To reduce laboratory​ costs, water samples from two public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past​ results, there is a 0.009 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from twotwo public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?

The probability of a positive test result is _____.

Is the probability low enough so that further testing of the individual samples is rarely​ necessary?
A. The probability is quite​ low, indicating that further testing is necessary for all of the combined samples.
B. The probability is quite​ low, indicating that further testing is not necessary for any of the combined samples.
C. The probability is quite​ low, indicating that further testing of the individual samples will be a rarely necessary event.
D. The probability is quite​ low, indicating that further testing of the individual samples will not be a rarely necessary event.

Answers

Answer 1
i believe the answer is either b or c

Answer 2

Answer:

The probability of a positive test result is 0.017919

Option C is correct.

The probability is quite​ low, indicating that further testing of the individual samples will be a rarely necessary event.

Step-by-step explanation:

Probability of finding bacteria in one public swimming pool = 0.009

We now require the probability of finding bacteria in the combined test of two swimming pools. This probability is a sum of probabilities.

Let the two public swimming pools be A and B respectively.

- It is possible for public swimming pool A to have bacteria and public swimming pool B not to have bacteria. We would obtain a positive result from testing a mixed sample of both public swimming pools.

- It is also possible for public swimming pool A to not have bacteria and public swimming pool B to have bacteria. We would also obtain a positive result from testing a mixed sample of both public swimming pools.

- And lastly, it is possible that both swimming pools both have bacteria in them. We will definitely get a positive result from this too.

So, if P(A) is the probability of the event of bacteria existing in public swimming pool A

And P(B) is the probability of the event of bacteria existing in public swimming pool B

P(A') and P(B') represent the probabilities of bacteria being absent in public swimming pool A and public swimming pool B respectively.

P(A) = P(B) = 0.009

P(A') = P(B') = 1 - 0.009 = 0.991

Since the probabilities for each public swimming pool is independent of the other.

P(A or B) = P(A n B') + P(A' n B) + P(A n B)

= P(A)×P(B') + P(A')×P(B) + P(A)×P(B)

= (0.009×0.991) + (0.991×0.009) + (0.009×0.009)

= 0.008919 + 0.008919 + 0.000081

= 0.017919

Evidently, a probability of 0.017919 (1.7919%) indicates an event with a very low likelihood. A positive result is expected only 1.7919% of the time.

Hence, we can conclude that the probability is quite​ low, indicating that further testing of the individual samples will be a rarely necessary event.

Hope this Helps!!!


Related Questions

He area of a rectangle is 27 m2 , and the length of the rectangle is 3 m less than twice the width. find the dimensions of the rectangle.

Answers

The width of the rectangle is 4.5 meters, and the length is 6 meters.

Let's denote the width of the rectangle as [tex]\( w \)[/tex] and the length as [tex]\( l \)[/tex].

1. The area [tex]\( A \)[/tex] of a rectangle is given by the product of its length and width, so we have the equation:

[tex]\[ A = l \times w \][/tex]

Since the area is given to be 27 square meters, we can write:

[tex]\[ l \times w = 27 \][/tex]

2. The length of the rectangle is 3 meters less than twice the width.

This relationship can be expressed as:

[tex]\[ l = 2w - 3 \][/tex]

This is our second equation.

Now we have a system of two equations with two variables:

[tex]\[ \begin{cases} l \times w = 27 \\ l = 2w - 3 \end{cases} \][/tex]

We can substitute the expression for [tex]\( l \)[/tex] from the second equation into the first equation:

[tex]\[ (2w - 3) \times w = 27 \][/tex]

Expanding the equation, we get:

[tex]\[ 2w^2 - 3w - 27 = 0 \][/tex]

To solve this quadratic equation, we can factor it:

[tex]\[ (2w - 9)(w + 3) = 0 \][/tex]

Setting each factor equal to zero gives us two possible solutions for [tex]\( w \)[/tex]:

[tex]\[ 2w - 9 = 0 \quad \text{or} \quad w + 3 = 0 \][/tex]

Solving for [tex]\( w \)[/tex], we get:

[tex]\[ w = \frac{9}{2} \quad \text{or} \quad w = -3 \][/tex]

Since the width of a rectangle cannot be negative, we discard [tex]\( w = -3 \)[/tex].

Thus, [tex]\( w = \frac{9}{2} \)[/tex] meters, which simplifies to [tex]\( w = 4.5 \)[/tex] meters.

Now we can find the length [tex]\( l \)[/tex] by substituting [tex]\( w = 4.5 \)[/tex] into the second equation:

[tex]\[ l = 2(4.5) - 3 \][/tex]

[tex]\[ l = 9 - 3 \][/tex]

[tex]\[ l = 6 \][/tex]

solve and graph |2x+10|>26

Answers

The answer is x > 8 or x < -18 then to graph it you would put a dot at 8 on a number line and put a line from the dot to every number greater than 8. then put a dot at -18 and put a line from that dot to every number less than -18. I tried my best to explain it, hope this helps!

Triangle ABC has vertices A(–2, –3), B(–5, –3), and C(–4, –2). The triangle is rotated 90° counterclockwise around the origin.


A) A’(3, 2), B’(3, 5), C’(2, 4)

B) A’(3, –2), B’(3, –5), C’(2, –4)

C) A’(–3, –2), B’(–3, –5), C’(–2, –4)

D) A’(–3, 2), B’(–3, 5), C’(–2, 4)


Answers

The rule for this rotation is (x, y) converted into (-y, x). So, to find the answer you would make the y negative and switch the values in the ordered pair. A would be (3, -2), B would be (3, -5), and C would be (2, -4). So, your answer would be B. Hope this helps!

An aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour. Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? Recall the formula d = rt. 0.75(x + y) = 120 x − y = 120 0.75(x − y)= 120 x + y = 120 120(x + y) = 0.75 120(x − y) = 1 120(x − y) = 0.75 120(x + y) = 1 Mark this and return

Answers

n aircraft travels with the wind for 120 miles in 0.75 of an hour. The return trip is flown against the wind and takes exactly 1 hour.
Which system of linear equations represents x, the speed of the plane in miles per hour, and y, the speed of the wind in miles per hour? 
---
With wind DATA:
distance = 120 miles ; time = (3/4)hr ; rate = 120/(3/4) = 160 mph
----
Against wind DATA:
distance = 120 miles ; time = 1 hr ; rate = 120 mph
-----

Equation::
Let p be speed of the plane in still air
Let w be speed of the wind
==================================
With wind:: p + w = 160 mph
Against wind:: p - w = 120 mph
================================

Answer:

System of equation: 0.75(x+y)=120 and x-y=120

A is correct

Step-by-step explanation:

An aircraft travels with the wind for 120 miles in 0.75 of an hour.

The return trip is flown against the wind and takes exactly 1 hour.

Let speed of aircraft be x mph and speed of wind y mph

Formula:

[tex]speed=\dfrac{Distance}{Time}[/tex]

Case 1: When aircraft along with wind

Speed = x+y

Time = 0.75

Distance = 120

[tex]x+y=\dfrac{120}{0.75}[/tex]

[tex]0.75(x+y)=120[/tex]

0.75(x+y)=120

Case 2: When aircraft against with wind

Speed = x-y

Time = 1

Distance = 120

[tex]x-y=\dfrac{120}{1}=120[/tex]

x-y=120

Hence, The system of equation are 0.75(x+y)=120 and x-y=120

In a shopping mall, shoppers who use a reward points card get a 10% discount on every transaction. If the average transaction is $450 for customers with these cards, and $500 for other customers, what happens to the expected value of a transaction?

Answers

Final answer:

The expected value of a transaction decreases by 10% for customers using a rewards points card, going from $500 to $450 per transaction as they receive a 10% discount.

Explanation:

The question pertains to the expected value of a transaction at a shopping mall considering different discounts for customers who use a rewards points card. The expected value takes into account the average (mean) value of transactions and the discounts applied to those transactions. With shoppers using the rewards card receiving a 10% discount, the average transaction value for these customers is $450, compared to $500 for those without the card.

If we calculate the expected value for a transaction without considering the card, it would simply be the average transaction amount of $500. However, when including the rewards card usage, we have to account for the discount. Therefore, the expected value for a transaction from a customer using the rewards card is 10% less than $500, which equals $450. This means the expected value for a transaction with the card has decreased by $50 compared to customers without the card.

To summarize the effect, use of the rewards card reduces the expected value of transactions for the business, given that a discount is provided. On the other hand, it incentivizes customers with savings, potentially increasing customer loyalty and the frequency of visits, which might offset the decrease in expected transaction value in a broader business strategy.

If f(x)=x+8 and g(x) = -4x - 3, find (f+g)(x)

Answers

(f + g) (x)= -3 x+ 5

(f + g)(x) = -3x + 5

What is function?"It defines a relation between input and output values.""In function, for each input there is exactly one output."

For given question,

We have been given two functions.

f(x) = x+8 and g(x) = -4x - 3

We need to find the value of (f + g)(x)

This means, we need to find the addition of functions f(x) and g(x)

⇒ (f + g)(x) = f(x) + g(x)

⇒ (f + g)(x) = (x + 8) + (-4x - 3)

⇒ (f + g)(x) = x - 4x + 8 -3

⇒ (f + g)(x) = -3x + 5

Therefore, (f + g)(x) = -3x + 5

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What is the sum of the coefficients of the expression 3x4+5x2+x3x4+5x2+x?

Answers

The answer is 9.
The coefficients are 3,5, and 1 and when you add them up you get 9.

 add like terms

 x^3x^4 = x^7

5x^2 + 5x^2 = 10x^2

you end up with x^7 +3x^4 + 10x^2 +x


Evaluate 4(6) + 7 (5 - 3 )
A: 118
B: 80
C: 10
D: 38

Answers

4(6) + 7 (5 - 3 ) 
= 24 + 7(2)
= 24 + 14
= 38

answer
D: 38
4(6)+7(5-3)
We need to first follow the order of operations, so first do those in parenthesis.
4(6)+7(2)
24+14
38
The correct answer is D.

What is the area of a section of pavement that is 20 ft wide and 50 yd​ long? give your answer in square feet?

Answers

Since this is supposed to be square feet, you need to multiply 50 by 3 to convert yards to feet. So, this is 20x150 square feet, which is 3000 square feet.

Find the product (x-y) (3x-4y)

Answers

(x - y)(3x - 4y)

= x(3x - 4y) - y(3x - 4y)

= 3x^2 - 4xy - 3xy + 4y^2

= 3x^2 - 7xy + 4y^2
(x-y) (3x-4y)
x(3x-4y)-y(3x-4y)
3x²-4xy-3xy+4y²
3x²-7xy+4y²
or
3x²+4y²-7xy

If a number is divisible by both two and three then we can say the number is divisible by

Answers

Simple....

if it's divisible by BOTH 2 and 3.....

Then we can say the number is divisible by 6...

Thus, your answer.

simple it is divisible by both


is the answer is both 2 and 3

Long Beach California has an elevation of -7 ft New Orleans Louisiana is 8 feet below sea level which city has lower elevation

Answers

new orleans lousiana is the answer

New Orleans has the lower elevation at -8 feet compared to Long Beach, which is at -7 feet, since a lower numerical value below zero indicates a further drop below sea level.

To determine which city has the lower elevation, we need to compare the elevations of Long Beach, California and New Orleans, Louisiana. A lower elevation means that it is further below sea level. Long Beach is at an elevation of -7 feet, while New Orleans is at 8 feet below sea level. In numerical terms, New Orleans’ elevation can be considered as -8 feet because the word 'below' indicates a negative elevation.

Comparing the two elevations:

Long Beach, California: -7 feet

New Orleans, Louisiana: -8 feet

Since -8 is less than -7, we determine that New Orleans has the lower elevation compared to Long Beach.

1.For the function y = f(x), what is the ordered pair for the point on the graph when x = b - 2? (3 points)

a. (b - 2, f(b -2))
b. (x, f(b))
c. (x, b - 2)
d. (b - 2, f(b))

Answers

A is the answer
^^^^^^^^^^^

Answer:

A

Step-by-step explanation:

BIG BRAIN

you pay $14.82 for 1.5 pound of ham. you buy 2.25 pounds of roast beef for $12.40 per pound. How much less does ham cost per pound than roast beef?

Answers

a pound of ham is 9.88$ and a pound of beef 5.51$ answer ham doesn't cost less roast beef is 4.37$ cheaper a LB.

We _____ when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.

Answers

Subtract because it has to deal with the many signs

We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.

What is a mean?

It is the average value of the set given.

It is calculated as:

Mean = Sum of all the values of the set given / Number of values in the set

We have,

The average deviation is calculated by taking the absolute value of the deviations from the mean, summing them, and then dividing by the total number of observations.

This gives us a measure of the average distance between each observation and the mean.

The formula for the average deviation is:

average deviation = Σ |x - mean| / n

where x is an observation, mean is the mean of the observations, and n is the total number of observations.

By taking the absolute value of the deviations, we ensure that negative and positive deviations do not cancel each other out when we sum them.

Thus,

We do not square the deviations when calculating the average deviation, because the sum of all deviation scores around the mean equals zero.

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How to find the equation of a parabola given the vertex and one point?

Answers

first, write down y=a(x-the x coordinate of the vertex)^2+the y coordinate of the vertex)
second, plug the x coordinate and coordinate of the given point in the above equation to find out a
For example, vertex is (1,2), the point is (3,4)
y=a(x-1)^2+2 
then plug in x=3, y=4 in the above equation to find out a
4=a(3-1)^2+2
4=4a+2
4a=2
a=1/2
the equation of the parabola with a vertex at (1,2) and passes through the point (3,4) is 0.5(x-1)^2+2
Final answer:

To find the equation of a parabola given the vertex and one point, use the vertex form of a parabola equation: y = a(x - h)² + k.

Explanation:

To find the equation of a parabola given the vertex and one point, you can use the vertex form of a parabola equation: y = a(x - h)² + k. Here's how:

Determine the values of h and k from the given vertex.Use the given point to substitute the values of x and y in the vertex form.Solve for a to find the equation of the parabola.

For example, if the vertex is (2, 3) and the point is (4, 5), the equation of the parabola would be y = 1(x - 2)² + 3.

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Calculate the loss on selling 50 shares of stock originally bought at 13 3/4 and sold at 12

Answers

50times 13.75 bc that's what 13 3/4 is so that gives u 68750

Then u do 50times12 that gives u 600


Then u subtract 600 from 68750and it gives u 87.50
Cost per share:

13 3/4 = 13 + 3/4 = (13 * 4 + 3 ) / 4 = (52 + 3 ) / 4 = 55 / 4

Selling price:

12

Loss per share: 55 / 4 - 12 = ( 55 - 48 ) / 4 = 7 /4

7 / 4 = 4 / 4 + 3 / 4 = 1 + 3/4 = 1 3/4 = 1.75

Total loss = loss per share * number of shares

=> 50 * 1.75 = 87.5

Answer: 87.5

Mr. Mask suggested contacting a travel agent to see whether they could get a lower price. The agent found a price that was 30% lower than $2075. What was the price the travel agent found? Explain and Show your work.

Answers

30% lower means it is 100-30 = 70% of the original price.

So the answer is (2075 * 70) / 100  = $1452.50
price 30% lower than $2075 = 70% of $2075
1) 70% of $2075?
2)convert 70% into a decimal( 0.70)
3)multiply $2075 by 0.70
4)$1452.00
5)The price the travel agent found was $1452.50

PLEASE HELP ASAP!
Write each equation in slope-intercept form of the equation of a line. Underline the slope and circle the y-intercept in each equation.

a)2x–y=4

b) 2x–y=0

c) x+3y=0

d) 2y–6=0

Answers

Final answer:

To write each equation in slope-intercept form and identify the slope and y-intercept, rearrange the given equations. a) 2x - y = 4: slope = 2, y-intercept = -4. b) 2x - y = 0: slope = 2, y-intercept = 0. c) x + 3y = 0: slope = -1/3, y-intercept = 0. d) 2y - 6 = 0: slope = 0, y-intercept = 3.

Explanation:

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. To write each equation in slope-intercept form and identify the slope and y-intercept, we can rearrange the given equations.

a) 2x - y = 4
First, we rearrange the equation to isolate y: -y = -2x + 4, then we rewrite as y = 2x - 4. Therefore, the slope is 2 and the y-intercept is -4.

b) 2x - y = 0
Rearranging the equation gives y = 2x. The slope is 2 and the y-intercept is 0.

c) x + 3y = 0
Isolating y, we get y = -1/3x. The slope is -1/3 and the y-intercept is 0.

d) 2y - 6 = 0
Solving for y, we find y = 3. The slope is 0 and the y-intercept is 3.

The glee club has a set of 48 classical cds and a set of 42 show tune cds. each set can be divided equally among the club members. what is the greatest possible number of club members?

Answers

We have to find the GCF (Greatest Common Factor) of 48 and 42 here... 

Factors of 48:
1,2,3,4,6,8,12,16,24,48

Factors of 42: 
1,2,3,6,7,14,21,42

The largest common factor of these two numbers is 6. 


So, there can be a maximum of 6 members in the club.. 

Hope this helped!

The greatest possible number of club members that we can divide 48 classical CDs and 42 show tune CDs is 6.

What is HCF?

HCF is the highest common number or factor that divides two or more than two given numbers completely.

These types of questions can be solved by the concept of HCF.

Given that the glee club has a set of 48 classical CDs and a set of 42 show tune CDs and we have to determine the highest number of club members so that we can distribute these two types of CDs to the club members equally.

∴ The HCF of 42 and 48 is 6, we know 2 and 3 also divides 42 and 48 but they are not the largest number.

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Tanner walked a total of 8 kilometers by making 2 trips to school. How many trips will Tanner have to make in all to walk a total of 12 kilometers?

Answers

3. every trip it's 4 kilometers, and 4 times 2 equals 8 so 4 times 3 equals 12 so yeah :))

The total number of trips is x to walk a total of 12 kilometers is 3 trips if Tanner walked a total of 8 kilometers by making 2 trips to school.

What is a fraction?

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

Tanner walked a total of 8 kilometers by making 2 trips to school.

Let the total number of trips be x to walk a total of 12 kilometers.

8 km → 2 trips

12 km → x trips

8x = 24

x = 24/8

x = 3 trips

Thus, the total number of trips is x to walk a total of 12 kilometers is 3 trips if Tanner walked a total of 8 kilometers by making 2 trips to school.

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What form would you use to write the equation of a line if you knew the slope and x-intercept? Explain.

Answers

You know the slope and the point (x1,0) where x1 is the x  coordinate of the x intercept.

You use the point slope form of the line:-

y - y1  = m(x - x1)  where m = slope and (x1,y1) is a point on the line.

here y1 = 0  so the  equation would be

y = m(x - x1)

The form used  to write the equation of a line if you knew the slope and x-intercept y=mx−k/m

What is slope?

The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it

According to the given situation we have given :a slope of 'm' and an x-intercept of 'k'

we can write

y=mx−k/m

and generally, To find the x-intercept, set y = 0 and solve for x.

For example,

Let k be some constant such that

y=mx + k

where

m is the slope.

m=3/4 and the x-intercept is 4

If the x-intercept is 4 this means that x=4 when y=0

So equation:

y=mx + k becomes

0=3/4+ k

k=−3

and our equation is

y=3/4x−3

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An integer x is divided by an integer y, and quotient is 24.the sum of these two integers is 75. what is the value of x?

Answers

72/3= 24. 72+3=75. I hope that helped

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of x is 72.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Let the integer be x and y.

An integer x is divided by an integer y, and the quotient is 24.

This can be written as:

x ÷ y
x/y = 24

x = 24y _____(1)

Now,

The sum of the integer is 75.

x + y = 75

From (1) we get,

24y + y = 75

25y = 75

Divide both sides by 25.

y = 3

Now,

From (2 ) we get,

x + y = 75

x + 3 = 75

Subtracting 3 on both sides.

x = 75 - 3

x = 72

We can also cross-check:

x = 72 and y = 3

= x ÷ y

= 72/3

= 24

Thus,

The value of x is 72.

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Write a polynomial function of least degree with zeroes 0 and - 2. write your answer using the variable x and in standard form with a leading coefficient of 1.

Answers

x(x+2) = 0
x² + 2x = 0

Jina purchased a prepaid phone card for $30 . Long distance calls cost 22 cents a minute using this card. Jina used her card only once to make a long distance call. If the remaining credit on her card is $25.82 , how many minutes did her call last?

Answers

19 minutes. subtract the new balance from the original total. divide by .22

Brain weight bb as a function of body weight ww in fish has been modeled by the power function b=.007w2/3b=.007w2/3, where bb and ww are measured in grams. a model for body weight as a function of body length ll (measured in cmcm) is w=.12l2.53w=.12l2.53. if, over 1010 million years, the average length of a certain species of fish evolved from 15cm15cm to 20cm20cm at a constant rate, how fast was the species' brain growing when the average length was 18cm18cm? round your answer to the nearest hundredth.

Answers

Final answer:

To find the rate of brain growth, we calculate the derivatives of the brain weight and body weight functions. Then, we find the rate by multiplying the derivatives and substituting the average length of 18cm. The rate of brain growth is approximately 0.04 grams/cm.

Explanation:

To find the rate at which the species' brain was growing when the average length was 18cm, we need to find the derivative of the brain weight function with respect to body weight and then multiply it by the derivative of body weight with respect to body length.

First, let's find the derivative of the brain weight function, b = 0.007w^(2/3), with respect to body weight, w.

Taking the derivative, we get db/dw = (2/3) * 0.007 * w^(-1/3).

Next, let's find the derivative of the body weight function, w = 0.12l^(2.53), with respect to body length, l.

Taking the derivative, we get dw/dl = 2.53 * 0.12 * l^(1.53).

Finally, to find the rate of brain growth when the average length was 18cm, we plug in the value 18 for l in the derivative of the body weight function and multiply it by the derivative of the brain weight function:

Rate of brain growth = (2/3) * 0.007 * (18)^(-1/3) * 2.53 * 0.12 * (18)^(1.53).

Rounding to the nearest hundredth, the rate of brain growth when the average length was 18cm is approximately 0.04 grams/cm.

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Consider the probability distribution of a random variable x. is the expected value of the distribution necessarily one of the possible values of x?

Answers

The expected value of a distribution is considered as a mean, or average, for a probability distribution. It represents the center of the possible values of a variable. That doesn't necessarily mean it would be one of the possible values of x. 

Answer:

No. The expected value can be a value different from the exact value of x.

What is the measure of A and what is the measure of B

Answers

5y - 3 = 3y + 27
2y = 30
y = 15

m<A= 5(15) - 3 = 75 - 3 = 72

m<B = [360 - 2(72)]/2
m<B = [360 - 144] / 2
m<B = 216 / 2
m<B = 108

(5y-3) = (3y+27)   -3y from both sides

2y-3 =  27    +3 to both sides

2y= 30   divide both sides by 2

y=15

check

5X15-3 = 3x15+27

72 = 72

correct that y=15 and that each angle is 72

in that shape correlating angles are the same so...

360-72-72= 216

216 divided by 2= 108 degrees

B is equal to 108 degrees

A is equal to 72 degrees

The average of your first three test grades is 78. what grade must you get on your fourth and final test to make your average 80?

Answers

You need to score 86

What is the area of a triangle with vertices at (0, −2) , ​ (8, −2) ​ , and ​ (9, 1) ​ ? Enter your answer in the box

Answers

The area of a triangle is A=1/2*b*h

When we graph the vertices of the triangle on a graph, we see that the lowest points are at y=-2, and the highest point is at y=1.  Therefore, our height is 3.
The base of the triangle goes from (0,-2) to (8,-2), which gives us a length of 8 for our base.

A=1/2*(8)*(3)
A=12

Answer:

12 square unit.

Step-by-step explanation:

Since, the area of a triangle having vertices [tex](x_1, y_1)[/tex], [tex](x_2, y_2)[/tex] and [tex](x_3, y_3)[/tex] is,

[tex]A=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Here, the vertices of the triangle are (0, −2), ​(8, −2) and ​ (9, 1),

Hence, area of the given triangle is,

[tex]A=\frac{1}{2}|0(-2-1)+8(1+2)+9(-2+2)|[/tex]

[tex]=\frac{1}{2}| 0+24+0|[/tex]

[tex]=\frac{24}{2}[/tex]

[tex]=12\text{ square unit}[/tex]

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