Two players take turns putting pennies on a round table, one penny per turn, withoutpiling one penny on top of another. The player who cannot place a penny loses. Design a winningstrategy for the first player.
The first player will eventually win, when the second player runs out of free slots.
On the first move place the coin on the center of the table.
Then player B will place his coin anywhere on the table.
Now, you put your coin on the line of diameter passing through the coin placed by player B, at the same distance away from the boundary of the circle ( mimic his placement on the opposite side of the table).
If player A has space to place a coin, so will player B. Player B will run out of place before player A.
The first player will eventually win, when the second player runs out of free slots.
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event a happens with probability 0.8 and event b happens with probability 0.6. the probability that at least one of the events happens is 0.9. find the probability of event b, given that event a happened.
On solving the provided question, we can say that probability P(B)(1–0.6)=0.3 =>P(B)=3/4= 0.75
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
If two events A and B are independent then,
[tex]P(A n B)= P(A).P(B)\\P(A u B)= P(A)+P(B)-P(A n B)[/tex]
Since A and B are independent, so
[tex]P(A u B)= P(A)+P(B)-P(A).P(B)\\0.9=0.6+P(B)-(0.6 * P(B))\\P(B)(1–0.6)=0.3\\P(B)=3/4= 0.75[/tex]
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Work out the value of
(a) 64 -1/2
(b) 81 -1/2
(c) 64 -1/3
(d) 125 -1/3
Answer:
Step-by-step explanation:
(a) To work out the value of 64 - 1/2, we first need to understand that -1/2 is the same as raising the number to the power of -1/2. So, 64 -1/2 can be written as 64^(-1/2)
The value of 64^(-1/2) is equal to 1/√(64) = 1/8
(b) To work out the value of 81 - 1/2, we can write it as 81^(-1/2)
The value of 81^(-1/2) is equal to 1/√(81) = 1/9
(c) To work out the value of 64 - 1/3, we can write it as 64^(-1/3)
The value of 64^(-1/3) is equal to 1/∛(64) = 1/4
(d) To work out the value of 125 - 1/3, we can write it as 125^(-1/3)
The value of 125^(-1/3) is equal to 1/∛(125) = 1/5
Note: √ represents square root and ∛ represents cube root
The total amount of garbage y is proportional to the number of days x, as shown in the graph.
Write an equation to represent this relationship
(Help please
The equation that represent this relationship shown in the graph is y = 4.5x having a slope of 4.5
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
Let y represent the total amount of cabbage and c represent the number of days
From the graph, Using point (0, 0) and (3, 13.5):
y - 0 = [(13.5 - 0)/(3 - 0)](x - 0)
y = 4.5x
The equation that represent this relationship is y = 4.5x
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HELP ASAP PLEASE! Find all the cube roots of -512.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The real cube root(s) of -512 is/are [}.
B. There are no real cube roots of -512.
Answer:
A; -8
Step-by-step explanation:
Well, the cube root of 512 is just 8, and because the root is an odd number, we can allow negative numbers as the answer instead of imaginary numbers. Therefore the real cube root of -512 is just -8
negative 3 plus negative 5
Answer: -8
Hope this helps :)
Step-by-step explanation:
Adding two negative integers is just like adding two regular numbers
Answer:
negative 8
Step-by-step explanation:
calculator
Give an example of a search problem you encounter in everyday life. Does it use sequential, binary, or some other search algorithm?
One example of a search problem I encounter in everyday life is finding a specific item in a grocery store.
What is algorithm?An algorithm is a set of instructions designed to perform a specific task. Algorithms are a key component of computer programming, used to create programs that can solve problems and perform tasks. Algorithms are typically used to solve complex problems and can be thought of as a set of steps that must be followed in order to achieve a desired goal. Algorithms can range from simple, such as a basic sorting algorithm, to complex, such as an artificial intelligence algorithm.
This search problem generally uses a sequential search algorithm, where I must search through the aisles of the store in order to locate the item. This is a linear search, where I may have to search each aisle until I find the item. This type of search is effective for larger stores with many items, as it is relatively simple and efficient.
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ben participates in a prize draw. he receives one prize that is equally likely to be worth $5, $10 or $20. jamie participates in a different prize draw. she receives one prize that is equally likely to be worth $30 or $40. what is the probability that the total value of their prizes is exactly $50?
The probability of getting a total value of $50 is 1/6.
There are three possible outcomes for Ben's prize: $5, $10, or $20.
There are two possible outcomes for Jamie's prize: $30 or $40.
Therefore, there are 3 x 2 = 6 total possible outcomes for the combined value of their prizes.
To find the probability that the total value of their prizes is exactly $50, we need to find the number of outcomes that result in a total value of $50, and divide that by the total number of possible outcomes.
The only way to get a total value of exactly $50 is that Ben wins $20 and Jamie wins $30. This is only one combination out of 6 possible combinations. So the probability of getting a total value of $50 is 1/6 or approximately 0.166.
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6. Kori and Mue decided to start a business. Korir contributed shs.40, 000 and Mue shs.64000. The two men agreed that in any year, 15% of the profit shall be divided equally between them and 20% of the profit will be used to meet the cost of running the business the following year. They also agreed to share the rest of the profit in the ratio of their contributions. The profit made after the first year was shs.43200. How much did they set aside towards the cost of running the business for the second year? How much did Mue receive at the end of the first year? Korir bought cows with his share of the profit. If each cow cost shs.1800, how many cows did he buy?
The answer to each part is given above.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign {%}.Given is a business collaboration between Kori and Mue.
( 1 ) -The amount set aside for running the business is -
{A} = 20% of 43200
{A} = 20/100 x 43200
{A} = 20 x 432
{A} = 8640
( 2 ) -15% of 43200
(15/100) x 43200
15 x 432
6480
Amount recieved after sharing 15% of profit equally = 6480/2 = 3240
Ratio of contributions -
Kori : Mue = 40000 : 64000 = 40000/64000 = 5 : 8
Kori : Mue = 5 : 8
So, we can write -
5x + 8x = 43200
13x = 43200
x = (43200/13)
x = 3323.1
Amount recieved by Kori will be -
3323.1 + 3240
$6563.1
Therefore, the answer to each part is given above.
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PLEASE HELP! THIS IS TIMED.. (WILL GIVE BRAINLIEST IF ANSWER IS CORRECT)
Answer: A
Step-by-step explanation:
1/5k-2/3j=-2/3j+1/5k
Let U = (a, b, c, d, e, f, g, h, i, j, k}.
Let A = {a, b, c, d, e, j}.
Let B={b, c, d, e, h}.
Let C= {a, c, f, j, k}.
Determine An C.
....
B
Choose the correct answer below and, if necessary, fill in the answer box in your choice.
A. An C= {aj) (Use a comma to separate answers as needed.)
B. An C is the empty set.
Answer:
See below
Step-by-step explanation:
[tex]A\cap C=\{a,c,j\}[/tex] because elements a, c, and j are contained in both sets A and C
In AMNO, m = 270 cm, ZM-8° and ZN=108°. Find the area of AMNO, to the
nearest square centimeter.
Therefore , the solution of the given problem of triangle comes out to be Area = 2700 cm square .
A triangle is what exactly?An triangle is a polygon since it has four or more parts. It is a simple geometric shape. A square having angles A, B, and C is referred to as a triangle ABC. When the sides are not collinear, Euclidean geometry generates a single plane and square. If a triangle has three sides and three corners, it is a polygon. The corners of a triangle are where its three sides meet. The sum of the angles in a triangle is 180 degrees.
Here,
Given : we have
In ΔMNO, m = 270 cm
=> Area = 1/2 * b *h
=> Area = 1/2 * 270 * 20
=> Area = 2700 cm square
Therefore , the solution of the given problem of angles comes out to be
Area = 2700 cm square .
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at a party there are only single women and married men with their wives. the probability that a randomly selected woman is single is $\frac{2}{5}$. what fraction of the people in the room are married men?
60% of the people in the room are married men.
We can use the information that the probability of a randomly selected woman being single is 2/5 to find the fraction of people in the room who are married men.
Let's call the fraction of people in the room who are married men x. The fraction of people in the room who are single women is (2/5) and the fraction of people in the room who are married men and their wives is (1-x)
Since there are only single women and married men with their wives at the party, we know that the sum of the fractions of single women and married men and their wives must be 1.
(2/5) + (1-x) = 1
We can solve this equation for x:
x = 1 - (2/5) = 3/5
So the fraction of people in the room who are married men is 3/5 or 0.6
So, 60% of the people in the room are married men.
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Are the ratio 1 is to 2 is to 3 equivalent?
the ratio 1 is to 2 is equivalent to 3: 6
What is an equivalent ratios?
A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.
Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.
Given ratios are 2:1 and 3:1
we can write it as 2/1 and 3/1.
The lcm of 2 and 3 is 6.
Multiply denominator of both ratio with 6, we get
2/6 and 3/6 And we can see both the ratios are not equal.
Hence, there are not equivalent ratios.
4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2
11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)
3:1 and 9:3 are equivalent ratios ------> is true
because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3
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what is the area of a triangle if the legs ar5e x and y long. if the first leg of the triangle is x and the length of the second leg is y, the formula
The area of a triangle is Area = sqrt(s(s-x)(s-y)(s-c)).
The area of a triangle can be found using the Heron's formula if we know the lengths of all three sides, or using the formula (1/2) * x * y if we know the lengths of two legs and the triangle is a right triangle.
In the case where the legs of the triangle are x and y long, if we don't know if the triangle is a right triangle, we can't use the formula (1/2) * x * y. However, we can use Heron's formula to calculate the area. Heron's formula states that the area of a triangle is equal to the square root of s(s-a)(s-b)(s-c), where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the three sides.
In this case, since we know the lengths of the two legs x and y, we can find the area of the triangle using Heron's formula as follows:
s = (x + y + c)/2
Area = sqrt(s(s-x)(s-y)(s-c))
Where c is the length of the hypotenuse of the triangle, this information is not provided, so we cannot calculate the area of the triangle.
Therefore, The area of a triangle is Area = sqrt(s(s-x)(s-y)(s-c)).
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2 multiples of eight that are squared in numbers
Find TU.
5
T
U
S
24°
Write your answer as an integer or as a decimal rounded to the nearest tenth.
TU =
The value of TU is 11 units rounded to the nearest tenth.
In triangle STU, SU=5units and angle T is 24 degrees.
To find TU use the ratio of tan to get:
tan24= SU/TU
TU = SU/tan24
TU= 5/0.445228
TU = 11.2302 ≈ 11.
Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The boldface Z is a common way to represent the set of integers in mathematical terms.
Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers. In this essay, we will learn more about integers, their definition, and their characteristics.
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Given: \overline{DC} DC bisects \angle ACB∠ACB and \overline{AC} \cong \overline{BC}. AC ≅ BC . Prove: \triangle ACD \cong \triangle BCD△ACD≅△BCD.
The congruent angles, ∠ACD and ∠BCD formed by the angle bisector [tex]\overline{DC}[/tex] the congruent segments [tex]\overline{AC}[/tex] and [tex]\overline{BC}[/tex], and the segment [tex]\overline{DC}[/tex] (congruent to itself, indicates that ΔACD ≅ ΔBCD by SAS
What is the SAS congruency rule?The SAS (Acronym for Side-Angle-Side) congruency rule states that two triangles, A and B are congruent if two sides and an included angle of the triangle A are congruent to the two sides and an included angle of the other triangle B.
The specified information are;
The bisector of ∠ACB = [tex]\overline{DC}[/tex]
Segment [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]
Required; to prove that ΔACD ≅ ΔBCD
The two-column method can be used to prove the congruency of the triangles as follows;
Step [tex]{}[/tex] Statement [tex]{}[/tex] Reasons
1. [tex]{}[/tex] [tex]\overline{DC}[/tex] bisects ∠ACB Given
[tex]{}[/tex] [tex]\overline{AC}[/tex] ≅ [tex]\overline{BC}[/tex]
2. [tex]{}[/tex] ∠ACD ≅ ∠BCD Definition of bisected angles
3. [tex]{}[/tex] [tex]\overline{CD}[/tex] ≅ [tex]\overline{CD}[/tex] Reflexive property of congruency
4. [tex]{}[/tex] ΔACD ≅ ΔBCD SAS congruency rule
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Determine the value of X
The two angles are (x+10) and the other number is 96
Answer: 43
Step-by-step explanation:
x+x+10 = 96
2x = 86
x = 43
in how many ways can a president, vice-president, and treasurer be chosen from a group of freshmen and sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions? one person cannot serve in more than one position.
Average There are 120 ways to choose the three positions so that at least one freshman and one sophomore is chosen.
There are a total of 4 possible combinations of freshman and sophomore for the three positions, with at least one of each:
1. Freshman President, Sophomore Vice-President, Sophomore Treasurer
2. Sophomore President, Freshman Vice-President, Sophomore Treasurer
3. Freshman President, Sophomore Vice-President, Freshman Treasurer
4. Sophomore President, Freshman Vice-President, Freshman Treasurer
For each of the four combinations, there are 10 possible ways to choose the specific freshmen and sophomores for the positions (5 freshmen and 5 sophomores). That means there are 40 possible ways to choose the three positions with at least one freshman and one sophomore. Multiplying this by the 3 possible orders of the positions (President-Vice-President-Treasurer, President-Treasurer-Vice-President, Vice-President-President-Treasurer) gives us a total of 120 possible ways to choose the three positions so that at least one freshman and one sophomore is chosen.
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Answer:
288 good ways
Step-by-step explanation:
:)
Which point is an approximate extrapolation for x = 30 from the line of best fit?
(30,38) is an approximate extrapolation for x = 30 from the line of best fit.
The equation of the Linear Regression line is
y=1.14 x + 3.805
A line of regression is that line that passes through none of the points, few points, or all the points in the two-dimensional coordinate plane. It tells the value of one variable when another variable is known.Q asking 4 an approximate for x=30
So (23,30) and (44,30) are out.
From the line of best fit:
x=0, y=4
x=16, y=22
x increases by 16 and y increases by 22-4=18
so at x=32, y=22+18 ⇒y=40
at x=30, the nearest best answer is (30,38).
Therefore, (30,38) is an approximate extrapolation for x = 30 from the line of best fit.
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Please somone explain how to do these algebraic expressions pleasease. i mean linear functions
Proven that expressions x = -1 in the quadratic function (2x + 1)(2x - 1) - 4(x + 2)² = -1.
What is algebraic expression?Using coefficients, unknowable variables, algebraic operations, and constants, a mathematical expression is called an algebraic expression. A sign of equality, however, is not permitted in an expression.
Mathematical expressions and phrases can be of many different kinds. Let's look at the connections between algebraic expressions and numerical expressions and equation.
Given that
(2x + 1)(2x - 1) - 4(x + 2)² = -1
Apply a² - b² = (a + b)(a - b)
(2x)² - (1)² - 4(x + 2)² = -1
4x² - 1 - 4(x + 2)² = -1
Apply (a + b)² = a² +b² + 2ab
4x² - 1 - 4 (x² + 2² + 2x×2) = -1
4x² - 1 - 4x² -16 - 16x = -1
4x² - 4x² - 16x -16 - 1 = -1
-16x -16 - 1 = -1
-16x -16 = -1 + 1
-16x = 16
x = 16/-16
x = -1
Hence, proven that expressions x = -1 in the quadratic function (2x + 1)(2x - 1) - 4(x + 2)² = -1.
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Solve the given differential equation by separation of variables.y ln x * (dx/dy) = [(y+1)/x]^2[(y^2)/2] + 2y + ln|y| =
The solution of the given differential equation is
x ln x - (x/2)(y+1)^2 + (y^3)/3 + 2y^2 + y ln|y| + c = 0
The given differential equation can be written as
ln x * (dx/dy) = [(y+1)/x]^2[(y^2)/2] + 2y + ln|y|
To solve this equation, we will use separation of variables. This means that we need to separate the terms containing 'x' and the terms containing 'y' on different sides of the equation.
We can rearrange the equation as,
ln x * (dx/dy) - [(y+1)/x]^2[(y^2)/2] - 2y - ln|y| = 0
Now, let us separate the terms containing 'x' from terms containing 'y':
ln x * (dx/dy) = [(y+1)/x]^2[(y^2)/2] + 2y + ln|y|
On one side of the equation, we have ln x * (dx/dy) and on the other side, we have [(y+1)/x]^2[(y^2)/2] + 2y + ln|y|.
Now, we can integrate both sides of the equation with respect to 'y':
∫ ln x * (dx/dy) dy = ∫ [(y+1)/x]^2[(y^2)/2] + 2y + ln|y| dy
Integrating both sides of the equation, we get
x ln x - (x/2)(y+1)^2 + (y^3)/3 + 2y^2 + y ln|y| + c = 0
where c is a constant of integration.
Therefore, the solution of the given differential equation is
x ln x - (x/2)(y+1)^2 + (y^3)/3 + 2y^2 + y ln|y| + c = 0
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during the 2000 season, the home team won 138 of the 240 regular season national football league games. is this strong evidence of a home field advantage in professional football? test an appropriate hypothesis and state your conclusion. be sure the appropriate assumptions and conditions are satisfied before you proceed.
A) The 95% confidence interval is:
0.58 ± 0.062
B) At the 0.01 probability value, there is neither substantial evidence of a home-field advantage in professional football (they won and over half of the games).
Now, According to the question:
A) Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × [tex]\frac{\sqrt{pq} }{n}[/tex]
Where:
z = The z score corresponds to the amount of confidence.
p = sample proportion.
q = probability of failure
q = 1 - p
p = x/n
Where
n = the number of samples
x = the number of success
From the information given,
n = 240
x = 138
p = 138/240 = 0.58
q = 1 - 0.58 = 0.42
To determine the z score, The confidence level from 100% to get α
α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025
Thus,
1 - 0.025 = 0.975
The z -score associated with the area just on z table approximately 1.96. Therefore, the z score with a 95% confidence level is 1.96.
As a result, the 95% confidence interval becomes
0.58 ± 1.96√(0.58)(0.42)/240
Confidence interval is
0.58 ± 0.062
B) Earning more than half of the games equates to winning 120 games or more.
p = 120/240 = 0.5
The hypothesis test will be
For the null hypothesis,
P ≥ 0.5
For the alternative hypothesis,
P < 0.5
Probability of success, p = 0.5
q = probability of failure = 1 - p
q = 1 - 0.5 = 0.5
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 138
n = number of samples = 240
P = 138/240 = 0.58
We need to find the values of the test statistic which will be the z score
z = (P - p)/√pq/n
z = (0.58 - 0.5)/√(0.5 × 0.5)/240 = 2.48
Remember that this is a two-tailed test. We would use the normal distribution table to calculate the probability potential of the property to the right of both the z score.
P value will be = 1 - 0.9934 = 0.0066
Since alpha, 0.01 > the p value, 0.0066, then we would reject the null hypothesis.
The given question is incomplete, The complete question is this:
__"During the 2000 season, the home team won 138 out of 240 regular season National Football League games. (15 points) a) Construct a 95% confidence interval for the winning proportion of the home team during this season. b) At the 0.01 significance level, is there strong evidence of a home field advantage (they win more than half of the games) in professional football? State hypotheses, calculate the test statistic and p-value, and make a conclusion in context"__
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Mr.Gardener wants to have an annual interest of $1000.0. If the annual interest rate is 5%, how much money should he invest?
Answer:
20,000
Step-by-step explanation:
1,000/ 5% = 20,000
How do I solve this?
Answer:
DB = 15
Step-by-step explanation:
∠ C and ∠ D are the base angles of Δ BCD
since they are congruent , that is ∠ D = ∠ C
Then the triangle is isosceles with the legs being congruent, so
DB = BC = 15
Can 2.5 cm 6.5 cm 6 cm be the sides of a right triangle?
2.5 cm, 6.5 cm, and 6 cm are the sides of a right triangle.
The sides of a triangle are 2.5 cm, 6.5 cm, and 6 cm in length.
The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.
[tex](Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}[/tex]
[tex](2.5)^{2}+(6)^{2}=(6.5)^{2}[/tex]
6.25 + 36 = 42.25
42.25 = 42.25
The sides offered satisfy the specifications for a right triangle.
Given that it satisfies the Pythagorean theorem, a right triangle with sides of 2.5 cm, 6.5 cm, and 6 cm can be built.
Hence, 2.5 cm 6.5 cm 6 cm can be the sides of a right triangle.
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A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
What statement best compares the theoretical and experimental probability of landing on orange?
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.
Answer:
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.
Step-by-step explanationThe theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.:
Answer:
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
Step-by-step explanation:
Since the 4 sections are equal, theoretical probability is given by:
p = 1/4
Out of 20 trials, 4 resulted in pink, hence experimental probability is given by:
p = 4/20 = 0.2 = 20%.
Hence,
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
If 10% of a number is 26 and 25% of the same number is 65, what is 15% of that number
15% of that number is 39.
What is a percentage?
A percentage is a way to express a number as a fraction of 100. It is commonly used to represent a proportion or ratio of a number to a whole. For example, 10% of a number means 10/100 or 1/10 of that number, 25% means 25/100 or 1/4 of that number, and 15% means 15/100 or 3/20 of that number.
To find 15% of a number, if we know that 10% of it is 26, and 25% of it is 65, we can use algebra:
Let X be the number we're trying to find
10% of X = 0.10X = 26
25% of X = 0.25X = 65
We know that 15% is between 10% and 25% so we can use the proportionality between them:
15% of X = 0.15X = (15/10)*26 = 39
Hence, 15% of that number is 39.
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∠P measures 30° more than the measure of its supplement. What is the measure of ∠P in degrees?
Applying the definition o a supplement of an angle, the measure of angle P in degrees is: 105°.
What is the Supplement of an Angle?The supplement of an angle is defined as the angle measure that is added to the angle to give a sum of 180 degrees.
For example, the supplement of angle X is 180 - measure of angle X.
Given the following:
Supplement of angle P = 180 - measure of angle P
Measure of angle P = (180 - measure of angle P) + 30 degrees
Therefore:
(180 - m<P) + [(180 - m<P) + 30] = 180
Open the parentheses:
180 - m<P + 180 - m<P + 30 = 180
Combine like terms:
390 - 2(m<P) = 180
390 - 180 = 2(m<P)
210 = 2(m<P)
210/2 = 2(m<P)/2
105 = m<P
m<P = 105°
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