Your name is Galileo Galilei, and you toss a weight upward at 16 feet per second from the top of the Leaning Tower of Pisa (height 186 ft). (a) Neglecting air resistance, find the weight's velocity as a function of time t in seconds. v(t) = Correct: Your answer is correct. ft/s (b) Find the height (in feet) of the weight above the ground as a function of time. s(t) =

To find the volume of a cone, we use the formula:

[tex]V = (1/3)\pi r^2h[/tex]

where V is the volume, r is the radius of the circular base, h is the height of the cone, and [tex]\pi[/tex] is approximately 3.14159.

In this problem, the height of the cone is given as 10 ft and the radius of the circular base is given as 6 ft.

First, we need to find the slant height of the cone. We can use the Pythagorean theorem:

[tex]l = \sqrt{(r^2 + h^2)[/tex]

[tex]l = \sqrt{(6^2 + 10^2)[/tex]

[tex]l = \sqrt{\\(36 + 100)[/tex]

[tex]l = \sqrt{136[/tex]

[tex]l = 11.66 ft[/tex]

Now we can substitute the values into the formula for the volume:

[tex]V = (1/3)\pi r^2h[/tex]

[tex]V = (1/3)\pi (6^2)(10)[/tex]

[tex]V = 120\pi /3[/tex]

[tex]V = 40\pi[/tex]

[tex]V= 125.6 cubic feet[/tex]

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The distance that the bees cover in feet is 10.84 feet.

The speed at which the bees travel is given in the unit inches per min but the required solution is in feet so we need to convert the unit from in/min to ft/min using the unit conversion method.

We know that

1 inch=1/12feet.

so 32 inches/min=32.5 *(1/12) feet/min.

which is roughly equal to 2.71 feet/min (rounded to two decimal places).

Now by using the speed, distance, and time formula which is:

distance=speed*time

we can calculate the distance covered by bees at the given speed and time.

Substituting the values in the equation.

distance=2.71 feet/minute * 4.0 minutes.

=10.84 feet

Therefore, the bee's distance in feet will be 10.84 feet (rounded off to 2 digits).

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The salesman's actual profit earnings after suffering a 5% loss due to damages when assembling the computer is $14,820.

Let's first calculate the original cost price of the computer to the salesman. We know that the salesman sold the computer for $15,600 and made a profit of 25%, which means that the selling price is 125% of the cost price.

Let the cost price of the computer be x.

Selling price = 125% of cost price

$15,600 = 1.25x

Solving for x, we get:

x = $12,480

So, the salesman's cost price of the computer was $12,480.

Now, the salesman suffered a loss of 5% due to damages when assembling the computer.

Loss = 5% of cost price

Loss = 5% of $12,480

Loss = $624

So, the actual earnings of the salesman after the loss is: $15,600 - $624 = $14,820.

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The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.

The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.

Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]

Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for  [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]

Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]

So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

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There is a vertical asymptote at x = 0.

A vertical asymptote is a vertical line that the graph of a function approaches but never touches or crosses. In the case of a rational function such as f(x) = x^3/(x^2-4), vertical asymptotes occur where the denominator of the function is equal to zero.

In this case, the denominator is x^2 - 4, which is equal to zero when x = ±2. However, we need to check whether these values are in the domain of the function. Since the interval of interest is (–18, 19), we see that only x = 2 is in the domain of the function.Therefore, the only vertical asymptote of the function f(x) = x^3/(x^2-4) on the interval (–18, 19) is at x = 0, which is the value of x where the denominator is closest to zero.

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The equation of the line passing through the given points is y = 3x-1.

Given that is a line passing through two points (0, 2) and (-1, -1) we need to find the equation of the line using them,

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (0, 2) and (-1, -1),

Therefore, the required equation is =

y+1 = -1-2/-1 (x-0)

y+1 = 3x

y = 3x-1

Hence, the equation of the line passing through the given points is y = 3x-1.

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The value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.

To evaluate the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex], where E is the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid becomes:

[tex]z = 9 - (r^2)[/tex]

The limits of integration are:

0 ≤ r ≤ 3 (since the paraboloid intersects the xy-plane at z = 0 when r = 3)

0 ≤ θ ≤ 2π

0 ≤ z ≤ 9 - (r^2)

The triple integral becomes:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r√(r^2) dz dθ dr[/tex]

Simplifying, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r^2 dz dθ dr[/tex]

Evaluating the innermost integral, we get:

∫[tex]0^(9-r^2) r^2 dz = (9-r^2)r^2[/tex]

Substituting this back into the triple integral, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π (9-r^2)r^2 dθ dr[/tex]

Evaluating the remaining integrals, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 (9r^2 - r^4) dθ[/tex]

= 2π [243/5]

= 486π/5

Therefore, the value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] dV over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.

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The percent increase in the interstate highway system from 1960 to now is 381%.

option A.

The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.

percent increase =  100% x (new value - old value) / old value

percent increase = 100% x  (77,000 - 16,000) / 16,000

percent increase = 100% x 61,000 / 16,000

percent increase = 381.25%

Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.

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1) If there are 2500 tickets sold, and you buy 1 ticket, then the probability of your ticket being the winning ticket is 1/2500 or 0.04%.

2) If you buy 5 tickets, then the probability of having a winning ticket is 5/2500 or 0.2%.

3) If you and your 4 friends each buy 5 tickets, then there will be a total of 25 tickets. The probability of having a winning ticket in this scenario is 5/25 or 20%.

4) The chances of holding a winning ticket have not changed. This is because the consolation prizes are separate from the main prize, and the probability of winning the main prize is still the same.

The addition of consolation prizes does not affect the probability of winning the main prize.

Assuming the same raffle is held every year and you and your 4 friends buy 5 tickets each year, the average net winnings would be calculated as follows:

Total cost of tickets = $1 x 5 x 5 = $25

Total prize money = $1200 + ($400 x 2) = $2000

Probability of winning = 5/2500 = 0.2%

Expected value of winning = $2000 x 0.2% = $4

Average net winnings = ($4 - $25)/year = -$21/year

This means that on average, you and your friends would lose $21 per year if you participate in the raffle every year.

However, it is important to note that this is just an average and there is a chance of winning a larger prize which would make the net winnings positive.

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The probability of a sophomore attending the prom, given that they were selected from the group of sophomores, is:

P(will attend the prom|sophomore) = (number of sophomores attending the prom) / (total number of sophomores)

From the table, we see that the number of sophomores attending the prom is 10, and the total number of sophomores is 54 (10 + 17 + 27). Therefore:

P(will attend the prom|sophomore) = 10 / 54

Simplifying the fraction, we get:

P(will attend the prom|sophomore) = 5 / 27

So the probability of a sophomore attending the prom is 5/27 (18.519%).

The percentage is 9.0% of the senior class are either members of the Key Club, enrolled in AP Physics, or both.

We need to find the percentage of seniors who are either members of the Key Club, enrolled in AP Physics, or both. We can use the formula:

Total percentage = Key Club percentage + AP Physics percentage - Both percentage

Step 1: Identify the given percentages
Key Club percentage = 2.3%
AP Physics percentage = 8.6%
Both percentage = 1.9%

Step 2: Apply the formula
Total percentage = 2.3% + 8.6% - 1.9%

Step 3: Calculate the result
Total percentage = 9.0%

So, 9.0% of the senior class are either members of the Key Club, enrolled in AP Physics, or both.

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The length of l is approximately 6.1 inches to the nearest tenth of an inch.

To find the length of l, we can use the Law of Cosines which states that:

                     c^2 = a^2 + b^2 - 2ab*cos(C)

where c is the side opposite angle C, and a and b are the other two sides.

In this case, we want to find the length of l, which is opposite the given angle ∠L. So we can label l as side c, and label m and n as sides a and b, respectively. Then we can plug in the values we know and solve for l:

                      l^2 = m^2 + n^2 - 2mn*cos(L)

l^2 = (2.1)^2 + (8.2)^2 - 2(2.1)(8.2)*cos(85°)

l^2 = 4.41 + 67.24 - 34.212

l^2 = 37.438

l = sqrt(37.438)

l ≈ 6.118

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A. Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.

B. In this case, the overall cost of the sofa would be approximately $2,284.08

To find the initial value of the home when Zahir purchased it, we can use the compound interest formula:

Future Value = Initial Value * (1 + (interest rate))^years

Let Initial Value be P. We are given the Future Value as $548,900, the interest rate as 4.8%, and the number of years as 15.

548,900 = P * (1 + 0.048)^15

Now, we'll solve for P:

P = 548,900 / (1 + 0.048)^15

P ≈ 305,113.48

a. Future Value = Initial Value * (1 + (interest rate / number of periods))^(years * number of periods)

Initial Value = $1,791.99

Interest Rate = 27.93% (0.2793)

Number of periods = 12 (monthly)

Years = 1

Future Value = 1,791.99 * (1 + (0.2793 / 12))^(1 * 12)

Future Value ≈ 2284.33

Kiran will be billed approximately $2,284.33 one year after the date of purchase if she does not make any payments.

b.  interest were compounded annually:

Future Value = Initial Value * (1 + interest rate)^years

Future Value = 1,791.99 * (1 + 0.2793)^1

Future Value ≈ 2284.08

In this case, the overall cost of the sofa would be approximately $2,284.08, which is slightly lower than if the interest were compounded monthly ($2,284.33).

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The student's error could be in the wrong formula he used. The  area of the sector is 245.043 sq.

The formula for area of a sector is

A = (θ/360) * π * r^2

where:

θ is the central angle of the sector in degrees

r is the radius of the circle

In this case, the central angle θ is 45 degrees and the radius r is 25 cm. So the area of the sector should be:

A = (45/360) * π * (25)^2

A = (1/8) * π * 625

A = 78.125π ≈ 245.043 sq. cm

The student could have made an error during any step of the calculation.

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Answer: Dude, I think its B. but I wouldn't use this site, its not a good rabbit hole to go down.

Step-by-step explanation:

if you meant simplification

[tex]4^3\sqrt{-88}\implies 64\sqrt{-88}\implies 64\sqrt{(-1)(2^2)(2)(11)}\implies 64(2)\sqrt{(-1)(2)(11)} \\\\\\ 128\sqrt{(2)(11)}\cdot \sqrt{-1}\implies 128\sqrt{22}~i[/tex]

Answer:

a. n < 14

b.  n ≥ 14

Step-by-step explanation:

a.

We see the line to the left of 14, meaning it will be smaller than 14. So, the inequality is n < 14

b.

The line goes to the right of 14, meaning it will be bigger than 14. This has a close circle meaning there will be an equal sign. So, the inequality is n ≥ 14

Answer:

< 3 = 3x + 105°

Step-by-step explanation:

There is remot angle theory which is the exterior angle is congrent to the other non adjecent angle in triangle.

so <1 + <EDF = <3

(3x + 15 ) ° + 90° = <3

3x°+ 105° = <3

< 3 = 3x + 105° .... so the measur of angle 3 interms of x is 3x + 105°

The mean decreases, and the median remains the same from plot 1 to plot 2.

In the first box-and-whisker plot, the hourly wages earned by 20 employees are displayed, with a range from $8.70 per hour to $11.50 per hour. The median, which is the value that separates the higher half of the data from the lower half, is $10 per hour. The mean, which is the average of all the wages, is calculated by adding up all the wages and dividing the total by 20.

When one employee earning $15 per hour quits and is replaced by a new employee earning $8 per hour, the second box-and-whisker plot is created. The range of wages extends from $8 per hour to $15 per hour, with a median of $9.50 per hour. Since the new employee is earning a lower wage, the mean hourly wage decreases.

Therefore, the correct answer to the question is that the mean decreases, and the median remains the same. It is important to note that while the median does not change in this case, it is not always the case in other situations where data is added or removed from a set. It is also important to note that box-and-whisker plots are helpful in visualizing the spread of data and identifying any outliers.

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Answer:

part a: The slope of the function represents the rate of change of the balance in the bank account per day. To find the slope, we can use the formula: slope = (change in y)/(change in x).

Using the values from the table, we have: slope = (720-600)/(3-0) = 120/3 = 40. Therefore, the slope of the function g(x) is 40.

part b: Using the point-slope form of the equation of a line, we can write: g(x) - 600 = 40(x-0). Simplifying, we get: g(x) = 40x + 600. This is the slope-intercept form of the equation, where the y-intercept is 600 and the slope is 40.

To write in standard form, we can rearrange the equation as: -40x + g(x) = 600.

part c: Using function notation, we can write the equation as: g(x) = 40x + 600.

part d: To find the balance in the bank account after 7 days, we can use the equation we found in part c and substitute x = 7: g(7) = 40(7) + 600 = 880. Therefore, the balance in the bank account after 7 days is $880.

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Your answer is D. 1/18  is the probability that she will choose a chocolate bar and then a piece of gum

First, let's determine the total number of snacks in the bag:
4 bags of chips + 5 fruit snacks + 6 chocolate bars + 3 pieces of bubble gum = 18 snacks

Next, let's find the probability of choosing a chocolate bar:
There are 6 chocolate bars and 18 snacks total, so the probability is 6/18, which simplifies to 1/3.

Since she puts the chocolate bar back, the total number of snacks remains the same. Now, let's find the probability of choosing a piece of gum:
There are 3 pieces of gum and 18 snacks total, so the probability is 3/18, which simplifies to 1/6.

Finally, to find the probability of both events happening, multiply the probabilities together:
(1/3) * (1/6) = 1/18

So, the probability that Debra will choose a chocolate bar and then a piece of gum is 1/18. Your answer is D. 1/18.

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The probability of the complement of the event of Ignacio chooses a plant at random that does not have a white bloom is 0.7692.

The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more probable it is that the event will take place.

Probability is a way to gauge how likely something is to happen. Several things are difficult to forecast with absolute confidence. With it, we can only make predictions about the likelihood of an event happening, or how likely it is.

The probability that Ignacio chooses the plant which have white bloom in it is,

P = number of white bloom / total number of flowers

P = 21 / 91

So the probability that the chosen flower is not white is,

1 - P = 1 - 21/91 = 70/91 = 0.7692.

Therefore, the probability of not choosing white is 0.7692.

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Answer:

[tex] \sqrt{3 {x}^{3} } = x \sqrt{3x} [/tex]

We note that x>0 here.

Answer:

The answer is x√3x

Step-by-step explanation:

√3x³=x√3x

A value that is less than 2 1/5% from the given data is 0. 0215. Option A is the correct answer.

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.

To find a value that is less than 2 1/5% we need to find the decimal number of a given fraction. to convert the given fraction into decimal form we need to divide the given fraction by 100.

= 2 1/5% / 100

= (2 + (1/5)) / 100

= 0.022

A value that is less than 0.022 from the given data is 0. 0215.

Therefore, a value less than 2 1/5% is 0. 0215.

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The equivalent expression is $\left(\dfrac{4^{3}}{5^{-2}}\right)^{5} = 102400000000000000000$.

We can simplify the expression inside the parentheses first:

\begin{aligned} \frac{4^3}{5^{-2}} &= 4^3 \cdot 5^2 \ &= (2^2)^3 \cdot 5^2 \ &= 2^6 \cdot 5^2 \ &= 2^5 \cdot 2 \cdot 5^2 \ &= 2^5 \cdot 10^2 \ &= 3200 \end{aligned}

Now we can substitute this value into the original expression and simplify further:

\begin{aligned} \left(\frac{4^3}{5^{-2}}\right)^5 &= (3200)^5 \ &= (2^8 \cdot 5^2)^5 \ &= 2^{40} \cdot 5^{10} \ &= (2^4)^{10} \cdot 5^{10} \ &= 16^{10} \cdot 5^{10} \ &= (16 \cdot 5)^{10} \ &= 80^{10} \ &= 102400000000000000000 \end{aligned}

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Alexander stacked  16 unit cubes required to build the rectangular prism.

A three-dimensional solid object called a prism has two identical ends. It consists of equal cross-sections, flat faces, and identical bases. Without bases, the prism's faces are parallelograms or rectangles.

Here we need to find the number of cubes required to build the rectangular prism.

Here first we need to find how many cubes stack in the base layer

Number of unit cubes in the base layer = Number of cubes along the length * Number of cubes along the width

The number of unit cubes in the base layer = 2 * 4 = 8 cubes.

Total number of unit cubes in prism =Number of unit cubes in the base layer *Number of layers = 8 * 2 = 16 unit cubes

So, there are 16 unit cubes are required to build the rectangular prism.

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Complete question :

Alexander stacked unit cubes to build the rectangular prism below. Use the rectangular prism to answer​ the question.

How many cubes are required to build the rectangular prism?

A circle with a circumference of 40π and a chord of the circle is 24 units, then the chord is 16 units from the center of the circle,

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Here, we are given that the circumference is 40π. That is

40π = 2πr

Dividing both sides by 2π, we get:

r = 20

Now, we need to find the distance between the chord and the center of the circle. Let O be the center of the circle, and let AB be the chord. We know that the perpendicular bisector of a chord passes through the center of the circle. Let P be the midpoint of AB, and let OP = x.

By the Pythagorean Theorem,

x^2 + 12^2 = 20^2

Simplifying,

x^2 + 144 = 400

x^2 = 256

x = ±16

Since OP is a distance, it must be positive. Therefore, x = 16, and the chord is 16 units from the center of the circle.

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Where the above figures are given, The right triangles are: B and C.

Using the phythagoren theorem, we can determind the options that represent a right ttriangle.


A 5,8, and 9:

5^2 + 8^2 = 25 + 64 = 89

9^2 = 81

Not a right triangle.

B 20, 21, and 29:

20^2 + 21^2 = 400 + 441 = 841

29^2 = 841

It is a right triangle.

C 9, 12, and 15:

9^2 + 12^2 = 81 + 144 = 225

15^2 = 225

It is a right triangle.

D 5, 6, and 11:

5^2 + 6^2 = 25 + 36 = 61

11^2 = 121

Not a right triangle.

The right triangles are: B and C.

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