A square pyramid's height is three times the side of the base of a cube if they have the same base and volume, due to their differing volume formulas.
If a square pyramid and a cube have the same base and volume, the relationship between their heights can be determined using the formulas for their volumes. The volume of a cube is given by [tex]V = s^3,[/tex] where s is the length of a side of the cube's base. The volume of a square pyramid is [tex]V = (1/3) * b^2 * h,[/tex] where b is the length of the base side and h is the pyramid's height. Since both have the same volume, we can set these equations equal to each other and solve for h.
Setting the volumes equal: [tex]s^3 = (1/3) * s^2 * h,[/tex] simplifying to h = 3s. Thus, the height of the pyramid is three times the side of the base of the cube. This is because a cube's volume grows as a cube of its side length, while a pyramid's volume is one third of the base area times the height. Therefore, since they have the same volume, the height of the pyramid must be three times larger to compensate for the 1/3 factor in its volume formula.
What is the product of 3/4x1/3x2/5
Final answer:
To find the product of 3/4, 1/3, and 2/5, multiply the numerators to get 6 and the denominators to get 60, resulting in 6/60. This simplifies to 1/10.
Explanation:
The question asks us to find the product of the three fractions: 3/4, 1/3, and 2/5. To calculate this, we multiply the numerators together and then the denominators together:
Numerators: 3 times 1 times 2 = 6
Denominators: 4 times 3 times 5 = 60
Therefore, the product of 3/4, 1/3, and 2/5 is:
6/60, which can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 6. This gives us 1/10.
A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square
Suppose two angles of one triangle are congruent to two angles of another triangle. What can you conclude about the relationship between the third angles in each triangle? What does this tell you about the two triangles? Justify your answer.
how many one thirds are in seven halves?
2. Two angles are supplements if their sum is 180 degrees. The measure of one angle is seven-fifths the measure of its supplement. What is the measure of the smaller angle?
factor as the product of two binomials x^2-3x+2
What is 485=? Tens +5units
an everyday meaning of corresponding is "matching". How can this help you find the corresponding parts of two triangles?
Which of the following expressions could be used to estimate the difference between -12.34 and -4.8?
-12 - 5
-12 + 5
-12 - 4
-12 + 4
Answer:
-12-(-5)
=-12+5
The ans is -12+5
Step-by-step explanation:
Which statement about the ordered pairs (3,-8) and (4,4) is true for the equation 3x-y/4=11
0.003 is 1/10 of ____
0.4 is 10 times as much as _____
0.2 is 10 times as much as _____
0.2 is 1/10 of __________
Miss Jones has 18 boys and 27 girls in choir. She wants them to stand in equal rows. Only boys or girls will be in each row ( meaning no mixed rows). What is the greatest number of students that can stand in each row
The quotient of x and 7 is equal to 13. Define variable and then write an expression to model the situation
Final answer:
The expression for the given situation "The quotient of x and 7 is equal to 13" is modeled by the linear equation x/7 = 13. By multiplying both sides by 7, we find that x equals 91.
Explanation:
The question "The quotient of x and 7 is equal to 13" can be modeled as an expression in the form of a linear equation. To define variables in this context, we let x represent the unknown number we're trying to find. The quotient of x and 7 means x divided by 7, and this is equal to 13. Therefore, we can write the linear equation as x/7 = 13.
To solve for x, we perform algebraic operations. We multiply both sides of the equation by 7 to get rid of the denominator. The expression becomes 7 * (x/7) = 13 * 7, which simplifies to x = 91.
Someone help please!
the sum of three consecutive even numbers is 66. what is the smallest of these numbers
In a single season, the New York Yankees sell an average of 42,362 tickets for each of their 81 home games. About how many tickets do they sell for an entire season of home games?
3,200,000
Further explanationWe will solve the problem of rounding to estimate the product.
Given:
In a single season, the New York Yankees sell an average of 42,362 tickets for each of their 81 home games.
Question:
About how many tickets do they sell for an entire season of home games?
The Process:
Let us round off the factors before multiplication.
42,362 = 40,000
81 = 80
Next we multiply 40,000 by 80.
[tex]\boxed{ \ 40,000 \times 80 = ? \ }[/tex]
[tex]\boxed{ \ = (4 \times 10,000) \times (8 \times 10) \ }[/tex]
[tex]\boxed{ \ = (4 \times 8) \times (10,000 \times 10) \ }[/tex]
[tex]\boxed{ \ = 32 \times 100,000 \ }[/tex]
[tex]\boxed{\boxed{ \ 3,200,000 \ }}[/tex]
Thus, the New York Yankees sell 3,200,000 tickets for an entire season of home games.
Learn more4 times as much as 3 is https://brainly.com/question/573729 How much money will the school spend for the tickets? brainly.com/question/11541124How many gallons of water flow over the falls in 1 minute brainly.com/question/6246525Keywords: in a single season, the New York Yankees, sell, an average of 42,362 tickets, for each, 81 home games, how many, they sell, for an entire season, rounding, factors, to estimate the product
How to cross cancel fractions for example 3/5 •15/18
All of our employees speak at least 2 languages and many of them (45%) speak 3. We have even got few (8%) persons, that speak 4 languages.
What is the average number of languages spoken at our team?
The average number of languages spoken by the employees is calculated as a weighted average and equals 2.61.
To determine the average number of languages spoken by the employees, we need to calculate the weighted average. This takes into account the percentage of people speaking a different number of languages. Let's denote the number of languages spoken as L, and the percentage of people speaking that many languages as P.
According to the information provided, we have the following groups:
People who speak 2 languages, which is 100% - 45% - 8% = 47% of the employees.People who speak 3 languages, which is 45% of the employees.People who speak 4 languages, which is 8% of the employees.Now, we calculate the average with the formula:
Average = (L1 * P1 + L2 * P2 + L3 * P3) / 100
Where:
L1 = 2 languagesL2 = 3 languagesL3 = 4 languagesP1 = 47%P2 = 45%P3 = 8%Substituting the values we get:
Average = (2 *47 + 3 * 45 + 4 * 8) / 100
Average = (94 + 135 + 32) / 100
Average = 261 / 100
Average = 2.61
So, the average number of languages spoken by the employees is 2.61.
Help with at least one of these ?
At a flower store, the price of a bunch of roses is $25 and the price of a bunch of carnations is $20. If one day it sold a total of 60 bunches of the two flowers and made $1375. How many bunches of roses and carnations did it sold? bunches of
Overnight the temperature dropped 1.3 degrees every hour how many hours did it take the temperature to drop 7.8 degrees
To calculate how long it took for the temperature to drop 7.8 degrees at a rate of 1.3 degrees per hour, divide 7.8 by 1.3, which equals 6 hours.
Explanation:This problem can be solved using simple division. The question tells us that the temperature dropped 1.3 degrees every hour and we want to know how long it took for the temperature to drop 7.8 degrees. So, divide the total drop in temperature (7.8 degrees) by the rate of temperature drop (1.3 degrees per hour).
7.8 / 1.3 = 6
So, if the temperature dropped 1.3 degrees every hour, it would take 6 hours for the temperature to drop 7.8 degrees.
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Harry's fitness trainer recommends that Harry drink 8 fluid ounces of water 8 times a day.Harry has a water bottle that's holds 1 1/4 pints of water then filled. Today, he has filled the water bottle three times and drank all of the water each time . Harry claims that he drank the total amount of water recommended by his fitness trainer. Explain why Harry's claim is not true?
An electrician has 4.1 meters of wire how man 7/10 strips can he make
What are multiples of the factors of 15
What are the lengths of sides KN and NM of the kite
Answer: KN=15 and NM=20.
Step-by-step explanation: i got it right on edg2020
Calculate the kinetic energy of an 88-kg scooter moving at 18 m/s .
Answer:
kinetic energy of the scooter is 14256 joule.
Step-by-step explanation:
Since kinetic energy of an object is represented by the formula
Kinetic energy = [tex]\frac{1}{2}(\text{Mass})(\text{Velocity}^{2})[/tex]
Mass of the scooter = 88 kg
Velocity of the scooter = 18 meter per second.
Kinetic energy = [tex]\frac{1}{2}\times 88\times (18)^{2}[/tex]
= 44×(18)²
= 14256 Joule
Therefore, kinetic energy of the scooter is 14256 joule.
teo worked for 42.5 h at $70.75 per hour. how much did he earn? show the process
The total earning for Teo is $3006.88 if teo worked for 42.5 h at $70.75 per hour, the answer is 3006.88.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Teo worked for 42.5 h at $70.75 per hour.
Let x be the total earnings.
The value of x can be found as follows:
x = 42.5(70.75)
x = 3006.875
Or
x = 3006.88
Thus, the total earning for Teo is $3006.88 if teo worked for 42.5 h at $70.75 per hour, the answer is 3006.88.
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Translate the word phrase into a variable expression:
The difference of twice a number and 3.
*Note, there are no provided answers. What you write is the real answer.*
How many sixteenth notes would be needed to have the same duration as 3 quarter notes? Represent this as a fraction.
How do u guys solve this problem