the elisa test is known to have probability 0.05 of producing a false positive result and probability 0.10 of producing a false negative result for a single chicken. a. if no chicken in the flock is infected with the h6n2 virus, what is the probability that the veterinarian will conclude that the h6n2 virus is not present in the flock? show how you found your answer. b. if no chicken in the flock is infected with the h6n2 virus, what is the probability that the veterinarian will conclude that the h6n2 virus is present in the flock? show how you found your answer. c. if every chicken in the flock is infected with the h6n2 virus, what is the probability that the veterinarian will conclude that the h6n2 virus is present in the flock? show how you found your answer. d. if 20 percent of the chickens in the flock are infected with the h6n2 virus and the other 80 percent are not infected, what is the probability that the veterinarian will conclude that the h6n2 virus is present

Answer:

First account: $16,000

Second account: $4,000

Step-by-step explanation:

Let x be the amount Christine invested in the 8% account and y be the amount she invested in the 10% account. We know from the problem that:

x + y = $20,000 (the total amount she had to invest)

0.08x + 0.1y = $1920 (the total amount of interest she received)

We can use the first equation to solve for one variable in terms of the other.

x = $20,000 - y

Now we substitute this expression into the second equation:

0.08($20,000 - y) + 0.1y = $1920

Solving for y:

0.08x + 0.1y = $1920

0.08($20,000 - y) + 0.1y = $1920

1,600 - 0.08y + 0.1y = $1920

-0.08y = -320

y = $4,000

Now, we know that Christine invested $4,000 in the 10% account, we can use the first equation again to find out how much she invested in the 8% account:

x + y = $20,000

x + $4,000 = $20,000

x = $16,000

So Christine invested $16,000 in the 8% account and $4,000 in the 10% account

Answer:

Step-by-step explanation:

Distance between top of the tower and point of observation = 100 meters
Angle of Elevation = 45 degrees

Let's draw a right angle triangle with the following specifications.

tan(45 degrees) = x/100

tan(45 degrees) = 1

100(1) = x

x =  100 meters

The height of the tower is 100 meters.

The correct equations to represent Ted's total September costs are: (3600+ 1.50) x 12.000 1.50(3600+) 12,000.

Cost is the total expenditure or loss incurred in the production, acquisition, or use of a product or service. It can be calculated as the sum of fixed costs (such as rent and labor costs) plus variable costs (such as materials and energy). Cost can be expressed both in monetary terms (such as dollars or euros) or in terms of resources (such as time or effort). In business, cost is a crucial factor for determining profitability and should be taken into consideration when making decisions about production, sales, and pricing strategies.
The first equation calculates the cost of the fixed monthly costs plus the cost of the 16 ounce bags of coffee multiplied by the total number of bags sold. The second equation calculates the cost of the 16 ounce bags of coffee multiplied by the fixed monthly costs plus the total number of bags sold.

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Answer:

240 seats with tables

Step-by-step explanation:

Let's start by making our fraction out of 10 on the first train to make it easier on us, this fraction would be [tex]\frac{6}{10}[/tex]. Then, to get the number of seats on this train that would have a table, we need to multiply 400 by our fraction, giving us:

[tex]400 * \frac{6}{10} = 2400/10 = 240[/tex]

So, the 1st train should have approximately 240 seats with tables.

Hope this helped!

Answer:

[tex]\frac{3}{16}[/tex] f - [tex]\frac{3}{2}[/tex] g

Step-by-step explanation:

[tex]\frac{3}{8}[/tex] ( [tex]\frac{1}{2}[/tex] f - 4g )

multiplying each of the terms inside the parenthesis by [tex]\frac{3}{8}[/tex]

[tex]\frac{3}{8}[/tex] × [tex]\frac{1}{2}[/tex] f

= [tex]\frac{3(1)}{8(2)}[/tex] f

= [tex]\frac{3}{16}[/tex] f

and

[tex]\frac{3}{8}[/tex] × - 4g ( cancel 4 and 8 by 4 )

= [tex]\frac{3}{2}[/tex] × - g

= - [tex]\frac{3}{2}[/tex] g

combining the 2 products, gives

[tex]\frac{3}{16}[/tex] f - [tex]\frac{3}{2}[/tex] g

Answer:

[tex]\textsf{Orange partial product}=\dfrac{3}{16}\;f[/tex]

[tex]\textsf{Pink partial product}=-\dfrac{3}{2} \;g[/tex]

[tex]\textsf{Product}=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)[/tex]

Calculate the partial products then add these together to find the product of the given expression.

Orange partial product

[tex]\implies \dfrac{3}{8} \times \dfrac{1}{2}f[/tex]

[tex]\implies \dfrac{3 \times 1}{8\times 2}\;f[/tex]

[tex]\implies \dfrac{3}{16}\;f[/tex]

Pink partial product

[tex]\implies \dfrac{3}{8} \times (-4g)[/tex]

[tex]\implies \dfrac{3 \times -4}{8} \;g[/tex]

[tex]\implies \dfrac{-12}{8} \;g[/tex]

[tex]\implies -\dfrac{\diagup\!\!\!\!4 \times 3}{\diagup\!\!\!\!4 \times 2} \;g[/tex]

[tex]\implies -\dfrac{3}{2} \;g[/tex]

Product:

[tex]\implies \dfrac{3}{8}\left(\dfrac{1}{2}f-4g\right)=\dfrac{3}{16}\;f-\dfrac{3}{2} \;g[/tex]

Given ,

[tex]\bold\red{zeroes \: of \: a \: cubic \: polynomial \: are \: - 2 \:, \: 0 \: and \: 7} \\ [/tex]

[tex]let \:, \\ \boxed{\alpha \: = - 2} \\ \boxed{\beta \: = 0} \\ \boxed{\gamma \: = 7} [/tex]

Now ,

[tex]sum \: of \: zeroes \: = \alpha \: + \: \beta \: + \: \gamma \: \\ \dashrightarrow \: sum = - 2 + 0 + 7 = \underline{5} \\ \\ sum \: of \: product \: of \: zeroes \: taken \: two \: at \: a \: time \: = \alpha\beta \: + \beta\gamma \: + \: \alpha\gamma \\ \dashrightarrow \: ( - 2)(0) \: + \: (0)(7) \: + \: (7)( - 2) \: = \: \underline{ - 14} \\ \\ product \: of \: zeroes \: = \: \alpha\beta\gamma \\ \dashrightarrow \: ( - 2)(0)(7) = \underline{0}[/tex]

We know that ,

[tex] \boxed{cubic \: polynomial \: = {x}^{3} - (\alpha \: + \: \beta \: + \: \gamma \:) \:{x}^{2} + (\alpha\beta \: + \: \beta\gamma \: + \: \alpha\gamma) \:x \: - \: \alpha\beta\gamma} [/tex]

Plugging in the values , we get

[tex]\boxed{f(x) = {x}^{3} - 5 {x}^{2} - 14x + 0}[/tex]

since this polynomial has degree 3 , it is called a cubic polynomial.

hope helpful! :)

The values of the expression are given by the inequality below:

11/3 < 5/x + 2 < 9/2

Here we want to find the possible values of the expression:

5/x + 2

Where we have the restriction:

2 < x < 3

Notice that x is on the denominator, so when x takes the largest value x = 3, we will have a lower bound for the expression:

5/3 + 2 = 5/3 + 6/3 = 11/3

When x takes the smallest value, we will get the upper bound:

5/2 + 2 = 5/2 + 4/2 = 9/2

Then the possible values of the expression are:

11/3 < 5/x + 2 < 9/2

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The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).

Take the common terms in the numerator and denominator and remove them from the expression to make it simpler.

The simplification of rational expressions can be achieved by using the Greatest Common Factor (GCF).Similar to fractions with variables in the denominators, rational expressions appear like them (and often numerators too).

For instance, the expression x 2 x + 3 is a rational expression: x squared, divided by x, plus 3, end fraction.

1)2m^2-4m)/2(m-2)

=[2m(m-2m)]/2(m-2)

= 2m/2

=m

2)m^2-2m+1/m-1

= (m-1)^2/(m-1)

=(m-1)(m-1)/(m-1)

=(m-1)

3)m^2-3m+2/m^2-m

=m^2-m-2m+2/m(m-1)

=m(m-1)-2(m-1)/m(m-1)

= (m-1)(m-2)/m(m-1)

=(m-2)/m

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The coordinates of the circumcenter of a triangle with vertices A(0,1),

B(2, 1) , and C(2, 5)  is (1,3).

What is circumcenter of triangle?

The point at which the perpendicular bisectors of a triangle's sides come together is known as the circumcenter of that triangle. The circumcenter is, in other words, the point at which the bisector of a triangle's sides coincides. P serves to indicate it (X, Y).

Given:  A triangle with vertices A(0,1), B(2, 1) , and C(2, 5).

Using distance formula:

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

AB = 2 units

BC = 4 units

AC = √20 units

The midpoint of AC:

[tex]= (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )\\= (\frac{2+0}{2}, \frac{5+1}{2}) \\= (\frac{2}{2} , \frac{6}{2})\\ = (1, 3)[/tex]

The midpoint of AC is (1, 3).

Hence, The coordinates of the circumcenter of a triangle with vertices A(0,1),  B(2, 1) , and C(2, 5)  is (1,3).

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The value of j by solving with one-step equation solution method will be of the option C i.e. 2/30.

What are one-step equations?

A one-step equation is an algebraic equation you can solve in only one step. Once you've solved it, you've found the value of the variable that makes the equation true.

To solve one-step equations, we do the inverse (opposite) of whatever operation is being performed on the variable, so we get the variable by itself. The inverse operations are:

Addition and subtraction

Multiplication and division

The most important thing to remember is that whatever you do to one side of the equation, you have to do the same thing to the other side.

Now,

given that,

19/30=j+17/30

To find j, subtract 17/30 from both side,  (Using one-step equation method)

19/30-17/30=j+17/30-17/30

2/30=j

Hence, the value of j will be 2/30.

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Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.

The original capital is multiplied by the interest rate, the loan term, and other factors to calculate simple interest. A simple return is equal to the principal plus interest hrs. This method of calculating interest is the simplest. The most typical method is to calculate it as a fraction of the principal amount. For instance, he was only liable for paying his portion of the interest if he acquired $100 from a buddy and agreed to repay the money on 5% interest. $x (0.05) = $5. When you make loans or lend money, you both have to pay interest. Interest is frequently determined as a percentage of a loan.

Here,

Given  :  interest = 9%

time  =35 years

amount = 800000

Using formula :

=> FV.( r / [tex](1+r) ^{n}[/tex] -1)

=>  800000 (0.09/12 / [tex](1 + 0.09/12 )^{12*35}[/tex] - 1 )

=> 271.94

Therefore,

the total amount you deposit will only be

=> 35*12 times $271.94, or

roughly total amount => 35*12*271.94= 114214.8 dollars, out of the estimated $800,000.

The balance will be what the account earns or accumulates over the next 35 years.

Therefore , the solution of the given problem of interest rate comes out to be $271.94 you will be depositing every month.

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Answer:

D= dependent. T= independent

Step-by-step explanation:

I would say this bc the total distance depends on the amount of time he ran

d is distance

t is time (how long he ran)

$2094.28 interest will she pay by the time the loan is repaid.

What is compounded monthly?

Theoretically, continuously compounded interest means that an account balance continuously earns interest as well as reinvesting that interest into the balance so that it too earns interest.

As we know the formula of per month installments

[tex]E.M.I = \frac{P*r*(1+r)^n}{(1+r)^n^-^1}[/tex]

By putting the value of P (loan applied for)=$5500

r (Monthly rate of interest)  [tex]= \frac{6.8}{12*100}[/tex]

n = number of monthly installments = 10 × 12 = 120

[tex]E.M.I = \frac{5500*(\frac{6.8}{12*100} )(1+\frac{6.8}{1200} )^1^2^0}{(1+\frac{6.8}{1200} )^1^2^0-1}\\ E.M.I= \frac{5500*0.00567*1.971}{1.971-1}\\ E.M.I = \frac{61.461}{0.971} \\E.M.I = 63.29[/tex]

E.M.I.=$63.29

Total Installments of loan =120

Therefore total amount paid against loan = $63.39 × 120 = 7594.28

So interest paid = 7594.28 - 5500= $2094.28

Hence, $2094.28 interest will she pay by the time the loan is repaid.

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∠3 is congruent to ∠1. Hence, proved.

Two angles are said to be complementary angles if they add up to 90 degrees. In other words, when complementary angles are put together, they form a right angle (90 degrees).

Given that, ∠3 and ∠2 are complementary; m∠2 + m∠3 = 90°---------(I)

From the given figure,

m∠1 + m∠2 = 90°---------(II)

From the given equation (I) and (II), we get

m∠1 + m∠2=m∠2 + m∠3

m∠1 ≅ m∠3

Hence, proved.

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The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The quadratic regression equation y = –0.1x² + 143.99x – 13,242.84 models expected company profits in terms of the number of pairs of shoes sold.

The profit can the company expect if it sells 400 pairs of shoes will be given as,

y = –0.1(400)² + 143.99(400) – 13,242.84

y = – 16,000 + 57,596 – 13,242.84

y = 28,354

y ≈ 28,400

The approximate profit can the company expect if it sells 400 pairs of shoes will be 28,400. Then the correct option is A.

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Answer:

I don't know the answer to this question

Answer:

Step-by-step explanation:

180 total

180-3=177

ratio of angle 1 to angle 2:

2:1

we need to divide 177 by 3 since there are 3 parts in the ratio above

177/3=59

angle 1 = 59x2=118

angle 1=118 degrees

angle 2=59+3=62

angle 2 =62 degrees

we can check by adding 62 and 118

62+118=180

The required values of the events are P(Sum > 5) = 0.72 , P (sum is even) = 0.5.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

We have,

According to empirical or relative frequency probability, probabilities are determined by dividing the total number of potential outcomes of an experiment by the number of ways an event could occur.

There are a total of 36 possible results when a fair die is rolled twice consecutively, which is

(1,1), (1, 2), (1,3), (1,4), (1, 5), (1, 6)

(2,1), (2, 2), (2, 3), (2,4), (2,5), (2,6)

(3, 1), (3,2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4,2), (4,3), (4, 4), (4, 5), (4, 6)

(5, 1),(5, 2), (5, 3), (5,4), (5,5), (5, 6)

(6,1), (6, 2), (6,3), (6,4), (6,5), (6,6)

Event A: The total exceeds 5. We find 26 numbers in the table that are bigger than 5, so

P(A) = P(Sum > 5) = 0.72 Event

B: The results of the total are even from the table are 18

P(B) = P (sum is even) = 0.5

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Answer:

D

Step-by-step explanation:

There are no black shoelaces

Find the difference between the two lower numbers. If the total is more than the greatest integer, the three numbers can represent the lengths of the triangle's sides.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees.

Here,

Find the sum of the two smaller numbers. If the aggregate is more than the greatest number, the three numbers can represent the lengths of the sides of a triangle.

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By completing squares in both the variables and try to get the general equation of the form:

(x - a)^2 + (y - b)^2 = R^2

A general circle equation for a circle whose center is (a, b) and the radius is R, is:

(x - a)^2 + (y - b)^2 = R^2

So, if we have an equation like:

x^2 + cx + d + y^2 + h*y + l = m

We just need to complete squares in both x and y, such that we end with an equation of the form of:

(x - a)^2 + (y - b)^2 = R^2

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Answer: z=23

Step-by-step explanation:

Since the sum of all interior angles of a triangle is 180, let's use that to solve this problem.

First, let's set up an equation.

z+62+95=180

Next step is to simplify the left side of the equation, which leaves us with:

z+157=180

Lastly, subtract 157 from both sides of the equation and we get the final answer:

z = 23

The height of the prism is 5x + 3 units.

What is volume?

A measurement of three-dimensional space is volume. It is frequently expressed numerically using SI-derived units, as well as different imperial or US-standard units. Volume and the definition of length are related.

Given:

The volume of a rectangular prism is given by the expression

10x^3 + 46x^2 – 21x – 27. The area of the base of the prism is given by the expression 2x^2 + 8x – 9.

We have to find the height of prism.

Volume of the rectangular prism = Base × Height

The expression is in the Question be

10x ³ + 46 x² - 21x -27

And the  area of the base of the prism is given by the expression

2x² + 8x - 9 .

Put in the formula

10x ³ + 46 x² - 21x -27  = 2x² + 8x - 9  × Height

The factor of 10x ³ + 46 x² - 21x -27 are (5x +3 )(2x² + 8x - 9) .

put in the formula

(5x +3 )(2x² + 8x - 9) = (2x² + 8x - 9) × Height

Cancelled 2x² + 8x - 9 on both side.

(5x+3)unit = Height

Hence, the height of the prism is 5x + 3 units.

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an incline plane to lift a heavy object to the top of a shelving unit with a height of 5 ft. The base of the incline plane is 221 ft from the shelving unit

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The probability of being born on a Tuesday is= 18/343

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability.

A straightforward illustration is tossing a fair (impartial) coin.

The coin is fair, thus the outcomes "heads" and "tails" are equally likely; the likelihood of "heads" is equal to the likelihood of "tails"; and because there are no other conceivable outcomes, the likelihood of either "heads" or "tails" is 1/2 (which is also an acceptable spelling).

Hence, The probability of being born on a Tuesday is= 18/343.

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According to Westgard and CLIA , 40-100  specimens should be run by each method on the same day for 8 to 20 days to compare a test method with a comparative method.

CLIA stands for  Clinical Laboratory Improvement Amendments  . The regulations under CLIA includes, the federal standards which is applicable to all U.S. facilities or sites which are test human specimens for health assessment or it is used to diagnose, prevent, or treat disease.

The Federal Register is the official daily publication for federal agencies and the organization's notices, proposed regulations, and final rules, as well as executive orders and other presidential papers. The regulations published in the Code of Federal Regulations and enforced by federal agencies are known as final rules.

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Answer:

the sum of two adjacent angle measures will equal the angle measure of the larger angle that they form together

Step-by-step explanation:

angle addition postulate formula is ∠AOB + ∠BOC = ∠AOC

If a translation of (x,y) → (x+6,y-10) is applied to figure ABCD, the coordinates of D are (1,-12).

What is translation?

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes.

The points of the original image is -

A(-3,4), B(3,4), C(1,-2), D(-5,-2)

The translation of (x,y) → (x+6,y-10) is applied -

A(-3,4) = (-3+6,4-10) = (3,-6)

B(3,4) =  (3+6,4-10) = (9,-6)

C(1,-2) = (1+6,-2-10) = (7,-12)

D(-5,-2) = (-5+6,-2-10) = (1,-12)

Therefore, the new points are -

A'(3,-6), B'(9,-6), C'(7,-12) and D'(1,-12).

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Answer: The expression X^2 + _x + 100 is the square of a binomial if the missing number is -b/2 and b^2 - 4ac = 0.

Step-by-step explanation: The general form of the square of a binomial is (x + b)^2 = x^2 + 2bx + b^2.

In this case, the missing number is -b/2, and the expression becomes X^2 - x + 100.

Now to find the value of x, we can use the equation b^2 - 4ac = 0

The equation becomes x^2 - 41100 = 0

Which gives x^2 - 400 = 0

So x = ± 20.

So the possible values for the missing number that make the expression the square of a binomial is -20/2 = -10 and 10.

Answer:

To find the missing number in the given expression, we will see the operation used. Step 1: Recall the concept of addition. We need to find the first addend. Step 2: Think of the number which when added to 3 gives the sum equal to 8. Step 3: 5 + 3 = 8. So, the missing number is 5. Step 4: Write the missing number: 5 + 3 = 8.

Step-by-step explanation: