Given the equation 47=38+n, tell which value is a solution from the solution set n={7, 9, 11, 13}

Answer:

31

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

[tex]\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}[/tex] or [tex]\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}[/tex]

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

[tex]\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}[/tex]

Therefore, the solution is 31.

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as [tex]\displaystyle \large{a_{n-1} \cdot r = a_n}[/tex] meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

[tex]\displaystyle \large{r=\frac{a_{n+1}}{a_n}}[/tex]

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

[tex]\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}[/tex]

Above should be applied for series that have common ratio not equal to 1.

[tex]\displaystyle \large{S_n=a_1 \cdot n}[/tex]

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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The mean and mean absolute deviation of the given data are;

B. Mean: 72; mean absolute deviation: 2.

The mean absolute deviation of a data set is the average distance of each data point in the data set from the mean of the data set.

Given the data, 68, 70, 72, 73, 74, 75:

Mean = (68 + 70 + 72 + 73 + 74 + 75)/6 = 432/6

Mean = 72

Mean absolute deviation = [(68 - 72) + ( 70 - 72) + ( 72 - 72) + ( 73 - 72) + ( 74 - 72) + ( 75 - 72)] / 6

Mean absolute deviation = [(4) + (2) + (0) + (1) + (2) + (3)] / 6

Mean absolute deviation = 12/6

Mean absolute deviation = 2

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The value of the equation is A = x² ( 4 + x )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = 4x squared + x cubed

Substituting the values in the equation , we get

A = 4x² + x³   be equation (1)

On simplifying the equation , we get

Taking the common factor as x² in the equation , we get

A = x² ( 4 + x )

Therefore , the value of A is x² ( 4 + x )

Hence , the factorized equation is x² ( 4 + x )

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Step-by-step explanation:

about circle R

arc angle MP = angle MRP = 78°

angle M = angle LMP.

according to the rules of inscribed angles, LMP is half of angle LRP.

LRP + MRP = 180° because together they cover the whole LM segment (half-circle).

LRP = 180 - MRP = 180 - 78 = 102°

so, LMP = angle M = 102/2 = 61°

also circle R (with arc ULNP)

the arc ULNP = arc UL + arc LN + arc NP = 160°

due to the congruent definition of JU and MP we know that arc UL = arc NP.

and we know arc LN = arc JM = 18°.

so,

160 = 2×arc NP + 18

142 = 2×arc NP

arc NP = 71° = arc UL

now, because arc MP + arc LP = 180 (half-circle),

arc MP = 180 - arc LP = 180 - arc LN - arc NP =

= 180 - 18 - 71 = 91°

about the circle R with 2 congruent chords :

the second answer : they are equidistant from R (the center of the circle).

about circle W

arc MK + arc KL = 180° (half-circle).

and we see

arc HL = arc KL = 53°.

so,

arc MK + 53 = 180°

arc MK = 180 - 53 = 127°

about circle M

arc QTS = 204°.

therefore, arc QRS = 360 - arc QTS = 360 - 204 =

= 156° = angle QMS.

according to the rules of inscribed angles

angle QTS = QMS/2 = 156/2 = 78°

Answer:

4 dollars per friend

Step-by-step explanation:

So, if 4 friends are paying 12 dollars, to find the total, we do 4 * 12 = 48

48 is how much the 4 friends paid

If 12 friends pay to hire the same group, (resemble for the same price of 48 dollars), is we do, 48 dollars ÷ 12 friends = 4 dollars per friend

x^2 - 9x - 3x + 27

x^2 - 12x + 27

Step-by-step explanation:

78.50 in^2 I am pretty sure

Answer:

78.50 in squared

Step-by-step explanation:

To find the area of a circle, you need to use the equation area = pi * r^2, or pie multiplied by the radius squared. The radius is half of the diameter, which means the radius is 5. 5 squared is 25. Pi times 5 is about 78.50 inches squared.

Answer:

26,160.00

Step-by-step explanation:

24,000 + 9% = 26,160.00

Have a wonderful day! Dream a good dream of good people. :)

Answer:

The answer is

→ $26,160

Step-by-step explanation:

In this problem, it says that the total cost of the new car is the price of $24,000 plus a sales tax of 9%. For the problem, it's obvious to use addition, because when you buy something, most of the time they add taxes.

So,

24,000

+ 9%

‾‾‾‾‾‾‾‾‾‾

26,160

Therefore, 26,160 is the correct answer for your problem.

Answer:

4units is the answer to the question

Answer:

4

Step-by-step explanation:

took the k12 test

Using the Empirical Rule, it is found that there is a 68% probability that a student scored between 66 and 82.

It states that, for a normally distributed random variable:

In this problem, considering the mean of 74 and the standard deviation of 8, we have that:

74 - 8 = 66

74 + 8 = 82.

Hence, there is a 68% probability that a student scored between 66 and 82.

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Answer:

10

Step-by-step explanation:

To  find,

HCF of 50 & 70 using Euclid's Division Algorithm.

Solution,

HCF(50 & 70) --  70 = 50 × 1 + 20.

                           50 = 20 × 2 + 10

                           20 = 10 × 2 + 0.

Therefore their HCF is 10.

Answer:

10

Step-by-step explanation:

According to Euclid's Algorithm, c = dq + r ,  0 ≤ r < d  (where r is the remainder)

As 70 > 50, c = 70 and d = 50

Substituting values of c and d:

   70 = (50 x 1) + 20

⇒ 50 = (20 x 2) + 10

⇒ 20 = (10 x 2) + 0

Therefore, the HCF is 10

Answer:

3.1%

Step-by-step explanation:

2.20/2.35 = 3.1%

Have an amazing day!!

Please rate an dmark brainliest!!

Answer:

Your answer is C.

239-92

Step-by-step explanation:

If shes giving AWAY then it would be a subtraction problem.

Answer:

30.42 in^2.

Step-by-step explanation:

Find the height:

sin 45 = 1/√2 = h/7.8

h = 7.8 /√2

the base = height = 7.8 /√2

Area = h * b

= (7.8 /√2)2

= 30.42.

Answer:

VOL_cone is 70.7

which is LESS THAN

the vol of cylinder. VOL_cyl is 71.6

Step-by-step explanation:

Volume of a cone:

V= (1/3)pi•r^2 • h

=(1/3)pi•3^2 • 7.5

= 70.7 cubic inches

(rounded to tenths this is the same if you use a pi key on the calculator or if you use 3.14)

The Volume of a cylinder:

V = pi•r^2 • h

= pi• 2.25^2 • 4.5

= 71.6 cubic inches

(more accurate with pi key, using 3.14 it rounds to 71.5)

The last blank could be the words "less than" but if they are asking for a fraction or percent, calculate by putting the big number on the bottom and the smaller number on top.

Answer:

  A: geometric; 4 times

  B: arithmetic: 4 more

Step-by-step explanation:

An arithmetic model is a linear model, where the rate of change is constant.  Growth or decay is by a constant amount from one interval to the next.

A geometric model is an exponential model, in which the rate of change is proportional to the amount. Growth or decay is by a constant factor from one interval to the next.

__

The equation for the sequence is given in "explicit" form:

  [tex]A_n=2^{2n}[/tex]

The exponent can be split so this can be rewritten as ...

  [tex]A_n=(2^2)^n=4^n[/tex]

If this were written in recursive form, it would look like ...

  [tex]A_0=1,\ A_n=4\times A_{n-1}[/tex]

The fact that terms are related by a constant factor tells you the model is geometric. The factor tells you each hour the population is 4 times what it was in the previous hour.

__

The given equation is in "recursive" form. It tells you each term is 4 more than the previous one. This constant difference between terms means the model is arithmetic.

_____

Additional comment

In general, words like "more" or "increase" refer to addition, and the words "times" or "factor" refer to multiplication.

No photo attached, but no need.

We're given that f(0) = 1 and f(2) = 5, and that

[tex]\displaystyle \int_0^2 f(x) \, dx = 7[/tex]

Integrate x f'(x) by parts, with

[tex]u = x \implies du = dx[/tex]

[tex]dv = f'(x) \, dx \implies v = f(x)[/tex]

Then

[tex]\displaystyle \int_0^2 x f'(x) \, dx = uv\bigg|_{x=0}^{x=2} - \int_0^2 v \, du \\\\ = x f(x) \bigg|_{x=0}^{x=2} - \int_0^2 f(x) \, dx[/tex]

Now just plug in everything you know:

[tex]\displaystyle \int_0^2 x f'(x) \, dx = 2f(2) - 0f(0) - \int_0^2 f(x) \, dx = 10 - 0 - 7 = \boxed{3}[/tex]

Answer: Altitude

Step-by-step explanation:

Answer

C. 49 fl oz

Step-by-step explanation:

I took the quiz.

Answer:

y + 8

Step-by-step explanation:

8 more than y is y plus 8.

Answer:

x= 12

Step-by-step explanation:

Hope u understood it

"PLEASE MARK ME THE BRAINLIEST"

Answer:

14x + 23

Step-by-step explanation:

The lengths of three sides of a triangle are 5x + 9 feet, 2x + 14 feet, and 7x feet.

The perimeter of a triangle: the sum of all of its sides.

5x + 9 + 2x + 14 + 7x

14x + 23

It's the expression of the perimeter of the triangle. Once you will be asked to find x, you'll probably be given the exact perimeter of the triangle.

The amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.

Monthly payment is the payment which has to paid against the loan amount or the borrowed money calculated with interest rate.

It can be calculated with the following formula.

[tex]M=P\left (\dfrac{r}{1-(1+r)^{-nt}}\right)[/tex]

Here, (P) is the principal amount, (r) is the interest rate and (t) is time.

Brandon has two credit cards and would like to consolidate the two balances into one balance on the card with the lower interest rate.

The table below shows the information about the two credit cards Brandon currently uses.    

Interest rate for the card a is,

[tex]r=\dfrac{13}{12\times100}=0.01083[/tex]

The time period is 8 years and there are 12 months in one year. Thus, the monthly payment of card A will be,

[tex]M=1157.98\left (\dfrac{0.01083}{1-(1+0.01083)^{-12(8)}}\right)\\M=19.47[/tex]

In the 8 years, there is total 96 monthly payments. Thus, the total payment by card A is,

[tex]P_a=19.47\times96=1869.12[/tex]

For the card B the monthly payment is $22.14. Thus the total payment by card B is,

[tex]P_b=22.14\times96=2125.44[/tex]

The difference in the payment is,

[tex]d=2125.44-1869.12\\d=256.12[/tex]

Hence, the amount which Brandon have saved in interest by consolidating the two balances on the card with the lower interest rate is $256.12.

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Answer:

C. 256.32

Step-by-step explanation:

Answer:

y=4x-9

Step-by-step explanation:

Slope-intercept form is y=mx+b where y is the y vale, m is the slope, x is the x value and b is the y-intercept.

We need to find the slope and y-intercept.

To find slope we will do rise/run

If we start from (3,3) and go up 4 and over 1 we get to (4,7)

4 over 1 is also 4

So m=4 or slope is 4

Now lets find the y-intercept

We can plug in our values and solve for b

3=4*3+b

3=12+b

-9=b

y-intercept is -9

so our answer will be y=4x-9

Answer:

  y = 4x -9

Step-by-step explanation:

The equation of this line is requested in slope-intercept form. The y-intercept is off the bottom of the graph, so we much develop the equation from what we can see.

Exact values are best determined from points where the line crosses grid intersections. We observe two of those are (1, -5) and (2, -1). The slope formula can tell us the slope:

  m = (y2 -y1)/(x2 -x1)

  m = (-1 -(-5))/(2 -1) = 4/1 = 4

The formula for the y-intercept can be used with the first point:

  b = y -mx

  b = -5 -4(1) = -9

Then the equation of the line y = mx +b is ...

  y = 4x -9

Answer:

-1.7

Step-by-step explanation:

8.7 + X =7

incorporate the shoes and socks method. We must do the opposite of what is being done. If we are adding X, we will subtract X on both sides leaving you with 8.7=7-x. We want X on one side of the equation so now we take the 8.7 and subtract on both sides giving 7-x-8.7. we must add X on both sides so we can have a X on one side thus X= 7-8.7. we can ordinary subtract and will give us -1.7.

X=-1.7

8.7+(-1.7) =7

A finite, nonzero area formed by the lines would have a fixed measurement

The number of separate region that have a finite, nonzero area is 64

The given parameters are:

The number (n) of separate region that have a finite, nonzero area is calculated as:

n = (h - 1) * (v - 1)

This gives

n = (9 - 1) * (9 - 1)

Evaluate the product

n = 64

Hence, the number of separate region that have a finite, nonzero area is 64

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The amount of plywood needed to build the garbage bin is the surface area. Therefore, the amount of plywood needed is 90884 cm².

The wooden box is a rectangular prism. The amount of plywood used to construct the wooden box is the surface area of the box.

Therefore,

surface area of rectangular prism = 2(lw + lh + hw)

where

l = 156 cm

w = 122 cm

h = 95 cm

surface area of rectangular prism = 2((156 × 122) + (156 × 95) + (122 × 95))

surface area of rectangular prism = 2(19032 + 14820 + 11590)

surface area of rectangular prism = 2(45442)

surface area of rectangular prism = 90884 cm²

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