Answer:
probability result of sample space would result in 12/144
Step-by-step explanation:
as result there is 12 numbers on each dice, blth have exact same numbers, resulting in 144 combinations ti be thrown as sample space event outcome wluld be;
1/1 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 1/11 1/12
2/1 2/2 2/3 2/4 2/5 2/6 2/7 2/8 2/9 2/10 2/11 2/12
3/1 3/2 3/3 3/4 3/5 3/6 3/7 3/8 3/9 3/10 3/11 3/12
4/1 4/2 4/3 4/4 4/5 4/6 4/7 4/8 3/9 4/10 4/11 4/12
5/1 5/2 5/3 5/4 5/5 5/6 5/7 5/8 5/9 5/10 5/11 5/12
6/1 6/2 6/3 6/4 6/5 6/6 6/7 6/8 6/9 6/10 6/11 6/12
7/1 7/2 7/3 7/4 7/5 7/6 7/7 7/8 7/9 7/10 7/11 7/12
8/1 8/2 8/3 8/4 8/5 8/6 8/7 8/8 8/9 8/10 8/11 8/12
9/1 9/2 9/3 9/4 9/5 9/6 9/7 9/8 9/9 9/10 9/11 9/12
10/1 10/2 10/3 10/4 10/5 10/6 10/7 10/8 10/9 10/10 10/11 10/12
11/1 11/2 11/3 11/4 11/5 11/6 11/7 11/8 11/9 11/10 11/11 11/12
12/1 12/2 12/3 12/4 12/5 12/6 12/7 12/8 12/9 12/10 12/11 12/12
giving 12 matching numbers in a 144 possible rolled outcome
mathematic formula would be P(A) = n(A)/n(S)
As P(A)= probabolity of event A
n(A)= number of favouravle outcome
n(S)= total number of outcome in sample space
giving
12=2/144=0,0138888889
X – 3 = 7 so X = thank
Answer:
x=10
Step-by-step explanation:
x-3(+3)=7+3
We need to add 3 to both sides to isolate x.
x=10
Answer:
x = 10Step-by-step explanation:
x - 3 = 7
x = 7 + 3
x = 10
The sky wheel has 42 glass enclosed gondolas. What is the measure of each central angle between gondola cars, to the nearest hundredth degree?
A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus, the measure of each central angle required in the question is [tex]8.6^{o}[/tex].
A sky wheel is a mechanical device that has a shape of a circle divided into a given number of equal sectors. Thus each sector has an equal central angle. Since the sum of the internal angles of a circle is [tex]360^{o}[/tex].
From the given question, it has been stated that the sky wheel has 42 glass-enclosed gondolas. This implies that the sky wheel has been divided into 42 equal sectors.
Therefore,
the measure of each central angle = [tex]\frac{360^{o} }{n}[/tex]
where n represents the number of gondolas (42).
Thus,
the measure of each central angle between gondolas cars= [tex]\frac{360}{42}[/tex]
= 8.5714
The measure of each central angle between gondolas cars is approximate [tex]8.6^{o}[/tex].
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please help if u can! greatly appreciated
don't answer if u dont know PLEASE
a. log₈8 = 1
b. log₇6/5
c. log₉3¹
The solution to the problem are1. log₈ 2 * 4 would produce an integer
= log₈8 = 1
The output is an integer
2. log₇6/5 would give us an irrational number
= log₇1.2
This would give us an irrational number
3. log₉3¹ would give us a rational number
= log₉9^[tex]^\frac{1}{2}[/tex] = 1/2 log⁹9
= 1/2
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A bowling ball weighs 15 pounds on earth and weighs 4 pounds on the planet saturn. you could determine a 100–pound earthling's weight on saturn using the proportion: a. startfraction 15 over 4 endfraction = startfraction b over 100 endfraction c. startfraction 4 over 15 endfraction = startfraction 100 over b endfraction b. startfraction 15 over 4 endfraction = 100 over b endfraction d. either a or c
100–pound earthling's weight on Saturn using the proportion is (B)
15/4 = 100/x.
What is proportion?The size, number, or quantity of one object or group of things in comparison to another thing or group of things In our class, the ratio of guys to girls is two to one (2:1).To find the 100–pound earthling's weight on Saturn using the proportion:
Weight of ball on Earth = 15 poundsWeight of ball on Saturn= 4 poundsLet 100 pounds of earthling weight on Saturn be x pounds.Thus, the proportion is 15:4 = 100:x15/4 = 100/xTherefore, 100–a pound earthling's weight on Saturn using the proportion is (B) 15/4 = 100/x.
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The correct question is given below:
A bowling ball weighs 15 pounds on earth and weighs 4 pounds on the planet Saturn. you could determine a 100–pound earthling's weight on Saturn using the proportion:
a. start fraction 15 over 4 end fraction = start fraction x over 100 end fraction
b. startfraction 15 over 4 endfraction = 100 over x endfraction
c. startfraction 4 over 15 endfraction = startfraction 100 over x endfraction
d. either a or c
Carrie spent
1
4
of her allowance on a shirt,
1
3
of her allowance on a skirt, and $8 on a belt. If she spent $22 in all, how much was Carrie’s allowance?
Answer:
24 dollars.
Step-by-step explanation:
1/4 + 1/3 = 3/12 + 4/12 = 7/12
7/12 a + 8 = 22
7/12 a = 14
a = 14 x 12/7
a = 24
How to factorise completely please help this is algebra
Answer:
Below in bold.
Step-by-step explanation:
9t^2 - u^2 (the difference of 2 squares)
= (3t - u) (3t + u).
2c - 4d - pc + 2pd
= 2(c - 2d) - p(c - 2d)
c -2d is common to both parts so the factors are:
(2 - p)(c - 2d)
2 Question is down below.
The height of the flagpole is 12.4 meters and the altitude of the balloon is 29.1 meters
How tall is the flagpole?See attachment for the diagram, when redrawn
Start by calculating the length AB using the following tangent function
tan(22) = BC/AB
This gives
tan(22) = 9/AB
Make AB the subject
AB = 9/tan(22)
Evaluate the quotient
AB = 22.3
The length DB is then calculated using:
tan(9) = DB/AB
This gives
tan(9) = DB/22.3
Make DB the subject
DB = 22.3 * tan(9)
Evaluate
DB = 3.35
The height of the flagpole is then calculated as:
Height = DB + BC
This gives
Height = 3.35 + 9
Evaluate
Height = 12.35
Approximate
Height = 12.4
Hence, the height of the flagpole is 12.4 meters
How to determine the altitude of the balloon?The diagram that illustrates the scenario is added as an attachment
Calculate the value of y using the following tangent functions
tan(57) = x/y and tan(72) = (15 + x)/y
Make y the subject in tan(57) = x/y and tan(72) = (15 + x)/y
y = x/tan(57) and y = (15 + x)/tan(72)
Substitute y = x/tan(57) in y = (15 + x)/tan(72)
x/tan(57) = (15 + x)/tan(72)
Evaluate the tangent ratios
x/1.5 = (15 + x)/3.1
Cross multiply
3.1x = 22.5 + 1.5x
Evaluate the like terms
1.6x = 22.5
Divide by 1.6
x = 14.1
The altitude of the balloon is then calculated as:
Altitude = 14.1 + 15
Altitude = 29.1
Hence, the altitude of the balloon is 29.1 meters
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Which value is a solution for the equation tan/2=-1
The value of the solution is 3π/2.
What is a trigonometric equation?
An equation involving one or more trigonometric ratios of unknown angles is called a trigonometric equation.
tan x/2 = -1
tanx/2 = tan(-π/4)
tanx=tanФ
⇒ The general equation of tanx=tanФ is
⇒ x=nπ+Ф
x/2=nπ+(-π/4)
at n=0
x/2=-π/4
x=-π/2
at n=1
x/2=π-π/4
x/2=3π/4
x=3π/2
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Disclaimer: The question was given incomplete on the portal. Here is the complete question.
Questions: Which value is a solution for the equation tan x/2 = -1?
A. 5pi/4
B. 7pi/4
C. 3pi/4
D. 3pi/2
Given a polynomial function f(x) = 2x2 7x 6 and an exponential function g(x) = 2x 5, what key features do f(x) and g(x) have in common?
f(x) = 2x² + 7x + 6 and g(x) = 2^x + 5 have -
Equal y-intercept at (0,6)Same end behavior as x approaches positive infinityHow to determine the common features of the polynomial equations?
The equation of the functions are given as:
f(x) = 2x² + 7x + 6 &
g(x) = 2^x + 5
Next, we plot the graph of both functions (see attachment)
From the graph, we have the following highlights
The y-intercept of both functions is (0,6)Both functions approach positive infinity as x approaches positive infinityTo learn more about polynomial functions from given link
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The answer to question 5 is “x(x-2y)(3x-2y)” and the answer to question 6 is “(x-y)(2-x+y)”. I know these answer cause I have the answer book but I don’t know how to get the answer . Can some one solve questions 5 and 6 with the steps to get these answers cause I have to show my work but I don’t understand how to get the answers . Also use the substitution method like I did in question 4.(urgent !!)
What is an algebraic expression?
An expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, etc.
What is the substitution method?
The substitution method is generally used to solve the system of equations. In this method, first, solve the equation for one variable, and substitute the value of the variable in the other equation
5th question :
⇒ x(2y-x)²+2x²(x-2y)
let (x-2y) = A
⇒we can also write (2y-x)² as (x-2y)² as both have the same value
x(x-2y)²+2x²(x-2y)
x(A)²+2x²(A)
By taking xA common
⇒ xA(A+2x)
On putting the value of A=(x-2y)
⇒ x(x-2y) (x-2y+2x)
⇒x(x-2y) (3x-2y)
6th question :
2(x-y)-(y-x)²
let (x-y) = B
⇒we can also write (y-x)² as (x-y)² as both have the same value
2(x-y)-(x-y)²
2B-(B)²
By taking B common
⇒ B(2-B)
On putting the value of B=(x-y)
⇒(x-y) (2-{x-y})
⇒(x-y) (2-x+y)
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Dario is the kicker for his high school football team. The path of the football when kicked can be
represented by the quadratic function y = -16x²
-16x2 +85x, where x is the horizontal distance (in
feet) and y is the height (in feet). How far does Dario kick the football? Express your answer as a
decimal rounded to the nearest hundredth.
Answer:
Assunming that the equation is y = -16x² +85x, I suggest Dario find a new profession. He kicks the ball 133 feet high, but it only travels 2.7 feet downfield at that point. It will have travelled 2*2.7 feet or 5.4 feet horizontal when it returns to ground.
Step-by-step explanation:
We can answer the question of how hiogh and far the ball travels (in feet) by either of two methods. The first is to differentiate the equation and set it equal to 0, and the second is the graph it and look for the vertex and x intercept.
Differentiate
y = -16x² +85x
The first derivative produces an equation that gives us the slope of the line at any point x. At the ball's top height, it stops and reverses direction, a point at which the slope is zero.
y = -16x² +85x
d(y)/d(x) = -32x + 85
0 = -32x + 85
32x = 85
x = 2.66 feet horizontal distance when the ball reaches its peak.
At x = 2.66, y is 112.9 feet high
When the ball returns, it adds amnother 2.66 feet to the horizontal distance, for a total of 5.4 feet.
Graph:
See attached plot of the function.
Horizontal distance is 2.66 feet and height is 133 feet. The x-intercept is at 5.4 feet.
After all that, the ball only travelled downfield (we hope downfield) a total of 5.4 feet.
PLEASE HELP, I REALLY NEED IT!!!
The number which is express in each of the models as given in the image attached to the task content are as follows;
a). 1.37
b). 1.37
c). 1.37.
What numbers are expressed according to the given models in the task content?It follows from the task content that the models describe that One flat represents 1 whole, One rod represents 1 tenth and one unit represents 1 hundredth.
It therefore follows from the task content that in each of the models, the algebraic sum of flat(s), rods and units as the case may be results in the value; 1.37 as the utmost number represented by the models.
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2. G.GPE.7 Consider ∆ABC below. What is the perimeter of ∆ABC? * A. 16.9 B. 12.9 C. 18.6 D. 17.4
Answer:B
Step-by-step explanation:
Matrix a is a 6 × 5 matrix. which order of matrix can be multiplied by matrix a to create matrix ab?
Order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
What is a matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions that are organized in rows and columns to represent a mathematical object or an attribute of such an object in mathematics. For instance, consider a matrix with two rows and three columns.To find the order of matrix:
We must first check the dimension of two matrices, say matrix A by matrix B, before we may multiply them.Multiplication is achievable if the number of columns in the first matrix, A, equals the number of rows in the second matrix.Dimension is assigned to the provided matrix: 6 × 5This means the given matrix contains six rows and five columns.As a result, the second matrix MUST have 5 rows in order for multiplication to be POSSIBLE.The only matrix with 5 rows among the above alternatives is the matrix with dimension (B) 5 × 6.To prove:
In other words, the inner products of the dimensions should be equal.That is; (a × b)(b × a) is possible but (a ×b)(c × b) is impossible.The dimensions of the matrix are given by, row × column.Therefore, order (B) 5 × 6 of the matrix can be multiplied by matrix a to create matrix ab.
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Instructions: Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
The volume of the cone is 84.9 km³
How to find the volume of a cone?Volume of a cone = 1 / 3 πr²h
where
h = heightr = radiusTherefore,
radius = 3 km
height = √9.5² - 3²
height = √81.25
height = 9.01387818866
height = 9.014 km
Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014
volume of the cone = 254.732197612 / 3
volume of the cone = 84.9107325372
volume of the cone = 84.9 km³
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Which graph represents the function f(x)= 2x-1 x-1 ?
Answer:
The bottom graph.
Step-by-step explanation:
The asymptote ( in between the 2 curves) on the bottom graph is at x = 1, because when x = 1 the denominator = 0.
I don't understand this question... Can anyone explain this to me please?
Answer:
First answer lol
Step-by-step explanation:
is the domain by any chance x ≥-2?
Please Solve the following #6 and #7. Answer: C, A
6) For the inverse to be a function, f(x) needs to be one to one. To accomplish this, restrict the domain to one side of the axis of symmetry
7) The y-intercept of the inverse is when x=0. This means we want to find when f(x)=0.
[tex]4(1/3)^x = 16 \\ \\ (1/3)^x= 4 \\ \\ x=\log_{1/3}(4) \approx -1.26[/tex]
need some help, please
Answer:
c = 15
Step-by-step explanation:
expand the left side and compare with like terms on the right side
2x(4x + 5) + 3(4x + 5) ← distribute parenthesis
= 8x² + 10x + 12x + 15 ← collect like terms
= 8x² + 22x + 15
compare to ax² + bx + c
then c = 15
Find the value of z.
Applying the angle of intersecting chords theorem, the value of z is: D. 100.
What is the Angle of Intersecting Chords Theorem?According to the angle of intersecting chords theorem, in a circle like the one shown in the image above, where two chords intersect to form vertical angles, the theorem states that the angle formed equals half of the sum of the measures of the arcs intercepted by the angles.
Applying the angle of intersecting chords theorem, let's find x first:
73 = 1/2(96 + x)
Multiply both sides by 2
2 × (73) = 1/2(96 + x) × 2
146 = 96 + x
Subtract both sides by 96
146 - 96 = 96 + x - 96
50 = x
x = 50°
Therefore:
x + z + 96 + 114 = 360° [full circle measure]
Plug in the value of x
50 + z + 96 + 114 = 360
z + 260 = 360
Subtract both sides by 260
z + 260 - 260 = 360 - 260
z = 100°
The answer is: D. 100°.
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NEED HELP ASAP
let h(x)=-1/3x+2. Find -4h(9)
Answer:
4
Step-by-step explanation:
h(x) = -1/3x+2 where we need to find -4h(9)
h(9): x = 9
h(x) = -1/3(9) + 2
h(x) = -3 + 2
h(x) = -1
-4h(9) is -4h(x):
-4(-1) = 4
4√2/9+√2+√1/18. 1/√3-1-1/√3+1
Answer:
Exact form: 78√2 - 17√3 / 54
Decimal form: 1.49747766
Step-by-step explanation:
Rationalize and simplify the expression.
Based on the graph which congruence theorems or postulates are reasons why these graphs are equal?
Triangles DEF and JKL can be proven to be congruent triangles based on:
C. ASA
E. AAS
F. LA
What is the ASA Congruence Theorem?The ASA congruence theorem states that if two triangles that are have two pairs of corresponding congruent angles and a pair of corresponding included congruent sides, then both triangles are congruent to each other.
What is the LA Congruence Theorem?The LA congruence theorem states that two right triangles are congruent if they have a pair of congruent legs and a pair of congruent angles that are corresponding to each other.
What is the AAS Congruence Theorem?The AAS congruence theorem states that two triangles with two pairs of congruent angles and a pair of congruent non-included sides are congruent.
From the image given, triangles DEF and JKL can be proven to be congruent triangles using the LA, AAS, and ASA congruence theorems.
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On saturday evening 5450 people visited india gate. out of these 1265 were men 1150 were woman and rest were children. how many children visited the india gate?
3435 were children visited the India gate.
What is a linear equation in math?
A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.Given,
men = 1265
women = 1150
Total women and men -
men + women = 2415
= 5450-2415 ⇒ 3435
Therefore, 3435 were children visited the India gate.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, Tysm!
Answer:
x=1
Step-by-step explanation:
2/3(9x-6) = 1/4(12-4x)
We want to solve for x
Distribute
6x-4=3-x
Add x to each side
6x-4+x = 3-x+x
7x-4 = 3
Add 4 to each side
7x-4+4 = 3+4
7x=7
Divide by 7
7x/7 = 7/7
x=1
Answer:
x = 1
Step-by-step explanation:
[tex]\frac{2}{3}[/tex] (9x - 6) = [tex]\frac{1}{4}[/tex] (12 - 4x) ← distribute parenthesis on both sides
6x - 4 = 3 - x ( add x to both sides )
7x - 4 = 3 ( add 4 to both sides )
7x = 7 ( divide both sides by 7 )
x = 1
Joel wanted his mom to buy a super-sized box of his favorite cereal, but his mom didn't think it would fit in her cupboard. The box had a volume of 6900 cm3, and the base was 23, the depth, 10. How high was it?
The height of the box would be = 30cm.
How to calculate the height of the box from the given volume?The volume of the box = 6900 cm3
The base of the box = 23 cm
The depth of the box = 10cm
Therefore the height of the box can be gotten from the formula used to calculate the volume of the box. That is;
Volume = base×depth×height
6900 = 23×10×h
make h the subject of formula;
height = 6900/230
= 30cm
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9) In the standard co-ordinate system, which of the following points in the greatest distance from origin? A. (-4, -1) B. (-3, 3) C. (4,0) D. (2, 3)
The point with the greatest distance to the origin is given by:
B. (-3, 3).
What is the distance between two points?Suppose that we have two points, [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The distance between them is given by:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The origin is given by point (0,0), hence the distance of a point (x,y) to the origin is given by:
D = sqrt(x² + y²).
Hence the distances for each point given in the problem are:
A. Distance = sqrt((-4)² + (-1)²) = sqrt(17).B. Distance = sqrt((-3)² + (3)²) = sqrt(18).C. Distance = sqrt((4)² + 0²) = sqrt(16).D. Distance = sqrt((2)² + 3²) = sqrt(13).Hence option B has the greatest distance.
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Which measurements of triangle BAC are correct
The measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
Trigonometrical ratiosFrom the question, we are to determine which of the given trigonometrical ratios for the given triangle are correct
The given triangle is a right angle triangle
Using SOH CAH TOA
sin C = 9/15
∴ The option sin C = 9/15 is correct
Also,
Using SOH CAH CAH
tan B = 12/9
∴ The option tan B = 9/12 is NOT correct
To determine the measure of angle B (m ∠B)
From tan B = 12/9
Then,
tan B = 1.33333
B = tan⁻¹(1.33333)
∴ B ≈ 53.13°
Thus, the option B ≈ 53.13° is correct
Hence, the measurements that are correct for the given triangle are
sin C = 9/15
B ≈ 53.13°
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How would you find the area or perimeter of this shape?
The perimeter of a given shape implies the sum of all its sides. While the area of a given shape is the total value of space it would cover on a 2-dimensional plane.
The perimeter of the shape is 104 cm.
The area of the shape is 640 [tex]cm^{2}[/tex].
The perimeter of a given shape implies the sum of all its length of sides., such that the value of each individual side is summed to a total value.
The area of a given shape is the total value of space it would cover on a 2-dimensional plane. The area of shapes depends on the type of shape.
In the given question, the given shape has 12 sides. Some of these sides can sum up to a given length as shown in the diagram.
So that;
perimeter = 2 + 32 + 10 + 10 + 2 + 32 + 8 + 8
= 104 cm
Thus, the perimeter of the shape is 104 cm
ii. The area of the shape = length x width
= 32 x 20
= 640 [tex]cm^{2}[/tex]
Therefore, the area of the given shape is 640 [tex]cm^{2}[/tex].
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Evacuate the following using suitable identities (102)^3
The value of [tex](102)^3[/tex] exists 1061208.
How to estimate the value of [tex](102)^3[/tex]?Let us rewrite [tex](102)^3[/tex] as [tex](100+2)^3[/tex]
Now utilizing the identity [tex](a+b)^3=a^3+b^3+3ab(a+b)[/tex], we get
a = 100 and b = 2 then substitute the values of a and b then
[tex](100+2)^3=100^3+2^3+[(3\times100\times2)(100+2)][/tex]
= 1000000 + 8 + (600 × 102)
= 1000000 + 8 + 61200
= 1061208
Hence, [tex](102)^3=1061208[/tex]
Therefore, the value of [tex](102)^3[/tex] exists 1061208.
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