Can you identify the domain and range of the functions y=x²-2x-3 and y=-x²+ 4x -1

Solving a system of equations we can find the exponential function, then we can evaluate it to get:

f(10.4)= 1,427.2

We know that f(x) is a exponential function, then we can write it as:

f(x) = A*b^x

First, we know that:

f(3) = 11

f(5.5) = 57

Then we can write a system of equations:

11 = A*b^3

57 = A*b^5.5

Taking the quotient between the two equations we will get:

57/11 = (A*b^5.5)/(A*b^3)

5.18 = b^(5.5 - 3)

5.18 = b^2.5

Solving for b we will get:

(5.18)^(1/2.5) = b

1.93 = b

with that, we can get the value of b.

11 = A*(1.93)^3

A = 11/(1.93)^3

A = 1.53

So the function is:

f(x)= 1.53*(1.93)^x

Then:

f(10.4) = 1.53*(1.93)^10.4 = 1,427.2

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The equation of the function g(x) is g(x) = 1/2x²

If we want to stretch or compress the function f(x) = x^2, we can multiply or divide the input variable x by a constant value a.

Specifically, if we use g(x) = f(ax), then g(x) is a stretched or compressed version of f(x).

To find the value of a that will make g(x) pass through the point (2,2), we can substitute these values into the equation g(x) = f(ax):

[tex]g(2)=f(a*2)=f(2a)=(2a)^2 =4a^2 =2[/tex]

So, we have

a = 1/2

Recall that

g(x) = f(ax)

So, we have

g(x) = f(1/2x)

This means that

g(x) = 1/2x²

Hence. the function is g(x) = 1/2x²

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Answer:

Step-by-step explanation:

I think its 42 because 7/20ths of 120 is 42

7/20 x 120 =42

A timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.

What is the unit conversion?

Unit conversion is the process of converting a quantity expressed in one unit of measurement to another unit of measurement that is equivalent in value. The need for unit conversion arises because different units are used to measure the same physical quantity in different countries or regions, or in different fields of study.

Making a model of the geologic time scale with a scale of 1 centimeter equals 1 million years means that each centimeter on the timeline represents 1 million years of geologic time.

To create the model, we can start by determining the total length of the timeline we want to create.

Let's say we want to include the entire Phanerozoic Eon, which spans approximately 541 million years.
To represent this on our timeline, we would need a total length of 541 centimeters.

However, we need to keep in mind that 100 cm is equal to 1 meter, which is a little longer than 3 feet.

Therefore, a timeline that spans 541 centimeters would be equivalent to a length of 5.41 meters or approximately 17.75 feet.

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a. It will take 7 months to pay off the credit card. b. it will take 4 months to pay off the credit card.

APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.

a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance. We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:

PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)

where:

PV is the present value of the debt

PMT is the payment amount per period

r is the monthly interest rate

n is the number of periods

Substituting the values, we get:

754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV ×r / PMT)) / log(1 + r)

= log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)

= 6.18

Therefore, it will take approximately 7 months to pay off the credit card if you put half of the available money each month toward the credit card.

b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.

754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)

Simplifying and solving for n, we get:

n = log(1 + (PV × r / PMT)) / log(1 + r)

= log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)

= 3.43

Therefore, it will take approximately 4 months to pay off the credit card if you put all of the available money each month toward the credit card.

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We cannot determine the value of d for the difference between the two group means.

In statistics, in addition to the mode and median, the mean is one of the measures of central tendency. Simply put, the mean is the average of the values in the given set.

To calculate the effect size d for the difference between the Intervention and Control group means, we can use the following formula:

d = (M₁ - M₂) / SDpooled

where M₁ is the mean for the Intervention group, M₂ is the mean for the Control group, and SDpooled is the pooled standard deviation.

Since we do not have the standard deviations for the two groups, we cannot calculate SDpooled. However, we can estimate d using the difference between the means and the assumption that the standard deviation for each group is equal. This is known as the pooled variance estimate.

To calculate d using the pooled variance estimate, we can use the following formula:

d = (M₁ - M₂) / Spooled

where Spooled is the pooled standard deviation estimate, which is calculated as follows:

Spooled = sqrt[((n₁-1) * S₁² + (n₂-1) * S₂²) / (n₁ + n₂ - 2)]

where n₁ and n₂ are the sample sizes for the Intervention and Control groups, respectively, and S₁ and S₂ are the sample standard deviations for the two groups.

Since we do not have the sample sizes or standard deviations for the two groups, we cannot calculate Spooled or d using the pooled variance estimate. Therefore, we cannot determine the value of d for the difference between the two group means.

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Answer: 46 ft by 92 ft

Step-by-step explanation:

The largest area is enclosed when half the fence is used parallel to the wall and the other half is used for the two ends of the fenced area perpendicular to the wall. Half the fence is 184 ft/2 = 92 ft. Half that is used for each end of the enclosure.

Answer:

90 cubic feet

Step-by-step explanation:

3 feet × 5 feet × 6 feet = 90 cubic feet

The equation which shows how many cases c you can buy is $250 = $15.50 * c.

An equation is a mathematical statement that shows the equality between two expressions. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation represents a relationship between quantities, and it is often used to describe or model real-world situations or problems.

According to the given information:

Let's denote the number of cases of assorted candy snacks as "c". The price of one case of assorted candy snacks is $15.50. The goal is to sell $250 worth of candy per week.

The total cost of buying "c" cases of assorted candy snacks can be calculated by multiplying the price per case ($15.50) by the number of cases (c):

Total Cost = Price per case * Number of cases = $15.50 * c

The goal is to sell $250 worth of candy per week. So, we can set up an equation to represent this goal:

$250 = $15.50 * c

This equation shows the relationship between the number of cases of candy snacks (c) that you can buy and the total cost of buying those cases, which is equal to $250, your goal for weekly candy sales.

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Answer: 76 pages

Step-by-step explanation:

700 photo spaces = 100%

-The total

168 photo spaces = 24%

-The number of empty spaces in the album.

- Find 24% of 700:

70(10%) x 2 = 140

7(1%) x 4 = 28

140 + 28 = 168

532 photo spaces = 76%

- The number of photos in the album

700 - 168 = 532

Finding the number of pages.

-As we know 1 page holds 7 photos, if we had 532 photos we'd have to divide it by 7 to see how many pages all the photos would be held in.

532 ÷ 7 = 76.

The side lengths will all make up a triangle, each can be classified as:

6. Isosceles triangle 7. Obtuse triangle 8. Scalene triangle

To determine whether the given numbers can represent the side lengths of a triangle or not, we need to check if the sum of the two smaller sides is greater than the largest side.

If this condition is satisfied for all three pairs of sides, then the numbers can represent the side lengths of a triangle.

6. The numbers 4, 5, and 5 can represent the side lengths of a triangle because 4 + 5 > 5, 5 + 4 > 5, and 5 + 4 > 5. This triangle is isosceles because two sides have the same length.

7. The numbers 10, 17, and 26 can represent the side lengths of a triangle because 10 + 17 > 26, 17 + 26 > 10, and 26 + 10 > 17. This triangle is obtuse because the square of the longest side (26^2 = 676) is greater than the sum of the squares of the other two sides (10^2 + 17^2 = 369).

8. The numbers 2, 10, and 12 can represent the side lengths of a triangle because 2 + 10 > 12, 10 + 12 > 2, and 12 + 2 > 10. This triangle is scalene because all three sides have different lengths.

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Since each curve is a transformation of the graph of the parent function y = √x, an equation for each curve are as follows;

A. y = √(-x + 2)

B. y = -√(x - 1) + 3

C. y = √(x - 3)

D. y = √x - 2

E. y = -√(x + 2)

In Mathematics and Geometry, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.

In Mathematics and Geometry, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (downward) is modeled by this mathematical equation g(x) = f(x) - N.

Where:

In order to write an equation that models curve A, we would have to apply a reflection and horizontal translation to y = √x by 2 units left.

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The answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

(a) What is the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years?

To answer this question, we need to standardize the values of 18 and 20 using the mean and standard deviation provided. Let X be the age at which growth plates fuse for males. Then,

Z = (X - mean) / standard deviation

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Z for X = 20 is (20 - 18.8) / (15.1/12) = 0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -0.53 and 0.53, which is approximately 0.351.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 18 and 20 years is 0.351.

(b) What is the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years?

We need to standardize the values of 16 and 18 using the mean and standard deviation provided.

Z for X = 16 is (16 - 18.8) / (15.1/12) = -2.03

Z for X = 18 is (18 - 18.8) / (15.1/12) = -0.53

Using a standard normal distribution table or a calculator, we can find the probability of Z being between -2.03 and -0.53, which is approximately 0.317.

Therefore, the probability that a randomly selected male has growth plates that fuse between the ages of 16 and 18 years is 0.317.

(c) What is the age at which growth plates fuse for the top 5% of males?

We need to find the age X such that the probability of a male having growth plates fuse at an age less than X is 0.95 (since 5% is the complement of 95%).

Using a standard normal distribution table or a calculator, we can find the Z-score corresponding to the 95th percentile, which is approximately 1.645.

Then, we can solve for X using the formula:

Z = (X - mean) / standard deviation

1.645 = (X - 18.8) / (15.1/12)

Simplifying the equation, we get:

X = 18.8 + (1.645)(15.1/12) = 20.24

Therefore, the age at which growth plates fuse for the top 5% of males is approximately 20.24 years.

(d) What percentage of males have growth plates that fuse before the age of 16?

We need to find the probability of a male having growth plates fuse before the age of 16, which is equivalent to finding the probability of Z being less than -2.03 (calculated in part (b)).

Using a standard normal distribution table or a calculator, we can find the probability of Z being less than -2.03, which is approximately 0.0228.

Therefore, approximately 2.28% of males have growth plates that fuse before the age of 16.

hence, the answers to each question are:

(a)  0.351.

(b)  0.317.

(c)  20.24 years.

(d)  16.

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The value or measure of following are :-

x = 17.18°

∠JK = 143.78°

∠MJ = 116.48°

∠LMK = 47.17°

A segment of a circle called an arc is made up of two endpoints on the circle and the curve that connects them.

Since the two lines JL and MK intersect at the center of the circle at point N, the angles formed by them are inscribed angles of the circle. Moreover, the angles formed by an inscribed angle and its corresponding arc are equal. Therefore, we can write:

∠JNK = ½ arc JNK = ½(5x+23)° = 2.5x + 11.5°

∠KNL = ½ arc KNL = ½(17x-41)° = 8.5x - 20.5°

We are also given that arc MNJ and LNK are similar, so their corresponding angles are equal. Similarly, arc MNL and JNK are similar, so their corresponding angles are equal. Let's use these facts to find x:

∠MNJ = ∠LNK

The arc MNJ is equal to the sum of arcs MNL and LNK. Therefore, we have:

½(5x+23)° + ½(17x-41)° = ∠MNJ + ∠LNK

2.5x + 11.5° + 8.5x - 20.5° = 2∠MNJ

11x - 9° = 2∠MNJ

∠MNL = ∠JNK

The arc MNL is equal to the sum of arcs MNJ and JNK. Therefore, we have:

½(5x+23)° + ½(8.5x-20.5°) = ∠MNL + ∠JNK

2.75x + 1.5° = 2∠JNK

1.375x + 0.75° = ∠JNK

Since ∠MNJ = ∠LNK and ∠MNL = ∠JNK, we can write:

2∠MNJ + 2∠JNK = 360°

Substituting the expressions we found for ∠MNJ and ∠JNK, we get:

22x - 18° = 360°

22x = 378°

x = 17.18° (rounded to two decimal places)

Now that we know x, we can find the values of the other angles of arc-

∠JNK = 1.375x + 0.75° = 24.43°

∠KNL = 8.5x - 20.5° = 119.35°

∠MNJ = (11x - 9°)/2 = 92.05°

∠LNK = ∠MNJ = 92.05°

∠MNL = 360° - ∠MNJ - ∠JNK = 243.52°

∠JK = ∠JNK + ∠KNL = 143.78°

∠MJ = ∠MNJ + ∠JNK = 116.48°

∠LMK = 360° - ∠MNJ - ∠JNK - ∠KNL = 47.17°

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Answer:

5x (x + 7)

Step-by-step explanation:

5x² + 35x

First, we find the GCF! In this case, the GCF is 5x

Factor out 5x

5x (x + 7)

So, the answer is 5x (x + 7)

Answer:

y = 163 since vertical angles are congruent.

   40°

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

Given a quadrilateral with four angles of:

We know the sum of interior angles for quadrilateral, it is 360°. Let us set up an equation as follows:

Solve it for k:

So the missing angle is 40°.

Answer:

Answer to your question ; f(t) = 55 = 4t

Answer: The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91. Brainliest?

Step-by-step explanation:

To round 87.71 to the nearest whole number, we look at the digit in the ones place, which is 1. Since 1 is less than 5, we round down to 87. To round 5.8 to the nearest whole number, we look at the digit in the ones place, which is 8. Since 8 is greater than or equal to 5, we round up to 6.

Using these rounded values, Yasmine estimated the difference between the numbers to be 87 - 6 = 81.

The actual difference between the numbers is:

87.71 - 5.8 = 81.91

Therefore, Yasmine's estimate was 81, and the actual difference between the numbers is 81.91.

Answer:

Yasmine estimated the difference to be 82. The actual difference is 81.91.

Step-by-step explanation:

The rounded whole number of 87.71 is 88 and the rounded whole number of 5.8 is 6.

So, the difference between the numbers 87.71 and 5.8 by rounding each number to the nearest whole numbers will be

(88 - 6) = 82.

The actual difference between the numbers 87.71 and 5.8 is (87.71 - 5.8) = 81.91.

Therefore, Yasmine estimated the difference to be 82. The actual difference is 81.91.

$14,000 was invested at 5% and $49,500 was invested at 9%.

what is system of equations?

A system of equations is a collection of two or more equations that are to be solved simultaneously. In other words, it is a set of equations that must be satisfied by a common set of variables. These equations can be linear or nonlinear, and they can have one or more variables.

The goal of solving a system of equations is to find the values of the variables that satisfy all the equations in the system. This can be done by using various methods, such as substitution, elimination, or matrix methods. The number of equations in a system can be greater than or equal to the number of variables in the system.

Systems of equations are used in various fields such as engineering, physics, economics, and many more. They are also an essential part of algebra and mathematics education, as they provide a powerful tool for solving real-world problems that involve multiple variables and relationships.

Let's assume that x is the amount invested at 5% and y is the amount invested at 9%. We can write two equations based on the given information:

x + y = 63,500 (the total amount invested)

0.05x + 0.09y = 5155 (the total annual income)

We can use these equations to solve for x and y.

First, we can rearrange equation 1 to solve for one of the variables in terms of the other:

x = 63,500 - y

Then, we can substitute this expression for x into equation 2:

0.05(63,500 - y) + 0.09y = 5155

Simplifying this equation:

3175 - 0.05y + 0.09y = 5155

0.04y = 1980

y = 49,500

So we now know that $49,500 was invested at 9%. We can substitute this value into equation 1 to solve for x:

x + 49,500 = 63,500

x = 14,000

Therefore, $14,000 was invested at 5% and $49,500 was invested at 9%.

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The data set with the greater range is greater for girls. The median is greater for girls.

What is the range of a dataset?

The range of a dataset is the difference between the maximum and minimum values in the set. The median is the middle value in a sorted dataset, or the average of the two middle values if the set has an even number of elements.

To determine which dataset has a greater range, you need to compare the difference between the highest and lowest values of the two datasets.

To determine which dataset has a larger median, you need to sort the datasets and find the middle value(s).

The range for boys is 60 as for girls the range is 80. The median for boys is 90 and for girl 110.

Hence, The data set with the greater range is greater for girls. The median is greater for girls.

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Complete question:

A survey asked 10 boys and 10 girls how many text messages they sent the previous day. The number of texts is given in the line plots.

Select from the drop-down menus to complete each statement.

The data set with the greater range is __________The median________

Boys Greater for Boys

Girls Greater for Girls

Neither Same

The number line is in the attached image.

Answer: slope = -10/3

Step-by-step explanation:

Answer:

slope = - [tex]\frac{10}{3}[/tex]

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (5, - 5 ) and (x₂, y₂ ) = (2, 5 )

m = [tex]\frac{5-(-5)}{2-5}[/tex] = [tex]\frac{5+5}{-3}[/tex] = [tex]\frac{10}{-3}[/tex] = - [tex]\frac{10}{3}[/tex]

to find the mean you add al the numbers together and divide it by how many numbers there were. so to find the mean it would be (682+612+756+674+714+790+668+652+776)÷9=702.6 which can be rounded up to 703. Also pls mark as brainliest answer

Answer:

One possible rational function that satisfies the given properties is:

r(x) = (x-2)(x-6) / [(x-3)(x-5)]

Step-by-step explanation:

x-intercepts at (2,0) and (6,0)

The x-intercepts are the points where the function crosses the x-axis, i.e., where the function value is zero. Since we are given that the function has x-intercepts at (2,0) and (6,0), we know that the function can be factored as:

r(x) = A(x-2)(x-6)

where A is a constant that we need to determine.

A hole at x=1 and vertical asymptotes at x=5 and x=3

A hole in a rational function occurs when there are factors in the numerator and denominator that cancel out, leaving a "hole" in the graph. In this case, we are given that there is a hole at x=1, which means that there must be a common factor of (x-1) in both the numerator and denominator. So, we can write:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))

where B is another constant that we need to determine.

We are also given that there are vertical asymptotes at x=5 and x=3, which means that the denominator must have factors of (x-5) and (x-3) that do not cancel out with any factors in the numerator. So, we can write:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5)) = [A(x-2)(x-6)] / [(B(x-1))(x-3)(x-5)]

End behavior given by x → ∞ ,f(x) → 1 and x → -∞ ,f(x) → 1

The end behavior of a rational function is determined by the degree of the numerator and denominator. Since the numerator and denominator in this case have the same degree (3), we know that the end behavior is given by the ratio of the leading coefficients, which is A/B. We are told that the end behavior approaches 1 as x approaches infinity or negative infinity, so we can set A/B = 1 and solve for A in terms of B:

A/B = 1, so A = B

Putting it all together

We now have enough information to write the equation for the rational function with the given properties:

r(x) = A(x-2)(x-6) / (B(x-1)(x-3)(x-5))

Using A = B, we get:

r(x) = A(x-2)(x-6) / [A(x-1)(x-3)(x-5)]

Canceling out the common factor of (x-1) in the numerator and denominator, we get:

r(x) = (x-2)(x-6) / [(x-3)(x-5)]

which is the equation for the desired rational function.

A 90% confidence interval for µ is (8.92, 9.28).

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.

The formula for a confidence interval for the population mean is:

CI = x ± z * (σ / sqrt(n))

where x is the sample mean, σ is the population standard deviation, n is the sample size, z is the z-score associated with the desired confidence level, and CI is the confidence interval.

Given the values provided:

c = 0.90

x = 9.1

σ = 0.6

n = 45

First, we need to find the z-score associated with a 90% confidence level. We can use a standard normal distribution table or a calculator to find that z = 1.645.

Then, we can plug in the values and calculate the confidence interval:

CI = 9.1 ± 1.645 * (0.6 / sqrt(45))

= 9.1 ± 0.176

= (8.92, 9.28)

Therefore, a 90% confidence interval for µ is (8.92, 9.28).

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Answer:

2,139 seats

Step-by-step explanation:

the seats increase by 3 every row so I'm going to make a chart to show you how much the seats increase to 31 rows then add all off them to find total.

1 : 24

2: 27

3 : 30

4 : 33

5 : 36

6 : 39

7 : 42

8 : 45

9 : 48

10 : 51

11 : 54

12 : 57

13 : 60

14 : 63

15 : 66

16 : 69

17 : 72

18 : 75

19 : 78

20 : 81

21 : 84

22 : 87

23 : 90

24 : 93

25 : 96

26 : 99

27 : 102

28 : 105

29 : 108

30 : 111

31: 114

You can see from the chart that the number of seats increases by 3 for each row, starting from 24 seats in the first row and ending with 114 seats in the 31st row. To find the total number of seats, you can add up all the numbers in the chart:

24 + 27 + 30 + 33 + ... + 111 + 114

This is an arithmetic series with a first term of 24, a common difference of 3, and 31 terms. You can use the formula for the sum of an arithmetic series to find the total:

Sum = n/2 * (a + l)

where n is the number of terms, a is the first term, and l is the last term.

n = 31, a = 24, and l = 114, so you can substitute these values into the formula and simplify:

Sum = 31/2 * (24 + 114)

Sum = 15.5 * 138

Sum = 2139

Therefore, the theater has a total of 2,139 seats, which agrees with the result obtained earlier.

Answer:

2139 seats

Step-by-step explanation:

24,27,30,.......

n = 31

This forms an arithmetic series. Sum of arithmetic series will give the number of seats in the theater.

 a = first term = 24

d = difference = second term - first term

  = 27 - 24

  = 3

         [tex]\sf \boxed{S_n=\dfrac{n}{2}[2a+(n-1)*d]}[/tex]

                 [tex]=\dfrac{31}{2}[2*24+30*3]\\\\=\dfrac{31}{2}[48+90]\\\\=\dfrac{31}{2}*138\\\\=31*69\\\\=2139[/tex]

For the given graph:

A. f(x) > 0 at x = x₁, x₂, x₃, x₄ and x₅

B. f'(x) > 0 at x = x₃, x₄

C. f(x) is increasing at x = x₃, x₄

D. f'(x) is increasing at x = x₁, x₂,

E. The slope of f(x) is negative at x = x₁, x₂ and x₅

F. The slope of f'(x) is negative at x = x₃, x₄ and x₅

The steepness of the hill is called slope. The same applies to the steepness of the line. Slope is defined as the ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two points.

The slope of a straight line is usually expressed in m.

m = (y₂ - y₁)/(x₂ - x₁)

It's important to keep the x and y coordinates in the same order in both the numerator and denominator. Otherwise you will get the wrong gradient.

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The probability that a person has the virus given that they have tested positive is 3.24%.

The probability that a person does not have the virus given that they test negative is 99.93%.

Here we have following probabilties:

P(A)=1/300, P(A')=1-(1/300)=299/300

P(B|A)=0.80, P(B|A')= 0.08

From the law of total probability is

P(B)=P(B|A)P(A)+P(B|A')P(A')

[tex]=0.80\cdot \frac{1}{300}+0.08\cdot \frac{299}{300}\\\\=0.0824[/tex]

By the Baye's theorem we have

P(A|B) = [tex]\frac{P(B|A)P(A)}{P(B)}\\\\=\frac{0.80\cdot \frac{1}{300}}{0.0824}\\\\=0.0324[/tex]

So the probability that a person has the virus given that they have tested positive is 3.24%.

(b)

From the law of total probability is

P(B')=P(B'|A)P(A)+P(B'|A')P(A')

[tex]=0.20\cdot \frac{1}{300}+0.92\cdot \frac{299}{300}\\\\=0.9176[/tex]

By the Baye's theorem we have

P(A'|B')=[tex]\frac{P(B'|A')P(A')}{P(B')}\\\\=\frac{0.92\cdot \frac{299}{300}}{0.9176}\\\\=0.9993[/tex]

So the probability that a person does not have the virus given that they test negative is 99.93%.

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Sam's longest run before starting training was 0.6 miles.

A scatter diagram is used to investigate the relationship between both axes (X and Y) and a single variable. If the variables on the graph are correlated, the point will decrease down a curve or line. A scatter diagram or scatter plot depicts the nature of a relationship.

A linear model is represented by the equation y = 0.2x + 0.6, where "y" is the longest distance Sam ran after "x" weeks of training. The y-intercept in this model is 0.6, which reflects the longest distance Sam could run before starting training.

As a result, the solution is:

Sam's longest run before starting training was 0.6 miles.

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The probability of drawing a marble that is green or even-numbered is  28/35

The total number of marbles in the jar is 35, of which 10 are blue, 12 are green, and 13 are red.

We need to find the probability of drawing a marble that is green or an even number.

First, let's find the number of even-numbered marbles.

Out of 35 marbles, 17 of them are even-numbered (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34).

There are 12 green marbles, and 17 even-numbered marbles,

Therefore, there are 12 + 17 - 1 = 28 marbles that are either green or even-numbered.

The probability of drawing a marble that is green or even-numbered is

28/35

So the probability of drawing a marble that is green or even-numbered is  28/35

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