Your average waiting time will be approximately 1 minute.
As the first passenger, you will not have to wait for any other passengers to get in the taxi. However, the taxi will wait for 2 passengers to arrive or 3 minutes to pass since your boarding.
Since passengers arrive according to a Poisson process with an average of 60 passengers per hour, the arrival rate lambda can be calculated as:
lambda = average number of passengers per time unit = 60/60 = 1 passenger per minute
The time between two consecutive passenger arrivals follows an exponential distribution with parameter lambda. Thus, the probability of waiting less than t minutes for the second passenger to arrive can be calculated as:
P(wait < t) = 1 - e^(-lambda*t)
We need to find the average waiting time until the second passenger arrives. This can be calculated as the area under the probability distribution curve divided by the arrival rate lambda:
average waiting time = integral from 0 to infinity of t*(1 - e^(-lambda*t)) dt / lambda
Using integration by parts, we can solve this integral to get:
average waiting time = 1/lambda + (1 - e^(-lambda*t))/(lambda^2)
Plugging in the values, we get:
average waiting time = 1/1 + (1 - e^(-1*3))/(1^2) = 1 + (1 - 0.0498) = 1.9502 minutes
Therefore, as the first passenger, your average waiting time until the second passenger arrives is 1.9502 minutes.
To answer your question, let's consider the two possible scenarios:
1. Two passengers are collected: In this case, the first passenger (you) waits for the second passenger to arrive. Since the arrival rate is 60 passengers per hour, the average time between arrivals is 1 minute (60 minutes / 60 passengers).
2. Three minutes have expired: In this case, the taxi departs after 3 minutes even if only one passenger (you) is in the taxi.
On average, the waiting time for the first passenger (you) will be the minimum of these two scenarios. Thus, your average waiting time will be approximately 1 minute.
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the conditions are met for use of a normal model to represent the distribution of sample means. which of the following are used to verify normality conditions for this scenario?
There are several methods that can be used to verify the normality conditions for a scenario where a normal model is used to represent the distribution of sample means.
One common method is the visual inspection of a histogram or a normal probability plot. Another method is to use statistical tests such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test to assess the normality of the sample data. Additionally, the sample size and the presence of outliers can also impact the normality conditions and should be taken into consideration when verifying normality.
Hi! To verify the normality conditions for the distribution of sample means, you should consider the following criteria:
1. Randomness: The sample data must be collected randomly to ensure independence of observations.
2. Sample size: The sample size should be sufficiently large (typically, n ≥ 30) to allow the Central Limit Theorem to apply.
3. Underlying distribution: If the population distribution is known to be normal, the sample means will also be normally distributed regardless of sample size.
These criteria help ensure the use of a normal model is appropriate in representing the distribution of sample means.
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The following probability model describes the number of golf balls ordered by customers of a pro shop and the corresponding probabilities. What is the mean number of golf balls? Round your answer to 2 decimal places if needed. Х P(X) 3 0.14 6 0.29 9 0.36 12 0.11 15 0.10
The mean number of golf balls ordered by customers is 8.22 (rounded to 2 decimal places).
To find the mean number of golf balls, we need to multiply each possible value of X by its corresponding probability, and then sum up the products. That is:
Mean number of golf balls = E(X) = Σ[X*P(X)] where Σ is the summation symbol.
Using the given probability model, we have:
E(X) = 30.14 + 60.29 + 90.36 + 120.11 + 15*0.10
E(X) = 0.42 + 1.74 + 3.24 + 1.32 + 1.50
E(X) = 8.22
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Find the tangent of
G
3
√33
H
F
The tangent of G is given by the trigonometric relation tan G = √24 / 3
Given data ,
Let the triangle be represented as ΔFGH
Now , the measure of side GH = 3 units
The measure of side GF = √33 units
So , the measure of side HF = √ ( √33 )² - ( 3 )²
HF = √ ( 33 - 9 )
HF = √24 units
Now , from the trigonometric relations , we get
tan θ = opposite / adjacent
tan G = HF / GH
tan G = √24 / 3
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The human resources department of the Mean Corporation would like to estimate the size of the annual salary that they should offer to university graduates. The CEO of the Mean Corporation has suggested that the salary offered (W) should be calculated based on the Grade Point Average (G) of a student. Based on a random sample of university graduates, the human resources department has calculated the mean salary offered to university graduates to be W and the mean Grade Point Average of university graduates to be G. The Mean Corporation will carry out a regression analysis to investigate the relationship between salary and Grade Point Average. Select the dependent variable in the regression analysis that will be conducted:___________
The dependent variable in the regression analysis that will be conducted is the salary offered (W) to university graduates.
It is considered the dependent variable because it is the variable that is predicted or explained by the Grade Point Average (G), which is the independent variable. The regression analysis will help to determine how much the salary offered varies with changes in the Grade Point Average, and the mathematical equation derived from the analysis will be used to predict the salary offered based on a given Grade Point Average.
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how many different types of products sold in ar? multiple choice 3 5 6 7 4 4. which product sold the most in ar? multiple choice 4 stout imperial stout ipa pale ale
There are 6 different types of products sold in AR. Among these products, the one that sold the most is IPA (India Pale Ale). IPA is a popular choice among consumers due to its distinct flavor and versatility.
AR, or Arkansas, is known for its growing craft beer scene, so it's no surprise that there are many different types of products sold in the state. According to recent data, there are a total of six different types of products sold in AR.
The answer is imperial stout, which is a type of beer known for its high alcohol content and rich, roasted flavors. While pale ale and IPA are also popular choices among beer enthusiasts in AR, imperial stout seems to be the clear winner in terms of sales.
In conclusion, if you're looking to try some of the most popular products sold in AR, be sure to give imperial stout a try. Its complex flavors and high alcohol content make it a perfect choice for those who appreciate a strong and bold beer.
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A random sample of 111 people was taken. 80 of the people in the sample favored candidate a. we are interested in determining whether or not the proportion of the population in favor of candidate a is significantly more than 70%. the test statistic is:__________
The test statistic is z = 2.75. Since the test statistic is greater than 1.96, we reject the null hypothesis and conclude that the proportion of the population in favor of candidate a is significantly more than 70%.
To calculate the test statistic, we first need to find the proportion of the sample that favored candidate a:
Proportion = 80/111 = 0.72
Next, we calculate the standard error of the proportion:
SE = sqrt[(0.7)(0.3)/111] = 0.045
Finally, we calculate the test statistic using the formula:
z = (Proportion - Hypothesized Proportion) / SE
z = (0.72 - 0.7) / 0.045 = 2.75
Since the test statistic is greater than 1.96 (the critical value for a two-tailed test at the 5% level of significance), we reject the null hypothesis and conclude that the proportion of the population in favor of candidate a is significantly more than 70%.
To determine whether the proportion of the population in favor of candidate A is significantly more than 70%, we'll use the test statistic formula for proportions:
Test statistic = (Sample proportion - Hypothesized proportion) / Standard error
In this case, a random sample of 111 people was taken, and 80 of them favored candidate A. We are interested in finding if the proportion favoring candidate A is more than 70% (0.7).
First, calculate the sample proportion:
Sample proportion = Favored candidate / Total sample
Sample proportion = 80 / 111 ≈ 0.7207
Next, calculate the standard error using the formula:
Standard error = √(p(1-p)/n), where p is the hypothesized proportion and n is the sample size.
Standard error = √(0.7 * (1-0.7) / 111) ≈ 0.0452
Finally, calculate the test statistic:
Test statistic = (0.7207 - 0.7) / 0.0452 ≈ 0.4581
The test statistic for determining whether the proportion of the population in favor of candidate A is significantly more than 70% is approximately 0.4581.
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(6x10^1) + (9x10^1) in scientific notation
The requried, (6x10¹) + (9x10¹) in scientific notation is 1.50x10²
To add (6x10^1) + (9x10^1) in scientific notation, we need to first make sure that the exponents of 10 are the same.
Now we can add the two numbers:
6.0x10¹ + 9.0x10¹ = 15.0x10¹
To express the result in scientific notation, we need to write 15.0 as 1.50 and move the decimal point one place to the left, which gives:
1.50x10²
Therefore, (6x10¹) + (9x10¹) in scientific notation is 1.50x10².
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HELPPPP ME PLEASE
4^-x+1=2^2x
The solution to the equation 4⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ is x = 1/2.
What is the solution to the equation?Given the equation in the question:
4⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ
To solve the equation 4⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ using the equal base method, we can rewrite the right side with base 4, since 4 is a power of 2:
4⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ
2²⁽⁻ˣ ⁺ ¹⁾ = 2²ˣ
Now both sides have the same base, so we can equate their exponents and solve for x:
2( -x + 1 ) = 2x
-2x + 2 = 2x
2x + 2x = 2
4x = 2
x = 1/2
Therefore, the value of x is 1/2.
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Create an equation to show the relationship between m and g.
Answer:
Step-by-step explanation:
m = 32g
find the angle measures of trapezoid BCED
Answer:
BCDE= 100+ 80+100+80 = 360 degree
BAC = 20 degree
DBC = 100 degree
BDE = 80 degree
Step-by-step explanation:
Shows all is correct
We associate isosceles trapezoid in this question, this helps us prove with angle A in the triangle vertices how we can find one of the adjacent angles from the trapezoid by subtraction when all angles within one single trapezoid = 360 degrees. We can use 20 degree angle A to subtract and find each alternative angle easier.
Step-by-step explanation:
The semi circle shows 9 stones
Where angles are interior to the trapezoid
Where all 4 sided shapes add up to 360 degree
We draw a line of symmetry on BCED angle
To make midway points BC and DE = 90 degree
The two new formed shapes are still 4 sided and add up to 360 degree.
BC + DE = 180 degree
BDE = Triangle 180 -20/2 = 160/2 = 80
BCDE = Trapezoid = 360
Trapezoid angle DBC = 360-80-80/2 = 360-160/2 = 200/2 = 100 degree
Finding interior angle A (BAC)
BAC = 180/9 = 20 degree
BAC * (2) = 360 degree circle
BAC = 360/18 = 20 degree
Proves BAC = 20 degree
20 degree is used in BAC workings above in bold and proves all trapezoid angles are correct. We now know this is an isosceles trapezoid and that is why symmetry and midway points can help us find the angles without any given length.
What is the value of x?
61
Why my answer is sixty one Because the Triangle ls the same size Of the other sixty one
Answer:
61
Step-by-step explanation:
Given u = 144i − 17j, what are the magnitude and direction of −3u? Round to the nearest whole number.
The magnitude of the vector is 435 units.
The direction of the vector is 173.3⁰ .
What is the magnitude of the vector?
The magnitude of the vector -3u is calculated as follows;
The new vector - 3u is determined as;
u = 144i - 17j
-3u = -3(144i - 17j )
= -432i + 51j
The magnitude of the vector is calculated as;
|u| = √ (-432² + 51²)
|u| = 435 units
The direction of the vector is calculated as follows;
θ = tan⁻¹ (uy / ux)
θ = tan⁻¹ (-51/432)
θ = -6.7⁰ = 173.3⁰
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Consider a population having a standard deviation equal to 10. We wish to estimate the mean of this population.(a) How large a random sample is needed to construct a 95 percent confidence interval for the mean of this population with a margin of error equal to 1? (Round your answer to the next whole number.)A= 385(b) Suppose that we now take a random sample of the size we have determined in part a. If we obtain a sample mean equal to 295, calculate the 95 percent confidence interval for the population mean.What is the interval's margin of error? (Round your answers to 3 decimal places.)B=?
(a) The answer of the question "What is the interval's margin of error (Round your answers to 3 decimal places.)" to part (b) is B = 0.978.
(b) margin of error = 1.96*(10/sqrt(385)) = 0.978
(a) To find the sample size needed to construct a 95% confidence interval with a margin of error of 1, we use the formula:
margin of error = z*(standard deviation/sqrt(sample size))
where z is the critical value from the standard normal distribution for a 95% confidence level, which is approximately 1.96.
Plugging in the given values and solving for the sample size, we get:
[tex]1 = 1.96*(10/sqrt(sample size))[/tex]
[tex]sqrt(sample size) = 1.96*10/1[/tex]
[tex]sample size = (1.96*10)^2 = 384.16[/tex]
Rounding up to the nearest whole number, we need a sample size of 385.
Therefore, the answer to part (a) is 385.
(b) To calculate the 95% confidence interval for the population mean given a sample size of 385 and a sample mean of 295, we use the same formula as above with the values we have:
1 = 1.96*(10/sqrt(385))
Solving for the margin of error, we get:
margin of error = 1.96*(10/sqrt(385)) = 0.978
The 95% confidence interval for the population mean is then:
295 - 0.978 to 295 + 0.978
or
(294.022, 295.978)
Therefore, the answer to part (b) is B = 0.978.
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which of the following is an example of systematic sampling? a) using a random number table, people are chosen and then only the people with even numbers are selected. b) in a population of 500, the first and last 100 for a total of 200 people are chosen. c) in a population of 1000 at a school, every 64th person is chosen. d) a government official uses a list of all the people that have returned tax forms and uses those people that h
The example of systematic sampling is option c) in a population of 1000 at a school, every 64th person is chosen.
In systematic sampling, the population is first divided into a sampling frame (for example, a list or a map) and then every kth individual is selected from the list. In this example, every 64th person is chosen from the list of 1000 individuals, which is an example of systematic sampling. In the example given, there is a list of 1000 individuals, and every 64th person is chosen from the list. This means that the sampling interval k is 64, and the first individual is selected randomly from the first 64 individuals in the list. From then on, every 64th individual is selected to be included in the sample. For instance, if the first individual selected is number 8, then the individuals selected for the sample would be 8+64=72, 8+264=136, 8+364=200, and so on.
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omg itss more and still coming check my page
The solution is : the measure of angle A is 150°.
We have,
First a diagram which looks like a 12 sided figure where all the sides are equal.
Now draw 2 consecutive radii.
There are 12 such triangles in a 12 sided polygon.
These triangles have an apex angle of 360 / 12 = 30 degrees.
The other two angles making up the triangle are both equal.
Therefore x + x + 30 = 180
2x = 150
x = 75
But 75 is 1/2 of the interior angle.
There are 2 such angles making up the interior angle 75 + 75 = 150.
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a parallelipiped has six faces that are parallelograms. in the parallelipiped shown, two parallel sides of the base are 5 inches long and 2 inches apart. the height of the parallelipiped is 8 inches. find the volume of the parallelipiped.
The volume of the parallelepiped is 80 cubic inches.
To find the volume of the parallelepiped, we need to multiply the area of the base by the height. We are given that two parallel sides of the base are 5 inches long and 2 inches apart, which means that the base is a parallelogram with base length of 5 inches and height of 2 inches. The area of the base is therefore:
Area of base = base length x height = 5 inches x 2 inches = 10 square inches
The height of the parallelepiped is given as 8 inches. Therefore, the volume of the parallelepiped is:
Volume = area of base x height = 10 square inches x 8 inches = 80 cubic inches
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Un bolígrafo pesa 6,4 g. Cuantos bolígrafos necesitamos para superar el kilogramo?
Based on th mentioned iinformations, we would be requiring about 157 pens (rounded up) in order to exceed the weight of 1 kilogram.
There are 1000 grams in a kilogram. To find out how many pens are needed to exceed 1 kilogram, we need to divide 1000 grams by the weight of one pen:
1000 g / 6.4 g = 156.25 pens
Therefore, we would need 157 pens (rounded up) to exceed 1 kilogram.
Dividing 1000 grams by the weight of one pen gives us the number of pens that would weigh 1000 grams or 1 kilogram, which turns out to be 156.25 pens. Since we cannot have a fractional part of a pen, we round up to 157 pens to ensure that their total weight exceeds 1 kilogram.
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The complete question is :
A pen weighs 6.4 g. How many pens do we need to exceed the kilogram?
Two linear functions, f and g, are defined as follows
Answer ALL true or false statements below
The linear function f(x) and g(x) have different intercept and slope.
What is true about the linear functions?To find what true or false about the given statements, we need to write out the equations for both functions.
f(x) = x + 9
To find the function g(x), we need to find the slope and y-intercept.
The slope of the function is given as;
m = y₂ - y₁ / x₂ - x₁
Taking two points from the table;
m = 14 - 10 / 3 - 1
m = 4 / 2
m = 2
Using the slope, we can find the y - intercept with any one point;
y = mx + c
10 = 2(1) + c
10 = 2 + c
c = 10 - 2
c = 8
The equation is y = 2x + 8
Now, we can write out the functions again;
f(x) = x + 9
g(x) = 2x + 8
Let's observe each of the given statements;
a. f(x) has a greater y - intercept than g(x) which is true because f(x) has intercept at 9 and g(x) has intercept at 8.
b. f(x) has greater x -intercept than g(x). This is false as f(x) has a lower x-intercept than g(x)
c. f(x) has a greater slope than g(x). This is also false as g(x) has a slope of 2 and f(x) has a slope of 1
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asteak at a restaurant actually weighs 17 ounces (the true value),but the menu claims that it is a 15-ounce steak. Find the values ofabsolute and relative errors.
The absolute error is 2 ounces, and the relative error is approximately 11.76%.
The absolute error is the difference between the claimed weight and the true weight of the steak, which is:
Absolute error = |15 - 17| = 2 ounces
The relative error is the absolute error divided by the true weight of the steak, which is:
Relative error = (2/17) x 100% = 11.76%
So, the absolute error of the claimed weight is 2 ounces, and the relative error is 11.76%.
To find the absolute error, you'll need to subtract the true value (17 ounces) from the claimed value (15 ounces):
Absolute error = |True value - Claimed value| = |17 - 15| = 2 ounces
Now, to find the relative error, you'll divide the absolute error by the true value, and then multiply by 100 to get a percentage:
Relative error = (Absolute error / True value) x 100 = (2 / 17) x 100 ≈ 11.76%
So, the absolute error is 2 ounces, and the relative error is approximately 11.76%.
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A rectangular prism has a volume of 7800 cubic feet width of 40 feet and a height of 13 feet, find its length in feet
The length of the rectangular prism is 15 feet.
What is the length of the rectangular prism?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
Given that: the volume of the rectangular prism is 7800 cubic feet, the width is 40 feet, and the height is 13 feet.
We can substitute these values into the formula and solve for the length:
V = w × h × l
7800 = 40 × 13 × l
7800 = 520 × l
l = 7800 / 520
l = 15 ft
Therefore, the measure of the length is 15 feet.
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What is the distance from Point A to Point B? Round your answer to the nearest tenth if necessary.
(Hint: sketch a right triangle and use the Pythagorean theorem.)
A coordinate is (4,6)
B coordinate is (5,-5)
The distance from Point A to Point B is
9.1 units (to the nearest tenths)How to find length of lineThe length of line in an ordered pair is calculated using the formula
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
where
d = distance between the points
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
distance between points (4, 6) and (-5, 5) is calculated by
d = √{(x₂ - x₁)² + (y₂ - y₁)²}
substituting the values
d =√{(4 - (-5))² + (6 - 5)²}
d =√{81 + 1}
d = √82
d = 9.055 units
d = 9.1 units (to the nearest tenths)
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Please help me with this is urgent!!!
Answer:
(681) 20.115
I think that's the answer
T/F : Find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other
False.
It is not possible to find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other.
It is not possible to find a 3 by 3 matrix A which is not invertible, but where no two columns are scalar multiples of each other, and no two rows are scalar multiples of each other.
This is because if no two columns of A are scalar multiples of each other, then the columns are linearly independent, and the rank of A is at least 3. Similarly, if no two rows of A are scalar multiples of each other, then the rows are linearly independent, and the rank of A is also at least 3. Since A is a 3 by 3 matrix, it follows that the rank of A is at most 3. Therefore, the only way for A to have rank 3 is for A to be invertible.
So, any 3 by 3 matrix A that is not invertible must have either two columns that are scalar multiples of each other, or two rows that are scalar multiples of each other.
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Calculate the lower confidence limit (LCL) and upper confidence limit (UCL) of the mean for each of the following. bar x= 160, n = 436, sigma = 30, and alpha = 0.01 bar x = 70, n = 323, sigma = 4, and alpha = 0.05 LCL =
LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.
To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:
LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))
where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).
First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01
1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.
2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39
First Scenario Result:
LCL = 158.61
UCL = 161.39
Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05
1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.
2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35
Second Scenario Result:
LCL = 69.65
UCL = 70.35
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a. A kicker punts a football. The height (in yards) of the football is represented by f(x)=-1/9(x-30)^2+25 , where x is the horizontal distance (in yards) from the kicker's goal line.
Find the domain and range.
b. On the next possession, the kicker punts the football again. The height of the football is represented by g(x)=f(x+5) .
Find the domain and range.
c. Compare the graphs.
d. On which possession does the kicker punts closer to his goal line? Explain.
The kicker's ability to punt the ball any distance from the goal line means that the domain is unlimited in range.
How to explain the informationAs a transformation of f(x), g(x) carries the same infinity of values within its range as well with a limit up to 25.
Decidedly opening downwards, f(x)'s parabola possesses a vertex located at (30, 25). For playing according to territory: representing the kicker’s goal line, x = 30 houses the vertex of f(x) , so punting happens closer there.
In sum, while f(x) equips football players to strategically understand their field posisioning ranging across all heights, trajectory of direction & ranges, executing effective plays based on the available resources; along with g(x) which offers a modified visual representation- they both obey the constraints of physics-based rules.
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(6) The figure shows a rectangle and 6 identical semicircles in a circle. Find the area of the shaded part. (Take π = 3.14.)
[tex]\blue{\boxed{\bold{\mathbb{SOLUTION}}}}[/tex]
Area of the biggest circle:
[tex]\pi r^{2}=\pi \times 6^{2}=\pi \times 36 \ cm^2[/tex].
Area of the rectangle:
[tex]4 \times (2+2+2+2) = 4 \times 8 = 32 \ cm^2[/tex].
Area of the 6 semicircles:
[tex]6 \times \dfrac{1}{2} \times \pi \times r^2 = 3 \times \pi \times 2^2 = \pi \times 12 \ cm^2.[/tex]
Total shaded area:
Biggest circle area - rectangle area - 6 semicircles area
[tex]= \pi \times 36 - 32 - \pi \times 12\\= \pi \times (36-12) - 32\\= \pi \times 24 - 32\\= 3.14 \times 24 - 32\\= 75.36 - 32\\= \boxed{43.36 \ cm^2}[/tex]
Therefore, the shaded part area is [tex]43.36 \ cm^2[/tex].
[tex]\aqua{\boxed{\mathfrak{Thank \: You}}}\\\aqua{\boxed{\bold{answered \: by: \: akbarsdtazm}}}[/tex]
Using a calculator, work out the value of (8.8 × 10-4) x (7.4 x 1011) Give your answer in standard form
The required value of (8.8 × 10⁻⁴) × (7.4 x 10¹¹) in standard form is 6.512 × 10⁸.
The expression is given as follows:
(8.8 × 10⁻⁴) × (7.4 x 10¹¹)
When multiplying numbers in scientific notation, we can multiply the coefficients and add the exponents of 10.
(8.8 × 10⁻⁴) × (7.4 x 10¹¹)
= (8.8 × 7.4) × 10⁽⁻⁴⁺¹¹⁾
= 65.12 × 10⁷
To convert to standard form, we can write 65.12 as 6.512 × 10¹:
= 6.512 × 10¹ × 10⁷
= 6.512 × 10⁸
Therefore, the value of (8.8 × 10⁻⁴) × (7.4 x 10¹¹) in standard form is 6.512 × 10⁸.
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n/(sqrt(16n^2 5) find the limit of the following sequence or determine that the sequence diverges.
The expression does not have any variable term (n) in it, the sequence converges to a constant value. The limit of the sequence as n approaches infinity is: Limit = 1/(sqrt(80))
To find the limit of the sequence n/(sqrt(16n^2 5)), we can simplify the expression by dividing both the numerator and denominator by n:
n/(sqrt(16n^2 5)) = 1/(sqrt(16*5/n^2)) = 1/(4sqrt(5/n^2))
As n approaches infinity, 5/n^2 approaches zero. Therefore, the denominator of the expression approaches infinity, and the whole expression approaches zero.
Therefore, the limit of the sequence is 0.
To find the limit of the given sequence n/(sqrt(16n^2 * 5)), we'll apply some algebraic simplification and use the properties of limits.
First, simplify the expression:
n/(sqrt(16n^2 * 5)) = n/(sqrt(80n^2))
Now, divide both the numerator and denominator by n:
n/(sqrt(80n^2)) = 1/(sqrt(80))
Since the expression does not have any variable term (n) in it, the sequence converges to a constant value. The limit of the sequence as n approaches infinity is:
Limit = 1/(sqrt(80))
This is the final answer.
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How many ordered quadruplets (a1,a2,a3,a4) of non-negative integers, where at least one of the integers is even, satisfy the equation a1+a2+a3+a4=100 ? Please express your answer in the form (wx)−(yz). (Note that the values of w,x,y and z will be integers, but not necessarily all distinct.)
The number of ordered quadruplets of non-negative integers that satisfy the given condition is:
|A| - |B| = 161,700 - 16,215 = 145,485
To solve this problem, we need to use the Principle of Inclusion-Exclusion (PIE). Let A be the set of all quadruplets (a1,a2,a3,a4) of non-negative integers that satisfy the equation a1+a2+a3+a4=100, and let B be the set of all quadruplets where all four integers are odd. Then the number of quadruplets that satisfy the given condition is given by:
|A| - |B|
To find |A|, we can use stars and bars. If we consider 100 stars and 3 bars, we can partition the stars into 4 groups, corresponding to the four integers. There will be 99 gaps between the stars and bars, and we need to choose 3 of them to place the bars. This gives us:
|A| = (99 choose 3) = 161,700
To find |B|, we can use a similar approach. If all four integers are odd, then they must be of the form 2k+1, where k is a non-negative integer. Substituting this into the equation a1+a2+a3+a4=100, we get:
2k1 + 1 + 2k2 + 1 + 2k3 + 1 + 2k4 + 1 = 100
Simplifying this equation, we get:
k1 + k2 + k3 + k4 = 48
This is now an equation in non-negative integers, which we can solve using stars and bars. We need to partition 48 stars into 4 groups, and there will be 3 bars separating them. This gives us:
|B| = (47 choose 3) = 16,215.
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Un granjero tiene para vender 1800 pollo primero vende 2/5 del total luego los 5/6 del resto y si se mueren 37 pollo¿ ¿cuantos pollos le quedan todavia?
Based on the mentioned informations, the farmer is calculated to have 143 chickens left after selling 2/5 and 5/6 of the initial 1800 chickens and 37 chickens died.
The farmer starts with 1800 chickens.
He sells 2/5 of the total, which is:
(2/5) x 1800 = 720 chickens.
So he has 1080 chickens left.
He then sells 5/6 of the remaining chickens, which is:
(5/6) x 1080 = 900 chickens.
So he has 180 chickens left.
Unfortunately, 37 chickens die, so the final number of chickens he has left is:
180 - 37 = 143 chickens.
Therefore, the farmer has 143 chickens left after selling 2/5 and 5/6 of the initial 1800 chickens and 37 chickens died.
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The complete question is :
A farmer has to sell 1800 chickens, first he sells 2/5 of the total, then 5/6 of the rest and if 37 chickens die, how many chickens does he still have left?