64200x0.12 with work!

Answer: Here are three specific examples of public health problems that epidemiologists may investigate:

Obesity: Epidemiologists may investigate the causes and risk factors for obesity, as well as the prevalence and trends in obesity rates over time. They may also evaluate the effectiveness of interventions to prevent or treat obesity, such as diet and exercise programs, policy changes, or medical treatments.

Environmental exposures: Epidemiologists may investigate the health effects of exposure to environmental toxins, such as air pollution, lead, or pesticides. They may evaluate the risks associated with exposure to these toxins, identify populations that are particularly vulnerable, and assess the effectiveness of interventions to reduce exposure or mitigate health effects.

Injury prevention: Epidemiologists may investigate the causes and risk factors for injuries, such as motor vehicle crashes, falls, or firearm injuries. They may identify populations that are at higher risk for injuries, evaluate the effectiveness of injury prevention programs or policies, and develop strategies to reduce the incidence or severity of injuries.

Step-by-step explanation:

The  true about the volumes of the triangular prism and the triangular pyramid is D; triangular pyramid has a volume one-third the volume of the triangular prism.

Suppose a triangle. Now, strech it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, about triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

In order for us to know the volume of the triangular pyramid, first we need to know the ratio of the volume of triangular prism and the volume of the triangular pyramid.

Take a traingle as a base then take 3 triangles such that each of them are connected to one-one side of the first traingle and when they're taken together, they form a closed object, called as a triangular pyramid.

Volume of the pyramid = 1/3 volume of the prism.

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The triangular pyramid has a volume one-third the volume of the triangular prism .

Correct option is D.

Volume is the measure of the capacity that an object holds. Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains. The best way to visualize volume is to think of it in terms of the space enclosed/occupied by any 3-dimensional object or solid shape.

Given,

A triangular prism and a triangular pyramid have the same base and height.

Let the height be h unit and area of base be x square unit

Volume of triangular prism

= base area × height

= Ah cubic unit

Volume of triangular pyramid

= (1/3)× base area × height

= (1/3)Ah

= (1/3) volume of triangular prism

Hence, volume of triangular pyramid is one-third of  volume of triangular prism.

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The balance in your account after 10 years will be $2,473.08.

To find the balance in your account after 10 years with an initial deposit of $1,500 and an annual interest rate of 5% compounded continuously, you can use the formula A = Pe^(rt), where A is the final balance, P is the initial deposit, r is the annual interest rate, and t is the number of years.

In this case, P = $1,500, r = 5%, and t = 10. Plugging these values into the formula, we get:

A = $1,500 * e^(0.05 * 10)
A = $1,500 * e^(0.5)
A = $1,500 * 1.64872
A = $2,473.08

the balance in your account after 10 years will be $2,473.08.

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F(prime) = 30

Given the information in the question, we can calculate \(F^{\prime}(2)\) using the chain rule. The chain rule states that \(F^{\prime}(x) = f^{\prime}(g(x))\cdot g^{\prime}(x)\). Thus, \(F^{\prime}(2) = f^{\prime}(-5)\cdot g^{\prime}(2)\). Plugging in the given values, we get \(F^{\prime}(2) = 6 \cdot 5 = 30\). Therefore, \(F^{\prime}(2) = 30\).

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Answer:

Step-by-step explanation:

It seems like the problem is asking about a sequence of shapes rather than a sequence of matches, so I will assume that the correct information for the problem is:

Number of shapes:

n=1 n=2 n=3

m-4 m=7 m+2

i) Sequence table for the first six patterns:

Pattern number Number of shapes

1                               m-4

2                               m

3                               m+2

4                               m+6

5                               m+10

6                               m+14

ii) Formula for the number of shapes in terms of the pattern number:

From the table, we can see that the number of shapes used in each pattern is increasing by a constant amount of 4. Therefore, we can write the formula as:

Number of shapes = (pattern number - 1) * 4 + m

where m is the number of shapes in the first pattern.

iii) Number of shapes used in the 300th pattern:

To find the number of shapes used in the 300th pattern, we can use the formula and substitute pattern number = 300:

Number of shapes = (300 - 1) * 4 + m

Since we don't know the value of m, we can't determine the exact number of shapes. However, we do know that the number of shapes in the first pattern is either m-4, m, or m+2, depending on the value of m. If we assume the smallest possible value of m, which is 1 (since the number of shapes can't be negative), then the number of shapes in the 300th pattern would be:

Number of shapes = (300 - 1) * 4 + 1-4 = 1195

Therefore, if m = 1, then the number of shapes used in the 300th pattern is 1195. However, if m is greater than 1, then the number of shapes in the 300th pattern would be higher.

Answer:

every other 3

Step-by-step explanation:

a) f(x) = x^3 -x^2 + 3x +7 is the correct answer

Landon would make a salary of $96,000 in his 23rd year working at this job.

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

If Landon starts with a salary of $30,000 and gets a raise of $3,000 every year going forward, then his salary in the 23rd year can be calculated as follows:

Salary in 2nd year = $30,000 + $3,000 = $33,000

Salary in 3rd year = $33,000 + $3,000 = $36,000

Salary in 4th year = $36,000 + $3,000 = $39,000

and so on...

So, we can see that Landon's salary increases by $3,000 every year.

His salary in the 23rd year would be:

Salary in 23rd year = $30,000 + ($3,000 x 22) = $30,000 + $66,000 = $96,000

Therefore, Landon would make a salary of $96,000 in his 23rd year working at this job.

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Answer:

-85

Step-by-step explanation:

Surface area of the triangular prism which is a compound shape has an area of: 878mm².

The combined area of one or more circles and simple polygons is known as the area of the composite forms. The areas of every basic shape can be added together to determine the area of the composite shapes. Simply calculate each shape's area separately, then put them together to get the area of composite shapes.

Now in the question, we have 2 triangles with base, b =31mm and height, h = 14mm

Now area of both the triangles = 2 × 1/2 × b × h

= 2×1/2×14×31

=434mm²

Now we have three different rectangles.

In the first rectangle, length, l = 27mm and breadth, b = 6mm

Area of the rectangle as we know = l × b

= 27 × 6

= 162mm²

In the second rectangle, l = 16mm and b = 6mm

Area = 16 × 6

= 96mm²

In the final rectangle, l = 31mm and b = 6mm

Area = 31 × 6

= 186mm²

Therefore, the total surface area = 162 + 434 + 96 + 186 = 878mm².

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As a result, the balance in the account at the end of seven years is, to the closest cent, $116177.20.

The term "amount" in mathematics typically denotes a sum, total, or quantity. It could be a numerical value or some other kind of measurement. Depending on the context, the word "amount" may also be used to refer to quantity, total, sum, volume, or magnitude. \

The term "amount" is used in algebra and calculus to describe the outcome of an operation, such as the amount of change in a function or the quantity of a variable needed to satisfy an equation. In many disciplines, including finance, science, and engineering, the word "amount" is frequently used to refer to quantities or measurements.

given

The amount of money in the account after 7 years can be calculated using the formula V = Pe(rt), where V is the value of a account in t years, P is the principal implementation, e is the base of a natural log, and r is the rate of interest:

V = P*e(rt) = 67700*e(0.077*7)

[tex]V = 67700 * e^{(0.539) (0.539)[/tex]

V = 67700 * 1.716

V = 116177.20

As a result, the balance in the account at the end of seven years is, to the closest cent, $116177.20.

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The solution to the equation |9a+5|=68 is a = 7, -8.111. To solve the equation |9a+5|=68, we can use the property of absolute value that states that |x| = x or |x| = -x. This means that we can set up two equations to solve for a:

9a+5 = 68 or 9a+5 = -68

Now we can solve each equation separately:

9a+5 = 68
9a = 63
a = 7

9a+5 = -68
9a = -73
a = -8.111

So the solutions are a = 7 and a = -8.111. We can write these solutions separated by a comma as follows:

a = 7, -8.111

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The solution of equation x² = 30 will be √30 and -√30. And the solution of equation x³ = 30 is ∛30.

In other words, the collection of all achievable values for the parameters that fulfill the specified mathematical equation is the suitable repository of the bunch of equations.

The equations are given below.

x² = 30 and x³ = 30

From equation x² = 30, then we have

x² = 30

x = ±√30

x = +√30, -√30

From equation x³ = 30, then we have

x³ = 30

x = ∛30

The solution of equation x² = 30 will be √30 and -√30. And the solution of equation x³ = 30 is ∛30.

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Answer:

C, E

Step-by-step explanation:

Answer choice A implies that [tex]42 +22 \geq 50 + 27[/tex], which is false

Answer choice B implies that 50 is half of the population, however the population is 200, so it is false

Answer choice C implies that [tex]50 + 27\geq[/tex] all other combinations, which is true.

Answer choice D implies that [tex]33 + 22\leq 50[/tex], which is false

Answer choice E implies that [tex]42 \leq 22+22[/tex], which is true

So, C & E are correct

Answer:

it is 2,475

Step-by-step explanation:

Answer:

4 number x value is 10 in

5 number x value is 12mi

use formula of h2=p2+b2

Answer:

60m^2

Step-by-step explanation:

15.1×10.3=155.53

155.53÷2=77.765

2.8×6.5=18.2

77.765-18.2= 59.565

rounded to nearest 10th = 60m^2

Answer:

  BD = 5√3

  AD = 10

  CD = 10√3

Step-by-step explanation:

You want the missing side lengths in a right-triangle geometry that shows the hypotenuse divided into lengths 5 and 15 by the altitude.

In this geometry, all of the right triangles are similar. The similarity proportions can be solved to give three geometric mean relationships:

  BD = √(AB·CB) = √(5·15) = 5√3

  AD = √(AB·AC) = √(5·20) = 10

  CD = √(CB·CA) = √(15·20) = 10√3

__

Additional comment

It can be handy to remember the geometric mean relations. They can be thought of as "each side is equal to the geometric mean of the hypotenuse segments it touches." (Note that touching the end is interpreted as touching the nearest part and the whole.)

For example, the similarity proportion for AD is ...

  hypotenuse/(short side)

  AD/AB = AC/AD   ⇒    AD² = AB·AC   ⇒   AD = √(AB·AC)

These are called "geometric mean" relations because the geometric mean of two numbers is the square root of their product.

The general solution to the differential equation y''+4y=0 is y(x) = c₁ cos ₂x + c₂ sin ₂x and the value of β is 2.

To find the value of β, we substitute the general solution into the differential equation and solve for β. We start by finding the first and second derivatives of y(x):

y'(x) = -c₁β sin βx + c₂β cos βx

y''(x) = -c₁β² cos βx - c₂β² sin βx

Substituting these expressions into the differential equation, we get:

-c₁β² cos βx - c₂β² sin βx + 4(c₁ cos βx + c₂ sin βx) = 0

Simplifying this equation, we get:

(c₁β² + 4c₁) cos βx + (c₂β² + 4c₂) sin βx = 0

This equation must hold for all values of x, which means that the coefficients of cos βx and sin βx must both be zero. Therefore, we have the following system of equations:

c₁β² + 4c₁ = 0

c₂β² + 4c₂ = 0

We can solve for β by dividing the second equation by c₂ and substituting c₁ = -4β²/c₂ from the first equation:

β² = -4c₁/c₂ = 4

Since β>0, we take the positive square root of 4, which gives β=2.

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The amount he would pay back in total is $126,000.

The amount he would pay back is the sum of the amount borrowed and the interest rate on the loan.

Amount that would be paid back = amount borrowed + interest

Simple interest is a linear function of the amount borrowed, interest rate and the duration of the loan. The simple interest is the cost of borrowing.

Interest = amount borrowed x interest rate x time

$90,000 x 0.04 x 10 = $36,000

Amount that would be paid back = interest + amount that is borrowed

=  $36,000 + $90,000 = $126,000

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To find the value of r that makes the statement an identity, we need to set the two sides of the equation equal to each other and solve for r.

First, let's multiply both sides of the equation by (x-10) to eliminate the denominator:

(x^(2)-x-8) = (x-10)(x+9) + r

Next, let's expand the right side of the equation:

x^(2)-x-8 = x^(2) + 9x - 10x - 90 + r

Now, let's rearrange the equation and solve for r:

r = x^(2)-x-8 - x^(2) - 9x + 10x + 90

r = 90

Therefore, the value of r that makes the statement an identity is 90.

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The theater sold 1875 regular tickets and 625 discount tickets.

Let x be the number of regular tickets sold and y be the number of discount tickets sold. We can symbolize the given information as a system of equations:
x + y = 2500 (total number of tickets sold)
28x + 20y = 65000 (total revenue)
To solve this system, we can use the substitution method. First, we can isolate one variable in one equation. Let's isolate x in the first equation:
x = 2500 - y
Now, we can substitute this expression for x into the second equation:
28(2500 - y) + 20y = 65000
Simplifying this equation gives:
70000 - 28y + 20y = 65000
-8y = -5000
y = 625
Now, we can substitute this value of y back into the first equation to find x:
x + 625 = 2500
x = 1875
So, the theater sold 1875 regular tickets and 625 discount tickets.

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According to the information, the mathematical expression with which the problem is solved is 8x < 672.

To find the expression that solves this problem we must take into account that it is an inequality. So we must use the symbols greater than > or less than <. Additionally, we must read the information in the statement to identify how it goes to the inequality.

According to the above, there are less than 84 students who answered that they had never bought online (x). Then the expression would start like this:

Subsequently, they do not say that x equals one eighth of the total number of students. Then the expression would be modified like this:

Finally, if we simplify this expression, it would look like this:

So, that would be the expression of this inequality.

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We can estimate that 900 people in attendance would prefer mustard on a hot dog.

What is proportion?

Proportion is a mathematical concept that refers to the relationship between two quantities, expressed as a ratio or a fraction. It represents the size of one quantity relative to another quantity, typically within a larger population or sample.

To determine the number of people who would prefer mustard on a hot dog, we need to use the proportion of people in the sample who prefer mustard and apply it to the total number of people in attendance.

The proportion of people in the sample who prefer mustard is:

27/150 = 0.18

To estimate the number of people who prefer mustard in the entire population of 5,000 attendees, we can multiply this proportion by the total number of attendees:

0.18 x 5,000 = 900

Therefore, we can estimate that 900 people in attendance would prefer mustard on a hot dog.

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1,800,000

We have to do 6 x 300,000, which gives us 1,800,000

The minimum number of people is not possible for the given situation operator has to revise the cost.

Let us consider the minimum number of people ride the Double Shot be x.

Cost per ride = $6.00

Revenue earned from the ride = $6.00x

Rental fee of the ride = ($200).

Safety inspection fee = ($65)

Cost of the rides  = 6x

⇒ Total Cost = $200 + $65 + ($6.00)x

Profit of at least $1,000 each day.

This implies,

Revenue ≥ Total Cost + Desired Profit

Substituting the expressions for revenue and total cost,

$6.00x ≥ $200 + $65 + ($6.00)x + $1,000

Simplifying the above expression we get,

$6.00x ≥ $1,265 + ($6.00)x

Subtracting ($6.00)x from both sides we get,

$0.00x ≥ $1,265

⇒No solution for x, because the number of riders cannot be negative.

⇒Operator must either increase the price per ride, decrease the costs, or revise their profit goal.

Therefore, for the given cost it is impossible to get the minimum number of people.

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Answer:

Step-by-step explanation:

24 (56) *

The arrow travels a distance of 2145 meters into the bale of paper after 3 seconds.

The distance an arrow travels into a bale of paper is given by the equation \[ s(t)=2401-(7-t)^{4}, 0 \leq t \leq 7 \]. To find the distance the arrow travels at a specific time, we simply plug in the value of \( t \) into the equation and solve for \( s \).

For example, if we want to find the distance the arrow travels after 3 seconds, we would plug in \( t=3 \) into the equation:
\[ s(3)=2401-(7-3)^{4} \]
\[ s(3)=2401-(4)^{4} \]
\[ s(3)=2401-256 \]
\[ s(3)=2145 \]

Similarly, we can find the distance the arrow travels at any time \( t \) by plugging in the value of \( t \) into the equation and solving for \( s \). This will give us the distance the arrow travels horizontally into the bale of paper at that specific time.

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The Synthetic divison is (2x^(3)-10x^(2)+14x-24) ÷ (x-4) = 2x^(2) - 2x + 6.

To divide (2x^3 - 10x^2 + 14x - 24) by (x - 4) using synthetic division, the following steps should be taken:

1. Write the coefficients of the dividend in a row, placing the divisor to the extreme left of the row.
2. Bring the first coefficient of the divisor down.
3. Multiply the divisor by the number directly below it in the row and write the answer to the right of the number.
4. Add the two numbers to the right of the divisor and write the answer below.
5. Repeat steps 3 and 4 until the last number in the row is reached.
6. The last number in the row is the remainder, while the numbers to its left form the quotient.

For the example given, the process is as follows:

Therefore, the quotient is

.
To divide (2x^(3)-10x^(2)+14x-24) by (x-4) using synthetic division, we can follow the steps below:

Step 1: Write down the coefficients of the dividend polynomial in descending order of the exponents. In this case, the coefficients are 2, -10, 14, and -24.

Step 2: Write down the constant term of the divisor polynomial with the opposite sign. In this case, the constant term is -4, so we write down 4.

Step 3: Bring down the first coefficient of the dividend polynomial, which is 2.

Step 4: Multiply the number brought down by the constant term of the divisor polynomial, and write the result under the next coefficient of the dividend polynomial. In this case, 2 * 4 = 8, so we write 8 under -10.

Step 5: Add the numbers in the column, and write the result below. In this case, -10 + 8 = -2.

Step 6: Repeat steps 4 and 5 until all the coefficients of the dividend polynomial have been used. In this case, we get:

-2 * 4 = -8, 14 + (-8) = 6

6 * 4 = 24, -24 + 24 = 0

Step 7: The numbers in the last row are the coefficients of the quotient polynomial, and the last number is the remainder. In this case, the quotient polynomial is 2x^(2) - 2x + 6, and the remainder is 0.

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The volume of the cylinder is approximately 40,107.6 cubic yards.

What is the volume of the cylinder?

The formula for the volume of a right circular cylinder is:

[tex]V = \pi r^2h[/tex]

The formula for the volume of a right circular cylinder is:

[tex]V = \pi r^2h[/tex]

Substituting the given values:

V = 3.14 x 17.2² x 45.3

V = 3.14 x 296.84 x 45.3

V = 40,107.6152 cubic yards

Rounding to the nearest tenth:

V ≈ 40,107.6 cubic yards

Therefore, the volume of the cylinder is approximately 40,107.6 cubic yards.

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Answer: 42080.87328 or 42,080.9 rounded to the nearest tenth

Step-by-step explanation:

V=πr2

V= 3.14 x 17.2 x 45.3

V= 3.14 x 17.2 squared x 45.3

= 17.2 squared is 295.84

V= 3.14 x 295.84 x 45.3

V= 42,080.87328

round it to nearest tenth and get 42,080.9 yd

The evaluation of the functions for data in the table and the graphs of the data, created using MS Excel, indicates that we get;

a. Equation 3 appears to be exponential

b. The reason is that as the value of x increases, the output values of the equation increases exponentially

c. The population of a bacteria is most likely modeled by Equation 3, which is an exponential function, because as the number of bacterium increases, the number of offspring they can produce in the next period increases, resulting in an exponential growth

d. Equation 4, which can be modeled using a linear equation, with a positive slope most likely models a tub collecting water from a leak faucet.

A function can be used to model an observation by specifying the relationship between the input and output values of the observation.

a. The function in the table that appears to be exponential is Equation 3

b. An exponential function is a function that has an equation of the following forms;

f(x) = [tex]a\cdot b^{c\cdot x}[/tex]

f(x) = [tex]p\cdot e^{k\cdot x}[/tex]

The values in the table for Equation 3 indicates that the as the value of x increases, the values of f(x) increases several times more, which is an exponential increase, such that an equation that can model the data, obtained using MS Excel is; f(x) = 0.1982 × e^(0.3092·x)

Plugging in the values of x, we get;

The value of f(x) at x = 9 is; f(9) = 0.1982 × e^(0.3092 × 9) ≈ 3.2

The value of f(x) at x = 10 is; f(10) = 0.1982 × e^(0.3092 × 10) ≈ 4.36

The value of f(x) at x = 17 is; f(17) = 0.1982 × e^(0.3092 × 17) ≈ 38.0

Therefore, the function for Equation 3 appears to be exponential

Please find attached the graph for the Equation 3 data values, created with MS Excel

c. The growth of a population is best modelled by an exponential function, therefore, the function that most likely models a bacteria growth in a lab culture is Equation 3.

d. The tub collecting water from a leaking faucet collects water at the steady rate at which the faucets leaks, which can be modelled by a linear equation with a positive slope, because the amount of water in the tub increases steadily.

The graph and trendline obtained from values of the data for Equation 4, indicates that the line of best fit is a line with the equation;

The square of the regression coefficient is; R² = 0.9993

The slope of the line of best fit of Equation 4 is positive, and therefore increasing at a steady rate and can therefore model collecting water from a leaky faucet using a tub

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