A certain disease has an incidence rate of 0.2%. If the false negative rate is 8% and the false positive rate is
1%, compute the probability that a person who tests positive actually has the disease.
Give your answer accurate to at least 3 decimal places

A summation, also known as a sum, is the result of arithmetic addition of numbers or quantities.

The value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.

Any of the following algebraic expressions should be used: addition, subtraction, multiplication, and division. Bring the variable to the left and all the remaining values to the right to find the value of x.

From the given information, we get

x - y = 6 ...............(1)

"if five times the smaller number is two times the larger number"

from the above information, we get

5y = 4x + 2

5) To simplify the value of y:

y = (4x +2) / 5 ...............(2)

Substitute  y = (4x +2) / 5 in (1), then we get

x - (4x + 2) / 5 = 6

5x / 5 - (4x + 2) / 5 = 6

simplifying the above equation, we get

(5x - 4x - 2) / 5 = 6

x - 2 = 5 x 6

x -2 = 30

x = 32

Substitute the value of x in (2)

y = 4(32) + 2 / 5

simplifying the above equation, we get

y = 130 / 5

y = 26

From (1), we get

x - y = 6

substitute the value of x and y in the above equation,

32 - 26 = 6

6 = 6

6) T is the 10s digit

X is the one's digit

The two digit number is 10T + X

It is 7 times the sum of the digits, so the 2 digit number is 7 times as large as the sum of the digits

10T + X = 7(T+X)

By using distributive law

10T + X = 7T + 7X

10T + X - 7T - 7X = 0

simplifying the above equation, we get

3T - 6X = 0

3(T - 2X) = 0

T - 2X = 0

T = 2X

The tens digit is 3 more than the one's digits, so

T = X + 3

Then we have  

T = 2X = X  + 3

Subtracting X from both sides,

T - 3 = X  + 3 - 3

X = 3

The Tens digit is 6.

The number is 63.

The sum of the digits is 9.

9 × 7 = 63.

Therefore, the value of x = 6 and y = 6 then the number exists 6 and the sum of the digits is 9.

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Answer:

Rector, Pine, Taylor

Step-by-step explanation:

The opposite side of each angle's lengths depend on how large the angle is. The larger the angle is, the longer the side. Because the angle opposite to Rector is the greatest, then it is the longest. Thus, then follows Pine and Taylor. Hope this helps!

The other names of AB in the given figure are

Collinear points refers to points that lies on the same plane and on the same straight line.

The figure shows two planes and point A, B and C are collinear points, while points Q and R are collinear

Points A, B and C are non colinear to points Q and R

Points AB are still part of line AC hence can be noted as part of line segment BC.

The line has arrow head and may also be called rays. In this case the are part of an arrow

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It could be said that the normal probability plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.

If the data from a simple random sample with 25 observations was used to construct the plots given below. The normal probability plot that was constructed has a correlation coefficient of 0.975., on analysing

The normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.

Therefore,  It could be said that the normal plot does not suggest that the data could come from a normal population, even though the boxplot does not show any outliners, so a t- interval could not be constructed.

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The orthocenter of the triangle with vertices  P(-1,2), Q(5,2), R(2,1) is

Orthocenter is calculated by

formula for slope is

m = (y₂ - y₁) / (x₂ - x₁)

slope of the perpendicular = -1/m

Using side PR  P(-1,2)  R(2,1) ,

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

m = 1 / 3

slope of the perpendicular = -1/m = - 1 / (1/3) = -3

using point-slope formula for equation of line passing through Q (5, 2)

point slope formula

(y - y₁) = m (x - x₁)

(y - 5) = -3 (x - 2)

y - 5 = -3x + 6

y = -3x + 6 + 5

y = 11 - 3x

Using side PQ  P(-1, 2), Q(5, 2)

m = (2 - 2) / (5 - -1)

m = 0

slope of horizontal line is zero for horizontal line the perpendicular is a vertical line

using point-slope formula for vertical line passing through R (2, 1)

point slope formula

(y - y₁) = m (x - x₁)

0 = (x - 2)

x =  2

The two equations are

y = 11 - 3x

x = 2

solving both equations with x already known

y = 11 - 3 * 2

y = 11 - 6

y = 5

Therefore the orthocenter is (2, 5)

The triangle is attached

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Answer: [tex]5^{2} + 4[/tex]

Step-by-step explanation:

[tex]2 + 3^3[/tex] =?

2 + 27 = 29

10 * 2 - 9 = 20 - 9 = 11

[tex]5^2 + 4[/tex] = 25 + 4 = 29

[tex]5^3\\[/tex] = 5 * 5*5 = 125

3+ 4 * 3 = 3 + 12 = 15

Answer:

[tex]2,8,14,20[/tex]

Step-by-step explanation:

If the first term of a sequence is [tex]2[/tex] and the common difference is [tex]6[/tex], then each successive term in the sequence is [tex]6[/tex] more than the previous term:

[tex]a_n=6n-4[/tex]

Therefore, the first term is [tex]2[/tex], followed by [tex]8[/tex], [tex]14[/tex], and [tex]20[/tex].

When a person from this group is selected at random, the probability that this person has type AB blood is 3/40

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates 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. In this case, 0 denotes the impossibility of the event and 1 represents certainty.

It should be noted that in this case, the number of people with AB blood is 15 and there are 200 people. The probability will be:

= Number of AB blood type / Total number of people

= 15 / 200

= 3/40

The probability is 3/40.

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The solution to the given equation is 5.630.

What is a logarithmic equation?

An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.

Here, we have

2^(x+1) = 3^(2x-5)

Taking logarithms on both sides, we get

(x+1)log2 = (2x - 5)log3

xlog2 + log2 = 2xlog3 - 5log3

log2 + log3⁵ = 2xlog3 - xlog2

log 2* 243 = x(log6 - log2)

log486 = x(log6/2)

log486 = xlog3

x = log486/log3

x = 5.630

Hence, the solution to the given logarithmic equation is 5.630.

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The true statement when the frozen yogurt stand charges per ounce of frozen yogurt purchased is B. Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.

In the scenario, the total cost (c), in dollars, for f ounces of frozen yogurt in a waffle bowl, is described by the function c = 0.45f + 1.

In this case, it is important to note that Each ounce of frozen yogurt costs $1 and a waffle bowl is $0.45 extra.

For example, for 2 ounces, this will be:

= 0.45f + 1

= 0.45(2) + 1

= 0.9 + 1

= $1.9

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The integer in the set S:{−32, −8, 16, 32} will make the inequality one fourth times the difference of m and four is less than or equal to one eighth times the difference of m and sixteen false is 32

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this case, based on the information we will replace m with 32. This will be illustrated thus:

1/4(32 - 4) ≤ 1/8 (32 - 16)

= 1/4(28) ≤ 1/8(16)

= 7 ≤ 2

In this case, 7 isn't less than or equal to 2. Therefore, 32 is the correct integer.

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Answer: Yes, Probably

64x³+125y³

= (4x+5y)( 16x²-20xy+25y²)

a³ + b³ = ( a + b )( a² - ab + b² )

64x³ + 125y³

= ( 4x )³ + ( 5y )³

= ( 4x+5y )[ (4x)²- (4x)(5y)+(5y)²]

= (4x+5y)( 16x²-20xy+25y² )

The zeros of the polynomial x⁴ - 6x³ - 21x² - 150x - 100  are 0.6511 and 8.262 respectively

Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively.

The zeros of a polynomial f(x) are the values of x which satisfy the equation f(x) = 0. Here f(x) is a function of x, and the zeros of the polynomial are the values of x for which the f(x) value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation f(x) = 0. All such domain values of the function, for which the range is equal to zero, are called the zeros of the polynomial.

To find the zeros of this polynomial function, we have to write the function appropriately.

x⁴ - 6x³ - 21x² = 150x - 100

x⁴ - 6x³ - 21x² - 150x - 100 = 0

The roots of this function is 0.6511 and 8.262 respectively

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Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

According to the map, North America makes up [tex]\frac{16}{100}[/tex] of the world's land surface area, while Europe makes up [tex]\frac{7}{100}[/tex]. Since both fractions already have a common denominator ( [tex]\frac{n}{100}[/tex] ), we can simply subtract the two to find how much greater the fractional part of North America is than the fractional part of Europe:

[tex]\frac{16}{100}-\frac{7}{100}=\frac{9}{100}[/tex]

The equation in slope intercept form of the line that passes through the graph is y = 2/3x + 2

From the graph, we have the points to be given as

(-3,0) and (0,2)

Start by calculating the slope of the points using the following slope equation

m = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (-3,0) and (0,2)

So, we have

m = (2 - 0)/(0 + 3)

Evaluate

m = 2/3

The equation is then calculated as

y = m(x - x₁) + y₁

Where

(x, y) = (0, 2) and m = 2/3

So, we have

y = 2/3(x - 0) + 2

Expand

y = 2/3x + 2

Hence, the equation in slope intercept form of the line is y = 2/3x + 2

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If Sebastian filled 10 gallons of gas, the total amount he spent at the gas station was C. $40.50.

Using the mathematical operations of multiplication and addition, we can compute the total amount that Sebastian spent at the gas station.

We first determine the total cost of gas that Sebastian bought by multiplying the unit cost by the quantity.

Secondly, we add the above total cost to the total cost of other items he bought at the station to arrive at the total amount spent.

The cost of gas per gallon = $2.91

The number of gallons of gas bought = 10

The total cost of gas = $29.10 ($2.91 x 10)

The total cost of granola bars and tissues = $11.40

The total amount spent = $40.50 ($29.10 + $11.40)

Thus, mathematically, Sebastian spent C. $40.50 at the gas station.

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The rate at which the tip of the woman's shadow is moving, found by making use of the relationships between similar triangle and differentiation is 10 ft/s

Similar triangles are triangle in which all three sides of one proportional to three sides of the other triangle

Height of the woman = 6 ft.

The speed with which the woman walks towards the streetlight = 8 ft/s
The length of the shadow of the woman

Height of the street light = 30 ft.

Let a represent the horizontal distance from the woman to the street light, and let b represent the horizontal distance from the woman to the tip of her shadow, from the similar triangles formed by the shadow, we have;

[tex]\dfrac{30}{x+y} =\dfrac{6}{y}[/tex]
Which gives;

[tex]y = \dfrac{x}{4}[/tex]

The length of the tip of the woman's shadow to the street light, l, in terms of x is therefore;

[tex]l =x + y = x + \dfrac{x}{4} = \dfrac{5\cdot x}{4}[/tex]

[tex]\dfrac{dx}{dt} = 8[/tex]

Therefore, dx = 8·dt

x(t) = 8·t

Writing the function for the l in terms of time t gives;

[tex]l = \dfrac{5\cdot x}{4}[/tex]

[tex]l = \dfrac{5\times 8\cdot t}{4} = \dfrac{40\cdot t}{4} = 10\cdot t[/tex]

The speed at which the tip of the shadow is moving,

[tex]\dfrac{dl}{dt} = \dfrac{d}{dt} \left (10\cdot t ) = 10[/tex]

The speed of the shadow dl/dx = 10 ft./s

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If the company wants to keep the cost of operation under $14,000 per month, The maximum number of units they can produce is: D. 349.

Given function:

C = $3,173 + $31u

Hence,

Let u represent number of  units

Let c represent the operation cost

Where c = $14,000 per month

$14,000 = $3,173 + $31u

Combine like terms

$14,000 - $3,173 = $31u

$10,827 = $31u

Divide both side by $31u

u = $10,827 / 31

u = 349 units

Therefore the correct option is D.

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The 10 forms 1/8 can be written is as follows;

A fraction refers to a number which consists of a numerator and a denominator.

A numerator is the upper value of a fraction.

A denominator is the lower value of a fraction.

1 over 8 can be written in the following ways;

1/8

1 ÷ 8

1/2³

= 1 / 2×2×2

= 1/8

1/√64

= 1/8

[tex]{8}^{ - 1} [/tex]

= 1/8

1 : 8

= 1/8

[tex]{√64}^{ - 1} [/tex]

= 1/√64

= 1/8

[tex]{2}^{ - 3} [/tex]

= 1/2³

= 1/8

2/16

= 1/8

4 : 32

= 4/32

= 1/8

In conclusion, 1/8 can be written in different forms including using square root and ratios.

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The probability that the sample proportion surviving for at least 3 years will be less than 67% is of:

0.1131 = 11.31%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The proportion and the sample size are given as follows:

p = 0.73, n = 80.

Hence the mean and the standard error are given as follows:

The probability that the sample proportion surviving for at least 3 years will be less than 67% is the p-value of Z when X = 0.67, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (0.67 - 0.73)/0.0496

Z = -1.21

Z = -1.21 has a p-value of 0.1131.

Hence the probability is:

0.1131 = 11.31%.

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By using set notation, the elements of the given data set in ascending order include {-4, -3, -3, -1, 0, 1, 2, 2}.

In Mathematics, a listing method can be defined as a technique which is used to list all the elements or members of a data set, while separating each of them with a comma and enclosing the data set within curly braces.

Generally speaking, set notation is typically used in mathematics for listing the elements of a set such as objects, numbers, or outcomes, especially by making use of curly brackets.

For this exercise, the elements of the given data set would be listed in ascending order as follows:

Set = {-4, -3, -3, -1, 0, 1, 2, 2}

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Step-by-step explanation:

Given the inequality 4x ≤ 28, determine the value of x.

4x ≤ 28

divide both sides by 4:

4x/4 ≤ 28/4

x ≤ 7

set builder notation: (-∞, 7]

answer:

The value of x is 7.

Step-by-step explanation:

4x ≤ 28 | divide both sides by 4

4x / 4 = x  and 28 / 4 = 7

therefore, x ≤ 7

The single fraction in its lowest terms will be;

⇒ - 7(2x - 1)/2

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Or, A number which is expressed as a quotient is called fraction.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The fraction is,

⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2

Now,

Solve the fraction as;

The fraction is,

⇒ 3 (2x - 1)/5 - 2 (4x - 2)/2

⇒ 3 (2x - 1)/5 - (4x - 2)

⇒ 3 (2x - 1)/5 - 2 (2x - 1)

⇒ (2x - 1) (3/5 - 2)

⇒ (2x - 1) (3 - 10)/2

⇒ (2x - 1) (- 7/2)

⇒ - 7(2x - 1)/2

Thus, The single fraction in its lowest terms will be;

⇒ - 7(2x - 1)/2

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The actual weekly labor cost compared to the target is 240 hours

What are Time and Work?

According to fundamental mathematical concepts, time may be described as the amount of time that a specific activity occurs, whereas work can be described as the collection of actions carried out in order to attain a specific activity or outcome. It should go without saying that time is needed to accomplish a task. It implies that time and work have a certain relationship.

The task completed is calculated as the sum of the number of people participating in the work and the number of days it took to finish. The fundamental time and work equation is W = N X D.

Target costing is a system under which a company plans in advance for the price points, product costs, and margins that it wants to achieve for a new product.

Given

Regular Rate $15.00/hr

Overtime Rate $22.50/hr

Targeted Labour Cost $12,000/wk

Labour Hours Needed 800/wk

According to the question:

Overtime means each employee can work beyond the input of 40 hrs. Per week.

Labor requirement = 800 hrs.

14 men labor capacity = 14× 40 = 560 hrs.

So overtime hours required = 800-560=240 hrs

Hence,

The actual weekly labor cost compared to the target is 240

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Answer: 3 busses

Step-by-step explanation:

Answer:

£27839

Step-by-step explanation:

O×M=N (original x multiplier = original value)

£28000×0.97%=£27160< 1st year decrease

£27160x1.025=£27839<2nd year increase

Answer:

  78°

Step-by-step explanation:

You want the measure of base angle x in an isosceles triangle with a.pex angle 24°.

The two base angles of an isosceles triangle are congruent. The sum of all angles is 180°, so we have ...

  24° +2x = 180°

  12° +x = 90° . . . . . . divide by 2

  x = 78° . . . . . . . subtract 12°

The measure of angle x is 78°.

Using the corresponding angle theorem, the value of x is 15 and y is 12.

In the given question we have to find the value of x and y.

From the graph we can see that

From the corresponding angle theorem

4x+2=62

Subtract 2 on both side, we get

4x=60

Divide by 4 on both side, we get

x=15

So the value of x is 15.

Similarly from the corresponding angle theorem

12y=144

Divide by 12 on both side, we get

y=12

So the value of y is 12.

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After simplifying an equation the value of x is x = 3.

What is solving an equation?

Unifying Principle for Equation Solving

By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.

The variable term on one side of the equation can be separated using addition or subtraction.

To find the variable, use multiplication or division.

Consider, the given equation

     5(2x - 4) = 10

      10x - 20 = 10                                  Removing parenthesis

10x -20 + 20 = 10 + 20                         Adding 20 on both sides

              10x = 30                                 Simplifying

                  x = 3                                    Dividing both sides by 10

Hence, the value of x is, x = 3.

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