(1/6)30x+(1/6)24-(1/7)63-(1/7)7x

Answer:

y ≈ 13,9

Step-by-step explanation:

Use trigonometry:

[tex] \tan(60°) = \frac{y}{8} [/tex]

Cross-multiply to find y:

[tex]y = 8 \times \tan(60°) = 8 \times \sqrt{3} = 8 \sqrt{3} ≈13.9[/tex]

Answer:

y ≈ 13.9

Step-by-step explanation:

using the tangent ratio in the right triangle

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{y}{8}[/tex] ( multiply both sides by 8 )

8 × tan60° = y , then

y ≈ 13.9 ( to the nearest tenth )

The probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience, is 53/115, or approximately 0.4609 when rounded to four decimal places.

What is probability?

We can use conditional probability to find the probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience:

P(Graduate degree | Over 5 years of experience) = P(Graduate degree and Over 5 years of experience) / P(Over 5 years of experience)

We are given that 53 applicants have both a graduate degree and over 5 years of experience, so:

P(Graduate degree and Over 5 years of experience) = 53/491

We are also given that 115 applicants have over 5 years of experience, so:

P(Over 5 years of experience) = 115/491

Now we can substitute these values into the formula:

P(Graduate degree | Over 5 years of experience) = (53/491) / (115/491)

Simplifying, we get:

P(Graduate degree | Over 5 years of experience) = 53/115

So the probability that a randomly chosen applicant has a graduate degree, given that they have over 5 years of experience, is 53/115, or approximately 0.4609 when rounded to four decimal places.

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After answering the presented question, we can conclude that This equation also has solutions x = -5 and x = -1: |x + 5| - |x + 1| = 4

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

[tex]|x + 3| - 2 = 0\\|x + 3| = 2\\x + 3 = 2 or x + 3 = -2\\x = -5 or x = -1\\|x + 2| + 4 = 1\\|x + 2| = -3\\|x + 5| - |x + 1| = 4\\[/tex]

This equation also has solutions x = -5 and x = -1:

|x + 5| - |x + 1| = 4

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For the given figure the absolute value equation | [tex]x+3[/tex] | = [tex]2[/tex] has the solution set x={[tex]-5,-1[/tex]}.

An absolute value equation is an equation that involves an absolute value expression. An absolute value expression is denoted by enclosing the expression inside vertical bars, like this: |expression|. The absolute value of a real number x is defined as:

|x| = x if x is non-negative (i.e.,[tex]x\geq 0[/tex])

|x| = -x if x is negative (i.e., [tex]x < 0[/tex])

A quadratic equation is a second-degree polynomial equation of the form:

[tex]ax^{2} +bx +c = 0[/tex]

where a, b, and c are constants, and x is the variable. The highest power of the variable x is[tex]2[/tex], which means that the equation represents a curve called a parabola. The constant a is called the leading coefficient and determines the shape and direction of the parabola.

According to the given information

An absolute value equation with solution set x={[tex]-5,-1[/tex]} can be written as:

| [tex]x+3[/tex] | = [tex]2[/tex]

To see why this equation has the given solution set, we can substitute [tex]-5[/tex] and [tex]-1[/tex] for x and check that they satisfy the equation:

| [tex]-5+3[/tex] | = [tex]2[/tex], which is true since |[tex]-2[/tex]| = [tex]2[/tex]

| [tex]-1+3[/tex] | = [tex]2[/tex] which is also true since |[tex]2[/tex]| = [tex]2[/tex]

Therefore, the absolute value equation | [tex]x+3[/tex] | = [tex]2[/tex] has the solution set x={[tex]-5,-1[/tex]}.

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The shape given below consists of a rectangle and a triangle, and its area is 91 m²

Based on the image, we can see that the shape is composed of a rectangle and a triangle.

In order to find the width of rectangle we have to subtract the height of the triangle from the total length:

9m - 4m = 5 m .

Area of Rectangle:

Length = 13 m

Width = 5 m

Area of Rectangle = Length x Width

= 13 m x 5 m

= 65 m²

Triangle:

Base = 13 m

Height = 4 m

Area of Triangle = (1/2) x Base x Height

= (1/2) x 13 m x 4 m

= 26 m²

Total area of the shape = Area of Rectangle + Area of Triangle

= 65 m² + 26 m²

= 91 m²

Therefore, the area of the shape is 91 square meters (m²)

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The radio station gave away 43 tickets to employees, and they gave away 3 times as many tickets (3x) to listeners, which is 3 * 43 = 129 tickets. We can calculate it in the following manner.

Let's assume that the radio station gave away "x" tickets to employees.

According to the problem, they gave away three times as many tickets to listeners as to employees. So the number of tickets given to listeners would be 3x.

We know that the total number of tickets given away is 172. Therefore, we can set up an equation based on this:

x + 3x = 172

Simplifying and solving for x, we get:

4x = 172

x = 43

Therefore, the radio station gave away 43 tickets to employees, and they gave away 3 times as many tickets (3x) to listeners, which is 3 * 43 = 129 tickets.

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Each function's rate of change across the interval [1, 4] is 3 for f(x) and 26 for g(x), respectively. As a result, g(x) is the function that is expanding more quickly.

To calculate the rate of change for each function over the interval [1, 4], we need to find the slope of the secant line between the points (1, f(1)) and (4, f(4)) for function f(x) and between the points (1, g(1)) and (4, g(4)) for function g(x).

For function f(x) = 3x + 1:

f(1) = 3(1) + 1 = 4

f(4) = 3(4) + 1 = 13

The slope of the secant line is:

(f(4) - f(1))/(4 - 1) = (13 - 4)/3 = 3

Therefore, the rate of change for f(x) over the interval [1, 4] is 3.

For function g(x) = 3^x + 1:

g(1) = 3^1 + 1 = 4

g(4) = 3^4 + 1 = 82

The slope of the secant line is:

(g(4) - g(1))/(4 - 1) = (82 - 4)/3 = 26

Therefore, the rate of change for g(x) over the interval [1, 4] is 26.

Comparing the rates of change, we see that the rate of change for f(x) is 3 and the rate of change for g(x) is 26. Therefore, the correct answer is (d) f(x) has a rate of change of 3 and g(x) has a rate of change of 26, so g(x) is growing faster.

The complete question is:-

Calculate the rate of change for each function over the interval [1, 4], then tell which function is growing faster.

f (x)=3x+1

g(x)=3^x+1

a) f(x) has a rate of change of 3

g(x) has a rate of change of 1

so f(x) is growing faster

(b) f(x) has a rate of change of 3

g(x) has a rate of change of 3

so they are growing at the same rate

(c) f(x) has a rate of change of 3

g(x) has a rate of change of 26

so f(x) is growing faster

d) f(x) has a rate of change of 3

g(x) has a rate of change of 26

so g(x) is growing faster

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Answer:

3,3,0,3

Step-by-step explanation:

because it's right

Step-by-step explanation:

The vertical line exactly between them     x = -1   is the axis of rotation

Answer:

The overall gain is $604.30.

Step-by-step explanation:

A summary of two stocks is shown.

52W high 52W low Name of Stock Symbol High Low Close

37.18 29.39 Zycodec ZYO 39.06 32.73 34.95

11.76 7.89 Unix Co UNX 16.12 12.11 15.78

Last year, a stockholder purchased 40 shares of Zycodec at its lowest price of the year and purchased 95 shares of Unix at its highest price of the year. If the stockholder sold all shares of both stocks at their respective closing price, what was the overall gain or loss?

The overall loss is $604.30.

The overall gain is $604.30.

The overall loss is $660.35.

The overall gain is $660.35.

Got It Right.

Answer: Don't use the other message below it's AI generated..

Step-by-step explanation:

The exponential growth function can be written as P0 * [tex]e^(rt)[/tex] where P0 is the initial population, r is the annual growth rate expressed as a decimal, t is the time in years, and e is the mathematical constant e. To estimate the population in 2018, we need to find the value of P(t) when t = 6 (since 2018 is six years after 2012).

An exponential growth function is a mathematical function that models the growth of a quantity at an exponential rate over time.

a) The exponential growth function can be written as:

P(t) = P0 * [tex]e^(rt)[/tex]

where P0 is the initial population, r is the annual growth rate expressed as a decimal, t is the time in years, and e is the mathematical constant e (approximately equal to 2.71828).

In this case, P0 = 5.94 million, r = 0.0377 (3.77% expressed as a decimal), and t is the time in years. Therefore, the exponential growth function for this city is:

P(t) = 5.94 * [tex]e^(0.0377t)[/tex]

b) To estimate the population in 2018, we need to find the value of P(t) when t = 6 (since 2018 is six years after 2012). So, we plug in t = 6 into the exponential growth function:

P(6) = 5.94 * [tex]e^(0.0377 * 6)[/tex] ≈ 7.58 million

Therefore, the estimated population of the city in 2018 was 7.58 million.

c) To find when the population of the city will be 9 million, we need to solve the exponential growth function for t when P(t) = 9. So, we plug in P(t) = 9 into the exponential growth function:

9 = 5.94 * [tex]e^(0.0377t)[/tex]

Divide both sides by 5.94:

1.516835016835017 = [tex]e^(0.0377t)[/tex]

Take the natural logarithm of both sides:

ln(1.516835016835017) = 0.0377t

Solve for t:

t ≈ 8.39

Therefore, the population of the city will reach 9 million approximately 8.39 years after 2012, which is around 2020.

d) The doubling time is the amount of time it takes for the population to double. We can use the exponential growth function to find this time by solving for t when P(t) = 2P0 (twice the initial population):

2P0 = P0 * [tex]e^(rt)[/tex]

Divide both sides by P0:

2 = [tex]e^(rt)[/tex]

Take the natural logarithm of both sides:

ln(2) = rt

Solve for t:

t = ln(2) / r

Substituting r = 0.0377, we get:

t = ln(2) / 0.0377 ≈ 18.38

Therefore, the doubling time for the population of this city is approximately 18.38 years.

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Answer:

The answer is 5

Step-by-step explanation:

You divide 175 divided by 7 to find the hourly rate of how many oranges Leah peels. 60 minutes are in a hour. So 12 times 5 is 60. If 175 divided by 7 is 25. And that's hour much she peels in an hour. You divide it by five to find the 12 minute rate, because 12 times 5 is 60 that is equivalent to your hourly rate.

Answer:

Step-by-step explanation:

--> If 7 hrs= 175 oranges

1 hr= 175/7=25

1hr= 60 minutes

So, leah can peal 25 oranges in 60 mins.

Let the number of oranges peeled in 12 mins be x.

60x=25*12

x= 25*12/60

x=300/60

x=5

Leah can peel 5 oranges in 12 minutes,

Therefore, for every passing hour, the amount of drug in the body is multiplied by approximately 0.7937 or 79.37% based on factor.

The half-life of a drug refers to the amount of time it takes for the concentration of the drug in the body to decrease by half. In this case, with a half-life of 3 hours, we can assume that the concentration of the drug in the body decreases by 50% every 3 hours.

To determine the factor by which the amount of drug in the body is multiplied for each passing hour, we can use the formula:

[tex]b = 0.5^(1/t)[/tex]

where b: factor by which the amount of drug in the body is multiplied for each passing hour, and t: half-life of the drug in hours. Substitute t = 3 hours into formula gives:

[tex]b = 0.5^(1/3) = 0.7937[/tex]

Therefore, for every passing hour, the amount of drug in the body is multiplied by approximately 0.7937 or 79.37%. This means that after one hour, the amount of drug in the body is reduced to 79.37% of its original amount, after two hours it is reduced to 62.86% (0.7937^2), after three hours it is reduced to 50%, and so on.

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The slope of the line passing through A(0,-5) and B(3,1) is 2.

what is slope?

In mathematics, slope is a measure of how steep a line is. It is the ratio of the change in the y-coordinates to the change in the x-coordinates between two points on the line.

The slope formula is given by:

slope = (change in y)/(change in x)

The change in y is the difference between the y-coordinates of two points on the line, while the change in x is the difference between the x-coordinates of the same two points. The slope is a single number that represents the degree of steepness of the line.

To find the slope of the line passing through two given points A(0,-5) and B(3,1), we can use the slope formula:

slope = (change in y)/(change in x)

We first need to find the change in y and the change in x between the two points:

change in y = y-coordinate of B - y-coordinate of A

= 1 - (-5)

= 6

change in x = x-coordinate of B - x-coordinate of A

= 3 - 0

= 3

Now, we can substitute these values into the slope formula:

slope = (change in y)/(change in x)

= 6/3

= 2

Therefore, the slope of the line passing through A(0,-5) and B(3,1) is 2.

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In order to have $140,000 in 20 years, you should deposit $371 each month.

$89,040 of the $140,000 comes from deposits and $50,960 comes from interest.

In Mathematics and Financial accounting, the periodic deposit (payment) for an investment can be calculated by using the following mathematical equation (formula):

[tex]FV=PMT(\frac{(1+\frac{r}{n})^{nt} -1}{\frac{r}{n} })[/tex]

Where:

By substituting the given parameters into the formula for the periodic deposit (payment), we have:

[tex]140,000=PMT(\frac{(1+\frac{0.0425}{12})^{12 \times 20} -1}{\frac{0.0425}{12} })[/tex]

140,000(0.0425/12) = PMT(1.33613612561)

495.8333333333 = PMT(1.33613612561)

PMT = 495.8333333333/1.33613612561

PMT = $371.0949 ≈ $371.

For the amount that comes from deposits, we have:

Total deposit = $371 × 12 × 20

Total deposit = $89,040

For the amount that comes from interest, we have:

Interest = $140,000 - $89,040

Interest = $50,960.

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The probability of drawing a penny dated 1977 is 0.24 or 24%.

Probability is a branch of mathematics that deals with the study of random events. It is used to measure the likelihood or chance of a particular event occurring.

Probability is expressed as a fraction or a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain.

The probability of drawing a penny dated 1977 can be found by dividing the number of pennies dated 1977 by the total number of pennies.

Here we have

Total number of pennies = 50

Number of pennies dated 1977 = 12

Probability of drawing a penny dated 1977

= Number of pennies dated 1977 / Total number of pennies

= 12 / 50

= 0.24

Therefore,

The probability of drawing a penny dated 1977 is 0.24 or 24%.

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the temperature at 9 P.M. is 38 degrees Fahrenheit, and the equation that represents this temperature is T(9) = 53 - 3(9-4).

How to determine the temperature ?

To determine the temperature at 9 P.M., we need to calculate how much the temperature drops from 4 P.M. to 9 P.M. We know that the temperature drops 3 degrees per hour, and since there are 5 hours between 4 P.M. and 9 P.M., the temperature will have dropped 3 x 5 = 15 degrees.

Therefore, to calculate the temperature at 9 P.M., we need to subtract 15 degrees from the temperature at 4 P.M.:

Temperature at 9 P.M. = Temperature at 4 P.M. - 15

Substituting the given temperature of 53 degrees Fahrenheit at 4 P.M.:

Temperature at 9 P.M. = 53 - 15 = 38 degrees Fahrenheit

Thus, the equation that accurately represents the temperature at 9 P.M. is:

T(9) = 53 - 3(9-4)

Simplifying the equation:

T(9) = 53 - 15

T(9) = 38

In conclusion, the temperature at 9 P.M. is 38 degrees Fahrenheit, and the equation that represents this temperature is T(9) = 53 - 3(9-4).

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The two equations that are true for the value x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16.

For x = -2, substituting into equation 1 gives:

(-2)² - 4 = 0

4 - 4 = 0

Adding x = -2 to equation 2 results in:

4(-2)² = 16

4(4) = 16

For x = 2, substituting into equation 1 gives:

(2)² - 4 = 0

4 - 4 = 0

Adding x = -2 to equation 2 results in:

4(2)² = 16

4(4) = 16

Therefore, the equations is true.

The equation 3x² + 12 = 0 is not true for either x = -2 or x = 2 since substituting either value into the equation yields a non-zero result.

The equation 2(x - 2)² = 0 is only true for x = 2, but not for x = -2, since substituting x = -2 yields a non-zero result.

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The definite integrals associated with the piecewise function have the following values:

Case 1: 1.5

Case 2: - 2 + 0.5π

Case 3: 5.5

In this problem we find the representation of a piecewise function formed by four parts, whose definite integrals must be determined by means of the following formulas:

[tex]I = \int\limits^b_a {f(x)} \, dx[/tex]

Graphically speaking, the definite integral is equal to the area below the curve.

Case 1

I = 0.5 · 2² - 0.5 · 1²

I = 1.5

Case 2

I = - 2 · 1 + 0.5π · 1²

I = - 2 + 0.5π

Case 3

I = - 0.5 · 0.5 · 1 + 0.5 · 1.5 · 3 + 1 · 3

I = - 0.25 + 2.75 + 3

I = 5.5

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So, Tom would have earned *Ksh (137465.91 + x) and John would have earned Ksh (202533.09 - x)

What exactly is markup?

The sum that is added to a product's cost price to cover expenses and profit is known as a markup.

We are aware that John banks 100,000 and Tom 230,000 Kenyan shillings.

Assume that both product A and B have a cost price of x.

Tom spends 5x because he BUYS 5 of Product A.

Tom sells two times as much of B. He SELLS 2 * (2x) = 4x as a result.

Hence, Tom's gain is:

4x - 5x = -x

Tom suffers a loss of x as a result of this.

John sells product A for three times what Tom BOUGHT. Thus he SELLS 3 * 5 = 15 times.

John purchases 13 of B Product. He therefore spends 13 times.

John thus makes a profit of:

15x - 13x = 2x

John thereby benefits by a factor of two.  

As a result, the cost of goods A and B is:

42,727.27 + (25/100) * 42,727.27 = Ksh 53,409.09

44,363.63 + (25/100) * 44,363.63 = Ksh 55,454.54

We also know that the sale price was discounted by 15%.

After discounts, the sale price for item

A is (85/100) * Ksh 53,409.09, which is Ksh 45,397.73.

After discounts, the sale price for item

B is (85/100) * Ksh 55,454.54 = Ksh 47,136.36.

Tom's product loss

Ksh 45,397.73 - x = cost price - selling price

John's profit on item A is calculated as follows:

sale price less cost price = Ksh 45,397.73 - x

Cost price minus sale price equals Tom's loss on item B, which is Ksh 47,136.36.

John's profit on item B is calculated as follows: sale price less cost price = Ksh 47,136.36 - x

Therefore:

Total loss for Tom is (x - Ksh 45,397.73) + (x - Ksh 47,136.36)

= 2x - Ksh (45,397.73 + 47,136.36)

= = 2x - Ksh (92,534.09) (92,534.09)

(Ksh 45,397.73 - x) + John's total profit (Ksh 47,136.36 - x)

= Ksh (92,533.09) -2x

After discount and markup, Tom's bank balance equals Tom's bank balance plus his overall loss.

= [2x - Ksh (92,534.09)] + Ksh (230000)

= Ksh (137465.91 + x)

After discount and markup, John's bank balance equals John's bank balance plus his overall profit.

= [Ksh (92,533.09) -2x) + Ksh (110000)]

= Ksh (202533.09 - x)

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Step-by-step explanation:

Looks like 24.634

Therefore, we can say that there is a 95% chance that a randomly selected light bulb will last between 675 and 900 hours.

Probability is a measure of the likelihood of an event occurring. It is a mathematical concept that is used to quantify the chance of a specific outcome in a given situation. Probability is typically expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.

Here,

To solve this problem, we can use the z-score formula:

z = (x - mu) / sigma

where x is the value we want to find the probability for (in this case, between 675 and 900 hours), mu is the mean (750 hours), and sigma is the standard deviation (75 hours). We can then use a standard normal distribution table or calculator to find the probabilities associated with the calculated z-scores.

First, let's find the z-score for x = 675:

z = (675 - 750) / 75

= -1

Next, let's find the z-score for x = 900:

z = (900 - 750) / 75

2

Since the data is normally distributed, we can use this rule to estimate the probability that a randomly selected light bulb will last between 675 and 900 hours.

Thus, the probability that a randomly selected light bulb will last between 675 and 900 hours is approximately:

P = 95%

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Answer: The answer is 4.64$

Step-by-step explanation:

9 pencils is 2.25$. and we have 2.39$ for the notebook. 2.25 + 2.39 = 4.64

if you purchased one ticket, your expected gross winnings are $0.36.

what is gross winnings  ?

Gross winnings refer to the total amount of money won before any taxes or fees are deducted. In other words, it is the total amount of money won by an individual in a lottery or other type of game of chance, without taking into account any deductions that may be made

In the given question,

To calculate the expected gross winnings, we need to multiply the probability of winning each prize by the value of the prize and then add up these values.

First, let's find the probability of winning each prize:

First prize: There is only one first prize, and there are 15,000 tickets sold, so the probability of winning the first prize is 1/15,000.

Second prize: There are two second prizes, so the probability of winning a second prize is 2/15,000.

Third prize: There are three third prizes, so the probability of winning a third prize is 3/15,000.

Now we can calculate the expected gross winnings:

First prize: The probability of winning the first prize is 1/15,000, and the value of the prize is $3,000, so the expected value of the first prize is (1/15,000) x $3,000 = $0.20.

Second prize: The probability of winning a second prize is 2/15,000, and the value of each prize is $750, so the expected value of a second prize is (2/15,000) x $750 = $0.10.

Third prize: The probability of winning a third prize is 3/15,000, and the value of each prize is $300, so the expected value of a third prize is (3/15,000) x $300 = $0.06.

Now we can add up these value to find the total expected gross winnings:

$0.20 + $0.10 + $0.06 = $0.36

Therefore, if you purchased one ticket, your expected gross winnings are $0.36.

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Answer:

soln;Here

Given,

f(x)=2x² + 4x - 14

g(x)= x³ + 15x

(f + g)(3)= ?

Now,

(f + g)(3) = f(3) + g(3)

=2×3³- 14 + 3³ + 15 × 3

=2 × 27 - 14 + 27 + 45

= 54 - 14 + 27 + 45

= 54 - 14 + 7

=61 - 14

= 47..

Hence the value of f + g)(3)= 47

Answer:

u = 12;

v = 6

Step-by-step explanation:

Use trigonometry:

[tex] \tan(60°) = \frac{6 \sqrt{3} }{v} [/tex]

Use the property of proportion to find v:

[tex]v = \frac{6 \sqrt{3} }{ \tan(60°) } = \frac{6 \sqrt{3} }{ \sqrt{3} } = 6[/tex]

Use the Pythagorean theorem to find u:

[tex] {u}^{2} = {v}^{2} + ( {6 \sqrt{3}) }^{2} [/tex]

[tex] {u}^{2} = {6}^{2} + ( {6 \sqrt{3}) }^{2} = 36 + 36 \times 3 = 36 + 108 = 144[/tex]

[tex]u > 0[/tex]

[tex]u = \sqrt{144} = 12[/tex]

Answer: [tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]

Step-by-step explanation:

Half angle formula for sine is  

sin([tex]\frac{x}{2}[/tex])=[tex]\sqrt{1-cosx}/2[/tex]

If x is 150, then sin 75=[tex]\sqrt{1-cos150}/2[/tex] =[tex]\sqrt{1-\frac{cos(180-30)}{2} }[/tex]=[tex]\sqrt{1+cos30}/2[/tex]

=[tex]\sqrt{(1/2)+(\sqrt{3}/4)}[/tex] =[tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]

A sum is divisible by 3 if and only if both of the dice rolls are either 1 and 2 or 2 and 1, or both of the dice rolls are either 1

How to solve the problem?

To solve this problem, we first need to determine the total number of possible outcomes when rolling the die twice. Each roll has six possible outcomes, so the total number of outcomes when rolling the die twice is 6 x 6 = 36.

Next, we can create a table to list all possible outcomes and their corresponding sums:

Die 1 Die 2 Sum

1 1 2

1 2 3

1 3 4

1 4 5

1 5 6

1 6 7

2 1 3

2 2 4

2 3 5

2 4 6

2 5 7

2 6 8

3 1 4

3 2 5

3 3 6

3 4 7

3 5 8

3 6 9

4 1 5

4 2 6

4 3 7

4 4 8

4 5 9

4 6 10

5 1 6

5 2 7

5 3 8

5 4 9

5 5 10

5 6 11

6 1 7

6 2 8

6 3 9

6 4 10

6 5 11

6 6 12

Using this table, we can calculate the probability of each event:

Event A: The sum is greater than 9.

There are four possible outcomes where the sum is greater than 9: 10, 11, and 12. The probability of getting each of these outcomes is:

P(sum = 10) = 3/36

P(sum = 11) = 2/36

P(sum = 12) = 1/36

Therefore, the probability of Event A is:

P(Event A) = P(sum = 10) + P(sum = 11) + P(sum = 12)

= (3/36) + (2/36) + (1/36)

= 6/36

= 1/6

Event B: The sum is not divisible by 3.

A sum is divisible by 3 if and only if both of the dice rolls are either 1 and 2 or 2 and 1, or both of the dice rolls are either 1

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the population of Bolivia in 2030, if it continues to grow at a rate of 1.6% continuously, will be approximately 14.45 million.

To solve this problem, we need to use the formula for continuous compounding, which is:

[tex]A = Pe^(rt)[/tex]

Where:

A = the final amount

P = the initial amount

r = the annual growth rate (as a decimal)

t = the number of years

We know that Bolivia had a population of 10.5 million in 2010 and a growth rate of 1.6%, or 0.016 as a decimal. We want to find the population in 2030, which is 20 years after 2010.

So, we plug in the values into the formula:

[tex]A = 10.5 million * e^(0.016 * 20)[/tex]

Using a calculator, we get:

[tex]A = 10.5 million * e^(0.32)[/tex]

A = 10.5 million * 1.3775

A = 14.45 million

Therefore, the population of Bolivia in 2030, if it continues to grow at a rate of 1.6% continuously, will be approximately 14.45 million.

Continuous compounding is a mathematical concept used to calculate the growth of a quantity that grows at a constant rate over time. It is different from simple interest, which is calculated based on a fixed rate over a certain period of time. In continuous compounding, the growth rate is applied infinitely many times over an infinite time period, resulting in exponential growth. The formula we used is a standard formula for continuous compounding, and it can be used to calculate the growth of various quantities, such as population, money, or investments.

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The probability that the 4th or 5th student you stop is the first to have the jumper cables is 0.2417 or about 24.17%.

This is an example of a negative binomial probability problem, where we want to know the probability of obtaining a certain number of failures before obtaining a certain number of successes in a series of independent trials. In this case, the "success" is finding a student with jumper cables, and the "failure" is finding a student without jumper cables.

Let p be the probability of success (finding a student with jumper cables) on any given trial, which is 0.18 according to the problem. Let k be the number of successes we want to obtain, which is 1 in this case (since we only need to find one student with jumper cables). Let x be the number of trials it takes to obtain k successes, which is either 4 or 5 in this case.

Then, the probability of finding the first student with jumper cables on the 4th or 5th stop is:

P(X = 4 or X = 5) = P(X = 4) + P(X = 5)

We can calculate these probabilities using the negative binomial distribution formula:

[tex]P(X = x) = (x-1) choose (k-1) * p^k * (1-p)^{x-k}[/tex]

For x = 4:

[tex]P(X = 4) = (4-1) choose (1-1) * 0.18^1 * (1-0.18)^{4-1} = 0.1778[/tex]

For x = 5:

[tex]P(X = 5) = (5-1) choose (1-1) * 0.18^1 *(1-0.18)^{5-1} = 0.0639[/tex]

So, the probability of finding the first student with jumper cables on the 4th or 5th stop is:

P(X = 4 or X = 5) = 0.1778 + 0.0639 = 0.2417

Therefore, the probability that the 4th or 5th student you stop is the first to have the jumper cables is 0.2417 or about 24.17%.

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