The probability that the sum is a multiple of three is 0.2778
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event will definitely occur.
If a pair of six-sided dice is rolled, and the sum is recorded, then the possible sum is the numbers from (1 + 1) = 2 to (6 + 6) = 12.
From 1 to 12, the multiples of 3 are 3, 6, 9, and 12. These can be resulted from having the following dice rolled.
3 : 1 & 2, 2 & 1
6 : 1 & 5, 2 & 4, 3 & 3, 4 & 2, 5 & 1
9 : 3 & 6, 6 & 3
12 : 6 & 6
Since there are 10 possible outcomes wherein the sum is a multiple of 3, and there are (6 x 6) total outcomes, then the probability is
p = 10 / 36 = 0.2778
Hence, the probability that this sum is a multiple of three is 0.2778.
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Define and distinguish among mean, median, and mode. Choose the correct description of the mean below. O A. The mean is the most common value in a data set. It can be strongly affected by outliers. O B. The mean is the sum of all the values divided by the number of values. It can be strongly affected by outliers. O C. The mean is the most common value in a data set. It is not affected by outliers. O D. The mean is the sum of all the values divided by the number of values. It is not affected by outliers. O E. The mean is the middle value in a data set. It can be strongly affected by outliers O F. The mean is the middle value in a data set. It is not affected by outliers.
Answer:
As far as I know
Mode: The most frequent number—that is, the number that occurs the highest number of times. Example: The mode of {4 , 2, 4, 3, 2, 2} is 2 because it occurs three times, which is more than any other number.
The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
Ajar contains 24 blue marbles, 16 red marbles, and 14 white marbles. Find the simplified ratio
of total marbles to red marbles.
Answer:
Answer: 27:8
Step-by-step explanation:
There are 24 + 16 + 14 = 24+16+14= 54
54 marbles in total.
The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.
Answer: 27:8
Identify the focus and directrix of the parabola represented by the equation (y-3)^2=-4(x 3)
The focus is at (3,3+1/4) and the directrix is the equation of a line is 2.75.
A parabola is defined as the set of all points that are equidistant to the focus (F) and the directrix (d).
In the case of this parabola represented by the equation (y-3)² = 4(x-3), the vertex is located at the point (3,3) which means that this parabola opens horizontally to the left. Since the coefficient of x² is positive the parabola opens up.
The focus is located at the point (3,3+1/4) which is (3,3.25) and the directrix is the line x = 2.75. These two elements are crucial in understanding the shape and behavior of the parabola, The focus is where the parabola bends, and the directrix is where it opens.
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If x:y = 1/2:1/3 and y:z = 1/5:1/6, find x:y:z
The value of the ratio x : y : z is 1/2 : /3 : 5/18
How to determine the ratioFrom the question, we have the following parameters that can be used in our computation:
x:y = 1/2:1/3 and y:z = 1/5:1/6
Express the ratio properly
So, we have the following representation
x : y = 1/2 : 1/3 and y : z = 1/5 : 1/6
Multiply the ratio y : z = 1/5 : 1/6 by 5/3
So, we have
y : z = 1/3 : 5/18
So, we have
x : y : y : z = 1/2 : 1/3 : 1/3 : 5/18
Remove the repetition
This gives
x : y : z = 1/2 : /3 : 5/18
Hence, the ratio is 1/2 : /3 : 5/18
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rika gives away samples of a new fragrance and a new scented hand lotion to customers. she must hand out a total of 114 samples during her shift she has already handed out 36 samples which represent 1/3 the number of fragrances samples and 1/4 the number of hand lotion samples she must hand out, write a system of equations for this problem situation.
Answer:
Let F be the number of fragrance samples and L be the number of hand lotion samples.
We know that F + L = 114, since Rika must hand out a total of 114 samples.
We also know that F = (1/3)L and L = (1/4)F, since the number of fragrance samples is 1/3 of the number of hand lotion samples, and the number of hand lotion samples is 1/4 of the number of fragrance samples.
Substituting the second equation into the first equation, we get:
F + (1/4)F = 114
Combining like terms, we get:
(5/4)F = 114
Dividing both sides by (5/4), we get:
F = 92
Substituting this value back into the second equation, we get:
L = (1/4)(92) = 23
Therefore, the system of equations is:
F + L = 114
F = (1/3)L
L = (1/4)F
The solution to this system is F = 92 and L = 23
It costs $31 for 3 visitors to take a tour. It costs $80 for 10 visitors to take the same tour. What is the rate of change?
The rate of change is $2.33 per visitor
What is rate of change?Rate of change refers to how quickly something changes over time. For example, acceleration is the rate of change of velocity with time.
Velocity is also the rate of change in position with time.
Rate of change means difference or changes with time.
It cost $31 for 3 visitor. This means that the cost per visitor is $31/3 = $10.33
It cost $80 for 10 visitor. This means that the cost for one visitor is 80/10 = $8
The rate of change is the difference in rate. This means that rate of change = $10.33 - $8
= $2.33/visitor
Therefore the rate of change is $ 2.33 per visitor.
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If A(2,3),B(4,6),C(7,4) and D(a,b) are vertices of quadrilateral
It can be concluded that the given coordinates of A(2,3), B(4,6), C(7,4) and D(a,b) can be used to determine the length of the sides as well as the angles of the quadrilateral ABCD.
What is quadrilateral?A quadrilateral is a four-sided polygon with four angles. It is a two-dimensional shape that is bounded by four line segments, each of which is called a side. The sum of the angles of a quadrilateral is 360 degrees. Types of quadrilaterals include rectangles, squares, trapezoids, parallelograms, and kites.
First of all, ABCD is a quadrilateral, which means it has four sides and four vertices. A, B, C and D are the vertices of this quadrilateral. It can be seen that A(2,3), B(4,6), C(7,4) and D(a,b) given in the question are coordinates of the vertices. Therefore, from these coordinates, we can conclude that A, B, C and D are the vertices of the quadrilateral ABCD.
Moreover, these coordinates can also be used to determine the length of the sides of the quadrilateral. The distance between A and B can be calculated by using the Pythagorean theorem. Similarly, the lengths of other sides can also be calculated by using the same theorem. Furthermore, the coordinates will also help us to calculate the angles formed by the sides of the quadrilateral ABCD.
Therefore, it can be concluded that the given coordinates of A(2,3), B(4,6), C(7,4) and D(a,b) can be used to determine the length of the sides as well as the angles of the quadrilateral ABCD.
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complete questions as follows-
If A(2,3),B(4,6),C(7,4) and D(a,b) are vertices of quadrilateral prove its true.
The height of parallelogram whose area is 35 cm2 and altitude 7 cm
Answer:
altitude is same as height =7cm
Step-by-step explanation:
area of parallelogram=height (altitude) × base length
Determine the number of unique triangles that can be made from the following information: For ∆LMN, ∠ = 31°, /LM = 6.9, and /MN = 3.4.
Answer:
Step-by-step explanation:
There is only one unique triangle that can be made with this information.
I know where u stay;)
Answer:
ok
Step-by-step explanation:
Wich of this relations is a function?
Pls Help
The relations depicted in graph 1 is a function as every input value has exactly one output value.
What are functions?A relation called a function is one in which every potential input value results in exactly one possible output value. They are set of ordered pairs.
What are relations?Relations indicate the relationship between the indicated input and output value.
Graph 1:
In graph 1 each input value has exactly one output hence relations in graph 1 is a function.
Graph 2:
Graph 2 represents a circle, in this each input value does not have exactly one output value and hence it is not a function.
Graph3:
In graph 3, each input value does not have exactly one output value and hence it is not a function.
Graph 4:
In graph 4, each input value does not have exactly one output value and hence it is not a function.
Hence, relations in graph 1 is a function.
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Solve and graph.
-4p>-28
Answer:
p < -7
Step-by-step explanation:
-4p > 28 Divide both sides by -4 and flip the sign
p < -7
Whats the answer for this
the value of the Perpendicular distance of F from Chord AB is 10.
What is the right-angle triangle?A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.
Given a circle, Where F makes a right angle triangle with the chord CD and also with Chord AB.
We know that,
Equal chords of a circle are equidistant from the center of a circle.
Here,
Chords AB and CD are equal to 18.
So, Chords AB and CD are equidistant from F(center of the circle).
Thus, x = 10
therefore, the value of the Perpendicular distance of F from Chord AB is 10.
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Solve the equation.
20=r+11
r=?
Answer:
9
Step-by-step explanation:
The answer is 9
Answer: 8
Step-by-step explanation:
20=r+11
-11 -11
8=r
A carpenter is making a wooden window frame that has a width of 1 inch. A window with a one-inch frame is shown. The frame is comprised of a rectangle and a semicircle. The rectangle has side lengths of 12 inches and 48 inches. The semicircle has a radius of 6 inches. The frame is 1-inch wider than the window. How much wood does the carpenter need to build the frame
The carpenter needs 1602.76 inches of wood to build the frame, which includes a 13x49 inch rectangle, a 12x48 inch rectangle, and a 7 inch radius semicircle.
Rectangle 1:
13 x 49 = 637 inches
Rectangle 2:
12 x 48 = 576 inches
Semicircle:
3.14 x 7 x 7 = 153.94 inches
Total = 637 + 576 + 153.94 = 1602.76 inches of wood
The second piece will be a rectangle with sides of 12 inches and 48 inches. The third piece will be a semicircle with a radius of 7 inches. Therefore, the carpenter will need a total of
(13 x 49) + (12 x 48) + (3.14 x 7 x 7)
= 1602.76 inches of wood to build the frame.
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A minor league baseball stadium offers general admission seats and premier seats. During the season opener, the stadium sold 1,348 tickets and had $12,748.30. The price of a premiere seat was 30% more than the $8.50 general admission seat. How many premiere seats and how many general admission seats were sold for the season opener?
The number of general admission seat sold is 842 and the number of premiere seat sold is 506.
How many of each seats were sold?The system of equations that represent the information provided in the question are:
a + b = 1348 equation 1
8.5a + (1.30 x 8.5)b = 12,748.30
8.5a + 11.05b = 12,748.30 equation 2
Where:
b = number of premiere seat solda = number of general admission seat soldThe elimination method would be used to solve these equations
Multiply equation 1 by 8.5
8.5a + 8.5b = 11,458 equation 3
Subtract equation 3 from equation 2
1290.30 = 2.55b
b = 1290.30 / 2.55
b = 506
Substitute for b in equation 1 :
a + 506 = 1348
a = 1348 - 506
a = 842
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Find the perimeter and area of these shapes asap!
Answer: #1 a=226
Step-by-step explanation:#1, split the shale into 2 parts. A small square with the 6 and 16. Then subtract six from sixteen and you have the height of the rectangle. Then take your difference (10) and multiply it with your width (19)= 190
Then do the little square which is 6x6=36. Add 190 and 36
Answer:
The area and the perimeter is 225 and 152. I'll show you how to do the rest below:
Step-by-step explanation:
For the Area you Multply all the numbers together
And for the perimeter you multiply the numbers by four
I hope you understand! let me know in the reply box
A dog kennel charges $30 per night to board your dog and $6 for each hour of playtime. The amount of money you spend is given by 30x+6y=180, where x is the number of nights and y is the number of hours of playtime. Graph the equation and interpret the intercepts. Keyboard Instructions Initial graph state The horizontal axis goes from -0.9 to 10.4 with ticks spaced every 1 unit(s). The vertical axis goes from -3.9 to 34.4 with ticks spaced every 5 unit(s).
The graph of the equation 30x+6y=180 will be a line in the xy-plane.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It is composed of one or more terms and an equal sign, and can contain constants, variables, and operators. Equations are used to represent relationships between different values, quantities, and objects, and to solve for unknowns. Equations are a fundamental tool of mathematics and can be used to describe physical processes as well as abstract concepts.
The line will pass through the origin, since the equation is satisfied when both x and y are 0. The intercepts of the line on the x-axis and y-axis represent the values of x and y that will make the equation true, regardless of the values of the other variable.
For this equation, the y-intercept is 30, since when x=0, the equation becomes 30(0)+6y=180, and so y=30. This means that if you do not board your dog, you would need to play with it for 30 hours in order to meet the requirement of spending a total of 180 dollars.
The x-intercept is 6 since when y=0, the equation becomes 30x+6(0)=180, and so x=6. This means that if you do not play with your dog, you would need to board it for 6 nights in order to meet the requirement of spending a total of 180 dollars.
Therefore, the graph of the equation 30x+6y=180 shows that it is possible to meet the requirement of spending a total of 180 dollars either by boarding your dog for 6 nights or by playing with it for 30 hours, regardless of the values of the other variable.
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The owner of a movie theater was counting the money from I day's ticket sales. He knew that a total of 150 tickets were sold. Adult tickets cost $7 each and children's tickets cost $4 each. II the total receipts for the day were $855, how many of each kind of ticket were sold?
The solution to the system of equations are
The number of adult tickets x = 85
The number of children's ticket y = 65
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 first equation be represented as A
Let the number of adult tickets be = x
Let the number of children's tickets be = y
A total of 150 tickets were sold
Substituting the values in the equation , we get
x + y = 150 be equation (1)
And , Adult tickets cost $7 each and children's tickets cost $4 each
So , 7x + 4y = 855 be equation (2)
Multiply equation (1) by 7 , we get
7x + 7y = 1050 be equation (3)
Subtracting equation (2) from equation (3) , we get
3y = 1050 - 855
3y = 195
Divide by 3 on both sides of the equation , we get
y = 65
Substitute the value of y in the equation (1) , we get
x + 65 = 150
Subtracting 65 on both sides of the equation , we get
x = 150 - 65
x = 85
Hence , the number of adult tickets x is 85 and the number of children's ticket y is 65
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When a rational number and an
irrational number are multiplied, the
product is always ___.
Answer: irrational number
Step-by-step explanation:
What is the factorization of the polynomial below?
x^2 - 5x - 36
OA. (X-9)(x+4)
OB. (x+9)(x-4)
OC. (x+9)(x+4)
OD. (X-9)(x-4)
The factorization of the polynomial is ( x - 4 ) ( x + 9 )
What is factorization?factorization is the method of breaking a number into smaller numbers that multiplied together will give that original form.
We are given the function as
x² + 5x - 36
We have to find out the two numbers when multiplied results to 36 & when subtracted results to 5.
The numbers are 9 and 4
x²+ ( 9 - 4)x - 36
Distribute x :
x² + 9x - 4x - 36
Take the common :
x ( x + 9 ) - 4 (x + 9 )
( x - 4 ) ( x + 9 )
Hence, The right answer is of Option C [ ( x - 4 ) ( x + 9 ) ]
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PLEASE HELP ME NOW THANK YOU I WILL GIVE YOU BRAINLIEST
[tex]-2(6x+36)-7x\leq 23 and 6x+10\ \textgreater \ 40[/tex]
Answer:
The first inequality can be solved by combining like terms and isolating x on one side:
-2(6x + 36) - 7x <= 23
-12x - 72 - 7x <= 23
-19x - 72 <= 23
-19x <= 95
x >= -5
The second inequality can be solved by subtracting 10 from both sides:
6x + 10 > 40
6x > 30
x > 5
The solution to both inequalities is x >= -5 and x > 5, which means that x is a real number greater than 5.
Which graph correctly shows the solution to the inequality
7- 3> 8-2003 Show or explain
your reasoning.
The given inequality can be correctly shown in the graph containing all the numbers greater than or equal to 3. The correct option is (D).
What is a number line?A number line is a graphical representation of numbers on a line.
The number line has one convention that the positive numbers are always on the right side of the origin and the negative numbers are on the left side.
The inequality is given as below,
[tex]\frac{7x-3}{9} \geq 8 - 2x[/tex]
It can be solved as follows,
[tex]\frac{7x-3}{9} \geq 8 - 2x[/tex]
Multiply both sides by 9 to get,
⇒ 7x - 3 ≥ 9(8 - 2x)
⇒ 25x ≥ 75
⇒ x ≥ 3
It implies that the solution is the set of numbers greater than or equal to 3.
Hence, the solution of inequality is obtained as number line satisfying x ≥ 3.
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A sequence is defined by the term-to-term rule
U(n+1) = U₁² +3
Given that u0= 1,
a) find u₁
b) find u₂
c) find u3
The terms of sequences are u₁ = 4, u₂ = 19 and u₃ = 364.
What is a sequence?An ordered list of things is a sequence (or events). Similar to a set, it has members (also called elements, or terms). The length of the sequence is the number of ordered items (potentially infinite).
Given:
A sequence is defined by the term-to-term rule
uₙ₊₁ = u₁² + 3
And u₀ = 1,
a). The second term
u₁ = u₀² + 3
u₁ = (1)² + 3
u₁ = 4
b). The third term
u₂ = u₁² + 3
u₂= (4)² + 3
u₂ = 19
c). The fourth term
u₃ = u₂² + 3
u₃ = (19)² + 3
u₃ = 364
Therefore, The values, u₁ = 4, u₂ = 19 and u₃ = 364.
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Find length of third side help please
Length of third side = 10 units.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
Here, given that,
Height = 7 units
Base = √51 units
And, we have, it is a right angle triangle
and we have to find the hypotenuse.
By Pythagorean theorem we get,
Hypotenuse = √7²+ 51
=√100
=10 units.
Hence, Length of third side = 10 units.
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8 dm to 3.2 dm
pls helppp
Answer:
8 dm decreased 60%
Step-by-step explanation:
8-3.2=4.8
4.8/8=0.6
0.6=60%
Natalia spent an eighth of the money in her
account on a shopping spree plus an
additional $20 on gas. If she spent $320, how
much did she originally have in her account?
Answer:
2420
Step-by-step explanation:
since it’s an eighth, you need to multiply 300 by 8 but not 320 since it’s separate. so you get 2400 but then add the 20 and get 2420
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. Find the ratio of the volume of the balloon in both the cases.
Solve for y 6x+2y=10
On solving the provided question, we can say that - the value of the following equations is 6(0) + 2y = 10y = 5
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
6x + 2y = 10
so, x = 0;
6(0) + 2y = 10
y = 5
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PLS HELP WILL MARK BRAINIEST
The given figure is a polygon, a quadrilateral and a trapezoid.
What is a polygon?A polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.
Given is a figure,
The figure is a polygon, a quadrilateral and a trapezoid.
It can not be a parallelogram, rhombus or a rectangle, because none of their properties are shown in the figure.
Hence, the given figure is a polygon, a quadrilateral and a trapezoid.
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