An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.
What is probability?Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.
The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.
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Luke bought 4 kilograms of apples and 0.29 kilograms of oranges. How much fruit did he buy
in all?
He bought 4.29 Kilos of fruit.
4+0.29=4.29
Luke bought 4.29 kilograms of fruit in all
Step-by-step explanation:
Simple addition will be used to find the total fruit Luke bought.
Given
Amount of apples he bought = 4 kilograms
Amount of oranges he bought = 0.29 kilograms
so the total fruit will be:
[tex]\text{total fruit}=\text{Apples}+\text{oranges}[/tex]
[tex]=4+0.29[/tex]
[tex]=4.29[/tex]
So,
Luke bought 4.29 kilograms of fruit in all
Keywords: Measurement, addition
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In a regular pentagon PQRST. PR intersects QS
at O. Calculate angle ROS.
Answer: 72°
Step-by-step explanation:
To find the interior angle of this shape, use the formula 180(n-2)/n, where n is the amount of sides. Plugging 5 in for the interior angle of a pentagon, you get 180(3)/5, or 108°.
Using the statement that PR intersects QS, we can see that triangle QOR is isosceles (to get this, look at triangle PQR, and note that because it has 2 equal side lengths, and its last length is not equivalent to the other 2 sides, it is isosceles). Solving for angle PRQ, we know one angle is 108°, and the other two are equal. The total angle in a triangle is 180°, so (180°-108°)/2 = 36° (angles QPR and PRQ).
Since the angle of R = 108°, we can find angle PRS as 108° - 36°, or 72°. Since triangles PQR and QRS are similar (share the same angles and side lengths), we can see that angle RQS and RSQ are both 36°.
Since ORS is a triangle, its angle total is 180°. Since we know the angles ORS and OSR (respectively) already as 72° and 36°, we can subtract these angles to find angle ROS. 180°-72°-36° = 72°
Smoothie Activity
6. Using the relative frequency table, create a segmented bar graph by employee type using technology or by hand. If using Excel technology the columns may need to be switched after inserting the chart. Click on the chart and the "Chart Design" ribbon will pop up. Then select "Switch Row/Column." (10 points)
By answering the presented question, we may conclude that I used the following procedures to produce this graph.
What is graphs?Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph contains vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle.
I used the following procedures to produce this graph:
I classified the personnel as full-time, part-time, and temporary.
I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."
I used the following procedures to produce this graph:
I classified the personnel as full-time, part-time, and temporary.
I estimated the proportion of employees who assessed the company's work-life balance as "very good" or "excellent" for each employee category, as well as the percentage who rated it as "good" or "fair/poor."
I made the segmented bar graph using these percentages.
The graph was made using Excel technology. You may make a similar graph with Excel or any other software that supports segmented bar graphs.
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Question
Find the value of y
for the given value of x
.
y=x+5;x=3
Answer: y is equal to 8
Step-by-step explanation:
by substituting the x for its vale of three we can add the two values to get 8 or y=8
a parachutist rate during a free fall reaches 132 feet per second. what is this rate in meters per second? at this rate, how many meters will the parachutist fall during 10 seconds of free fall. in your computations, assume that 1 meter is equal to 3.3 feet. (do not round your answer)
Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.
How to convert feet to meters?First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:
[tex]$\frac{3meter}{3.3 feet}[/tex]
To convert feet per second to meters per second, we can multiply by the conversion factor:
[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]
Therefore, the parachutist's rate during free fall is 40 meters per second.
Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:
distance =[tex]\frac{1}{2}[/tex] * acceleration * time²
where acceleration due to gravity is approximately 9.8 meters/second^2.
Substituting the given values, we get:
distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²
distance = 490 meters
Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.
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What are the zeros of the function? Set the function = 0, factor, and use the zero-product property. Show your steps!
f(x) = x² + 7x – 60
(100 POINTS AND BRAINLIEST)
The zeroes of the function are -12 and 5.
What is meant by Zeros of the function?Zeros of a function are the values of the input variables that make the output of the function equal to zero. The zeros are the solutions of equation f(x) = 0.
According to the question:
To find the zeros of the function
f(x) = x² + 7x - 60, we must set f(x) equal to zero and solve for x.
So we start with the equation:
x² + 7x - 60 = 0
Next, we need to factor the left side of the equation. We are looking for two numbers that multiply to -60 and add to 7. After some trial and error, we find that the numbers are 12 and -5:
x² + 7x - 60 = (x + 12)(x - 5) = 0
Now we can apply the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x:
x + 12 = 0 or x - 5 = 0
Solving for x, we get:
x = -12 or x = 5
The zeros of the function f(x) = x² + 7x - 60 are therefore x = -12 and x = 5.
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Will make you brainlist!
Answer:
x = -2 , y = 2
Step-by-step explanation:
label your equations (1) and (2) the question mention to use elimination method and make x the same for both. To do that multiply equation (1) by 2. than label it (3)so 3x becomes 6x adding the equation (2)+(3) cancels out -6x and 6x so you can find value of yuse value of y to find xhope this helps :)
What’s -9.1 times 3.75
The tires on Mavis’ car will have to be replaced when they each have 160 000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25 000 km?
Answer:
If the tires on Mavis’ car have to be replaced when they each have 160 000 km of wear, then the total distance Mavis can drive on a set of tires is:
4 tires * 160,000 km = 640,000 km
If Mavis drives 25,000 km in a year, she will need to replace her tires after:
640,000 km ÷ 25,000 km/year = 25.6 years
Since Mavis will need to replace her tires once every 25.6 years, the cost of the wear on her tires for a single year is:
$140.00/tire * 4 tires = $560.00
So the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km is $560.00.
Step-by-step explanation:
source: trust me bro
A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.
Find the probability that a 0 is received. (Enter the value of the probability in decimal format and round the final answer to one decimal place.)
P(0 received correctly) = P(0 sent) × P(0 received correctly | 0 sent)= [tex](2/3) × 0.8= 0.5333[/tex] (rounded to 1 decimal place)Thus, the probability that a 0 is received is 0.5333 (rounded to 1 decimal place).
0.5333
A space probe near Neptune communicates with Earth using bit strings. Suppose that in its transmissions it sends a 1 one-third of the time and a 0 two-thirds of the time. When a 0 is sent, the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 1) is 0.2. When a 1 is sent the probability that it is received correctly is 0.8 and the probability that it is received incorrectly (as a 0) is 0.2.The probability that a 0 is received correctly is given in the problem as 0.8, and the probability that a 0 is sent is 2/3. Therefore, the probability that a 0 is received correctly
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What geometric shapes can you draw that have exactly one pair of parallel sides? Use pencil and paper. Sketch examples for as many different types of shapes as you can. Use appropriate marks to show the pairs of parallel sides.
A. regular pentagon
B. square
C. Trapezoid
D. parallelogram
Let A, B, and C be subsets of some universal set U. (a) Draw two general Venn diagrams for the sets A, B, and C. On one, shade the region that represents A - (B nC), and on the other, shade the region that represents (A -B) U (A C). Based on the Venn diagrams, make a conjecture about the relationship between the sets A-(BnC) and (A -B)U (A -C). (b) Use the choose-an-element method to prove the conjecture from Exer- cise (5a). (c) Use the algebra of sets to prove the conjecture from Exercise (5a).
In conclusion, we can prove that[tex](A -B) U (A C)[/tex] is a superset of[tex]A - (B nC)[/tex] using both the choose-an-element method and the algebra of sets.
To answer this question, let's first draw two Venn diagrams to represent the sets A, B, and C. In the first Venn diagram, shade the region that represents[tex]A - (B nC)[/tex].
This is the region outside of the intersection of B and C and inside of A. In the second Venn diagram, shade the region that represents [tex](A -B) U (A C).[/tex] This is the union of the region outside of B and the region outside of C, both of which are inside of A. Based on these diagrams, we can make the conjecture that (A -B) U (A C) is a superset of A - (B nC).
To prove this conjecture, we can use the choose-an-element method. Let a be an element of A - (B nC). This means that a is in A, but not in B or C. Since a is in A, it is also in (A -B) U (A C), and therefore (A -B) U (A C) is a superset of A - (B n C).
We can also use the algebra of sets to prove this conjecture.[tex]A - (B n C) = (A -B) U (A -C) since A - (B n C)[/tex]is the union of the regions outside of B and outside of C, both of which are inside of A. This implies that (A -B) U (A C) is a superset of A - (B nC).
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Use the following function to find d(0)
d(x)=-x+-3
d(0)=
Answer:
d(0) = -3
Step-by-step explanation:
d(x) = -x + -3 d(0)
d(0) = 0 - 3
d(0) = -3
So, the answer is d(0) = -3
6. 4 The point Q (3, -1) has been translated from P by the vector (3) What are the coordinates of the point P?
The coordinates of the point P is (-1,2) .
What is translation?
In mathematics, a translation is a geometric transformation that moves every point of a figure or a space by the same amount in a given direction. The amount and direction of the movement can be described using a vector, which is a mathematical object that has both magnitude and direction.
Finding the coordinates of the point P :
The coordinates of point P can be found by subtracting the vector from point Q.
To find the coordinates of point P, we need to subtract the vector [tex]\begin{pmatrix}4\\-3\end{pmatrix}[/tex] from the coordinates of point Q, which are (3, -1).
Subtracting the x-coordinate of the vector from the x-coordinate of point Q gives us:
3 - 4 = -1
Similarly, subtracting the y-coordinate of the vector from the y-coordinate of point Q gives us:
-1 - (-3) = 2
Therefore, the coordinates of point P are (-1, 2).
So, the correct answer is (C) (-1, 2).
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I NEED HELPP PLEASEEEEEEEE
The slope between the points (-3, 0) and (0, -1) is -1/3.
What is slope?The slope of a line serves as a gauge for its steepness. It may be calculated by dividing the difference in y-coordinate by the difference in x-coordinate between any two points on a line. A line's slope might be zero, positive, negative, or undefinable. A line with a positive slope is moving upward from left to right, a negative slope is moving downward from left to right, and a line with a zero slope is level. The line is vertical if the slope is undefinable.
Let us consider the first two points (-3, 0) and (0, -1).
The slope of the line is given as:
m = (y2 - y1) / (x2 - x1)
Substituting the values we have:
m = (-1 - 0) / (0 - (-3)) = -1/3
Hence, the slope between the points (-3, 0) and (0, -1) is -1/3.
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using the net below find the area of the triangular prism
6 cm
3 cm
4 cm
6 cm
5 cm
2 cm
Answer:153
Step-by-step explanation:
One number is 13 less than another number. Let x represent the greater number. What is the sum of these two numbers?
Answer:
2x - 13
Step-by-step explanation:
If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:
x + (x - 13) = 2x - 13
Alfonso wants to purchase a pool membership
for the summer. He has no more than y dollars to
spend. The Aquatics Club charges an initial fee
of $75 plus $20 per month. The Swimming Hole
charges an initial fee of $15 plus $65 per month.
Write a system of inequalities that you can use to
determine which company offers the better deal.
Let x represent the number of months.
The system of inequalities of the company with the better offer is 75 + 20x ≤ y and 15 + 65x ≤ y
Identifying the system of inequalitiesLet's use A to represent the total cost (in dollars) of purchasing a pool membership from the Aquatics Club,
Let S represent the total cost of purchasing a pool membership from the Swimming Hole.
Then we can write the following system of inequalities:
A = 75 + 20x (total cost of Aquatics Club membership)
S = 15 + 65x (total cost of Swimming Hole membership)
Alfonso has no more than y dollars to spend
So, we have
75 + 20x ≤ y
15 + 65x ≤ y
Hence, the system is 75 + 20x ≤ y and 15 + 65x ≤ y
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What is an equation for the quadratic function represented by the table shown?
A straw that is 15cm long leans against the inside of a glass. The diameter of a glass is
5cm, and has a height of 8cm. How far past the edge of the glass would the straw extend?
Round your answer to the nearest tenth.
The straw will extend past the edge of the glass in a straight line. To find the answer, subtract the diameter of the glass (5cm) from the length of the straw (15 cm): 15 cm - 5 cm = 10 cm. This is the distance the straw will extend past the edge of the glass. To round to the nearest tenth, round 10.0 up to 10.1. Therefore, the straw will extend past the edge of the glass 10.1 cm.
Please help quick with this question.
Answer:
b = [tex]\frac{S-2la}{h+l}[/tex]
Step-by-step explanation:
S = bh + lb + 2la ( reversing the equation )
bh + lb + 2la = S ( subtract 2la from both sides )
bh + lb = S - 2la ← factor out b from each term on the left side
b(h + l) = S - 2la ← divide both sides by (h + l)
b = [tex]\frac{S-2la}{h+l}[/tex]
what is the value of y in the solution to the system of equations below.
y=-x+6
2x-y=-9
Answer:
I gave a couple solutions as I wasn't sure if you were asking for graphing purposes or substituting y=-x+6 into the second equation 2x-y=-9. So I gave both solutions just in case.
for the first equation y=-x+6, y intercept is (0,6)
for equation two 2x-y=-9, y intercept is (0,9)
In both of the equations the x value is 1.
Solving for y without graphing. Y=9+2x
and x=-1
Step-by-step explanation:substitute i
HOWEVER, if you are saying that the top equation is the value of y, then you substitute it into the bottom equation. 2x--x+6=-9 which would be x=-5
It really depends on what is expected of the question. I wasn't sure which one, so I gave a couple different approaches. If you could give more information, such as, are you graphing, that would be great. I'll keep an eye out for any comments.
Jayden evaluated the expression a + (2 + 1. 5) for a = 14. He said that the value of the expression was 8. 5. Select all the statements that are true. Jayden's solution is incorrect. Jayden added inside the parentheses before dividing. Jayden substituted the wrong value for a. Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.
It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
1) The correct solution is
Given,
a ÷ (2 + 1. 5)
Substituting the value of a which is 14
= 14 ÷ (2 + 1. 5)
= 14 ÷ 3.5
= 4
2) As there is no term which needs to be divided so, the second statement is false.
3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.
4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
i.e. a ÷ (2 + 1. 5)
14 ÷ 2 + 1. 5
7+1.5
8.5
This is the way Jayden solved the equation due to which he arrived at the wrong solution.
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The Correct question is as below
Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.
1. Jayden's solution is incorrect.
2. Jayden added in the parentheses before dividing.
3. Jayden substituted the wrong value for a.
4. Jayden divided 14 by 2 and added 1.5
in how many ways can a class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer and a secretary g
The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040
A class of 40 students select a committee from the class that consists of a president, a vice president, a treasurer, and a secretary in the following way:Step-by-step explanation:The number of ways that a class of 40 students can choose a committee consisting of a president, vice president, treasurer, and a secretary can be found by using the permutation formula.If we assume that the positions of the committee members are different, the number of ways can be calculated as follows:The number of ways of selecting the president from 40 students is 40.The number of ways of selecting the vice president from the remaining 39 students is 39.The number of ways of selecting the treasurer from the remaining 38 students is 38.The number of ways of selecting the secretary from the remaining 37 students is 37.The total number of ways of selecting the committee is, therefore,40 x 39 x 38 x 37= 7,903,040Thus, secretary.
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The average between 3. 15 and x is 40 what is x?
The value of x that makes the average between 3.15 and x equal to 40 is 76.85.
In this problem, we are given two numbers, 3.15 and x, and told that the average between them is 40. We can set up an equation to solve for x as follows:
(3.15 + x) / 2 = 40
To find the average between 3.15 and x, we add the two numbers together and divide by 2, which gives us the equation above.
To solve for x, we can start by multiplying both sides of the equation by 2:
3.15 + x = 80
Next, we can subtract 3.15 from both sides of the equation:
x = 76.85
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Please help it’s for tmr
Leo has a number of toy soldiers between 27 and 54. If you want to group them four by four, there are none left, seven by seven, 6 remain, five by five, 3 remain. How many toy soldiers are there?
The answer is 48 but I need step by step explanation
Hence, 28 toy soldiers are the correct answer.
In mathematics, how is a group defined?A group in mathematics is created by combining a set with a binary operation. For instance, a group is formed by a set of integers with an arithmetic operation and a group is also formed by a set of real numbers with a differential operator.
Let's refer to the quantity of toy soldiers as "x".
We are aware that x is within the range of 27 and 54 thanks to the problem.
x can be divided by 4 without any remainders.
The residual is 6 when x is divided by 7.
The leftover after dividing x by five is three.
These criteria allow us to construct an equation system and find x.
Firstly, we are aware that x can be divided by 4 without any residual. As a result, x needs to have a multiple of 4. We can phrase this as:
x = 4k, where k is some integer.
Secondly, we understand that the remaining is 6 when x is divided by 7. This can be stated as follows:
x ≡ 6 (mod 7)
This indicates that x is a multiple of 7 that is 6 more than. We can solve this problem by substituting x = 4k:
4k ≡ 6 (mod 7)
We can attempt several values of k until we discover one that makes sense for this equation in order to solve for k. We can enter k in to equation starting using k = 1, as follows:
4(1) ≡ 6 (mod 7)
4 ≡ 6 (mod 7)
It is not true; thus we need to attempt a next value for k. This procedure can be carried out repeatedly until the equation is satisfied for all values of k.
k = 2:
4(2) ≡ 6 (mod 7)
1 ≡ 6 (mod 7)
k = 3:
4(3) ≡ 6 (mod 7)
5 ≡ 6 (mod 7)
k = 4:
4(4) ≡ 6 (mod 7)
2 ≡ 6 (mod 7)
k = 5:
4(5) ≡ 6 (mod 7)
6 ≡ 6 (mod 7)
k = 6:
4(6) ≡ 6 (mod 7)
3 ≡ 6 (mod 7)
k = 7:
4(7) ≡ 6 (mod 7)
0 ≡ 6 (mod 7)
We have discovered that the equation 4k 6 (mod 7) is fulfilled when k = 7. Thus, we can change k = 7 to x = 4k to determine that:
x = 4(7) = 28
This indicates that there are 28 toy troops. Yet we also understand that the leftover is 3 when x is divided by 5. We don't need to take into account any other values of x because x = 28 satisfies this requirement.
28 toy soldiers are the correct response.
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Use the following function to find d(0)
d(x)=-x+-3
d(0)=
When the function d(x) = -x +(-3), then the value of d(0) is -3
In mathematics, a function is a relationship between two sets of numbers, called the domain and range. A function assigns each element of the domain to exactly one element of the range.
In the given problem, we are given a function d(x)=-x-3. The notation d(0) represents the value of the function d(x) when x = 0.
To find d(0), we need to substitute x = 0 in the function d(x)=-x-3, which gives:
d(0) = -(0) - 3
The first term -(0) is equal to zero, and the second term -3 is a constant value that remains the same regardless of the value of x. Therefore, we can simplify the expression as
d(0) = -3
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what is the messure or the vertex angle of an isosceles triangle if one of its base angle measures 16 degrees
A man sells an article at rs 600and makes a profit of 20%. Calculate his profit percentage
Answer:
120
Step-by-step explanation:
20 percent of 600 is 120 so he will get 120
A coffee maker is on sale for 45$. If the sales tax is 7%, how much will the buyer spend altogether?
Answer: 38 I think if it's not right I'm sorry I'm bad at math that's like the only thing I suck at
Step-by-step explanation: