find the probability of choosing a letter other than the letter s from a bag that contains the eighteen letters of the name srinivasa ramanujan. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Step-by-step explanation:

The sum of 2 and 2 can be derived using basic arithmetic operations.

Starting with 2, we can add 1 to get 3:

2 + 1 = 3

Then, we can add another 1 to get 4:

3 + 1 = 4

Therefore, the derivation of 2 + 2 is:

2 + 2 = (2 + 1) + 1 = 3 + 1 = 4

Hence, 2 + 2 is equal to 4.

Answer:

4

Step-by-step explanation:

The scale factor used to create the dilated polygon is 4.

What is scaler factor?

Scale factor is a numerical ratio that describes how much a geometric figure has been enlarged or reduced. It is the ratio of the length of a side, diagonal, or any other linear dimension of the new (dilated) figure to the corresponding dimension of the original figure.

The distance between two points can be calculated using the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.[/tex]

To determine the scale factor, we need to compare the distances between corresponding points in the original and dilated polygons. Let's start by finding the distance between points A and B in the original polygon:

[tex]$d_{AB}=\sqrt{(3-1)^2+(-1+1)^2}=\sqrt{4}=2$[/tex]

Now let's find the distance between corresponding points A' and B' in the dilated polygon:

[tex]$d_{A'B'}=\sqrt{(12-4)^2+(-4+4)^2}=\sqrt{64}=8$[/tex]

To find the scale factor, we divide the corresponding distances:

[tex]$scale\ factor=\frac{d_{A'B'}}{d_{AB}}=\frac{8}{2}=4$[/tex]

Therefore, the scale factor used to create the dilated polygon is 4.

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By probability , 3 Apples are left .

What does a probability simple definition entail?

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

                             The probability is a metric for determining how likely an event is to occur. It gauges how likely an event is. The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.

Jhoney ate =  3 apples

           = 2 left

  he eat = ³C₂

              =  3!/(3-2)! 2!

              = 3

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we have found that in the given right triangle with sides 10, 24, and 26, the tangent of the larger acute angle (angle B) is 2.4.

In a right triangle, the tangent of an acute angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Let us label the sides of the right triangle as follows:

The hypotenuse (the longest side) is 26

One of the acute angles (let's call it angle A) has opposite side length of 10

The other acute angle (let's call it angle B) has opposite side length of 24

To find the tangent of the larger acute angle, which is angle B, we use the formula:

tan(B) = opposite / adjacent

In this case, the opposite side of angle B is 24, and the adjacent side is 10. So we have:

tan(B) = 24 / 10 = 2.4

Therefore, the tangent of the larger acute angle (angle B) is 2.4.

This means that if we draw a line that is tangent to the circle with radius 10 centered at the vertex of angle B, the length of that line will be 24. This is a geometric interpretation of the tangent function, where the tangent of an angle is the length of a line tangent to the unit circle at that angle.

In conclusion, we have found that in the given right triangle with sides 10, 24, and 26, the tangent of the larger acute angle (angle B) is 2.4.

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the number of more 4's printed than 8's is 188 - 59 = 129.

We can approach this problem by counting the number of times the digit 4 appears and the number of times the digit 8 appears in the page numbers from 1 to 488.

First, let's count the number of times the digit 4 appears. We can break down the counting into three cases:

The digit 4 appears in the units place (page numbers 4, 14, 24, ..., 484): there are 49 such page numbers (from 4 to 484, incrementing by 10).

The digit 4 appears in the tens place (page numbers 40 to 49, 140 to 149, ..., 440 to 449): there are 50 such page numbers.

The digit 4 appears in the hundreds place (page numbers 400 to 488): there are 89 such page numbers.

Thus, the total number of times the digit 4 appears is 49 + 50 + 89 = 188.

Next, let's count the number of times the digit 8 appears. We can break down the counting into two cases:

The digit 8 appears in the tens place (page numbers 80 to 89, 180 to 189, ..., 480 to 489): there are 50 such page numbers.

The digit 8 appears in the hundreds place (page numbers 800 to 880): there are 9 such page numbers.

Thus, the total number of times the digit 8 appears is 50 + 9 = 59.

Therefore, the number of more 4's printed than 8's is 188 - 59 = 129.

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we will use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the distance across the lake is the hypotenuse, and the given measurements a and b are the other two sides.

Solution:

1. Write the Pythagorean theorem:

c² = a² + b²,

where c is the distance across the lake.
2. Substitute the given measurements:

c² = (2.62)² + (3.51)²
3. Calculate the squares:

c² = 6.8644 + 12.3201
4. Add the squared values:

c² = 19.1845
5. Find the square root of the sum:

c = √19.1845
6. Calculate the distance:

c ≈ 4.38 miles

The distance across the lake is approximately 4.38 miles

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The evaluation of the algebraic expression 8a-1+0.5b when a=1/4 and b=10 is 6.

We are given an expression 8a−1+0.5b8, and we are asked to evaluate it when a = 1/4 and b = 10. Substituting these values, we get:

8(1/4) - 1 + 0.5(10) = 2 - 1 + 5

Simplifying the expression on the right-hand side, we get:

8a−1+0.5b8 = 6

Therefore, when a = 1/4 and b = 10, the value of the expression 8a−1+0.5b8 is 6.

This means that if we substitute the given values for a and b, the resulting expression will have a value of 6. It is important to correctly substitute the values before evaluating the expression to obtain the correct answer.

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

Evaluate 8 a − 1 + 0.5 b 8a−1+0.5b8, a, minus, 1, plus, 0, point, 5, b when a = 1 4 a= 4 1 a, equals, start fraction, 1, divided by, 4, end fraction and b = 10 b=10b, equals, 10.

Answer:

= 58/33

= 1 25/33

Step-by-step explanation:

12/11 - (-2/3) =

= 12/11 + 2/3

= 36/33 + 22/22

= 58/33

= 1 25/33

In approximately 11.41% of years, the rainfall will be between 50 and 70 centimeters in that town.

To solve this problem, we need to find the percentage of years where the rainfall is between 50 and 70 centimeters. We can do this by standardizing the rainfall values and using a standard normal distribution table.

First, we need to standardize the rainfall values of 50 and 70 centimeters using the formula

z = (x - μ) / σ

where

z is the standardized value

x is the rainfall value

μ is the mean

σ is the standard deviation

For x = 50

z = (50 - 95) / 28

z = -1.607

For x = 70

z = (70 - 95) / 28

z = -0.893

Next, we use a standard normal distribution table or calculator to find the area under the curve between these two standardized values. This represents the percentage of years where the rainfall is between 50 and 70 centimeters.

Using a standard normal distribution table, we can find that the area under the curve between z = -1.607 and z = -0.893 is 0.1141. This means that approximately 11.41% of years will have rainfall between 50 and 70 centimeters in this town.

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Step-by-step explanation:

2x + 2y  = 28   <=====given

x * y = 40     <===given .....  re-arrange to :

           y = 40 / x    <===substitute this 'y'  into the first equation

2x + 2 ( 40/x) = 28   <=====solve for x

2x^2 -28x + 80 = 0

x^2 -14x +40 = 0

(x -10)(x-4) = 0                        shows x = 10 or 4    then y = 4 or 10

dimensions    10    and 4   inches

Answer:

4 or 10 inches

Step-by-step explanation:

I added a photo of my solution

Answer:

x= 2

Step-by-step explanation:

² means times the number itself 2 times.

2×2=4

The chance of rolling two 5s and flipping two heads can be calculated by multiplying the odds together because each cube and coin flip is independent. the probability that Kyle wins the prize is [tex]1/144[/tex]

The probability of rolling a 5 on a number cube is 1/6, and the probability of flipping heads on a coin is 1/2.

Since each roll of the cube and flip of the coin is independent, we can find the probability of rolling two 5's and flipping two heads by multiplying the probabilities together:

P(rolling two 5's and flipping two heads) = P(rolling a 5) * P(rolling a 5) * P(flipping heads) * P(flipping heads)

[tex]= (1/6) \times (1/6) \times (1/2) \times (1/2)[/tex]

[tex]= 1/144[/tex]

Therefore, the probability that Kyle wins the prize is ,[tex]1/144[/tex] or approximately  [tex]0.0069[/tex] (rounded to four decimal places).

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The CPA Practice Advisor reports that the mean preparation fee for federal income tax returns was 261. Use this price as the population mean and assume the population standard deviation of preparation fees is 120.

We need to find the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.

We use the central limit theorem that states that, regardless of the shape of the population, the sampling distribution of the sample means approaches a normal distribution with mean μ and standard deviation

σ/√n

where μ is the population mean, σ is the population standard deviation, and n is the sample size.

Therefore, we have:

[tex]\mu = 261\]\\sigma = $120\]\\n = 20\][/tex]

[tex]S.E.= \frac{\sigma}{\sqrt{n}}\\S.E =\frac{\ 120}{\sqrt{20}}\\S.E =26.83[/tex]

The probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is given by:

[tex]P(Z < \frac{X - \mu}{S.E})\][/tex]

where X is the sample mean, μ is the population mean, and S.E is the standard error of the mean.

To calculate the probability, we standardize the distribution of the sample means using the z-score formula, i.e.,

[tex]\[z = \frac{X - \mu}{S.E} = \frac{\50 - \261}{\26.83} = -7.91\][/tex]

Therefore, the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less is zero because the z-score is less than the minimum z-score (i.e., -3.89) that corresponds to the probability of selecting a random sample of 20 tax returns and a standard deviation of the sample preparation fees of 50 or less.

Thus, it is impossible to obtain such a sample.

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The probability that the coin will land on the same side in all three tosses is 1/8.

There are two possible outcomes for each coin flip: heads or tails. Therefore, there are 2 × 2 × 2 = 8 possible outcomes for flipping a coin three times in a row.To find the probability that the coin will land on the same side in all three tosses, we need to count the number of outcomes that satisfy this condition.

There are only two such outcomes: either all three tosses are heads or all three tosses are tails. Therefore, the probability of this happening is 2/8 or 1/4.But we are asked for the probability that the coin will land on the same side in all three tosses, not just one specific side.

Therefore, we need to divide our previous result by 2 (the number of sides of the coin) to get the final answer: 1/4 ÷ 2 = 1/8. The probability that the coin will land on the same side in all three tosses is 1/8.

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The graph at the end of the response provides the dilated figure, which has the same format as the original figure but reduced side lengths as a result of the dilation with a scale factor of less than 1.

To make an opening or hollow structure wider or larger than usual, such as a blood vessel or the pupil of an eye.

The process of dilation entails growing an object's size without changing its shape.

The size of the object may rise or decrease depending on the scale factor.

Using dilation maths, a square with a side of 5 units can be made wider to have a side of 15 units, yet the square retains its original shape.

So, the coordinates of each vertex of the figure are multiplied by the scale factors to create a dilatation in the image.

The vertices for the original figure that was graphed are listed as follows:

I(0,6).

H(3,6).

G(9,0).

F(-6,-9).

E(-6,-6).

The coordinates of the resulting image are presented as follows since the dilation has a scale factor of 1/3, which means that the coordinates are multiplied by 1/3:

I'(0,2).

H'(1,2).

G'(3,0).

F'(-2,-3).

E'(-2,-2).

Therefore, the graph at the end of the response provides the dilated figure, which has the same format as the original figure but reduced side lengths as a result of the dilation with a scale factor of less than 1.

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Correct question:

The figure below is dilated by a factor of centered at the origin. Plot the resulting image. -109 -11 E Click twice to plot a segment. Click a segment to delete it. 4 -5 7 F A -9 10 9 B 4 I d 3 P BI 1 9 H 3 4 6 6 M​

The compound inequality is -7 < y/3 - 2 < 4 and the solution is -15 < y < 18

To write the compound inequality that represents the statement, we can first translate the words into symbols:

The quotient of a number y and 3, less 2: y/3 - 2

Is between -7 and 4: -7 < y/3 - 2 < 4

So the compound inequality that represents the statement is:

-7 < y/3 - 2 < 4

To solve this compound inequality, we can first add 2 to all parts of the inequality:

-7 + 2 < y/3 - 2 + 2 < 4 + 2

Simplifying, we get:

-5 < y/3 < 6

To isolate y/3, we can multiply all parts of the inequality by 3:

-15 < y < 18

Therefore, the solution to the compound inequality is: -15 < y < 18

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A) Jane's share is 12% of X, which is equal to 0.12X.

B) the total cost of the insurance is $20,691.67

C)  the employer's share is $18,208.67.

Total cost is the collective term for the cost of production as a whole, which encompasses both fixed and variable costs. The expense necessary to produce a good is referred to in economics as the total cost. There are two parts that make up the total cost: a set price The expense is what never changes.

Let X be the total cost of Jane's individual health care, then:

A) Jane's share is 12% of X, which is equal to 0.12X.

B) We know that Jane's deduction from each biweekly paycheck is $95.50, so she pays a total of:

$95.50 * 26 = $2,483

This amount is equal to 0.12X, so we can set up an equation:

0.12X = $2,483

Solving for X, we get:

X = $20,691.67

Therefore, the total value of the insurance is $20,691.67.

C) The employer's share is the difference between the total cost of the insurance and Jane's share:

Employer's share = Total cost - Jane's share

Employer's share = $20,691.67 - $2,483

Employer's share = $18,208.67

Therefore, the employer's share is $18,208.67.

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Jane's share of the total cost of her individual health care is $795.83, The total value of the insurance is $795.83 + 0.88x and the employer's share is 0.88x.

What is cost?

In mathematics, cost refers to the amount of resources (such as money, time, effort, or materials) that are required to produce or obtain something.

A) To find Jane's share of the total cost of her individual health care, we can use the information that she contributes 12% of the cost, and that this is a $95.50 deduction from each of her biweekly paychecks.

Let x be the total cost of Jane's individual health care. Then:

12% of x = $95.50

0.12x = $95.50

x = $95.50 / 0.12

x = $795.83

Therefore, Jane's share of the total cost of her individual health care is $795.83.

B) To find the total value of the insurance, we can add up both Jane's share and the employer's share.

If Jane is contributing 12% of the total cost, then the employer is contributing the remaining 88% of the cost. So the employer's share can be calculated as:

88% of x = 0.88x

The total value of the insurance is then:

Total value = Jane's share + Employer's share

Total value = $795.83 + 0.88x

C) To calculate the employer's share, we can use the same information as above. The employer is contributing 88% of the total cost, so:

88% of x = 0.88x

Therefore, the employer's share of the total cost of Jane's individual health care is $0.88x, or approximately $700.33 (if we use the value of x that we found in part A).

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The probability that a person chosen at random has run a red light in the last year can be calculated by taking the number of people who said “yes” to running a red light and dividing it by the total number of people in the group.

For example, if 10 people said “yes” and 20 said “no”, the probability of a person chosen at random running a red light in the last year is 10/30, or 1/3.

The probability of an event happening is calculated using the formula:

Probability = Number of Favorable Outcomes / Total Number of Outcomes

In this case, the favorable outcome is running a red light in the last year, and the total number of outcomes is the total number of people asked.

To calculate the probability, we take the number of people who said “yes” to running a red light in the last year and divide it by the total number of people in the group. In our example, 10/30 = 1/3, so the probability that a person chosen at random has run a red light in the last year is 1/3.

In conclusion, the probability of a person chosen at random having run a red light in the last year is calculated by taking the number of people who responded “yes” and dividing it by the total number of people in the group.

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Answer:

x=8

Step-by-step explanation:

8 x 8 = 64

You can find this answer by using inverse operations.

64/8 = 8

To check your work, you can multiply...

8x8 = 64.

Hope this helps!

The percent decrease in the price of the headphones is 26.32%.

Explanation:

To find the percent change in price, we can use the following formula:

percent change = (new value - old value) / old value * 100%

     
In this case, the old value is the original price of the headphones, which is $95.
   

The new value is the sale price, which is $70. Plugging these values into the formula, we get:percent change = (70 - 95) / 95 * 100%

percent change = -25 / 95 * 100%

percent change = -0.2632 * 100%

percent change = -26.32%

   
The negative sign indicates that the price has decreased, and the magnitude of the percent change is 26.32%, which means that the sale price is 26.32% lower than the original price.

The width of the rectangle is 5 meters.

To find the width of the rectangle, let's use the formula for the area of a rectangle, which is:

Area = length x width

We know that the area of the rectangle is 65 square meters. We also know that the length of the rectangle is 8 meters more than the width. Let's call the width "w". Then, the length can be expressed as:

length = w + 8

Substituting this expression for length into the formula for the area, we get:

65 = (w + 8) x w

Simplifying and solving for w, we get:

w² + 8w - 65 = 0

Using the quadratic formula, we get:

w = (-8 ± √(8² + 4(1)(65))) / (2(1))

w = (-8 ± √(324)) / 2

w = (-8 ± 18) / 2

We take the positive value for w since the width cannot be negative:

w = (-8 + 18) / 2

w = 5

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A horizontal curve is to be designed with a 2000 feet radius. The curve has a tangent length of 400 feet and its pi is located at station 103+00. Determine the stationing of the PT.

A horizontal curve is a curve that is used to provide a transition between two tangent sections of a roadway. To connect two tangent road sections, horizontal curves are used. Horizontal curves are defined by a radius and a degree of curvature. The curve's radius is given as 2000 feet. The tangent length is 400 feet.

The pi is located at station 103+00.

To determine the stationing of the PT, we must first understand what the "pi" means. PC or point of curvature, PT or point of tangency, and PI or point of intersection are the three primary geometric features of a horizontal curve. The point of intersection (PI) is the point at which the back tangent and forward tangent of the curve meet. It is an important point since it signifies the location of the true beginning and end of the curve. To calculate the PT station, we must first determine the length of the curve's arc. The formula for determining the length of the arc is as follows:

L = 2πR (D/360)Where:

L = length of the arc in feet.

R = the radius of the curve in feet.

D = the degree of curvature in degrees.

PI (103+00) indicates that the beginning of the curve is located 103 chains (a chain is equal to 100 feet) away from the road's reference point. This indicates that the beginning of the curve is located 10300 feet from the road's reference point. Now we need to calculate the degree of curvature

:Degree of curvature = 5729.58 / R= 5729.58 / 2000= 2.8648 degrees. Therefore, the arc length is:

L = 2πR (D/360)= 2π2000 (2.8648/360)= 301.6 feet.

The length of the curve's chord is equal to the length of the tangent, which is 400 feet. As a result, the length of the curve's long chord is: Long chord length = 2R sin (D/2)= 2 * 2000 * sin(2.8648/2)= 152.2 feet To determine the stationing of the PT, we can use the following formula: PT stationing = PI stationing + Length of curve's long chord= 10300 + 152.2= 10452.2Therefore, the stationing of the PT is 10452+2.

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Therefore, the total number of sets of four marbles, including exactly two green marbles, is 720.

The given bag contains a total of [tex](2+4+1+6+5)=18[/tex] marbles.

There are two possibilities of selecting two green marbles and the other two marbles in a set, as shown below;GG -- NN (No Green Marbles)GG -- RR (No Green Marbles)GG -- YY (No Green Marbles)GG -- OO (No Green Marbles)GG -- GL (Lavender)GG -- RG (Red)GG -- OG (Orange)

The first two options have no green marbles; thus, they are eliminated. We can select non-green marbles in C(16,2) = 120 ways, then multiply by C(4,2) = 6 to choose two green marbles out of four.So, the total number of such sets is

[tex]120 × 6 = <<120*6=720>>720.[/tex]

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Answer:

Step-by-step explanation:

Circle centre: (4,7)

Radius: 3

Equation is:

  [tex](x-h)^2+(y-k)^2=r^2[/tex]   (where (h,k) is center, r is radius)

  [tex](x-4)^2+(y-7)^2=3^2[/tex]

  [tex](x-4)^2+(y-7)^2=9[/tex]     (This is the general standard form )

in expanded form,

  [tex](x^2-8x+16)+(y^2-14y+49)=9[/tex]

  [tex]x^2+y^2-8x-14y+56=0[/tex]

Note: Unless stated either form is an acceptable answer.

Answer:

Step-by-step explanation:

It takes 3.1 hour  for half of the drug dose to be left in the body.

In the metric system the unit measurement of mass is known as mg .

mg is equal to one thousandth of a gram ie.1/1000. The unit is often used in medical field for weighing out small quantities of  ingredients.

prons

it is precise and it can be used to measure small quantities of items.

It is easy to convert mg to other units of measure.

cons:

It is a very small unit of measurement, it is difficult to measure the values accurately.

It is also a very commonly used unit of measurement, it get easily  confuse with other units

10*1/2=10(0.8)^t

0.8^t=1/2

t=log0.8*1/2

t=3.1

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6.81 is the Ph of a neutral aqueous solution.

To calculate the pH of a neutral aqueous solution at 37°C with a KW of 2.4×10⁻¹⁴, follow these steps:

1. Identify that in a neutral aqueous solution, the concentrations of hydrogen ions (H⁺) and hydroxide ions (OH⁻) are equal. Therefore, [H⁺] = [OH⁻].

2. Use the KW expression, which is the product of [H⁺] and [OH⁻] concentrations. In this case, KW = 2.4×10⁻¹⁴.

3. Since [H⁺] = [OH⁻], you can rewrite the KW expression as KW = [H⁺]². Now, solve for [H⁺] by taking the square root of KW: [H⁺] = sqrt(KW) = sqrt(2.4×10⁻¹⁴).

4. Calculate the square root: [H⁺] ≈ 1.55×10⁻⁷ M.

5. Use the pH formula: pH = -log[H⁺]. Plug in the [H⁺] value: pH = -log(1.55×10⁻⁷).

6. Calculate the pH: pH ≈ 6.81.

The pH of a neutral aqueous solution at 37°C with a KW of 2.4×10⁻¹⁴ is approximately 6.81.

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we can expect that approximately 815 employees owned a petrol car in 2019 (rounded to the nearest integer).

We can model the number of employees owning petrol cars in the years 2010 and 2013 using the exponential decay formula:

[tex]$$N(t) = N_0 e^{-kt}$$[/tex]

where N(t) is the number of employees owning petrol cars at time t, [tex]$N_0$[/tex] is the initial number of employees owning petrol cars (in 2010), k is the decay constant, and t is the time elapsed since 2010 (in years).

We can use the given information to find the value of k:

In 2013 (3 years after 2010), the number of employees owning petrol cars decreased from 2187 to 1536:

[tex]$$1536 = 2187 e^{-3k}$$[/tex]

Dividing both sides by 2187 gives:

[tex]$$e^{-3k} = \frac{1536}{2187}$$[/tex]

Taking the natural logarithm of both sides gives:

[tex]$$-3k = \ln\left(\frac{1536}{2187}\right)$$[/tex]

Solving for k gives:

[tex]$k = -\frac{1}{3} \ln\left(\frac{1536}{2187}\right) \approx 0.1565$$[/tex]

Now we can use the exponential decay formula to find the number of employees owning petrol cars in 2019 (9 years after 2010):

[tex]$$N(9) = 2187 e^{-0.1565 \cdot 9} \approx 815$$[/tex]

Therefore, we can expect that approximately 815 employees owned a petrol car in 2019 (rounded to the nearest integer).

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Since the range of observed values is 1, which is less than two standard deviations away from 10, the observed value is not significantly different from the expected value and thus the number of girls in 10 births is not significantly low.

Standard deviation is a measure of how spread out numbers are in a data set. It is calculated by taking the square root of the variance. Variance is the average of the squared differences from the mean. Standard deviation provides an indication of how much variation there is in the data set, and is often used in statistical analysis.

The range rule of thumb is a statistical method used to determine whether a given phenomenon is significantly different from an expected value. It states that if the range of observed values is greater than two standard deviations of the expected value, then the observed values are significantly different from the expected value.

In this particular case, the expected value is 10 girls in 10 births, and the observed value is 1 girl in 10 births. Since the range of observed values is 1, which is less than two standard deviations away from 10, the observed value is not significantly different from the expected value and thus the number of girls in 10 births is not significantly low.

The range rule of thumb is one way to determine whether observed values are significantly different from expected values, but there are other methods available as well.

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