The growth constant is 0.69 and the population will increase to 12900 after approximately 3.7 years.
We have, Sunset Lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. Assuming logistic growth with a carrying capacity of 25000,
The logistic growth model is given by the equation
dN/dt=rN[(K-N)/K]
where, dN/dt = rate of change of population with respect to time,
N = population size at time t,
r = intrinsic rate of natural increase (growth constant),
K = carrying capacity.
The population size, "N" after 1 year = 7050
The initial population, "N₀" = 2500
The carrying capacity, K = 25000
We can use the following formula to find the value of the growth constant,
r = 2.303/t{ln(N_t/N₀) }........... (1)
Where, t = time taken for the population to increase from N_0 to N_t= 1 year (given)
Substituting the given values in equation (1), we get
r = 2.303/1 ln(7050/2500) ⇒ 0.688 ≈ 0.69
The value of the growth constant is 0.69.
Now, we can use the logistic growth equation to find the time required for the population to reach 12900.
dN/dt=rN[(K-N)/K]
Given, N₀ = 2500 and K = 25000
Differentiating both sides with respect to t,
dN/dt = rN[(K-N)/K] + Ndr/dt
Substituting the values of N, r, and K in the above equation, we get,
dN/dt= 0.69N[(25000-N)/25000] + N{dN/dt}
Let the population N become 12900 at time t = t₁
Therefore, at time t = 0, the population N₀ = 2500
Also, at time t = 1, the population N₁ = 7050
Substituting these values in the above equation, we get,
dN/dt= 0.69N[(25000-N)/25000] + N₁
dN/dt= 0.69(2500)[(25000-2500)/25000] + N₁
Solving for N₁, we get, N₁ = 7825
Substituting N₁ = 7825 in the above equation,
dN/dt= 0.69(7825)[(25000-7825)/25000] + N₁
dN/dt= 3263.25/1.69 ⇒ 1930.4
Now, to find t1, we can use the following formula;
ln[(K-N₁)/(K-N₀)] = rt₁
Substituting the given values, we get,
ln[(25000-12900)/(25000-2500)] = 0.69t₁
On solving for t₁, we get;
t₁ = ln[(1575/22500)]/0.69 ≈ 3.7 years
Hence, the population will increase to 12900 after approximately 3.7 years.
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4) Hamid purchased some educational stationary and paid GST of Rs.1800. He sold all
educational stationary Nishaben and collected GST of Rs.2100. Find the GST CGST and
SGST to be paid
Answer: Therefore, Hamid needs to pay Rs. 1050 as both CGST and SGST.
Step-by-step explanation:
Assuming the GST rate is the same for both the purchase and the sale, we can calculate the GST rate as follows:
GST rate = GST paid / Cost of stationary purchased
= 1800 / Cost of stationary purchased
Since we don't have the cost of stationary purchased, we can't calculate the GST rate or the CGST and SGST amounts directly. However, we know that the GST collected from Nishaben was Rs. 2100, which is equal to the GST paid plus the profit earned on the sale. We can express this mathematically as follows:
GST collected = GST paid + Profit
Profit = GST collected - GST paid
= 2100 - 1800
= Rs. 300
Since the profit earned is Rs. 300, we can find the cost of the stationary purchased by subtracting the profit from the amount collected from Nishaben:
Cost of stationary purchased = GST collected - Profit
= 2100 - 300
= Rs. 1800
Now that we know the cost of the stationary purchased, we can calculate the GST rate as follows:
GST rate = GST paid / Cost of stationary purchased
= 1800 / 1800
= 1
Since the GST rate is 1 (or 100%), we can divide the total GST collected equally between CGST and SGST:
CGST = SGST = GST collected / 2
= 2100 / 2
= Rs. 1050
Therefore, Hamid needs to pay Rs. 1050 as both CGST and SGST.
A video game sells for $59.99 and the sale tax is 13% what would the sale tax be on the game?
Answer: $7.7987 or round it to be $7.80
Step-by-step explanation:
hope this helps
Answer : 7.79 Or 7.80
Explanation : 59.99 × 13/100
(5x-2y)(a-b) -(2x-y)(a-b)
Answer:
3xa−3xb−ya+yb
Step-by-step explanation:
The answer to the given equation will be 3xa-ay-3xb-by
How to get to itOne can apply the simplification property of like terms since both terms are being multiplied by (a-b).
Party forms, the term will multiply the other two that accompany it.
Check it out(a-b)×(5x-2y-(2x-y))
(a-b)×(5x-2y-2x+y)
(a-b)×(3x-y)
=> 3xa-ay-3xb-by
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One of your friends wants to buy a pair of binoculars to look at the birds and animals, however, she cannot afford the R4999 at once. She pays a deposit of R999 and the rest over 3 years using simple interest.
Write down the total that she paid for the binoculars.
Hint: Consider the deposit and the accumulated amount
The interest rate she got from the bank is 0.83% and the monthly repayment she needs to make is 99.6 dollars.
What is simple interest?
Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
What kinds of simple interests are there?
When the time is measured in days, simple interest can be divided into two groups. They have common and straightforward interests. The comparable number of days in a year for ordinary simple interest is 360 days. In contrast, precise simple interest (SI) is a SI that requires exactly 365 days in a regular year or 366 days in a leap year.
The simple interest is given by the formula:
SI = PRT/ 100
where, P is the principal = $4999 - $999 = $4000.
R is the rate.
T is the time = 3.
Given that the total accumulated amount is $7000.
That is:
4000 + SI(3) = 7000....(1)
SI = (4000)(R)(3)/100
SI = 120R.......(2)
Substitute the value of SI in equation 1:
4000 + 120(3)R = 7000
36R = 3000
R = 83.33
R = 0.83%
The monthly repayments are:
SI = (4000)(0.83)(3)/100
SI = 99.6
Hence, the monthly payments are 99.6.
The interest rate she got from the bank is 0.83% and the monthly repayment she needs to make is 99.6 dollars.
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Please help me find the surface area of this shape
Answer:
1570 in²
Step-by-step explanation:
You want the total surface area of the irregularly-shaped prism shown.
DimensionsThe single hash mark on some segments indicates those are all the same length (congruent). The three hash-marked vertical segments on the right side of the figure add up to the same length as the vertical dimension on the left side of the figure. If each of those hash-marked segments is 'x', then we have ...
3x = 15
x = 5 . . . . . divide by 3
The dimensions of the base edges of the figure can now be seen to match those shown in the attachment.
Base areaThe shaded front face (base) of the prism has overall dimensions of 15 inches high by 5 +11 = 16 inches wide. That's an area of ...
A = BH = (16 in)(15 in) = 240 in²
From that area we can subtract rectangles from the upper right and lower right to find the shaded area. Those rectangles have a total area of ...
upper right + lower right = (4 in)(5 in) +(11 in)(5 in) = (20 +55) in² = 75 in²
Then the shaded base (front face) area is ...
A = (240 in²) -(75 in²) = 165 in²
The back face is identical in shape and area, so the total base area of the prism is ...
Base area = 2 × 165 in² = 330 in²
Lateral areaThe total area of the rectangular faces is the product of the perimeter of the base and the distance between the two bases.
The perimeter is (working clockwise from lower left) ...
15 in +12 in +5 in +4 in +5 in +11 in +5 in +5 in
= 62 in
Then the lateral area is ...
LA = Ph = (62 in)(20 in) = 1240 in²
Surface areaThe surface area is the sum of the base area and the lateral area:
SA = B +LA = 330 in² +1240 in² = 1570 in²
The surface area of the shape is 1570 square inches.
__
Additional comment
In effect, the perimeter is the sum of the lengths of horizontal edges and vertical edges. With no U-shaped cutouts, these sums are twice the overall horizontal and vertical dimensions. Here, that is ...
2(16 in +15 in) = 2(31 in) = 62 in
This is an easier computation than adding the individual side lengths.
A 3rd grade math test included this rather tough challenge. Can you solve it? If 5*3=4 2*8=2 and 6*3=3 find the value of 1*7=?
Without a clear pattern or rule from the given examples, it is difficult to determine the value of 1*7 in this problem.
This problem appears to involve some sort of pattern or rule that relates the multiplication of two numbers to a resulting value. Let's examine the given examples to try to identify the pattern:
5*3=4: The product of 5 and 3 is 15, but the answer is 4. This means that some sort of operation was performed on 15 to produce 4. One possibility is that the digits of 15 were added together: 1 + 5 = 6, and then the result was subtracted from 10: 10 - 6 = 4. So, this pattern involves adding the digits of the product and subtracting the result from 10.
2*8=2: The product of 2 and 8 is 16, but the answer is 2. Again, we need to perform an operation on 16 to get 2. One possibility is to divide 16 by the sum of the digits: 1 + 6 = 7, so 16 / 7 = 2.28 (rounded to 2 decimal places). However, this pattern doesn't quite fit the given examples perfectly, so there may be other rules or variations involved.
6*3=3: The product of 6 and 3 is 18, but the answer is 3. Applying the same approach as before, we could try dividing 18 by the product of the digits: 6 * 3 = 18, so 18 / 18 = 1. However, this pattern doesn't match the previous examples either.
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Solve for side length x. Round to the nearest tenth.
Answer:
x=3.1
Explanation:
x is an opposite sine of 15°
sin = opposite side ÷ hypotenuse
sin(15°)=0.259
hypotenuse =12
0.259 × 12 = 3.1
Need help really bad. I need 2 answers
There are 55 vehicles in a parking lot. The frequency table shows data about the types and colors of the vehicles. Complete a relative frequency table to show the distribution of the data with respect to color. Use pencil and paper. Explain why the first two numbers in each row must add up to 100%
In order to complete a relative frequency table to show the distribution of data with respect to color in a parking lot with 55 vehicles, you must first understand the concept of frequency. Frequency is the number of times a particular element appears in a given set of data. In this case, the elements are the colors of the vehicles in the parking lot.
To begin, you must count the number of vehicles of each color in the parking lot and record the number in the appropriate column. Then you must calculate the relative frequency for each color. Relative frequency is calculated by dividing the frequency of a color by the total number of vehicles. To find the total number of vehicles in the parking lot, simply add up the number of vehicles of each color. Once you have the relative frequency for each color, you can complete the relative frequency table.The first two numbers in each row of the relative frequency table must add up to 100%. This is because they represent the percentages of the total number of vehicles in the parking lot. If the percentages do not add up to 100%, then the table would not accurately reflect the distribution of data with respect to color. In conclusion, to complete a relative frequency table to show the distribution of data with respect to color in a parking lot with 55 vehicles, you must understand the concept of frequency, count the number of vehicles of each color, calculate the relative frequency for each color, and ensure that the first two numbers in each row add up to 100%.
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Infinite solution
The answer is 0. Therefore, there is Infinite solutions
Work out the size of angle x in the diagram
below.
Give your answer in degrees (°).
35°
44°
X
Not drawn accurately
Therefore , the solution of the given problem of triangle comes out to be angle x has a magnitude of 101°.
What is a triangle?A triangle is a polygon since it possesses two or so additional components beyond that. It is plainly rectangular in form. A and B are the only two of either a triangle's three edges that can distinguish it from a typical triangle. When bounds are still not precisely collinear, Euclidean geometry yields a single region rather than a cube. Three edges and three angles are what make a triangle.
Here,
Because a triangle's angles sum up to 180 degrees, we can determine the size of angle x by deducting the other two angles from 180 degrees:
=> x = 180° - 35° - 44°
=> x = 101°
As a result, angle x has a magnitude of 101°.
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Answer:
See explanation below
Step-by-step explanation:
1/(sec - tan) - 1/cos = 1/cos - 1(sec + tan)
=> 1/(sec - tan) + 1(sec + tan) = 1/cos + 1/cos
Left side
(sec + tan)/[(sec - tan)(sec + tan)] + (sec - tan)/[(sec - tan)(sec + tan)]
= [sec + tan + sec - tan]/[(sec - tan)(sec + tan)]
= [2sec]/[(sec - tan)(sec + tan)]
since (a+b)(a-b) = a^2 - b^2
=> 2sec/(sec^2 - tan^2)
let's work on the denominator (sec^2 - tan^2)
we know sec = 1/cos and tan = sin/cos
=> (1/cos)^2 - (sin/cos)^2
=> 1/cos^2 - sin^2/cos^2
=> (1 - sin^2)/cos^2 = cos^2/cos^2 = 1
so 2sec/(sec^2 - tan^2) => 2sec/1
=> 2sec
since sec = 1/cos => 2sec = 2(1/cos) = 2/cos
Right side
1/cos + 1/cos = 2/cos
In △ABC, A=27∘, a=37 and c=28. Which of these statements best describes the triangle?
If in △ABC, A=27degree, a=37 and c=28, then the statements best describes the triangle is (B) △ABC is obtuse.
We can use the Law of Cosines to determine the length of side b:
b^2 = a^2 + c^2 - 2ac cos(A)
b^2 = 37^2 + 28^2 - 2(37)(28) cos(27°)
b ≈ 27.88
Now we can use the Law of Sines to determine the measure of angle B:
sin(B)/b = sin(A)/a
sin(B) = (b/a)sin(A)
sin(B) = (27.88/37)sin(27°)
B ≈ 46.18°
Finally, we can find the measure of angle C using the fact that the angles in a triangle sum to 180°:
C = 180° - A - B
C ≈ 106.82°
Since angle C is greater than 90°, we know that △ABC is obtuse triangle. Therefore, the best statement that describes the triangle is (B) △ABC is obtuse.
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The given question is incomplete, the complete question is:
In △ABC, A = 27 degree, a = 37 and c = 28. Which of these statements best describes the triangle? A) △ ABC is acute. B) △ABC is obtuse. C) △ABC can be either acute or obtuse. D) △ABC is a right triangle. E) △ABC cannot be constructed.
Determine the two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution. -1.39, 1.39 -1.46,1.46 -1.53, 1.53 -1.45, 1.45
The two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution are -1.46 and 1.46.
To find these z-scores, we need to first determine the area in the tails of the distribution. Since the middle 87.4% of the distribution is separated from the tails, the area in the tails is 100% - 87.4% = 12.6%. This means that there is 12.6% / 2 = 6.3% in each tail.
Next, we can use a standard normal table or a calculator to find the z-scores that correspond to the 6.3% in the tails. We want to find the z-scores that have an area of 0.063 to the left and to the right of them.
According to a standard normal table, the z-score that has an area of 0.063 to the left of it is -1.46, and the z-score that has an area of 0.063 to the right of it is 1.46.
Therefore, the two z-scores that separate the middle 87.4% of the distribution from the area in the tails of the standard normal distribution are -1.46 and 1.46.
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ANSWER ASAP
Use the data sets above to complete the sentence and answer the questions below.
The number of football games with a score less than or equal to 29 is equal to half the number of basketball games with a score greater than or equal to ____.
For both sports, if the only games won were those with scores of 30 or higher, how many more basketball games were won compared to football games won? _____
What is the difference between the total maximum possible points scored by the basketball team last year and the total maximum possible points scored by the football team last year? ____ points
Answer:
1. Tbh, I actually don't know lolol
2. Basketball games were 1. They won 1 more then Football.
3. The answer would be 20.
Step-by-step explanation:
3. The answer is 20 cause the highest of Football games were 49, whereas Basketball was 69. There fore, your difference is 20.
Keep in mind, Im trying my hardest, and I apologize if I get it wrong.
Please complete the following questions either by hand or typing answers into provided response locations. When asked to use R to calculate values, or to construct a plot, copy and paste both the values or plot and the R command you used to obtain the values or plot. Show work where appropriate. 1. A post-mix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. In order to estimate the population, mean amount of syrup dispensed, a random sample of 50 beverages was found that have mean syrup content of 1.098 fluid ounces. Assume syrup content (fluid ounces) is normally distributed with a standard deviation of 0.016 fluid ounces. A. Is the data collected in this situation qualitative or quantitative? B. What is the parameter of interest in this situation? C. How do you know that the sample mean is normally distributed? D. Calculate the appropriate critical value (z α/2 ) for a 98% confidence interval for population mean for this situation. E. Using the appropriate formula, find a 98% (two-sided) confidence interval for the population mean amount of syrup dispensed. F. Provide an interpretation for the interval found.
The interpretation for this interval is that we can be 98% confident that the population mean amount of syrup dispensed is between 1.092 and 1.104 fluid ounces.
A. The data collected in this situation is quantitative.
B. The parameter of interest in this situation is the population mean amount of syrup dispensed.
C. We know that the sample mean is normally distributed because the population of syrup content (fluid ounces) is assumed to be normally distributed with a standard deviation of 0.016 fluid ounces.
D. The appropriate critical value (z α/2 ) for a 98% confidence interval for population mean in this situation is 2.05.
E. Using the appropriate formula, the 98% (two-sided) confidence interval for the population mean amount of syrup dispensed is (1.092, 1.104).
F. The interpretation for this interval is that we can be 98% confident that the population mean amount of syrup dispensed is between 1.092 and 1.104 fluid ounces.
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Isabelle takes out a loan that gathers
compound interest.
The table shows the value of the loan
over time.
What is the rate of interest per annum?
Give your answer as a percentage to 1
d.p.
Start
After 1 year
After 2 years
£5500.00
£5698.00
£5903.13
*use photo*
Answer:
3.6% per annum
Step-by-step explanation:
The formula for accrued amount on a loan(value of loan) is given by the formula if compounded yearly is
[tex]A = P\left(1 + r)^t[/tex]
where
P = original loan amount
r = interest rate in decimal
t = number of years
We are given that the original loan amount
P = £5500
After 1 year the accrued amount
[tex]A = 5500(1 + r)^1[/tex]
and we know that after 1 year, the value of the loan is £5698
Therefore
5698 = 5500(1 + r)
1+ r = 5698/5500 = 1.036
r= 1.036 - 1 = 0.036
In percentage terms 0.036 = 0.036 x 100 = 3.6%
decreased by ___% = decreased by 10% and decreased by 10% again
Answer:
is this a trick question? Because if you lose 10 bucks but earn ten bucks its like nothing happened so Its going to be 0% because nothing changed
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1 ), complete parts (a) through (d). Click here to view page 1 of the cumulative standardized normal distribution table. Click here to view page 2 of the cumulative standardized normal distribution table. a. What is the probability that Z is less than 1.56? The probability that Z is less than 1.56 is 0.9406. (Round to four decimal places as needed.) b. What is the probability that Z is greater than 1.81 ? The probability that Z is greater than 1.81 is 0.0351. (Round to four decimal places as needed.) c. What is the probability that Z is between 1.56 and 1.81 ? The probability that Z is between 1.56 and 1.81 is (Round to four decimal places as needed.) d. What is the probability that Z is less than 1.56 or greater than 1.81 ? The probability that Z is less than 1.56 or greater than 1.81 is (Round to four decimal places as needed.)
From the given data, the probability of Z less than 1.56, greater than 1.56, between 1.56 and 1.81 and less than 1.56 or greater than 1.81 is 0.9406, 0.0359, 0.0235 and 0.9765 respectively.
a. From the cumulative standardized normal distribution table, we can look up the value 1.56 in the left column and find the corresponding value of 0.9406 in the intersecting row. Therefore, the probability that Z is less than 1.56 is 0.9406.
b. From the cumulative standardized normal distribution table, we can look up the value 1.81 in the left column and find the corresponding value of 0.9641 in the intersecting row. Since we want the probability that Z is greater than 1.81, we subtract this value from 1 to get 1 - 0.9641 = 0.0359 (rounded to four decimal places as needed). Therefore, the probability that Z is greater than 1.81 is 0.0359.
c. To find the probability that Z is between 1.56 and 1.81, we need to subtract the probability that Z is less than 1.56 from the probability that Z is less than 1.81. From the table, we know that the probability that Z is less than 1.56 is 0.9406 and the probability that Z is less than 1.81 is 0.9641. Therefore, the probability that Z is between 1.56 and 1.81 is 0.9641 - 0.9406 = 0.0235 (rounded to four decimal places as needed).
d. The probability that Z is less than 1.56 or greater than 1.81 is the sum of the probabilities that Z is less than 1.56 and Z is greater than 1.81, since these events are mutually exclusive. From parts (a) and (b), we know that the probability that Z is less than 1.56 is 0.9406 and the probability that Z is greater than 1.81 is 0.0359. Therefore, the probability that Z is less than 1.56 or greater than 1.81 is 0.9406 + 0.0359 = 0.9765 (rounded to four decimal places as needed).
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Baseball Players' Salaries. We have access to data regarding the salaries of all professional baseball players in 2015. That is, if we consider all professional baseball players in 2015 our subjects of interest, then we have information on every individual in the population. In this problem, we are going to examine how varying the sample size impacts the sampling distribution of the sample mean. We will be using an applet called StatKey to complete this problem. Start by opening a web browser on your computer and going to the following website: http://lock5stat.com/statkey/sampling.1_quant/sampling_1_quant.html (a) In the top left corner of the page, under StatKey, click on the button with the words Percent uith Internet Access (Countries) and select Baseball Players-2e (2015 Salary in millions) The top graph on the right hand side displays the distribution of the population as well as some numerical summaries describing the population. Use this graph and the numerical summaries to answer the following questions i. Report the mean (in millions of dollars) for all 868 salaries of 2015 professional baseball players to 3 decimal places ii. Report the standard deviation (in millions of dollars) for all 868 salaries of 2015 pro- fessional baseball players to 3 decimal places iii. The values in parts (a) and (b) above are (Choose all that apply) . Parameters o Statistics o Estimates . Numerical summaries of the sample . Numerical summaries of the population iv. (Free Response) Describe the shape of the distribution of salaries for professional baseball players in 2015. Be sure to comment on skewness and modality.
Previous question
The values in parts (a) and (b) are numerical summaries of the population.
Regarding the question on baseball players' salaries in 2015, the mean salary for all 868 professional baseball players is 3.856 million dollars and the standard deviation is 1.589 million dollars. The values in parts (a) and (b) are numerical summaries of the population.
The shape of the distribution of salaries for professional baseball players in 2015 is positively skewed, with the majority of the salaries clustering at the lower end of the salary range and a few salaries on the upper end. There is only one mode to the distribution.
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The spinner below was spun 20 times. The frequency that the spinner landed on each color is shown in the table below. What are the experimental and theoretical probabilities of landing on a red portion.
Work for the experimental probability and the theoretical probability shown. Show work!
A. Experimental: 80%; theoretical: 30.5%
B. Experimental: 8%; theoretical: 8%
C. Experimental: 40%; theoretical: 37.5%
D. Experimental: 30%; theoretical: 62.5%
The correct option for the probability of landing in the color red is:
Experimental: 40%; theoretical: 37.5%
What is probability?
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
We will get
p = 8/20 = 2/5 = 0.4
In percentage form this is:
p = 100%*0.4 = 40%
While the theoretical probability depends on the quotient between the number of red sections and the total number of sections.
There are 3 red sections and 8 sections in total, so here the probability is:
p = 100%*3/8 = 37.5%
So the correct option is C.
Experimental: 40%; theoretical: 37.5%
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A clinic examines 100,000 Covid-19 test samples in one month and finds that 25,000 are positive and 75,000 are negative. A PCR test is available which is accurate 82% of the time (whether the coronavirus is present or not). A lab technician reports finding evidence of the coronavirus in a randomly selected patient. Complete your answers in the space provided below. You must show your steps for complete credit.
a. In the absence of any test, what is the probability that the patient is Covid-19 positive?
b. In the absence of any test, what is the probability that the patient is Covid-19 negative?
c. What is the probability that the patient will test positive for Covid-19?
d. What is the probability that the patient will test negative?
e. What is the probability that the patient does not have Covid-19 if he or she tests positive for it?
f. What is the probability that the patient has Covid-19 if he or she tests negative?
Therefore , the solution of the given problem of probability comes out to be there is a 0.73 percent chance that a patient will test clear for Covid-19.
What is probability exactly?The primary goal of the designs inside a practice known as criteria is the evaluation of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1 can be used to represent chance, with 1 usually representing a range level of certainty and 0 typically representing possibility. A probability diagram shows the chance that a specific event will occur. Just the digits 0% and approximately 100% make up the decimal 1, 0, and 0.
Here,
a. P(Covid-19 positive) of 25,000/100,000 equals 0.25
b. P(Covid-19 negative) = 75,000/100,000 = 0.75
c. P(positive test) equals P(positive test | Covid-19 positive) * P(Covid-19 positive) + P(positive test | Covid-19 negative) * P(positive test | Covid-19 positive) (Covid-19 negative)
P (positive test | Covid-19 positive) = 0.82, while P (positive test | Covid-19 negative) = 0.18
When we enter the numbers, we obtain:
P(positive test) is equal to 0.82 * 0.25 + 0.18 * 0.75 = 0.31.
As a result, there is a 0.31 percent chance that a patient will test positive for Covid-19.
d. P(negative test) = P(negative test | Covid-19 negative) * P(Covid-19 negative) + P(negative test | Covid-19 positive) * P(negative test | Covid-19 negative) * P (Covid-19 negative)
Since the test is correct 82% of the time, we know that if a patient has Covid-19, the test will be negative 18% of the time, so:
P(positive test, negative Covid-19) = 0.18 P(negative test, positive Covid-19) = 0.95
When we enter the numbers, we obtain:
P(negative test) = 0.18*0.025+0.95*0.075=0.73
Therefore, there is a 0.73 percent chance that a patient will test clear for Covid-19.
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Can sum1 help please?
The zeroes of the polynomial f(x) = x⁴ - 2x³ - 6x² + 22x - 15 are x = 1, x = 3, x = -3
Describe Polynomial?Polynomials can be classified by degree, which is the highest power of the variable in the polynomial. For example, the polynomial f(x) = 3x^4 - 2x^3 + x^2 - 5x + 2 is a fourth-degree polynomial, as the highest power of x is 4.
Polynomials can be added, subtracted, multiplied, and divided using a variety of techniques, including factoring, synthetic division, and long division. They can also be evaluated at specific values of the variable, which can be useful in solving problems or analyzing data.
We can find the zeroes of the polynomial function f(x) = x⁴ - 2x³ - 6x² + 22x - 15 by factoring it or by using numerical methods such as the Newton-Raphson method or the bisection method. Here, we will use the factoring method.
First, we can observe that x = 1 is a zero of the polynomial, since f(1) = 1 - 2 - 6 + 22 - 15 = 0. Therefore, we can factor out (x - 1) from the polynomial:
f(x) = x⁴ - 2x³ - 6x² + 22x - 15
= (x - 1)(x³ - x² - 7x + 15)
Therefore, we have:
x³ - x² - 7x + 15 = (x - 1)(x² - 9)
= (x - 1)(x - 3)(x + 3)
Therefore, the zeroes of the polynomial f(x) = x⁴ - 2x³ - 6x² + 22x - 15 are:
x = 1, x = 3, x = -3
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Calculate the size of the label to fit around the tin of soup assuming it's glued
on with no overlap.
Remember- The label is NOT on the top or bottom of the can!
The Campbell soup can is 12. 5 cm in height and 7. 5 cm in width
The sample size of the label needed to fit around the tin of soup is 24.5 cm, calculated by multiplying the diameter (7.5 cm) by pi (3.14) and adding 1 cm for overlap.
In order to calculate the size of the label to fit around the tin of soup, you will need to measure the circumference of the can. The circumference of the can is the total length of the can along the curved edge. To do this, you will need to measure the diameter of the can, which in this case is 7.5 cm, and then multiply it by pi (3.14). This will give you the circumference of the can, which is 23.5 cm. To find the size of the label, you will need to add 1 cm onto the circumference of the can to allow for a small overlap. This will give you a label size of 24.5 cm.
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The terminal side of an angle in standard position passes through P(-3,-4). What is the value of tan0
If MNO IS NMO what statement best describes triangle MON?
If MNO is NMO, it means that the second and third vertices of the triangle have switched places, but the first vertex remains the same. Therefore, triangle MON is congruent to triangle NMO.
as they have the same side lengths and angles. Specifically, the sides MO, ON, and NM are congruent, and the angles at vertices M, O, and N are also congruent. We can represent this relationship between the two triangles using the symbol ≅, so we can say that triangle MON ≅ triangle NMO. The concept of congruent triangles is a fundamental principle in geometry. Two triangles are said to be congruent if their corresponding sides and angles are equal. When two triangles are congruent, we can say that they have the same size and shape, but they may be oriented differently in space. here are several ways to prove that two triangles are congruent, such as the side-angle-side (SAS), angle-side-angle (ASA), side-side-side (SSS), angle-angle-side (AAS), and hypotenuse-leg (HL) congruence criteria.
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Mr. Lawson purchased 24 cartons of eggs. Each carton contained 36 eggs. Mr.
Lawson used 79 eggs to make cookies for the local grocery store.
Write an equation that can be used to find e the number of eggs that Mr. Lawson did not use in making cookies
Answer:
(24x36)-79=785
Step-by-step explanation:
Answer: (24 x 36) - 79 = e
Step-by-step explanation: to find the number of eggs he had starting out, multiply the number of cartons, c, by the number of eggs inside each carton, e. C x e = 864. He has 864 eggs before he used 79. The answer, e, is 864 - 79
HELP BRAINLIEST AND 5 STAR IF YOU GET ALL BLANKS CORRECT
Two trains simultaneously left points M and N and headed toward each other. The distance between point M and N is 380mi. The speed of the train, which started, from point N was 5 mph faster than the speed of the other train. In two hours after the departure the distance between the trains was 30 mi. What is the speed of each train?
Answer:
Using the quadratic formula, we find that:
x = 0.555 or x = 89.445
We can ignore the first solution since it doesn't make sense for the speed of a train. Therefore, the speed of the slower train is approximately 89.445 mph, and the speed of the faster train is approximately 94.445 mph.
So, the answer is:
The speed of the slower train is approximately 89.445 mph, and the speed of the faster train is approximately 94.445 mph.NOT SURE
Step-by-step explanation:
Solve the following equations by using the properties of logarithms
Log 2x = 5
Lnx-In (2x+1)=2
Log x= log (2/x) +1
The value of the following equations by using the properties of logarithms: 1.x = 50000 2. x = (1 ± √5) / 4 3. x= 2√5.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions, usually separated by an equal sign (=). An equation typically consists of one or more variables, coefficients, constants, and mathematical operations, such as addition, subtraction, multiplication, division, exponentiation, and roots. The purpose of an equation is to find the values of the variables that satisfy the equation. These values are called solutions or roots of the equation. Equations are used in many branches of mathematics, including algebra, calculus, geometry, and statistics, to model and solve various problems and phenomena in the natural and social sciences, engineering, and finance.
Here,
1. Log 2x = 5
We can rewrite this equation using the property that log_a(b) = c is equivalent to b = aˣ:
2x = 10⁵
Simplifying the right-hand side, we get:
2x = 100000
Dividing both sides by 2, we get:
x = 50000
Therefore, the solution is x = 50000.
2. Lnx - In(2x+1) = 2
Using the fact that ln a - ln b = ln(a/b), we can simplify the left-hand side of the equation:
ln(x/(2x+1)) = 2
Next, we can rewrite the equation in exponential form:
e² = x/(2x+1)
Multiplying both sides by 2x+1, we get:
e²(2x+1) = x
Expanding and simplifying the left-hand side, we get a quadratic equation:
4xe² + 2e² - x = 0
Solving for x using the quadratic formula, we get:
x = (-2e² ± √((2e²)² - 4(4e²)(-1))) / (2(4e²))
Simplifying, we get:
x = (-e² ± √(e⁴ + 4e₂)) / (4e²)
x = (-e² ± e²√5) / (4e²)
x = (1 ± √5) / 4
Therefore, the solutions are x = (1 + √5) / 4 and x = (1 - √5) / 4.
3. Log x = log (2/x) + 1
Using the fact that log_a(b) = log_a(c) is equivalent to b = c, we can simplify the equation:
x = 2/x * 10
Multiplying both sides by x, we get:
x² = 20
Taking the square root of both sides, we get:
x = ±√(20)
Since x cannot be negative (because log of a negative number is undefined), the only solution is:
x = √(20) = 2√5
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Here is a rectangle. Here is the same rectangle. It has some unit squares inside. Find the area of the rectangle
Here is the same rectangle. It has some unit squares inside. The area of the rectangle is 10 Square unit.
Area of Rectangle:
The area of a rectangle is the area occupied within the bounds of the rectangle. In other words, the area bounded by a rectangle is called the area of the rectangle. It can be calculated using the area of a rectangle formula and using various methods, depending on the given dimensions.
According to the Question:
Area of each small square = 1 sq cm
Area of rectangle in figure 2 by counting the squares = 10 sq. cm
Area = 10 square cm
Length of rectangle = 5 cm
Breadth of rectangle = 2 cm
Area = 5 × 2 = 10 sq. cm
Hence, area of rectangle = length × breadth
A = l × b where, A is the area, l and b are length and breadth of a rectangle.
Complete Question:
You are given 10 squares with side length of 1 to 10 units each. You want to put them in a rectangle such that there is no overlapping and no piece of a square is outside the rectangle. Here is the same rectangle. It has some unit squares inside. Find the area of the rectangle?
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