The graphs shows the amount of a chemical in a water
sample at different times after it was first measured.
Select all statements that are true.
(Select all that apply)
A) The amount of the chemical in the water sample is
decreasing exponentially
B) The amount of the chemical in the water sample is not
decreasing exponentially.
C) It is not possible to tell for certain whether or not the amount
of the chemical is decreasing exponentially.
D) When it was first measured, there were 2,000 mg of the
chemical in the water sample.
E) After 4 hours, there were 100 mg of the chemical in the
water.

If the sequence defines a function, the range is all integers. Option D

The given sequence is an arithmetic Progression. An arithmetic progression is the sequence in which the terms are gotten by the addition of a constant term known as the common difference.

The given sequence is 3,8,13,18,23,28,......

The first term (a) = 3

The common difference (d) = 8-3=5

The last term L= a+(n-1)d

Input the values in the formula to get

Last term = 3+(n-1)5

L= 3+5n-5

L=  -2+5n

In conclusion from the solution, the last term ranges from -2 to positive showing all integers. therefore the range is all integers positive and negative

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Answer:

b

Step-by-step explanation:

you can take the rectagel and you x the rectagel

Answer:

0.93

Step-by-step explanation:

Answer:

B. -6

Step-by-step explanation:

We basically just need to solve for p by isolating it!

The most simple way to do this is shown through these steps:

6p+4 = 4p-8

-4p -4p

2p + 4 = -8

- 4 - 4

2p = -12

÷2 ÷2

p = -6

The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by \(S = 24000 * (1.035)^t\).

What is a function?

You can use the fact that the raise is done on the previous year's salary.

Let the initial salary be P = $24000

After 1 year, her salary increased by R = 3.5% which, thus,

Total salary = P + increment

Similarly going on, we get

\(P_t = P(1+ \frac{R}{100})^t = S\) (we can say)

Putting values of P(value of P) and R(value of R), we get

\(S = 24000(1 + 0.035)^t = 24000 *(1.035)^t\)

Thus,

The function that Ngozi's salary s(t) in dollars, t years after she starts to work as an interpreter is given by

\(S = 24000 * (1.035)^t\)

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The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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\( \red { \orange {\boxed {\boxed{Answer}}}}\)

\( = 65\% \times 35\)

\( = \frac{65}{100} \times 35\)

\( = \frac{65 \times 35}{100} \)

\( = \frac{2275}{100} \)

\( = 22.75\)

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Answer:

Step-by-step explanation:

Diameter = 18cm

18 / 2 = Radius

Radius = 9cm

Formula: A=2πrh+2πr^2

2 x pi x 9 x 0.3 + 2 x pi x 9^2 = 525.90261

Nearest hundredth = 525.90

The family size has the lowest price compared to the family price per ounce which the amount is $0.21 / ounce.

To compare the box of cereal price we need to know the price per ounce first. It can be written as

Price per ounce = price /  total ounces

From the text above, we know that :

large size price = $3.34

large size ounces = 15

family size price = $5.14

family size ounces = 24

By substituting the parameter we can get the price per ounce of large size and family size

Large size

Price per ounce = price /  total ounces

Price per ounce = 3.34 / 15

Price per ounce = $0.22 / ounce

Family size

Price per ounce = price /  total ounces

Price per ounce = 5.14 / 24

Price per ounce = $0.21 / ounce

Hence, the family size has the lowest price compared to the family price per ounce which the amount is $0.21 / ounce.

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Answer:

Interest: $1440

Total Account Balance: $5440

Step-by-step explanation:

First, converting R percent to r a decimal

r = R/100 = 1.2%/100 = 0.012 per year,

then, solving our equation

I = 4000 × 0.012 × 30 = 1440

I = $ 1,440.00

The simple interest accumulated

on a principal of $ 4,000.00

at a rate of 1.2% per year

for 30 years is $ 1,440.00.

The simple Interest is $1440 and the total Account Balance: $5440.

Simple interest is calculated just on the loan's principal amount, whereas compound interest is calculated on both the principal and the cumulative interest.

First, converting R percent to r a decimal,

r = R/100 = 1.2%/100 = 0.012 per year,

Then, solving our equation,

I = 4000 × 0.012 × 30 = 1440

I = $ 1,440.00

The simple interest accumulated,

on a principal of $ 4,000.00

at a rate of 1.2% per year

for 30 years is $ 1,440.00.

Therefore, the simple Interest is $1440, and the total Account Balance: $5440.

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The total cost to build a 3-on-3 court, using area and perimeter formula is obtained as $528.

What is perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

As the court area is 165 square meters, we need to calculate the perimeter to determine the amount of asphalt needed for the court.

Assuming the court is rectangular, we can use the formula -

Perimeter = 2 × (length + width)

To find the length and width, we need to know the aspect ratio of the court.

According to FIBA regulations, a 3-on-3 court should have an aspect ratio of 1:1.5, meaning the length should be 1.5 times the width.

Let's assume the width of the court is x meters.

Then, the length of the court would be 1.5x meters.

The area of the court is given by -

Area = length × width

165 = 1.5x × x

165 = 1.5x²

x² = 165 / 1.5

x² = 110

x = √110

x ≈ 10.49

Therefore, the width of the court is approximately 10.49 meters, and the length is 1.5 times that, or approximately 15.73 meters.

The perimeter of the court is -

Perimeter = 2 × (length + width)

Perimeter = 2 × (15.73 + 10.49)

Perimeter = 52.42 meters

Now, we need to convert the perimeter to the amount of asphalt needed. According to industry standards, one ton of asphalt covers 9.29 square meters at a thickness of 5 cm.

The thickness of the asphalt will depend on the existing ground conditions, but assuming we need a thickness of 5 cm, the amount of asphalt needed is -

Asphalt needed = (Perimeter × Thickness) / 9.29

Asphalt needed = (52.42 × 0.05) / 9.29

Asphalt needed = 0.28 tons

Therefore, the amount of asphalt is 0.28 tons.

If the cost of asphalt is $100 per ton, then the cost of the required amount of asphalt would be -

Cost of asphalt = Asphalt needed × Cost per ton

Cost of asphalt = 0.28 × $100

Cost of asphalt = $28

We also need to factor in the cost of hoops and paint.

As per the problem statement, the quantity of hoops and paint required is the same as that for a 5-on-5 court.

Assuming the cost of hoops and paint for a 5-on-5 court is $500, the total cost of building the 3-on-3 court would be -

Total cost = Cost of asphalt + Cost of hoops and paint

Total cost = $28 + $500

Total cost = $528

Therefore, the total cost to build a 3-on-3 court with an area of 165 square meters, assuming the cost of asphalt is $100 per ton and the cost of hoops and paint is $500, is $528.

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What is the cost to build a 3-on-3 court with an area of 165 square metres? The hoops and the paint will still be needed in the same quantities as the 5-on-5 court. However, the quantity of asphalt will be less. Complete your calculations and circle the final answer.​ The cost of asphalt is $100 per ton.

Thus, the total number of ways is 52 * 51 * ... * 41.                                                                                                                                          For the first problem, we need to find the number of ways to reward the 1st and 2nd places among the six people. Since order matters (i.e., the 1st and 2nd positions are distinct), we can use the concept of permutations. The number of ways to select the 1st place is 6, and after that, we have 5 remaining people to select the 2nd place from. Thus, the total number of ways is 6 * 5 = 30.

In the second problem, we want to determine the number of pairs that can be made from a group of 7 people. To do this, we can use combinations since the order does not matter in a pair. The formula for combinations is nCr, where n represents the total number of items and r represents the number of items we want to choose. In this case, we have 7 people, and we want to choose 2 for a pair. Thus, the number of pairs is 7C2 = (7!)/(2!(7-2)!) = 21.
For the third problem, Miss Mendoza wants to choose 3 students out of a class of 10 to clean the room. Again, we can use combinations since the order does not matter. Using the combination formula, we have 10C3 = (10!)/(3!(10-3)!) = 120 ways to choose the students.
In the fourth problem, Miss Bravo needs to choose a president, a vice president, and a secretary from a group of 9 excellent students. Since the order matters, we can use permutations. The number of ways to select the president is 9. After that, we have 8 remaining students to choose the vice president from, and then 7 remaining students for the secretary position. Thus, the total number of ways is 9 * 8 * 7 = 504.
In the fifth problem, we need to determine the number of ways to distribute 3 P1000 prizes among a group of 7 people. Here, the order doesn't matter, and we can use combinations. Using the combination formula, we have 7C3 = (7!)/(3!(7-3)!) = 35 ways to distribute the prizes.
Lastly, in the sixth problem, we want to find the number of ways to draw 12 cards from a standard deck of 52 cards.

Since the order matters (drawing one card after another), we can use permutations. The number of ways to draw the first card is 52, the second card is 51, and so on until the twelfth card, which is 41.

Thus, the total number of ways is 52 * 51 * ... * 41.

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1. The number of ways to reward the 1st and 2nd place in a contest with 6 people, we can use permutations.  The number of ways to reward the 1st and 2nd place in a contest with 6 people is 30.

2. The number of pairs that can be made from a group of 7 people is 21.

3. The number of ways to choose 3 students out of 10 to clean the room is 120.

4. The number of ways Miss Bravo can choose a president from 9 excellent students, we can use permutations. The number of ways to choose a president, a vice president, and a secretary from 9 excellent students is 504.

5. The number of ways to distribute 3 P1000 prizes among 7 people is 35.

6. The number of ways to draw 12 cards from a standard deck of 52 cards is calculated using factorials.

1. To find the number of ways to reward the 1st and 2nd place in a contest with 6 people, we can use permutations. Since the order of the rewards matters, we need to use the formula for permutations. The number of ways to choose the 1st place is 6, and once the 1st place is chosen, there are 5 remaining people to choose from for the 2nd place. Therefore, the total number of ways is 6 * 5 = 30.

2. To find the number of pairs that can be made from a group of 7 people, we can also use permutations. However, in this case, the order of the pairs doesn't matter. So, we need to use the formula for combinations. The number of ways to choose 2 people from a group of 7 is given by the combination formula: C(7, 2) = 7! / (2! * (7-2)!) = 7! / (2! * 5!) = (7 * 6) / (2 * 1) = 21.

3. To find the number of ways Miss Mendoza can choose 3 students out of 10 to clean the room, we can use combinations again. The number of ways to choose 3 students from a group of 10 is given by C(10, 3) = 10! / (3! * (10-3)!) = 10! / (3! * 7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.

4. To find the number of ways Miss Bravo can choose a president, a vice president, and a secretary from 9 excellent students, we can use permutations. The number of ways to choose the president is 9, and once the president is chosen, there are 8 remaining students to choose from for the vice president. Similarly, there are 7 remaining students to choose from for the secretary. Therefore, the total number of ways is 9 * 8 * 7 = 504.

5. To find the number of ways to distribute 3 P1000 prizes among 7 people, we can use combinations. The number of ways to choose 3 people from a group of 7 is given by C(7, 3) = 7! / (3! * (7-3)!) = 7! / (3! * 4!) = (7 * 6 * 5) / (3 * 2 * 1) = 35.

6. To find the number of ways to draw 12 cards from a standard deck of 52 cards, we can use permutations. The number of ways to choose the first card is 52, and once the first card is chosen, there are 51 remaining cards to choose from for the second card. Similarly, there are decreasing numbers of cards to choose from for each subsequent card until the 12th card. Therefore, the total number of ways is 52 * 51 * 50 * ... * 41, which can be simplified using factorials as 52! / (52-12)!.

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Answer:

24

Step-by-step explanation:

A=LxW

6x4=24

Answer:

24 feet

Step-by-step explanation:

I hope this helps!

The angle of Sonny's line of sight to both Sam and Sal, we can use the Law of Cosines. The angle of Sonny's line of sight to both Sam and Sal is approximately 77 degrees (rounded to the nearest degree).

Let's consider the triangle formed by Sam, Sonny, and Sal. Let's label the sides of the triangle:

The side opposite Sam as side a (distance between Sonny and Sal)

The side opposite Sonny as side b (distance between Sam and Sal)

The side opposite Sal as side c (distance between Sam and Sonny)

According to the Law of Cosines, we have the formula:

c^2 = a^2 + b^2 - 2ab * cos(C)

Where C is the angle opposite side c.

We want to find angle C, which is the angle of Sonny's line of sight to both Sam and Sal.

Plugging in the given distances:

c = 175 ft

a = 201 ft

b = 153 ft

Using the Law of Cosines:

175^2 = 201^2 + 153^2 - 2 * 201 * 153 * cos(C)

Simplifying and solving for cos(C):

cos(C) = (201^2 + 153^2 - 175^2) / (2 * 201 * 153)

cos(C) = 0.228

To find the angle C, we can take the inverse cosine (cos^-1) of 0.228:

C ≈ cos^-1(0.228) ≈ 77.08 degrees

Therefore, the angle of Sonny's line of sight to both Sam and Sal is approximately 77 degrees (rounded to the nearest degree).

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Answer:

Wednesday

Step-by-step explanation:

1. First find the position of each variable on the number line.

2. The average temperature is 0 because it is in the center.

3. The answer cannot be Monday because it is above so it is Wednesday.

Answer:

wensday

Step-by-step explanation:

Answer:

= − 7 /1 1  in fraction form

Step-by-step explanation:

STEP 1: Multiply by 1

1 + 1 0 + 2 5 = 1 8

+ 1 0 + 2 5 = 1 8                                                                                                                               STEP 2: Combine like terms

+ 1 0 + 2 5 = 1 8

1 1 + 2 5 = 1 8                                                                                                                       STEP 3: Subtract  2 5   from both sides of the equation

11x+25=18

1 1 + 2 5 − 2 5 = 1 8 − 2 5

STEP 4: Simplify  by subtracting the numbers

1 1 + 2 5 − 2 5 = 1 8 − 2 5

11x+25−25=18−25                                                                                                   1 1 = 1 8 − 2 5                                                                                                                                   1 1 =  -7

STEP 5: Divide both sides of the equation by the same term                                                     1 1 = − 7                                                                                                                         11x/ 11x = −7/ 1 1 (set up as a fraction)                                                                       STEP 6: Cancel terms that are in both the numerator and denominator

=  − 7 /1 1                                                                                                                      SOLUTION

=  − 7 /1 1

The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.

The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).

Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.

In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.

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Assuming the randomly throw is equally distributed along the rectangle area, the probability of hitting the square is the fraction of the area of the square with respect to the total are of the rectangle.

The area of the square is the square of its side:

And the area of the rectangle is the product of its lengths by its height:

So, the probability is the area of the square divided by the area of the rectangle:

The probability if 9%.

We have that the 80% of this type of seeds germinate, if we plant 90 seeds, the 80% is: 90 * 80/100 = 72

Then we know that 72 seeds will germinate.

a) The probability that fewer than 75 seeds germinate is 1 or 100%, having in count that at least 72 seeds will germinate.

Then the correct answer is 1 (100%)

b) The probability of 80 or more seeds germinating is 0, again, having in mind the percent of seeds that germinate. In other words, as just 72 of 90 seeds will germinate, it's impossible that 80 or more seeds will germinate.

Then the correct answer is 0 (0%).

c) To approximate the probability that the number of seeds germinated is between 67 and 75 is the average of the probability that 67 seeds have been germinated and the maximum probability because 72 are the seed that will germinate.

Then the correct answer is 0.965

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Step-by-step explanation:

length = 2×width + 6

84 = 2×length + 2×width

now using the first in the second equation :

84 = 2×(2×width + 6) + 2×width = 4×width + 12 + 2×width

84 = 6×width + 12

72 = 6×width

width = 12 cm

length = 2×width + 6 = 2×12 + 6 = 24 + 6 = 30 cm

Answer:

2

Step-by-step explanation:

yes it actually works >□<

good day♡

Answer:

1 + 1 = 2

Step-by-step explanation:

:)

The power to which a number or expression is raised is called the exponent.

1. An exponent is a mathematical notation that represents the power to which a number or expression is raised. It is written as a superscript number or variable placed above and to the right of the base number or expression.

2. The base number or expression is the number or expression that is being multiplied repeatedly by itself, raised to the power of the exponent.

3. The exponent tells us how many times the base number or expression should be multiplied by itself. For example, in the expression \(2^3\), the base is 2 and the exponent is 3. This means that 2 should be multiplied by itself three times: 2 * 2 * 2 = 8.

4. The exponent can be a positive whole number, a negative number, zero, or a fraction. Each of these cases has different interpretations:

  - Positive exponent: Indicates repeated multiplication. For example, \(2^4\)means 2 multiplied by itself four times.

  - Negative exponent: Indicates the reciprocal of the base raised to the positive exponent. For example, \(2^{-3\) means 1 divided by \(2^3\).

  - Zero exponent: Always equals 1. For example, \(2^0\) = 1.

  - Fractional exponent: Represents a root. For example, \(4^{(1/2)\)represents the square root of 4.

5. Exponents follow certain mathematical properties, such as the product rule \((a^m * a^n = a^{(m+n)})\), the quotient rule \((a^m / a^n = a^{(m-n)})\), and the power rule \(((a^m)^n = a^{(m*n)})\).

Remember to use these rules and definitions to correctly interpret and evaluate expressions involving exponents.

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Answer:

(-2, 5), 6, 12

Step-by-step explanation:

Center: (-2, 5)

Radius: 6

Diameter: 12

The fifth number is 120

the fifth number can be calculates as follows

mean = \(\frac{sum of each value in the population}{number of values in the population}\)

so the sum of the number is mean x number of values

sum of the 4 number = 70 x 4 = 280, while,

sum of the 5 number = 80 x 5 = 400

so the fifth number = 400 - 280 = 120

so, the fifth number is 120

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Cows with eyes painted on their rears: This group experienced no deaths due to lion attacks.

Cows with cross-marks on their rear: This group suffered four deaths as a result of lion attacks.

Cows with no marks on their rear: This group experienced 15 deaths caused by lion attacks.

The researchers in Africa conducted a study to assess the effectiveness of using painted eyes on the rear of cattle as a means to protect them from lion attacks. The study included three treatment groups: cows with eyes painted on their rears, cows with cross-marks on their rear, and cows with no marks on their rear. After a period of four years during which the cattle roamed the plains, the researchers observed the following outcomes:

Cows with eyes painted on their rears: This group experienced no deaths due to lion attacks.

Cows with cross-marks on their rear: This group suffered four deaths as a result of lion attacks.

Cows with no marks on their rear: This group experienced 15 deaths caused by lion attacks.

Based on these findings, it appears that painting eyes on the cows' rears was an effective method for reducing lion attacks. The cows with eyes painted on their rears had a significantly lower risk of being attacked and killed by lions compared to the other two groups. The group with cross-marks also fared better than the group with no marks, but the difference in outcomes between these two groups was less pronounced.

This creative approach of using painted eyes as a deterrent demonstrates the potential for innovative and non-traditional methods to address human-wildlife conflicts and protect livestock. It could provide valuable insights for developing strategies to mitigate conflicts between predators and domestic animals, which could be particularly relevant in regions where such conflicts are common.

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There are total 10 ordered pairs of (a,b) , where a , b are subsets of {1,2,3,4,5}.such that |a| * |b| = 4.

To find this, we need to consider the possible values for |a| and |b|.

The only pairs that multiply to 4 are (1, 4) and (2, 2).

Case 1: |a| = 1 and |b| = 4.
There are 5 ways to choose a single element for set 'a' from the given set.

For each choice of 'a', there will be only one set 'b' consisting of the remaining 4 elements. So, there are 5 ordered pairs for this case.

Case 2: |a| = 2 and |b| = 2.
There are 10 ways to choose 2 elements for set 'a' from the given set (by using combinations: ⁵C₂). For each choice of 'a', the set 'b' will consist of the remaining 3 elements.

However, we only need to count distinct ordered pairs, and switching the elements between 'a' and 'b' gives us the same ordered pair. So, we divide by 2 to account for this duplication. Thus, there are 10 / 2 = 5 ordered pairs for this case.

In total, there are 5 (Case 1) + 5 (Case 2) = 10 ordered pairs (a, b) where a, b are subsets of {1, 2, 3, 4, 5}, and |a| * |b| = 4.

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Jack has a total of 35 different combinations of fruits to choose from at the store.

To calculate the number of combinations Jack can choose, we need to use the concept of combinations in mathematics. Since Jack can buy any three fruits out of the seven available options, we need to calculate the number of combinations of 7 fruits taken 3 at a time.

The formula to calculate combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of options and r is the number of options to be chosen.

In this case, n = 7 (total number of fruits) and r = 3 (fruits to be chosen). Plugging these values into the formula, we get:

C(7, 3) = 7! / (3! * (7 - 3)!)

        = (7 * 6 * 5 * 4!) / (3 * 2 * 1 * 4!)

        = (7 * 6 * 5) / (3 * 2 * 1)

        = 35

Jack has a total of 35 different combinations of fruits to choose from at the store. He can select any three fruits out of the available options, which include apples, oranges, pears, bananas, plums, grapefruit, and kiwis.

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Using pythagoras' theorem in the right-angled triangle

A right-angled triangle is a polygon with 3 sides in which one angle is a right angle

Now, since we have 3 triangles, using Pythagoras' theorem in all three triangles, we have

h² + (12 - x)² = 12² - 6² (1)

Also, h² + x² = 6²  (2)

So, h² + (12 - x)² = 12² - 6²

h² + (12 - x)² = 144 - 36

h² + (12 - x)² = 108  (3)

From equation (2), h² = 36 - x²

Substituting this into equation (3), we have that

h² + (12 - x)² = 108  (3)

36 - x² + (12 - x)² = 108  (3)

Expanding the brackets, we have that

36 - x² + 144 - 24x + x² = 108

36 + 144 - 24x = 108

180 - 24x = 108

-24x = 108 - 180

-24x = -72

x = -72/-24

x = 3

Since  h² = 36 - x²

h = √(36 - x²)

So, substituting the value of x = 3 into the equation, we have that

h = √(36 - x²)

h = √(36 - 3²)

h = √(36 - 9)

h = √27

h = 3√3

So,

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Statment b. If you buy groceries for $50, then you PIBP for them is equal to $50 is always true.

PIBP stands for "price paid in buyer's perspective," which means the amount that the buyer pays to purchase a product or service. In this case, if you buy groceries for $50, then your PIBP for them is indeed $50 since that is the price you paid as the buyer.

Option a is incorrect because PISP stands for "price in seller's perspective," which means the value the seller receives in exchange for a deal they own. Option c is incorrect because PIBP stands for "price paid in buyer's perspective," not "value in use." Option d is incorrect because PIBP and PISP can change around a cycle of ownership depending on the negotiation and agreement between the buyer and seller.

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