Write an explicit formula that represents the sequence defined by the following recursive formula

The answer of the following options are as 50, 64, 36, 40, 100, 9, 12, 12 100, 27, 150 42, 50 72, 28.3.

Suppose the fraction is proper (the numerator is smaller than the denominator).

Let it be

[tex]\dfrac{a}{b}[/tex]

Then, we can interpret it as:

a parts out of b parts of a thing.

[tex]1. \dfrac{2}{5} t = 20\\\\t = 20 \times \dfrac{5}{2}\\\\t= 50[/tex]

[tex]2. \frac{7}{8} p = 56\\\\p = 56 \times \frac{8}{7} \\\\ p= 64[/tex]

[tex]3. \frac{5}{6} x = 30 \\\\x = 30 \times \frac{6}{5} = 36[/tex]

[tex]4. \frac{1}{2} x = 20\\\\x = 20 \times 2 = 40[/tex]

[tex]5. \frac{3}{5} s = 60\\\\s = 60 \times \frac{5}{3} = 100[/tex]

[tex]6. \frac{1}{3} t = 3 \\\\t = 3\times 3 = 9[/tex]

[tex]7. \frac{3}{4} x = 9\\\\x = 12[/tex]

[tex]8. \frac{11}{12} x = 11\\\\x = 11 \times 12/11 = 12[/tex]

[tex]9. \frac{8}{10} t = 80\\\\t = 80 \times 10/8 = 100[/tex]

[tex]10. \frac{p}{3} = 9 \\\\p = 9 \times 3 = 27[/tex]

[tex]11. \frac{n}{5} = 30\\\\n = 30 \times 5 = 150[/tex]

[tex]12. \frac{6a}{7} = 36 \\\\a = 36 \times 7/6 = 42[/tex]

[tex]13. \frac{1}{2} t + 3 = 28\\\\t = (28 - 3)2 = 50[/tex]

[tex]14. \frac{1}{6} r = 12\\\\r = 12\times 6 = 72[/tex]

[tex]15. \frac{11}{12} b = 32\\ \\b = 32 \times 11/12 = 29.33[/tex]

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Answer:

  78

Step-by-step explanation:

The number of correct problems is found by multiplying the percentage that were correct by the total number of problems.

__

  number correct = fraction correct × number of problems

  number correct = 0.39 × 200 = 78

Serenity answered 78 problems correctly.

_____

Additional comment

The symbol % is fully equivalent to /100. That is 39% = 39/100 = 0.39 (pronounced "thirty-nine hundredths"). Using a percent symbol is just another way to write a fraction.

Answer:

i think the answer is 25q - 5 / 4

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find how many terms are in [tex]\pmb{10y^2-3y+8}[/tex].

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

So let's compute the number of terms in this expression.

The first term is [tex]\pmb{10y^2}[/tex].

Is anything added or subtracted from 10y²?

Sure! [tex]\pmb{-3y}[/tex] is subtracted from 10y².

Also, 8 is added to -3y.

Thus, this expression has 3 terms.

Hope it helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

The equivalent expression of 14r^4y^6/7r^8y^2 is 2y^4/r^4

The expression is given as:

14r^4y^6/7r^8y^2

Start by dividing 14 by 7

2r^4y^6/r^8y^2

Next divide y^6 by y^2

2r^4y^4/r^8

Lastly divide r^4 by r^8

2y^4/r^4

Hence, the equivalent expression of 14r^4y^6/7r^8y^2 is 2y^4/r^4

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His average monthly expenses are: $750

The given parameters are:

The average monthly expenses are calculated using:

Average = Total expenses/Number of months

So, we have:

Average = (700 + 700 + 800 + 800)/4

Evaluate

Average = 750

Hence, his average monthly expenses are: $750

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Answer:

Its a for me

Step-by-step explanation:

trust me fuys

Upon searching for your question, I believe there are 8 [tex]\frac{1}{4}[/tex] cups, and not 814 cups.

Answer: 6 [tex]\frac{3}{4}[/tex] cups of water

Step-by-step explanation:

    First, we will turn 12 ounces into units of cups.

         12 / 8 = 1.5 cups

    Now, we will subtract the start of the month from the end of the month.

         8.25 cups - 1.5 cups = 6.75 cups

   Lastly, we will turn it into a mixed number.

         .75 = [tex]\frac{3}{4}[/tex]

         6 [tex]\frac{3}{4}[/tex] cups

     6 [tex]\frac{3}{4}[/tex] cups of water were added to the barrel during the month.

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Answer:

Sorry po Hindi ko po alm :(

Answer:

V = 1607.7 in^3

V = 0.94 ft^3

Step-by-step explanation:

To find the volume of a traffic cone, use the formula for the volume of a cone: (1/3)*π*h*r^2

h = height

r = radius of cone

Step 1: determine variables and units

2 feet = 24 inches

diameter = 2 * radius

radius = (1/2) * diameter = (1/2)*16 in = 8 inches

Step 2: determine volume

V = (1/3)*π*h*r^2

V = (1/3)*3.14*24*(8)^2

V = 1607.7 in^3

Optional step 3: determine volume in ft^3

h = 2 ft

r = 0.67 ft

V = (1/3)*π*h*r^2 = (1/3)*3.14*2*(0.67)^2

V = 0.94 ft^3

Answer:

1-250 i think

Answer: B

Step-by-step explanation:

trust me bro

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The time for which the person must leave the money in the bank until it reaches $2500 is 1.2.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,

[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]

where A is the final amount

P is the principal amount

r is the rate of interest

n is the number of times interest is charged in a year

t is the number of years

The principal amount is 1000 dollars, while the rate of interest is 6.75% which is compounded monthly. Therefore, the time it will need for the account to reach $2500 is,

2500 = 1000[1+(0.0675/12)¹²ˣⁿ

2.5 = (1.0675)¹²ⁿ

log(2.5)\ log(1.0675) = 12n

14.0278 = 12n

n = 1.1689 ≈ 1.2

Hence, the time for which the person must leave the money in the bank until it reaches $2500 is 1.2.

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Answer: 13.6 years

Step-by-step explanation: Dealta Math Answer

The value of x is 7 and the measure of ∠1 is 99

The given parameters are:

The sum of angles in a triangle is 180.

So, we have:

5x + 19 + 8x - 11 + 11x + 4 = 180

Evaluate the like terms

24x = 168

Divide both sides by 24

x = 7

Hence, the value of x is 7

The angles on a straight line add up to 180.

This means that:

∠1 + ∠QNM = 180

Subtract ∠QNM from both sides

∠1 = 180 - ∠QNM

Substitute ∠QNM = 11x + 4

∠1 = 180 - 11x - 4

Substitute x = 7

∠1 = 180 - 11 * 7- 4

Evaluate

∠1 = 99

Hence, the measure of ∠1 is 99

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The time taken for the candle to burn down to a height of 1.3 inches is 4.5 hours

A linear function is what can be written in the form of

y =mx+c

The rate at which the candle is burning is 0.6 inches/ hour

The initial height is 4 inches at t=0

The straight line equation can be written for this as

y =mx +c

as m = -0.6

at x = 0 , y = 4 therefore c =4

y = -0.6x +4

The time at which y = 1.3 inches is

1.3 = -0.6x +4

-2.7 = -0.6 x

x =4.5

4.5 hours is the time taken for the candle to burn down to a height of 1.3 inches.

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Answer:

a = 63

b = 117

c = 63

Step-by-step explanation:

The sum of interior angles in a triangle is = 180

so the measure of a:

85 + 32 + a = 180 add like terms

117 + a = 180 subtract 117 from both sides

a = 63

a and be are supplementary angles so their sum is equal to 180

180 - 63 = 117 is the b's value

since a and c are on a pair of parallel lines, their value must be equal therefore the value of c is also 63

a) A × B is the Cartesian product of A and B, given by the set

A × B = {(a, b) | a ∈ A and b ∈ B}

Then for A = {4, 6, 8} and {4, 5, 6}, we have the product

A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}

b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...

Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is

A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}

and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set

Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}

By assuming that the motion of the plastic disc thrown by Mary is a projectile motion, the missing values are 4 and 3 respectively.

Since we're assuming that the motion of the plastic disc thrown by Mary is a projectile motion, it simply means that the motion can be represented by a quadratic function (parabolic).

For a projectile motion, the height of the disc at the time when it's at the top would be the same (equal). Thus, we can logically deduce that:

Height at time (t = 1 seconds) = Height at time (t = 5 seconds)

4 = A.

Similarly, Height at time (t = 0 seconds) = Height at time (t = 6 seconds)

3 = B.

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Answer:

a. median is 8

b. first quartile is 7

c. third quartile is 9.5

d. below

e. below

Step-by-step explanation:

7, 10, 10, 6, 7, 8, 8, 7, 9.

Place number in order least to greatest

6, 7, 7, 7, 8, 8, 9, 10, 10

a. What is the median?

The median is the middle number in a data set

number of terms in data set (n) + 1 / 2 =

9 + 1 / 2 = 10 / 2

6, 7, 7, 7, 8, 8, 9, 10, 10

The median is 8

b. What is the first quartile?

Q1 is the central point between the smallest score and the median

6, 7, 7, 7

since there is even number of data points you find the average,

7 + 7 / 2 = 14 / 2 = 7

c. What is the third quartile?

Q3 is the central point between the median and the largest score

8, 9, 10, 10

since there is even number of data points you find the average,

9 + 10 / 2 = 19 / 2 = 9.5

d. Draw a box plot of the data.

below

e. Write two conclusions about the data shown in the box plot.

There are no outliers with a minimum of 6 and a maximum of 10. The Interquartile Range is 2.5 (9.5 - 7)

Complete the square:

x² - 4x + 6 = 0

x² - 4x = -6

x² - 4x + 4 = -6 + 4

(x - 2)² = -2

But the left side is positive for any real number x, so there are no real solutions.

If you're solving over the complex numbers, we can go on to say

x - 2 = ± √(-2)

x - 2 = ± 2i

x = 2 ± 2i

where i = √(-1).

The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The question is: Consider the function f(x) = (-2/3)x - 24  Which conclusions can be drawn about f⁻¹(x) Select two options:

f⁻¹(x) has a slope of -2/3

f⁻¹(x) has a restricted domain.

f⁻¹(x) has a y-intercept of (0, –36).

f⁻¹(x) has an x-intercept of (–36, 0).

f⁻¹(x) has a range of all real numbers.

f(x) = (-2/3)x - 24

To find the inverse of a function:

interchange the x and y

x = (-2/3)y - 24

y = (-3/2)(x + 24)

y = (-3/2)x - 36

The slope of a function f⁻¹(x) is -3/2

From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.

Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.

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Answer:

D and  E

Step-by-step explanation:

did the test

Answer:

  0.513671875 = 263/512 inches

  easier to use: depends on the measurement tool

Step-by-step explanation:

The model dimension is found by multiplying the actual dimension by the scale factor.

__

  model frame dimension = actual frame dimension × 1/64

  = (32.875 inches)/64 = 0.513671875 inches

In fractional form, this is ...

  (32 7/8) / 64 = (263/8) / 64 = 263/512 . . . inches

__

It is unlikely that a casual hobbyist will have access to tools that measure with a resolution finer than 0.0001 inches. More common would be a measurement resolution of 0.001 inches. Using such tools, the rounded decimal value 0.5137 or 0.514 inches would be more useful than the fractional measurement.

It is possible that an optical measuring device could be available that would present its result as a fraction of an inch. If such a tool were used, the fractional measurement value would provide an appropriate point of comparison.

In short, the measurement easiest to work with depends on the tool being used to make the measurement.

Answer:

n² blocks are needed to build a staircase with n steps.

Step-by-step explanation:

Answer:

[tex]\frac{1}{24}[/tex]

Step-by-step explanation:

(1/3)/(8/1)

cross multiply

(1*1=1)/(3*8=24)

1/24

Answer:



= 1/24

One third divided by eight is 1/24.





Step-by-step explanation:



first we make an equation then simplfy it further

⇒1/3 ÷ 8

convert the division sign into multiplication by using the mutiplicative inverse of 8

⇒1/3 × 1/8

multiply the numerators together and denominators together

⇒1/24 ...answer...

hope that helps...

Answer: 0.5 or - 0.834

Step-by-step explanation: Here is the explanation!

The graph of the two given system of inequalities y > 2x - 5

y < -3x is; Attached below

We are given two inequalities;

y > 2x - 5

y < -3x

The graph that represents the 2 inequalities has been attached and from the graph, we see that;

The solution of the system of inequalities is the shaded pink area between the two dotted lines.

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Answer:

In the right triangle, the side a=[tex]4[/tex] and the hypotenuse c=[tex]7[/tex].

To find: the value of x

We have,

[tex]a=6[/tex] and [tex]c=7[/tex]

Now,by the pythagorean theorem,

[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]

Substitute the values,

[tex] {6}^{2} + {x}^{2} = {7}^{2} [/tex]

[tex]36 + {x}^{2} = 49[/tex]

Subtract 36 from each sides,

[tex] {x}^{2} = 13[/tex]

Take square root from each sides,

[tex]x = \sqrt{13} [/tex]

Hence, the value of x is [tex]\sqrt{13}[/tex].

Answer:

r = - 18/5

I hope this helps! ^^

( This problem has 13 steps, so it would take a lot of time to type them in ^^)

Answer:

Hi,

Step-by-step explanation:

sin(a-b)=sin(a) cos(b)+ cos(a) sin(b)

a=45° and b=30°

[tex]sin(45^o-30^o)=sin(45^o)*cos(30^o)+cos(45^o)*sin(30^o)\\\\=\dfrac{\sqrt{2}}{2}* \dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{2}*\dfrac{1}{2}\\\\\\\boxed{sin(15^o)=\dfrac{\sqrt{2}}{4}*(1+\sqrt{3} )}\\[/tex]