A truck can be rented from Company A for $100 a day plus $0.30 per mile. Company B charges $20 a day plus $0.80 per mile to rent the same truck. Find the number of
miles in a day at which the rental costs for Company A and Company B are the same.
At miles, the rental costs are the same from either company.

The important to select the appropriate value of alpha based on the characteristics of the data and the goals of the forecasting model.

The statement "for a time series for simple exponential smoothing, a larger alpha is smoother than a shorter period" is true.

In simple exponential smoothing, the forecast for the next period is based on the previous forecast and the difference between the actual value and the previous forecast. The smoothing parameter alpha controls the weight given to the most recent observation compared to the previous forecasts.
A larger alpha places more weight on the most recent observation, resulting in a forecast that is more responsive to recent changes in the data. As a result, the forecast will exhibit less volatility or variability, making it smoother. This means that a larger alpha will lead to a more stable forecast with less fluctuation around the trend.
On the other hand, a smaller alpha places less weight on the most recent observation, resulting in a forecast that is less responsive to recent changes in the data.

As a result, the forecast will be more volatile or variable, making it less smooth. This means that a smaller alpha will lead to a forecast that is more susceptible to fluctuations around the trend.
In summary, the choice of alpha is a trade-off between stability and responsiveness to changes in the data. A larger alpha will lead to a smoother forecast, while a smaller alpha will lead to a more volatile forecast.

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Answer: 49.5

Step-by-step explanation:

All triangles equal 180 degrees

We know two of these degrees

73+57.5=130.5

180-130.5=49.5 degrees

The sample size required is approximately 47. Hence, option B is the correct answer.

Given the standard deviation is assumed to be 18 minutes, the desired margin of error is 5 minutes.

We want to estimate the mean weekly amount of time consumers spend watching television with a 95% confidence level.

The formula for the sample size is as follows:

\([\ Large n=\frac{{Z}^2\cdot {\sigma }^{2}}{E^2}\]\)

where

\(n = sample sizeZ = z-score, i.e., 1.96 (for a 95% confidence level)σ = standard deviation\)

E = margin of error, i.e., 5 minutes

Putting in the values,

\([\begin{aligned}n&= \frac{{(1.96)}^{2}\cdot {(18)}^{2}}{{(5)}^{2}} \\&= 46.6096 \end{aligned}\].\)

Therefore, the sample size required is approximately 47.

Hence, option B is the correct answer.

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Answer:

so the(g) semicircle should go up top with

3) The extra number of feet of coiled tubing Tom needs to run into the well is: 5445 ft

4) The total length of coiled tubing Brendan ran in the wellbore is: 994 ft

5) The distance that the coiled tubing has reached after the first four hours is:  a depth of 16,776 feet in the well.

3) Initial amount of coiled tubing he had after 81 minutes = 9,153 feet

Amount of tubing after another 10 minutes = 10,283 feet

The total tubing required = 15,728 feet.

The extra number of feet of coiled tubing Tom needs to run into the well is: Needed tubing length - Current tubing length

15,728 feet - 10,283 feet = 5,445 feet

4) Speed at which Brendan is running coiled tubing = 99.4 feet per minute.

Coiled tubing inside the wellbore after 8 minutes is: 795.2 feet

Coiled tubing inside the wellbore after 2 more minutes is: 198.8 feet

The total length of coiled tubing Brendan ran in the wellbore is:

Total length = Initial length + Additional length

Total length =  795.2 feet + 198.8 feet

Total Length = 994 feet

5) Rate at which coiled tubing is being run into a 22,000-foot wellbore = 69.9 feet per minute. After the first four hours, we need to determine how deep the coiled tubing has reached.

A time of 4 hours is same as 240 minutes

Thus, the distance covered in the first four hours is:

Distance = Rate * Time

Distance = 69.9 feet/minute * 240 minutes

Distance = 16,776 feet

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a) Yes, It does. The scatterplot support the newspaper report about number of semesters and starting salary.

b) The value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables.

a) The scatterplot appears to show a positive association between the number of semesters needed to complete an academic program and the starting salary in the first year of a job. As the number of semesters increases, the starting salary generally increases as well. Therefore, the scatterplot supports the newspaper report.

b) The coefficient of determination, or R-squared value, represents the proportion of the variation in the dependent variable (starting salary) that is explained by the independent variable (number of semesters). A value of 0.335 means that 33.5% of the variation in starting salary is explained by the number of semesters. This value is relatively low, indicating that there are other factors that also contribute to starting salary.

c) The correlation coefficient is a value between -1 and 1 that measures the strength and direction of the linear association between two variables. A value of 1 indicates a perfect positive correlation, a value of -1 indicates a perfect negative correlation, and a value of 0 indicates no correlation. The correlation coefficient for this data is not provided in the problem, so it is not possible to determine it. Without the correlation coefficient, it is not possible to interpret the strength and direction of the association between number of semesters and starting salary.

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For the given function,

Vertical asymptote = -5/4

Horizontal asymptote = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Range =  (-∞,-5/4) ∪ (-5/4,∞)

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given function is

\(f(x) = \frac{-5x+2}{4x+5}\)

The given function has a vertical asymptote at x = -5/4. This is because the function tends to ∞ as x tends to -5/4.

The horizontal asymptote of the function is when x tends to ∞ .

\(\lim_{x \to \infty} \frac{-5x+2}{4x+5} = \frac{-5+2/x}{4+5/x} = \frac{-5}{4}\)

The horizontal asymptote of function is at y = -5/4.

Since at x = -5/4, the function becomes undefined.

The domain is all real numbers except x = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Since the function is not defined at y = -5/4 as well, the range is also

(-∞,-5/4) ∪ (-5/4,∞) .

Therefore for the given function,

Vertical asymptote = -5/4

Horizontal asymptote = -5/4

Domain =  (-∞,-5/4) ∪ (-5/4,∞)

Range =  (-∞,-5/4) ∪ (-5/4,∞)

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The expected value for one field goal attempt is 1.25 points.

To calculate the expected value for one field goal attempt in basketball, we need to multiply each possible outcome by its corresponding probability and sum them up. In this case, we have three possible outcomes: scoring 0 points, 2 points, or 3 points.

Let's denote the points scored by X and their respective probabilities as follows:

X = 0, with a probability of 0.45 (45%)

X = 2, with a probability of 0.40 (40%)

X = 3, with a probability of 0.15 (15%)

To calculate the expected value (E), we can use the formula:

E = (X1 * P1) + (X2 * P2) + (X3 * P3)

Plugging in the values, we have:

E = (0 * 0.45) + (2 * 0.40) + (3 * 0.15)

E = 0 + 0.80 + 0.45

E = 1.25

Therefore, the expected value for one field goal attempt is 1.25 points.

The expected value represents the average value we would expect to obtain over multiple attempts. In this case, if we were to repeat the field goal attempt numerous times under the same conditions, we would expect the player to score an average of 1.25 points per attempt. It provides an understanding of the central tendency of the outcomes and helps evaluate the overall performance of the player in terms of scoring.

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The vertex of the quadratic function 3x² - 6x + 13 has the coordinates given as follows:

(-1, 22).

The function for this problem is defined as follows:

y = 3x² - 6x + 13.

The coefficients are given as follows:

a = 3, b = -6, c = 13.

Then the x-coordinate of the vertex is given as follows:

x = -b/2a

x = -6/6

x = -1.

The y-coordinate of the vertex is found with the numeric value at the x-coordinate of the vertex, which is of x = -1 for this case, hence:

y = 3(-1)² - 6(-1) + 13

y = 22.

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Answer:

186.17

Step-by-step explanation:

Answer:

132

Step-by-step explanation:

That is an 180 degree angle so just do:

180-42=a

a=132

Answer:

138 degrees.

Step-by-step explanation:

A straight line is equal to 180 degrees. 42 is some, so you would subtract 180 and 42. That is 138 degrees. (When two or more angles add up to 180 it's called supplementary angle) Hope this helps

Answer:

142

Step-by-step explanation:

angle <3 is supplementary to 5x + 3

5x + 3 + 21x - 5 = 180 (because two angles are supplementary as well)

26x  - 2 = 180 add 2 to both sides

26x = 182 divide both sides by 26

x = 7

<3 + 5x + 3 = 180 replace x with 7 and rewrite equation

<3 + 38 = 180 subtract 38 from both sides

<3 = 142

Answer:

Step-by-step explanation:

1. -10+18+6=8+6=14

2. -1+84=83

3. -2×(−6)2 +7=12×2+7=24+7=31

4. 50-(−6)2 +(−8)=50+12-8=62-8=54

5. (-2+2)× (−3)3=0× (−3)3=0

6. 30+8-42=38-42=-4

7. -9-2-1=-12

8. -32+6+6=-20

9. -10×3÷5+9=-30÷5+9=-6+9=3

10. -24÷ 8 + 33=-3+33=30

a) The proportion of the students scored at least 26 points on this test is 0.02275.

b) The 71 percentile of the distribution of test scores is 24.073

A low standard deviation suggests that values are often close to the mean of the collection, whereas a large standard deviation suggests that values are dispersed over a wider range.

Standard deviation, often known as SD, is most frequently represented in mathematical texts and equations by the lower case Greek letter (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.

Let the scores be X and X is normally distributed with a mean of 22 and standard deviation of 2.

μ=22

σ=2

X≈N(22,2)

a) P(X≥26)=P(((X-μ)/σ)≥(26-μ)/σ)

=1-P(Z≥2)

=1-P(Z<2)

=1-0.97725

=0.02275

b) Let a is the 71th percentile of X,

P(X≤a)=0.71

P((X-μ)/σ)≤(a-μ)/σ)=0.71

P(Z≤z)=0.71

From the standard normal table by calculating with z value, we get

a=24.073

Therefore,

a) The proportion of the students scored at least 26 points on this test is 0.02275.

b) The 71 percentile of the distribution of test scores is 24.073.

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The midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0. To approximate the area under the curve using a midpoint approximation, we divide the interval [0, 4) into four subintervals of equal width.

The width of each subinterval is (4 - 0) / 4 = 1.

Now, we need to evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval.

The midpoints of the subintervals are: 0.5, 1.5, 2.5, and 3.5.

Evaluating the function at these midpoints, we get:

f(0.5) = 2 * 0.5 * (0.5 - 4) * (0.5 - 8) = 6

f(1.5) = 2 * 1.5 * (1.5 - 4) * (1.5 - 8) = -54

f(2.5) = 2 * 2.5 * (2.5 - 4) * (2.5 - 8) = 54

f(3.5) = 2 * 3.5 * (3.5 - 4) * (3.5 - 8) = -6

Now, we calculate the sum of these values and multiply it by the width of the subinterval:

Area ≈ (6 + (-54) + 54 + (-6)) * 1 = 0.

Therefore, the midpoint approximation of the area under the curve f(x) = 2x(x - 4)(x - 8) over the interval [0, 4) with 4 subintervals is 0.

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Function g(x) is \(-3x^{2}\)

It is given that function g(x) is transformation of function f(x).

F(x) = \(x^{2}\)

At x = 0,

F(x) = \(0^{2}\)

      = 0

G(x) = 0 (According to graph)

At x = 1,

F(x) = \(1^{2}\)

      = 1

G(x) = -3 (According to graph)

At x = -1,

F(x) = \((-1)^{2}\)

      = 1

G(x) = -3 (According to graph)

As g(x) = -3f(x)

Therefore, g(x) = \(-3x^{2}\)

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A node is visited only once for each time and the number of times a node is visited is equivalent to the number of in-degree of the node.

Breadth First Search (BFS) is a type of graph traversal algorithm that explores or "searches" through a graph by visiting all of the nodes in the graph in a systematic way. It starts at a given vertex or node and explores the nodes at each level of the graph before moving on to the next level. During the search, each node is visited only once, and the goal is to find the shortest path from the starting node to the goal node.

In BFS, a node is visited once for each time it is encountered in the search. For example, if a node is encountered twice in the search, then it will be visited twice. The number of times a node is visited depends on the number of edges or connections that a node has. If a node has two edges, then it will be visited twice. If a node has three edges, then it will be visited three times.

The number of times a node is visited in BFS is also equivalent to the number of in-degree of the node. In-degree is the number of edges that point towards a node. Thus, if a node has three edges pointing towards it, then it will be visited three times.

In conclusion, in BFS, a node is visited only once for each time it is encountered in the search, and the number of times a node is visited is equivalent to the number of in-degree of the node.

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Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

Answer:

  0.253 m/s

Step-by-step explanation:

You want to know the horizontal component of motion of a passenger riding a Ferris wheel when they are 1/27 of the way around the circle and their rate of rise is 0.06 m/s.

The wheel makes one revolution in 27 minutes, so the angular displacement is changing at the rate of (360°)/(27 min) = 13 1/3°/min.

After 1 minute, the passenger is following a path that has an angle of elevation of 13 1/3°.

The ratio of vertical speed to horizontal speed will be the tangent of the angle of elevation:

  Vv/Vh = tan(13 1/3°)

Then the horizontal speed will be ...

  Vh = Vv/tan(13 1/3°) = (0.06 m/s)/0.237004

  Vh ≈ 0.253 m/s

The passenger's horizontal motion is about 0.253 m/s.

Answer:

28

Step-by-step explanation:

5+5=10

9+9=18

10+18=28

The length of BC in this problem is given as follows:

BC = 3.6.

Two triangles are defined as similar triangles when they share these two features listed as follows:

The similar triangles for this problem are given as follows:

ABC and ADE.

Hence the proportional relationship for the side lengths is given as follows:

3/5 = BC/6.

Applying cross multiplication, the length BC is given as follows:

BC = 6 x 3/5

BC = 3.6.

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the answer would be 9.88372093e-7

1 )Simplify.

\(\frac{850000000000000000}{8.6E}\)+23

2 )Answer

9.88372093e-7

Answer:

D

Step-by-step explanation:

Differentiate the function and set it to zero:

f'(x) = -10x + 13

0 = -10x + 13

x = 1.3 seconds

Plug the x value into f(x):

f(1.3) = -5(1.3)^2 + 13(1.3) + 6 = 14.45 meters

Answer:

Your answer would be the third one

Step-by-step explanation:

Triangle 1 - 73, 45

Triangle 2 - 47, 30

Triangle 1: 105°, 23° and Triangle 2: 52°, 105 are similar.

Option (4) is correct.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

As per the given data:

We are given two angles for each pair of triangles, and we have to find out which of the pair of triangles are similar.

For any two triangles to be similar, it must have 2 angles which are having the same measure.

For, Triangle 1: 55°, 45° and Triangle 2: 55°, 80°

Only one angle is same, hence not similar.

Triangle 1: 103°, 32° and Triangle 2: 103°, 25°

Only one angle is same, hence not similar.

Triangle 1: 73°, 47° and Triangle 2: 47°, 30°

Only one angle is same, hence not similar.

Triangle 1: 105°, 23° and Triangle 2: 52°, 105

By using angle sum property in Triangle 1 the remaining angles is:

= 180 - (105 + 23) = 52°

By using angle sum property in Triangle 2 the remaining angles is:

= 180 - (52 + 105) = 23°

2 angles are same, hence similar.

Triangle 1: 99, 41° and Triangle 2: 40°, 99°

Only one angle is same, hence not similar.

Hence, Triangle 1: 105°, 23° and Triangle 2: 52°, 105 are similar.

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Answer:

60 minutes

Step-by-step explanation:

Latitude and longitude are measuring lines used for locating places on the surface of the Earth. They are angular measurements, expressed as degrees of a circle. A full circle contains 360°. Each degree can be divided into 60 minutes, and each minute is divided into 60 seconds.

One degree of latitude is equal to approximately 60 nautical miles or 69 statute miles. Since a minute of latitude is one-sixtieth of a degree, it follows that one degree of latitude is equal to 60 minutes.

This means that there are 60 nautical miles or 69 statute miles between two points that differ by one minute of latitude.

The minute of latitude is a widely used unit for measuring distances on Earth, particularly in navigation and aviation. It allows for precise calculations and is crucial for determining positions accurately. Understanding the relationship between degrees of latitude and minutes helps in determining distances, estimating travel times, and ensuring accurate navigation across the globe.

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The series involves the reciprocal of the sum, the individual terms become smaller and tend towards zero as k approaches infinity.The series converges to a finite value, indicating convergence.

To determine whether the series

Σ (n → ∞) 1/(1+2+...+k)

converges or diverges, we need to analyze its behavior as the number of terms approaches infinity.

Let's break down the series:

1/(1+2+...+k) represents the reciprocal of the sum of the terms 1 to k.

As k increases, the denominator (1+2+...+k) also increases, meaning the value of each term in the series becomes smaller.

We can observe that the sum of the terms in the denominator grows at a rate of O(k^2).

Since the series involves the reciprocal of the sum, the individual terms become smaller and tend towards zero as k approaches infinity.

Therefore, the series converges to a finite value, indicating convergence.

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