What is the step by step process of solving for the GCF from a list of terms.
Ex. (see picture)
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Related Questions
A rubber ball has a radius of about 2.86 in. Can the ball be packaged in a box shaped like a cube with a volume of 125 in3?
Answers
volume of the ball = 4/3 * PI *r^3 =
4/3 * 3.14 * 2.86^3 = 97.99 cubic inches
this is less than the volume of the box, so yes it will fit
A water well is to be drilled in the desert where the soil is either rock, clay or sand. The probability of rock P(R)equals=0.53. The clay probability is P(C)equals=0.21. The sand probability is P(S)equals=0.26. If the soil is rock, a geological test gives a positive result with 35% accuracy. If it is clay, this test gives a positive result with 48% accuracy. The test gives a 75% accuracy for sand.
Given the test is positive, what is the probability that the soil is clay, P(clay | positive)? Use Bayes' rule to find the indicated probability.
Answers
To find the probability of the soil being clay given a positive test result, we can use Bayes' rule. Given the probabilities of the different types of soil and the accuracy of the test in each soil type, we can calculate the probability using the law of total probability and Bayes' rule.
Explanation:To find the probability of the soil being clay given a positive test result, we can use Bayes' rule. Bayes' rule states that P(A|B) = (P(B|A) * P(A)) / P(B), where P(A|B) is the probability of event A happening given that event B has occurred, P(B|A) is the probability of event B happening given that event A has occurred, P(A) is the probability of event A happening, and P(B) is the probability of event B happening. In this case, event A is that the soil is clay and event B is that the test result is positive.
Given that the soil is clay, the test gives a positive result with 48% accuracy. Therefore, P(B|A) = 0.48. The probability of the soil being clay is P(A) = 0.21. To find P(B), we need to consider the probabilities of the test result being positive in each type of soil.
If the soil is rock, the test gives a positive result with 35% accuracy, so the probability of the test result being positive in rock soil is P(B|rock) = 0.35. Similarly, if the soil is sand, the test gives a positive result with 75% accuracy, so the probability of the test result being positive in sand soil is P(B|sand) = 0.75. We can calculate P(B) using the law of total probability: P(B) = P(B|rock) * P(rock) + P(B|clay) * P(clay) + P(B|sand) * P(sand).
Plugging in the given values, we have P(B) = 0.35 * 0.53 + 0.48 * 0.21 + 0.75 * 0.26. Now we can substitute the values into Bayes' rule:
P(clay | positive) = (P(positive | clay) * P(clay)) / P(positive) = (0.48 * 0.21) / P(B).
So the probability that the soil is clay given a positive test result is (0.48 * 0.21) / P(B).
other form to write 600,000+80,000+10
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hope this helps
or 680,010
Malia is observing the velocity of a cyclist at different times. After two hours, the velocity of the cyclist is 15 km/h. After five hours, the velocity of the cyclist is 12 km/h.
Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. Show your work and define the variables used. (5 points)
Part B: How can you graph the equations obtained in Part A for the first 12 hours? (5 points)
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Ax+By+C=0. A,B and C it's coefcients; x and y - it's variables.A and B must not be equal to zero at same time.This condition can be writen like this: (A^2+B^2) not equal to zero.
We know that x=2 ("after two hours") and y=15 ("velocity of the cyclist is 15 km/h")
AND
x=5 ("after five hours") and y=12 ("velocity of the cyclist is 12 km/h").
Lets look at standart form and give the values on variables.1. 2A+15B+C=0
2. 5A+12B+C=0and it is system.let's subtract the bottom equation from the top -3A+3B=03A=3BA=B.So we can choose any value for A and B, just A=B.I choose for A=B=1.Our equation takes the formx+y+C=0
x+y=-C
and if we giving the value to variables, we can find coefficients "C".
5+12=-CC=-17.
Standart form is:x+y-17=0. ---- answer for Part A.
and the graph of this function is a straight line.For find the answer to Part B, we need to prolong our straight line into the perpendicular vertical line wich contain x=12.
In the point of the intersection of the lines, you must to turn at right angle to axis OY and to come at the value in the axis OY, it's will be the velocity after 12 hours.
In the rhombus, m<1=8y-6. Find the value of y. Please help!!
Answers
Answer: 12
The value of y= 12.
Step-by-step explanation:
We know that the diagonal of rhombus are perpendicular bisector of each other.
i.e. the angle made at the intersection of diagonal is 90 degrees.
Thus , for the given figure m∠1 = 90°
Since it is given that m∠1 = 8y-6
Thus , 8y-6= 90
⇒8y=96 [Adding 6 both sides]
⇒ y = 12 [Dividing both sides by 8]
Hence, the value of y= 12.
The building of Jim's Hardware is assessed at $109,000. The tax rate is $86.95 per $1,000 of assessed valuation. The tax due is A. $8,695.45. B. $947.75. C. $9,477.55. D. $8,659.54. E. 94,698.23.
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109,000 / 1,000 = 109
109 x 86.95 = 9,477.55
Express the ratio of A's to N's in the word SAVANNAH, in simplest form
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You have taken over an abandoned drilling project. After drilling for 2 hours, the depth is 110 feet. After 5 hours, the depth has increased to 114.5 feet. Write an equation in the form y = mx + b to describe the relationship between x, the hours of drilling, and y, the depth of the well.
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slope = (114.5 - 110) / (5 - 2) = 4.5 / 3 = 1.5
y = mx + b
slope(m) = 1.5
use either of ur points..(2,110)...x = 2 and y = 110
now we sub and find b, the y int
110 = 1.5(2) + b
110 = 3 + b
110 - 3 = b
107 = b
so ur equation is : y = 1.5x + 107 <==
Tickets for a school play sold for $7.50 for each adult and $3 for each child the total receipts for the 113 tickets sold were $663 find the number of adult ticket sold
Answers
a+c=113
Write a literal equation for c using the second equation.
c=-a+113
Substitute the value of c into the first equation
7.5a+3(-a+113)= 663
7.5a-3a+339=663
4.5a+339=663
4.5a=324
a=72
Final answer: 72 adult tickets sold
Check by finding the value of c and plugging both values in
(72)+c=113
c=41
7.5(72)+3(41)
663
True
A rectangular prism has the following dimensions: l = 5a , w = 2a ,
h = ( a^3 - 3a^2 + a ) Use the formula V = l ⋅ w ⋅ h to find the volume of the rectangular prism.
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The volume of a shape is the amount of space in it.
The volume of the rectangular prism is: [tex]\mathbf{10a^5 -30a^4 + 10a^3}[/tex]
The dimensions of the rectangular prism are:
[tex]\mathbf{l = 5a}[/tex]
[tex]\mathbf{w = 2a}[/tex]
[tex]\mathbf{h = (a^3 - 3a^2 + a)}[/tex]
The volume (v) of the rectangular prism is:
[tex]\mathbf{v = l\cdot w \cdot h}[/tex]
So, we have:
[tex]\mathbf{v = 5a \cdot 2a \cdot (a^3 -3a^2 + a)}[/tex]
[tex]\mathbf{v = 10a^2 \cdot (a^3 -3a^2 + a)}[/tex]
Expand
[tex]\mathbf{v = 10a^5 -30a^4 + 10a^3}[/tex]
Hence, the volume of the rectangular prism is: [tex]\mathbf{10a^5 -30a^4 + 10a^3}[/tex]
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Two linear equations are shown.
What is the solution to the system of equations?
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2 + 5 = 4/3x - 1/3x
7 = x
y = 1/3(7) + 2
y = 7/3 + 2
y = 7/3 + 6/3
y = 13/3
solution is : (7,13/3) <=
Answer:
B.
Step-by-step explanation:
What is 1/4 of 268 ?
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Answer: 67
To find 1/4 of 268, you divide 268 by 4. The result of this operation is 67.
Explanation:Calculating 1/4 of a number involves a simple mathematical operation known as division. In this case, we want to find out what is 1/4 of 268. To do this, you simply divide 268 by 4.
The calculation is as follows:
Divide the number 268 by 4.268 ÷ 4 equals 67.This means that 1/4 of 268 is 67.
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Which statement is true?
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f(x) = 9x-6
g(x) =√(x-4)
(f0g)(x) = f(g(x)) exist if g(x) exist and f(g(x)) exist.
g(1) no exist because : √(1-4) =√(-3) ... no real
conclusion : 1 is not in the domain of : f0g
A and B are mutually exclusive events. P(A) = 1/3 and P(B) = 1/2. What is the P(A or B)?
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1/3+1/2=5/6
Final answer: 5/6
answer
P(A or B) = 5/6
(APEX) If a product is equal to zero, we know at least one of the factors must be zero. And the constant factor cannot be zero. So set each binomial factor equal to 0 and solve for x, the width of your project (-2x^-6x-4)
Answers
(x-q)(x-r) = 0
where q and r are the roots of the equation. Because their product is zero, the Zero Product Property states that x-q - 0 and x-r = 0
Thus, for the given equation above, a = -2, b = -6 and c=-4. Then, we find the roots using the quadratic formula.
[tex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} [/tex]
[tex]x= \frac{-(-6)+/- \sqrt{ (-6)^{2}-(-2)(-4) } }{2(-2)} [/tex]
x = -1 and -2. That means q=-1 and r=-2. Hence, the two binomials are (x+1) and (x+2).
There are two aircraft carriers, A and B, and the carrier A is longer in length the carrier B. The total length of these two carriers is 4178 feet, while the difference of their lengths is only 14 feet.
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Answer:
Length of carrier A = 2096 feet Length of carrier B=2082 feet.Step-by-step explanation:
Given , two air craft carriers are A and B . The carrier A is longer than the carrier B in length.
Total length of two carriers =4178 feet
Difference of two carriers = 14 feet
Let
Length of carrier A =x feet
And
Legth of carrier B =y feet
According to question
The I equation is
x+y=4178
The II equation is
x-y= 14
Substitution method: In this method step I : we find value of x or y from the equation I
Step II: put the value of x or y in II equation then we get the value of another varaiable x or y
Step : Again put the obatined value of variable x or y from step II in equation I then we get value of other variable x or y .
By using substitution method ,
we find value of x from equation I
x= 4178-y
Now, put the value of x in equation II then we get
4178-y-y=14
4178-2y=14
4178-14=2y
4164=2y
[tex]y=\frac{4164}{2}[/tex]
y= 2082
Again , put the value of y in equation I
2082 +x=4178
x= 4178-2082
x=2096
Hence, the length of carrier A = 2096 feet
The length of carrier B= 2082 feet
Final answer:
To solve the problem, we set up two equations based on the given total length and the length difference of the two aircraft carriers. By solving these equations, we find that carrier A is 2096 feet long and carrier B is 2082 feet long.
Explanation:
The student's question involves solving a system of linear equations to find the lengths of two aircraft carriers, A and B. Given that the total length is 4178 feet and the length difference is 14 feet, we can set up the following equations:
Equation 1: A + B = 4178
Equation 2: A - B = 14
To solve for A and B, we can add the two equations together to eliminate B.
This gives us 2A = 4192, hence A = 2096 feet.
Substituting A back into one of the equations, we find B = 2082 feet.
Therefore, carrier A is 2096 feet long and carrier B is 2082 feet long.
What's the correct answer for this?
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[tex]\bf \textit{\underline{N} is inversely proportional to \underline{A}}\qquad N=\cfrac{k}{A} \\\\\\ \textit{we also know that } \begin{cases} A=3\\ N=16 \end{cases}\implies 16=\cfrac{k}{3}\implies 16\cdot 3=k \\\\\\ 48=k\qquad thus\qquad \boxed{N=\cfrac{48}{A}}\\\\ -------------------------------\\\\ \textit{if \underline{A} is 4, what is \underline{N}?}\qquad N=\cfrac{48}{4}[/tex]
A parallelogram has an area of 48 m². If the base is 12 m long, what is the height?
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A school graduation class wants to hire buses and vans for a trip to Jasper National Park. Each bus
holds 40 students and 3 teachers and cost $1200 to rent. Each van holds 8 students and 1 teacher
and costs $100 to rent. The school has at least 400 students wanting to go, but at most 36 teachers.
What is the minimum transportation cost?
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A bus can hold 40 students and 3 teachers.
A van can hold 8 students and 1 teacher.
The number of students riding in buses and vans is at least 400, therefore
40x + 8y ≥ 400 (1)
The number of teachers riding in buses and vans is at most 36, therefore
3x + y ≤ 36 (2)
Write (1) and (2) as
y ≥ 50 - 5x (3)
y ≤ 36 - 3x (4)
The equality portion of the solution of (3) and (4) is
36 - 3x = 50 - 5x
2x = 14
x = 7 => y = 36 - 3*7 = 15
A graph of the inequalities indicates the acceptable solution in shaded color, as shown below.
The minimum cost of renting buses and vans is
7*$1200 + 15*$100 = $9900
Answer: The minimum cost is $9,900
A set of equations is given below:
Equation A: y = x + 1
Equation B: y = 4x + 5
Which of the following steps can be used to find the solution to the set of equations?
x + 1 = 4x + 5
x = 4x + 5
x + 1 = 4x
x + 5 = 4x + 1
Answers
Answer:
x + 1 = 4x + 5
Step-by-step explanation:
To solve this set of equation you can just equalize them ot one another, as you can see they are already in Y form, which means that they have already been solved for Y, so that makes things easier for us, we just insert the second equation in the place of Y in the first one, and we can solve for "x".
A class tossed coins and recorded 165 heads and 172 tails. What is the experimental probability of tails?
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172/337 is the experimental probability of tails.
Hope this helps!
Answer:
Probability of tails = 0.51
Step-by-step explanation:
Probability is the ratio of number of favorable outcome to the total number of outcomes.
Total number of outcomes = Total number of heads + Total number of tails
= 165 + 172 = 337
Number of favorable outcome = Total number of tails = 172
[tex]\texttt{Probability}=\frac{172}{337}=0.51[/tex]
Explain the place value relationship when the same two digits are next to each other in a multi-digit number.
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Partitioning this value,
5664 = 5000 + 600 + 60 + 4
Notice that one digit of 6 worth 100 and the other worth 10
Take another example, 78869 where there are two digits of '8'
Partitioning this value, we have
78869 = 70000 + 8000 + 800 + 60 + 9
Notice that one digit of '8' worth 8000 and the other worth 800
One other characteristic that we can tell from both example, is that when two same digits are placed next to each other in a value, one digit's value is always worth ten times than the other digit.
for example, the value 600 and 60 from the first example, 600 = 10 × 60
a class voted for either kayaking, fishing, or hiking as their favorite summer activity. if hiking got 17% percent of the vote and fishing got 33%, what percentage of the class voted kayaking?
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100-17-33
Just the difference after subtraction
The percentage of the class that voted for kayaking is 50%.
Given data:
To find the percentage of the class that voted for kayaking, use the fact that the total percentage of votes adds up to 100%.
Hiking got 17% of the vote.
Fishing got 33% of the vote.
Let x be the percentage of the class that voted for kayaking.
Since the total percentage of votes is 100%:
17% + 33% + x = 100%
On solving for x:
x = 100% - (17% + 33%)
x = 100% - 50%
x = 50%
Hence, 50% of the class voted for kayaking.
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Devaughn is 13 years older than Sydney. The sum of their ages is 77 . What is Sydney's age?
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53 ℃ below zero degrees
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hope this helps
how to solve this linear equation step by step please
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[tex]\bf \cfrac{3}{c(c-4)}-\cfrac{9}{c(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{3(2c+3)-9(c-4)}{c(c-4)(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{6c+9-(9c-36)}{c(c-4)(2c+3)}=\cfrac{2}{(2c+3)(c-4)} \\\\\\ \cfrac{6c+9-9c+36}{1}=\cfrac{2[c(c-4)(2c+3)]}{(2c+3)(c-4)} \\\\\\ -3c+45=2c\implies 45=5c\implies \cfrac{45}{5}=c\implies 9=c[/tex]
write 103,727,495 in word form and expanded
Answers
One hundred three million, seven hundred twenty seven thousand, four hundred ninety five
Expanded Form:
100,000,000 + 3,000,000 + 700,000 + 20,000 + 7,000 + 400 + 90 + 5
Hope this helped
Manuel is choosing a 3 -letter password from the letters A, B, C, D, and E. The password cannot have the same letter repeated in it. How many such passwords are possible?
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What is the equation of the line that passes through (4,3) and (2,2)
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Answer:
The equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].
Step-by-step explanation:
Given information: The line passes through the point (4,3) and (2,2).
If a line passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through the point (4,3) and (2,2), so the equation of line is
[tex]y-3=\frac{2-3}{2-4}(x-4)[/tex]
[tex]y-3=\frac{-1}{-2}(x-4)[/tex]
[tex]y-3=\frac{1}{2}(x-4)[/tex]
Using distributive property, we get
[tex]y-3=\frac{1}{2}(x)+\frac{1}{2}(-4)[/tex]
[tex]y-3=\frac{1}{2}(x)-2[/tex]
Add 3 on both sides.
[tex]y=\frac{1}{2}(x)-2+3[/tex]
[tex]y=\frac{1}{2}(x)+1[/tex]
Therefore the equation of line is [tex]y=\frac{1}{2}(x)+1[/tex].
From 1980 to 1990, the consumer price index (CPI) increased from 82.4 to 130.7. If a bottle of dish soap cost $0.74 in 1980 and the price of dish soap increased at the same rate as the CPI from 1980 to 1990, by approximately how much did the price of a bottle of dish soap increase from 1980 to 1990?
Answers
Using proportions, it is found that the price of a bottle of dish soap increased $0.43 from 1980 to 1990.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The percent increase, as a proportion, of the CPI is given by:
P = 130.7/82.4 = 1.5862.
Hence, for the price of the bottle:
Pb = $0.74 x 1.5862 = $1.17.
The difference is:
1.17 - 0.74 = $0.43.
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Answer: $0.43
Step-by-step explanation:
The cool dude above me already explained it