We fail to reject H0. So there is enough evidence to state that the hypothesis H1 has the risk to make an error equal to α.
What do you mean by standard deviation?
The term "standard deviation" refers to a measurement of the data's dispersion from the mean. A lower number deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
What does it mean if standard deviation is negative?The standard deviation is positive, or greater than zero, whenever there are two uneven terms in the observations. The standard deviation is exactly zero if all of the observations are equally distributed. Thus, the standard deviation can never be negative or less than zero.
We have two hypotheses:
H0: μ= 120
H1: μ≠ 120
where μ is the mean weight and per apple the value of α is 0.05. If conditions are met we will run sample a.
random: 49 apples are randomly selected
normal: 49>=30 so CLF holds. Now,
formula of z-test for μ
Test statistic: z-test=(¯x−μ)/( σ/√n)
We are given with:
n=49
¯x=122.5
σ=12
putting values in formula:
z-test=(122.5-120)/(12/√49)
=1.458
P-value: P(z>1.458)=normal df(1.458, ∞,1)
=0.0724
And it is a two tailed test so
=2(0.0724)
=0.1448
Since P-value> α ; (0.0724>0.05)
So, we fail to reject H0. We do not have convincing evidence that there is a difference in mean weight per apple. So here we would say that there is enough evidence to state that the hypothesis H1 has the risk to make an error equal to α.
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Zoe goes to a restaurant and the subtotal on the bill was xx dollars. A tax of 5% is applied to the bill. Zoe decides to leave a tip of 15% on the entire bill (including the tax). Write an expression in terms of xx that represents the total amount that Zoe paid.
The expression in terms of x that represents the total amount that Zoe paid is 1.2x
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
A tax of 5% is applied to the bill.
Zoe decides to leave a tip of 15% on the entire bill (including the tax).
let the bill cost $x.
So, the price after tax and tip
= x+ 5% of x+ 15% of x
= x + 0.05x + 0.15x
= x + 0.20x
= 1.2x
Hence, the expression in terms of x that represents the total amount that Zoe paid is 1.2x
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A team of A4 paper contain 500 heet. The ize of each paper i 297mm long and 210mm wide. The volume of the team i 37422cm cube. Find the thickne of each heet of paper,leaving your anwer in cm
Using the conversion factor, we can say that each sheet of paper is 0.0012mm thick.
What is the conversion factor?A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.
The amount is often expressed as a fraction or ratio with a multiplication factor.
So, 500 sheets of A4 paper make up a conventional ream. Each paper measures 297mm in length by 210mm broad, and one ream contains 3742.2cm of paper.
to change cm to mm
3742.2cm = 37422 mm
Sheet 1's surface
(297mm) X 210mm) = 62370mm²
1st volume sheet:
37422mm : 500 = 74.844mm
One sheet's thickness is:
74.844mm : 62370mm = 0.0012mm
Therefore, each sheet of paper is 0.0012mm thick.
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Correct question:
A ream of A4 paper contains 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm find the thickness of each sheet of paper answer in millimeters
What type of pair of angles are∠2 and angle∠11 ?
The type of pair of angles that are∠2 and angle∠11 is an alternate interior angles.
What is an alternate interior angle?When a transversal intersects two coplanar lines, alternate interior angles are formed. They are on the inside of the parallel lines, but on the outside of the transversal.
Angles with the same size that occur on opposite sides of the transversal line are known as alternate angles. The following alternate angles are equal: By drawing a Z shape, we can frequently identify interior alternate angles: Alternate angles are classified into two types: alternate interior angles and alternate exterior angles.
To understand alternate interior angles, imagine a set of parallel lines and then a line intersecting them. The intersecting line is known as a transversal, and all of the angles formed by the parallel lines are known as interior angles.
Both angles are interior angles that lie alternately to each other on the transversal line r. Therefore, they are alternate interior angle.
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suppose that you have 600 feet of rope and want to use it to make a rectangle. what dimensions should you make your rectangle if you want to enclose the maximum possible area?
The dimensions of the rectangle should be 150 feet by 400 feet in order to enclose the maximum possible area.
To explain this step by step:
Step 1: We know that the perimeter of a rectangle is equal to 2*length + 2*width.
Step 2: Since we have 600 feet of rope, we can plug this number into the equation: 2*length + 2*width = 600
Step 3: To solve for the length and width, we can divide both sides by 2: length + width = 300
Step 4: We can then separate the equation into two equations: length = 300 - width and width = 300 - length
Step 5: Since we want to find the maximum possible area, we should set width equal to the larger number, 300, and set length equal to the smaller number, 300 - width.
Step 6: Plugging this into the equation, we get: width = 300 and length = 300 - width = 300 - 300 = 0.
Step 7: Therefore, the maximum possible area that can be enclosed with 600 feet of rope is 150 feet by 400 feet dimensions.
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assume that blood pressure readings are normally distributed with a mean of 123 and a standard deviation of 9.6. if 144 people are randomly selected, find the probability that their mean blood pressure will be less than 125.
The probability that the mean blood pressure will be less than 125 is 0.9938
The mean of the pressure readings = 123
The standard deviation = 9.6
Total population = 144
The value is less than 125
The equation of the z-score is
z-score = (Observed value - Mean ) / (Standard deviation /[tex]\sqrt{N}[/tex])
Substitute the values in the equation
z-score = (125 - 123) / (9.6/[tex]\sqrt{144}[/tex])
= 2 / (9.6/12)
= 2 / 0.8
= 2.5
Using the statistical table
The probability of that their mean blood pressure less than 125
P(z < 2.5) = 0.9938
Therefore, the probability is 0.9938
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A hot chocolate recipe calls for 2/3 cup of milk.Slade wants to make 1/2 of the recipe.How much milk should Slade use?
Answer: Slade should use 1/3 cup of milk
Step-by-step explanation:
2/3 divided by 1/2 = 1/3
In other words, if you have 2 of something and you give someone half, you would give them 1.
Select the correct answer. What is the average rate of change of f(x), represented by the table of values, over the interval [-2, 3]? x f(x) -6 2.5 -2 2.5 0 2 2 0 3 5 A. 5 B. 2.5 C. 1 D. 0.5\
The average rate of change of f(x), represented by the table of values, over the interval [-2, 3] is: D. 0.5.
What is an average rate of change?An average rate of change is sometimes referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity changes with respect to another quantity, over a given interval.
In Mathematics, the average rate of change of f(x) on a closed interval [a, b] is given by this formula:
Average rate of change = [f(b) - f(a)]/(b - a)
Next, we would determine the average rate of change of the function f(x) over the interval [-2, 3]:
a = -2; f(a) = 2.5
b = 3; f(b) = 5
Substituting the given parameters into the formula, we have the following;
Average rate of change = (5 - 2.5)/(3 - (-2))
Average rate of change = 2.5/5
Average rate of change = 0.5.
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because the sample size is 81, do you need to be concerned about the shape of the population distribution when conducting the t test in (a)? explain. choose the correct answer below. a. no, because n is equal to 81, the sampling distribution of the t test is approximately normal. in general, the t test is appropriate for a large sample size. b. yes, because n is equal to 81, the sampling distribution of the t test cannot be determined. in general, the t test is only appropriate for a normally distributed sample. c. no, because n is equal to 81, the sampling distribution of the t test is approximately normal. in general, the t test is appropriate for this sample size unless the population is skewed. d. yes, because n is equal to 81, the sampling distribution of the t test cannot be determined. in general, the t test requires a larger sample size.
As per the given sample size, the shape of the population distribution when conducting t test is approximately normal.
Sampling.
in statistics, sampling refers the statistical procedure that is concerned with the selection of the individual observation; it helps us to make statistical inferences about the population.
Given,
Here we have the sample size is 81.
Now, we need to find the shape of the population distribution when conducting the t test.
Let us consider you are the manager of a restaurant for a fast-food franchise. And in last month, the mean waiting time at the drive-through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.9 minutes.
Now, you are selecting a random sample of 81 orders.
As per the sample size, the sample mean waiting time is 3.72 minutes, with a sample standard deviation of 0.8 minute.
Now, we complete parts (a) and (b) below.
a. here at the 0.01 level of significance, is there evidence that the population mean waiting time is different from 3.9 minutes.
And state the null and alternative hypotheses.
H0: μ▼ H1: μ ▼
So, H0 is sufficient insufficient evidence to conclude that the population mean waiting time is different from 3.9 minutes .
b. According to the sample size is 81,
The shpe of the population distribution when conducting t test is approximately normal. As in the t test is appropriate for a large sample size.
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One hundred people purchase lottery tickets. Three winning tickets will be selected at random. If first prize is $100, second prize is $50, and third prize is $25, in how many different ways can the prizes be awarded?.
The number of different ways the prizes can be awarded is 161700
How to determine the number of different ways can the prizes be awarded?From the question, we have the following parameters that can be used in our computation:
Total number of people, n = 100Total numbers of winners, r = 3 i.e. the first, the second, the thirdThe number of different ways the prizes can be awarded is calculated using the following combination formula
Total = ⁿCᵣ
Where
n = 100 and r = 3
Substitute the known values in the above equation
Total = ¹⁰⁰C₃
Apply the combination formula
ⁿCᵣ = n!/(n - r)!r!
So, we have
Total = 100!/97!3!
Evaluate
Total = 161700
Hence, the number of ways is 161700
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For the following pairs of assertions, indicate which do not
comply with our rules for setting up hypotheses and why (the
subscripts 1 and 2 differentiate between quantities for two
different populations or samples): (a) H0: μ = 100, Ha: μ > 100
These hypotheses comply with our rules. H0 cannot include equality,
so these hypotheses are not in compliance. Each μ is a statistic,
so these hypotheses do not comply with our rules. The asserted
value in H0 should not appear in Ha, so these hypotheses are not in
compliance. (b) H0: σ = 20, Ha: σ ≤ 20 These hypotheses comply with
our rules. Ha cannot include equality, so these hypotheses are not
in compliance. Each σ is a statistic, so these hypotheses do not
comply with our rules. The asserted value in H0 should not appear
in Ha, so these hypotheses are not in compliance. (c) H0: p ≠0.25,
Ha: p = 0.25 These hypotheses comply with our rules. Ha cannot
include equality, so these hypotheses are not in compliance. Each p
is a statistic, so these hypotheses do not comply with our rules.
The asserted value in H0 should not appear in Ha, so these
hypotheses are not in compliance. (d) H0: μ1 − μ2 = 25, Ha: μ1 − μ2
> 100 These hypotheses comply with our rules. H0 cannot include
equality, so these hypotheses are not in compliance. Each μ is a
statistic, so these hypotheses do not comply with our rules. The
asserted value in H0 should also appear in Ha, so these hypotheses
are not in compliance. (e) H0: S12 = S22, Ha: S12 ≠S22 These
hypotheses comply with our rules. H0 cannot include equality, so
these hypotheses are not in compliance. Each S is a statistic, so
these hypotheses do not comply with our rules. The asserted value
in H0 should not appear in Ha, so these hypotheses are not in
compliance. (f) H0: μ = 120, Ha: μ = 150 These hypotheses comply
with our rules. Ha cannot include equality, so these hypotheses are
not in compliance. Each μ is a statistic, so these hypotheses do
not comply with our rules. If μ appears in H0, then it should not
appear in Ha, so these hypotheses are not in compliance. (g) H0:
σ1/σ2 = 1, Ha: σ1/σ2 ≠1 These hypotheses comply with our rules. H0
cannot include equality, so these hypotheses are not in compliance.
Each σ is a statistic, so these hypotheses do not comply with our
rules. The asserted value in H0 should not appear in Ha, so these
hypotheses are not in compliance. (h) H0: p1 − p2 = −0.1, Ha: p1 −
p2 < −0.1 These hypotheses comply with our rules. H0 cannot
include equality, so these hypotheses are not in compliance. Each p
is a statistic, so these hypotheses do not comply with our rules.
The asserted value in H0 should not appear in Ha, so these
hypotheses are not in compliance.
a)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is right tailed. And null hypothesis can include equality. Further mu is not a statistics,
So option a) i.e these data comply with our rules, is correct and all other are incorrect.
b)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further sigma is not a statistics,
So option d) is correct and all other are incorrect.
C)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further p is not a statistics,
So option (b) is correct and all other are incorrect.
d)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further mu1 and mu2 is not a statistics,
So option a) i.e these data comply with our rules, is correct and all other are incorrect.
e)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further sigma is not a statistics,
So option (c) correct and all other are incorrect.
f)
Since alternative hypothesis can be of either right tailed or left tailed or a simple hypothesis. Here alternative hypothesis is a simple hypothesis And null hypothesis can include equality. Further mu is not a statistics,
So option a) i.e these data comply with our rules, is correct and all other are incorrect.
g)
Since alternative hypothesis can be of either right tailed or left tailed or two tailed. Here alternative hypothesis is two tailed. And null hypothesis can include equality. Further sigma1 and sigma 2 is not a statistics,
So option a) i.e these data comply with our rules, is correct and all other are incorrect.
h)
Since alternative hypothesis can be of either right tailed or left tailed. Here alternative hypothesis is left tailed. And null hypothesis can include equality. Further p is not a statistics, and asseter value of H0 should not appear in asserted value in Ha.
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PLEASE HELP!! HURRY!!
Answer:
B
Step-by-step explanation:
Its the second one, Answer B
3x + 2 ≥ 4x + 8 solve and graph the solution to the inequality
answer : x≤-6
steps:
3x+2≥4x+8
-x≥6
x≤-6
Answer:
x≤−6
View graph below
Step-by-step explanation:
x≤−6
Solution Steps
3x+2≥4x+8
Subtract 4x from both sides.
3x+2−4x≥8
Combine 3x and −4x to get −x.
−x+2≥8
Subtract 2 from both sides.
−x≥8−2
Subtract 2 from 8 to get 6.
−x≥6
Divide both sides by −1. Since −1 is negative, the inequality direction is changed.
x≤−6
X could be from -6 to -infinity.
The wholesale price for a desk is $144 .A certain furniture store marks up the price by 20%.Find the price of the desk in the furniture store. Round the nearest cent,as necessary
The printed price of the desk on the furniture store is $173. It can be solved by the concept of cost price and selling price.
What is cost price and selling price?
Cost price is the price of the object at which it is purchaged and selling price is the price of the object at which it is sold. If cost price is more than the selling price then the seller will earn a loss. If the cost price is less than then the selling price then the seller will earn a profit.
The cost price of the furniture = $144
Now, 20% of cost price is,
[tex]=\$ 144\times\frac{20}{100}\\=\$28.8[/tex]
Now, price of furniture on the store = Cost price + 20% of cost price
= $144 + $28.8
= $172.8$
Round off the price = $173
Hence, the printed price of the desk on the furniture store is $173.
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a hot-air balloon has a 1414-foot diameter that is being deflated at a rate of 0.250.25 feet per minute. how many minutes, xx, will it take before the balloon has shrunk to a diameter of 88 feet?
The amount of time it would take for the balloon's diameter to decrease to 8 feet is 56 minutes.
What is an example of diameter?
If you look at the cycle wheel, the spikes that run through the center from one end to the other are an illustration of diameter. This is comparable to a circle's diameter, which is a line segment that extends from one end of the circle to the other end while passing through the center.
In how long would the diameter have decreased to 8 feet?
A circle's diameter is determined by drawing a line across its center, touching both ends of its circumference.
Minutes are calculated as diameter/decline.
56 minutes from 14/0.25
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When building a house, the number of days required to build varies inversely with with the number of workers. One house was built in 55 days by 15 workers. How many days would it take to build a similar house with 33 workers?
Answer: 25 days
Step-by-step explanation:
We know that it takes 55 days with 15 workers, so we need to find how many days it takes with 1 worker by taking 55 timed 15 = 825 days for 1 worker.
Then we take 825 divided by 33 and get 25 days for 33 workers.
If you can please give me a Brainliest, I only need 3 more to become an Ace, thank you!
i don't know how to start
Using the equation of the proportional relationship, the number of miles she would drive on 50 gallons is: 1,660 miles.
What is a Direct Proportional Relationship?A direct proportional relationship can be defined by the equation, y = kx, where the constant of proportionality between the variables is given as the value of k.
First, we need to write an equation that defines the table of values given. To do this, find the constant of proportionality by using any pair of values from the table, say (6, 199.2):
Number of gallons used = x
Number of miles driven = y
Constant of proportionality, k = y/x = 199.2/2
k = 33.2
To write the equation for the proportional relationship, substitute k = 33.2 into y = kx:
y = 33.2x
To find the how many miles she would drive on 50 gallons, substitute x = 50 into y = 33.2x:
y = 33.2(50)
y = 1,660 miles.
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You go to a store that is offering a 20% discount for students! You
decide to buy a book for $15.40. You also have a coupon for $5 off after
the discounted price. What is the cost of the book after the discount and
coupon?
The cost of the book after the discount and coupon is $7.32
How to determine the cost of the book?From the question, we have the following parameters that can be used in our computation:
Amount = $15.40
Coupon = $5 offer
Discount = 20% off
This means that
Total amount = Amount * (1 - Discount) - Coupon
So, we have
Total amount = 15.40 * (1 - 20%) - 5
Evaluate
Total amount = 7.32
Hence, the total amount = 7.32
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For the given equation, find the values of a, b, and c, determine the direction in which the parabola opens, and determine the y-intercept. Decide which table best illustrates these values for the equation: f (x) = negative 9 x squared + 7 x Table A a b c up or down y-intercept -9 -7 0 down (0,0) Table B a b c up or down y-intercept 2 7 0 down (0,0) Table C a b c up or down y-intercept 9 7 0 down (0,0) Table D a b c up or down y-intercept -9 7 0 down (0,0) a. Table A c. Table C b. Table B d. Table D
Examining the function -9x² + 7x the parabolic curve is opening downwards and the y intercept is 7/9 and 0
How to find the y interceptsWhere a parabolic curve opens up or down in this case depends on the sign on the coefficient of the x².
The coefficient of x² is a and in this function is -9
A negative coefficient leads to opening downwards while a positive coefficient will result to opening upwards
The y intercept
-9x² + 7x = 0
x(-9x + 7) = 0
x = 0
-9x + 7 = 0
-9x = -7
x = 7/9
the y intercept is 0 ad 7/9
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Math Question Attached
Answer:
D
Step-by-step explanation:
A simpler way to see it, of course, is that the mentioned line segments lie on the same line, so they must have the same slope.
Solve for x in this figure.
x = 111°
Interior angles of a polygon
The formula for the sum of the interior angles of a polygon with n sides is: (n-2) x 180°.
The mentioned polygon has 7 sides, so we can put this in the formula:
The sum of the interior angles = (n – 2) x 180°
= (7 – 2) x 180°
= 5 x 180°
= 900°
We already had the value of the 6 interior angles, so we can calculate the 7th angels (x) as follow:
900° = 136° + 118° + 135° + 139° + 141° + 120° + x
= 789° + x
x = 900° – 789°
= 111°
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Answer:
As we than it is a diagram of heptagon. so the sum of its angles is 900°
according to the diagram,
x+136°+118°+135°+139°+141°+120°=900°[total sum of heptagon angles]
or, x+ 789°=900°
or, x=900°-789°
or, x=111°
Rewrite 16a4b + 8ab3 using a common factor.
2a4b(8 + 4ab3)
4ab(4a3 + 8ab3)
8ab(2a4b + 8ab3)
8ab(2a3 + b2)
The expression 16a⁴b + 8ab³ can be written as 8ab(2a³ + b²). Option (D) is correct.
What is GCF?GCF is the greatest common factor, that is the highest common number that is common in two or more numbers.
The given expression is,
16a⁴b + 8ab³
Simplify the expression, by factor method,
8 x 2 x a x a x a x a x b + 8 x a x b x b x b
The common term is 8ab,
8ab(2a³ + b²)
The required expression is 8ab(2a³ + b²).
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Solve the system by graphing and identify and state the number of solutions y=-x+1. Y=1/3x-3
By graphing the system of equations, we will see that the solution is x = 3 and y = -2
How to solve the system of equations graphically?
Here we have te following system of equations:
y = -x + 1
y = (1/3)*x - 3
To solve the system we can graph bot equation in the same coordinate axis and try to identify the intersection points between the graphs.
Below you can see the graph
We can see that the interception point is (3, - 2), then the solution to the system of equations is x = 3 and y = -2.
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Which of the following is NOT true of the sample variance when the samples are independent and normally distributed?
it decreases as the number of sample values increases it is an unbiased point estimate of the population variance
it has a normal sampling distribution it remains constant as the number of sample values increases
it has a skewed sampling distribution
Option C, which states that the sample variance is constant as the number of sample values rises when the samples are independent and regularly distributed
Each sampling distribution's variability declines as the sample size go up, becoming more and more leptokurtic. The sample distribution's range is less than the original population's range.
The margin of error & sample size has an inverse relationship, meaning that as sample size rises, sampling error falls. It is because the findings would be more accurate the more evidence you had.
The distribution's dispersion is gauged by the standard error. The dispersion decreases as the sample size increases and the distribution's mean moves closer to the population mean.
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Solve for x.
y=69
5x+15=y+2x-5
The solution of x in the equation is 79/3
How to determine the solution of x?From the question, we have the following parameters that can be used in our computation:
y = 69
5x + 15 = y + 2x - 5
Substitute y = 69 in the equation 5x + 15 = y + 2x - 5
So, we have
5x + 15 = 69 + 2x - 5
Collect the like terms
This gives
5x - 2x =69 - 5 + 15
Evaluate the like terms
This gives
3x = 79
Divide both sides by 3
x = 79/3
Hence, the solution is 79/3
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A barn is 100 feet long and 40 feet wide (see figure). A cross section of the roof is the inverted catenary given below. Find the number of square feet of roofing on the barn. (Round your answer to the nearest whole number.)
The number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.
What is integration?
It is defined as the mathematical approach to calculating the smaller parts or components.
It is given that:
A barn is 100 feet long and 40 feet wide.
Find the first derivative of the given function:
After solving the above integration:
= 20(e - 1/e)
The roofing = 100(20(e - 1/e))
= 4701 square feet
Thus, the number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.
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Terry has a goal of making $300 in commission for the week if her commission is based on 18% of sales how much does she need to sell to make her goal
The amount of sales Terry must make is $1667
How to determine the amount in sales?
From the question, we have the following parameters that can be used in our computation:
Commission = 18% of sales
Commission = $300
These parameters mean that
Commission = 18% of sales
Substitute the known values in the above equation, so, we have the following representation
18% of sales = 300
Divide both sides by 18%
Sales = 1667
Hence, the amount is $1667
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which of the following statements about regression analysis is false? multiple choice it uses information on the explanatory variables to predict the value of the response variable. it can establish cause-and-effect relationships. it is related to correlation analysis. it can have multiple explanatory variables.
It is untrue that it can build cause-and-effect relationships.
When the following criteria are met, a cause-and-effect relationship is asserted: the two occurrences take place at the same time and location; one event occurs right before the other; and it seems doubtful that the second event would have happened without the first event first occurring.
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Sean runs 2600 meters in 10 minutes.How many meters can Sean run in one minute?
Answer:
Sean can rub in one minute:
260 meters
Step-by-step explanation:
2600 meters ⇒ 10 minutes
A meters ⇒ 1 minute
A = 2600 meters * 1 minute / 10 minute
A = 260 meters
Answer: The correct answer is Sean can run 260 meters in 1 minute
Step-by-step explanation:
What we know:
Sean runs 2600 meters in 10 minutesWhat we need to find out:
How many meters can Sean run in one minute?Divide the total meters by the total minutes to find out the meters per minute
2600 meters / 10 minutes = 260 meters per minute
Distance in 1 minute
Time * meters per minute = distance
1 * 260 = 260 meters in 1 minute
The coupon rate of a bond determines the percentage of interest earned on the bond each year. Samantha purchased a five-year municipal bond for $600. After the bond matured five years later, she had received a total of $720 in principal plus interest payments. What is the coupon rate of Samantha's bond?
4%
5%
10%
12%
20%
The required coupon rate of Samantha's bond is 4%.
Explain coupon rate of bond.The coupon rate is the annual income an investor can expect to receive while holding a particular bond. It is fixed when the bond is issued and is calculated by dividing the sum of the annual coupon payments by the par value. At the time it is purchased, a bond's yield to maturity and its coupon rate are the same.c
According to question:We have,
principal amount = $600
Amount after five year = $720
Interest of five year = $(720 - 600) = $120
Then,
Interest of one year = $120/5 = $24
Now,
Coupon rate = ($24/600)×100 = 4%
Thus, required coupon rate is 4%.
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In a study of helicopter usage and patient survival, among the 56,074 patients transported by helicopter, 235 of themleft the treatment center against medical advice, and the other 55,839 did not leave against medical advice. If 40 of
the subjects transported by helicopter are randomly selected without replacement, what is the probability that none
of them left the treatment center against medical advice?
The probability is
(Round to three decimal places as needed.)
The probability, which is calculated using the hypergeometric distribution, is 0.845, or 84.5%.
Given,
The answer to this question involves using the hypergeometric distribution because the patients are randomly selected from the sample without replenishment.
Hypergeometric distribution:
The probability of x successes is given by:
P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]
The parameters are:
x is the number of successes.
N is the size of the population = 56074
n is the size of the sample = 40
k is the total number of desired outcomes = 235
The number of unique combinations of x objects from a set of n elements is provided by the following formula:
Cₙ,ₓ = n! / x! (n - x)!
The probability that none left against medical advice is P(X = 0), so:
P(X = x) = h(x, N, n, k) = [tex]\frac{C_{k,x}*C_{N-k,n-x} }{C_{N, n} }[/tex]
P(X = 0) = h(0, 56074, 40, 235) = (C₂₃₅, ₀ × C₅₆₀₇₄₋₄₀, ₄₀₋₀) / C₅₆₀₇₄, ₄₀
= (C₂₃₅, ₀ × C₅₅₈₃₉, ₄₀) / C₅₆₀₇₄, ₄₀
= 0.845
The probability is 0.845 = 84.5%.
Therefore,
The probability that none of them left the treatment center against medical advice is 0.845 = 84.5%
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