The maximum possible number of points where two polygons can intersect is [tex]$n = 4$[/tex]. This is achieved when the two polygons are tangent to each other at four points.
Maximum Intersection Point CountThere are different ways to approach the problem of determining the maximum possible number of points where two polygons can intersect, but one possible method is to use geometric principles and constructive examples. Here is one possible way to do it:
Start with a heptagon and a hexagon that are both regular (i.e., all sides and angles are equal).Place the heptagon in the plane so that one of its vertices coincides with the center of the hexagon.Draw an equilateral triangle with sides of the same length as the heptagon's sides, and one of its vertices at the center of the hexagon.Connect the center of the hexagon to each vertex of the triangle, forming six congruent isosceles triangles.Draw a line segment from the center of the hexagon to the middle point of each side of the heptagon. This divides the heptagon into 14 congruent isosceles triangles.Now, it is clear that the heptagon and hexagon intersect at 4 points.This is a constructive example for showing that the maximum possible number of intersection points between heptagon and hexagon is 4.
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Given the geometric sequence where a1 = 7 and the common ratio is 3, what is the domain for n?
All integers where n ≥ 1
All integers where n ≥ 0
All integers where n > 7
All integers
The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.
What is a geometric sequence?A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The geometric sequence where a₁ = 7 and the common ratio is 3. Then the formula is given as,
aₙ = 7 · (3)ⁿ⁻¹
In the geometric sequence, the value of the exponent should be greater than or equal to zero. Then we have
n - 1 ≥ 0
n ≥ 1
The domain for 'n' will be all integers where n ≥ 1. Then the correct option is A.
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You measure the mass of a ring three times using the same balance and get slightly different values: 17.46 g, 17.42 g, 17.44 g
The variation in the values is due to random error. Hence, it can be reduced by taking more observations to estimate the measure of the mass of the ring.
One way to minimize experimental error in this situation is to take multiple measurements and use the average of those measurements as the final value. This helps to account for any small fluctuations or inaccuracies in the individual measurements.
Also, it is important to ensure that the balance is properly calibrated and that the ring is placed on the balance in the same way each time.
Other ways to minimize experimental error include using a more precise measuring instrument, such as a digital scale, and ensuring that the lab environment is controlled and stable (i.e. no drafts or vibrations that could affect the measurements).
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The complete question is -
You measure the mass of a ring to be used in your experiment three times using the same balance and get slightly different values: 17.46 g, 17.42 g, and 17.44 g. How can you minimize experimental error?
I need the answer as soon as possible!
3x + 4y^2 ; x = -3 and y = 5
Thank You!
The value of the expression 3x + 4y² when x = -3 and y = 5 is 91.
What is the value of the given expression?Given the expression in the question;
3x + 4y²
x = -3y = 5To determine the value of the expression when x = -3 and y = 5, plug in x = -3 and y = 5 for every x and values in the expression and simplify.
3x + 4y²
3( -3 ) + 4( 5 )²
Simplify
Take the square of 5
3( -3 ) + 4( 25 )
Multiply 3 and -3
-9 + 4( 25 )
Multiply 4 and 25
-9 + 100
Add -9 and 100
91
Therefore, the value of the expression is 91.
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Find the following for the given functions.
f(x): =
X/X + 9 ,
g(x) = x³
The results of operations between functions:
Case A: (f + g) (x) = x / (x + 9) + x³
Case B: (f - g) (x) = x / (x + 9) - x³
Case C: (f · g) (x) = x⁴ / (x + 9)
Case D: (f / g) (x) = 1 / [x² · (x + 9)]
Function (f / g) (x) has the following domain: x ∈ R - {- 9, 0}.
How to find the result of operations between two functions
According to function theory, we can obtain a function with more complexity by operations between two functions, the most common operations are listed below:
Addition: (f + g) (x) = f (x) + g (x)Subtraction: (f - g) (x) = f (x) - g (x)Multiplication: (f · g) (x) = f(x) · g(x)Division: (f / g) (x) = f (x) / g (x)Now we proceed to determine the resulting function:
Case A:
(f + g) (x) = f(x) + g(x)
(f + g) (x) = x / (x + 9) + x³
Case B:
(f - g) (x) = f(x) - g(x)
(f - g) (x) = x / (x + 9) - x³
Case C:
(f · g) (x) = f (x) · g (x)
(f · g) (x) = [x / (x + 9)] · x³
(f · g) (x) = x⁴ / (x + 9)
Case D:
(f / g) (x) = f(x) / g(x)
(f / g) (x) = [x / (x + 9)] / x³
(f / g) (x) = 1 / [x² · (x + 9)]
The domain of (f / g) (x) is the set of all values of x-values such that the function exists. In this case, we must determine the values of the denominator of (f / g) (x) such that it is not equal to zero.
x² · (x + 9) = 0
x = 0 or x = - 9
The domain of (f / g) (x) is: x ∈ R - {- 9, 0}.
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help me with 6th grade math
The value of x that solves the equation is x = 28.10, and there are 4 eggs per batch.
Which value satisfies the equation?Particularly x is not in that equation, but we can write:
5x = 140.50
To solve for x, we need to divide both sides by 5, then we will get:
5x/5 = 140.50/5
x = 140.50/5
x = 28.10
How many eggs are needed per batch?To find this, we need to take the quotient between the number of eggs and the number of batches, so we will get:
12 eggs.
3 batches.
12/3 = 4
This means that you need 4 eggs per batch.
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6=7/w-3 solve for w??????
Answer:
w=7/9
Step-by-step explanation:
6=7/w-3
Move the terms
6=7/w-3, w [tex]\neq[/tex] 0
Calculate
-7/w=-3-6
Multiply both sides
-7/w=-9
Swap the sides
7=9w
Divide both sides
9w=7
w=7/9, w [tex]\neq[/tex] 0
w=7/9
3.3x0.14 = ?
hazgxjklkkspkoxdh
Answer:
Step-by-step explanation:
0.462
Answer:
0.462 :) hope this helps and please put me as brainiest thankyou !!
Step-by-step explanation:
Determine the slope of the linear relationship
The increase in the y-coordinatesis then calculated by dividing it by the change in the x-coordinates.
How can you determine a linear graph's slope?Locating Slope using a graphChoose two random spots on the line's graph (preferably with integer coordinates).Identify them as A and B. (in any order).The "rise" from A to B should be calculated. If necessary, when moving vertically from point A to point B.Determine the "run" distance from A to B.Apply the following equation: slope = rise/run.You need the coordinates for two points on a line in order to calculate its slope. The increase in the y-coordinates (also known as the slope) is then calculated by dividing it by the change in the x-coordinates (referred to as the run).-6 to 29-2 to 152 to 18 to -20To learn more about linear relationship refer to:
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At a local pizza shop, the delivery person earns $2 for every pizza delivered, plus $70 per day. How many pizzas must the delivery person deliver to earn more than $100 in one day? Write an inequality to represent this situation.
70 + 2x > 100 is an inequality to represent this situation.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
Given, At a local pizza shop, the delivery person earns $2 for every pizza delivered, plus $70 per day.
Let "x" be the number of pizzas he delivers
Thus, the Total money he earns by delivering pizza = 70 + 2x
To earn more than 100$ inequality represents
70 + 2x > 100
So,
2x > 30
x > 15
Therefore, to earn more than 100$ every day he needs to deliver at least 15 pizzas.
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If you borrow $220,000 at an APR of 3.5% for 25 years, you will pay $1,101.37 per month. If you borrow the same amount at the same APR for 30 years, you will pay $987.90 per month.
a. What is the total interest paid on the 25-year mortgage?
b. What is the total interest paid on the 30-year mortgage?
a. The total interest paid on the 25-year mortgage is $110411.
b. The total interest paid on the 30-year mortgage is $135644.
What is the meaning of APR?
Annual percentage rate (APR) is the term used to describe the annual interest produced by a sum that is levied against borrowers or distributed to investors. APR is a percentage that expresses the actual yearly cost of borrowing money over the course of a loan or the income from an investment. This does not account for compounding and includes any fees or additional costs related to the transaction. Consumers can compare lenders, credit cards, or investment products using the APR as a benchmark figure.
Given that, the amount that is borrowed is $220,000.
If you borrow it for 25 years, you will pay $1,101.37 monthly.
The amount that you need to pay is (1,101.37×12×25) = 330411.
The total interest is = (330411 - 220,000) = $110411.
If you borrow it for 30 years, you will pay $987.90 monthly.
The amount that you need to pay is (987.90×12×30) = 355644.
The total interest is = (355644 - 220,000) = $135644
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I can’t fit the whole question but if anybody knows this it would be great
The glide reflection that maps triangle ABC into triangle A'B'C' is given as follows:
Shift right of 7 units and reflection over the x-axis.
What is a glide reflection?The glide reflection is a combination of a reflection with a translation.
The vertices of the original triangle are given as follows:
A(-3,-2), B(-6,-5) and C(-1,-4).
The vertices of the reflected triangle are given as follows:
A'(4,2), B'(1,5) and C'(6,4).
Hence the composite rule is given as follows:
(x,y) -> (x + 7, -y).
Meaning that the glide reflection is defined as follows:
x -> x + 7: translation of 7 units right.y -> -y: reflection over the x-axis.More can be learned about glide reflections at brainly.com/question/5612016
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Which set of numbers could be the side lengths that will form a triangle?
All u have to do is use the Traingle Inequality theorem, which states that the sum of two sides lenghts of a triangle is always greater than the third side. if this is true for all three combinations of added side lengths then you will have a triangle
Hope this helps :>
Answer:
3, 5, 7
Step-by-step explanation:
given 3 sides, for a triangle to be formed, then the sum of any 2 sides must be greater than the third side.
4 , 4 , 8
4 + 4 = 8 , not greater than 8, so does not form a triangle
1 , 2 , 3
1 + 2 = 3 , not greater than 3, so does not form a triangle
3 , 9 , 14
3 + 9 = 12 < 14 , so does not form a triangle
3 , 5 , 7
3 + 5 = 8 > 7
3 + 7 = 10 > 5
5 + 7 = 12 > 3
condition is satisfied , so will form a triangle
what is the largest power of 10 that is a factor of the following numbers, i.e., how many zeroes are at the end of the decimal representation? a. 50! b. 1000!
In 50! will have 12 leading zeroes so the power of 10 will be 12 And for 1000! will have 249 Zeroes so here the power of 10 will be 249.
We calculate the leading zeroes by knowing the numbers 2 And 5 So
This number must end with 249 zeroes since there are 249 fives (and more than 249 twos) in its prime factorization. Thus 10 249 is the highest power of 10 that divides 1000!
To see why we have 249 powers of five:
there are 200 numbers ≤ 1000 that are multiples of 5there are 40 numbers ≤ 1000 that are multiples of 5^2 = 25there are 8 numbers ≤ 1000 that are multiples of 5^3 = 125there is 1 number ≤ 1000 is a multiple of 5^4 = 625200 + 48 + 8 + 1 = 249
And also we can do this with a formula n−σp(n)/(p−1) where σp(n) is the sum of the digits of n written in base-p
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.
What is the Puzzle code for puzzle 2.
Linear equation Digital Escape!!!
Please need the puzzle code for PUZZLE 2. WILL GIVE BRAINLIST.
All the equations are matched with the line graph are given below.
And the letter code is AEBG.
What is graph?In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.
The relationships between two or more items are frequently represented by the points on a graph.
Given:
All the equations are matched with the line graph:
A: y = 3x + 1 → Line 1
B: y = -2x + 2 → Line 3
G: y = -1/2x + 2 → Line 4
E : y = x+ 4 → Line 2
The letter code is AEBG.
Therefore, the letter code is AEBG.
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Solve the equation
1
4
(4x − 24) + x = 14.
The solution to an equation is 10.Solving an equation refers to the process of determining its solution.
Which one provides an answer to the problem?A variable's value that, when substituted into the equation, results in a true assertion is known as the solution. Solving an equation refers to the process of determining its solution. Finding the value of the variable that causes an equation to hold true is referred to as finding the solution to an equation.Solving an equation refers to the process of determining its solution. Finding the value of the variable that causes an equation to hold true is referred to as finding the solution to an equation.Make the available
14to obtain the desired amount:
x – 6 + x = 14
Put similar phrases together to get:
2x – 6 = 14
Adding 6 to both sides yields:
2x = 20
x = 10.
The complete question is,
1 4 (4x 24) + x = 14 must be solved.
By dividing the 1 by 4, you can obtain:
Put similar phrases together to get:
Adding 6 to both sides yields:
x =
Consequently, is the necessary response.
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5. Over the last 35 years, the average price of computers has dropped 76%. People now spend an average of $1,456 less for a computer today. How much did the average computer cost 35 years ago? Round to the nearest cent O$1,899.79 O $2,262.79 O $459.79 O$1,915.79
The average of cost computers was $1,915.79 35 years ago. The correct answer would be an option (D).
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Let the average computer cost was x 35 years ago.
As per the question, we have
76% of x = $1,456
76% is expressed as 0.76 in decimal form
0.76x = 1,456
x = 1,456/0.76
x = 1,915.7947
Rounded to the nearest cent, and we get
x = 1,915.79
Thus, the average of cost computers was $1,915.79.
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12. The ratio of dolphins to penguins is 2:5. So, for every 2 dolphins, there are 5 penguins. If there are 30 penguins, how many dolphins would there be?
If the ratio of dolphins to penguins is 2:5, then for every 2 dolphins, there are 5 penguins. If there are 30 penguins, you can use this ratio to find out how many dolphins there are. To find out how many dolphins there are, you can set up a proportion:
(number of dolphins) / (number of penguins) = (2) / (5)
You know that the number of penguins is 30, so you can substitute that in and solve for the number of dolphins:
(number of dolphins) / 30 = 2 / 5
Multiply both sides by 30 to solve for the number of dolphins:
number of dolphins = (2/5) * 30 = 6
So, if there are 30 penguins, there would be 6 dolphins.
Which expression is equivalent to 64x - 16?
O 16(4x + 1)
O-16 (4x - 1)
16(4x - 1)
- 16(4x + 1)
whoever answers first will be brainlyist
delta airlines quotes a flight time of hours, minutes for its flights from cincinnati to tampa. suppose we believe that actual flight times are uniformly distributed between hours and hours, minutes.
The required probability for the given delta airlines is given by :
a. Probability of flight late no more than 5 minutes is 0.25.
b. Probability of flight late more than 10 minutes is 0.5
c. Expected flight time is equal to 130 minutes.
Flight time from Cincinnati to Tampa = 2 hours 5 minutes
Actual time distributed between 2 hours and 2 hours 20 minutes
2 hours = 120 minutes
2 hours 20 minutes = 140 minutes
f(x) = [tex]\left \{ {{\frac{1}{( 140 - 120)} , 120 \leq x\leq 140\atop {0 , x = 0 }} \right.[/tex]
a. Probability of flight no more than 5 minutes late
[tex]\int_{130}^{125} \frac{1}{20} dx[/tex]
= 1 / 4
= 0.25
b. Probability of flight more than 10 minutes late
[tex]\int_{135}^{125} \frac{1}{20} dx[/tex]
= 1/2
= 0.5
c. Expected flight time in minutes
= [tex]\int_{140}^{120} \frac{x}{20} dx[/tex]
= 130 minutes
Therefore, the required probability are given by :
a. Probability of flight late no more than 5 minutes is 0.25.
b. Probability of flight late more than 10 minutes is 0.5
c. Expected flight time is equal to 130 minutes.
The above question is incomplete , the complete question is :
Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. What is the probability that the flight will be no more than 5 minutes late (to 2 decimals)? What is the probability that the flight will be more than 10 minutes late (to 2 decimals)? What is the expected flight time, in minutes?
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Find the midpoint between (-1, -5) and (-5, 9) by using the Midpoint Formula.
Answer: Midpoints (-3/2)
Step-by-step explanation:
Midpoint formula is (x1+x2)/2 , (y1+y2)/2
Plugin x values and solve
(-1 +-5)/2 = -3
Plugin y values and solve
(-5+9)/2 = 2
The midpoint is -3/2
I hope this helped you :D
please please please help
Answer:
[tex]\underline{x\quad \:\:\:\:\:\:-8\quad\quad\;\;-6\quad\quad0\quad\quad\quad\;\; \;\;2}\\y\quad\quad\;\;\;\boxed{\dfrac{1}{3}}\quad\quad\quad \boxed{0} \quad\;\boxed{-1} \quad\quad \boxed{\dfrac{4}{3}}[/tex]
Step-by-step explanation:
The strategy is to substitute the value of each of the given x values into the equation
[tex]y = -\dfrac{x}{6} - 1[/tex]
and find the corresponding value for [tex]y[/tex]
[tex]x\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{x}{6} - 1\\\line(1,0){180}\\\\[/tex]
[tex]-8\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-8}{6} - 1 = \bf{{\dfrac{1}{3}[/tex]
[tex]-6\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{-6}{6}-1 = \bf{0}[/tex]
[tex]0\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{0}{6}-1 = \bf{-1}[/tex]
[tex]2\quad\quad\quad\quad\quad\quad\quad\quad\quad y = -\dfrac{2}{6} -1 =\bf{-}\dfrac{4}{3}[/tex]
[tex]\line(1,0){180}\\\\[/tex][tex]\line(1,0){180}\\\\[/tex]
Describe the y-intercept and end behavior of the following graph: The graph starts on the top left and curves down to the right, crosses the x axis at negative 2, then crosses the y axis at negative 4 and continues decreasing to the bottom right. a (−2, 0); The graph approaches y = −6 to the right. b (0, −5); The graph approaches y = −6 to the right. c (−2, 0); The graph decreases to the left. d (0, −5); The graph decreases to the left.
The correct alternative is -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the graph of the function.
The correct alternatives are -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).Therefore, the correct alternative is -
The graph starts on the top left and curves down to the right, crosses the {x} axis at -2, then crosses the {y} axis at -4 and continues decreasing to the bottom right to (−2, 0).To solve more questions on graphs, visit the link below-
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Imagine a study that looks at nutrition and memory. Each subject is randomly assigned to one of three groups: high-protein diet; high-fiber diet; standard diet (control). After a month on this diet, each subject undergoes a memory test. The initial statistical analysis of this study would be conducted using __________ because __________.
A. Analysis of variance (ANOVA) / there are more than two levels of the independent variable
B. Analysis of variance (ANOVA) / there are more than two levels of the dependent variable
C. A t test / there are only two experimental conditions (plus a control condition)
D. A t test / the goal would be to compare high-protein with control and high-fiber with control
Options
at westville high school there are 315 seniors and 389 juniors. 65% of the seniors have parkign passes and 42% of teh juior have parking passes. the statistics teacher selects a srs of 30 seniors and a seperate srs of 30 juniors.
a. The shape of the sampling distribution is normal by the Central Limit Theorem.
b. The mean is 0.23.
c. The standard error is 0.125, which means that the sample proportions differ by around 0.125 from the mean of 0.23.
d. The probability is 0.2877 = 28.77%.
By the Central Limit Theorem, each sample has at least 10 successes and at least 10 failures, and the shape of the distribution is normal.
For each sample, the mean and the standard error are specified as follows:
Seniors : [tex]p_{s} = 0.65, s_{s} =\sqrt{\frac{0.65(0.35)}{30} } = 0.087[/tex]Juniors : [tex]p_{j}= 0.42, s_{j} =\sqrt{\frac{0.42(0.58)}{30} } = 0.09[/tex]Hence, the distribution of differences, the mean, and the standard error are specified as follows:
Mean= 0.65 - 0.42 = 0.23.Standard error: [tex]s =\sqrt{0.087^{2}+0.09^{2} } = 0.125[/tex]Using the z-score formula, the probability that the difference is greater than 30 is 1 subtracted by the p-value of Z when X = 0.3, Therefore:
Z = (0.3 - 0.23)/0.125
Z = 0.56
Z = 0.56
1 - 0.7123 = 0.2877 = 28.77%.
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The complete question is:
At Westville High School there are 315 seniors and 389 juniors. 65% of the seniors have parking passes and 42% of the juniors have parking passes. The statistics teacher selects an SRS of 30 seniors and a separate SRS of 30 juniors. Let ^ps-^pj be the difference in the sample proportion of seniors and juniors that have parking passes.
a. What is the shape of the sampling distribution of ^ps-^pj? Why?
b. Find the mean of the sampling distribution.
c. Calculate and interpret the standard deviation of the sampling distribution.
d. What is the probability that the difference in sample proportions (senior-junior) of students with parking passes is greater than 30%?
In a closed bottle, the product of the pressure and volume is constant. By what percent mist the volume be decreased to increse the pressure by 25%?
Answer: This is known as Gay-Lussac's Law.
The relationship states that the pressure and volume of a gas are directly proportional at constant temperature. Therefore, if the pressure is increased by 25%, the volume must be decreased by 25% to maintain the constant product of pressure and volume.
during a severe storm, electrical transformers that function independently are expected to operate 85 percent of the time. suppose 20 electrical transformers are randomly selected from the population. let the random variable t represent the number of electrical transformers operating during a severe storm. which of the following is the best interpretation of the random variable t ?
The binomial variable with mean 17 transformers and standard deviation √2.55 transformers.
In math standard deviation is defined as a measure of how dispersed the data is in relation to the mean.
Here we have know that the good electrical transformers operate at approximate 85% of the total time and 20 electrical transformers are chosen at random.
Here let us assuming the variable is a binomial variable.
Then we have written it as in the following form,
=> Mean = number of samples * probability
And the value of standard deviation is calculated as
=> Standard Deviation = √mean (1 − probability)
Here we know that the value of mean is calculated as,
=> 85% * 20 = 0.85*20 = 17 transformers
Then the value of Standard deviation is calculated as,
=> √mean * (1 − 0.85)
Apply the values on the formula, then we get,
=> √17 * 0.15 =√2.55 transformers.
Hence the random variable is a binomial variable.
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NO LINKS!!!
Please help me #49 and 50
Answer:
49. a) A - C - 1
49. b) 1 - 2R
49. c) 2Q - P
50. x = 103
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{5cm}\underline{Log laws}\\\\$\log_axy=\log_ax + \log_ay$\\\\$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\$\log_ax^n=n\log_ax$\\\\$\log_ab=c \iff b=a^c$\\\\&\log_aa=1$\\ \end{minipage}}[/tex]
Question 49Part a
Given:
[tex]\log_5 9=A[/tex]
[tex]\log_5 6=B[/tex]
[tex]\log_5 11=C[/tex]
[tex]\begin{aligned}\log_5 \dfrac{9}{55}&=\log_5 9 - \log_5 55\\&=\log_5 9 - \log_5 (11 \cdot 5)\\&=\log_5 9 - (\log_5 11 + \log_5 5)\\&=\log_5 9 - \log_5 11 - \log_5 5\\&=A-C-1\\\end{aligned}[/tex]
Part b
Given:
[tex]\log_3 10=R[/tex]
[tex]\log_3 4=S[/tex]
[tex]\log_3 11=T[/tex]
[tex]\begin{aligned}\log_3 \dfrac{3}{100}&=\log_3 3 - \log_3 100\\&=\log_3 3 - \log_3 (10 \cdot 10)\\&=\log_3 3 - \log_3 10^2\\&=\log_3 3 - 2\log_3 10\\&=1-2R\\\end{aligned}[/tex]
Part c
Given:
[tex]\log_3 4=P[/tex]
[tex]\log_3 10=Q[/tex]
[tex]\log_3 7=R[/tex]
[tex]\begin{aligned}\log_3 25&=\log_3 \dfrac{100}{4}\\&=\log_3 100 - \log_3 4\\&=\log_3 (10 \cdot 10) - \log_3 4\\&=\log_3 10^2 - \log_3 4\\&=2 \log_3 10 - \log_3 4\\&=2Q-P\end{aligned}[/tex]
Question 50The error was in line 4 of the calculation. The log law
[tex]\log_ab=c \iff b=a^c[/tex]was not applied correctly.
The correct solution is:
[tex]\begin{aligned}3 \log (x-3) + 1 & = 7\\3 \log (x-3) & = 6\\\log (x-3) & = 2\\x-3&=10^2\\x&=3+10^2\\x&=103\end{aligned}[/tex]
Function Tables
Thank you!
The complete function tables are written above.
What is a function? What is a quadratic function?A function describes a relationship between a dependent and independent variable. Example -
y = f(x) = 5x + 9
A quadratic function is of the form -
f(x) = ax² + bx + c
Given are the function tables as shown in the image attached.
{ 4 } -
Rule : h = 8c
{c} 2 3 4 5 6 7
{h} 16 24 32 45 48 56
{5} -
Rule : k = 2r
{r} 6 7 8 9 12 11 14
{k} 12 14 16 18 24 22 28
{6} -
Rule : k = 2r
{r} 6 7 8 9 12 11 14
{k} 12 14 16 18 24 22 28
Therefore, the complete function tables are written above.
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His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without the tax?
The amount that he pays for the cooler alone without the tax will be $7.37.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
His total bill, with tax, was $7.95. He paid 6 percent sales tax.
Let 'x' be the total bill without the sales tax. Then the equation is given as,
107.95% of x = $7.95
1.0795x = $7.95
x = $7.37
The amount that he pays for the cooler alone without the tax will be $7.37.
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MAKING FAIR DECISIONS
2. A group of 6 students are in the school chess club. Their teacher has 2 tickets to a chess tournament She wants to make sure she has a fair way of deciding which 2 students will win the tickets. She decides that every time a student wins a chess match, that student's name will be put in a hat for a chance to win the tickets. She will choose two names from the hat at the end of the week
Part A: Is the teacher's method fair? Explain. If it is not fair, explain how you would change her method to make it fair. (5 points: 1 point for correctly deciding whether the method is fair or unfair, 4 points for the explanation and, if it is unfair, for a correction to the method)
Part B: Two new students join the chess club. The teacher wants to include them in the chance to win the tickets. How can she set up a fair way to make the decision that includes everyone? Explain why this method is fair (5 points)
Part A: The teacher's method is partially fair.
Part B: She can set up a fair way to make the decision that includes everyone by making it an open tournament for all such that all can participate.
How can she make the decision to be fair?Part A: The teacher's method is fair in terms of giving all students an equal opportunity to win the tickets by playing chess matches and having their names put into the hat.
However, it does not take into account the skill level of the students, which could result in a less skilled student winning the tickets over a more skilled student. To make the method more fair, the teacher could use a combination of wins and chess ratings to determine which students have the best chance to win the tickets.
Part B: To include the new students in the chance to win the tickets, the teacher could have them play chess matches against the current club members and use a combination of wins and chess ratings to determine the two students who will win the tickets.
This method is fair because it gives all students, including the new ones, the opportunity to compete and be recognized for their chess skills, rather than simply giving the tickets to the two students who have been in the club the longest. Additionally, using a combination of wins and ratings ensures that the most skilled players have a better chance of winning the tickets.
Therefore, the correct answer is as given above
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