4. What is Probability?
(ii) State the axioms of probability
(iii)Two fair dice are thrown, what is the probability of getting
(a) the sum of 9
(b) two odd numbers
(c) two prime numbers
(d) two factors of 12
4c. What is Statistics?
(i) Probability is a notion in Mathematics which describes the likelihood of an event or a set of events occurring. It is a measure of uncertainty when estimating the outcome of an experiment or an observation.
(ii) The axioms of probability are:
the non-negativity (that the probability of an event is greater than or equal to zero), and
the additivity (that the probability of the union of two or more mutually exclusive events is equal to the sum of their individual probabilities).
(iii) When two fair dice are thrown the probability of getting:
a) The sum of 9 = 1/9
b) Two odd numbers = 1/4
c) two prime numbers = 1/9
d) two factors of 12 = 1/9
(iv) Statistics is a branch of mathematics that deals with data collection, analysis, interpretation, presentation, etc.
How to find probability when two dice are thrown?To find probability when two dice are thrown, we have:
(a) The sum of 9:
We will estimate the number of ways to get a sum of 9: (3,6), (4,5), (5,4), and (6,3) = 4 ways
A die has 6 possible outcomes, the total number of possible outcomes is 6x6=36 = 4/36 = 1/9.
(b) Two odd numbers:
We count the number of ways to get two odd numbers: (1,3), (1,5), (1,7), (3,1), (3,5), (3,7), (5,1), (5,3), and (5,7).
possible outcomes = 9,
So, the total possible outcomes = 6x6=36 = 9/36 = 1/4.
(c) Two prime numbers
We estimate the number of ways we can get two prime numbers: (2,3), (3,2), (5,2), and (2,5)
possible outcomes = 4,
So, the total possible outcomes = 6x6 =36 = 4/36, = 1/9.
(d) Two factors of 12:
We count the number of ways and divide by the total possible outcomes.
The factors of 12 are 1, 2, 3, 4, 6, and 12: (2,6), (3,4), and (4,3) = 3 ways
possible outcomes = 6
Therefore, the total number of possible outcomes = 6x6=36 = 3/36, = 1/12
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Elsie bought a dress that was discounted 35% off of the original price of $140. What was the amount of the dress after 8% sales tax? $
Answer:
$98.28
Step-by-step explanation:
35% of $140=49
140-49=91
8% of 91=7.28
91+7.28= 98.28
1345667-123445=?answer first
Answer:
1,222,222 is the answer
Step-by-step explanation:
You can use a calculator to find out.
Write an inequality for the graph
The inequality that represents the line in the figure will be y > - (2/3) x + 3.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
From the figure, the points of the line are (0, 3) and (3, 1). And the region above the line is a consideration. Then the equation of the line is given as,
(y - 3) > [(3 - 1) / (0 - 3)](x - 0)
Simplify the equation, then we have
(y - 3) > [(3 - 1) / (0 - 3)](x - 0)
(y - 3) > - (2/3)x
y > - (2/3) x + 3
The disparity that addresses the line in the figure will be y > - (2/3) x + 3.
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Solve for x.
OA. 9
OB. 1
OC. 4
OD.7
The value x in the secant line using the Intersecting theorem is 4.
What is the value of x?Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.
From the figure:
First sectant line segment = ( x - 1 ) + 5
External line segment of the first secant line = 5
Second sectant line segment = ( x + 2 ) + 4
External line segment of the second secant line = 4
Using the Intersecting secants theorem:
5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )
Solve for x:
5( x - 1 + 5 ) = 4( x + 2 + 4 )
5( x + 4 ) = 4( x + 6 )
5x + 20 = 4x + 24
5x - 4x = 24 - 20
x = 4
Therefore, the value of x is 4.
Option C) 4 is the correct answer.
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I really need help with this
Find all real zeros of
f
(
x
)
=
x
3
-
x
2
-
68
x
+
186
.
x
=
(Enter the zeros as a list, e.g.
1
,
2
,
3
. Use exact forms, not decimal approximations.)
The real zeros of the function f(x) = x³ - x² - 68x + 186 are x = 3, x = -1 + 3√7 and x = -1 - 3√7
Finding all real zeros of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x³ - x² - 68x + 186
To find the real zeros of the function, we set the function to 0
Using the above as a guide, we have the following:
x³ - x² - 68x + 186 = 0
Next, we solve by graphing (see attachment for graph)
With the use of a graph, the real zeros of the function are
x = 3, x = -1 + 3√7 and x = -1 - 3√7
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Complete questions
Find all real zeros of f(x)=x3-x2-68x+186.x=(Enter the zeros as a list, e.g. 1,2,3. Use exact forms, not decimal approximations.)
-5/2 (3x + 4) < 6 - 3x
Step-by-step explanation:
here is the ans
please check
How do I solve for this?
Answer: \(cosx =- \sqrt{ 1 - sin^2x}\)
Step-by-step explanation:
Generally speaking; \(cos^2x + sin^2x = 1\)
rearranging this gives us all sorts of cool things.
for now, we will use: \(cosx = \sqrt{ 1 - sin^2x}\)
This however, is general.
In the third quadrant, cosine is negative. So cosx in QIII will be:
\(cosx =- \sqrt{ 1 - sin^2x}\)
and thats the answer :)
solving and graphing inequalities
Answer:
wssp i can help
Step-by-step explanation:
Divide N6.00 in the
ratio of 1:2
Answer:
2:4
Step-by-step explanation:
6
Ratio: 1:2
6/3 = 2
2*1=2
2*2=4
2:4 is the answer
If TUV is isosceles, find the value of X
Answer:
x = 17
Step-by-step explanation:
Since the triangle is isoceles that means angle UTV is also 43 degrees. The sum of all angles in a triangle is 180 degrees. So construct this equation. 43 + 43 + 43 + 8x - 42 = 180. Now solve for x.
Find the missing side x
Answer:
x = 21.52
Step-by-step explanation:
Given:
hypotenuse (That has to be found out)
Side adjacent to the given angle
and an angle,
Hence we can say that Cos ratio would be used;
Cos(28) = 19 / x
x = 19 / Cos(28)
x = 21.52
Hope this helps!
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
The amount of a radioactive substance remaining as it decays over time is A = A0(0.5)t/h ,where a represents the final amount
Ao represents the original amount, t represents the number of years, and h represents the half-life of the sibstance.
The half-life of the radioactive isotope carbon-14 is 5,730 years. Approximately how many years will it take a 50-gram mass of
carbon-14 to decay to 5 grams?
Carbon-14 will take 19,035 years to decay to 10 per cent.
What is the time of decay?
A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay.
An exponential decay can be described by the following formula:
\(N(t)=N_oe^{-\lambda t}\)
Where:
No = The quantity of the substance that will decay.
N(t) = The quantity that still remains and has not yet decayed after a time t
\(\lambda\) = The decay constant.
One important parameter related to radioactive decay is the half-life:
\(t_{1/2}=\dfrac{Ln(2)}{\lambda}\)
If we know the value of the half-life, we can calculate the decay constant:
\(\lambda =\dfrac{ln(2)}{t_{1/2}}\)
Carbon-14 has a half-life of 5,730 years, thus:
\(\lambda =\dfrac{ln(2)}{5730}\)
\(\lambda\) = 0.00012097
The equation of the remaining quantity of Carbon-14 is:
\(N(t)=N_oe^{-0.00012097t}\)
We need to calculate the time required for the original amount to reach 10%, thus N(t)=0.10No
\(0.10N_o=-N_oe^{-0.00012097t}\)
Simplifying:
\(0.10=e^{0.00012097t}\)
Taking logarithms:
ln(0.10) = -0.00012097t
Solving for t:
\(t=\dfrac{Log0.10}{-0.00012097}\)
t = 19035 years
Carbon-14 will take 19,035 years to decay to 10 per cent.
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Giselle works as a carpenter and as a blacksmith.
She earns
$
20
$20dollar sign, 20 per hour as a carpenter and
$
25
$25dollar sign, 25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of
30
3030 hours, and earned a total of
$
690
$690dollar sign, 690.
How long did Giselle work as a carpenter last week, and how long did she work as a blacksmith?
Giselle worked as a carpenter for
hours and as a blacksmith for
hours last week.
Answer:
Giselle worked as a carpenter for 12 hours and as a blacksmith for 18 hours last week
Step-by-step explanation:
Let's assume that Giselle worked as a carpenter for x hours and as a blacksmith for y hours last week.
We know that she earns $20 per hour as a carpenter and $25 per hour as a blacksmith, and that she worked a total of 30 hours, so we can write two equations based on this information:
x + y = 30 (total hours worked)
20x + 25y = 690 (total earnings)
To solve for x and y, we can use substitution or elimination. Let's use substitution.
From the first equation, we can solve for x in terms of y:
x = 30 - y
Substitute this expression for x in the second equation:
20(30 - y) + 25y = 690
Simplify and solve for y:
600 - 20y + 25y = 690
5y = 90
y = 18
So Giselle worked as a blacksmith for 18 hours last week.
To find how long she worked as a carpenter, we can substitute y = 18 into the first equation and solve for x:
x + 18 = 30
x = 12
Therefore, Giselle worked as a carpenter for 12 hours last week.
a bus traveled 60 km of north of its terminal. From this point, it traveled km east. How far is the bus from the terminal?
maybe 61km from northeast
helpppp...........................
Answer:
see explanation
Step-by-step explanation:
the sum of the interior angles of a polygon is
sum = 180° (n - 2) ← n is the number of sides
a hexagon has 6 sides , then
sum = 180° × (6 - 2) = 180° × 4 = 720°
12
the polygon has 5 sides , so
sum = 180° × (5 - 2) = 180° × 3 = 540°
sum the interior angles and equate to 540
y + 90 + 120 + 90 + 110 = 540
y + 410 = 540 ( subtract 410 from both sides )
y = 130
13
the polygon has 7 sides , so
sum = 180° × (7 - 2) = 180° × 5 = 900°
sum the interior angles and equate to 900
p + 90 + 141 + 130 + 136 + 123 + 140 = 900
p + 760 = 900 ( subtract 760 from both sides )
p = 140
In a class of pupils, 7 play the flute and
piano.
14 play the flute only.
10 play the piano only.
6 play neither instrument.
How many pupils are in the class?
Answer:
aassass
Step-by-step explanation:
aassav
aadke
ddwvme
Given ΔACP≅ΔLNX, find each missing measure.
Answer:
XL = PC
AC = NX
PC = XL
Angle L = Angle C
Angle C = Angle L
Angle X = Angle P
Step-by-step explanation:
Algebra- I need help with this problem, I don't really get it.
Answer:
29
Step-by-step explanation:
First, replace v with 6 and k with 12
12/6 + 5 - 4(6) + 12
12/6= 2
2 + 5 - 4(6) + 12
4(6) = 24
2 + 5 - 24 + 12
2+ 5 = 7
24 + 12 = 36
7 - 36 = 29
hope this helps!
Matthew examines the relation shown in the below.
{(4,-11), (3,1), (0,1), (2,6), (3, -1)}
Is the relation a function? Why or why not?
No. There are x values which map to more than 1 y-value.
Yes. Every y-value maps to exactly 1 x-value.
No. There are y-values which map to more than 1 x-value.
Yes. Every x-value maps to exactly 1 y-value.
No, there are x values which map to more than 1 y-value.
Given that Matthew examines the relation as shown in the below.
{(4, -11), (3,1), (0,1), (2,6), (3, -1)}
We need to check whether the relation is a function or not,
So, we know that,
A relation can map inputs to multiple outputs. It is a function when it maps each input to exactly one output. The set of all functions is a subset of the set of all relations.
If any x values are repeated, and the corresponding y values are different, then we have a relation and not a function.
Here we can see that the y values are repeated, so it is not a function.
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Which of the following equations represents an ellipse having vertices
located at (2,9) and (2,-5) and foci located at (2,5) and (2,-1)?
Answer:
(x-2)^2/40 + (y-2)^2/49 = 1
Step-by-step explanation:
PLEASE ANSWER ASAP! NO SCAM LINKS! OR REPORTED.
Answer:
im pretty sure its A
Step-by-step explanation:
how many positive perfect square integers are factors of the product $\left(2^{10}\right)\left(3^{12}\right)\left(5^{15}\right)$?
By the multiplication principle of counting, the total number of positive perfect square factors of the product is the product of the number of choices for each prime factor, which is $6\times7\times8=336$. Therefore, 336 positive perfect square integers are factors of(2¹⁰ )(3¹² )(5¹⁵)
We can find the number of positive perfect square integers that are factors of the given product by first considering the prime factorization of the product, which is (2¹⁰ )(3¹² )(5¹⁵)
To get a perfect square factor, we need each prime factor to have an even exponent. Therefore, we can choose any even exponent for the prime factors of 2, 3, and 5, respectively, as long as the exponents are not greater than 10, 12, and 15, respectively.
For the factor of 2, we can choose any even exponent from 0 to 10, so there are 6 choices. Similarly, for the factor of 3, we can choose any even exponent from 0 to 12, so there are 7 choices. Finally, for the factor of 5, we can choose any even exponent from 0 to 15, so there are 8 choices.
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Select a personal or professional example of a measurement you use routinely. Convert the measurement either from U.S customary units to metric units, or from metric units to U.S. customary units. You may choose more than one measurement and may choose among weight, length, temperature, etc. Show each step of your conversion and be sure to include all units from the original and converted measurements (for example, yards to meters, degrees Celsius to degrees Fahrenheit).
A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.
To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.
For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:
150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms
Therefore, 150 pounds is approximately equal to 68.0388 kilograms.
In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.
It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.
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Select the correct answer. Which statement best describes the zeros of the function h(x) = (x – 6)(x2 + 8x + 16)? A. The function has two distinct real zeros. B. The function has three distinct real zeros. C. The function has one real zero and two complex zeros. D. The function has three complex zeros.
We can see here that the statement that best describes the zeros of the function h(x) = (x – 6)(x² + 8x + 16) is: C. The function has one real zero and two complex zeros.
What is a function?In mathematics, a function is a special type of relation. A relation is a set of ordered pairs, where each ordered pair consists of two elements.
To determine the zeros of the function h(x) = (x - 6)(x^2 + 8x + 16),
we can set the function equal to zero and solve for x.
Setting h(x) = 0, we have:
(x - 6)(x^2 + 8x + 16) = 0
Setting x - 6 = 0, we find:
x = 6
Setting x^2 + 8x + 16 = 0,
we can attempt to factor or use the quadratic formula.
Therefore, the function:
h(x) = (x - 6)(x^2 + 8x + 16) has one real zero (x = 6) and two complex zeros.
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Stephen is combining all juice shown to make fruit punch. Does the expression (64+28+76)/6 make sense’s
Yes, the expression (64+28+76)/6 makes sense as it represents the average quantity of juice per unit when combining all the shown juices.
To determine whether the expression (64+28+76)/6 makes sense, we need to evaluate the components of the expression and consider whether the mathematical operations are valid.
The expression (64+28+76)/6 represents the sum of three numbers (64, 28, and 76), divided by 6. Let's break it down step by step:
Addition: We have three numbers being added together: 64, 28, and 76. The sum of these numbers is 168 (64 + 28 + 76 = 168).
Division: The sum of the three numbers, 168, is then divided by 6. Division is a valid mathematical operation.
Now, let's analyze whether the expression makes sense in the context of Stephen combining all the juice to make fruit punch. The numbers 64, 28, and 76 may represent quantities of juice (in some units) that Stephen is combining. However, without further information or context, we cannot determine if the expression accurately represents the combination of these juices.
If the numbers 64, 28, and 76 represent quantities of juice in the same units (such as milliliters or liters), then the expression (64+28+76)/6 would represent the average quantity of juice per unit. The result, 168/6, would be 28. This would imply that each unit (e.g., glass or serving) of the fruit punch contains an average of 28 units of juice.
In summary, mathematically, the expression (64+28+76)/6 is valid. However, without additional context regarding the units or quantities being represented, it is not possible to determine whether the expression accurately describes the process of combining the juices to make fruit punch.
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Someone help me please
Step-by-step explanation:
i think c is your answer
A man bought two pencils and three biros at a cost of 50, Again he bought three pencils and four biros for 70. find the cost of a pencil and a biro