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The actual distance between the two cities is given as follows:

17 miles.

The actual distance between the two cities is obtained applying the proportions in the context of the problem.

The scale factor is given as follows:

1 inch = 17 miles.

The length of the drawing is given as follows:

1 inch.

Hence the actual distance between the two cities is given as follows:

1 x 17 = 17 miles.

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The graph of f(x) = (x - 1)/(4(x - 4)) is plotted to represent f(x) = (x - 1)/(4x - 16)

From the question, we have the following parameters that can be used in our computation:

f(x) = (x - 1)/(4x - 16)

Factor out 4 from the denominator

So, we have

f(x) = (x - 1)/(4(x - 4))

This means that

f(x) = (x - 1)/(4(x - 4)) is equivalent to f(x) = (x - 1)/(4x - 16)

So, we can plot the graph of f(x) = (x - 1)/(4(x - 4)) to represent f(x) = (x - 1)/(4x - 16)

See attachment for the graph

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The part of a pyramid include the following: E. lateral faces.

In Mathematics and Geometry, the volume of a pyramid can be calculated by using the following formula:

Volume = 1/3 × b × h

Where:

Generally speaking, a pyramid is composed of three main parts and these include the following:

In conclusion, we can reasonably infer and logically deduce that lateral face is a part of any pyramid.

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To find the length of a row of bookshelves, we can use the square root function, as the length of a row of bookshelves will be proportional to the square root of the area of the space that Isabel rents.

Mathematically, we can express f(x) as: f(x) = √(x)

Where x represents the area of the space that Isabel rents, and f(x) represents the total length of a row of bookshelves.

The above function takes the square root of the area x, which gives us the length of a row of bookshelves in feet, assuming that the area is in square feet. As x increases, f(x) will also increase, indicating that the length of the row of bookshelves will also increase as Isabel rents a larger area in the warehouse.

To find the length of a row of bookshelves, we can use the square root function, denoted as √(x), where x represents the area of the space that Isabel rents.

For example, if Isabel rents an area of 324 square feet, we can find the length of a row of bookshelves as follows:

x = 324

f(x) = √(x) = √(324) = 18

So, the length of a row of bookshelves would be 18 feet in this case.

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Part 2: Solve a real-world problem using a square root function.

When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square.

The total length of each row of bookshelves will be of the length of the storage space.

Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves? (3 points)

Write a function that expresses f(x). (10 points)

Using the average daily balance, the total balance on the next billing date, April 1 is $5,059.73.

The average daily balance is a credit card method of computing finance charges.

To determine the average daily balance, the sum of the daily balances over your billing cycle is divided by the number of days in the billing cycle.

The finance charge is then the product of the average daily balance multiplied by the APR and the number of days involved, divided by 365 days.

Average daily balance = $1,900

Unpaid balance at month-end = $1,700

APR = 32.4%

The finance charge for the month = $9.73 ($1900 x 32.4% x 30/365)

The total balance on the next billing date, April 1 = $5,059.73 ($5,050 + $9.73)

Thus, on April 1, the next billing cycle, the balance on the card is $5,059.73.

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Answer:

Step-by-step explanation:

(a) π/4

(b) 0

(c) 1

(d) 1

(e) 2/3

(f) 1/2

Answer:

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively. We are given that the volume of the pan is 252 cubic inches, the length is 12 inches, and the width is 10-1/2 inches.

So, 252 = 12 x 10.5 x h

Simplifying the right side of the equation, we get:

252 = 126h

Dividing both sides by 126, we get:

h = 2

Therefore, the height of the pan is 2 inches.

Answer:

(-6,3)

Step-by-step explanation:

reflect over x=2, so you. move Y up by 2. 1+2 =3

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

[tex]\stackrel{f(x)}{y}~~ = ~~x^3+9\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~y^3+9} \\\\\\ x-9=y^3\implies \sqrt[3]{x-9}=y=f^{-1}(x)[/tex]

Answer choice C is correct. That is the total population of wild hogs in that particular area is 100.

Total population in an area refers to the number of individuals of a particular species or group living in a specific geographical region or habitat. This can include both visible and hidden individuals, such as animals that are difficult to spot or track. Total population is an important measure for conservation and management efforts, as it helps determine the size of a population and whether it is growing or declining.

Given that 20 wild hogs were tagged and later they saw 8 tagged wild hogs out of 40 recaptured wild hogs. We need to find the total population of wild hogs in that area.

From the given information we can see,

(Number of hogs tagged) / (Total population) = (Number of tagged hogs recaptured) / (Number of hogs recaptured)

⇒ 20 / x = 8 / 40

⇒ 8x = 20 × 40

⇒ 8x = 800

⇒ x = 100

Therefore, the wildlife group can estimate that the total population of wild hogs in the area is 100.

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Answer:

152 teenagers attended the game.

Step-by-step explanation:

Write the formula:

4% of 3800 people = total teens

Evaluate:

4/100 x 3800

Calculate:

4 x 38

= 152 teens

Answer:

Step-by-step explanation:

The polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be formed as follows:

Since the zero 6 has a multiplicity of 2, it appears twice in the factored form of f(x), i.e., (x-6)(x-6) = (x-6)^2.

The other zero is 3i, which means its complex conjugate, -3i, is also a zero. Therefore, the factored form of f(x) can be written as:

(x-6)^2(x-3i)(x+3i)

Expanding this expression, we get:

f(x) = (x-6)^2(x^2 + 9)

Multiplying this out, we get:

f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324

Therefore, the polynomial f(x) with real coefficients, degree 4, and zeros 6 (multiplicity 2), 3i can be written as:

f(x) = x^4 - 12x^3 + 81x^2 - 216x + 324.

If Scott planted 20% of a garden with roses then the area of

the section of the garden that is planted with roses is 10 square feet

The garder is in rectangle shape

We have to find the area of the garden

The length of the garden is 10 ft and width of garden is 5 ft

Area of garden = 10×5

=50 square feet

Now  Scott planted 20% of a garden with roses

Convert 20% to decimal by dividing 20 by 100

Area of garden which has roses = 50×0.2

=10 square feet

Hence, if Scott planted 20% of a garden with roses then the area of

the section of the garden that is planted with roses is 10 square feet

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Answer:

Impossible to know, or best guess

Step-by-step explanation:

It is impossible to determine exactly how many bucket loads it would take to empty the world's ocean because the volume of the ocean is constantly changing due to factors such as tides, currents, and sea level rise. However, we can estimate the approximate volume of the ocean and calculate the number of bucket loads needed based on that estimate.

The approximate volume of the world's ocean is 1.332 billion cubic kilometers (km³) or 332.5 million cubic miles (mi³). Assuming that each bucket can hold 10 liters or 0.01 cubic meters (m³) of water, we can calculate the number of bucket loads needed to empty the ocean as follows:

1 km³ = 1,000,000,000 m³

1,332,000,000 km³ = 1.332 x 10¹⁸ m³

1.332 x 10¹⁸ m³ / 0.01 m³ per bucket = 1.332 x 10²⁰ bucket loads

Therefore, it would take approximately 1.332 x 10²⁰ or 133,200,000,000,000,000,000 bucket loads to empty the world's ocean. This number is so large that it is practically impossible to even visualize, let alone accomplish.

Another answer provided by our lord and savior (That one green ai)

There were 24 students working in area B in the morning, and 3 times as many, or 72 students, working in area A. The total number of students is then 24 + 72 = 96.

In geometry, an area is the measurement of the amount of space inside a two-dimensional flat surface such as a square, rectangle, triangle, circle, or any other shape. It is usually expressed in square units, such as square centimeters (cm²) or square meters (m²), and is calculated by multiplying the length and width of a rectangular shape or by using specific formulas for different geometric shapes such as the base times the height divided by 2 for a triangle or pi times the radius squared for a circle. The concept of area is fundamental in many branches of mathematics, physics, engineering, and other fields where the measurement of the extent of a surface is important.

Let's assume that the number of students working in area b is x. Then the number of students working in area A is 3x (since there are three times as many students working in area A as in area b in the morning).

Let A be the area of area a, and B be the area of area b. We know that A = 1.5B (since area a is 1 1 2 times the area of area b).

In the morning, the total number of students is x + 3x = 4x.

In the afternoon, 7/12 of the students work in area a, and the rest work in area b. So, the number of students working in area A in the afternoon is 7/12 * 4x = 7x/3, and the number of students working in area b is (1 - 7/12) * 4x = 5x/12.

Since area a was finished at the end of the day, we know that the total area cleaned by the students is A + B = 1.5B + B = 2.5 B. This means that the number of students working in area b is enough to finish 0.5B (since area a was already finished), but 4 more students are needed to finish the remaining 0.5B.

So, we can set up the following equation:

(5x/12) / x = 0.5 / (0.5 + 4/x)

Simplifying this equation, we get:

5x = 6x + 24

x = 24

Therefore, there were 24 students working in area b in the morning, and 3 times as many, or 72 students, working in area A. The total number of students is then 24 + 72 = 96.

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33.3/11 = 3.02727272727...

Then, rounding to the nearest hundredth means keeping only two decimal places. The third decimal place is 7, which is greater than or equal to 5, so we round the second decimal place up:

3.03

Therefore, 33.3/11 rounded to the nearest hundredth is 3.03.

Okay, let's analyze the two functions based on the options:

Function A:

X f(x)

0 5

1 10

2 20

3 40

4 80

Options:

Neither function A nor function B has an x-intercept. - False, function A has an x-intercept at x=0.

Neither function A nor function B has a y-intercept. - False, function A has a y-intercept at f(x)=5.

The domain and range of both functions contain only positive numbers. - False, function A has values that include 0.

The domain and range of both functions contain only positive numbers and zero. - True, the domain and range of both functions contain only non-negative numbers including 0.

Therefore, the correct choice is:

O The domain and range of both functions contain only positive numbers and zero.

Let me know if you have any other questions!

Step-by-step explanation:

y=mx+b

y= -5 x= 10

-5 = 2/5 (10) + b

-5 = 4 + b

b= -9

the equation of aline is y = 2/5(x) -9

or 2x = 5y + 45

15.048 deciliters is equivalent to 1 quart.

Conversion is the process of changing a quantity from one unit of measure to another unit of measure using a conversion factor or a formula.

We have:

To convert meters to feet, multiply by 3.28.

To convert liters to gallons, multiply by 0.26.

To convert kilograms to pounds, multiply by 2.20.

To convert deciliters to quarts, divide by 15.048.

Let's use these conversions to convert the given measurement:

15.048 dL = qt

Dividing both sides by 15.048, we get:

1 dL = qt/15.048

Multiplying both sides by 0.946353, which is the number of quarts in a liter, we get:

0.946353 dL = qt/15.048 * 0.946353

Simplifying the right-hand side, we get:

0.946353 dL = qt/15.961

Multiplying both sides by 3.78541, which is the number of liters in a gallon, we get:

3.78541 * 0.946353 dL = 3.78541 * qt/15.961

Simplifying the left-hand side, we get:

3.58702 L = qt/4.22676

Multiplying both sides by 4.22676, we get:

15.1485 L = qt

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Answer:

161

Step-by-step explanation:

angle 5 is supplementary to the given angle 180-1

Answer:

1/16

Step-by-step explanation:

(1/4)x(1/4)= 1/16

Answer: A is 36 cm^2

Step-by-step explanation:

The freighter is approximately 164.33 miles from the city.

We can use the Law of Cosines to solve this problem. Let's label the distances as follows:

d: distance between the city and the freighter

x: distance between the city and the island

y: distance between the island and the freighter

First, we need to find x using the given coordinates:

N23°38'W is equivalent to S23°38'E, so we have:

cos(23°38') = x/48

x = 48cos(23°38') ≈ 42.67 miles

Next, we can use the coordinates of the freighter to find y:

N11°26'E is equivalent to E11°26'N, and N12°16'W is equivalent to S12°16'E. This means that the angle between the island and the freighter is:

23°38' + 11°26' + 12°16' = 47°20'

cos(47°20') = y/d

We can rearrange this equation to solve for y:

y = dcos(47°20')

Now we can use the Law of Cosines to solve for d:

d² = x² + y² - 2xy cos(90° - 47°20')

d² = 42.67² + (d cos(47°20'))² - 2(42.67)(d cos(47°20')) sin(47°20')

d² = 1822.44 + d² cos²(47°20') - 2(42.67)(d cos(47°20')) sin(47°20')

d² - d² cos²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² (1 - cos²(47°20')) = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² sin²(47°20') = 1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')

d² = (1822.44 - 2(42.67)(d cos(47°20')) sin(47°20')) / sin²(47°20')

d ≈ 164.33 miles

Therefore, the freighter is approximately 164.33 miles from the city.

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Where the above conditions existing, the probability that a randomly selected site will have a    snow depth between 2.25 and 2.7 inches is 68.3 %.

t the value The value one standard deviation below the mean is 2.25 inches.

The  value one standard deviation above the  mean is 2.75 in.

To find the probability , calculate the z-scores for these values

z1 = (2.25  - 2.5 ) /0.25 = -1

z2= ( 2.7 -2.5 )   / 0.25 = 0.8

Using a standard normal distribution table ....

we can see that the probability of a z-  score between -1 and 0.8 is approximately 0.683, or 68.3%.

Hence,  the probability that a randomly chosen location will have a snow depth between 2.25 and 2.7 inches is 68.3%.

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Danny had the sales of total $16,000.

We have,

He earns a 2.5% commission on his first $4000 in sales.

He earns a 7.5% commission on any amount of sales beyond $4000.

Commission earned = $1000

So, 6.25% of x = 1000

6.25/10 x = 1000

0.0625x = 1000

x= 1000/ 0.0625

x= $16,000

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Danny had the sales of total $16,000.

We have,

He earns a 2.5% commission on his first $4000 in sales.

He earns a 7.5% commission on any amount of sales beyond $4000.

Commission earned = $1000

So, 6.25% of x = 1000

6.25/10 x = 1000

0.0625x = 1000

x= 1000/ 0.0625

x= $16,000

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The maximum value of the objective functions are 2600, 27 and 1980

Given that

Max Z = 8x + 16y

Where the constraints are

3x + 6y ≤ 900

x + y ≤ 200

y ≤ 125

x, y ≥ 0

Plotting the constraints 3x + 6y ≤ 900, x + y ≤ 200 and y ≤ 125 on the same graph, the coordinates of the feasible region are:

(x, y) = (100, 100), (75, 125) and (50, 125)

So, we have

Z = 8(100) + 16(100) = 2400

Z = 8(75) + 16(125) = 2600

Z = 8(50) + 16(125) = 2400

Hence, the maximum value is 2600

Given that

Max Z = 6x + 3y

Where the constraints are

2x + y ≤ 8

3x + 3y ≤ 18

y ≤ 3

x, y ≥ 0

Plotting the constraints 2x + y ≤ 8, 3x + 3y ≤ 18 and y ≤ 3 on the same graph, the coordinates of the feasible region are:

(x, y) = (3, 3), (2.5, 3) and (2, 4)

So, we have

Z = 6(3) + 3(3) = 27

Z = 6(2.5) + 3(3) = 24

Z = 6(2) + 3(4) = 24

Hence, the maximum value is 27

Given the objective function, the constraints and the final simplex tableau

We have the final values to be

Z = 1980

This means that the maximum value is 1980

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Therefore, the total volume of the two prisms is 10,404 cubic inches.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters (m³), cubic feet (ft³), or cubic centimeters (cm³). The volume of an object is calculated by multiplying its length, width, and height or by using an appropriate formula for the shape of the object.

Here,

The two prisms have the same dimensions of 17 inches in height, 18 inches in base, and 17 inches in length and width.

To find the volume of a prism, we multiply the area of the base by the height. The base of the prism is a rectangle with length 18 inches and width 17 inches, so the area of the base is:

Area of base = length × width

= 18 in × 17 in

= 306 in²

Therefore, the volume of one prism is:

Volume = area of base × height

= 306 in² × 17 in

= 5202 in³

The volume of the two prisms combined is simply twice the volume of one prism:

Total volume = 2 × 5202 in³

= 10404 in³

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Step-by-step explanation:

We can use the standard normal distribution to calculate probabilities for a normal distribution with mean 33 and standard deviation 4. We just need to standardize the intervals using the formula:

z = (x - mu) / sigma

where x is the specific value in the interval, mu is the mean, sigma is the standard deviation, and z is the corresponding z-score.

a. Between 29 and 37:

z1 = (29 - 33) / 4 = -1

z2 = (37 - 33) / 4 = 1

Using a standard normal distribution table, the cumulative probability of z being between -1 and 1 is approximately 0.6827.

So the probability that a randomly selected x-value from the distribution is between 29 and 37 is approximately 0.6827.

b. Between 33 and 45:

z1 = (33 - 33) / 4 = 0

z2 = (45 - 33) / 4 = 3

The cumulative probability of z being between 0 and 3 is approximately 0.4987.

So the probability that a randomly selected x-value from the distribution is between 33 and 45 is approximately 0.4987.

c. At least 29:

z = (29 - 33) / 4 = -1

The cumulative probability of z being less than -1 is approximately 0.1587. So the probability that a randomly selected x-value from the distribution is at least 29 is approximately 1 - 0.1587 = 0.8413.

d. At most 21:

z = (21 - 33) / 4 = -3

The cumulative probability of z being less than -3 is very close to 0. So the probability that a randomly selected x-value from the distribution is at most 21 is approximately 0.