This example using cluster sampling, how do we know whether these estimates are considered valid?
The estimates are not correct because we are to find the proportion and sample error of the given values. The proportion expresses the number of opposing votes to the total number of voters. Also, the sampling error follows the formula of [tex]SE = Z\sqrt{P(1 - P/n)}[/tex]
The right estimate to use
The exact formula used in the expression is quite different from the standard formula for calculating the standard error. We are supposed to find the root of the standard deviation but that is not the case as can be seen in the formula above.
So, the main issue with this formula is that the square root is not considered in the proportion formula used by the council, so it is not a valid estimate.
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If the mass of a proton is 1.67 × 10-24 gram, what is the mass of 2,000 protons?
Answer:
3.34 * 10^-21 g
Step-by-step explanation:
1.67*10^-24 * 2000 = 1.67 * 10^-24 * 2 *10^3 = 3.34 * 10^-21 g
Find the surface area of the prism.
A. 78 in2
B. 158 in2
C. 120 in2
D. 119 in2
Answer:
119in^2
Step-by-step explanation:
formula= 2(width×length+hight×length+hight×5
2×(5×8+3×8+3×5) = 119in^2
me movement o
Which choice shows (3+9) + 13 correctly rewritten using the associative property and then
correctly simplified?
O 13+(3+9) = 13 + 12 = 25
13+(9+ 3) = 13 + 12 = 25
O 3+ (91+3) = 3 +94 = 97
O 3+ (9+13) = 3 +22= 25
(3+9) + 13 correctly rewritten using the associative property and then correctly simplified is 13+(9+3) = 13 + 12 = 25.
1. Start with the expression (3+9) + 13.
2. According to the associative property of addition, we can group the numbers in any order without changing the result.
3. Rearrange the expression by grouping the numbers differently: (9+3) + 13.
4. Now simplify the grouped numbers: 9+3 = 12.
5. The expression becomes 12 + 13.
6. Finally, simplify the addition: 12 + 13 = 25.
Therefore, the correct rewritten expression using the associative property and the simplified result is 13+(9+3) = 13 + 12 = 25.
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(-14)+x=14[/tex] what is the answer
The equation (-14) + x = 14 is solved by adding 14 to both sides of the equation, resulting in x = 28. This means that 28 is the value of x that satisfies the equation and makes it true.
To solve the equation (-14) + x = 14, we need to isolate the variable x on one side of the equation. Let's go through the steps:
Step 1: Add 14 to both sides of the equation to eliminate the -14 on the left side.
(-14) + x + 14 = 14 + 14
x = 28
The solution to the equation (-14) + x = 14 is x = 28.
In this equation, we start with (-14) on the left side, and we want to determine the value of x that makes the equation true. To do that, we need to isolate x. By adding 14 to both sides of the equation, we cancel out the -14 on the left side, leaving us with just x. On the right side, 14 + 14 simplifies to 28.
Therefore, the solution to the equation is x = 28. This means that if we substitute 28 for x in the original equation, (-14) + 28 will indeed equal 14. Let's verify this:
(-14) + 28 = 14
14 = 14
The left side of the equation simplifies to 14, and the right side is also 14. Since both sides are equal, it confirms that x = 28 is the correct solution to the equation.
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what is the midpoint of 70 and 90
Answer:
80
Step-by-step explanation:
Just average the two numbers to get (70+90)/2 = 160/2 = 80
Answer:
Step-by-step explanation:
To find the midpoint between two numbers, you add them together and divide the sum by 2.
In this case, the midpoint between 70 and 90 would be:
(70 + 90) / 2 = 160 / 2 = 80.
Therefore, the midpoint between 70 and 90 is 80.
NO LINKS!! URGENT HELP PLEASE!!
Answer:
a. 5π cm
b. 144π in²
c. 6 ft
Step-by-step explanation:
a.
The circumference of a circle is given by:
Circumference pf circle= πd
where d is the diameter.
In this case, d = 5 cm,
Therefore, Circumference of circle = π*5=5π cm
b.
The area of a circle is given by:
Area of circle=πr²,
where r is the radius. In this case, the diameter is d = 24 in,
so, the radius is r = d/2 = 24/2=12in
Therefore, Area of circle=π*12²=144π in²
c.
The area of a circle is given by:
Area of circle=πr²,
where r is the radius. In this case, Area is 36π ft²
Now substituting value
36π=πr²
dividing both side by π, we get
36=r²
[tex]r=\sqrt{36}=6[/tex]
r=6 ft.
Therefore, Radius is 6 ft.
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct representations of the inequality –3(2x – 5) < 5(2 – x) are options 1 (x < 5) and 3 (–6x + 15 < 10 – 5x).
To determine the correct representations of the inequality –3(2x – 5) < 5(2 – x), let's simplify the expression and analyze the options:
First, we simplify the inequality:
–3(2x – 5) < 5(2 – x)
–6x + 15 < 10 – 5x
Now let's analyze the options:
x < 5: This option represents the solution to the inequality. It indicates that x must be less than 5 for the inequality to hold true.
–6x – 5 < 10 – x: This is not a correct representation of the inequality. The sign of the x-term on the right side of the inequality is incorrect.
–6x + 15 < 10 – 5x: This option represents the solution to the inequality. It correctly represents the simplified inequality we obtained earlier.
A number line from negative 3 to 3 in increments of 1, with an open circle at 5 and a bold line starting at 5 and pointing to the right: This representation does not accurately represent the solution to the inequality. The inequality is not satisfied at x = 5, so the circle should be closed.
A number line from negative 3 to 3 in increments of 1, with an open circle at negative 5 and a bold line starting at negative 5 and pointing to the left: This representation is not correct as it does not represent the solution to the inequality.
Therefore, choices 1 (x 5) and 3 (-6x + 15 10 - 5x) are the proper expressions of the inequality -3(2x - 5) 5(2 - x).
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Can you use the ASA postulate or the AAS theorem to prove the triangles are congruent
which of the following is equivalent to x^2 -5x +6
Hello!
x² - 5x + 6
= (x² - 2x) + (-3x + 6)
= x(x - 2) - 3(x - 2)
= (x - 2)(x - 3)
A building contractor is building a backyard playground and wishes to put down rubber mulch to provide safety from falls. The contractor wishes to put the mulch in a pit in the shape of a rectangular solid 24 feet long, 13 feet wide, and 6 inches deep.
a) Determine the volume, in cubic feet, of mulch the contractor will need.
b) If mulch costs 9$ per cubic foot, what will the cost of mulch be?
Answer:
A= 220.5ft
B= $2425.5
Step-by-step explanation:
A= 220.5ft
B= $2425.5
Pls help I need this answer now
Answer:
The correct answer is A. As x increases, the rate of change of f(x) exceeds the rate of change of g(x)
Step-by-step explanation:
A bacteria culture triples every 5 minutes. At 4:27 P.M. the population is . Determine what the population was 27 minutes earlier, at 4:00 P.M.
The population at 4:00 P.M., 27 minutes earlier, is[tex]3^3[/tex] times the initial population P.
To determine the population of a bacteria culture 27 minutes earlier, we need to calculate the population growth from 4:00 P.M. to 4:27 P.M. given that the bacteria culture triples every 5 minutes.
Let's break down the time period into intervals of 5 minutes:
From 4:00 P.M. to 4:05 P.M., the population triples once.
From 4:05 P.M. to 4:10 P.M., the population triples again.
From 4:10 P.M. to 4:15 P.M., the population triples for the third time.
From 4:15 P.M. to 4:20 P.M., the population triples for the fourth time.
From 4:20 P.M. to 4:25 P.M., the population triples for the fifth time.
From 4:25 P.M. to 4:27 P.M., the population undergoes partial growth.
Since the population triples every 5 minutes, we can express the population at 4:27 P.M. as 3^5 times the initial population at 4:00 P.M.
Let's denote the initial population at 4:00 P.M. as P. Then, the population at 4:27 P.M. is [tex]3^5[/tex] * P.
To find the population 27 minutes earlier, we need to reverse the growth from 4:27 P.M. to 4:00 P.M. Since the population triples every 5 minutes, we need to divide the population at 4:27 P.M. by [tex]3^{(27/5).[/tex]
Therefore, the population at 4:00 P.M., 27 minutes earlier, can be calculated as:
Population at 4:00 P.M. = (Population at 4:27 P.M.) / [tex]3^{(27/5)[/tex]
[tex]= (3^{5} * P) / 3^{(27/5)\\\\\\\\= 3^{(25/5)} * P\\= 3^5 * P / 3^2\\= 3^3 * P[/tex]
Hence, the population at 4:00 P.M., 27 minutes earlier, is 3^3 times the initial population P.
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According to the Committee for the Study of the American Electorate, the voter turnout in the 2004 presidential election was higher in all but four states than it was in the 2000 election. The four states with lower voter turnout are listed below.
According to the Committee for the Study of the American Electorate, the four states with lower voter turnout in the 2004 presidential election compared to the 2000 election were Arkansas, Hawaii, Maryland, and Tennessee.
In the 2004 presidential election, voter turnout increased in most states compared to the 2000 election. However, Arkansas, Hawaii, Maryland, and Tennessee experienced a decrease in voter participation. This means that fewer eligible voters in these states cast their ballots in the 2004 election compared to the previous one.
The reasons behind the lower voter turnout in these states could vary and might be influenced by factors such as changes in voter registration laws, campaign strategies, voter demographics, or the overall political climate in each state during that particular election cycle.
It is worth noting that while voter turnout increased in most states, overall voter participation in the United States has been historically lower compared to some other democracies.
Efforts to increase voter engagement and turnout, such as expanding access to voting and improving voter education, continue to be important in ensuring that more eligible citizens exercise their right to vote and have their voices heard in the democratic process.
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A simple random sample of size n is drawn from a normally distributed population, and the mean of the sample is (x with a line over it), while the standard deviation is s. What is the 99% confidence interval for the population mean? Use the table below to help you answer the question.
The 90% confidence interval for the population variance (σ^2) is approximately [7.19, 20.19].
To construct a 90% confidence interval for the population variance (σ^2), given a sample size of 20 and a sample variance (s^2) of 12.5, we need to utilize the chi-square distribution.
The formula for constructing a confidence interval for the population variance is:
[ (n - 1)s^2 / χ^2_upper, (n - 1)s^2 / χ^2_lower ]
Where n is the sample size, s^2 is the sample variance, χ^2_upper is the upper critical value from the chi-square distribution, and χ^2_lower is the lower critical value from the chi-square distribution.
For a 90% confidence interval, we need to find the critical values from the chi-square distribution that correspond to the upper and lower tails of 5% each (since the confidence level is divided equally into two tails).
(a) Degrees of freedom:
The degrees of freedom (df) for the chi-square distribution is equal to n - 1. In this case, n = 20, so df = 20 - 1 = 19.
(b) Chi-square critical values:
We need to find the upper and lower critical values from the chi-square distribution table for df = 19 and a significance level of 0.05/2 = 0.025 (for each tail).
From the chi-square distribution table or using a statistical software, the upper critical value for a significance level of 0.025 and df = 19 is approximately 32.852. Similarly, the lower critical value is also approximately 8.907.
(c) Confidence interval calculation:
Substituting the values into the formula, we can construct the confidence interval:
[ (n - 1)s^2 / χ^2_upper, (n - 1)s^2 / χ^2_lower ]
[ (20 - 1) * 12.5 / 32.852, (20 - 1) * 12.5 / 8.907 ]
[ 19 * 12.5 / 32.852, 19 * 12.5 / 8.907 ]
[ 7.19, 20.19 ]
Therefore, the [7.19, 20.19] is roughly inside the 90% confidence interval for the population variance (2).
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Question
A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample variance, s^2, is determined to be 12.5.Complete parts (a) through (c).Construct a 90% confidence interval for
σ2 if the sample size, n, is 20.
Answer:
B :3
Step-by-step explanation:
good luck <3
i need help!!!! does anyone know this..!!???
The period of oscillation is 3 seconds
What is period of oscillation?A Oscillation is the periodic change of a measure around a central value or between two or more states, usually in time.
The time taken for an oscillating particle to complete one cycle of oscillation is known as the Period of oscillating particle. It is measured in seconds
Oscillation can also be vibration or revolution or cycle.
Therefore, using the graph to determine the period. Then the wave particle made a complete oscillation at 3 second.
This means that the period of the particle is 3 seconds.
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A container holds 2 pounds of peanuts. How many ounces of peanuts are in the container? (1 pound = 16 ounces)
16 ounces
32 ounces
36 ounces
40 ounces '
PLEASEEE HELPPP
please help quickly
Which two values of x are roots of the polynomial below?
Answer:
A, C
Step-by-step explanation:
x² + 3x - 5 = 0
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{3^2 - 4(1)(-5)}}{2(1)} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{29}}{2} [/tex]
How to make 1001 from nine 9. Use can use 9 in any way
Using the given operations and nine 9s, you can make 1001.
How to make 1001 from nine 9. Use can use 9 in any wayTo make 1001 using nine 9s, you can use the following mathematical operations:
1. (9 + 9 + 9) * 9 * 9 - 9 - 9 - 9 = 1001
- Adding three 9s together: (9 + 9 + 9) = 27
- Multiplying the sum by two 9s: (27 * 9 * 9) = 2187
- Subtracting three 9s: (2187 - 9 - 9 - 9) = 2160
- Adding one 9: (2160 + 9) = 2169
- Adding 832 (which is (9 * 9 * 9 + 9 * 9 + 9)) to 2169: (2169 + 832) = 3001
- Subtracting two 9s: (3001 - 9 - 9) = 2983
- Adding nine 9s: (2983 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9 + 9) = 1001
Therefore, using the given operations and nine 9s, you can make 1001.
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In square $ABCD,$ $P$ is on $\overline{BC}$ such that $BP = 4$ and $PC = 1,$ and $Q$ is on $\overline{CD}$ such that $DQ = 4$ and $QC = 1.$ Find $\sin \angle PAQ.$
In triangle PAD, using the Pythagorean theorem, we find AD = 5√2. Given that ∠PAQ's opposite side is PQ, which equals 3, we have sin∠PAQ = PQ/AQ = √2/10.
Explanation:In square ABCD, we are given that points P and Q are on lines BC and CD respectively such that BP=4 and PC=1, DQ=4 and QC=1. Considering triangle PAD, it is a right triangle in the given square, and, using the Pythagorean theorem, we can find the hypotenuse AD as AD = √(5² + 5²) = 5√2. The same reasoning, AD = AQ.
Because ∠PAQ is the angle we are interested in finding the sine of, we know that sin∠PAQ = opposite/hypotenuse. In this case, the opposite side is PQ which we determine is 3 using the given distances (PC+QC). So, sin∠PAQ = PQ/AQ = 3/(5√2) = √2/10. Thus, the sine of angle PAQ is √2/10.
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i need help!!!! does anyone know this..!!???
The period of the frequency factor b that is given in the diagram above would be = 0.2 sec.
How to determine the period of the frequency factor b given above?The frequency of a water wave is defined as the number of times the wave completes a cycle within a given period of time. While the period is the time it takes for the completion of a cycle.
The dot the represents the frequency factor b is the green dot on the wave table. Therefore the period as traced from the graph= 0.2 sec.
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a 4-foot length of ribbon costs $1.32. how much will it cost to buy 10 yards of ribbon?
Answer:
$3.3
Step-by-step explanation:
4x = 1.32
x = 0.33$ / ft
10x = 10 * 0.33 = 3.3$
If f(x) = 16x2, what is the value of f(2.5)?
Answer:
f(2.5) = 100
Step-by-step explanation:
to evaluate f(2.5) substitute x = 2.5 into f(x)
f(2.5) = 16(2.5)² = 16 × 6.25 = 100
See Picture:
Given :
Prove :
Answer:
statmen there for this should me solved and abcd are proof
reason bcz this is not equal square
Find a function of the form or whose graph matches this one:
The function that matches the graph is of the form:
4cos((pi x)/7) + 1
Graphs of trigonometric functionsGraphs of trigonometric functions are graphs used in representing trigonometric functions.
From these graphs, some basic properties such as Amplitude, phase difference, period and vertical shift can be deduced.
From the given graph in the question, it can be seen that the graph crosses the y-axis at it's amplitude (highest point), so its easier to use the cosine relation.
To calculate the midline M:
Use the formula,
M = (maximum + minimum)/2
= (5 + -3)/2 = 2/2 = 1
Vertical shift: It can be seen from the graph that there is a vertical upward shift of 1 unit. C = 1
Amplitude: Maximum value - vertical shift is:
A = 5 - 1 = 4
Period = spacing between repeating patterns. There are 14 units between each peak (peak when x = -14, next peak when x = 0).
k = 2pi/Period;
So: k = 2pi/14 = pi/7
Therefore y = 4cos(pix/7) + 1 is the function that matches the given graph.
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Find the center and radius of the circle represented by the equation below.
Answer:
centre = (5, - 6 ) , radius = 7
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
given
x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )
x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )
x² - 10x + y² + 12y = - 12
using the method of completing the square
add ( half the coefficient of the x/ y terms )² to both sides
x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36
(x - 5)² + (y + 6)² = 49 = 7² ← in standard form
with centre (5, - 6 ) and radius = 7
Answer:
Center = (5, -6)
Radius = 7
Step-by-step explanation:
To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.
To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:
[tex]x^2-10x+y^2+12y=-12[/tex]
Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:
[tex]x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2[/tex]
Simplify:
[tex]x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2[/tex]
[tex]x^2-10x+25+y^2+12y+36=-12+25+36[/tex]
[tex]x^2-10x+25+y^2+12y+36=49[/tex]
Factor the perfect square trinomials on the left side:
[tex](x-5)^2+(y+6)^2=49[/tex]
The standard equation of a circle is:
[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]
where:
(h, k) is the center.r is the radius.Comparing this with the rewritten given equation, we get
[tex]h = 5[/tex][tex]k = -6[/tex][tex]r^2 = 49 \implies r=7[/tex]Therefore, the center of the circle is (5, -6) and its radius is r = 7.
Can some please help me I don’t understand this?
Please due tmr morning thanks!
The numbers to complete the pythagorean triple in the equation (n² - 1)² + k² = (n² + 1)² are B. 35 and 37
What is the pythagorean triple?A pythagorean triple is a set of 3 numbers that obey the pythagorean theorem.
Given the equation
(n² - 1)² + k² = (n² + 1)², we need to find the remaining numbers generated by the equation when k = 12. So, we proceed as follows/
Since we have the equation
(n² - 1)² + k² = (n² + 1)²
Subtracting (n² + 1)², from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = (n² + 1)² - (n² + 1)²
(n² - 1)² - (n² + 1)² + k² = 0
Now, subtracting k from both sides, we have that
(n² - 1)² - (n² + 1)² + k² = 0
(n² - 1)² - (n² + 1)² + k² - k² = 0 - k²
(n² - 1)² - (n² + 1)² + 0 = - k²
(n² - 1)² - (n² + 1)² = - k²
Using the difference of two squares a² - b² = (a + b)(a - b)
(n² - 1)² - (n² + 1)² = - k²
(n² - 1 + n² + 1)[n² - 1 - (n² + 1)] = - k²
(n² + n² - 1 + 1)[n² - n² - 1 - 1)] = - k²
(2n² + 0)[0 - 2)] = - k²
(2n²)(- 2) = - k²
-4n² = - k²
4n² = k²
n² = k²/4
Taking square root of both sides, we have that
n = √(k²/4)
n = k/2
Since k = 12, we have that
n = 12/2
n = 6
So, the first number is (n² - 1) = (6² - 1)
= 36 - 1
= 35
The second number is (n² + 1) = (6² + 1)
= 36 + 1
= 37
So, the numbers are B. 35 and 37
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complete the table of values for y=3/x
The table of values for the equation y = 3/x can be completed as follows:
x | y
1 | 3/1 = 3
2 | 3/2 = 1.5
3 | 3/3 = 1
4 | 3/4 = 0.75
5 | 3/5 = 0.6
To complete the table of values for the equation y = 3/x, we substitute different values of x into the equation and calculate the corresponding values of y.
When x = 1:
Substitute x = 1 into the equation: y = 3/1 = 3
So, when x = 1, y = 3.
When x = 2:
Substitute x = 2 into the equation: y = 3/2 = 1.5
So, when x = 2, y = 1.5.
When x = 3:
Substitute x = 3 into the equation: y = 3/3 = 1
So, when x = 3, y = 1.
When x = 4:
Substitute x = 4 into the equation: y = 3/4 = 0.75
So, when x = 4, y = 0.75.
When x = 5:
Substitute x = 5 into the equation: y = 3/5 = 0.6
So, when x = 5, y = 0.6.
By substituting different values of x into the equation y = 3/x, we can complete the table of values as shown above.
Hence, the completed table of values for y = 3/x is:
x | y
1 | 3
2 | 1.5
3 | 1
4 | 0.75
5 | 0.6
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Joint probability of independent events J and K is equal to
Select one:
a. P(J) * P(K) - P(J * K)
b. P(J)- P(K)
c. P(J) * P(K)
d. P(J) * P(K) + P(J-K)
e. P(J) + P(K)
Note: Answer A is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
The joint probability is found by multiplying the probability of event J by the probability of event K P(J and K) = P(J) * P(K) Option C.
When two events J and K are independent, it means that the occurrence or non-occurrence of one event does not affect the probability of the other event. In other words, the probability of event J happening is completely unrelated to the probability of event K happening.
The joint probability of two independent events J and K is the probability that both events J and K occur simultaneously. Since the events are independent, the probability of their intersection is equal to the product of their individual probabilities.
The joint probability is found by multiplying the probability of event J by the probability of event K.
This formula holds true for independent events because there is no interaction or dependency between the events. Each event has its own probability, and when they occur together, the joint probability is simply the product of their individual probabilities. Option C is correct.
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Suppose you have entered a 48-mile biathlon that consists of a run and a bicycle race. During your run, your average
velocity is 5 miles per hour, and during your bicycle race, your average velocity is 23 miles per hour. You finish the race
in 6 hours. What is the distance of the run? What is the distance of the bicycle race?
The distance of the run is miles.
The distance of the bicycle race is approximately 24.61 miles.
Let's assume the distance of the run is 'x' miles and the distance of the bicycle race is 'y' miles.
We know that average velocity is equal to the total distance divided by the total time taken.
We can use this information to form two equations based on the given average velocities and total time.
For the run:
Average velocity = Distance of the run / Time taken for the run
5 mph = x miles / T hours ---(Equation 1)
For the bicycle race:
Average velocity = Distance of the bicycle race / Time taken for the bicycle race
23 mph = y miles / (6 - T) hours ---(Equation 2)
Since the total time for the race is 6 hours, we can substitute (6 - T) for the time taken during the bicycle race.
Now, we can solve these equations simultaneously to find the values of 'x' and 'y'.
From Equation 1, we have:
5T = x
From Equation 2, we have:
23(6 - T) = y
Now, we substitute the value of 'x' in terms of 'T' from Equation 1 into Equation 2:
23(6 - T) = 5T
138 - 23T = 5T
138 = 28T
T = 138 / 28
T ≈ 4.93 hours
Substituting this value back into Equation 1, we can find 'x':
5(4.93) = x
x ≈ 24.65 miles
Therefore, the distance of the run is approximately 24.65 miles.
To find the distance of the bicycle race, we substitute the value of 'T' back into Equation 2:
23(6 - 4.93) = y
23(1.07) = y
y ≈ 24.61 miles
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