What is the volume of a cone with a radius of 2.5 and a height of 4 answer in terms of pi

options:
-20 5/6π
-25π
-8 1/3π
-15 5/8π

To create a story context for the given expressions, which are (5 1/4 - 2 1/8) divided by 4 and 4 x (4.8/0.8).

Imagine there is a fruit store where you have to prepare fruit baskets for a local charity event. The first expression (5 1/4 - 2 1/8) divided by 4 can be a story about the number of apples to be distributed equally among four baskets.

You initially have 5 1/4 dozen apples, but you realize that 2 1/8 dozen of them are not suitable for the baskets.

To find out how many dozens of apples should be put into each basket, you need to subtract the unsuitable apples and divide the result by 4:

(5 1/4 - 2 1/8) / 4

Now, let's move on to the second expression, 4 x (4.8/0.8). This can be a story about the number of oranges you need to purchase for the fruit baskets. You already have 4.8 dozen oranges, but you need to add more to reach the desired ratio of oranges to apples.

Your friend suggests that for every 0.8 dozen oranges you currently have, you should add 4 more dozen oranges. To find out how many dozens of oranges you need to buy, you can use this formula:

4 x (4.8/0.8)

By creating these story contexts, you can use the given expressions to solve real-life problems, such as distributing fruits among charity baskets.

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The unit price in dollars per centimeter is 80 cents.

:: Total wire length = 19.5 cm

:: Total amount paid = $15.60

Per unit price = [ (total amount paid) / (total wire length) ]

Per unit price = (15.60 / 19.5) $/cm

Per unit price = 0.8 ($/cm)

And as we know, $1 = 100 cents,

So,

$0.8 = 0.8 x 100 cents = 80 cents.

Therefore, the unit price in dollars per centimeter is 80 cents.

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The order of the volumes of the boxes from least to greatest is  Box D, Box B, Box C, Box A. Therefore, the correct option is D.

To determine the order of the volumes of the boxes from least to greatest, we will first calculate the volume of each box using the formula:

Volume = Length × Width × Height.

Hence,

1. Box A: Volume = 2in × 4.5in × 6in = 54 cubic inches

2. Box B: Volume = 6in × 2.5in × 3in = 45 cubic inches

3. Box C: Volume = 5in × 4.5in × 2.25in = 50.625 cubic inches

4. Box D: Volume = 2.5in × 2.25in × 3in = 16.875 cubic inches

Now, arrange the volumes in ascending order:

Box D (16.875), Box B (45), Box C (50.625), Box A (54)

Thus, the correct answer is D: Box D, Box B, Box C, Box A.

Note: The question is incomplete. The complete question probably is: The table shows the dimensions of four boxes. Which is the order of the volumes of the boxes from least to greatest?

          Length Width Height

Box A 2in; 4.5in; 6in

Box B 6in; 2.5in; 3in

Box C 5in; 4.5in; 2.25in

Box D 2.5in; 2.25in; 3in

A) Box A Box B, Box C, Box D B) Box A, Box C, Box B, Box D C) Box B, Box D, Box A, Box C D) Box D, Box B, Box C, Box A.

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To write the given expression in factored form using the greatest common factor and distributive property, we need to find the largest common factor of 9 and 6, which is 3. Then we can factor out 3 from both terms, giving us 3(3d+2e). Therefore, the equivalent expression in factored form is 3(3d+2e).

This expression is simplified and shows that 3 is a common factor of both terms. In 100 words, this process involves identifying the greatest common factor between the terms and then using the distributive property to factor it out. This simplifies the expression and allows for easier calculations in further operations.

It is important to always look for common factors and simplify expressions whenever possible.

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Answer:

To calculate the amount of money spent in interest alone over the course of a 30-year mortgage, we can use the formula:

Total Interest = (Monthly Payment x Number of Payments) - Principal

For a 3.5% 30-year mortgage with a principal of $180,000, the monthly payment can be calculated using the formula:

Monthly Payment = (Principal x Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))

where Monthly Interest Rate = Annual Interest Rate / 12, and Number of Payments = 30 years x 12 months per year = 360.

Plugging in the values, we get:

Monthly Payment = (180,000 x 0.0035) / (1 - (1 + 0.0035)^(-360)) = $808.28

Using this monthly payment, we can calculate the total interest over the 30-year period:

Total Interest = ($808.28 x 360) - $180,000 = $101,020.80

Therefore, the correct answer is A. $110,880 (which is not one of the options given).

The exponential function y = [tex]2700(1.02)^t[/tex] models the growth of bacteria cells in a petri dish over time, with an initial population of 2700 cells and a growth rate of 2% per hour.

Exponential functions are often used to model situations where the growth or decay of a quantity depends on a constant proportionality factor.

In this case, the proportionality factor is the growth rate, which is represented by the constant 0.02 in the function. The factor (1 + r) represents the growth factor, which is the multiplier for the initial population to calculate the population after t hours. The larger the growth rate, the faster the population will grow, and the steeper the graph of the exponential function will be.

The equation y = [tex]2700(1.02)^t[/tex] can be used to make predictions about the growth of the bacteria population over time. For example, after one hour, the number of bacteria cells would be y = [tex]2700(1.02)^1[/tex] = 2754 cells. After two hours, the number of cells would be y = [tex]2700(1.02)^2[/tex] = 2812 cells, and so on.

It's worth noting that exponential growth cannot continue indefinitely, as there are always limiting factors that will eventually constrain the growth of a population. In the case of bacteria, the petri dish may eventually become overcrowded or run out of nutrients, which will slow or stop the growth of the bacteria population. Therefore, the exponential function y = [tex]2700(1.02)^t[/tex] is a model that is only valid for a certain range of values of t, beyond which other factors may come into play.

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The equation in standard form for the circle with center (8,0) and radius 3/3 is (x - 8)² + y² = 1

To write the equation in standard form for the circle with center (8,0) and radius 3/3, we can use the following formula for a circle in standard form:
(x - h)² + (y - k)² = r²
Where (h, k) is the center of the circle and r is the radius. In this case, the center is (8,0) and the radius is 3/3, which simplifies to 1. Now, we can substitute the values of h, k, and r into the equation:
(x - 8)² + (y - 0)² = 1²

Since (y - 0) is just y, we can simplify the equation to:
(x - 8)² + y² = 1
So, the equation in standard form for the circle with center (8,0) and radius 3/3 is:
(x - 8)² + y² = 1
In summary, we used the standard form equation for a circle, substituted the given values for the center and radius, and simplified the equation to obtain the final answer.

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It would take Jose approximately 3232 minutes (or about 53.87 hours) to read 2020 pages at the same rate of 2.5 pages every four minutes.

To determine how long it would take Jose to read 2020  runners at the same rate of2.5  runners every four  twinkles, we can use a proportion.   Let x be the number of  twinkles it would take Jose to read 2020  runners. also, we can set up the following proportion:

2.5 pages / 4 minutes = 2020 pages / x minutes

To solve for x, we can cross-multiply and simplify:

2.5 pages * x minutes = 4 minutes * 2020 pages

2.5x = 8080

x = 8080 / 2.5

x = 3232

Therefore, it would take Jose approximately 3232 minutes  to read 2020 pages at the same rate of 2.5 pages every four minutes.

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Answer:

Obese

Step by Step Explanation:

looked it up :)

The area of one garden using each side of the lounging area is 15 feet long is equal to 56.25 square feet.

Shape of the garden landscape is square.

If the lounging area is a square with sides of length 15 feet,

Area of lounging area

= (15 feet) × (15 feet)

= 225 square feet

Four congruent sections of the landscape plan .

Three indoor gardens and one walkway.

Divide the lounging area into four equal square sections.

Each of the congruent sections has an area equal to,

Area of lounging area = 4 × area of one garden

Let's call the area of one garden be x.

⇒225 = 4x

Solving for x, we divide both sides by 4

⇒x = 225/4

⇒x  = 56.25 square feet

Therefore, the area of one garden is 56.25 square feet.

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Answer:

a.x=100 equation: 540=(125·2)+90+(2x)

b. x=3 equation: 6x+18=2x+30

Step-by-step explanation:

a. We know that the interior angles of a pentagon have to equal 540 degrees.

So:

540=125+125+90 (hence the square) + x + x

simplify:

540=340+2x

simplify:

200=2x

x=100

b. Using the alternate exterior angles theorem we can say:
6x+18=2x+30

simplify:

4x+18=30

4x=12

x=3

Answer:

89.6°

Step-by-step explanation:

180-90.4=89.6°

Answer: 89.6

Step-by-step explanation:

Supplementary means angles adding up to 180

180-90.4  = x

x=89.6   this is your supplemental angle

1. For the solid bounded by the panes 2 = 1 - x and z=1-y in the first octant, one triple integral that describes the volume of the solid. The region is bounded by the x-axis and the curve y = √(2x-x^2), which is the top half of a circle centered at (1,0) with radius 1.

One possible order of integration is:
∫0^1 ∫0^(1-x) ∫0^(1-y) dzdydx
This means we integrate over z first, then y, then x. Another order of integration could be:
∫0^1 ∫0^x ∫0^(1-x-y) dzdydx
Here we integrate over z first, then x, then y.
Another possible order of integration is:
∫0^1 ∫0^1-x ∫0^1-y dzdxdy
Here we integrate over z first, then x, then y. This order of integration can also be rewritten in polar coordinates as:
∫0^(π/4) ∫0^(secθ-1) ∫0^(cscθ-1) r dzdrdθ
2. Compute by switching the order of integration:
∫0^2 ∫0^√(2x-x^2) dydx

First, let's sketch the region of integration. The region is bounded by the x-axis and the curve y = √(2x-x^2), which is the top half of a circle centered at (1,0) with radius 1.
We can switch the order of integration to integrate over x first, then y:
∫0^1 ∫0^(2-2y^2) dxdy
To find the limits of integration for x, we set y = √(2x-x^2) and solve for x:
y^2 = 2x - x^2
x^2 - 2x + y^2 = 0
(x-1)^2 = 1 - y^2
x = 1 ± √(1-y^2)
Since the curve is the top half of the circle, we take the positive square root:
x = 1 + √(1-y^2)
So the limits of integration for x are 0 to 2-2y^2. Integrating with respect to x first gives:
∫0^1 ∫0^(2-2y^2) dxdy = ∫0^1 (2-2y^2)dy = 4/3
3. Write the following integral in polar coordinates, then solve:
arctan (dy/dx)
We can write dy/dx in terms of polar coordinates using the chain rule:
dy/dx = (dy/dr)(dr/dθ)(1/dx/dθ)
Using the relationships x = rcosθ and y = rsinθ, we have:
dx/dθ = -rsinθ
dy/dθ = rcosθ, So
dy/dx = (dy/dr)(dr/dθ)(1/dx/dθ) = (cosθ)/(sinθ) = cotθ
Therefore, the integral becomes:
∫arctan(cotθ) dθ

To solve this integral, we use the identity arctan(x) + arctan(1/x) = π/2 for x > 0:
arctan(cotθ) = π/2 - arctan(tanθ)
So the integral becomes:
∫(π/2 - arctan(tanθ)) dθ
Integrating, we get:
(π/2)θ - ln|cosθ| + C
Where C is the constant of integration.
1. To find three other orders of integration for the solid bounded by the planes z = 1 - x, z = 1 - y, x = 0, y = 0, and z = 0 in the first octant, we can rearrange the given triple integral, which is given as:
∫∫∫_D dz dy dx
Now, we can find three other orders of integration:
a) ∫∫∫_D dx dz dy
b) ∫∫∫_D dy dx dz
c) ∫∫∫_D dy dz dx
2. To compute the volume of the solid by switching the order of integration, we can rewrite the given integral ∫∫ dy dx as: ∫∫ dx dy

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Answer:

(1, 4)

Don't worry, I feel the same way sometimes, :)

Step-by-step explanation:

Substitute the bottom equation into the top.

If y=3x+1, than the first y will equal 3x+1.

3x+1 = x+3

Subtract 1 from 3

3x = x+2

Subtract x from 3x.

2x=2

Divide everything by 2.

x=1

Now substitute it in the equation.

1. y=1 + 3

y=4

2. y= 3(1) + 1

y=3+1

y=4

(1, 4)

The total area of the composite figure is 1650 mm

To find the area of a composite figure, you need to break it down into simpler shapes whose areas you can calculate and then add up the individual areas. In this case, the composite figure consists of two shapes: a rectangle and a trapezoid.

To find the area of the rectangle, you multiply its length by its width. From the given dimensions, the length of the rectangle is 40 mm and the width is 30 mm. So the area of the rectangle is 40 x 30 = 1200 mm².

To find the area of the trapezoid, you use the formula for the area of a trapezoid: (base1 + base2) x height / 2. From the given dimensions, the two bases of the trapezoid are 25 mm and 35 mm, and the height is 15 mm. So the area of the trapezoid is (25 + 35) x 15 / 2 = 450 mm².

Now you add the areas of the two shapes together to get the total area of the composite figure: 1200 + 450 = 1650 mm².

Therefore, the total area of the composite figure is 1650 mm², rounded to the nearest hundredth.

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To arrange the books in the specified order (Mathematics, Science, and English), you need to determine the number of arrangements for each subject's books and then multiply them together.

For the 4 mathematics books, there are 4! (4 factorial) ways to arrange them, which is 4 × 3 × 2 × 1 = 24 ways.

For the 5 science books, there are 5! (5 factorial) ways to arrange them, which is 5 × 4 × 3 × 2 × 1 = 120 ways.

For the 3 English books, there are 3! (3 factorial) ways to arrange them, which is 3 × 2 × 1 = 6 ways.

To find the total number of ways to arrange all the books in the required order, multiply the arrangements for each subject together: 24 (Mathematics) × 120 (Science) × 6 (English) = 17,280 ways.

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45% is the experimental probability that only 1 of 4 children in a family is a girl.

To find the experimental probability that only 1 of 4 children in a family is a girl, we need to count the number of times this outcome occurs in the sample and divide it by the total number of outcomes. In this case, we have 20 coin tosses, and we are looking for sequences with exactly 1 "tails" (girl) and 3 "heads" (boys).

Here are the sequences with exactly 1 girl:
HTHH
HHTT
HHHT
THHT
HTTH
TTHH
THTT
TTHH
THTT

There are 9 such sequences out of the total 20 coin tosses. Therefore, the experimental probability is:

(9/20) * 100% = 45%

The experimental probability that only 1 of 4 children in a family is a girl is 45%.

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The percent of the customers at Harris Teeter that are adults is 70%

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

Customers = 160

Children = 48

using the above as a guide, we have the following:

Adults = Customers - Children

substitute the known values in the above equation, so, we have the following representation

Adults = 160 - 48

So, we have

Adults = 112

Next, we have

Percentage = 112/160 * 100%

Evaluate

Percentage = 70%

Hence, the percentage is 70%

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The dimensions of the original square is 8 by 8.

Let x be the original side length of the square. The area of the square is x². When one side is doubled and the adjacent side is diminished by 3, the rectangle's dimensions become 2x and (x-3). The area of the rectangle is (2x)(x-3) = 2x² - 6x.

According to the problem, the area of the rectangle is greater than the area of the square by twice the original side of the square, which is 2x. So we can set up the equation:

2x² - 6x = x² + 2x

Now, solve for x:

2x² - x² = 6x + 2x
x² = 8x
x = 8

So the dimensions of the original square are 8 by 8.

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ - 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{- 7}(x-\stackrel{x_1}{2}) \\\\\\ y-7=-7x+14\implies {\Large \begin{array}{llll} y=-7x+21 \end{array}}[/tex]

The 95% confidence interval for the true proportion of defective chips is between 0.043 and 0.197.

To calculate the 95% confidence interval for the true proportion of defective computer chips, the quality control specialist would use the formula:

proportion +/- z ×√(proportion x (1-proportion)/sample size)

In this case, the proportion of defective chips is 12/100 or 0.12. The sample size is 100. To find the value of z for a 95% confidence level, we look at a standard normal distribution table or use a calculator and find that it is 1.96.

So the calculation for the confidence interval would be:

0.12 +/- 1.96 × √(0.12 × (1-0.12)/100)

Simplifying this gives us:

0.12 +/- 0.077

This means that if we repeated this sampling process many times, we would expect the true proportion of defective chips to fall within this interval 95% of the time.

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Deli should charge $24.50 for the 50-inch family sub.

In a transaction, the price of something refers to amount of money that you have to pay in order to buy it. To make the prices comparable, we can use the unit price which is as follows>

The price per inch of 6-inch sub is:

= $2.95 / 6 inches

= $0.49/inch

To make 50-inch sub price, we will solve as:

= $0.49/inch * 50 inches

= $24.50

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Only the statement "One machine is considerably more unreliable than the rest." is valid for the data.

Total number of correct cuts = 42 + 55 + 13 + 24 + 17 = 151

Total number of cuts = 100 + 100 + 100 + 100 + 100 = 500

Percentage of correct cuts = (151/500) * 100 = 30.2%

This statement is not valid, as only 30.2% of the cuts are the correct length.

One machine is considerably more unreliable than the rest."

By examining the number of correct cuts for each machine, we can see that Machine 3 has only 13 correct cuts, while the other machines have more than 17. This statement is valid.

3. When a machine misses the correct length, it tends to cut too long."

We need to compare the number of cuts that are too long (1.26-1.27 feet) with those that are too short (1.23-1.24 feet) across all machines:

Total number of cuts too long = 4 + 2 + 3 + 6 + 4 = 19

Total number of cuts too short = 980 + 72 + 67 = 1119

This statement is not valid, as the machines tend to cut too short rather than too long.

4. "Machine 5 will cut every batch the correct length at least 92% of the time."

To check this statement, we need to find the percentage of correct cuts for Machine 5:

Percentage of correct cuts for Machine 5 = (17/100) * 100 = 17%

This statement is not valid, as Machine 5 only cuts the correct length 17% of the time, which is less than 92%.

only the statement "One machine is considerably more unreliable than the rest." is valid for the data.

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The maximum height of Marsha's math book is 36 feet.

To find the maximum height of Marsha's math book, we need to find the vertex of the parabolic equation h = [tex]-16x^2 + 24x + 30[/tex]. The vertex of a parabola is the highest or lowest point on the curve, depending on whether the parabola opens upward or downward.

To find the x-coordinate of the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation [tex]ax^2 + bx + c[/tex]. In this case, a = -16 and b = 24, so we have:

x = -b/2a = -24/(2*(-16)) = 0.75

To find the y-coordinate of the vertex, we can substitute x = 0.75 into the equation h = [tex]-16x^2 + 24x + 30[/tex], which gives us:

h = [tex]-16(0.75)^2 + 24(0.75) + 30 = 36[/tex]

Therefore, the maximum height of Marsha's math book is 36 feet.

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Answer:

-----------------------

Given:

(i) We know 60 out of 110 can speak both languages, so as 60 out of 85. The number 60 is counted twice if we add them together.

Find the number of those speak either language:

(ii) Find the number of thise who can talk neither of these languages:

r = 4.0 units

Given that,

A cylinder has a radius of r units, and that the height of the cylinder is also r units.

The lateral area of the cylinder is 98 square units.

We need to find the value of r.

The formula for the lateral area of the cylinder is given by:

[tex]\text{A}=2\pi \text{rh}[/tex]

Put all the values,

[tex]2\pi \text{rh}=98[/tex]

[tex]\text{r}=\sqrt{\dfrac{98}{2\pi} }[/tex]

[tex]\text{r}=4.0 \ \text{units}[/tex]

So, the value of r is equal to 4.0 units.

The minimum number of dots that could lie on the whole surface of four standard dice glued together is 56.

This can be achieved by placing the faces with 1 dot opposite the faces with 6 dots, the faces with 2 dots opposite the faces with 5 dots, and the faces with 3 dots opposite the faces with 4 dots on all four dice. Since the sum of the numbers on opposite faces of each individual die is always 7, the sum of the numbers on opposite faces of the four glued-together dice is also always 7. Therefore, the minimum number of dots on the whole surface is 7 times the number of faces, which is 7 x 8 = 56.

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Since 2 is greater than 1, it would have been faster for Daniel to swim directly to the campsite. Therefore, Daniel's sister is incorrect.

We can solve this problem using the formula for distance, rate, and time, which is:

distance = rate x time

Let's assume that Daniel swims at a rate of s feet per second and jogs at a rate of j feet per second. If he swims directly to the campsite, the distance he needs to cover is the distance d between the campsite and the boat ramp, which is 200 feet. If he swims to the boat ramp and then jogs to the campsite, he will need to cover the distance d twice, once while swimming and once while jogging. The total distance he will cover is 2d = 400 feet.

If Daniel swims directly to the campsite, the time it will take him to cover the distance is:

time1 = d/s

If he swims to the boat ramp and then jogs to the campsite, the time it will take him to cover the distance is:

time2 = d/s + d/j

To compare the two times, we can take their ratio:

time2/time1 = (d/s + d/j)/(d/s) = 1 + j/s

If this ratio is less than 1, then Daniel's sister is correct, and he would have arrived quicker by swimming to the boat ramp and then jogging. If the ratio is greater than 1, then it would have been faster for him to swim directly to the campsite.

Substituting d = 200, we get:

time2/time1 = 1 + j/s = 1 + (j/s)*(200/200) = 1 + (200j)/(ds)

Since Daniel arrives at the campsite out of breath from his swim and jog, we can assume that his rates of swimming and jogging are roughly equal. Let's assume s = j = r, where r is the common rate of swimming and jogging. Substituting this into the ratio, we get:

time2/time1 = 1 + (200r)/(dr) = 1 + 200/d

To determine if Daniel's sister is correct, we need to compare this ratio to 1. If time2/time1 is less than 1, then Daniel's sister is correct. If it is greater than 1, then it would have been faster for Daniel to swim directly to the campsite.

Substituting d = 200, we get:

time2/time1 = 1 + 200/200 = 2

Since 2 is greater than 1, it would have been faster for Daniel to swim directly to the campsite. Therefore, Daniel's sister is incorrect.

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Answer:

6 30/31 as fraction and with Long Division its 6 with 30 Remainder