Given:
Volume of Large cube = 1 cubic unit
Volume of small cube = [tex]\dfrac{1}{27}[/tex] cubic unit
To find:
The difference between the edge length of the large cube and the edge length of the small cube.
Solution:
Let the edges of large and small cubes are [tex]a_1[/tex] and [tex]a_2[/tex] respectively.
We know that, volume of a cube is
[tex]V=(edge)^3[/tex]
Volume of Large cube = 1 cubic unit
[tex](a_1)^3=1[/tex]
Taking cube root on both sides, we get
[tex]a_1=1[/tex]
So, edge of large cube is 1 unit.
Volume of small cube = [tex]\dfrac{1}{27}[/tex] cubic unit
[tex](a_2)^3=\dfrac{1}{27}[/tex]
Taking cube root on both sides, we get
[tex]a_2=\dfrac{1}{3}[/tex]
So, edge of large cube is [tex]\dfrac{1}{3}[/tex] unit.
Now, difference between them is
[tex]d=a_1-a-2[/tex]
[tex]d=1-\dfrac{1}{3}[/tex]
[tex]d=\dfrac{3-1}{3}[/tex]
[tex]d=\dfrac{2}{3}[/tex]
Therefore, the difference between the edge length of the large cube and the edge length of the small cube is [tex]\dfrac{2}{3}[/tex] unit.
The annual enrollment of a university for the last nine years is recorded in the table. What quadratic function best models this set of data?
Answer:
y = 0.14 x^2 - 1.43 x + 10.75
Step-by-step explanation
got it correct on the test
The quadratic function best models this set of data is y = 10.75x² - 1.43x + 0.14.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have data shown in the table:
It is required to find the quadratic function best models this set of data.
Let the quadratic function is:
y = ax² + bx + c
We can find the values of a, b, and c from the table, which are constants.
From the table:
a = 10.75
b = -1.43
c = 0.14
The quadratic function is:
y = 10.75x² - 1.43x + 0.14
Thus, the quadratic function best models this set of data is y = 10.75x² - 1.43x + 0.14.
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Recycling Tim's family was collecting aluminum cans to recycle. They found out that they would get two.cents for every three cans they collected. If they collected 2,187 cans, how much money did they receive? EXPLAIN YOUR ANSWER PLEASE
Answer: They received $14.58
Step-by-step explanation:
Set up a proportional relationship
If 2 cents equal to 3 cans then we will represent how 2,187 will be worth by x.
[tex]\frac{0.02}{3} / \frac{x}{2187}[/tex] Cross multiply
3x = 43.74 Divide both sides by 3
x = 14.58
combine these radicals
[tex] - 12 \sqrt{12} - 2 \sqrt{3} [/tex]
he results of a survey are shown below. In the survey, 12 students said that they would like to learn French. How many of the students surveyed would like to learn Spanish?
A drawing shows a result of a survey on a piece of paper. It shows the percent of students who like to learn different languages. It shows the percentages as Spanish, 36; French; 24; German, 18; other, 22.
Answer:
18 students
Step-by-step explanation:
Now think of it in this form. 12 students wanna learn french which is 24% and in this problem we have to find 24% of "x" is 12. The answer is obviously 50. Now go to German and you can see that 18% want to learn German. All you have to do is find 50% of 18 to get your answer which is 9. Now follow that same pattern with the Spanish one. If 36% want to learn Spanish, just find 50% of it or half of it and that could be done by doing 36 divided by 2 to get 18 as your answer. Another way to do it is my turning 50% into 0.5 and multiplying it by 36 to get your answer. As a result, your answer is 18 students want to learn Spanish.
if your a single boy look at the pic below
Answer:
im not a boy nor single but an fyi it doesn't show a photo just letting you know
Step-by-step explanation:
Answer:
df
Step-by-step explanation:
During the day, Lola's dog is tied by rope to a tree in the center of her yard. The scale drawing below shows the area that the dog has to run. If the actual length of the rope is 12 1/2 feet, what is the scale used in the drawing? 1 9/16
Answer:
[tex]Actual\ Length : Scale\ Length = 8 : 1[/tex]
Step-by-step explanation:
Given
[tex]Actual\ Length = 12\frac{1}{2}ft[/tex]
[tex]Scale\ Length = 1\frac{9}{16}ft[/tex] --- See attachment
Required
Determine the scale used
The scale of the drawing can be represented using the following ratio
[tex]Scale = Actual\ Length : Scale\ Length[/tex]
Substitute values for actual and scale lengths
[tex]Scale = 12\frac{1}{2}: 1\frac{9}{16}[/tex]
Convert to improper numbers
[tex]Scale = \frac{25}{2}: \frac{25}{16}[/tex]
Convert to division:
[tex]Scale = \frac{25}{2}/\frac{25}{16}[/tex]
[tex]Scale = \frac{25}{2}*\frac{16}{25}[/tex]
[tex]Scale = \frac{1}{2}*\frac{16}{1}[/tex]
[tex]Scale = \frac{16}{2}[/tex]
[tex]Scale = \frac{8}{1}[/tex]
Convert to ratio
[tex]Scale = 8 : 1[/tex]
Hence, the scale of the drawing is:
[tex]Actual\ Length : Scale\ Length = 8 : 1[/tex]
What is 3 divided by 48
Answer:
uhhh 16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
Work out 1 2/3x 1 1/5
1 2/3 × 1 1/5
Convert into improper fraction !
5/3 × 6/5
30/15
6/3
2
Hola !
I think this is an Australian site !
Nice meeting you people !
☺️✌️
Enter an expression which would represent the simplified form of 4x + 8 subtracted from 2x - 10?
Answer:
2x - 2
Step-by-step explanation:
Move the numbers to be near their mates
4x - 2x + 8 - 10
Then solve as much as you can
4x - 2 = 2x, 8 - 10 = -2
2x - 2
In ANOP, NP is extended through point P to point Q, mZPNO = (x + 14),
mZOPQ = (5x – 2)°, and mZNOP = (x - 1)º. Find mZOPQ.
Answer:
Step-by-step explanation:
m∠OPQ = 23°
What is the slope-intercept form of the linear equation x+4y=12?
Answer:
y = -x/4 + 3
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptStep-by-step explanation:
Step 1: Define
Standard Form: x + 4y = 12
Step 2: Rewrite
Find slope-intercept form
Subtract x on both sides: 4y = 12 - xDivide 4 on both sides: y = 3 - x/4Rearrange: y = -x/4 + 3we know that
The equation of the line in the slope-intercept form is equal to
we have
Solve for y
Subtract both sides
Divide by both sides
therefore
the answer is
Y= 1/4x+3
PLEASE HELP SOLVE THIS!!!!!!!!!!!
9514 1404 393
Answer:
a) yes; 12/15/17 ~ 20/25/x; SAS
b) x = 28 1/3
Step-by-step explanation:
The left-side segments are in the ratio ...
top : bottom = 12 : 8 = 3 : 2
The right side segments are in the ratio ...
top : bottom = 15 : 10 = 3 : 2
These are the same ratio, and the angle at the peak is the same in both triangles, so the triangles are similar by the SAS postulate.
Normally, a similarity statement would identify the triangles by the labels on their vertices. Here, there are no such labels, so we choose to write the statement in terms of the side lengths, shortest to longest:
12/15/17 ~ 20/25/x
__
The sides of similar triangles are proportional, so the ratio of longest to shortest sides will be the same in the two triangles. In the smaller triangle, the longest side is 17/12 times the length of the shortest side. The value of x will be 17/12 times the length of the shortest side in the larger triangle:
x = 17/12 · 20 = 340/12
x = 28 1/3
Plis help me first one to reply gets brainless
Answer:
1.>
2.>
3.=
4. >
Step-by-step explanation:
Transversal t cuts parallel lines a and b as shown in the diagram. Which equation is necessarily true?
A. m∠1 = m∠2
B. m∠4 = m∠6
C. m∠1 + m∠5 = 90°
D. m∠3 + m∠5 = 180°
E. m∠7 = m∠8
Answer:
D is true
Step-by-step explanation:
A, B, C, and E are supplementary pairs so they cant equel each other.
Answer:
the answer would be d! got it right on plato.
Step-by-step explanation:
Candice is playing an online trivia game. She has 75 points and earns 3 points for each correct answer. She will advance to the next round if her score is over 90 points which statement best describes how antibiotics are used?a75x + 3 > 90 b3x + 90 90 d3x + 75 < 90
Using a linear function, the statement that best describes when she advances to the next phase is: 75 + 3x > 90.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering that she already has 75 points, and earns 3 points for each correct answer, her score is modeled by the following function:
T = 75 + 3x.
She advances to the next phase if she scores over 90 points, hence the statement is:
T > 90
75 + 3x > 90.
More can be learned about linear functions at https://brainly.com/question/24808124
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Answer:
c.3x+75>90
Step-by-step explanation:
A painting is on sale at 40% off.the sale price is $320 what was the original price
Answer:
$533.33
Step-by-step explanation:
$533.33 multiplied by 0.6 = $319.998 which rounds to $320
533.33 ÷ 100 = 5.33 so this is 1 percent
5.33 x 40 = $213.332 which rounds to $213.33
$320 + $213.33 = $533.33
I give brainlest if you answer my question correctly!
Answer:
C the third one
Step-by-step explanation:
It is equal to the demo
Which of the following does NOT show an identity property?
2 + 1 = 3
5 ÷ 1 = 5
3 − 0 = 3
4 × 1 = 4
Answer:
2+1 = 3
Step-by-step explanation:
The first one
2+1 = 3
the identity properties are :
n+0=n
n-0=n
n/1=n
n*1=n
and the one that does NOT show an identity is 2+1=3
a $380 television cost $411.35 after tax is added. What is the percentage of the tax
Answer:
The tax percentage is 8.25 percent
Step-by-step explanation: After multiplying multiple tax percentages I found that 8.25 was the right tax percentage.
Hope this helps.
If f(x) = 5x^2– 3 and f(x + a) = 5x^2+ 30x + 42,
what is the value of a ?
Answer:
The zeros are x=0,3,-2
There is a multiplicity of 1 for all of them.
Step-by-step explanation:
The required value of a is 3 for the given function.
What are the functions?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
The function is given as follows:
f(x) = 5x²– 3
Substitute the value of x = x + a in the above function,
f(x + a) = 5(x + a)²– 3
f(x + a) = 5(x² + a² + 2ax) - 3
f(x + a) = 5x² + 5a² + 10ax - 3
f(x + a) = 5x² + 10ax + 5a² - 3 ....(i)
As per the question, we have f(x + a) = 5x²+ 30x + 42 ....(ii)
Equating the equations (i) and (ii),
So, 10a = 30
a = 30/10
a = 3
Therefore, the required value of a is 3.
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Solve by Graphing. y = 4x y = x + 3
Answer: 99% sure its (1,4)
Step-by-step explanation:
Being a bullfrog, Lilly is good at hopping. She can hop 9 inches with each hop! How
many hops will it take for her to hop across a sidewalk that is 60 inches wide?
7
8
6
5
Answer:
Step-by-step explanation:
60 / 9 = 6.66666...
it will take lily 7 hops to make it across
help mee pleaseee this doesnt even make sense lol
Answer: 2 is less than or equal to x which is less than 4
Step-by-step explanation:
how many times can 15 fit into 25
Answer:
1 time
Step-by-step explanation:
15x2=30
and 30 is more than 25, therefore, 15 only fits in 25 one time
Answer:
only 1 time
you can divided the answer but it will just keep repeating
1.6666666666667
PLz answer fast with picture of your work on a blank piece of paper
Answer:2/3
Step-by-step explanation:
I need help plis I'm struggling in this math problem
Answer:
D) 13x + 5
Step-by-step explanation:
Combine like terms
Here, 6x and 7x are like terms
5 + 6x + 7x = 5 + 13x
=13x + 5
A rectangular field is 348 inches long and 7 yards wide. What is the perimeter of the field in feet? plz help me
Answer:50 feet
Step-by-step explanation:
16. Solve the equation. ( point)
R/4 -1=4
O 1.3
O 0.8
O 12
O 20
Answer:
D. 20
Step-by-step explanation:
Since you are subtracting, you can add 4 and 1. The sum is 5. 20/4 is equal to 5 so R = 20.
14 Divide 2+3(4)-(61/2-3)
5 of the 25 players on the soccer team are 7th graders. Find the Percent of 7th graders