the probability that one of the three will be elected = [tex]\frac{19}{30}[/tex]
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.
As per the question, it is given that :
Probability of John (A) = [tex]\frac{1}{8}[/tex]
Probability of Beth (B) = [tex]\frac{2}{5}[/tex]
Probability of Avery (C) = [tex]\frac{1}{3}[/tex]
The probability that one of the three will be elected :
P(A) * P(B') * P(C') + P(A') * P(B) * P(C') + P(A') * P(B') * P(C) = P(A) * (1 - P(B)) * (1 - P(C)) + (1 - P(A)) * P(B) * (1 - P(C)) + (1 - P(A)) * (1 - P(B)) * P(C).
here, P(A) = Probability of A happening
P(A') = Probability of A not happening
= [tex](\frac{1}{8} * \frac{3}{5} * \frac{2}{3}) + (\frac{7}{8} * \frac{2}{5} * \frac{2}{3}) + (\frac{7}{8} * \frac{3}{5} * \frac{1}{3})[/tex]
= [tex]\frac{1}{20} + \frac{7}{30} + \frac{7}{20}[/tex]
= [tex]\frac{3 + 14 + 21}{60}[/tex]
= [tex]\frac{38}{60}[/tex] = [tex]\frac{19}{30}[/tex]
Therefore, the probability that one of the three will be elected = [tex]\frac{19}{30}[/tex]
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A tv show had 3.6 x 104 viewers in the first week and 4.1 x 104 viewers in the second week. determine the average number of viewers over the two weeks and write the final answer in scientific notation. 3.85 x 104 7.7 x 104 3.85 x 108 7.7 x 108
The average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8. option C
Scientific notationFirst week = 3.6 x 10⁴Second week = 4.1 x 10⁴Average number of viewers over the two weeks = (First week + Second week) / 2
= {(3.6 x 10⁴) + (4.1 x 10⁴)} / 2
= {3.6 + 4.1 × 10^(4×4) } / 2
= (7.7 × 10^16) / 2
= 3.85 × 10^8
Therefore, the average number of viewers over the two weeks written in scientific notation is 3.85 × 10^8.
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isabelle is mixing red paint with blue paint to make purple paint. She 3/10 adds of 1 1/10 a fluid ounce of red to of a fluid ounce of blue to make 1 1/30 fluid ounces of purple. How many fluid ounces of red paint will she need to make 3 fluid ounces of purple paint?
27/31 ounce of red paint should she really have to make 3 fluid ounces of purple paint.
common denominator in math's:Any arithmetic operation involving two or more fractions, such as addition or subtraction, is achievable if the denominators of both fractions are equal. This is referred to as the common denominator. A common denominator is an integer that has at least one element in common with both denominators other than 1.
According to the given data:Given:
3 /10 red + 11 /15 blue makes 1 1/30 purple
Get a common denominator of 30
3/10 * 3/3 = 9/30 red
11/15 *2/2 = 22/ 30 blue
1 1/30 = 31/30 purple
the amount of paint required to make 3 fluid ounce of purple color of paints:
So,
((3/10) * (31/30)) * 3
= (3/10 * 30/31) * 3
= 27/31 ounce.
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I need help on this ASAP
Answer:
assuming you wanted the value of m
[tex]m=\frac{5D}{9}+36[/tex]
__________
Solve[tex]D=\frac{9}{5}\left(m-36\right)\\=\frac{9}{5}\left(m-36\right)=D\\5\cdot \frac{9}{5}\left(m-36\right)=5D\\=9\left(m-36\right)=5D\\\frac{9\left(m-36\right)}{9}=\frac{5D}{9}\\=m-36=\frac{5D}{9}\\m-36+36=\frac{5D}{9}+36\\m=\frac{5D}{9}+36[/tex]
__________
Hope this helps.
Suppose that 11 inches of wire costs 44 cents. At the same rate, how many inches of wire can be bought for 32 cents?
Answer:
8 inches
Step-by-step explanation:
So if 11 in. cost 44 cents, then each inch cost 4 cents.
32/4=8
a student receives test scores of 62, 83, and 91. the student's term project score is 88 and her homework score is 76. each test is worth 20% of the final grade, the term project is 25% of the final grade, and the homework grade is 15% of the final grade. what is the student's mean score in the class?
Student's mean score of the class is 80.6.
Mean:
Mean or the average of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Given,
A student receives test scores of 62, 83, and 91. the student's term project score is 88 and her homework score is 76. each test is worth 20% of the final grade, the term project is 25% of the final grade, and the homework grade is 15% of the final grade.
Here we need to find the student's mean score in the class.
First, we have to convert the percentage into decimal,
Then
=> 20% = 0.20
=> 25% = 0.25
=> 15% = 0.15
Then we have to find the scores from it,
Test A is 0.20 of the total and scores 62.
Test B is 0.20 of the total and scores 83.
Test C is 0.20 of the total and scores 91.
Project F is 0.25 of the total and scores 88.
Work H is 0.15 of the total and scores 76.
Multiply across:
=> A = (0.2 * 62) = 12.4
=> B = (0.2 * 83) = 16.6
=> C = (0.2 * 91) = 18.2
=> F = (0.25 * 88) = 22
=> H = (0.15 * 76) = 11.4
Now we have to add all these values to find the mean,
=> A + B + C + F + H
=> 12.4 + 16.6 + 18.2 + 22 + 11.4
=> 80.6
Therefore, the mean of that student is 80.6
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Solve inequality.
-n/7 ≥ 3
To solve the inequality, multiply both sides by -7 and flip the inequality direction. The solution is n ≤ -21 or (∞, -21]
Tips to solve linear inequalities:
Isolate the variable on one side by using subtraction or addition. Subtraction and addition will not change the inequality.Use division or multiplication to find the solution. Multiplication and division by a positive number will not the inequality. However, if we multiply or divide both sides with a negative number, we need to flip the inequality direction.Interval notation is often used for the solution(s). Recall the differences between a bracket [ or ], and a parenthesis ( or ). A bracket means the endpoint is included in the solution while a parenthesis means the endpoint is not included in the solution. Remember, infinity ∞ always use a parenthesis.
Example: x ≥ 2 can be written as [2, ∞), while
x > 0 is written as (2, ∞)
The given problem:
-n/7 ≥ 3
Multiply both sides by -7. Since we multiply it by a negative number, flip the inequality.
-n/7 . (-7) ≤ 3 . (-7)
n ≤ -21
Using the interval notation, the solution is (∞, -21]
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If 2000 pizzas were split between 4 people, how long would they last?
Answer:
It depends, each person gets 500 pizzas, and since there is no info on how long it takes for each of them to eat one pizza, there is no possible answer,
Step-by-step explanation:
Answer:
Each person would have 500 pizzas but how long they last would depend how fast they eat 'em lol
Step-by-step explanation:
2000 / 4 is 500
joyce paid $210 for an item at the store that was 55 percent of the original price. what was the original price?
Answer:
Step-by-step explanation:
Answer : Original price 382
55% of 382 = $210
The perimeters of the triangles shown are equal. Find the side lengths of each triangle.
A
B
C
2x+7
2x+6
2x
2x
2x
3x+9
P
Q
R
AB = 15, AC = 14, BC = 8
PQ = 8 , QR = 24, PR = 8
The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence. If the yard is 50 ft × 50 ft your fence is 200 ft long.
Perimeter of Δ ABC = Length of AB + Length of BC + Length of AC.
Perimeter of ΔABC = (2x + 7) + (2x) + (2x + 6) = 6x + 13
Perimeter of ΔPQR = (2x) + (3x + 9) + (2x) = 7x + 9
So, 6x + 13 = 7x + 9
Therefore, x = 4
AB = 2(4) + 7 = 15 PQ = 2(4) = 8
AC = 2(4)+6 = 14 QR = 3(5) + 9 = 24
BC = 2(4) = 8 PR = 2(4) = 8
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the following are amounts of total snow falls (in inches) in different midwestern cities in the united states in a certain year: 20 40 31 7 15 29 25 20 17 32 28 12 34 29 20 17 33 23 find the sample mean.
The sample mean of snowfalls in the 18 midwestern cities of the United States is 24. This is calculated by applying the formula of arithmetic mean or average to the given sample of data.
What is arithmetic mean?
An arithmetic mean is examined as very similar to an average. Mathematically, it is obtained by dividing the sum of all objects by the total number of objects.
Calculation of the sample mean for given data
Given the total number of cities = 18
The total amount of snow falls = 20 + 40 + 31 + 7 + 15 + 29 + 25 + 20 + 17 + 32 + 28 + 12 + 34 + 29 + 20 + 17 + 33 + 23
The sample mean = total amount of snowfalls / total number of cities
= 432 / 18
= 24
Hence, the sample mean of the given data is 24.
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please solve correctly!
in a class of 50 students, 28 participate in mathcounts, 21 participate in science club, and 6 students participate in neither. how many students participate in both mathcounts and science club?
Answer:
5
Step-by-step explanation:
28+21+6=55
Answer:55-50
ointwise characterization of angle bisector. a point p lies on the bisector of ! †bac if and only if p is in the interior of †bac and the distance from p to ab !
According to the given information the Pointwise Characterization of Perpendicular Bisectors.
What are Perpendicular Bisectors?A line known as a perpendicular bisector divides a specified line segment precisely in half, creating a 90° angle at the intersection. The intersection of a line segment's midpoint with a perpendicular bisector. It can be built with a compass and a ruler. On both sides of the line segment being divided, it forms a 90° angle.
The perpendicular bisector seems to be a mathematical construct that is being explored along with its creation in this article. We'll also look at the perpendicular bisector of a triangle and its properties. We will solve some few cases at the end to help you understand the subject better.
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Evaluate expression if r=3, q=1 , and w=-2 .
r + 3q / 4r
Answer:
3+3×1/4×3
3+3/12
3×12+3/12
39/12
Least to greatest 6.3 630% -6.1
Answer:
-6.1, 6.3, 630%
Step-by-step explanation:
-610%, 630%, 630%
there are six members on a student council. three of these members will serve on a spring formal committee. how many possible spring formal committees are there?
There are 20 possible combinations are there for spring formal committees.
Combination:
The process of determining the number of ways in which r objects can be selected from n distinct objects without regard to the order in which they are selected. Such selections are called combinations.
[tex]^nC_r=\frac{n!}{(n-r)!r!}[/tex]
Where
n refers the total number of ways
r refers the selected one
Given,
There are six members on a student council.
Three of these members will serve on a spring formal committee.
Here we need to find the possible number of members in spring formal committees.
We know that the value of,
n = 6
and r = 3
So, apply the values on the formula,
Then we get,
[tex]^6C_3=\frac{6!}{(6-3)!3!}[/tex]
[tex]^6C_3=\frac{6!}{3!3!}[/tex]
⁶C₃ = 720/36
⁶C₃ = 20
Therefore, the resulting value is 20.
Therefore, there are 20 possible combinations are there for spring formal committees.
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Can someone help me with this?
Answer:
x = 6
Step-by-step explanation:
21 : 28
27 : 6x
Cross multiply
21*6x = 27*28
126x = 756
756/126 = x
x = 6
Express the relation , below graph .
100 points , will give brainliest
Answer: 6 8
Step-by-step explanation:
the dot will be line 6 and 8
if that makes sence
??
does anyone kno the value of x??
Answer:
x=12
Step-by-step explanation:
x÷4=3
x=4x3
x=12
12÷4=3
Tell whether x and y show a positive correlation, a negative correlation, or relatively no correlation.
2.) No correlation
3.) Negative correlation
Step-by-step explanation:
Marsha gave the cashier $20.00 to pay for three pairs of socks and received $6.20 in change. If all three socks were equally priced, what was the cost in dollars and cents for each pair of socks?
PLS Help !!!
Answer:
$4.60
Step by Step:
First, you have to subtract $20 from $6.20 which is the change you got back. Once you remove that, you will get $13.80, the actual amount of all three pairs of socks. Now, you have to figure out how much each pair of socks is. So you need to divide 13.80 by 3 which is $4.60. So each pair of socks was $4.60
Hope that helps :D
State a) whether each graph is a function, b) whether the relation is
continuous, discrete, or neither, and c) the domain and range in the notation
indicated.
For the given graph, we have that:
a) It is not a function.
b) The function is discrete.
c) The domain is {-5,2} and the range is all real values.
When does a graph represents a function?A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y.
For this problem, we can see that it is not a function, as the values of x = -5 and x = 2 are mapped to multiple values of y.
When a function is discrete and when it is continuous?A function is discrete when it is defined for only integer values of x.A function is continuous when it is defined for real values of x.For this problem, the function is defined only for x = -5 and x = 2, which are integer values, hence it is a discrete function.
What are the domain and the range of a function?The domain of a function is the set that contains all possible input values for the function. Hence, in a graph, it is the set that contains the values of x.The range of a function is the set that contains all possible output values for the function. Hence, in a graph, it is the set that contains the values of y.Thus, the domain is {-5,2} and the range is all real values.
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A group of 12 dance competitions contestants are wearing the numbers 1 through 12. What is the probability that the winners will be wearing numbers 2, 4 and 7?
The probability is 1/4 that the winners will be wearing numbers 2, 4, and 7.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
We have been given that a group of 12 dance competition contestants is wearing the numbers 1 through 12.
To determine the probability that the winners will be wearing numbers 2, 4 and 7
Here are favorable outcomes that the contestants wearing numbers 2, 4, and 7
So the number of favorable outcomes = 3
And there is a total number of outcomes = 12
Required probability = 3/12
Required probability = 1/4.
Thus, the probability is 1/4 that the winners will be wearing numbers 2, 4, and 7.
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please help with problem 22
I am writing this because the app says the answer is to short :)))
Answer:
Step-by-step explanation:
-2x+3y
-1/9 + (-5/7) =
will give brainiest
Answer:-0.825 or 52/63
Samantha is a farmer and the other day she was on her way to sell eggs at the
market she got into an accident and all her eggs broke. In order for her to collect
money from the insurance company, she had to give the exact amount of eggs she
had. She doesn't remember how many eggs there were but when she was packing
them she remembered when she put them in groups of 2, 3, 4, 5, or 6, one egg was
left over. But in groups of 7 no eggs were left over.
How many eggs did she have?
Answer: 6
Step-by-step explanation: 6+1 Is 7 and there are no eggs left in the group of 7 so if they need one egg left and 7-1 is 6 the answer is 6.
write out the form of the partial fraction decomposition of the function (as in this example). do not determine the numerical values of the coefficients. (a) x − 30 x2 x − 30 (x−5)b (x 6)a (x−5)(x 6) (b) x2 x2 x 30
The form of the partial fraction decomposition of the given function is:
[tex]\frac{A}{x+5}+\frac{B}{x-4}[/tex]
What do we mean by rational expression?The ratio of two polynomials is a rational expression.If f is a rational expression, it can be expressed as p/q, where p and q are polynomials.To find the form of the partial fraction:
The rational expression given is: [tex]\frac{x-20}{x^2+x-20}[/tex]
Factor the provided rational expression's denominator:
[tex]\begin{aligned}\frac{x-20}{x^2+x-20} &=\frac{x-20}{x^2+5 x-4 x-20} \\&=\frac{x-20}{x(x+5)-4(x+5)} \\&=\frac{x-20}{(x+5)(x-4)}\end{aligned}[/tex]
Apply the partial fraction decomposition method now:
[tex]\begin{aligned}\frac{x-20}{x^2+x-20} &=\frac{x-20}{(x+5)(x-4)} \\&=\frac{A}{x+5}+\frac{B}{x-4}\end{aligned}[/tex]
Therefore, the form of the partial fraction decomposition of the given function is:
[tex]\frac{A}{x+5}+\frac{B}{x-4}[/tex]
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The correct question is given below:
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.
[tex]\frac{x-20}{x^2+x-20}[/tex]
xy - 2; use x = 3, and y = 5
Please explain step by step how to solve this type of problem.
Answer: 13
Step-by-step explanation:
x = 3, y = 5
xy - 2=
(3)(5)-2=
15-2=13
help!!!!!!!! Solve x/5 -3<5
A company orders 11 boxed lunches from a deli for $108.90. If each boxed lunch costs
the same amount, how much do 17 boxed lunches cost?
Answer:
$7.95
Step-by-step explanation:
The equation c = 7.95b represents the total cost of the boxed lunches
c represents the total cost
b represents the number of boxed lunches
To find the total cost of multiple items, you generally multiply the cost of a single item by the number of items there are.
Using this, we can find the cost per item is 7.95 dollars, or 7 dollars and 95 cents.