I need help on khan academy write and expression for "the quotient of 9 and c."​

The 12th term of the geometric  sequence is -341796875.

The common ratio (r) is:

\(\frac{a_{1} }{a_{2} } =-\frac{35}{7} =-5\)

\(\frac{a_{3} }{a_{2} } =\frac{175}{-35} =-5\)

(r)=-5

The sum is :

\(S_{n}\)=a·{\(\frac{1-r^{n} }{1-r^{} }\)}

\(S_{3}\)= 147

So. The general form is:

\(a_{n}\)=7·-\(5^{n-1}\)

Now, The nth term is:

\(a_{1}\)=7

\(a_{2}\) = \(a_{1}\)·\(r^{n-1}\) = 7· \(-5^{2-1}\) = 7 · \(-5^{1}\) = 7 · -5 = -35

\(a_{3}\) = \(a_{1}\)·\(r^{n-1}\) = 7· \(-5^{3-1}\) = 7 · \(-5^{2}\) = 7 · 25 = 175

\(a_{4}\) = \(a_{1}\)·\(r^{n-1}\) = 7· \(-5^{4-1}\) = 7 · \(-5^{3}\) = 7 · -125 = -875

\(a_{5}\) = 4375

\(a_{6}\) = -21875

.......  so, \(a_{12}\) = - 341796875

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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In data analytics, a population refers to all possible data values in a certain dataset

Data analysis is a systematic computer-aided analysis of data or statistics. [1] It is used to discover, interpret, and convey meaningful patterns in the data. It also includes applying data patterns for effective decision-making.

It may be useful in areas where there is a lot of recorded information. The analysis relies on the simultaneous application of statistics, computer programming, and operations research to quantify performance.

Organizations can apply analytics to business data to describe, predict, and improve business performance. Areas within the analysis include descriptive analysis, diagnostic analysis, predictive analysis, prescriptive analysis, and cognitive analysis in particular. [2] Analysis can be applied in various fields such as marketing, management, finance, online systems, information security, and software services.

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Answer:

A=28

B=18

C=18

D=28

E=28

F=18

G=10

H=5

Step-by-step explanation:

The value of [r] will be 5 units.

What is equation modelling? What is a mathematical equation and expression?

According to the given question:

Given is a line segment as shown in the image.

We can write the equation as -

(4r - 3) + (r + 7) = 29

4r + r - 3 + 7 = 29

5r + 4 = 29

5r = 25

r = 5

Therefore, the value of [r] will be 5 units.

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Answer:

B

Step-by-step explanation:

1. The piecewise-defined function is as follows:

For 0 ≤ x ≤ 50: F(x) = 2x + 20

For 50 ≤ x ≤ 100: F(x) = x + 10

For x > 100: F(x) = 0 - 5x

2. Evaluating the function for the given values:

F(101) = -505

F(75) = 85

F(10) = 40

1. The piecewise-defined function is as follows:

For 0 ≤ x ≤ 50:

F(x) = 2x + 20

For 50 ≤ x ≤ 100:

F(x) = x + 10

For x > 100:

F(x) = 0 - 5x

2. Evaluating the function for different values:

a) F(101):

Since 101 is greater than 100, we use the third equation:

F(101) = 0 - 5(101) = -505

b) F(75):

Since 75 falls within the range 50 ≤ x ≤ 100, we use the second equation:

F(75) = 75 + 10 = 85

c) F(10):

Since 10 is less than 50, we use the first equation:

F(10) = 2(10) + 20 = 40

Therefore, F(101) = -505, F(75) = 85, and F(10) = 40.

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The simplified form of the expression -10g - 4h² +15g -8h² -4 is -12h² +5g -4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is -10g - 4h² +15g -8h² -4. The expression will be simplified as below,

E = -10g - 4h² +15g -8h² -4

E = - 4h²-8h² -10g +15g - 4

E = -12h² + 5g - 4

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Answer:

-12h² +5g -4.

Step-by-step explanation

i just did it

w = l - 3

w = 9 - 3

w = 6

//

l = 9

w = 6

//

p = 2(9) + 2(6)

p = 30

x = 4 and y = 9 and z = 7

x(y + z - 32) = 4 · (9 + 7 - 32) =

= 4 · (16 - 32) = 4 · (-16) = -64

Answer:

x=20

Step-by-step explanation:

3x-1+31+90=180

Combine like terms

3x+120=180

Subtract by 120 on both sides

3x=60

x=20

Answer:

59 degrees

Step-by-step explanation:

so first things first you have the tringle it has a right angle meaning that this triangle will equal 90 degrees so here is what our equation would look like:

90=31+(3x-1)

So in order to solve this equation you must subtract add and divide.

First Rule in doing these equations: what you do to one side of the equal sign you do to the other side.

so we subtract 31 from 90 to equal 59 so the equation looks like this:

59=(3x -1)

you then add a one to the negative one and the 59 to get 60 making the equation look like this

60= 3x

we then divide 60 by 3 to get 20

so 20= x

But this is not our answer this is simply the solvation for x in (3x - 1)

so the equation now looks like this (3(20) - 1) and this equals 59 degrees

now to check our work!

31 + 59 = 90 or 90- 31 = 59

Answer:

s (score) = 89

Step-by-step explanation:

We find the average (or mean) by dividing the sum of the data points by the total number of points (4 in this problem)

With s representing the final score needs to get an average score of 70, we have (59 + 64 + 68 + s) / 4 = 70

191 + s = 280

s = 89

Answer:

\( - 24\)

Step-by-step explanation:

\(( - 4)( - 2)( - 3) \\ ( + 8)( - 3) \\ = - 24\)

I hope I helped you^_^

Answer:

15 < X > 31

Step-by-step explanation:

From triangle theorem,a triangle with sides X, Y, Z, the sum of any 2 sides must be greater than the third side i.e;

1. X + Y > Z

2. Y + Z > X

3. X + Z > Y

We are given 2 sides say Y = 8 and Z = 23.

Thus,Range of values is expressed as;

Z - Y < X > Z + Y

23 - 8 < X > 23 + 8

15 < X > 31

By taking quotients between the prices and the numbers of boxes, we can see that the pack of 16 boxes is the better buy.

To identify which one is the better buy, we need to see which pack gives a smaller price per juice box.

To get that, we need to take the quotient between the price and the number of boxes for each case.

The pack of 14 boxes costs $11.34, then the price per box is:

P = $11.34/14  =$0.81

For the pack of 16 boxes the price is $12.64, in this case we will have:

P' = $12.64/16 = $0.79

We can see that the second option is cheaper, so that is the better buy.

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The number of distinct ways in which the digits of the number 7,511,111 can be arranged is of:

42.

The total number of arrangements of n elements is given by the factorial of n, as follows:

A(n) = n!

When a few of the elements repeat, the number of arrangements with repetition is given by the equation presented as follows, also involving factorials.

\(A_n^{n_1, n_2, \cdots n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}\)

In which \(n_1, n_2, \cdots n_n\) is the number of times that each element repeats.

For the number 7,511,111, we have that:

Hence the number of distinct arrangements of the number 7,511,111 is given as follows:

7!/5! = 7 x 6 = 42 distinct arrangements.

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Answer:

7

Step-by-step explanation:

Plug it in.....

h(0) = 2.5 * 0 + 7 = 7

Markov analysis is used for analyzing the performance and reliability of complex systems, while replacement charts are used for optimizing the replacement timing of deteriorating assets.

Markov Analysis:

Markov analysis is a probabilistic model that is used to predict the future state of a system based on its current state.

It involves the use of Markov chains to model the transitions between different states of a system over time.

Markov analysis is commonly used when the equipment or system under consideration can be in multiple states with varying probabilities of transition.

It is suitable for analyzing systems that have a continuous or non-repairable nature, such as complex machinery, infrastructure, or systems with multiple failure modes.

The primary objective of Markov analysis is to assess the reliability, availability, and performance of the system and make decisions regarding maintenance, replacement, or repair strategies.

Replacement Chart:

A replacement chart, also known as a replacement model or replacement policy, is a decision-making tool used to determine the optimal time to replace a piece of equipment or system.

It involves comparing the costs associated with continuing to use the existing equipment (including maintenance and repair costs) with the costs of replacing it.

The replacement chart provides a visual representation of the costs over time and helps identify the point at which replacement becomes more cost-effective than continued use.

Replacement charts are commonly used for assets that are subject to wear and tear, aging, or deterioration over time, such as vehicles, machinery, or equipment with a defined lifespan.

The primary objective of a replacement chart is to minimize costs associated with the asset's life cycle by optimizing the replacement timing.

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Answer:

so you wold do I=t×r×A ok so I=6,500 t=5 r=4.3 and u have to find A so you wolf multiple 5×4.3=21.5 and than you wold divide 6500÷21.5=302.3255813953488×21.5= 6500 so A=302.3255813953488

(a) The equation ||2 - r/7|| = 3 can be split into two separate equations without using absolute value::

1. 2 - r/7 = 3

2. 2 - r/7 = -3

(b) Solving these equations gives us the following solutions for r: -7, 35.

Let us discuss each section separately:

(a) The equation ||2 - r/7|| = 3 can be split into two separate equations as follows:

1. 2 - r/7 = 3

2. 2 - r/7 = -3

(b) Solving the first equation:

Subtracting 2 from both sides gives -r/7 = 1. Multiplying both sides by -7 yields r = -7.

Solving the second equation:

Subtracting 2 from both sides gives -r/7 = -5. Multiplying both sides by -7 gives r = 35.

Thus, the solutions to the equations are r = -7, 35.

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Answer:

8x + 36

Step-by-step explanation:

Answer:

8 and 36

Step-by-step explanation:

Answer: 3/10

Step-by-step explanation:

Since the rest of the trees are pears trees and plum trees in the ratio of 7:5 and there are 175 plum trees, the number of pear trees will be:

= 175 ÷ 5/7

= 175 × 7/5

= 245

Plum trees = 175

Pear trees = 245

Apple trees = 600 - (175 + 245)

= 600 - 420

= 180

Fraction of apple trees = Number of apple trees / Total number of trees

= 180/600

= 3/10

Summer would need 4 classes for the costs of both plans to be the same

Equation is an expression used to show the relationship between two or more variables and numbers.

Let y represent the total pay for x membership classes.

At gym A:

y = 12x

For gym B:

y = 6x + 24

Hence for both plans to be the same:

12x = 6x + 24

x = 4

Summer would need 4 classes for the costs of both plans to be the same

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The equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

The equation of the tangent to the curve y = f(x), passing through the point (a, b) can be written as -

(y - b) = (dy/dx) (x - a)

Given is the curve y = f(x) = x⁴ + 6x² − x.

The given curve is -

y = x⁴ + 6x² − x

f'(x) = dy/dx = d(x⁴ + 6x² − x)/dx

f'(x) = dy/dx = 4x³ + 12x + 1

Now -

f'(x){1, 6} = (dy/dx){1, 6} = 4 x 1 x 1 x 1 + 12 x 1 + 1

f'(x){1, 6} = 17

We can write the equation as -

(y - 6) = 17(x - 1)

Therefore, the equation of the line tangent to the curve is -

(y - 6) = 17(x - 1).

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To calculate the gain on the sale of the office furniture, we need to determine the asset's book value and compare it to the sale price.

First, let's calculate the accumulated depreciation on the furniture. The furniture was purchased on January 1, 2014, and the straight-line depreciation method is used over 10 years with a salvage value of $80,200.

Depreciation per year = (Cost - Salvage Value) / Useful Life

Depreciation per year = ($746,800 - $80,200) / 10 years

Depreciation per year = $66,160

Next, we need to calculate the accumulated depreciation for the period from January 1, 2014, to May 1, 2021 (the date of the sale). This is approximately 7.33 years.

Accumulated Depreciation = Depreciation per year × Years

Accumulated Depreciation = $66,160 × 7.33 years

Accumulated Depreciation = $484,444.80

Now, we can calculate the book value of the furniture:

Book Value = Cost - Accumulated Depreciation

Book Value = $746,800 - $484,444.80

Book Value = $262,355.20

Finally, we can calculate the gain on the sale:

Gain on Sale = Sale Price - Book Value

Gain on Sale = $300,000 - $262,355.20

Gain on Sale = $37,644.80

Therefore, the gain that should be recognized on the sale of the office furniture is approximately $37,644.80.

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The gain that should be recognized on the sale of the office furniture is $84,080.

The gain is calculated by subtracting the equipment's book value from the sale price. This gain will be reported on the company's income statement. Here is how to calculate the gain:First, find the equipment's book value using the straight-line method of depreciation.

Straight-line depreciation is calculated by taking the difference between the equipment's original cost and its salvage value, and then dividing it by the number of years the equipment is used. The annual depreciation expense is then multiplied by the number of years the equipment is used to find the equipment's book value at the end of its useful life.

For this question, the book value of the equipment at the time of sale is:Cost of equipment: $746,800Salvage value: $80,200Depreciable cost: $746,800 - $80,200 = $666,600Annual depreciation: $666,600 ÷ 10 years = $66,660Book value at the end of 2020: $666,600 - ($66,660 x 7) = $156,420

Next, subtract the equipment's book value from the sale price to find the gain:Sale price: $300,000Book value: $156,420Gain: $143,580Finally, round the gain to the nearest dollar:$143,580 ≈ $143,580.00So the gain that should be recognized on the sale of the office furniture is $84,080.

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Answer:

24 pounds of garlic

Step-by-step explanation:

if she spends 3$ per pound, you divide 72 by 3. the answer to that is 24, so if she spends 72 dollars on only garlic, she can buy 24 pounds.

Jennifer can buy 24 pounds of garlic

we see here, that if she spends 3$ per pound, you divide 72 by 3.

The answer would be 24, so if she spends 72 dollars on only garlic,

she can buy 24 pounds.

1: any of various units of mass and weight specifically: a unit now in general use among English-speaking peoples equal to 16 avoirdupois ounces or 7000 grains or 0.4536 kilogram — see Weights and Measures Table

2: the basic monetary unit of the United Kingdom.

In maths, a division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each

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