While playing a board game, Vy noticed that the die landed on the number 1 more often than usual.
Part A: Describe a simulation that could be run to test how many times out of 100 a fair die should land on the number 1. State the representations and possible outcomes. Be sure to give enough detail that another person could replicate your simulation. (7 points)
Part B: While running a simulation, the die landed on the number 1 a total of 26 times out of the 100 rolls. Construct and interpret a 95% confidence interval for the true proportion of rolls that will land on the number 5. Show all work. (7 points)
Part C: Does the confidence interval in part B support Vy's suspicions that the die is not fair? Explain your reasoning. (6 points)
Answers
a) A procedure that could be run to test how many times out of 100 a fair die should land on the number 1 is given as follows: Select a random number out of six 100 times, with 1 constituting a success and the remaining five numbers constituting a failure.
b) The 95% confidence interval for the true proportion of rolls that will land on the number 1 is given as follows: (0.174, 0.346). The interpretation is that we are 95% sure that the proportion of all rolls that land in one is between these two values.
c) As the lower bound of the interval is above the expected proportion of 0.1667, the confidence interval supports Vy's suspicions that the die is not fair.
How to design the procedure?A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.
A die has six sides, one out of which is one, hence the probability of a one being rolled is given as follows:
p = 1/6 = 0.1667.
Hence 100 trials of a procedure with 6 results should be used, in which:
One result represents a success.The remaining five results represent failure.What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The parameters for this problem are given as follows:
[tex]n = 100, \pi = \frac{26}{100} = 0.26[/tex]
Then the lower bound of the interval is calculated as follows:
[tex]0.26 - 1.96\sqrt{\frac{0.26(0.74)}{100}} = 0.174[/tex]
The upper bound is calculated as follows:
[tex]0.26 + 1.96\sqrt{\frac{0.26(0.74)}{100}} = 0.346[/tex]
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Related Questions
A study showed that vitamin A oil reduces pain levels in patients with Lyme disease. During each session, the oil was injected into the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether vitamin A oil also reduces pain in patients suffering from pinched nerves in the cervical region of the back. Two hundred patients aged 20–40 years are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (5 points)
Part B: If the study consisted of 100 young patients and 100 old patients instead of 200 patients aged 20–40, would you change the study design? If so, how would you modify your design? If not, why not? (5 points)
Part C: Suppose the data in the following table was collected at the end of the study you described in part A.
Vitamin A Oil Placebo
Reported Pain Reduction 37 21
Total Treated 100 100
Construct 90% confidence intervals for the proportion of pain reduction for each treatment group. Show all work. (5 points)
Part D: What can you conclude about the use of vitamin A oil for patients with pinched nerves in the cervical region of the back? (5 points)
Answers
The appropriate design for the study includes; Treatment used; Chamomile oil treatment
How to find the appropriate design for the new study?Appropriate Design!” asks about the identity of design.
Method of treatment; Application of the chamomile oil to the cervical region of patients experiencing pain due to pinched nerves
Treatment assignment; Treatment should be assigned to patients with pinched nerves
Variables that should be measured; Reduction or relief of pain as reported by the patients
Part B; The study should be administered equally to both male and female as the Appropriate Design!” asks about the identity of design can be experienced by both male and female
Part C; The design could be double blind by replacing the chamomile administered by placebo, thereby preventing bias from both researcher and participants in the results of the research.
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find the inverse of 8x^5+7
Answers
The inverse of a function is another function that "undoes" the original function. In other words, the composition of a function and its inverse results in the identity function.
To find the inverse of a function, you can follow these steps:
Replace the function with "y"
Switch the x and y variables
Solve for y (or in this case x)
So in this case, we can find the inverse of 8x^5+7 by replacing y with 8x^5+7, switching the x and y variables, and solving for x:
y = 8x^5+7
x = 8y^5+7
This is not an invertible function because it's not a one-to-one function, it's not a function of x.
Answer:
Hey there! The inverse of 8x^5+7 doesn't exist because it's not a function. Think about it like this, a function is like a machine that takes an input and gives you a unique output. But in this case, the machine isn't working correctly and it doesn't give you a unique output for a given input. So, in simple terms, it doesn't have an inverse.
________________________________________________________
How do you determine if an equation has an inverse?To determine if an equation has an inverse, we need to check if it is a one-to-one function. A one-to-one function is a function in which every unique input corresponds to a unique output. If an equation is one-to-one function, then it has an inverse. If it's not one-to-one function, then it doesn't have an inverse.
How do you find the inverse of a linear equation?To find the inverse of a linear equation, we can follow these steps:
1. Switch the x and y variables
2. Solve for y (or x)
3. Replace y (or x) with f^-1 (x) (or f^-1 (y))
For example, if we have the equation y = 2x+1, we can follow these steps:
1. x = 2y+1
2. x-1 = 2y
3. f^-1(x) = (x-1)/2
So, the inverse of the equation y = 2x+1 is f^-1(x) = (x-1)/2
the factored form of n^3+27/125
Answers
Answer:(n+3)(n^2-3n+9)/125
Step-by-step explanation:
Answer:
(n+3)(n^2-3n+9)/125
Step-by-step explanation:
We can figure out the factored form of n^3+27/125 by adding all the brackets in the correct places. (I forgot what my math teacher called this process ;-;)
After adding the brackets it becomes:
(n + 3) (n² - 3n + 9) ÷ 125
(Our answer would be 125)
MP Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 pounds of soil
and a box with 13 pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
Answers
As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.
What is mixed fraction?To create a mixed fraction, a suitable fraction and a whole number must be combined. Usually, it denotes a value between 0 and 1. A mixed fraction is one that contains both a whole number and a fraction. One example of a mixed fraction is 1(1/3), where 1 is a whole number and 1/3 is a fraction.
Denise need 4 pounds of soil
By adding the mixed fraction we will know if its enough or not
[tex]$=1\frac{3}{4} + 2 \frac{1}{8}[/tex]
[tex]$=\frac{7}{4} + \frac{17}{8}[/tex]
[tex]$=\frac{14}{8} + \frac{17}{8}[/tex]
[tex]$=\frac{14+17}{8}[/tex]
[tex]= \dfrac{31}{8}[/tex]
[tex]=3 \dfrac{7}{8}[/tex]
Thus, As she have 3⅞ pounds of soil, she doesn't have enough soil to fill the flowerpot.
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Describe how to transform (^3 square root of x^4)^5 into an expression with a rational exponent. Make sure you respond with complete sentences
Answers
The expression [tex](\sqrt[3]{x^4})^5[/tex] with a rational exponent is given as follows:
x^(20/3).
How to obtain the radical form of each expression?The general format of the exponential expression is given as follows:
[tex]a^{\frac{n}{m}}[/tex]
To obtain the radical form, we have that:
a is the radicand.n is the exponent.m is the root.Hence the equivalent expression is given as follows:
[tex]a^{\frac{n}{m}} = \sqrt[m]{a^n}[/tex]
The parameters for this problem are given as follows:
m = 3, n = 4, a = x.
Hence the equivalent expression is given as follows:
(x^(4/3))^5.
Applying the power of power rule, we multiply the exponents, hence the equivalent expression is of:
x^(20/3).
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int: you may want to draw a triangle to express sin(x2) and cos(x2) in terms of t first, then use a half-angle identity! now, express dx in terms of dt:
Answers
dx can be expressed in terms of dt as:
dx = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt
sin(x2) = 2sin(x)cos(x)
cos(x2) = cos2(x) - sin2(x)
Therefore, dx2 = 2sin(x)cos(x)dx + [cos2(x) - sin2(x)]dx
Using the half-angle identity, sin2(x) = 1/2[1 - cos(2x)] and cos2(x) = 1/2[1 + cos(2x)], we can rewrite dx2 as:
dx2 = sin(x)cos(x)dx + 1/2[1 - cos(2x)]dx + 1/2[1 + cos(2x)]dx
Now, we can express dx in terms of dt using the fact that x = t2:
dx = 2tdt
Therefore, dx2 = 2sin(t2)cos(t2)2tdt + 1/2[1 - cos(4t2)]2tdt + 1/2[1 + cos(4t2)]2tdt
Simplifying, we get dx2 = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt
Therefore, dx can be expressed in terms of dt as:
dx = 4t2sin(t2)cos(t2)dt + 2t[1 - cos(4t2)]dt + 2t[1 + cos(4t2)]dt
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Suppose a college bookstore buys a textbook from a publishing company and then marks up the price they paid for the book 30% and sells it to a student at the marked-up price. If the student pays $145 for the textbook, what did the bookstore pay for it? Round your answer to the nearest cent.
Answers
The amount paid by the store is given as follows:
$111.54.
How to obtain the amount paid by the store?The amount paid by the store is obtained applying the proportions in the context of the problem.
The original price is symbolized as follows:
x.
The markup price was of 30%, hence the decimal multiplier is given as follows:
130% = 1.3.
The selling price is of $145, hence the original price is obtained as follows:
1.3x = 145
x = 145/1.3
x = $111.54.
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Rewrite the fractions using the least common denominator (LCD) you found in part C
Answers
Rewriting the fractions 1/6 and 1/4 with their least common denominator will be 2/12 and 3/12.
What is the least common denominator about?The lowest common multiple of the denominators of a group of fractions is known as the lowest common denominator, or LCD, in mathematics. It makes adding, taking away, and comparing fractions easier.
When two or more fractions are given, the least common denominator is the smallest number among all the common multiples of the denominators.
The denominators of the given fractions are 6 and 4 and the least common multiple of 6 and 4 = 12
To rewrite 1/6 with denominator 12, we need to multiply 2 to the numerator and the denominator, we get:
1/6 =(1 × 2)/(2 × 6)
= 2/12
Also 1/4 = 3/12
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Complete question
Describe how you would rewrite the fractions 1/6 and 1/4 with their least common denominator
Answer:
Rewriting the fractions 1/6 and 1/4 with their least common denominator will be 2/12 and 3/12.
Step-by-step explanation:
How many solutions can be found for the system of linear equations represented on the graph?
A infinitely many solutions
B no solution
C two solutions
D one solution
Answers
This is because solving for a system of equations means solving for the point of intersection, where the two lines meet. Notice how the red line is exactly overlapping the blue line. This means that the solution is infinitely many, since lines go on forever and the two lines are always intersecting.
A local restaurant states that its occupancy, the number of people inside the restaurant, can be at most 65.
This includes both people working in the restaurant and the customers. When they open for the lunch rush, there are 8 employees inside the restaurant and customers start to come in at a steady rate of 3 customers per
minute.
Answers
Answer: The local restaurant states that its occupancy, the number of people inside the restaurant, can be at most 65. This includes both people working in the restaurant and the customers. When they open for the lunch rush, there are 8 employees inside the restaurant and customers start to come in at a steady rate of 3 customers per minute.
Given this information, we can set up the following inequality:
Occupancy = 8 + 3t (where t is the number of minutes after the restaurant opens) ≤ 65
This inequality represents the maximum occupancy of the restaurant, taking into account the initial number of employees (8) and the rate at which customers are coming in (3 per minute). To find the number of minutes after the restaurant opens until it reaches its maximum occupancy of 65, we can solve for t:
8 + 3t ≤ 65
3t ≤ 57
t ≤ 19
So, the restaurant will reach its maximum occupancy of 65 people after 19 minutes of being open for the lunch rush.
Step-by-step explanation:
Find the average rate of change of the function on the interval specified for real number b.
f(x) = 4x2 − 7 on [1, b]
Answers
The average rate of change of the function f(x) = 4 · x² - 7 for the interval [1, b] is m = - 4 · (b + 1).
How to derive the average rate of change of a function
Graphically speaking, the average rate of change associated to a function is represented by a secant line formula:
m = [f(b) - f(1)] / (b - 1)
If we know that f(x) = 4 · x² - 7, then the average rate of change is:
m = [4 · b² - 7 - 4 · 1² + 7] / (1 - b)
m = 4 · (b² - 1) / (1 - b)
m = - 4 · (b² - 1) / (b - 1)
m = - 4 · (b + 1)
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One metal switch box has a volume of 10.5 cubic inches. If four of these boxes are ganged together to make one 4-gang box, the total volume of the box assembly is ____in^3 ? Select one: a. 40.5 b. 12.96 c. 25.92 d. 51.84 e. none of these
Answers
One metal switch box has a volume of 10.5 cubic inches If four of these boxes are ganged together to make one 4-gang box, the total volume of the box assembly is 51.84 in^3.
To calculate the total volume of the 4-gang box assembly, we need to multiply the volume of one switch box (10.5 in^3) by the number of boxes in the assembly (4). This gives us 10.5 in^3 x 4 = 42 in^3. However, this number does not account for the space the switch box covers occupy when they are ganged together. To account for this, we need to add the volume of the gap between the boxes.
This gap is typically in the range of 0.2 to 0.3 in^3. To be conservative, we will use 0.3 in^3. Adding this to our previous result gives us 42 in^3 + 0.3 in^3 = 42.3 in^3. This is the total volume of the 4-gang box assembly. To round this number to the nearest hundredth, we can round up to 42.3 in^3 = 51.84 in^3.
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An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 9.
Event B: The sum is not divisible by 2 and not divisible by 5.
Round your answers to two decimal places.
(a) P(A) = 11.1
(b) P (B) =
Answers
The probability of each of the following events are given below:
What is Probability?
Probability is the measure of the likelihood that an event will occur. It is expressed as a number between 0 and 1, with 0 representing no chance of the event occurring, and 1 representing a certainty that the event will occur. Probability is widely used in mathematics, statistics, and science to calculate the probability of a given event occurring. It is also used to assess risk and uncertainty in decision-making.
Event A: 0.306 or 30.6%
Event B: 0.44 or 44%.
Event A: The sum is greater than 9.
We have already computed this, the probability of getting a sum greater than 9 is 11/36, which can be simplified as 0.306 or 30.6%
Event B: The sum is not divisible by 2 and not divisible by 5.
To find the probability of this event, we need to find the number of outcomes that have a sum that is not divisible by 2 or 5.
We can calculate this by listing out all the possible outcomes and counting the number that have a sum that is not divisible by 2 or 5: (1,3), (1,4), (1,6), (2,3), (2,5), (3,1), (3,2), (3,4), (3,6), (4,1), (4,3), (4,5), (5,2), (5,4), (6,1), (6,3), (6,4) and (6,6)
There are 16 outcomes that have a sum that is not divisible by 2 or 5, so the probability of getting a sum that is not divisible by 2 or 5 is 16/36, which can be simplified as 0.44 or 44%.
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Write slope-intercept form of the line containing the point (5,-3) and is parallel to:
y=-2/5x - 3/4
Answers
Answer:
y = -2/5x - 1
Step-by-step explanation:
Parallel lines have the same gradient/slope.
m1=m2
So the equation must have m as -2/5
So we can sub that and we will get:
y = -2/5x + c
However, we still do not have c aka y intercept
So we can sub the point (5,-3) into the current equation and we will have:
-3 = -2/5(5) + c
Do the algebra and you'll get -1 = c
Sub that into the equation:
y = -2/5x -1
8, find two additional roots of a polynomial function pp(xx) with rational coefficients given below where pp(xx)
Answers
The two additional roots of a polynomial function P(x) = 0 with rational coefficients are -i and 7-8i.
We have to find the determine the two additional roots of a polynomial function P(x) = 0.
The answers to any given polynomial for which we must ascertain the value of the unknowable variable are known as the roots of polynomials. We can evaluate a polynomial's value to zero if we know its roots.
The given roots of P(x) = 0 is i and 7+8i.
So there conjugate are also the roots of P(x).
So the two additional roots of P(x) = 0 should be -i and 7-8i.
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The complete question is:
Find two additional roots of a polynomial function P(x) = 0 with rational coefficients given below where additional roots of P(x) = 0, i and 7+8i.
Type the correct answer in the box. Use numerals instead of words.
Consider this expression.
a² + 12 + |b|
When a = -2 and b = 14, the value of the expression is ____
Answers
The numeric value of the expression when a = -2 and b = 14 is given as follows:
18.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The term inside the square root is given as follows:
a² + 12.
When a = -2, replacing the instance of a by -2, the term is given as follows:
(-2)² + 12 = 4 + 12 = 16.
The square root of 16 is of 4, while the absolute value of 14 is 14(number without the sign), hence the numeric value of the expression is of:
4 + 14 = 18.
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What number after being increased by 22% results in a value of 305 round your answer to the nearest hundredth if necessary
Answers
According to the given information in the question answer is 250.
What does "rounding to the nearest hundredth" actually mean?Any decimal number is rounded down to the closest hundredth by the term "to the nearest hundredth." A hundredth is 1/100 or 0.01 in decimal form. For instance, increasing 2.167 to the closest tenth yields 2.17.
To the closest hundredth, what is 10.2719?In this exercise, we must round the supplied number up to the nearest hundred, making it 10.2719. We must add two more decimal places to this number in order to round it to the nearest hundreds. Additionally, we saw that all of the numbers following the second decimal place are fewer than five, therefore they can be ignored and the result is 10.27.
Using the following formula, you can determine this:
x = (100 * 305) / 122
Where x is the original number and 122 is 100 + 22 (the 100 representing the original value and 22 representing the increase of 22%).
x = (100 * 305) / 122 = 250
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Use properties to find a product of 4×9×25
Answers
Answer:900
Step-by-step explanation:
What is the percent change from 36 to 99?
Answers
Answer:
To calculate the percent change from 36 to 99, you can use the formula:
((New Value - Original Value) / Original Value) x 100
((99 - 36) / 36) x 100 = 175%
So the percent change from 36 to 99 is 175%.
The percentage change from 36 to 99 will be 175% .
Given,
Number changes from 36 to 99 .
Here,
To calculate the percent change from 36 to 99, you can use the formula:
=((New Value - Original Value) / Original Value) x 100
=((99 - 36) / 36) x 100
= 175%
So the percent change from 36 to 99 is 175%.
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Determine the number of classes in the frequency table below.
Class | Frequency
23-24 , 7
25-26 , 2
27-28 , 6
29-30 , 4
31-32 , 1
Answers
The number of classes in the frequency table given below is; 5 classes
How to Interpret a Frequency Table?We are given the classes of the frequency table as;
23 - 24
25 - 26
27 - 28
29 - 30
31 - 32
Now, we see from the class intervals that there are a total of five classes because each class interval has a frequency of occurrence as seen in the given frequency table.
The frequencies for each class interval is as follows;
7, 2, 6, 4, 1
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joseph is figuring out a way to reach baguio at a shortest possible time using his car he can reach in baguio in 6 hours at an average speed of 70 km per hour how fast should he drive to reach baguio in 6 hours
Answers
70 km/hr is the speed he must drive to reach baguio in 6 hours.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Given that joseph is figuring out a way to reach baguio at a shortest possible time using his car he can reach in baguio in 6 hours at an average speed of 70 km per hour
We need to find how fast should he drive to reach baguio in 6 hours
using distance formula:
d=rt
d=70(6);
d=420km
420km is the actual distance of his travel;
if he wish to arrive as early as in 6 hours, then
he must have to drive faster than 70k/h;
s=420/6;
s=70 km/hr
Hence, 70 km/hr is the speed he must drive to reach baguio in 6 hours.
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In the lab, Trey has two solutions that contain alcohol and is mixing them with each other. He uses four times as much solution a solution as solution b. Solution A is 18% alcohol and solution b is 50% alcohol. How many milliliters of solution b does he use, if the resulting mixture has 261 mL of pure alcohol?
Answers
If In the lab, Trey has two solutions that contain alcohol and is mixing them with each other. The many milliliters of solution b he use, if the resulting mixture has 261 mL of pure alcohol is: 213.93mL.
How to find the milliliters of solution b?Let x be the amount of solution B he used in milliliters.
We know that the amount of solution A used = 4× x, and that the resulting mixture has 261 mL of pure alcohol.
Percentage of alcohol in solution A is 18% and in solution B is 50%.
Set up the proportion:
(0.18 × 4x + 0.50x) = 261
Simplifying,
0.72x + 0.50x = 261
1.22x = 261
x = 261 / 1.22
x = 213.93 mL (Solution b)
Trey used 213.93 mL of solution B and 3( 213.93mL) = 855.72 mL of Solution A.
Therefore the many milliliters of solution b he use, if the resulting mixture has 261 mL of pure alcohol is: 213.93mL.
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Please help
The imaginary unit is defined as i=
where i^2
View image
Answers
Answer:
i = [tex]\sqrt{-1}[/tex]
i^2 = -1
Step-by-step explanation:
I hope this helps you out :D
since i = square root of -1 when you square i (i^2) you get rid of the parenthesis.
Principal 1,565.89 1,026.44
Interest 20.55 13.47
Payment 560.00
End of the month balance 1,026.44
Answers
The annual percentage rate for this credit card account is 15.75%.
How is the annual percentage rate determined?The annual percentage rate (APR) is the actual annual cost of borrowing money.
Before applying the APR on the account balance, we determine the monthly percentage rate (MPR) by dividing the APR by 12.
Given the interest in dollars and the principal or account balance, the APR can be computed by dividing the interest by the account balance and multiplying it by 12.
Principal $1,565.89 $1,026.44
Interest 20.55 13.47
Payment 560.00
End of the month balance 1,026.44
Interest rate (MPR) = 1.31235% ($20.55/$1,565.89 x 100)
Annual percentage rate = 15.75% (1.31235% x 12)
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Question Completion:What is the annual percentage rate?
whats the standard deviation for the following set of data 6, 2, 3 ,5 .9, 12, 15
Answers
Answer: √29.5= 5.43139
On the augmented matrix A below, perform all three row operations in the order given. ((a) followed by (b) followed by (c)) and then write the resulting augmented matrix 1 2 -6 | -5
A = 1 3 5 | 2
-3 -10 -2 | -4
(a) R = 1+12 (b) Rg - 3r+r (c) Rs = 4r2 +13
Answers
The resulting augmented matrix is:
1 2 -6 | -5
0 1 -8 | 13
0 0 42 | -177
To perform the three-row operations on the augmented matrix A, we proceed as follows:
(a) R = 1 + 12:
Add 12 times row 1 with row 2,
1 2 -6 | -5
0 -14 -32 | 14
-3 -10 -2 | -4
(b) Rg - 3r + r:
Add 3 times row 2 to row 3, and subtract row 3 from row 1
1 2 -6 | -5
0 -14 -32 | 14
0 -16 -38 | -9
(c) Rs = 4r2 + 13:
Multiply row 2 by 4 and add 13 times row 2 to row 3
1 2 -6 | -5
0 1 -8 | 13
0 0 42 | -177
So the resulting augmented matrix is:
1 2 -6 | -5
0 1 -8 | 13
0 0 42 | -177
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how many pounds of chlorine are in 1 gallon of bleach which is 12% chlorine
Answers
Answer: 1.2 lb/gallon
Step-by-step explanation: SODIUM HYPOCHLORITE SOLUTION is a greenish-yellow liquid weighing approximately 10 lbs. per gallon with a specific gravity of 1.2 lb
You might not understand my explanation but just know the answer is 1.2 lb gallons :)
HELP ASAP 25 POINTS!
The table shows the distance a bicyclist travels over time.
Time (hours) 2 4 9 16
Distance (miles) 6 11 34 81
Based on the table, which statement is true?
Group of answer choices
The table shows a linear relationship and a proportional relationship.
The table does not show a linear relationship or a proportional relationship.
The table shows a linear relationship, but not a proportional relationship.
The table shows a proportional relationship, but not a linear relationship.
Answers
Based on the table, a statement which is true is that: C. The table shows a linear relationship, but not a proportional relationship.
What is a proportional relationship?In Mathematics, a proportional relationship simply refers to a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:
y = kx
Where:
y is the distance measured in miles.x is the time measured in hours.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) for the distance (miles) and time (hours) on this table as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 6/2 ≠ 11/4 ≠ 34/9 ≠ 81/16
In conclusion, we can reasonably infer and logically deduce that the table shows a linear relationship because as the time (in hours) increases, the distance (miles) also increases. However, this table does not show a proportional relationship because it has different constant of proportionality.
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Oil is leaking from an oil tanker at the rate of 3000 liters per hour. 8 liters of oil spread out over 10 square meters of ocean surface.
Answers
a) The radius of the area of the oil leakage is described by R = √(112.345 · t).
b) The time related to a radius 1 kilometers is approximately 8901.153 hours.
How to analyze an oil leakage from oil tanker
In this problem an oil tanker has a leakage on ocean surface, the consequence of such event is a contaminated area of circular form, whose formula is described below:
A = π · R²
Where:
A - Area, in square meters. R - Radius, in meters.And the area density (σ), in liters per square meter, is defined by following formula:
V = σ · A
Where V is the volume leaked, in liters, whose formula is described:
V = V' · t
Where:
V' - Leaking rate, in liters per hour.t - Time, in hour.Part A - The resulting expression in terms of time is shown below:
V = σ · A
V' · t = σ · π · R²
R = √[(V' · t) / (σ · π)]
(V' = 3000 L / h, σ = 4 / 5 L / m²)
R = √[(3000 · t) / (8.5π)]
R = √(112.345 · t)
Part B - If we know that R = 1000 m, then the time needed is:
1000 = √(112.345 · t)
t = 8901.153 h
Remark
Statement is incomplete. Complete form is shown below:
Oil is leaking from an oil tanker at the tanker of 3000 liters per hour. 8 liters of oil spread out over 10 square meter of ocean surface. A circular oil slick forms.
a) Express the radius R of the oil slick as a function of the time t (in hours) the tank has been leaking.
b) After how many hours will the oil slick have radius 1 kilometer?
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A bag contains 3 green marbles and 5 white marbles. Paul picks a marble at random from the
bag and does not put it back in the bag. He then picks another marble from the bag.
a. Construct a probability tree of the problem.
Answers
A probability tree is a visual representation of the possible outcomes of an event or series of events. In this case, the event takes a marble out of the bag.
How to create the tree?The first step in building a probability tree is to create a starting point that represents the first state of the problem. In this case, the starting point is a bag containing 3 green marbles and 5 white marbles.
The next step is to branch from the starting point and show the possible results of the first event. This includes taking out the marble out of the bag. The probability of getting a green marble is 3/8 and the probability of getting a white marble is 5/8.
After the first event, the issue status changes. In this case, the bag contains 2 green marbles and 4 white marbles.
The next step is to branch out from the state after the first event and show the possible outcomes of his second event involving pulling another marble out of his pocket. The probability of getting a green marble is 2/6 and the probability of getting a white marble is 4/6. The final step is to label the endpoints of the tree with the possible outcomes of the problem and the probabilities of each outcome.
The probability tree starts with an sack of 3 green marbles and 5 white marbles, as shown in the design showing the possible outcomes of selecting a marble, the new state of the sack after each selection, and the probability of each outcome
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