how to find the trigonometric ratio

Answer:

0.621

Step-by-step explanation:

Number of people that have run a red light in the last year = 290

Number of people that have not run a red light in the last year = 177

Total number of respondents = 290 + 177

                                                 = 467

Pr(if a person is chosen at random, they have run a red light in the last year) = \(\frac{number of people who has run the red light last year}{total number of respondents}\)

                   = \(\frac{290}{467}\)

                   = 0.621

The probability that if a person is chosen at random, they have run a red light in the last year is 0.621.

The probability that the athlete has actually been using the prohibited drug given that they tested positive is approximately 0.5789 or 57.89%.

To solve this problem, we can use Bayes' theorem, which relates the conditional probabilities of two events.

Let A be the event that the athlete has been using the prohibited drug, and let B be the event that the athlete tests positive.

We want to find the probability of A given B, which we can write as P(A | B).

Using Bayes' theorem, we have:

P(A | B) = P(B | A) * \(\frac{P(A) }{P(B)}\)

where P(B | A) is the probability of testing positive given that the athlete has been using the prohibited drug, P(A) is the prior probability of the athlete using the prohibited drug, and P(B) is the overall probability of testing positive, which can be calculated using the law of total probability:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

where P(B | not A) is the probability of testing positive given that the athlete has not been using the prohibited drug, and P(not A) is the complement of P(A), i.e., the probability that the athlete has not been using the prohibited drug.

Using the given information, we can plug in the values:

P(B | A) = 1 - 0.12 = 0.88 (probability of testing positive given the athlete is using the drug)

P(A) = 0.05 (prior probability of the athlete using the drug)

P(B | not A) = 0.04 (probability of testing positive given the athlete is not using the drug)

P(not A) = 1 - P(A) = 0.95 (probability that the athlete is not using the drug)

Then, we can calculate P(B) as:

P(B) = P(B | A) * P(A) + P(B | not A) * P(not A)

= 0.88 * 0.05 + 0.04 * 0.95

= 0.076

Finally, we can calculate P(A | B) as:

P(A | B) = P(B | A) * \(\frac{P(A) }{ P(B)}\)

= 0.88 * \(\frac{0.05 }{ 0.076}\)

= 0.5789

Therefore, the probability that the athlete has actually been using the prohibited drug given that they tested positive is approximately 0.5789 or 57.89%.

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To serve 50 people, the minimum square footage needed would be 750 square feet.

Let us analyze the given question and solve the problem given. The problem is asking about the minimum square footage of the multi-story building that is required to open a small restaurant on the lowest floor. The building is already zoned for mixed use.

John wants to open a small, by-reservation-only restaurant on the lowest floor. He needs to calculate the minimum square footage he needs to serve 50 people. Let's calculate the minimum square footage that John needs to open the restaurant. If local code requires 15 square feet per person, then 15 x 50 = 750 square feet are needed for 50 people. In other words, John needs at least 750 square feet of space to serve 50 people at his restaurant.

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A. Liam sets a goal to score a 720 on the GMAT test in October.

B. Liam develops an action plan to study for a month and take a practice test. After studying for a month, he takes a practice test and scores 40 points higher than he did on his first practice test.

C. Based on the average test scores of students at his target schools, Liam decides he wants to earn a 710 on the GMAT.

D. To achieve his goal, Liam will spend one hour each weeknight and three hours every Saturday and Sunday studying GMAT practice questions. He will also review progress regularly to ensure that he is on track to achieve his goal.

E. Finally, Liam will appraise his performance by comparing his scores on practice tests with his goal score of 710. If he finds that he is not making enough progress, he may adjust his study schedule or seek additional help.

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Rate is the same thing as gradient so to work out the gradient you need to use the formula

change in y / change in x

Change in y = y2 - y1

Pick any two points on the graph

Change in y = 30 - 15

Change in y = 15

Change in x = x2 - x1

Change in x = 2 - 1

Change in x = 1

15/1

= 15 dollars per day.

We can double check this by seeing the increase of money per day, for example, here from day two to day three, the money needed increases by 15, so our answer is correct.

Step-by-step explanation:

Graph 1 is a parabola and has 2 x points and a turning point

meaning it has a minimum and a maximum point.

conclave points are the highs and lows, once you show this in table then you can interpreted them on a graph see the examples attached.

Graph 1 is opposite to shown interpreted conclave so instead of --c++

we write  + + c - - and draw on quadrant 1 instead of quadrant 3

graph 2 is decreasing so instead of -+ c then + + it would show + -  c then - - so the curve stays in quadrant 3 and 4. Also where c is we draw a 0 and say whether it is minimum or maximum point.

Both graph 1 and 2 demonstrate minimum points for their f(x) for c.

so in your workings within the table you write min as seen in red within the attachment. They wrote max, but you write min as you are in decreasing conclave fx values that reach min point c then they increase and become parabolas.

Answer 24a + 6

Step-by-step explanation:

8 + 18a -2 + 6a

18a + 6a = 24a

8 - 2 = 6

24a + 6

Answer:

it will be equal to = 1/2 or

\(2 {}^{ - 1} \)

Step-by-step explanation:

\(2 {}^{ - 1} \times 4 {}^{ - 1} \div 2 {}^{ - 2} \)

\(\frac{1}{2} \times \frac{1}{4} \div \frac{1}{4} \)

\( = \frac{1}{2} \)

or

\( {2}^{ - 1} \)

Answer: D

Step-by-step explanation:

2x - 14 + x= 46

3x = 60

x= 20

Answer:

Frances will complete 131,444,313 oil changes.

Step-by-step explanation:

919191 oil changes=777days

         ?                     =111111 days

=(919191*111111)/777

=131,444,313 oil changes

The theory behind Euler's equation and the boundary conditions for a column with one fixed end and the other end free. Therefore, the answer to the question is d) 1/2, as x = π/2L = (2(1) - 1)π/2L = (2n - 1)π/2L when n = 1/2.

Euler's equation is derived from the Euler-Bernoulli beam theory, which states that a slender column under axial compression will buckle when the compressive stress exceeds a certain critical value. The buckling load is given by the equation P= xt^2π^2Et, where P is the buckling load, x is a dimensionless factor called the slenderness ratio (the ratio of the column length to its cross-sectional dimensions), t is the thickness of the column wall, E is the modulus of elasticity of the column material, and π is the mathematical constant pi.

For a column with both ends pinned, the value of x is given by x = nπ/L, where n is an integer and L is the length of the column. For a column with one end fixed and the other end free, the value of x is given by x = (2n - 1)π/2L, where n is an integer.  In this case, we have a column with one fixed end and the other end free, so we need to use the equation x = (2n - 1)π/2L to find the value of x. Since n can be any integer, we can choose n = 1 to simplify the equation and get x = π/2L.

Substituting this value of x into Euler's equation, we get P = (π/2L)²π²Et = π²Et/4L². This means that the buckling load for a column with one fixed end and the other end free is proportional to the modulus of elasticity and inversely proportional to the square of the length of the column.

Therefore, the answer to the question is d) 1/2, as x = π/2L = (2(1) - 1)π/2L = (2n - 1)π/2L when n = 1/2

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2x + 5 = 3x - 1

x = 6

y = 17

please give brainliest

Answer: There are 24 ways.

Step-by-step explanation:

All the numbers are divisible by 11, so divide all the numbers by 11 to make the problem simpler: Jo climbs a flight of 6 stairs. Jo can take the stairs 1, 2, or 3 at a time.

A recursive approach can now solve this problem. The number of ways to climb one stair is 1. There are two ways to climb 2 stairs: (1, 1) or (2). For 3 stairs, there are 4 ways: (1, 1, 1), (1, 2), (2, 1), and (3). Extending this pattern, there are 1+2+4 = 7 ways to climb up 4 stairs, 2+4+7 = 13 ways to climb up 5 stairs, and 4+7+13 = 24 ways to get up 6 stairs.  

The total number of ways by which Jo climbs the stairs at school when he can take the stairs 1, 2, or 3 at a time.

Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways. The number of possible ways to arrange is n!.

Here, n is the number of objects.

Every day at school, Jo climbs a flight of 6 stairs.  Jo can take the stairs 1, 2, or 3 at a time. For example, Jo could climb 3, then 1, then 2.

With one stair, there is one way to climb. With two stairs, the ways to climb are two 1-1 at a time or 2 at a time. For the three stair, there are 4 ways,

\(1+1+1,1+2,2+1,3\)

For the three stair, there are 7 possibilities he can climb the stair.

\(1+1+1+1,\;1+1+2,\;1+2+1,\;2+2\;,2+1+1\;1+3.\;3+1\)

In the same way for the 5 the stair there are 6 additional steps add in it, which makes it 13.

For the six stair for single step, we have 13 ways, for double step we have 7 ways and for triple step we have 4 ways. Thus,

\(\rm Number\; of \; ways=13+7+4\\\rm Number\; of \; ways=24\)

Thus, the total number of ways by which Jo climbs the stairs at school when he can take the stairs 1, 2, or 3 at a time.

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By solving a system of equations, we can see that there are 17 children and 8 parents in the room.

Let's define the variables:

x = number of children.

y = number of parents.

We know that there are 9 more children than parents, then:

x = y + 9

And there is a total of 25 people, so:

x + y = 25

So we have a system of equations:

x = y + 9

x + y = 25

Replacing the first equation into the second one, we get:

(y +9) + y = 25

2y + 9 = 25

2y = 25 - 9 = 16

y = 16/2 = 8

then the value of x is:

x = y + 9 = 8 + 9 = 17

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The Interquartile Range (IQR) of the given data set, consisting of the yields of hay from a farmer's last 10 years (375, 210, 150, 147, 429, 189, 320, 580, 407, 180), is 227 bushels.

IQR stands for Interquartile Range which is a range of values between the upper quartile and the lower quartile. To find the IQR of the given data, we need to calculate the first quartile (Q1), the third quartile (Q3), and the difference between them. Let's start with the solution. Find the IQR. Given data are the yields, in bushels, of hay from a farmer's last 10 years: 375, 210, 150, 147, 429, 189, 320, 580, 407, 180

Sort the given data in order.150, 147, 180, 189, 320, 375, 407, 429, 580

Find the median of the entire data set. Median = (n+1)/2  where n is the number of observations.

Median = (10+1)/2 = 5.5. The median is the average of the fifth and sixth terms in the ordered data set.

Median = (210+320)/2 = 265

Split the ordered data into two halves. If there are an odd number of observations, do not include the median value in either half.

150, 147, 180, 189, 210 | 320, 375, 407, 429, 580

Find the median of the lower half of the data set.

Lower half: 150, 147, 180, 189, 210

Median = (n+1)/2

Median = (5+1)/2 = 3.

The median of the lower half is the third observation.

Median = 180

Find the median of the upper half of the data set.

Upper half: 320, 375, 407, 429, 580

Median = (n+1)/2

Median = (5+1)/2 = 3.

The median of the upper half is the third observation.

Median = 407

Find the difference between the upper and lower quartiles.

IQR = Q3 - Q1

IQR = 407 - 180

IQR = 227.

Thus, the Interquartile Range (IQR) of the given data is 227.

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a. Ashley would need to invest approximately $49,302.55 in one lump sum today. b. Ashley would need to put away approximately $9,167.42 annually to accumulate the required capital in 6 years. c. Ashley already has $20,000 saved, she would need to put away approximately $6,111.57 annually to accumulate the required capital in 6 years.

a. To determine how much Ashley would need to invest today, in one lump sum, to end up with $70,000 in 6 years, we can use the future value formula:

Future Value (FV) = Present Value (PV) * (1 + interest rate)^time

In this case, FV = $70,000, interest rate = 7% (0.07), and time = 6 years. Plugging in these values into the formula, we can solve for PV:

$70,000 = PV * \((1 + 0.07)^6\)

PV = $70,000 /\((1.07)^6\)

PV ≈ $49,302.55

Therefore, Ashley would need to invest approximately $49,302.55 in one lump sum today.

b. If Ashley is starting from scratch, we need to calculate how much she would have to put away annually to accumulate the needed capital in 6 years. This can be calculated using the present value of an ordinary annuity formula:

PV = Annual Payment * [(1 - (1 + interest rate)^(-time)) / interest rate]

In this case, PV = $70,000, interest rate = 7% (0.07), and time = 6 years. Plugging in these values, we can solve for the annual payment:

$70,000 = Annual Payment *\([(1 - (1 + 0.07)^(-6)) / 0.07]\)

Annual Payment ≈ $9,167.42

Therefore, Ashley would need to put away approximately $9,167.42 annually to accumulate the required capital in 6 years.

c. If Ashley already has $20,000 saved, we can subtract this amount from the required capital and calculate the annual payment for the remaining amount:

Remaining Amount = Required Capital - Initial Savings

Remaining Amount = $70,000 - $20,000 = $50,000

Using the same formula as in part b, we can calculate the annual payment:

$50,000 = Annual Payment\(* [(1 - (1 + 0.07)^(-6)) / 0.07]\)

Annual Payment ≈ $6,111.57

Therefore, if Ashley already has $20,000 saved, she would need to put away approximately $6,111.57 annually to accumulate the required capital in 6 years.

d. Ashley can use an investment plan to help reach her objective by following these steps:

- Set a specific financial goal, such as accumulating $70,000 in 6 years.

- Determine the required investment amount, whether it's a lump sum or an annual payment.

- Consider her risk tolerance and investment options. Since she estimates a 7% return, she can explore various investment vehicles like stocks, bonds, mutual funds, or other investment instruments.

- Develop an investment plan that aligns with her financial goals and risk tolerance. This plan may involve diversifying her investments, considering different time horizons, and regularly monitoring her progress.

- Continuously track the performance of her investments and make adjustments if needed.

- Stay disciplined and committed to her investment plan, making regular contributions or adjusting investments as necessary to reach her desired capital.

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Answer:

if you dont know the answer you can downlode the brainly app and take pics of your work and it will translate the answer

Step-by-step explanation:

Answer:

44

Step-by-step explanation:

4 times 8 = 20

8 times 3 = 24

20 + 24 = 44

Also, if you could label this brainliest that would be a great help!

Thanks xx 

-Dante

The expression (16x^3y^2) - (24x^4y^4) can be written as the product of the greatest common factor (8x^3y^2) and the binomial (2 - 3x^1y^2).

To rewrite the expression (16x^3y^2) - 24x^4y^4 as a product of the greatest common factor multiplied by a binomial, we need to find the greatest common factor of the two terms. The greatest common factor of 16x^3y^2 and 24x^4y^4 is 8x^3y^2.

We can factor out 8x^3y^2 from both terms to get:

(16x^3y^2) - (24x^4y^4) = 8x^3y^2(2 - 3x^1y^2)

Therefore, the expression (16x^3y^2) - (24x^4y^4) can be written as the product of the greatest common factor (8x^3y^2) and the binomial (2 - 3x^1y^2).

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The break-even point is the point where the profit and the loss are the same (equal). To calculate it, we have the following formula:

where "Price" denotes the value estimate (per unit) by the company. In this case, such a value is $50. And "Variable costs" denotes the variable cost per table; in this case, it's $22. Then,

Now, note that the obtained number of sales is not an entire number. In such cases, we choose the next integer (for we prefer no loss); in this particular case, it's 465.

The total sales the company needs to break even are 465.

Answer:

35 rabbits

Step-by-step explanation:

hens : rabbits : total

3     : 5 :  3+5

3     : 5 :  8

We have 56 total animals

56/8 = 7

Multiply each term by 7

hens : rabbits : total

3*7     : 5*7 :  8*7

21       : 35     : 56

There are 21 hens and 35 rabbits    

Answer:

−1/7

Step-by-step explanation:

Answer:

The answer is vv

Step-by-step explanation:

The 3rd answer, ab+ac, that expression is wrong. ac+bc may be correct or wrong,

The correct option regarding the scale factor and the statement in this problem is given as follows:

D. The statement is false. Because there are 3 feet in one​ yard, there are 9 square feet in one square yard.

The scale factor between the length dimensions of the yard are given as follows:

3 feet = 1 yard.

(as these length dimensions are given in yards).

Then for the square units, the correct scale factor is found applying the proportion as follows:

(3 feet)² = (1 yard)².

9 feet squared = 1 square yard.

Hence the statement given in this problem, that because there are 3 feet in one​ yard, there are also 3 square feet in one square yard, is false, and the correct option is given by option D.

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Answer:

Co me he re tjyvynoqtu guys

Answer:

True.

Step-by-step explanation:

\(\frac{(10)-2}{4}=2\\\\\frac{8}{4}=2\\\\2=2\)

Part a)Given, utility function of the consumer as:U(x1, x2) = log(x1) + log(x2)X1 ≤ 0.5Let p2 = 1 and m = 1, and p1 is unknown. The consumer has a budget constraint as: p1x1 + p2x2 = m = 1Now we have to find the minimal p1 such that the consumer consumes x1 strictly less than 0.5.

We need to find the value of p1 such that the consumer spends the entire budget (m = 1) on the two goods, but purchases only less than 0.5 units of the first good. In other words, the consumer spends all his money on the two goods, but still cannot afford more than 0.5 units of good 1.

Mathematically we can represent this as:

p1x1 + p2x2 = 1......(1)Where, x1 < 0.5, p2 = 1 and m = 1

Substituting the given value of p2 in (1), we get:

p1x1 + x2 = 1x1 = (1 - x2) / p1Given, x1 < 0.5 => (1 - x2) / p1 < 0.5 => 1 - x2 < 0.5p1 => p1 > (1 - x2) / 0.5

Now we know, 0 < x2 < 1.So, we will maximize the expression (1 - x2) / 0.5 for x2 ∈ (0,1) which gives the minimum value of p1 such that x1 < 0.5.On differentiating the expression w.r.t x2, we get:d/dx2 [(1-x2)/0.5] = -1/0.5 = -2

Therefore, (1-x2) / 0.5 is maximum at x2 = 0.

Now, substituting the value of x2 = 0 in the above equation, we get:p1 > 1/0.5 = 2So, the minimal value of p1 is 2.Part b)Now, we have to show mathematically that whether the threshold on p1 found in Part a increases/decreases/stays the same when p2 increases.

That is, if p2 increases then the minimum value of p1 will increase/decrease/stay the same.Since p2 = 1, the consumer’s budget constraint is given by:

p1x1 + x2 = m = 1Suppose that p2 increases to p2′.

The consumer’s new budget constraint is:

p1x1 + p2′x2 = m = 1.

Now we will find the minimal p1 denoted by pi, such that the consumer purchases less than 0.5 units of good 1. This can be expressed as:

p1x1 + p2′x2 = 1Where, x1 < 0.5

The budget constraint is the same as that in Part a, except that p2 has been replaced by p2′. Now, using the same argument as in Part a, the minimum value of p1 is given by:

p1 > (1 - x2) / 0.5.

We need to maximize (1 - x2) / 0.5 w.r.t x2.

As discussed in Part a, this occurs when x2 = 0.Therefore, minimal value of p1 is:

pi > 1/0.5 = 2

This value of pi is independent of the value of p2′.

Hence, the threshold on p1 found in Part a stays the same when p2 increases.

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Answer:

(9×3)+(4×2)

Step-by-step explanation:

Let a represent the price of books

Let b represent the price of magazines

Alicia purchase 3 books for $9

She also purchased 2 magazines for $4

(9×a) +(4×b)

= (9 ×3) + (4×2)

= 27+8

= 35

The answer is 16/3, which is obtained by evaluating the integral of (8x² - 4x) over the interval [-1,1].

To express the limit of limn→[infinity]∑i=1n(4(x∗i)2−2(x∗i))δx over [−1,1] as an integral, we can use the definition of a Riemann sum.

First, we note that delta x, or the width of each subinterval, is given by (b-a)/n, where a=-1 and b=1. Therefore, delta x = 2/n.

Next, we can express each term in the sum as a function evaluated at a point within the ith subinterval. Specifically, let xi be the right endpoint of the ith subinterval. Then, we have:

4(xi)² - 2(xi) = 2(2(xi)² - xi)

We can rewrite this expression in terms of the midpoint of the ith subinterval, mi, using the formula:

mi = (xi + xi-1)/2

Thus, we have:

2(2(xi)² - xi) = 2(2(mi + delta x/2)² - (mi + delta x/2))

Simplifying this expression gives:

8(mi)² - 4(mi)delta x

Now, we can express the original limit as the integral of this function over the interval [-1,1]:

limn→[infinity]∑i=1n(4(x∗i)2−2(x∗i))δx = ∫[-1,1] (8x² - 4x) dx

Evaluating this integral gives:

[8x³/3 - 2x²] from -1 to 1

= 16/3

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The number of burger sam bought = x

Let the number of burgers for mike be = y

the equation for the total number of burgers will be

Mike brought 5 more than 2 times as many burgers as sam will be represented as

By substituting Eqn 2 in Eqn 1 we will have

Therefore,

The value of x= 15

To calculate the number of burgers mike brought to the BBQ =y,

We will substitute the value of x in (Eqn 1) above