given the geometric sequence 1/3,2/9,4/27,8/81,... determine the formula for the nth term and find a10​

Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Pat ran more miles by the end of the week with a total of 8.25 miles. Pat ran 0.5 miles more than Toby.

Algebra is a branch of mathematics that deals with mathematical expressions and equations, using letters and symbols to represent numbers and quantities. It involves the manipulation and solving of equations and inequalities involving variables.

In algebra, variables are represented by letters, usually x, y, or z, and they can represent any number or quantity. Algebraic expressions are formed by combining variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division.

To determine who ran more miles by the end of the week, we need to calculate the total number of miles each person ran. We can do this by adding up the miles from each day:

Pat: 2.75 + 3 + 2.5 = 8.25 miles

Toby: 2 + 2.25 + 3.5 = 7.75 miles

Therefore, Pat ran more miles by the end of the week with a total of 8.25 miles. Pat ran 0.5 miles more than Toby.

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The complete question is:

After alcohol is fully absorbed into the body, it is metabolized with a half-life of about 1.5 hours. This means that every 1.5 hours, the concentration of alcohol in your blood will decrease by half.

In this scenario, you have had three alcoholic drinks and an hour later, at midnight, your blood alcohol concentration (BAC) is 0.4 mg/ml. To determine how long it will take for your BAC to reach zero, we need to calculate the number of half-lives it will take.

Given that the half-life of alcohol metabolism is 1.5 hours, we can divide the time elapsed since your last drink (1 hour) by the half-life to determine the number of half-lives.

1 hour / 1.5 hours per half-life = 0.67 half-lives

Since you have consumed three drinks, your initial BAC would have been much higher. Assuming that your BAC after three drinks was 0.4 mg/ml at the time of consumption, we can estimate that your BAC would have been:

Initial BAC = 0.4 mg/ml * (2^0.67) = 0.4 mg/ml * 1.467 = 0.587 mg/ml

Now, to estimate how long it will take for your BAC to reach zero, we need to calculate the number of half-lives it will take to decrease from 0.587 mg/ml to zero.

0.587 mg/ml / 0.4 mg/ml = 1.47 half-lives

So, it will take approximately 1.47 * 1.5 hours = 2.2 hours for your BAC to reach zero.

Please note that these calculations are estimations and can vary based on individual factors such as metabolism and other variables. It is important to prioritize safety and avoid driving or operating machinery until you are certain that your BAC is at zero.

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Answer:

Step-by-step explanation:

Answer 3700

Answer:

Step-by-step explanation:

si...  yono  em usho de cmopu preo sloo estoy usand una jjssjsjsj jsjsj  c

Answer:A) no solutions

Step-by-step explanation:

1) set both problems equal to each other

2) subtract four from each side

3) subtract 2x from each side

4) 10 does not equal 0

Answer:

No solution

Step-by-step explanation:

As soon as you minus the equations from each other, the y's and x's cancel out therefore there is no solution

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

Answer:

Step-by-step explanation:

you do -8 x 14, which will give you -112, and then divide -112 by -7. The negatives will cancel out and you can do 112 divided by 7, which is 16.

so, x = 16

Answer:14=7x/-8

   14(-8)=7x

   -112/7 =x

    -16=x

Step-by-step explanation:

Answer:

Stanley needs 31 feet and 2 inches of fencing.

Step-by-step explanation:

In order to answer this problem, you need to find the perimeter of the dog run.

Since: \(P=2(l+w)\)

and \(l=149\) inches & \(w=56\) inches

Plug in what we know :

\(P=2(149+56)\)

and solve:

\(P=410\) inches

The dog run has a perimeter of 410 inches.

However, now we need to subtract 36 inches since the gate doesn't need fencing.

\(410-36=374\) inches.

The dog run needs 374 inches of fencing.

In order to find out how many feet of fencing that is, divide it by 12.

\(\frac{374}{12}\) = 31.16666667 OR \(31\frac{2}{12}\), meaning 31 feet and 2 inches.

Answer:

31 feet and 2 inches of fencing :))<3

Step-by-step explanation:

Answer:

-2/5

Step-by-step explanation:

Answer:

Part-to-part ratios provide the relationship between two distinct groups. For example, the ratio of men to women is 3 to 5, or the solution contains 3 parts water for every 2 parts alcohol.

Part-to-whole ratios provide the relationship between a particular group and the whole populations (including the particular group). For example, 3/5 of the students in the class are girls, or the mixture is 40% rye grass (40% is equivalent to saying 40 of every 100 parts).

Answer:

Area: T = 18

a.  The triangle area using Heron's formula: T=  sqrt(s(s−a)(s−b)(s−c) )

​b. 2\(\sqrt{10}\)  

c. h = 5.69

d. T = 18

Step-by-step explanation:

a. T=  sqrt(s(s−a)(s−b)(s−c) )

T=sqrt( 11.16(11.16−10)(11.16−6)(11.16−6.32) )

​T=  sqrt(324 )

​T =18

b. We compute the base from coordinates using the Pythagorean theorem

c=  sqrt( ((−2−4)^2)+ ((1−3) ^2) )

c= sqrt(40) = 2sqrt(10)

c. Calculate the heights of the triangle from its area

​  

The vector equation is: x1 * (5, 7) + x2 * (-1, 9) = (6, )
- The matrix equation is: | 5  -1 | | x1 | = |  6  | and | 7   9 | | x2 | = |      |

To write the given system first as a vector equation and then as a matrix equation, follow these steps:

1. Write the given system of equations:
5x1 - x2 = 6
7x1 + 9x2 =

2. Rewrite the system as a vector equation:
x1 * (5, 7) + x2 * (-1, 9) = (6, )

3. Write the matrix equation:
A * X = B

where A is the matrix of coefficients, X is the matrix of variables, and B is the matrix of constants.

4. Create matrix A using the coefficients of x1 and x2:
A = | 5  -1 |
   | 7   9 |

5. Create matrix X using the variables x1 and x2:
X = | x1 |
   | x2 |

6. Create matrix B using the constants of the system:
B = |  6  |
   |      |

So the matrix equation is:
| 5  -1 | | x1 | = |  6  |
| 7   9 | | x2 | = |      |

To summarize:

- The vector equation is: x1 * (5, 7) + x2 * (-1, 9) = (6, )
- The matrix equation is: | 5  -1 | | x1 | = |  6  | and | 7   9 | | x2 | = |      |

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Inherent limitations are factors that are beyond the control of an organization and that may limit the effectiveness of its internal control system. The correct option is, "human judgment in the decision-making process".

While all of the options listed could be potential limitations to an entity's internal control, the one that is most likely to be considered inherent is human judgment in the decision-making process. This is because humans are inherently fallible and subject to biases, errors, and mistakes.

Even with the best policies, procedures, and controls in place, there is always the risk that human judgment will lead to errors or fraud. Therefore, organizations must implement additional controls, such as independent oversight, to mitigate this inherent limitation.

The other options listed may also be limitations to internal control, but they are not inherent limitations. For example, the complexity of the information processing system can be managed through proper design, testing, and monitoring of the system. The ineffectiveness of the board of directors can be addressed through improvements in governance practices, training, and accountability.

The lack of management incentives to improve the control environment can be addressed through changes in compensation and performance measurement systems.

However, these factors are not inherent limitations because they can be addressed through changes in the organization's practices or structure.

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Answer:

Step-by-step explanation:

Answer:

Yes please upload the pic

Step-by-step explanation:

:)

Answer:

(g o f)(8)

Step-by-step explanation:

First we find f(8).

f(8) = 8 - 1 or 7.

We now find g(f(8)), which means g(7).

g(7) = 7^3 or 343

Answer:

y = 2x - 4

Step-by-step explanation:

Given:

x1 = 5

y1 = 6

slope (m) = 2

Solution:

y - y1 = m ( x - x1 )

y - 6 = 2 ( x - 5 )

y - 6 = 2x - 10

y = 2x - 10 + 6

y = 2x - 4

The statement that shows a discrepancy between the check register and bank statement is: C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.

The check register shows a balance of $500, while the bank statement shows a balance of $510.

In the case of Gavin, where the balance in his check register is $500 and the balance in his bank statement is $510, there is a $10 discrepancy between the two.

A possible explanation for this discrepancy could be outstanding checks or deposits that have not yet cleared or been recorded in either the check register or the bank statement.

For example, Gavin might have written a check for $20 that has not been cashed or processed by the bank yet. Therefore, the check register still reflects the $20 in his balance, while the bank statement does not show the deduction. Similarly, Gavin may have made a deposit of $10 that has not yet been credited to his account in the bank statement.

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The two percentages do not agree. Hence, option D is correct.

a) The mean time was 103.59 seconds, with a standard deviation of 5.16 seconds. If the Normal model is appropriate, the percentage of times that will be less than 98.43 seconds can be calculated as follows:

z = (x - μ) / σz = (98.43 - 103.59) / 5.16z = -1.00Using z-score table, we can determine that the percentage of times that will be less than 98.43 seconds is approximately 15%.

Therefore, the percentage of times that will be less than 98.43 seconds is 15%.

(Round to the nearest integer as needed)Hence, option A is correct.b) The actual percentage of times less than 98.43 seconds can be calculated by finding the number of competitors that finished with a time less than 98.43 seconds and dividing that number by the total number of competitors.

98.06, 98.09, 98.46, 98.47, 98.96, 98, 99, 99.12, 99.35, 99.57, 99.98, 100.08, 100.11, 100.28, 100.64, 101.32, 101.06, 101.25, 101.34, 101.39, 102.48,

101.99, 103.01, 103.87, 104.11, 103.64, 104.15, 104.27, 104.37, 104.33, 104.52, 105.47, 105.48, 105.69, 105.61, 113.02, 105.73, 109.65, 106.92, 116.11, 117.43, 117.59, 99.09, 100.67, 103.12, 105.02, 114.55, 99.11, 100.77, 103.18, 105.39, 115.97

There are no competitors who finished with a time less than 98.43 seconds. Therefore, the actual percentage of times less than 98.43 seconds is 0%. (Round to one decimal place as needed)Thus, option D is correct.c) The two percentages do agree.

This is because the Normal probability plot shows that the Normal model is not appropriate.

Therefore, the actual percentage of times less than 98.43 seconds is 0%, which is different from the percentage that was calculated using the Normal model. Since the Normal model is not appropriate, the actual percentage of times is more accurate.

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The percentage of the total cost for the finance charges is 36.47%

Computation:

Given,

\(P\) Principal amount= $35,125

\(r\) Interest rate =7.44%

\(t\) Compounding period = quarterly 4

\(n\) Time period =10 years

The formula of the annuity will be used to determine the total cost:

\(\begin{aligned}A&=P\times\dfrac{(1+\frac{r}{n})^{n-1}}{r\times(1+\frac{r}{n})^n}\\&=\$35,125\times\dfrac{(1+\frac{0.0744}{10})^{10-1}}{0.0744\times(1+\frac{0.0744}{10})^{10}}\\&=\$1,252.70\end{aligned}\)

\(\begin{aligned}\text{Total cost}&=A\times(n\times t)\\&=\$1,252.70\times(10\times 4)\\&=\$50,108\end{aligned}\)

Now, the percentage of finance charges will be determined as follows:

\(\begin{aligned}\text{\% of Finance Charges}&=\dfrac{\text{Total Cost+ Service Charges-Principal Amount}}{\text{Total Cost+ Service Charges}}\times100\\&=\dfrac{\$50,108+\$5,180.0-\$35,125}{\$50,108+\$5,180.70}\times100\\&=36.47\%\end{aligned}\)

Therefore, the percentage of finance charges is correct in option b. 36.47%.

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Answer:

C

Step-by-step explanation:

The profit calculations provided include information on marginal revenue (MR), market price, marginal cost (MC), total revenue, quantity, and total cost. The market price is stated as $30.00, while the marginal cost is slightly higher at $30.16. The total revenue is given as $1,950.00, and the quantity is listed as 65.

However, the total cost is not provided in the given information. To determine the profit, the total cost would need to be subtracted from the total revenue. Without the total cost, a definitive profit calculation cannot be made.

To calculate profit, the total cost needs to be deducted from the total revenue. Unfortunately, the total cost is not provided in the given information, so a precise profit calculation cannot be determined. Profit represents the financial gain obtained by subtracting the total cost of production from the total revenue generated. If the total cost is lower than the total revenue, a profit is generated, while if the total cost exceeds the total revenue, a loss is incurred. In this case, without knowledge of the total cost, it is not possible to determine the profit or loss incurred from the given information.

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The linear model that represents the cost of any number of candy bars can be written as: C = $1.90B + $0.95

To write the linear model that models the cost of any number of candy bars, we need to find the equation of a line that best fits the given data points. We'll use the variables B for the number of candy bars purchased and C for the total cost of the candy bars.

Looking at the given data, we can see that there is a linear relationship between the number of candy bars and the total cost. As the number of candy bars increases, the total cost also increases.

To find the equation of the line, we need to determine the slope and the y-intercept. We can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.

First, let's find the slope (m) using two points from the given data, for example, (3, $6.65) and (25, $48.45):

m = (C2 - C1) / (B2 - B1)

 = ($48.45 - $6.65) / (25 - 3)

 = $41.80 / 22

 ≈ $1.90

Now, let's find the y-intercept (b) using one of the data points, for example, (3, $6.65):

b = C - mB

 = $6.65 - ($1.90 * 3)

 = $6.65 - $5.70

 ≈ $0.95

Therefore, the linear model that represents the cost of any number of candy bars can be written as:

C = $1.90B + $0.95

This equation represents a linear relationship between the number of candy bars (B) and the total cost (C). For any given value of B, you can substitute it into the equation to find the corresponding estimated total cost of the candy bars.

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The ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x.

The correct option is A: (-2, 2).

To determine which ordered pairs satisfy both inequalities y < -x + 1 and y > x, we need to check each pair's coordinates in both inequalities.

Let's test each ordered pair:

A: (-2, 2)

For y < -x + 1: 2 < -(-2) + 1 → 2 < 3 (True)

For y > x: 2 > -2 → 2 > -2 (True)

B: (1, 1)

For y < -x + 1: 1 < -(1) + 1 → 1 < 0 (False)

For y > x: 1 > 1 → 1 > 1 (False)

C: (0, 0)

For y < -x + 1: 0 < -(0) + 1 → 0 < 1 (True)

For y > x: 0 > 0 → 0 > 0 (False)

D: (-1, -1)

For y < -x + 1: -1 < -(-1) + 1 → -1 < 2 (True)

For y > x: -1 > -1 → -1 > -1 (False)

From the above calculations, we can see that only the ordered pair (-2, 2) satisfies both inequalities y < -x + 1 and y > x. Therefore, the correct answer is option A: (-2, 2).

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The complete question:

Which ordered pairs make both inequalities y < -x + 1 and y > x true?

A: (2, 2)

B: (1, 1)

C: (0,0)

D: (-1, -1)

the particle's position at any time l is given by: x(t) = (21/2)t^2 - (17/2) y(t)  (7/2)t^3 - (5/2) z(t) = (1/2)t^2 - (1/2) w(t) = (1/4L)t^2 - (1/4L)

To find the particle's position at any time l, we can integrate its velocity vector with respect to time. Given that v(1) = (21, 21, 1, 2/4L), let's perform the integration.

(a) Position at any time l:

Integrating the velocity vector, we have:

∫(v(t)) dt = ∫((21t, 21t^2, t, (2/4L)t)) dt

To find the position, we integrate each component of the velocity vector separately:

∫(21t) dt = (21/2)t^2 + C1

∫(21t^2) dt = (7/2)t^3 + C2

∫(t) dt = (1/2)t^2 + C3

∫((2/4L)t) dt = (1/4L)t^2 + C4

Adding the constant terms, we get:

x(t) = (21/2)t^2 + C1

y(t) = (7/2)t^3 + C2

z(t) = (1/2)t^2 + C3

w(t) = (1/4L)t^2 + C4

Now, we need to determine the values of the constants C1, C2, C3, and C4. To do so, we'll use the initial conditions provided.

Given that the particle starts at the point (2, 1, 0) when t = 1, we substitute these values into the position equations:

x(1) = (21/2)(1)^2 + C1 = 2

y(1) = (7/2)(1)^3 + C2 = 1

z(1) = (1/2)(1)^2 + C3 = 0

w(1) = (1/4L)(1)^2 + C4 = 0

From these equations, we can solve for the constants C1, C2, C3, and C4.

C1 = 2 - (21/2) = -17/2

C2 = 1 - (7/2) = -5/2

C3 = 0 - (1/2) = -1/2

C4 = 0 - (1/4L) = -1/4L

Therefore, the particle's position at any time l is given by:

x(t) = (21/2)t^2 - (17/2)

y(t) = (7/2)t^3 - (5/2)

z(t) = (1/2)t^2 - (1/2)

w(t) = (1/4L)t^2 - (1/4L)

(b) To find the cosine of the angle between the velocity vector v(1) and the position vector at t = 1, we can calculate their dot product and divide it by the product of their magnitudes.

Let's calculate the cosine:

cosθ = (v(1) · r(1)) / (|v(1)| |r(1)|)

Substituting the values:

v(1) = (21, 21, 1, 2/4L)

r(1) = (2, 1, 0, 0)

|v(1)| = √((21)^2 + (21)^2 + (1)^2 + (2/4L)^2) = √(882 + 882 + 1 + (1/2L)^2) = √(1765 +

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Answer:

4 months

Step-by-step explanation:

Let

x = number of months

Double Mint Mobile = 100 + 30x

BT&T = 20 + 50x

After how many months will both cell phone plans cost the same?

Equate the cost of both phone plans

Double Mint Mobile = BT&T

100 + 30x = 20 + 50x

100 - 20 = 50x - 30x

80 = 20x

x = 80/20

x = 4 months

Number of months = 4 months

Answer:

The equation representing how old Monique son is \(\mathbf{a = 2 + \dfrac{8}{21}(q-34)}\)

Step-by-step explanation:

From the given information:

A linear function can be used to represent the constant growth rate of Monique Son.

i.e.

\(q(t) = \hat q \times t + q_o\)

where;

\(q_o\) = initial height of Monique's son

\(\hat q\) = growth rate (in)

t = time

So, the average boy grows approximately 2 5/8 inches in a year.

i.e.

\(\hat q = 2 \dfrac{5}{8} \ in/yr\)

\(\hat q = \dfrac{21}{8} \ in/yr\)

Then; from the equation \(q(t) = \hat q \times t + q_o\)

\(34 = \dfrac{21}{8} \times 0 + q_o\)

\(q_o = 34\ inches\)

The height of the son as a function of the age can now be expressed as:

\(q(t) = \dfrac{21}{8} \times t + 34\)

Then:

Making t the subject;

\(q - 34 = \dfrac{21}{8} \times t\)

\(t = \dfrac{8}{21}(q-34)\)

and the age of the son  i.e. ( a (in years)) is:

a = 2 + t

So;

\(\mathbf{a = 2 + \dfrac{8}{21}(q-34)}\)

SO;

if q (growth rate) = 50 inches tall

Then;

\(\mathbf{a = 2 + \dfrac{8}{21}(50-34)}\)

\(\mathbf{a = 2 + \dfrac{8}{21}(16)}\)

a = 2 + 6.095

a = 8.095 years

a ≅ 8 years

i.e.

Monique son will be 8 years at the time Monique is 50 inches tall.

Answer:

On sale at a deficit of -20% from the original price is saying that the item is at 80% of its original value.

Converting percentages using decimals is a very easy way to fine original values.

So:

$76.80 = 80% of the original value

convert the 80% into a decimal = 0.80

The maths:

$76.80 ÷ 0.8 = $96.00

$96.00 = the original value.

Answer: The original price is $96

Step-by-step explanation:

Since 76.8 is the discounted price after 20% was taken off, we know that 76.8 is 80% of the original price. My way is to set up a equivalent fractions relation thing (I don’t know what to call it), and for this problem it looks like this:

80/100 = 76.8/?
the numerator is the part, or discounted price, and the denominator is the whole, or original price.

Using equivalent fractions, we can find out that ? = 96.

The two linearly independent solutions are y₁(x) = x(1 + (5/3)x + a₂x² + a₃x³ + ...) and y₂(x) = √x(1 + (5/2)x + a₂x² + a₃x³ + ...).

To find two linearly independent solutions of the given differential equation 2x²y" - xy' + (-5x + 1)y = 0, we can use the method of Frobenius. Let's solve it step by step:

Step 1: Assume a power series solution:

y(x) = \(x^{r(1 + a_1x + a_2x^2 + a_3x^3 + ...)\)

Step 2: Calculate the derivatives of y(x):

y'(x) = \(rx^{(r-1)(1 + a_1x + a_2x^2 + a_3x^3 + ...)\) + \(x^{r(a_1 + 2a_2x + 3a_3x^2 + ...)\)

y''(x) = r(r-1)\(x^{(r-2)(1 + a_1x + a_2x^2 + a_3x^3 + ...)\) + r\(x^{(r-1)(a_1 + 2a_2x + 3a_3x^2 + ...)\)

Step 3: Substitute y(x), y'(x), and y''(x) into the differential equation:

2x²[r(r-1)\(x^{(r-2)(1 + a_1x + a_2x^2 + a_3x^3 + ...)\)] - x[r × \(x^{(r-1)(1 + a_1x + a_2x^2 + a_3x^3 + ...)\)] + (-5x + 1)[\(x^r\)(1 + a₁x + a₂x² + a₃x³ + ...)] = 0

Step 4: Simplify and collect terms with the same powers of x:

2r(r-1)(1 + a₁x + a₂x² + a₃x³ + ...) - r(1 + a₁x + a₂x² + a₃x³ + ...) + (-5x + 1)(1 + a₁x + a₂x² + a₃x³ + ...) = 0

Step 5: Equate coefficients of like powers of x to zero:

For the term without x:

2r(r-1) - r + 1 = 0

For the term with x:

2(r+1)a₁ - a₁ - 5 = 0

For the term with x²:

2(r+2)a₂ - a₂ = 0

For the term with x³:

2(r+3)a₃ - a₃ = 0

Step 6: Solve the equations obtained in Step 5 to find the values of r and a₁, a₂, a₃, etc.

For the term without x:

2r(r-1) - r + 1 = 0

2r² - 3r + 1 = 0

(r-1)(2r-1) = 0

So, we have two possible values for r: r₁ = 1 and r₂ = 1/2.

For the term with x:

2(r+1)a₁ - a₁ - 5 = 0

2a₁(r+1) - a₁ - 5 = 0

For the term with x²:

2(r+2)a₂ - a₂ = 0

2a₂(r+2) - a₂ = 0

For the term with x³:

2(r+3)a₃ - a₃ = 0

2a₃(r+3) - a₃ = 0

Step 7: Solve the equations obtained in Step 6 to find the values of a₁, a₂, a₃, etc.

For r₁ = 1:

2a₁(1+1) - a₁ - 5 = 0

4a₁ - a₁ - 5 = 0

3a₁ = 5

a₁ = 5/3

For r₂ = 1/2:

2a₁(1/2+1) - a₁ - 5 = 0

3a₁ - a₁ - 5 = 0

2a₁ = 5

a₁ = 5/2

Step 8: Write the two linearly independent solutions using the values of r and a₁, a₂, a₃, etc.

For r₁ = 1:

y₁(x) = \(x^1\)(1 + (5/3)x + a₂x² + a₃x³ + ...)

= x(1 + (5/3)x + a₂x² + a₃x³ + ...)

For r₂ = 1/2:

y₂(x) = \(x^{(1/2)\)(1 + (5/2)x + a₂x² + a₃x³ + ...)

= √x(1 + (5/2)x + a₂x² + a₃x³ + ...)

Learn more about the linearly independent solutions at

https://brainly.com/question/31479221

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