Answer:
population in 2003 is 234 million.
Step-by-step explanation:
A country's population in 1991 was 231 million
In 1999 it was 233 million.
We have to calculate the population in 2003.
Since population growth is always represented by exponential function.
It is represented by [tex]P(t)=P_{0}e^{kt}[/tex]
Here t is time in years, k is the growth constant, and is initial population.
For year 1991 ⇒
233 = [tex]P_{0}e^{8k}[/tex] = 231 [tex]e^{8k}[/tex]
[tex]\frac{231}{233}= e^{8k}[/tex]
Taking ln on both the sides ⇒
[tex]ln(\frac{233}{231})=lne^{8k}[/tex]
ln 233 - ln 231 = 8k [since ln e = 1 ]
5.451 - 5.4424 = 8k
k = [tex]\frac{0.0086}{8}=0.001075[/tex]
For year 2003 ⇒
[tex]P(t)=P_{0}e^{kt}[/tex]
P (t) = 231 × [tex]e^{(0.001075)(12)}[/tex]
= 231 × [tex]e^{0.0129}[/tex]
= 231 × 1.0129
= 233.9 ≈ 234 million
Therefore, population in 2003 is 234 million.
Sixty-five percent of men consider themselves knowledgeable football fans. if 12 men are randomly selected, find the probability that exactly four of them will consider themselves knowledgeable fans.
Answer:
P(x)= 0.0198
Step-by-step explanation:
Given : 65% men are knowledgeable football fans, 12 are randomly selected ,
To find : Probability that exactly four of them will consider themselves knowledgeable fans.
Solution : Let P is the success rate = 65% = 0.65
Let Q is the failure rate = 100-65= 35%= 0.35
Let n be the total number of fans selected = 12
Let r be the probability of getting exactly four = 4
Formula used : The binomial probability
[tex]P(x)= \frac{n!}{(n-r)!r!}P^rQ^{n-r}[/tex]
putting values in the formula we get ,
[tex]P(x)= \frac{12!}{(12-4)!4!}(0.65)^4(0.35)^{12-4}[/tex]
[tex]P(x)= (495)(0.1785)(o.ooo22 )[/tex]
P(x)= 0.0198
The probability that exactly four out of the twelve randomly selected men will consider themselves knowledgeable football fans is approximately 0.236 or 23.6%.
Step 1: Model Selection (Binomial Distribution)
This scenario can be modeled using the binomial distribution if the following conditions are met:
Fixed number of trials (n): In this case, we have a fixed number of men being selected (n = 12).Binary outcome: Each man can be classified into two categories: either a "knowledgeable fan" (success) or a "not knowledgeable fan" (failure).Independent trials: The knowledge level of one man doesn't affect the selection of another.Constant probability (p): The probability (p) of a man being a knowledgeable fan remains constant throughout the random selection (given as 65%).Since these conditions seem reasonable, the binomial distribution is a suitable model for this scenario.
Step 2: Formula and Values
The probability (P(x)) of exactly x successes (knowledgeable fans) in n trials (men selected) with probability p of success (knowledgeable fan) can be calculated using the binomial probability formula:
P(x) = nCx * p^x * (1 - p)^(n-x)
where:
n = number of trials (12 men)x = number of successes (4 knowledgeable fans - what we're interested in)p = probability of success (knowledgeable fan - 65% converted to decimal: 0.65)(1 - p) = probability of failure (not knowledgeable fan)Step 3: Apply the Formula
We are interested in the probability of exactly 4 men being knowledgeable fans (x = 4). Substitute the known values into the formula:P(4) = 12C4 * 0.65 ^ 4 * (1 - 0.65) ^ (12 - 4)Step 4: Calculate Using Calculator or Software
While it's possible to calculate 12C4 (combinations of 12 choosing 4) by hand, using a calculator or statistical software is often easier.12C4 = 495 (combinations of 12 elements taken 4 at a time)Step 5: Complete the Calculation
Now you have all the values to complete the calculation:P(4) = 495 * 0.65 ^ 4 * (1 - 0.65) ^ 8Using a calculator or software, evaluate the expression. You'll get an answer around 0.236.Find the slope in line perpendicular x-y=16
The three sides of a triangle are consecutive odd integers. If the perimeter of the triangle is 39 inches find the lengths of the sides of the triangle
Approximately 7% of people are left-handed. if two people are selected at random, what is the probability of p(one is right-handed and the other is left-handed)
The required probability that one is right-handed and the other is left-handed is 217/1650.
Given that,
Approximately 7% of people are left-handed. if two people are selected at random, what is the probability of p(one is right-handed and the other is left-handed) is to be determined.
What is probability?
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
Total number of left-handed people out of 100 = 7
Total number of right-handed people out of 100 = 100 - 7 = 93
Now,
Probability of picking 2 person(one is right-handed and the other is left-handed) = 7 / 100 (93/99) = 217/1650.
Thus, the required probability that one is right-handed and the other is left-handed is 217/1650.
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what is the product? 3x^5 (2x^2+4x+1)
Answer:
The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex] is [tex]6x^7+12x^6+3x^5[/tex]
Step-by-step explanation:
Given: Polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
We have to find the product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
Consider the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex]
Apply distributive rule, [tex]a(b+c)=ab+ac[/tex]
Multiply [tex]3x^5[/tex] with each term in brackets, we have,
[tex]=3x^5\cdot \:2x^2+3x^5\cdot \:4x+3x^5\cdot \:1[/tex]
[tex]=3\cdot \:2x^5x^2+3\cdot \:4x^5x+3\cdot \:1\cdot \:x^5[/tex]
Apply exponent rule, [tex]a^b\cdot \:a^c=a^{b+c}[/tex]
Simplify, we have,
[tex]=6x^7+12x^6+3x^5[/tex]
Thus, The product of the given polynomial [tex]3x^5(2 x^2+4x+1)[/tex] is [tex]6x^7+12x^6+3x^5[/tex]
find the area of triangle QRS.
Answer: 140 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\ and\ (x_3,y_3)[/tex] is given by
[tex]\text{Area}=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2][/tex]
Then area of triangle QRS with vertices (6,10), (2,-10) and (-9,5) is given by :-
[tex]\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-10-5)+2(5-10)-9(10-(-10))]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[6(-15)+2(-5)+-9(20)]|\\\\\Rightarrow\text{Area}=|\frac{1}{2}[280]|\\\\\Rightarrow\text{Area}=140\text{ square units}[/tex]
Answer:
the answer is 140. I did the assignment
9log9(4) =
A. 3
B. 4
C. 9
D. 81
Rectangle R has varying length l and width w but a constant perimeter of 4 ft. A. Express the area A as a function of l. What do you know about this function? B. For what values of l and w will the area of R be greatest? Give an algebraic argument. Give a geometric arguement.
Factor the expression
4b^2+28b+49
Which graph represents the solution to the system of inequalities? x + y ≥ 4 2x + 3y < 12
Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
What is the length of segment QM'?
Answer: 6 units
Step-by-step explanation:
Given: Line segment LM is dilated to create L'M' using point Q as the center of dilation and a scale factor of 2.
Since in dilation , to calculate the distance of a point on image from center point we need to multiply scale factor to the distance of corresponding point on pre-image from center point .
Thus we have,
[tex]QM'=2\times QM\\\\\Rightarrow QM'=2\times3\\\\\Rightarrow QM'=6[/tex]
Hence, the length of segment QM' = 6 units.
Answer:
6 units
Step-by-step explanation:
find the point on the terminal side of θ = negative three pi divided by four that has an x coordinate of negative 1
The point on the terminal side is (1,-1) and this can be determined by using the trigonometric functions.
Given :
The point on the terminal side of θ = negative three [tex]\pi[/tex] divided by four that has an x coordinate of negative 1.
The following steps can be used in order to determine the point on the terminal side:
Step 1 - Write the given expression.
[tex]\theta = -\dfrac{3\pi}{4}[/tex]
Step 2 - The value of the trigonometric function is given by:
[tex]\rm tan \dfrac{3\pi}{4} =-1[/tex]
Step 3 - The trigonometric function can also be written as:
[tex]\rm tan \theta=\dfrac{y}{x}=-1[/tex]
Step 4 - Substitute the value of 'x' in the above expression.
y = -1
So, the point on the terminal side is (1,-1).
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To answer that question
Determine the value of a so that the line whose equation is ax+y-4=0 is perpendicular to the line containing the points (2,-5) and (-3,2)
When simplified, the expression (x ^1/8) (x^3/8) is 12. Which is a possible value of x?
Find the slopes of the asymptotes of the hyperbola with the following equation.
36 = 9x ^{2} - 4y^{2}
The given equation is a hyperbola, and by converting it to standard form we find a = 2 and b = 3. Therefore, the slopes of the asymptotes are ±3/2.
Explanation:The equation given is in the form of a hyperbola equation which could be written as [tex]x^2/a^2 - y^2/b^2 = 1.[/tex] This suggests that the transverse axis is horizontal meaning the hyperbola opens to the left and right. The slopes of the asymptotes for hyperbola is given by ±b/a.
First, we need to rewrite our equation in standard form. The equation given is [tex]36 = 9x^{2} - 4y^{2}.[/tex] To convert it into the standard form, we divide whole equation by 36 to isolate 1 on one side. This yields [tex](x^2/4) - (y^2/9) = 1.[/tex] Now, it is in the standard form of hyperbola.
By comparing it with the standard equation, we see that [tex]a^2 = 4 \ and\ b^2 = 9[/tex]which gives a = 2 and b = 3. Based on these, we can now find the slope of the asymptotes which is ±b/a = ±3/2.
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determine which of the following logarithms is condensed correctly
rationalize the denominator. write it in simplest terms
3
------
√12x
What is the value of X that makes the given equation true? 4x-16=6(3+x)
How many radians are contained in the angle AOT in the figure? Round your answer to three decimal places.
A. 0.459 radian
B. 2.178 radians
C. 1.047 radians
D. 0.955 radian
Answer:
Option C. 1.047 radians
Step-by-step explanation:
We have to find the measure of angle AOT in radians.
To convert measure of an angle from degree to radians we use the formula
[tex]\text{radians}=\frac{\pi(\text{degrees})}{180}[/tex]
= [tex]\frac{\pi(60)}{180}=\frac{\pi }{3}[/tex]
(Since measure of angle AOT is 60°)
= [tex]\frac{3.14}{3}[/tex] (since π = 3.14)
= 1.047 radians
Therefore, option C. 1.047 radians is the correct option.
06.01 LC)
Four graphs are shown below:
Which graph represents a positive nonlinear association between x and y?
Graph A
Graph B
Graph C
Graph D
Answer:
d
Step-by-step explanation:
a tower casts a 450 ft shadow at the same time that a 4 ft child casts a 6 ft shadow. Write and solve a proportion to find the height of a tower
Answer:
[tex]x=300[/tex]
Step-by-step explanation:
Set up the proportion;
[tex]\frac{x}{450} =\frac{4}{6}[/tex]
then cross multiply;
[tex]6x=450[/tex] · [tex]4[/tex]
[tex]6x=1800[/tex]
[tex]x=\frac{1800}{6} =300[/tex]
[tex]x=300[/tex]
Find all solutions in the interval [0, 2π).
sin^2 x + sin x = 0
A rectangular picture frame measures 4.0 inches by 5.5 inches. To cover
the picture inside the frame with glass costs $0.99 per square inch.
What will be the cost of the glass to cover the picture?
area = 4 x 5.5 = 22 square inches
cost is 0.99 per sq. inch
22 * 0.99 = 21.78
cost is $21.98
To find the cost of the glass for a 4.0 inch by 5.5 inch picture frame, calculate the frame's area and multiply it by the cost per square inch. The glass would cost $21.78.
To calculate the cost of the glass needed to cover the picture, you first need to determine the area of the glass required. The frame measures 4.0 inches by 5.5 inches, so the area can be found using the formula for the area of a rectangle, which is length multiplied by width.
The area is therefore 4.0 inches × 5.5 inches = 22.0 square inches. With the cost of glass being $0.99 per square inch, the total cost can be calculated by multiplying the area of the glass by the cost per square inch:
Total cost = 22.0 square inches × $0.99/square inch = $21.78.
Therefore, the cost of the glass to cover the picture would be $21.78.
Solve the inequality.
The figures in each pair are similar. Find the value of each variable. Show your work.
x - 2(x + 10) = 12 what's x
Write a segment addition problem using three points that asks the student to solve for x but has a solution x = 20
The segment addition problem was given below which gives the value of x as 20.
Segment addition problem:
Consider three points on a line: A, B, and C. Point B is located between points A and C.
The lengths of the line segments are as follows:
Length of segment AB: 12
Length of segment BC: x
Length of segment AC: 32
Find the value of x.
We have the equation for segment addition: AB + BC = AC
Substitute the given values:
12 + x = 32
Now, solve for x:
x = 32 - 12
x = 20
Therefore, the value of x is indeed 20, and the lengths of the segments satisfy the segment addition property.
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To construct a segment addition problem with a solution of x = 20, use three collinear points A, B, and C and set AB = x and BC = 20 - x, with the entire segment AC being 20 units. Solving the equation x + (20 - x) = 20 confirms that x = 20 is the solution.
Explanation:To write a segment addition problem that solves for x where the solution is x = 20, let’s use three collinear points A, B, and C with point B between A and C. We can then express the lengths of segments AB and BC in terms of x. For instance, if AB is x units long and BC is 20 - x units long, the total length of AC would be 20 units. We can write an equation based on this:
AB + BC = AC
x + (20 - x) = 20
By simplifying, x cancels out on the left-hand side, leaving 20 = 20, which is true for x = 20. Therefore, this is a valid segment addition problem where solving for x yields 20 as the solution.
Here is the step-by-step problem phrased as a question:
Let points A, B, and C be collinear with B between A and C.If AB = x and BC = 20 - x, and AC = 20, find the value of x.Probability theory predicts that there is a 44% chance of a water polo team winning any particular match. If the water polo team playing 2 matches is simulated 10,000 times, in about how many of the simulations would you expect them to win exactly one match?
Tim bought a soft drink for 2 dollars and 5 candy bars. He spent a total of 22 dollars. How much did the candy bar costs?