The greatest common factor of polynomial 64xyz−36xy + 24x is 4x
The greatest common factor of a polynomial is a monomial that divides all terms of the polynomial.
The given polynomial is:
64xyz−36xy + 24x
Notice that there are 3 terms:
64xyz
−36xy
24x
To find the greatest common factor, notice that each terms contain x.
Next, find the gcf of 64, 36, 24.
Using prime factorization:
64 = 2⁶
36 = 2² × 3²
24 = 2³ × 3
Hence the gcf (64, 36, 24) = 2² = 4
Therefore the gcf of 64xyz−36xy + 24x is 4x
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suppose that 45% of people own dogs. if you pick two people at random, what is the probability that they both own a dog? give your answer as a decimal (to at least 3 places) or fraction
Answer:
0.2025 or 20.25%
Step-by-step explanation:
The problem says the probability of ONE person having a Dog is 45%
This is 0.45 in decimal form
But what are the chances TWO random people BOTH have Dogs. The chances would decrease!
To find the probability, you need to multiply the probability of one person by the probability of another person. They both have the same probability of having a Dog.
This looks like:
0.45 (person 1) × 0.45 (person 2) = 0.2025
The number of times 0.45 is in the equation above is the same number as the people in the problem!
Use given information to prove that angle DHF = EHG. Write in two-column proof.
After solving the equation the required solution is ∠DHG = ∠EHG
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given, ∠1 = ∠3
now,
∠DHF = ∠1 + ∠2
and, ∠EHG = ∠3 + ∠2
∠EHG = ∠1 + ∠2 (As ∠1 = ∠3)
Hence, ∠DHG = ∠EHG
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Two sides of a triangle measure 8 inches and 10 inches respectively which of these is NOTa possible length for the thirds side of a triangle . Please show ur work Bc I have too !!
A) 12 inches
B) 16 inches
C) 17 inches
D) 18 inches
18 inches is not a possible length for the thrid side of a triangle.
What is Triangle is?A triangle is a polygon with the 3edges and 3 vertices. It is 1 of the basic shaped on geometry. A triangle with vertices A, B, and C is denoted ∆ ABC. In Euclidean geometry, any 3 points, when non-colli early, determined a uniquely ∆ and simultaneously, to unique plane.
As we know in a ∆ if the measurement of two sides are given than the sum of these 2 sides.
Otherwise buliding of a triangle is never possible.
Here two side are 10 and 8 inches.
So, 3rd side of the triangle should be less than
10+8 = 18
Third sides=
2<x<18
Now we have to calculate the range of 3rd sides
2<x<18
Thus,3rd side of the measurement with 18 inches is not possible.
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Please help with this
Answer:
x=45
Step-by-step explanation:
89+112+114+x=360(Sum of angles of a quadrilateral)
315+x=360
x=360-315
x=45
Hope this helps u
I need help to understand this problem cause I forgot how to do it.
Answer:
f (-4) = -5
Step-by-step explanation:
Look at the graph and see the y coordinates when x = -4.
Here, when x = -4, y = -5.
f(x) = (4x/9) -8
Find
f-¹(-10)
Answer:
Step-by-step explanation:
f x = (4x/9)
so it will be x into 4x = 9/f
so 4x square = 9/f
Let X = {x|x is a whole number less than 10} and Y= {-3, -2, 1, 3, 5, 7, 20). Find XU Y.
The number of elements of set (XUY) = 8
What is set?A set is simply an organized collection of distinct objects forming a group and can be expressed in set-builder form or roaster form.
Let X = {x|x is a whole number less than 10} and Y= {-3, -2, 1, 3, 5, 7, 20). .
Means write all the elements in X and Y, then
X = {x|x is a whole number less than 10}
Means write the common elements in X and Y
Y= {-3, -2, 1, 3, 5, 7, 20).
Since there are no common elements in X and Y, then
(XUY) is null set.
The number of elements in (XUY) is 4 + 4 = 8 elements
Then (XUY) = 8
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Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.
What is the range of this relation?
Answer:
c. 3 [tex]\leq[/tex] y [tex]\leq[/tex] 5
Step-by-step explanation:
Rosalie is training for a marathon. She jogs for 30 minutes at a rate of 5 miles per hour, then she decreases her speed over a period of time and walks for 60 minutes at a rate of 3 miles per hour.
Therefore, the speed (y) of Rosalie ranges from 5 mph to 3 mph including the values.
So, the range of this relation is 3 ≤ y ≤ 5.
Answer:
c
Step-by-step explanation:
the maximum of y is 5 the minimum of y is 3
For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean, and compare the result to the expected percentage of a normal distribution. {50, 46, 54, 51, 29, 52, 48, 54, 47, 48}.
According to the normal distribution, 68% of values should fall in one standard deviation from the mean.
Define the term standard deviation?The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the identical mean however a different range, it is helpful.The standard deviation and the mean of the provided data must first be determined.
Below are the standard deviation and mean
Mean = (50 + 46 + 54 + 51 + 29 + 52+ 48 + 54 + 47 + 48)/10
Mean x = 47.9
Standard deviation: √∑(x - x')²/(n - 1)
s = √(50 - 47.9)² + (46 - 47.9)² + (51 - 47.9)² + .....+ (48 - 47.9)²)/(9)
s = 7.20
We possess:
x' ± s = (47.9 ± 7.2)
x' ± s = (40.7, 55.1)
The proportion of values that are within 1 standard deviation of that mean is thus:
9/10 * 100 = 90%.
According to the normal distribution, 68% of values should fall in one standard deviation from the mean.
As a result, the percentage of values seen to be within 1 standard deviation of a mean is significantly larger than the percentage a normal distribution would predict.
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Write a system of equations and then solve by the method of your choice:substitution or elimination
How to solve a system of equations by elimination.
Write both equations in standard form. If any coefficients are fractions, clear them.Make the coefficients of one variable opposites.Decide which variable you will eliminate.Multiply one or both equations so that the coefficients of that variable are opposites.Add the equations resulting from Step 2 to eliminate one variable.Solve for the remaining variable.Substitute the solution from Step 4 into one of the original equations. Then solve for the other variable.Write the solution as an ordered pair.Check that the ordered pair is a solution to both original equations.How to solve a system of equations by Substitution.
Let us take an example :
y = 3x - 4
2y = -x + 6
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionStep 1: Define Systems
y = 3x - 4
2y = -x + 6
Step 2: Solve for x
Substitution
Substitute in y: 2(3x - 4) = -x + 6[Distributive Property] Distribute 2: 6x - 8 = -x + 6[Addition Property of Equality] Add x on both sides: 7x - 8 = 6[Addition Property of Equality] Add 8 on both sides: 7x = 14[Division Property of Equality] Divide 7 on both sides: x = 2Step 3: Solve for y
Substitute in x [Original Equation]: y = 3(2) - 4Multiply: y = 6 - 4Subtract: y = 2Learn more about Substitution method at:
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Solve the equation included in the picture
Answer:
[tex]C[/tex]
Step-by-step explanation:
[tex]|2x+2|=10\\\\2x+2=10,2x+2=-10\\\\2x=8,2x+2=-10\\\\x=4,2x=-12\\\\x=4,x=-6[/tex]
Select the correct answer.
Which number line represents the solution to |x - 5] <3?
Answer:
A.
Step-by-step explanation:
since we are using the absolute value this means the result to be between 0 and 3.
the difference to C. is that the endpoints are not included (empty dots). that is correct, because the inequality uses the "<" sign. being equal to 3 is not valid.
but any real number higher than 2 and lower than 8 will provide a valid solution.
the higher or lower numbers used in B. and D. will not create anything between 0 and 3.
Answer:
A
Step-by-step explanation:
HELPPPPP!! A company makes different sized shoeboxes in the shape of rectangular prisms. Match the area of the material needed to make each box to the box’s dimensions.
The area of the material needed to make each box to the box’s dimensions 14in× 5in× 5in = 330in², 16in× 6in× 4in = 368in², 10in× 6in ×6in = 312in², 12in× 5in× 6in = 324in².
What is a rectangular prism?
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
Here, we have
Given
A company makes different-sized shoeboxes in the shape of rectangular prisms.
We have to match the area of the material needed to make each box to the box’s dimensions.
S₁ = 12in× 5in× 6in
S₁ = (12×5+12×6+6×6)×2
S₁ = 162×2
S₁ = 324in²
S₂ = 10in× 6in ×6in
S₂ = (10×6+10×6+6×6)×2
S₂ = 156×2
S₂ = 312in²
S₃ = 16in× 6in× 4in
S₃ = (16×6+16×4+6×4)×2
S₃ = 184×2
S₃ = 368in²
S₄ = 14in× 5in× 5in
S₄ = (14×5×2+5×5)×2
S₄ = 165×2
S₄ = 330in²
Hence, the area of the material needed to make each box to the box’s dimensions 14in× 5in× 5in = 330in², 16in× 6in× 4in = 368in², 10in× 6in ×6in = 312in², 12in× 5in× 6in = 324in².
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the table below shows the flight of a golf ball after it was hit from the tee toward the green
a) The graph is drawn and attached below by using graphing calculator:
b) The equation of the curve of best fit is y=0.75x
c) The horizontal distance of the ball travelled with this hit is 58.33
d) It does not touch the hall land on the green.
What is a graph?A relation is shown graphically in a function graph. In set theory and modern mathematics, a function is truly equivalent to its graph. For instance, a codomain should be considered while determining whether or not a function is onto (surjective). A function's graph by itself does not show the codomain.
a) The graph is drawn and attached below by using graphing calculator:
b) The equation of the line of best fit is:
Consider any points from the table,
(0,0) and(30,22.5)
y=mx+c
(0,0) -----> 0=0+c
c=0
(30, 22.5)
m=0.75
y= (0.75)x
c) The horizontal distance of the ball travelled with this hit is 58.33
d) For 10m ------>5.8m
For 20m ------->x
x=11.6m
For 120m it will be near to the ground,
16.7-11.6
=5.1m
It does not touch the hall land on the green.
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At a book fair the ratio of the number of tudent to the number of adult i 4:3 after 169 tudent left the book fair the ratio became 4:5 how many adult were there at the book fair
If the ratio of the number of students and adults in the book fair is 4:3, the new ratio when 169 students left the fair is 4:5, then the number of adults in the book fair is 318
Let the number of students be 4x
Let the number of adults be 3x
When 169 students left the fair, number of students left = 4x - 169
According to question,
(4x-169)/3x = 4/5
⇒ 5(4x-169) = 4×3x
⇒ 20x - 845 = 12x
⇒ 20x - 12x = 845
⇒ 8x = 845
⇒ x = 845/8
⇒ x = 105.625
⇒ x = 106
Number of adults = 3x = 3×106 = 318
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Algebra 1: Write and solve two-variable linear equations: word problems
Riley plans to join a members-only speaker series for $50. As a member, she will pay just $12.50 for each event she attends.
Write an equation that shows how the total cost, y, depends on the number of events Riley attends, x.
Do not include dollar signs in the equation.
Answer:
y = 12.50x + 50
Step-by-step explanation:
The linear equation is y=mx + b
b in this one is 50
And the x or the slope is 12.50
Which value represents a percentage between 11% and 17%?
Answer: 0.159
Step-by-step explanation:
0.159
The value of a percentage between 11% and 17% is,
⇒ 0.14
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100.
Given that;
To find value of a percentage between 11% and 17%.
Now, We can formulate;
The value of a percentage between 11% and 17% is,
⇒ (11% + 17%) /2
⇒ 28% / 2
⇒ 14%
⇒ 0.14
Thus, The value of a percentage between 11% and 17% is,
⇒ 0.14
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Calculate the perimeter of the irregular shape . Please show ur work Bc I have too !!
Therefore, the perimeter of the irregular shape is 34cm .
What is perimeter?Whether it be a two-dimensional shape or a one-dimensional length, a perimeter is a closed path that contains, surrounds, or delineates it. The outermost border of an ellipse or circle is its circumference.
Here,
The perimeter of the irregular shape is
Given:
9 cm is the length of the below line and 4cm , 3cm and x is the length of the above line .
So x value is => 9 = 4 + 3+x
=> 9-7 = x
=>x= 2cm
and
thus we get all the length of the irregular shape
so adding =>
=> 4+2+3+2+3+6+5+9= 34 cm
Therefore, the perimeter of the irregular shape is 34cm .
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if x and t represent distance and time, respectively, the c in x = 1/2ct 2 must
C have dimension of [tex]\frac{L}{T^2}[/tex] in the given equation.
What is dimension of physical quantity?The term "dimension" refers to the power to which the fundamental quantities are magnified in order to express a physical quantity. The letters [M], [L], and [T] stand for mass, length, and time, respectively.
given the equation is:
x = [tex]\frac{1}{2}Ct^2[/tex]
and given that x represents distance and t represents time
as we know Dimension of x id L and dimension of time is T
and according to dimensional analysis dimesion of Left side must be equal to dimension to Right side.
let [x] denote dimension of x
so [x] = [C] [[tex]t^2[/tex]]
as [x] = L and [[tex]t^2[/tex]] = [tex]T^2[/tex]
L = [C] * [tex]T^2[/tex]
so [C] = [tex]\frac{L}{T^2}[/tex]
so dimenstion of C is [tex]\frac{L}{T^2}[/tex]
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A pattern ue both addition and ubtraction a it rule. The rule i "Add 12, Subtract 3. " The pattern begin with 41. What i the ixth number in the pattern?
When the rule reads, "Add 12, Subtract 3," and the pattern begins at 41, the sixth number in the pattern is 71.
What is pattern?A pattern is defined in mathematics as a sequence of repeated objects, forms, or numbers. A pattern can be associated with any form of event or object. A pattern has a rule that informs us which items belong to the pattern and which objects do not. Patterns are items that repeat logically, such as vertical stripes on a shirt. They can take the form of numbers, pictures, or forms. A pattern constructed of plastic animals, for example, can alternate between two and four legged creatures, or animals that swim and animals that fly.
Here,
pattern begin at 41,
=41+12
=53
=53-3
=50
=50+12
=62
=62-3
=59
=59+12
=71
The 6th number in the pattern is 71 when the rule says, "Add 12, Subtract 3." and pattern start at 41.
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Isabella is building a tree fort. The base of the fort is 78 inches wide by 92 inches long.
a What is the area of the base in square inches? Show your work
Answer: 7,176 inches
Step-by-step explanation:
Areas equation is Length times width so applying that we have 78 times 92 giving you the answer of 7,176
Please respond to this two questions. Help me improve my grade :)
The percentile rank of a score of 71 on this test will be 33.33% and the score of the 60th percentile will be 84.
What is a percentile?Percentile is the amount to measure the rank of a student in respect to the other students.
For example, the 90 percentile score means that there is 10 percent of members higher than you.
As per the given test scores,
The score of 71 from left to is at the 5th number.
Percentile = 5/15 x 100 = 33.33%
If the percentile is 60%.
x/15 = 60/100
x = 9
The 9th from left to is 84
Hence "On this test, a score of 71 will yield a percentile rank of 33.33%, while an outcome of 84 will represent the 60th percentile.".
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Use the display of data items to find the mean, median, mode, and midrange.
Stems
Leaves
The statistical measures for the data-set are given as follows:
Mean: 69.6.Median: 74.Mode: 74.Mid range: 37.5.How to obtain the statistical measures?From the stem plot, the observations of the data-set are given as follows:
45, 46, 48, 74, 74, 75, 76, 93, 95.
The mean is given by the sum of all observations divided by the number of observations, hence:
Mean = (45 + 46 + 48 + 74 + 74 + 75 + 76 + 93 + 95)/9 = 69.6
The median is the middle element of the data-set. The data-set has 9 elements, hence the median is the 5th element, which is of 74.
The mode is the element that appears the most times in the data-set, which is also 74.
The first quartile is the median of the first half of the distribution, which is the median of the first four elements, hence:
Q1 = (46 + 48)/2 = 47.
The third quartile is the median of the last four elements, hence:
Q3 = (76 + 93)/2 = 84.5.
Then the midrange is given as the difference of the quartiles, as follows:
IQR = Q3 - Q1 = 84.5 - 47 = 37.5.
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The scale is 1ft:1.26cm and your school is 30 feet tall how tall will a model be with 6.3 cm tall toothpicks
Answer:
it will be 37.8 cm tall
What is the equation of the line that passes through the point (1,1) and has a slope of −5?
Answer: y=-5x+6
Step-by-step explanation:
Write an equation of the line that passes through the points
(-1,7) (6,7)
Answer: y=7
Step-by-step explanation:
Slope intercept form
y=mx+b
m=slope
b= y-intercept
find the slope with the slope formula
y2-y1/x2-x1
7-7/6-(-1)
0/7
the slope is 0, meaning this is a horizontal line.
Find the y-intercept
7=0(-1)+b
b=7
y=7
Avicenna, a major inurance company, offer five-year life inurance policie to 65-year-old. If the holder of one of thee policie die before the age of 70, the company mut pay out $23,900 to the beneficiary of the policy. Executive at Avicenna are conidering offering thee policie for $956 each. Suppoe that for each holder of a policy there i a 4% chance that they will die before the age of 70 and a 96% chance they will live to the age of 70
Answer:
Step-by-step explanation:
E(x) = 791*0.97 - 23600*0.03 = 59.27. The answer is positive so they will make a profit of $59.27 for each policy sold.
However the correct answer is $83. By trial and error.
Determine the domain and the range of the function.
f = {(2,4),(29,-7),(44, 4), (54, 2)}
The domain of the given function is {2, 29, 44, 54} and the range is {-7, 2, 4}.
What are the domain and range of functions?The domain of a function represents the set of input values to the function and the range of a function represents the set of output values for the domain of the function.
Domain - {x coordinates of the points in a function}
Range - {y coordinates of the point in a function}
Calculation:The given function is
f = {(2, 4), (29, -7), (44, 4), (54, 2)}
So, the x coordinates of the function are formulated in a set as {2, 29, 44, 54} and the y coordinates are {-7, 2, 4}
Where output 4 is repeated.
Then, the domain of the function is given by the set {2, 29, 44, 54} and the range of the function is given by the set {-7, 2, 4}.
The mapping of the given function is shown in the figure below.
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A diver is at an elevation of -18 feet relative to sea level. The diver descends to an undersea cave that is 4 times as far from the surface
What is the elevation of the cave?
A: -14 feet
B: -18 feet
C: -22 feet
D: -72 feet
The elevation of the cave in feet will be negative 72 feet. Then the correct option is D.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
A jumper is at a height of - 18 feet comparative with ocean level. The jumper plunges to an undersea cavern that is 4 times as distant from the surface
The elevation of the cave is given as,
Elevation = - 18 x 4
Elevation = - 72 feet
The elevation of the cave in feet will be negative 72 feet. Then the correct option is D.
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If John ha 54 time a many car a Noah' car. How much car doe Noah have if the anwer i 4266?
If John has 4266 cars, then Noah will have 79 cars
We can solve this question in the following way,
We have been given the condition that John owns 54 times more cars than Noah.
That means,
If Noah owns 1 car, John will own 1*54 = 54 cars
Similarly, if Noah owns 2 cars, John will own 2*54 = 108 cars
This will follow the pattern,
when Noah owns n cars, John will own n*54= 54n cars
In the question, we know that John owns 4266 cars,
That means we know that
54 * n= 4266
We have to calculate how many cars Noah owns, which is n
therefore the value of n will be
n= [tex]\frac{4266}{54}[/tex]
n= 79 cars
Therefore Noah will own 79 cars while John will have 4266 cars.
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