Andy Mann is building a garden fence out of planks. The planks are 15 cm wide to the nearest cm. He needs to make 61m of fencing altogether, correct to the nearest metre.

Answer:

19.72

Step-by-step explanation:

The probability of at least one appearance in a 21-alternate period is 0.969803

(a) The appearance  rate is 10 passengers nanosecond , so the anticipated number of advents  in nanosecond is also 10. The probability of no advents  in one minute is given by the Poisson distribution with parameter lambda = 10:

P(X = 0) = [tex]e^{(-lambda)}[/tex] [tex]lambda^{0}[/tex] / 0! =  [tex]e^{(-10)}[/tex]* [tex]10^{0}[/tex] / 1! = 0.000045 (rounded to 6 decimal places)

Therefore, the probability of no arrivals in one-minute period is 0.000045.

(b) To compute the probability that three or fewer passengers arrive in one-minute period, we can use the cumulative distribution function (CDF) of the Poisson distribution:

P(X <= 3) = sum from i=0 to 3 of P(X = i)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= [tex]e^{-10}[/tex] *[tex]10^{0}[/tex] / 0! + [tex]e^{(-10)}[/tex] * [tex]10^{1}[/tex]/ 1! + [tex]e^{(-10)}[/tex] * [tex]10^{2}[/tex] / 2! + [tex]e^{(-10) }[/tex]* [tex]10^{3}[/tex]/ 3!

= 0.010336 (rounded to 6 decimal places)

Therefore, the probability that three or fewer passengers arrive in one-minute period is 0.010336.

(c) The arrival rate is 10 passengers per minute, which is equivalent to 10/60 = 1/6 passengers per second. Therefore, the expected number of arrivals in a 21-second period is (1/6) * 21 = 3.5 passengers. The probability of no arrivals in a 21-second period is given by the Poisson distribution with parameter lambda = 3.5:

P(X = 0) = [tex]e^{(-lambda)}[/tex] * l[tex]lambda^{0}[/tex] / 0! = [tex]e^{(-3.5)}[/tex] * [tex]3.5^{0}[/tex]/ 1! = 0.030197 (rounded to 6 decimal places)

Therefore, the probability of no arrivals in a 21-second period is 0.030197.

(d) The probability of at least one arrival in a 21-second period is equal to 1 minus the probability of no arrivals:

P(at least one arrival) = 1 - P(no arrivals)

= 1 - 0.030197

= 0.969803 (rounded to 6 decimal places)

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Answer: 50 meters

Perimeter = 2W x 2L OR W+W+L+L (the measurement of all sides of a shape)

Width = 9 meters

Length = 16 meters

9(2) + 16(2) = 50 meters

190 pounds is approximately equal to 86.1826 kg ( rounded to four decimal places )

To convert 190 pounds to kg, we can use the following formula:

1 pound = 0.453592 kg

The conversion factor is 0.453592

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The mass in kg = conversion factor × The mass in pounds

Substitute the values in the equation

The mass in kg = 0.453592 × 190

Multiply the numbers

= 86.1826 kg  ( rounded to four decimal places )

Therefore, 190pounds is 86.1826 kg

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The IQR measures the spread of the middle 50% of the data.

Without knowing the actual values of the fuel economy ratings or the summary statistics, we cannot provide an exact answer. However, we can make some general observations about the effects of removing an extreme outlier on the standard deviation and the interquartile range (IQR).

First, the standard deviation measures the spread of the data around the mean. Removing an extreme outlier that is far from the mean could potentially decrease the standard deviation, as the remaining values may be more tightly clustered around the mean. However, the effect on the standard deviation will depend on the exact values of the data points and how much they vary from the mean.

Second, the IQR measures the spread of the middle 50% of the data. Removing an extreme outlier that is far from the bulk of the data may not have a significant effect on the IQR, as the remaining.

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Answer:

34/5

Step-by-step explanation:

Press fit is calculated by determining the required force to assemble two cylindrical parts, using the interference between them and their material properties.

Press fit is calculated by determining the amount of interference between two cylindrical parts and their material properties. The interference is the difference between the diameter of the shaft (male part) and the diameter of the hole (female part). The required force to assemble the parts is then calculated using the material properties of both parts and the amount of interference. The interference is typically expressed as a percentage of the shaft diameter, and the required force is expressed in pounds or newtons.

Calculating the press fit is important for ensuring that the parts are securely and correctly assembled, and for preventing excessive stress or deformation in either part. Press fit calculations are commonly used in mechanical engineering and manufacturing applications.

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the value of a is 7/6 and the value of b is 0.

The tangent is an immediate line that simply touches the curve at a given point. The regular is an immediate line this is perpendicular to the tangent. the slope of any line perpendicular to a line with slope m is the terrible reciprocal −1/m.

Given a curve y = ax + b/√x.

with the constant value of a and b.

First, we need to find the derivative of the curve y = ax + b/√x in order to find the gradient of the tangent to the curve at any given point. We can use the quotient rule to differentiate the equation:

dy/dx = a - (b/2)x^(-3/2)

Now we can find the gradient of the tangent to the curve at the point (4, 12) by substituting x = 4 into this equation:

dy/dx = a - (b/2)4^(-3/2) = a - b/16

The gradient of the normal to the curve at this point is the negative reciprocal of the gradient of the tangent, so:

-1/m = -(a - b/16)

We know that the equation of the normal is given by:

3y + 2x = 44

We can use this to substitute in y in terms of x:

y = (44 - 2x)/3

Now we can substitute this into the expression for -1/m:

-1/m = -(a - b/16) = -(dy/dx) = -(a - b/2x^(3/2)) = -(a - b/2(4)^(3/2))

-1/m = -(a - b/8)

Simplifying this equation, we get:

1/m = a - b/8

Substituting the value of m = -3 into this equation (because the gradient of the normal is -3), we get:

-1/3 = a - b/8

Multiplying through by 8, we get:

-8/3 = 8a - b

We also know that the curve passes through the point (4, 12), so we can substitute this into the equation for the curve:

12 = 4a + b/2

Multiplying through by 2, we get:

24 = 8a + b

Now we have two equations in two variables:

-8/3 = 8a - b

24 = 8a + b

Adding the two equations together, we get:

56/3 = 16a

Dividing through by 16, we get:

a = 7/6

Substituting this into one of the equations, we get:

24 = 8(7/6) + b

b = 0

Therefore, the value of a is 7/6 and the value of b is 0.

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Applying the angles addition postulate, m<KJL = 132°.

The Angles Addition Postulate is a fundamental property of angles in geometry that explains how to find the measure of an angle that is formed by two adjacent angles. According to this postulate, the measure of the larger angle, which is formed by two adjacent angles, is equal to the sum of the measures of the two smaller adjacent angles.

Given the following:

m <1 =79°

m<2 = 53°

Thus, we have:

m<KJL = m<1 + m<2

Substitute:

m<KJL = 79 + 53

m<KJL = 132°

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The angles m∠1 = 79° and m∠2 = 53° make up the angle m∠KJL and the measure of m∠KJL = 132°.

We can observe that the angles m∠1 and m∠2 are between the angle m∠KJL hence the sum of the two angles m∠1= 79° and m∠2 = 53° will give the measure of m∠KJL as follows:

m∠1 + m∠1 = m∠KJL

79° + 53° = 132°

m∠KJL = 132°

Therefore, the angles m∠1 = 79° and m∠2 = 53° make up the angle m∠KJL and the measure m∠KJL = 132°

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The coordinates of Room 1314 are given as follows:

(2, 13).

We are going to label the rooms are follows:

Then the coordinates of Room 1314 are obtained applying the proportions in the context of the problem.

Room 1314 is located five-sevenths of the distance from Room 1305 to Room 1324, hence the equation is given as follows:

Z - X = 5/7(Y - X).

Then the x-coordinate is obtained as follows:

x + 8 = 5/7(6 + 8)

x = 10 - 8

x = 2.

The y-coordinate is obtained as follows:

y + 2 = 5/7(19 + 2)

y + 2 = 15

y = 13.

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The conversion of 65 kilos in pounds is equivalent to approximately 143.3 pounds.

Its name derives from the Latin word "poundus" meaning "weight". The £ symbol comes from an ornate L in Libra. The pound was a unit of currency as early as 775AD in Anglo-Saxon England, equivalent to 1 pound weight of silver.The approximation we use for kilograms (kg) to pounds (lb) is 1 kg = 2.2 lb. To convert from kilogram to pound, we multiply by 2.2. To convert from pound to kilogram, we divide by 2.2.

To convert 65 kilograms to pounds, you can use the conversion factor of 1 kilogram = 2.20462 pounds.

Therefore,65 kilograms = 65 x 2.20462 pounds= 143.3003 pounds (rounded to 4 decimal places)

So, 65 kilograms is equivalent to approximately 143.3 pounds.

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The height of the silo, to the nearest meter is, 84.9 m

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A surveyor needs to determine the height of a large grain silo.

And,  He positions his transit 65 m from the silo and records an angle of elevation of 52º.

Now, By the given condition we can formulate;

tan 52° = x / 65

x = 83.2 m

Here, the height of the transit is 1.7 m,

Thus, The height of the silo, to the nearest meter is,

83.2 + 1.7 m

84.9 m

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Answer:

6 US tablespoons

Step-by-step explanation:

A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).

To find integer matrices A and B that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B), we can start with the following matrices:

A = [1 0 0; 0 1 0; 0 0 0]

B = [1 1 0; 0 0 0; 0 0 0]

The null space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the null space of B also consists of all vectors of the form [x; y; 0]. Therefore, Nul(A) = Nul(B).

The column space of A consists of all vectors of the form [x; y; 0], where x and y are integers. Similarly, the column space of B also consists of all vectors of the form [x; y; 0]. Therefore, Col(A) = Col(B).

We can verify that A and B are not multiples of each other by computing their determinants. The determinant of A is 0, while the determinant of B is 0 as well. However, A and B are not multiples of each other because the first column of A is [1; 0; 0], while the first column of B is [1; 0; 0] + [0; 1; 0], which is a linear combination of the columns of A.

Therefore, A = [1 0 0; 0 1 0; 0 0 0] and B = [1 1 0; 0 0 0; 0 0 0] are two integer matrices that are not multiples of each other such that Nul(A) = Nul(B) and Col(A) = Col(B).

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Find integer matrices A, B not multiples of each other such that Nul(A)=Nul(B)andCol(A)=Col(B)?

Step-by-step explanation:

The prime factor of the 144 is 24 x 32. The exponents in the prime factorisation are 4 and 2. Add the number 1 with the exponents and multiply it. (4+1)(2+1) = 5 x 3 = 15.

The probability of selecting the integer 318 is 0

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

Sample space = 1 to 50

The integer 318 is not in the range of integers that the random number generator can select from (1 to 50).

Hence, the required probability of selecting the integer 318 is 0.

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Quadrilateral MNOP is similar to quadrilateral QRST. The measure of side RS is approximately 39.2 units.

If two quadrilaterals are similar, their corresponding sides are in proportion. Therefore, we can set up a proportion between the corresponding sides of quadrilaterals MNOP and QRST as follows:

MN / QR = NO / ST = OP / RS

We are given the lengths of MN, NO, and OP, but we need to find the length of RS. We can solve for RS by rearranging the proportion as follows:

OP / RS = MN / QR

RS = OP / (MN / QR)

We can substitute the given values to get:

RS = 58 / (19 / 13)

Simplifying this expression gives:

RS = 58 * (13 / 19) = 39.241 ≈ 39.2

Therefore, the measure of side RS is approximately 39.2 units.

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____The given question is incomplete, the complete question is given below:

Quadrilateral MNOP is similar to quadrilateral QRST. Find the measure of side RS. Round your answer to the nearest tenth if necessary. Figures are not drawn to scale. QT =58, PM= 19 ON=13.

The coordinates of C are (-6, -3)

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

A = (-9, -5)

B = (6, 5)

m : n = 1 : 4 i.e. 1/5

The coordinate is then calculated as

C = 1/(m + n) * (mx2 + nx1, my2 + ny1)

So, we have

C = 1/5 * (1 * 6 + 4 * -9, 1 * 5 + 4 * -5)

Evaluate

C = (-6, -3)

Hence, the coordinate is (-6, -3)

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Josiah invested $96,000 in an account paying an interest rate of 3.5% compounded continuously. Assuming no deposits or withdrawals are made, the value of the account will reach $153,400 after 9 years.

To calculate this, we can use the formula for the future value of a single sum invested with an inverted interest rate compounded continuously.

Future Value = Present Value × (1 + r)n

Where:

We can solve for n to find out how many years it will take to reach $153,400.

153,400 = 96,000 × (1 + 0.035)n

153,400/96,000 = (1 + 0.035)n

Taking the natural log of both sides and simplifying:

ln(153,400/96,000) = n × ln(1.035)

n = ln(153,400/96,000)/ln(1.035)

n ≈ 8.99

To the nearest year, it will take 9 years for the value of the account to reach $153,400.

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The value of minutes can be converted to hours by dividing the value of minute by 60 so 115000 minutes means 1916.66 hours.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

With the help of our conversion tools, you can convert 115000 Minutes to Days (min to d). Use the direct conversion formula below to convert 115000 min to d.

115000 min = 79.861111111111 d.

Also, you can change 115000 Minutes into other Time (common) units.

We will create an equation to convert 115000 minutes to hours, then utilise the equation to perform the conversion. Since there are 60 minutes in an hour, we can construct our equation as follows:

Hours = Minutes / 60

In the equation above, we may convert 115000 minutes to hours by substituting 115000 minutes, giving the following result:

115000 / 60 = Hours

1916 2/3 hours divided by 115000 minutes is 1916.66667 hours.

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The characteristics of a data set are enumerated by descriptive statistics. You can test a hypothesis or determine whether your data can be applied to a larger population by using inferential statistics.

To summarize a given data set, which may be a sample of a population or a representation of the entire population, brief informational coefficients known as descriptive statistics are used.

The two primary subcategories of descriptive statistics are measures of central tendency and measures of variability (spread). Descriptive statistics are thus used to summarize the data. Descriptive statistics can only ever make claims about the data set from which they were derived, using only the data that you have.

Statistical inference is the process of determining characteristics of an underlying probability distribution through the use of data analysis. Inferential statistical analysis, for instance, infers characteristics of a population by testing hypotheses and producing estimates.

Inferential statistics looks to identify some characteristic or overarching pattern about a large group through the study of a smaller sample size in the hopes that the results will apply to the larger group.

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The required number of dollars in a year per 37 dollars in an hour equals 324,120 dollars.

Number of dollars in one hour is equal to 37 dollars.

Relation between year and hour .

1 year = 12 months

1 month = 31, 30 or 28 days

Total number of days in a year = 365 days

Number of hours in 1 day = 24 hours

Number of hours in 365 days = ( 365 × 24 ) hours

                                                 = 8760 hours

In 1 hour = 37 dollars

⇒ 8760 hours = ( 37 × 8760 ) dollars

⇒ 8760 hours = ( 324,120 ) dollars

⇒ 1year = (  324,120  ) dollars

Therefore, the number of dollars in a year is equal to  324,120 dollars.

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Answer:

Step-by-step explanation:

first step you want round that into decimal

Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We can use trigonometry to solve this problem.

Let's call the horizontal distance from the observatory to the island "x".

Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -

tan(25) = opposite / adjacent

tan(25) = 150 / x

Solving for x, we get -

x = 150 / tan(25)

Using a calculator, we find that -

x ≈ 322 feet

Therefore, the horizontal distance value is 322 feet.

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Answer:

Step-by-step explanation:

Using trigonometric ratios the approximate horizontal distance from the observatory to the island is option A: 322 feet.

What is trigonometric ratio?

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios.

We can use trigonometry to solve this problem.

Let's call the horizontal distance from the observatory to the island "x".

Since we know the opposite side (150 ft) and the angle of depression (25 degrees), we can use the tangent function -

tan(25) = opposite / adjacent

tan(25) = 150 / x

Solving for x, we get -

x = 150 / tan(25)

Using a calculator, we find that -

x ≈ 322 feet

Therefore, the horizontal distance value is 322 feet.

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Answer:

25 / 2

Step-by-step explanation:

12.5% = 125 / 10 ( simplify the fraction with 5 )

= 25 / 2

A long division polynomials calculator is an online tool used to perform polynomial long division for dividing polynomials.

A long division polynomials number cruncher is an internet based device that performs polynomial long division, a strategy used to separate one polynomial by another. This cycle is like long division with numbers, yet rather than partitioning by single-digit numbers, it includes separating by a polynomial of at least one terms. The interaction includes partitioning the most extensive level term of the profit by the most extensive level term of the divisor, then increasing the divisor by the remainder and taking away the outcome from the profit. The subsequent articulation is the rest of the division. The interaction is then continued involving the rest of the new profit, until the level of the rest of not exactly the level of the divisor. An internet based long division polynomials mini-computer robotizes this interaction, permitting clients to enter the profit and divisor polynomials and get the remainder and remaining portion. This can be helpful for understudies and experts in fields like math, physical science, and designing, who need to partition polynomials for computations and critical thinking.

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