The sum of the weight of the empty box and the 940 feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kg.
What is a scientific notation?A number is expressed using scientific notation when it contains a number larger than 1 but less than 10, that multiplies a power of 10
The empty weight of the box = 56.7 grams
The number of feathers added = 940 feathers
Mass of one feather (unit weight) = 0.000567 kilogram
The total weight of the box with the 940 feathers is found as follows;
56.7 grams = 0.0567 kilograms
Mass of the empty box in kilograms = 0.0567 kilograms
Total mass of the 940 feathers 0.000567 × 940 = 0.53298 kilograms
The total weight of the box with the 940 feathers inside is; 0.0567 kilograms + 0.53298 kilograms = 0.58968 kilograms
The total weight of the box and the feathers = 0.58968 kilograms =
[tex]5.8968 \times {10}^{ - 1} [/tex]
kilograms
Rounding the coefficient to the nearest tenth gives;
The total weight of the box and the feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kilograms
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I need to find the one real answer
The missing value for which there is one solution of the equation are 13, -11 and 11.
What is defined as the solution of the equation?A mathematical equation expresses that two expressions seem to be equal. 4+4=8 is a mathematical formula. A mathematical formula with one or more variables is known as an algebraic equation. It has a first-degree variable (x) and a straight line graph.The method of identifying the number that what a variable represents is known as solving an equation. The value obtained is known as the equation's solution. An equation is a mathematical language that claims that two algebraic expressions has to be equal in nature.For the given question,
The expression is given as;
(4/3)(-9x + 12) - x = _x - 9
Putting, 13, -11 and 11 will given the one solution of the equation.
Except -13 as expression is not defined for it.
Put -13 at the blank space and solve it,
-12x + 48 - x = - 13 x - 9
- 13x + 48 = -13x - 9
-13x will get cancelled.
Thus,
48 = -9
But,
48 ≠ -9
Thus, -13 is not a solution of the expression.
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The ratio of chocolate chip cookies to oatmeal raisin cookies in the cookie box is 1 to 4. If there are 2 chocolate chip cookies in a cookie box, how many the total chocolate chip and oatmeal raisin cookies are there in the cookie box?
Based on the given ratio, the total number of chocolate chip and oatmeal raisin cookies in the cookie box is 10.
What is the ratio?The ratio refers to the numerical relationship that one value or number bears to another.
Ratios are fractional values, showing how much a value is contained in another, or in relation to another.
Ratios are depicted using the ratio sign (:), fractions, decimals, or percentages, like proportions.
The ratio of chocolate chip cookies to oatmeal raisin cookies = 1:4
The sum of ratios = 5 (1 + 4)
The number of chocolate chip cookies in the cookie box = 2
Using the above ratio, there will be 8 oatmeal raisin cookies, that is 2/1 x 4
The total number of cookies (both types) in the cookie box = 10 (2/1 x 5).
Thus, we can conclude that based on the relative sizes of both cookies, the total number in the box is 10.
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if p varies directly as q.for p =4.5 when q=12 .find(1) the relationship between p and q (2) p and q=16
( 1 ) If p varies directly as q, for p = 4.5 when q = 12, then the relationship between p and q is p = kq represented as 4.5 = (8/3)12
( 2 ) If p and q is 16 then the direct variation is 1
What is direct variation?Any time one quantity directly affects the other, such as when one quantity rises relative to the other and vice versa, there is a direct variation between the two variables. It is the relationship between two variables where one of the variables is a fixed multiple of the other. Since the two variables are directly correlated, they are also known as directly proportional.
There are two kinds of proportionalities: direct variation and inverse variation. When two quantities are multiplicatively connected by a constant, the relationship is said to be proportional. In a direct variation, the ratio of the two quantities stays the same, whereas in an inverse variation, the product of the two quantities stays the same.
If p varies directly as q
for p = 4.5
when q = 12
Then p = kq
4.5 = 12k
k = 12/4.5
k = 8/3
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What is the image of the point ( − 1 , 2 ) after a rotation of 270 counterclockwise about the origin?
The mass of Earth is 5.97 × 10^24 kg.
The mass of Mercury is 3.29 × 10^23 kg.
The ratio of the mass of Earth to the mass
of Mercury can be written in the form
1: n.
Calculate the value of n.
Give your answer as an ordinary number
to 2 significant figures.
The value of n is 0.06.
What is the ratio between two quantities?A fraction that demonstrates how many times one quantity is of the other is the ratio of two quantities of the same kind and in the same units. The ratio is represented by the sign ":". The expression a/b, which stands for the ratio of two quantities a and b (b ≠0), is used.Given:
The mass of Earth is 5.97 × 10²⁴ kg.
The mass of Mercury is 3.29 × 10²³ kg.
The ratio of the mass of Earth to the mass of Mercury is represented as 1: n.
The ratio of the mass of Earth to the mass of Mercury can be calculated as,
= mass of Earth/mass of Mercury
⇒ [tex]\frac{5,97*10^{24} }{3.29*10^{23} } = \frac{1}{n}[/tex]
⇒ n = 0.0551
⇒ n ≅ 0.06 ( 2 significant figures)
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Determine the momentum of a system that consists of two objects. One object, m1, has a mass of 6 kg and a velocity of 13 m/s in the direction of the positive x-axis and a second object, m2, has a mass of 14 kg and a velocity 7 m/s in the direction of the negative x-axis.
Answer:
The solution to the question will be explained better using the image below
Concept:
The formula to calculate momentum is given below as
[tex]\begin{gathered} momentum=mass\times velocity \\ m=mv \end{gathered}[/tex]The first momentum will be
[tex]\begin{gathered} m_1=m_1v_1 \\ m_1=6\times13 \\ m_1=78kg\text{ m/s} \end{gathered}[/tex]The second momentum will be
[tex]\begin{gathered} m_2=m_2v_2 \\ m_2=14kg\times7 \\ m_2=98kg\text{ m/s} \end{gathered}[/tex]Since they are moving in different directions,
We will substract both momentums
[tex]\begin{gathered} momentum=m_1v_1-m_2v_2 \\ momentum=78-98 \\ momentum=-20kg\text{ m/s} \end{gathered}[/tex]Hence,
The momentum of a system that consists of two objects should be 20 kg m/s in the direction of the negative x-axis
please help me with this
The angle 4 is an alternate angle to 80° and this tells us that; ∠4 = 80°
How to find alternate angles?Alternate angles are defined as the angles that occur on opposite sides of the transversal line and have the same size. Thus, Alternate angles are always equal.
These interior alternate angles can be gotten by drawing a Z shape which produces two different types of alternate angles namely alternate interior angles and alternate exterior angles.
Now, we are given that only one known angle in the image which is 80°. However, we see that the angle we want to find which is angle 4 is an alternate angle to the known angle.
Thus, by definition of alternate angles, we can say that ∠4 = 80°
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The product 7 and the square of a number
The algebraic expression for the statement the product 7 and the square of a number is 7x²
What are algebraic expressions?Algebraic expressions are described as mathematical expressions that consist of arithmetic terms, factors, constants, variables and coefficients.
These expressions are also composed of arithmetic operations which may include;
SubtractionMultiplicationAdditionBracketDivisionParentheses, etcFrom the information given, we have that;
The product 7 and the square of a number
Now, let the number be x
The square of x is x²
This statement is expressed as;
7x²
Thus, the expression is 7x²
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The complete question:
The product 7 and the square of a number. Write the algebraic expression
I have a problem what is 27 divided by 655
Answer:
0.04122137404 is the answer
Answer: 0.041221374
Step-by-step explanation: According to Bing, 0.041221374 is your answer.
1. no association 2. negative association 3. positive association 4. nonlinear association
From the graph it can be observed that line fits curve and line has positive slope as increase in hours cause increase in miles.
The line with postive slope represent the positive relation between the variables. So there is postive association between miles and time spent for running.
Answer: positive association
test score hours studying 2 3 4 test score 44 66 88 test score ratio hours studying 22 1 ? ?
The test score ratio for studying 2 : 2 : 1 hours is represented as
44 : 44 : 22
What is a ratio?The comparison of two similar quantities or the relationship between them is known as a ratio. Using ratio symbols or words, ratios can be expressed in three different ways while maintaining their meaning.
To put it another way, ratios can be expressed by putting a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.
If 2 hours of studying = 44 marks
If 3 hours of studying = 66 marks
If 4 hours of studying = 88 marks
Then total sum of hours of studying = 9 hours
9 hours of studying = Sum of all marks
= 44 + 66 + 88
= 198
1 hour of studying = 198/9
= 22 marks
So, the test score ratio for studying 2 : 2 : 1 hours is represented as
44 : 44 : 22
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Represent the quadratic function
For the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to y = x² - 14x + 48 .
As given in the question,
From the table of ordered pairs, it is observed that the zeros of the quadratic function are at x = 6 and x = 8. The zeros are the points where the y value of the function becomes zero.
An equation of the function in the standard form is given by :
y = (x - 6)(x - 8)
⇒y = x (x - 8) - 6 (x - 8)
⇒ y = x² -8x -6x +48
⇒ y = x² -14x + 48
The quadratic function is represented as the product of the zeros of the graph when plotted on a Cartesian plane.
Therefore, for the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to y = x² - 14x + 48 .
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Find the lateral surface area and volume of the solid object in picture
Notice that s stands for the slant height of the pyramid, and this height is the height of each one of the lateral triangular faces.
We will need to use the next formulas
[tex]\begin{gathered} A_{\text{hex}}=\frac{3\sqrt[]{3}}{2}a^2\to\text{Area of a regular hexagon (a is one of its sides)} \\ A_{\text{tri}}=\frac{bh}{2}\to\text{Area of a triangle} \end{gathered}[/tex]Therefore, the surface area is
[tex]\begin{gathered} A_{\text{figure}}=A_{\text{hex}}+6\cdot A_{\text{tri}}=\frac{3\sqrt[]{3}(3)^2}{2}+6\cdot\frac{(3\cdot10.3)}{2} \\ =\frac{27\sqrt[]{3}}{2}+92.7 \\ \Rightarrow A_{\text{figure}}=\frac{27\sqrt[]{3}}{2}+92.7 \\ \Rightarrow A_{\text{figure}}\approx23.4+92.7=116.1 \\ \Rightarrow A_{\text{figure}}=116.1 \end{gathered}[/tex]Lateral Area=116.1 m^2
As for the volume, the volume of a regular pyramid is
[tex]V=\frac{A_{\text{base}}\cdot h}{3}[/tex]In our case,
[tex]V=\frac{3\sqrt[]{3}a^2}{2}\cdot\frac{h}{3}=\frac{\sqrt[]{3}}{2}a^2h[/tex]Therefore,
[tex]\Rightarrow V=\frac{\sqrt[]{3}}{2}(3)^2\cdot10=45\sqrt[]{3}[/tex]Volume= 77.9 m^3
suppose that 15 inches of wire cost 60 cents. at the same rate, how much (in cents) will 11 inches of wire cost
The cost of 11 inches of wire will be 44 cents
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
The 15 inches of wire costs 60 cents, so the cost of 1 inch of wire is;
Rate = 60/15 =4 cents
So the cost of 1 inch of wire which is the rate of 4 cents.
Now we have to find the cost (in cents) of 11 inches wire.
We know the cost of 1 inch of wire cost 4 cents so the cost of 11 inches of wire is;
= Total inches of wire x Price of 1 inch of wire
= 4 x 11
= 44
Tehrefore, The cost of 11 inches of wire is 44 cents
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Solve the formula for the small base b
Value of b is 2Ah - B.
What is area?The area that an object's shape designates as being within it. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area. Area is the entire amount of space occupied by the shape of an object or a flat (2-D) surface.
On a piece of paper, draw a square with a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.
Numerous 2-D shapes, such as circles, triangles, squares, rectangles, parallelograms, and trapezoids, may be found all around us. On paper, you can trace each of these shapes. Since every shape is distinct and varied, its area is also determined in a different way.
Given Data
A= [tex]\frac{1}{2}[/tex]h ( B + b)
For the value of b
b + B = 2Ah
b = 2Ah - B
Value of b is 2Ah - B.
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7 lorries can carry 987 cartons of books. How many cartons of books can each lorry carry
Answer:
141 each
Step-by-step explanation:
The points H(3,-1), I(-6, -1), and J(3,-9) form a triangle. find the
perimeter of the triangle?
The perimeter of the given triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
The points which form a triangle are:
H(3,-1) ; I(-6,-1) and J(3,-9)
Perimeter of the given triangle with vertices H(3,-1); I(-6,-1) and J(3,-9) is required:
To find the length we have to find the distance between the points.
Using distance formula i.e.
[tex]\sqrt{ [ (x2 - x1)^2 + (y2 - y1)^2 ][/tex]
Let the length of the sides be A1, A2 , A3
On applying the distance formula to H(3,-1) and I(-6,-1) ;
We get,
A1 = [tex]\sqrt{[ (-6-3)^2 + (-1+1)^2 ][/tex]
= [tex]\sqrt{ [ (-9)^2 + (0)^2 ][/tex]
= [tex]\sqrt[ 81 + 0 ]}[/tex][tex]\sqrt{[ 81 + 0 ][/tex]
= [tex]\sqrt{81}[/tex]
= 9
On applying the distance formula to I(-6,-1) and J(3,-9);
We get,
A2 = [tex]\sqrt{ [ (3+6)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (9)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{[ 81 + 64 ][/tex]
= [tex]\sqrt{145}[/tex]
= 12.04
On applying the distance formula to J(3,-9) and H(3,-1);
We get,
A3 = [tex]\sqrt{[ (3-3)^2 + (-9+1)^2 ][/tex]
= [tex]\sqrt{[ (0)^2 + (-8)^2 ][/tex]
= [tex]\sqrt{ [ 0 + 64 ][/tex]
=[tex]\sqrt{64}[/tex]
= 8
Hence,
The perimeter is 9 + 12.04 + 8 = 29.04
The perimeter of the triangle having vertices H(3,-1); I(-6,-1) and J(3,-9) is 29.04.
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A hang glider dropped his cell phone from a height of 450 feet. How many seconds did it take for the cell phone to reach the ground? Use radical equations and round to the nearest tenth.
The cell phone will takes about 4.7 seconds to reach the ground.
What are equations of motion?There are three equation of motions that can be used when motion of the object is under constant acceleration and on a straight path.
They are listed below as:
[tex]v = u + at\\\\s = ut + \dfrac{1}{2} at^2\\\\v^2 = u^2 + 2as[/tex]
where u = initial velocity of the considered object
v = final velocity of the object
a = acceleration of the object
s = distance traveled by the object in 't' time.
Given that hang glider dropped his cell phone from a height of 450 feet:
Acceleration is rate of change of velocity.
[tex]s = ut + \dfrac{1}{2} at^2[/tex]
Height = h = 450 feet
Gravitational Acceleration = g = 9.8 feet/s²
Initial Velocity = u = 0 m/s
h = 1/2at²
h = √2h/g
h = √2 x 450/ 9.8
h = 9.58 s.
Therefore, the cell phone will take 9.58 seconds to reach the ground.
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On a number line, what is the distance between −17 and 9?
Responses
A 2020
B -26-26
C -8-8
D 88
E 26
Using the subtraction between integers, it is found that the distance between -17 and 9 is given by:
B. -26.
How to subtract two numbers of different signals?When we subtract a positive by a negative, the result is always positive.
This is because the result will take the negative makes the signal of the negative number being inverted, then the negative becomes a positive and is added to the first amount.
For this problem, the numbers are given by:
-17 and 9.
The distance between two points on a number line is given by the subtraction between them, hence:
9 - (-17) = 9 + 17 = 26.
The negative meant that the signal of the -17 was inverted and the number became 17, then it was added with 9 resulting in 26.
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The following are the temperatures in °C for the first 12 days of January: 4.5 , − 3 , − 2 , 2 , 2.5 , 3 , − 1 , 4 , − 2.5 , 7 , − 4 , 3.5 What is the median temperature for those 12 days? Give your answer as a decimal.
Answer:
First you will put the numbers in order least to greatest. So, it would be -4.5, -4, -3.5, -2, -1, 0, 1.5, 2, 2.5, 4, 6. 0 is the median because it in in the middle here’s how. You cross out -4.5 and 6 then 4 and -4 then -3.5 and 2.5 then 2 and -2 then -1 and 1.5 and you’re left with just the 0
Step-by-step explanation:
Evaluate 1.5 X 3 - 0.5 ²
A. 2
B. 3.5
C. 4.25
D. 31.25
Answer:
c is the answer
Step-by-step explanation:
1.5 x 3 =4.5
4.5 - 0.25
= 4.25
65 randomly selected students were asked the number of pairs of shoes they have. Let X represent the number of pairs of shoes. The results are as follows:
# of Pairs of Shoes 4 5 6 7 8 9 10 11 12 13
Frequency 8 5 4 4 7 14 6 7 6 4
The mean of the number of shoes according to the obtained results is; 8.49.
The median of the number of pairs of shoes obtained is; 9.
What is the mean and median of the frequency distribution?It follows from the complete task content that the mean and median of the data set are to be evaluated;
Since the mean is the average of all obtained data values, it follows from the mean formula;
Mean = Sum Total/Total Frequency
Mean = { ( 8 × 4 ) + ( 4 × 5 ) + .......+ (13 × 4) } / 65
Mean = 552/65
Mean = 8.49.
Also, the median of the set of 65 data values can be guessed to be the 33rd term.
On this note, the data value which corresponds to a cumulative frequency of 33 upon orderly arrangement is the median term.
Hence, since; 8 + 5 + 4 + 4 + 7 = 28; Hence, upon addition of 14, we have; 42.
Therefore, the median of the number of pairs of shoes is; 9 pairs of shoes.
Remark; The complete task requires that the mean and median be determined.
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Fully factorise 8x+24y+16z
Answer:
8 ( x + 3y + 2z) we can take 8 common in the whole expression
Finding Distance Using Absolute Value
3) Find the difference between each set of points on the number line. Confirm your answer by writing an absolute value statement for each example.
Points
Difference Between
Absolute Value Statement
23 and -45
23 – (-45) = 23 + 45 = 68
|23 – (-45) |= 68
-15 and 35
47 and -12
-43 and 27
-10 and 4
50 and -25
36 and -19
-30 and -40
-2 and 45
18 and 46
-10 and -44
-28 and 41
7 and -9
-52 and 28
22 and -50
-4 and -31
19 and 51
0 and -38
2 and -14
Distance using absolute value for each example are given below:
205916147555104328346916807227323816As given in the question,
Distance Using Absolute Value
Difference between each set of points on the number line and also confirming it by writing an absolute value statement for each.
1) –15 and 35
Distance Using Number Line –15 – (–35) = –15 + 35 = 20
Absolute Value Statement |–15 – (–35)| = 20
2) 47 and –12
Distance Using Number Line 47 – (–12) = 47 + 12 = 59
Absolute Value Statement |47 – (–12)| = 59
3) –43 and 27
Distance Using Number Line –43 – (–27) = –43+27 = – 16
Absolute Value Statement |–43 – (–27)| = 16
4) –10 and 4
Distance Using Number Line –10 – 4 = –14
Absolute Value Statement |–10 – 4| = 14
5) 50 and –25
Distance Using Number Line 50 – (–25) = 50 + 25 = 75
Absolute Value Statement |50 – (–25)| = 75
6) 36 and –19
Distance Using Number Line 36 – (–19) = 36+19 = 55
Absolute Value Statement |36 – (–19)| = 55
7) –30 and –40
Distance Using Number Line –30 – (–40) = –30 + 40 = 10
Absolute Value Statement |–30 – (–40)| = 10
8) –2 and –45
Distance Using Number Line –2 – (–45) = –2 + 45 = 43
Absolute Value Statement |–2 – (–45)| = 43
9) 18 and 46
Distance Using Number Line 18 – 46 = –28
Absolute Value Statement |18 – 46| = 28
10) –10 and –44
Distance Using Number Line –10 – (–44) = –10 + 44 = 34
Absolute Value Statement |–10 – (–44)| = 34
11) –28 and 41
Distance Using Number Line –28 – 41 = –69
Absolute Value Statement |–28 – 41| = 69
12) 7 and –9
Distance Using Number Line 7 – (–9) = 7+9 = 16
Absolute Value Statement |7 – (–9)| = 16
13) –52 and 28
Distance Using Number Line –52 – 28 = –80
Absolute Value Statement |–52 – 28| = 80
14) 22 and –50
Distance Using Number Line 22 – (–50) = 22 + 50 = 72
Absolute Value Statement |22 – (–50)| = 72
15) –4 and –31
Distance Using Number Line –4 – (–31) = –4 + 31 = 27
Absolute Value Statement |–4 – (–31)| = 27
16) 19 and 51
Distance Using Number Line 19 – 51 = –32
Absolute Value Statement |19 – 51| = 32
17) 0 and –38
Distance Using Number Line 0 – (–38) = 0+ 38 = 38
Absolute Value Statement |0 – (–38)| = 38
18) 2 and –14
Distance Using Number Line 2 – (–14) = 2+14 = 16
Absolute Value Statement |2 – (–14)| = 16
Therefore, distance using absolute value for each example are given below:
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Given f(x) = 4x – 1, find ƒ(4).
The final answer to the function given as here can be answered as 15 when formulated properly with the formulas substituted to it.
What does a function mean to you?Any kind of mathematical phrase, rule, or law that can be used to establish the link between an independent variable and a dependent variable.
This function can be solved as
Given f(x) = 4x – 1,
as in here f (4) = 4 x 4 – 1
f (4) = 15
An example of a function is what?A function is a kind of rule that has the ability to produce one output for a single input. This is illustrated by the equation y=x2. Any kind of input present for x results in an absolute single output for y. Considering that x is the input value, we would state that y is a function of x.
What is the straightforward definition of function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to the output.
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a stack of 20 identical boxes. The stack is 180cm tall, Julia then removes 3 boxes from the top. How tall is the stack now
A stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
As given in the question,
Number of identical boxes in a stack=20
Stack of 20 identical boxes are 180 cm tall
Height of 1 box=180/20
=9cm
Julia removes 3 boxes from the top
Height of 3 identical boxes=9 × 3
=27 cm
Height of stack after removing 3 boxes from the top
=Original height - height of 3 boxes
=180 -27
=153cm
Therefore, a stack of 20 identical boxes are 180 cm tall, then after removing 3 boxes from the top it is 153 cm tall.
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The balance sheet for Tempest, Inc., is shown here in market value terms. There are 19,000 shares of stock outstanding.
Based on the number of shares outstanding and the market value, the price the stock is currently selling for is $31.40
How to find the selling price of the stock?To find the selling price of the stock the formula is:
= Equity value of stock / Number of stock outstanding
The number of stock outstanding is 19,000 shares. The equity value of the stock is $596,600.
The selling price of the stock today then is:
= Equity value of stock / Number of stock outstanding
= 569,600 / 19,000
= $31.40
Full question is:
What is the stock selling for today?
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Let g (x) be the reflection across the y-axis of the function f (x) = 5x + 8. Identify the rule for g (x). g(x) = 5x + 8g (x) = -5x+8g (x) = -5x -8g (x) = 5x - 8
Given a function f(x), we can write the function g(x), where g(x) is the reflection over teh y-axis of f(x) by:
[tex]g(x)=f(-x)[/tex]In this case, the function given is:
[tex]f(x)=5x+8[/tex]Thus the reflection over the y-axis is:
[tex]g(x)=f(-x)=5(-x)+8[/tex]Now simplify:
[tex]g(x)=-5x+8[/tex]hus the answer is:
g (x) = -5x+8 (second option)
b. The product (a - b)(a + b) is called the
when simplified, it is called
of two squares and, when simplified it is equivalent to
The product (a - b)(a + b) is called the special binomial product, when simplified it is called algebraic identity of two squares and, when simplified it is equivalent to a² - b²
What is simplification?An equivalent, simpler (typically shorter) mathematical expression is substituted for the original one through the process of simplification.
Computer algebra's simplification of algebraic expressionsLogic optimization involves simplification of boolean expressions.A more straightforward but typically non-equivalent formula results from simplification of conjunction elimination in inference in logic.simplification of fractionsIn propositional logic, simplification is a valid immediate inference, argument form, and inference rule that draws the conclusion that if the conjunction A + B is true, then A + B is true as well. By deriving one of the conjuncts of a conjunction on a line by itself, the rule enables the brevity of longer proofs.
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We are flipping three coins. Outcomes in the sample space are represented by strings of Hs and Ts such as TTH and
HHT.
Todes!
a. How many elements are in this sample space?
b. Express the event "there are more heads than tails" as a set.
c. What is the probability that there are more heads than tails?
d. What is the probability that there are an equal number of heads and tails?
a. The elements are in this sample space = 8.
b. "there are more heads than tails" = 1.
c. Probability that there are more heads than tails = 1/8.
d. Probability for equal number of heads and tails = 0.
What is described the term probability?In a sample space, the probability of the an outcome is a number ranging from zero and 1, inclusive. The sum of all the probabilities inside the sample space should always equal 1. The probability of an event E, denoted by the symbol P(E), is defined as the total of the probabilities of a outcomes that comprise E.The formula for calculation the probability is;
P(E) = number of times E occurs/ number of times experiment is performed
The sample space of flipping three coins.
S = HHH, HHT, HTH, HTT, THH, THT, TTH, TTT
a. The elements are in this sample space.
The total element present on the sample space is 8.
b. "there are more heads than tails"
Sample space for more heads than tails is only HHH.
S = 1
c. The probability that there are more heads than tails.
Probability = number of heads than tails/total outcome
Probability = 1/8
d. The probability that there are an equal number of heads and tails
S = 0; Non outcome has equal number of head ans tail.
Probability = 0.
Thus, the probabilities of different situations are obtained.
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