The probabilities for each case in this problem are given as follows:
a) A and B disjoint -> P(B and not A) = 1/2.
b) A is contained in B -> P(B and not A) = 1/6.
c) P(A and B) = 1/8 -> P(B and not A) = 3/8.
How to obtain the probabilities?The probability that we want to obtain in this problem is given as follows:
P(B ∩ Ac).
Which is the probability of B and the complement of A, that is:
P(B and not A).
If A and B are disjoint, it means that their intersection is of 0, hence:
P(B and not A) = P(B) = 1/2.
If A is contained in B, all elements of A are contained in B, hence the proportion of elements that are in B but not A is given as follows:
P(B and not A) = 1/2 - 1/3 = 1/6.
If the probability of the intersection is of 1/8, the proportion of elements that are in B but not A is given as follows:
P(B and not A) = 1/2 - 1/8 = 4/8 - 1/8 = 3/8.
(as 1/8 of them belong to both B and A, hence they do not belong to the complement of A).
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A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. At the end of the questionnaire is an (optional) invitation to donate money to the organization. Which of the following statements about this survey is true?
A) The survey results are invalid because it’s impossible to word questions about politics without creating bias.
B) The survey results are invalid because only surveys conducted by phone are free from bias.
C) The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money.
D) The survey results will overestimate support for this political action committee in the entire population because people more likely to respond if they are prepared to donate money.
E) Since the survey was sent to randomly-selected households, it should be free of bias.
Option c; The survey results will underestimate support for this political action committee in the entire population because people who respond are less likely to support an organization that asks for money. This is the correct statement about the survey.
What is politics?
Politics is a category of activities that are related to group decision-making or other types of power dynamics between people, such as the allocation of resources or status. Political science is the name of the area of social science that focuses on politics and governance.
Given,
A political action committee sends out a questionnaire to randomly-selected mailing addresses, asking people to rate the importance of a variety of economic and social issues facing the country. at the end of the questionnaire is an (optional) invitation to donate money to the political action committee.
We have to find the correct statement about the survey from the given options;
Because respondents are less inclined to support a group that solicits donations, the survey results will understate public support for this political action committee.
The correct statement about the survey is option c;
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Fill in the missing digits to find the base 2 representation of 59.
To find the base 2 representation of 59, we need to express 59 as a sum of powers of 2.
The powers of 2 are: 1, 2, 4, 8, 16, 32, 64, 128, etc.
The largest power of 2 that is less than or equal to 59 is 32. The next largest power of 2 is 16. The largest power of 2 that is less than or equal to the remaining value (59 - 32 = 27) is 16. The largest power of 2 that is less than or equal to the remaining value (27 - 16 = 11) is 8. The largest power of 2 that is less than or equal to the remaining value (11 - 8 = 3) is 2. The largest power of 2 that is less than or equal to the remaining value (3 - 2 = 1) is 1.
The base 2 representation of 59 is therefore:
32 + 16 + 8 + 2 + 1
which can be written as:
111011
Therefore, the base 2 representation of 59 is 111011.
Answer:
0111011
Step-by-step explanation:
By doing L.C.M of 59 by 2 only
__2__[_59__
__2__{_29__ ----->remainder=1
__2__{__14__ ----->remainder=1
__2__{__7___----->remainder=0
__2__{__3___----->remainder=1
__2__{__1___------>remainder=1
__2__{__0__------->remainder=1
__2__{__0__------->remainder=0
answer: 0111011
Two mobile phone companies have different data rates. Company A has a rate of
$100 for unlimited data, and Company B has a flat fee of $20 plus $5 per gigabyte of data. The point of intersection between these two linear relations is (16, 100).
What does this point of intersection represent?
a) Both phone companies would charge $16 per gigabyte used with a bill of $100.
b) Both phone companies would charge $100 if the customer used 16 gigabytes of data.
c) Both companies would charge $100 with a flat fee of $16.
d) Both companies would charge $16 per gigabyte if the customer used 100 gigabytes.
Explanation:
x = number of gigabytes of data used
y = total price
Company A has the equation y = 100. The x variable is not involved since the cost is $100 no matter what.
Meanwhile, company B has the equation y = 5x+20
The slope of 5 indicates how much per gigabyte is charged. The 20 at the end is the flat fee, aka y intercept.
If we were to graph those equations, then we'd find they intersect at (16,100) as mentioned.
This means x = 16 and y = 100 pair up together.
It further tells us that both companies charge the same ($100) when x = 16 gigabytes of data are used.
This points us to choice B as the final answer.
Mr. Freeze is a freelance ice artist who creates ice sculptures. He is paid $30 per pound of ice he uses. Last week it took him 73 hours to sculpt 5 sculptures weighing a total of 530 pounds. Based on this, what is his approximate hourly wage?
Answer:
$217.81/hr
Step-by-step explanation:
The 5 sculptures contain 530 lbs of ice, which Nr. Freeze sells at $30/lb:
His total income is: (530 lbs)*($30/lb) = $1590
The sculptures required 73 hours to create. Mr Freeze's hourly wage is therefore ($1590/73 hr) = $217.81/hr (!)
8188.8
A new washing machine used 3½ gallons of water per full load to clean clothes. If Sam
washed 3% loads of clothes, how many gallons of water would be used?
The wholesale price for a shirt is 5.50. A certain department store marks up the wholesale price by 90%. Find the price of the shirt in the department store.
Round your answer to the nearest cent, as necessary.
The price of the shirt if The wholesale price for a shirt is 5.50 and A certain department store marks up the wholesale price by 90% is $10.45.
What is the Wholesale price?The cost price of a certain product plus the profit margin earned by the manufacturer equals the wholesale price.
Given:
The wholesale price for a shirt is $5.50,
The markup price = 90%
Calculate the markup price as shown below,
The markup price = 90% of $5.50
The markup price = 90 / 100 × 5.50
The markup price = $4.95
Calculate the price of the shirt as shown below,
The price of a shirt = The markup price + The wholesale price of the shirt
The price of a shirt = $5.50 + $4.95
The price of a shirt = $10.45
Therefore, the price of the shirt if The wholesale price for a shirt is 5.50 and A certain department store marks up the wholesale price by 90% is $10.45.
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Which of the following is a polynomial ? (a) 1/x+1 (b) 1/√x+1 (c) 1/x²+x+1 (d) x³+1
Answer:
Before you get into classifying polynomials, let’s define what polynomials are!
Polynomials are a specific type of mathematical expression that has all of the following:
One or more terms
Variables with only positive whole-number exponents
No variables in the denominators of any term
So, let's discuss the questions:
A)1/x+1 is not a polynomial
B)1/√x+1 is not a polynomial
C)1/x²+x+1 is not a polynomial
D) x^3+1 is a polynomial bc it has positive whole number exponent, their no variables in the denominators and its more than 1 terms
Step-by-step explanation:
hope this helps <3
on the 9th of february 2012, the heights of the water in the bristol channel in cardiff, uk were as follows. low tide was 1.2 m at 2:00 am and high tide was 12.4 m at 7:56 am. assuming sinusoid periodicity, estimate the height of the water at sunset (5:16 pm on that day). give your answer as a decimal (in metres) rounded to 1 decimal place.
It should be close to 7m at around 5pm. In fact, this is the time of day when the water rises the fastest, so perhaps 8m
What is the period of the sinusoidal signal?The interval between successive peaks in the sinusoidal signal graph, or period, is only the number of seconds needed for one cycle of the sinusoid.
Are all sinusoidal sequences periodic?Depending on the values of angular frequency (), discrete-time sinusoidal sequences may or may not be periodic. A discrete-time sinusoidal signal must have an angular frequency () that is a multiple of 2 to be considered periodic.
It takes roughly 6 hours from low tide to high tide, or 12 hours for the entire tide cycle. Since low tide was at 2 a.m., low tide will be at around 2 p.m. as well. Three hours later, or at around 5 p.m., the water should be at the average level, which should be at (12.4+1.2)/2=6.8 m. Therefore, it should be close to 7m around 5:45. Actually, this is when the water rises the fastest, so it's probably close to 8m. Your 5.5m is obviously too low, regardless of where it is.
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choose r for a qualification for a member of the house of representatives, s for a qualification for a senator, or b for both.
Qualifications for members of house of representatives and senate
r ;- Be a resident of the state from which they are elected, be at least 25 years old, and have been citizens for at least 7 years.
s ;- Be a resident of the State from which he or she is elected, at least 30 years old, and a citizen for at least 9 years.
Given,
The House of Representatives is the lower body of the United States Congress, and the United States Senate is its upper chamber. The United States' national bicameral legislature is made up of them all. Washington DC
Then,
Qualification for a member of the house of representatives, r ;-
Be a resident of the state from which they are elected, be at least 25 years old, and have been citizens for at least 7 years.
Qualification for a senator, s ;-
Be a resident of the State from which he or she is elected, at least 30 years old, and a citizen for at least 9 years.
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The differential treatment of individuals or groups without reference to behavior, qualifications, or other legal factors, resulting in a difference in outcome, is known as discrimination. Discrimination can occur based on various factors such as race, gender, age, religion, disability, or nationality.
There are different forms of discrimination, including: 1. Direct discrimination: This occurs when someone is treated less favorably because of a specific characteristic or attribute. For example, if an employer refuses to hire someone solely based on their gender, it would be considered direct discrimination. 2. Indirect discrimination: This happens when a seemingly neutral policy, criterion, or practice puts individuals with a particular characteristic at a disadvantage. For instance, if a job requires a height requirement that disproportionately affects a certain racial group, it would be considered indirect discrimination.
3. Systemic discrimination: This refers to discrimination that is built into the structures, policies, and practices of an organization or society. It may be unintentional but still leads to unequal outcomes. An example is when certain communities consistently receive lower funding for education compared to others, leading to systemic disadvantages for students in those areas.
Discrimination can have negative impacts on individuals and society as a whole, perpetuating inequality and hindering social progress. It is important to promote equality, fairness, and inclusivity to create a just and equitable society.
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Please help. I tried and couldn’t solve it
Using the law of cosines, the measure of the angles are
α ≈ 127°
β ≈ 28°
γ ≈ 25°
Law of Cosines: Calculating the angles in a triangleFrom the question, we are to solve the triangle.
To solve the triangle, we will determine the value of the unknown angles.
Using the law of cosines, we can write that
cosα = (b² + c² - a²)/2bc
From the given information,
a = 34
b = 20
c = 18
Thus,
cosα = (20² + 18² - 34²)/2(20)(18)
cosα = -432/720
cosα = -0.6
α = cos⁻¹(-0.6)
α = 126.8699°
α ≈ 127°
Calculating angle β
cosβ = (a² + c² - b²)/2ac
cosβ = (34² + 18² - 20²)/2(34)(18)
cosβ = 1080/1224
β = cos⁻¹(1080/1224)
β = 28.0724°
β ≈ 28°
To determine angle γ
α + β + γ = 180° (Sum of angles in a triangle)
127° + 28° + γ = 180°
155 ° + γ = 180°
γ = 180° - 155°
γ ≈ 25°
Hence,
α ≈ 127°
β ≈ 28°
γ ≈ 25°
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Can a triangle have sides with the given lengths? 11, 12, 15
what is the result of the following boolean expression, if x equals 5, y equals 3, and z equals 8? not (x < y or z > x) and y < z
False Reason:...This is false if (x=5) (y=3). and denotes the requirement that both be true.
This is true: (z=8) > (x=5) The entire statement is false because it relies on the and condition rather than the OR condition.
What is an example of a Boolean expression?
A Boolean expression(named for mathematician George Boole) is an articulation that assesses to one or the other valid or misleading. Let's take a look at some examples from common speech: Pink is my favorite color. valid • I'm anxious about PC programming. False This book is a laugh-out-loud good read.
Which three Boolean expressions are there?
There are three fundamental Boolean operators: What's more, OR, and NOT.
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Roberto's employer offers a sliding paid vacation. when he started work, he was given three paid days of vacation. For each six-month period he stays at the job, his vacation is increased by two days. Let x represent the number of 6-month periods worked and y represent the total number of paid vacation days. Write an equation that modes the relationship between these two variables.
Answer:
telecomunication of te following
if opposite angles of a quadrilateral are supplementary then the quadrilateral is a parallelogram? true or false?
False. If opposite angles of a quadrilateral are supplementary then the quadrilateral is not a parallelogram.
What are supplementary angles?Two angles are said to be supplementary angles if their sum is equal to 180 degrees.
What are the angle properties of a parallelogram?In a parallelogram the sum of adjacent angles is equal to 180 degrees which means that the adjacent angles are supplementary. Whereas, the opposite angles in a parallelogram are congruent (equal). Hence, the statement is false.
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Function A is represented by the equation y= 2x+1. Function B is a linear function that goes through the points shown in the table. X 1 3 4 6 3 11 15 23 Which statement correctly compares the rates of change of the two functions?
A. the rate of change of function a is 1
The rat of change of function b is 4
B. the rate of change of function a is 2
the rate of change of function b is 8
C. the rate of change of function a is 1
the rate of change of function b is 8
D. the rate of change of function a is 2
the rate of change of function b is 4
The rate of change of the linear function A is 2, and the one of function B is 4, then the correct option is D.
Which statement correctly compares the rates of change?A general linear function is written as:
y = a*x + b
Where a is the rate of change and b is the y-intercept.
In this case, we know that function A is:
y = 2x + 1
Then the rate of change is 2, and the y-intecept is 1.
We also know that if a line passes through two points (x₁, y₁) and (x₂, y₂), then the rate of change of that line is given by the formula:
a = (y₂ - y₁)/(x₂ - x₁)
In the case of function B we have the table:
x: 1 3 4 6
y: 3 11 15 23
We can use any two points on the table, if we use the first two ones:
(1, 3) and (3, 11) we will get:
a = (11 - 3)/(3 - 1) = 8/2 = 4
The rate of change of function B is 4, then the correct statement is the one in option D.
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In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°, what is the value of x?
A: 35
B: 37
C: 44
D: 71
The required simplified value of the x is given as 5.
Given that,
In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
for the triangle sum of the interior angles is equal to 180°.
∠D + ∠E + ∠F = 180
2x + 2x - 4 + x + 9 = 180
5x + 5 = 180
5x = 175
x = 35
Thus, the required simplified value of the x is given as 5.
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I need help with this problem
Step-by-step explanation:
of the following is the correct arrangement of the following atoms in order of DECREASING first ionization energy?
O>Te>Se>Po
Po>Te>Se>O
O>Se>Te>Po
Po>Se>Te>O
Find an equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5.
Equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5 is (x+3)²/25+(y-5)²/16=1
What is Ellipse?An ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
Given,
center −3, 5,
Major axis of length 8
Endpoint of minor axis 0, 5.
Standard form of equation for an ellipse with vertical major axis:
(x-h)²/b²+(y-k)²/a²=1, a>b
(h,k)=(x,y) coordinates of center.
(-3, 5) are coordinates of centre
given length of vertical major axis:=8=2a=4
a=4
a²=16
Length of minor axis=b=5
b²=25
Hence, equation of the ellipse that has center −3, 5, a major axis of length 8, and endpoint of minor axis 0, 5 is (x+3)²/25+(y-5)²/16=1
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Draw a graph with at least 5 nodes and 15 edges.
It is possible to draw graph with 5 nodes and 15 edges.
What are nodes and edges?
Nodes are points on graph in where curves, lines or scatters are met.
Edges are curves, lines or arcs presented on the graph connected by one or more nodes.
How to draw graph with nodes and edges?So as to draw graph using nodes and edges, we have to follow a formula that allow us about how many nodes and edges can be used at a time.
If we have N nodes, then we have N-1 edges available connect directly to other nodes. Therefore, maximum number of edges available in such case for connecting directly or indirectly to the nodes is calculated by the formula below.
Maximum number of edges =N×(N-1), when we have N nodes.
in the question, we are said to draw graph with 5 nodes and 15 edges.
we have maximum number of edges = 5×(5-1) = 20 edges
hence, it is possible to draw graph with 5 nodes and 15 edges.
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which is not true about the pascals triangle
The statement which not true about the Pascal’s Triangle is that it is not symmetrical.
What are the correct statements about Pascal’s Triangle?It is symmetrical.The first diagonal is all 1’s.The second diagonal is the counting numbers.Any number in the triangle is the sum of the two numbers directly above it.Each row adds to a power of 2.The first and last numbers of a row are always 1.The nth row gives the coefficients in the expansion of (x+y)^n.Pascal's Triangle presents us how many ways heads and tails can combine. This can then show us the probability of any combination.
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2. The equation and the graph represent two functions. Use the equation
y 4 and the graph to answer the questions, Besson 5-7)
6 7 8 9 10 11 12
a. When x is 4, is the output of the equation or the graph greater?
b. What value for x produces the same output in both the graph and
the equation?
The equation y = 4 has a greater output at x = 4
The graph and the equation have the same output at x = 6
The greater output at x = 4From the question, we have
The linear graph The equation y = 4From the graph, we can see that
When x = 4, the output is 3
The equation y = 4 implies that, the output is always 4 irrespective of the input value
Hence, the equation has a greater output.
The value of x for same outputHere, we have the same parameters above
From the graph, we can see that
When y = 4, the input is 6
The equation y = 4 implies that, the output is always 4 irrespective of the input value
Hence, they have the same output at x = 6
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How long does it take to finish A Christmas Carol?; How many stages are in A Christmas Carol?; How did Scrooge change from the beginning to the end?; What is the time and place of A Christmas Carol?
Average one hour 45 minutes time is taken to read A Chirstmas Carol Novel.
There is total five chapters in this novel. In the ed of of beginning, Scrooge has completely transformed into a charitable, altruistic man. A chirstmas Carol is at a time when the British were investigating and reassessing past Christmas
traditions and place is Washington.
A Christmas Carol:The average reader will spend 1 hour 4 minutes reading this book at 250 WPM (words per minute). A Christmas Carol is set in London during the Victorian era. The events of the story take place on Christmas Eve at Ebenezer's Scrooge home, where various events are shown by three visiting spirits. Charles Dickens wrote A Christmas Carol at a time when he was very critical of his writing and the world around him.
Dickens wrote A Christmas Carol at a time when the British were investigating and reassessing past Christmas traditions, including carols, and more recent practices such as Christmas cards and Christmas trees. He was influenced by his own adolescent experiences and by other writers' Christmas stories, such as Washington in his Irving and Douglas in his Jerold.
The book is divided into his five chapters, which Dickens entitled "Staves".
By the end of the novel, Scrooge has completely transformed into a charitable, altruistic man, rather than a misanthrope. This concept becomes apparent when you say, "I'm light as a feather, happy as an angel, and so baby." Scrooge changed his attitude and behavior.
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QUESTION 12/15 Which tools would you use to make Chart 1 look like Chart 2? Select all that apply.
The tool that is used to make Chart1 look like Chart2 is data lables .
What are Charts ?
Charts can be defined as graphical way that represents data elements.
the forms of charts are tables and graph .
From the attachment we can see that both the charts are circle graphs .
and the chart2's data label is visible and chart's 1 data label is not visible .
The data label of chart1 needs to be visible for both the chart to look alike .
Therefore , the tool that is used to make both the charts lookalike is data labels .
The given question is incomplete , the complete question is
Which tools would you use to make Chart 1 look like Chart 2 ?
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what is the value of the estimated standard error for the following set of d-scores? scores: 2, 2, 10, 2. a) 3 b) square root 3 c) 4 D) 2
The value of the estimated standard error for the following set of D scores 2, 2, 10, 2 is 4 .
The standard error of a statistic is the standard deviation of the sample distribution, or a close approximation of that standard deviation. A statistic that is the sample mean is referred to as having a "standard error of the mean."
The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. In statistics, a sample mean deviates from the actual mean of a population; this deviation is the standard error of the mean.
Consider the following set of D scores,
2, 2, 10, 2
We will calculate ∑D and ∑D² to find the SS for the D scores.
Therefore,
∑D = 2 + 2 + 10 + 2
We can sum or difference of the coefficients,
∑D = 4 + 10 + 2
∑D = 14 + 2
∑D = 16
Then,
∑D² = 2² + 2² + 10² + 2²
∑D² = 4 + 4 + 100 + 4
∑D² = 8 + 100 + 4
∑D² = 100 + 12
∑D² = 112
So,
The formula for the standard score is given as:
SS = ∑[tex]D^{2}[/tex] - (∑D*∑D) / n
SS = 112 - [ (16)² /4 ]
SS = 112 - [ 256 /4 ]
SS = 112 - 64
SS = 48
Then,
[tex]S_{D}[/tex] = [tex]\sqrt{\frac{SS}{n-1} }[/tex]
[tex]S_{D}[/tex] = [tex]\sqrt{\frac{48}{4-1} }[/tex]
[tex]S_{D}[/tex] = [tex]\sqrt{\frac{48}{3} }[/tex]
[tex]S_{D}[/tex] = [tex]\sqrt{16}[/tex]
[tex]S_{D}[/tex] = 4
Therefore,
The value of the estimated standard error for the following set of D scores 2, 2, 10, 2 is 4 .
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find the future value of an annuity due of $200 each quarter for 2 1 2 years at 13%, compounded quarterly. (round your answer to the nearest cent.) $
The Future value of an annuity due of $200 each quarter for 2 1 2 years at 13%, compounded quarterly is $10263.734 ..
The future value of an annuity is the value of a group of regular payments at some point in the future. It assumes a particular rate of return, or discount rate. The higher the discount rate, the greater the annuity's future value.
P = PMT× ((1+r)ⁿ −1)/r
where:
P---> Future value of an annuity stream
PMT---->Dollar amount of each annuity payment
r -->Interest rate (also known as discount rate)
n--->Number of periods in which payments will be
We have given that
Present value for an Annuity = $200
compounded rate , r = 13%
but compounded quarterly, then, r = 13%/4
= 0.13/4 = 0.325
Number of years , n = 2 + 1/2 = 5/2
then change into quarterly, n = 5/2 × 4 = 10
Future value formula ,
F.V = PMT ( (1+i)ⁿ - 1)/r
=> Future value = 200((1+0.325)^10/0.325)
=> F.V = 10263.734
Hence, the future value of an annuity is $10263.734..
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a grocery store is interested in determining whether or not a difference exists between the shelf life of two different brands of doughnuts. a random sample of 100 boxes of each brand was selected and the shelf life in days was determined for each box. the sample results are given below. brand a brand b mean
Therefore ,Based on this sample, of 90% confidence interval that Hot'n Now doughnuts will remain fresher for an additional 1.1 to 2.4 days than Sugar Yum doughnuts.
What is confidence interval ?An estimation range for an unknowable parameter is referred to as a confidence interval in frequentist statistics. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals.
Here,
Given: random sample of 100 boxes of each brand
The difference of the means,μhn−μsy had a 90% confidence interval that was calculated as follows: (1.1,2.4).
Therefore,
Based on this sample, we are 90% confidence interval that Hot'n Now doughnuts will remain fresher for an additional 1.1 to 2.4 days than Sugar Yum doughnuts.
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Suppose that survey is planned to estimate the proportion of population that is left-handed The sample data will be used to form confidence interval: Which one of the following combinations of sample size and confidence leve will give the widest interval? n E 500, confidence level 909 n = 1,000, confidence level 909 n = 500, confidence level 959 n = 1,000, confidence level 959 Explain why this sample size and confidence level will give the widest interval: The Select-- sample size and Select- confidence level will both tend to increase the width of the confidence interval:
The 500 sample size and 95% confidence level will both tend to increase the width of the confidence interval.
In this question, we have been given the combinations of sample size and confidence level.
We need to select a combinations of sample size and confidence level that will give the widest interval.
We know that the confidence level is typically set in the range of 99% to 80%. The 95% confidence interval will be wider than the 90% interval and which will be wider than the 80% interval.
As we know increasing the confidence will increase the margin of error which results in a wider interval.
But increasing the sample size decreases the width of confidence intervals, as it decreases the standard error.
This means, for the widest interval we need to select a high confidence interval and small sample size.
Therefore, the sample size = 500 and the confidence interval = 95% will give the widest interval.
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Bones from the skeleton of a fish have lost 22 percent of their carbon-14. Note that for carbon-14,the constant of proportionality is approximately k = 0.000124. Estimate the age of the bones: Round to the nearest tenth of ayear. Answer How to enter your answer Keypad years
The age of the bones from the skeleton of s fish is 2000 years.
The formula to be used for calculation of age is-
ln (N/No) = - kt, where N/No represents remaining time, k represents constant of proportionality and t refers to the age or time period.
The remaining time = 100 - 22
Remaining time = 78% or 0.78
Keep the values in mentioned formula to find the time.
ln 0.78 = - 0.000124t
Keeping the value of ln 0.78 on Left Hand Side of the equation
- 0.248 = - 0.000124t
Negative sign will be cancelled as it is present on both sides of the equation
t = 0.248/0.000124
Performing division on Right Hand Side of the equation
t = 2000
Hence, the age is around 2000 years.
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A cement mix calls for 2 cups of water and 1 1/4 pounds of mix to make five large tiles stick to the ground, Yolanda has plenty of water but only 4 3/8 pounds of mix. How many large tiles (including parts of a tile) can she stick to the ground? You MUST think conceptually and illustrate your thinking with a model. Do NOT use proportional reasoning.
175/26 large tiles can she stick to the ground.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
A cement mix calls for 2 cups of water and [tex]1\frac{1}{4}[/tex] pounds of mix to make five large tiles stick to the ground,
2+ [tex]1\frac{1}{4}[/tex]=5
2+5/4
13/4
Which means 13/4 is needed for 5 large tiles.
Yolanda has plenty of water but only [tex]4\frac{3}{8}[/tex] pounds of mix
We need to find how many large tiles can she stick to the ground.
Let x be the number of tiles.
[tex]4\frac{3}{8}[/tex] =35/8
So
(13/4)/5=(35/8)/x
Apply cross multiplication
13/4x=35/8×5
13/4x=175/8
x=175/8×4/13
x=700/104=350/52=175/26
Hence, 175/26 large tiles can she stick to the ground.
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The variable p varies inversely as the square of q. When p = 36, q = 25.
When p = 4, q=
When q = 10, p =
Answer:
p=4: q = 75q=10: p = 225Step-by-step explanation:
You want to know various values of p and q when p varies inversely as the square of q, and p=36 when q=25.
VariationA formula describing the variation of one variable with another will generally have a constant of variation, which we choose to represent here by the letter k.
Since p varies inversely as the square of q, the formula can be written as ...
[tex]p=\dfrac{k}{q^2}[/tex]
Multiplying by q² gives us a way to find the value of k from known values of p and q:
k = p·q²
k = 36·25² = 22500 . . . . . . using the given values of p and q
We can also rearrange the formula to give q as a function of p:
q = √(k/p)
Table of valuesWe are interested in q for p=4, and in p for q=10.
q = √(22500/4) = 75
p = 22500/10² = 225
When p=4, q = 75When q=10, p = 225