex]\frac VW = \frac1{12,150}[/tex] of the total amount of coffee in the can, so you can make 12,150 cups of coffee.
find the values of a and b such that
x2-4x+9=(x+a)2+b
Answer:
x = [tex]-\frac{1}{2}a-\frac{1}{4}b+\frac{9}{4}[/tex]
Step-by-step explanation:
A cylinder has a base radius of 3 centimeters and a height of 15 centimeters.
What is its volume in cubic centimeters, to the nearest tenths place?
Answer: 424.12
Step-by-step explanation:
Cual es la respuestas de esta?
Pregunta:
Al inicio del mess, el valor de una inversion ero de $48.45. Al final del mass, el valor de la inversion cambio con una perdida de $13.80. Cual fue el valor, en dolares, de la inversion al finalizer el mass? escribe tu respuesta en el recuardo
Question in English:
At the beginning of the month, the value of an investment is $48.45. At the end of the mass, the value of the investment changed with a loss of $13.80. What was the value, in dollars, of the investment at the end of the mass? write your answer in the box
Respuesta:
34.65
Answer in English:
34.65
Explicación paso a paso:
Todo lo que necesitas hacer es restar. Reste 48.45 por 13.80. y su respuesta será 34.65
Step-by-step explanation in English:
All you need to do is subtract. Subtract 48.45 by 13.80. and your answer will be 34.65
Your welcome!!!
¡¡¡De nada!!!
HELP ILL GIVE BRAINLIEST
An equation is shown.
4c + 2c = 4c + 11/2
What value of 2c makes the equation true?
Answer:
[tex]\huge\boxed{\bf\:c = \frac{11}{4}}[/tex]
Step-by-step explanation:
[tex]4c + 2c = 4c + \frac{11}{2}[/tex]
Cancel 4c on both the sides of the equation.
[tex]2c = \frac{11}{2}[/tex]
Bring the 2 in the denominator of 11/2 to the left hand side of the equation.
[tex]2*2c = 11\\4c = 11[/tex]
Bring 4 to the right hand side if the equation.
[tex]\boxed{\bf\:c = \frac{11}{4}}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Which one is it?
Btw this is a Math Question.
Answer:
$1.5
Step-by-step explanation:
9÷6= 1.5
1.5× 1 = 1.5
Stan has made a $125.30 monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years. he would now like to draw a monthly salary from the account. determine the amount that stan can withdraw each month for 20 years, if he plans on not having anything in the account at the end of the 20 year period and no future deposits are made to the account. a. $69,242.49 b. $69,159.05 c. $333.29 d. $333.71
The annuity of the monthly deposit into an account that pays 1.5% interest, compounded monthly, for 35 years is $333.71
What is annuity?An annuity is a series of payments made at equal period of time.
future value = annuity x [(1 + i)ⁿ - 1] / i
annuity = $125.30
i = 1.5% / 12 = 0.00125
n = 35 years x 12 months = 420
future value = $125.30 x [(1 + 0.00125)⁴²⁰ - 1] / 0.00125
future value = $69,156.049 ≈ $69,156.05
annuity = [i x (present value)] / [1 - (1 + i)⁻ⁿ]
i = 1.5% / 12 = 0.00125
n = 20 years x 12 months = 240
present value = $69,156.05
annuity = (0.00125 x $69,156.05) / [1 - (1 + 0.00125)⁻²⁴⁰]
annuity = $86.45 / 0.25904
= $333.71
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The two data sets below depict random samples
of the management salaries in two companies.
Based on the salaries below which measure of
center will provide the most accurate estimation
of the salaries for each company?
• Company A:
1.2 million, 242,000, 265,500, 140,000,
281,000, 265,000, 211,000
• Company B:
5 million, 154,000.250,000, 250,000,
200,000, 160,000, 190,000
Answer:
the anwser is company A ( dont know if you need explanation)
Step-by-step explanation:
Kaitlynn needs 3 pounds of fruit for a salad.
She already has 34 pound of apples and 13 pound of grapes.
How many more pounds of fruit does she need to buy?
If I'm right, none of answer choices are correct. I used substitution and factoring, but couldn't find a solution. I just want anyone's conformation. Thanks!
Answer:
Yes, none of these are correct.
Step-by-step explanation:
We can easily see that none of these are correct just by looking at the second piece of criteria and substituting x and y for their respective numbers.
The radius of a circle is 2 yards. What is the circle's area? r=2 yd Use 3.14 for .
Answer:
12.56
Step-by-step explanation:
pi(r)^2
3.14(2)^2
12.56
f(x)=2x-1
g(x)=3
h(x)=x²+1
Compute the following:
Find f(3)
DP
In a board game, students draw a number, do not replace it, and then draw a
second number. Determine the probability of each event occurring.
The probability of drawing a two and another 2 is 1/72
What is probability?Probability is the likelihood or chance that an event will occur
Since the total number in the board game is 9, hence the probability of drawing a 2 will be 1/9The probability of drawing the second 2 will be 1/8Pr(drawing a 2, then drawing another 2) = 1/9 * 1/8Pr(drawing a 2, then drawing another 2) = 1/72
Hence the probability of drawing a two and another 2 is 1/72
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You buy a watch that cost $45.50. The tax on the watch is 7.5%. What is the final cost of the watch? *
-2-0.5b+12=0.3b+6.2
Step-by-step explanation:
-2 -0.5b + 12 = 0.3b + 6.2
-2 + 12 - 6.2 = 0.3b + 0.5b
3.8 = 0.8b
b = 3.8/0.8
= 4.75
Answer:
4.75
Step-by-step explanation:
-2-0.5b + 12 = 0.3b + 6.2
Move all terms to the left:
-2-0.5b + 12 - (0.3b + 6.2) = 0
Add all the numbers together, and all the variables
-0.5b - (0.3b + 6.2) + 10 = 0
Get rid of parentheses
-0.5b - 0.3b - 6.2 + 10 = 0
Add all the numbers together, and all the variables
-0.8b + 3.8 = 0
Move all terms containing b to the left, all other terms to the right
-0.8b = -3.8
b= -3.8/-0.8
b= 4+0.6/0.8
b= 4.75