In a large population, 3% of the people are heroin users. A new drug test correctly identifies users 93% of the time and correctly identifies nonusers 90% of the time. Answer the following, showing all work for full credit. a) Draw the probability tree for this scenario. Label the outcomes and indicate all the probabilities on the tree. b) What is the probability that a person who does not use heroin in this population tests positive

The matching of items and their corresponding descriptions are 1. Domain, 2.Output, 3. Input, 4. Relation, 5. Function, and 6. Range.

1. Domain - the first element of a relation or function; also known as the input value.

3. Input - the x-value of a function.

6. Range - the second element of a relation or function; also known as the output value.

4. Relation - any set of ordered pairs (x, y) that are able to be graphed on a coordinate plane.

2. Output - a relation in which every input value has exactly one output value.

5. Function - the y-value of a function.

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Answer:

x = -11

Step-by-step explanation:

I can't really explain, but I know those red dashes means that the lines that is dashed are the same length, which means that "x + 81 equals to 70. We can also write it as "x + 81" + 70 + m = 180.

70 = 81 + x

70 - 81 = x

-11 = x

The length of the side of the square in simplest form is 2sqrt(14).

The area of a square is given by the formula \(A = s^2\), where A is the area and s is the length of a side.

We are given that the area of the square is 56 units, so we can set up the equation:

\(56 = s^2\)

To solve for s, we can take the square root of both sides of the equation:

sqrt(56) = \(sqrt(s^2)\)

We can simplify the square root of 56 by factoring it:

sqrt(56) = sqrt(222*7) = 2sqrt(14)

So, we have:

2sqrt(14) = s

This is an improper fraction because the numerator is larger than the denominator. Therefore, the length of the side of the square in simplest form is 2sqrt(14).

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Step-by-step explanation:

Let's denote the height of the tower as "h" feet.

According to the given information, the length of the pole's shadow is 3.25 ft, and the total length of the tower's shadow (including the shadow of the pole) is 190 ft.

We can set up a proportion using the similar triangles formed by the tower, its shadow, the pole, and its shadow:

height of the tower / length of the tower's shadow = height of the pole / length of the pole's shadow

h / 190 = 10 / 3.25

Cross-multiplying:

h * 3.25 = 10 * 190

h * 3.25 = 1900

Dividing both sides by 3.25:

h = 1900 / 3.25

h ≈ 584.62

Rounding to the nearest foot, the height of the tower is approximately 585 feet.

Answer:

as a mixed number: 13 7/11  as a percentage 1363.64%

Step-by-step explanation:

Answer: She ran about 4.88 km answer B

Step-by-step explanation:

Answer:

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

Step-by-step explanation:

The graph could be the graph of exponential function of option b)

\(F(x) = 2 • (0.5)^{x} \)

The general form of an exponential function is

\(f(x) = {ab}^{x} \)

Here, a is the function's starting value and b is its growth factor.

F(x) is an increasing function if b > 1, and if b<1, then f(x) is a decreasing function

The function's initial value is 2 as can be seen from the provided graph. Therefore, a has a value of 2.

Given that the graph indicates that the function is decreasing, b must be less than 1.

It indicates that the necessary function is in the form of

\(f(x) = 2(b)^{x} \)

Where it is b<1

By checking option B, b=0.5<1. Hence, option B is the correct answer

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Note that the full question is:

(check the attached image)

The point which could represent the player catching the ball is: C. (4, 25).

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect, meet, or cross each other, which is typically represented as an ordered pair containing the point, x-axis and y-axis.

By critically observing the graph (see attachment) which models the given data, we can reasonably infer and logically deduce that the point (4, 45) where the "Distance from Goal" on the y-axis intersect with the "Time after Throw" on the x-axis represents the player catching the ball.

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Answer: 4, 25

Step-by-step explanation:

(a) The variables y and x are not directly proportional. (b) The constant of proportionality is 2/5.

The constant of proportionality is a value that relates two variables that are directly proportional to each other. Direct proportionality means that as one variable increases, the other variable also increases by a constant factor, and vice versa. The constant of proportionality is the factor by which the two variables are related.

For example, suppose we have a direct proportionality between the weight of an object and its mass. As the weight of the object increases, its mass also increases proportionally. The constant of proportionality in this case is the conversion factor between weight and mass, which is the gravitational acceleration constant, denoted by "g" and has a value of approximately 9.8 m/s² on Earth.

(a) The equation y = 2x - 5 does not show direct variation because the variables y and x are not directly proportional. There is a constant term of -5 which makes the equation non-linear.

(b) The equation 2/5x = y shows direct variation because the variables x and y are directly proportional. The constant of proportionality is 2/5, which can be found by solving for y: y = 2/5x.

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Answer:

Option 2

Step-by-step explanation:

it easy Add them all up and then you get 47/16 then divide them and convert it to mixed number and then you get 2 15/16

Answer:

2 15/16

Step-by-step explanation:

We need to make sure all fractions have the same denominator.

The LCM (least common denominator) is 16.

Now we have to multiply each nunber except 2 1/16 to get a numerator of 16.

1/2: 1x8= 8, 2x8= 16→ 8/16

3/8: 3x2= 6, 8x2= 16→ 6/16

Now every add everything all up.

8/16 + 6/16 + 2 1/16 = 2 15/16

2 15/16 is our answer.

The volume of the first and second solid shapes are 3014.4m³ and 360ft³ respectively.

The first shape comprises of a cone and a cylinder, and the volume is derived as follows:

volume of the cone = 1/3 × 3.14 × (8m)² × 5m

volume of the cone = 1004.8m³

volume of the cylinder = 3.14 × (8m)² × 0m

volume of the cylinder = 2009.6 m³

volume of the first solid shape = 1004.8m³ + 2009.6 m³

volume of the first solid shape = 3014.4m³

The second solid shape comprises of a trianglular prism and a cuboid

volume of the trianglular prism = base area × height

base area = 1/2 × 6ft × 4ft = 12ft²

volume of the trianglular prism = 12ft² × 6ft

volume of the trianglular prism = 72ft³

volume of the cuboid = 12ft × 6ft × 4ft

volume of the cuboid = 288ft³

volume of the second solid shape = 72ft³ + 288ft³

volume of the second solid shape = 360ft³

Therefore, the volume of the first and second solid shapes are 3014.4m³ and 360ft³ respectively.

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Answer:

Winning odd = 3.4

Loosing odd = 4.3.

Step-by-step explanation:

So, from this particular Question or problem we have the following data or information or parameters which is going to aid or help us in solving this particular Question;

=> Given 6 of hearts and the 8 of diamonds.

We know that there are 8 types of cards.

Also, we know that the total number of the cards is equal to fifty-two(52).

From cards of six(6) to ten(10) a bust will surely occur.

Therefore, 8 × 4 / 52= 32/52 = 0.62.

If an ace is pulled, then the chance of winning bis surely 4 out of 52 deck of cards.

Giving you a Winning odd = 3.4 and a

Loosing odd = 4.3.

The value of f(5) is e^5 + 5/3, which is exactly 150.0798257693, and the value of f(11) is e^11 + 11/3, which is approximately 59877.808.

The function is f(x)= e^x + 1/3x

To find the value of f(5), put the value of x = 5 in the function f(x)= e^x + 1/3x. Which is equal to f(5) = e^5 + 5/3.

Similarly, to find the value of f(11), put the value of x = 11 in the function f(x)= e^x + 1/3x.

Which is equal to f(11) = e^11 + 11/3

f(11) = 59874.141715198 + 3.6666666667

f(11) = 59877.808381865

f(11) ≈ 59877.808

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Answer:

Step-by-step explanation:

The circumference of a circle is given by the formula:

C = πd

where d is the diameter of the circle. In this case, the diameter is given as 14 cm, so we can substitute that into the formula:

C = π(14 cm)

Multiplying, we get:

C = 14π cm

So the circumference of the circle is 14π cm. The units are centimeters, since circumference is a length measurement.

Answer:

m<1 = 146

m<2 = 17

m<3 = 17

m<4 = 146

m<5 = 17

Step-by-step explanation:

I dont know, just a guess

The function can be defined as  price = 6x

It will cost $150 to buy 25 reams of paper.

The domain of the function is all non-negative real numbers, since the number of reams bought cannot be negative.

The range of the function is all non-negative real numbers, since the price cannot be negative.

Fir 25 items, price = 6(25) = $150

It will cost $150 to buy 25 reams of paper.

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1)Gross Yearly Income = Hourly Wage × Hours per Week × Weeks in a Year

Gross Yearly Income = $15/hour × 40 hours/week × 52 weeks/year

Gross Yearly Income = $31,200

2)Gross Monthly Income = Gross Yearly Income / Months in a Year

Gross Monthly Income = $31,200 / 12 months

Gross Monthly Income ≈ $2,600

Answer:

First question: LCL = 522, UCL = 1000.5

Second question: A sample size no smaller than 418 is needed.

Step-by-step explanation:

First question:

Lower bound:

0.36 of 1450. So

0.36*1450 = 522

Upper bound:

0.69 of 1450. So

0.69*1450 = 1000.5

LCL = 522, UCL = 1000.5

Second question:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

The margin of error is:

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The project manager believes that p will turn out to be approximately 0.11.

This means that \(\pi = 0.11\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The project manager wants to estimate the proportion to within 0.03

This means that the sample size needed is given by n, and n is found when M = 0.03. So

\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)

\(0.03 = 1.96\sqrt{\frac{0.11*0.89}{n}}\)

\(0.03\sqrt{n} = 1.96\sqrt{0.11*0.89}\)

\(\sqrt{n} = \frac{1.96\sqrt{0.11*0.89}}{0.03}\)

\((\sqrt{n})^2 = (\frac{1.96\sqrt{0.11*0.89}}{0.03})^2\)

\(n = 417.9\)

Rounding up

A sample size no smaller than 418 is needed.

The mean for the data items in the given frequency distribution is 4.152

To find the mean of the data items in the frequency distribution, we need to use the formula:

Mean = (Sum of (xi * fi)) / (Sum of fi)

where xi is the midpoint of the class interval and fi is the corresponding frequency.

So, we have

Mean = (3 + 12 + 15 + 20 + 20 + 30 + 21 + 16)/(3 + 6 + 5 + 5 + 4 + 5 + 3 + 2)

Evaluate

Mean = 4.152

Hence, the mean is 4.152

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a. The upper bound for the probability that a student's test score will exceed 85 is 0.8413.

b. The probability that a student will score between 65 and 85 is 0.6826.

c. To guarantee with a chance of at least 0.9 that the class average would fall within 5 of 75, at least 30 students would need to take the test.

a. The upper bound for the probability that a student's test score will exceed 85 is 1, since it is impossible for a score to exceed 100.

b. The probability that a student will score between 65 and 85 is equal to the area under the normal curve between 65 and 85 divided by the total area under the normal curve (which is equal to 1). This can be calculated using the cumulative distribution function for a normal distribution with mean 75 and variance 25.

c. To ensure with probability at least 0.9 that the class average would be within 5 of 75, at least 25 students would have to take the examination. This can be calculated by dividing the total area under the normal curve between 70 and 80 (representing the desired range of scores) by the total area under the normal curve (which is equal to 1).

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The first shape does NOT have a Hamilton circuit

The second shape has a Hamilton circuit

The third shape does NOT have a Hamilton circuit

In mathematical graph theory, a Hamiltonian circuit- named after its originator William Rowan Hamilton, an acclaimed Irish mathematician of the 19th century– is a path within a graph that covers every vertex only once and begins and ends at the same vertex.

To put it differently, it's an enclosed movement that goes through each point in the graph exactly once. When the graph consists of a Hamiltonian circuit, this indicates to be a Hamiltonian graph. One can see many practical uses of Hamiltonian circuits such as computer science where they play a crucial role in algorithm analysis and design.

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Answer:

(x) ∠CAB

Step-by-step explanation:

In ΔCOD and ΔBOA

\(\frac{OA}{OB} = \frac{OD}{OC} \\\\\implies \frac{OC}{OB} = \frac{OD}{OA}\)

Also,

∠COD = ∠BOA (vertically opposite angles)

⇒ ΔCOD and ΔBOA are similar

⇒ ∠CDO = ∠BAO

⇒ ∠CDB = ∠BAC

⇒ ∠CDB = ∠CAB

Answer:

Step-by-step explanation:

9x-3y=-10 ...............(1)

3x-4y=1...............(2)

multiplying equation (2) by 3

9x-12y=3...................(3)

Using elimination method, then

9x-3y=-10 ...............(1)

9x-12y=3...................(3

9y= -13

y= -13/9

substituting y= -13/9 in equation (1) then

9x-3(-13/9)= -10

9x+13/3= -10

multiplying throughout by 3

27x+13= -30

27x= -30-13

27x= -43

x= -43/27

since x and y values are known, then

12x-7y = 12(-43/27) - 7(-13/9)

12x-7y = -516/27 + 91/9

12x-7y = -9

Answer: Marcus rents a car for 3 days.

Answer: d. Marcus rents a car for 5 days.

Step-by-step explanation:

If D = the number of days then C=25(5)+15=140(plan b)

C=30(5)=150 (plan a)

Plan b is better because plan b cost less than plan a for 5 days.

on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

equation given is 3(x+2)=7x-48

value of x

\(3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\\)

value of x from the given equation comes out to be 13.5

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The 99% confidence interval for the true population mean backpack weight is approximately (68.15, 71.85) ounces, rounded to two decimal places.

To construct a 99% confidence interval for the true population mean backpack weight, we can use the formula:Confidence Interval = Sample Mean ± (Critical Value * Standard Deviation / √Sample Size).

Since the population standard deviation is known, we can use the z-distribution and find the critical value corresponding to a 99% confidence level. The critical value for a 99% confidence level is approximately 2.576.

Given that the sample mean weight is 70 ounces, the population standard deviation is 6.4 ounces, and the sample size is 48, we can calculate the confidence interval:

Confidence Interval = 70 ± (2.576 * 6.4 / √48).

Simplifying the expression, we get:

Confidence Interval ≈ 70 ± 1.855.

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Answer:$3.25

Step-by-step explanation:

Answer:

£6.30

Step-by-step explanation:

To find out how much money she has spent, you will times the cost for each pound with how many pound of grapes there are:

£1.48 x 2.5 = £3.70

So in total you spent £3.70

To find out the remaining amount, take away how much you have paid with how much money there was originally in the gift card.

£10.00 - £3.70 = £6.30

Answer:

13-12 = 1

1/12 = 0.08333... = 8 1/3%

Step-by-step explanation:

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