Find the quotient z₁/z₂of the complex numbers. Leave your answer in polar form
z₁ = 32(cos 42° + i sin 42°) z₂=4(cos 6+ i sin 6°)
Choose the correct answer below.
A. 8( cos 7+ i sin 7°)
B. 8[(cos 42-cos 6°)+ (sin 42°- sin 6°)
C. 8( cos 36+ sin 36")
D. 8( cos 42° sin 6+ / sin 42° cos 6°))

The height of the building is approximately 38.601 feet.

To find the height of the building, we can use the tangent function, which relates the angle of elevation to the height and distance. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the building, and the adjacent side is the distance from the person to the building.

Let's denote the height of the building as h and the distance from the person to the building as d.

From the problem, we have the following information:

Angle of elevation = 65 degrees

Distance from the person to the building (adjacent side) = 18 ft

Using the tangent function, we have:

tan(angle) = opposite/adjacent

tan(65 degrees) = h/d

We can rearrange the equation to solve for the height:

h = d * tan(angle)

Plugging in the values:

h = 18 ft * tan(65 degrees)

Using a scientific calculator or a calculator with trigonometric functions, we can find the value of tan(65 degrees) and calculate the height:

h ≈ 18 ft * 2.1445

h ≈ 38.601 ft

Therefore, the height of the building is approximately 38.601 feet.

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Chuck's interpretation of the problem seems to have some inaccuracies. He incorrectly assumed a linear growth model, which assumes a constant rate of increase over time.

However, the problem statement mentions a "growing" deer population, suggesting a non-linear growth pattern. In reality, the deer population would likely exhibit exponential growth.

A clue to Chuck that something was wrong should have been the constant growth rate of 6 animals per year. In a linear model, the population would increase by the same amount every year. However, in a real-life scenario, the population growth rate would likely change over time due to factors such as limited resources, predation, or natural constraints.

To accurately model the deer population, Chuck should consider using an exponential growth equation. This type of model takes into account a growth rate that is proportional to the current population size. It would be helpful to incorporate additional information or data to determine the most appropriate growth model for the deer population.

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Answer:A

Step-by-step explanation:

The term that could be defined as the standard deviation adjusted to take into account the use of sampling is A. Standard Error.

The plane must fly approximately 42,108 feet horizontally to be directly over the tree

we can use trigonometry and the concept of tangent.

Let's denote the distance horizontally from the plane to the tree as "x". We can consider a right triangle formed by the plane, the tree, and a point directly below the plane on the ground.

The angle of depression is the angle formed between the line of sight from the plane to the tree and the horizontal line. In this case, the angle of depression is 13°50'.

In a right triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In this scenario, the opposite side is the height of the plane above the ground (10,500 feet), and the adjacent side is the horizontal distance from the plane to the tree (x).

We can use the tangent function to express this relationship:

tan(13°50') = opposite/adjacent

tan(13°50') = 10,500/x

To find the value of x, we can rearrange the equation:

x = 10,500 / tan(13°50')

Using a calculator, evaluate the tangent of 13°50':

tan(13°50') ≈ 0.2493

Now, substitute this value into the equation to find x:

x = 10,500 / 0.2493

x ≈ 42,108.25

Therefore, the plane must fly approximately 42,108 feet horizontally to be directly over the tree.

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The calculated percentiles are as follows:

10th percentile: 21

50th percentile (Median): 40

100th percentile: 115

To calculate the 10th, 50th (also known as the median), and 100th percentiles from the given set of observations: 42, 29, 40, 21, 115, we need to sort the data in ascending order.

Ascending order: 21, 29, 40, 42, 115

Now we can calculate the desired percentiles:

10th percentile: The 10th percentile is the value below which 10% of the data falls. To calculate it, we multiply 10% (0.1) by the total number of observations (5) and round up to the nearest whole number. In this case, 10% * 5 = 0.5, which rounds up to 1. Therefore, the 10th percentile is the first observation in the sorted data, which is 21.

50th percentile (Median): The 50th percentile represents the middle value of the data set when arranged in ascending order. Since we have an odd number of observations (5), the median will be the middle value. In this case, the middle value is the third observation, which is 40.

100th percentile: The 100th percentile represents the maximum value in the data set. Since the maximum value in the given data set is 115, it is also the 100th percentile.

Therefore, the calculated percentiles are as follows:

10th percentile: 21

50th percentile (Median): 40

100th percentile: 115

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a)  2,546.48 gallons of regular gasoline were sold.

b) The station's total profit is $775.33.

Let's set up and solve the equation for the given business situation.

Let's assume that x represents the number of gallons of premium gasoline sold. Since the station sold 360 more gallons of regular than premium, the number of gallons of regular gasoline sold would be x + 360.

(a) To find the number of gallons of each type of gasoline sold, we can set up the equation:

3.45x + 3.30(x + 360) = 15,970.50

Now, we can solve this equation for x:

3.45x + 3.30x + 1188 = 15,970.50

6.75x + 1188 = 15,970.50

6.75x = 15,970.50 - 1188

6.75x = 14,782.50

x = 14,782.50 / 6.75

x ≈ 2,186.48

So, approximately 2,186.48 gallons of premium gasoline were sold.

To find the number of gallons of regular gasoline sold, we can substitute the value of x back into the expression x + 360:

x + 360 = 2,186.48 + 360

x + 360 ≈ 2,546.48

So, approximately 2,546.48 gallons of regular gasoline were sold.

(b) To calculate the station's total profit, we need to multiply the number of gallons of each type of gasoline sold by their respective profit per gallon and then sum them up:

Profit from regular gas = 2,546.48 gallons * $0.15/gallon = $381.97

Profit from premium gas = 2,186.48 gallons * $0.18/gallon = $393.36

Total profit = Profit from regular gas + Profit from premium gas

Total profit = $381.97 + $393.36 = $775.33

Therefore, the station's total profit is $775.33.

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The value of arctan(-1) as a simplified fraction is -π/4.

The arctan function, or inverse tangent function, returns the angle whose tangent is a given number. In this case, we want to evaluate arctan(-1).

The tangent function represents the ratio of the length of the side opposite an angle to the length of the adjacent side in a right triangle. The tangent of an angle is negative when the angle is in the second or fourth quadrant of the unit circle.

For arctan(-1), we are looking for the angle whose tangent is -1. In the unit circle, the tangent of -π/4 (negative pi/4) is -1.

Therefore, the value of arctan(-1) can be expressed as -π/4, which represents an angle of -45 degrees or -π/4 radians.

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The domain is x > 0 and the range is y < 0. In interval notation, the domain is (0, ∞) and the range is (-∞, 0). In set-builder notation, the domain is {x | x > 0} and the range is {y | y < 0}.

To graph the logarithmic function represented by the table, we plot the given points (x, y) on a coordinate plane. The x-values are the inputs, and the y-values represent the outputs or the function values. The graph will help us understand the behavior of the function.

The table provides us with five points: (-3, 1/125), (-2, 1/25), (-1, -2/5), (0, -1), and (1, 25/125). Plotting these points and connecting them, we see that the graph starts from the bottom left, passes through the point (0, -1), and curves upwards as x increases. The graph approaches positive infinity as x approaches infinity.

The domain of the logarithmic function f(x) is the set of all x-values for which the function is defined. In this case, since logarithms are only defined for positive numbers, the domain is x > 0.

The range of the logarithmic function f(x) is the set of all possible y-values that the function can attain. Looking at the table and the graph, we observe that the y-values are negative and approach negative infinity as x approaches zero. Therefore, the range is y < 0.

These notations express the conditions that define the domain and range of the logarithmic function.

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Answer:

Domain: (0, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

Given table representing a logarithmic function f(x):

[tex]\begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}x&y\\\cline{1-2}\vphantom{\dfrac12}\frac{1}{125}&-3\\\cline{1-2}\vphantom{\dfrac12}\frac{1}{25}&-2\\\cline{1-2}\vphantom{\dfrac12}\frac{1}{5}&-1\\\cline{1-2}\vphantom{\dfrac12}1&0\\\cline{1-2}\vphantom{\dfrac12}5&1\\\cline{1-2}\vphantom{\dfrac12}25&2\\\cline{1-2}\vphantom{\dfrac12}125&3\\\cline{1-2}\end{array}[/tex]   [tex]\implies \begin{array}{|c|c|}\cline{1-2}\vphantom{\dfrac12}x&y\\\cline{1-2}\vphantom{\dfrac12}5^{-3}&-3\\\cline{1-2}\vphantom{\dfrac12}5^{-2}&-2\\\cline{1-2}\vphantom{\dfrac12}5^{-1}&-1\\\cline{1-2}\vphantom{\dfrac12}5^0&0\\\cline{1-2}\vphantom{\dfrac12}5^1&1\\\cline{1-2}\vphantom{\dfrac12}5^2&2\\\cline{1-2}\vphantom{\dfrac12}5^3&3\\\cline{1-2}\end{array}[/tex]

Observe that the values of x in the given table are the reciprocals of powers of 5, while the values of y are the corresponding exponents. This indicates that the logarithm base is 5. Therefore, the function can be written as:

[tex]\boxed{f(x) = log_5(x)}[/tex]

To graph the logarithmic function based on the given table, plot the points provided in the table and draw a continuous curve passing through the points. (See attachment).

The domain of a function is the set of all possible input values (x-values).

The logarithmic function is a continuous, one-to-one function. It is not defined for negative numbers or for zero. Therefore, its domain is always positive.

The range of a function is the set of all possible output values (y-values).

The range of a logarithmic function is unrestricted and therefore includes all real numbers.

In summary, the graph of the logarithmic function based on the given table would resemble an increasing curve passing through the provided points. The domain of the function is (0, ∞), and the range is (-∞, ∞).

For the graph y =  eˣ,

(a) y = e^x - 6

(b) y = e^(x - 4)

(c) y = -e^x

(d) y = e^(-x)

(e) y = -e^(-x)

Starting with the graph of y = e^x, we will apply the given changes to obtain the new transformations.

(a) Shifting 6 units downward:

To shift the graph 6 units downward, we subtract 6 from the original equation:

y = e^x - 6

(b) Shifting 4 units to the right:

To shift the graph 4 units to the right, we replace x with (x - 4) in the original equation:

y = e^(x - 4)

(c) Reflecting about the x-axis:

To reflect the graph about the x-axis, we multiply the original equation by -1:

y = -e^x

(d) Reflecting about the y-axis:

To reflect the graph about the y-axis, we replace x with (-x) in the original equation:

y = e^(-x)

(e) Reflecting about the x-axis and then about the y-axis:

To reflect the graph about the x-axis and then about the y-axis, we multiply the equation from part (d) by -1:

y = -e^(-x)

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Suppose you choose a number at random from [−1,2] and let X(ζ)=−ζ+2, a) P([-1,2]) = 0, b) P([-0.5,0.5]) = 0 c) P({X≤1}) = 1, d) P({X>3}) = 0.

a) To find P([-1,2]), we need to calculate the probability of selecting a number from the interval [-1,2]. Since the interval includes both -1 and 2, we can say that the range of possible outcomes is 2 - (-1) = 3. The total possible outcomes when selecting a number at random from [-1,2] is infinite, but the probability can be calculated using the formula:

P([-1,2]) = (length of the interval) / (total possible outcomes).

In this case, the length of the interval is 2 - (-1) = 3, and the total possible outcomes are infinite. Therefore, the probability of selecting a number from the interval [-1,2] is 3/infinity, which is 0.

b) To find P([-0.5,0.5]), we need to calculate the probability of selecting a number from the interval [-0.5,0.5]. Again, the range of possible outcomes is 0.5 - (-0.5) = 1. The total possible outcomes when selecting a number at random from [-0.5,0.5] is infinite.

Therefore, the probability of selecting a number from the interval [-0.5,0.5] is 1/infinity, which is also 0.

c) To find P({X≤1}), we need to calculate the probability of X being less than or equal to 1. We can substitute

X(ζ) = -ζ + 2 into the inequality.
-ζ + 2 ≤ 1
Simplifying, we get -ζ ≤ -1
Multiplying both sides by -1 (and reversing the inequality since we multiplied by a negative number), we get ζ ≥ 1.

Therefore, P({X≤1}) is the probability of selecting a number greater than or equal to 1, which is 1.

d) To find P({X>3}), we need to calculate the probability of X being greater than 3. Again, we substitute

X(ζ) = -ζ + 2 into the inequality.
-ζ + 2 > 3
Simplifying, we get -ζ > 1
Multiplying both sides by -1 (and reversing the inequality), we get ζ < -1.

Therefore, P({X>3}) is the probability of selecting a number less than -1, which is 0.

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a.
i. Δx = 6.5
ii. Δy = 25
iii. The change in y is approximately 3.85 times as large as the change in x.

b.
i. Δx = -0.1
ii. Δy = -0.4
iii. The change in y is 4 times as large as the change in x.

a.
i. To find how much x changes over the interval from x=2 to x=8.5, we subtract the initial value of x from the final value: Δx = 8.5 - 2 = 6.5.

ii. To find how much y changes over the same interval, we substitute the initial and final values of x into the equation y = 4x + 9.
When x = 2, y = 4(2) + 9 = 17.
When x = 8.5, y = 4(8.5) + 9 = 42.
So, Δy = 42 - 17 = 25.

iii. To find how many times larger the change in y is compared to the change in x, we divide Δy by Δx: Δy/Δx = 25/6.5 ≈ 3.85.

b.
i. To find how much x changes over the interval from x = -5 to x = -5.1, we subtract the initial value of x from the final value: Δx = -5.1 - (-5) = -0.1.

ii. To find how much y changes over the same interval, we substitute the initial and final values of x into the equation y = 4x + 9.
When x = -5, y = 4(-5) + 9 = -11.
When x = -5.1, y = 4(-5.1) + 9 = -11.4.
So, Δy = -11.4 - (-11) = -0.4.

iii. To find how many times larger the change in y is compared to the change in x, we divide Δy by Δx: Δy/Δx = -0.4/-0.1 = 4.

In summary:
a.
i. Δx = 6.5
ii. Δy = 25
iii. The change in y is approximately 3.85 times as large as the change in x.

b.
i. Δx = -0.1
ii. Δy = -0.4
iii. The change in y is 4 times as large as the change in x.

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The present value for the following compounding periods are:
296.46 (nearest cent),
295.11 (nearest cent),
456.65 (nearest cent).

Given: Nominal rate = 9%
Discounted time:
  5 years for semiannual compounding,
  5 years for quarterly compounding,
  1 year for monthly compounding
Future Value = 500
      We have to calculate the present value of the future value using the compound interest formulae for different compounding periods.
A) For semi-annual compounding, the interest rate will be (9% / 2) = 4.5%
Number of compounding periods will be 2 × 5 = 10
FV = PV × (1 + i)n where PV is the present value
PV = FV / (1 + i)n
PV = 500 / (1 + 0.045)10 = 296.46 (nearest cent)

B) For quarterly compounding, the interest rate will be (9% / 4) = 2.25%
Number of compounding periods will be 4 × 5 = 20
FV = PV × (1 + i ) n where PV is the present value
PV = FV / (1 + i ) n
PV = 500 / (1 + 0.0225)20 = 295.11 (nearest cent)

C) For monthly compounding, the interest rate will be (9% / 12) = 0.75%
Number of compounding periods will be 12 × 1 = 12
FV = PV × (1 + i)n where PV is the present value
PV = FV / (1 + i)n
PV = 500 / (1 + 0.0075)12 = 456.65 (nearest cent).

Therefore, the present value for the following compounding periods are:
296.46 (nearest cent)
295.11 (nearest cent)
456.65 (nearest cent)

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The distance of the person from the base of the plateau is 5.76 meters.

Given that a person is heading towards a plateau that is 20.7 meters high. The angle of elevation to the top of the plateau is 14.5°. We need to find out how far the person is from the base of the plateau and what is the distance from the base of the plateau?The diagram for the given problem is as follows:Let AB be the height of the plateau and C be the point where the person is standing, and draw CD ⊥ AB.So, in right ∆CDB,We haveCD = AB * tan14.5°CD = 20.7 * tan14.5° = 5.76 metersThus, the person is 5.76 meters from the base of the plateau.The distance of the person from the base of the plateau is 5.76 meters.

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The simple average of the given data set is 3.72 g, and the weighted average cannot be determined without knowing the weights assigned to each data point.

To calculate the simple average, we sum up all the data points and divide the sum by the number of data points. In this case, the sum of the data points (3.50 g + 3.72 g + 3.72 g + 3.50 g + 3.72 g + 3.72 g + 3.50 g + 3.72 g) is 29.1 g. Dividing this sum by the number of data points (8), we get the simple average of 3.72 g.

The weighted average requires the weights assigned to each data point. Without knowing the weights, we cannot calculate the weighted average.

The weighted average takes into account the importance or significance of each data point by multiplying the data point by its corresponding weight, summing up the weighted data points, and dividing by the sum of the weights.

Since the question does not provide any information about the weights assigned to each data point, we cannot determine the weighted average in this case. So B is correct.

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The total length of the cut boards is 7.92 inch.

To find the total length, we add up the lengths of the four boards. We convert the mixed radicals to decimal form and then add all the lengths together.

Step-by-step explanation:
1. Convert the mixed radicals to decimal form:
  - 7^((1)/(2)) inches is approximately 2.646 inches
  - 10^((1)/(2)) inches is approximately 3.162 inches
  - 9 inches remains the same
  - 5^((1)/(2)) inches is approximately 2.236 inches

2. Add up the lengths:
  2.646 + 3.162 + 9 + 2.236 = 17.044 inches

3. Round the total length to the nearest hundredth:
  The total length is approximately 17.04 inches, which can be rounded to 17.0 inches or 17 inches.

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Vector is a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces. The new vector →u + →v is ⟨ 3,-6 ⟩.

→u = ⟨ 2,−7 ⟩ and →v = ⟨ 1,1 ⟩ , to find the new vector →u + →v, we can add the corresponding components of the given vectors using the formula below:→u + →v = ⟨u₁+v₁,u₂+v₂⟩Where u₁ and v₁ are the first components of →u and →v, respectively, and u₂ and v₂ are the second components of →u and →v, respectively.

Substituting the given values, we get:→u + →v = ⟨ 2,−7 ⟩ + ⟨ 1,1 ⟩  →u + →v = ⟨ 2+1,−7+1 ⟩   →u + →v = ⟨ 3,-6 ⟩.Therefore, the new vector →u + →v is ⟨ 3,-6 ⟩.

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Part a:

The value of the gradient G for the royalty stream is $5,143.

To find the value of the gradient G, we need to calculate the present worth of the 7-year royalty stream. The present worth represents the equivalent value of all future cash flows discounted to the present time using an interest rate of 9% per year.

Let's denote the value of the gradient G as G. The royalty stream begins at the end of the first year with a payment of $12,000. From year 2 to year 7, the royalty stream changes by G each year. Therefore, the cash flows for each year are as follows:

Year 1: $12,000

Year 2: $12,000 + G

Year 3: $12,000 + 2G

Year 4: $12,000 + 3G

Year 5: $12,000 + 4G

Year 6: $12,000 + 5G

Year 7: $12,000 + 6G

To calculate the present worth, we need to discount each cash flow to the present time. Using the TVM (Time Value of Money) factor table or calculator, we can find the discount factors for each year based on the interest rate of 9% per year.

Calculating the present worth of each cash flow and summing them up, we find that the present worth of the 7-year royalty stream is $45,000. Therefore, we can set up the following equation:

$45,000 = $12,000/(1+0.09)^1 + ($12,000+G)/(1+0.09)^2 + ($12,000+2G)/(1+0.09)^3 + ($12,000+3G)/(1+0.09)^4 + ($12,000+4G)/(1+0.09)^5 + ($12,000+5G)/(1+0.09)^6 + ($12,000+6G)/(1+0.09)^7

Solving this equation will give us the value of the gradient G, which is approximately $5,143.

Part b:

The value of the gradient G for the royalty stream, given a future worth at the end of year 7 of $130,000, cannot be determined based on the information provided.

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Answer:

c

Step-by-step explanation:

1 nanogram is  1 x 10^-12 kg

16.3 nanogram  *  1 x 10^-12  kg/ nanogram = 16.3 x 10^-12 = 1.63 x 10^-11 kg

Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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Given tan(t) > 0 and sin(t) < 0, the terminal point determined by t lies in Quadrant III, making the answer c) III.

In the coordinate plane, the trigonometric functions have specific signs in each quadrant.

For tan(t) > 0, it means that the tangent of angle t is positive. In Quadrant III, the x-coordinate is negative and the y-coordinate is also negative. Since tan(t) = sin(t)/cos(t), if sin(t) < 0, it implies that both sin(t) and cos(t) are negative in Quadrant III.

Therefore, in Quadrant III, tan(t) is positive (as given) because the ratio of a negative value for sin(t) and a negative value for cos(t) yields a positive result. Additionally, sin(t) is negative (as given) because the y-coordinate is negative in Quadrant III.

By analyzing these conditions, we conclude that the terminal point determined by t lies in Quadrant III.

Hence, the correct answer is c) III.

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The quadratic equation x² - 10x + 25 = 0 has two equal roots which is x=5.

To solve the quadratic equation, follow these steps:

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The length of the rectangular plot of land is 153 feet. This problem will be solved using the basics of rectangles. The width of the rectangular plot of land is w. As given, the length of the fence is 32 feet longer than the width. So, the length of the rectangular plot of land is w + 32 feet. If the landowner has a total of 548 feet of fence that he can use, then the perimeter of the rectangular plot of land can be calculated using the given data.

The perimeter of the rectangular plot of land can be calculated as follows: Perimeter of a rectangle = 2(l + w)Here, l is the length of the rectangular plot of land and w is the width of the rectangular plot of land. So, the equation can be written as follows:2(w + 32 + w) = 548Simplifying the above equation:2w + 32 = 2742w = 242w = 121So, the width of the rectangular plot of land is 121 feet. As per the given data, the length of the rectangular plot of land can be calculated as follows: l = w + 32l = 121 + 32l = 153. So, the length of the rectangular plot of land is 153 feet.

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Water makes up roughly 60% of your total body weight. This means that if you weigh 150 pounds, about 90 pounds of that is water.

Water is essential for the functioning of our bodies. It plays a vital role in maintaining temperature, transporting nutrients and oxygen, and removing waste products. The percentage of water in the human body varies depending on factors such as age, sex, and body composition. On average, water makes up about 60% of an adult's total body weight. This percentage can be higher in infants and lower in elderly individuals.

For example, a person weighing 150 pounds would have approximately 90 pounds of water in their body. It's important to stay hydrated by drinking enough water to replenish the water that our bodies constantly lose through processes like sweating, urination, and breathing.

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The volume of the moving box is 8,018,968 cubic inches.

To find the volume of the moving box, we need to multiply its length, width, and height. Given that the dimensions are:

Length = 2214 inches

Width = 1812 inches

Height = 22 inches

The volume (V) of the box can be calculated as follows:

V = Length x Width x Height

V = 2214 inches x 1812 inches x 22 inches

V = 8,018,968 cubic inches

Therefore, the volume of the moving box is 8,018,968 cubic inches.

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To find the abscissa of point B in the parallelogram with vertices O(0; 0), A(10; 8), C(2; 6), we can use the fact that opposite sides of a parallelogram are equal in length and parallel.

First, let's find the length and slope of the line segment AC. The length of AC can be calculated using the distance formula:
AC = sqrt((10-2)^2 + (8-6)^2) = sqrt(64 + 4) = sqrt(68)
The slope of AC can be found using the formula:
m = (y2 - y1) / (x2 - x1)
mAC = (6-8) / (2-10) = -2 / -8 = 1/4
Since opposite sides of a parallelogram are parallel, the slope of the line segment BC will also be 1/4. Now, let's find the equation of the line passing through C with slope 1/4. Using the point-slope form:
y - y1 = m(x - x1)
y - 6 = 1/4(x - 2)
y - 6 = 1/4x - 1/2
y = 1/4x + 5.5
Finally, let's find the x-coordinate of point B by substituting y = 8 into the equation of the line:
8 = 1/4x + 5.5
1/4x = 8 - 5.5
1/4x = 2.5
x = 2.5 * 4
x = 10
Therefore, the abscissa of point B is 10.
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Answer:

672 had dark hair, 592 had blond hair, and 48 had red hair

Step-by-step explanation:

To solve this problem, we need to first find the total number of people for each hair color based on the given ratio.

Let's start by finding the common factor that we can use to scale the ratio up to the total number of people, which is 1,312:

42 + 37 + 3 = 82

We can then divide 1,312 by 82 to get the scaling factor:

1,312 ÷ 82 = 16

This means that for every 16 people, there are 42 with dark hair, 37 with blond hair, and 3 with red hair.

To find the actual number of people with each hair color in the town meeting, we can multiply the scaling factor by the number of people for each hair color in the ratio:

Dark-haired people: 42 × 16 = 672

Blond-haired people: 37 × 16 = 592

Red-haired people: 3 × 16 = 48

Therefore, there are 672 people with dark hair, 592 people with blond hair, and 48 people with red hair at the town meeting.

The result of the operation is -1.594×10⁻²).

To solve the given expression, we start by dividing 3.25×10⁻⁴ by 8.012×10⁻²). This can be done by dividing the coefficients (3.25 ÷ 8.012) and subtracting the exponents (10⁻⁴ ÷ 10⁻²).

The division of the coefficients gives us 0.4047, and subtracting the exponents gives us 10 (-4-(-2)) = 10⁻² = 0.01. Therefore, the division of the two numbers results in 0.4047 × 0.01 = 0.004047.

Next, we subtract 2.000×10⁻² from the result obtained above. This is done by subtracting the coefficients (0.004047 - 2.000) and keeping the same exponent (-2).

Performing the subtraction gives us -1.995953, and the common exponent remains -2. Therefore, the final result is -1.995953 × 10⁻² = -1.594×10⁻².

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We then subtracted the area of the doorway and window to get the final answer which is 301ft².

The approximate area that Rick paints in the room can be calculated by finding the total surface area of the four walls and subtracting the area of the doorway and window.

First, let's calculate the surface area of the four walls. The room has a length of 12ft and a width of 10ft, so the perimeter of the room is 2 * (12ft + 10ft) = 44ft. The height of the walls is 8ft, so the total surface area of the four walls is 44ft * 8ft = 352ft².

Next, we need to subtract the area of the doorway and window. The area of the doorway is 3ft * 7ft = 21ft², and the area of the window is 6ft * 5ft = 30ft². Therefore, the total area that Rick paints is 352ft² - 21ft² - 30ft² = 301ft².

To find the area that Rick paints in the room, we calculated the surface area of the four walls by finding the perimeter of the room and multiplying it by the height of the walls.

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The correct scientific notation for the number 0.00050210 is 5.0210 x 10^(-4).

Here's a step-by-step explanation:

1. To convert a decimal number to scientific notation, we need to move the decimal point until we have a number between 1 and 10. In this case, we need to move the decimal point 4 places to the right to get 5.0210.

2. Next, we determine the power of 10 by counting the number of places we moved the decimal point. In this case, since we moved it 4 places to the right, the power of 10 is -4.

3. Finally, we write the number in the form of "a x 10^n", where "a" is the number between 1 and 10 (5.0210 in this case), and "n" is the power of 10 (-4 in this case).

So, the correct scientific notation for 0.00050210 is 5.0210 x 10^(-4).

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Question- The correct scientific notation for the number 0.00050210 is: a. 5.0210 x 10° b. 5.021 x 10 c. 5.021 x 10 d. 5.0210 x 10 e. None of the choices listed are correct.

The scientific notation for 0.00050210 is 5.0210 x 10^-4. It was calculated by moving the decimal point 4 places to the right, resulting in 5.0210, and then multiplying by 10 to the power of -4.

The given number is 0.00050210. We're trying to express it in scientific notation which is a shorthand way to write numbers that are either very large or very small by representing them as the product of a number (between 1 and 10) and a power of ten.

First, let's consider the number 0.00050210. We shift the decimal point 4 places to the right until we have a number that is between 1 and 10. So, we get 5.0210. Then, we multiply by 10 to the power of minus the number of places we moved the decimal (in this case, -4) to write the scientific notation.

So, the scientific notation of 0.00050210 is 5.0210 x 10^-4.

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a. f(-9) = -65
b. f(x+9) = 8x + 79
c. f(-x) = -8x + 7

The function f(x) = 8x + 7 represents a linear equation. To evaluate this function, we need to substitute the given values of the independent variable (x) into the function and simplify the expression.

a. To evaluate f(-9), we substitute -9 for x in the function:

f(-9) = 8(-9) + 7

Now we simplify the expression:

f(-9) = -72 + 7

f(-9) = -65

Therefore, f(-9) = -65.

b. To evaluate f(x+9), we substitute (x+9) for x in the function:

f(x+9) = 8(x+9) + 7

Now we simplify the expression:

f(x+9) = 8x + 72 + 7

f(x+9) = 8x + 79

Therefore, f(x+9) = 8x + 79.

c. To evaluate f(-x), we substitute (-x) for x in the function:

f(-x) = 8(-x) + 7

Now we simplify the expression:

f(-x) = -8x + 7

Therefore, f(-x) = -8x + 7.

In summary:
a. f(-9) = -65
b. f(x+9) = 8x + 79
c. f(-x) = -8x + 7

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