Answer:
[tex]6\frac{1}{5}[/tex] or [tex]\frac{31}{5}[/tex]
Step-by-step explanation:
Answer:
31/5 OR 6 1/5 (Depends if your teacher wants an improper fraction or a mixed number.)
Step-by-step explanation:
First, rewrite the decimal as a fraction with 1 as the denominator.
6.2 = 6.2/1
Nest, multiply to remove one decimal place so it's easier to solve.
6.2 x 10 = 62 and 1 x 10 = 10 so... that would be 62/10
Find to GCF of both 62 and 10, or in other words something that they are both divisible by. That would be 2, and now you can simplify the fraction further.
62/2 = 31 and 10/2 = 5 so that would be 31/5, which is 6 1/5 as a mixed number.
I hope this was useful!! :)
If the denominator is a friendly number, you can Up or down, or use a
If the denominator is a friendly number, you can easily multiply it with another integer.
What is a Friendly Number in math?In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and the number itself.
Friendly numbers are numbers that are easy to work with. For example, multiples of 10 are “friendly” because they are easy to work with when we add or subtract.
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on a circle of radius 9 feet, give the degree measure of the angle that would subtend an arc of length 6 feet. round your answer to the nearest hundredth, or two decimal places.
The circumference of the circle is 2 * pi * 9 = 56.5 feet. So, the degree measure is (6/56.5) x 360 = 51.1 degrees. Rounded to two decimal places, the degree measure is 51.1 degrees.
To find the degree measure of an angle that subtends an arc of length 6 feet on a circle of radius 9 feet, use the formula: degree measure = (arc length / circumference) x 360 degrees.
The degree measure of the angle that would subtend an arc of length 6 feet on a circle of radius 9 feet can be found by using the formula:
degree measure = (arc length / circumference) * 360
The circumference of the circle is 2 * pi * 9 = 18 * pi
So, degree measure = (6 / (18 * pi)) * 360 = (6 / 18) * (360 / pi) = 60 / pi
To convert this to degrees, we can use an approximation of pi as 3.14, so
degree measure = 60 / 3.14 = 19.11
Rounding to two decimal places, the degree measure is 19.11, which can be rounded to 19.11 degrees.
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Write the ratio 12 :30 in the form 1: n
Answer: 1:2.5
Step-by-step explanation:
Step by step explanation:
12:30
÷ by 12
= 1:2.5
The diameter of a cone's circular base measures 10 inches, and the slant height of the cone is 8 inches.
What is the approximate surface area of the cone?
Responses
146.3 in²
204.1 in²
314.2 in²
565.2 in²
The surface area of Cone is 204.1 inch².
What is Surface area of Cone?The surface area of a cone is equal to the curved surface area plus the area of the base: π r² + πlr
where r is the radius and l is the slant height
Given:
Radius= 5 inches
Slant height= 8 inches
So, the Surface area of Cone
= πr (l +r)
= 3.14 x 5 ( 8 + 5)
= 15.7 x 3
= 204.1 inch²
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use markov's inequali5y 5o get an upper bound on the tail probability p(x>-t) nonegative random variable
The maximum value of P(X > -t) is 1 and the upper bound of P(X > -t) is -E[X]/t.
Markov's inequality states that if X is a non-negative random variable and c is a positive constant, then P(X > c) ≤ E[X]/c.
For example, let X be a non-negative random variable and let c = -t. Then the tail probability P(X > -t) can be upper bounded by Markov’s Inequality as: P(X > -t) ≤ E[X]/(-t).
To calculate P(X > -t) in terms of E[X], we can solve for P(X > -t) in the inequality. Therefore, P(X > -t) ≤ E[X]/(-t) can be rewritten as P(X > -t) ≤ -E[X]/t.
Since the left side of the inequality is a probability, it must be between 0 and 1. Therefore, the maximum value of P(X > -t) is 1 and the upper bound of P(X > -t) is -E[X]/t.
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Learn before you teach Select an adult at random. Define events A: person
has earned a college degree, and T: person has chosen teaching as his or her
career. Rank the following probabilities from smallest to largest. Explain your
reasoning.
P(A) P(T) P(AT) P(TA)
The order of the probabilities from smallest to largest is P(T) < P(T|A) < P(A) < P(A|T).
A represents the event "Person earned a college degree"
T represents the event "Person's career is teaching"
P(A) represents the probability of event A (Person earned a college degree)
P(T) represents the probability of event T (Person's career is teaching)
P(T|A) represents the conditional probability of event T given event A (Probability of a degree holder being a professional teacher)
P(A|T) represents the conditional probability of event A given event T (Probability of a teaching career being held by a degree holder)
It is a universal fact that all teachers have a college degree, so:
P(A|T) > P(A) as having a college degree is a necessary condition for being a teacher
P(T|A) < P(A) as not all degree holders choose to become teachers
P(T|A) > P(T) as a smaller number of degree holders become teachers compared to the total number of teachers
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Find the next three terms
1.5, 4.5, 13.5, 40.5
Answer:
121.5, 364.5, 1093.5
Step-by-step explanation:
Divide 4.5 and 1.5 to find out how we get our next terms:
4.5 / 1.5 = 3
Every number is multiplied by 3 to become the next term, thus:
40.5 * 3
[121.5]
121.5 * 3
[364.5]
364.5 * 3
[1093.5]
Answer:
121.5, 364.5, 1093.5
Step-by-step explanation:
In this problem, we are asked to find the next three terms of the given geometric sequence.
To solve this simply, we can first identify the change, or difference, between the sequence's terms.
1.5, 4.5, 13.5, 40.5, ...
From 1.5 to 4.5, the difference is 3.
From 4.5 to 13.5, the difference is 9.
From 13.5 to 40.5, the difference is 27.
We can see that the difference between each term is one more power of three each time. So, we can continue the pattern.
For the next three terms, the difference from the previous term will be be 3 times the previous difference.
So, the differences will be: 81, 243, and 729.
We can add these numbers in a recursive sequence to get the next three terms of the sequence:
40.5 + 81 = 121.5
121.5 + 243 = 364.5
364.5 + 729 = 1093.5
What’s the difference between slope-intercept form and and point slope formula
Point slope form and slope intercept form of a line are y - y₁ = m (x - x₁) and y = mx + c respectively.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
The point slope form of a line is given by,
y - y₁ = m (x - x₁),
where (x₁, y₁) is a point on the line, m is the slope and (x, y) be any point.
The slope intercept form of a line is given by,
y = mx + c
where m is the slope and c is the y intercept.
y intercept is the point where the line touches the Y axis. x coordinate will be 0 at that point.
The slope intercept form of a line can be found from the point slope by substituting (x₁, y₁) = (0, c)
y - c = m (x - 0)
y - c = mx
y = mx + c
Hence the slope intercept form of a line is y = mx + c and the point slope form is y - y₁ = m (x - x₁).
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(12.) The population of Michigan is nearly 10,000,000 people as Massachusetts has nearly 6,000,000
people. The number of state representatives is 15 and 10, respectively.
a. Write the equation of the line given the state population and appointed state representatives.
b. What does the slope represent?
c. What does the y-intercept represent?
d. Use your model to predict how many state representatives that the state of New York will be
assigned if they have a population of 19,000,000.
If Triangle PQR ~ Triangle VST with a scale factor of 2:5, find the value of x.
The value of x that makes Triangle PQR ~ Triangle VST is 5
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
Triangle PQR ~ Triangle VST
Scale = 2 : 5
So, we have the following equivalent ratio
6 : 2x = 15 : 25
So, we have
2x/6 = 25/15
Make x the subject
So, we have the following representation
x = 6 * 25/(15 * 2)
Evaluate the expression
x = 5
Hence, the value is 4
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Complete question
If Triangle PQR ~ Triangle VST with a scale factor of 2:5, find the value of x.
PQ = 6
QR = 2x
VS = 15
ST = 25
Determine whether the data set is a population or a sample. Explain your reasoning The grades of 5 students in a classroom of 30 Choose the correct answer below. O A. Population, because it is a subset of all students in the class O B. Sample, because it is a collection of grades for all students in the classroom, but there are other classrooms ° O C. Sample, because the collection of 5 students' grades is a subset of all students in the class. O D. Population, because it is a collection of grades for all students in the classroom
The data set is a sample, because the collection of 5 students' grades is a subset of all students in the class. This is indicated by choice "C."
The grades of 5 students in a class of 30 represent only a portion of the total data and do not include all of the grades in the class. Thus, it is a sample and not a population. A sample is a part of the population that is selected for analysis. In this case, the grades of 5 students are a subset of the grades of all students in the classroom, which is the population. A sample is used to make inferences about the population, and the results from the sample are used to estimate the characteristics of the population. However, the sample is not representative of the entire population, so the results from the sample may not reflect the true characteristics of the population. This is why it is important to use a random sample that is representative of the population to ensure accurate results.
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(co 3) consider the following table: age group frequency 18-29 983 30-39 784 40-49 686 50-59 632 60-69 541 70 and over 527 if you created the probability distribution for these data, what would be the probability of 30-39?
The probability of 18-29 is 0.2213 or 22.13%, the probability of 30-39 is 0.1765 or 17.65%.
The probability of 30-39 can be calculated using the following formula:
P(30-39) = Frequency of 30-39 / Total Frequency
P(30-39) = 784 / 4443
P(30-39) = 0.1765
Therefore, the probability of 30-39 is 0.1765 or 17.65%.
To calculate the probability of any age group, the formula is the same. The probability is determined by dividing the frequency of the age group by the total frequency. To calculate the probability of any age group, you must first calculate the total frequency by adding up the frequencies of all the age groups. Then you can use the formula to calculate the probability of any age group.
For instance, to calculate the probability of 18-29, the formula would be:
P(18-29) = Frequency of 18-29 / Total Frequency
P(18-29) = 983 / 4443
P(18-29) = 0.2213
Therefore, the probability of 18-29 is 0.2213 or 22.13%.
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What is the probability of getting 4 kings when 5 cards are drawn from a standard deck of cards?
The probability of drawing four kings from a standard deck of cards in a single draw is 0.000001515, or 0.001515%.
The probability of drawing four kings from a standard deck of cards is extremely unlikely, as there are only four kings in a standard deck. This means that the probability of drawing four kings in a single draw of five cards is expressed mathematically as:
P(4 kings) = (4C4)*(48C1)/(52C5)
In this equation, 4C4 is the number of ways to select four kings from four kings, 48C1 is the number of ways to select one card of any other rank, and 52C5 is the total number of ways to select five cards from the deck.
Plugging in the numbers, we get the following equation:
P(4 kings) = (4!)*(48C1)/(52C5)
= (24)*(48C1)/(2598960)
= 0.000001515
Therefore, the probability of drawing four kings from a standard deck of cards in a single draw is 0.000001515, or 0.001515%.
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Melanie invests a total of $35,500 in two accounts. The first account earned a rate of return of 12%
(after a year). However, the second account suffered a 4% loss in the same time period. At the end
of one year, the total amount of money gained was $1,300.00. How much was invested into each
account?
$15,500 was invested in the first account
$20,000 was invested in the second account.
Solution
Let's call the amount invested in the first account "x". The amount invested in the second account would be $35,500 - x.
At the end of one year, the first account would have x * 1.12 = x + 0.12x = 1.12x dollars.
And the second account would have (35,500 - x) * 0.96 = 34,320 - 0.96x dollars.
The total amount of money gained at the end of one year would be 1.12x + 34,320 - 0.96x = 35,500 + $1,300 = $36,800.
We can set up an equation to solve for x:
1.12x + 34,320 - 0.96x = $36,800
0.16x = $2,480
x = $15,500
So, $15,500 was invested in the first account, and $35,500 - $15,500 = $20,000 was invested in the second account.
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what is the sum that I'm supposed to do?
Answer:
a: 1/8 and 1/4. b: 1/2 1/4. c: 1/1 and 5/12. d: 1 1/2 and 3/4
Step-by-step explanation:
You had to find 2 fractions that add up to a number between the two numbers listed.
A race car driver won a 300 mile race with a speed of
170.9 miles per hour. Find the driver's time.
Answer:
2.59hours
Step-by-step explanation:
Answer:2.59 hours.
Step-by-step explanation:
Speed = Distance/Time
Speed here is 115.7 mph
Distance here is 300 miles
Time here is unknown (t)
Plug the values into the equation
115.7 miles per hour = 300 miles/ t
Multiply both sides by t
115.7(t) = 300 miles
Divide both sides by 115.7 to get t alone
t = 300 miles/115.7mph
The miles here cancel out, so you'll be left with hours only. Hours is a time unit, so that's good1
t = 2.59 hours
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10) The temperature is below 80 degrees.
Answer:
ok so I don't get what you're trying to say but ok
Z-scores are useful with regard to inferential statistics primarily because they offer a tool by which to determine whether _____. a. a sample is noticeably different from a population. b. a distribution of scores is standardized. c. a distribution of scores is symmetrically shaped. d. an individual is different from a sample.
Z-scores are useful with regard to inferential statistics primarily because they offer a tool by which to determine whether a sample is noticeably different from a population. The answer is A.
Inferential statistics is a branch of statistics that deals with making predictions, generalizations, or inferences about a population based on a sample of data collected from that population.
Z-scores are a measure of the number of standard deviations away from the mean that a particular score lies. By standardizing a distribution of scores, Z-scores allow us to compare scores from different distributions or from different populations. By determining the Z-score of a particular sample, we can determine whether it is noticeably different from a population based on its distance from the population mean.
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Cynthia Besch wants to buy a rug for a room that is 25ft wide and 34ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 360 square feet of carpeting. What dimensions should the rug have?
The dimensions of the rug are: width is 15 feet length is 21 feet.
Let's call the width of the strip of floor around the rug "x". Then the width of the rug would be 25 - 2x, and the length of the rug would be 34 - 2x.
The total area of the rug should not exceed 360 square feet, so we can set up an equation to represent this:
(25 - 2x)(34 - 2x) = 360
Expanding and simplifying the left-hand side:
25 × 34 - 2 × 25 × x - 2 × 34 × x + 4 × x² = 360
850 - 118x + 4x² = 360
4x² - 118x+ 490 =0
Now we have a quadratic equation that we can solve using the quadratic formula or by factoring. Either way, we find that x = 24.5 or x = 5. Since x represents the width of the strip of flooring, x must be positive. Therefore, x = 5 is the solution.
So the width of the strip of flooring is 5 feet, and the dimensions of the rug are:
width: 25 - 2 × 5 = 15 feet
length: 34 - 2 × 5 = 21 feet
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(20 POINTS) The area of the right triangle shown below is 200 ft^2. The segment XY has a length of 10 ft. Find the length of the hypotenuse. Round to the tenths place if necessary. Show or explain your work. (20 POINTS)
The length of the hypotenuse is given as follows:
41.23 ft.
How to obtain the length of the hypotenuse?The area of a right triangle is given by half the multiplication of the two side lengths of the triangles.
The parameters are given as follows:
Side lengths of 10 and x.Area of 200 ft².Hence the side length x is given as follows:
0.5 x 10x = 200
5x = 200
x = 200/5
x = 40 ft.
Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:
h² = 10² + 40²
h = sqrt(10² + 40²)
h = 41.23 ft.
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A researcher found that for the years 2010 to 2018, the equation, y=-0.2(x-5)²+35, models the average gas mileage of new vehicles sold in Switzerland, where x is the number of years since 2010 and y is the average gas mileage, in miles per gallon (mpg).
During what year was the average gas mileage for new vehicles sold in Switzerland the greatest?
Please help me, I need help I didn't understand this!!!
The average gas mileage for new vehicles sold in Switzerland was the greatest in the year 2013.
How did we arrive at the answer?The equation models the average gas mileage of new vehicles sold in Switzerland as a parabolic function, y=-0.2(x-5)²+35.
To find the year in which the average gas mileage was the greatest, we need to find the vertex of this parabolic function.
The x-coordinate of the vertex is given by x = 5 + (-b/2a) = 5 - (-0.2/2(-0.2)) = 5 - (0.2/0.4) = 5 - 0.5 = 4.5 years since 2010, or the year 2013. The y-coordinate of the vertex can be found by substituting x = 4.5 years into the equation, y = -0.2(4.5-5)² + 35 = -0.2(0.5)² + 35 = 0.2 * 0.25 + 35 = 0.05 + 35 = 35.05 mpg.
So the average gas mileage for new vehicles sold in Switzerland was greatest in the year 2013, with a value of 35.05 mpg.
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A crew of painters are hired to paint a house. The cost of the pain is estimated to
be $250 and each of the (p) painters will get paid $15 per hour. If the crew of
painters will work a 7 hour day and the job is estimated to take (d) days.
12.)What is the equation to determine the cost of 1 painter per day
13.) What is the cost in dollars per day for painting if the are 5 painters working.
14.) Which expression will represent the total cost of painting the house for the
5 painters working?
a. C-250pd + 775
b.) C=250 + 525d
c. C=250(7)(15) (5)d
d. C= 7d + 285 +5
15.) What is the total cost of 5 painters working for 4 days?
12. The cost of 1 painter per day is
C = 15 * 7 hours
13. cost in dollars per day for painting if the are 5 painters working is $525
14. The expression will represent the total cost of painting the house for the 5 painters working is C = 250 + 525d
15. the total cost of 5 painters working for 4 days is $2350
How to solve for the cost12. The workers are to work for 7 hours in a day and the pay for each worker at 1 hour is 15 dollars.
The cost of 1 painter per day is
C = 15 * 7 hours
C = $105
13. If 1 person is 105 dollars, then 5 painters would be 105 * 5
= $525
14. The expression that would tell us the total cost of painting the house is cost of paint + cost of 5 painters * number of days
cost of paint = $250
cost of 5 painters = $525
hence
C=250 + 525d
15. The total cost of 5 workers in 4 days is
C=250 + 525 * 4
C = 250 + 2100
C = $2350
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x=2y in evryday words mean
In everyday words x = 2y means that twice of y makes x
What is multiplication by two?The general rule for solving all multiplication by two problems is to multiply the integer by two by adding the number to itself.
The order of your numbers doesn't matter while solving multiplication issues.
In the problem, x = 2y represents that twice of y is x
the inverse of this is half of x is y
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training the eccentric phase of plyometric movements with a new client will help them improve which of the following?
The eccentric phase of plyometric movements can help a new client improve power, agility, speed, balance, coordination, and stability.
The eccentric phase of plyometric movements can be an effective way to help a new client improve their overall performance. When training the eccentric phase, the client will be performing exercises that involve quickly stretching and contracting their muscles. This helps to increase power, agility, speed, balance, coordination, and stability. It also helps to reduce the risk of injury by strengthening the muscles and tendons around the joints. By training the eccentric phase of plyometric movements, the client will be able to improve muscular strength and endurance as well. Proper instruction and form should be explained and emphasized to ensure the client is performing the exercises safely and correctly. The client should also be encouraged to progress gradually as they become more comfortable with the exercises. With proper technique, consistent training, and progression, a new client can benefit greatly from training the eccentric phase of plyometric movements.
The complete question: Training the eccentric phase of plyometric movements with a new client will help them improve which of the following?
Select one:
a. Core stability
b. Power development
c. Landing mechanics
d. Force production
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5x (2x + 6) in its equivelant form
Answer:
[tex]10x {}^{2} + 30x[/tex]
||
2. Complete the steps for factoring 2x3 - 36x² + 162x by writing words, numbers,
or expressions in the blanks.
2x336x2 + 162x=
(x2-18x+81)
_2x [x²-2(____)x+ (__________)²]
=
11
(x-.
_)(x-____
_2=(x-_9_) ²
Factor out
Rewrite the trinomial.
Use the
pattern.
Simplify.
The complete factorization of the given expression is 2x³ - 36x² + 162x = 2x (x - 9)².
What is factorization?An algebraic expression is factorised when it is written as the product of its factors. These variables, factors, or algebraic expressions could be present. The breaking or decomposition of an entity (such as a number, a matrix, or a polynomial) into a product of another entity, or factors, whose multiplication results in the original number, matrix, etc., is known as factorization or factoring in mathematics.
The steps to factorize the given expression is:
2x³ - 36x² + 162x
= 2x (x² - 18x + 81) Factor out 2x.
= 2x (x² - 2(9)(x) + (9)²) Rewrite the trinomial.
= 2x (x - 9) (x - 9) Use the whole square formula.
= 2x (x - 9)² simplify.
Hence, the complete factorization of 2x³ - 36x² + 162x = 2x (x - 9)².
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there are 22 cherry trees in vince's orchard, and he wants to plant more. it takes him an hour to plant each tree. let h represent the number of hours vince spent planting and c represent the total number of cherry trees he will have. find the value of c when h
When h = 4, Vince will have 26 cherry trees in his orchard.
A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.
If it takes Vince an hour to plant each tree, and h represents the number of hours Vince spent planting, then the total number of cherry trees he will have is given by the equation:
c = 22 + h
So when h = 4, the value of c can be found by substituting h = 4 into the equation:
c = 22 + 4 = 26.
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How do you find the sample standard deviation when given the population standard deviation? What formula do you use? If you can make up an example that would be great.
The estimate of the population standard deviation will be the estimated sample standard deviation
You must use sample data when you don't have access to population data. Consider the following hypothetical research question: What is the standard deviation of student heights in Azerbaijan? All of the residents are Azerbaijani students. To gather data on every student in Azerbaijan might be impossible or expensive.
As a result, you measure the heights of 100 pupils who were chosen at random. You next figure out the sample standard deviation. Keep in mind that the lack of population statistics prevents you from calculating the population standard deviation.
In this case, your best estimate of the population standard deviation will be the estimated sample standard deviation.
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A country’s population in 1993 was 127 million
The population in 2008 is approximately 138 million.
To solve it, we will use the exponential growth formula:
P(t) = P0 *[tex]e^(rt)[/tex]
where
P(t) = population at time t
P0 = initial population (127 million)
e = natural logarithm base (approximately 2.71828)
r = rate of growth
t = number of years
To find the rate of growth, we can use the population in 2000 as a reference point.
P(7) = 132 million = P0 * [tex]e^(7r)[/tex]
Divide both sides by P0:
132 million / 127 million = [tex]e^(7r)[/tex]
Take the natural logarithm of both sides:
ln (132 million / 127 million) = 7r
Solve for r:
r = ln (132 million / 127 million) / 7
Now that we have the rate of growth, we can use it to estimate the population in 2008:
P(15) = 127 million * [tex]e^(15r)[/tex]
Plug in the value of r:
P(15) = 127 million * [tex]e^(15 * ln (132 million / 127 million) / 7)[/tex]
Using a calculator, the population in 2008 is approximately 138 million.
Round to the nearest million: 138 million.
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The correct question is:
A country's population in 1993 was 127 million. In 2000 it was 132 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million.
g decide whether or not the following are propositions. please also determine the truth value of all the propositions (if any):
1. "I am tired." Proposition: Yes, Truth Value: True
2. "7 + 8" Proposition: No, Truth Value: N/A
A proposition is a statement that is either true or false. In order to determine whether or not something is a proposition, we need to consider if the statement can be evaluated as true or false. For example, in the first statement, "I am tired," this is a proposition because it can be evaluated as true or false. It is true because the speaker is likely tired. In this case, the truth value of the proposition is true. In the second statement, "7 + 8," this is not a proposition because it cannot be evaluated as true or false. It is simply an arithmetic expression. Therefore, in this case, the truth value of the proposition is N/A.
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