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The first scenario described is an example of a retrospective cohort study.  The second scenario suggests a retrospective cohort study as well. The third scenario represents a cross-sectional study, where researchers conduct a survey among high school students to assess the prevalence of obesity and diabetes.

1. In the first scenario, a retrospective cohort study is conducted by tracking individuals over a 20-year period. The study begins in 1960 and collects data on cigar smoking practices. After 20 years, the participants are followed up to determine if they developed any cancers. This type of study design allows researchers to examine the long-term effects of smoking Cuban cigars.

2. The second scenario involves a retrospective cohort study as well. The objective is to study the long-term neurological effects of a discontinued anesthetic agent. The researchers identify patients who received the drug before it was discontinued and then assess the occurrence of subsequent neurological disorders. This study design allows for the examination of the relationship between exposure to the anesthetic agent and the development of neurological disorders.

3. The third scenario represents a cross-sectional study. Researchers aim to assess the prevalence of obesity and diabetes among high school students during their junior year. They conduct a survey to gather information on the students' current weight, diabetes status, and other relevant factors. A cross-sectional study provides a snapshot of the population at a specific point in time, allowing researchers to examine the prevalence of certain conditions or characteristics.

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Answer:

they sold 1,397,262,266 less seeds this season but made 1,397,262,266 last season

Step-by-step explanation:

2,995,748,111 - 1,598,485,845 = 1,397,262,266

Answer:

The answer is 2

Step-by-step explanation:

2x3=6 +1 =7

Answer:

answer is : 2

Step-by-step explanation:

2x3=6+1=7

Step-by-step explanation:

The variable is n, which can have different values. 9 is the coefficient of the variable term and -2 is the constant term

Answer:

C)N.

Because variables represent an unknown number.

Answer: A) No, because it has a constant rate of change

=============================================================

Explanation:

Each time x goes up by 1, y drops by 2.

This means,

slope = rise/run

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

slope = (y drops by 2)/(x goes up by 1)

slope = -2/1

slope = -2

-----------

We can pick two points from the table to plug into the slope formula. I'll pick the first two rows

m = slope

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

m = (2-4)/(7-6)

m = -2/1

m = -2

If you tried every pair of rows possible for this table, you'll get the same slope each time. This is why the rate of change is constant.

This means the data is linear instead of nonlinear. Plotting the points leads to a single straight line going through all four points. See the diagram below. The graph was made with GeoGebra.

The equation of that red line is y = -2x+16 which is equivalent to 2x+y = 16.

In the graph, going from A to B has us go down 2 and to the right 1, which is one visual way of seeing the slope is -2/1 = -2.

Answer:

Red = 43 more picket

Green = 49 more picket

Yellow = 66 more picket

Blue = 75 more picket

Step-by-step explanation:

Red = 32

Green = 26

Yellow = 9

Blue = 0

Total picket Dana needs = 300

She wants equal amounts of each of her four selected colors.

Each color = 300/4

= 75 picket per color

How many more of each color does Dana need to buy?

Red = 32

= 75 - 32

= 43 more

Green = 26

= 75 - 26

= 49 more

Yellow = 9

= 75 - 9

= 66 more

Blue = 0

= 75 - 0

= 75 more

Red = 43 more picket

Green = 49 more picket

Yellow = 66 more picket

Blue = 75 more picket

The length of opposite side is 34.5 meters. The length of opposite side is 132 feet. Therefore, the height of the plane above the level of the atoll is approximately 460 meters to the nearest meter.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving triangles, such as finding the unknown sides or angles of a triangle, or finding the distance or height of an object that is too far away to measure directly.

Here,

6. To find the horizontal distance Viola has covered, we need to use trigonometry. The angle of 9° is the angle between the hill and the horizontal, so we can use the tangent function:

tangent(9°) = opposite/hypotenuse

where the opposite side is the horizontal distance we want to find and the hypotenuse is the distance Viola has driven, which is 200 meters.

Solving for the opposite side, we get:

opposite = tangent(9°) x hypotenuse

opposite = tan(9°) x 200

opposite ≈ 34.5 meters

7. Using trigonometry again, we can find the height of the building. The angle shown in the diagram is the angle of elevation from the students' location to the top of the building, and the distance shown is the horizontal distance between the students' location and the base of the building. We can use the tangent function again:

tangent(angle of elevation) = opposite/adjacent

where the opposite side is the height of the building we want to find, and the adjacent side is the horizontal distance from the students to the building, which is given as 150 feet.

Solving for the opposite side, we get:

opposite = tangent(angle of elevation) x adjacent

opposite = tan(41°) x 150

opposite ≈ 132 feet

8. In this problem, we can use trigonometry to find the height of the plane. We know the angle of depression from the plane to the atoll is 7°, which means the angle of elevation from the atoll to the plane is also 7°. We also know the horizontal distance from the plane to the atoll is 3,729 meters. Let h be the height of the plane above the level of the atoll. Then we can set up the following equation using the tangent function:

tan(7°) = h / 3,729

Solving for h, we get:

h = 3,729 * tan(7°)

Using a calculator, we get:

h ≈ 460 meters

9. In this problem, we can use trigonometry to find the height of the pole. Let h be the height of the pole above the ground, and let d be the horizontal distance from the surveyor to the base of the pole. Then we can set up the following right triangle:

The opposite side is the height of the pole h.

The adjacent side is the horizontal distance d = 140 feet.

The angle of elevation to the top of the pole is 44°.

We can use the tangent function to find the height of the pole:

tan(44°) = h / 140

Solving for h, we get:

h = 140 * tan(44°)

Using a calculator, we get:

h ≈ 157 feet

10. In a 30°-60°-90° triangle, the sides are in a ratio of 1:√3:2, where the hypotenuse is twice the length of the shorter leg. Let x be the length of the shorter leg, then the longer leg is x√3 and the hypotenuse is 2x. In this problem, we are given that the hypotenuse has a length of 18, so we can set up the following equation:

2x = 18

Solving for x, we get:

x = 9

Therefore, the shorter leg has a length of 9, and the longer leg has a length of 9√3.

The perimeter of the triangle is the sum of the lengths of its sides, so we have:

Perimeter = 9 + 9√3 + 18

Using the fact that √3 ≈ 1.732, we can simplify this expression to:

Perimeter ≈ 9 + 9(1.732) + 18

Perimeter ≈ 9 + 15.588 + 18

Perimeter ≈ 42.588 meters

Therefore, the perimeter of the triangle is approximately 42.588 units.

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The relation that is a function is (d) the graph

The list of options represents the given parameter

As a general rule;

For a relation to be considered a function, the following must be true:

One x value must not point to several y values

Using the above as a guide, the ordered pair in (a), relation in (b) and table in (c) are not functions

This is because one x value must not point to several y values

However, there are unique values in the graph of (d)

Hence, (d) the graph is a function

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The 14.9% increase in Sylvia's lead lathe tech's hourly wage of $18.50 results in a $2.75 per hour increase. Assuming the lead lathe tech works 2,080 hours per year, the additional cost to Sylvia's annual wages budget would be approximately $5,720, excluding benefits or taxes.

First, we need to find the percentage increase in the lead lathe tech's hourly wage. The increase requested is $2.75, which is 14.9% of the current wage rate ($18.50). To calculate the percentage increase, we divide the increase by the current wage rate and multiply by 100: ($2.75 / $18.50) * 100 ≈ 14.9%.

To determine the additional cost to Sylvia's annual wages budget, we need to know the total number of hours worked by the lead lathe tech in a year. Let's assume the lead lathe tech works 40 hours per week and there are 52 weeks in a year, resulting in a total of 2,080 hours.

To calculate the annual cost of the wage increase, we multiply the hourly increase ($2.75) by the total number of hours worked (2,080): $2.75 * 2,080 ≈ $5,720.

Therefore, the 14.9% increase in the lead lathe tech's hourly wage will cost Sylvia an additional $5,720 in her annual wages budget, excluding benefits or taxes.

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Rate: 12 students. Unit Rate: 1 page for every 3 students, 3 pages per student. Neither: 320 words per page, 450 words, 500 words on 2 pages.

In this task, we are given five items with different values. Our goal is to classify each item as a rate, a unit rate, or neither.

A unit rate is a rate that has a denominator of 1. For example, if we say that a car is traveling at a speed of 30 miles per hour, this is a unit rate since it can also be expressed as 1 mile per 1/2 hour.

An item can be classified as neither if it is not a ratio or comparison of two different kinds of quantities.

- "12 students" is a rate since it compares the number of students to some other quantity that is not specified.

- "1 page for every 3 students" is a unit rate since it compares the number of pages to the number of students and has a denominator of 1.

- "320 words per page" is neither since it is not a comparison of two different kinds of quantities.

- "3 pages per student" is a unit rate since it compares the number of pages to the number of students and has a denominator of 1.

- "450 words" is neither since it is not a comparison of two different kinds of quantities.

- "500 words on 2 pages" is neither since it is not a ratio or comparison of two different kinds of quantities.

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Answer:

A

Step-by-step explanation:

Answer:

up to 5 candy bars

Step-by-step explanation:

Answer:

p = 26

Step-by-step explanation:

(p+4)/6 = 5

Multiply each side by 6

(p+4)/6 *6 = 5*6

p+4 = 30

Subtract 4 from each side

p+4-4 = 30-4

p = 26

a. ln(7x) can be expanded as ln(7) + ln(x). b. ln(x + 3) remains as it is, since it cannot be simplified further. c. ln(x^8) can be expanded as 8ln(x). d. 15,000ln(xy^4) can be expanded as ln(x) + 4ln(y) + ln(15,000).

a. To expand the logarithmic expression ln(7x), we can use the property of the natural logarithm that states ln(ab) = ln(a) + ln(b).

Therefore, ln(7x) can be expanded as ln(7) + ln(x).

b. Similarly, the logarithmic expression ln(x + 3) can be expanded using the property ln(ab) = ln(a) + ln(b).

Hence, ln(x + 3) remains as it is since we cannot simplify it further.

c. Expanding the logarithmic expression ln(x^8) can be done using the property ln(a^b) = b * ln(a).

Thus, ln(x^8) becomes 8 * ln(x).

d. Expanding the logarithmic expression 15,000ln(xy^4) can be done by applying the property ln(ab) = ln(a) + ln(b).

Therefore, 15,000ln(xy^4) can be expanded as 15,000[ln(x) + ln(y^4)].

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a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

(5b-4)1/5 = 5b * 1/5 - 4 * 1/5 = b - 4/5

Answer:

\(\frac{1}{2}\)x-4

Step-by-step explanation:

Answer:

1/2 (x)-4

Step-by-step explanation:

Hopes this helps

Based on the two-tangent theorem, the measure of TH is also: 4.2 cm.

According to the two-tangent theorem, the length of two tangents (TG and TH) that are drawn from a circle to intersect at an external point are equal. That is, they are congruent to each other.

Thus, we are given that, TG = 4.2 cm. Therefore, based on the two-tangent theorem, the measure of TH is also: 4.2 cm.

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∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.

We are given that:

AB = BC

Now, draw a angle bisector from point B to the line AC in a way that it intersects AC at D.

Now, we get that:

∠ABD = ∠CBD ( BD is the angle bisector)

BD = BD ( common line)

So, ΔABD ≅ Δ CBD ( SAS property)

So,

∠A = ∠ C ( CPCT rule)

Also, it will be true for every isosceles triangle.

Therefore, we get that, ∠A = ∠C for every isosceles triangle and not only for this specific isosceles triangle.

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Your question was incomplete. Please refer the content below:

There is an isosceles triangle with AB = BC. Prove that ∠A = ∠C.

Did we prove the conclusion true for every isosceles triangle or only for this specific isosceles triangle.

Using the elimination method, the price of one t-shirt is $30 and one key-chain is $11.

In the given question, Elizabeth's family went to NYC for their vacation.

At the gift shop on Liberty Island, Valerie bought three t-shirts and four key chains for $134, and Jennifer bought four t-shirts and five key chains for $175.

We have to find the price of each item.

Let the price of one t-shirt = $x

Let the price of one Key chain = $y

According to question

Price of three t-shirts and four key chains = $134

So the equation is

3x + 4y = $134……………….(1)

Also,

Price of four-shirts and five Key chains = $175

So the equation is

4x+5y = $175……………………..(2)

Now solving the equation using the elimination method.

Multiply Equation (1) by 5 and Equation (2) by 4, we get

15x+20y = 670....................(3)

16x+20y = 700......................(4)

Subtract equation 4 and 3, we get

x = 30

Now put the value of x in equation 1,

3*30 + 4y = $134

90+4y=$134

Subtract 90 on both side, we get;

4y = 44

Divide by 4 on both side, we get;

y = 11

Hence, the price of one t-shirt is $30 and one key-chain is $11.

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Answer:

1

Step-by-step explanation:

a negative plus a positive is equal to a negative minus a negative. -29+30=-29-(-30)

Take away negative 30 from -29 and you get 1.

Answer: 2)The probability of drawing a red cube is 3/5 and the probability of drawing a blue cube us 2/5.

  3) No the probability of selecting a red cube is not equal to probability of selecting a blue cube because the outcomes 3/5 and 2/5 are not equal.

Step-by-step explanation:

The probability of each outcome in the sample space is:

Probability of drawing a red cube = 3/5

Probability of drawing a blue cube = 2/5

No, the probability of selecting a red cube is not equal to the probability of selecting a blue cube.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required event / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The sample space of this experiment consists of the possible outcomes of randomly drawing a cube from the bag.

There are two possible outcomes: either a red cube is drawn or a blue cube is drawn.

So, the probability of each outcome in the sample space is:

Probability of drawing a red cube = 3/5

Probability of drawing a blue cube = 2/5

No, the probability of selecting a red cube is not equal to the probability of selecting a blue cube.

This is because there are more red cubes in the bag than blue cubes, so the probability of drawing a red cube is higher than the probability of drawing a blue cube.

Specifically, the probability of drawing a red cube is 3/5, which is greater than the probability of drawing a blue cube, which is 2/5.

Thus,

The probability of each outcome in the sample space is:

Probability of drawing a red cube = 3/5

Probability of drawing a blue cube = 2/5

No, the probability of selecting a red cube is not equal to the probability of selecting a blue cube.

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Answer:

17

Step-by-step explanation:

the step by step process is on the pics

When Myriam was flying in the plane at a cruising altitude of 10 km, she felt no different sitting in her seat than she had felt on the ground. This is because both the plane and its occupants, including Myriam, are moving at the same speed and direction relative to each other. In other words, there is no relative motion between Myriam and the plane's interior.

From the perspective of the passengers inside the plane, they are essentially moving together as a single unit. The air inside the cabin is also moving with the same velocity as the plane. Therefore, there is no noticeable change in sensation or feeling of motion. This is similar to how we don't feel the motion of being inside a moving car if we are not looking outside or feeling any external forces.

The sensation of motion primarily arises when there is a change in velocity or when there are external forces acting on our bodies. In the case of an airplane flying smoothly at a constant speed and altitude, there are no significant forces or changes in velocity experienced by the passengers, so they feel no different than if they were on the ground.

The magician's trick of pulling a tablecloth out from under a set of dishes on a table is explained by the principle of inertia, which is a fundamental concept of Newton's First Law of Motion. According to Newton's First Law, an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and direction, unless acted upon by an external force.

When the magician pulls the tablecloth rapidly, the key is to apply a quick and forceful pull in a horizontal direction. By doing so, the frictional force between the tablecloth and the dishes is overcome, and the tablecloth slides out from underneath the dishes. Due to the inertia of the dishes, they tend to resist changes in their state of motion, so they remain relatively stationary even as the tablecloth is rapidly removed.

The magician's trick is more successful when the tablecloth is pulled rapidly rather than slowly. Pulling the tablecloth slowly would increase the time over which the frictional force acts, causing a greater chance for the dishes to be affected by the force and potentially get disturbed or toppled. A rapid pull reduces the duration of the force acting on the dishes, allowing them to maintain their state of motion (or rest) due to inertia and minimizing the likelihood of disruption.

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Given: A parallelogram with the dimension below

To Determine: The area of the given parallelogram

The area of a paralleogram is given by the formula

Substitute the base and the height into the formula

Hence, the area of the given parallelogram is 117yd²

Answer:

18 cm each side

Step-by-step explanation:

Square has 4 sides. So, 72/4=18

18 cm each side

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x + 2/9 = 8

x = 8 - 2/9

x = 72/9 - 2/9 (We converted 8 to 72/9)

x = 70/9

x = 7 7/9 if we can write the answer as a mixed number