There are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.
What is a combination?
A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.
Here, we
Consider lining up all the blue marbles and placing one red marble in between them. Let that arrangement be fixed. The remaining red marbles will be 5 red marbles. Note that the arrangement will be:
x BR x BR x BR x BR x BR x BR x BR x B x
Note that this is the same even if our arrangement is
x B x RB x RB x RB x RB x RB x RB x RB x
There is a total of 13 places to arrange 8 blue marbles among 12 red marbles.
8 marbles can be placed in ¹³C₈ ways
Total possible arrangements = ¹³C₈ = 1287
Hence, there are 1287 ways of arranging 8 blue marbles and 12 red marbles without placing 2 blue marbles next to each other.
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which of the correlation values represent a perfect linear relationship between x and y? A. 0,5 B. 100 C. 1 D. -1 E. 0
The correlation coefficient that represents a perfect linear relationship between x and y is 1 and -1. (Option C and D)
The correlation coefficient refers to a statistical measure of the strength of a linear relationship between two variables and lies with the range from -1 to 1. In other words, a correlation coefficient is a statistical measure of the degree to which changes to the value of one variable predict change to the value of another.
A linear relationship is a statistical term which is used to describe a straight-line relationship between two variables. A perfect linear relationship refers to a relationship in which one of the variables can be perfectly explained by a linear function of the other and can be achieved by the correlation coefficient of 1. A correlation of -1.0 indicates a perfect negative correlation, and a correlation of 1.0 indicates a perfect positive correlation.
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How do you use the sine rule to work out an obtuse angle?
The value of the obtuse angle by applying sine rule for the attached diagram is equal to x° = 38.2°.
As given in the question,
Diagram of the obtuse angle triangle is attached.
In the given triangle,
Name the vertex of angle x as 'C' and side opposite to angle x as AB.
Draw a perpendicular from point A to BC at point D such that AD = z .
Given m ∠ACB = x°
AB = 2y
AC = y
m ∠ABC = 18°
In ΔADB,
sinB = AD / AB
⇒ sin 18° = z / 2y __(1)
In ΔACD,
sin ACD = AD / AC
⇒ sin ( 180 - x )° = z / y __(2)
Divide (1) by (2) we get,
sin18° / sin ( 180 - x )° = ( z / 2y ) / ( z / y )
⇒ sin 18° / sinx° = 1 / 2
⇒ sinx° = 2sin18°
⇒ sinx° = 2 (0.309 )
⇒ x° = sin⁻¹( 0.618)
⇒x° = 38.2°
Therefore, the obtuse angle for the given attached diagram using sine rule is equal to 38.2°.
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find the sum or different 2b+8
This cannot be furtherly simplified because the sum or difference of 2b+8 depends upon the value of b.
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 2b+8.
In the given expression b is the variable and 2 is the coefficient of the variable b. eight is the constant value and plus is the operator.
As there is a plus sign we need to add the two terms 2b and 8.
We do not know the value of b so we cannot simplify the expression further. The value of 2b plus eight depends upon the value of b, if it is positive then we add two terms and if it is negative we use difference,
Hence, the sum or difference of 2b+8 depends upon the value of b and cannot be furtherly simplified.
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Is it possible to write an equation for such a parabola in the form f(x)=(x-a)(x-b).
Yes. Parabola is possible to write an equation in the form f(x) = (x-a)(x-b)
Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.
A parabola can be described in the form of a general equation
[tex]y=ax^{2} +bx+c[/tex], with a, b, c is integers.
The form f(x)=(x-a)(x-b) can be made in other forms :
[tex]y=(x-a)(x-b)[/tex]
[tex]y=x^{2} -bx-ax+ab[/tex]
[tex]y=x^{2} -(b+a)x+ab[/tex]
That form of the equation is the same as : [tex]y=ax^{2} +bx+c[/tex]
With :
a = 1
b = -(b+a)
c = ac
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what is the null hypothesis of the dickey-fuller test 1? the series is stationary around a 0 mean the series is stationary around a non 0 mean the series is non-stationary and has 0 mean the series is non-stationary and has a non 0 mean
If you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.
What is Null hypothesis?
The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.
Consider the given process:
[tex]x_{t} = c+\alpha x_{t-1}+\beta _{t} \\E[\beta _{t}]=0\\[/tex]
Obtain mean,
[tex]E[x _{t}]=\frac{c}{1-\alpha }[/tex]
This works only when |α|<1. If α=1 this doesn't work, it blows up, because , [tex]E[x _{t}]\neq E[x _{t-1}][/tex] i.e. the process is not stationary.
The constant refers to the term c.
The trend is easy too:
[tex]x_{t} +c+\alpha t+\alpha x_{t-1} +\beta_{t}[/tex]
In this case,
[tex]E[x _{t}]=\frac{c+\alpha t}{1-\alpha }[/tex]
So, if you have a trend then the process is non-stationary, but if you account for the time trend, it's still stationary around the line.
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8. A square has an area of 40 square feet. What is the length of a side of the square, in feet? PLEASE HELP I NEED IT ASAP
A
[tex] \sqrt[4]{10} [/tex]
B
[tex]10[/tex]
C
[tex]20[/tex]
D
[tex] \sqrt[2]{10} [/tex]
Answer:
The length of the side of the square should be 10ft
Step-by-step explanation:
Calculation of the length of the side:
Since A square has an area of 40 square feet.
As we know that the square does have 4 sides
So, the length of the side of the square should be
40 divided by 4
= 10ft
the margin of error of a confidence interval is the error from biased sampling methods. True or False
It is false, that the margin of error of a confidence interval is the error from biased sampling methods.
The margin of error of a confidence interval is the amount of accuracy in a sample with respect to the population. It is calculated by taking the sample standard deviation and dividing it by the square root of the sample size. The margin of error helps to quantify the reliability of estimates and provides a range within which the population parameter is likely to fall. It does not refer to errors in sampling methods, which are typically a result of bias. Bias is a systematic error that arises from the sampling procedure, resulting in estimates that are not an accurate representation of the population.
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A snack food company advertises that they have increased the size of their standard tortilla chips bag to 16.8 ounces, which is 20% more than the original size.
What is the original size of the bag?
A tortilla chip bag labeled x ounces. A tortilla chip bag that has 20 percent more is labeled 16.8 ounces.
The original size of the bag is given by the equation A = 14 ounces
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the original size of the bag be = A
Now , the equation will be
The increased size of the bag = 16.8 ounces
The percentage increase in the size of the bag = 20 %
So , the equation for the percentage increase in the size of the bag is
Original size of the bag + ( 20/100 ) x percentage increase in the size of the bag = increased size of the bag
Substituting the values in the equation , we get
A + ( 20/100 ) x A = 16.8
( 120 / 100 ) A = 16.8
On simplifying the equation , we get
Multiply by 100 on both sides of the equation , we get
120A = 1680
Divide by 120 on both sides of the equation , we get
A = 14 ounces
Therefore , the value of A is 14 ounces
Hence , The original size of the bag is 14 ounces
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a 5.0L v8 pickup truck takes 7.7 quarts of oil with a tolerance of 0.2 quarts. Write an equation representing the minimum and maximum fill capacity tolerated by this truck.
Answer:
Step-by-step explanation:
cdcdfcdfvdsfdf
I need help please! Describe how the graph of g(x) is related to graph of f(x) = x³.
a. g(x) = (x-4)³
b. g(x) = -5x³
Answer:
Step-by Graph the line using the slope and y-intercept, or two points
Slope=3
y-intercept=18-step explanation:
Find f(3)-(5) given f(x) = 8(.5) and gix) = 2x+1
Answer:
Hope it helps
Step-by-step explanation:
f(3)-g(5) = 8(.5) - (2(5)+1) = 4 - 11 = -7
a box with a square base and open top must have a volume of 4,000 cm3. find the dimensions of the box (in cm) that minimize the amount of material used. sides of base cm height
Therefore width = 10cm
height = 20cm
length = 20cm
given that
volume = 4,000[tex]cm^{3}[/tex]
let height = h
width = w
length = l
width and length are equal
height = length = h
volume of box = height × width × height
4000 = h × w × h
4000 = [tex]h^{2}[/tex]w
w = 4000/[tex]h^{2}[/tex]
surface area(SA) = area of base + sum of area of each side
= [tex]h^{2}[/tex] + hw + hw + hw + hw
= [tex]h^{2}[/tex] + 4hw
substitute y = 4000/[tex]h^{2}[/tex]
SA = [tex]h^{2}[/tex] + 4x(4000/ [tex]h^{2}[/tex] )
SA = [tex]h^{2}[/tex] + 16000/h
Taking the derivative:
SA' = 2h - 16000/ [tex]h^{2}[/tex]
making SA' = 0:
0 = 2h - 16000/ [tex]h^{2}[/tex]
2h = 16000/ [tex]h^{2}[/tex]
2[tex]h^{3}[/tex] = 16000
[tex]h^{3}[/tex] = 8000
h = 20 cm
w = 4000 / [tex]h^{2}[/tex] = 4000 / 20² = 10 cm
Therefore width = 10cm
height = 20cm
length = 20cm
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before i can open my gym locker, i must remember the combination. two of the numbers of this three-term sequence are 17 and 24, but i have forgotten the third, and do not know which is which. there are 40 possibilities for the third number. at ten seconds per try, at most how long will it take me to test every possibility? the answer is not 40 minutes!
Therefore, 6 minutes and 40 seconds are needed to test possibilities.
Describe combination.Combinations are sometimes known as selections. Combinations are the results of selecting elements from a set assortment. Nothing specific is being organized here. We are choosing them. To denote the number of unique r-selections or combinations among a set of n items, we write n C r. Combinations are distinct from arrangements or permutations.
Here,
The first two numbers in this three-term series are 17 and 24, and the third one remains a mystery.
Given that there are 40 options for the third number and that each try takes 10 seconds, we have 40 x 10 seconds, or 400 seconds, to try every possible combination.
Thus,
=> 400 seconds is equals to 6 minutes and 40 seconds
Therefore, 6 minutes and 40 seconds are needed to test every scenario.
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a cruise director schedules 4 different movies, 2 bridge games, and 3 tennis games for a two-day period. if a couple selects 3 activities, find the probability that they attend 2 movies and 1 tennis game.
I need help:/
………………
Using system of linear equations, the number of students in year book is 25 and that of film making are 39
System of Linear EquationSystem of linear equations can be defined as the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.
Using variables x and y to represent to unknown values;
x = number of students in film makingy = number of students in year bookx + y = 64 ...eq(i)
x = 14 + y ...eq(ii)
Put eq(iii) into eq(i)
14 + y + y = 64
14 + 2y = 64
2y = 64 - 14
2y = 50
y = 25
Put y = 25 into eq(ii)
x = 14 + 25
x = 39
The number of students in film making is 39 and year book is 25
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Solve using elimination.
4× - 3y = -8
9x - 3y = 12
Step-by-step explanation:
Simulteanous EquationsSimulteanous Equations are multiple equations with corresponding number of unknown variables.
They can be solved by 2 methods: Substitution and Elimination Method.
Solutionx = 4
y = 8
We will use the Elimination Method since the question specify as so.
4x - 3y = -8 (Equation 1)
9x - 3y = 12 (Equation 2)
By using Equation 1 - Equation 2,
4x - 9x - 3y - (-3y) = - 8 - 12
-5x - 3y + 3y = - 20
-5x = - 20
x = - 20 ÷ - 5 = 4
Now we substitute x = 4 into Equation 1.
4(4) - 3y = - 8
16 - 3y = - 8
-3y = - 8 - 16
-3y = - 24
y = - 24 ÷ - 3
= 8
Therefore the varables are:
x = 4
y = 8
Find KL in the image below
By Midsegment theorem we find the length of KL is 8.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
We know by midsegment theorem, the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.
The length of midsegment KL =1/2 of the length of the third segment FH.
KL = 1/2(FH)
KL = 1/2(16)
KL is sixteen divided by 2.
KL = 8
Hence, the length of KL is 8.
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a group spends $277.50 to rent 15 tubes for a float down the ichetucknee river. how many of each type of tube does the group rent?
Answer: $18.50
Step-by-step explanation:
Take 277.50 divided by 15 = $18.50
The required price of each tube for rent is given as $18.6.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Renting 15 tubes for a float down the Ichetucknee River costs $277.50 for a group.
So,
Let the rent of each tube be x,
According to the question,
15x = 277.50
x = 277.50 / 15
x = 18.6
Thus, the required price of each tube for rent is given as $18.6.
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Tabitha planted an evergreen tree in her front yard. It was 12 feet tall. The next year it was 20% taller. How much taller, in feet, was the evergreen tree in Tabitha’s yard?
The evergreen tree grew 2.4 feet taller the next year.
What are Percentages?Percentage can be derived by dividing the given value by the total value, and then multiplying the result by 100.
Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".
Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
It is given by:
Percentage = (given value / total value) * 100%
From the question, the tree has a base height of 20m, if it grew 20% taller then;
tree height = 12 x (20/100)
tree height = 12 x 0.2
tree height = 2.4
Therefore, the tree grew 2.4 feet taller the next year.
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the area of a rectangle is 105 sq in and the length of one side is 7 in. what is the length of the perimeter?
The length of the perimeter of the rectangle = 112 cm or 44 inches
Given in the question,
Area = [tex]105in^{2}[/tex]
= 677.4 [tex]cm^{2}[/tex]
Length of one side of the rectangle = 7 inches
= 17.7 cm
∴ Since the length of one side of the rectangle is given in the question we need to find the width of the rectangle to calculate the total perimeter of the rectangle
⇒ Area = length x width
⇒ 677.4 = 17.7 x width
⇒ Width = [tex]\frac{Area}{Length}[/tex]
⇒ Width = [tex]\frac{677.4}{17.7}[/tex]
⇒ Width = 38.2 cm
As we got both the length and the width of the rectangle, now we can calculate the perimeter,
⇒ Perimeter = [tex]2( length + width)[/tex]
⇒ Perimeter = [tex]2(17.7 + 38.3)[/tex]
⇒ Perimeter = 2 x 56 cm
⇒ Perimeter = 112 cm
⇒ In inches = 44 inches
Therefore, the length of the perimeter is = 112cm or 44 inches
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Write 45% as a fraction or mixed number in simplest form.
The simplest form is ?
Answer:
9/20
Step-by-step explanation:
hope it helps!
Could you please give me brainliest for this? Thank you!
Do linear equations have 2 answers?
The Linear equations can have 2 or more answers if the lines overlap each other .
In the question ,
it is asked that can two linear equations have 2 answers or solutions .
We know that ,
(1) two linear equations can have No Solution / Zero Solution if two lines are parallel .
(2) two linear equations can have One Solution/Unique Solution if two line intersect at a point .
(3) two linear equations can have infinitely many solution if lines overlap on each other .
So from (3) , we can conclude that linear equations can have 2 or more solutions when the line are overlapping .
Therefore , Yes, the linear equations can have two answers .
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factor the following expression using imaginary numbers : 100x^2+1
Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].
What are the factorization?
Factorisation or factoring is defined as the breaking or decomposition of an entity into a product of another entity, or factors, which when multiplied together give the original number.
Here given expression is
[tex]100x^2+1[/tex]
[tex](10x)^2+(1)^2[/tex]
[tex](10x+1)^2[/tex]
As we know that,
[tex](a+b)^2=a^2+b^2+2ab[/tex]
Here
[tex]a=10x\\b=1[/tex]
So,
[tex](10x+1)^2=(10x)^2+(1)^2+2(10x(1))\\\\(10x+1)^2=(10x)^2+(1)^2+20x\\\\(10x+1)^2=100x^2+1+20x[/tex]
Hence, the factors of [tex](10x+1)^2=100x^2+1+20x[/tex].
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The factors of the expression 100x² + 1 are (10x+i) (10x-i).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
The given expression is 100x² + 1.
The given expression is a quadratic function.
The standard form of quadratic function:
ax²+bx +c, where a is not equals to zero.
Comparing with the standard form we get,
a = 100, b = 0 and c = 1
Simplifying,
100x² + 1
= 100x² - (-1)
= (10x)² - (-1)
= (10x)² - (i)² ,{i² = -1}
= (10x+i) (10x-i)
Therefore, (10x+i) (10x-i) are the factors.
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HELPPP PLSSS!!!
agile minds
Answer:
A = 2; B = 3; C = -3
Step-by-step explanation:
The curve goes to negative infinity as x decreases and positive infinity as x increases.
This looks like a 3rd degree polynomial.
f(0) = -3
f(x) = Ax^B + x + C
f(0) = A(0^B) + 0 + C = -3
C = -3
f(x) = Ax^B + x - 3
f(1) = A(1^B) + 1 - 3 = 0
A - 2 = 0
A = 2
f(x) = 2x^B + x - 3
f(1.125) = 2(1.125)^B + 1.125 - 3 = 1
2(1.125)^B + 1.125 - 3 = 1
2(1.125)^B = 2.875
(1.125)^B = 1.4375
log (1.125)^B = log 1.4375
B × log (1.125) = log 1.4375
B = (log 1.4375)/(log 1.125)
B = 3
f(x) = 2x^B + x - 3
Answer: A = 2; B = 3; C = -3
What are 3 rules that prove two triangles are similar?
Three rules that prove two triangles are similar AA, SAS, SSS.
When two shapes in geometry have the same shape but different sizes, they are said to be comparable. A square with sides of 21 cm and one with sides of 14 cm would be comparable. A square with sides of 14 cm and an equilateral triangle with sides of 21 cm are not comparable because they are different shapes.
Applying three triangle-specific theorems makes it simple to distinguish between similar triangles.
In geometry, correspondence refers to the exact relationship between a specific part on one polygon and a part that is similarly positioned on another polygon.
These theorems knows as
Angle-Angle (AA) = Two pairs of corresponding angles are equal.
Side-Angle-Side(SAS) = Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.
Side-Side-Side(SSS) = Three pairs of corresponding sides are proportional.
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Find the value of x and y (8x-14) (5y+16) (5x34)
Answer:
x=16
y=10
Step-by-step explanation:
(8x-14) + (5y+16) =180, because together they make a straight line.
(5x+34) = (8x-14), because they are alternate exterior angles.
Solve for x:
48=3x
x=16
Let's plug that into the first equation, then solve for y.
(8(16)-14) + (5y+16) =180
128-14+5y+16=180
130+5y=180
5y=50
y=10
Rotate these ordered pairs around the origin
90° Counter clockwise.
(2,3)
(-4,7)
(5,-4)
(-8,-6)
Answer:
After rotating the ordered pairs 90° counterclockwise around the origin, they will become:
(3, -2)
(-7, -4)
(-4, 5)
(-6, 8)
To rotate a point 90° counterclockwise around the origin, you can use the following transformation matrix:
[[0, -1],
[1, 0]]
To rotate a point (x, y) by 90° counterclockwise, you can multiply the transformation matrix by the point, which will give you the new coordinates of the point after the rotation. For example, to rotate the point (2, 3) 90° counterclockwise, you can multiply the transformation matrix by the point:
[[0, -1],
[1, 0]] * [2, 3] = [3, -2]
Similarly, you can rotate the other points 90° counterclockwise using the same transformation matrix.
~Describe the transformation(s) shown:
What is the solution to this equation? –1.3x = 52
Answer:
Step-by-step explanation:
x=-40
6. Annie orders a coke for $1.75, pasta primavera for $14.50, and ice cream for $3.25 when out to dinner with friends. If the tax rate is 8.25%, and Annie plans to leave a 17% gratuity, what will be the total cost for her meal?
Answer:
Step-by-step explanation:
1.75+ 14.50+ 3.25= 19.5
8.25% of 19.5= 1.60875
19.5 + 1.60875= 19.7 rounded
19.7+ 17%= 19.87
$19.87 is the total
I rounded so the closest to this might be the answer