Identify which of the following measures would be best to use in the below situations.
A. Odds ratio D. Etiologic fraction (attributable risk)
B. Relative risk E. Sensitivity
C. Attack rate F. Specificity
28. ______Determining an association between eating junk food and Type II diabetes in a cohort study
29. ______Determining the contributing effect of smoking in coronary heart disease
30. ______Determining how well a new test which screens for prostate cancer finds all cases of the disease
31. ______Determining an association between wearing seat belts and death in motor vehicle accidents in a case-control study
32. ______Determining which item may be the cause of food poisoning during a local outbreak
33. ______Determining how well a new secondary prevention test determines that a person does not have the disease

The angular coordinate, angular velocity, and angular acceleration of the flywheel are: (a) At t = 0, θ = θ0 = 0.5 rad, ω = 0, and α = 12π²θ0 = 23.55 rad/s².

(b) At t = 0.125 s, θ = 0.267 rad, ω = 4.116 rad/s, and α = -69.08 rad/s².

The given equation for the angular displacement of the flywheel is θ=θ0e(-3πcos(4πt)). Here, θ0 = 0.5 rad. To find the angular velocity and angular acceleration, we need to differentiate θ with respect to time.

θ = θ0e(-3πcos(4πt))

ω = dθ/dt = -12π²θ0e(-3πcos(4πt))sin(4πt)

α = d²θ/dt² = -48π³θ0e(-3πcos(4πt))(cos(4πt) - 2)sin(4πt)

Substituting t = 0, we get:

(a) At t = 0, θ = θ0 = 0.5 rad, ω = dθ/dt = 0, and α = d²θ/dt² = 12π²θ0 = 23.55 rad/s².

(b) At t = 0.125 s, θ = 0.267 rad, ω = dθ/dt = 4.116 rad/s, and α = d²θ/dt² = -69.08 rad/s².

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Considering the given system of equations, it is found that:

B. They intersect at the point (2,9000).

C. The x-value of the point of intersection represents the time in which they intersect.

D. The y-value of the point of intersection represents the altitude in which they intersect.

A system is equations is composed by a number of curves, and the solution to the system of equations is the point where all these curves intersect each other on the graph.

In the context of this problem, the curves are given as follows:

In which the variables are as follows:

From the graph given in this problem, it is found that they intersect at point (2,9000), that is, they intersect a height of 9000 feet at a time of 2 seconds.

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Answer:  Considering the given system of equations, it is found that:

B. They intersect at the point (2,9000).

C. The x-value of the point of intersection represents the time in which they intersect.

D. The y-value of the point of intersection represents the altitude in which they intersect.

How to solve a system of equations graphically?

A system is equations is composed by a number of curves, and the solution to the system of equations is the point where all these curves intersect each other on the graph.

In the context of this problem, the curves are given as follows:

Plane A descent: y = -2500x + 14000.

Plane B ascent: y = 4000x + 1000.

In which the variables are as follows:

Variable x: time in minutes.

Variable y: altitude of the plane, in feet.

From the graph given in this problem, it is found that they intersect at point (2,9000), that is, they intersect a height of 9000 feet at a time of 2 seconds.

Step-by-step explanation:

Answer:

ypotenuse squared = adjacent squared + opposite squared

Step-by-step explanation:

sin θ =opposite/hypotenuse

tan θ = opp/adjacent

cos θ = adj/hyp

Pythagoras Theorem states that hypotenuse squared = adjacent squared + opposite squared

Answer: A

Step-by-step explanation:

The main limitation of a cross-sectional study design is that researchers cannot infer the temporal sequence between exposure and disease when the exposure is a changeable characteristic.

Cross-sectional studies are observational studies that measure the prevalence of a disease or health outcome at a specific point in time and assess the association between the outcome and exposure to certain risk factors. However, because the data is collected at a single time point, it is impossible to determine the order of events between exposure and outcome. This is particularly problematic when the exposure is a changeable characteristic such as diet or lifestyle habits. In such cases, it is difficult to determine whether the exposure caused the outcome or whether the outcome led to changes in exposure. Despite this limitation, cross-sectional studies can still provide valuable information about the prevalence and distribution of diseases and risk factors in a population.

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Answer:

6

Step-by-step explanation:

Answer: -10 and 68

Step-by-step explanation:

We have the numbers, ordered from least to greatest:

11, 26, 29, 31, 43, 44, 47 and x.

The range is equal to the difference between the largest number and the smallest number, so, x can take two values.

The smallest number:

here we have that:

47 - x = 57

x = 47 - 57 = -10

The other possibility is that x is the largest number, in this case, we have that:

x - 11 = 57

x = 57 + 11 = 68.

Then the two possibla values of x are -10 and 68

Answer:

3/5

Step-by-step explanation:

72/2 =36

120/2 =60

=36/60

36/2 = 18

60/2 = 30

=18/30

18/2=9

30/2 =15

= 9/15

9/3=3

15/3 =5

= 3/5

Answer:

-212

Step-by-step explanation:

an = a1 + (n-1)d, so

a52 = a1 + 51d

a1= - 8

d = -4 ( because you take away 4 every time)

so a52 = -8 + 51(-4) = -212

The length of the other leg is (c) √43

From the question, we have the following parameters that can be used in our computation:

Hypotenuse = 7

One leg = √6

The length of the other leg can be calculated using

The length of the other leg = √(Hypotenuse^2 - One leg^2)

So, we have

The length of the other leg = √(7^2 - √6^2)

Evaluate

The length of the other leg = √43

Hence, the length is (c) √43

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Complete question

A right triangle has a leg length of √6 and a hypotenuse length of 7. Determine the length of the other leg of the right triangle.

Answer:

B. No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP.

Step-by-step explanation:

I took the test.

The correct option is B. No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP.

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

We are given that Deepak is measuring sides and angles of triangle FGH to determine whether it is congruent to triangle MNP,

In Triangle M N P.

Side P N = 26.7 centimeters,

M N is 18.3 centimeters,

P M is 14.2 centimeters.

Angle P is 40 degrees, angle N is 30 degrees, and angle M is 110 degrees.

He found that Angle G has a measure of 50° and Segment F H is 18.3 centimeters long.

Based on the definition, two triangles are congruent if the three sides are equal and the three angles are equal.

Hence, he need to know the other lengths of the sides of the triangle and the others angles to know if they are congruent or not.

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Answer:

= 44j+32

j = -8/11

geometric figure it is called a line.

Step-by-step explanation:

Expand the following:

4 (6 j + 5 j + 8)

Grouping like terms, 5 j + 8 + 6 j = (5 j + 6 j) + 8:

4 (5 j + 6 j) + 8

5 j + 6 j = 11 j:

4 (11 j + 8)

4 (11 j + 8) = 4×8 + 4×11 j:

4×8 + 4×11 j

4×8 = 32:

32 + 4×11 j

4×11 = 44:

Answer: 32 + 44 j

The pitch of the roof is 0.3.

Pitch:

The pitch can be expressed numerically as a fraction. The pitch fraction represents a certain amount of vertical rise over the entire span.

Here it is given that the rise in the roof is 3.6m and a rum of 12m,

We have to find the pitch of the roof.

As is already given in the statement that the slope of a roof is called its pitch.

By this we get the slope:

Slope = 3.6/12

= 3/10

= 0.3

Therefore we get the pitch of the roof at 0.3.

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Answer:

(8w+96)

Step-by-step explanation:

(w+12)8

8(w+12)

8•w

8•12

(8w+96)

If the initial population is 3800. The population of cockroaches after 3 years will be 1603.

Consider the function:

y = a(1 ± r)ⁿ

where n is the number of times growth/decay, a = initial amount, and r = fraction by which this growth/decay occurs.

If there is a plus sign, there is exponential growth happening by r fraction or r%.

If there is a minus sign, there is exponential decay happening by r fraction or r%.

If the population is currently 3,800 cockroaches.

The expression is given as

y = 3800(0.75)ⁿ

The population of cockroaches after 3 years will be

y = 3800(0.75)³

y = 3800 x 0.4218

y = 1603.125

y ≅ 1603

Hence, the population of cockroaches after 3 years will be 1603.

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The complete question is:

Colette has an exterminator visit regularly to control an ongoing cockroach problem. it's been working, and the population has declined by 15% every year. if the population is currently 3,800 cockroaches, how many will there be in 3 years? if necessary, round your answer to the nearest whole number.

Answer:

Step-by-step explanation:

The formula for exterior angles of a regular polygon is that they must add up to 360. They are also equal for a regular polygon.

Exterior angle = 360 / number of sides

The first one (a pentagon) has 5 sides

Exterior angle = 360/5

Exterior angle = 360/5 = 72

The second one has 8 sides.

Exterior angle = 360/8

Exterior angle = 360/8 = 45

SOLUTION

For 10 days, Mario measured the amount of food that his cat Toby ate each day.

The amount he recorded are shown in the table at the right

Graph the results on the line plot

Amount Toby ate each day for 10 days

Amount of food Days

1/ 4 c 2

3/ 8 c 1

1/ 2 c 3

5/ 8 c 3

3/ 4 c 1

TOTAL AMOUNT OF FOOD TOTAL NUMBER OF DAYS

1/ 4 c + 3/ 8 c + 1/2 c + 5/ 8 c + 3/ 4 c = 5/ 2 c = 2 1/2 c 10

What is the total amount of food Toby ate over the 10 days?

Toby ate 2 1/ 2 c over 10 days.

Answer:

B. 171

Step-by-step explanation:

Answer:

The answer is 171

Step-by-step explanation:

You do the math in the parentheses first, then the sum to the power of two, then multiply by 4, and then subtract by 5^2.

4×(2+5)^2-5^2

4×(7^2)-5^2

4×(49)-5^2

4×49-5^2

196-5^2

196-25=

171

Answer:

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Step-by-step explanation:

Answer:

The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

Step-by-step explanation:

Natural Numbers are known as 1, 2, 3, 4, ..., ∞

Now,

For Cube of first six natural numbers

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Thus, The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

-TheUnknownScientist

In Andrew's coordinate proof relating isosceles triangle the coordinates required are :

Isosceles triangle refers to a class of triangles which have two sides equal

The coordinates are calculated using the mid point calculation. as the triangle is isosceles triangle the points P and Q should be mid points of line ED and line FD

mid point of ED = P

E (0, 0) and D (2a, 2b)

\(P=(\frac{0+2a}{2} ,\frac{0+2b}{2} )\)

\(P=(\frac{2a}{2} ,\frac{2b}{2} )\)

P= (a, b)

mid point of FD = P

F (4a, 0) and D (2a, 2b)

\(Q=(\frac{4a+2a}{2} ,\frac{0+2b}{2} )\)

\(Q=(\frac{6a}{2} ,\frac{2b}{2} )\)

Q = (3a, b)

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An example of an exponential function is y = 2^x. In this function, the base is 2, and x is the exponent.

The rate of change in an exponential function depends on the base. In this case, since the base is 2, the function will experience exponential growth. As x increases, the value of y will double each time. For example, when x = 0, y = 1 (2^0 = 1), when x = 1, y = 2 (2^1 = 2), when x = 2, y = 4 (2^2 = 4), and so on. The rate of change increases exponentially as x increases.

The graph of an exponential function with a base greater than 1, like in this example, will start with a shallow slope near the y-axis but quickly become steeper as x increases. The graph will never touch or cross the x-axis, as 2^x is always positive. The graph will show exponential growth, getting steeper and steeper as x increases. It will have a concave shape, curving upward.

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Step-by-step explanation:

hope this helps you out good luck

The value of the x of the equation x² + 2x = 24 is negative 6 and 4, then the correct option is C.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The expression equation is given below.

x² + 2x = 24

x² + 2x – 24 = 0

On factorization, we have

       x² + 2x – 24 = 0

x² + 6x – 4x – 24 = 0

       (x – 4)(x + 6) = 0

                         x = –6, 4

The value of x is –6 and 4.

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Given:

\(\sin (x)=-\dfrac{1}{2}\)

\(\cos (y)=-\dfrac{1}{3}\)

x is an angle in quadrant III, and y is an angle in quadrant II.

To find:

The value of sin(x+y).

Solution:

We know that, only sin and cosec are positive in II quadrant. Only tan and cot are positive in III quadrant.

x is an angle in quadrant III,

\(\cos x=-\sqrt{1-\sin^2 x}\)

\(\cos x=-\sqrt{1-(-\dfrac{1}{2})^2}\)

\(\cos x=-\sqrt{1-\dfrac{1}{4}}\)

\(\cos x=-\sqrt{\dfrac{4-1}{4}}\)

\(\cos x=-\dfrac{\sqrt{3}}{2}\)

y is an angle in quadrant II.

\(\sin y=\sqrt{1-\cos^2x}\)

\(\sin y=\sqrt{1-(-\dfrac{1}{3})^2}\)

\(\sin y=\sqrt{1-\dfrac{1}{9}}\)

\(\sin y=\sqrt{\dfrac{9-1}{9}}\)

\(\sin y=\sqrt{\dfrac{8}{9}}\)

\(\sin y=\dfrac{2\sqrt{2}}{3}\)

Now,

\(\sin(x+y)=\sin x\cos y+\cos x\sin y\)

\(\sin(x+y)=(-\dfrac{1}{2})\times (-\dfrac{1}{3})+(-\dfrac{\sqrt{3}}{2})\times (\dfrac{2\sqrt{2}}{3})\)

\(\sin(x+y)=\dfrac{1}{6}-\dfrac{2\sqrt{6}}{6}\)

\(\sin(x+y)=\dfrac{1-2\sqrt{6}}{6}\)

Therefore, the correct option is B.

Answer:

Choice B

Step-by-step explanation:

The definition of percent helps you write fraction and decimal equivalents by understanding that "per cent" means "per hundred".

For example, if you are asked to write the fraction and decimal equivalent of 25%, you would divide 25 by 100 to get the fractional equivalent of ¼, and divide 25 by 100 to get the decimal equivalent of 0.25.

The decimal equivalent of a fraction or percentage is the numerical value expressed in decimal form. For example, the decimal equivalent of 1/2 is 0.5 and the decimal equivalent of 25% is 0.25. Decimal equivalents are useful for calculations and can be used to convert fractions and percentages into decimal form.

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Answer:69

Step-by-step explanation:

kp(x) satisfies the condition of U, and it is in U. Since U satisfies all three properties of a subspace, we can conclude that U is a subspace of P2.

of c₁ and c₂, which are both real numbers.

Therefore, the sum p(x) + q(x) satisfies the condition of U, and it is in U.

Closure under scalar multiplication:

Let's take a polynomial p(x) = a + bx + cx² in U, where a = -b.

We need to show that if we multiply p(x) by a scalar k, the result kp(x) is also in U.

(kp(x)) = k(a + bx + cx²)

= ka + kbx + kcx²

Since a = -b, we can rewrite the expression as:

(kp(x)) = k(-b) + kbx + kcx²

= -kb + kbx + kcx²

Notice that the coefficient of x is kb, and the coefficient of x² is kc, which are both real numbers.

Therefore, kp(x) satisfies the condition of U, and it is in U.

Since U satisfies all three properties of a subspace, we can conclude that U is a subspace of P2.

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