1. The number of people living with HIV infections increased exponentially worldwide from 1990 to 2005. The formula for the number of HIV infections, H, in millions, as a function of years, t, since 1990 is given by H = 2.3e ^(0.1343t) A) How many people were living with HIV infection in 1990? Show how you calculated this value.B) Use functional notation to express the number of people infected in the year 2003, then calculate thatC) Explain the meaning of H (5) and calculate H (5)
Answers
1) In this problem, let's work with an exponential model.
a) To find out how many people were living with HIV infection we're going to consider 1990 as the first year. The year "0"
So we can write out
\(\begin{gathered} H(t)=2.3e^{0.1343t} \\ H=2.3e^{0.1343\times0} \\ H=2.3\cdot1 \\ H=2.3 \end{gathered}\)Note that we plugged into t, t=0 then we know that according to that exponential model there were 2.3 million people HIV positive in 1990.
b) Now we can evaluate the function, 13 years later in 2003, so we'll plug into that t=13:
\(\begin{gathered} H(t)=2.3e^{0.1343t} \\ H(13)=2.3e^{0.1343\cdot13} \\ H(13)=13.18143 \end{gathered}\)So 13 years later there were more than 13 million people infected
c) In this case, the meaning of H(5) is the number of HIV positive 5 years later since t is given in years. In other words, H(5) is the number of HIV positive in 1995.
Related Questions
If you have a statistical calculator or computer, use it to find the actual sample mean and sample standard deviation. Otherwise, use the values Σx = 2769 and Σx2 = 132,179 to compute the sample mean and sample standard deviation. (Round s to four decimal places.)
Answers
By using a statistical calculator, the actual sample mean and sample standard deviation are:
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
How to calculate the sample mean for the set of data?In Mathematics and Geometry, the sample mean for any set of data can be calculated by using the following formula:
Mean = ∑x/(n - 1)
∑x represents the sum of all data values.(n - 1) represents the number of data contained in a sample.In Mathematics and Geometry, the sample standard deviation for any set of data can be calculated by using the following formula:
Standard deviation, δx = √(1/N × ∑(x - \(\bar{x}\))²)
x represents the observed values of a sample.\(\bar{x}\) is the mean value of the observations.N represents the total number of of observations.By using a statistical calculator, the actual sample mean and sample standard deviation are as follows;
Actual sample mean = 46.1500.
Actual ample standard deviation = 8.6256.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Katerina runs 15 miles in 2 1/2 hours what is the average number of minutes it takes her to run 1 mile?
Answers
We have that The average number of minutes it takes her to run 1 mile
\(X=42min\)
From the Question we are told that
Katerina runs 15 miles in 2 1/2 hours
Average number of minutes it takes her to run 1 mile
Generally
\(2 1/2 hour=10.5h\)
\(10.5hours=630minutes\)
Therefore
The average number of minutes it takes her to run 1 mile
\(X=\frac{630}{15}\)
\(X=42min\)
In conclusion
The average number of minutes it takes her to run 1 mile
\(X=42min\)
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prove that there is a 1-1 correspondence between the set of all positive integers and the set of all rational numbers
Answers
A one-to-one correspondence between the set of all positive integers and the set of all rational numbers exists.
By definition, any rational number can be expressed as a fraction a/b, where a and b are integers and b is nonzero. Since any positive integer can be expressed as the fraction a/1, each positive integer can be associated with a rational number a/1.
Thus, there is a one-to-one correspondence between the set of all positive integers and the set of all rational numbers. Furthermore, since any rational number a/b can be expressed as the product of a and b, it can also be associated with the product of two positive integers a and b.
Thus, there is also a one-to-one correspondence between the set of all rational numbers and the set of all positive integers.
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Two cars leave the same parking lot, one heading north and the other east. After several minutes, the eastbound car traveled 5 kilometers. If the two cars are now a straight-line distance of 13 kilometers apart, how far has the northbound car traveled?
Answers
Based on the information given, we can use the Pythagorean theorem to determine the distance traveled by the northbound car.
Let's denote the distance traveled by the northbound car as 'x' kilometers.
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse (the straight-line distance between the two cars) is equal to the sum of the squares of the other two sides (the distances traveled by each car).
In this case, the northbound car's distance is 'x' kilometers and the eastbound car's distance is 5 kilometers.
So we have the equation:
x^2 + 5^2 = 13^2
Simplifying, we get:
x^2 + 25 = 169
Subtracting 25 from both sides, we get:
x^2 = 144
Taking the square root of both sides, we get:
x = 12
So the northbound car has traveled 12 kilometers.
Answer: 12 km
Step-by-step explanation:
As seen in the figure the distance that the northbound car traveled equals to the distance from point N to the parking lot.
pythagorean: \(\sqrt{13^{2}-5^{2} }=12km\)
if we know the value of b, the slope of the regression line, we can accurately guess the value for the correlation coefficient without looking at the scatterplot or making any calculations.
Answers
Yes, knowing the value of b, the slope of the regression line, allows us to predict the correlation coefficient value with accuracy.
Regression and correlation techniques can be used to establish links between variables.
Every day, we refer to any form of association as a "correlation," using that word.
To determine whether or if there is a relationship between the variables under investigation, correlation analysis is used.
Although regression illustrates how the variables are related,
Correlation and regression analysis can be shown graphically using scatter plots.
According to the question,
If we know the value of the slopes of the regression line say byx and bxy
We can Calculate the value of Correlation coefficient by using the relation
=> r = √(byx × bxy)
Hence , Yes We can accurately guess the value of correlation when slope of regression line is given
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PLEASE HELP 100 POINTS Consider two integers p and q. Explain why p x (-q) = (-p) x q = -pq.
Answers
Answer:
Step-by-step explanation:
When two variables are together, this means they are supposed to be multiplied. This is why -pq and p x (-q) are equivalent. (-p) x q is the same thing as p x (-q). When two numbers are being multiplied and one is negative, it doesn't matter which one is negative, the ending result will still be a negative number.
I hope you understand what I am trying to say. I explained the best I could, and I hope this helps you. Do well on the test!
I want you to remember this rule:
When multiplying or dividing two different integers that have different signs which are: + (positive sign) and - (negative sign). You get a negative number
However, if you are multiplying or dividing two different integers but they have the same signs. You end up with a positive number
Also multiply are associative, means that they can change the numbers around but they still end up in the same answer
So in this question p x (-q) = (-p) x q = -pq (they put a bracket in the negative number so the question could be easier to be reconize)
We can make:
p = 3
q = 4
So: 3 x -4 = -12
-3 x 4 = -12
-3(4) = -12 (it's a different way to write multiply)
You can see here using the facts that I gave up there supports that
p x (-q) = (-p) x q = -pq
what is the meaning of sequence in mathematic and
Answers
Answer:
A list of numbers or objects in a special order. Example: 3, 5, 7, 9, ... is a sequence starting at 3 and increasing by 2 each time.
Step-by-step explanation:
HELP PLEASE DUE IN 10 MIN
Answers
The correct statement regarding the measure of variability used to represent the data is given as follows:
The IQR of 10 is the most accurate to use, as the data is skewed.
How to obtain the interquartile range?The interquartile range of a data-set is given by the difference of the third quartile by the first quartile of the data-set.
It is the measure of variability to be used when a data-set contains outliers, or is skewed, as is the case for this problem.
The charity received 18 donations, hence the quartiles are given as follows:
First quartile: 0.25 x 18 = 4.5th element = median of 10 and 15 = 12.5.Third quartile: 0.75 x 18 = 13.5th element = median of 20 and 25 = 22.5.Hence the IQR is given as follows:
IQR = 22.5 - 12.5
IQR = 10.
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A sample of 300 subscribers to a particular magazine is selected from a population frame of 9,000 subscribers. If, upon examining the data, it is determined that no subscriber had been selected in the sample more than once:________.
A. the sample could not have been random
B. the sample may have been selected without replacement or with replacement
C. the sample had to have been selected without replacement
D. the sample had to have been selected with replacement
Answers
Answer:
C
Step-by-step explanation:
It is determined that no subscriber had been selected in the sample more than once the sample had to have been selected without replacement.
What is the sample?A sample is a subset of data drawn from a larger population by a researcher using a predetermined selection process. These components are referred to as sample points, sampling units, or observations.
If it is determined that no subscriber had been selected in the sample more than once, this means that each subscriber was only included once in the sample. This can only occur if the sample was selected without replacement, meaning that each subscriber was selected once and only once from the population frame.
Therefore, the correct answer is C. the sample had to have been selected without replacement.
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Match each function on the left to all points on the right that would be located on the graph of the function. Help!! thanks
Answers
Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;
f(x) = 2x + 2 ⇒ (0, 2).
f(x) = 2x² - 2 ⇒ (-1, 0).
\(f(x) = 2\sqrt{x+1}\) ⇒ (0, 2).
What is a function?In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.
Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;
For the ordered pair (0, 2), we have:
f(x) = 2x + 2
2 = 2(0) + 2
2 = 2 (True).
For the ordered pair (-1, 0), we have:
f(x) = 2x² - 2
0 = 2(-1)² - 2
0 = 2 - 2
0 = 0 (True).
For the ordered pair (0, 2), we have:
\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)
2 = 2 (True).
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What are the solutions to the quadratic equation x2-16=0
Answers
Answer:
x = -4, 4
Step-by-step explanation:
Hi there!
\(x^2-16=0\)
Rewrite 16:
\(x^2-4^2=0\)
The difference of squares rule states that \(a^2-b^2=(a+b)(a-b)\). With this, apply the difference of squares to the equation:
\((x+4)(x-4)=0\)
The zero-product property states that if the product of two numbers is 0, then one of the numbers must be equal to zero. Set each term equal to 0 and find the solutions:
\(x+4=0\\x=-4\)
\(x-4=0\\x=4\)
Therefore, the solutions are -4 and 4.
I hope this helps!
Identify a pattern in each list of numbers. Then use this pattern to find the next number.
5, 12, 33, 96, 285, ___
Answers
=====================================================
Explanation:
The given sequence is 5, 12, 33, 96, 285, ...
The jump from 5 to 12 is +7The jump from 12 to 33 is +21The jump from 33 to 96 is +63The jump from 96 to 285 is +189The sequence of increases is: 7, 21, 63, 189
Then notice,
The jump from 7 to 21 is "times 3"The jump from 21 to 63 is also "times 3"The jump from 63 to 189 is also "times 3".Assuming this pattern keeps up, the next increment will be 189*3 = 567
We add this increment to the last term of the original sequence
285+567 = 852
The sequence is now 5, 12, 33, 96, 285, 852, ...
19. Ram and Rahim are partners in a firm sharing profits in the ratio of 3: 2. Kabir is admitted as a partner for 1/5th share of profits. Machinery would be appreciated by 10% (Book Value of 80,000) and Building would be depreciated by 20% (Book Value of 2,00,000). Unrecorded Debtors of 1,250 would be brought to books. There is a liability of 2,750 included in Sundry Creditors that is not to be paid. What will be the Gain (Proñt Loss on revaluation? (a) Loss of 28,000. (c) Profit 28,000. (6) Loss 40,000. (d) Profit of 40,000.
Answers
Answer:
make me brainlist
Step-by-step explanation: firm sharing profits and losses in the ratio of 3
2. From Ist April, 2020 they decided to share the future profits equally. On this date, the General Reserve
showed a balance of 1,60,000; Revaluation of fixed assets resulted into a gain of "1,02,000 and stock resulted
to a loss of 22,000. On this date, the goodwill of the firm was valued at $3,60.000
Pas necessary journal entries for the above transactions on reconstitution of the form
Bolutions
PLEASE HELP (must show work) Show all work to factor x4 - 17x2 + 16 completely.
Answers
Determine the missing side of a right triangle if one side
length is 15 and the hypotenuse measures 17 units.
Answers
Answer:
215 units
Step-by-step explanation:
Find the midpoint of the line segment from (1,-3) to(-5,2)
Answers
Midpoint of the line segment from (1,-3) to(-5,2) is (-2,-1/2).
What is straight line?A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.
The midpoint of a line segment is a point that lies exactly halfway between two points
The formula for midpoint (x,y)=(x₁+x₂/2,y₁+y₂/2)
We need to find midpoint of the line segment from (1,-3) to(-5,2)
Midpoint=(1-5/2,-3+2/2)
=(-4/2, -1/2)
=(-2,-1/2)
Hence, midpoint of the line segment from (1,-3) to(-5,2) is (-2,-1/2).
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(a+b square)-(a-b square)
Answers
Answer:
\( {(a + b)}^{2} - {(a - b) }^{2} \\ = 1\)
In algebra 0 is written as 1 according to rule.
Yo can anyone help me with this question I cant find where Ive gone wrong and math is hard
Answers
Answer:
Try to divide 5/8 and what you get subtract it from 24 that should be the answer
Which of the following statements can be assumed from the diagram?
Answers
Answer:
the last answer choice is one of them for sure.
Step-by-step explanation:
Line A and F intersects line BC
What is the slant height I of the
triangular face of the pyramid?what
is the surface area of the pyramid
Please
Help
Me
Answers
Answer:
Answer explained in image
Step-by-step explanation:
Solve. Write the solution in interval notation.
9 − 6(x + 2) ≤ 6 + 6(5x + 6)
Answers
Answer:
x ≥ 1.25
Step-by-step explanation:
9 − 6(x + 2) ≤ 6 + 6(5x + 6)
9 - 6x - 12 ≤ 6 + 30x + 36
-3 - 6x ≤ 42 + 30x
-3 - 36x ≤ 42
-36x ≤ 45
x ≥ 1.25
What is the approximate value of x in –2 ln (x + 1) − 3 = 7?
Answers
Answer:
x = 1/e^-5 - 1
Step-by-step explanation:
–2 ln (x + 1) − 3 = 7
–2 ln (x + 1) = 10
ln (x + 1) = –5
x + 1 = e^-5
x = e^-5 - 1
x = 1/e^-5 - 1
the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
To solve the equation -2 ln(x + 1) - 3 = 7 for the approximate value of x, we will follow these steps:
1. Begin with the given equation: -2 ln(x + 1) - 3 = 7.
2. Move the constant term to the other side of the equation: -2 ln(x + 1) = 7 + 3.
3. Simplify: -2 ln(x + 1) = 10.
4. Divide both sides of the equation by -2 to isolate the natural logarithm term: ln(x + 1) = -5.
5. Rewrite the equation using the exponential form of natural logarithm: e⁻⁵ = x + 1.
6. Calculate the value of e⁻⁵: e⁻⁵ ≈ 0.0067.
7. Subtract 1 from both sides of the equation: x = 0.0067 - 1.
8. Simplify: x ≈ -0.9933.
Therefore, the approximate value of x in the equation -2 ln(x + 1) - 3 = 7 is x ≈ -0.9933.
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A particular fruit's weights are normally distributed, with a mean of 509 grams and a standard
deviation of 26 grams.
If you pick 6 fruit at random, what is the probability that their mean weight will be between 496
grams and 544 grams
Answers
The mean weight of a fruit is normally distributed with a mean of 509 grams and a standard deviation of 26 grams.
When 6 fruits are picked at random, the mean weight of the 6 fruits will also be normally distributed.
How do we find the probability?To find the probability that the mean weight of the six fruits will be between 496 grams and 544 grams, we need to calculate the z-scores for each of these values using the formula:
z = (x - μ) / (σ / √n)
where x is the value we are interested in (either 496 or 544),
μ is the population mean (509),
σ is the population standard deviation (26),
n is the sample size (6).
For x = 496:
z = (496 - 509) / (26 / √6) = -1.50
For x = 544:
z = (544 - 509) / (26 / √6) = 1.30
Using a normal distribution table or a calculator, we can find the probabilities associated with the z-scores which are between -1.50 and 1.30 is approximately 0.867.
Therefore, the probability that the mean weight of six fruits picked at random will be between 496 grams and 544 grams is approximately 0.867 or 86.7%.
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if it is 5:00 will the clock show a right angel
Answers
Answer:
the clock hands do not form a right angle at 5:00.
Step-by-step explanation:
For every 2 hours, approximately $1,087 worth of product is sold to consumers. How much money will the company for an entire month (30 days)?
Answers
Answer:
391,248 dollars
Step-by-step explanation:
Answer:
the answer is $39,128
Step-by-step explanation:
$1087 divided by 2 = 543.4
$543.4 worth of products is sold in 1 hour
$543.4 x 720 = $39,128
i got the 720 for the hours from 30 day so there is 720 hours in 30 days a whole month (24 x 30 =720)
i hope this helps ;)
sorry if im wrong
What is the answer please help
Answers
Answer:
is the number 4
so 13/16 3/16
Step-by-step explanation:
what is
(-1/3)+1/4+(-1/5)
Answers
Answer:
-17/60
Step-by-step explanation:
(-1/3)+1/4+(-1/5)
Please help! I need this answered by tommorrow!
Answers
Answer:
You could use rate reasoning because, one day is 405 miles traveled. It is 3,272 miles from Sacramento to Key West, and when you use rate reasoning, you can tell that it will take about 8 days from Sacramento to Key West (3 more days if your counting the 5 days that they have already traveled)
Hope this helps
Find c.
Round to the nearest tenth:
Answers
Answer:
Step-by-step explanation:
2/Sin(105) = c / sin(15)
2 * sin(15) = c * sin(105) Divide by Sin(105)
2 * sin(15)/Sin(105) = c
2 * 0.2679 = c
c = 0.539
c = 0.5
la o intalnire sportivaau patricipat 6 persoane. fiecare dintre cele 6 persoane a dat mana o singura data cu fiecare dintre ceilaltiparticipanti. Caite strangeri de mana au avut loc ?
Answers
Answer:
I believe the answer would be 15
Step-by-step explanation: