Suppose a novel infectious disease reaches the portland-metro area. This disease takes 9 days to recover from, and has a basic reproduction number of R0=4.5. Suppose the disease is 0.3% fatal. We'll model the disease outbreak with an SIR model.
i) Find a value for N, the total population of the portland-metro area.
ii) Determine the values of a and b, the constants for the SIR model.
iii) Suppose on day 0, there are 5 cases of the disease. If 15% of the initial population has immunity to the disease, determine the initial values S(0), I(0) and R(0).
iv) Solve the SIR model numerically, over a time interval that shows the whole course of the disease outbreak. Create a graph showing S, I and R vs time. The remaining questions can all be answered by reading and interpreting the graph:
v) How many people ultimately will be infected?
vi) How many will die from the disease?
vii) When is the peak of the outbreak?
viii) When is the outbreak is over?
ix) For this disease, what is the herd immunity threshold? Find the time at which the number of R individuals reaches the herd immunity threshold.
x) How many people die of the disease, after the herd immunity threshold is reached?

For a dish party, Alia needs to seat four people at a round table. There are 24 possible combinations of seating arrangements.

This is because each person has 3 options (clockwise, counter-clockwise, opposite), for a total of 34 or 81 combinations. However, due to symmetry, half of these are the same combinations with the people just shifted around the table, so we are left with 24 total combinations.

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The expression (122two _ 202three)_ 1001three can be evaluated by breaking it down into its constituent parts.

Expression in math is a combination of numbers, symbols, and/or operations that represent a mathematical statement. Expressions can be used to calculate values, solve equations, and to model real-world problems. Expressions can be simple or complex and can range from basic arithmetic operations to more complex functions and equations. Expressions are an essential part of mathematics and are used to represent equations, formulas, and even solutions to complex problems.

The first part, 122two, is a number and can be evaluated to 122. The second part, 202three, is also a number and can be evaluated to 203. The third part, 1001three, is also a number and can be evaluated to 1002. Taking the evaluation of each part (122, 203 and 1002), the overall expression (122two _ 202three)_ 1001three can be evaluated to 121.

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Function Family: quadratic

Domain: all real numbers

x-int: (0,0) and (2,0)

y-int: (0,0)

The object will have a height of 100 feet after 100 seconds.

The equation for the height of the object in feet after T seconds is H(T) = A(T - h)2 + k, where A and h are constants. Given that the object has a height of 0 feet after 10 seconds, and a maximum height of 200 feet at 0 seconds, we can solve for A and h.

We know that H(0) = 200, so k = 200.

We also know that H(10) = 0, so A(10 - h)2 + 200 = 0. Solving for A, we get A = -(h2 + 200) / 102.

Now we have an equation with two unknowns, A and h, so we can use substitution to solve for h. We can substitute -(h2 + 200) / 102 for A in our original equation, and solve for h. This gives us h = 10.

We now know A = -(102 + 200) / 102 = -20.

So, our equation for the height of the object in feet after T seconds is H(T) = -20(T - 10)2 + 200.

To find the height of the object after 100 seconds, substitute 100 for T in the equation. This gives us H(100) = -20(100 - 10)2 + 200 = 100.

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Answer:

Step-by-step explanation:

the answer is eitehr b or a

The equation of the function g(x) in terms of the function f(x) has the equation of g(x) = -2f(x + 2) + 3

Given the graph of functions f(x) and g(x)

Where

y = f(x) -- the parent function

y = g(x) --- the transformed function (the dashed line)

The transformation of f(x) to g(x) is as follows

First, the graph of y = f(x) is moved 2 units to the left

This is represented as f(x + 2)

Next, the shifted graph of y = f(x) is reflected across the x-axis and then stretched vertically by a factor of 2.

This is represented as -2f(x + 2)

Lastly, the reflected and stretched graph is moved 3 units up

This is represented as -2f(x + 2) + 3

This means that

g(x) = -2f(x + 2) + 3

So, the function g(x) is g(x) = -2f(x + 2) + 3

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Mason spends one half of an hour lifting weights and one third of an hour on the treadmill, so the ratio of time Mason spends lifting weights to time Mason spends on the treadmill is 1:2.

A treadmill is a machine used for walking or running while staying in one place. It usually has a belt and a platform to stand on, and the belt moves at a speed determined by the user. It is a great way to get a good cardio workout.

The question asks which are correct descriptions of the relationship of time Mason spends lifting weights and on the treadmill.

Mason spends one half of an hour lifting weights and one third of an hour on the treadmill, so the fraction of time Mason spends lifting weights is 2/3.

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So the equation of the circle is (x+4)^2 + (y+4)^2 = 4^2 with center (-4, -4) and radius 4

The equation of a circle is given by (x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center of the circle and r is the radius. We need to rearrange the given equation to match this form.

2x^2 + 2y^2 + 16x + 16y + 32 = 0

Divide both sides of the equation by 2:

x^2 + y^2 + 8x + 8y + 16 = 0

Rearrange the terms:

x^2 + 8x + y^2 + 8y = -16

Complete the square for both x and y terms:

(x^2 + 8x + 16) + (y^2 + 8y + 16) = -16 + 16 + 16

(x+4)^2 + (y+4)^2 = 16

Now the equation is in the standard form of a circle equation, and we can find the center (h,k) and radius r:

h = -4, k = -4, r = 4

So the equation of the circle is (x+4)^2 + (y+4)^2 = 4^2 with center (-4, -4) and radius 4.

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Answer: $135

Step-by-step explanation:

    We know that:

         Selling price = [tex](100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})[/tex]

    Using the given cost price and loss%, we can solve.

         Selling Price = [tex](100 - \text{Loss}\%)(\frac{\text{Cost Price}}{100})[/tex]

         Selling Price = (100 - 10)([tex]\frac{\text{150}}{100}[/tex])

         Selling Price = (90) * (1.5)

         Selling Price = $135

    This means the selling price of the dress is $135.

The maximum amount you can earn is $540

a. y = 13.50x , 10 <= x <= 40
b. x = 10, y = 135; x = 20, y= 270; x = 30, y = 405; x = 40, y = 540
c. Domain: 10 <= x <= 40; Range: 0 <= y <= 540
d. The minimum amount you can earn in a week with this job is $135. The maximum amount you can earn is $540.

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The correct statement about the functions f(x) and g(x) include the following: B. f(x) has a steeper slope than g(x).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m of g(x) = (1 - (-3))/(0 - (-2))

Slope, m of g(x) = 4/2

Slope, m of g(x) = 2.

Slope of f(x) = 3. Therefore, 3 is greater than 2.

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Uncle Moneybags can withdrawal approximately $583.67 per month.

To find out how much Uncle Moneybags can withdraw each month, we can use the formula for the future value of an annuity:

FV = PMT × [(1 + i)ⁿ - 1] / i

Where:
FV = future value
PMT = payment amount
i = interest rate per period
n = number of periods

In this case, we want to solve for PMT, so we can rearrange the formula to:

PMT = FV × i / [(1 + i)ⁿ - 1]

We know that FV = $500,000, i = 8% / 12 = 0.00667, and n = 25 × 12 = 300. Plugging these values into the formula, we get:

PMT = $500,000 × 0.00667 / [(1 + 0.00667)³⁰⁰ - 1]

PMT = $500,000 × 0.00667 / 5.7435

PMT = $583.67

Therefore, Uncle Moneybags can withdraw $583.67 each month for 25 years.

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The exact value of the expression is √3.

To find the exact value of the given expression, we can use the sum formula for tangent. The formula is:

Tan (A + B) = (tan A + tan B) / (1 - tan A tan B)

Where A and B angle.

In this case, A = 41° and B = 19°. Plugging these values into the formula, we get:

Tan (41° + 19°) = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)Simplifying the left side of the equation gives us:

Tan 60° = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)We know that tan 60° = √3.

Substituting this value into the equation gives us:√3 = (tan 41° + tan 19°) / (1 - tan 41° tan 19°)

Cross-multiplying and simplifying gives us:

√3 (1 - tan 41° tan 19°) = tan 41° + tan 19°√3 - √3 tan 41° tan 19° = tan 41° + tan 19°

We can rearrange the terms to get:

√3 = tan 41° + tan 19° + √3 tan 41° tan 19°

This is the same expression that we were given in the question.

Therefore, the exact value of the expression is √3.

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The algebraic expression that translates the given phrase is 2c + 15, where c is the amount of Chrissy's savings.

To translate the phrase "15 more than twice Chrissy's savings" into an algebraic expression:

1. First, we need to identify the variable. In this case, the variable is c, which represents Chrissy's savings.
2. Next, we need to identify the operations and numbers involved in the phrase. The phrase "twice Chrissy's savings" means that we need to multiply c by 2.
3. The phrase "15 more than" means that we need to add 15 to the result of the multiplication.
4. Putting these steps together, we get the algebraic expression 2c + 15.

So the final answer is 2c + 15.

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The coordinates of N can be estimated as: (-8, -12)

Scale factor is a mathematical term, which we use to scale 2-dimensional and 3-dimensional shapes. Scale factor is a measure of similar figures. Those figures who look the same but are in different sizes.

If point N is dilated with a scale factor of 5/4 centered at the origin, the coordinates of the image point, let's call it N', can be found by multiplying the coordinates of N by the scale factor:

N' = (5/4)N

We also know that the image point N' is located at (-10, -15), so we can substitute these values into the equation:

(-10, -15) = (5/4)N

Solving for N, we can multiply both sides by the reciprocal of 5/4, which is 4/5:

N = (4/5)(-10, -15)

N = (-8, -12)

Therefore, the coordinates of point N are (-8, -12).

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Answer: y > 2/5x - 4

Step-by-step explanation:

The slope intercept form is y = mx + b

To get the inequality to that, we have to get y alone.

Starting:

2x - 5y < 20

Subtract 2x from each side leaves you:

- 5y < -2x + 20

Dividing by -5 leaves you:

(Remember that when dividing by a negative in an inequality, the sign flips.)

y > 2/5x - 4

Hope this helps!

Answer:

see below

Step-by-step explanation:

84

i took the test

The solution is, (x + 6) and (2x - 5) are the factors of polynomial

2x^2 + 7x - 30.

Polynomials are sums of k-xⁿ terms, where k can be any number and n can be any positive integer.

3x+2x-5, for example, is a polynomial.

A binomial is a two-term polynomial.

For instance, x²ˣ-2ˣ² and x⁶ˣ-6ˣ⁶ are both binomials.

here, we have,

given that,

2x^2 + 7x - 30 is the polynomial .

now, we have to factorize it.

so, we get,

2x2 + 7x - 30

2x2 + 12x - 5x - 30

2x( x + 6) - 5( x + 6)

so, we have,

(x + 6) and (2x - 5) are the factors.

Hence, The solution is, (x + 6) and (2x - 5) are the factors of polynomial

2x^2 + 7x - 30.

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Some of the questions to ask grade 12 students on a questionnaire about taking a gap year after school​ are:

A questionnaire refers to a set of questions or items used to collect information about respondents' attitudes, experiences, or opinions. Questionnaires can be used to collect both quantitative and qualitative data. Questionnaires are widely used in market research, as well as social and health sciences.

As the researcher's study focus on semester taken after high school and prior to post-secondary education, such questionnaire involve will focus on variables on the student gap year.

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We have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

We can use the properties of logarithms to show that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

First, recall that the arithmetic mean of two numbers is half their sum:
arithmetic mean = (v + w)/2

And the geometric mean is the square root of their product:
geometric mean = √(v*w)

Now, let's take the log of the geometric mean:
log(geometric mean) = log(√(v*w))

Using the property of logarithms that log(a*b) = log(a) + log(b), we can expand the expression:
log(√(v*w)) = log(√v) + log(√w)

Using the property of logarithms that log(a^b) = b*log(a), we can simplify the expression:
log(√v) + log(√w) = (1/2)*log(v) + (1/2)*log(w)

Now, we can see that the log of the geometric mean is the arithmetic mean of the logs of the two numbers:
log(geometric mean) = (log(v) + log(w))/2

So, if we let p = log(v) and q = log(w), we can see that the log of the geometric mean of v and w is the arithmetic mean of p and q:
log(geometric mean) = (p + q)/2

Therefore, we have shown that the log of the geometric mean of two numbers is the arithmetic mean of the logs of those two numbers.

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The values of x and y that satisfy the given equation are x = 2 and y = 1.

One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.

Since a and b span R², any vector in R² can be expressed as a linear combination of a and b.

Let's call the coefficients of this linear combination c₁ and c₂ so that any vector v in R² can be expressed as:

v = c₁a + c₂b

Now let's use this fact to solve the given equation:

(2-x)a + b = ya + (x-3)b

We can rearrange this equation to get all the terms with an on one side and all the terms with b on the other side:

(2-x)a - ya = (3-x)b

Now we can write both sides of the equation as linear combinations of a and b:

(2-x)a - ya = 2a - xa - ya = (2-x)a - (x-2)a - ya = (2-x - x + 2)a - ya = (4 - 2x)a - ya

(3-x)b = 3b - xb = 3b - xb + 3b - 3b = (6 - x)b - 3b = (6 - x - 3)b = (3 - x)b

So now we have:

(4 - 2x)a - ya = (3 - x)b

Since a and b span R², we know that any vector in R² can be expressed as a linear combination of a and b. Therefore, we can write:

(4 - 2x)a - ya = c₁a + c₂b

(3 - x)b = c₁a + c₂b

Now we can set the coefficients of a and b equal to each other and solve for x and y:

4 - 2x = c₁

-y = c₂

3 - x = c₂

Substituting the third equation into the second equation, we get:

-y = 3 - x

Solving for x and y, we get

x = 2

y = 1

Therefore, the values are x = 2 and y = 1.

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The values of x and y are determined by solving the equation

The values of x and y can be found by solving the equation x(23) + y(-10) = (106). This can be done by isolating one variable and solving for the other. For example, isolating x gives us x = (106 + 10y)/23. We can then plug this value of x back into the original equation and solve for y. Once we have the value of y, we can plug it back into the equation for x to find the value of x.

The value of −2p2s2v​−qtw​−rux​​ can be found by plugging in the given values of p, s, v, q, t, w, r, and u into the equation and simplifying.

The value of ∣3AB∣ can be found by using the properties of determinants of matrices. Specifically, the determinant of a product of matrices is equal to the product of the determinants of the individual matrices. Therefore, ∣3AB∣ = ∣3∣∣A∣∣B∣ = 3(-1)(3) = -9.

So, the values of x and y are determined by solving the equation x(23) + y(-10) = (106), the value of −2p2s2v​−qtw​−rux​​ is found by plugging in the given values and simplifying, and the value of ∣3AB∣ is found by using the properties of determinants of matrices.

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From  the function φ(x)=31​x3−21​x,  0 is a fixed point of φ(x) it shows in calculation below.  The iteration xk+1 = φ(xk) converges locally to 0 shows below. The iteration diverges as k increases.

(a) To show that 0 is a fixed point of φ(x), we need to show that φ(0) = 0. Substituting x = 0 into the function gives us:

φ(0) = (3/1)(0)3 - (2/1)(0) = 0 - 0 = 0

Therefore, 0 is a fixed point of φ(x).

(b) To show that the iteration xk+1 = φ(xk) converges locally to 0, we need to show that |φ'(x)| < 1 for x near 0. Taking the derivative of φ(x) gives us:

φ'(x) = (9/1)x2 - (2/1)

At x = 0, φ'(0) = 0 - 2 = -2. Since |φ'(0)| > 1, the iteration does not converge locally to 0.

(c) By numerical tests, we can find an initial guess x0 such that the iteration converges to 0 and an initial guess x0 such that the iteration diverges. For example, if we choose x0 = 0.5, the iteration converges to 0:

x1 = φ(0.5) = (3/1)(0.5)3 - (2/1)(0.5) = -0.625

x2 = φ(-0.625) = (3/1)(-0.625)3 - (2/1)(-0.625) = 0.8203125

x3 = φ(0.8203125) = (3/1)(0.8203125)3 - (2/1)(0.8203125) = -0.4625244140625

And so on. The iteration converges to 0 as k increases.

On the other hand, if we choose x0 = 2, the iteration diverges:

x1 = φ(2) = (3/1)(2)3 - (2/1)(2) = 20

x2 = φ(20) = (3/1)(20)3 - (2/1)(20) = 23980

x3 = φ(23980) = (3/1)(23980)3 - (2/1)(23980) = 3.47119332792e+13

And so on. The iteration diverges as k increases.

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The area of the shaded shape WXZY s equal to 381.4 cm².

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = θπr²/360

Where:

In order to determine the area of the shaded shape WXZY, we would have to subtract the area of sector OYZ from the area of the sector OWX.

Area of sector OWX = 75 × 3.14 × 32²/360 = 669.87 cm²

Area of sector OYZ = 75 × 3.14 × 21²/360 = 288.49 cm²

Area of shaded shape WXZY = Area of sector OWX - Area of sector OYZ

Area of shaded shape WXZY = 669.87 cm² - 288.49 cm²

Area of shaded shape WXZY = 381.4 cm².

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She gets $114 to work at grocery store for 6 hours and $200 at the nursery.

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute.

We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

Eli has two summer jobs. During the week he works in the grocery store, and on the weekend he works at a nursery. He gets paid $20 per hour to work at the grocery store and $17 per hour to work at the nursery.

14 hours at the grocery store and 9 hours at the nursery? How much does he earn if he works

Therefore, She gets $114 to work at grocery store for 6 hours and $200 at the nursery.

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The price per pound of the apples is $3.50. This is calculated by dividing the total cost, $7.00, by the weight of the apples, 2 pounds.

The price per pound of the apples can be found by dividing the total cost by the weight of the apples. In this example, the total cost of the apples is $7.00 and the weight is 2 pounds. To calculate the price per pound, divide 7.00 by 2. This gives us 3.50, which is the price per pound of the apples. Knowing the price per pound is useful when you are trying to figure out how much a certain amount of apples will cost. For example, if you wanted to buy 5 pounds of apples, you would multiply 5 by 3.50, which would give you $17.50. This is the total cost of the 5 pounds of apples. In addition to helping you figure out how much certain amounts of apples will cost, knowing the price per pound can also help you compare prices between stores. For example, if you found apples for $4.00 per pound at one store, and $3.50 per pound at another store, you could easily determine which store has the better deal.

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The chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.

The chain rule is a formula for calculating the derivative of a composite function. It states that the derivative of a composite function f(g(x)) is equal to the derivative of f with respect to g times the derivative of g with respect to x. In mathematical notation, this is expressed as (f(g(x)))' = f'(g(x)) * g'(x).

In the case of the first equation, we can use the chain rule to reduce it to the second equation by applying the formula mentioned above. First, we need to identify the composite function and its components. In this case, the composite function is f(g(x)) and the components are f and g.

Next, we need to find the derivative of f with respect to g and the derivative of g with respect to x. Once we have these derivatives, we can multiply them together to get the derivative of the composite function.

Finally, we can reduce the first equation to the second equation by substituting the derivative of the composite function for the original composite function. This will give us the second equation, which is a simplified version of the first equation.

In conclusion, the chain rule allows us to reduce the first equation to the second equation by finding the derivative of the composite function and substituting it for the original function. This provides a simpler and more concise explanation of the relationship between the two equations.

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