Answer: Percent of interest paid on this loan annually = 351% p.a
Step-by-step explanation:
Given that,
principal amount = $100(loan)
time period = 14 days
interest amount (SI) = $13.50
we have to calculate the rate of interest (i),
Simple interest(SI) = principal amount × rate of interest (i) × time period
13.50 = 100 × i × [tex]\frac{14}{365}[/tex]
i = [tex]\frac{4927.5}{1400}[/tex]
i = 3.51
i = 351% p.a.
Final answer:
The student paid a 13.5% interest on the $100 loan from the local cash center.
Explanation:
Percent of interest paid:
Initial loan amount: $100
Amount to be repaid: $113.50
Interest paid: $113.50 - $100 = $13.50
Percent interest paid = (Interest paid / Initial loan amount) * 100%
Percent interest paid = ($13.50 / $100) * 100% = 13.5%
You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $15 for the ace of clubs. Find the standard deviation of the amount you might win drawing a card.
Answer:
a) The probability is the number of favorable outcomes divided by the number of possible outcomes. There are 52 cards in a deck.
Step-by-step explanation
hope this helps.
25 points T a classroom there are 15 men and 3 women. If teams of 4 members are formed and X is the random variable of the number of men in the team. a. Provide the probability function for X. X f(x) b. What is the expected number of men in a team?
Suppose that neighborhood soccer players are selling raffle tickets for $500 worth of groceries at a local store, and you bought a $1 ticket for yourself and one for your mother. The children eventually sold 1000 tickets. What is the probability that you will win first place while your mother wins second place?
Answer:
The probability is 0.001001.
Step-by-step explanation:
Players are selling raffle tickets for $500 worth of groceries at a local store.
You bought a $1 ticket for yourself and one for your mother.
The children eventually sold 1000 tickets.
We have to find the probability that you will win first place while your mother wins second place.
We can find this as :
P(winning) =[tex]1/999=0.001001[/tex]
The following situation can be modeled by a linear function. Write an equation for the linear function and use it to answer the given question. Be sure you clearly identify the independent and dependent variables. Is a linear model reasonable for the situation described? You can rent time on computers at the local copy center for an $8 setup charge and an additional $5.50 for every 10 minutes. How much time can be rented for $25?
Select the correct choice below and fill in the answer box to complete your choice. A. The independent variable is rental cost (r), in dollars, and the dependent variable is time (t), in minutes. The linear function that models this situation is t equals to . (Simplify your answer. Do not include the $ symbol in your answer.)
B. The independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. The linear function that models this situation is r equals .
(Simplify your answer. Do not include the $ symbol in your answer.)
How many minutes can be rented for $25. (Round to the nearest minute as needed.)
A linear model reasonable for this situation
The situation can be modelled by the linear function r = $5.50t/10 + $8, where 't' is time and 'r' is cost. For a $25 rental, approximately 31 minutes can be rented. A linear model is appropriate as the cost increases steadily with time.
Explanation:In this case, the independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. Here, 't' is the time on the computer, and 'r' is the total cost.
The linear function for this situation would be r = $5.50t/10 + $8. Note that $5.50t/10 is the cost per minute (as the rate is $5.50 every 10 minutes), and $8 is the setup fee.
To calculate how much time can be rented for $25, we solve for 't' when r = $25. $25 = $5.50t/10 + $8 gives t = (25 - 8) x 10/5.5, or roughly t = 31 minutes.
A linear model is reasonable for this situation as the cost of renting the computer increases steadily with time.
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The correct option is B. The independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. The linear function that models this situation is r equals . The cost equation is r = 8 + 0.55t, with t as the independent variable and r as the dependent variable. For $25, approximately 31 minutes can be rented.
The given situation can be modeled by a linear function where the total rental cost depends on the time rented. Here, the independent variable is time (t) in minutes, and the dependent variable is rental cost (r) in dollars.
Option B: The linear function that models this situation is:
→ r = 8 + 0.55t
To find the time that can be rented for $25:
→ Set r = 25 and solve for t:
→ 25 = 8 + 0.55t
Subtract 8 from both sides:
→ 17 = 0.55t
Divide both sides by 0.55:
→ t = 30.91 (approximately)
Rounding to the nearest minute, the time that can be rented is 31 minutes.
Which of the following is a true statement about the self-interest assumption?
a.
Self-interest players always maximize money.
b.
Self-interest players will never perform an act of charity.
c.
Self-interest players may sacrifice to punish others.
d.
Self-interest implies that players are selfish.
Answer:
d
Step-by-step explanation:
Self-interest assumption means that an action taken by a person can be termed as self interest if he or she has any basis or reason behind taking such action. The individual always looks for profit and self benefit.Hence they can be treated as selfish.
So, if a person sacrifices his or her own interest so that others can be punished then such act can be termed as self-interest as person concerned is taking such action with a reason behind such act.
Hence, the correct answer is the option (d).
The measurement of the circumference of a circle is found to be 68 centimeters, with a possible error of 0.9 centimeter. (a) Approximate the percent error in computing the area of the circle. (Round your answer to two decimal places
Answer: 2.65%
Step-by-step explanation:
Given : The measurement of the circumference of a circle = 68 centimeters
Possible error : [tex]dC=0.9[/tex] centimeter.
The formula to find the circumference :-
[tex]C=2\pi r\\\\\Rightarrow\ r=\dfrac{C}{2\pi}\\\\\Rightarrow\ r=\dfrac{68}{2\pi}=\dfrac{34}{\pi}[/tex]
Differentiate the formula of circumference w.r.t. r , we get
[tex]dC=2\pi dr\\\\\Rightarrow\ dr=\dfrac{dC}{2\pi}=\dfrac{0.9}{2\pi}=\dfrac{0.45}{\pi}[/tex]
The area of a circle :-
[tex]A=\pi r^2=\pi(\frac{34}{\pi})^2=\dfrac{1156}{\pi}[/tex]
Differentiate both sides w.r.t r, we get
[tex]dA=\pi(2r)dr\\\\=\pi(2\times\frac{34}{\pi})(\frac{0.45}{\pi})\\\\=\dfrac{30.6}{\pi}[/tex]
The percent error in computing the area of the circle is given by :-
[tex]\dfrac{dA}{A}\times100\\\\\dfrac{\dfrac{30.6}{\pi}}{\dfrac{1156}{\pi}}\times100\\\\=2.64705882353\%\approx 2.65\%[/tex]
To approximate the percent error in computing the area of the circle, calculate the actual area using the given circumference and radius formula. Then find the difference between the actual and estimated areas, and divide by the actual area to get the percent error.
Explanation:To approximate the percent error in computing the area of the circle, we need to first find the actual area of the circle and then calculate the difference between the actual area and the estimated area. The approximate percent error can be found by dividing this difference by the actual area and multiplying by 100.
The actual area of a circle can be calculated using the formula A = πr^2, where r is the radius. Since the circumference is given as 68 cm, we can find the radius using the formula C = 2πr. Rearranging the formula, we have r = C / (2π). Plugging in the given circumference, we get r = 68 / (2π) = 10.82 cm.
Now we can calculate the actual area: A = π(10.82)^2 = 368.39 cm^2.
The estimated area is given as 4.5 m^2, which is equal to 45000 cm^2 (since 1 m = 100 cm). The difference between the actual and estimated areas is 45000 - 368.39 = 44631.61 cm^2. The percent error can be found by dividing this difference by the actual area (368.39 cm^2) and multiplying by 100:
Percent error = (44631.61 / 368.39) * 100 ≈ 12106.64%.
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34. A MasterCard statement shows a balance of $510 at 13.9% compounded monthly. What monthly payment will pay off this debt in 1 year 4 months? (Round your answer to the nearest cent.)
Answer:
The monthly payment is $35.10.
Step-by-step explanation:
p = 510
r = [tex]13.9/12/100=0.011583[/tex]
n = [tex]12+4=16[/tex]
The EMI formula is :
[tex]\frac{p\times r\times(1+r)^{n} }{(1+r)^{n}-1 }[/tex]
Now putting the values in formula we get;
[tex]\frac{510\times0.011583\times(1+0.011583)^{16} }{(1+0.011583)^{16}-1 }[/tex]
=> [tex]\frac{510\times0.011583\times(1.011583)^{16} }{(1.011583)^{16}-1 }[/tex]
= $35.10
Therefore, the monthly payment is $35.10.
When the positive integer "n" is divided by 3, the remainder is 2 and when "n" is divided by 5, the remainder is 1. What is the least possible value of "n" I really need this done out step by step and explained in detail. im not grasping it...
Answer:
The number would be 11.
Step-by-step explanation:
Dividend = Divisor × Quotient + Remainder
Given,
"n" is divided by 3, the remainder is 2,
So, the number = 3n + 2,
"n" is divided by 5, the remainder is 1,
So, the number = 5n + 1
Thus, we can write,
3n + 2 = 5n + 1
-2n = -1
n = 0.5,
Therefore, number must be the multiple of 0.5 but is not divided by 3 or 5,
Possible numbers = { 1, 2, 4, 7, 8, 11...... }
Since, 1 and 4 do not give the remainder 2 after divided by 3,
And, 2, 7 and 8 do not give the remainder 1 after divided by 5,
Hence, the least positive integer number that gives remainder 2 and 1 after divided by 3 and 5 respectively is 11.
Wolfe Camera Shop pays $78.50 for a Panasonic® 16.1 MP digital camera. The camera sells for $179.99. What is the percent of markup to the nearest tenth percent?
Answer:
129.3% of cost
Step-by-step explanation:
cost + markup = selling price
$78.50 + markup = $179.99 . . . . fill in given information
markup = $101.49
The markup as a percentage of cost is ...
markup/cost × 100% = $101.49/%78.50 × 100% ≈ 129.3%
__
As a percentage of selling price, the markup is ...
markup/selling price × 100% = $101.49/$179.99 × 100% ≈ 56.4%
The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. Admissions Probability 1,040 0.3 1,320 0.2 1,660 0.5 1. What is the expected number of admissions for the fall semester
Answer: 1406
Step-by-step explanation:
Given Table :
Admissions Probability
1,040 0.3
1,320 0.2
1,660 0.5
Now, the expected number of admissions for the fall semester is given by :-
[tex]E(x)=p_1x_1+p_2x_2+p_3x_3\\\\\Rightarrow\ E(x)=0.3\times1040+0.2\times1320+0.5\times1660\\\\\Rightarrow\ E(x)=1406[/tex]
Hence, the expected number of admissions for the fall semester = 1406
Give an approximation of underroot(3) correct to hundredths. (Round to two decimal places as needed.)
Answer: 1.75
Step-by-step explanation:
To find the value of [tex]\sqrt{3}[/tex]
[tex]\text{Let , }y=\sqrt{x}[/tex]
[tex]\text{And Let x = 4 and }\Delta x=-1[/tex]
Now,
[tex]\Delta y=\sqrt{x+\Delta x}-\sqrt{x}\\\\=\sqrt{3}-\sqrt{4}=\sqrt{3}-2\\\\\Rightarrow\ \sqrt{3}=\Delta y+2[/tex]
Since dy is approximately equals to [tex]\Delta y[/tex] then ,
[tex]dy=\dfrac{dy}{dx}\Delta x\\\\=\dfrac{1}{2\sqrt{x}}\times(-1)=\dfrac{1}{2\sqrt{4}}\times(-1)=-0.25[/tex]
Thus , the approximate value of [tex]\sqrt{3}=-0.25+2=1.75[/tex]
The road map indicates that it is 10 miles from Vacaville to Fairfield. From the information on the road map, it follows that Vacaville and Fairfield really are 10 miles apart. what type of argument?
Answer: Inductive argument.
Step-by-step explanation:
An argument can have one or more premises but there is only one conclusion to it.The arguments are of two types : Inductive (uses pattern or signs to get a conclusion ) and deductive (Uses general facts or defines or theory to decide any conclusion)
The given argument : The road map indicates that it is 10 miles from Vacaville to Fairfield. From the information on the road map, it follows that Vacaville and Fairfield really are 10 miles apart.
The given argument is the argument that is based on signs (maps are signs) which comes under inductive arguments.
Thus, the given argument is an inductive argument.
The argument which concludes that Vacaville and Fairfield are 10 miles apart based on the information from a road map is an example of a deductive argument, specifically, a syllogism.
Explanation:The argument you're describing here falls under the category of a deductive argument. Specifically, it is an example of a syllogism, which is a form of deductive reasoning consisting of two premises and a conclusion. The premises in this case are 'The map says there are 10 miles between Vacaville and Fairfield' and 'The map is correct'. Therefore, the conclusion is 'There are 10 miles between Vacaville and Fairfield'.
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Question: 57 mod 6
A) 3
B) 0
C) 6
D) 9
Explain how.
Answer: A) 3
Step-by-step explanation:
We know that [tex]p\ mod\ q[/tex] gives the remainder when p is divided by q.For example : 1) When we divide 21 by 4 , then the remainder is 1.
Therefore we say that [tex]21\ mod\ 4 =1[/tex]
2) When we divide 10 by 7 , we get 3 as remainder.
Then , we say [tex]10\ mod\ 7=3[/tex]
The given problem : [tex]57\ mod\ 6[/tex]
When we divide 57 by 6 , we get 3 as remainder [as [tex]57=54+3=6(9)+3[/tex]]
Therfeore , [tex]57\ mod\ 6=3[/tex]
Hence, A is the correct option.
The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean? 14.7 and 16.9 10.0 and 20.0 16.1 and 18.1 13.2 and 17.6
Answer:
14.7 and 16.9
Step-by-step explanation:
We want to find the confidence interval for the mean when the population standard deviation [tex]\sigma[/tex], is known so we use the [tex]z[/tex] confidence interval for the mean.
The following assumptions are also met;
The sample is a random sample [tex]n\ge 30[/tex]The z confidence interval for the mean is given by:
[tex]\bar X-z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )\:<\:\mu\:<\bar X+z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )[/tex]
The appropriate z-value for 95% confidence interval is 1.96 (read from the standard normal z-distribution table)....See attachment.
From the question, we have [tex]n=49[/tex], [tex]\sigma=3.8[/tex] and [tex]\bar X=15.8[/tex]
We substitute all these values to get:
[tex]15.8-1.96(\frac{3.8}{\sqrt{49} } )\:<\:\mu\:<\bar 15.8+1.96(\frac{3.8}{\sqrt{49} } )[/tex]
[tex]15.8-1.96(\frac{3.8}{7 } )\:<\:\mu\:<15.8+1.96(\frac{3.8}{7} )[/tex]
[tex]14.7\:<\:\mu\:< 16.9[/tex] correct to one decimal place.
To calculate the 95% confidence interval for the population mean of truck weights on I-475, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / Square Root of Sample Size). Plugging in the given values, we find that the 95% confidence interval is approximately 14.7 to 16.9 tons.
Explanation:To calculate the 95% confidence interval for the population mean, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / Square Root of Sample Size). In this case, the sample mean is 15.8 tons, the population standard deviation is 3.8 tons, and the sample size is 49. The critical value for a 95% confidence level is approximately 1.96. Plugging in these values, we get:
Confidence Interval = 15.8 ± (1.96) * (3.8 / √49)
Confidence Interval ≈ 15.8 ± (1.96) * (3.8 / 7)
Confidence Interval ≈ 15.8 ± (1.96) * 0.543
Confidence Interval ≈ 15.8 ± 1.06
Therefore, the 95% confidence interval for the population mean is approximately 14.7 to 16.9 tons.
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Are Sin(x) and e^x linearly independent? Justify.
Answer:
yes they are linearly independent
Step-by-step explanation:
By definition of linear dependence we have if f(x) and g(x) be 2 functions
if they are linearly dependent then we can write
f(x) = αg(x)...........(i) where α is an arbitrary constant
in our case we can see that the range of sin(x) is only from [-1,+1] while as [tex]e^{x}[/tex] has range from [0,∞]
thus we cannot find any value of α for which (i) is valid
Find a parametric representation for the surface. The part of the hyperboloid 4x2 − 4y2 − z2 = 4 that lies in front of the yz-plane. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of u and/or v.)
"in front of the [tex]y,z[/tex] plane" probably means [tex]x\ge0[/tex], in which case
[tex]4x^2-4y^2-z^2=4\implies x=\sqrt{1+y^2+\dfrac{z^2}4}[/tex]
We can then parameterize the surface by setting [tex]y(u,v)=u[/tex] and [tex]z(u,v)=v[/tex], so that [tex]x=\sqrt{1+u^2+\dfrac{v^2}4}[/tex].
The part of the hyperboloid in front of the yz-plane is represented parametrically by x(u,v)=2*cos(u), y(u,v)=-2*sinh(v), and z(u,v)=sinh(u).
Explanation:The surface of the hyperboloid lies in front of the yz-plane and is described by the equation 4x² − 4y² − z² = 4. A common form of parameterization for this type of surface uses hyperbolic functions. Therefore, a parametrization for the part of the hyperboloid lying in front of the yz-plane can be given in terms of u and v as follows:
x(u,v) = 2*cos(u) y(u,v) = -2*sinh(v) z(u,v) = sinh(u)
In this parametric form, u can range over all real numbers to cover the entire surface in front of the yz-plane, while v can oscillate between -∞ to +∞ to provide a full representation of the surface.
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An attendant at a car wash is paid according to the number of cars that pass through. Suppose the probabilities are 1/12, 1/12, 1/4, 1/4, 1/6, and 1/6, respectively, that the attendant receives $7, $9, $11, $13, $15, or $17 between 4:00 P.M. and 5:00 P.M. on any sunny Friday. Find the attendant’s expected earnings for this particular period.
Answer:
The expected earnings of the attendant for this particular period are: $12.66
Step-by-step explanation:
We have to calculate expected mean here:
So,
E(x) = ∑x*f(x)
[tex]E(X) = \{(7 * \frac{1}{12} )+(9 * \frac{1}{12} )+(11 * \frac{1}{4} )+(13 * \frac{1}{4} )+(15 * \frac{1}{6} )+(17 * \frac{1}{6})\\= 0.58+0.75+2.75+3.25+2.5+2.83\\=12.66\ dollars[/tex]
Therefore, the expected earnings of the attendant for this particular period are: $12.66 ..
Considering the discrete distribution, it is found that the attendant’s expected earnings for this particular period are of $12.67.
What is the expected value of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Hence, considering the probability of each earning amount, the expected earnings are of the attendant is given by:
[tex]E(X) = 7\frac{1]{12} + 9\frac{1}{12} + 11\frac{1}{4} + 13\frac{1}{4} + 15\frac{1}{6} + 17\frac{1}{6} = \frac{7 + 9 + 33 + 39 + 30 + 34}{12} = 12.67[/tex]
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Find the slope and the y -intercept of the line.
Write your answers in simplest form.
-7x - 2y = -4
Answer:
So the y-intercept is 2 while the slope is -7/2.
Step-by-step explanation:
We are going to write this in slope-intercept form because it tells us the slope,m, and the y-intercept,b.
Slope-intercept form is y=mx+b.
So our goal is to solve for y.
-7x-2y=-4
Add 7x on both sides:
-2y=7x-4
Divide both sides by -2:
[tex]y=\frac{7x-4}{-2}[/tex]
Separate the fraction:
[tex]y=\frac{7x}{-2}+\frac{-4}{-2}[/tex]
Simplify:
[tex]y=\frac{-7}{2}x+2[/tex]
If we compare this to y=mx+b, we see m is -7/2 and b is 2.
So the y-intercept is 2 while the slope is -7/2.
Answer:
the slope m is:
[tex]m = -\frac{7}{2}[/tex]
The y-intersection is:
[tex]b = 2[/tex]
Step-by-step explanation:
For the equation of a line written in the form
[tex]y = mx + b[/tex]
m is the slope and b is the intersection with y-axis.
In this case we have the equation
[tex]-7x - 2y = -4[/tex]
So we rewrite the equation and we have to:
[tex]2y = -7x + 4[/tex]
[tex]y = -\frac{7}{2}x + 2[/tex]
the slope m is:
[tex]m = -\frac{7}{2}[/tex]
the y-intersection is:
[tex]b = 2[/tex]
Consider a rectangle of length L inches and width W inches. Find a formula for the perimeter of the rectangle. Use upper case letters. P = L+L+W+W (b) If the length and width of the rectangle are changing with respect to time, find dP dt . Use dL dt and dW dt and not L ' and W ' . dP dt = 2( dL dt)+2( dW dt) (c) Suppose the length is increasing at 2 inches per hour and the width is decreasing at 3 inches per hour. How fast is the perimeter of the rectangle changing when the length is 40 inches and the width is 104 inches?
Answer:
a) P=2(L+W)
b)[tex]\frac{dp}{dt}=2\frac{dL}{dt}+2\frac{dW}{dt}[/tex]
c)-2 inch/hour
Step-by-step explanation:
given:
length of the rectangle as L inches
width of the rectangle as W inches
a) The perimeter is defined as the measure of the exterior boundaries
therefore, for the rectangle the perimeter 'P' will be
P= length of AB+BC+CD+DA (A,B,C and D are marked on the figure attached)
Now from figure
P= L+W+L+W
OR
=> P=2L+2W .....................(1)
b)now dp/dt can be found as by differentiating the equation (1)
[tex]\frac{dP}{dt}=2(\frac{dL}{dt} )+2(\frac{dW}{dt} )[/tex] .............(2)
c)Now it is given for the part c of the question that
L=40 inches
W=104 inches
dL/dt=2 inches/hour
dW/dt= -3 inches/hour (here the negative sign depicts the decrease in the dimension)
substituting the above values in the equation (2) we get
[tex]\frac{dP}{dt}=2(2)+2(-3)[/tex]
[tex]\frac{dP}{dt}=4-6=-2 inches/hour[/tex]
The formula for the perimeter of a rectangle is P = 2L + 2W. By differentiating this formula, we find that dP/dt = 2(dL/dt) + 2(dW/dt). When the length is increasing at 2 inches per hour and the width is decreasing at 3 inches per hour, the perimeter is changing at a rate of -2 inches per hour.
Explanation:To find the perimeter of a rectangle, we add the lengths of all four sides of the rectangle. Given that the length is L inches and the width is W inches, the formula for the perimeter is P = 2L + 2W.
To find the rate of change of the perimeter with respect to time, we differentiate the formula with respect to time, using the chain rule. Thus, dP/dt = 2(dL/dt) + 2(dW/dt).
For the specific case where the length is increasing at 2 inches per hour and the width is decreasing at 3 inches per hour, we substitute these values into the formula for the rate of change of the perimeter to find that dP/dt = 2(2) + 2(-3) = -2 inches per hour.
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A study to determine the sensitivity and specificity of a new test for celiac disease is conducted on 7642 people. Studies have shown that celiac disease occurs at a rate of 1.32%. Your sample has the same prevalence of celiac disease. You find that 99 people with celiac disease tested positive with the new test. You also have a total of 7495 negative test results in your study. CALCULATE THE SENSITIVITY of this test.
Question 1 options:
A) 68.71%
B) 99.97%
C) 98.02%
D) 99.36%
E) 67.35%
Final answer:
The sensitivity of the new test for celiac disease is 98.02% (Option C).
Explanation:
The question asks us to calculate the sensitivity of a new test for celiac disease. Sensitivity is the ability of a test to correctly identify those with the disease (true positive rate), and it is calculated as the number of true positives divided by the number of true positives plus the number of false negatives, which is essentially all the actual disease cases.
According to the provided data, the new test for celiac disease has 99 true positive results. To find out the total number of disease cases, we first need to calculate the expected number of people with celiac disease in the sample, which is 1.32% of 7642. That is approximately 100.87, or about 101 people (since we can't have a fraction of a person). Given that, we can assume there are 101 actual cases of celiac disease in the sample.
The sensitivity can be calculated as:
Sensitivity = (True Positives) / (True Positives + False Negatives)
= 99 / 101
= 0.9802 or 98.02%
Therefore, the sensitivity of the test is 98.02%, matching option C).
What is the measure of ∠X?
69°
111°
180°
21°
The height of a photograph is 40 cm greater than the width, and the area of the photograph is 896 cm2what is the height of the photograph?
Answer:
Height = 56 cm
Step-by-step explanation:
let the width of photograph be = 'w' cm
let the Height of photograph be = 'h' cm
Now it is given that height is 40 cm greater than width
=> h = w + 40 cm.............................(i)
Now it is given that area of photograph = [tex]896cm^{2}[/tex]
We know that area = [tex]Width^{}[/tex]x[tex]Height^{}[/tex]
Thus we have [tex]h^{}[/tex] x [tex]w^{}[/tex]=[tex]896cm^{2}[/tex]
Applying value of 'h' from equation i we get
[tex](w+40^{})[/tex]x[tex]w^{}[/tex]=[tex]896cm^{2}[/tex]
[tex]w^{2} +40w=896cm^{2}[/tex]
This is a quadratic equation in 'w' whose solution in standard form is given by
w=[tex]\frac{-b\mp\sqrt{b^{2}-4ac}}{2a}[/tex]
upon comparing with standard equation we see that
a =1
b=40
c=896
applying values in the formula we get
w=[tex]\frac{-40\mp\sqrt{40^{2}-4\times 1\times- 896}}{2 \times1 }[/tex]
w1 = 16 cm
w2 = -56 cm
We discard -56 cm since length cannot be negative thus
width = 16 cm
Height = 40+16 cm = 56 cm
Consider the differential equation 4y'' â 4y' + y = 0; ex/2, xex/2. Verify that the functions ex/2 and xex/2 form a fundamental set of solutions of the differential equation on the interval (ââ, â). The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) = â 0 for ââ < x < â.
Check the Wronskian determinant:
[tex]W(e^{x/2},xe^{x/2})=\begin{vmatrix}e^{x/2}&xe^{x/2}\\\frac12e^{x/2}&\left(1+\frac x2\right)e^{x/2}\end{vmatrix}=\left(1+\frac x2\right)e^x-\frac x2e^x=e^x\neq0[/tex]
The determinant is not zero, so the solutions are indeed linearly independent.
To verify a fundamental set of solutions for the given differential equation, one must demonstrate that the functions e^{x/2} and xe^{x/2} satisfy the equation and that their Wronskian is non-zero, indicating linear independence.
Explanation:The student's question pertains to verifying whether a given set of functions, e^{x/2} and xe^{x/2}, form a fundamental set of solutions for the differential equation 4y'' - 4y' + y = 0. A set of solutions is fundamental if the functions are linearly independent and satisfy the differential equation. Linear independence can be proved by calculating the Wronskian, which must be non-zero over the given interval. To show that these functions are solutions, they must be substituted into the differential equation to check if it holds true.
To check for linear independence, we can compute the Wronskian:
W(e^{x/2}, xe^{x/2}) = |which simplifies to e^{x} (1 - (x/2)) that is non-zero for all real numbers x, proving linear independence.
To verify if the functions satisfy the differential equation, we substitute each function into the equation. The derivatives of e^{x/2} and xe^{x/2} are taken, and then these are plugged into the equation to confirm that it yields zero.
A bag contains 1 gold marbles, 10 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
The expected value of the game is approximately $0.09375. This is the long-term average value one might expect to gain for each play of the game.
Explanation:The question involves determining the expected value of a game involving the random selection of marbles. Expected value, in probability, is the long-term average value of repetitions of the experiment. It can be computed using the formula:
Expected Value (E) = ∑ [x * P(x)]
where x represents the outcomes and P(x) is the probability of those outcomes. In this case, our outcomes and their corresponding probabilities are as follows:
$4 (winning) with a probability of 1/32 (since there's one gold marble out of 32) $2 (winning) with a probability of 10/32 (since there are 10 silver marbles out of 32) -$1 (losing) with a probability of 21/32 (since there are 21 black marbles out of 32)
Calculating our expected value, we get:
E = $4*(1/32) + $2*(10/32) - $1*(21/32) = $0.09375
This means you can expect to win about $0.09 each time you play the game in the long run.
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The sides of a rhombus with angle of 60° are 6 inches. Find the area of the rhombus.
9√3 in2 1
8√3 in2
36 in2
Answer:
18 sqrt(3) in^2
Step-by-step explanation:
If we know the length of a side and the angle
area = s^2 sin a
Since the side length is 6 and the angle a is 60
= 6^2 sin 60
= 36 sin 60
= 36 * sqrt(3)/2
= 18 sqrt(3)
Given the Arithmetic sequence A1,A2,A3,A4 53, 62, 71, 80 What is the value of A38?
Answer:
[tex]A_{38} = 350[/tex]
Step-by-step explanation:
The 5th term of the arithmetic sequence is 53. We can write the equation:
[tex]a + 4d = 53...(1)[/tex]
The 6th term of the arithmetic sequence is 62. We can write the equation:
[tex]a + 5d = 62...(2)[/tex]
Subtract the first equation from the second one to get:
[tex]5d - 4d = 62 - 53[/tex]
[tex]d = 9[/tex]
The first term is
[tex]a + 4(9) = 53[/tex]
[tex]a + 36 = 53[/tex]
[tex]a = 53 - 36[/tex]
[tex]a = 17[/tex]
The 38th term of the sequence is given by:
[tex] A_{38} = a + 37d[/tex]
[tex]A_{38} = 17+ 37(9)[/tex]
[tex]A_{38} = 350[/tex]
Answer:
[tex]A_{38}=386[/tex]
Step-by-step explanation:
We have been given an arithmetic sequence gas [tex]A_1,A_2,A_3,A_4[/tex] as :53,62,71,80. We are asked to find [tex]A _{38}[/tex].
We know that an arithmetic sequence is in format [tex]a_n=a_1+(n-1)d[/tex], where,
[tex]a_n[/tex] = nth term,
[tex]a_1[/tex] = 1st term of sequence,
n = Number of terms,
d = Common difference.
We have been given that 1st term of our given sequence is 53.
Now, we will find d by subtracting 71 from 80 as:
[tex]d=80-71=9[/tex]
[tex]A_{38}=53+(38-1)9[/tex]
[tex]A_{38}=53+(37)9[/tex]
[tex]A_{38}=53+333[/tex]
[tex]A_{38}=386[/tex]
Therefore, [tex]A_{38}=386[/tex].
A property contained ten acres. How many lots of not less than 50 feet by 100 feet can be subdivided from the property if 26,000 square feet were dedicated for roads?
Answer:
81 lots of 5,000 square feet fits in the property.
Step-by-step explanation:
The first step is calculate the square feet of the minimum area:
[tex]50 \: feets \times 100 \: feet = 5,000 \:square \: feet[/tex]
Second, from the ten acres we subtract the 26,000 feets of roads:
[tex]1 \: acre = 60 \: feet \times 660\:feet = 43,560\:square\:feet\\43,560 \times 10 = 435,600\\435,600 - 26,000 = 409,600 \:square \: feet\:available[/tex]
Third, we divide the lot area over the available square feet
[tex]\frac{409,600}{5,000} = 81.92[/tex]
81 lots of 5,000 square feet fits in the property.
A piece of wire 6 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. (a) How much wire should be used for the square in order to maximize the total area? Correct: Your answer is correct. m (b) How much wire should be used for the square in order to minimize the total area? Incorrect: Your answer is incorrect. m
To maximize the area, a 2m length of wire should be used for the square and the rest for the triangle. To minimize the area, nearly all the wire should be used for the triangle, leaving a negligible amount for the square.
Explanation:The problem described is a classic example of Mathematics optimization. In this case, we have two geometric shapes, a square and an equilateral triangle. To answer this question effectively, one needs to understand the relationship between the perimeter and area of these two shapes.
For the square, the area is given by A=s2, where s is the length of a side. For the equilateral triangle, the area is given by A=0.433*s2, where s is the length of a side. We want to understand how to divide the 6m wire so that we either maximize or minimize the total area of these two shapes.
The total length of wire used is fixed at 6m. Let's designate x as the length of wire used for the square. This means the length for the triangle would be 6-x. For the maximum area, the result generally comes around 2m for the square and 4m for the triangle. However, for the minimum area, the answer would be essentially 0m for the square and 6m for the triangle.
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(a) For maximizing total area, use [tex]\( s \approx 3.76 \)[/tex] meters in square.
(b) For minimizing area, use [tex]\( s = 0 \)[/tex] for maximum utilization of wire to the triangle, least yielding area near zero or minimal non-zero.
(a) Maximizing the Total Area
To maximize the total area, we need to determine the length of the wire to be used for the square [tex](\( s \))[/tex] and the length used for the equilateral triangle [tex](\( t \))[/tex].
(b) Minimizing the Total Area
To minimize the total area, confirm whether interiors of boundary values might be critical points. Specifically, see if using all the wire for one shape minimizes the area.
The newly elected president needs to decide the remaining 5 spots available in the cabinet he/she is appointing. If there are 15 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed
To calculate the number of different ways the members of the cabinet can be appointed, we can use the concept of permutations. Using the formula for permutations, it is found that there are 3003 different ways the members of the cabinet can be appointed.
Explanation:To calculate the number of different ways the members of the cabinet can be appointed, we can use the concept of permutations. Since there are 15 eligible candidates for the remaining 5 spots, and the order in which the members are appointed matters, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of candidates and r is the number of spots available. In this case, we have:
P(15, 5) = 15! / (15 - 5)!
Calculating this gives us:
P(15, 5) = 15! / 10!
P(15, 5) = (15 × 14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)
P(15, 5) = 3003
Therefore, there are 3003 different ways the members of the cabinet can be appointed.
A project manager can interpret several things from data displayed in a histogram. If something unusual is happening, the histogram might be ___________. a. Flat b. Skewed c. Bell-shaped d. S-shaped
Answer:
Skewed
Step-by-step explanation:
A project manager can interpret several things in a histogram. If something unusual happening, the histogram is said to Skewed. When the histogram is Skewed it means that many of the values of the graph are falling on only one side of the mean. It can be either on left side( left skewed) or on the right side called right skewed