A television station would like to measure the ability of its weather forecaster. Past data have been collected that indicate the following:
Probability of sunshine on sunny days is 0.8
Probability of sunshine on rainy days is 0.4
Probability of a sunny day is 0.6
Find the probability of
(I)sunshine
(II)sunny given that the forecaster has predicted sunshine
Final answer:
The probability of sunshine on any given day is 0.64, and the probability that it is sunny given that sunshine has been forecasted is 0.75.
Explanation:
To address the question, we'll first define the given probabilities:
Probability of sunshine on sunny days (P(S|Sunny)) = 0.8Probability of sunshine on rainy days (P(S|Rainy)) = 0.4Probability of a sunny day (P(Sunny)) = 0.6Probability of a rainy day is the complement of a sunny day (P(Rainy)) = 0.4, since P(Sunny) + P(Rainy) = 1
Part I: Finding the probability of sunshine
To find the overall probability of sunshine, we use the law of total probability:
P(S) = P(S|Sunny) × P(Sunny) + P(S|Rainy) × P(Rainy)P(S) = 0.8 × 0.6 + 0.4 × 0.4 = 0.48 + 0.16 = 0.64Part II: Finding the probability of sunny given sunshine
To find the probability of sunny given that the forecaster has predicted sunshine, we use Bayes' theorem:
P(Sunny|S) = [P(S|Sunny) × P(Sunny)] / P(S) = (0.8 × 0.6) / 0.64 = 0.48 / 0.64 = 0.75X+y/3 =5 solve for (x)
angle LMP and angle PMN are complementary. Find the value of x.
A. 22.5
B. 7.5
C. 15
D. 30
The last step in a proof contains the
Use the properties of logarithmic functions to simplify the expression on the left side of the equation and determine the values of x and y. Then evaluate the simplified expression. The value of x is , and the value of y is. The value of the expression, rounded to nearest hundredth, is .
To simplify the equation using logarithmic functions, take the natural logarithm of both sides and use properties of logarithms to solve for x and y. Then substitute the values in the simplified expression to evaluate it.
Explanation:To simplify the expression on the left side of the equation using the properties of logarithmic functions, let's work step by step:
Take the natural logarithm (ln) of both sides of the equation. The natural logarithm cancels the exponential function.The natural logarithm of 5.6/16.0 is -1.050.Now, we have the equation ln(x) - ln(2y) = -1.050.Using the property of logarithms, subtracting the logarithms of two numbers is equivalent to dividing the numbers. So we have ln(x/2y) = -1.050.To find the value of x/2y, take the inverse natural logarithm (e^) of both sides.So we have x/2y = e^(-1.050).To solve for x, multiply both sides of the equation by 2y.Therefore, x = 2y * e^(-1.050).Once you have the values for x and y, substitute them into the simplified expression to find its value.Which of the following is the correct expanded form for the series below?
A. 1+1+1/2+1/6
B.1+1/2+1/6+1/24
C.1+2/3+1/2+2/5
D.4+2+2/3+1/6
Answer: Option A is correct that is [tex]1 +1+\frac{1}{2} +\frac{1}{6}[/tex]
Explanation:
we will substitute the values of n in given expression
[tex]\sum_{n=1}^{4}\frac{n}{n!}[/tex]
when substituting n=1 we get in [tex]\sum_{n=1}^{4}\frac{n}{n!}[/tex]=[tex]\frac{1}{1!}[/tex]
when n=2 we get [tex]\frac{2}{2!}[/tex]
when n =3 we get [tex]\frac{3}{3!}=\frac{3}{6}=\frac{1}{2}[/tex] ;3 factorial that is 3! = 3 *2*1 = 6
when n=4 we get [tex]\frac{4}{4!}=\frac{4}{24}=\frac{1}{6}[/tex];4! = 4*3*2*1 = 24
Note: factorial means the product of the terms getting multiplied till 1
suppose n! will be equal to n(n-1)(n-2)(n-3).......1
The correct expanded form for the series is Option B, which represents the sum of inverse factorials up to 1/3! The other options do not accurately depict the factorial series.
Explanation:The correct expanded form for the series given would be the option that correctly represents the sum of the factorial terms in the sequence. The series in the choices seems to depict a sum of inverse factorials. Factorials are mathematical expressions that involve multiplying a series of descending natural numbers. The factorial of a number n is represented as n! and is equal to n × (n-1) × (n-2) × … × 1. Therefore, 0! and 1! are both equal to 1, while 2! is equal to 2, 3! equals 6, and 4! equals 24, and so on.
By applying this logic to the options:
Option A is incorrect because 1/6 is equivalent to 1/3! not 1/4!.Option B, 1 + 1/2 + 1/6 + 1/24, correctly represents the sum 1/0! + 1/1! + 1/2! + 1/3!.Option C is incorrect as the sequence of numbers does not represent factorials.Option D is incorrect because the numbers do not follow the pattern of the inverse factorial sequence.Therefore, the correct answer is Option B.
Alice wants to buy some paper towels. She has two options. She can either buy a package of four rolls or she can buy one roll now and buy another when she runs out. Which of these options is better? Give reasons for your answer.
Answer:
Correct Answer: Alice should buy the package of four paper towels because buying in bulk means she gets each roll of towels for less money.
Step-by-step explanation:
a lab researcher wants to find out whether mice will run through a maze quicker during the day or at night, after training. Describe what is being measured in this experiment and what variable is being manipulated?
A normal curve is ___________ about the mean. consequently, 50% of the total area under a normal distribution curve lies on the left side of the mean, and 50% lies on the right side of the mean.
At maximum speed, an airplane travels 2460 miles against the wind in 6 hours. Flying with the wind, the plane can travel the same distance in 5 hours.
Let x the maximum speed of the plane and y be the speed of the wind. What is the speed of the plane with no wind?
The speed of the plane with no wind is 451 miles per hour.
Explanation:Let's solve this problem step-by-step:
We are given that the airplane travels 2460 miles against the wind in 6 hours at maximum speed. This means that the speed of the airplane relative to the ground is its maximum speed minus the speed of the wind. So, the equation is: x - y = 2460/6 or x - y = 410 (where x is the maximum speed of the plane and y is the speed of the wind). We are also given that the airplane can travel the same distance with the wind in 5 hours. This means that the speed of the airplane relative to the ground is its maximum speed plus the speed of the wind. So, the equation is: x + y = 2460/5 or x + y = 492. To find the speed of the plane with no wind, we can add the two equations: (x - y) + (x + y) = 410 + 492. This simplifies to: 2x = 902. Dividing both sides by 2, we get: x = 451. Therefore, the speed of the plane with no wind is 451 miles per hour.
True or false? in order to inscribe a circle in a triangle, the circle's center must be placed at the circumcenter of the triangle
Answer:
False.Step-by-step explanation:
A inscribe circle in a triangle means to draw the biggest circle possible inside such triangle. To do that perfectly, we first have to find the incenter of the circle, which is the intersection of all three internal bisector of the triangle, that point is the center of the inscribed circle.
Therefore, the statement is false.
In addition, a circumcenter allow to perfectly draw a circumscribed circle, which is outside the triangle, which is not the case here.
An image showing the inscribed circle is attached.
Answer:
false
Step-by-step explanation:
What is the solution of y − 4x = 0 and 3x + 6y = 9?
Who can help me with that one please ? Thanks!
The average of six numbers is 4. a seventh number is added and the new average is 5. what is the seventh number?
According to the question, the seventh number is 11.
Use the concept of average defined as:
Average, also known as the mean, is a statistical measure that represents the central value of a set of numbers. It is calculated by summing up all the numbers in the set and dividing the sum by the total count of numbers.
To find the seventh number,
If the average of six numbers is 4, then the total sum of those six numbers would be 6 multiplied by 4, which is 24.
Assume the seventh number is 'x'.
If the new average (after adding the seventh number) is 5, then the total sum of all seven numbers would be 7 multiplied by 5, which is 35.
To find the seventh number 'x',
Subtract the sum of the initial six numbers (24) from the sum of all seven numbers (35).
This gives us 35 - 24 = 11.
Hence,
The seventh number is 11.
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A city’s annual rainfall totals are normally distributed, and the probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668. If the standard deviation of the city’s yearly rainfall totals is 1.8 inches, what is the city’s mean annual rainfall?
Answer: 40.5 inches
Step-by-step explanation:
Given: A city’s annual rainfall totals are normally distributed.
The probability that the city gets more than 43.2 inches of rain in a year is given by P(z≥1.5)=0.0668
Thus, X=43.2 inches
z=1.5
Standard deviation [tex]\sigma[/tex]=1.8 inches
We know that [tex]z=\frac{X-\mu}{\sigma}[/tex]
[tex]\Rightarrow\mu=X-z\sigma\\\Rightarrow\mu=43.2-1.5\times1.8\\\Rightarrow\mu=43.2-2.7\\\Rightarrow\mu=40.5\ inches[/tex]
Hence, the city’s mean annual rainfall is 40.5 inches.
PLEASE HELP!!! IMAGE ATTACHED FIND THE AREA OF THE FIGURE ABOVE
Answer:
231in
Step-by-step explanation:
The original price of a couch is $650. It is on sale for $546. What is the percent change in the price off the couch?
The probability that an american industry will locate in shanghai, china, is 0.7, the probability that it will locate in beijing, china, is 0.4, and the probability that it will locate in either shanghai or beijing or both is 0.8. what is the probability that the industry will locate
Two numbers have a sum of 30 and a product of 209. what is the positive difference between them?
y + x = 30
xy = 209
y = 30 -x
x(30-x) = 209
30x - x^2 = 209
x^2 - 30x + 209 = 0
x = 19
y = 11
the difference is 19-11 = 8
The numbers are 11 and 19.
Given to us,Sum of the two numbers = 30,Product of the two numbers = 209,AssumptionLet's assume that the first number be a and the second is b.
equation 1,a + b = 30
equation 2,ab = 209
Therefore, in equation 1,
[tex]a\times b = 209\\b= \dfrac{209}{a}[/tex]
substitute the value of b in equation 1,
[tex]a+b=30\\\\a+\dfrac{209}{a}=30\\\\\dfrac{a^2+209}{a} =30\\\\a^2 +209 = 30a\\a^2-30a +209 = 0[/tex]
[tex]a^2 -30a+209= 0\\a^2 -19a-11a+209= 0\\a(a-19)-11(a-19)=0\\(a-11)(a-19)=0[/tex]
Substituting the factor against 0,
[tex](a-11) = 0\\a = 11\\\\(a-19)=0\\a = 19[/tex]
Therefore, the numbers are 11 and 19.
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A model rocket is launched with an initial upward velocity of 67/ms. The rocket's height h (in meters) after t seconds is given by the following.
h= 67t-5t^2
Find all values of t for which the rocket's height is 30 meters.
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Step-by-step explanation:
The rocket's height h (in meters) after t seconds is given by:
[tex]h=67t-5t^2[/tex]
67 m/s is the initial upward velocity of the rocket. We need to find the values of t for which the rocket's height is 30 meters. So equation (1) becomes :
[tex]67t-5t^2=30[/tex]
[tex]67t-5t^2-30=0[/tex]
The above equation is a quadratic equation. We need to find the value of t.After solving the quadratic equation, we get the values of t are :
t = 0.464 seconds = 0.46 seconds
or
t = 12.936 seconds = 12.94 seconds
Hence, this is the required solution.
The rocket's height is 30 meters at t = 3.79 seconds or t = 0.54 seconds after launch, when solved using the quadratic formula applied to the given equation.
Explanation:To find all values of t for which the rocket's height is 30 meters according to the given quadratic equation h = 67t - 5t2, we need to set the equation equal to 30:
30 = 67t - 5t2
Moving all terms to one side, we obtain:
0 = 5t2 - 67t + 30
Now, we can solve this quadratic equation using the quadratic formula:
t = (-b ± sqrt(b2 - 4ac)) / (2a)
Here, a = 5, b = -67, and c = 30. Plugging these values into the formula we get:
t = (67 ± sqrt(672 - 4 * 5 * 30)) / (10)
Calculating the discriminant and then computing the values for t:
t = 3.79 or t = 0.54
Therefore, the rocket is at 30 meters at approximately t = 3.79 seconds or t = 0.54 seconds after launch, rounded to the nearest hundredth.
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At an amusement park, Corey spends 7 minutes on a ride for every 20 minutes he spends waiting in lines. If he waits in line for 60 minutes, how many minutes does he spend on rides? [Type your answer as a number.]
Answer:
21
Step-by-step explanation:
On a 10-item test, three students in professor hsin's advanced chemistry seminar received scores of 2, 5, and 8, respectively. for this distribution of test scores, the standard deviation is equal to the square root of
salas little brother is learning to talk. he has a vocabulary of 30 words. each week his vocabulary grows by about 6%. at this rate how many words will he know 5 weeks from now
30 * (1+0.06)^5=
30* 1.338225578 = 40.146
he will know 40 words in 5 weeks
reflecting over which line will map the rhombus onto itself
-8-(3x+6)=4-x
Wow I'm dumb lol
Raina makes eight dollars for each hour of work. Write an equation to represent her total pay p after working h hours
Two way Frequency table question
(NEED HELP!!!)Which of the following lines is perpendicular to y= 3x + 2?
A. y=3x -1/2
B. y=-1/3x+6
C. y=1/3x+2
D. y=3x+1/2
Answer:
[tex]y=\frac{-1}{3}x+6[/tex]
Step-by-step explanation:
We have to find the equation of the line from the options given which is perpendicular to the line y=3x+2.
In order to do so we must know that , the product of the slope of the two perpendicular lines is always -1
Hence
if the slope of line A is "m" and the line B which is perpendicular to A, will have [tex]-\frac{1}{m}\\[/tex]
Also , in the slope intercept form of any equation the coefficient of x is our slope. Hence the slope of y=3x+2., is 3
Hence the slope of any line perpendicular to this will be [tex]\frac{-1}{3}[/tex]
as the product of two slopes is -1
Hence in the given options only c options has the line whose slope is [tex]\frac{-1}{3}[/tex]
Which graph best represents the solution to the system of equations shown below?
y = -2x + 14
y = 2x + 2
Answer:
solution is (3,8)
option A
Step-by-step explanation:
[tex]y = -2x + 14[/tex]
[tex]y = 2x + 2[/tex]
Lets graph each equation
Given equation is in the form of y=mx+b
LEts graph each equation using a table
[tex]y = -2x + 14[/tex]
x y
0 14
1 12 points are (0,14) and (1,12)
[tex]y = 2x + 2[/tex]
x y
0 2
1 4 points are (0,2) and (1,4)
Graph both the table
The graph is attached below. both graph intersects at (3,8)
To the nearest hundredth, what is the circumference of a circle with a radius of 4 units.
A. 201.06
B. 50.27
C. 12.57
D. 25.13
Answer:
it Is D
Step-by-step explanation:
just did it