Answer:
X= -12 +6√10
X= 6.973
Step-by-step explanation:
Volume of the box= (36-2x)(24-2x)x
Volume of the box
=( 864 -96x -4x²)x
But 864 -96x -4x²
=216 - 24x-x²
Solving for x quadratically
X= (24+12√10)/-2
X= -12 -6√10
X= -30.97
Or
X= (24-12√10)/-2
X= -12 +6√10
X= 6.973
X will definitely be a positive number
So X= -12 +6√10
X= 6.973
Increasing or decreasing the side length of the square that gives the
maximum volume, gives a volume that is less than the maximum.
The side length of the cut out square to get a box with the maximum volume is approximately 4.71 in.Reasons:
The given dimensions of the box = 24 in. by 36 in.
Let x represent the dimensions of the square removed from the corners, we have;
Width of box = 24 - 2·x
Length of box = 36 - 2·x
Height of the box = x
Volume of a box = Width × Length × Height
Therefore;
Volume of the box, V = (24 - 2·x)·(36 - 2·x)·x = 4·x³ - 120·x² + 864·x
At the maximum or minimum point of the volume, we have;
[tex]\displaystyle \frac{dV}{dx} = \mathbf{ \frac{d}{dx} \left(4 \cdot x^3 - 120 \cdot x^2 + 864 \cdot x \right )} = 0[/tex]Which gives;
12·x² - 240·x + 864 = 0
x² - 20·x + 72 = 0
Which gives;
[tex]\displaystyle x = \dfrac{20\pm \sqrt{(-20)^{2}-4\times 1\times 72}}{2\times 1} = \mathbf{10 \pm 2\cdot \sqrt{7}}[/tex]
At x = 10 + 2·√7, we have;
[tex]\displaystyle 10 + 2 \cdot \sqrt{7} > \frac{24}{2}[/tex]
2 × (10 + 2·√7) in. > 24 in. which is the width of the cardboard
Therefore, (10 + 2·√7) is too long to be cut from the cardboard
At x = 10 - 2·√7, we have;
V = 4·(10 - 2·√7)³ - 120·(10 - 2·√7)² + 864·(10 - 2·√7) ≈ 1,828.3
Therefore;
The maximum volume corresponds with a cut out square of side length x = 10 - 2·√7 inches ≈ 4.71 inches
The size of the square to be cut out each corner is x ≈ 4.71 inchesLearn more here:
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Help I’m dying I’m giving 20 points plz help
Answer:
20.25
Explanation:
We first need to find the length of one side of the square. We can do this by dividing the area by 4 (27/4), since a square has four sides. You should get 6.75. Now you can multiply 6.75 by three since one side of the square is the same as one side of the triangle. Also, it is an equilateral triangle and all sides are the same. If you multiply correctly, you should get 20.25. Hope this helped!
Answer:
9 sqrt(3)
Step-by-step explanation:
Since the area of the square is 27 cm^2
A = s^2
27 = s^2
Take the square root of each side
sqrt(27) = s
sqrt(9) sqrt(3) = s
3 sqrt(3) =s
We know the the side length of the triangle is s
The perimeter of the triangle is
P =3s = 3 ( 3 sqrt(3))
= 9 sqrt(3)
Paul owns 8 CDs, 6 of which are rock-and-roll. What percent of Paul's CDs are rock-and-roll?
Answer:
75% are rock and roll
Step-by-step explanation:
6 /8 = 3/4 = 0.75 = 75%
I need help please no one helps me
Answer:
Frank worked 80 hours
Step-by-step explanation:
40x4=160
160 divied by 2 is 80
If Daniel ate 36 Snicker bars, what does he have now? Diabetes???
His stomach is gonna hurt really bad
In the class election, the student who gets the highest number of votes will become the class president and the one who gets the second highest
number of votes will become the class vice president. Tabitha and four other students were candidates. Tabitha's teacher announces the election
results as percentages of the total number of votes. Two hundred votes were cast in the election. In this activity, you will relate the percentages of
the votes received to the actual numbers.
Question 1
The table gives the percentage of votes each candidate received. Use the information in the table to understand the results of the election
Candidate Percentage of Votes
Tabitha
30%
Vincent
12%
Esmeralda
22%
Nancy
5%
Tyler
31%
Part A
How many votes did Tabitha receive?
Answer:
Tabitha received 60 votes.
Step-by-step explanation:
200 votes × .30 = 60 votes
The given percentage of votes shows that Tyler win the class elections (has the highest percentage of votes - 31%), and Tabitha received 60 votes (30% of 200).
What are percentages?A percentage is a fraction of a whole number represented as a number out of 100.
How do we solve the given question?We are given the percentages of votes received by the candidates in a class election. We are also informed that a total of 200 votes were cast in the elections.
The percentages are as follows:
Tabitha = 30%
Vincent = 12%
Esmeralda = 22%
Nancy = 5%
Tyler = 31%.
We are asked to find the winner of the election and the number of votes Tabitha received.
As Tyler receives the highest percentage of votes (31%), he is the winner of the elections.
Tabitha received 30% of the votes, and the total number of votes = 200
∴ Number of votes Tabitha received = 30% of 200 = (30/100)*200 = 0.3*200 = 6.
∴ Tabitha received a total of 60 votes.
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2635 divided by 17 in long form
Answer:
155
Step-by-step explanation:
17 can go into 26. 1 time then 26-17=9
bring down the 3 and it turns into 93
17 can go into 93 5 times. that equals 85
93-85=8 then add the 5 that make 85
85 divided by 17 =5
so the answer is 155
The sum of 18 and a number
Answer:
The expression you are looking for is: 18+x
Step-by-step explanation:
The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 13. According to the standard deviation rule, only (what?) % of people have an IQ over 126.
Answer: 2.5% of people have an IQ over 126.
Step-by-step explanation:
Given: The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 13.
126 = 100 + 2(13) = Mean +2 ( standard deviation)
To find : % of people have an IQ over 126.
i.e. % of people have an IQ over Mean +2 ( standard deviation).
According to the standard deviation rule,
95% of data fall within two standard deviations.
Now, 100% - 95% = 5%
and Half of 5% is 2.5%.
So 2.5% of the data lies below 2 standard deviations of mean and 2.5% of the data lies above 2 standard deviations of mean .
i.e. 2.5% of people have an IQ over 126.
The cost of 1.00 Liters of gas is 26.9 cents. How many dollars will 12.0 gallons cost?
The cost of 12 gallons of gas will be 1221.80 cents.
It is given that 1 liter of gas cost 26.9 cents.
We have to calculate the cost of 12 gallons of gas.
What will be the cost of 10 pens if 1 pen costs 2 cent ?
The cost of 10 pens will be 10 × 2 = 20 cent.
As per the question ;
Cost of 1 liter of gas = 26.9 cent
∵ 1 gallon = 3.785 liters
So ,
The cost of 1 gallon of gas = 3.785 × 26.9
The cost of 12 gallons of gas will be ;
= 12 × 3.785 × 26.9
= 1221.80 cents
Thus , the cost of 12 gallons of gas will be 1221.80 cents.
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Please help me with some math im stuck
y = - 40
- 40 since theres no letters it gonna be -40.
John has $90 in the bank. Every time herides the bus he spends
$2.50. Write an equation that John can use to see how many times
he can ride the bus. Let x = the number of times he can ride the bus.
Answer:90 divided by 2.50= X
36 = X
Step-by-step explanation:
What is the distance between (2,8) and (7,7)
Answer:
5.1 units
Step-by-step explanation:
Hey there!
To find the distance of points,
(2,8) and (7,7).
We need to use the Pythagorean Theurom formula which is,
[tex]a^2 + b^2 = c^2[/tex]
So we need to find the rise/run or a and b to find c or the distance.
x - 2 and 7, distance of 5 units
y - 8 and 7, distance of 1 unit.
Plug those numbers in.
[tex]5^2 + 1^2 = c^2[/tex]
25 + 1 = c^2
26 = c^2
c = 5.09901
c = 5.1 rounded to the nearest tenth.
Hope this helps :)
Here is how i did it
k=6
c=2
5 • k - 10c + 8
Answer:
22-10c
Step-by-step explanation:
The simplified value of the expression is 18
Given the expression :
5 * k - 10c + 8k = 6c = 2To solve , substitute the values of k and c into the equation
Now we have ;
5 * 6 - 10(2) + 8
5 * 6 - 20 + 8
30 - 20 + 8
30 - 12
= 18
Hence, the. simplified value of the expression is 18
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What is the area of a rhombus whose diagonals have lengths D1=12 inches and D2=14 inches? Show your work.
Answer:
Answer:
84inches^2
Step-by-step explanation:
Step-by-step explanation:
Area of a rhombus = pq/2
From the question
p= 12 inches
q = 14 inches
Therefore Area = 12x14 /2
= 168/2
= 84 inches^2
How many 1-1 functions from a set with five elements to a set with 4 elements?
Answer:
The number is zero
Step-by-step explanation:
From the question we are told to state the number of on-to-one that exist from the set of 5 element to the set 4 element
Generally there are no one-to-one function from a set with a higher number of elements to a set with the lower number of elements
So the correct answer to the question is there are no one-to-one function from the set of 5 elements to the set of 4 elements
According to a family-oriented lobbying group, there is too much crude language and violence on television. Forty-two percent of the programs they screened had language they found offensive; 27% were too violent, and 10% were considered excessive in both language and violence. What percentage of programs did comply with the group's standards? Give your answer as a percentage and do not put the % sign in your answer.
Its C because its a loaded language
In the city of Lawrenceville, how many phone numbers are possible using the area code 678? The restrictions for the phone company are listed below. · The first digit of the phone number cannot be numbers 0-5. · The second number cannot be a zero. · The third and fourth numbers cannot be a zero or one · The fifth number cannot be a zero, one or two How many phone numbers are possible using the area code 678? a.2000 b.1,6128 c.1,612,800 d.300
Answer:
Hey there!
If there were no restrictions, there would be 10x10x10x10x10 phone numbers.
The first number can only be a 6-9, so that is four options.
The second number can have nine options.
The third and fourth numbers have eight options.
The fifth number has seven options
4x9x8x8x7=16128.
16128 numbers are possible.
Let me know if this helps :)
1. Find the ratio of oranges to apples if there are 2 pineapples, 4 apples,
6 bananas, and 3 oranges in a fruit bowl.
a. 1 to 2
b. 2 to 4
c. 3 to 4
d. 3 to 2
Answer: the answer is C because there are 3 oranges and 4 apples
How many tablets of 6 mg can be made from 0.6 kg of medicine?
Answer:
100 000 tablets
Step-by-step explanation:
1 mg = 0.001 g ⇒ 6 mg = 0.006 g
1 kg = 1000 g ⇒ 0.6 kg = 600 g
600 g / 0.006 g = 100 000 tablets
BAKED GOODS Mary sells giant chocolate chip and peanut butter cookies for
$1.25 and $1.00, respectively, at a local bake shop. She wants to make at least
$25 a day
a. Write and graph an inequality that represents the number of cookies Mary
needs to sell each day.
Answer:
(1.25c) + (1p) ≥ 25
c is the amount of chocolate chip cookies
p is the amount of peanut butter cookies
Inequalities help us to compare two unequal expressions. The inequality that represents the number of cookies Mary needs to sell each day is 1.25x + 1y ≥ 25.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
Let the number of chocolate chips sold be represented by x, while the number of peanut butter cookies is represented by y.
Given that the selling cost of chocolate chips and peanut butter cookies is $1.25 and $1.00, respectively. Also, Mary needs to make $25 a day, therefore, the inequality can be written in the form as,
1.25x + 1y ≥ 25
Hence, the inequality that represents the number of cookies Mary needs to sell each day is 1.25x + 1y ≥ 25.
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|x+6|=|x−12| Graph the solution
Answer:
Step-by-step explanation:
[tex]\left|x+6\right|=\left|x-12\right|\\\\\mathrm{For\:each\:absolute\:find\:positive\:and\:negative\:intervals}\\ \\\mathrm{For\:}x<-6:\quad \mathrm{No\:Solution}\\\\\mathrm{For\:}-6\le \:x<12:\quad x=3\\\\\mathrm{For\:}x\ge \:12:\quad \mathrm{No\:Solution}\\\\\mathrm{Combine\:Solutions:}\\\\\mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=3\\\\x=3[/tex]
Please help me!!!!!!!!
Answer:
10) 1/11
11) 18/8 or 2 2/8 or 2 1/4
12) -8/5 or -1 3/5
Step-by-step explanation:
10) -6/11-(-5/11)=-6/11+(5/11)=1/11
11) 1 3/8-(-7/8)=11/8+7/8=18/8 or 2 2/8 or 2 1/4
12) -4/5-4/5=-8/5 or -1 3/5
A bag contains 8 green, 4 black and 6 yellow marbles. How could you use the complement to determine the probability of randomly selecting a green or black marble?
Answer:
12/18=2/3
Step-by-step explanation:
You should add up every marbles to find out how many marbles are in total. Then, you should add the green and black marbles. There are 4 black marbles, and 8 green marbles, which results 12 black+green marbles. Then you should make a fraction 12/18, because you are finding the probability of the green+black marbles out of the total marbles. If you simplify, you get 2/3.
The probability of randomly selecting a green or black marble is 12/18.
What is probability?Probability is the ratio that determines how likely an event is to occur from a set of possible events.
We can find the probability of randomly selecting a green or black marble as shown below:Total number of green marbles = 8
Total number of black marbles = 4
Total number of yellow marbles = 6
Total number of marbles = Total number of green marble + Total number of black marbles + Total number of yellow marbles = 18
P(selecting a green marble) = Total number of green marbles/Total number of marbles
= 8/18
P(selecting a black marble) = Total number of black marbles/Total number of marbles
= 4/18
P(selecting a green or black marble) = (Total number of green marbles + Total number of black marbles)/Total number of marbles
= (8 + 4)/18
= 12/18
Therefore, we have found the probability of randomly selecting a green or black marble to be 12/18.
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The length of the carpet is 2a2 and width is 3a. Find the area of the carpet.
HELP ME PLEASE
Answer:
[tex]6a^{3}[/tex]
Step-by-step explanation:This is a very simple question.
We all know that the equation or formula for area is...
A= L*W
So multiply...
[tex]2a^{2} *3a[/tex]= [tex]6a^{3}[/tex]
Since 3a has an exponent power of 1 and you add the exponent power when multiplying...
The result would be... [tex]6a^{3}[/tex].
Hope this helps:)
please help, i will give brainliest
Answer:
24
Step-by-step explanation:
hope i helped
Evaluate the numerical expression. 30 - [(9 X 2) - (3 X 4)]
Answer:
Step-by-step explanation:
30 - [(9 X 2) - (3 X 4)]
30 - [ 18 - 12 ]
30 - 18 + 12
= 42 - 18
= 24
Hope this helps
plz mark as brainliest!!!!!!
Answer:
24
Step-by-step explanation:
30-[18-12]
30-18+12
12+12
=24
x+3 divided by 5=30 i need help
Answer:
x = 147
147 + 3 = 150
150 ÷ 5 = 30
Answer:
See answer in the explanation below.
Step-by-step explanation:
x = 147
147 + 3 = 150
150 ÷ 5 = 30
True or False? The absolute value of any number the same as absolute value of its additive inverse
Answer:
true
Step-by-step explanation:
that is true i need twenty charcters
Using every day knowledge which of the following statements is an if/then statement whose reverse is also correct.
A. if an ambulance has emergency lights on, then cars on the road pull over.
B. if the TV is unplugged, then the TV will not turn on.
C. if the wind is blowing, then the weather is chilly
D. if the light bulb was recently on, then the lightbulb is hot
B. if the TV is unplugged, then the TV will not turn on.
A conditional statement has two parts: hypothesis (if) and conclusion (then).
The converse is when we switch or interchange our hypothesis and conclusion.
So, we have given statements as:
A. if an ambulance has emergency lights on, then cars on the road pull over.
B. if the TV is unplugged, then the TV will not turn on.
C. if the wind is blowing, then the weather is chilly.
D. if the light bulb was recently on, then the lightbulb is hot.
If we see the converse statement of C.
If the tv does not turn on it’s unplugged.
So the statement is true in both the ways.
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PLEASE ANSWER QUICK, ITS URGENT!
Step-by-step explanation:
which part of the question do you need