To find the two consecutive odd integers, let's set up an equation using the given information. Let x be the smaller odd integer, then the next consecutive odd integer is x+2.
The problem states that the product of these two integers is 77 more than twice the larger integer. In equation form, this can be written as:
x * (x + 2) = 2(x + 2) + 77
Now, let's solve for x:
x * (x + 2) = 2x + 4 + 77
x^2 + 2x = 2x + 81
x^2 = 81
To find the value of x, take the square root of both sides:
√(x^2) = √81
x = 9
So, the smaller odd integer is 9. The next consecutive odd integer is 9 + 2 = 11.
Therefore, the two consecutive odd integers are 9 and 11.
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The two consecutive odd integers are 9 and 11.
How to find consecutive integers?To find the two consecutive odd integers whose product is 77 more than twice the larger, we can set up the following equation:
x * (x + 2) = 2(x + 2) + 77
Here, x represents the first odd integer, and x + 2 represents the second consecutive odd integer. Now, let's solve the equation step by step:
1. Expand the equation: x^2 + 2x = 2x + 4 + 77
2. Simplify the equation: x^2 + 2x = 2x + 81
3. Subtract 2x from both sides: x^2 = 81
4. Take the square root of both sides: x = ±9
Since we're looking for positive integers, x = 9. Therefore, the two consecutive odd integers are 9 and 11.
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A frustum is made by removing a small cone from the top of a large cone. In the diagram shown, the height of the small cone is half the height of the large cone. Work out the curved surface area of the frustum
It depends on whether the frustum is formed by slicing a cone or a pyramid. If it is a cone, then the area of frustum consists of two circular bases and a curved surface.
Curved surface area ≈ [tex]81.5 cm^2[/tex] (rounded to one decimal place)
What is the area of frustum?Curved surface area [tex]= (1/2) \times (C1 + C2) \times L[/tex]
Where C1 and C2 are the circumferences of the bases of the frustum, and L is the slant height.
From the diagram, you can see that C1 = 2πr and C2 = 2πR, where r and R are the radii of the bases. You can also see that L = √(H² + (R - r)²), where H is the height of the frustum.
Substituting these values into the formula, you get:
Curved surface area = (1/2) × (2πr + 2πR) × √(H² + (R - r)²)
Simplifying, you get:
Curved surface area = π(r + R) × √(H² + (R - r)²)
Now you just need to plug in the values given in the question. The height of the large cone is 12 cm, so [tex]H = 12 - 6 = 6[/tex] cm. The radius of the small base is 3 cm, so r = 3 cm. The radius of the large base is 4 cm, so [tex]R = 4[/tex] cm.
Curved surface area = π(3 + 4) × √(6² + (4 - 3)²)
Curved surface area ≈ π × 7 × √[tex]37[/tex]
Therefore, Curved surface area ≈ [tex]81.5 cm^2[/tex] (rounded to one decimal place)
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the physician orders lanoxin elixir 0.175 mg po q.am for the patient. the pharmacy sends a bottle labeled: lanoxin elixir 0.05 mg/ml. how many milliliters will the nurse administer to the patient? write your answer as a decimal number.
The nurse should administer 3.5 mL of Lanoxin elixir 0.05 mg/mL to the patient to achieve the desired dose of 0.175 mg.
First, we need to convert the prescribed dose of 0.175 mg to milligrams per milliliter (mg/mL) using the concentration of the Lanoxin elixir, which is 0.05 mg/mL.
To determine how many milliliters of Lanoxin elixir 0.05 mg/mL the nurse should administer to the patient, we need to use a simple formula:
Dose = Desired dose / Stock strength
Where:
Desired dose is 0.175 mg
Stock strength is 0.05 mg/mL
So, substituting the values into the formula:
Dose = 0.175 mg / 0.05 mg/mL
Dose = 3.5 mL
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The perimeter of a rectangular parking lot is 364 m. If the length of the parking lot is 98 m, what is its width?
First we have to remember what the perimeter of a rectangle is. The perimeter is the outside edges of the rectangle, think of it as the fence around a yard. This means that the perimeter of a rectangle or a square has four sides: two widths and two lengths.
This problem tells us that the length of this rectangular parking lot is 98m. Since this parking lot is a rectangle, each of the parallel lengths are the same size. Therefore, each length is 98m and that takes care of 196m of the perimeter [tex](98\text{m} \times 2)[/tex].
To find the width, we know that the lengths take up 196m of the total 364m of the perimeter which leaves 168m for the widths. Again, since this parking lot is a rectangle, each parallel width is the same size so we can find one width by dividing the left over perimeter by 2: [tex]168\text{m} \div 2 = \bold{84m}[/tex].
I hope that helps!
Please answer this question
The perimeter of parallelogram ABCD in which AM ,BN are angle bisector and DM = 4ft and MN = 3ft is: P = 2(AB + BN) = 2(2 + 2) = 8 ft.
What is perimeter?Perimeter is the total length of the boundary or the distance around the edge of a two-dimensional shape such as a polygon or a circle.
To find the perimeter of parallelogram ABCD, we need to find the length of each side of the parallelogram.
Since AM and BN are angle bisectors of parallelogram ABCD, we know that they intersect at the diagonals' midpoint. Therefore, we can say that DM = MB and MN = NA.
Using this information, we can label the sides of the parallelogram as follows:
AB = CD = x (opposite sides of a parallelogram are equal)
AM = MC = BM = MD = x/2 (diagonals of a parallelogram bisect each other)
BN = ND = NA = NC = y (angle bisectors of a parallelogram bisect opposite angles and sides)
DM = 4 ft and MN = 3 ft (given)
Since DM = MB, we can write:
x/2 + 4 = y + 3
x/2 - y = -1
Since BM = MC, we can write:
x/2 + y = x
y = x/2
by substituting-
x/2 + 4 = x/2 + 3
x = 2
Therefore, AB = CD = 2 ft and BN = ND = NA = NC = x/2 = 1 ft.
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Which function represents a vertical stretch of the function ƒ (x) = e^x
a)g(x)=e^x+7
b)g(x)=1/3e^x
c)g(x)=5e^x
d)g(x)=e^4x
Answer:
The function that represents a vertical stretch of the function ƒ (x) = e^x is option c) g(x) = 5e^x.
To see why, we can compare the graphs of the two functions. The graph of ƒ(x) = e^x is an exponential function that starts at the point (0,1) and increases rapidly as x increases. The graph of g(x) = 5e^x is also an exponential function, but it starts at the point (0,5), which is five times higher than the starting point of ƒ(x). This means that g(x) is a vertical stretch of ƒ(x) by a factor of 5.
Option a) g(x) = e^x + 7 is a vertical shift of ƒ(x) by 7 units, but it does not represent a vertical stretch.
Option b) g(x) = 1/3e^x is a vertical compression of ƒ(x) by a factor of 1/3, rather than a vertical stretch.
Option d) g(x) = e^4x represents a horizontal stretch of ƒ(x) by a factor of 1/4, but it does not represent a vertical stretch.
How many ways can you make chance. 45 cents
Answer:
There are several ways to make 45 cents using different coins:
Nine nickels
Four dimes and one nickel
Three dimes and six nickels
Two dimes and one quarter
One dime, two nickels, and three pennies
One quarter and two dimes
One quarter, one dime, and four nickels
One quarter, three nickels, and five pennies
45 pennies
So there are 9 ways to make 45 cents.
I Hope This Helps!
I need help the answer that was put is incorrect I need the right answer
Answer:
Step-by-step explanation: Its 6x, you add the 6 + 1 then keep the x.
I need the answer help pls
Answer:
Step-by-step explanation:
among a student group 49% use chrome, 20% internet explorer, 10% firefox, 5% mozilla, and the rest use safari. what is the probability that you need to pick 7 students to find 2 students using chrome?
The probability that you need to pick 7 students to find 2 students using Chrome is approximately 65%.
To calculate this, we can use the formula P = (n!/r!(n-r)!) * p^r * q^(n-r), where n = 7 (number of students to pick), r = 2 (number of Chrome users to find), p = 0.49 (probability of Chrome user), and q = 0.51 (probability of non-Chrome user). By plugging the numbers into the equation, the probability of finding 2 Chrome users is 0.649.
In other words, if you randomly pick 7 students from the group, there is a 65% chance that you will find 2 students using Chrome.
This is because 49% of the group use Chrome, so if you pick 7 students randomly, the probability of picking 2 Chrome users is high.
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a sample of test scores is normally distributed with a mean of 120 and a standard deviation of 10. what score is located 2 standard deviations below the mean? g
The score located 2 standard deviations below the mean is 100. This score can be found by subtracting 2 standard deviations (20) from the mean (120).
The normal distribution is a bell-shaped curve that is symmetrical around the mean. This means that if you calculate the number of standard deviations away from the mean, you can use the same number to calculate how many standard deviations away from the mean the score is.
For example, in this question, the mean is 120 and the standard deviation is 10. To find the score located 2 standard deviations below the mean, subtract 2 standard deviations from the mean. This means the score is 120 - 20 = 100.
In general, the formula for calculating the score located x standard deviations away from the mean is:
Score = Mean + (x * Standard Deviation)
For example, to find the score located 4 standard deviations away from the mean, the formula is:
Score = Mean + (4 * Standard Deviation)
In this example, the score is 120 + (4 * 10) = 160.
In summary, to find the score located x standard deviations away from the mean, use the formula:
Score = Mean + (x * Standard Deviation)
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No notes. No Book. No Phone. No Ipad
Calculator allowed. Homework allowed
Quiz 6.1
1) Which expression is equivalent to 83
√834
5
√835
a.
b.
4
c. (√83) 5
d. (√83)*
2) Which expression is equivalent to V30'
a. 307
7
b. 305
c. 304
d. 3021
6) Write (b) as a radical expression.
Simplify completely.
Name:
Block:
3) Write x¹/5 in radical form.
Date:
Guinn
4) Write √45 in rational exponent form.
5) What is the value of n if va = a"?
7) Write √-64x as a rational exponent.
Simplify completely.
Part B:
How many times faster (round to the nearest tenth)?
8) The power function H(m) = 240m models an animal's approximate resting heard rate H
(in beats per minute) given its mass m (in kilograms). Consider a gorilla with a mass of 200
kilograms and a chimpanzee with a mass of 50 kilograms.
Part A:
Which animal has a faster heart rate when resting (Show all work)?
The gorilla has a heart rate that is four times faster than the chimpanzee's when they are resting.
What is expression in math?Expression in math is a combination of numbers, variables, operations and/or symbols that represent a value, quantity or an equation. It can either be a single term, or several terms connected by mathematical operations such as addition, subtraction, multiplication and division. Expressions are typically used in equations, formulas and problems to help solve them.
To calculate the heart rate of the gorilla, we use the power function given: H(m) = 240m. Substituting in m = 200, we get H(200) = 240(200) = 48,000 beats per minute.
To calculate the heart rate of the chimpanzee, we use the same power function: H(m) = 240m. Substituting in m = 50, we get H(50) = 240(50) = 12,000 beats per minute.
Therefore, the gorilla has a heart rate that is four times faster than the chimpanzees when they are resting.
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Find the distance between points B and C on the graph.
A√5
B18
C5
D√34
E √146
The distance between points B and C on the graph is equal to: D. √34 units.
What is Pythagorean theorem?In Mathematics, Pythagorean's theorem is represented by the following mathematical expression:
c² = a² + b²
Where:
a, b, and c represent the side length of any right-angled triangle.
How to determine the distance between points B and C?In order to determine the distance between points B and C in right-angled triangle ABC, we would have to apply Pythagorean's theorem.
BC² = AB² + AC²
BC² = 5² + 3²
BC² = 25 + 9
BC² = 34
BC = √34 units.
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Determine the domain of the following graph:
Answer:
domain is [-11 , -3]
Step-by-step explanation:
domain is x
range is y
x values are from -11 to -3
during a typical friday, the west end donut shop serves 2400 customers during the 10 hours it is open. each customer spends (on average) 5-minutes in the shop. on average, how many customers are in the shop simultaneously?
The average number of customers in the West End Donut Shop simultaneously is 30, which is obtained by using the arrival rate and service rate formulas for a queueing system.
To find the average number of customers in the shop simultaneously, we can use the concept of the arrival rate and the service rate.
The arrival rate is the rate at which customers arrive at the shop, and can be calculated as:
arrival rate = number of customers / time
arrival rate = 2400 customers / 10 hours
arrival rate = 240 customers per hour
The service rate is the rate at which customers are served by the shop, and can be calculated as:
service rate = 60 minutes / 5 minutes per customer
service rate = 12 customers per hour
Using the formula for the average number of customers in a queueing system, we get:
average number of customers = arrival rate / (service rate - arrival rate)
average number of customers = 240 / (12 - 240/60)
average number of customers = 240 / 8
average number of customers = 30
Therefore, on average, there are 30 customers in the West End Donut Shop simultaneously.
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Russia has
23,400 miles
of what?
A. continuous coast
lines
B. continuous
highways
C. continuous
mountain ranges
identify three strategies that the federal government could implement to encourage the use of bevs. assume that the fuel efficiency of the ice vehicle is 235 miles per gallon and that gasoline costs $3.75 per gallon.calculate the cost of gasoline per mile.
Three strategies that implement to encourage the use of BEVs are incentives, Infrastructure and Regulations. The cost of gasoline per mile for an ICE vehicle is $0.016 per mile.
Incentives: The federal government could offer financial incentives such as tax credits, rebates, or grants to consumers who purchase BEVs. This would make BEVs more affordable and help to offset the higher upfront cost of these vehicles.
Infrastructure development: The federal government could invest in the development of charging infrastructure for BEVs, such as public charging stations. This would help to alleviate range anxiety and make BEVs more convenient and practical for consumers.
Regulations: The federal government could implement regulations that incentivize or require automakers to produce more BEVs. This could include emissions standards that are more favorable to BEVs, or mandates for automakers to produce a certain percentage of their vehicles as electric.
To calculate the cost of gasoline per mile for an ICE vehicle with fuel efficiency of 235 miles per gallon and gasoline cost of $3.75 per gallon, we divide the cost of gasoline by the fuel efficiency:
Cost per mile = $3.75 / 235 miles per gallon
Cost per mile = $0.016 per mile
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0.5878. Find the measure of angle B, in degrees, for
Let cos 54° =
sin B = 0.5878.
simplify 4+5(3x - 2) - 3x
Answer:
12x - 6
Step-by-step explanation:
[tex] \rm \: 4 + 5(3x - 2) - 3x[/tex]
[tex] \rm \: = 4 + 15x - 10 - 3x \: \sf (distribute \: the \: 5)[/tex]
[tex] \rm= 12x - 6 \: \sf (combine \: like \: terms)[/tex]
[tex] \rm= 6(2x - 1) \: \sf (factor \: out \: a \: 6)[/tex]
[tex] \rm \: = 6(2x) - 6(1) \: \sf (distribute \: the \: 6)[/tex]
[tex] \rm \:= 12x - 6 \: \sf (simplify)[/tex]
students who study for 7 hours over the course of a week (spaced learning) will perform better than students who cram for 7 hours the night before the exam. the independent variable in this hypothesis is:
The independent variable in this hypothesis is the method of studying, specifically whether students engage in spaced learning or cramming.
In the hypothesis that students who study for 7 hours over the course of a week using spaced learning will perform better than students who cram for 7 hours the night before the exam, the independent variable is the method of studying.
This variable is independent because it is being manipulated and controlled by the researcher. In this case, the researcher is comparing two different methods of studying and measuring the effect on exam performance.
Spaced learning involves breaking up the study time into smaller, more manageable chunks over a period of time, such as a week. Cramming, on the other hand, involves trying to learn all the material in a short period of time, such as the night before the exam.
The dependent variable in this hypothesis is exam performance, which is expected to be better for students who engage in spaced learning compared to those who cram.
The hypothesis suggests that the method of studying has a causal relationship with exam performance, but it is the independent variable, the method of studying, that is being manipulated to test this hypothesis.
Therefore the independent variable in the hypothesis that students who study for 7 hours over the course of a week using spaced learning will perform better than students who cram for 7 hours the night before the exam is the method of studying, specifically whether the student engages in spaced learning or cramming.
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10 points question at position 1 samples of rejuvenated mitochondria are mutated (defective) with a probability 0.15. find the probability that at most one sample is mutated in 10 samples
The probability that at most one sample is mutated in 10 samples is 0.746.
To calculate this probability, we use the binomial distribution formula.
The binomial distribution formula is used to calculate the probability of a certain number of successes (in this case, samples that are mutated) in a certain number of trials (10 samples). We need to find the probability of 1 success or fewer in 10 trials.
This is equal to P(x<=1) = 1 - P(x>1), where x is the number of successes.
For this calculation, we need the following parameters: n = 10 (number of trials), p = 0.15 (probability of a single sample being mutated), and x = 1 (number of successes). So, P(x<=1) = 1 - P(x>1) = 1 - P(x = 2) - P(x = 3) - P(x = 4) - P(x = 5) - P(x = 6) - P(x = 7) - P(x = 8) - P(x = 9) - P(x = 10).
The probability of at most one sample being mutated in 10 samples is calculated by adding the individual probabilities of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 samples being mutated, which equals 0.746.
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Can someone explain this correctly to me?
Answer:
2.80
Step-by-step explanation:
It asks to find the shipping and handling price.
The first step is take that percentage, 20% and convert into decimal form. Then you need to multiply that by the original price. So it would be 0.2 x 14.
That gives you 2.80 which is the shipping and handling price. That's all you have to do.
if you have $11 and save $5 each week how much money you will have after 6 weeks
Answer: 41$
Step-by-step explanation:
This is because 5x6=30 (To find how much money is made)
then 11+30=41 (add both amounts)
Identify the factors of 9x² +49y²
A. prime
B. (3x + 7y)(3x - 7y)
C. (3x - 7y)(3x - 7y)
D. (3x + 7y)(3x + 7y)
Step-by-step explanation:
The factors of 9x² +49y² are:
D. (3x + 7y)(3x + 7y) and C. (3x - 7y)(3x - 7y)
We can use the identity:
a² + b² = (a + b)(a - b)
To factor the expression 9x² + 49y², let a = 3x and b = 7y. Then we have:
9x² + 49y² = (3x)² + (7y)² = (3x + 7y)(3x - 7y)
So the factors of 9x² + 49y² are (3x + 7y) and (3x - 7y). We can see that these factors are not prime, as they can be factored further into (3x + 7y)(3x + 7y) and (3x - 7y)(3x - 7y).
pleas help meeeeee thank
you
Answer:
angle "E" =70°
Step-by-step explanation:
<ABC=<ADC
<ADC=<EAD (alternate angles)
<EAD=<DEA (because /DA/=/DE/
and <DEA=angle E, therefore answer=70°
a cargo ship carries only 5-ton trucks and 12-ton trucks. for each shipment, the cargo ship must carry at least 750 trucks and the total weight of the trucks can be at most 5,000 tons. what is the maximum number of 12-ton trucks that the cargo ship can carry per trip?
The maximum number of 12-ton trucks that the cargo ship can carry per trip is 750. This is obtained by solving the linear programming problem subject to the given constraints.
Let's denote the number of 5-ton trucks and 12-ton trucks that the cargo ship carries by x and y, respectively. Then, we can write the following two constraints based on the requirements.
x + y ≥ 750 (constraint 1: the ship must carry at least 750 trucks)
5x + 12y ≤ 5000 (constraint 2: the total weight of the trucks can be at most 5,000 tons)
We want to maximize the number of 12-ton trucks y, subject to these two constraints.
To solve this problem, we can use linear programming techniques.
The feasible region is the set of all (x,y) pairs that satisfy the two constraints
The feasible region is bounded by the x-axis, the y-axis, and the two lines 5x + 12y = 5000 and x + y = 750.
We want to find the point in the feasible region where the number of 12-ton trucks y is maximized. This point will lie on one of the corners of the feasible region.
We can calculate the coordinates of the corners of the feasible region by solving the system of equations formed by the two constraint lines:
x + y = 750 (equation 1)
5x + 12y = 5000 (equation 2)
Multiplying equation 1 by 5, we get:
5x + 5y = 3750 (equation 3)
Subtracting equation 1 from equation 2, we get:
7y = 1250
y = 178.57 (rounded to 2 decimal places)
Substituting this value of y into equation 1, we get:
x = 571.43 (rounded to 2 decimal places)
The coordinates of this corner point are (571.43, 178.57).
Similarly, we can calculate the coordinates of the other corner points:
(750, 0), (500, 250), and (0, 750)
We can now evaluate the objective function (the number of 12-ton trucks y) at each of these corner points:
At (571.43, 178.57), y = 178.57
At (750, 0), y = 0
At (500, 250), y = 250
At (0, 750), y = 750
The maximum value of y is 750, which occurs at the point (0, 750).
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PLEASE HELP!!
Write a function that represents the situation: A population of 5 fruit flies increases by 12.5% each day.
P(t) = 5(1 + 0.125)^t
where P(t) is the population of fruit flies after t days.
4x-1 4x+1 11 813 4x+1 8 4x-1-3
Answer: x = squrt (1/20
Step-by-step explanation:
The sum of a number and 12 squared
Answer:
x = the unknown number. Its square is x2. The sum of a number and its square is 12:
x + x²= 12
Putting the quadratic into standard form:
x2 + x - 12 = 0
(x+4)(x-3) = 0
x = -4 and 3
Let's check x=-4:
x + x2 = 12
(-4) + (-4)2 = 12
-4 + 16 = 12
12 = 12
Now let's check x= 3:
x + x2 = 12
3 + 32 = 12
3 + 9 = 12
12 = 12
Yup, they both work. There are two answers, x = -4 and x = 3
the goal of the calculating an acceptance interval is to: a. find the probability that the true mean lies between two values. b. determine a range within which sample means are likely to occur, given a population mean and variance. c. determine a range within which no sample means would occur, given a population mean and variance. d. none of the above.
The goal of calculating an acceptance interval is to find the probability that the true mean lies between two values, hence the correct answer is option a.
The acceptance interval is a method for developing a tolerance interval for a specified percentage of future measurements in a distribution. The tolerance interval specifies the interval into which a specified percentage of future measurements will fall.
An acceptance interval is a quality control tool for assessing whether the characteristics of a production lot meet predetermined quality criteria. These predetermined criteria are usually in the form of upper and lower limits for the interval.
The acceptance interval is utilized to detect whether a production lot's results are within the tolerances or specifications of the quality criteria.
The purpose of calculating an acceptance interval is to locate the probability that the true mean falls between two values. In conclusion, the goal of calculating an acceptance interval is to find the probability that the true mean lies between two values.
Therefore, option a is the correct answer.
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Which expression is equivalent to
-5
28p9q5
12pq
7 ? Assume P≠0,q≠0.
The expression -5 + 28p9q5 - 12pq + 7 is equivalent to 7. Since all the terms except the last one contain variables, we can use algebra to solve for the value of the expression.
What is algebra?Algebra is a branch of mathematics which deals with the manipulation of equations, inequalities, and other mathematical expressions. Algebra is used to solve equations, simplify expressions, and model real-world problems.
To begin, we can add -5 and 7 to obtain 2. This means that the expression is now equal to 2 + 28p9q5 - 12pq. We can then simplify this expression by combining like terms.
Since 28p9q5 and -12pq are both products of the same variables, we can add them together. When we do so, we obtain 16p9q5, which means that the expression is now equal to 2 + 16p9q5.
Finally, we can simplify the remaining term by breaking down the product. We can divide 16 by 8 to obtain 2, and then divide 9 by 3 to obtain 3. This means that the expression is now equal to 2 + 2p3q5. Since there are no more terms to simplify, we can conclude that the answer is 2.
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