You randomly select 500 students and observe that 85 of them smoke. Estimate the probability that a randomly selected student smokes.
a.) .27
b.) .50, since there are two possible outcomes for every student surveyed (smoke, don't smoke)
c.) 0.17
d.) 1.2

We used the chain rule and derivative of an inverse tangent function to find [tex]\frac{dy}{dx} &= \frac{d}{dx} \left[\tan^{-1}\left(\frac{2x}{1+x^2}\right)\right][/tex] and got [tex]$\frac{dy}{dx} = 2\left(\frac{1}{1+4x^2}\right)\left(\frac{1}{1+x^2}\right)$[/tex].

To find [tex]\frac{dy}{dx}[/tex] for [tex]$y = \tan^{-1}\left(\frac{2x}{1+x^2}\right)$[/tex], we can use the chain rule and the derivative of the inverse tangent function:

[tex]$\frac{dy}{dx} = \frac{d}{dx}\left[\tan^{-1}\left(\frac{2x}{1+x^2}\right)\right]$[/tex]

[tex]$= \frac{1}{\left(\frac{2x}{1+x^2}\right)^2+1} \cdot \frac{d}{dx}\left[\frac{2x}{1+x^2}\right] \quad $[/tex] [chain rule]

[tex]$= \frac{1}{\left(\frac{2x}{1+x^2}\right)^2+1} \cdot \frac{(1+x^2)\cdot2 - 2x\cdot2x}{(1+x^2)^2} \quad[/tex] [quotient rule]

[tex]$= \frac{2}{1+4x^2} \cdot \frac{1}{1+x^2}$[/tex]

Therefore, [tex]\frac{dy}{dx} = \frac{2}{1+4x^2} \cdot \frac{1}{1+x^2}$[/tex].

(a) To find [tex]\frac{dy}{dx} = (e^x\sqrt{2x})^4$[/tex], we can use the chain rule and the power rule:

[tex]\frac{dy}{dx} = \frac{d}{dx}\left[(e^x\sqrt{2x})^4\right][/tex]

[tex]= 4(e^x\sqrt{2x})^3 \frac{d}{dx}[e^x\sqrt{2x}][/tex]

[tex]= 4(e^x\sqrt{2x})^3 \left(e^x\frac{1}{2}(2x)^{-1/2} + e^x\sqrt{2x}\frac{1}{2}(2x)^{-3/2}\right) \quad[/tex] [chain rule]

[tex]= 2(e^x\sqrt{2x})^2\frac{1+\sqrt{2x}}{x}[/tex]

Therefore, dy/dx = [tex]= 2(e^x\sqrt{2x})^2\frac{1+\sqrt{2x}}{x}[/tex]

(b) To find [tex]\frac{dy}{dx} \quad[/tex] for [tex]\quad e^{xy} + \ln(xy) = 0[/tex] we can use implicit differentiation:

[tex]\quad e^{xy} + \ln(xy) = 0[/tex]

Taking the derivative of both sides with respect to x, we get:

[tex](e^{xy})(y + x\frac{dy}{dx}) + \frac{1}{xy}(xy' + y) = 0[/tex]

Simplifying and solving for [tex]\frac{dy}{dx}[/tex], we get:

[tex]\frac{dy}{dx} = \frac{-e^{xy} - \frac{y}{x^2y+1}}{xe^{xy}}[/tex]

Therefore, [tex]\frac{dy}{dx} = \frac{-e^{xy} - \frac{y}{x^2y+1}}{xe^{xy}}[/tex].

To find the indefinite integral of [tex]e^x sin2x[/tex], we can use integration by parts:

Let u = sin2x and [tex]\frac{dv}{dx} = e^x[/tex]. Then du/dx = 2cos2x and v = e^x.

Using the formula for integration by parts, we get:

[tex]\int e^x \sin 2x \ dx = e^x \sin 2x - \int 2e^x \cos 2x \ dx[/tex]

We can now integrate by parts again, letting u = cos2x and dv/dx = e^x. Then du/dx = -2sin2x and v = e^x.

Using the formula again, we get:

[tex]\int e^x \sin 2x \ dx = e^x \sin 2x - 2e^x \cos 2x + 4\int e^x \sin 2x \ dx[/tex]

Rearranging terms and dividing by 5, we get:

[tex]\int e^x \sin 2x \ dx = \frac{e^x}{5} (\sin 2x - 2\cos 2x) + C[/tex]

Therefore, the indefinite integral of e^x sin2x is [tex]\frac{e^x}{5} (\sin 2x - 2\cos 2x) + C[/tex]

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Answer: x ≅ 0.5, and x ≅ −3.7

Step-by-step explanation:

[tex]4x^2 + 11x - 19 = -2x - 12[/tex]

[tex]4x^2 + 13x - 7 = 0[/tex]

Now use the quadratic formula with a = 4, b = 13, and c = -7

(if you dont know what that is, you should probably search it and understand/memorize).

Using the formula, we get two values:

x ≅ 0.5, and x ≅ −3.7

The simplified expressions are:

In order to solve the algebraic expressions:

a. 3x(x²+2x-6)

Distribute 3x across the terms inside the parenthesis:

= 3x^3 + 6x^2 - 18x

b, -5x (2x² - 4x - 8)

In order to solve this too, we would do the same thing as the first one and distribute -5x

= -10x^3 + 20x^2 + 40x

c.  -2x(3x² + 7x + 1)

We also distribute -2x

This would give us the expression which is

= -6x^3 - 14x^2 - 2x

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The measure of ∠DBA is 96 degrees.

The angle between a tangent and a chord is equal to the angle in the alternate segment.

An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.

Therefore, the measure of ∠DBA can be defined as follows:

Hence,

∠DBA = 1 / 2 (192)

∠DBA = 96 degrees

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Suppose A and B are dependent events. If P(A|B) = 0.25 and P(B) = 0.6, then  P(AuB) = 0.2

The probability of an event is described as a number that indicates how likely the event is to occur which is usually  expressed as a number in the range from 0 and 1, or preferably using percentage notation ranging  from 0% to 100%.

The relationship between two dependent events is expressed in the following equation below according to the rules of probability,

P(A|B) = P(A∩B) / P(B)

we then substitute ,

0.25 = P(A∩B) / 0.8

P(A∩B)  = 0.2

In conclusion, If P(A|B) = 0.25 and P(B) = 0.6, then  P(AuB) = 0.2

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Answer: Surface Area = 7 m * 8.2 m = 57.4 m2

Step-by-step explanation:

The integer which represents the location of the man when he is moved down to look at the coral is -37.

Given that,

A man went scuba diving.

He dove down 12 feet initially.

The he spotted an interesting coral formation and dove down another 25 feet to inspect it.

So from the top, he is at a distance of 12 feet + 25 feet = 37 feet down.

Since it is down, the integer represented here is -37 feet.

Hence the required integer value is -37.

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At the value of x = 3, functions f (x) is equal to g (x).

We have to given that;

Functions are,

f (x) = 2³x

g (x) = 6x + 6

Now, We can equate the functions we get;

2³x = 6x + 6

8x = 6x + 6

8x - 6x = 6

2x = 6

x = 3

Thus, At the value of x = 3, functions f (x) is equal to g (x).

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The slope of the line is 4/5.

Option C is the correct answer.

We have,

The slope of the line that passes through the points (3, -1) and (-2, -5) can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the coordinates, we get:

slope = (-5 - (-1)) / (-2 - 3) = -4 / (-5) = 4/5

Therefore,

The slope of the line is 4/5.

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The events "model YZ-99 is chosen" and "model XB-50 is chosen", these would be mutually exclusive events, because a bike cannot be both models at the same time.

a. To find the probability that a mountain bike is brown using the relative frequency assessment method, we need to divide the number of brown mountain bikes by the total number of mountain bikes:

Total number of brown mountain bikes = 105 + 205 = 310

Total number of mountain bikes = 302 + 105 + 200 + 40 + 205 + 130 = 982

Therefore, the probability that a mountain bike is brown is:

P(brown) = 310/982 ≈ 0.316

b. To find the probability that the mountain bike is a YZ-99, we need to divide the total number of YZ-99 bikes by the total number of mountain bikes:

Total number of YZ-99 bikes = 40 + 205 + 130 = 375

Therefore, the probability that the mountain bike is a YZ-99 is:

P(YZ-99) = 375/982 ≈ 0.382

c. To find the joint probability that a randomly selected mountain bike is a YZ-99 and brown, we need to find the number of YZ-99 bikes that are also brown, and divide by the total number of mountain bikes:

Number of YZ-99 bikes that are brown = 205

Total number of mountain bikes = 982

Therefore, the joint probability that a randomly selected mountain bike is a YZ-99 and brown is:

P(YZ-99 and brown) = 205/982 ≈ 0.209

d. Two events are mutually exclusive if they cannot occur at the same time. In this case, the events "model YZ-99 is chosen" and "a white product is chosen" are not mutually exclusive, because there are white YZ-99 bikes. Therefore, it is possible for both events to occur at the same time.

However, if the question was about the events "model YZ-99 is chosen" and "model XB-50 is chosen", these would be mutually exclusive events, because a bike cannot be both models at the same time.

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This is because there are mountain bikes that are both YZ-99 and white, so it is possible to choose a mountain bike that belongs to both events at the same time.

a. Based on the relative frequency assessment method, the probability that a mountain bike is brown is:

Total number of brown bikes / Total number of bikes

= (105 + 205) / (302 + 105 + 200 + 40 + 205 + 130)

= 310 / 982

= 0.3156 (rounded to 4 decimal places)

So the probability that a mountain bike is brown is 0.3156.

b. The probability that the mountain bike is a YZ-99 is:

Total number of YZ-99 bikes / Total number of bikes

= (40 + 205 + 130) / (302 + 105 + 200 + 40 + 205 + 130)

= 375 / 982

= 0.3819 (rounded to 4 decimal places)

So the probability that the mountain bike is a YZ-99 is 0.3819.

c. The joint probability that a randomly selected mountain bike is a YZ-99 and brown is:

Number of brown YZ-99 bikes / Total number of bikes

= 205 / 982

= 0.2088 (rounded to 4 decimal places)

So the joint probability that a randomly selected mountain bike is a YZ-99 and brown is 0.2088.

d. The events "model YZ-99 is chosen" and "a white product is chosen" are not mutually exclusive. This is because there are mountain bikes that are both YZ-99 and white, so it is possible to choose a mountain bike that belongs to both events at the same time.

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Answer:

67.6 grams

Step-by-step explanation:

First, find the volume of the cylindrical container which should provide the volume of water in the sample

Volume, V,  of a cylinder is given by the formula

[tex]V = \pi r^2h[/tex]

where,
r = radius of the cylinder
h = height of the cylinder

Given r = 8 cm and h = 11.6 cm. the volume of the container used by Parker
V = π · 8² · 11.6

   = 2332.31838 cubic centimeters

There are 0.029 grams of trace element for every cubic centimeter of water

Therefore the amount of trace element in 2332.31838 cc of water
= 2332.31838 x 0.029
= 67.63723302 grams'

Rounded to the nearest tenth that would be 67.6 grams

Answer:

Step-by-step explanation:

2332.31838 x 0.029

= 67.63723302 grams'

there the asnwer

We fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean number of days before visible results begin to show is different between the three types of facial creams.

c. We fail to reject the null hypothesis and conclude that there is insufficient evidence at a 0.025 level of significance to support the claim that the mean number of days before visible results begin to show is different between the three types of facial creams.

To test the hypothesis, we use a one-way ANOVA test since we have three independent samples. The null hypothesis is that there is no difference in the mean number of days for the three creams, and the alternative hypothesis is that at least one of the means is different. We can perform the ANOVA test and obtain an F-statistic and p-value. If the p-value is less than our significance level of 0.025, we reject the null hypothesis.

Using statistical software or a calculator, we obtain an F-statistic of 1.52 and a p-value of 0.249. Since the p-value is greater than 0.025, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean number of days before visible results begin to show is different between the three types of facial creams.

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Suppose P, Q, and R are statements, P + (QR) and (P + Q) + R are logically equivalent.

To determine if P + (QR) and (P + Q) + R are logically equivalent, we can use a truth table.

First, we need to define the truth values for P, Q, and R. Let's say P is true, Q is false, and R is true.

Using these truth values, we can evaluate both statements:

P + (QR) = true + (false true) = true
(P + Q) + R = (true false) + true = true

Since both statements have the same truth value with these truth values for P, Q, and R, we can say that P + (QR) and (P + Q) + R are logically equivalent.

We can also prove this algebraically:

P + (QR) = (P + 0) + (0Q + R) = (P + (Q + 0)) + R = (P + Q) + R

Therefore, P + (QR) and (P + Q) + R are logically equivalent.

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We have proven that:

cost = Jo - 2J2 +2J4 – = .......

[infinity]

= Jo(x) + Σ (-1)^n j2n (x).

n=1

To prove this identity, we first start with the formula for the exponential function:

e^ix = cos(x) + i*sin(x)

where i is the imaginary unit.

Now, we can rewrite the right-hand side of the desired identity using this formula:

Jo(x) + Σ (-1)^n j2n (x)

= Jo(x) + Σ (-1)^n [i^nJn(x) - i^nYn(x)] (using the Bessel function identity j_n(x) = cos(x)J_n(x) - sin(x)Y_n(x))

= Jo(x) + Σ (-i)^nJn(x) + Σ i^nYn(x)

= Jo(x) + Σ (-i)^nJn(x) + Σ (-i)^{n+1}Jn(x) (using the Bessel function identity Y_n(x) = (J_n(x)cos(npi) - J_{-n}(x))/sin(npi))

= Jo(x) + 2Σ (-i)^nJn(x)

= Jo(x) + 2Σ (-1)^n*J2n(x) (since Jn(x) is real for all n)

Therefore, we have proven that:

cost = Jo - 2J2 +2J4 – = .......

[infinity]

= Jo(x) + Σ (-1)^n j2n (x).

n=1

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Answer:

x = 9

Step-by-step explanation:

Ratios!! Since both triangles are in the same triangle, they are proportinate in size. from there, we can match the sides of the small triange to the sides of the large.

[tex] \frac{4}{10} = \frac{6}{6 + x} [/tex]

Then, you can cross multiply and solve the equation algebraicly for x.

4(6+x) = 60

24+4x = 60

4x = 36

x = 9

The perimeter of the L shape is: AB + BC + CD + AC = x + x + x √2 + x = 2x + x √2

To find the perimeter of the L shape, we need to add up the lengths of all the sides.

Starting from the top left corner, we can label the four vertices of the L shape as A, B, C, and D, as shown in the diagram below.

The length of side AB is simply x, and the length of side BC is also x.

To find the length of side AC, we can use the Pythagorean theorem. Since triangle ABC is a right triangle, we have:

[tex]AC^2 = AB^2 + BC^2[/tex]

[tex]AC^2 = x^2 + x^2\\AC^2 = 2x^2\\\\AC = sqrt(2x^2) = x sqrt(2)\\\\[/tex]

Finally, to find the length of side CD, we can use the fact that it is parallel to AB and has the same length as BC, which is x.

Therefore, the perimeter of the L shape is:

AB + BC + CD + AC = x + x + x √2 + x = 2x + x √2

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What is an expression in terms of x for the greatest perimeter for a shape made of L regular hexagons?

The type of association you are referring to is called a spurious correlation. In a spurious correlation, there is a relationship between two variables, but the relationship is actually caused by a third variable, also known as a confounding variable. This can lead to misleading conclusions if the third variable is not taken into account.

The type of association that occurs when there is a relationship between two variables, but the relationship is caused by a third variable is called a spurious association or a confounding variable. In this case, the relationship between the two variables is not a direct causal relationship, but is instead influenced by the third variable. It is important to identify and control for confounding variables in order to accurately interpret the relationship between the two variables of interest.

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Answer: 3/40

Step-by-step explanation:

To change 7 1/2% to fraction percent

multiply 7x2  then add 1

=15/2%  but this is still a percent,  in order to change to a decimal we still need to divide by 100

=[tex]\frac{15}{2} / 100[/tex]   rules for dividing is Keep the first, change the sign, flip the second

=[tex]\frac{15}{2} *\frac{1}{100}[/tex]          reduce by dividing 15 by 5 and 100 by 5

=[tex]\frac{3}{2} *\frac{1}{20}[/tex]             that is all you can reduce so multiply across

=[tex]\frac{3}{40}[/tex]                  since we reduced earlier this is lowest term

Jim prepared a few pancakes. He used 9 cups of milk for every 5 cups of flour. Jim's pancakes have a flour-to-milk ratio of 5:9.

To see why, let's break down what this ratio means. The colon in the ratio notation indicates a comparison between two quantities, in this case, flour and milk. The first number before the colon (5) represents the amount of flour, while the second number after the colon (9) represents the amount of milk. So the ratio 5:9 tells us that for every 5 cups of flour Jim used, he added 9 cups of milk.

We can also express this ratio as a fraction, by dividing the amount of flour by the amount of milk. Using Jim's recipe, this would be:

5 cups of flour / 9 cups of milk

Simplifying this fraction by dividing both the numerator and denominator by 5 gives:

1 cup of flour / (9/5) cups of milk

Multiplying the denominator by 5/5 to get a common denominator gives:

1 cup of flour / 45/5 cups of milk

Simplifying again by dividing both the numerator and denominator by 5 gives:

1/9 cup of flour / 1 cup of milk

So we can see that the ratio of flour to milk in Jim's pancakes is indeed 5:9, or equivalently 1/9 cup of flour to 1 cup of milk.

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The equation would have three roots.

The highest power term in a cubic equation is a variable raised to the third power, making it a polynomial equation of degree three. A cubic equation's general form is as follows:

Ax3 + Bx2 + Cx+ D = 0

There can be one, two, or three real roots in a cubic equation. Complex roots, which come in pairs called complex conjugates, are possible for cubic equations. The equation still has three roots in this instance, although they could not be true roots.

The roots of the equation are;

x1 = -2.19682

x2 = 0.14684

x3 = 1.54998

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The area of a parallelogram with the following vectors: v1=[1,-2,0], v2=[2,8,-2] is determined to be 20.

A function is a block of code that performs a specific task. It takes in some input, called arguments, and produces an output. In this case, we want to write a function that calculates the area of a parallelogram given two adjacent vectors starting from the origin.

To do this, we first need to calculate the cross-product of the two vectors. The cross product of two vectors gives us a new vector that is perpendicular to both of them. The magnitude of this vector is equal to the area of the parallelogram formed by the two original vectors.

Here is the code for the parallelogram function:

```
function area = parallelogram(v1,v2)
   cross_prod = cross(v1,v2);  % calculate cross product of v1 and v2
   area = norm(cross_prod);  % calculate magnitude of cross product
end
```

In this function, we take in two arguments, v1 and v2, which are the two adjacent vectors. We then use the cross() function to calculate the cross product of these two vectors. Finally, we use the norm() function to calculate the magnitude of the resulting vector, which is equal to the area of the parallelogram.

To use this function to calculate the area of the parallelogram formed by the vectors v1=[1,-2,0] and v2=[2,8,-2], we simply call the function with these vectors as arguments:

```
v1 = [1,-2,0];
v2 = [2,8,-2];
area = parallelogram(v1,v2);
disp(area);
```

This will output the area of the parallelogram, which is 20.

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There is a data set with data values 18, 16, _, 9, 12, 23. If mean of data set is 15, then the misssing number is equals to the twelve.

Mean means the average of a data set. It is calculated by adding all numbers together and then dividing the resultant sum by the number of numbers, i.e, count of numbers. It is denoted by

[tex] \bar X .[/tex] Mathematcally formula,

[tex]\bar X = \frac{\sum X_n}{n }[/tex]

Where, Xₙ --> data values or numbers

n --> count of values

We have a data set with data values : 18, 16, _, 9, 12, 23. Mean of this data set = 15

We have to determine the missing number. Let the missing number be x. The sum of numbers = 18 + 16 + x + 9 + 12 + 23 = 78 + x

Count of values = 6

Using above mean formula, [tex] 15 = \frac{ 78+ x}{6}[/tex]

=> 90 = 78 + x

=> x = 90 - 78

=> x = 12

So, required value is 12.

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For a piece of string art created by 16 evenly spaced nails around the circumference of a circle. The measure of angle BXC is equals to the 90°.

We have a piece of string art is made by placing 16 evenly spaced nails around the circumference of a circle. See the above figure. We have to determine the measure of angle BXC. Now, using the inscribed angle theorem , the measure of angle BXC, [tex] m\angle BXC = \frac{ 1}{2} ( m \hat {AD} + m \hat {BC}) [/tex]

Measure of AD = [tex] 2(\frac{ 1}{16})360°[/tex] = 45°

The measure of BC = [tex] 6(\frac{ 1}{16} )360°[/tex]

= 135°

Now, Using the above formula the measure of angle BXC [tex] = \frac{ 1}{2} ( m \hat {AD} + m \hat {BC})[/tex]

[tex]= \frac{ 1}{2} ( 45° + 135°)[/tex]

= 90°

Hence, required value is 90°.

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Complete question:

The above figure complete the question.

28. A piece of string art is made by placing 16 evenly spaced nails around the circumference

of a circle. A piece of string is wound from A to B to C to D. What is measure of angle BXC.

The weighted mean for Joe's milk purchases for the week is $2.05 per gallon.

To calculate the weighted mean, you need to multiply each quantity by its corresponding weight, sum up the products, and divide by the total weight. In this case, the quantity represents the number of gallons of milk purchased, and the weight represents the cost per gallon.

Using the given data, the total weight is calculated by summing up the quantities for each day, which is 10 + 5 + 15 + 20 + 8 = 58 gallons. The products of the quantities and weights for each day are as follows:

Monday - 10 * 3.00 = 30.00
Tuesday - 5 * 4.00 = 20.00
Wednesday - 15 * 1.50 = 22.50
Thursday - 20 * 1.25 = 25.00
Friday - 8 * 3.50 = 28.00

The sum of these products is 30.00 + 20.00 + 22.50 + 25.00 + 28.00 = 125.50. Dividing this by the total weight of 58 gallons gives a weighted mean of 125.50 / 58 = $2.05 per gallon.

Therefore, the weighted mean for Joe's milk purchases for the week is $2.05 per gallon, which takes into account both the quantity and cost of milk purchased each day.

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The value of the cos z is 12/13.

We have,

Perpendicular = 36 unit

Hypotenuse = 39

Base = 15

Using Trigonometry

cos Z = YZ / XZ

cos Z = 36 / 39

cos Z = 12 / 13

Thus, the value of cos Z is 12/13.

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The compute limit value of

[tex]lim_{n→\infty} \frac{6a_n b_n}{ 4 a_n - 3 b_n}[/tex] where, [tex]lim_{n → \infty} a_n [/tex], [tex]lim_{n → \infty} b_n = - 2[/tex] is equal to the [tex] \frac{ - 12}{5} [/tex]. So, option(3) is correct choice for answer.

The limit of a sequence is a numeric value that occur when a sequence approaches as the number of terms goes to infinity. This value depends on the sequence.

We have nᵗʰ terms of two sequence aₙ and bₙ. The limit of sequence aₙ is

[tex]lim_{n → \infty} a_n = 6 [/tex] and for bₙ, [tex]lim_{n→\infty} b_n= -2 [/tex]. We have to determine the limit value for the following: [tex]lim_{n→\infty} \frac{6a_n b_n}{ 4 a_n - 3 b_n}[/tex]

Solving the above expression step by step, [tex] = \frac{ 6 \: lim_{n → \infty} a_n .lim_{n → \infty}b_n }{4 \: lim_{n → \infty} a_n - 3 \: lim_{n → \infty} b_n } \\ [/tex]

Using the above values in formula,

[tex]= \frac{ 6 ×6 × -2}{4 ×6 \: - \: 3 ×- 2}[/tex]

[tex]= \frac{ -72 }{30} [/tex]

[tex]= \frac{ -12 }{5} [/tex]

Hence, required value is [tex]= \frac{ -12 }{5} [/tex].

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Complete question:

Compute the value, [tex]lim_{n→\infty} \frac{6a_n b_n}{ 4 a_n - 3 b_n}[/tex]

where [tex]lim_{n -> \infty} a_n = 6 [/tex]

[tex]lim_{n → \infty} b_n = - 2 [/tex]

1) Limit = -37/15

2) limit = 12/5

3) limit = - 12/5

4) limit does not exist

5) limit = 37/15

The original size of the bottle was 13.5 ounces in the given case

Let x be the original size of the bottle in ounces.

In the context of this problem, "original size" refers to the size of the bottle of hand soap before the manufacturer reduced its size

According to the problem, the new size of the bottle is 20% less than the original size, so we can set up the equation:

x - 0.2x = 10.8

Simplifying the left side:

0.8x = 10.8

Dividing both sides by 0.8:

x = 13.5

Therefore, the original size of the bottle was 13.5 ounces.

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Answer:

11668

2+2 = 4

+2*6*6*6*3*3*3

= 11668

Step-by-step explanation:

Answer:

Please mark me the brainliest.

Step-by-step explanation:

11668, trust me i used the calculator

The correct answer is option B: "Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe when the boat is loaded with 16 passengers."

a) Using the given mean and standard deviation, we can standardize the weight of the passengers to find the z-score:

z = (x - μ) / σ

z = (178.2 - 140) / 39.2

z = 0.9719

Using a standard normal distribution table or calculator, we can find the probability of a z-score greater than 0.9719:

P(z > 0.9719) = 1 - P(z <= 0.9719) = 1 - 0.8349 = 0.1651

So the probability that the boat is overloaded because the mean weight of the 70 passengers is greater than 140 lb is 0.1651.

b) The new load limit is 2,736 lb, which means the average weight per passenger should be no more than 2736/16 = 171 lb. We can standardize the weight of the passengers again:

z = (171 - 178.2) / (39.2 / sqrt(16))

z = -2.3155

Using a standard normal distribution table or calculator, we can find the probability of a z-score less than -2.3155:

P(z < -2.3155) = 0.0104

So the probability that the boat is overloaded because the mean weight of the 16 passengers is greater than 171 lb is 0.0104.

Since the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe when the boat is loaded with 16 passengers. Therefore, the correct answer is option B: "Because the probability of overloading is lower with the new ratings than with the old ratings, the new ratings appear to be safe when the boat is loaded with 16 passengers."

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the findings of the study highlight the importance of maintaining a sterile environment in medical facilities and the need to take measures to prevent the spread of bacteria and other microorganisms.

It is important for medical personnel to maintain a sterile environment to prevent the spread of bacteria and other microorganisms. The findings of the research suggest that neckties worn by physicians, physician assistants, and medical students may harbor microorganisms that can cause illness.

The fact that 47.6% of the neckties tested positive for microorganisms is concerning, as it suggests that there is a significant risk of contamination. However, it is important to note that the study only sampled neckties at one hospital, so it is unclear if the findings can be generalized to other hospitals or medical facilities.

It is also worth noting that only one of the 10 ties worn by security guards tested positive for microorganisms. This suggests that there may be differences in the level of contamination between different types of clothing or between different groups of people.

Overall, the findings of the study highlight the importance of maintaining a sterile environment in medical facilities and the need to take measures to prevent the spread of bacteria and other microorganisms. This may include implementing dress codes that require medical personnel to avoid wearing neckties or other clothing items that cancan harbor bacteria, as well as ensuring that proper sterilization procedures are followed.

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