The interpretation of v(4) = 64 for a cube's volume means a cube with 4-unit sides has a 64 cubic unit volume. Doubling the sides to 8 units leads to a volume of 512 cubic units, resulting in a volume ratio of 8:1 because volume scales with the cube of the side length increase.
The statement v(4) = 64 indicates that a cube with side length 4 units has a volume of 64 cubic units. When each side of the cube is doubled, the new side length becomes 8 units. The volume of a cube is calculated as the cube of its side length (s³). So, the new volume is 8³ or 512 cubic units.
The ratio of the new volume to the old volume is 512:64, which simplifies to 8:1. This ratio is not simply 2 because the volume of a cube increases by the cube of the factor by which the side is increased. Since the sides are doubled (a factor of 2), the volume increases by 2³ or 8 times, not 2 times.
This reasoning outlines why the ratio of the volumes of two cubes, when one cube has sides twice as long as the other, is not 2 but 8:1. The surface area to volume ratio is also affected by changes in the side length, which is significant not only in geometry but also in disciplines such as biology.
What is the area of a banner with 4 2/3 ft and 1 1/2 ft
Use the result from part c to find the two solutions to the equation 2x2−3x−5=0. enter the two solutions separated by a comma. (the order is not important.)
The quadratic formula can be used to find the solutions of a quadratic equation. In this case, the equation is 2x² - 3x - 5 = 0. Using the quadratic formula, the two solutions are x = 2 and x = -1.
Explanation:To find the solutions to the equation 2x² - 3x - 5 = 0, we can use the quadratic formula. The formula states that the solutions of any quadratic equation ax² + bx + c = 0 can be calculated using the formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 2, b = -3, and c = -5. Substituting these values into the formula, we get:
x = (-(-3) ± √((-3)² - 4(2)(-5))) / (2(2))
Simplifying further, we have:
x = (3 ± √(9 + 40)) / 4
x = (3 ± √49) / 4
x = (3 ± 7) / 4
Therefore, the two solutions to the equation 2x² - 3x - 5 = 0 are x = (3 + 7) / 4 = 2 and x = (3 - 7) / 4 = -1.
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wes has six errands to run (picking up the dry cleaning, going to the grocery store, getting gas, going to the bank, going to the library, and going to the video store). he only haves time to run 3 errands this afternoon. how many different combinations of three errands could he choose to run?
Answer: 120 different combinations .
Step-by-step explanation:
The combination of n things taking m things at a time is given by :-
[tex]C(n,m)=\dfrac{n!}{m!(n-m)!}[/tex]
Given : The total numbers of errands = 6
Now, the combination of 6 errands taking 3 at a time is given by :-
[tex]C(6,3)=\dfrac{6!}{3!(6-3)!}\\\\=\dfrac{6\times5\times4\times3!}{3!}=120[/tex]
Hence, he could choose to run 120 different combinations of three errands .
The decimal equivalent to the binary number 0 0 0 1 0 1 1 0 is ______________.
Need help with number 6. Also could you tell me if I did number 5 right? Thanks
use multiplication and the Distributive property to find the quotient
70 divided by 5 =
A tank can be filled by one pipe in four hours and by a second pipe in six hours; and when it is full, the tank can be drained by a third pipe in three hours. If the tank is empty and all three pipes are open, in how many hours will the tank be filled?
A. 8 hours
B. 12 hours
C. 24 hours
Suppose that it costs $25 to place a classified advertisement in the newspaper, plus $3 for each line. Then the cost to place an ad x lines long is given by y dollars, where y=3x+25. Express an ordered pair the fact that a 2 line ad cost $31
F(x)=x-2/x^3+x find the domain
Let a and b be the solutions of the quadratic equation $2x^2 - 8x + 7 = 0. Find 1/(2a)+(1/2b).
Please help me!
Which of the following gives an example of a set that is closed under multiplication? CHOOSE ALL THAT APPLY !!!! 15 PTS
A. The product of an even number and an even number
B. The product of 0 and 0
C. The product of a negative number and a negative number
D. The product of a perfect square and a perfect square
In October Greg and Thomas had the same amount of money in their savings account in November Greg deposited $120 into his account Thomas increased the money in his account by 20% when they compare their bounces they found out they were still equal
what is the exponent used in cubing a number
Use this equation to find dy/dx. 3y cos x = x2 + y2
Drag the blue labels onto the table to identify the data that is relevant to each hypothesis. then use the pink labels to indicate whether each hypothesis is supported or not supported by the data answers
Hypothesis 1 supported (potentially adapted wings), 2 needs more data, 3 and 4 not supported (scavengers and traffic constant).
Here's how to proceed:
1. Match Data to Hypotheses:
Hypothesis 1:
Relevant Data: "The wing shapes of swallows killed on roads differ from those of the general population."
Hypothesis 2:
Relevant Data: Not directly provided in the given options. More information is needed about the actual population size of cliff swallows living near roads over time.
Hypothesis 3:
Relevant Data: "Avian scavengers did not increase during this time, and terrestrial scavengers probably did not increase."
Hypothesis 4:
Relevant Data: "Car traffic stayed the same or increased during this time."
2. Evaluate Hypothesis Support:
Hypothesis 1:
Supported (additional data may be needed). The wing shape difference suggests potential adaptation, but more evidence would strengthen the conclusion.
Hypothesis 2:
Cannot be determined without direct data on population size changes.
Hypothesis 3:
Not supported (probably not a factor). The data indicates scavenger populations haven't increased, suggesting they aren't significantly affecting the number of road-killed swallows found.
Hypothesis 4:
Not supported (probably not a factor). The data shows car traffic has remained steady or increased, making it less likely to be the cause of a decrease in observed road-killed swallows.
Complete Question:
What Is 22/55 in lowest terms
p=21+2w (solve for w)
How can knowing the multiplication properties help you multiply 5x(2x6)?
what is 150% as a fraction
Time measured in minutes is an example of a(n) _______________ scale.
The answer can be written in statement form as,"Time measured in minutes is an example of a(n) interval scale."
What is an interval scale?A numerical scale known as an interval scale is one in which both the order of the variables and their differences are known. Using the Interval scale, variables with recognizable, consistent, and calculable differences are categorized.
It is easy to remember the primary role of this scale too, ‘Interval’ indicates ‘distance between two entities’, which is what Interval scale helps in achieving.
The value of time is given in minutes.
The given quantity can be measured on interval scale.
Hence, the required scale is known as interval scale.
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The function d(x) =3x +2 determine how many donuts need to be purchased for a meeting, where x is the number of people at the meeting. The office manager uses h(d(x)) to find the amount of money to bring for the donuts purchase. The function h(x) = 2x + 7 . Solve for how much money to bring when there are 8 people In the meeting.
A.25
B.26
C.52
D.59
Chelsea has four hours of free time on Saturday. She would like to spend no more than 2/3 of an hour on each activity. How many activities can she do during her time?
The number of sofas a factory produces varies directly with the number of hours the machinery is operational. Suppose the factory can produce 455 sofas in 48 hours. What is an equation that relates the number of sofas produced, n, with the amount of time, t, in hours? What is the graph of your equation?
Any proposed solution of a rational equation that causes a denominator to equal _______ is rejected.
Answer:
Any proposed solution of a rational equation that causes a denominator to equal __ZERO__ is rejected.
Step-by-step explanation:
We will show this statement is true by an example:
Consider the expression : [tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
Now, solved the rational expression and check its proposed solution
[tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
x cannot equal to 4, as it makes both denominators equal to zero.
Multiply both the sides by (x-4),
[tex]\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot\left ( \frac{x}{x-4}+4 \right )\\[/tex]
Now, use the distributive property on Right hand side,
[tex]\left ( x-4 \right )\cdot \frac{x}{x-4}=\left (x-4 \right )\cdot \left ( \frac{x}{x-4} \right )+\left (x-4 \right )\cdot 4\\[/tex]
Simplify the above expression,
[tex]x=x+4x-16[/tex]
Combine like terms,
[tex]x-x-4x=-16[/tex]
[tex]-4x=-16[/tex]
Divide both sides by -4, we get
[tex]\frac{-4x}{-4}=\frac{-16}{-4}[/tex]
[tex]x=4[/tex].
As we know that x cannot equal to 4, replacing x=4 in the original expression causes the denominator equal to 0.
Check the solution: [tex]\frac{x}{x-4}=\frac{x}{x-4}+4[/tex]
Substitute the value of x=4 in the original expression,
[tex]\frac{4}{4-4}=\frac{4}{4-4}+4[/tex]
[tex]\frac{4}{0}=\frac{4}{0}+4[/tex]
Thus, 4 must be rejected as the solution, and the solution set is only 0.
A proposed solution of a rational equation that causes a denominator to equal zero is rejected because division by zero is not possible.
Explanation:Any proposed solution of a rational equation that causes a denominator to equal zero is rejected. When the denominator of a rational equation is zero, the fraction becomes undefined because division by zero is not possible. In mathematics, division by zero is an undefined operation.
Do I add the lenghs of the sides of a figure and multiply them by the height to get the area?
An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?
A. C(t) = 145 for 5 < x ≤ 6
B. C(t) = 145 for 6 < x ≤ 7
C. C(t) = 170 for 5 < x ≤ 6
D. C(t) = 170 for 6 < x ≤ 7
Find f(5) for f(x). ... .. ... ....
what is 77.0 divided by 200
The average weight of a mature human brain is approximately 1400 grams. What is the equivalent weight in pounds? Use the conversion equivalency 1 kilograms (kg) = 1000 grams (g) and 2.20 pounds (lb) = 1 kg.
Maree is 8 years older than Aaron.
Aaron is twice as old as Rick.
All their ages add up to 28.
What are their ages?
Maree is
Aaron is
Rick is
what is the answer? this is hard