Complete the description of the piecewise function graphed below. Use interval notation to indicate the intervals.

Geometric series is convergent if the |r|<1 where r is the common ratio.

Let Sn=∑ni=0(−3/4)i then

Sn=(−3/4)n+1−1(−3/4)−1

Now take n→∞ then

Sn→0−1(−3/4)−1=4/7

because |−3/4|<1 and so (−3/4)n→0. Now note that your sum is

lim ∑i=1n+1(−3)i−14i=lim 14∑i=1n+1(−3)i−14i−1=1/4.lim Sn=1/7.

Geometric series: A geometric series is the result of adding together geometric sequences indefinitely. Depending on the sequence given to us, such infinite sums can either be finite or infinite. A series is considered to be convergent if the partial sums gravitate to a certain value, also known as a limit. In contrast, a divergent series is one whose partial sums do not reach a limit. Divergent series frequently reach, reach, or avoid a particular number.

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Hope you could understand.

If you have any query, feel free to ask.

Answer:

3^3 - 3^2 is greater than 17.

Step-by-step explanation:

2^2 + 3^2 = 13

Given that the terminal side of 8 passes through the point (6, 8).We need to find the exact value of the given trig functions.

The point (6,8) lies on the terminal side of 8.The distance from the origin to (6,8) is r = sqrt(6²+8²)

= 10.From this, we know that sinθ=y/r

=8/10

=4/5cosθ

=x/r

=6/10

=3/5tanθ

=y/x

=8/6

=4/3.

We know that sin²θ + cos²θ = 1, substitute the above values, we get:(4/5)² + (3/5)² = 16/25 + 9/25

= 25/25

= 1tanθ

= y/x

= 8/6

= 4/3.

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The total arc length AB that the pendulum travels is approximately 13.96 inches.

To find the total arc length traveled by the pendulum, we can use the formula for the arc length of a pendulum given by:

Arc length (s) = θ × r

where θ is the angle in radians and r is the length of the pendulum.

However, in this case, we are given the angle in degrees, so we need to convert it to radians. The formula for converting degrees to radians is:

θ (in radians) = (π/180) × θ (in degrees)

Given that the angle is 80°, we can convert it to radians as follows:

θ (in radians) = (π/180) × 80° = (4π/9) radians

Now, we can calculate the arc length:

Arc length (s) = (4π/9) radians × 10 inches

The total arc length traveled by the pendulum is therefore:

Arc length (s) = (40π/9) inches

To approximate the answer, we can use the value of π as approximately 3.14:

Arc length (s) ≈ (40 × 3.14/9) inches

Arc length (s) ≈ 13.96 inches

Therefore, the total arc length AB that the pendulum travels is approximately 13.96 inches.

Please note that this calculation assumes that the pendulum swings in a perfect arc without any friction or external factors affecting its motion. In reality, there may be slight variations due to factors such as air resistance or imperfections in the pendulum's motion.

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Answer:

15

Step-by-step explanation:

720 divided by 48 equal 15

Step-by-step explanation:

a thing or situation that is annoying because it is complicated or involves a lot of effort

the combined weight of the two pieces of leaf is 1.47 x 10⁻²grams.

HOW TO FIND WEIGHT ?

To find the combined weight of the two pieces of leaf, we simply need to add the weights of the individual pieces of leaf. We are given that one piece of leaf weighs 1.25 x 10⁻² grams and the other piece of leaf weighs 2.3 x 10⁻³ grams.

Adding these two weights, we get:

1.25 x 10⁻²grams + 2.3 x 10⁻³ grams = 1.47 x 10⁻² grams

Therefore, the combined weight of the two pieces of leaf is 1.47 x 10⁻²grams.

It's important to note that when working with scientific notation, we need to pay attention to the exponents and perform the operations according to the rules of exponents. In this case, we add the numbers in front of the exponent (1.25 and 2.3) and keep the exponent (10⁻²) the same.

It's also worth mentioning that this problem involves very small weights, as the values are expressed in grams using scientific notation. This is a common approach when dealing with very large or very small values in scientific contexts, as it allows us to easily express and compare values using a standardized format

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The tank is filled in gallons per second at 0.158 gal/s, in cubic meters per second is 0.000600 m³/s, and the time interval required to fill a 1.00 m³ volume at the same rate is approximately 14.72 hours.

A. To calculate the rate at which the tank is filled in gallons per second, we can use the given information that it takes 5.25 minutes to fill a 50.0 gal gasoline tank. First, we convert the time from minutes to seconds by multiplying 5.25 by 60, which gives us 315 seconds. Then, we divide the volume of the tank (50.0 gals) by the time in seconds (315 s) to obtain the rate of filling in gallons per second, which is approximately 0.158 gal/s.

B. To calculate the rate at which the tank is filled in cubic meters per second, we need to convert the volume from gallons to cubic meters. One gallon is equal to 0.00378541 cubic meters. Thus, we multiply the rate in gallons per second (0.158 gal/s) by the conversion factor to obtain the speed in cubic meters per second, which is approximately 0.000600 m³/s.

C. To determine the time interval required to fill a 1.00 m³ volume at the same rate, we can set up a proportion using the rate in cubic meters per second (0.000600 m³/s). We can cross-multiply and solve for the time interval, which is approximately 14.72 hours.

In conclusion, the tank is filled at a rate of 0.158 gal/s, which is equivalent to 0.000600 m³/s. It would take approximately 14.72 hours to fill a 1.00 m³ volume at the same rate.

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Answer:

A. 30 minutes

Step-by-step explanation:

30 minutes - strength training

90 minutes - treadmill

His new grade will be 85.838 , this can be calculated using simple fraction.

What is fraction?

As the components of a whole, fractions are by definition. The entire can be a single item or a collection of items.

Main Body:

Initial percentage of child = 93.73%

Child's percentage at test = 74%

according to the question his 40% of test grade is accounted

Parts of grade is from test = 4/10

So his new grade = (4/10)*74 + (6/10) *93.73

New grade = 29.6 +56.238

Hence the new grade for the child will be 85.838%

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a) The critical points of the function f are x = 8 and x = -9, which is option A. b) The function f is increasing on the open interval (-9, 8) and never decreasing i.e., option C and c) the function f may assume local maximum or minimum values at the endpoints x = -9 and x = 8.

a) To find the critical points of f, we need to find the values of x where the derivative f'(x) equals zero or is undefined. From the given derivative f'(x) = (x-8) ²(x+9), we can see that it is defined for all values of x. To find the critical points, we need to set f'(x) equal to zero and solve for x:

(x-8) ²(x+9) = 0

By setting each factor equal to zero, we can find the critical points:

x-8 = 0 or x+9 = 0

Solving these equations, we get:

x = 8 or x = -9

Therefore, the critical points of f are x = 8 and x = -9.

b) To determine where f is increasing or decreasing, we can examine the sign of the derivative f'(x) in different intervals. Considering the critical points x = 8 and x = -9, we can divide the number line into three intervals: (-∞, -9), (-9, 8), and (8, +∞).

c) Since f is increasing on the interval (-9, 8), it does not have any local maximum or minimum values within that interval. However, at the endpoints x = -9 and x = 8, f may assume local maximum or minimum values. To determine if these points correspond to local maximum or minimum, we need to examine the behavior of f around those points by evaluating f(x) itself.

Therefore, the answers to the questions are:

a) The critical points of f are x = 8 and x = -9. (Choice A).

b) The function is increasing on the open interval (-9, 8) and never decreasing. (Choice C).

c) The function f may assume local maximum or minimum values at x = -9 and x = 8, the endpoints of the interval.

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Answer:

an = 196,608 nth term

Hope it's helped

Answer:

an = -3 • 4^(n - 1)

Step-by-step explanation:

The appropriate domain for this scenario would be the set of days on which Carson measures the height of the flower.

In mathematics, the domain of a function is the set of input values for which the function is defined. For example, in the scenario you described, the function could be the height of the flower as a function of the number of days that have passed since the flower was planted. In this case, the domain would be the set of days on which Carson measures the height of the flower, and the range would be the set of possible heights that the flower can have.

Range is the set of output values for which the function is defined.

The appropriate domain for this scenario would be the set of days on which Carson measures the height of the flower. This would typically be a set of consecutive integers, such as {1, 2, 3, ..., 30}.

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The input and the output of a function are key components in understanding how a function operates. The input refers to the value or values that are given to the function as an argument, while the output refers to the result or results that the function returns after processing the input.

In other words, the input is what you provide to the function, and the output is what you get in return. The input can be a single value or a set of values, depending on the requirements of the function. The output can also be a single value or a collection of values, again depending on the function's purpose.

It's important to note that the input and output of a function are not always the same. The function may perform calculations or transformations on the input, and the output may be different from the input. This transformation is what gives functions their ability to perform specific tasks and solve problems.

In summary, the input is what you give to a function, and the output is what you get in return after the function processes the input.

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Answer:

\(\frac{23\pi }{18}.\)

Step-by-step explanation:

1) the rule of transformation [degr → rad] is:

\(\alpha [rad]=\alpha [degr] *\frac{\pi }{180};\)

2) according to the formula above:

230°=230*π/180=23π/18 [rad].

Answer:

x = 240

Step-by-step explanation:

Apply the leg rule to find the value of x.

Leg rule is given as:

Hypotenuse/leg 1 = leg 1/part 1

Hypotenuse = 400

Leg 1 = x

Part 1 = 144

Plug in the known values into the formula

400/x = x/144

Cross multiply

x*x = 144*400

x² = 57,600

Take the square root of both sides

√x² = √57,600

x = 240

For a normally distributed variable X representing homework grades with a mean (μ) of 90 and a standard deviation (σ) of 2, the probability of a randomly selected student scoring above 92 can be calculated using the Z-score.

To find the probability of a randomly selected student scoring above 92, we first need to calculate the Z-score. The Z-score measures how many standard deviations an individual data point is from the mean. It is calculated using the formula Z = (X - μ) / σ, where X represents the value (92 in this case), μ is the mean (90), and σ is the standard deviation (2). Plugging in the values, we get Z = (92 - 90) / 2 = 1.

To calculate the probability of a score between 88 and 92, we repeat the process for both lower and upper limits. For the lower limit (88), we calculate the Z-score as Z = (88 - 90) / 2 = -1. Similarly, for the upper limit (92), the Z-score is 1 as calculated earlier. Using the standard normal distribution table or calculator, we find the area to the left of the Z-score of -1 and the area to the left of the Z-score of 1. Subtracting the former from the latter gives us the probability of scoring between 88 and 92.

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Answer:

It’s 2+2=x 3x3=18 that’s the answer

Step-by-step explanation:

Answer:

\(w=-9/8\)

Step-by-step explanation:

We are given the equation \(-2 \frac{1}{4} = 2w\). To solve this equation, we can divide both sides by 2 to get that \(w = -2\frac{1}{4} \div 2 = -\frac{9}{8}\).

Answer:

w = - \(\frac{9}{8}\)

Step-by-step explanation:

Given

- 2 \(\frac{1}{4}\) = 2w ( change the mixed number to an improper fraction )

- \(\frac{9}{4}\) = 2w ( multiply both sides by 4 to clear the fraction )

- 9 = 8w ( divide both sides by 8 )

- \(\frac{9}{8}\) = w

Answer: the answer is 70

Step-by-step explanation:

The value of x is 70.

According to the triangle's "angle sum property," a triangle's angles add up to 180 degrees. Three sides and three angles, one at each vertex, make up a triangle. The sum of the interior angles in a triangle is always 180, regardless of whether it is acute, obtuse, or right.

Given:

As, the two sides of Triangles are and angles opposite to equal sides are also equal.

So, the measure of two angles are x.

Now, using Angle Sum Property

x+ x + 40= 180

2x + 40= 180

2x = 140

x= 70

Hence, the value of x is 70.

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Answer:

To find out how much money is allotted for each of these items, we can multiply the percentage of the income allocated to each item by the total income.

Food: 20% of $25,000 = $25,000 x 0.20 = $5000

Shelter: 25% of $25,000 = $25,000 x 0.25 = $6250

Clothing: 15% of $25,000 = $25,000 x 0.15 = $3750

So the family has $5000 for food, $6250 for shelter and $3750 for clothing.

The schedule is as follows:

T1 -> T2 -> T1 -> T3 -> T1 -> T2 -> T1.

To construct a schedule using the Earliest Deadline First (EDF) scheduling algorithm, we need to consider the execution time, period, and deadline of each task and assign them priorities based on their deadlines. The task with the earliest deadline will be scheduled first. Let's create a schedule for the given task set:

Task T1: Execution time (e) = 2 ns, Period (P) = 5 ns, Deadline (D) = 5 ns

Task T2: Execution time (e) = 4 ns, Period (P) = 7 ns, Deadline (D) = 7 ns

Task T3: Execution time (e) = 7 ns, Period (P) = 7 ns, Deadline (D) = 7 ns

We have a period of 22 ns, and we need to schedule these tasks within that period. Let's start with the task with the earliest deadline:

At time 0 ns: Execute T1 (2 ns)

At time 2 ns: Execute T2 (4 ns)

At time 6 ns: Execute T1 (2 ns)

At time 8 ns: Execute T3 (7 ns)

At time 15 ns: Execute T1 (2 ns)

At time 17 ns: Execute T2 (4 ns)

At time 21 ns: Execute T1 (2 ns)

This completes the execution of all tasks within the given period of 22 ns. The schedule is as follows:

T1 -> T2 -> T1 -> T3 -> T1 -> T2 -> T1

In this schedule, we have followed the EDF algorithm by selecting tasks based on their deadlines. The task with the earliest deadline is always scheduled first to meet the timing requirements of the system.

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Answer:

A-51.91 technically but 52

B- 25.9 so 26

The dollar number that defines where the lowest values falls is

20% percentile value =$20

This is further explained below.

Generally,  Now we need to determine the 20th percentile ($20). It indicates that we need to locate a dollar amount that marks the point at which the 20 % data has a value lower than that number.

i=(p/100)*n

Where i is the position of p^th

percentile when the data is presented in ascending order.

i=20/100*50

i=1000/100

i=10

Therefore

n=50

p=20

In conclusion, the 10th position for given data is 20,

Therefore, 20% percentile value =$20

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Answer:

3 1/2

3 whole trapezoids and half trapezoid

The CPI increased by 2.78%.

Thus, the purchasing power of household income decreased between 2007 and 2008. Therefore, the correct option is D. 1.02%; fell.

Between 2007 and 2008, the cost of living in this economy increased by 2.78% (choose the closest answer), and the purchasing power of household income decreased between 2007 and 2008.

What is CPI:

CPI stands for consumer price index.

It is a measure of the change in prices of a specified set of goods and services in a particular country.

It calculates the change in prices of goods and services purchased by households.

CPI is calculated by comparing the prices of a basket of goods in a base year to their prices in the current year.

Therefore, the increase in CPI from 180 to 185 means that the price level of the basket of goods and services consumed in the economy increased by 2.78 percent (calculated as [(185-180)/180] x 100).

The household income rose by 3% in this period.

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Answer:

i'm sorry if i get it wrong but i think it's c

Step-by-step explanation: