Let lim f(x) = 3 and lim g(x)= 12. Use the limit rules to find the following limit. X-5 X-5 lim f(x) X-75 g(x) f(x) lim = *-—5 g(x) (Type an integer or a simplified fraction.)

a) The resulting true speed of the boat is approximately 5.39 m/s.

b) The compass direction of the boat is 21.8° south of east.

c) The distance downstream the boat will land on the shore if the river is 800 meters wide is 320 meters.

a) To find the true speed of the boat, we can use the Pythagorean theorem. Since the boat's speed is 5 m/s due east and the current's speed is 2 m/s due south, we can treat these as perpendicular vectors. The true speed can be found using the formula:

True Speed = √((5 m/s)² + (2 m/s)²) = √(25 + 4) = √29 ≈ 5.39 m/s

b) To find the compass direction of the boat, we can use the inverse tangent function. The angle θ can be calculated using:

θ = arctan(opposite/adjacent) = arctan(2 m/s / 5 m/s) ≈ 21.8°

Since the boat is headed east and the current is pushing it south, the true direction is 21.8° south of east.

c) To find the distance downstream where the boat will land, we first need to calculate the time it takes to cross the river. The boat's speed across the river (due east) is 5 m/s and the width of the river is 800 meters. The time taken to cross the river is:

Time = Distance / Speed = 800 m / 5 m/s = 160 seconds

Now, we can use the time to find the distance downstream by multiplying the current's speed (2 m/s) by the time:

Distance downstream = 2 m/s × 160 s = 320 meters

So, the boat will land 320 meters downstream from its starting point on the opposite shore.

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The best prediction possible for the number of times you will roll a one number when a 6-sided die is rolled 12 times = (0.167)¹²

Events occur as the outcome of an experiment. But one cannot be satisfied with these events until a degree of measurement of the likeliness of its occurrence is not provided. Probability is a statistical tool used widely to obtain predictive value.

Here, 6-sided die rolled 12 times.

If a 6-sided die is rolled, possible outcomes are {1, 2, 3, 4, 5, 6}

So, total number of outcomes = 6

So, number of favorable outcomes = 1

Probability of getting 1 is 1/6 = 0.167

The best prediction possible for the number of times you will roll a one number when a 6-sided die is rolled 12 times = (0.167)¹²

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Answer:3:58 p.m.

Step-by-step explanation:

809,304 people live in Charlotte, rounded to the nearest person.

To calculate the approximate population of Charlotte, you can use the given information:

Population density = 2,720 people per square mile
Area of Charlotte = 297.7 square miles

To find the total population, multiply the population density by the area:

Total population = Population density × Area
Total population = 2,720 people/sq mile × 297.7 sq miles

Total population ≈ 809,304 people

So, approximately 809,304 people live in Charlotte, rounded to the nearest person.

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The expression to represent the situation is 2.85g + 3.15c.

Joe bought g gallons of gasoline for $2.85 per gallon and c cans of oil for $3.15 per can.

An algebraic expression is made up of variables and constants, along with algebraic operations such as addition, subtraction, division, multiplication etc.

Therefore, the expression that can be used to determine the total amount Joe spent on gasoline and oil can be calculated as follows:

Therefore,

total cost = 2.85g + 3.15c

where

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To determine how many times a day we would need to fill the container shown below, we need to calculate its capacity in cubic centimeters. Let's assume that the container is a rectangular prism with dimensions of 30 centimeters (length) x 20 centimeters (width) x 25 centimeters (height). The formula for calculating the volume of a rectangular prism is:

Volume = length x width x height

Plugging in the values we have, we get:

Volume = 30 cm x 20 cm x 25 cm

Volume = 15,000 cubic centimeters

Therefore, the container has a capacity of 15,000 cubic centimeters. To determine how many times we would need to fill it each day, we need to divide the amount of pellets and hay we feed the okapi daily (5,024 cubic centimeters) by the capacity of the container (15,000 cubic centimeters):

5,024 / 15,000 = 0.3356

This means that we would need to fill the container approximately 0.3356 times a day, which is not a practical answer. We need to round this up to the nearest whole number.

The options given to us are 80 times, 40 times, 16 times, and 4 times. Out of these options, the closest whole number to 0.3356 is 1, which means we would need to fill the container once a day.

Therefore, the answer is that we would need to fill the container shown below 1 time a day to feed the okapi their daily amount of pellets and hay.

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It should be noted that f(25) represents the quantity of items sold when the price is $25. In other words, if the price of the item is $25, then f(25) gives the number of units that customers will buy.

Also, f⁻¹(30) represents the price at which q = 30 units will be sold. In other words, if the number of items sold is 30, then f⁻¹(30) gives the price at which these 30 units will be sold.

This quantity is also known as the inverse demand function, which gives the price as a function of quantity demanded. . f(25) represents the quantity of items that will be sold at a price of $25. This means that if the item is sold at a price of $25, the function f will return the number of items that will be sold.

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a) The price of the old model is P22,289.

b) The dimensions of the rectangle are 16 by 32.

a) Let x be the price of the old model. According to the problem, the price of the new 32'' LED television is P15,500 less than twice the price of the old model.

This can be expressed as 2x - P15,500 = P29,078. Solving for x, we can add P15,500 to both sides to get 2x = P44,578, and then divide both sides by 2 to get x = P22,289.

b) Let w be the width of the rectangle. According to the problem, the length of the rectangle is twice the width, so the length is 2w. The perimeter of a rectangle is the sum of the lengths of all four sides, which in this case is 2w + 2(2w) = 6w.

We are given that the perimeter is 96, so we can set up an equation: 6w = 96. Solving for w, we can divide both sides by 6 to get w = 16. Since the length is twice the width, the length is 2(16) = 32.

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Using the formula V = k*T/P to get the volume, the required volume in the given situation is 1.77L.

The measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

Volume and the notion of length are connected.

The area that any three-dimensional solid occupies is known as its volume.

These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

So, the volume can be obtained using the equation:

V = k*T/P

The value of the constant k is:

K = PV/T = 16N/cm²*2.2L/340K = 0.104N*L*K⁻¹*cm⁻²

We can now determine the volume when:

T = 408 K

P = 24 N/cm²

V = k*T/P = 0.104N*L*K⁻¹*cm⁻²*408K/21Ncm = 1.77L

Therefore, using the formula V = k*T/P to get the volume, the required volume in the given situation is 1.77L.

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Correct question:

The volume of a gas varies inversely to the pressure and direction of the temperature (in degrees Kelvin). If a certain gas occupies a volume of 2.2 liters at a temperature of 340 K and a pressure of 16 newtons per square centimeter, find the volume when the temperature is 408 K and the pressure is 24 newtons per square centimeter.

The volume of the composite figure is 152 m³.

The volume of a rectangular prism can be found using the formula V = lwh, where l is the length, w is the width, and h is the height.

For the rectangular prism:

V_prism = lwh = 9m * 8m * 3m = 216 m³

For the cube:

V_cube = s^3 = 4m * 4m * 4m = 64 m³

Now, subtract the volume of the cube from the volume of the prism:

V_composite = V_prism - V_cube = 216 m³ - 64 m³ = 152 m³

The volume of the composite figure is 152 m³.

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Answer: 26/100   OR     0.26  (I would put the answer as a fraction)

Step-by-step explanation:

We need both fractions to have the same denominator before we add them. The denominator of 6/100 is 100. The denominator of 2/10 is 10. We need to turn 10 into 100. To do that, we can do 10*10. This gives us 100. However what we do to the bottom must be done to the top therefore we have 20/100 + 6/100

Now the two fractions can be added together. 20/100 + 6/100 = 26/100.

Normally we would simplify this down to 13/50 but if you want it unsimplified 26/100 would be your answer.

Answer: B, C and E

Step-by-step explanation: the term growing means the value is increasing, and a number multiplied by 1 gives the same number; therefore in order for that number to increase, it need to be multiplied by a bigger number which is greater than 1, in this case it can not be a number less than 0 like 0.85, so all the number which are greater than 1 in the bracket are correct.

the number before the bracket is the population before increasing, so you can substitute any value for t and try out different outcomes, you will get only B, C and E as number greater than the original number

Astha's account was greater than the amount of money in Henry's account is:

5700 + 100x > 75x

Let's start by finding the total amount of money deposited by Astha and Henry after x weeks.

Astha deposited $100 into her account each week for x weeks, so the total amount she deposited is 100x.

Similarly, Henry deposited $75 into his account each week for x weeks, so the total amount he deposited is 75x.

To find the inequality that represents the situation when the amount of money in Astha's account was greater than the amount of money in Henry's account, we need to compare the total amount of money each of them deposited.

Astha started with $5,700 and deposited $100 each week for x weeks, so the total amount of money in her account after x weeks is:

5700 + 100x

Henry started with zero dollars and deposited $75 each week for x weeks, so the total amount of money in his account after x weeks is

75x

Therefore, the inequality that represents the situation when the amount of money in Astha's account was greater than the amount of money in Henry's account is:

5700 + 100x > 75x

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The maximum height of Anna's golf ball is approximately 7.81 units.

The equation y = [tex]x - 0.04x^2[/tex] represents the height of Anna's golf ball, where x is the horizontal distance the ball has traveled.

To find the maximum height of the ball, we need to determine the vertex of the parabolic equation. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -0.04 and b = 1.

x = -b/2a = -1/(2(-0.04)) = 12.5

So, the maximum height of the ball occurs when it has traveled a horizontal distance of 12.5 units. To find the maximum height, we substitute x = 12.5 into the equation:

[tex]y = 12.5 - 0.04(12.5)^2 = 7.81[/tex]

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Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:

x(t) = 57t
y(t) = -7t
z(t) = -3

To find the parametric equations for a line in the direction of the vector 57 - 7 and through the point (0, 0, - 3), we can use the vector form of the equation of a line:

r = r0 + tv

where r is a point on the line, r0 is the given point (0, 0, -3), t is a parameter, and v is the direction vector (57, -7, 0).

Substituting the given values, we have:

r = (0, 0, -3) + t(57, -7, 0)

Expanding, we get:

x(t) = 0 + 57t
y(t) = 0 - 7t
z(t) = -3 + 0t

Simplifying, we have:

x(t) = 57t
y(t) = -7t
z(t) = -3

Therefore, the parametric equations for the line in the direction of the vector 57 - 7 and through the point (0, 0, - 3) are:

x(t) = 57t
y(t) = -7t
z(t) = -3

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1. Chelsea Menken's debt-to-income ratio is 35.7%.

2. Her debt situation is concerning because she accumulated significant student loan debt and credit card debt.

The debt-to-income ratio means percentage of gross monthly income that goes to paying your monthly debt payments

Her total monthly debt payments is:

= $385 (Student loans) + $240 (Credit card) + $1,100 (Rent)

= $1,725.

Her total monthly income after taxes is:

= $58,000 / 12 months

= $4,833.33 per month.

The debt-to-income ratio will be:

= Total monthly debt payments / Monthly income after taxes

= $1,725 / $4,833.33

= 0.357

= 35.7%.

Her debt situation is concerning, so, it important for to develop a plan to pay off the debts in order to avoid accruing more interest and damaging her credit score.

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If Franco's Pizza Parlor knows that the marginal cost of the 500th pizza is $3.50 and that the average total cost of making 499 pizzas is $3.30, then Average total costs are rising at Q = 500. The correct answer is (c)

The marginal cost is the additional cost of producing one more unit. In this case, the marginal cost of the 500th pizza is $3.50.

The average total cost is the total cost of producing all units up to a certain level, divided by the number of units produced. In this case, the average total cost of making 499 pizzas is $3.30.

If the marginal cost of producing the 500th pizza is greater than the average total cost of making the first 499 pizzas, then the average total cost will increase when the 500th pizza is produced.

Therefore, the correct answer is (c) average total costs are rising at Q = 500.

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Answer:

$15.

Step-by-step explanation:

9 + 3*2

= $15.

The perimeter of Koch's snowflake fractal will be infinite.

Koch's snowflake fractal is created by adding triangular bumps to the sides of an equilateral triangle at progressively smaller scales. At each stage, the number of sides of the resulting figure increases by a factor of 4, and the perimeter of the figure increases as well.

To see how the perimeter changes as bumps are added to all sides of the figure, we can use the fact that each bump adds a segment of length 1/3 to the original side. So if we start with a triangle of side length 1 and add a bump to each side, the new perimeter is:

P = 3(1 + 1/3) = 4

Now we have a figure with 12 sides. If we add a bump to each of these sides, the new perimeter is:

P = 12(1 + 1/3 + 1/9) = 16/3

In the next stage, we have 48 sides, and each side has a length of 1/3^2, so the new perimeter is:

P = 48(1 + 1/3 + 1/9 + 1/27) = 64/3

At each stage, we can see that the perimeter is multiplied by a factor of 4/3. So if we carry on this process forever, the perimeter of Koch's snowflake fractal will be infinite.

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The function f(x) = (x + 6)/(2-6) does not have any critical values. A critical value of a function is a value of x where the derivative of the function is either zero or undefined.

However, in this case, the denominator of f(x) is a constant, so the derivative of f(x) is simply the derivative of the numerator divided by the constant denominator.

The derivative of the numerator is 1, so the derivative of f(x) is simply 1/(2-6) = -1/4. Since the derivative is a constant, it is never zero or undefined, and so there are no critical values for this function.Explanation: To find the critical values of a function, we need to find the values of x where the derivative of the function is either zero or undefined. However, in this case, the denominator of f(x) is a constant, so the derivative of f(x) is simply the derivative of the numerator divided by the constant denominator. The derivative of the numerator is 1, so the derivative of f(x) is simply 1/(2-6) = -1/4. Since the derivative is a constant, it is never zero or undefined, and so there are no critical values for this function. Therefore, the answer is None.

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When a multiple regression model created incorrectly then leaves out one and more than one important factors are omitted.

Multiple regression is a statistical way that can be used to analyze the relationship between a single dependent variable and several independent variables. Equation is written as y =

We have regressors x₁ and x₂ where both variables are determinants of the dependent variable. you first regressor y on x₁ only and find no relationship. however when regressing y on x₁ and x₂.

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Complete question:

consider the multiple regression model with two regressors x1 and x2, where both variables are determinants of the dependent variable. you first regress y on x1 only and find no relationship. however when regressing y on x1 and x2, the slope coefficient changes by a large amount. this suggests that your first regression suffers from:

The percentage of males attending the sporting events that are adults is:

65.10%.

A percentage is one example of a proportion, as it is obtained by the number of desired outcomes divided by the number of total outcomes, and then multiplied by 100%.

The number of males attending sporting events is given as follows:

1235.

Of those 1235 males, 804 are adults, hence the percentage of males attending the sporting events that are adults is given as follows:

p = 804/1235 x 100%

p = 65.10%.

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To calculate the relative frequency for each category, divide the number of marked mountain goats in each category by the total number of marked mountain goats.

Total marked mountain goats = 71 (male) + 93 (female) = 164
Total marked mountain goats = 103 (adult) + 61 (baby) = 164

Relative frequency for male goats = Male goats / Total marked mountain goats = 71/164
Relative frequency for female goats = Female goats / Total marked mountain goats = 93/164
Relative frequency for adult goats = Adult goats / Total marked mountain goats = 103/164
Relative frequency for baby goats = Baby goats / Total marked mountain goats = 61/164

Your answer:
Relative frequency for male goats = 71/164
Relative frequency for female goats = 93/164
Relative frequency for adult goats = 103/164
Relative frequency for baby goats = 61/164

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After 2 years, the total amount is approximately $642.45. After 4 years, the total amount is approximately $690.27.

1. Define variables:
A = total amount after a certain number of years
P = initial amount ($600)
r = annual interest rate (3.5% or 0.035)
t = number of years

2. Substitute into formula:
A = 600(1+0.035)^t

3. Evaluate:

For 2 years (t=2):
A = 600(1+0.035)^2
A = 600(1.035)^2
A ≈ 642.45

The total amount after 2 years is approximately $642.45.

For 4 years (t=4):
A = 600(1+0.035)^4
A = 600(1.035)^4
A ≈ 690.27

The total amount after 4 years is approximately $690.27.

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The amount which is greater than the given amount four hundred forty-five and fifty-seven hundredths is given by option b. 445.7.

Amount representing the  number is 445.57.

Amount greater than this number,

Compare the decimal parts of the numbers given in the options.

445.5 has a decimal part of 0.5, which is not greater than 0.57.

Option a is not greater than 445.57.

445.7 has a decimal part of 0.7, which is greater than 0.57.

Option b is greater than 445.57.

445.005 has a decimal part of 0.005, which is less than 0.57.

Option c is not greater than 445.57.

445.057 has a decimal part of 0.057, which is not greater than 0.57.

Option d is not greater than 445.57.

Therefore, the only option that is greater than 445.57 is option b. 445.7.

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The size of the measure of the angle X is calculated to be equal to 37° to the nearest degree using trigonometric ratios of sine

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

For the given triangle;

sin X = 3/5 {opposite/hypotenuse}

X = sin⁻¹(3/5) {cross multiplication}

X = 36.8699°

Therefore, the measure of the angle X is calculated to be equal to 37° to the nearest degree using trigonometric ratios of sine

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The calculated value of x is 8 and the perimeter is 80 units

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

The figure

If the lines that appear to be tangent are tangent, then we have the following equation

x = 26 - 18

Evaluate the like terms

x = 8

The perimeter is the sum of the side lengths

So, we have

Perimeter = 26 + 18 + 14 + 14 + x

This gives

Perimeter = 26 + 18 + 14 + 14 + 8

Evaluate

Perimeter = 80

Hence, the perimeter is 80 units

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The quotient of the expression (5.04×10^12)÷(6.3×10^9) written in scientific notation is 8 × 10^2.

To divide two numbers written in scientific notation, we can divide their coefficients (the decimal parts) and subtract their exponents. So, we have:

(5.04 × 10^12) ÷ (6.3 × 10^9) = (5.04 ÷ 6.3) × 10^(12-9) = 0.8 × 10^3

Since 0.8 is less than 1, we can write this number in scientific notation by moving the decimal point one place to the right and subtracting 1 from the exponent:

0.8 × 10^3 = 8 × 10^2

Therefore, the quotient of the expression (5.04×10^12)÷(6.3×10^9) written in scientific notation is 8 × 10^2.

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The value of the median is 18. The range of this plot is 6. The 25th percentile is 17 and the 75th percentile is 20. The interquartile range is 3.

We are given a box-and-whisker plot and we have to find the correct value of the median, range, 25th percentile, 75th percentile, and inter-quartile range with the help of this box-and-whisker plot.

We find the median with the help of the box. The line which splits the box into two halves is the median for the given data. Therefore, the median will be 18. To find the range, we subtract the minimum value from the maximum value. The minimum value is 15 and the maximum value is 21. Therefore, the range will be (21 - 15) = 6.

From the plot, we can see that the 25th percentile is 17, Q1, and the 75th percentile is 20, Q3. Now, we have to find the interquartile range. To find the interquartile range, we subtract Q1 from Q3. Therefore, our interquartile range will be (20 -17) = 3.

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