Find the sum of the geometric sequence. (1 point) 1, one divided by two, one divided by four, one divided by eight, one divided by sixteen

Answers

Answer 1

GP = 1/2 , 1/4 , 1/8 , 1/16
1st) the common ratio is (1/4 : 1/2 ) = 1/2, so r =1/2
2nd) the sum of a GP is:

S= a(1-rⁿ)/(1-r)

S=(1/2).[1-(1/2)⁴]/(1-1/2) = 15/16

Answer 2

Answer:

31/16

Step-by-step explanation:

Related Questions

What is the 32nd term of the arithmetic sequence where a1 = −32 and a9 = −120?

Answers

firstly we have to find d:
[tex]d = \frac{a_{n}-a_{m}}{n-m} [/tex] ⇒
[tex]d = \frac{-120-(-32)}{9-1} = \frac{-88}{8} = -11[/tex]
now, when we know d, we can find the 32nd term by using a following formula:
[tex]a_{n}=a_{1}+(n-1)*d[/tex]
[tex]a_{32} =-32+31*(-11) = -32-341 = -373[/tex]
the answer is [tex]a_{32} = -373[/tex]

Answer:

-373

Step-by-step explanation:

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120

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341

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373

Salvage system algebraically. Show all your work in circle your answers

Answers

Use substitution for x
2(y+2)+4y=-2
2y+4+4y=-2
6y+4=-2
6y=-6
y=-1

Plug the y value in to find x
x= (-1)+2
x=1

Final answer: (1,-1)

select all tht apply
If n-^2 = 1/16, then n could be which of the following?

-8
-4
-1/4
1/4
4

Answers

[tex] n^{-2}= \cfrac{1}{16} \\ \\ \cfrac{1}{n^2} = \cfrac{1}{16}; \ \ \ n \neq 0 \\ \\ n^2=16 \\ \\ n=б \sqrt{16} \\ \\n=б4[/tex]

what is the proportion for 2/3 and 8/10

Answers

there is no solution I believe since 2/3 and 8/10 cross multiplied are 2 times 10 and 3 times 8 which is 20 = 24 which does not equal and there is no answer

(3x/4)>51 ( line underneath >)

Answers

quick and easy steps that you (may understand it better)

So, firstly let's multiply the fraction [tex] (\frac{4}{3} )[/tex] on your sides

[tex] \frac{4}{3} ( \frac{3}{4}x )[/tex] ← cancel this out because it would give you the quotient of [tex]1 [/tex]

[tex] \frac{4}{3} (52) [/tex] keep this because this would give you [tex]68 [/tex]

[tex]Answer: x \geq 68[/tex]

[tex]good \\ luck \\ on \\ your \\ assignment \\ \\ \\ \\ Enjoy \\ your \\ day \\ \\ \\ \\ MeIsKaitlyn :) [/tex]

PLZ HELP I NEED THIS TODAY!!!!Write an expression for the perimeter of the triangle shown below: A triangle is shown with side lengths labeled 2.3x plus 14, 2x, and negative 0.2x plus 15.

Answers

The perimeter of the triangle:
P = a + b + c, where a, b, and c are sides of the triangle.
Here is:
a = 2.3 x + 14, b = 3 x and c = - 0.2 x + 15
P = ( 2.3 x + 14 ) + 2 x + ( - 0.2 x + 15 ) =
= 2.3 x + 14 + 2 x - 0.2 x + 15 = 4.1 x + 29
Answer: The perimeter of the triangle is 4.1 x + 29

Suppose A and B are independent events if P(A) = 0.4 And P(B) = 0.1, what is P(A'uB)? APEX

Answers

For Independent Events, P(A) × P(B) = P(A∩B)

so we have, P(A∩B) = 0.4×0.1 = 0.04

P(A') = 1 - 0.4 = 0.6

This information can be represented on a Venn diagram as shown below

P(A'∪B) means the union of everything that is not A with everything that is B

P(A'∪B) = 0.06 + 0.54 + 0.04 = 0.64

Answer:0.6

Step-by-step explanation:

A line with a slope of 0 passes through the point (0, -5) . what is its equation i n slope -intercept form?

Answers

It should be y=x-5 because the slope is 0 and the y-intercept is -5.

which of the following is an example of conditional probability.
A: probability of hitting a home run
B: Probability of getting an A on a test, given that you didn't fail the test
C: probability of drawing a club from a deck of 52 cards
D: probability of getting an A on a test

Answers

it would be b because first off it is different from all the others and it has probability of a given b

The example of conditional probability is Probability of getting an A on a test, given that you didn't fail the test.

What is conditional probability?

Conditional probability is known as the possibility of an event or outcome happening, based on the existence of a previous event or outcome.

For Conditional probability, the event should be dependent events.

Also, the probability of an event and the condition is that the other event has already been occurred.

Here, in Probability of getting an A on a test, given that you didn't fail the test is example of conditional probability because " you didn't fail the test " already occurred and now find the probability of getting A.

Learn more about conditional probability here:

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A box has dimensions of 17 inches long.1.3 feet wide, and 8 inches high. What is the valine of the box? The formula for the volume is V = l• w •h.

Answers

convert the feet to inches so all 3 dimensions are in the same measurement

1.3 x 12 = 15.6 inches

now multiply them all

17 x 15.6 x 8 = 2121.6 cubic inches

round the answer if you need to

A golfer would like to test the hypothesis that the variance of his golf score equals 10.0. a random sample of 28 rounds of golf had a sample standard deviation of 3.5. what is the number of degrees of freedom for this hypothesisâ test?

Answers

It depends on which statistic test we wish to perform, the formula to find a degree of freedom could be different.

for Normal Distribution test, we do not need to find a degree of freedom

for T-test and Chi-Square test, we do n - 1 to find the degree of freedom, where 'n' is the sample size.

if we have two different sample size, then the degree of freedom is given by (n₁ + n₂) - 2

We are given only one sample size, n = 28, hence the degree of freedom is 28 - 1 = 27

How to factor x^2+27

Answers

Hello,

If you know complex, than:

x²+27=x²-i²*3*9=(x-i*3√3)(x+i*3√3)

ABCDEFGHIJ is a regular decagon. Find the length of the apothem. Round the answer to the nearest tenth.

A.

8.0

B.
20.5

C.

24.7

D.

26.0

Answers

you find apothem with the formula [tex] \left[a = fn*S] [/tex]

fn is the fixed number (1,539) and S the side of the polygon.

a = 16*1,539 = 24,624 = 24,7

Answer C

Solution:(α=∫nₓS)Use this formula to find apothem

∫n is the fixed number (1,539) and S the side of the polygon.

a = 16 × 1,539 = 24,624 = 247

Answer: C 24.7

One way to recognize a line of symmetry is to look for a line that divides the original image into

Answers

yes that is correct
like a square if you half it both sides equal each other but if you half a elephant then it is not equal

2 equal halves

for example a line of symmetry fro an isosceles triangle is a line from vertex to midpoint of the opposite side.

The mass of mercury is 330,200,000,000,000,000,000,000 kilograms. how can this number be written in scientific notation?

Answers

Final answer:

The mass of mercury, 330,200,000,000,000,000,000,000 kg, can be written in scientific notation as 3.302 × 10²⁰ kg. Scientific notation helps to express very large numbers in a more manageable form, using a coefficient between 1 and 10 multiplied by a power of ten.

Explanation:

To write the mass of mercury in scientific notation, we need to express it as a number between 1 and 10 multiplied by a power of ten. The mass given is 330,200,000,000,000,000,000,000 kilograms, which can be written as 3.302 × 10²⁰. Since there are 20 digits to the right of the first digit (3), the exponent in the scientific notation will be 20.

In scientific notation, the mass of mercury is thus written as 3.302 × 10²⁰ kg.

When converting to scientific notation, we use multiplication and division techniques to adjust the original number, so the resulting coefficient is a value from 1 up to, but not including, 10. This method is commonly used by scientists and astronomers when dealing with astronomical numbers, as in this case with the mass of a planet or in chemistry with the mass of an atom.

If vertex T' is at (2,-2) what are the coordinates of vertex s

Answers

wheres the grid????????

Samantha loves to download new music. She originally had 52 songs but plans to purchase 2 new songs each week. She wants to know how many songs she will have after 93 weeks. Which equation should she use?

a93 = 93 + 2(52 − 1)
a93 = 93 + 2(52 + 1)
a93 = 52 + 2(93 + 1)
a93 = 52 + 2(93 − 1)

Hint: It's either A, B, C, or D

Answers

[tex]a_1=52\\ d=2\\ n=93\\\\ a_n=a_1+(n-1)\cdot d\\\\ a_{93}=52+(93-1)\cdot2=52+2(93-1) [/tex]

They want to construct this in the form of an arithmetic sequence which as the form:

a(n)=a+d(n-1), where a=initial value, d=common difference.

In this case a=52 and d=2, so our formula is:

a(n)=52+2(n-1) and if we are looking for the 93 term we have

a(93)=52+2(93-1)

2. Richmond Appliance repairs washing machines. The revenue that the company earns is given by the function R(h) = 20 + 45h dollars for every h hours spent repairing washing machines. The company’s overhead cost is given by the function C(h) = 5h2 – 30 dollars. For what number of hours does the company break even? Show your work.

Answers

The number of hours needed for the company to break even happens when
[tex]R(h)=C(h)[/tex]

[tex]20+45h= 5h^{2}-30 [/tex], rearranging to make the equation 'zero' on LHS
[tex]0= 5h^{2}-30-20-45h [/tex]
[tex]0= 5h^{2}-45h-50 [/tex], divide each term by 5
[tex]0= h^{2}-9h-10 [/tex], factorise
[tex]0=(h+1)(h-10)[/tex], equate each factor to zero
[tex]h=-1 [/tex] and [tex]h=10[/tex]

We choose the positive value of [tex]h[/tex]

Hence, the number of hours needed to break even is [tex]h=10[/tex]

Answer:

The number of hours needed for the company to break even happens when

, rearranging to make the equation 'zero' on LHS

, divide each term by 5

, factorise

, equate each factor to zero

and

We choose the positive value of

Hence, the number of hours needed to break even is

Step-by-step explanation:

HELP PLEASE..answer fast please and show all work and explain how to solve

Answers

[tex] \cfrac{a}{sinA}= \cfrac{b}{sinB} \ \ \to \\ sinB= \cfrac{b*sinA}{a} = \cfrac{10*sin15^o}{9}= 0.2875 \ \ \to \ m \angle B=16.7^o \\ \\ \\ m \angle C=180- m \angle A- m \angle B=180-15-16.7=148.3^o \\ \\ \\ \cfrac{a}{sinA}= \cfrac{c}{sinC} \ \ \to \ c= \cfrac{a*sinC}{sinA}= \cfrac{9*sin148.3^o}{sin15^o} \approx 18.3[/tex]

(02.07)Solve for L: A = L ⋅ W ⋅ H

Answers

A = LWH
/WH = L

Therefore L = A / WH

A = L ⋅ W ⋅ H
Let's solve for l.a=lwhStep 1: Flip the equation.hlw=aStep 2: Divide both sides by hw.hlw/hw=a/hwl=ah/w

Find the zeros of the function. f(x) = 4x3 - 12x2 - 40x

Answers

first take out the GCF which is 4x

4x (x^2 - 3x - 10) = 0

4x(x - 5)(x + 2) = 0

4x = 0 so x = 0

x - 5 = 0 so x = 5

x+2 = 0 so x = -2

zeros are -2, 0 and 5

is this correct? if not please let me know how to solve it

Answers

It's correct.

All you had to do was distribute and you did that perfectly.

it is correct. you had to use the distributive property and you did that correctly.

What's the 6th term in a sequence that starts with -7.5 and has a common ratio of 9?

Answers

[tex]\bf n^{th}\textit{ term of a geometric sequence}\\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=-7.5\\ r=9\\ n=6 \end{cases}\implies a_6=-7.5\cdot 9^{6-1}[/tex]

7x7-9exponent x 7 7exponent

Answers

7 x 7 (-9) exponent x 7(7) exponent:
[tex]7 * 7 ^{-9}* 7 ^{7}= \\ =7 ^{1-9+7}= \\ = 7 ^{-1} [/tex] = 1/7
Answer: 1/7

Answer:

1/7

Step-by-step explanation:

Gabby solved x2 - 3x = 4 as shown below:
x2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = -4 and x = 1

Caitlyn says Gabby is wrong and believes this is the solution:
x2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x = 4 and x = -1

Is Gabby or Caitlyn correct? What mistake was made by the incorrect girl? Type your response in the box provided.

Answers

Caitlyn is correct.
Both factored correctly but the reason Gabby is wrong is because of the Zero Product Property, which says if (x-4)(x+1)=0, then (x-4)=0 or (x+1)=0.

If (x-4)=0, then the value of x must be 4.
If (x+1)=0, then the value of x must be -1.

what is the solution to y=x+16 and y=-x+4??

Please show work and explanation in how its done...
so i can understand better cause I'm new to these problems...
so i can get all the help i can get (:

Answers

y=x+16
y=-x+4

All you have to do is substitute.
Put the second equation into the first equation.

-x + 4 = x + 16
4 = 2x + 16
-12 = 2x
-6 = x

Now substitute the x into one of the equations to get y.

y = (-6) + 16
y = 10

The solution to these equations is (-6, 10).

What is the square root of 75 in simplified form?

Answers

√75 = 5√3

so yeah this is filler text

Answer:The answer is

5 3

Step-by-step explanation:

Lana Powell has cumulative earnings of $110,000 at the end of September. In the first week in October she earns $2,000. The amount deducted for Social Security and Medicare from her check is (assume Social Security rate of 6.2% on $110,100 and Medicare of 1.45%):

Answers

Answer:

Step-by-step explanation:

In the first week of October on the $ 2,000, we must deduct the two expenses, that of 6.2% and 1.45%, and then add them between them and subtract them from the $ 2000.

It would be the following: 2000 x 6.2% = $ 124; 2000 x 1.45% = 29; 124 + 29 = $ 153 is the amount to be deducted from the $ 2,000; $ 2000 - $ 153 = $ 1847.

Final answer:

Lana Powell's paycheck for the first week in October would have $124 deducted for Social Security and $29 for Medicare, resulting in a total deduction of $153. Her cumulative earnings are not considered here as she has exceeded the earnings threshold of $110,100 for Social Security tax.

Explanation:

Lana Powell's earnings for the first week in October are subject to deductions for Social Security at a rate of 6.2% and Medicare at a rate of 1.45%. To calculate these deductions, you multiply her weekly earnings by the respective rates:

Social Security deduction = $[tex]2000*6.2/100 = $124[/tex]Medicare deduction = $[tex]2000*1.45/100 = $29[/tex]

Therefore, the total amount deducted from Lana Powell's paycheck for Social Security and Medicare is $124 + $29 = $153.

Note that you do not consider her cumulative earnings in this case. The Social Security tax is applicable only up to a wage base limit of $110,100 and since her cumulative earnings have already exceeded this limit, she would not be paying any additional Social Security tax beyond this earnings threshold.

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Prove or disprove the identity. If you find the identity is true, state the first line of the proof. If you find the identity is false, write the correct equation by replacing the right side.
sin x cos x tan x cot x = 1

A) the identity is true. sin x cos x tan x cot x = cos x
B) the identity is true. sin x cos x tan x cot x = sin x tan x
C) the identity is false. sin x cos x tan x cot x = sin x cos x
D) the identity is false. sin x cos x tan x cot x = sin x

Answers

sin x cos x tan x cot x

Change to sin's cos's:-

= sin x cos x sin x cos x
------- -------
cos x sin x

= sin x cos x

C is correct

Final answer:

The identity sin x cos x tan x cot x = 1 is false. By using the definitions of tan and cot, we can show that sin x cos x tan x cot x simplifies to sin x cos x.

Explanation:

The student has asked to prove or disprove the identity sin x cos x tan x cot x = 1. To verify this identity, we need to remember the definitions of the trigonometric functions. The tangent (tan) of an angle is the ratio of the sine (sin) to the cosine (cos) of that angle, and the cotangent (cot) is the reciprocal of the tangent.

Therefore, tan x = sin x / cos x, and cot x = cos x / sin x. When we multiply tan x by cot x, we get:

tan x × cot x = (sin x / cos x) × (cos x / sin x) = 1

Now, multiplying this result by sin x cos x gives:

sin x cos x tan x cot x = sin x cos x × 1 = sin x cos x

Therefore, the correct equation is sin x cos x tan x cot x = sin x cos x, which means the correct answer is:

A runner is running 5 miles per hour. how many feet is the runner running per second.

Answers

For this problem, you want to make conversions from meters to feet and hours to seconds. So, you start out with 5 miles/ hour, and you divide by a unit factor of 5280 feet / miles, getting 5*5280 feet/ hour. Then, you multiply by a unit factor of 1 hour / 60*60 seconds, getting 5*5280/360 feet/second. Simplify, and your final answer is
73.33.

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