The volume of the square frustrum, the volume of the pyramid and the volume of the obelisc are 1018791.667 ft³, 22019.625 ft³ and 1040811.292 ft³, respectively.
How to determine the volume of the Washington Monument
In this problem we must determine the volume of a obelisc, which is equal to the sum of the volumes of a square frustrum and a pyramid with a square base. First, sum the volumes of the frustrum and the pyramid:
V' = (1 / 3) · 500 · (55² + 55 · 34.5 + 34.5²)
V' = 1018791.667 ft³
V'' = (1 / 3) · (34.5)² · 55.5
V'' = 22019.625 ft³
Second, calculate the volume of the obelisc:
V = V' + V''
V = 1018791.667 ft³ + 22019.625 ft³
V = 1040811.292 ft³
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answer all with appropriate answer
Answer:
1.900 2(i)1260 (ii)9 3.20 4.80 5.36 6(i)540 (ii)100
Step-by-step explanation:
1.(7-2)*180
=5*180
=900
2(a)(i) (9-2)*180
=7*180
=1260
(ii) 9
3 360/x=18
x=20
4 (5-2)*180
=3*180
=540
2y+y+y+110+110=540
4y=320
y=80
5 360/x=30
x=36
6(i) (5-2)*180
=3*180
=540
(ii)x+95+115+115+115=540
x=100
) a mathematical organization is producing a set of commemorative license plates. each plate contains a sequence of five characters chosen from the four letters in aime and the four digits 2007. no character may appear in a sequence more times than it appears among the four letters in aime or the four digits in 2007. a set of plates in which each possible sequence appears exactly once contains n license plates. find n
The correct answer or possible sequence is the value of N/10 is 372.
The letters can be selected from the words "AIME" or "2007."
The only number that can be repeated twice is 0; there are seven different characters that can be chosen.
There are two potential scenarios.
Here is the first instance:
There are 7!/(7-5) potential sequences if 0 appears 0 or 1 times in the sequence.
There are 2520 possible sequences if 0 appears 0 or 1 times in the sequence.
Here is the second example:
If 0 occurs twice in the sequence, there must be a 0 in ⁵C₂. positions.
If 0 occurs twice in the sequence, 10 spots must be filled with 0.
The remaining three characters can be arranged in 6!/(6-3)! different ways.
There are 120 different arrangements for the final three characters.
In the second scenario, there are a total of 1200 possible possibilities, or 10*120.
There are 2520 methods in total plus 1200.
There are 3720 different ways in all.
N = 3720
We must ascertain the value of (N/10)
⇒ N/10 = 3720/10
⇒ N/10 = 372
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The mass
a cube, M (kg),
is proportional to the cube of
the length of its edge,
L (m).
The mass
the cube is 40
kg when the length of its
edge is 35 cm.
Work out M (to 2 DP) when L
=
0.6 m
Thanks
The mass when L = 0.6 is given as follows:
M = 68.57 kg.
How to obtain the mass of the cube?The mass of the cube is modeled according to a proportional relationship, as follows:
M = kL.
In which k is the constant of proportionality.
The mass the cube is 40 kg when the length of its edge is 35 cm = 0.35 m, hence the constant is obtained as follows:
0.35k = 40
k = 40/0.35
k = 114.28.
Hence the mass when L is of 0.6 m is given as follows:
M = 114.28 x 0.6
M = 68.57 kg.
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Jason has 4 gallons of hand sanitizer that contains 25% alcohol. He wants to make a hand sanitizer that contains 50% alcohol. How many gallons of pure alcohol should he add?
A school purchased sand to fill a sandbox on its playground. The dimensions of the sandbox in meters and the total cost of the sand in dollars are known. Which units would be most appropriate to describe the cost of the sand?
The most appropriate units to describe the cost of the sandbox would indeed be dollars.
When describing the cost of an item or service, it is essential to use the unit that represents the currency being used for the transaction. In this case, the total cost of the sand for the school's sandbox is given in dollars. To maintain consistency and clarity, it is best to express the cost in the same unit it was provided.
Using dollars as the unit for the cost allows for clear communication and understanding among individuals involved in the transaction or discussion. Dollars are widely recognized as the standard unit of currency in many countries, including the United States, where the dollar sign ($) is commonly used to denote monetary values.
Using meters, the unit for measuring the dimensions of the sandbox, to describe the cost would be inappropriate and could lead to confusion or misunderstandings. Mixing units can cause ambiguity and hinder effective communication.
Therefore, it is most appropriate to describe the cost of the sand in dollars, aligning with the unit of currency provided and commonly used in financial transactions. This ensures clarity and facilitates accurate comprehension of the cost associated with the sand purchase for the school's sandbox.
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✓ get this
22_1034 number/
Divisible
By 9
The number 22_1034 is not divisible by 9.
What is divisibility ?
Divisibility is a mathematical concept that describes whether one integer (a whole number) can be divided evenly by another integer, without leaving a remainder.
In other words, if we have two integers a and b, we say that a is divisible by b if and only if a can be expressed as a product of b and another integer without leaving a remainder. This is typically denoted by writing a divided by b as a fraction, and if the remainder is zero, we say that a is divisible by b.
According to the question:
To check if the number 22_1034 is divisible by 9, we can add up its digits and see if the sum is divisible by 9.
2 + 2 + 1 + 0 + 3 + 4 = 12 + 4 = 16
Since 16 is not divisible by 9, the number 22_1034 is not divisible by 9.
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on the island of mumble, the mumblian alphabet has only $5$ letters, and every word in the mumblian language has no more than $3$ letters in it. how many words are possible? (a word can use a letter more than once, but $0$ letters does not count as a wor
The total number of possible words is 155.
How many words are possible? (A word can use a letter more than once, but 0 letters do not count as a word)
There are 5 letters in the mumblian alphabet, and each word must contain 1, 2, or 3 letters.
The number of 1 letter words is 5 since every letter is a word.
The number of 2 letter words is 5 × 5 = 25 because there are 5 options for the first letter and 5 options for the second letter.
The number of 3 letter words is 5 × 5 × 5 = 125 because there are 5 options for the first letter, 5 options for the second letter, and 5 options for the third letter. Therefore, the total number of possible words is:
\($5 + 25 + 125 = \boxed{155}$\)
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Order the numbers from least to greatest. 15, 20, –13, –20, –9, 7 A. 20, 15, 7, –9, –13, –20 B. –20, –9, 15, 20, –13, 7 C. 7, –13, –20, 15, 20, –9 D. –20, –13, –9, 7, 15, 20
Answer:
D
Step-by-step explanation:
the numbers on answer D are in order on the number line from LEAST to GREATEST
You hear on the news that over the next 5 years the inflation rate will skyrocket to 12% if today a new blu-ray movie costs $19.99 assuming continuous compounding how much will the same disk cost in 5 years?
The Blu-ray movie will cost approximately $36.42 in 5 years with an inflation rate of 12% and continuous compounding.
To calculate the future cost of the Blu-ray movie in 5 years with an inflation rate of 12% and continuous compounding, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = Future value
P = Present value
e = Euler's number (approximately 2.71828)
r = Annual interest rate (in decimal form)
t = Time period in years
In this case, the present value (P) is $19.99, the inflation rate (r) is 12% or 0.12, and the time period (t) is 5 years. Substituting these values into the formula, we get:
A = 19.99 * e^(0.12 * 5)
Calculating the exponent first:
0.12 * 5 = 0.6
Then:
e^0.6 ≈ 1.82212
Finally:
A = 19.99 * 1.82212 ≈ 36.42
Using the formula for continuous compound interest, we calculated that a Blu-ray movie that costs $19.99 today will cost approximately $36.42 in 5 years, assuming an inflation rate of 12% and continuous compounding.
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Find the solution(s) to the system of equations. Select all that apply.
A. (0,-3)
B. (-1,0)
C. (3,0)
D. (4,5)
Answer:
A
Step-by-step explanation:
it should be A
Solve the following equation: -3 = 1 3/5+ m.
Answer:
m=-4 3/5
Step-by-step explanation:
I don't have the steps sorry
If p and q vary inversely and p is 29 when q is 25, determine q when p is equal to 5.
Answer:If p and q vary inversely, it means that their product remains constant. So we can set up the equation:
p * q = k
where k is the constant of variation.
Given that p is 29 when q is 25, we can substitute these values into the equation:
29 * 25 = k
725 = k
Now, let's determine the value of q when p is equal to 5:
p * q = k
5 * q = 725
Dividing both sides of the equation by 5:
q = 725 / 5
q = 145
Therefore, when p is equal to 5, q is equal to 145.
Step-by-step explanation:
Answer:p1q1=p2q2
q1=25,p1=29;
p2=5,q2=?;
q2=p1q1/p2;
q2=25*29/5;
q2=29*5;
q2=145.
Step-by-step explanation:
66.6666666667 as a mixed number in simplest form
Answer:
66 67/100
Step-by-step explanation:
Answer:
Mix Number form: 66 2/3
Simplest Form: 6.66
Hope this helps.
determine whether the function is continuous on the entire real number line. explain your reasoning. 8x f(x) = x2 + 3
The function 8x f(x) = x² + 3 is a polynomial function, which means it is continuous on the entire real number line, that is, it has no holes, jumps, or vertical asymptotes in its graph
Polynomial functions, in general, are continuous on the entire real number line. The definition of a continuous function is one that can be drawn without lifting your pencil from the paper. The polynomial function is a function of x of the form: f(x) = a₀ + a₁x + a₂x² + … + anxn, where a₀, a₁, a₂, …, an are real numbers and n is a non-negative integer. The polynomial function can be written in factored form as: f(x) = a (x – r₁) (x – r₂) … (x – rn), where r₁, r₂, …, rn are the roots or zeros of the function and a is the leading coefficient. In this case, the function f(x) = x² + 3 is a polynomial function of degree 2.
Since all polynomial functions are continuous on the entire real number line, the given function is also continuous on the entire real number line. Thus, we can conclude that the function f(x) = x² + 3 is continuous on the entire real number line.\
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-118 = -5 ( 4 + 7x ) + 7
A. -5
B. -9
C. 3
D. -1
Answer:
X=3
Step-by-step explanation:
A plane is flying at an elevation of 25000feet. It is within the sight of the airport and the pilot finds that the angle of depression to the airport is 14 degrees. Find the diagonal distance between the plane and the base of the airport.
Answer:
The distance between the plane and the base of the airport = 103339.14 ft
Step-by-step explanation:
Consider the diagram attached.
We can notice that the a triangle (ABC) can be formed between the plane, the airport, and a vertical line drawn from the ground to the plane showing its altitude.
The angle of depression is 14 degrees. This means that angle BAC is 90 - 14 = 76 degrees.
From triangle laws, we will have that \(cos 76 = \frac{Altitude}{AC}\)
\(AC = \frac{25000}{(cos 76)} = 103339.14 ft\)
Hence, the distance between the plane and the base of the airport = 103339.14 ft
The diagonal distance between the plane and the base of the airport is 103339.14 ft.
This situation forms a right angle triangle.
The plane is flying at an elevation of 25000 ft.
The elevation is the height or opposite side of the triangle.
The diagonal distance between the plane and the base of the airport is the hypotenuse of the triangle.
Therefore, using trigonometric ratio,
sin 14° = opposite / hypotenuse
sin 14° = 25000 / d
d = 25000 / sin 14
d = 25000 / 0.2419218956
d = 103339.137361 ft
Therefore, the diagonal between the plane and the base of the airport is 103339.14 ft.
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In a certain state's lottery, 22 balls numbered 1 through 22 are placed in a machine and 5 of them are drawn at random. If the 5 numbers drawn match the numbers that a player had chosen, the player wins $30,000. In this lottery, THE ORDER THE NUMBERS ARE DRAWN DOES MATTER. Compute the probability that you win the prize if you purchase a single lottery ticket.
The probability that you win a prize is 0.00003797372
How to determine the probability that you win a prize?From the question, we have the following parameters:
Sample Space = 1 to 22
This means that
Sample size, n = 22 i.e. the count of numbers from 1 to 22
The count of numbers to be drawn is 5
So, the individual probabilities are
P(1) = 5/22
P(2) = 4/21
P(3) = 3/20
P(4) = 2/19
P(5) = 1/18
The probability of winning is the product of the above
So, we have
p = 5/22 * 4/21 * 3/20 * 2/19 * 1/18
Evaluate
p = 0.00003797372
Hence, the probability is 0.00003797372
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let v, w ∈ rn. if v = w , show that v w and v − w are orthogonal.
If two vectors, v and w, are equal, then the dot product between them (v•w) and the difference between them (v - w) is 0, making them orthogonal.
To prove this mathematically, we can start by stating that if v = w, then the dot product between them will be equal to 0:
v•w = v1w1 + v2w2 + ... + vnwn = 0
The same applies to the difference between them:
v - w = v1 - w1 + v2 - w2 + ... + vn - wn = 0
As a result, the dot product between v•w and the difference between them (v - w) is 0, which is the definition of orthogonality, meaning that these two vectors are orthogonal.
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your quidditch league has 5 teams. you will play a tournament next week in which every team will play every other team once. each team can play at most one match each day, but there is plenty of time in the day for multiple matches. what is the fewest number of days over which the tournament can take place?
The fewest number of days over which the tournament can take place is 5 days.
How to calculate the number of days?As each team plays with other team Once and we have total 5 teams so number of matches will be (4+3+2+1)
Counted as team 1 plays with all other teams = 4 matches
Team 2 plays with team 3,4,5 =3 matches
Team 3 play with team 4,5=2 match
And the last match is between team 4 and team5
Total match = 10 and can be played two matches per day:
Number of days = 10/2
= 5 days.
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Let C be the circle relation defined on the set of real numbers. For every x, y ϵ R, x Cy <=> x^2 + y^2 = 1. (a) Is C reflexive justify your answer. C is reflexive for a very real number x, x C x. By definition of C this means that for every real number x, ____ -1. This is ____.
Find an example x and x^2 + x^2 that show this is the case. (x, x^2 + x^2) = ( ____ ) Since this ____ 1, C ____ reflexive
About the circle relation C on the set of real numbers:
To determine if circle (C) is reflexive, we need to examine if for every real number x, x C x holds true. By definition of C, this means that for every real number x, x^2 + x^2 = 1.
Now, let's simplify this equation: x^2 + x^2 = 2x^2, so we get 2x^2 = 1. To satisfy this equation, x^2 must equal 1/2. However, there is no real number x for which x^2 = 1/2.
As we cannot find an example of x such that (x, x^2 + x^2) = (x, 1), we conclude that since this does not equal 1, C is not reflexive.
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Carrie apartment building ramp has a 2-foot height and a 4-foot base the new building code says the ramp must have a 1:4 height base ratio . How Can Carrie adjust her ramp base to meet the new code ?
The height of building ramp is h = 2 foot.
The base of the building ramp is b = 4 foot.
The code for new bulding is,
\(\begin{gathered} \frac{h}{b}=\frac{1}{4} \\ h=\frac{b}{4} \end{gathered}\)Let the new base be x for new building code and height remain same h = 2.
\(\begin{gathered} 2=\frac{x}{4} \\ x=8 \end{gathered}\)So Carrie increase the base from 4 foot to 8 foot.
Detemine the adjustment in base.
\(\begin{gathered} b^{\prime}=8-4 \\ =4 \end{gathered}\)Thus Carrie increase the base by 4 foot to meet the new code for the building.
Your bedroom measures 278
meters by 314
meters. What is the area?
Answer:
The area is 278 m × 314 m = 87,292 m^2.
$84 to 40 please please please
Answer:
The answer would be 34
Step-by-step explanation:
85 x 40 = 3400 so the discount would be 34
A store is having a sale on almonds and jelly beans today. The table below shows the amount of each type of food (in pounds) and the total cost (in dollars) of
two purchases today.
First
purchase
Second
purchase
Amount of
almonds
(In pounds)
3
12
Amount of
jelly beans
(In pounds)
5
2
Total cost
(in dollars)
17
23
O
Cost for each pound of almonds is $1.5 and cost for each pound of jelly beans is $2.5.
What is a System of Linear Equations?Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.
System of linear equations involve two or more linear equations.
Let x be the cost of each pound of almond and y be the cost of each pound of jelly beans.
Then from the first purchase, we have the equation,
3x + 5y = 17
Similarly, from the second purchase, we have,
12x + 2y = 23
So the system of equations are
3x + 5y = 17 and 12x + 2y = 23
Solving these, we will get the values of x and y which is the cost of each pound of almond and jelly beans.
3x + 5y = 17
12x + 2y = 23
Multiplying the first equation with 4, we get,
12x + 20y = 68
Subtracting 12x + 2y = 23 from 12x + 20y = 68,
18y = 45
y = $2.5
Substituting y = 2.5 in any of the equation above, we get,
x = $1.5
Hence the cost for each pound of almond and jelly beans are $1.5 and $2.5 respectively.
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A cylindrical tin filled with oil has a diameter of 12cm and a height of 14cm. The oil is then poured in rectangular tin 16cm long and 11cm wide. What is the depth of the oil in the tin
The volume of cylindrical tin is 1584 \(cm^3\). The depth of the oil in the tin is 9cm.
\(V_1 =\) VOLUME OF CYLINDRICAL TIN
\(= \pi r^2 h\)
\(=\frac{22}{7}\) x 6 x 6 x 14
= 44 x 36
= 1584 \(cm^3\)
\(V_2 =\) VOLUME OF RECTANGULAR TIN
= lbh = 1584
= (16)(11)(h) = 1584
= 176h =1584
= h = 1584 / 176
= h = 9 cm
A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.
To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.
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volunteers for a human performance study were randomly divided into two groups. the first group had their flexibility measured in the morning after a short meditation session while the second group had their flexibility measured in the afternoon with no previous meditation session. the flexibility scores of the two groups were compared. to improve the design of this experiment, one part of it should be done in a blind way. that is, we should
To improve the design of this experiment, the researchers could have used a double-blind design, where both the participants and the researchers are unaware of the group allocation.
In the given experiment, the researchers have not employed any form of blinding, which could be a potential source of bias. Blinding is a critical aspect of experimental design, where the participants or the researchers are unaware of the group allocation or the treatment being administered. Blinding is used to eliminate any potential sources of bias that may arise due to the expectations or beliefs of the researchers or participants. In this particular study, the lack of blinding could have led to two possible sources of bias. Firstly, the participants in the first group who received the meditation session could have had higher expectations of improvement in their flexibility due to the meditation. These expectations could have led to higher motivation and effort during the flexibility measurement, leading to an artificial improvement in their flexibility scores. Secondly, the researchers who were measuring the flexibility of the participants could have been biased towards finding a difference between the groups due to their knowledge of the group allocation. This could have led to a subconscious alteration in the measurement process, leading to a false conclusion about the effect of meditation on flexibility.
hence To improve the design of this experiment, the researchers could have used a double-blind design, where both the participants and the researchers are unaware of the group allocation. For instance, the participants could have been assigned a unique identification number, and the researchers could have used coded labels to differentiate the groups. This would have eliminated any potential sources of bias due to expectations or beliefs and would have made the results more reliable.
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Indicate whether each situation involves a combination or a permutation.
a. A team of 6 chosen from a class of 36
The factorial values and simplifying the expression, we find that there are 1,947,792 possible combinations of selecting a team of 6 from a class of 36.
In the situation described, a team of 6 is chosen from a class of 36. To determine whether this is a combination or a permutation, we need to consider if the order in which the individuals are selected matters.
A combination is used when the order does not matter. In this case, the order in which the team members are chosen does not affect the outcome. As long as the same 6 individuals are selected, it doesn't matter in what order they are chosen. Therefore, this situation can be classified as a combination.
To calculate the number of combinations, we can use the formula for combinations: C(n, r) = n! / (r!(n-r)!), where n is the total number of items (36 in this case) and r is the number of items being chosen (6 in this case). Plugging in the values, we get:
C(36, 6) = 36! / (6!(36-6)!)
= 36! / (6!30!)
Calculating the factorial values and simplifying the expression, we find that there are 1,947,792 possible combinations of selecting a team of 6 from a class of 36.
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Landon reads for 45 minutes 5 times a week. Marisa reads for 100 minutes 3 times a week. Daniel reads for 25 minutes 7 times a week. Out of the three students who reads the most per week? What is the difference between the person who reads the most and the person who reads the least?
Answer:
Marisa
Step-by-step explanation:
a closed rectangular box with volume 8 ft3 has length twice the width. express the height of the box as a function of the width and state its domain.
The height of the box can be represented as a function of the width, h = 4/w², where the domain of the function is (0, +∞).
Let's assume the width of the rectangular box is represented by the variable 'w'. Given that the length of the box is twice the width, we can express the length as '2w'. The height of the box can be represented by the variable 'h'.
The volume of a rectangular box is given by the formula: V = lwh, where V represents the volume, l represents the length, w represents the width, and h represents the height.
We are given that the volume of the box is 8 ft³. Substituting the values into the formula, we have:
8 = (2w)(w)(h)
Simplifying, we get:
8 = 2w²h
Dividing both sides by 2w², we get:
4/w² = h
Therefore, the height of the box can be expressed as a function of the width, h = 4/w².
The domain of the height function is determined by the width. Since the width of a rectangular box cannot be zero or negative (as it represents a physical dimension), the domain of the height function is the set of positive real numbers, excluding zero. In interval notation, the domain can be expressed as (0, +∞).
In conclusion, the height of the box can be represented as a function of the width, h = 4/w², where the domain of the function is (0, +∞).
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Select the correct answer
Which table corresponds to the graph below?