The largest square that Mr. Stanley can use to plant in his farm is a square with a side length of 8 meters.
To find the greatest common factor of 24 and 40, we can list the factors of both numbers and find the highest factor that they have in common:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
The highest factor that 24 and 40 have in common is 8.
Factors are numbers that can be multiplied together to get a given number. For example, the factors of 6 are 1, 2, 3, and 6 because 1 x 6 = 6 and 2 x 3 = 6. Factors can be prime or composite. Prime factors are those that are only divisible by 1 and themselves. Composite factors are those that have more than two factors.
Factors are important in math because they can be used to simplify fractions, find common denominators, and solve equations. They also play a crucial role in number theory and cryptography, where they are used to encrypt and decrypt messages. 150 is a composite number, which means it has factors other than 1 and itself. The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150. To find these factors, you can divide 150 by each number smaller than it and see if the remainder is 0.
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the perimeter of a square with side length $x$ units is equal to the circumference of a circle with radius 2 units. what is the value of $x$? express your answer as a decimal to the nearest hundredth.
The value of $×$ is 3.14 units
What is perimeter ?Perimeter is the distance around the edge of a shape. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.
The perimeter of a square is expressed as 4l
The circumference of a circle = 2πr
This means that;
4l = 2πr
4l = 2× 3.142 × 2
4l = 12.57
divide both sides by 4
l = 12.57/4
l = 3.14 units(nearest hundredth)
therefore the value of the side length is 3.14 units
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F(x) equals -3(x-1) to the power of 2 + 2 and g(x) equals -3(x-1) to the power of 2 -5 . The vertex of g(x) is
The vertex of the function g(x) is (1,-5).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are f(x)=-3(x-1)²+2 and g(x)=-3(x-1)²-5.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(1,-5)
Focus:
(1,-61/12)
Axis of Symmetry:
x=1
Directrix:
y= -59/12
Therefore, the vertex of g(x) is (1,-5).
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interior angle measures of a 20-gon
The required interior angle of 20-gon measures 162 degrees.
What is a generalized formula to calculate the interior angle of the polygon?The interior angle measure for the n-sided polygon is given by
Interior angle measure = (n-2) x 180° / n, where n is the number of sides (or vertices) of the polygon.
Here,
To find the measure of each interior angle of a 20-gon (icosagon), we can use the formula:
For a 20-gon, n = 20. Substituting this into the formula, we get:
Interior angle measure = (20-2) x 180° / 20
= 18 x 180° / 20
= 162°
Therefore, each interior angle of 20-gon measures 162 degrees.
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three students are chosen at random from a class of ten girls and twelve boys. what is the probability that at least one is a boy, given that at least one is a girl?
The probability that at least one is a boy, given that at least one is a girl is 0.823
To solve this problem, we can use conditional probability.
Let A be the event that at least one student is a boy, and let B be the event that at least one student is a girl.
We want to find the probability of A given B, denoted as P(A|B).
Let total student is,
Total girls (10) + Total boys (12) = 22
First calculating the probability of event B, which is probability that all three students are boys. This can be calculated as:
P(B) = 1 - (10/22)^3 = 1 - 0.214 = 0.906
The probability of event A intersecting B is then calculated, which is the probability that at least one student is a boy and at least one student is a girl. We can use the complement of this event, which is the likelihood that all three students are male or female:
P(A intersect B) = 1 - P(all girls) - P(all boys)
= 1 - (10/22)^3 - (12/22)^3
= 1 - 0.077 - 0.245
= 0.743
Finally, we use the formula for conditional probability to calculate P(A|B):
P(A|B) = P(A intersect B) / P(B)
= 0.743 / 0.906
= 0.822
Therefore, the probability that at least one student is a boy, given that at least one is a girl, is 0.862.
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Which graph represents the solution to the inequality −0.25 is greater than or equal to the product of a number and −0.5?
number line with a closed circle on 0.5 with an arrow shaded right
number line with an open circle on point on negative 0.5 with an arrow shaded left
number line with a closed circle on negative 2 with an arrow shaded right
number line with an open circle on 2 with an arrow shaded left
As we can see from graph for given linear inequality -0.25≥-0.5x, the graph will be a number line with a closed circle on 0.5 with an arrow shaded right.
What exactly are linear inequalities?
Inequality is a mathematical statement in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers. The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠). In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.
The symbols "< and '>' represent severe inequalities, whereas ‘≤’ and ‘≥’ represent slack inequalities. A linear inequality appears to be the same as a linear equation, however there is a difference.
Now,
Given linear inequality is -0.25≥-0.5x
0.25≤0.5x
1/4≤1/2x
x≥1/2
hence,
graph will be a number line with a closed circle on 0.5 with an arrow shaded right.
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6 (72(x - 2)) = 4(15 - 3x)
What is the solution to the equation above?
00
02
O The equation has no solutions.
O The equation has infinitely many solutions.
The solution to the equation 6(72(x - 2)) = 4(15 - 3x) is x = 77/37.
What is the solution to the given equation?Given the equation in the question
6(72(x - 2)) = 4(15 - 3x)
To solve the equation, remove the parenthesis by applying distributive property.
6( 72 × x - 72 × 2 ) = 4 × 15 - 4 × 3x
6( 72x - 144 ) = 60 - 12x
6( 72x - 144 ) = 60 - 12x
6 × 72x - 6 × 144 = 60 - 12x
432x - 864 = 60 - 12x
Collect like terms
Add -12x to both sides
432x + 12x - 864 = 60 - 12x + 12x
432x + 12x - 864 = 60
Add 864 to both sides
432x + 12x - 864 + 864 = 60 + 864
432x + 12x = 60 + 864
444x = 924
x = 924/444
x = 77/37
Therefore, the value of x is 77/37.
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Which digit(s) makes 3,71_ divisible by 3?
A. 3 only
B. 7 only
C. 1 only
D. 1, 4, and 7
Answer: I think B. 7 only
Step-by-step explanation: I hope this helps and I hope everyone is having a good day/Friday&weekend^^
there are two urns containing colored balls. the first urn contains 50 red balls and 50 blue balls. the second urn contains 30 red balls and 70 blue balls. one of the two urns is randomly chosen (both urns have equal probability of being chosen) and then a ball is drawn at random from one of the two urns. if a red ball is drawn, what is the probability that it came from the first urn?
If a red ball is drawn from two urns containing colored balls , then the probability that it came from the first urn is 0.625 or 62.5% .
Let A = the event that the first urn is chosen, and
B is = the event that a red ball is drawn.
We have to find P(A|B), which means , the probability that the first urn was chosen given that a red ball was drawn.
So , By Bayes' theorem:
we have , P(A|B) = P(B|A) × P(A) / P(B) ;
Since each urn has an equal probability of being chosen, we have P(A) = P(B) = 1/2 ; and
the probability of drawing a red ball is the same regardless of which urn was chosen.
We need to find P(B|A), the probability of drawing a red ball from the first urn is 50/100 = 0.5 ;
To find P(B), the overall probability of drawing a red ball, we can use the law of total probability:
that is ; P(B) = P(B|A) × P(A) + P(B|A') × P(A') ;
where A' = event that the second urn was chosen.
Now , we find P(B|A'), which is the probability of drawing a red ball from the second urn is = 30/100 = 0.3 ;
We know that P(A') = 1/2 = 0.5 , because there are only 2 urns.
So , we have : P(A|B) = P(B|A)×P(A) / P(B) ;
= (0.5×0.5) / (0.5×0.5 + 0.3×0.5)
= 5/8
= 0.625
Therefore, the probability that the red ball came from the first urn is 0.625 or 62.5% .
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Calculate the amount of US dollars you can buy for R12 500 at an exchange
rate of 1 US$ R8,76.
Answer: To calculate the amount of US dollars you can buy for R12,500 at an exchange rate of 1 US$ = R8.76, you can use the following formula:
US$ = R12,500 / R8.76
Plugging in the values, we get:
US$ = R12,500 / R8.76 = 1,421.51
So, with R12,500, you can buy 1,421.51 US dollars at an exchange rate of 1 US$ = R8.76.
Step-by-step explanation:
2. Use the Rational Root Theorem to list all possible rational roots for the equation.
3x³ +9x-6=0
2
O±1, 12, 13, 16, ±, ± -
6,±3⁄3,±0
T
تانی
O±1, ±3, ±6
2
O±1, ± 2, ±3, ±6, ± -, ± -, ±=
3 3
NI
3
1/3
WIN
112
±1, +2, +3, +9,-,-
, -, ±一,土
13
MIN
3
2
The possible rational roots of the equation 3x³ + 9x - 6 = 0 are given as follows:
± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.
How to obtain the potential zeros of the function?To obtain the possible rational zeros of the function, we use the Rational Zero Theroem.
The rational zero theorem states that all the possible rational zeros of a function are given by plus/minus the factors of the constant by the factors of the leading coefficient.
The parameters for this function are given as follows:
Leading coefficient of 3.Constant term of 6.The factors are given as follows:
Factors of 3: {1, 3}.Factors of 6: {1, 2, 3, 6}.Hence the possible roots are given as follows:
± 1/3, ± 2/3, ± 1, ± 2, ± 3, ± 6.
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according to the american diabetes association (links to an external site.), 34.2 million americans, or 10.5% of the population, had diabetes in the year 2018. what is the probability that a randomly chosen person has diabetes?
The probability that a randomly chosen person has diabetes is 34.2 million / (0.105 * total population).
The probability that a randomly chosen person has diabetes is equal to the number of people who have diabetes divided by the total population:
probability = number of people with diabetes / total population
Substituting the given values:
probability = 34.2 million / (10.5% of the total population)
To calculate this, we need to convert the percentage to a decimal by dividing by 100:
probability = 34.2 million / (0.105 * total population)
Assuming the total population remains constant between 2018 and now, and that the percentage of people with diabetes has also remained constant, we can use this probability to estimate the current number of people with diabetes in the United States.
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An 18- ounce jar of peanut butter retails for $1.30. What is the unit price in dollars? Round to the nearest cent
Answer:
7 cents
Step-by-step explanation:
0.072222 rounded to the nearest cent is 0.07
to collect data on the signal strengths in a neighborhood, tracy must drive from house to house and take readings. she has a graduate student, dave, to assist her. tracy figures it would take her eight hours to complete the task working alone, and that it would take dave 12 hours if he completed the task by himself. how long will it take tracy and dave to complete the task together? 3.6 hours 7.2 hours 4.8 hours 6.0 hours
It would take Tracy and Dave approximately 4.8 hours to complete the task together. So, the correct option is C.
To solve this problem, we can use the formula:
time = work / rate
where work is the amount of work to be done (in this case, collecting signal strength data from each house), and rate is the rate at which the work is being done.
Let's start by finding Tracy's and Dave's individual rates:
Tracy's rate: 1 job / 8 hours = 0.125 jobs per hour
Dave's rate: 1 job / 12 hours = 0.0833 jobs per hour
Now, let's find their combined rate when they work together:
Combined rate = Tracy's rate + Dave's rate
Combined rate = 0.125 + 0.0833
Combined rate = 0.2083 jobs per hour
Finally, we can use the formula time = work / rate to find how long it would take them to complete the task together:
time = 1 job / 0.2083 jobs per hour
time ≈ 4.8 hours
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Using the F’(x) Graph shown, find the Integral from 0 to 1 F’(x)dx if f(5) = -7.8, and f(0) = 3.
Answer:
[tex]-22.8[/tex]
Step-by-step explanation:
[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]
Do anybody know this?
The proof for the congruence of triangles GHI and GFJ are given below.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
From the figure,
1) Line segment FJ ⊥ line segment FH (given)
2) ∠HGI = ∠FGJ (It is also given)
3) HI = FJ (Given). So HI ≅ FJ
4) HI ⊥ FH (given)
5) Since both the angles F and H are right angles,
∠F ≅ ∠H (since all right angles are congruent)
6) So we get that two angles and a non included side of ΔGHI are equal to the corresponding two angles and a non included side of ΔGFJ.
So by AAS congruence theorem, ΔGHI ≅ ΔGFJ.
Hence the given two triangles are congruent.
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(SAT Prep) Find the value of x
FIND THE VALUE OF x IT IS NOT 5x
statistics is a rigorous branch of mathematics that deals with group of answer choices data mining visualization understanding data linear regression all of the above
Statistics is a rigorous field that provides a set of tools and techniques for understanding and making decisions based on data. Correct option is C.
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. Statistics is used in a wide range of fields, from business and finance to social sciences, engineering, and healthcare.
One of the key goals of statistics is to summarize and make sense of complex data, and this is often done through the use of visualization techniques such as histograms, scatterplots, and box plots.
Statistics also involves techniques such as data mining, which involves the use of algorithms and computational methods to analyze large data sets, and linear regression, which is a technique for modeling the relationship between two variables.
In addition to its practical applications, statistics is also important for understanding the world around us. It can be used to test hypotheses, evaluate the reliability of data, and make predictions about future events. Overall, statistics plays a vital role in modern society by helping us make sense of the vast amounts of data that we encounter every day.
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Complete question is:
Statistics is a rigorous branch of mathematics that deals with
group of answer choices
A. data mining
B. visualization
C. understanding data
D. linear regression
E. all of the above
The figure below is a square. Find the length of side x in simplest radical form with a rational denominator.
Answer:
[tex]\frac{5\sqrt{2} }{2}[/tex]
Step-by-step explanation:
The square cut in half makes the right side a right triangle.
The equation for these types of questions is short side * square root of 2 = long side
So that means that x * [tex]\sqrt{2}[/tex] = 10
So then divide by square root of 2 on both sides to cancel it out
x = 10/[tex]\sqrt{2}[/tex]
Then to simplify it multiply the top and bottom by square root of 2, since you can't have an irrational number in the denominator
That makes it [tex]\frac{10\sqrt{2} }{2}[/tex]
Divide 10/2 to make [tex]\frac{5\sqrt{2} }{2}[/tex]
Can anyone help me out please I really need it…
Answer:
x= 39.549°
Step-by-step explanation:
please review answer.
Four children take part in a swimming relay race.
The table shows their times in the race.
Name Time taken
(seconds)
Manjit: 92.4
Pierre: 86.7
Safia: 85.1
Chen: 91.8
Work out the total time taken by the team in minutes and seconds.
.................minutes ...............seconds
Answer:
5 Minutes and 56 Seconds
Step-by-step explanation:
Manjit= 1 Minute and 32.4 Seconds
Pierre = 1 Minute and 26.7 Seconds
Safia = 1 Minute and 25.1 Seconds
Chen = 1 Minute and 31.8 Seconds
4 X 1 Minute = 4 Minutes
32.4 + 26.7 +25.1 +31.8 = 116 or 1 Minute and 56 Seconds
Therefore, the answer is 5 Minutes and 56 Seconds
The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39. 48, 56, 95, 81 and 75. Find the
Range of the marks obtained
Mean marks obtained by the group
Answer: To find the range of the marks obtained, we need to find the difference between the highest and lowest marks:
Range = highest mark - lowest mark
To find the highest and lowest marks, we can simply sort the marks in ascending or descending order:
39, 48, 56, 75, 76, 81, 85, 85, 90, 95
So, the highest mark is 95 and the lowest mark is 39. Then, the range is:
Range = 95 - 39 = 56
To find the mean marks obtained by the group, we need to add up all the marks and divide by the number of marks:
Mean = (85 + 76 + 90 + 85 + 39 + 48 + 56 + 95 + 81 + 75) / 10
= 745 / 10
= 74.5
So, the mean marks obtained by the group is 74.5.
Step-by-step explanation:
Transformation Question
Translate point (5, -6) based on vector V.
V:(-2,10)
The updated positions are (5, -6) + (-2, 10) = (3, 4)
Describe vector.A vector is a mathematical concept that has both magnitude and direction. The vector's size is determined by size. An arrow-depicted line serves as this representation. The vector's magnitude is represented by the line's length, and its direction is shown by the arrow. additionally referred to as geometric, Euclidean, spatial, or just "vectors."
You can add the components of the vector to the corresponding components of the point to translate point (5, -6) based on vector V:(-2,10).
The updated positions are (5, -6) + (-2, 10) = (3, 4)
Thus, the translated message is (3, 4).
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Over the summer, a Bee Keeper and their bees was able to produce 636 jars of honey over the course of 12 week.
Answer: I assume you are trying to find how many jars the beekeeper has produced per week.
The answer is: 53
Step-by-step explanation:
We know that he produced 636 jars of honey over 12 weeks.
Therefore, to find out the number of jars he made each week, we divide the amount by the time.
So 636/12
Answer 53.
Pls help can u please answer 4 and 5
4A. The number of whole pie shaded are 2
4B . The number of partial pie shaded is 3
4C. The mixed number formed is 2 3/5
5A. The whole number part which is 2 is the quotient
5B. The remainder is 3
What are fractions in math?
In mathematics, a fraction is a number that represents a part of a whole. It consists of two parts: a numerator, which is the part of the fraction that represents the number of parts being considered, and a denominator, which is the number that represents the total number of parts in the whole.
A mixed number is a combination of a whole number and a fraction. It represents a quantity that is greater than the fraction but less than the next whole number.
For example, In the division problem, the dividend is 13 and and the divisor is 5. the division results to mixed number of value 2 3/5.
The mixed number 2 3/5 represents a quantity that is equal to
two whole and three fifths.
converting to improper fractions gives 13/5
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at a football match , there are 29800 people correct to the nearest 100.
at the end of the football match, the people leave at a rate of 400 people per minute , correct to the nearest 50 people
calculate the lower bound for the number of minutes it takes for all the people to leave
The lower bound for the number of minutes it takes for all the people to leave is 67 minutes.
What is lower bound?
Lower bound refers to the smallest possible value in a range or interval of values. In the context of measurements or estimates, it represents the minimum value that a quantity or measurement is expected to be, based on the precision or accuracy of the measuring instrument or method.
To calculate the lower bound for the number of minutes it takes for all the people to leave, we need to use the following formula:
Lower bound = (total number of people - 0.5) / departure rate (in people per minute)
Using the given information, we have:
Total number of people = 29800 (correct to the nearest 100)
Departure rate = 400 (correct to the nearest 50)
To ensure we have a conservative estimate, we will round down the total number of people to 29750 and round up the departure rate to 450.
Therefore, the lower bound for the number of minutes it takes for all the people to leave is:
Lower bound = (29750 - 0.5) / 450
= 66.1 (rounded up to the nearest minute)
So the lower bound for the number of minutes it takes for all the people to leave is 67 minutes.
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Who is funnymike fav badkid?
Answer: badkid jay
Step-by-step explanation: because he gets him everything he ask for and shows favoritism towards him
Answer:
Step-by-step explanation:
PennyWise
NickleSmart
DimeSharp
QuarterIntelligent
the area of a square is 64 square yards. find the length of 1 side of the square
Answer:
Step-by-step explanation:
The formula for the Area of a square is:
A=[tex]s^{2}[/tex] Where s is the length of the side of the square.
Substituting and solving for s gives:
64 units2 = [tex]s^{2}[/tex]
√64 units2 =√s2
8 units = s
The formula for the perimeter of a square is:
p=4s
Where s is the length of the side of the square.
The equation 7(2W + 3) = 14W + 20 has no solutions. Change one term in the original equation to create a new equation with one solution.
Answer:
change the 2w value
Step-by-step explanation:
first, check the equation:
14w + 21 = 14w + 20
when subtracting the 14w from both sides you can see that
21 is NOT EQUAL to 20, making the answer NS.
now, reread the question... create a new equation with ONE solution.
to fix this, we need to change the amount of W's, NOT the amount of constant.
let's try out another number in place of 2w
7 ( 3w + 3 ) = 14w + 20
21 w + 21 = 14w + 20
7 w = -1
w = -1/7
so now it is clear. to change the outcome of the equation, try out another value instead of 2w. Maybe try 3w, 3.5w, or maybe even 1w, or 1.5w .
Answer:
change the 2w
Step-by-step explanation:
=> 7 ( 3w + 3 ) = 14w + 20
=> 21 w + 21 = 14w + 20
=> 7 w = -1
=> w = -1/7
So everything is now evident. Change the value of 2w to anything else to alter the equation's result. Try 3w, 3.5w, or even 1w or 1.5w if you can.
Hope it have been helpful.
8.70% of is 14?
O 10
O 20
O 30
O 50
what number solves the equation 1/3x = -20
Answer:
x=-60
Step-by-step explanation:
Answer:
-60
Step-by-step explanation:
1/3 x = -20 Multiply both sides by 3
3(1/3) x = 3(-20)
x = -60
Check
1/3(-60) = -20
-20 = -20
