How many cubes with side lengths of 1/3 cm does it take to fill the prism?
Answers
Answer:
120 tiny cubes
Step-by-step explanation:
Find the volume of both the tiny cubes and the big cube. Then we will take big volume cube and divide it by tiny cube volume.
So big cube has volume (5/3*4/3*2)=40/9 cm^3
Tiny cube volume is (1/3*1/3*1/3)=1/27 cm^3
(40/9) divided by (1/27)
is the same as 40/9 time 27=40(27)/9=40(3)=120
Answer:
120
Step-by-step explanation:
Related Questions
Does anyone know the answer to this question
Answers
ANSWER
[tex]\cos B = \frac{ \sqrt{3} }{3} [/tex]
EXPLANATION
The given triangle is a right triangle.
It was given that,
[tex]a = 1[/tex]
and
[tex]b = \sqrt{2} [/tex]
Using the Pythagoras Theorem, we can determine the value of c.
[tex] {c}^{2} = {( \sqrt{2} )}^{2} + {1}^{2} [/tex]
[tex] {c}^{2} = 2 + 1[/tex]
[tex]{c}^{2} = 3[/tex]
[tex]c = \sqrt{3} [/tex]
The ratio is the adjacent over the hypotenuse.
[tex]\cos B = \frac{1 }{ \sqrt{3} } [/tex]
We rationalize to get:
[tex]\cos B = \frac{ \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \frac{ \sqrt{3} }{3} [/tex]
A right cylinder has a diameter of 8 M and a height of 6M. What is the volume of the cylinder
Answers
Answer:
V=301.59 M^3
Step-by-step explanation:
The volume of a cylinder is 3.14r^2h
3.14(4^2)6=V
3.14(16)6=V
50.24(6)=301.59
Sara has a piece of string measuring 3 yards. How many 1-inch strips can be cut from the string?
A- 108 strips
B- 72 strips
C- 36 strips
D- 12 strips
Answers
Answer:
A - 108 strips
Step-by-step explanation:
1 yard = 36 inches
3 yards = 108 inches.
If Sara cuts 1-inch strips, she will have 108 strips in total.
Hope this helps!
Answer:
A 108 strips
Step-by-step explanation:
1 yd = 3 ft
3 ft = 3 * 12 inches = 36 inches
3 yds = 3 * 36 = 108
If each strip is 1 inch, we can cut 108 1 inch strips
NEED HELP ASAP (WILL MARK BRAINLYEST)
Answers
Answer:
The true statements are the third and fifth. [not sure about the second one!]
Step-by-step explanation:
1.) (7u + 4) is written as a sum of three terms.
This is false since 7u is one term, and 4 is one term, making a total of two terms, not three.
2.) 2 is a factor
I'm not sure on this but I don't think its true.
3.) In 7u, 7 is a coefficent
This is true. The coefficent is the number in front of a variable, or in this case, 7.
4.) In (7u + 4), 7u is a constant.
This is false, as a constant is a number without any variable attached to it. The constant in this case would be 4.
5.) 8 and 1 are like terms.
This is true, since you can add 8 and 1, resulting in the sum of 9.
6.) None of these are true.
This is false, as at least 2 of these statements are true.
I hope this helps! :)
(−
6
11
)+m=−
9
2
Answers
To solve the equation (−6/11) + m = −9/2, you need to isolate the variable m. The solution to the equation is m = −33/22.
To solve the equation (−6/11) + m = −9/2, we need to isolate the variable m.
First, we can start by subtracting (−6/11) from both sides of the equation: m = −9/2 - (−6/11)
Simplify the equation by finding a common denominator: m = −9/2 + 33/11
Combine the fractions: m = −99/22 + 66/22
Finally, add the numerators and keep the common denominator: m = −33/22
Therefore, the solution to the equation is m = −33/22.
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To rent a car, you must pay $0.30 per mile plus a maintenance fee of $35. Write and equation to represent this function.
Answers
Let y be the total cost and x be the miles taken:
y = 0.30x + 35
35 is a fixed cost. No matter how many miles you drive the car you will still need to pay $35
.30 is a cost that depends on the miles taken (x).
Hope this helped!
~Just a girl in love with Shawn Mendes
Arianna is buying plants for her garden. She buys 15 flowering plants for $96. Pink flowering plants sell for $8, and purple flowering plants sell for $5. How many pink flowering plants did Arianna buy?
I figured out the answer! The answer is 7.
8x +5y = 96
plug in 7 for x
8 (7) + 5y = 96
56 + 5y = 96 subtract 56 from both sides
5y/y = 40/5
y = 8
She bought 7 pink and 8 purple plants
Answers
Answer:
7 & 8
Step-by-step explanation:
For this case we propose a system of equations:
x: Variable representing the plant with pink flowers
y: Variable representing the plant with purple flowers
We have as data that:
[tex]x + y = 15\\8x + 5y = 96[/tex]
From the first equation we have to:
[tex]x = 15-y[/tex]
Substituting in the second equation:
[tex]8 (15-y) + 5y = 96\\120-8y + 5y = 96\\-3y = 96-120\\-3y = -24\\y = \frac {-24} {- 3}\\y = 8[/tex]
Arianna bought 8 purple flowers.
Now we have:
[tex]x = 15-8\\x = 7[/tex]
Arianna bought 7 pink flowers.
Answer:
Arianna bought 7 pink flowers.
If U = {all positive integers) and A = {x|x EU and x is an odd positive integer}, which describes AC?
Aº = {xlx EU and is a negative integer}
AC = {x|x EU and is zero}
Aº = {x|x EU and is not an integer}
Aº = {xlx EU and is an even positive integer}
Answers
The option that describes the Complement A^c is; D: A^c = {x| x ∈ U and x is an even positive integer}
What is the correct set element description?If the Universal set, U = {all positive integers); and
A = {x|x ∈ U and x is an odd positive integer}.
Thus:
The complement of A is the set of the elements of the universal set which are not in A.
If a set is not odd, then it is even.
Thus:
A^c = {x| x ∈ U and x is an even positive integer}
Read more about Set Elements at; https://brainly.com/question/14528403
In the four-digit number ABCD, each letter represents a unique integer. When A is multiplied by B, the product is odd. When A is multiplied by C, the product is even. Which of the following four-digit numbers is even?
A. ABDC
B. CABD
C. ACDB
D. Cannot be determined from the information given.
Answers
Answer:
A
Step-by-step explanation:
Nice problem.
The only way you can get an odd number by multiplying two digits together is if they are both odd.
For example 5*7 = 35 which is odd. You cannot find 2 odd numbers that when multiplied will give an even.
That means that A and B are both odd.
Now if you multiply an odd and an even together, you always get an even.
For example 4 * 9 = 36 which is even.
Since A is known to be odd, C must be even. So the four digit number you want ends in C.
The Answer is A
Answer:
Step-by-step explanation:
The aaaa
Find an equation for the line parallel to y = 3 x - 2 y-intercept (0,5). Write the answer in slope-intercept form.
Answers
Y-5= 3x
Y= 3x + 5
Hope this helps!
Simplify into one fraction. -1/x-9 - -2/x+7
a. 1/(x-9)(x+7)
b. -3/(x-9)(x+7)
c. x-25/(x-9)(x+7)
d. -3x+11/(x-9)(x+7)
Answers
Answer: I think c but I am not sure
Step-by-step explanation: Hope this helps
[tex]\bf -\cfrac{1}{x-9}-\cfrac{-2}{x+7}\implies -\cfrac{1}{x-9}+\cfrac{2}{x+7}\implies \cfrac{2}{x+7}-\cfrac{1}{x-9}\impliedby \stackrel{\textit{our LCD is}}{(x+7)(x-9)} \\\\\\ \cfrac{(x-9)2~~-~~(x+7)1}{(x+7)(x-9)}\implies \cfrac{2x-18~~-~~x-7}{(x+7)(x-9)}\implies \cfrac{x-25}{(x+7)(x-9)}[/tex]
What is the value of x?
a.30
b.45
c.55
d.60
Answers
Answer:
b. 45deg
Step-by-step explanation:
see attached
Answer:
45
Step-by-step explanation:
We are seen with two lines crossing each other and the angle in which a line has is 180 degrees. Also, the angles labeled 3x and x are supplementary angles, which mean they add up to 180 degrees. Using this information, we can set up an equation.
[tex]x+3x=180[/tex]
[tex]4x=180[/tex]
[tex]x=45[/tex]
The function f is continuous on the interval [3,11] with some of its values given in the table below. Find the average rate of change in t over the interval [3,11].
X. | 3 | 5 | 8 | 10 | 11 |
F(x)| -4| 4 | 10 | 16 | 20 |
A. 1/3
B. 2
C. 3
D. None of these
Answers
Answer:
C
Step-by-step explanation:
The average rate of change of a function f(x) on the interval [a, b] is:
(f(b) − f(a)) / (b − a)
Here, the interval is [3, 11]. f(3) = -4 and f(11) = 20.
(f(11) − f(3)) / (11 − 3)
(20 − -4) / 8
24 / 8
3
The average rate of change in t over the interval [3,11] is C. 3.
What is the average rate of change of a function?The average rate of change function exists expressed as the average rate at which one quantity is changing regarding something else changing. In simple terms, an average rate of change function exists as a process that estimates the amount of change in one item divided by the corresponding amount of change in another.
The average rate of change of a function f(x) on the interval [a, b] is:
(f(b) − f(a)) / (b − a)
Here, the interval is [3, 11]. f(3) = -4 and f(11) = 20.
(f(11) − f(3)) / (11 − 3)
(20 − -4) / 8
24 / 8
3.
The average rate of change in t over the interval [3,11] is C. 3.
Hence, The correct answer is option C. 3.
To learn more about the average rate of change of a function
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Solve the equation:
9 - 7 — 29
Select one:
oz = 36
o -4
о - - 4
2
Answers
9x-7= 29
9x-7+7= 29+7
9x= 36
Divide by 9 for 9x and 36
9x/9= 36/9
x= 4
Check answer by using substitution method
9x-7= 29
9(4)-7=29
36-7= 29
29= 29
Answer is x=4 (second choice)
Answer:
38/9
Step-by-step explanation:
9x - 7 = 29⁰
9x = 38
x = 38/9
Which function is the inverse of function f? f(x)=9x^-12
Answers
Answer:
[tex](\frac{x}{9})[/tex]¹²
Step-by-step explanation:
The given function is f(x) = 9x⁻¹²
To find the inverse of f(x) we will write the function in a equation form y = 9x⁻¹²
Now we will replace x from y and y from x
x = 9y⁻¹²
Then we will find the value of y
y⁻¹² = [tex]\frac{x}{9}[/tex]
y = [tex](\frac{x}{9})[/tex]¹²
Now y will be replaced by f⁻¹(x)
f⁻¹(x) = [tex](\frac{x}{9})[/tex]¹²
Therefore inverse of the function f(x) is f⁻¹(x) = [tex](\frac{x}{9})[/tex]¹²
Which equation represents the graphed function?
y=-3x + 3
0 y = 3x-3
© y= 3x - 1
y=-3x+3
Answers
Answer:
y = -1/3x +3
Step-by-step explanation:
First we need to find the slope
m = (y2-y1)/(x2-x1)
= (2-3)/(3-0)
-1/3
Then we know the y intercept( where it crosses the y axis)
It crosses at y=3
The slope intercept form is
y= mx+b where m is the slope and b is the y intercept
y = -1/3x +3
Answer:
[tex]y=\frac{-1}{3} x+3[/tex]
Step-by-step explanation:
Let frame the equation of the line using the points given on the graph
(0,3) and (3,2)
Equation of the line is y=mx+b
where m is the slope and b is the y intercept
To find slope we use formula
[tex]slope =\frac{y_2-y_1}{x_2-x_1} =\frac{2-3}{3-0} =\frac{-1}{3}[/tex]
Y intercept b is the point where the graph crosses y axis
y intercept b = 3
The equation y=mx+b becomes
[tex]y=\frac{-1}{3} x+3[/tex]
determine the distance between -16 and -4
Answers
the answer would be 12
-4 - -16 = 12
the distance between -16 and -4 is 12.
The change from one number to the next in a geometric sequence is called
the:
A. common difference.
B. arithmetic difference.
C. common ratio.
D. geometric ratio.
Answers
Answer:
C. Third option
Step-by-step explanation:
C is the correct answer, because the common ratio is a change from one number into the next in a geometric sequence.
Hope this helps!
I checked
The town librarian bought a combination of new-release movies on DVD for $20 and classic movies on DVD for $8. Let x represent the number of new releases, and let y represent the number of classics. If the librarian had a budget of $500 and wanted to purchase as many DVDs as possible, which values of x and y could represent the number of new-release and classic movies bought?
Answers
Answer:
x = 1, y = 60
Step-by-step explanation:
Value of new-releases (x) = $20 each
Value of classic (y) = $8 each
Total budget = $500
Equation : 20x + 8y = 500
The librarian wants to purchase maximum DVDs. She can get more DVDs of classic movies for $8 as they are less costly.
Lets assume the librarian buys at least one new-release DVD.
x=1
20x + 8y = 500
8y + 20(1) = 500
y = 60
Therefore, in a budget of $500, the librarian can purchase 60 classic movies and 1 new-release.
!!
Answer: x=16 y=22
Step-by-step explanation:
Edge test math
How many variable terms are in the expression3x3y+5x2+y+9
Answers
Answer:
Four(4)
Step-by-step explanation:
The given algebraic expression is:
[tex]3x^3y+5x^2+y+9[/tex]
The variables in this expression are [tex]x[/tex] and/or [tex]y[/tex].
The variable terms in this expression are terms containing [tex]x[/tex] and [tex]y[/tex].
These terms are:
[tex]3x^3y[/tex]
[tex]5x^2[/tex]
and
[tex]y[/tex]
Therefore there are 4 variable terms.
Given the pay rate and hours worked, determine the gross earnings, Federal taxes (assuming 18% of gross earnings), state taxes (assuming 4% of gross earnings), social security deduction (assuming 7.05% of gross earnings), total deductions, and net pay.
Answers
Answer:
Let us assume that the pay rate per hour = x
no. of hours worked = n
Gross earnings = x*n
Federal taxes = 18% of gross earnings
= 0.18(x*n)
State taxes = 4% of gross earnings
= 0.04(x*n)
Social security deduction = 7.05% of gross earnings
= 0.0705(x*n)
Total deductions = Federal taxes + State taxes +SSD
= 0.18(x*n) + 0.04(x*n) + 0.0705(x*n)
= 0.2905(x*n)
Net pay = Gross earnings - Total Deduction
Net pay = x*n - 0.2905(x*n)
Net pay = 0.7095(x*n)
The gross earnings are $800. Deductions total $232.40, resulting in a net pay of $567.60 after federal, state taxes, and social security deductions.
Let's calculate various components of a paycheck, starting with the given pay rate and hours worked. Suppose the pay rate is $20 per hour and the employee works 40 hours per week.
1. Gross Earnings:
Gross Earnings = Pay Rate × Hours Worked
Gross Earnings = $20/hour × 40 hours
Gross Earnings = $800
2. Federal Taxes:
Federal Taxes = 18% of Gross Earnings
Federal Taxes = 0.18 × $800
Federal Taxes = $144
3. State Taxes:
State Taxes = 4% of Gross Earnings
State Taxes = 0.04 × $800
State Taxes = $32
4. Social Security Deduction:
Social Security Deduction = 7.05% of Gross Earnings
Social Security Deduction = 0.0705 × $800
Social Security Deduction = $56.40
5. Total Deductions:
Total Deductions = Federal Taxes + State Taxes + Social Security Deduction
Total Deductions = $144 + $32 + $56.40
Total Deductions = $232.40
6. Net Pay:
Net Pay = Gross Earnings - Total Deductions
Net Pay = $800 - $232.40
Net Pay = $567.60
Therefore, the gross earnings are $800, and after accounting for $232.40 in deductions for federal and state taxes along with social security, the net pay is $567.60.
Match the equivalent expressions.
x - 3y + 12
12 - 3y - 2x + x + 2x
3x + 2y - 2x + y + 12
3y + 12
3x + y - 12
4y + 3y + 3x - 6y - 10 - 2
x + 3y + 2x - 3x + 7 + 5
x + 3y + 12
5 + 2y + 7x - 4x + 3y - 17
Answers
Answer:
One pair of equivalent expressions is:
x - 3y + 12
12 - 3y - 2x + x + 2x
Second,
x + 3y + 12
3x + 2y - 2x + y + 12
third,
3y + 12
x + 3y + 2x - 3x + 7 + 5
four,
3x + y - 12
4y + 3y + 3x - 6y - 10 - 2
Step-by-step explanation:
In order to match the equivalent expressions we have to put each expression in its simplest form
So,
[tex]x-3y+12\\\\12 - 3y - 2x + x + 2x\\=12-3y+x\\=x-3y+12\\\\3x + 2y - 2x + y + 12\\=x+3y+12\\\\4y + 3y + 3x - 6y - 10 - 2\\=3x+y-12\\\\x + 3y + 2x - 3x + 7 + 5\\=3y+12\\\\5 + 2y + 7x - 4x + 3y - 17\\=5y+3x-12[/tex]
One pair of equivalent expressions is:
x - 3y + 12
12 - 3y - 2x + x + 2x
Second,
x + 3y + 12
3x + 2y - 2x + y + 12
third,
3y + 12
x + 3y + 2x - 3x + 7 + 5
four,
3x + y - 12
4y + 3y + 3x - 6y - 10 - 2
..
Answer:
x + 3y + 12 <--> x + 3y + 2x - 3x + 7 + 5
x − 3y + 12 <--> 12 - 3y - 2x + x + 2x
3x + 2y − 2x + y + 12 <--> 3x + y - 12
3y + 12 <--> 4y + 3y + 3x - 6y - 10 - 2
I need help with this
Answers
Answer:
X=6
Step-by-step explanation:
You need to cross multiply 2 by x+6. this Equals 2x+12. Then you cross multiply 8 by three which is 24. leading to the equation 2x+12=24 . Subtract 12 on both sides to get 2x=12. Divide by two to get 6 as your answer.
Find the nonpermissible replacement for bin
this expression.
b2/5b +5
Answers
Answer:
b ≠ - 1
Step-by-step explanation:
The denominator of the rational expression cannot be zero as this would make it undefined.
Equating the denominator to zero and solving gives the value that b cannot be.
solve
5b + 5 = 0 ( subtract 5 from both sides )
5b = - 5 ( divide both sides by 5 )
b = - 1 ← excluded value
Coach Johnson needs to buy shin guards for the Junior Varsity and Varsity basketball
players. The following packages of shin guards are available at The Athletic Store:
. 10 shin guards for $14.50
. 15 shin guards for $22.50
Coach Johnson needs to buy 30 shin guards. How much money will he save by purchasing
30 shin guards in packages with the lowest unit price compared to the highest unit price?
Answers
Answer:
Coach Johnson will save $1.50
Step-by-step explanation:
1. The first step is to calculate the unit price for each of the packages, ie. how much a single shin guard costs.
If we look at the package of 10 shin guards for $14.50, we can calculate the unit price by dividing the package price ($14.50) by the number of shin guards (10). Thus we get:
14.50/10 = $1.45
Now, if we do the same for the package of 15 shin guards for $22.50, we get:
22.50/15 = $1.50
2. Now we can see that the lowest unit price is $1.45 (package of 10 shin guards) and the highest unit price is $1.50 (package of 15 shin guards).
3. There are two ways to see how much he would save, so I will show both here.
1) First calculate how much the coach will have to pay for a pack of 30 shin guards for each of the packages:
3 packages of 10 shin guards for $14.50 = 3*14.5 = $43.50
2 packages of 15 shin guards for $22.50 = 2*22.5 = $45.00
Now subtract the second value from the first: 45-43.5 = 1.5
Therefor, he will save $1.50.
2) The second method is perhaps what I would personally use as it is a little quicker; so we already know that the unit price for the pack of 10 is $1.45 and the unit price for the pack of 15 is $1.50 - thus, we can say that there is a difference of $0.05 per shin guard in price. Now if we were going to calculate how much the coach would save in buying 30 shin guards, we could simply multiply how much he saves on a single shin guard by 30. Thus, we get:
0.05*30 = 1.5
Therefor, again we get the same answer that Coach Johnson would save $1.50.
Hope that helps :)
Assume that you have taken out an amortized loan for $10,000 to buy a new car. The yearly interest rate is 18% and you have agreed to pay off the loan in 4 years. What is your monthly payment?
Answers
Answer:
$293.75
Step-by-step explanation:
Any number of financial calculators, spreadsheets, and on-line calculators can compute the monthly payment for you. Or you can put the numbers into the formula and compute it yourself.
A formula I like is ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where A is the monthly payment, P is the loan amount, r is the annual interest rate, and t is the number of years. Filling in the given information and doing the arithmetic, we get ...
A = $10000(0.18/12)/(1 -(1 +0.18/12)^(-12·4)) = $150/(1 -1.015^-48) = $293.75
Your monthly payment is $293.75.
what is the correct way to find the distance between the points (9, 6) and (4, 1)?
Answers
Answer: Using the distance formula 5sqrt 2 is the answer
d=sqrt(x1-x2)^2+(y1-y2)^2
Step-by-step explanation:
d=sqrt(9-4)^2+(6-1)^2
d=sqrt(5)^2+(5)^2
d=sqrt 25+25
d=sqrt 50
d= 5 sqrt 2
Simplify (5a)(5b) help me plz
Answers
Answer:
25ab
Step-by-step explanation:
(5a)(5b) -> Expand the brackets (multiply like terms together, etc) When the brackets are expanded, values can be multiplied, etc easily
25ab -> 5 multiplied by the other 5 gives 25; a multiplied by b gives ab
Find the number of steel ball bearings, each of diameter 0.7 cm, that can be made from 1kg of steel, given that 1cm cubed of steel weighs 7.8 g
Answers
Answer:
Ball Bearing Volume = (4 / 3) * PI * radius ^3
Volume = (4 / 3) * 3.14159265 * (.35)^3
Volume = (4 / 3) * 3.14159265 * 0.042875
Volume = 0.17959438 cc
1 cc of steel = 7.8 g
Volume of 1 kg of steel = 1,000 cc / 7.8 g per cc
1 kg = 128.205 cc
Number of ball bearings we can make = 128.205 / 0.17959438
Equals 713.86
Step-by-step explanation:
Write the expiation of a circle with a center at (3,-5) and a radius of 4
Answers
[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{3}{ h},\stackrel{-5}{ k})\qquad \qquad radius=\stackrel{4}{ r}\\[2em] [x-3]^2+[y-(-5)]^2=4^2\implies (x-3)^2+(y+5)^2=16[/tex]