The measure of arc CAD is either 240 or 260.
How to do measure of arc?Without additional information, it is not possible to determine the measure of arc CAD with certainty. The measure of an arc depends on the central angle that subtends it.
If the central angle is known, the measure of the arc can be calculated using the formula: measure of arc = (central angle / 360) x circumference of the circle. However, without knowing the central angle, we cannot determine the measure of arc CAD.
Therefore, we need to be provided with additional information such as the measure of another angle that is related to the central angle, or the length of a chord that subtends the arc in order to determine the central angle and the measure of arc CAD.
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A cylindrical can without a top is made to contain 181 in^3 of liquid. Find the dimensions that will minimize the cost of the metal to make the can.
The dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.
How to find the dimensions that will minimize the cost of the metal to make the cylindrical can without a top?We can use the following steps:
Step 1: Write the volume formula for the cylinder.
The volume (V) of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. Since the volume is given as 181 in³, we have:
181 = πr²h
Step 2: Solve for h in terms of r.
Divide both sides by πr²:
h = 181 / (πr²)
Step 3: Write the surface area formula for the cylinder without a top.
The surface area (S) of a cylinder without a top is given by the formula S = 2πrh + πr², where r is the radius and h is the height.
Step 4: Substitute h from step 2 into the surface area formula.
Replace h with 181 / (πr²) in the surface area formula:
S = 2πr(181 / (πr²)) + πr²
Step 5: Simplify the surface area formula.
After simplifying the surface area formula, we get:
S = (362 / r) + πr²
Step 6: Minimize the surface area.
To minimize the surface area, differentiate S with respect to r and set the derivative equal to 0:
dS/dr = -362/r² + 2πr = 0
Step 7: Solve for r.
To find the value of r that minimizes the surface area, solve the equation for r:
r³ = 181/π
r = (181/π)¹/³
Step 8: Find the height h.
Substitute the value of r back into the equation for h from step 2:
h = 181 / (π((181/π)¹/³)²)
Step 9: Calculate the dimensions.
Calculate the dimensions r and h using the values obtained in step 7 and step 8:
r ≈ 2.82 inches
h ≈ 7.10 inches
So, the dimensions that will minimize the cost of the metal to make the can are approximately r = 2.82 inches and h = 7.10 inches.
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Find the height of a skyscraper if you know that its top is 1000 feet
from a point on the ground and its base is 200 feet from the same
point.
The 1,000 feet and 200 feet distances of the top and the base of the skyscraper from the point on the ground, indicates, using Pythagorean Theorem that the height of the skyscraper is 400·√6 feet
What is the Pythagorean Theorem?Pythagorean Theorem states that the square of the length of the hypotenuse side of a right triangle is equivalent to the sum of the squares of the other two sides.
The distance of the top of the skyscraper from a point on the ground = 1000 feet
The distance of the base of the skyscraper from the same point = 200 feet
Therefore, according to the Pythagorean Theorem, in the right triangle formed by the ray from the top of the skyscraper to the point on the ground, the height, h, of the skyscraper, and the distance of the point on the ground from the skyscraper, we get;
1000² = h² + 200²
h² + 200² = 1000²
h² = 1000² - 200² = 960,000
h = √(960,000) = 400·√6
The height of the skyscraper is 400·√6 feet
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(3. 5 points) use the given data in problem 33 (page 302) to answer the following questions. Assume that population data follow normal distribution. (a) (1. 5 points) calculate a two-sided 95% confidence interval for true average degree of polymerization. (b) (one points) does the interval suggest that 440 is a plausible value for true average degree of polymerization? explain. (c) (one point) does the interval suggest that 450 is a plausible value for true average degree of polymerization? explain
Joyner Company’s income statement for Year 2 follows:
Sales $ 703,000
Cost of goods sold 109,000
Gross margin 594,000
Selling and administrative expenses 151,700
Net operating income 442,300
Nonoperating items:
Gain on sale of equipment 9,000
Income before taxes 451,300
Income taxes 135,390
Net income $ 315,910
Its balance sheet amounts at the end of Years 1 and 2 are as follows:
Year 2 Year 1
Assets
Cash and cash equivalents $ 294,410 $ 55,900
Accounts receivable 228,000 141,000
Inventory 318,000 289,000
Prepaid expenses 10,000 20,000
Total current assets 850,410 505,900
Property, plant, and equipment 639,000 508,000
Less accumulated depreciation 165,300 130,200
Net property, plant, and equipment 473,700 377,800
Loan to Hymans Company 46,000 0
Total assets $ 1,370,110 $ 883,700
Liabilities and Stockholders' Equity
Accounts payable $ 311,000 $ 262,000
Accrued liabilities 49,000 57,000
Income taxes payable 84,200 80,700
Total current liabilities 444,200 399,700
Bonds payable 209,000 105,000
Total liabilities 653,200 504,700
Common stock 340,000 287,000
Retained earnings 376,910 92,000
Total stockholders' equity 716,910 379,000
Total liabilities and stockholders' equity $ 1,370,110 $ 883,700
Equipment that had cost $31,500 and on which there was accumulated depreciation of $10,400 was sold during Year 2 for $30,100. The company declared and paid a cash dividend during Year 2. It did not retire any bonds or repurchase any of its own stock.
Required:
1. Using the indirect method, compute the net cash provided by/used in operating activities for Year 2.
2. Prepare a statement of cash flows for Year 2.
3. Compute the free cash flow for Year 2
the free cash flow for Joyner Company in Year 2, we need to follow these steps:
Step 1: Calculate operating cash flow (OCF).
Operating cash flow is calculated by taking the company's net income, adding back non-cash expenses (depreciation and amortization), and adjusting for changes in working capital.
Step 2: Calculate capital expenditures (CapEx).
Capital expenditures are the funds used by the company to acquire, upgrade, and maintain physical assets, such as equipment or buildings. In this case, we need to find the net change in equipment and accumulated depreciation.
Step 3: Subtract the cash dividend.
The cash dividend paid by the company during Year 2 should be subtracted from the operating cash flow.
Step 4: Calculate the free cash flow.
Free cash flow is the remaining cash after deducting capital expenditures and cash dividends. It represents the cash available for the company to repay debt, reinvest in the business, or distribute to shareholders.
Unfortunately, the provided information is not sufficient to compute the free cash flow for Year 2. Specifically, the net income, changes in working capital, and complete equipment transactions are needed to perform these calculations. Please provide the missing information so that a detailed step-by-step explanation can be given to compute the free cash flow for Joyner Company in Year 2.
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What is the explicit formula for this sequence?
-7, -3, 1, 5, ...
A. an = 9+ (n − 1)(-4)
B. an-4+ (n-1)(-7)
C. an-7+ (n − 1)4
D. an-7+ (n-1)(-4)
Answer:
It is C
Step-by-step explanation:
It cannot be d bc - 7-4=-11 so rejected
Not b bc the first number is - 7
The same w a
Is 11:15 to 12:15 a hour or 30 minutes
Answer:
It’s an hour
Answer:
11:15 to 12:15 is 1 hour.
11:15 is 1 hour and 15 minutes after 10:00. 12:15 is 1 hour and 15 minutes after 11:00. Therefore, the time span between 11:15 and 12:15 is 1 hour.
Step-by-step explanation:
Help!!!
if abc is similar to xyz and yzx, what special type of triangle is abc? complete the explanation.
If ABC is similar to XYZ and YZX, then the corresponding angles of those triangles are same, and the corresponding sides are proportional. because of this triangle ABC is a special type of triangle known as a "similar triangle."
In a similar triangle, the angles of the triangle are equal, however the sides can be exclusive lengths. but, the ratios of the corresponding aspects are usually the same. This property is beneficial in lots of regions of mathematics and physics, which includes trigonometry and the study of geometric shapes.
inside the case of triangle ABC, the fact that it's far much like each XYZ and YZX tells us that its angles are same to those of these triangles, and its sides are proportional to the ones of these triangles. This property may be used to solve many issues regarding triangles and other geometric shape.
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Suppose that, using the simulation in Exercise 4 (Connections), you devise a patch configuration using stepping stones. In your first simulation run, you set the leave prairie probability to 0. 9 and turn probability in non-prairie to zero. You run the simulation once, with no fires. The simulated butterfly population size after 100 weeks increases from 25 to 132. What does this result tell you about the real-world Fender's blue butterfly population
The result should be interpreted with caution and cannot be directly extrapolated to the real-world Fender's blue butterfly populations, and the simulation does not take these factors into account.
Find out the result tell you about Fenders blue butterfly population?The result of the simulation suggests that in a hypothetical scenario where the Fender's blue butterfly population is restricted to stepping stones, and the leave prairie probability is set to 0.9, the population is likely to increase over time. However, it is important to note that the simulation represents an idealized scenario and may not reflect the complexity of real-world butterfly populations.
Furthermore, the absence of fires in the simulation may not reflect the natural habitat of Fender's blue butterfly, as fire is a crucial factor in maintaining prairie habitats. In the real world, fire suppression and habitat fragmentation are major threats to the survival of Fender's blue butterfly populations, and the simulation does not take these factors into account.
In summary, while the simulation result may provide insights into the potential effectiveness of using stepping stones to conserve butterfly populations, it should be interpreted with caution and cannot be directly extrapolated to the real-world Fender's blue butterfly population. Further research and monitoring of butterfly populations in their natural habitats are necessary to fully understand their dynamics and inform conservation efforts.
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A company is replacing cables with fiber optic lines in rectangular casing BCDE. If segment DE = 3 cm and segment BE = 3. 5 cm, what is the smallest diameter of pipe that will fit the fiber optic line? Round your answer to the nearest hundredth. Quadrilateral BCDE inscribed within circle A a 3. 91 cm b 4. 24 cm c 4. 61 cm d 4. 95 cm
Using the Pythagorean theorem, the smallest diameter of the pipe that will fit the fiber optic line is approximately 4.61 cm (Option C).
To determine the smallest diameter of the pipe that will fit the fiber optic line in rectangular casing BCDE, we need to find the diagonal AC of the rectangle. Since the rectangle is inscribed within circle A, the diameter of the circle will be equal to the diagonal of the rectangle.
Using the Pythagorean theorem, we can find the length of AC:
AC^2 = DE^2 + BE^2
AC^2 = (3 cm)^2 + (3.5 cm)^2
AC^2 = 9 + 12.25
AC^2 = 21.25
AC = √21.25 ≈ 4.61 cm
Therefore, the smallest diameter of the pipe that will fit the fiber optic line is approximately 4.61 cm (Option C).
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Eric sells hot apple cider at the Hendersonville Apple Festival each year. For a batch of cider that makes 25 servings, Eric uses 2 tablespoons of cinnamon. How much cinnamon is in each serving of cider?
Each serving of cider contains 0.08 tablespoons of cinnamon.
Eric uses 2 tablespoons of cinnamon for a batch of cider that makes 25 servings. To find out how much cinnamon is in each serving, we need to divide the total amount of cinnamon used by the number of servings.
tablespoons/tablespoons= tablespoons per serving
2 tablespoons / 25 tablespoons = 0.08 tablespoons per serving
Therefore, there is 0.08 tablespoons of cinnamon in each serving of cider.
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Math is not my best subject
The values are,
x = 15[tex]\sqrt{2}[/tex]([tex]\sqrt{2}[/tex] -1)/2
y = 15([tex]\sqrt{2}[/tex] -1)/2
z = 15
Labelling the given figure;
In ΔABC
Cos 60 = (y + z)/15[tex]\sqrt{2}[/tex]
⇒y + z = 15[tex]\sqrt{2}[/tex]/2 ....(i) (since cos 60 = 1/2)
In ΔADC
sin 45 = z/15[tex]\sqrt{2}[/tex]
⇒ z = 15 ....(ii) (since sin45 = 1/[tex]\sqrt{2}[/tex])
Now from (i) and (ii)
y = 15([tex]\sqrt{2}[/tex] -1)/2
In ΔABD
Sin 45 = y/x
⇒ 1/[tex]\sqrt{2}[/tex] = (15([tex]\sqrt{2}[/tex] -1)/2)/x
⇒ x = 15[tex]\sqrt{2}[/tex]([tex]\sqrt{2}[/tex] -1)/2
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The screen of a tablet has dimensions 8 inches by 5 inches. The
border around the screen has thickness z.
a. Write an expression for the total area of the tablet, including the
frame.
8 inches
5 inches
b. Write an equation for which your expression is equal to 50.3125. Explain what a solution to this
equation means in this situation.
c. Try to find the solution to the equation. If you get stuck, try guessing and checking. It may help to
think about tablets that you have seen.
(a) The expression for the total area of the tablet = (8 + 2z)(5 + 2z)
(b) Equation is: (8 + 2z)(5 + 2z) = 50.3125 and the solution to this equation refers to the thickness of frame for which the area of the tablet is 50.3125.
(c) Solution or the thickness of the frame must be 0.375 inches.
The dimensions of the screen of a tablets are 8 inches by 5 inches.
border around the screen has thickness z.
So the length with frame = 8 + 2z
and the width of the screen with frame = 5 + 2z
So the expression for the total area of the tablet = Length* Width = (8 + 2z)(5 + 2z)
Equation for which the expression is equal to 50.3125 is given by,
(8 + 2z)(5 + 2z) = 50.3125
So the solution to this equation refers to the thickness of frame for which the area of the tablet is 50.3125.
Solving the equation we get,
(8 + 2z)(5 + 2z) = 50.3125
40 + 10z + 16z + 4z² = 50.3125
4z² + 26z - 10.3125 = 0
Solving this quadratic equation we get the solutions,
z = -6.875, 0.375
Since the thickness cannot be negative so -6.875 must be neglected.
Hence the thickness of the frame is 0.375 inches.
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Help please! I'm really struggling here ((40 points))
Answer:
k = - 0.36 or k = 30.36
Step-by-step explanation:
k² - 30k = 11
to complete the square
add ( half the coefficient of the k- term )² to both sides
k² + 2(- 15)k + 225 = 11 + 225
(k - 15)² = 236 ( take square root of both sides )
k - 15 = ± [tex]\sqrt{236}[/tex] ≈ ± 15.36 ( to the nearest hundredth )
add 15 to both sides
k = 15 ± 15.36
Then
k = 15 - 15.36 = - 0.36
or
k = 15 + 15.36 = 30.36
let s be a finite minimal spanning set of a vector space v. that is, s has the property that if a vector is removed from s, then the new set will no longer span v.
A finite minimal spanning set of a vector space V is a set S that satisfies the following properties:
S is a spanning set of V, i.e., every vector in V can be expressed as a linear combination of vectors in S.S is finite, i.e., it contains a finite number of vectors.S is minimal, i.e., no vector can be removed from S without destroying the spanning property.In other words, S is the smallest set of vectors that can be used to generate V. If we remove any vector from S, the resulting set will not be able to generate V anymore.
The concept of a finite minimal spanning set is important in linear algebra, particularly in the context of basis and dimension. A basis is a linearly independent spanning set of a vector space V.
A finite minimal spanning set is also a basis of V. The dimension of a vector space is the number of vectors in any basis of V. Since a finite minimal spanning set is a basis, the dimension of V is equal to the number of vectors in S.
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Full Question: Let S be a finite minimal spanning set of a vector space V. That is, S has the property that if a vector is removed from S, then the new set will no longer span V. Prove that S must be a basis for V.
You want to know the approximate height of a tall oak tree. You place a mirror on the ground and stand where you can see the top of the tree in the mirror. How tall is the tree? The mirror is 24 feet from the base of the tree. You are 36 inches from the mirror and your eyes are 5 feet above the ground. Round your answer to the nearest tenth
The approximate height of the tall oak tree is 60.0 feet.
To find the height of the tree, follow these steps:
1. Convert the distance between you and the mirror from inches to feet: 36 inches = 3 feet.
2. Create a proportion using similar triangles, where the height of the tree (h) divided by the distance from the tree to the mirror (24 feet) equals your eye height (5 feet) divided by the distance from your eyes to the mirror (3 feet).
3. Set up the proportion: h / 24 = 5 / 3.
4. Solve for h: h = (5 / 3) * 24.
5. Calculate h: h = 40 feet (height of tree above your eye level).
6. Add your eye height (5 feet) to the height of the tree above your eye level: 40 + 5 = 60 feet.
7. Round the answer to the nearest tenth: 60.0 feet.
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Peter gets a part-time job cleaning and maintaining his community's swimming pool and spa. 40 Here are some facts about the pool and spa. There is an outlet for a vacuum halfway along the side of the pool. What is the approximate length the hose should be to reach any part of the pool surface from there? Show your work. Answer Between _and _ft.
The length of the hose to reach any part of the pool surface from there will be 22.36 feet.
How to calculate the length:Length of hose = √(L² + W²)
The pool is 20 feet long and 10 feet wide, the length of the hose needed would be approximately:
Length of hose = √(20² + 10²) = √500 = 22.36 feet
Therefore, Peter would need a vacuum hose that is approximately 22.36 feet long to reach any part of the pool surface from the outlet.
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Check all that are inequalities.
-3 = y
t > 0
-4. 3 < a
g = 5 and one-half
k less-than Negative StartFraction 5 Over 7 EndFraction
x = 1
Anwer: B C E
The inequalities in the given options are: B) t > 0, C) 3 < a, E) k < -5/7, The correct option is B,C,E.
B) t > 0: This represents an inequality because the symbol ">" indicates "greater than." It states that the variable "t" is greater than zero. In other words, it means that "t" has to be a positive number and cannot be zero or negative.
C) 3 < a: This represents an inequality because the symbol "<" indicates "less than." It states that the number 3 is less than the variable "a." In other words, it means that "a" has to be greater than 3 for the inequality to hold true.
E) k < -5/7: This represents an inequality because the symbol "<" indicates "less than." It states that the variable "k" is less than -5/7. In other words, it means that "k" has to be a value smaller than -5/7 for the inequality to be true.
The other options, such as -3 = y, g = 5 and one-half, and x = 1, do not represent inequalities because they either show an equation (equality) or simply assign values to variables without any comparison.
Therefore the correct option is B,C,E.
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Mason plays a game by flipping a fair coin. He wins the game if the coin lands facing heads up. If Mason plays 300 times, how many times should he expect to win?
Answer:
Step-by-step explanation:
A fair coin means that there is a 50% probability of heads and a 50% probability of tails.
Playing the game 300 times means that Mason will approach theoretical probability.
Therefore, playing 300 times, he should expect to win 50% of the time, so 50% x 300 = 150 times.
Mason should expect to win 150 times.
Identify the volume of a cube with edge length 8 ft.
V = 512 ft^3
V = 256 ft^3
V = 514 ft^3
V = 324 ft^3
The volume of a cube with edge length 8 ft are V = 512 ft³
The volume of a cube is calculated by multiplying the length of one of its sides by itself three times (V = s³). Therefore, for a cube with an edge length of 8 ft, its volume would be V = 8³ = 512 ft³.
Therefore, the correct answer is: V = 512 ft³
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in a survey of some people, it was found that the ratio of the people who liked pop songs and rap songs is 7:9. out of which, 60 people liked both songs, 30 liked rap songs only and 40 liked none of the songs. find the number of people who did not like pop songs.
Solve with steps.
The number of people who did not like pop songs is 175.
Given data :
In a survey, the ratio of people who liked pop songs and rap songs is 7: 9.
The number of people who liked both songs = 60.
The number of people who liked only rap songs = 30.
The number of people who liked none of the songs = 40
First of all, we will find the number of people who only like pop songs. We are given a ratio of 7:9 for the people who liked pop songs and rap songs. Let us assume that the number of people who liked pop songs is x and those who liked rap songs is y. According to the ratio given,
[tex]\frac{x}{y} = \frac{7}{9}[/tex] .....(1)
As we know the number of people who only liked rap songs are 30. Therefore, y - x = 30
x = y - 30
We will substitute the value of x in equation 1.
[tex]\frac{y - 30}{y} = \frac{7}{9}[/tex]
9y - 270 = 7y
2y = 270
y = 135
Now, x = 135 -30
x = 105
Total number of people in survey = x + y + 40
105 + 135 + 40 = 280
Out of 280, the number of people who liked pop songs is 105. So, the number of those who did not like pop songs is ( 280 - 105) = 175.
Therefore, the number of people who did not like pop songs are 175.
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Complete the statements below to explain two ways to convert miles to kilometers.
1
mile ≈1.61
kilometers
1
kilometer ≈0.62
mile
CLEARCHECK
Kilometers are
miles.
That means the number of kilometers in a distance will always be
the number of miles in that distance.
We can convert miles to kilometers by
by 1.61
.
We can convert miles to kilometers by
by 0.62
.
The number of miles travelled is 6.2 miles.
What is Kilometer ?
A kilometer (km) is a unit of length or distance measurement in the metric system. It is equivalent to 1,000 meters or approximately 0.62 miles. The prefix "kilo" means "thousand", so one kilometer is equal to 1,000 meters.
Completing the statements:
Kilometers are a larger unit of distance measurement compared to miles. That means the number of kilometers in a distance will always be greater than the number of miles in that distance.
We can convert miles to kilometers by multiplying the number of miles by 1.61. For example, if we have a distance of 5 miles, we can convert it to kilometers as:
5 × 1.61 = 8.05 kilometers
We can also convert kilometers to miles by multiplying the number of kilometers by 0.62. For example, if we have a distance of 10 kilometers, we can convert it to miles as:
10 × 0.62 = 6.2 miles
Therefore, The number of miles travelled is 6.2 miles.
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Brody is going to invest $350 and leave it in an account for 18 years. Assuming the interest is compounded daily, what interest rate, to the nearest tenth of a percent, would be required in order for Brody to end up with $790?
The interest rate is 4.5%, if the interest is compounded daily on an investment of $350.
To find the interest rate, compound interest formula
A= P(1+r/n)ⁿᵃ
where
A = The amount to be received
P = The Principal
r = The rate of interest
n = number of years (Here interest is compounded on daily basis. So, n =365)
a = Time period in years
Substitute the values in the formula,
790= 350(1+r/365)⁽³⁶⁵⁾⁽¹⁸⁾
790= 350(1+r/365)⁶⁵⁷⁰
790/350= (1+r/365)⁶⁵⁷⁰
Using logarithms property on both sides
ln(790/350)= 6570×ln(1+r/365)
By the property of logarithms, for small values of x ln(1+x) =x
(ln(790/350))/6570= r/365
Therefore
The rate of interest r = 4.5%
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A company makes cones out of solid foam. Each cone has a height of inches, and its base has a radius of inches. How much foam is needed to make cones?
The total foam needed to make n cones is (n/3)πr^2h cubic inches.
What is the total volume of foam required to manufacture a certain number of cones with a given height and base radius?The volume of a cone can be calculated using the formula:
V = (1/3)πr^2h
where r is the radius of the base, h is the height, and π is the mathematical constant pi.
In this case, the height of each cone is given as h inches, and the radius of the base is given as r inches. So, the volume of each cone can be calculated as:
V = (1/3)πr^2h
Now, let's assume that the company wants to make n cones. Then, the total amount of foam needed to make these cones would be:
Total foam needed = n × V
Substituting the expression for V, we get:
Total foam needed = n × (1/3)πr^2h
Therefore, the total foam needed to make n cones is (n/3)πr^2h cubic inches.
Note that the given values of h and r are necessary to compute the total foam required.
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im gonna be sending a lot of problems since i wasnt in my class for the lesson
Answer:
168
Step-by-step explanation:
Volume is the ''area'' of a 3d shape
to find the volume, multiply the length, width, and height of the shape.
6x7x4
=42x4
=168 cubic yards
hope it helps
pls mark brainliest!!!
Answer:
168 cubic yards
Step-by-step explanation:
The formula for a rectangular prism volume is:
[tex]V=lwh[/tex]
Since we have all 3, the length, the width, and the height, we can plug in the numbers to substitute:
V=6·7·4
=168
So, the volume of this rectangular prism is 168 cubic yards.
Hope this helps :)
The box plots show a summary of push–up scores for Group A and Group B in the same gym class. Both groups have the same number of students. Determine whether each statement is true based on these box plots. Select True or False for each statement. True False At least 50% of students in each group scored more than 165 push–ups. The median score of push–ups of Group A is 10 points greater than the median score of push–ups of Group B. The scores of Group A have less variability than the scores of Group B
Statement 2 is false because while the median score of Group A is higher than Group B, it is not 10 points greater as claimed.
Statement 1 is false because the box plots provide limited information, making it impossible to determine whether at least 50% of students in each group scored more than 165 push-ups.
Statement 3 is false because Group A has more variability in push-up scores than Group B, as indicated by the larger interquartile range (IQR) of Group A.
Looking at the box plots, we can see that the median score of Group A is higher than Group B, but it is not 10 points greater. Therefore, statement 2 is False.
We cannot determine whether at least 50% of students in each group scored more than 165 push-ups. The box plots only show us the quartiles and the minimum and maximum values, so we do not know the exact number of students who scored above 165 push-ups. Therefore, statement 1 is False.
The interquartile range (IQR) of Group A is greater than the IQR of Group B, indicating that Group A has more variability in push-up scores than Group B. Therefore, statement 3 is False.
Hence, All the statement are False.
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One of the teachers at a school is chosen at random. The probability that this teacher is female is 3/5 There are 36 male teachers at the school
If the probability that this teacher is female is 3/5 , there are a total of 90 teachers at the school.
Let's denote the total number of teachers at the school as T. We know that the probability of choosing a female teacher is 3/5. Therefore, the probability of choosing a male teacher is 1 - 3/5 = 2/5.
We are also given that there are 36 male teachers at the school. We can use this information to set up an equation:
36/T = 2/5
To solve for T, we can cross-multiply:
36 x 5 = 2 x T
180 = 2T
T = 90
Therefore, there are a total of 90 teachers at the school.
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Complete question is:
One of the teachers at a school is chosen at random. The probability that this teacher is female is 3/5 There are 36 male teachers at the school. Work out the total number of teachers at the school.
In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.
please help i'm having trouble answering this (70 points) (brainylist answer) thank you!
The hexagon will have six congruent sides of equal length and six congruent angles of 120 degrees each.
In order to produce a cross section of a regular hexagon, the plane should pass through the cube such that it intersects three pairs of opposite edges at equal distances from their endpoints, forming an equilateral triangle in each pair.
These three equilateral triangles will intersect at the center of the hexagon, forming six congruent triangles that make up the regular hexagon. Imagine the cube as a three-dimensional box with edges of equal length.
Imagine a plane passing through the box such that it intersects three pairs of opposite edges at equal distances from their endpoints. These three pairs of edges will form three equilateral triangles within the cube, and their intersections at the center of the cube will form a regular hexagon.
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A circular flower garden surrounds a sculpture on a square base as show being 6x and 4x. What is an expression for the area of the flower garden
A circular flower garden surrounds a sculpture on a square base as show being 6x and 4x. The expression for the area of the flower garden is π(26x - 12√2x).
Find the expression for the area of the flower garden, we need to first find the area of the square base.
The area of a square is calculated by multiplying the length of one side by itself. In this case, the length of one side is 4x, so the area of the square base is (4x)^2 = 16x^2.
Next, we need to find the area of the circular flower garden that surrounds the square base.
Since the flower garden is circular, we use the formula for the area of a circle, which is A = πr^2, where A is the area and r is the radius.
The radius of the flower garden is the distance from the center of the circle to any point on the circumference.
Since the flower garden surrounds the square base, we can find the radius by subtracting the side length of the square base from the diameter of the circle.
The diameter of the circle is equal to the diagonal of the square base, which is √(6x)^2 + (6x)^2 = √72x^2 = 6√2x. Therefore, the radius of the flower garden is (6√2x - 4x)/2 = (3√2x - 2x).
Now we can substitute this expression for the radius into the formula for the area of a circle to find the area of the flower garden: A = π(3√2x - 2x)^2 = π(18x - 12√2x + 8x) = π(26x - 12√2x).
Therefore, the expression for the area of the flower garden is π(26x - 12√2x).
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A hexagon has 4 sides of length 3x +5 and the other 2 sides are each 3 units shorter than the other 4 sides. What is the perimeter, P, of the hexagon in terms of x?
The perimeter, P, of the hexagon in terms of x is 18x + 24.
To find the perimeter, P, of the hexagon in terms of x, we'll consider the given side lengths.
The hexagon has 4 sides of length 3x + 5. The other 2 sides are each 3 units shorter than the other 4 sides, so their length is (3x + 5) - 3 = 3x + 2.
Now, we can calculate the perimeter by adding the lengths of all 6 sides:
P = (4 * (3x + 5)) + (2 * (3x + 2))
First, distribute the numbers to the expressions inside the parentheses:
P = (12x + 20) + (6x + 4)
Next, combine like terms:
P = 18x + 24
So, the perimeter, P, of the hexagon in terms of x is 18x + 24.
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A solid is made by a hemisphere and cylinder having equal radii. The volume of the solid is 2707 cm'. If the height of the cylinder is 80 cm, find the total surface area of the solid
The total surface area of the solid is approximately 1818 [tex]cm^{2}[/tex]. Let's call the radius of the hemisphere and cylinder "r".
The volume of the solid is the sum of the volumes of the hemisphere and cylinder: V = (2/3)π[tex]r^{3}[/tex] + π[tex]r^{2}[/tex]h. Substituting in the given values, we get: 2707 = (2/3)π [tex]r^{3}[/tex] + π[tex]r^{2}[/tex](80)
To solve for r, we can rearrange the equation and use a numerical method or calculator. We get: r ≈ 11.6 cm
Now, we can use the radius to find the surface area of the solid. The surface area is the sum of the curved surface areas of the hemisphere and cylinder, plus the area of the circular base of the cylinder: A = 2π[tex]r^{2}[/tex] + 2πrh + π[tex]r^{2}[/tex].
Substituting in the given values and solving for A, we get: A ≈ 1818 [tex]cm^{2}[/tex]. Therefore, the total surface area of the solid is approximately 1818 [tex]cm^{2}[/tex].
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