An investigator is studying the association between cell phone use and migraine headaches. She recruits 100 cases (migraine patients) and 100 controls (people who don't suffer from migraine), and asks each group how many hours they use their cell phones per day, on average. She obtains the following information:
cases controls
use cellphones
>3hrs/day
60 55
use cellphones
<3hrs/day
40 45
total 100 100
Calculate the observed odds ratio (the observed association between migraine headache and cell phone use).
OR = 0.82
OR = 1.23
OR = 1.11
OR = 3.45

Answer:

\(34\)

Step-by-step explanation:

Let the first number be \(x\)

The next number be \(2\) more than the previous as it is an even number

The second number is \(x+2\)

and the last number is \(x+4\)

The sum of the numbers is \(108\), so the expression will be

\(x+(x+2)+(x+4)=108\)

\(\Rightarrow 3x+6=108\)

\(\Rightarrow x=\dfrac{108-6}{3}\)

\(\Rightarrow x=34\)

The smallest of the three numbers is \(34\).

9514 1404 393

Answer:

  13 1/3 cups

Step-by-step explanation:

We assume flour is proportional to cookies, so we have ...

  cups/dozens = x/10 = 4/3

Multiplying by 10 gives ...

  x = 40/3 = 13 1/3

13 1/3 cups of flour are needed for 10 dozen cookies.

Answer:

13 1/2 cups of flour.

Step-by-step explanation:

Answer:

1 - z/3

Step-by-step explanation:

There are 96 ways for four people to sit in six chairs so that the leftmost chair is occupied and the rightmost is empty.

There are 4 guests and the leftmost seat is to be occupied, so there are 4  such ways to choose the occupant of that seat.

Then, for each of those 4 ways, there are 4 ways to decide the occupant for the second seat -- the remaining three people plus the possibility of that seat being empty, that makes a total of 16 ways to decide the configuration of the first two seats.

Then, for each of those 16 ways, there are 3 ways to choose the occupant for the third seat (either 3 remaining guests if the second seat was left empty, or the two remaining guests plus the possibility of leaving the 3rd seat empty). Hence, 16 times 3 is 48. For each of those ways, there are two choices for the next seat, i.e. 48 times 2 = 96, and finally one choice for the fifth seat. So in all, there are 96 ways.

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The average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

Given,

Benny's arcade has five video game machines

The average time between failures = 34 hours

The maintenance engineer can repair a machine in about = 13 hours

The failure time and repair times are both exponentially distributed

The formula for the mean of an exponential distribution is mean = 1/λ where λ is the rate parameter of the distribution.

In this problem, the rate parameter of both the failure time and repair time is the reciprocal of their respective averages. Therefore,

λ_f = 1/34λ_r = 1/13

Now, let's find the average time from when a machine breaks until it is fixed using the fact that the sum of two independent exponential distributions with rate parameters λ1 and λ2 is itself an exponential distribution with rate parameter λ1+λ2.

So, the rate parameter for the time from when a machine breaks until it is fixed is λ_f+λ_r = 1/34+1/13

= 0.0885 hours⁻¹ (approximately)

Hence, the average time from when a machine breaks until it is fixed is mean = 1/λ= 1/0.0885 ≈ 11.3 hours (approximately).

Therefore, the average time in hours from when a machine breaks until it is fixed is approximately 11.3 hours.

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Answer:

she can make 4 batches of brownies

Step-by-step explanation:

since she already made a batch of brownie with 1/2 cup and she has 3/2 cups left, that means she can make 3 more

3+1=4

hope this helps

The batches of brownies can Luisa make is 4 batches.

It is required to find the the batches of brownies can Luisa make.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

3 batches of brownies from 3/2 cups of chocolate left.

Step-by-step explanation:

From the question, we know that:

1/2 cups of chocolate = 1 batch of brownies

3/2 cups of chocolate = x

Cross Multiply

1/2 × x = 3/2

x = 3/2/1/2

x = 3/2 × 2/1

x = 3 batches.

That means she can make 3 more

3+1=4

Therefore, the batches of brownies can Luisa make is 4 batches.

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Answer:

A

Step-by-step explanation:

Given

- 2x² + 5x - 3 ← factor out - 1 from each term

= - 1(2x² - 5x + 3) ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 2 × 3 = 6 and sum = - 5

The factors are - 2 and - 3

Use these factors to split the x- term

2x² - 2x - 3x + 3 ( factor the first/second and third/fourth terms )

2x(x - 1) - 3(x - 1) ← factor out (x - 1) from each term

(2x - 3)(x - 1)

Then

- 2x² + 5x - 3 = - 1(2x - 3)(x - 1) → A

To find a recurrence relation for the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b, we can use the following approach.

Let's consider the last two letters of the sequence. There are three possible cases:

1. The last letter is not "a": In this case, we can append any of the three letters (a, b, or c) to the end of an (n-1)-letter sequence that satisfies the given condition. This gives us a total of 3 times the number of (n-1)-letter sequences that satisfy the condition.

2. The last letter is "a" and the second to last letter is "b": In this case, we can append any of the two letters (a or c) to the end of an (n-2)-letter sequence that satisfies the given condition. This gives us a total of 2 times the number of (n-2)-letter sequences that satisfy the condition.

3. The last letter is "a" and the second to last letter is not "b": In this case, we cannot append any letter to the end of the sequence that satisfies the condition. Therefore, there are no such sequences of length n in this case.

Putting all these cases together, we get the following recurrence relation:

f(n) = 3f(n-1) + 2f(n-2), where f(1) = 3 and f(2) = 9.

Here, f(n) denotes the number of n-letter sequences using the letters a, b, c such that any a not in the last position of the sequence is always followed by a b.

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Answer:

Step-by-step explanation:

Exponential Growth:

1). The value of a home in a growing community every year.

2). The amount of money in a saving account that earns interest annually.

Exponential decay:

1). The monthly sale of albums of a band whose popularity is declining.

2). The amount of radioactive element remaining in a sample every decade.

3). The temperature of a hot cup of coffee left on the counter every minute.

The percentage is obtained by multiplying by 100 and dividing the needed amount by the entire value.

Number of foreign coins:

84% of 275 = 231

There are 231 foreign coins available.

The percentage is obtained by multiplying by 100 and dividing the needed amount by the entire value.

Example:

The necessary percentage value is a.

value total = b

a/b x 100 Equals percentage

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We've got

There are 275 coins in all.

84% of the coins are foreign currency.

how many foreign coins there are.

= 84% of 275

= 84/100 x 275

= 231

Thus,

The number of foreign coins is 231.

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To evaluate the expression |2-r| + 17 when r=3, q=1, and w=-2, we substitute the given values into the expression and simplify.

Given that r=3, q=1, and w=-2, we substitute the value of r into the expression |2-r| + 17. Since r=3, the expression becomes |2-3| + 17. Evaluating the absolute value |2-3| gives us |-1|, which is equal to 1.

Therefore, the expression simplifies to 1 + 17. Adding 1 and 17, we get the final result of 18. Thus, when r=3, q=1, and w=-2, the expression |2-r| + 17 evaluates to 18.

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Answer:

15. 2

16. \(\frac{27}{16}\) or 1.6875

17. \(\frac{17}{30}\) or 0.5666666667

18. 5

19. \(\frac{35}{8}\) or 4.375

20. \(\frac{22}{5}\) or 4.4

Step-by-step explanation:

Find common denominators. Multiply then simplify (if possible).

9514 1404 393

Answer:

Step-by-step explanation:

The intercepts are ...

  x-intercept = -4/-9 = 4/9

  y-intercept = -4/5

Knowing these intercepts means we can put the equation in intercept form.

  x/(4/9) -y/(4/5) = 1

The fractional intercepts make graphing somewhat difficult. However, we observe that the sum of the x- and y-coefficients is equal to the constant:

  -9 +5 = -4

This means the point (x, y) = (1, 1) is on the graph. Knowing a point, we can write several equations using that point.

We like a positive leading coefficient (as for standard or general form), so we can multiply the given equation by -1.

  9x -5y = 4 . . . . . standard form equation

Adding -4, so f(x,y) = 0, puts this in general form.

  9x -5y -4 = 0

We can eliminate the constant by translating a line from the origin to the point we know:

  9(x -1) -5(y -1) = 0

This can be rearranged to the traditional point-slope form ...

  y -1 = 9/5(x -1)

Yet another equation can be written that tells you the slope is the same everywhere:

  (y -1)/(x -1) = 9/5

These are only a few of the many possible forms of a linear equation.

The amount of cardboard needed to cover the entire space on the ground is 40 square feet.

To find the amount of cardboard needed to cover the entire space on the ground, we need to calculate the surface area of the rectangular cardboard.

The surface area of a rectangle can be found by multiplying its length by its width. In this case, the width of the cardboard is 8 feet and the length is 5 feet.

Surface area = length × width

Surface area = 5 feet × 8 feet

Surface area = 40 square feet

Therefore, the amount of cardboard needed to cover the entire space on the ground is 40 square feet.

This means that a rectangular piece of cardboard with dimensions 8 feet by 5 feet would be sufficient to cover the entire ground area. The cardboard should be large enough to completely cover the 8 feet wide and 5 feet long space.

It's important to note that the surface area represents the two-dimensional space covered by the cardboard. If we were to consider the thickness of the cardboard, it would add a third dimension and result in a volume measurement rather than just an area. However, in this context, we are only concerned with the area being covered.

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Answer:

slope(m)=6

Step-by-step explanation:

(2 , -1)=(x1 , y1)

(3 , 5)=(x2 , y2)

use formula : y2 - y1/x2 - x1

=5-(-1)/3-2

=5+1/1

=6/1

=6

therefore slope of a line is 6.

Answer:

Find the volume of a concrete block that is 2.5 metres long,. 12 centimetres wide and. 10 centimetres high. Two of the dimensions, the width and height,

Answer:

480,000 cm3

Step-by-step explanation:

give crown please ( brainliest )

The given rational function is \(\frac{x^2-x-6}{x^2-2x-8}\). We need to find the points of discontinuity, vertical asymptotes, horizontal asymptotes, holes, x-intercepts, y-intercepts, and end behavior of the function.

Firstly, let's find the points of discontinuity. The function has a discontinuity where the denominator is equal to zero. Therefore, we need to solve the equation x^2-2x-8=0. Factoring the quadratic equation, we get (x-4)(x+2)=0. Hence, the points of discontinuity are x=4 and x=-2.

Next, we need to find the vertical asymptotes. The vertical asymptotes occur at the points of discontinuity. Therefore, the vertical asymptotes of the function are x=4 and x=-2.

To find the horizontal asymptote, we need to divide the leading coefficient of the numerator by the leading coefficient of the denominator. The degree of the numerator and denominator is the same, which is 2. Therefore, the horizontal asymptote of the function is y=1.

To find the holes in the graph, we need to simplify the function and check if there are any common factors in the numerator and denominator. Factoring the numerator and denominator, we get \(\frac{(x-3)(x+2)}{(x-4)(x+2)}\). We can cancel the common factor of x+2, which gives us \(\frac{x-3}{x-4}\). Hence, there is a hole at x=-2.

To find the x-intercepts, we need to set the numerator equal to zero. Therefore, x^2-x-6=0. Factoring the quadratic equation, we get (x-3)(x+2)=0. Hence, the x-intercepts are x=3 and x=-2.

To find the y-intercept, we need to set x=0 in the function. Therefore, the y-intercept is \(\frac{-6}{-8}\), which simplifies to \(\frac{3}{4}\).

Lastly, to determine the end behavior, we need to examine the behavior of the function as x approaches infinity and negative infinity. As x approaches infinity, the function approaches 1, which is the horizontal asymptote. As x approaches negative infinity, the function also approaches 1.

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The solution of the equation x³ = 16 will be;

⇒ x = 2.519

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

Given that;

The equation is,

⇒ x³ = 16

Now,

Since, The equation is,

⇒ x³ = 16

Solve for x as;

⇒ x = ∛ 16

⇒ x = 2.519

Thus, The solution of the equation is,

⇒ x = 2.519

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Using the critical values of t=+/-2.201 is less likely to lead to rejection of the null hypothesis than using the critical values of +/-2.093.

Critical Value Definition -

Critical value can be defined as a value that is compared to a test statistic in hypothesis testing to determine whether the null hypothesis is to be rejected or not.

If the value of the test statistic is less extreme than the critical value, then the null hypothesis cannot be rejected.

Critical values are essentially cut-off values that define regions where the test statistic is unlikely to lie; for example, a region where the critical value is exceeded with probability \alpha if the null hypothesis is true.

Using the critical values of t=±2.201 is more "conservative" than using the critical value of ±2.093 because it is more likely to reject the null hypothesis using the greater value i-e t=±2.201.

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Answer:

2 m.

Step-by-step explanation:

T = 8.0 s is the period of the pendulum

g = 9.81 m/s^2 is the acceleration due to gravity

True, the eventual success of any system solely depends on how users work with it.

A system's success is determined by various factors, such as its design, functionality, and compatibility with user needs.

However, user engagement, adaptability, and willingness to work with the system notably contribute to its success.

Users who understand the system's features and can efficiently adapt and utilize them in their workflow contribute to its overall effectiveness.

In contrast, a system with poor user adoption and engagement may not achieve its intended outcomes, regardless of its inherent quality.

So, even if a system is well-designed and has all the necessary features, if users are unable to effectively use it, the system will not achieve its intended purpose.

Thus, user adoption and effective usage are crucial for the success of any system.

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The length of the line segment TV is 30.

In this problem we have a geometrical system formed by two collinear line segments (TU, UV). Mathematically speaking, the geometrical system is described by the following equations:

TV = TU + UV       (1)

TU = 25                 (2)

UV = 2 · x + 15       (3)

TV = x + 35            (4)

By (1), (2), (3) and (4):

x + 35 = 25 + (2 · x + 15)

x + 35 = 2 · x + 40

35 - 40 = 2 · x - x

- 5 = x

x = - 5

Lastly, we evaluate (4) at x = - 5 and find the length of the line segment TV is:

TV = - 5 + 35

TV = 30

The length of the line segment TV is 30.

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Answer:

1. -3/4

2. -7

3. -9/5

4. -1/3

5. 4/5

6. -1/6

Answer:

First, we need to find the length of the slope connecting the shallow end and the deep end. We can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the slope and the bottom of the pool:

h = sqrt((12.5 - 9)² + 4.5²) = 6.08 feet

Next, we need to find the difference in depth between the shallow end and the deep end. We can use the tangent of the angle of depression to find this difference:

tan(16.5) = (4.5 - d) / 6.08

where d is the depth of the pool at the deep end. Solving for d, we get:

d = 4.5 - 6.08 * tan(16.5) = 2.24 feet

Therefore, the depth of the pool at the deep end is approximately 2.2 feet.

Answer:

im pretty sure a b g

Step-by-step explanation:

The length vector is 1. So the sketch vector field f is given below. So the option a is correct.

In the given question, the vector field F by drawing a diagram like this figure.

The given vector field F is:

F(x, y) = (yi + xj)/√(x^2 + y^2)

We can write the vector field as:

F(x, y) = yi/√(x^2 + y^2) + xj/√(x^2 + y^2)

Here

F(x, y) = [y/√(x^2 + y^2)]^2 + [x/√(x^2 + y^2)]^2

F(x, y) = y^2/(x^2 + y^2) + x^2/(x^2 + y^2)

F(x, y) = (y^2+ x^2)/(x^2 + y^2)

F(x, y) = 1

F(0, y) = y/|y| = ±1

F(x, 0) = x/|x| = ±1

So the length vector is 1.

So the sketch vector field f is given below:

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The complete question is:

Sketch the vector field F by drawing a diagram like this figure.

F(x, y) = (yi + xj)/√(x^2 + y^2)

In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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