what is the smallest integer that can possibly be the sum of an infinite geometric series whose first term is 9?

Cost of 15 liters of paint is, 630 Rs.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Five liters of paint cost = 210 Rs.

Hence, We get;

Cost of 1 liters of paint = 210/5

                                   = 42 Rs.

So, Cost of 15 liters of paint is,

⇒ 15 × 42

⇒ 630 Rs.

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The equation representing the temperature y in degrees Fahrenheit at x hours after sunset is:

y = -2x + 4

Since the temperature changes linearly with time after sunset, we can represent the temperature as a linear equation:

y = mx + b

where y is the temperature in degrees Fahrenheit, x is the number of hours after sunset, m is the rate of change of temperature and b is the y-intercept.

Given that at 2 hours before sunset, the temperature is 0°F and at 2 hours after sunset, the temperature is -4°F, we can use these points to find m and b.

At x = -2: y = 0°F

At x = 2: y = -4°F

So, m = (y2 - y1) / (x2 - x1) = (-4°F - 0°F) / (2 - (-2)) = -2°F/hour

And, b = y - mx = 0°F - (-2°F/hour * -2) = 4°F

Therefore, the equation representing the temperature y in degrees Fahrenheit at x hours after sunset is:

y = -2x + 4

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y = 1/2 x + 1

y = 3/2x + 4        Use first equation to sub in for y

1/2 x + 1  = 3/2 x + 4

-3 = x      then use this value in one of the equations to calc  y

y = 1/2 x + 1

y = 1/2 (-3) + 1 =  - 1/2

A geometric random variable is the number of 5s when rolling a die 35 times. (option 1)

This is due to the fact that rolling a 5 on any given roll has a probability of 1/6, and the number of 5s can be determined by counting the number of successes (rolling a 5) prior to the first failure (not rolling a 5).

If you roll a number other than 5, the expected number of unsuccessful iterations is 1/2pq, where p is the probability of success (1/6) and q is the probability of failure (5/6). Additionally, this can be expressed as (1-p)/p. Therefore, when rolling a die 35 times, the expected number of 5s is 35, or (1-1/6)/(1/6).

We can use the formula for the expected value of a geometric random variable, E[X] = (1-p)/p, where p is the probability of success, to demonstrate this mathematically. p is 1/6 in this case.

E[X] = (1-1/6)/(1/6) = 35 can be obtained by substituting this number into the formula. This indicates that 35 is the anticipated number of 5s after rolling a die 35 times.

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Complete Question:

which of the following random variables is geometric?

According to the solving the amount of the principal investment is, $1200.

option A is correct

Simple interest is calculated without taking the impact of compounding into consideration. In many circumstances, interests compounds with each specified time of a loan, whereas simple interest does not. Simple interest is calculated as the principal sum multiplied by that of the cost of borrowing, multiplied by the number of periods.

Simple Interest(I)

=  P × R × T/100

A = P(1 + RT)

Given that,

A = $1422

R =  3.7%

T =  5 year

P  = ?

After 5 year total amount

1422 = P (1 + 0.037 × 5)

P  =   1422/( 1 + 0.037 × 5)

  =    1422/1.185

P  =    1200

Hence, the principal amount is $1200

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According to the solving the amount of the principal investment is, $1200.

option A is correct

Simple interest is calculated without taking the impact of compounding into consideration. In many circumstances, interests compounds with each specified time of a loan, whereas simple interest does not. Simple interest is calculated as the principal sum multiplied by that of the cost of borrowing, multiplied by the number of periods.

According to the given data:

Simple Interest(I)

=  P × R × T/100

A = P(1 + RT)

Given that,

A = $1422

R =  3.7%

T =  5 year

P  = ?

After 5 year total amount

1422 = P (1 + 0.037 × 5)

P  =   1422/( 1 + 0.037 × 5)

 =    1422/1.185

P  =    1200

Hence, the principal amount is $1200

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The best tool for collecting data on which gas pump is used most frequently by customers would be a check sheet.

A check sheet is a simple tool used to collect and categorize data in a structured manner. In this case, the operator can use a check sheet to keep track of which gas pump is being used by customers by marking each time a customer uses a certain pump.

The operator can then tally the marks to determine which pump is used most frequently. This method provides an easy and efficient way to collect data and quickly see patterns and trends in the data.

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--The given question is incomplete; the complete question is

"A gas station operator is interested in determining which gas pump is used most frequently by customers. The best tool for collecting this data would be a

Run chart.

Check sheet.

Histogram.

Pareto diagram."--

Answer:

You can call them champion ice-skating sisters or identical champion ice-skaters.

The equations obtained from evaluation of the data in the table and the predicted cost of hiring the DJs are as follows;

Part B

The equation representing the cost of hiring Celinda is; c = 36·h + 16

The equation representing the cost of hiring Brian is; c = 38·h + 4

Part C

The cost of hiring Celinda for 5 hours is $196

Cost of hiring Brian for 5 hours is $194

A linear equation is an equation that has an highest index of 1.

Part B

The first difference in the cost of hiring each DJ is presented as follows;

Celinda; 160 - 124 = 124 - 88 = 88 - 52 = 36

Brian; 156 - 118 = 118 - 80 = 80 - 42 = 38

The first difference are constant, therefore, the relationship are linear, which can be represented by linear equations.

The difference between the subsequent values in the number of hours of 1 indicates that we get;

Slope of the equation for Celinda = 36

The equation representing the total cost for Celinda is therefore;

Where c represents the cost and h represents the number of hours, we get;

c - 52 = 36·(h - 1)

c = 36·h - 36 + 52

The equation for Brian, with a slope of 38, is therefore;

c - 42 = 38·(h - 1)

c = 38·h - 38 + 42 = 38·h + 4

Part C

The cost of hiring each DJ for 5 hours is therefore;

h = 5

The cost of hiring Celinda for 5 hours is; c = 36 × 5 + 16 = 196

The cost of hiring Celinda for 5 hours is $196

The cost of hiring Brian for 5 hours can be obtained by plugging in h = 5 in the equation; c = 38·h + 4

Therefore; c = 38 × 5 + 4 = 194

The cost of hiring Brian for 5 hours is $194

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Answer:

Z+12a−z+8+12−+8

Step-by-step explanation:

Z+8−6(z−2a)+5z

+8−6(−2)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8−6(−2a+z)+5z

+8−6(−2+)+5

Z+8+12a−z+8+12−

Answer:

Z + 8 + 12a − z

12a + 8

Step-by-step explanation:

Answer:

x = 8, y = 1

Step-by-step explanation:

11x - 20y = 28 ...(1)
3x + 4y = 36
or 15x + 20y = 180 ...(2)
Adding (1) and (2),
26x = 208
Or x = 8
Now, 3x + 4y = 36
3(8) + 4y = 36
4y = 36 - 32 = 4
so y = 1

The length of the shortest path the gecko can take to reach the fly is √170 feet.

The shortest path the gecko can take to reach the fly is a straight line from its starting position to the position of the fly. To find the length of this path, we can use the Pythagorean theorem.

Let's call the distance the gecko must travel along the ceiling x and the distance it must travel along the wall y. Then, using the Pythagorean theorem, we have:

x² + y² = d²

Where d is the distance between the two points.

We can find x and y by using the information given in the problem. The gecko starts one foot from the ceiling, so x = (8 - 1) = 7. It starts one foot from the back wall, so y = (12 - 1) = 11. The fly is one foot from the floor, so x = (8 - 1) = 7. It is one foot from the front wall, so y = (10 - 1) = 9.

Substituting these values into the equation, we have:

7² + 11² = d²

49 + 121 = d²

170 = d²

d = √170

Therefore, the length of the shortest path the gecko can take to reach the fly is √170 feet.

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Answer: y - ln2 = (1/2)(x - 2) or y = (1/2)x + ln2 - 1

Step-by-step explanation:

f(x) = lnx

f'(x) = 1/x

f(2) = ln 2 , so we have the slope = 1/2, and a point (2, ln2)

equation of tangent:

y - ln2 = (1/2)(x - 2)

y = (1/2)x + ln2 - 1

Answer:

Step-by-step explanation:

2+2=4

The diameter of Pool A is 26.84 meters. So, the diameter of Pool B is greater, and the circumference is greater by 0.56 meters.

The diameter is a straight line that passes through the center of a circle and touches two points on the circumference of the circle. The radius is half the length of the diameter.

The first step is to convert the radius of pool A to meters from feet:

44 x 0.305 = 13.42 meters

Diameter of Pool A = 2 x radius

2 x 13.42 = 26.84 meters

Circumference of a circle = πD

Where:

π  = 3.14

D = diameter

Circumference of Pool A = 3.14 x 26.84 meters = 84.28 meters

Circumference of Pool B = 3.14 x 27.02 = 84.84 meters

Difference = 84.84 - 84.28 = 0.56 meters

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To determine the price of the keyboard with the coupon, we need to know how much Tiana spent. Let's call the original price of the keyboard "x".

According to the coupon, Tiana will receive a discount of $150 for every $500 spent. So, if she spends x dollars, she will receive a discount of (x/500) * $150.

The price of the keyboard with the coupon will then be x - (x/500) * $150.

Since the original price is not specified, we cannot determine the exact price of the keyboard with the coupon.

It  is unknown what proportion of employees at it's-a-living are happy with their job. if we randomly sample 300 and 159 are happy, based on this sample for the proportion who are happy gives mean result.

An unknown statistical parameter's expected range of values is shown by a confidence interval, a statistical measure. The confidence interval is an estimate of the range of potential population mean values if the parameter is the population mean.

By using approximation to the binomial,

σ=√npq

= √300*.095*159

=212.8

When using observed (sample) data, a confidence interval is computed at a set degree of confidence (chosen prior to the computation of the confidence interval). This confidence level, like a 95% confidence level, represents the accuracy of the estimating process; it does not represent the degree to which it is confident that the computed confidence interval accurately represents the parameter under investigation.

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The amount of the down payment is:     $ 108.08

Step-by-step explanation:

It is given that:

You purchase a new LCD monitor for $1,351.

You put a 8% down payment and $59.56 per month on a 24 month purchase plan.

This means that the down payment made is 8% of the total amount of the LCD monitor.

i.e.

The amount of the down payment= 8% of 1,351

i.e.

The amount of the down payment= 0.08 of 1,351

i.e.

The amount of the down payment=0.08×1,351

i.e.

The amount of the down payment= $ 108.08

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According to the above, to draw a 1:2 scale we must divide the figure in 2.

The scale model is a way of drawing a figure that is smaller or larger in size. In this case, the size would be smaller, 1:2 means that for each unit of measurement (cm) of the original figure, there are 2 units on the scale.

According to the above, if the circle has a 12cm radius, then the scale model would have a 6cm radius, that is, it would be smaller than the original as shown in the second image.

Note: This question is incomplete. Here is the complete information:

Draw a scale of 1:2 of the following figure:

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The equation of the circle that meets the specified requirements is x^2 + y^2 = 89, with the center at the origin and going through P(5, 8).

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical phrase with two equal sides separated by an equal sign is called an equation. An example of an equation is 4 + 6 = 10.

Here,

The equation of a circle with center at the origin (0,0) and passing through the point (x1,y1) can be found using the distance formula.

The distance between a point (x1, y1) and the origin (0,0) is given by:

sqrt((x1-0)^2 + (y1-0)^2) = sqrt(x1^2 + y1^2)

Let's call the radius of the circle r. We know that the distance between the point (x1,y1) and the origin is equal to r. So, we can set up the equation:

sqrt(x1^2 + y1^2) = r

Substituting the values x1 = 5 and y1 = -8, we have:

sqrt(5^2 + (-8)^2) = r

Solving for r, we get:

r = sqrt(5^2 + (-8)^2) = sqrt(25 + 64) = sqrt(89)

Finally, we can write the equation of the circle in standard form using the center (0,0) and radius r:

(x - 0)^2 + (y - 0)^2 = r^2

x^2 + y^2 = r^2

x^2 + y^2 = 89

The  equation of the circle that satisfies the stated conditions that is center at the origin, passing through P(5, −8) is x^2 + y^2 = 89.

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Answer:

false

Step-by-step explanation:

Answer:

there were 13 dogs with ticks but not fleas.

Step-by-step explanation:

Let's call the number of dogs with fleas "x" and the number of dogs with ticks "y".

From the information given, we know:

x = 40 (dogs with fleas)

x + y = 75 (total number of dogs)

y = 27 (dogs with ticks)

So, the number of dogs with ticks but not fleas is equal to y - the number of dogs with both:

y - 14 = 27 - 14 = 13

Therefore, there were 13 dogs with ticks but not fleas.

The number of unique ways to complete a quiz with 5 questions and 4 possible answers to each question is [tex]4^5[/tex], or 1024.

This can be calculated using exponential notation, which states that a number raised to the power of another number is equal to the number multiplied by itself that many times. In this case, 4 to the power of 5 is equal to 4 x 4 x 4 x 4 x 4, or 1024.

In other words, the number of unique ways to answer a quiz with 5 questions and 4 possible answers to each question is equal to 4 multiplied by itself 5 times. This can also be written using the exponential notation as [tex]4^5[/tex]. There are 1024 unique ways to complete a quiz with 5 questions and 4 possible answers to each question.

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The area of the oil spill after 2 hours is 300 square  meters

A rate of change describes the rate at which one quantity changes in relation to another quantity.

Since the oil spill spreads 25 square meters every 1/6 hour. We can write:

rate = 25/(1/6) = 150 square meters per hour

In 2 hours:

area = 2 * 150

area = 300 square meters

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[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \pounds 3100\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=years\dotfill &3 \end{cases} \\\\\\ I = (3100)(0.08)(3) \implies I = 744[/tex]

Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2). Option D

Probability is a mathematical concept that describes the likelihood of an event happening in a given set of circumstances. It is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The closer the probability is to 1, the higher the likelihood of the event happening.

If we arrange the fractions in decreasing order we would have;

5/7 > 6/9 > 6/11

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In linear equation, The carbohydrate intake ranges between 129-286g

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

A diet with adequate proteins and carbohydrates can be given to an athlete (2-3 hours) before a sport.

Generally, 2-3g/kg body weight of Carbohydrates can be included in the diet (depending on the weight and height.

Here, the person weighs 86kgs (assuming the majority of the bodyweight is muscle mass)

Therefore, average carbohydrate intake can be – 85* 2 = 170g; or, 85*3 = 255g

Thus, the carbohydrate intake ranges between 129-286g

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The result of [tex] \frac{x - 3}{8} [/tex] is x = 8k + 3

To solve the fraction [tex] \frac{x - 3}{8} [/tex], you need to isolate the fraction on one side of the equation. Then, multiply both the numerator and denominator by the same number to make the denominator equal to 1. Finally, simplify the fraction by dividing the numerator by the denominator. The steps are as follows:

[tex] \frac{x - 3}{8} = k[/tex], where k is a constant.

Then, [tex](x - 3) \times {8}^{ - 1 } = k[/tex].

This simplifies to x-3 = 8k.

Finally, you have x = 8k + 3. This is the solution to the fraction [tex] \frac{x - 3}{8} [/tex].

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The set of observations on a variable measured at successive points in time or over successive periods of (c) time series .

A Time Series is a set of observations on a variable that is measured at successive points in time or over successive periods.

Which means that the values of the variable that are recorded at regular intervals or successive points, such as daily, weekly, monthly, or annually, and are analyzed to identify the patterns, trends, and relationships over time.

The Time series analysis can be used in various fields, including economics, finance, engineering, and the natural sciences, to make predictions, identify cause-and-effect relationships, and inform decision-making.

The given question is incomplete , the complete question is

A set of observations on a variable measured at successive points in time or over successive periods of

(a) geometric series

(b) time invariant set

(c) time series

(d) logarithmic series

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