Tutorial Exercise Determine wheter the geometric series is convergent or divergent. If it is convergent, find its sum 1000 81 100 10 9 9 - 10 + Part 1 of 5 100 1000 81 To see 9 - 10 + as a geometric series, we must express it as n=0 ar For any two successive terms in the geometric series arn- 1, the ratio of the the two terms, arn 1 n 1 simplifies into an algebraic expression given by Part 2 of5 100 9 1000 81 81 100 In our series 9-10+ + , the ratio is r= Enter a fraction, integer, or exact decimal. Do not approximate SubmitSkip (you cannot come back

Answer: its 56

Step-by-step explanation:

plug #'s in

t=72-8x2

t=56

Answer:

$2.20

Step-by-step explanation:

First you find how much money Meiling already has

2 dollars is $2.00

11 dimes is $1.10

5 pennies is $0.05

Add them all together

2 + 1.10 + 5 = 3.15

Then subtract how much Meiling need to how much Meiling has

5.35 - 3.15 = 2.20

Meiling still needs $2.20 for the ticket

Answer:

Let speed of slower car be xkm/h

Therefore rate of other car=x+20 km/h

After 4 hrs ,

Distance covered by Car A=4x

Distance covered by Car B=4x+80

4x+4x+80=760km

8x=680

x=45

The rate of the slower car=45km/h

The correct answer is mean.

The characteristic which is being calculated here is the mean or the average of the data set.

(20.73 + 20.76 + 20.68 + 20.75)/4

when we divide it by 4 because there are four data sets

= 82.92 / 4

= 20.73

The complete question is 'Francine makes several measurements of the mass of a metal block and the data set is shown in the table below. The measurement mass of metal blocks(g) are a) 20.73 b) 20.76 c) 20.68 d) 20.75 . After analyzing the given data set, Francine calculates a value of 20.73 g so which of these characteristics has been calculated?'

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The present value of the working capital cash flow expected to be received in year 10 is approximately $101,548.6.

The present value of the working capital cash flow expected to be received in year 10,  to discount it back to its present value using the after-tax cost of capital.

The present value (PV) :

PV = CF / (1 + r)²n

Where:

CF = Cash Flow in year 10

r = After-tax cost of capital

n = Number of years

The cash flow in year 10 is the liquidation of the working capital investment, which is $200,000. The after-tax cost of capital is 10%, which means the discount rate (r) is 0.10. The number of years (n) is 10.

After-tax cost of capital = Cost of capital × (1 - Tax rate)

= 10% × (1 - 30%)

= 0.10 × (1 - 0.30)

= 0.10 × 0.70

= 0.07

The present value of the cash flow:

PV = $200,000 / (1 + 0.07)²10

= $200,000 / (1.07)²10

= $200,000 / 1.967151

= $101,548.68

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Answer:

add 3.99 + 6.99 + 5.99 = 16.97 divide 14.50 by 16.97 you will get .854 multiply by 100 it is %85.4 that is the percentage he paid then he saves 100 - 85.4 = %14.6

Answer:

C.

Step-by-step explanation:

Take the equation for finding the volume of a sphere and plug in your radius

4π\(\frac{r^3}{3}\) = V

your equation would plug in 7 for the r. Then simplify the rest of the equation.

Answer:

c

Step-by-step explanation:

I'm not sure but i hope this helps

\(\sf \sqrt{\dfrac{15}{2} } = \dfrac{\sqrt{15} }{\sqrt{2} }\)

        \(\sf = \dfrac{\sqrt{15} }{\sqrt{2} } \ \cdot \ \dfrac{\sqrt{2} }{\sqrt{2} }\)        

        \(\sf = \dfrac{\sqrt{15 * 2} }{\sqrt{2} * \sqrt{2} }\)                [ apply radical rule: √a × √b = √ab ]

        \(\sf = \dfrac{\sqrt{30} }{2}\)                      [multiply the integers] [note: √2 × √2 is 2]

\(\sf x^2 -4 = 0 \\\\\sqrt{x^2-4} = 0\\ \\x^2 - 2^2 = 0^2 \ \quad \quad \quad \leftarrow third \ step \ should \ be \ this\\\\ (x-2)(x + 2) = 0 \\\\x = 2, x = -2 \\ \\ x = \pm 2\)

Answer:

  2. (√30)/2

  3. x = ±2

Step-by-step explanation:

For these, we will show the correct steps, and describe the error in words.

__

  \(\displaystyle\begin{aligned}\sqrt{\dfrac{15}{2}&=\dfrac{\sqrt{15}}{\sqrt{2}}\\&=\dfrac{\sqrt{15}}{\sqrt{2}}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}}\\ &=\dfrac{\sqrt{30}}{2}&\text{error in original work was here}\end{aligned}\)

The product of √2 and itself is 2, not √2.

__

  \(\displaystyle\begin{aligned}x^2-4&=0\\x^2&=4&\text{error was here}\\x&=\pm\sqrt{4}&\text{both square roots}\\x&=\pm2\end{aligned}\)

The expression (x²-4) does not have a square root of (x-2). To usefully take the square root, we need a perfect square involving the variable term.

Answer:

x=-3y

x=-3y + 5/2

Step-by-step explanation:

Answer:

540 are girls

Step-by-step explanation:

6 to 10 means 6/10

900/10 = 90

90 x 6 = 540

The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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The rule that show the relationship between the input (x) and the output (y) is y = 4x - 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Independent variables represent function inputs that do not depend on other values, while dependent variables represent function outputs that depends on other values.

Let x represent the input and y represent the output, hence using the point (8, 30) and (10, 38):

y - 30 = [(38 - 30)/(10 - 8)](x - 8)

y = 4x - 2

The rule that show the relationship between the input (x) and the output (y) is y = 4x - 2

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A car is traveling at the speed of 35 miles per hour, and its speed in feet per second will be equal to 51.33 feet per second.

The amount of the shift in approach per time unit or the size of the shift to the right over time for just an object can be used to describe speed, which in everyday language and kinematics is a scalar quantity.

As a time interval's duration goes closer to zero, the beginning speed serves as that of the maximum permitted speed.

The speed of the car in miles per hour = 35 miles/hour

Multiply it by 1.46 to convert the speed to feet/second.

35 × 1.46 = 51.33 feet/second.

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A continuous probability distribution for a real-valued random variable in statistics is known as a normal distribution or Gaussian distribution.

A normal distribution is an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution appears as a "bell curve" on a graph.

The median, mode, and means are the same. At its centre, or the mean, the curve is symmetric. To the left of centre, precisely half of the values are located, and to the right, exactly half. The curve has a total area under it of one.

The answer for normal distribution is 4

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Given that,

Then,

Therfore,

Answer:

5 because -20 divided by -4 is 5

Step-by-step explanation:

Answer:

-12,-16 is the answer for this graph

The square root x^4= x^2

Cruz had 672.13 in his checking account and a check that he wrote to his landlord for 650.00 was just deposited. this will result in none of this mentioned. Thus the correct answer is "none of the answer".

What is the landlord?

A landlord is a  person who refers to the owner of the land providing his property for rent to people by taking some charges.

Spending more money than you have in your bank account results in overdraft fees.

A  service fee is a cost that is gathered to cover services associated with a good or service that is being purchased.

ATM fees refer to charges applicable to the use of services related to ATM cards.

Therefore, none of the above is appropriate.

Step-by-step explanation:

Answer: None of the above

Step-by-step explanation:

Answer:

√50, 7.6, √65, √78.8, 8.2

Step-by-step explanation:

might be wrong but i'm pretty sure this is it

Aggregate Demand (AD) is a macroeconomic concept that represents the total demand for goods and services in an economy. The X factor in the AD equation represents exports, which are an important part of the economy.

AD is calculated by adding up the individual components of demand, which include consumer spending (C), investment spending (I), government spending (G), and net exports (X-M). The X-M component represents the difference between exports (X) and imports (M).

The X component in the equation represents exports, which are the goods and services produced domestically and sold to foreign countries. Exports are an important part of the economy as they generate income and create jobs. The M component in the equation represents imports, which are the goods and services purchased from foreign countries and consumed domestically. Imports can have a negative impact on the economy as they represent a drain on resources and can lead to a trade deficit. The X factor in the equation is used to represent exports because it is a variable that can change over time. Factors that can affect exports include exchange rates, tariffs, and global demand for certain products. If the exchange rate between two currencies changes, it can make exports more or less expensive for foreign buyers, which can affect the level of exports. Tariffs are taxes on imports, which can make domestic products more competitive in foreign markets.

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The car is going at 41.4 mi/h (approx.) when it travels 196 m in 10.5 seconds in the school zone with a 35mi/h speed limit.The given information is:Distance travelled = 196 mTime taken = 10.5 seconds.

The speed limit in the school zone = 35 mi/h. The conversion factor is:1 m/s = 2.24 mi/h. To calculate the speed of the car in mi/h, we need to convert the distance and time into the same unit as the speed limit (mi/h).Let's start by converting the distance:

Distance in miles = Distance in meters ÷ 1609.344

Distance in miles = 196 m ÷ 1609.344

Distance in miles = 0.121 mi

Next, we'll convert the time:Time in hours = Time in seconds ÷ 3600

Time in hours = 10.5 s ÷ 3600

Time in hours = 0.00292 h

Now, we can calculate the speed of the car in mi/h:

Speed in mi/h = Distance ÷ Time

Speed in mi/h = 0.121 mi ÷ 0.00292 h

Speed in mi/h = 41.4 mi/h (rounded to one decimal place)

Therefore, the car is going at 41.4 mi/h (approx.) when it travels 196 m in 10.5 seconds in the school zone with a 35mi/h speed limit.

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Answer:

10.

4(12x+1)

11.

10(9s+8)

........

The statements that are true about exponential functions are:

Exponential functions are mathematical functions in the form \(f(\text{x}) = \text{ax}\), where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

The domain of an exponential function consists of all real numbers. The range of an exponential function consists of only positive real numbers, that is, real numbers greater than zero. The graph of an exponential function has a horizontal asymptote at y = 0, not x = 0.

The input to an exponential function isn't necessarily an exponent. It can be any other variable in the function. The base of an exponential function represents the multiplicative rate of change of the function.

Hence, the correct options are A, D, and E.

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Which statements are true about exponential functions?

A. The domain is all real numbers.

B. The range always includes negative numbers.

C. The graph has a horizontal asymptote at x = 0.

D. The input to an exponential function is the exponent.

E. The base represents the multiplicative rate of change

Answer:

Step-by-step explanation:

she would need 36*2 doughnuts (72)

Then divide by 8

Answer - 9

The probability that the cook adds the right ingredients and cooks well is 0.75

From the question, we have the following parameters that can be used in our computation:

Right ingredients = 9 times

Errors = 3 times

using the above as a guide, we have the following:

Total = 9 + 3

Evaluate the sum

Total = 12

The probability that the cook adds the right ingredients and cooks well is

P = Right ingredients/Total

So, we have

P = 9/12

Evaluate

P = 0.75

Hence, the probability is 0.75

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The minimum possible value of the sum $xyz$ occurs when $x$, $y$, and $z$ are as close to each other as possible.

To find the minimum possible value of the sum $xyz$, we need to consider the factors of 2004 and distribute them as evenly as possible among $x$, $y$, and $z$. Since we want the sum to be minimum, we try to minimize the differences between the values of $x$, $y$, and $z$.

The prime factorization of 2004 is $2^2 \times 3 \times 167$. To minimize the sum, we allocate the prime factors evenly: $x = 2$, $y = 2 \times 3 = 6$, and $z = 167$. Therefore, the minimum value of the sum $xyz$ is $2 \times 6 \times 167 = 2004$.

In this case, $x$, $y$, and $z$ are as close to each other as possible, resulting in the minimum value of the sum. Any other allocation of factors would increase the sum, making this the optimal solution.

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Answer:

3.715

Step-by-step explanation:

7.802/2.1 = 3.715