Squares are cut out of the corners of a piece of 18*18 graph paper so that the sides can be folded to make an open box. What is the largest possible number of cubic units in the volume of the box if we require that the length of each edge is a whole number?
Answers
Answer:
432 mm²
Step-by-step explanation:
We need to cut out 3x3 squares from corners and make an open box. It's height will be 3mm(see the plan). So volume will be:
V = 12 * 12 * 3 = 432mm²
Related Questions
find the ratio of 4 days to 2 weeks
Answers
What is the value of StartFraction 6 Over x EndFraction + 2x2, when x = 3?
Answers
(6/X) + 2x^2 =
(6/3) + 2(3^2) =
2 + 2(9) =
2 + 18=
20
Answer:
D) 20
Step-by-step explanation:
Hope It Helps!!!
How does simplifying a square root expression differ from simplifying a cube root expression?
Answers
The square root contains two same numbers and the cubic root contains three same numbers.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The square root contains two same numbers and the cubic root contains three same numbers.
For an example:-
√9 = [tex]\sqrt{3\times 3}[/tex] = 3 as we can see in the example the value of the square root of 9 is 3 it consists of two threes in the roots.
∛27 = [tex]\sqrt[3]{3\times 3\times 3}[/tex] = 3 here we have found that 27 contains 3 times 3 so the cube root of 27 will be equal to 3.
Therefore square root contains two same numbers and the cubic root contains three same numbers.
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Show how you would convert 500 A.U. into light-years.
Someone please help I’m so lost
Answers
Answer:
0.00790625
Step-by-step explanation:
499.9997656975
Astronomical unit
=
0.00790625
Light-year
Formula
for an approximate result, divide the length value by 63240
Two players take turns removing a ball from a jar that initially contains m white and n black balls. The rst player to remove a white ball wins. Find the probability that the starting player wins.
Answers
½×½ which will be ¼
Step-by-step explanation:
because
Probability that the starting player wins:
[tex]P_{n} =[/tex] m /n + m + n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]
Let us say that the probability that the first player wins is [tex]P_{n}[/tex]. Then this can be happen in two ways:
If the first player wins in the first move which has a probability: m /n + m
If the first player wins after the second move which has a probability :
n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]
Therefore by the law of probability,
[tex]P_{n} =[/tex] m /n + m + n(n-1) /(n + m)(n+m -1) × [tex]P_{n-2}[/tex]
This will allow us to find out the probability of first player winning the game recursively.
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Tom was able to save 35% more this year than he did last year. If he saved $140 last year, how much did he save this year?
Answers
Answer:
$189
Step-by-step explanation:
35% of 140 = 49
140 + 149 = 189
Tom's total saving this year is $189.
It is a 35 percent increased saving from last year's $140.
What are percentages?Percentages are fractional values where the denominator is fixed to be 100.
To convert percentage into number, we multiply by 100.
How to solve the question?In the question, we are informed that Tom was able to save 35% more this year than he did last year.
We are asked if he saved $140 last year, then how much did he save this year.
The increase in Tom's savings = 35% of last year's savings,
or, the increase = 35/100 * 140 (To convert percentage into quantity, we divide by 100).
or, the increase = $49.
Therefore, Tom's total savings this year = Last year's savings + Increase,
or, Tom's total saving this year = $140 + $49 = $189.
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2. John and Jen went to the farmers market to buy fruit. John bought 3 boxes of oranges and 9 boxes of cherries for $78. Jen bought 8 boxes of oranges and 4 boxes cherries for $58. The system of equations ( shown in the pic i uploaded) can be used to represent this situation. A. Find how much does a box of oranges and a box of cherries cost ?
Answers
Answer:
Let the cost of orange be X and cost of cherry be y
3x + 9y = 78
8x + 4y = 58
Solving equation using elimination method
multiplying eq 1 with 8 and eq 2 with 3
8(3x + 9y ) = 78(8)
3( 8x + 4y) = 3(58)
24x + 72 y = 624
24x + 12y = 174
subtracting,
60 y = 450
y = 7.5
3x + 9(7.5) = 78
3x + 67.5 = 78
3x = 78 - 67.5
3x = 10.5
x = 3.5
Box of orange = $3.5 Box of cherry = $7.5Solve ly + 21 > 6
() {yly <-8 or y> 4]
O (yly<-4 or y> 4}
(yly <-6 or y> 6}
Answers
[tex] |y + 2| > 6 \\ y + 2 > 6 \: \: \: or \: \: \: y + 2 < - 6 \\ y > 6 - 2 \: \: \: or \: \: \: y < - 6 - 2 \\ y > 4 \: \: \: or \: \: \: y < - 8[/tex]
Solution : ] -♾️ , -8 [ U ] 4, + ♾️ [
PLEASE GIVE BRAINLIEST
Select the correct answer.
The graph of function f is shown.
If g(x) = -2f(x), which graph is the graph of function g?
Answers
Answer:
Step-by-step explanation:
Note that the new function, g(x), provides a value for y that is -2 times the value returned by f(x). That means that for the same value of x, the resulting value of g(x) will be -2 times that provided by f(x).
See the attached image. The table shows how the values of y change for each value of x used in the respective function. Plot those new values to produce the graph.
I need help with a question
Answers
Solution :-
Here we have been given with two equations :
x + 5y = 0 (Equation No.1)3y + 2x = -21 (Equation No.2)¤ From Equation No.1 :
>> x = -5y
¤ In Equation No.2 :
Substituting the value of x which we got above as -5y here.
>> 3y + 2(-5y) = -21
>> 3y + 2 × (-5y) = -21
>> 3y - 10y = -21
>> -7y = -21
>> 7y = 21
>> y = 21 / 7
>> y = 3
¤ Finding out value of x :
>> x = -5y
>> x = -5(3)
>> x = -15
Step-by-Step Explanation:
=> x + 5y = 0 (Eq. 1)
=> 2x + 3y = -21 (Eq. 2)
From Eq. 1 :-
x = 0 - 5y
=> x = -5y (Eq. 3)
Substitute value of ‘x’ from Eq. 3 in 2 :-
2x + 3y = -21
2(-5y) + 3y = -21
-10y + 3y = -21
-7y = -21
7y = 21
y = 21/7
=> y = 3
Therefore, y = 3
Substitute value of ‘y’ in Eq. 3 :-
x = -5y
x = -5(3)
x = -5 * 3
=> x = -15
Therefore, x = -15
Hence, x = -15, y = 3 (-15, 3)
Type the correct answer in each box. Use numerals instead of words.
The domain of this function is (-12.-6.3, 15).
y =
Complete the table based on the given domain.
X
-6
15
y
S
15
Answers
Answer:
ttttihbogfpvvovovibjnphgbpvvvohj
Simplify each expression
3+8b+4+7b-3
Answers
Answer:
9. 15b + 4
10. 4y + 6
11. 15r+72
12. 130n + 20
Step-by-step explanation:
9. Combine Like terms
10. Combine Like terms
11. Distribute the 8 into (r + 9) then combine like terms
12. Distribute 10 into (3n + 2 + 10n) then combine like terms
Answer:
[tex]\mathsf {9) 15b + 4}\\\mathsf {10) 4y + 6}\\\mathsf {11) 15r + 72}\\\mathsf {12) 130n + 20}[/tex]
Step-by-step explanation:
[tex]\textsf {Question 9}[/tex]
[tex]\mathsf {3 + 8b + 4 + 7b - 3}[/tex]
[tex]\mathsf {8b + 7b + 4 + 3 - 3}[/tex]
[tex]\mathsf {15b + 4}[/tex]
[tex]\textsf {Question 10}[/tex]
[tex]\mathsf {8 + 7y - 3y + 2 - 4}[/tex]
[tex]\mathsf {7y - 3y + 8 + 2 - 4}[/tex]
[tex]\mathsf {4y + 6}[/tex]
[tex]\textsf {Question 11}[/tex]
[tex]\mathsf {8(r + 9) + 7r}[/tex]
[tex]\mathsf {8r + 8(9) + 7r}[/tex]
[tex]\mathsf {8r + 7r + 72}[/tex]
[tex]\mathsf {15r + 72}[/tex]
[tex]\textsf {Question 12}[/tex]
[tex]\mathsf {10(3n + 2 + 10n)}[/tex]
[tex]\mathsf {10(13n + 2)}[/tex]
[tex]\mathsf {10(13n) + 10(2)}[/tex]
[tex]\mathsf {130n + 20}[/tex]
On a farm, there is a grain silo.The silo is cylindrical with a tile roof. The silo has a diameter of 8 metres and is 6 metres tall. The farmer wants to paint the curved surface of the silo.Each can of paint will cover 20m². The paint costs $11.75 per can. How much will it cost the farmer to paint the silo?
Answers
The paint that the farmer needs to paint his Silo will cost $152.75.
How to calculate the price of the paint that the farmer will require?To calculate the value of the total paint that the farmer will require, we must carry out the following procedure:
1. Identify the area you need to paint
2πrh + 2πr²2 * 3.14 * 4m * 6m + 2 * 3.14 *4m² = 251.32m²2. Find how many cans of paint he needs.
251.32m² ÷ 20m² = 12.56That is, he will need 13 cans of paint.
3. Find the price of 13 cans of paint.
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The height in feet, h, of a model rocket t seconds after launch is given by the equation h (t) = 3 + 70 t minus 16 t squared. The average rate of change in h(t) between t = 1 second and t = 3 second is 6. What does the average rate of change tell you about the rocket?
The rocket is traveling six times as fast when t = 3 than it is when t = 1.
The rocket is at a greater height when t = 3 than it is when t = 1.
The rocket is 6 feet higher above the ground when t = 3 than it is when t = 1.
The rocket is traveling at a constant rate of 6 feet per second between t = 1 and t = 3.
Answers
The average rate of change in h(t) is 6.
What is Average Rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
h(t) = 3 + 70t - 16t²
Average rate of change
At t = 1 second
h(1) = 3 + 70(1) - 16(1)^2
h(1) = 57
At t = 3 second
h(3) = 3 + 70(3) - 16(3)^2
h(3) = 69
Average rate of change = Δh / Δt
=[h(3) - h(1)] / (3 - 1)
= (69 - 57) / 2
= 12 / 2
= 6.
Hence, the rate of change is 6.
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A rational expression simplifies to 3. the denominator of the original expression is given. which polynomial is the numerator?
Answers
The polynomial within the numerator is 9x²+45x+54.
Given the denominator of the initial expression is [tex]\frac{?}{3x^2+15x+18}[/tex] and also the rational expression simplifies to three.
A mathematical expression which will be rewritten to a rational fraction, an algebraic fraction specified both the numerator and therefore the denominator are polynomials. and a polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Let's take the polynomial within the numerator is k.
So, rewrite the given expression as
[tex]\frac{k}{3x^2+15x+18}=3[/tex]
or it also can be written as
[tex]\frac{k}{3x^2+15x+18}=\frac{3}{1}[/tex]
Cross multiply either side as a×d=b×c where a=k, b=3x²+15x+18, c=3 and d=1 and acquire
k=3(3x²+15x+18)
Simplify the above expression,
k=9x²+45x+54
Hence, the polynomial within the numerator within the given expression [tex]\frac{?}{3x^2+15x+18}[/tex] which is simplified to 3 is 9x²+45x+54.
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Answer:a
Step-by-step explanation:
What is the ratio of the circumference of a circle to its radius?
Answers
Answer:
2 pi : 1
Step-by-step explanation:
for every one unit of radius, there are two pi units in the circumference!
The graph of a system of inequalities shown
Answers
Which is an exponential decay function
Answers
Answer:
should be either b or c
Step-by-step explanation:
ee ni mee ni my nee mo
In the first answer a > 1 so it is an exponential growth function
In the second answer (4/5)^-x = (5/4)^x so again a growth function
In the third answer (8/7)^-x = (7/8)^x so this is an exponential decay function
help please i need answer ASAP
Answers
If the result is reflected over x-axis and vertically stretched by a factor of 5, the result will be g(x) = -5(x - 1)²
Transformation of functionsTransformation is a way of changing the position of an object o the xy plane. Given the parent function expressed as
f(x) = x^2
If the function is shifted to the left by unit, then we will have h(x) = (x - 1)²
If the result is reflected over x-axis and vertically stretched by a factor of 5, the result will be g(x) = -5(x - 1)²
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Four complex numbers form the vertices of a square in the complex plane. Three of the numbers are $-19 32i,$ $-5 12i,$ and $-22 15i$. What is the fourth number
Answers
If the three numbers of a square in the complex plane are [tex]-19+32i,-5+12i and -22+15i[/tex] , then the fourth complex number [tex]-2+19i[/tex].
Given [tex]-19+32i,-5+12i and -22+15i[/tex] are three numbers.
Complex numbers are those numbers which extends the real numbers with an imaginary i. In this [tex]i^{2}=-1[/tex]. Major complex numbers are in the form a+ bi where a and b are real numbers.
let the fourth complex numbers be [tex]x+yi[/tex]. Then according to question;
=[tex](-22+15i)-(-5+12i)[/tex]
=(cos π/2+i sin π/2) [tex](x+yi)-(-5+12i)[/tex]
[tex]-17+3i=-y+12[/tex][tex]+(x+5)i[/tex]
Now solving for x and y by equating both sides.
x=-2 and y=29
Put the value of x and y in [tex]x+yi[/tex]
Z=-2+29i
Hence if the three numbers which forms vertices of a square are [tex]-19+32i,-5+12i,-22+25i[/tex] then the fourth complex numbers be [tex]-2+29i[/tex].
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Samuel Haskins uses his minivan primarily for his delivery business. He has 100/300 bodily injury, and $100,000 property damage coverage. His driver-rating factor is 3.55 because of his business use. His vehicle is classified A, 15.
Answers
In insurance, in a 100/300 policy, it should be noted that up to $100,000 bodily injury per single person injured in the accident will be covered.
What is insurance coverage?An insurance coverage simply means the amount of risk or liability for an individual.
In this case, in a 100/300 policy, up to $100,000 bodily injury per single person injured in the accident will be covered.
Also,an amount up to $300,000 in total will be for bodily injuries per accident. Finally, there's a $100,000 for damages to the property of others.
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What is the inverse of function f?
f(x) = 64x3 - 1
Answers
Step-by-step explanation:
f(x) = y = 64x³ - 1
y + 1 = 64x³
(y + 1)/64 = x³
[tex]x = \sqrt[3]{(y + 1) \div 64} [/tex]
[tex]x = \sqrt[3]{y + 1} \div 4[/tex]
that is the actual inverse function to calculate the original x value for a given y value of the original function.
but to make it a "normal" function, we need to rename the variables (x to y, y to x) :
[tex]y = \sqrt[3]{x + 1} \div 4[/tex]
this is now f^-1(x)
but careful, don't get confused, if dealing together with the original function, this "x" is actually standing for the "y" of the original function ...
What is the cosiner fade when the sign of fada equals 2/5
Answers
The value of cosine theta (cosθ) for the given triangle is determined as 4.58/5.
Complete side lengths of the triangleFor a given sine value of a triangle, the remaining side length of the triangle can be calculated as follows;
sinθ = opp/hypo = 2/5
opposite side = 2hypotenuse side = 5Adjacent side of the triangleb² = 5² - 2²
b² = 21
b = 4.58
Value of cosine θ
Cosθ = adj/hypo
Cosθ = 4.58/5
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help me solve this problem please.
Answers
-11, -6, -7 and -6.1 are the answers
The inequality is r lesser than or equal to -6
Select the correct answer.
The speed of a ship is given by , where d is the distance the ship travels in 3 hours. If the ship travels 48 miles in 3 hours, what is the speed of the ship?
A.
12 miles per hour
B.
16 miles per hour
C.
45 miles per hour
D.
51 miles per hour
Answers
There are 8 kids at a birthday party. If there are 6 girls and 2 boys at a party what fraction of the kids are girls?
Answers
Okay, so out of 8 kids, we know that 6/8 are girls and 2/8 are boys. Its asking us what fraction of the kids are girls. The denominator (the bottom part of the fraction will be the amount of kids at the party, 8) and the top part, the numerator, will be 6 as there are 6 girls at the party of the 8 attendees.
So the fraction is 6/8. However we can reduce this by dividing both sides of the fraction by a common factor, 2!
So your final answer is 3/4.
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Find the constant of proportionality
(
r
)
(r)left parenthesis, r, right parenthesis in the equation
y
=
r
x
y=rxy, equals, r, x.
Answers
The constant of proportionality is 0.1
Complete questionFind the constant of proportionality (r)in the equation y=rx.
r =
x y
14 1.4
16 1.6
21 2.1
How to determine the constant of proportionality?The equation is given as:
y = rx
When x = 14 and y = 1.4, we have:
1.4 = r * 14
Divide both sides by 14
r = 0.1
Hence, the constant of proportionality is 0.1
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for f(x) = 2x + 1 and g(x)=x^2 - 7, find (f - g)(x)
A. x^2 + 2x - 8
B. -x^2 + 2x + 8
C. 2x^2 - 15
D. -2x + 2x - 6
Answers
Answer: B
Step-by-step explanation:
[tex](f-g)(x)=f(x)-g(x)=(2x+1)-(x^{2}-7)=2x+1-x^{2}+7=\boxed{-x^{2}+2x+8}[/tex]
Use the FOIL method to evaluate the expression:
Answers
Answer:
[tex]\sf b.) \ 1 +2\sqrt{7}[/tex]
Explanation:
Foil method: (a + b)(c + d) = ac + ad + bc + bd
Solving steps:
[tex](4 - \sqrt{7} )(2 + \sqrt{7} )[/tex]
[tex](4)(2) + 4(\sqrt{7} ) + (-\sqrt{7} )(2) + (-\sqrt{7} )(\sqrt{7} )[/tex]
[tex]8 + 4\sqrt{7} - 2\sqrt{7} - 7[/tex]
[tex]8 -7 + 4\sqrt{7} - 2\sqrt{7}[/tex]
[tex]1 +2\sqrt{7}[/tex]
option b) 1 + 2√7
Step-by-step explanation:Foil property method :-
[tex] \red{ \boxed{ \orange{ \rm (a + b)(c + d) = ac + ad + bc + bd}}}[/tex]
then, on substituting the values,
[tex]\sf⇒ \: \: 8 + 4 \sqrt{7} - 2 \sqrt{7} - 7[/tex]
[tex]\sf⇒ \: \: \green{ \underline{\bold{ \red{1 + 2 \sqrt{7} }}}}[/tex]
Draw the graph of f(x) = (x − 1)2 − 2. Start by creating a table of ordered pairs for the function. Then plot the points from the table, and draw a curve connecting the points.
Answers
The attached graph represents the graph of f(x) = (x - 1)^2 - 2
How to plot the graph?The equation is given as:
f(x) = (x - 1)^2 - 2
Next, we set x to -2, -1, 0, 1 and 2.
So, we have:
f(-2) = (-2 - 1)^2 - 2 = 7
f(-1) = (-1 - 1)^2 - 2 = 2
f(0) = (0 - 1)^2 - 2 = -1
f(1) = (1 - 1)^2 - 2 = -2
f(2) = (2 - 1)^2 - 2 = -1
This means that the table of values is
x f(x)
-2 7
-1 2
0 -1
1 -2
2 -1
Next, we plot the above points and connect them.
See attachment for the graph of f(x) = (x - 1)^2 - 2
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