The probability of selecting a pen from the first box is 1/8 (since there is only 1 pen out of 8 items in the box). The probability of selecting a crayon from the second box is 3/6 (since there are 3 crayons out of 6 items in the box).
To find the probability of both events happening together, we multiply the probabilities:
P(pen and crayon) = P(pen) x P(crayon)
P(pen and crayon) = (1/8) x (3/6)
Simplifying the fraction 3/6 to 1/2:
P(pen and crayon) = (1/8) x (1/2)
Multiplying the numerators and denominators:
P(pen and crayon) = 1/16
Therefore, the probability of selecting a pen from the first box and a crayon from the second box is 1/16.
Use formula to find the area of the figure(show the formula,work,and units)
Answer:
25
Step-by-step explanation:
Formula 1/2(B1+B2)H
1/2(10)5
1/2 x 10=5
5 x 5 =25
What is the value of x?
Triangle A B C is shown with its exterior angles. Line B A extends through point D. Line A B extends through point E. Line A C extends through point F.
Which angle’s measure is equal to the sum of the measures of ∠BAC and ∠BCA?
The measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.
What is the exterior angle?An exterior angle is an angle that forms a linear pair with an interior angle of a polygon. It is formed by extending one of the sides of the polygon. In other words, it is the angle formed between a side of a polygon and the extension of an adjacent side.
Based on the problem description, we can see that the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA. Therefore, we need to find the measure of the exterior angle at vertex A.
We know that the sum of the measures of the angles in a triangle is 180 degrees. So, we can find the measure of angle BAC by subtracting the measures of angles BCA and ABC from 180 degrees:
angle BAC = 180 - angle BCA - angle ABC
We can find the measure of angle ABC by subtracting the measure of angle A from 180 degrees:
angle ABC = 180 - angle A
Similarly, we can find the measure of angle BCA by subtracting the measure of angle C from 180 degrees:
angle BCA = 180 - angle C
Substituting these expressions into the equation for angle BAC, we get:
angle BAC = 180 - (180 - angle A) - (180 - angle C)
= angle A + angle C
Therefore, the measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.
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is there a relationship between attendance at religious services and alcohol consumption? a random sample of 1000 adults was asked whether they regularly attend religious services and whether they drink alcohol daily
The relationship of those who attend religious services regularly are less likely to consume alcohol regularly.
Yes, there can be a relationship between attendance at religious services and alcohol consumption. In the given random sample of 1000 adults, both their attendance at religious services and daily alcohol consumption were recorded.
To analyze the relationship, you can follow these steps:
1. Organize the data: Create a contingency table that displays the frequency of each combination of attendance at religious services and alcohol consumption.
2. Calculate percentages: Determine the percentage of adults who attend religious services and drink alcohol daily, as well as the percentages for the other categories (e.g., attend services and don't drink daily, don't attend services and drink daily, etc.).
3. Identify trends or patterns: Compare the percentages to see if there is a relationship between attendance at religious services and daily alcohol consumption.
For example,
If the percentage of adults who attend religious services and drink daily is significantly lower than the percentage of those who don't attend services and drink daily, this suggests a relationship.
4. Statistical testing: Perform a chi-square test to determine if the observed relationship is statistically significant.
This test compares the observed frequencies in the contingency table to the frequencies that would be expected if there was no relationship between attendance at religious services and alcohol consumption.
5. Interpret the results: If the chi-square test shows that the relationship is statistically significant, this supports the hypothesis that there is a relationship between attendance at religious services and alcohol consumption in the sample of 1000 adults.
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how do we check for normality of the sampling distribution of for a one sample z confidence interval for proportions? group of answer choices large sample size (n>30) no skewness or outliers in sample data n > 10 and n(1- ) > 10 n > 10 and n(1- ) > 10
To check the normality of the sampling distribution for a one-sample z confidence interval for proportions, the sample size should be large (typically n > 30), and the number of successes and failures in the sample should both be at least 10.
To check for normality of the sampling distribution for a one-sample z confidence interval for proportions, we need to ensure that the following conditions are met:
Large sample size: The sample size should be sufficiently large (typically n > 30). This is because the central limit theorem states that for large enough sample sizes, the sampling distribution of the sample proportion will be approximately normal, regardless of the underlying distribution of the population.
Success-Failure Condition: The number of successes (np) and failures (n(1-p)) in the sample should both be at least 10. This condition ensures that the binomial distribution of the sample proportion is approximately normal.
If these conditions are met, then we can assume that the sampling distribution of the sample proportion is approximately normal, and we can proceed to construct a one-sample z confidence interval for proportions.
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Which equation of a circle represents the picture?
A) (x)^2+(y)^2=10
B) (x-5)^2+(y-5)^2=25
C) (x)^2+(y^2)=25
D) (x+5)^2+(y+5)^2=10
Answer:
C) x² + y² = 25
Step-by-step explanation:
the center is (0, 0).
so, the generic circle equation
(x−h)² + (y−k)² = r². The center is (h, k) and the radius is r units.
for (h, k) = (0, 0) this gives us the equation above.
and r we can easily see as the distance from the center to one of the points on the circle arc. which is 5, as the coordinates tell us.
You've decided you want a plant for your room. At the gardening store, there are
4
44 different kinds of plants (tulip, fern, cactus, and ficus) and
4
44 different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).
If you randomly pick the plant and the pot, what is the probability that you won't get a clay pot or a cactus?
The probability of not getting a clay pot or a cactus when randomly picking a plant and a pot from a selection of 4 plants and 4 pots is 0.75 or 75%.
There are a total of 4 x 4 = 16 possible outcomes when randomly picking a plant and a pot. Out of these, we need to count the number of outcomes where we don't get a clay pot or a cactus.
Let's start by counting the number of outcomes where we get a clay pot or a cactus. There are 4 possible outcomes for the plant (cactus or one of the three other plants) and 1 possible outcome for the pot (clay pot). So there are 4 x 1 = 4 outcomes where we get a cactus or a clay pot.
Therefore, the number of outcomes where we don't get a cactus or a clay pot is:
16 - 4 = 12
So the probability of getting a plant and a pot where neither the plant is a cactus nor the pot is a clay pot is:
P = number of outcomes where we don't get a cactus or a clay pot / total number of outcomes
= 12 / 16
= 0.75
Therefore, the probability of not getting a clay pot or a cactus is 0.75 or 75%.
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the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?
The average speed of a falling object during the first 3 seconds of its fall is h(3)-h(0)/3.
The model of the motion of the body is given by, and the function of the motion of the body is given by h(t) = 300 - 16t².
The speed of object after 3 seconds is given by . The falling speed of object during the first 3 seconds of falling is calculated as follows, v = dh(t)/dt = -32t.
So now the average speed of the movement is calculated as follows,
v = h(3)-h(0)/3.
Option d is therefore the correct option.
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Complete question - the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?
A.) h(3) – h(0)
B.) h(3/3)-h(0/3)
C.) h(3)/3
D.) (h(3)-h(0))/3
In a cooking contest, the mean score for taste was 20, with a standard deviation of 2.8. One of the contestants received a score of 14. Convert this score to a z score and tell if it is “usual” or “unusual.”
To convert the score of 14 to a z-score, we use the formula:
z = (x - μ) / σ
where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Substituting the given values, we get:
z = (14 - 20) / 2.8
z = -2.14
The z-score of -2.14 indicates that the score of 14 is quite far from the mean of 20, which makes it an unusual score. To determine how unusual it is, we can compare the z-score to the standard normal distribution table.
The table shows that a z-score of -2.14 corresponds to a probability of approximately 0.016. This means that only about 1.6% of contestants would receive a score of 14 or lower in this cooking contest. Therefore, we can conclude that the score of 14 is unusual.
Suppose that y varies directly as the square root of x, and that y=43 when x=289 . What is y when x=191 ? Round your answer to two decimal places if necessary.
Please hurry i need it asap
Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).
Define about the direct variation?When two quantities, including such time and distance or hours and compensation, change directly, they do so at a predictable rate.
The constant of variation is another name for the constant rate of increase or decline. We will examine three different methods of showing direct variation in this lesson: an equation, a table, and just a graph.
For the given question:
y varies directly as the square root of x.
y ∝ √x
y = k√x
Here, k is the constant of proportionality
Now,
y=43 when x=289 .
43 = k√289
k = 43/√289
k = 2.53
Now, y when x=191.
y = k√x
y = 2.53√191
y = 34.96
Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).
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since the mid 1950s both men and women in the u.s. have experienced a steady in the proportion of the population never married. group of answer choices decline decrease increase none of these options are correct.
Since the mid 1950s, both men and women in the U.S. have experienced an increase in the proportion of the population never married. The correct answer is "increase".
This trend has been attributed to various factors such as the rise of individualism, changing gender roles, economic factors, and the decline of traditional social norms. In 1960, only 9% of women and 6% of men aged 25-34 had never been married, while in 2020, these numbers increased to 33% for women and 23% for men.
Therefore, it is evident that the proportion of the U.S. population never married has increased steadily over the past few decades
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Help me with this question please?
The interval over which the function f(x) increase is {∞, 1}.
The interval over which the function f(x) decrease is {1, ∞}.
The interval over which the function g(x) increase is {3, ∞}.
The interval over which the function g(x) decrease is {∞, 3}.
What is a decreasing function?For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.
By critically observing the graph of f(x), we can logically deduce that the function f(x) increases over the interval {∞, 1}. On the other hand, the function f(x) decreases over the interval {1, ∞}.
By critically observing the graph of g(x), we can logically deduce that the function f(x) increases over the interval {3, ∞}. On the other hand, the function f(x) decreases over the interval {∞, 3}.
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A bag with 8 marbles has 2 yellow marbles, 3 red marbles and 3 blue marbles. A marble is chosen from the bag at random. What is the probability that it is yellow? Write your answer as a fraction in simplest form.
The probability that it is yellow is 1/4.
What is probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: A bag with 8 marbles has 2 yellow marbles, 3 red marbles, and 3 blue marbles. A marble is chosen from the bag at random.
We have to find the probability that it is yellow.
the probability that it is yellow:
= 2/8
= 1/4
Hence, the probability that it is yellow is 1/4.
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Write an inequality for the following statement. a is less than or equal to 2
Answer: a ≤ 2
Step-by-step explanation:
How to write an inequality statement:
Step 1: Write the two values being compared in the problem.
Step 2: Determine whether the first value is larger or smaller than the second value.
Step 3: Express the inequality with the right symbols:
≤ = less than or equal to
≥ = greater than or equal to
Therefore, the answer would be a≤2.
Hope this helped!
ASAP PLEASE 25 POINTS YALL
find the 43th term for the sequence -19, -15, -11
The 43rd term of the sequence is 149.
What is arithmetic progression?Arithmetic progression is a sequence of numbers in which the difference between any two consecutive numbers is a constant value. The constant value is called a common difference.
Equation:We can see that the common difference between consecutive terms in the sequence is 4. So, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
To find the 43rd term, we plug in the values:
a1 = -19, d = 4, n = 43
an = -19 + (43 - 1)4
an = -19 + 42(4)
an = -19 + 168
an = 149
Therefore, the 43rd term of the sequence is 149.
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it is known that 5% of the books bound at a certain bindery have defective bindings. find the probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution.
Answer:
Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.
Step-by-step explanation:
We can use the Poisson approximation to the binomial distribution when n (the number of trials) is large and p (the probability of success) is small. In this case, n = 100 and p = 0.05, so np = 5, which is not too small. However, we can still use the approximation as long as we adjust for continuity, by adding and subtracting 0.5 from the number of successes we're interested in.
Let X be the number of books with defective bindings out of 100. We want to find the probability that X = 2. Using the Poisson approximation, we have:
λ = np = 5
P(X = 2) ≈ P(1.5 < Y < 2.5), where Y is a Poisson random variable with parameter λ
To find this probability, we can use the cumulative distribution function (CDF) of Y:
P(X = 2) ≈ P(1.5 < Y < 2.5) = F(2.5) - F(1.5), where F(x) is the CDF of Y evaluated at x
The CDF of a Poisson distribution with parameter λ is given by:
F(x) = e^(-λ) * Σ(λ^k / k!, k = 0 to floor(x))
where floor (x) is the greatest integer less than or equal to x. Using this formula, we can calculate:
F(1.5) = e^(-5) * Σ(5^k / k!, k = 0 to 1) ≈ 0.0337
F(2.5) = e^(-5) * Σ(5^k / k!, k = 0 to 2) ≈ 0.1247
Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.
The probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution is 0.0842.
Since the number of books bound, n = 100, is large and the probability of defective bindings, p = 0.05, is small, we can use the Poisson approximation to the binomial distribution.
The mean, µ, of the Poisson distribution is µ = np = 100 x 0.05 = 5.
The probability of 2 defective bindings can be calculated using the Poisson probability formula:
P(X = 2) = (e^-µ) * (µ^x) / x!
= (e^-5) * (5^2) / 2!
= 0.0842 (rounded to four decimal places)
Using the Poisson approximation to the binomial distribution, the likelihood that 2 of the 100 volumes bound by this bindery will have faulty bindings is roughly 0.0842.
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3 divided by 4.93 show how you got the answer please
Answer:
0.986
Step-by-step explanation:
4.93 ×100÷5×100 = 493÷500=0.986
PLEASE HELP!!
Fill in the table below.
Level
3
7
Toothpicks
Part D Extension
Sum of
Toothpicks
sxordinoni 10 # IRIOL
120
100
80
60
40
20
Number of Levels
What do you notice about the points being graphed?
Do they appear linear, quadratic or exponential?
Defend your choice.
The table of values when completed using y = 10x is a linear function
Completing the table of valuesFrom the question, we have the following parameters that can be used in our computation:
The incomplete table
When completed, we have
Levels Toothpicks
1 10
2 20
3 30
4 40
5 50
6 60
7 70
8 80
The means that
Toothpicks = 10 * Level
So, we have the equation to be
y = 10x
This is a linear function
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-8x+y=25 system of equations help
if f(x) = -x-11 ; find the following.
the fraction of f(9) and f(-6)
Answer:
f(x) = -x -11
= -9-11 = -20
f(x) = -x-11
= -6-11= -17
Step-by-step explanation:
7. Roberta and Eugene were trying to work out how
much charge there was stored in different electric
toothbrush batteries. They measured the current
flowing into toothbrush when it was switched on
and timed how long it took to run the batteries
down. The toothbrush required two batteries.
They repeated their experiment twice.
(Results in picture attached)
a) Circle the anomalous result in the table.
b) Calculate the mean average for each brand of
battery.
c) Calculate the amount of charge stored by each
brand of battery.
d) How would you present the results of this
experiment? Justify your answer.
Please help I have a test tmrw
a) The anomalous result in the table is the Durablast battery in the second trial, which recorded a time taken of 768 seconds.
b) The mean averages for each brand of battery are 955.33, 852 and 908 seconds.
c) the amount of charge stored by each brand of battery is 1098.6 coulombs, 1065 coulombs and 1089.6 coulombs.
d) The results of this experiment can be presented in a table format, showing the current flowing, the mean time taken, and the amount of charge stored for each brand of battery.
What is anomalous result?It is an unexpected or unusual outcome that does not agree with the expected or accepted outcome. It may be a result of a mistake, an anomaly in the data, or a misinterpretation of the data.
a) The anomalous result in the table is the Durablast battery in the second trial, which recorded a time taken of 768 seconds.
b) The mean averages for each brand of battery are:
Longalast: 955.33 seconds
Durablast: 852 seconds
Morelife: 908 seconds
c) The amount of charge stored by each brand of battery can be calculated by multiplying the current flowing into the toothbrush (amps) by the mean time taken (seconds) for each battery:
Longalast: 1.15 amps x 955.33 seconds = 1098.6 coulombs
Durablast: 1.25 amps x 852 seconds = 1065 coulombs
Morelife: 1.20 amps x 908 seconds = 1089.6 coulombs
d) The results of this experiment can be presented in a table format, showing the current flowing, the mean time taken, and the amount of charge stored for each brand of battery. This would allow the reader to easily compare the performance of each battery, as well as to identify any anomalous results.
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2. ? 0.13 6.02 ? what are the two numbers to fill the question marks?
The missing numbers to fill the question marks are 2.1 and 7.11
Completing the missing numbersTo solve the question, we need to look for a pattern or relationship between the given numbers. One way to approach this is to consider the decimal representation of each number.
If we look at the first number, 0.13, we can see that it has 2 digits after the decimal point.
The second number, 6.02, has 2 digits before the decimal point.
So, it's possible that the missing numbers also follow a pattern where one number has 2 digits before the decimal point, and the other has n digits after the decimal point.
Using the decimal points, one possible pattern is 2, 2.1, 0.13, 6.02, 7.11
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Identify the slope and y-intercept of the following equation:
y = 1/3x
Answer: Slope: 1/3
Y-intercept: 0 (since there is no constant term)
The dance team is making banners to advertise an upcoming performance. (Screenshot)
Answer:
[tex]6.45ft^{2}[/tex]
Step-by-step explanation:
Shawn makes 15 1/5% of free throw shots he attempts. That means on average he makes 15 1/5 shots for every 100 shots he attempts. About how many free throw shots does Shawn make out of 300 shots?
Answer: To find how many free throw shots Shawn makes out of 300 shots, we can first find how many he makes out of 100 shots, and then multiply by 3 to get the number of shots he makes out of 300.
If he makes 15 1/5 shots out of 100, we can convert this to a decimal by dividing 15 by 100 and adding 1/5, which is the same as adding 0.2. This gives:
15/100 + 1/5 = 0.15 + 0.2 = 0.35
So, on average, Shawn makes 35% of the free throw shots he attempts.
To find how many shots he makes out of 300, we can multiply this percentage by 300:
0.35 x 300 = 105
Therefore, Shawn makes about 105 free throw shots out of 300 shots.
Step-by-step explanation:
If radius of a cylinder is 1.2cm and the height is 4cm find the total volume and total surface area
The volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.
What is a cylinder?
One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry.
We are given that the radius of the cylinder is 1.2 cm and the height is 4 cm.
So,
⇒ Volume = π[tex]r^{2}[/tex]h
⇒ Volume = π * [tex](1.2)^{2}[/tex] * 4
⇒ Volume = 3.14 * 5.76
⇒ Volume = 18.0864 cubic cm
Similarly,
⇒ Total surface area = 2πrh + 2π[tex]r^{2}[/tex]
⇒ Total surface area = 2π * 1.2 * 4 + 2π[tex](1.2)^{2}[/tex]
⇒ Total surface area = 2π * 4.8 + 2π * 1.44
⇒ Total surface area = 2π * (4.8 + 1.44)
⇒ Total surface area = 2 * 3.14 * 6.24
⇒ Total surface area = 39.1872 square cm
Hence, the volume of the cylinder is 18.0864 cubic cm and the surface area of the cylinder is 39.1872 square cm.
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he difference between the value of the number increased by 20% and the value of the number decreased by 25% is 36. what is the number? (1 point) 720 80 7.2 0.8
The number described in the question, whose stated percentage difference is 36, is 80.
Let us represent the number as x. So, the increased number will be -
Increased number = x + 20%×x
Simplify percentage
Increases number = x + 0.2x
Add the digits
Increased number = 1.2x
Similarly, decreased number = x - 25%×x
Converting percentage
Decreased number = x - 0.25x
Subtract the digits
Decreased number = 0.75x
Representing the difference
1.2x - 0.75x = 36
Subtract
0.45x = 36
Divide
x = 80
Hence, the number is 80.
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Solve 32 ≤ −5z − 32. z ≤ 0 z ≥ 0 z ≤ −12.8 z ≥ −12.8
The solution to the inequality 32 ≤ −5z − 32 is z ≥ -12.8.
To solve for z in the inequality 32 ≤ -5z - 32, we first add 32 to both sides:
32 + 32 ≤ -5z
64 ≤ -5z
Then, we can divide both sides by -5, but we need to reverse the inequality since we are dividing by a negative number:
-5z ≤ 64
z ≥ -64/5
z ≥ -12.8
Therefore, the solution to the inequality is z ≥ -12.8.
Option (d) is correct: z ≥ -12.8.
The complete question is:
Solve 32 ≤ −5z − 32.
Answer choices:
a) z ≤ 0
b) z ≥ 0
c) z ≤ −12.8
d) z ≥ −12.8
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PLS HELP THIS PROGRAM IS UNNECESSARY
Answer: -32.00
Step-by-step explanation:
Answer:
A) -32.00
Step-by-step explanation:
-32.00 would be more debt than -25
Helping in the name of Jesus.
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
It would be true
Step-by-step explanation:
A linear pair is two angles that are adjacent and whose non-common sides form a straight line. If two angles are a linear pair, then it would be supplementary.
in july 2008, the united states had a population of approximately 302,000,000 people. how many americans were there in july 2009, if the estimated 2008 growth rate was 0.88%?
There were approximately 304,657,600 Americans in July 2009.
To find out how many Americans were there in July 2009, we'll use the given data in the student question:
Initial population (July 2008): 302,000,000 people
Growth rate (2008): 0.88%
Step 1: Convert the growth rate percentage to a decimal.
0.88% = 0.0088
Step 2: Calculate the population increase for 2009.
Increase = Initial population × Growth rate
Increase = 302,000,000 × 0.0088
Increase ≈ 2,657,600 people
Step 3: Add the population increase to the initial population to get the population in July 2009.
Population (July 2009) = Initial population + Increase
Population (July 2009) ≈ 302,000,000 + 2,657,600
Population (July 2009) ≈ 304,657,600 people.
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