All subsets of the set s = {(i, 0), (0, i), (i, i)} that form a basis for r2 is
{( 0,1) (-1,1)}
{(1,0)(0,1)}
{(1,0)(-1,1)}
A fixed A is a subset of some other set B if all elements of set A are factors of set B. In other phrases, set A is contained within set B. The subset relationship is denoted as A⊂B.
Subsets are a part of one of the mathematical ideas known assets. a hard and fast is a set of items or factors, grouped within the curly braces, consisting of {a,b,c,d}. If a set A is a set of even numbers and set B includes {2, 4,6}, then B is stated to be a subset of A, denoted by B⊆A and A is the superset of B.
In mathematics, set A is a subset of a fixed B if all factors of A are also elements of B; B is then a superset of A. It's far possible for A and B to be equal; if they may be unequal, then A is a proper subset of B. The relationship of one set being a subset of every other is known as inclusion.
A set which is (is linearly independent andoil generates/ spans the space (like R) is called a baris.
S= (1,0), (0,1), (-1))}
option-1
As, dimension of R²=2, so, Ary set
conists of three vectors cannot be baris for R²
so, option-1 is wrong.
option-2
As, dimention of R2-2.
{(10), (-11)} is a linearly independent
subset of S. so And as, this subset
has 2 vectors so it will as also
span R se, it will be a baris
of IR?
So, option-6 is correct
{(0,1)} is linearly independent subset
option-7
As (LO) has one vector. So, it cannot
Span/generate R so, it also cannot be balis
for R2
of S.
But it cannot span R²
So ut cannot
be a baris of R2
se, option-2 is wrong.
Option-3
AS, {(0,1), (-1,1)} is linearly independent
So, option -7, is wrong.
Answer
[as fox amy KER, (-1,1) K (0,1)] subset of s
And also as dim {(0,1), (-11)}=2
which is same as the dimention of IR2
so {(0,1), (-11)} forms a baris of R2
{(1,0), (0,1), (-11)}
{(1,0)}
So, option-3 is
Connect
option-4
{(1,0), (3, 1)} is standard balis of R2
which is subset of S.
10
[{(1,0), (0,1)}]
So, option-4 is correct.
option-5
{(-11)}
consists of one vertex,
so, ut cannot span R², so, ut cannot
be a baris of R²
9090
LO {(1,0), (-1,1)}]
Learn more about subsets here https://brainly.com/question/2000547
#SPJ4
find the ratio with step
1] 900ml and 3L
2]8cm and 8mm
3] 2kg and 750gm
4] 1m and 7cm
please help me with step by step
please immediately
Answer:
3:10
10:1
8:1
100:7
Step-by-step explanation:
900:3000
300:1000
3:10
80:8
10:1
2000:750
8:1
100:7
Volume= cm3
What is the volume?
Help me please asap! Thanks so much :)
The volume of the similar triangular prism is: 1,280 cm³.
What is the Volume of a Right Triangular Prism?Volume of a right triangular prism = 0.5 × b × h × altitude, where:
b is the base length of the triangular base
h is the height of the triangular base
Find the of the first triangular prism
Base length of the triangular base (b) = 4 cm
Height of the triangular base (h) = 4 cm
Altitude of the prism = 20 cm
Volume of the first triangular prism = 0.5 × 4 × 4 × 20 = 160 cm³.
Volume of the first prism/Volume of the second prism = (leg of first prism)³/(leg of second prism)³
160/Volume of the second prism = (4)³/(8)³
160/Volume of the second prism = 64/512
160/Volume of the second prism = 0.125
Volume of the second prism = 1,280 cm³.
Thus, applying the volume formula for a right triangular prism, the volume of the given similar prism is calculated as: 1,280 cm³.
Learn more about volume of triangular prism on:
https://brainly.com/question/21173224
#SPJ1
Determine the qualities of the given set. (select all that apply. ){(x, y) | x > 0, y > 0}
The qualities of the set {(x,y): x>0,y>0} is as under:
All points lie in first quadrant.All values are positive and greater than zero.Given a set {(x,y),x>0,y>0}.
We are required to determine the qualities of the set.
We know that a set is a collection of things,numbers, fractions, etc.
In any set the values of x represents the domain of the function and the values of y represents the value of codomain of the function with which the set belongs to.
Set={(x,y): x>0,y>0}
From the above set we can find the qualities stated below:
All points lie in first quadrant as the first quadrant only contains positive values of x and y.All values are positive because it is given that they are greater than zeroHence the qualities of the set {(x,y): x>0,y>0} are that all values should be in first quadrant and all the values are positive.
Learn more about sets at https://brainly.com/question/2166579
#SPJ4
A company is replacing cables with fiber optic lines in rectangular casing bcde. if segment de = 2.5 cm and segment be = 3 cm, what is the smallest diameter of pipe that will fit the fiber optic line? round your answer to the nearest hundredth.
3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.
What is diameter?
Diameter is the full length of the circle running from the edge, through the midpoint, all the way to the other side. That is this whole length right here. The diameter of a circle is represented by the letter d.we know that
The diameter of the circle is equal to BD
Applying the Pythagoras Theorem
BD² = BE² + DE²
substitute the given values
BD² = (3)² + (2.5)²
BD² = 9 + 6.25
BD² = 15.25
BD = √15.25
BD = 3.9 cm
Therefore , 3.9 cm is the smallest diameter of pipe that will fit the fiber optic line.
Learn more about diameter
brainly.com/question/5830326
#SPJ4
Write the equation of the line passing through the point (a, b) and having a slope m.
The equation of the line is b = am + c
What are linear equations?Linear equations are equations that have a constant slope, average rate of change or gradients
How to determine the line equation?The point is given as
(x, y) = (a, b)
The slope is given as
Slope = m
A linear equation is represented as
y = mx + c
Where me represents the slope
Substitute (x, y) = (a, b)
b = am + c
Hence, the equation of the line is b = am + c
Read more about linear equations at:
https://brainly.com/question/14323743
#SPJ1
please help me with 3.2
The measure of the angle ∠PQR is 90 degrees
How to prove that ∠PQR is 90 degrees?The equation of the line PQ is given as:
3x - y - 2 = 0
The coordinates of the QR are given as:
(0, -2) and (6, -4)
Make y the subject in 3x - y - 2 = 0
y = 3x - 2
The slope of the above line is
m1 = 3
Next, we calculate the slope (m2) of points Q and R.
So, we have:
m2 = (y2- y1)/(x2 - x1)
This gives
m2 = (-4 + 2)/(6 - 0)
Evaluate
m2 = -1/3
The slopes of perpendicular lines are opposite reciprocals.
m1 = 3 and m2 = -1/3 are opposite reciprocals.
This means the lines PQ and QR are perpendicular lines.
The angle at the point of perpendicularity is 90 degrees
Hence, the measure of the angle ∠PQR is 90 degrees
Read more about linear equations at:
https://brainly.com/question/15602982
#SPJ1
The picture below shows a pole and its shadow:
A pole is shown with a right triangle side. The right triangle has hypotenuse 113 cm and base 15 cm.
What is the height of the pole?
112 centimeters
100 centimeters
98 centimeters
64 centimeters
The answer is 112 centimeters.
As this problem represents a right triangle, here we need to apply the Pythagorean Theorem.
h = √113² - 15²h = √12769 - 225h = √12544h = 112 centimetersFind the next two terms in this
sequence.
1, -3, 9, -27, 81, [ ? ], [ ? ]
Answer:
the answers are -243 and 729
Step-by-step explanation:
you multiply each by -3. 1x-3 gives you -3. -3x-3 gives you 9. -3x9 gives you -27. -27x-3 gives you 81. 81x-3 gives you -243 and -243x-3 gives you 729. i hope this helps.
Christen returned an overdue book to the library. her fine was the same as it would have been if she returned the book the previous day. which of the answer choices below could be the number of days christen’s book is overdue? 10 14 18 22
The number of days christen’s book is overdue is 22.
What do we mean by overdue?Overdue is defined as occurring after the due date for payment. The arrival of a train that is tardy is an illustration of anything that is past due.Despite the fact that it is after the due date, money that is past due has not yet been paid. The average small business owes outstanding payments of approximately £12,000.When you state that a change or event is overdue, you're implying that you believe it should have taken place sooner rather than later.The number of days christen’s book is overdue:
According to the graph, the fine levied stops rising after 20 overdue days and then stays at 10 for the remaining days.
Additionally, if Christen's fine was the same as yesterday, her late dates must be longer than 21 days (because the fine on day 20 will be the same).
22 might therefore be the number of days past due based on the options provided.
The number of days christen’s book is overdue is 22.
To learn more about overdue, refer to:
https://brainly.com/question/23785152
#SPJ4
Ben throws four identical darts. Each hits one of four identical dartboards on the wall. After throwing the four darts, he lists the number of darts that hit each board, from greatest to least. How many different lists are possible
Based on the fact that the identical darts were thrown at four identical dartboards and Ben took a list, the number of different lists possible is 5 lists.
How many lists are possible?If all the darts hit on dartboard then the list would be:
= 0004
If one dart hit a dartboard and three hit one dartboard the list would be:
= 0031
If two darts hit two boards:
= 0022
If two darts hit one board, 1 dart two others:
= 0211
If all darts hit separate boards;
= 1111
This means that 5 lists are possible to Ben.
Find out more on mathematical possibilities at https://brainly.com/question/6785393
#SPJ1
Help!!!!
A system of inequalities is shown.
Which system Is represented in the graph?
The system of inequalities represented on the graph is:
y > 2x + 3.y > (x + 1)² - 4.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.The linear function in this problem has y-intercept of b = 3, and also goes through the point (1,5), hence the slope is of 2. The line is dashed, hence it is not included in the solution, hence only the part greater than the line is, hence:
y > 2x + 3
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this graph, the vertex of the parabola is of (-1,-4), hence h = -1, k = -4, and the equation is:
y = a(x + 1)² - 4
When x = 0, y = -3, hence the leading coefficient is found as follows:
-3 = a - 4
a = 1.
Hence:
y = (x + 1)² - 4.
And the inequality is:
y > (x + 1)² - 4.
More can be learned about a system of inequalities at https://brainly.com/question/3656398
#SPJ1
A cone has a radius of 3 and a height given by the expression 2a. which expression represents the volume of the cone?2aπ units34a2π units36aπ units324aπ units3
The expression that represents the volume of the cone is 6aπ.
What is called cone?
A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the vertex.The volume of a cone is expressed as;V = (1/3)πr²hWhere r is the radius, h is height and π is pieGiven the data in the question;
Radius r = 3
Height h = 2a
Volume of the cone V = ?
We substitute our given values into the expression above.
V = (1/3) × π × r² × h
V = (1/3) × π × (3)² × 2a
V = (1/3) × π × 9 × 2a
V = 18aπ / 3
V = 6aπ
Therefore, the expression that represents the volume of the cone is 6aπ.
Learn more about cone
brainly.com/question/1778223
#SPJ4
A person draws a card from a hat. each card is one color, with the following probabilities of being drawn: 1/25 for white, 1/5 for black, 1/10 for red, and 1/15 for pink. what is the probability of pulling a black or red card, written as a reduced fraction?
The probability of pulling a black or red card = 3/10
We are informed that a card is pulled from a hat.Probability that a white card will be drawn, P(white) = 1/25
Probability that a blue card will be dealt, P(black) = 1/5
Probability that a black card will be dealt, P(red) = 1/10
Probability that a pink card will be revealed, P(pink) = 1/15
All of these occurrences are distinct from one another and do not relate to one another.
The likelihood that any one of any two events, A and B, with probability P(A) and P(B), will occur is:
P( A ∪ B ) = P(A) + P(B)
Here, event A can be compared to getting a black card, and
incident B is comparable to receiving a red card.
So, P(black or red) = P(black) + P (red)
= (1/5) + (1/10)
= ( 2 + 1 )/10
= 3/10
So, the likelihood that a black or red card will be pulled from the hat:
= 3/10
To know more about Probability visit:
https://brainly.com/question/16969946
#SPJ4
Which inequality is represented by the graph below? Check all that apply. A number line going from 4 to 14. An open circle is at 9. Everything to the left of the circle is shaded. x greater-than 9 x less-than 9 any rational number greater than or including 9 any rational number less than or including 9 any rational number greater than 9 any rational number less than 9
the correct inequality is"any rational number less than 9"
x < 9
Which inequality is represented by the graph?Remember that when we have a number line, an open circle means that we can use the symbols > or <.
While a closed circle uses the symbols ≤ or ≥.
Here we know that we have an open circle at 9, ant everything to the left of the circle is shaded.
To the left of 9 there are the numbers smaller than 9, then the inequality would be:
x < 9
Then the correct option is "any rational number less than 9"
If you want to learn more about inequalities:
https://brainly.com/question/18881247
#SPJ1
Answer: x<9
any rational number less than 9"
Step-by-step explanation:
Find, correct to the nearest minute, the angle subtended at the centre of a circle of radius 5 cm by an of length 13 cm.
[tex]\\ \tt{:}\dashrightarrow \ell=\dfrac{\Theta}{180}\pi r[/tex]
[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180\ell}{\pi r}[/tex]
[tex]\\ \tt{:}\dashrightarrow \Theta=\dfrac{180(13)}{5\pi}[/tex]
[tex]\\ \tt{:}\dashrightarrow \Theta=149^{\circ}[/tex]
1°=60'[tex]\\ \tt{:}\dashrightarrow \Theta=149(60)[/tex]
[tex]\\ \tt{:}\dashrightarrow \Theta=8940'[/tex]
The angle subtended at the center of a circle of radius 5 cm by a length of 13 cm is 149.1°.
Given that,
The angle is subtended at the center of a circle of radius 5 cm by a length of 13 cm.
Here, Lenght of an arc = 13 cm
The radius of an arc = 5 cm
Used the formula for the angles (θ);
Length of an arc = 2πrθ / 360°
Substitute all the values, we get;
13 = 2 × 3.14 × 5 × θ / 360°
Solve for θ;
13 × 360° = 31.4 × θ
4,680° = 31.4 × θ
θ = 4,680°/31.4
θ = 149.1°
To learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ7
(6.04)the equation of the line of best fit of a scatter plot is y = −5x − 2. what is the slope of the equation? −5 −2 2 5
Answer:
slope = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 5x - 2 ← is in slope- intercept form
with slope m = - 5
A person is looking up to the top of a pole at an angle of elevation of 32°. If their line of sight is at 6 ft, find the total height of the pole from the ground to the top. (HINT: you must find "h" first in order to find the total height): (Do not do any rounding during your calculations, just round your final answer)
The total height of the pole from the ground to the top is 3.2 added to the height of the person
How to determine the height of the pole?The given parameters are:
Elevation angle = 32 degreesLine of sight, L = 6 ftThe question is an illustration of elevation
Where the height of the building is the sum of the height of the person and the height from the person's sight to the top of the building (h)
Start by calculating the value of h using the following sine function
[tex]\sin(\theta) = \frac{h}{L}[/tex]
Substitute the values of L and ∅ in the above equation
sin(32) = h/6
Multiply both sides by 6
h = 6 * sin(32)
Evaluate sin(32)
h = 6 * 0.5299
Evaluate the product
h = 3.1794
Approximate
h = 3.2
Hence, the total height of the pole from the ground to the top is 3.2 added to the height of the person
Read more about elevation at:
https://brainly.com/question/21137209
#SPJ1
im confuse gusy can u help me?
Answer:
11. 333... which can also be written as 11 1/3.
Step-by-step explanation:
Sure.
√(6c - 4) = 8
Squaring both sides:
6c - 4 = 64
6c = 64 + 4 = 68
c = 68/6
= 11. 333...
Answer:
[tex]c=\dfrac{34}{3}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt{6c-4}=8[/tex]
Square both sides:
[tex]\implies (\sqrt{6c-4})^2=8^2[/tex]
[tex]\implies 6c-4=64[/tex]
Add 4 to both sides:
[tex]\implies 6c-4+4=64+4[/tex]
[tex]\implies 6c=68[/tex]
Divide both sides by 6:
[tex]\implies \dfrac{6c}{6}=\dfrac{68}{6}[/tex]
[tex]\implies c=\dfrac{34}{3}[/tex]
Verify the solution by inputting the found value of c back into the equation:
[tex]\implies \sqrt{6\left(\dfrac{34}{3}\right)-4}[/tex]
[tex]\implies \sqrt{\dfrac{204}{3}-4}[/tex]
[tex]\implies \sqrt{68-4}[/tex]
[tex]\implies \sqrt{64}[/tex]
[tex]\implies \pm 8[/tex]
Therefore, the solution of the found value of c is verified.
Find the midpoint of TU given the endpoints T(21.8, 9.3) and U(7.6, 1.7)
Answer:
Step-by-step explanation:
Remember the midpoint formula:
[tex](\frac{x2+x1}{2},\frac{y2+y1}{2} )\\[/tex]
Substitute in your values
[tex](\frac{7.6+21.8}{2},\frac{1.7+9.3}{2} )\\[/tex]
Solve
[tex](\frac{29.4}{2},\frac{11}{2} )\\(14.7,5.5)\\[/tex]
Answer: (14.7,5.5)
Step-by-step explanation: I got it right on the test...
4. Emily’s house has a chimney. What is the volume of her chimney? 4 in 12 in 9 in 3 in 4 in 6 in. please hurry ill give brainliest quickly
the total volume of the chimney is:
V =456 in^3
What is the volume of her chimney?
Remember that the volume of a rectangular prism of dimensions L, W, and H is:
V = L*W*H
If you look at the image of the chimney (bottom right image) you can see that the figure can be viewed as 2 rectangular prisms, one smaller of dimensions:
4in x 12in x 9 in
Then the volume of the larger part is:
V = (4in)*(12in)*(9in) = 432 in^3
The smaller prism has dimensions:
of (6in - 4in) = 2in x 3in x 4in
Then the volume is:
V = (2in)*(3in)*(4in) = 24 in^3
Then the total volume of the chimney is:
V = 432 in^3 + 24 in^3 = 456 in^3
If you want to learn more about volumes:
https://brainly.com/question/1972490
#SPJ1
What type of function is f(x) = 2 log5(3x)? exponential logarithmic polynomial rational
The type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)
What kind of function is a given expression?
In this problem we must check the characteristics of an expression and conclude what kind of function is. First, we need to find if any trascendent operator, it not, then the function may be either polynomial or rational. If the function has a trascendent operator, then we must check if it is logarithmic or exponential.
At first glance, we see that the function includes only one trascendent operator, a "log" operator that creates a function of the form f(x) = A · ㏒ₙ (B · x). Therefore, the type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)
RemarkThe statement is poorly formatted, correct form is shown below:
What type of function is f(x) = 2 · ㏒₅ (3 · x)? a) Exponential, b) Logarithmic, c) Polynomial, d) Rational.
To learn more on logarithmic functions: https://brainly.com/question/3181916
#SPJ1
Answer: Logarithmic
Step-by-step explanation: Got the question right on test.
Consider the graphed function.
What are the domain and the range of this function?
Hello and Good Morning/Afternoon:
Let's take this problem step-by-step
What does this problem want to find:
⇒ domain and range
Let's find domain
⇒ distance covered by graph horizontally
⇒ [-5, 1)
Let's find range
⇒ distance covered by graph vertically
⇒ [-4, 7)
*note
use parentheses when endpoint is hollow⇒ those points are not included in domain and range
use brackets when the endpoint is filled⇒ those points are included in domain and range
Answer:
Domain: [-5, 1) Range: [-4, 7)Hope that helps!
#LearnwithBrainly
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Domain of the function are the real values at which the function is defined, or has a unique value. generally domain is represented by the values that x - coordinate can take according to graph.
So, domain of given function is :
[ -5, 1 )here,
[ ] represents closed interval - that means it can have the extreme values too. ( ) represents open interval - that means it can have values between extremes but not extreme value.Similarly, range represents all the values that the function can have, and it is represented by the values that y - coordinate can have.
So, range of given function is :
[ -4, 7 )12 triangles outlined in blue are shown. A red square is drawn around 8 of the triangles.
The area of one of the small right triangles outlined in blue is A cm2, while the area of the square outlined in red is B cm2. Which expressions show the area of the shaded region in terms of A and B? Check all that apply.
4A + B
8A + B
2A + B
1.5B
12A
Answer:
A, D, E
Step-by-step explanation:
I got it right.
What is the slope of a line that is perpendicular to the line whose equation is 3x 2y=6?
2/3 is the slope of a line that is perpendicular to the line whose equation is 3x 2y=6.
What is slope?
Slope, Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).we can find the slope from the equation that is given buy solving the equation for y
3x+2y = 6
2y = 6-3x
y = 3-3/2x
y = -3/2x+3
now that the equation is in slope-intercept form, we can easily see that the slope of the given line is -3/2
perpendicular lines have slopes that are negative reciprocals, so we can just take the negative reciprocal of the slope we have
-3/2 → 3/2 → 2/3
Therefore, the slope of the perpendicular line is 2/3.
Learn more about slope
brainly.com/question/3605446
#SPJ4
Here are yesterday's high temperatures (in Fahrenheit) in 12 U.S. cities. 48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80 Notice that the temperatures are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set. Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.
According to the given statement
we have given data set and we have to find the five number summary.
So, For this purpose,
the given data set is:
48, 50, 54, 56, 63, 63, 64, 68, 74, 74, 79, 80
Firstly we have to find the upper quartile means median for it.
So, Median = n /2
median = 12/2
median = 6th term.
So, Upper quartile range for this data set is 63.
And
Lower quartile for data set is the lower value of the data set.
So, That's why
Lower quartile range for this data set is 48.
And now, we have to find the Interquartile range
so, Interquartile range means maximum value of data.
So, That's why
Interquartile range of this data is 80.
So, The median value is 63 and Lower quartile range is 48 and Interquartile range is 80.
Learn more about median here
https://brainly.com/question/16233946
#SPJ1
Does anyone know the last two? Match the correct property to the equation showing that property.
Explanation: The 4th one is the distributive property because it shows an equal sign and the 5th one is the inverse property of addition because it uses more than addition.
Answer: 4th one is distributive property 5th one is inverse property of addition
P.S. I am sure 95% sure that I am correct.
find the slope of (2,2), (-1,-2)
Answer:
4/3
Step-by-step explanation:
The slope is the change in y over the change in x.
Your y's from the point given is -2, and 2.
Your x's from the point given is -1, and 2. Since we want to know how much they have changed, we subtract these numbers to find the change.
Change in y's? -2 - 2 or -4
Change in x's -1 - 2 or -3
This gives me a slope of -4/-3 and a negative divided by a positive is a positive.
I could have found the change by going the opposite direction
Change in y's ? 2 - (-2) or 4
Change in x's? 2 - (-1) or 3
This gives me the same slope 4/3
A coin is flipped 15 times where each flip comes up either heads or tails. How many possible outcomes (a) contain exactly four tails (b) contain at least three heads?
Using the arrangements formula, it is found that:
a) There are 1365 possible outcomes that contain exactly four tails.
b) There are 1,307,674,399,889 possible outcomes that contain at least three heads.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
When there are repetitions, the number of ways is given as follows:
[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]
In which [tex]n_1, n_2, \cdots, n_n[/tex] are the numbers of repetitions.
Item a:
11 heads and 4 tails, hence:
[tex]A_{15}^{11,4} = \frac{15!}{11!4!} = 1365[/tex]
There are 1365 possible outcomes that contain exactly four tails.
Item b:
The total number is:
[tex]A_{15} = 15! = 1,307,674,400,000[/tex]
With no heads:
[tex]A_{15}^{15,0} = \frac{15!}{15!0!} = 1[/tex]
With one head:
[tex]A_{15}^{14,1} = \frac{15!}{14!1!} = 15[/tex]
With two heads:
[tex]A_{15}^{13,2} = \frac{15!}{13!2!} = 95[/tex]
Hence the number of outcomes with less than three heads is:
1 + 15 + 95 = 111
With at least three heads, the number of outcomes is:
[tex]1,307,674,400,000 - 111 = 1,307,674,399,889[/tex]
There are 1,307,674,399,889 possible outcomes that contain at least three heads.
More can be learned about the arrangements formula at https://brainly.com/question/24648661
#SPJ1
Coplanar circles that have the same center, but not necessarily the congruent radii are called?
Coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.
How to complete the blank?From the question, we have the following statements:
The circles are coplanar i.e. they are on the same planeThey have the same circleThe radii of the circles are differentAs a general rule, circles that have the above features are referred to as concentric circles.
This is so because concentric circles have the same center, and they do not intersect
Hence, coplanar circles that have the same center, but not necessarily the congruent radii are called concentric circles.
Read more about concentric circles at
https://brainly.com/question/960547
#SPJ1
Jack and Serena can write a lab report together in 12 hours. If all people work at the same rate, how many hours would it take to write a lab report if Kay joins Jack and Serena?
