Match the correct term to its definition.
Fomite E. Portal of exit
Vector F. Zoonotic
Reservoir G. Incubation period
Portal of entry
34. _______ Site where infectious agent enters the body
35. _______ Disease transmitted through an animal bite
36. _______ Population or environment in which pathogen lives and reproduces and on which it depends on its survival
37. _______ Inanimate object covered in disease-causing agent
38. _______ Interval between exposure to pathogen and first signs and symptoms of disease
39. _______ Site where infectious agent leaves the body
40. _______ Living insect or animal involved with disease transmission

Answer: 28

Step-by-step explanation:

28 is thhe missing number

Step-by-step explanation:

The factors of 9x² +49y² are:

D. (3x + 7y)(3x + 7y) and C. (3x - 7y)(3x - 7y)

We can use the identity:

a² + b² = (a + b)(a - b)

To factor the expression 9x² + 49y², let a = 3x and b = 7y. Then we have:

9x² + 49y² = (3x)² + (7y)² = (3x + 7y)(3x - 7y)

So the factors of 9x² + 49y² are (3x + 7y) and (3x - 7y). We can see that these factors are not prime, as they can be factored further into (3x + 7y)(3x + 7y) and (3x - 7y)(3x - 7y).

Answer:

12 + 3x = 24

Step-by-step explanation:

Simplifying

3x + 12 = 24

Reorder the terms:

12 + 3x = 24

Solving

12 + 3x = 24

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-12' to each side of the equation.

12 + -12 + 3x = 24 + -12

Combine like terms: 12 + -12 = 0

0 + 3x = 24 + -12

3x = 24 + -12

Combine like terms: 24 + -12 = 12

3x = 12

Divide each side by '3'.

x = 4

Simplifying

x = 4

Answer

x=12

Step-by-step explanation:

3 times 12 is 36

36 minus 12 is 24

Answer:

c. no real solutions

Step-by-step explanation:

because the x's will not be there

Answer:

x = 9

m∠1 = m∠2 = 54°

Step-by-step explanation:

Two lines r and s are the parallel lines and a transversal line is intersecting these lines at two distinct points.

a). ∠1 ≅ ∠2 [Corresponding angles]

    Therefore, m∠1 = m∠2

    (63 - x)° = (72 - 2x)°

    2x - x = 72 - 63

    x = 9

b). m∠1 = (63 - x)°

            = 63 - 9

            = 54°

    m∠2 = (72 - 2x)°

             = 72 - 18

             = 54°

The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7

Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle.  There are three common trigonometric ratios: sine, cosine, and tangent

For page 3 question 3,

a) <A + <B = 90 since <C = right angle

b) SinA = BC/AB and CosB = BC/AB

The ratio of the two angles BC/AB ÷ BC/AB = 1

I notice that the ratio of sinA and cosB gives 1

b) The ratio of CosA and SinB will give

BC/AB ÷ BC/AB

= BC/AB * AB/BC = 1

For page 5 number 3

Tan28 = g/i

g/12.2 = tan28

cross multiplying to have

g = 12.2*tan28

g = 12.2 * 0.5317

g = 6.5

b) the angle I is given as 90-28 degrees

<I = 62 degrees

To find the side h we use the Pythagoras theorem

h² = (12.2)² + (6.5)²

h² = 148.84 +42.25

h²= 191.09

h=√191.09

h= 13.8

For page 6

1) Sin42 = x/18

x=18*sin42

x = 18*0.6691

x = 12.0

2) cos28 = 6/x

xcos28 = 6

x = 6/cos28

x [= 6/0.8829

x = 6.8

3)  Tan63 = x/34

x = 34*tan63

x= 34*1.9526

x = 66.4

4) Sin50 123/x

xsin50 = 123

x = 123/sin50

x = 123/0.7660

x =160.6

5)  Sin57 = P/8

Pole = 8sin57

the pole = 8*0.8387

The pole = 6.7

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Answer:

-3, -3

Step-by-step explanation:

The coordinates of point B on line AC is (6/7, -30/7).

Given that, A(6, -6), C(-6,-2) and AB= 3/4 AC.

The section formula is P(x, y)\(=(\frac{mx_{2} +nx_{1}}{m+n}, \frac{my_{2} +ny_{1}}{m+n} )\).

Now, AB= 3/4 AC⇒AB:AC=3:4

P(x,y)\(=(\frac{3(-6)+4(6)}{3+4}, \frac{3(-2) +4(-6)}{3+4} )\)

=(6/7, -30/7)

Therefore, the coordinates of point B on line AC is (6/7, -30/7).

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The statement is not true in general. The correct formula relating the second differential equations of y with respect to x and t is:

(d²y)/(dx²) = [(d²y)/(dt²)] / [(d²x)/(dt²)]

This formula is known as the Chain Rule for Second Derivatives, and it relates the rate of change of the slope of a curve with respect to x to the rate of change of the slope of the curve with respect to t. However, it is important to note that this formula only holds under certain conditions, such as when x is a function of t that is invertible and has a continuous derivative.

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Answer:

The wind pushed the plane \(65.01\) miles in the direction of \(45.56 ^{\circ}\) East of North  with respect to the destination point.

Step-by-step explanation:

Let origin, O, br the starting point and point D be the destination at 250 miles at a bearing of 20° E of S, but due to wind let D' be the actual position of the plane at 230 miles away from the  starting point in the direction of 35° E of South as shown in the figure.

So, we have |OD|=250 miles and |OD'|=230 miles.

Vector \(\overrightarrow{DD'}\) is the displacement vector of the plane pushed by the wind.

From figure, the magnitude of the required displacement vector is

\(|DD'|=\sqrt{|AB|^2+|PQ|^2}\;\cdots(i)\)

and the direction is \(\alpha\) east of north as shown in the figure,

\(\tan \alpha=\frac{|PQ|}{|AB|}\;\cdots(ii)\)

From the figure,

\(|AB|=|OA-OB|\)

\(\Rightarrow |AB|=|OD\cos 20 ^{\circ}-OD'\cos 35 ^{\circ}|\)

\(\Rightarrow |AB|=|250\cos 20 ^{\circ}-230\cos 35 ^{\circ}|\)

\(\Rightarrow |AB|=45.52\) miles

Again, \(|PQ|=|OP-OQ|\)

\(\Rightarrow |PQ|=|OD\sin 20 ^{\circ}-OD'\sin 35 ^{\circ}|\)

\(\Rightarrow |PQ|=|250\sin 20 ^{\circ}-230\sin 35 ^{\circ}|\)

\(\Rightarrow |PQ|=46.42\) miles

Now, from equations (i) and (ii), we have

\(|DD'|=\sqrt{|45.52|^2+|46.42|^2}=65.01\) miles, and

\(\tan \alpha=\frac{|46.42|}{|45.52|}\)

\(\alpha=\tan^{-1}\left(\frac{|46.42|}{|45.52|}\right)=45.56 ^{\circ}\)

Hence, the wind pushed the plane \(65.01\) miles in the direction of \(45.56 ^{\circ}\) E astof North  with respect to the destination point.

Answer:

7.5 x 10⁵

Step-by-step explanation:

2.5x10^3)(3x10^2)= 750000

move decimal all the way to the left with one # in front of your decimal

Given the question: In how many ways can 7 people line up for play tickets?

The number of ways for the first = 7

The number of ways for the second = 6

The number of ways for the third = 5

The number of ways for fourth = 4

The number of ways for the fifth = 3

The number of ways for the sixth = 2

The number of ways for the seventh = 1

So, the total number of ways = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5,040

So, the answer will be option B. 5,040

Answer:

Step-by-step explanation:

The orthocenter of a triangle is the point of intersection of the lines containing its heights.

You find line like that leading line perpendicular to the side of the triangle and crossing the opposite vertex.

Point A is opposite to side BC so line perpendicular to BC that intersects point A is one of the lines needed to find orthocenter.

(a) The graph of r = 3sin(5θ) would have 5 petals.

(b) The graph of r = -4cos(6θ) would have 6 petals.

(c) The second derivative of the parametric equation x = 2t + 1, y = t^3 - 1 is 2/3.

(a) The equation r = 3sin(5θ) represents a polar graph. The number of petals in this graph is determined by the coefficient of θ, which is 5 in this case. So, the graph would have 5 petals.

(b) The equation r = -4cos(6θ) also represents a polar graph. The number of petals in this graph is determined by the coefficient of θ, which is 6 in this case. So, the graph would have 6 petals.

(c) To find the second derivative of the parametric equation x = 2t + 1, y = t^3 - 1, we need to differentiate the equation twice with respect to t. Taking the derivative of x = 2t + 1 gives dx/dt = 2, and taking the derivative of y = t^3 - 1 gives dy/dt = 3t^2. Taking the derivative of dx/dt = 2 gives the second derivative d^2x/dt^2 = 0, and taking the derivative of dy/dt = 3t^2 gives the second derivative d^2y/dt^2 = 6t. Therefore, the second derivative of the parametric equation is 6t.

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The result of the each of the following set is

A ∪ B = {1, 3, 5, 6, 7, 9}

A ∩ B = {3, 9}

A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A ∩ C = {∅}

A - B = {1, 5, 7}

B - A = {6}

B U C = {2, 3, 5, 6, 8, 9 }

B ∩ C = {6}

The given values are

A = {1, 3, 5, 7, 9}

B = {3, 6, 9}

C = {2, 4, 6, 8}

Then find the each given terms in set roaster notation

Union of the set, intersection of the set  and the difference of the set are the basic operations of set

A ∪ B = {1, 3, 5, 6, 7, 9}

A ∩ B = {3, 9}

A ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9}

A ∩ C = {∅}

A - B = {1, 5, 7}

B - A = {6}

B U C = {2, 3, 5, 6, 8, 9 }

B ∩ C = {6}

Therefore, all the given terms has been found

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Step-by-step explanation: it will be c because 45 divided by 15 = 3

Solution:

Given:

Using the simple interest formula;

At t = 0 years,

At t = 5 years,

At t = 10 years,

At t = 15 years,

At t = 20 years,

To get the amount,

The table can be represented below;

The graph to represent the simple interest account is shown below;

The zeros of the polynomial are: x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).We have found all three real zeros of the polynomial, which confirms that there are no complex zeros.

f(x) = 2x³ - 112x² + 27x - 41x + 15

To find the zeros and their multiplicities of this polynomial, we can begin by using Descartes' Rule of Signs. Let's consider the sign changes in the coefficients:

There are 2 sign changes in the coefficients (from 2x³ to -112x² and then to 27x, and finally to -41x and 15), which means there are either 2 or 0 positive real zeros.

There are no sign changes when we replace x with -x, which means there are either 0 or 2 negative real zeros.

Thus, there can be either 0, 2, or 4 real zeros, but we cannot determine their exact number or location with Descartes' Rule of Signs alone.

Next, we can use the Upper and Lower Bound Theorem to limit our search for rational zeros. According to this theorem, any rational zero of the polynomial must be of the form p/q, where p is a factor of the constant term (15 in this case) and q is a factor of the leading coefficient (2 in this case). Therefore, the possible rational zeros of the polynomial are:

±1/2, ±1, ±3/2, ±5, ±15/2, ±30

We can use synthetic division or long division to check these possible rational zeros and see which ones are actually zeros of the polynomial. Doing so, we find that the rational zeros of the polynomial are:

x = 1/2 (with multiplicity 1), x = 3 (with multiplicity 1), and x = 5/2 (with multiplicity 1).

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Answer:

x=\frac{6-y-z}{3}

Step-by-step explanation:

Answer:

x= 2-y/3-z/3

y=8+x+2z

z= -16/3+5x/3+y/3

Step-by-step explanation:

Answer:

When you add all the angles together you get 360 degrees because every circle equals 360.

a: 35 degrees

b: 40 degrees

c: 35 degrees

d: 70 degrees

Step-by-step explanation:

For "d":

To find a we see that 70 degrees is a bisector to "d" meaning that they are equal. Also the angle to the left of the 40 degree angle is equal to the angle to the right of "d". So we would add 40 and "d", which is 70 degrees. And since that whole line of angles creates a straight line, which is 180 degrees we take the sum of 40 and 70 then subtract that to 180 which is 180-110= 70.

Then we divide 70 by 2 because the 2 angles are the same. This makes 35.

So now that we know the angles that are not labeled we can find a,b, and c

For "a":

It is very simple to find "a" since we found that the unlabeled angles are both 35 degree. Angle "a" happens  to be a bisector of the 35 degree angle making them equal. This means that "a" is 35 as well.

For "b":

Since "b" is a bisector of the 40 degree angles this makes "b" 40 degrees.

For "c":

Angle "c" is exactly like Angle "a" because of them being being bisectors wiht the unlabeled angles. So "c" is 35 too.

Answer:

B. Yes.

C. Yes.

Step-by-step explanation:

B. In this, it is saying basically is "2b + b = 3b." Well yes, because 2b + b = 3b. So 3b = 3b? Yes.

C. So same thing. 2b + b = 3b. 3b = 3b. they are equivalent.

The maximum positive number that can be represented with 4-bit 2's complement representation is Decimal point 7 (0111).

In computing, 2's complement representation is a method for representing signed numbers in binary number system. It is used to represent both positive and negative numbers and it is the most common method for representing signed numbers in computers. In 2's complement representation, the leftmost bit of the binary number is the sign bit. If the sign bit is 0, it indicates that the number is a positive number. If the sign bit is 1, it indicates that the number is a negative number. In 4-bit 2's complement representation, 4 bits are used to represent a number. 4 bits can store numbers between 0 and 15 in decimal. In 2's complement representation, the range of numbers that can be represented is from -7 to 7 in decimal. The maximum positive number that can be represented with 4-bit 2's complement representation is 7 (0111). The maximum negative number that can be represented is -8 (1000).

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a) Value of function fx​(2,−9) = -32, fy(2,−9) = 18.

b) Solution of the differential equation is, y = ±\((x^{2} +1)^{1/2}\) \(e^{C}\).

c) The evaluated integral is -(1/4)\(e^{-4x}\) + C.

a) To find fx​(2,−9), we differentiate f(x, y) with respect to x, treating y as a constant:

fx​(x, y) = d/dx (64 − 8\(x^{2}\) − \(y^{2}\))

= -16x

Now substitute x = 2 and y = -9 into the expression:

fx​(2,−9) = -16(2)

= -32

The number -32 represents the slope of the function f(x, y) with respect to x at the point (2,−9). It indicates that for every unit increase in the x-coordinate, the function value decreases by 32 units.

Similarly, to find fy(2,−9), we differentiate f(x, y) with respect to y, treating x as a constant:

fy(x, y) = d/dy (64 − 8\(x^{2}\) − \(y^{2}\))

= -2y

Substituting x = 2 and y = -9:

fy(2,−9) = -2(-9)

= 18

The number 18 represents the slope of the function f(x, y) with respect to y at the point (2,−9). It indicates that for every unit increase in the y-coordinate, the function value increases by 18 units.

b) To solve the differential equation (x^2 + 1)y' = xy:

We can rewrite the equation as:

dy/dx = (xy) / (\(x^{2}\) + 1)

Now, we can separate the variables and integrate both sides:

∫(1/y) dy = ∫(x / (\(x^{2}\) + 1)) dx

Integrating, we get:

ln|y| = (1/2)ln(\(x^{2}\) + 1) + C

where C is the constant of integration.

Exponentiating both sides:

|y| = \(e^{ln(x^{2} +1)^{1/2} +C}\)

Simplifying further:

|y| = \(e^{ln(x^{2} +1)^{1/2} +C}\)

|y| = \(e^{ln(x^{2} +1)^{1/2}\) * \(e^{C}\)

|y| = \((x^{2} +1)^{1/2}\) * \(e^{C}\)

Considering the absolute value, we can write:

y = ±\((x^{2} +1)^{1/2}\) * \(e^{C}\)

where ± indicates two possible solutions.

c) To evaluate the integral ∫\(e^{-4x}\) dx using the substitution u = -4x:

Differentiating both sides of u = -4x with respect to x, we get du/dx = -4.

Rearranging the equation, we have dx = -du/4.

Substituting this back into the integral:

∫\(e^{-4x}\) dx = ∫\(e^{u}\) * (-du/4)

Pulling the constant out of the integral:

= -(1/4) ∫\(e^{u}\) du

Integrating \(e^{u}\) with respect to u, we get:

= -(1/4) * \(e^{u}\) + C

Now, substituting back u = -4x:

= -(1/4) * \(e^{-4x}\) + C

So, the evaluated integral is -(1/4) * \(e^{-4x}\) + C.

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The result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

To calculate log4 57 to the nearest thousandth, we can use a scientific calculator or a logarithmic table.

Using a calculator, we can find the logarithm of 57 to the base 4 directly:

log4 57 ≈ 3.682

Therefore, the correct answer is option C: 3.682.

If you prefer to verify the result using logarithmic properties, you can do so as follows:

Let's assume log4 57 = x. This means \(4^x\) = 57.

Taking the logarithm of both sides with base 10:

log (\(4^x\)) = log 57

Using the logarithmic property log (\(a^b\)) = b \(\times\) log a:

x \(\times\) log 4 = log 57

Dividing both sides by log 4:

x = log 57 / log 4

Using a calculator to evaluate the logarithms:

x ≈ 3.682

Thus, the result is consistent with the previous calculation, and option C, 3.682, is the correct answer.

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The salesman earned a total sum of $2,165.

Given that, a shoe salesman sold $4,125 in shoes and earns a 4% commission, his base salary is $2000.

The amount of commission earned by the shoe salesman is equal to the product of the total sales and the commission rate, which is 4% or 0.04 as a decimal:

Commission = Total sales x Commission rate

Commission = $4,125 × 0.04

Commission = $165

To find the total earnings of the salesman, we add his commission to his base salary:

Total earnings = Base salary + Commission

Total earnings = $2,000 + $165

Total earnings = $2,165

Therefore, the salesman earned $2,165.

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Answer:

C. 8

Step-by-step explanation:

( - 32 ) / ( - 4 ) =

( + 8 )

Two negatives always divide and make a positive.

Answer:

\(\frac{6363}{100}\)

Step-by-step explanation:

Answer:

700/11

I would say that's the answer

or 63 7/11

Answer:

See below.

Step-by-step explanation:

The set of all real numbers except for 100 in set builder notation (assuming the variable is x) is:

\(\{x|x\in\mathbb{R},x\neq100\}\)

The very first x represents the variable.

The second with the R represents the number. Here, we want all real numbers.

And the third is the constraint. We want all real numbers except for 100.

The required sample size is 44.

The central limit theorem (CLT) in probability theory states that even when separate random variables are added together and appropriately normalized, the resulting total frequently trends toward a normal distribution. The theorem is a fundamental idea in probability theory because it suggests that many problems involving other types of distributions can be solved using probabilistic and statistical techniques that are effective for normal distributions.

The required sample size is given by:

n = (Z² * σ² )/E²

where,

n = sample size

E = error

σ = standard deviation

n = (1.96² * 175² )/52²

n = 43.51

n = 44

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