A cylinder and cone having the same volume. The cylinder having radius x and height y. The cone has radius 12x. Then, the height of the cone in terms of y is 48h.
The volume of the cylinder will be given by the formula V_cylinder = [tex]πr^{2h}[/tex], where r is radius and h is height. The volume of a cone is given by the formula V_cone = (1/3)[tex]πr^{2h}[/tex], where r is the radius and h is the height.
Since the cylinder and cone have the same volume, we can set their volume formulas equal to each other and solve for the height of the cone;
[tex]πX^{2y}[/tex] = (1/3)[tex]π(12X)^{2h}[/tex]
Simplifying, we get;
[tex]πX^{2y}[/tex] = [tex]π144X^{2h/3}[/tex]
Dividing both sides by [tex]πX^{2}[/tex], we get;
y = 144h/3
Simplifying further, we get;
y = 48h
Therefore, the height of the cone in terms of y is h = (1/48)y.
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Sara is making a scale drawing of a clock tower. She knows the clock tower is 99 feet tall. If every 2 centimeters on her drawing equals 12 feet, what is the height of the clock tower in her drawing in centimeters?
The height of the clock tower in Sara's drawing is 16.5 centimeters.
What is a scale image?Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.
The scale factor is 12 feet per 2 centimeters, which simplifies to 6 feet per 1 centimeter.
First, we need to figure out how many centimeters on Sara's drawing represent one foot:
2 cm : 12 ft
We can simplify this ratio by dividing both sides by 2:
1 cm : 6 ft
Now we can use this ratio to find the height of the clock tower in centimeters:
99 ft × (1 cm/6 ft) = 16.5 cm
Therefore, the height of the clock tower in Sara's drawing is 16.5 centimeters.
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Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 8, 10}, and C = {2, 4, 5, 6, 7, 9}. List the elements of each set. (Enter your answers using roster notation. Enter EMPTY or ∅ for the empty set.)
The list of elements of each set are as follows:-
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 3, 5, 7, 9}
B = {2, 4, 6, 8, 10}
C = {2, 4, 5, 6, 7, 9}
What are sets?A set in mathematics is a collection of unique objects, referred to as elements or members, that are paired off according to some shared quality.
For instance, 1, 2, 3, 4, 5, 6, 7, and 8 make up the set of all natural numbers that are less than 10. There are several ways to describe sets, including by describing its components, using set builder notation, or by utilising set operations.
Given that-
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 3, 5, 7, 9}
B = {2, 4, 6, 8, 10}
C = {2, 4, 5, 6, 7, 9}
Set U contains all the numbers from 1 to 10, so U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Set A contains only the odd numbers from 1 to 10, so A = {1, 3, 5, 7, 9}.
Set B contains only the even numbers from 1 to 10, so B = {2, 4, 6, 8, 10}.
Set C contains the numbers that are in both A and B, so C = {2, 4, 5, 6, 7, 9}.
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Jeffery made a table of values
representing the ratios of side
lengths of some squares to their
perimeters. He made some
mistakes.
Part A:
Click the wrong answers.
Part B:
Drag numbers into each box to
produce the correct answers.
Place the smaller number in the
box on the left.
The ratio of the length of a side of a square to its perimeter is **1:4**. Therefore, any ratio that is not equivalent to 1:4 is a wrong answer. For example, 2:8 is equivalent to 1:4, but 3:8 is not.
| Side length | Perimeter | Ratio |
| ----------- | --------- | ----- |
| 2 cm | 8 cm | 2:8 |
| 3 cm | 12 cm | 3:12 |
| 4 cm | 16 cm | 4:16 |
| 5 cm | 20 cm | 5:20 |
Part A: Click the wrong answers.
The wrong answers are **3:12** and **5:20**, because they are not equivalent to 1:4.
Part B: Drag numbers into each box to produce the correct answers. Place the smaller number in the box on the left.
To produce the correct answers, we need to find two numbers that have a ratio of 1:4. For example, we can use 1 and 4, or 2 and 8, or 3 and 12, etc.
| Side length | Perimeter | Ratio |
| ----------- | --------- | ----- |
| [ ] cm | [ ] cm | [ ]:[ ]|
| [ ] cm | [ ] cm | [ ]:[ ]|
One possible way to fill in the blanks is:
| Side length | Perimeter | Ratio |
| ----------- | --------- | ----- |
| [1] cm | [4] cm | [1]:[4]|
| [2] cm | [8] cm | [2]:[8]|
Another possible way is:
| Side length | Perimeter | Ratio |
| ----------- | --------- | ----- |
| [3] cm | [12] cm | [3]:[12]|
| [4] cm | [16] cm | [4]:[16]|
There are other possible ways as well, as long as the ratio is equivalent to 1:4.
If the origin is the only point with 0 for both coordinates, what must be true about the origin?
Answer:
If the origin is the only point with 0 for both coordinates, then it must be the point of intersection of the x-axis and the y-axis. In other words, the origin is the point (0,0), where the x-coordinate and y-coordinate are both zero. It is the unique point in the Cartesian plane that satisfies this condition.
Step-by-step explanation:
Write an equivalent expression by distributing the " − −" sign outside the parentheses: p− ( 9.4 q + 3 ) p−(9.4q+3)
The equivalent expression by distributing the sign outside the parentheses: [tex]-( -9.4 \text{q} + 3 )\ -(-9.4\text{q}+3)[/tex] will be [tex]18.8\text{q} - 6[/tex].
How to calculate the value?It should be noted that based on the information given, the expression is illustrated as:
[tex]-( -9.4 \text{q} + 3 )\ -(-9.4\text{q}+3)[/tex]
The signs should be taken into consideration. This will be:
[tex]-( -9.4 \text{q} + 3 )\ -(-9.4\text{q}+3)[/tex]
[tex]= 9.4\text{q} - 3 + 9.4\text{q} -3[/tex]
[tex]\boxed{=\bold{18.8\text{q} - 6}}[/tex]
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18x=19+12x
F
G
H
J
................
The required situation that can be represented by the equation 18x = 19 + 12x is:
"J. Krystal can make $18 per hour by tutoring. Jondo can make $12 per hour by tutoring. Jondo already has $19. How many hours, x, would Krystal and Jondo need to tutor for them to have the same amount of money?"
Let Krystal and Jondo work for x hours. Then Krystal would make 18x dollars, and Jondo would make 12x + 19 dollars (Jondo already has 19 dollars).
The equation 18x = 12x + 19 represents the situation where Krystal and Jondo make the same amount of money. Solving this equation gives:
18x - 12x = 19
6x = 19
x = 19/6
So Krystal and Jondo would need to work for approximately 3.17 hours (or 3 hours and 10 minutes) to make the same amount of money.
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Please hurry and help me I’ll give points please tho
Click above the line to create a
histogram for the given numbers
of pencils in students' pencil
bags.
4, 6, 3, 7, 2, 8, 10, 5, 8, 10, 3, 7
Frequency
LO
5
4-
3
2
1
0
Histogram for Pencils
1-3
4-6 7-9 10-12
Pencils
The histogram is attached.
Given that, we need to draw a histogram,
Data :-
1-3 3, 2, 3 Frequency = 3
4-6 4, 6, 5 Frequency = 3
7-9 7, 8, 8, 7 Frequency = 4
10-12 10, 10 Frequency = 2
Hence, you can draw the histogram according to the table.
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The ideal way to organize electronically the raw data for a study is to:_________
The ideal way to organize electronically the raw data for a study is to use a spreadsheet or database management system.
A spreadsheet or database management system allows you to input, store, and manage large amounts of data in a structured and organized manner. This makes it easier to analyze and process the data, as well as share it with others working on the study. Using these tools, you can sort, filter, and manipulate the data to find patterns, trends, and insights, making it easier to draw conclusions from the raw data.
Utilizing a spreadsheet or database management system is the most effective and efficient way to organize raw data electronically for a study, as it provides structure, organization, and ease of data manipulation.
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(Adapted from NYEngage) Use similar triangles to find the length of the altitude
The measure of the altitude NE in the triangle CNE for the given similarity is equal to 4 units.
Here In the attached figure,
B is the unknown vertex where ray AM and DE intersects.
In the triangles,
Triangle ABE ~ Triangle CDE
⇒measure of ∠A = measure of ∠C __(1)
AE = 15
CE = 5
ME = 12
Let 'x' be the measure of altitude NE.
In ΔAME and ΔCNE,
Measure of ∠A = Measure of ∠C (from 1)
Measure of ∠AME = Measure of ∠CNE ( each 90° )
Measure of ∠AEM = Measure of ∠CEN ( vertically opposite angles)
By AAA corollary we have,
ΔAME ~ ΔCNE
In similar triangles corresponding sides are in proportion .
AE / CE = ME / NE
Substitute the values we have,
⇒ 15 /5 = 12/ x
⇒x =12/3
⇒x = 4
⇒NE = 4 units.
Therefore , the length of the altitude NE is equal to 4 units.
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The above question is incomplete, the complete question is:
Use similar triangles to find the length of the altitude.
Triangle ABE ~ Triangle CDE. Find the length of altitude for NE.
Attached figure.
I am greater than 6 if you multiply me with 6 I become 42 what number am i
Answer:
7 you would times 6 by 7 to get 42
Answer:
Step-by-step explanation:
Product is 42 after you multiply by
Here you do the reverse:
42 ÷ 6 =
7 is greater than 6 therefore your answer is
The heart rates (in beats per minute) for a random sample of 36 blue whales are shown in the table.
The mean of the heart rates is 9.20
Given that, the heart rates of 36 whales, we need to find the mean of the population,
Mean μ = ∑x / N
N = sample size
x = observed population
Mean μ = 11+10+12+12+8+10+13+11+13+9+11+8+12+6+8+13+5+8+9+8+12+6+9+7+6+8+7+9+9+5+12+9+11+7+8+9 / 36
= 331 / 36
= 9.20
Hence, the mean of the heart rates is 9.20
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Select the correct answer. Martin runs 100 meters in 15 seconds. What is the equation for d, the distance in meters that Martin covers per second? A. 15 + d = 100 B. 100 + d = 15 C. d × 15 = 100 D. d × 100 = 15
Answer:
To find the equation for d, the distance in meters that Martin covers per second, we need to use the formula:
distance = speed × time
Here, the distance covered by Martin is 100 meters, and the time taken is 15 seconds. Therefore, we can write:
distance = speed × time
100 meters = speed × 15 seconds
To find the speed, we can rearrange the equation as:
speed = distance / time
speed = 100 meters / 15 seconds
So the speed of Martin is:
speed = 6.67 meters per second
Therefore, the correct equation for d, the distance in meters that Martin covers per second, is:
d = speed
d = 6.67 meters per second
Answer: There is no option that matches the correct equation for d, which is simply d = 6.67 meters per second.
Step-by-step explanation:
scores on an english test are normally distributed with a mean of 37.6 and a standard deviation of 7.6. find the score that separates the top 53% from the bottom 47%
We can use the inverse normal distribution function to find the z-score corresponding to the desired percentile, and then use the formula for standardizing a normal variable to find the corresponding raw score.
The score that separates the top 53% from the bottom 47% on an English test with a normal distribution, mean of 37.6, and standard deviation of 7.6 can be found using the inverse normal distribution function.
We need to find the z-score that corresponds to the 53rd percentile. We can do this using a standard normal distribution table or a calculator. The z-score corresponding to the 53rd percentile is approximately 0.07.
We can use the formula for standardizing a normal variable to find the corresponding raw score: z = (X - mean) / standard deviation Rearranging this formula, we get: X = z * standard deviation + mean
Plugging in the values we have: X = 0.07 * 7.6 + 37.6 X ≈ 38.2 A score of approximately 38.2 separates the top 53% from the bottom 47% on this English test.
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what is the slop of the line passing through the points (-2,-8) and (-3,-9)
Answer: The slop is 1
Step-by-step explanation: The coordinates points:
(-2,-8), and (-3,-9)
x1 = -2 y1= -8
x2 = -3 y2= -9
m = y2 - y1/ x2 - x1
put the value
m= -9 - (-8) / -3 - (-2)
= -9 + 8 / -3 + 2
= -1/-1
= 1
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in order to develop an interval estimate of a population mean, the margin of error must be computed using:
In order to develop an interval estimate of a population mean, the margin of error must be computed using: either population standard deviation, σ or the sample standard deviation, s.
What is the margin of error?In Mathematics, the margin of error (MOE) can be defined as a measure of the difference that exist between an observed value and a true value of the population parameter.
This ultimately implies that, the margin of error (MOE) can be used to determine the confidence interval.
How to determine the sample size?In Mathematics and Statistics, a sample size that would result in a specific standard deviation can be calculated by using the following mathematical equation (formula):
Sample size, n = (zσ/ME)²
Where:
n represents the sample size.z represents the z-score of the desired confidence level. σ represents the standard deviation of the population.ME represents the margin of error.Read more on sample size here: brainly.com/question/30520316
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In a direct variation, y=12 when x=2. Write a direct variation equation that shows the relationship between x and y.
Answer:
Step-by-step explanation:
In direct variation, the relationship between two variables x and y can be represented by the equation y = kx, where k is the constant of variation.
To find the value of k, we can substitute the given values of x and y into the equation:
y = kx
12 = k(2)
Solving for k, we can divide both sides by 2:
k = 6
Now we can write the direct variation equation using the value of k:
y = 6x
Therefore, the direct variation equation that shows the relationship between x and y is y = 6x.
suppose that a simple random sample is used to estimate the proportion of families in a certain area that are living below the poverty level. if this proportion is roughly .15, what sample size is necessary so that the standard error of the estimate is .02?
The sample size for estimate the proportion of families in a certain area that are living below the poverty level is equals to the 318.75.
The standard error is a statistic term that is the standard deviation of its sampling distribution or an estimate of that standard deviation. In case of sample mean, it is called the standard error of the mean. Formula of standard mean is
[tex] SE =\sqrt{ \frac{\hat p (1 - \hat p)}{n}} [/tex]
where, n--> sample size
We have a simple random sample for estimate the proportion of families,
Sample proportion = 0.15
Standard error = 0.02
We have to determine the sample size for the standard error of the estimate is .02.
Here, SE = 0.02, \hat p = 0.15
Using the standard score formula,
[tex] 0.02 =\sqrt{ \frac{0.15 (1 - 0.15)}{n}} [/tex]
Squaring both sides
[tex] 0.02² = \frac{0.15 ×0.85 }{n} [/tex]
[tex] 0.0004 = \frac{0.1275 }{n} [/tex]
=> n = 318.75
Hence, required value is 318.75.
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Write a quadratic function h whose only zero is -5.
Answer:
Step-by-step explanation:
What is the value of x?
The value of x in the model expression is x = 10/8
What is the value of x?From the question, we have the following parameters that can be used in our computation:
The model
When represented as an equation, we have
4x - 4 = -4x + 6
Collect the like terms
So, we have
4x + 4x - 4 + 6
Evaluate the like terms
8x = 10
Divide by 8
x = 10/8
Hence, the solution is x = 10/8
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The height of a cylinder is 6 in. The diameter of the cylinder is 12 in. What is the
lateral area of the cylinder to the nearest square inch?
Given: BD || AE
Prove: CA/CB=CE/CD
What extra information could have been used to prove Angle-Angle similarity?
Answer choices:
Corresponding Angle Theorem
CBD ~ CAD
CBD ≅CAE
Vertical Angles Theorem
Angle C ≅ angle C
Reflexive Property
Alternate Interior Angle Theorem
The missing portions of the proof are:
2) ∠4 ≅ ∠1 ; ∠3≅∠2 - Corresponding Angles Theorem
3) CDB ≅CEA - AA Similarity
The other information that could have been stated to proof that Angle - Angle similarity is: Angle C ≅ angle C
Reflexive Property
The reflexive property of equality in algebra asserts that a number is always equal to itself. Equality has a reflexive attribute. If an is a positive integer, then a = a.
When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding angles with the transversal.
So in the above proof, ∠4 ≅ ∠1 ; ∠3≅∠2 because they are a pair of corresponding angels because they are created in matching corners.
Looking at the shape, we can see that CDB and CEA are triangles since we have established that their angles are similar, hence, the Angle Angle Similarity postulate.
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What is the distance between the two points plotted?
A graph with the x-axis starting at negative 10, with tick marks every one unit up to 10. The y-axis starts at negative 10, with tick marks every one unit up to 10. A point is plotted at 3, 5 and at 3, negative 6.
1 unit
11 units
−11 units
−1 unit
If point is plotted at (3, 5) and (3, -6), then the distance between the two points plotted is (b) 11 units.
The two points plotted are (3, 5) and (3, -6). We see that both the points have the same x-coordinate, which means that both points lie on the same "vertical-line" which is parallel to the y-axis.
The distance between these two points is the vertical distance between their y-coordinates, which is:
The "y-coordinate" of the points are 5 and -6,
So, the distance will be = |5 - (-6)| = 11 units,
Therefore, the correct option is (b).
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The given question is incomplete, the complete question is
A graph with the x-axis starting at -10, with tick marks every one unit up to 10. The y-axis starts at -10, with tick marks every one unit up to 10.
A point is plotted at (3, 5) and at (3, -6).
What is the distance between the two points plotted?
(a) 1 unit
(b) 11 units
(c) -11 units
(d) -1 unit
Find the area of the rectangle.
show a rectangle with the width and length measurements included. Width is b^2 and length is b^5.
Answer:
A=b^7
the area of the rectangle is b^
Step-by-step explanation:
To find the area of a rectangle, we use the formula:
Area = Length x Width
In this case, the width (W) is given as b^2 and the length (L) is given as b^5. Therefore, the area (A) can be calculated as:
A = L x W
A = b^5 x b^2
A = b^(5+2) (when we multiply two numbers with the same base, we add the exponents)
A = b^7
an insurance agent has appointments with 8 prospective clients tomorrow. from past experience the agent knows that the probability of making a sale on any appointment is one out of five. using the rules of probability, what is the likelihood that the agent will sell a policy to two of the eight prospective clients?
The likelihood of the agent making 2 sales out of 8 appointments is 0.132.
Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
The probability of making a sale on any appointment is 1/5, and the probability of not making a sale is 4/5.
We can use the binomial distribution to find the probability of making 2 sales out of 8 appointments
P(2 sales) = (8 choose 2) × (1/5)² × (4/5)⁶
where (8 choose 2) = 28 is the number of ways to choose 2 appointments out of 8.
So, plugging in the values, we get
P(2 sales) = 28 × (1/5)² × (4/5)⁶
= 0.132
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6 teaspoons of red paint are equal to 10 teaspoons of yellow paint.
How many teaspoons of red paint are equal to 15 teaspoons?
Answer: If the question is asking how many teaspoons of red paint does it take to have 15 teaspoons of yellow paint, then your answer would be 9 I believe, hope this helps:)
Step-by-step explanation:
Answer:
The answer to you question is 9 teaspoons of red paint.
Step-by-step explanation:
3 teaspoons of red paint = 5 teaspoons of yellow paint
6 teaspoons of red paint = 10 teaspoons of yellow paint
9 teaspoons of red paint = 15 teaspoons of yellow paint
I hope this helps and have a wonderful day!
ayo help me pls I'll make u brainliest
The two afternoon buses were 5 minutes late.
What is a median?In Mathematics, a median is the middle number (center) of a sorted data set, which is when the data set is either arranged in a descending order from the greatest to least or an ascending order the least to greatest.
How to calculate the median number of 10 observations?Since the mode is equal to 0, the frequency of 0 shall be greater than 2 of the given times in minutes and less than or equal to 4 given times in minutes.
Therefore, the frequency of 0 is equal to 3. Consequently, the number of time in minutes late for each bus after arranging them in ascending order is given by:
0, 0, 0, 2, 2, x, 6, 8, 8, 9
Median = (2 + x)/2
3.5 = (2 + x)/2
2 + x = 7
x = 7 - 2
x = 5
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Which of the equations shown will have infinitely many solutions? Select the TWO that apply. A 3x−1=3x+13 x minus 1 is equal to 3 x plus 1 B 2x−1=1−2x2 x minus 1 is equal to 1 minus 2 x C 3(x−1)=3x−33 times open paren x minus 1 close paren is equal to 3 x minus 3 D 2x+2=2(x+1)2 x plus 2 is equal to 2 times open paren x plus 1 close paren E 3(x−2)=2(x−3)
Answer:
A. 3x−1=3x+1 and D. 2x+2=2(x+1) have infinitely many solutions.
A peice of art is in the shape of a rectangular pyramid like a the figure shown below.
how much glass is needed to cover the entire pyramid?
Answer:
2nd choice: 144.53 ft²
Step-by-step explanation:
Area of base = 6 x 7 = 42
Area of 2 sides with 8 ft height = 2 · (1/2)(6)(8) = 48
Area of 2 sides with 7/79 ft height = 2 · (1/2)(7)(7.79) = 54.53
Total SA = 42 + 48 + 54.53 = 144.53 ft²
Solve the systems of equations by substituting
2.)
3x+3y=-18
2y=x
Answer:
x= 4 and y= 2
Step-by-step explanation:
3x+3y= 18 (1)
2y= x (2)
from (1):
x+y= 6
y= 6-x (3)
sub (3) into (2):
2(6-x)= x
12-2x= x
-3x= -12
x= 4 (4)
sub (4) into (3):
y= 6-4
= 2
a football quarterback has 2 more chances to throw a touchdown before his team is forced to punt the ball. he misses the receiver on the first throw 40% of the time. when his first throw is incomplete, he misses the receiver on the second throw 15% of the time. what is the probability of not throwing the ball to a receiver on either throw? (10 points)
The probability of not throwing the ball to a receiver on either throw is 0.66, or 66%.
Consider two conceivable scenarios for quarterback tosses.
1. He tosses the ball to the recipient on his to begin the endeavor.
2. He misses the collector on his to begin with endeavor and once more on his moment endeavor.
The likelihood of situation 1 is 1 – 0.4 = 0.6. Usually since the quarterback on the primary attempt he misses the collector 40% of the time.
The likelihood for Situation 2 can be calculated as
P(1st Endeavor Fizzled + 2nd Endeavor Fizzled) = P(1st Endeavor Fizzled) * P(2nd Endeavor Fizzled | 1st Endeavor Fizzled)
= 0.4 * 0.15 = 0.06
Subsequently, the likelihood of not tossing the ball to the recipient on any toss is the entirety of the probabilities of Scenarios 1 and 2.
P(Don't toss to recipient) = P(Scenario 1) + P(Scenario 2)
= 0.6 + 0.06
= 0.66
Hence, the likelihood of not tossing the ball to the collector on any toss is 0.66, or 66%.
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