suppose a certain drug test is 96% sensitive, that is, the test will correctly identify a drug user as testing positive 96% of the time, and 86% specific, that is, the test will correctly identify a non-user as testing negative 86% of the time. suppose a corporation decides to test its employees for drug use, and that only 0.3% of the employees actually use the drug. what is the probability that, given a positive drug test, an employee is actually a drug user? round your answer to 3 digits after the decimal point.

Answer:

Yep

Step-by-step explanation:

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The speeds of the car are 35 km/hr and 25 km/hr, if a car starts from A and another car starts from B at the same time. If both cars travel in the same direction, they cross in 8 hours, but if these cars travel in opposite directions, they meet each other in 1 hour 20 mins. A and B have a distance of 80 km.

Let the speed of the car at A be \(v_1\)

the speed of the car at B be \(v_2\)

In the first case, they travel in the same direction, the relative velocity is given by \(v_1-v_2\)

\(v_1-v_2\) = \(\frac{80}{8}\)

\(v_1-v_2\) = 10 -----(i)

In the second case, they travel in the opposite direction, the relative velocity is given by \(v_1+v_2\)

\(v_1+v_2\) = \(\frac{80}{1\frac{1}{3} }\)

\(v_1+v_2\) = \(\frac{80*3}{4}\)

\(v_1+v_2\) = 60 ------(ii)

Add equations (i) and (ii)

\(2v_1\) = 70

\(v_1\) = 35 km/hr

From equation (i)

\(v_2\) = 25 km/hr

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To determine whether the demand is elastic, inelastic, or has unit elasticity at the given price values, we need to calculate the price elasticity of demand (PED) using the price-demand equation.

The price-demand equation is given as:

x = f(p) = 1,875 - p^2

The formula to calculate PED is:

PED = (dx/dp) * (p/x)

Where dx/dp is the derivative of x with respect to p.

(A) When p = 15:

Substituting p = 15 into the price-demand equation, we get:

x = 1,875 - 15^2 = 1,875 - 225 = 1,650

Calculating PED at p = 15:

PED = (dx/dp) * (p/x) = (-2p) * (p/x) = (-2 * 15) * (15/1650) = -30 * 0.0091 ≈ -0.273

Since PED is negative and less than 1 in absolute value, the demand is inelastic at p = 15.

(B) When p = 25:

Substituting p = 25 into the price-demand equation, we get:

x = 1,875 - 25^2 = 1,875 - 625 = 1,250

Calculating PED at p = 25:

PED = (dx/dp) * (p/x) = (-2p) * (p/x) = (-2 * 25) * (25/1250) = -50 * 0.02 = -1

Since PED is negative and equal to -1, the demand has unit elasticity at p = 25.

(C) When p = 40:

Substituting p = 40 into the price-demand equation, we get:

x = 1,875 - 40^2 = 1,875 - 1600 = 275

Calculating PED at p = 40:

PED = (dx/dp) * (p/x) = (-2p) * (p/x) = (-2 * 40) * (40/275) ≈ -80 * 0.145 = -11.6

Since PED is negative and greater than 1 in absolute value, the demand is elastic at p = 40.

In summary:

(A) Demand is inelastic at p = 15.

(B) Demand has unit elasticity at p = 25.

(C) Demand is elastic at p = 40.

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Answer:

5 : 7

Step-by-step explanation:

groom's side: 40

bride's side: 56

ratio groom to bride = 40/56 = 20/28 = 10/14 = 5/7

Answer: 5 : 7

Answer:

m<X = \(126^{o}\)

Step-by-step explanation:

From the given isosceles triangle, we have;

<W and <V as the base angles

So that,

m<W = m<V = 27 (base angles of an isosceles triangle are equal)

Thus,

m<X + m<V + m<W = 180 (sum of angles in a triangle)

m<X + 27 + 27 = 180

m<X + 54 = 180

m<X = 180 - 54

       = 126

m<X = \(126^{o}\)

The values of the variables are represented below

Triangle (1)

This can be calculated using the following law of sines

x/sin(110) = 16/sin(27)

So, we have

x = sin(110) * 16/sin(27)

Evaluate

x = 33.1

Triangle (2)

This can be calculated using the following law of cosines

x² = 30² + 14² -  2 * 30 * 14 * sin(125)

So, we have

x² = 407.91

Evaluate

x = 20.20

Triangle (3)

This can be calculated using the following law of cosines

28² = 18² + 12² -  2 * 18 * 12 * sin(x)

So, we have

sin(x) = -0.7314

Evaluate

x = 133

Triangle (4)

This can be calculated using the following law of sines

29/sin(x) = 33/sin(91)

So, we have

29/sin(x) = 33.01

Evaluate

x = 61.46 degrees

The missing lengths

PR is calculated as

PR^2 = 18^2 + 27^2 - 2 * 18 * 27 * cos(76)

Evaluate

PR = 28.6

Then, we have

18^2 = 28.6^2 + 27^2 - 2 * 28.6 * 27 * cos(R)

R = 37.6

For P, we have

P = 180 - 37.6 - 76

P = 66,4

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The value of f(g(-3))  is 8.

The correct answer is b) 8.

Given:

f(x) = x² + 4

g(x) = √(1 - x)

First, let's find g(-3),

g(-3) = √(1 - (-3))

      = √(1 + 3)

      = √4

      = 2

Now, substitute g(-3) into f(x):

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

        = 2² + 4

        = 4 + 4

        = 8

we need to substitute -3 into the function g(x) and then substitute the result into the function f(x).

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The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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Answer: 11.9

Step-by-step explanation:

The opposite is across from the 35 degree angle and the ajacent is the side valued at 17.

Answer:

A. 11.9

Step-by-step explanation:

35° = opposite/adjacent

tan(35°) = x/17

tan(35) x 17 = 11.90352814

x = 11.90352814

x = 11.9

The value of the composite function is (f + g)(x) = 2x^2 + x - 4

The functions are given as:

f(x) = 4x - 4

g(x) = 2x^2 - 3x

The composite function is calculated as:

(f + g)(x) = f(x) + g(x)

This gives

(f + g)(x) = 4x - 4 + 2x^2 - 3x

Evaluate the like terms

(f + g)(x) = 2x^2 + x - 4

Hence, the value of the composite function is (f + g)(x) = 2x^2 + x - 4

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Answer:

4y^4 + 6y = 256y + 6 = 262y

Step-by-step explanation:

Remove the variables for a second and think of the problem as a normal expression; 4^4 + 6

Simplify the first term; 4^4 = 256

Now, add 6; 256 + 6 = 262

Add back in the variable; 262y

Answer:

2y(2y+3)

Step-by-step explanation:

2y(2y) +6y factor 2y out of 4y^2

2y(2y)+2y(3) factor 2y out of 6y

2y(2y + 3) factor 2y out of 2y(2y)+2y(3)

Answer:

a) 3 lemons = (0.3)^3 = 0.027

------------------------------------

b) No fruit symbols = (0.5)^3 = 0.125

c) 3 bells (the jackpot) = (0.1)^3 = 1/1000

d) No bells = (999/1000)

e) At least one bar (An automatic loser)= 1 - P(no bars)

= 1 - 3C0(0.4)^0*0.6^3 = 1-0.6^3 = 0.784

============================================

Cheers,

The expressions (3√-5 + 2)(4√-12 - 1) and (4i - 3)² have values of -24√5 - 2 + 16i√3 - 3i√5 and  -7 - 24i respectively.

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.

In the first expression;

(3√-5 + 2)(4√-12 - 1) will give us -24√5 - 2 + 16i√3 - 3i√5

In the second expression, we have (4i - 3)² which will give us -7 - 24i

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A system of equations with one linear equation and one quadratic equation has "zero or one or two" solutions.

Consider a system of equations with one linear equation and one quadratic equation as

Case (1): y = x² + 4x + 2 ...(1)

and x + y = 2 ...(2)

By the substitution method:

from (2), y = 2 - x; Substituting in (1)

⇒ 2 - x = x² + 4x + 2

⇒ x² + 4x + 2 + x - 2 = 0

⇒ x² + 5x = 0

⇒ x(x + 5) = 0

∴ x = 0 and x = -5

If x = 0, then y = 2 - 0 = 2

If x = -5, then y = 2 + 5 = 7

So, the system has two solutions at (0, 2) and (-5, 7).

Case (2): y = x² + 4x + 2 ...(1)

and x - y = 2 ...(2)

By the substitution method:

from (2), y = x - 2; Substituting in (1)

⇒ x - 2 = x² + 4x + 2

⇒ x² + 4x + 2 + 2 - x = 0

⇒ x² + 3x + 4 = 0

we know that b² - 4ac will decide the nature of roots.

So, (3)² - 4(1)(4) = 9 - 16 = -7 < 0

Since the determinant is less than 0, the roots are imaginary. Hence the system has no solution. That means the line and the parabola do not meet.

Case (3): y = x² + 4x + 2 ...(1)

and y = x - 1/4 ...(2)

Substituting (2) in (1), we get

⇒ x - 1/4 = x² + 4x + 2

⇒ x² + 4x + 2 - x + 1/4 = 0

⇒ x² + 3x + 9/4 = 0

⇒ 4x² + 12x + 9 = 0

⇒ (2x + 3)² = 0

⇒ 2x + 3 = 0

∴ x = -3/2

If x = -3/2 then y = -3/4 - 1/4 = -7/4

So, the system has one solution at (-3/2, -7/4).

Therefore, the given type of system has "zero or one or two" solutions.

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The function f(x) = 5 - 2x equals its average value at x = 1. To find the point(s) at which the function f(x) = 5 - 2x equals its average value on the interval [0,2], we first need to determine the average value of the function on that interval.

The average value of a function f(x) on the interval [a, b] is given by:

Avg = (1 / (b - a)) * ∫[a, b] f(x) dx

In this case, the interval is [0, 2]. So, the average value of f(x) on this interval is:

Avg = (1 / (2 - 0)) * ∫[0, 2] (5 - 2x) dx

Simplifying:

Avg = (1 / 2) * ∫[0, 2] (5 - 2x) dx

Avg = (1 / 2) * [5x - x^2] evaluated from 0 to 2

Avg = (1 / 2) * [(5 * 2 - 2^2) - (5 * 0 - 0^2)]

Avg = (1 / 2) * [10 - 4 - 0]

Avg = (1 / 2) * 6

Avg = 3

The average value of the function f(x) = 5 - 2x on the interval [0, 2] is 3.

To find the point(s) at which the function equals its average value, we set f(x) equal to the average value and solve for x:

5 - 2x = 3

Subtracting 3 from both sides:

2 - 2x = 0

Adding 2x to both sides:

2 = 2x

Dividing both sides by 2:

1 = x

Therefore, the function f(x) = 5 - 2x equals its average value at x = 1.

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Answer:

C = -D - B

Step-by-step explanation:

Step 1: Write out equation

B + C = -D

Step 2: Subtract B on both sides

C = -D - B

Answer:

a = 146

Step-by-step explanation:

0 . 1 5 + 2 8 . 1 = 5 0  

3 / 2 0 + 2 8 . 1 = 5 0

3 /2 0 = 2 1 . 9

Therefore, we conclude that 5 vectors in ℝ⁴ cannot be linearly independent.

In ℝ⁴, the dimension is 4, which means that at most we can have 4 linearly independent vectors. Therefore, it is not possible to have 5 linearly independent vectors in ℝ⁴.

To prove this, we can use the fact that the maximum number of linearly independent vectors in a vector space is equal to its dimension. In this case, the dimension of ℝ⁴ is 4.

Assume we have 5 vectors v₁, v₂, v₃, v₄, v₅ in ℝ⁴. If these vectors are linearly independent, it would imply that we have a set of 5 linearly independent vectors in a space with dimension 4, which is not possible.

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Answer:

I would think that 2x+3y+4 would be the answer.

Step-by-step explanation:

We need to  know about margin of error to solve the problem. The factors that influence margin of error are confidence level and sample size.

Margin of error is a statistic expressing the amount of random sampling error in the results of a survey. The larger the margin of error, the less confidence one should have that a poll result will reflect the result of a census of the entire population. Margin of error is influenced by three factors, confidence level, sample size and population standard deviation. In absence of population standard deviation, the margin of error is influenced by confidence level and sample size.

Therefore the margin of error is influenced by confidence level and sample size.

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Answer:

Activity 1:-

1) Pi (π) is the ratio of circumference and the diameter of the circle which is 22/7. So

\(\frac{c}{d} =\pi = \frac{22}{7}\)

\(=> c = \frac{22}{7} d\) where circumference is directly proportional to diameter (d).

2) Area of a parallelogram = Altitude × Base

Base = 10 cm. So ,

\(A = 10a\) where area (A) is directly proportional to altitude (a).

3) Let the fare of 1 unit distance be f

So, for distance d , total fare (F) will be \(F = fd\) where total fare (F) is directly proportional to distance (d).

4) Let the distance be 'D' , speed be 's' & time be 't' .

We know that \(s = \frac{D}{t}\) where speed (s) is directly proportional to distance (D) & inversely proportional to time (t).

5) We know that area of a square (A) = side² (s²)

\(=> A = s^{2}\) where area(A) is directly proportional to side(s).

Activity 2:-

1) p is directly proportional to sum of u & w.

⇒ p ∝ u + w

⇒ p = k (u + w)

Putting the values of p , u & w

⇒ 14 = k(4 + 3)

⇒ 7k = 14

⇒ k = 14/7 = 2

2) r is directly proportional to square of t.

⇒ r ∝ t²

⇒ r = k × t²

Putting the values of r & t

⇒ 16 = k × 16²

⇒ k = 16² ÷ 16 = 16

3) y is directly proportional to cube root of x.

⇒ y ∝ ∛x

⇒ y = k × ∛x

Putting the values of x & y ,

⇒ 2 = k × ∛27

⇒ 3k = 2

⇒ k = 2/3

4) z is directly proportional to cube of d.

⇒ z ∝ d³

⇒ z = k × d³

Putting the values of d & z ,

⇒ 5 = k × 2³

⇒ 8k = 5

⇒ k = 5/8

5) Total Surface Area (SA) is directly proportional to square of the sides (s).

⇒ SA ∝ s²

⇒ SA = k × s²

Putting the values of SA & s ,

⇒ 96 = k × 4²

⇒ 16k = 96

⇒ k = 96/16 = 6

Answer:

i think  -12,9 and you multiply it by x,-2

The standard error of the mean is approximately 0.79 (rounded to two decimal places).

Define standard error ?

The standard error is a statistical term that measures the variability of a sample mean or an estimate of a population parameter from its true value. It is the standard deviation of the sampling distribution of the mean. In simpler terms, the standard error measures how much the sample mean varies from the true population mean. A smaller standard error indicates that the sample mean is more likely to be representative of the population mean, while a larger standard error suggests that the sample mean may not be as reliable.

The formula for the standard error of the mean is:

\(SE = \frac{\sigma }{\sqrt{n}}\)

Where σ is the population standard deviation and n is the sample size.

Substituting the given values:

\(SE =\frac{5}{\sqrt{40}}\)

SE ≈ 0.79

Therefore, the standard error of the mean is approximately 0.79 (rounded to two decimal places).

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To construct a 4x2 matrix D such that AD=I2, we can use the following matrix: D = [0 0 1 0; 0 0 0 1]. It is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C.

Constructing a matrix D such that AD=I2

Let A = -1 be a 1x1 matrix. We want to construct a 4x2 matrix D such that their product AD is equal to the 2x2 identity matrix I2. We can use the following matrix for D:

D = [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

To verify that AD=I2, we can compute the matrix product:

AD = [-1 0 0 0; 0 -1 0 0] [0 0 1 0; 0 0 0 1; 1 0 0 0; 0 1 0 0]

= [0 0 -1 0; 0 0 0 -1]

= -I2

Note that D only uses 1 and 0 as entries.

Now, it is not possible for CA to be equal to 4 or 14 for any 4x2 matrix C. To see why, we can use the definition of matrix multiplication. Let C be a general 4x2 matrix:

C = [c11 c12; c21 c22; c31 c32; c41 c42]

Then, we can compute CA as:

CA = [-1 0; 0 -1] [c11 c12; c21 c22; c31 c32; c41 c42]

= [-c11 -c12; -c21 -c22; -c31 -c32; -c41 -c42]

Since CA is a 4x2 matrix and 4 is a scalar, it is not possible for CA to be equal to 4. Similarly, since the entries of C are only 0 or 1, it is not possible for CA to be equal to 14.

Therefore, there is no matrix C that satisfies the equations CA=4 or CA=14.

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If Naya is filling up the gas tank in her motorcycle she puts 4.145 gallons of gas in the tank if the gas cost $2.57 per gallon then she spend $10.65

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

The cost of one gallon of gas =$2.57

The quantity of gas she puts in the tank = 4.145 gallons

Apply unitary method

Then, the cost of 4.145 gallons of gas = Cost of one gallon of the gas × Quantity of gas

The cost of 4.145 gallons of gas= 2.57×4.145= $10.65

Hence, If Naya is filling up the gas tank in her motorcycle she puts 4.145 gallons of gas in the tank if the gas cost $2.57 per gallon then she spend  $10.65

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Answer:

i hope my answer is right for you

In the given triangle, the value of x is 60°.

So, the value of 'x':

Now,

Therefore, in the given triangle, the value of x is 60°.

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Answer: y=1/2x+4

Step-by-step explanation:

c rating

end by student

check rating

:)

Answer:

$5.84

Step-by-step explanation:

32/8= 4 so 4 x $0.71 = $2.84 So he paid $2.84 for the 8 ounce cans in total to be 32.

32/4=8 so 8 x 0.73 = $5.84 So he would've paid $5.84 for the 4 ounce can in total to be 32