(L7) A Pythagorean Triple is a set of three nonzero positive _____ numbers, a,b, and c, such that a²+b²=c².

The percentage strength of neomycin in the final compounded product is approximately 2.5%.

To determine the percentage strength of neomycin in the final compounded product, we need to calculate the weight of neomycin in the cream and divide it by the total weight of the cream.

Neomycin (5%) cream: 30g

The neomycin content is 5% of the total cream weight. To find the weight of neomycin in the cream, we multiply the cream weight by the neomycin percentage:

Weight of neomycin = 30g × 0.05 = 1.5g

Now, to calculate the percentage strength of neomycin in the final compounded product, we divide the weight of neomycin by the total weight of the cream and multiply by 100:

Percentage strength of neomycin = (Weight of neomycin / Total weight of cream) × 100

Percentage strength of neomycin = (1.5g / 60g) × 100 ≈ 2.5

Therefore, the percentage strength of neomycin in the final compounded product is approximately 2.5%.

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Answer:

Exponential functions are patterns that get continuously multiplied by some number. It's exponential growth when the base of our exponential is bigger than 1, which means those numbers get bigger. It's exponential decay when the base of our exponential is in between 1 and 0 and those numbers get smaller.

Step-by-step explanation:

Answer:

exponential growth

Step-by-step explanation:

Answer:

7 of 100 parts have been shaded, and 7 hundredths is written as 0.07

Step-by-step explanation:

Note that we have a grid of 100 squares and 7 of those squares are shaded. We can represent the shaded portion by saying 7/100 which is equivalent to .07.

With this information, we can say 7 out of 100 is shaded and is representative of 7 hundredths.

Note that each digit after the decimal is a multiple of (1/10). We can express this as (1/10)^n where n is the digit place after the decimal.

In this case, we have 7, two digits after the decimal so it will be equivalent to 7 * (1/10)^2 = 7 * (1/100) = 7/100.

Cheers.

Answer:

-3

Step-by-step explanation:

3x +7 =f(x+1)

3x +7=x+1

3x-x=-7+1

2x=-6

-3

The student's claim is incorrect because , ( x + 9 ) ( x - 9 ) = x² - 81 , therefore the right side of the equation does not equal to the left side of the equation

Given data ,

Let the polynomial equation be represented as A

Now , the value of A is

A = ( x + 9 ) ( x - 9 )

On simplifying , we get

A = ( x + 9 ) ( x ) - ( x + 9 ) ( -9 )

A = x² + 9x - 9x - 81

On further simplification , we get

A = x² - 81

Hence , the equation is solved and A = x² - 81

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Background:

"As much as" means that two quantities are being compared and is a keyword for division.

Procedure:

Answer: 2

The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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The functions covariance.p and covariance.s return different values because they use different formulas for calculating the covariance.

Covariance is a measure of how two variables are related to each other, and it is used to understand the linear relationship between two variables. The formula for calculating covariance depends on the type of data being analyzed. The covariance.p function calculates population covariance, while covariance.s calculates sample covariance.

The formula for population covariance uses N in the denominator, while the formula for sample covariance uses N-1 in the denominator. This is because the sample covariance formula is an unbiased estimator of the population covariance, and using N-1 instead of N corrects for the bias.

Therefore, the two functions return different values even when using the same data because they are calculating different types of covariance using different formulas.

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Answer:h=3/2

Step-by-step explanation:

-2h=-3

h=3/2 it changes to plus because two minus’s equal a plus

1. Althea needs 5.75 pounds and 12 ounces of cold cuts.

2.  Isabella's flight lasts 205 minutes.

3. Liam visited Europe for 1176 hours.

The following are the solutions to the given problems according to their respective terminologies:

1. Althea needs 92 ounces of cold cuts for a party.  The formula for converting ounces to pounds is: Pounds = Ounces ÷ 16 (There are 16 ounces in 1 pound.)

So, Pounds = 92 ÷ 16 = 5.75 pounds

To convert the remaining ounces from the above calculation into ounces again, use the following formula:

Ounces = Total ounces - (Pounds x 16)Therefore, Ounces = 92 - (5.75 x 16) = 12 ounces

Therefore, Althea needs 5.75 pounds and 12 ounces of cold cuts.

2. Isabella is on a flight that lasts 3 hours and 25 minutes.

To convert hours to minutes, multiply the given number of hours by 60. Then add any remaining minutes.

Therefore, the flight duration in minutes is:3 hours and 25 minutes = (3 x 60) + 25 = 205 minutes

Therefore, Isabella's flight lasts 205 minutes.

3. Mateo needs 88 cups of juice to make punch. The formula for converting cups to gallons is:

Gallons = Cups ÷ 16 (There are 16 cups in 1 gallon.)

Therefore, Gallons = 88 ÷ 16 = 5.5 gallons

Therefore, Mateo needs 5.5 gallons of juice.4. Liam visited Europe for 7 weeks.

The formula for converting weeks to hours is: Hours = Weeks x 7 x 24

Therefore, Hours = 7 x 7 x 24 = 1176 hours

Therefore, Liam visited Europe for 1176 hours.

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Given data:

Total packs 3x3 sticky notes: 24 packs

Cost of 24 packs: 28.99

Number of sticky notes in a pack: 100

With the information above, we can proceed to find the answers to the questions

Part A: What is the price for each pack?

Since 24 packs cost 28.99

Then 1 pack will cost =

Hence, a pack will cost $1.21

Part B: How much is every single sticky note?

Since each pack cost 1.21, and each pack has 100 sticky notes, then

each sticky note will cost

=> every single sticky note will cost $0.012

Revenue (R(x)) = -2x^2 + 30x, Profit (P(x)) = -2.5x + 30, Average Cost (AverageCost(x)) = 0.5x + 30, ROC(x) = -5, and x(p) = (30-p)/2.

Given the price function p(x) = -2x + 30 and the cost function C(x) = 0.5x + 30, we can calculate the revenue (R(x)), profit (P(x)), average cost (AverageCost(x)), return on cost (ROC(x)), and the demand function (x(p)).

The revenue (R(x)) is obtained by multiplying the price function p(x) by the quantity x: R(x) = p(x) * x = (-2x + 30) * x = -2x^2 + 30x.

The profit (P(x)) is calculated by subtracting the cost function C(x) from the revenue (R(x)): P(x) = R(x) - C(x) = (-2x^2 + 30x) - (0.5x + 30) = -2.5x + 30.

The average cost (AverageCost(x)) is the cost function C(x) divided by the quantity x: AverageCost(x) = C(x) / x = (0.5x + 30) / x = 0.5 + (30 / x).

The return on cost (ROC(x)) is the profit (P(x)) divided by the cost function C(x): ROC(x) = P(x) / C(x) = (-2.5x + 30) / (0.5x + 30) = -5.

The demand function (x(p)) represents the quantity demanded (x) given the price (p): x(p) = (30 - p) / 2.

These calculations provide the values for revenue, profit, average cost, return on cost, and the demand function based on the given price and cost functions.

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Answer:

Step-by-step explanation:

30% of 499 is 149.70

499+149.70=648.70

Answer:

quadrant 1 - (2,4)

quadrant 2 - (-3,4)

quadrant 3 - (-1, -5)

quadrant 4 - (6, -1)

Step-by-step explanation:

quadrant one consists of both x and y being positive.

quadrant two being the x is negative but the y is negative.

quadrant 3 has its x and y both negative.

finally, quadrant 4 has its x positive, but y is negative.

Answer:1700

Step-by-step explanation:

In total, he traveled 1700 feet. He had to get to the 250ft starting point somehow, so you would count that as the overall total distance traveled.

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

A. The triangles are congruent by SAS.

Step-by-step explanation:

Two sides of one triangle are congruent to two sides of the other triangle. The included angles of the two triangles are congruent.

The triangles are congruent by SAS.

Answer:

1539 ft^3

Step-by-step explanation:

3.5×3.5=12.25

12.25×3.14=38.465

38.465×40=1,538.6

1538.6 rounded to the nearest whole number is 1539.

The line is positive

The line is positive because it slants to the right.

It wouldve been negative if it slanted to the left.

Answer:

The slope is positive.

Step-by-step explanation:

With the line crossing over at -7 on the x-axis and 10 crossing over on the y-axis, you're able to form the two points. (-7, 0) & (0, 10).
0 - -7 = 7 & 10 - 0 = 10, so you get 10/7

The slope will be y = 10/7x + 10, therefore it's positive.

  The equation for a line that is perpendicular to \(z = -5z + 2\) and passes through the point (-10, 2) can be found. The equation is \(z = \frac{1}{5}y + \frac{3}{2}\).

To find the equation of a line perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line \(z = -5z + 2\) can be rewritten as \(y = -5z + 2\).
The slope of the given line is -5. The negative reciprocal of -5 is \(\frac{1}{5}\), which will be the slope of the perpendicular line.
Now, we can use the point-slope form of a linear equation, where \((x_1, y_1)\) is a point on the line and m is the slope. Plugging in the values \((-10, 2)\) for \((x_1, y_1)\) and \(\frac{1}{5}\) for m, we have:
\(z - 2 = \frac{1}{5}(y + 10)\)
To simplify the equation, we can multiply both sides by 5 to eliminate the fraction:
\(5z - 10 = y + 10\)
Rearranging the equation, we obtain:
(y = 5z - 20)
Therefore, the equation of the line perpendicular to (z = -5z + 2) and passing through the point (-10, 2) is (y = 5z - 20).

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Answer:

240

Step-by-step explanation:

24, 48, 72, 96, 120, 144,168, 192, 216, 240

80, 160, 240

Answer:

240

Step-by-step explanation:

multiples of

24= 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264,...

80= 80, 160, 240, 320,...

The lowest common multiple is 240

To determine where g has a local maximum, we need to find the critical points of g'(x) and analyze the sign changes around those points.

Here's a step-by-step explanation:
1. Identify the critical points of g'(x) by setting it equal to 0:
g'(x) = x(x - 5)(x + 1)^4 = 0
The critical points are x = -1, x = 0, and x = 5.

2. Determine the sign of g'(x) around the critical points:
For x < -1, g'(x) > 0 (since there are three negative factors)
For -1 < x < 0, g'(x) > 0 (since there are two negative factors)
For 0 < x < 5, g'(x) < 0 (since there is one negative factor)
For x > 5, g'(x) > 0 (since all factors are positive)

3. Analyze the sign changes and apply the First Derivative Test:
- At x = -1, there is no sign change, so it is not a local maximum.
- At x = 0, g'(x) changes from positive to negative, indicating a local maximum.
- At x = 5, there is no sign change, so it is not a local maximum.

So, g has a local maximum at x = 0 only. The correct answer is (c).

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The function f(x) = 2x2 - x + 2 is continuous at x = 2, the correct option is C. Yes, because the function is defined at x = 2 and approaches y = 8 on the left and right sides of x = 2.

A continuous function is a type of function in mathematics that has no abrupt changes or breaks in its graph. It is a function where the values change smoothly as the input values vary. In other words, a function is continuous if its graph can be drawn without lifting the pen from the paper.

Given the function f(x) = 2x² - x + 2.

Determine whether the function is continuous at x = 2.

Explanation: For a function to be continuous at x = a, it must satisfy the following conditions:

1. The function must be defined at x = a.

2. The limit of the function at x = a must exist.

3. The limit of the function at x = a must be equal to the value of the function at x = a.

Let us verify these conditions for the given function

f(x) = 2x² - x + 2 at x = 2.

1. The function is defined at x = 2.

2. We need to calculate the left-hand limit and the right-hand limit of the function as x approaches 2.

Let us first calculate the left-hand limit:

lim f(x) as x → 2- = lim (2x² - x + 2)

as x → 2- = 2(2)² - 2 + 2

= 6

Now, let us calculate the right-hand limit:

lim f(x) as x → 2+ = lim (2x² - x + 2)

as x → 2+ = 2(2)² - 2 + 2

= 6

Since both the left-hand limit and the right-hand limit of the function exist and are equal to 6, the limit of the function at x = 2 exists and is equal to 6.

3. We need to verify whether the limit of the function at x = 2 is equal to the value of the function at x = 2.

Let us calculate the value of the function at x = 2:

f(2) = 2(2)² - 2 + 2

= 8

Since the limit of the function at x = 2 is equal to the value of the function at x = 2,

we can say that the given function f(x) = 2x² - x + 2 is continuous at x = 2.

Thus, the correct option is C.

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Time-series plots are used for several reasons:

B. Time-series plots are used to identify any outliers in the data.

C. Time-series plots are used to identify trends in the data over time.

D. Time-series plots are used to present the relative frequency of the data in each interval or category.

First, we need to know that quantitative variable is required when drawing a time-series plot.

We need to also know that data points are graphically represented as time-series plots, with the variable of interest drawn on the y-axis and time commonly depicted on the x-axis. They demonstrate the variable's evolution over time.

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The simple reason why streets are usually designed parallel or perpendicular to each other is because that pattern makes it easy for users to connect people easily.

A perpendicular street can simply be defined as a street which intersect another streets. However, on the other end, two streets are said to be parallel to each other when they are in the same distance apart. The same is applicable in mathematics as a perpendicular line intercept another line and parallel lines don't meet.

That being said, when streets are parallel or perpendicularly designed, residents of the environment find it easy to communicate with each other. Business owners use this easy accessibility to easily describe their addresses to customers.

So therefore, it can be deduced from the given explanation above that when streets are designed with good planning, it makes people access it easily.

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Answer:

.

Step-by-step explanation:

.

Answer:

\(4 \frac{1}{2} \)

Step-by-step explanation:

Let's find the value of x first.

From the first sentence:

4x +13= 8

Subtract 13 from both sides:

4x= 8 -13

4x= -5

\(x = - \frac{5}{4} \)

\(x = - 1 \frac{1}{4} \)

2 times x is added to 7 → 2x +7

2x +7

\(= 2( - \frac{5}{4} ) + 7 \)

\( = - \frac{5}{2} + 7\)

\( = 4 \frac{1}{2} \)

Following are the correct match for each pair of statements.

What is statement?

In mathematics, a statement is a declarative sentence that can be either true or false, but not both.

#1

1.Selective Service - America's military draft

2.Nationalism - loyalty to one's own country

3.Monroe Doctrine - forbade European intervention in the Western Hemisphere

4.Spanish-American War - fight for Cuban independence

5.Big Stick Policy - America's defense of the Monroe Doctrine under Roosevelt

6.Boxer Rebellion - Chinese revolt against foreigners

7.Square Deal - Roosevelt's fair treatment of the common man

#2

1.Prohibition - ban on liquor sales

2.League of Nations - Wilson's peace proposal

3.Disarmament - limit on military equipment

4.Urbanization - mass movement to the city

5.New Deal - Roosevelt's Depression recovery plan

6.Treaty of Versailles - peace ending World War I

7.Fourteen Points - group for the peaceful settlement of world problems

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On factorizing each equation we get

a) x² + 6x + 9 =  (x + 3) (x + 3)  

b) x² - 6x + 8 = (x - 4) (x - 2)  

c) x² - 4x - 32 = (x - 8) (x + 4)  

d) x² + x - 42 = (x + 7) (x - 6)  

Factorization is the process of finding the factors of an expression or number. In algebra, factorization involves expressing an algebraic expression as a product of its factors.  

To factorize the following split the middle term and group out the common factors as given below.

Here we have four equations that can be factorized as follows

a) x² + 6x + 9  

=> x² +3x + 3x + 9         [ Split middles term ]

=> x(x + 3) +3(x + 3)      [ Grouping the terms ]

=> (x + 3) (x + 3)  

∴  a) x² + 6x + 9 =  (x + 3) (x + 3)  

b) x² - 6x + 8

=> x² - 4x - 2x + 8               [ Split middles term ]

=> x(x - 4) -2(x - 4)              [ Grouping the terms ]  

=> (x - 4) (x - 2)

∴ x² - 6x + 8 = (x - 4) (x - 2)  

c) x² - 4x - 32  

=> x² - 8x + 4x - 32         [ Split middles term ]  

=> x(x - 8) + 4(x - 8)         [ Grouping the terms ]    

=> (x - 8) (x + 4)

∴ x² - 4x - 32 = (x - 8) (x + 4)  

d) x² + x - 42  

=> x² + 7x - 6x - 42             [ Split middles term ]  

=> x(x + 7) - 6(x + 7)            [ Grouping the terms ]    

=> (x + 7) (x - 6)

∴ x² + x - 42 = (x + 7) (x - 6)  

Therefore,

On factorizing each equation we get

a) x² + 6x + 9 =  (x + 3) (x + 3)  

b) x² - 6x + 8 = (x - 4) (x - 2)  

c) x² - 4x - 32 = (x - 8) (x + 4)  

d) x² + x - 42 = (x + 7) (x - 6)  

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Answer:

The percentage of decrease 37.5%

Step-by-step explanation:

80-50=30

30*100 / 80$ = 37.5%

Answer:

37.5

Step-by-step explanation:

I took a test and that was the right answer