sally has a cube of side length units such that the number of square units in the surface area of the cube equals of the number of cubic units in the volume. she also wants to make a square for which the number of square units in the area of the square is equal to the number of cubic units in the volume of the cube. what should the side length of the square be?
The side of square is 216 units and side of cube is 36 units.
According to question we have given that Sally has a cube of some length in units. Let the length of side of cube is S units .
As we know , Area of cube = 6 (side)²= 6S² square units.
Volume of cube = (side)³ = S³ cubic units
Then, as given area in square units of cube = 1/6 of volume of cube in cubic units . That is 6S²= 1/6 S³ => S = 36 units
Area of cube with side 36 units = 6×36²=46656 square units
Volume of cube with side 36 units = 36 ³ cubic units
So, the side of cube is 36 units.
Also, the number of square units in area of Square = number of cubic units in volume of cube
Area of square (S²) = 46656
Side of square = sqrt (46656 ) = 216 units
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For the function f(x) =[tex]\sqrt{8x+10}[/tex] the inverse function [tex]f^{-1}[/tex](x) = [tex]\frac{x^2-10}{8}[/tex] x≥ 0 as can be calculated through the inverse function's formula.
What is an inverse in a function?In mathematics, any kind of inverse is a function that serves to “undo” any other function. That is, if f(x) produces y, then while putting y into the inverse off it produces the output x.
How do you find the inverse of a function?To find the inverse of a function, write the function y as a function of x i.e., y = f(x) and then solve for x as a function of y.
What is inverse example?Inverse operations are seen as opposite operations that provides undo to each other. For example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse operations.
What are the properties of inverse function?Every one-to-one function f has an inverse; this inverse is denoted by f−1 and read aloud as 'f inverse'. A function and its inverse 'undo' each other: one function does something, the other undoes it.
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Aiyana wrote the ratio 3:5 to compare a number of Paris of shorts that she owns to the number of pairs of jeans that she owns which ratio is equivalent to Aiyana’s ratio
3:5 is equivalent to Aiyana’s ratio
Since 3 and 5 are both prime numbers, you must multiply them by the same number (or any other integer) in order to have a ratio that is the same as Aiyana's. Ex 3:5=6:10=9:15 etc. The three ratios are identical.
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
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I need some help with my math please
Which answer choice correctly shows 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 in
exponential notation?
OA) 811
OB) 118
OC) 11⁹
OD) 1111
Answer:
it would be 11^8
Step-by-step explanation:
i dont see this as an option but i believe that there was a mistake i dont believe that any of theese are correct
what does 6/3 = and what does 30/10 =
Answer:
6/3=2
30/10=3
Step-by-step explanation:
For simple division like this, you can look and see how many times 3 can go into 6, and 10 into 30.
Question 3 options:
Premises:
If you have a cat, then it will chase mice.
You have a cat.
Conclusion:
Your cat will chase mice.
The Law of ___________________________makes this argument true.
The law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.
What is the law of syllogism?Legal syllogism is a legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
It is given that:
The statement is:
If you have a cat, then it will chase mice.
As we know, from the definition of the Law of Syllogism, the legitimate concept that deals with the law and how it is applied, specifically a type of argument that uses deductive reasoning to determine whether a given act is legal.
Your cat will chase mice.
The Law of syllogism makes this argument true.
Thus, the law of syllogism makes this argument true if you have a cat, then it will chase mice and your cat will chase mice.
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Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 2p − 8 < 5p + 4 true.
S:{−2, −3}
S:{−3, −4}
S:{−4, −5}
S:{−2, −5}
Answer:
s:[-2,-3] is the answer
The set S:{ - 2 , - 3 } will make the inequality 2p - 8 < 5p + 4 true
What is an Inequality Equation?
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
The set S : { - 2 , - 3 , - 4 , - 5 }
The inequality relation is 2p - 8 < 5p + 4
Now , substituting the value from set S in the inequality , we get
When p = - 2 :
2p − 8 < 5p + 4
2(-2) − 8 < 5(-2) + 4
-4 − 8 < -10 + 4
-12 < -6 TRUE
When p = - 3
2p − 8 < 5p + 4
2(-3) − 8 < 5(-3) + 4
-6 − 8 < -15 + 4
-14 < -11 TRUE
When p = - 4
2p − 8 < 5p + 4
2(-4) − 8 < 5(-4) + 4
-8 − 8 < -20 + 4
-16 < -16 FALSE
When p = - 5
2p − 8 < 5p + 4
2(-5) − 8 < 5(-5) + 4
-10 − 8 < -25 + 4
-18 < -21 FALSE
Therefore , the value of p = - 2 , - 3 will satisfy the given inequality relation
Hence , the set S:{ -2,-3 } is the solution
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Choose the best initial step in solving the following system by substitution.
2x + 3y = –12
6x + y = 18
Answers:
1.Solve the first equation for x.
2.Solve the first equation for y.
3.Solve the second equation for x.
4.Solve the second equation for y.
Using substitution method, the best initial step in solving the equation is solve the first equation for x.
How to solve equation by substitution method?The equation can be solved by substitution method as follows:
2x + 3y = -12
6x + y = 18
Hence, let's make y the subject of the formula in equation(ii)
6x + y = 18
y = -6x + 18
We have to substitute the value of y in equation(i)
2x + 3y = -12
2x + 3(-6x + 18) = -12
2x - 18x + 54 = -12
- 16x + 54 = -12
-16x = - 12 - 54
- 16x = -66
x = 66 / 16
x = 33 / 8
Therefore,
6(33 / 8) + y = 18
99 / 4 + y = 18
y = 18 - 99 / 4
y = - 27 / 4
From the solving above the best step to solve the equation is solving the first equation for x.
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Write an equation of each parabola in vertex form vertex : (1/2,1) point: (2,-8)
Answer: [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]
Step-by-step explanation:
Using the vertex form, the equation is
[tex]y=a \left(x-\frac{1}{2} \right)^2 +1[/tex]
Substituting in the coordinates (2, -8) to solve for a,
[tex]-8=a \left(2-\frac{1}{2} \right)^2 +1\\\\-8=\frac{9}{4}a+1\\\\-9=\frac{9}{4}a\\\\a=-4[/tex]
So, the equation is [tex]y=-4 \left(x-\frac{1}{2} \right)^2 +1[/tex]
Answer each part. If necessary, round your answers to the nearest hundredth.
(a) It takes 51 pounds of seed to completely plant a 9-acre field.
How many acres can be planted per pound of seed?
acres per pound
(b) Christine runs 4 miles in 22 minutes.
How many minutes does she take per mile?
minutes per mile
Answer:4
Step-by-step explanation:
Answer:a) Given :
51 pounds of seed can be planted in = 9 acre field.
Per pound of seed =
We can convert 9/51 in simplest fraction by dividing top and bottom by 3.
We get
Therefore, 3/17 of an acrs can be planted per pound of seed.
b) $10 amount = 16 pounds of sugar.
$1 amount = 16/10 = 1.6 pounds of sugar.
Therefore, 1.6 pounds of sugar she got per dollar.
Step-by-step explanation:
Please help me with parts C and D, I’m struggling with them
ANSWER
[tex]\begin{gathered} c)s\imaginaryI n\frac{\theta}{2}=\sqrt{\frac{1}{2}(1-\frac{\sqrt{13}}{7})} \\ decimal=0.49 \\ d)cos\frac{\theta}{2}=\sqrt{\frac{1}{2}(\frac{\sqrt{13}}{7}+1)} \\ decimal=0.87 \end{gathered}[/tex]EXPLANATION
Given;
[tex]\begin{gathered} sin\theta=\frac{6}{7} \\ 0<\theta<\frac{\pi}{2} \end{gathered}[/tex]c) Hence;
[tex]\begin{gathered} sin\frac{\theta}{2}=\sqrt{\frac{1}{2}(1-\frac{\sqrt{13}}{7}}) \\ \end{gathered}[/tex]In decimal form;
[tex]sin\frac{\theta}{2}=0.49[/tex]d)
[tex]\begin{gathered} cos\theta=\frac{\sqrt{13}}{7} \\ cos\frac{\theta}{2}=\sqrt{\frac{1}{2}(\sqrt{\frac{13}{7}+1})} \\ decimal=0.87 \end{gathered}[/tex]a college professor hands out a list of 10 questions, 5 of which will appear on the final examination for the course. one of the students taking the course is pressed for time and can prepare for only 9 of the 10 questions on the list. suppose the professor chooses the 5 questions at random from the 10.
one of the students taking the course is pressed for time and can prepare for only 9 of the 10 questions on the list. then the probability of all 5 questions prepared for appears is 2
Recall : nCr = n! ÷ (n-r)!r!
The total possible outcome ; 5 questions out of 10
10C5 = 10! ÷ 5!5! = (10*9*8*7*6)÷(5*4*3*2*1) = 252
Required outcome :
All 5 questions set being from the 9 questions covered and 0 from the 1
left uncovered
9C5 * 1C0
9C5 = 9! ÷ 4!5! = (9*8*7*6) ÷ (4*3*2*1) = 126
1C0 = 1! ÷ 1!0! = 1
Probability = required outcome / Total possible outcomes
P(All 5 questions prepared for appears) :
[9C5 * 1C0] ÷ 10C5
(126 * 1) / 252
= 126/ 252
=2
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Determine if the following representations or functions or not? Explain your reasoning.
The three relations given all represent functions because each has exactly one y-value that corresponds to each x-value.
What Relation can be Defined as a Function?A relation can be defined as a function if the x-values (input/domain element) each has exactly one y-value (output value/range element) that is related to or it corresponds to.
A function can have two x-values that have the same y-value but cannot have two y-values that corresponds to one x-value.
In the first relation showing a graph, each x-value on the graph has exactly one y-value it corresponds to. Therefore, it is a function.
In the second relation that is represented by the set of ordered pairs, every x-value also have only one y-value it is related to. Therefore, it represents a function.
The third function given shows a table of values of a relation that has exactly only one y-value that is assigned or related to each x-value. This also is a relation that represents a function.
Therefore, all three relations represent functions.
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14.14 / 14 Is what ? Please show work ┐( ∵ )┌
Answer:
1.01
Step-by-step explanation:
14.14/14
14/14=1
0.14/14=0.01
1+0.01=1.01
Write an equation in point-slope form of the line that passes through (-4,1) and (4,3) The equation is ?
Answer:
y = 4x+2
Step-by-step explanation:
To find an equation that runs through (-4,1) and (4,3) first find the difference between the two y numbers and x number to find the slope. between the two y numbers you go left or right 8 units, and difference between the two x numbers, which is 2. making the slope 4. looking at a graph and marking the two points, draw a line connecting the two given points, find the y intercept. the y intercept is at coordinates (0, 2) making the y intercept 2. making that into an equation is y = 4x + 2
48x35 in smtandard algorithm
48×35. By using standard algorithm we got 1680.
Given that,
48×35
We have to find the multiplication of the numbers by standard algorithm.
Standard algorithm is nothing but the words "Standard" and "Algorithm" make up the standard algorithm. Standard refers to the standard or standard way of doing anything, such as eating, bathing, or brushing one's teeth. Algorithms are nothing more than a task's sequential execution. As a result, solving a problem step by step is a common algorithm in mathematics. You will discover what a standard algorithm is in this article, along with the addition, subtraction, multiplication, and division standard algorithms.
If you don't use the standard algorithm , your answers will be incorrect.
48×35=1680
Therefore, By using standard algorithm we got 1680.
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example of an event which has a probability of 0. Explain why the probability equals 0.
The example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because it will not occur.
The probability is the branch of mathematics that shows the occurrence of the random event. The value of the probability varies from 0 to 1.
The equation of the probability is
Probability = Number of favorable outcomes / Total number of outcomes
The probability of getting number number 7 when you throw a die once is zero. Because when you throw a die the possible outcomes are 1, 2, 3, 4, 5 and 6. We wont get number 7. Therefore the probability is zero
Hence, the example of an event which has a probability of 0 is probability of getting number 7 when you throw a die once. The probability of this event is zero because it will not occur.
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Larry can carry a maximum of 60 pounds.
He is already carrying a chair that weighs 20 pounds. He has boxes as well to carry that weigh 5 pounds each.
Which inequality represents all possible values of x, the number of boxes that he can carry?
A. 20x +5 ≤ 60
B. 5x + 20 ≥ 60
C. 20x + 5 ≥ 60
D. 5x + 20 ≤ 60
Answer: Your answer would be D
Step-by-step explanation: The reason why is because in the question it said he is already carrying a 20 pound chair. It then say he can carry some boxes that weigh 5 pounds each. The word each is your keyword. With that you can replace the x variable with some single digit numbers. But you also need to make sure your total is less than or equal to 60 pounds. You would pick the less than or equal to sign since he can only carry 60 pounds or less.
NEED HELP ASAP - 100 POINTS
When solving quadratic equations, there are benefits to utilizing one method over the other. In your own words, explain what the advantages may be of using the method of completing the square to solve quadratic equations.
The advantages may be of using the method of completing the square to solve quadratic equations to estimate the values of x and y roots without calculating them.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Using Completing the square.
1. First of all we can find the minimum or maximum of the equation immediately.
2. Second is to cuts out the need to use the given ones (a, b, c) in the quadratic formula.
3. It allows estimating the values of x and y roots without calculating them.
Then Estimating on a test is a very valuable asset.
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The White family purchases a new pool table on a no-interest-for-one-year plan. The cost is $2,665. There is a d dollars down payment. If they make a minimum monthly payment of m dollars until the last month, express their last month's payment algebraically.
The last month's payment for White family can be algebraically expressed as;
⇒ 2665 - d - 11m.
What is an expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
Cost of a new pool table = $2,665
Down payment = d dollars
And, The monthly payment = m dollars.
Since, we have to given a duration of twelve months, we will have to subtract one month from 12 to give, 11 months.
Hence, We can formulate an algebraic equation as;
2665 - d - 11m.
Thus, The last month's payment for White family can be algebraically expressed as;
⇒ 2665 - d - 11m.
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Identify the location of the values √10. √13. and 22
on the number line.
A
B
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
A: Point A is 22 point B is √10. and point C is √13
B:Point A is √10. point B is √13, and point C is 22
C:Point A is 22, point B is 13. and point C is √10
D:Point A is √10. point B is
and point C is √13
Answer:
1
Step-by-step explanation:
Simplify the expression. Show your work.
[tex]\sqrt[3]{27x^6y^4}[/tex]
[tex]\sqrt[3]{27x^6y^4}\implies \sqrt[3]{3^3 (x^2)^3 y^3 y^1}\implies 3x^2 y\sqrt[3]{y}[/tex]
Nicole has a machine that will produce a number from 1 through 50 when she pushes a button. a. p (multiple of 10)? b. p (not 100)? c. p (not a multiple of 4)? d. p (one-digit number)?
Total outcome is 50 [because the number produced by the machine is from 1 to 50]
Question a:
Multiple of 10 are 10, 20, 30, 40, 50
There are five possible outcomes for multiple of 10
P(Multiple of 10) = 5/50 = 1/10
Question b:
Number 1 to 50 will be all the outcomes that are not 100
There are 50 possible outcomes
P(not 100) = 50/50 = 1
Question c:
Multiple of 4 that are less than 50 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48
There are 12 possible outcomes for multiple of 4
We want 'not multiple of 4' so we need to do 50 - 12 = 38 outcomes
P(not a multiple of 4) = 38/50 = 19/25
Question d:
One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9
There are 9 possible outcomes
P(one-digit number) = 9/50
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A stack of 12 sheets of gypsum board are 10.5 inches thick. If all the boards are uniform, how thick is each board?
Answer:
0.875 inches
Step-by-step explanation:
Pretty easy. Just divide how many inches thick the boards are by how many there are: inches-thick/amount
Now substitute 10.5/12 and find your answer
0.875 inches thick per board
A shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The store decides to discount the packs of socks by 40%. Is the discounted price $5? OA) yes: The packs of socks are marked up to $7 and then discounted to $5. OB) yes; The packs of socks are marked up to $9 and then discounted to $5. OC) no: The packs of socks are marked up to $7 and then discounted to $4.20. OD) no, The packs of socks are marked up to $5.20 and then discounted to $4.99.
Answer:
C) no: The packs of socks are marked up to $7 and then discounted to $4.20
Step-by-step explanation:
You want to know the price of a $5 pair of socks after markup by 40%, and again after that price is marked down 40%.
Marked-up priceWhen the $5 cost is marked up by 40%, the resulting price is ...
$5 + 0.40×5 = $5 +2 = $7.
The socks are marked up to $7.
Marked-down priceWhen the $7 price is marked down by 40%, the resulting price is ...
$7 - 0.40×7 = $7.00 -2.80 = $4.20
The socks are discounted to $4.20.
if you want to change m² to cm² what will you do
Answer:
Use this relation
Im^2 = 10000cm^2
Answer:
multiply m² by 10000
Step-by-step explanation:
1 m = 100 cm
1 m² = 100² = 10000 cm²
then to change m² to cm² , multiply m² by 10000
PLEASE HELP I AM GROUNDED AND MY MOTHER IS SO MAD AT ME FOR MY GRADE
Answer:
64°
Step-by-step explanation:
it's a right angle (90°) so u take away the other angle (26°) which gets you 64°
What is the value of this expression.
Answer:46
Step-by-step explanation:
A bicycle has cash price $16 319.50. It can be bought on hire purchase with a deposit of $6
900 and ten monthly installments of $1 224.50 each.
a. What is the total hire purchase price for the bicycle? [3 marks]
b. Find the difference between the hire purchase price and the cost price for the bicycle.
[1 mark]
c. Express your answer in (b) above as a percentage of the cash price.
The total cost of the hire purchase for the bicycle is $19,145.
The difference between the hire purchase price and the cost price for the bicycle is $2,825.50
The difference as a percentage of cash price 17.31%.
What is total cost?The total cost of the hire purchase is the sum of the deposit and the total monthly instalment.
Total cost of the hire purchase = amount deposited + total instalment paid
Total instalment paid = number of month x payment per month
$1224.50 x 10 = $12,245
Total cost of the hire purchase = $6,900 + $12,245 = $19,145
The difference = cost of hire purchase + cash price
$19,145 - $16 319.50 = $2,825.50
The difference as a percentage of cash price = (2,825.50 / $16,319.50) x 100 = 17.31%
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