the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation is 0.1, or 10%.
Let A be the event that Jim's vacation was in Alaska, and let S be the event that Jim went surfing during the vacation. We want to find P(A|S), the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation.
By Bayes' theorem, we have:
P(A|S) = P(S|A) * P(A) / P(S)
We can calculate each term as follows:
P(S|A) = 0.1: the probability that Jim went surfing during the vacation given that he was in Alaska.
P(A) = 0.5: the probability that Jim's vacation was in Alaska, since he tosses a fair coin to decide between Hawaii and Alaska.
P(S) = P(S|A) * P(A) + P(S|H) * P(H) = 0.1 * 0.5 + 0.9 * 0.5 = 0.5: the total probability of Jim going surfing during the vacation, since he either went surfing in Alaska with probability 0.1 or went surfing in Hawaii with probability 0.9.
Therefore, we have:
P(A|S) = P(S|A) * P(A) / P(S) = 0.1 * 0.5 / 0.5 = 0.1
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dont understand what m supposed to do at the radius = diameter/2 part
Step-by-step explanation:
Radius simply means half of the diameter. In other words radius is the distance between the center of the circle to the outside of the circle
A population has a mean μ=135 and a standard deviation Ï=28. Find the mean and standard deviation of the sampling distribution of sample means with sample size n=57.
A population has a mean μ=135 and a standard deviation Ï=28.
The mean of the sampling distribution of sample means is equal to the population mean, that is 135.
The standard deviation of the sampling distribution of sample means can be calculated by using the formula
SE = Ï /[tex]\sqrt{n}[/tex]
Where Ï is the population standard deviation and n is the sample size.
By putting the given values we get
SE = 28 / [tex]\sqrt{57}[/tex] = 3.7
Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.
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PLEASE HELP!!!
A principal of $4200 is invested at %8 interest, compounded annually. How much will the investment be worth after 12 years?
Answer:
$10,244.14 after 12 years
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
A = the final amount of the investment
P = the principal amount ($4200 in this case)
r = the annual interest rate (8% or 0.08 as a decimal)
n = the number of times the interest is compounded per year (once annually in this case)
t = the number of years the money is invested (12 years in this case)
Substituting the given values into the formula, we get:
A = 4200(1 + 0.08/1)^(1*12)
A = 4200(1.08)^12
A = 4200(2.44140625)
A = $10,244.14 (rounded to the nearest cent)
What is the total surface area of the square pyramid?
The surface area of the square pyramid is 384 cm squared.
How to find the surface area of a square base pyramid?The surface area of the square base pyramid can be found as follows:
surface area of the square base pyramid = base area + 2al
where
a = side length of the basel = height of the pyramidTherefore,
base area = 12 × 12
base area = 144 cm²
Hence,
surface area of the square base pyramid = 144 + 2 × 12 × 10
surface area of the square base pyramid = 144 + 240
surface area of the square base pyramid = 384 cm²
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Select the acceptable conclusions to a hypothesis test. a The value of the test statistic lies in the nonrejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true. b The value of the test statistic does not lie in the rejection region. Therefore, we accept the null hypothesis. c The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true. d The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true. e The value of the test statistic does not lie in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is true. f The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.
The acceptable conclusions to a hypothesis test are option a, c, d, f.
What is hypothesis test?
Hypothesis Testing is a way of statistical analysis in which a person can put his assumptions about a population parameter to the test. It usually used to estimate the relationship between two statistical variables.
By the property of hypothesis test the following can be stated.
⇒The value of the test statistic lies in the non rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.
⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true.
⇒The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.
⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.
Hence the correct options are a, c, d, f.
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9. A classroom table has a mass of 24 kg. Pulling with a force of 36 N, a student moves the table to the other side of the classroom. How much did the table accelerate? Record your answer and fill in the bubbles. Be sure to use the correct place value.
The acceleration of this classroom table is equal to 1.5 meter per seconds square.
How to calculate the acceleration of this classroom table?From Newton's Second Law of Motion, the force exerted on the classroom table is modeled or represented by this mathematical equation (formula):
F = ma
Where:
F represent the force.m represent the mass.a represent the acceleration.By making "acceleration" the subject of formula, we have the following:
Acceleration, a = force/mass
Acceleration, a = 36/24
Acceleration, a = 1.5 meter per seconds square.
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what is the surface area of a composite figure (square pyramid and rectangular prism) with the dimensions length 6 width 6 height 12 triangle height 4 slant height 5
The total surface area to paint is 22000 sq. ft.
What is surface area?Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).
Surface Area = 2(lw + lh + wh)
Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))
Surface Area = 2(5000' + 4000' + 2000')
Surface Area = 2(11000')
Surface Area = 22000 sq. ft.
Answer: The total surface area to paint is 22000 sq. ft.
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Answer:
2200
Step-by-step explanation:
Share oranges among three boys so that the first gets twice more oranges than the second and the second gets twice the third's amount of the third. What is each boy's share? l
The calculated value of each boy's share is shown below
Let's call the amount of oranges the third boy gets "x".
According to the problem, the second boy gets twice the amount of oranges as the third boy, so he gets 2x oranges.
And the first boy gets twice more oranges than the second boy, so he gets 2(2x) = 4x oranges.
So the total number of oranges is x + 2x + 4x = 7x, and we need to divide this equally among the three boys.
Therefore, the first boy gets 4/7 of the total oranges, which is 4x/3, the second boy gets 2/7 of the total oranges, which is 2x/3 and the third boy gets 1/7 of the total oranges, which is x/3.
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What is the surface area of this composite solid? Show your work.
According to the above, we have to add the surface area of each face. So, the surface area of this solid would be 127.
What is the surface area of the composite solid?To calculate the surface area of the composite solid we have to perform the following procedure:
Sides (a) area
4 * 3 = 1212 * 2 = 24Sides (b) area
7 * 3 = 2121 * 3 = 63Face (c) area
3 * 4 / 2 = 66 * 2 = 12Base area
4 * 7 = 28
Total surface area
To calculate the total surface area we have to add the value of each face as shown below:
28 + 12 + 63 + 24 = 127According to the above, the surface area of this solid would be 127.
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Two real numbers are defined as: a=0444444444444 b=0.354355435554 Determine whether each number is rational or irrational. Is the product of a and b rational or irrational? Justify your answers. Enter your answers and your justifications in the box provided.
The a is rational , b is irrational and product of a and b is rational.
The number a=0.444444444444 is rational
Because it can be expressed as the ratio of two integers.
a = 4/9
The number b=0.354355435554 is irrational
Because it cannot be expressed as the ratio of two integers.
It has an infinite non-repeating decimal expansion.
To determine whether the product of a and b is rational or irrational, we can simply multiply them together:
a × b = (4/9) × 0.354355435554
= 0.158919191574
This product is a rational number, because it can be expressed as the ratio of two integers.
Hence, a is rational , b is irrational and product of a and b is rational.
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an a normal distribution be used to approximate the distribution of the random variable x that counts the number of adults who have not visited a dentist in the last two years?
Yes, a normal distribution can be used to approximate the distribution of the random variable X, which counts the number of adults who have not visited a dentist in the last two years. This approximation can be done using the Central Limit Theorem (CLT), which states that if you have a large enough sample size, the distribution of the sample means will approach a normal distribution, regardless of the original distribution's shape.
To use a normal distribution for this approximation, you need to meet the following criteria:
1. The sample size (n) should be large enough, typically n > 30.
2. The random variable X should have a known mean (μ) and standard deviation (σ).
If these criteria are met, you can use the normal distribution to approximate the distribution of X by calculating the standard error (SE), which is equal to σ / √n. This will help you estimate probabilities and analyze the data for the number of adults who have not visited a dentist in the last two years.
In summary, using a normal distribution to approximate the distribution of the random variable X is possible through the Central Limit Theorem, as long as the sample size is large enough and the mean and standard deviation are known.
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At a company a copy machine prints 175 pages in 5 minutes. if the number of pages printed is proportional to the time in minutes what is the unite rate
Answer:
The unit rate is 35 pages per minute.
Step-by-step explanation:
Divide 175 by 5, or 175/5 to get the unit rate, which is 35.
Can I get the answer?
The meaning of the y - intercept in the context of the problem of the snow level in Moose Wyoming is the level of snow at the beginning of the time period in question.
What is the y - intercept ?The y-intercept of the function y = 2x + 14 is the value of y when x = 0. Substituting x = 0 into the equation, we get:
y = 2(0) + 14
y = 14
Therefore, the y-intercept is 14.
In terms of the problem, this means that at midnight (when x = 0), there is already 14 inches of snow on the ground in Moose, Wyoming. The y-intercept represents the initial or starting value of the snow level function, which in this case is the amount of snow already on the ground at the start of the time period being modeled.
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please help asap!! i need the help
Answer:
Step-by-step explanation:
angle L is 106 degrees
x= 2
angle LMK is 37 degrees
its equal, you can check by adding up all the angles to 360 degrees
ABC is a right triangle.
AC = 12
CB = 9
Blank #1 Find AB Do not label
Blank #2. Find ∠A Round your answer to the nearest whole number. Do not include a degree sign
Blank #3 Find ∠C Round your answer to the nearest whole number. Do not include a degree sign.
Blank #4 Find ∠B Round your answer to the nearest whole number. Do not include a degree sign
a) The length of the hypotenuse AB is 15.
b) The angle ∠A is approximately 53 degrees.
c) The angle ∠C is 90 degrees.
d) The angle ∠B is approximately 37 degrees.
a) To find the length of the hypotenuse AB, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. In this case, we have:
AB² = AC² + CB²
AB² = 12² + 9²
AB² = 144 + 81
AB² = 225
AB = √225
AB = 15
Therefore, the length of the hypotenuse AB is 15.
b) To find the angle ∠A, we can use trigonometry. The sine of an angle is the ratio of the opposite side to the hypotenuse. In this case, we have:
sin(∠A) = AC/AB
sin(∠A) = 12/15
sin(∠A) = 0.8
Taking the inverse sine of 0.8, we get:
∠A = sin⁻¹(0.8)
∠A ≈ 53
Therefore, the angle ∠A is approximately 53 degrees.
c) Since angle ∠C is the right angle, its measure is 90 degrees.
d) To find the angle ∠B, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:
∠B = 180 - ∠A - ∠C
∠B = 180 - 53 - 90
∠B ≈ 37
Therefore, the angle ∠B is approximately 37 degrees.
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what is the value of f(16)
Step-by-step explanation:
Put '16' where 'x' is and compute
3/4 ( 16 ) + 7 = f(16) = 19
Dave is buying popcorn and sodas for his son and his five friends that he brings to the movies (Six kids total). The needs to buy at least one of the two items for each of the six. Popcorn costs $2. 50 per bag and sodas cost $4. 00 each. Dave can spend at most $40. Lets represent the number of sodas he buys and p represent the number of bags of popcorn he buys
The system of equations that models this scenario is:
p + s ≥ 62.50p + 4.00s ≤ 40How can it be modeled using a system of equations?Let p be the number of bags of popcorn.
Let s be the number of sodas Dave buys.
Since Dave needs to buy at least one of each item for all six kids, we have:
p + s = 6 -----(1)
Given:
The cost of a bag of popcorn is $2.50.
The cost of a soda is $4.00.
The total cost of Dave's purchase can be expressed as:
2.50p + 4.00s = C -----(2) where the C is the total cost of Dave's purchase.
Since Dave can spend at most $40, we have:
2.50p + 4.00s ≤ 40 -----(3).
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(I NEED THIS ASAP)
2. Write a rule that
describes this transformation.
Answer:
the y is always gonna be a difrent like a negative and a postive
Step-by-step explanation:
the y on the left if it's a positive the y on the right Is nightie ect
How many planes of symmetry does a right pyramid with an isosceles triangle base have?
Answer: The amount of planes of symmetry a right pyramid with an isosceles triangle base has four.
Hope this helps!
please solve and explain
LaTisha's calculation of the distance for the brake anchor placement is incorrect because she didn't take into account the height at which the cable is attached to the starting tree.
What is the correct distance ?The bungee cord is attached 16 feet above the ground, which will also contribute to the length of the cable needed to reach the ending tree.
To correctly calculate the distance, we can use the Pythagorean theorem, considering the height (16 feet) and the length of the stretched bungee cord (24 feet + 18 feet = 42 feet). Let's denote the horizontal distance from the base of the ending tree to the brake anchor as 'd'. We have:
d² + 16² = 42²
Now, we can solve for d:
d² + 256 = 1764
d² = 1508
d = √1508 = 38.8 feet (rounded to one decimal place)
The brake anchor should be placed approximately 38.8 feet from the base of the ending tree.
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A piece of metal with a mass of 611 g is placed into a graduated cylinder that contains25.1 mL of water, raising the water level to 56.7 mL. What is the density of the metal?A) 2.70 g/cm3 B) 7.13 g/cm3 C) 8.96 g/cm3 D) 10.5 g/cm3 E) 19.3g/cm3
The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.
The given mass of the metal is 611 g and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal volume can be evaluated by subtracting the initial volume from the final volume of water released by the metal.
Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL
Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³
The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.
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Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. Explain what most likely happened in
Sandy's experiment.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 500 flips.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
And please give me the answer
Answer: option C - Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips, is the most likely scenario.
Step-by-step explanation:
Based on the Law of Huge Numbers, the more times a coin is flipped, the closer the test likelihood will be to the hypothetical likelihood of 0.5 for heads and 0.5 for tails. In this manner, Sandy's exploratory likelihood is most likely to be closest to the hypothetical likelihood within the test with 1,000 flips.
In spite of the fact that it is conceivable that Sandy's exploratory likelihood might be near to the hypothetical likelihood within the explore with 100 flips or 500 flips, it is more likely that the bigger test measure of 1,000 flips will result in a more precise representation of the hypothetical likelihood.
Solve: 11x - 24 = 7x + 76
Answer:
[tex] \sf \: x = 25[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 11x - 24 = 7x + 76
Then the value of x will be,
→ 11x - 24 = 7x + 76
→ 11x - 7x = 76 + 24
→ 4x = 100
→ x = 100 ÷ 4
→ [ x = 25 ]
Hence, the value of x is 25.
Hello and greetings Brainly users.
Answer:Therefore, the solution to the equation is x = 25.Step-by-step explanation:It is an exercise of linear equations with one variable is a fundamental topic in the study of algebra. These types of equations are characterized by being first-degree polynomials in one variable, and can be found in various contexts, such as physics, economics, engineering, among others. Therefore, the ability to solve these equations is essential in the training of any mathematics student and in the development of their ability to solve problems in real life situations.
A linear equation with a variable can be solved by means of a series of algebraic operations that allow us to simplify the expression and clear the variable to be solved. These operations include adding, subtracting, multiplying, and dividing, always maintaining equality between both sides of the equation. The ultimate goal is to find the numerical value that satisfies the equation, that is, the value that makes the equality true.
Solving linear equations with one variable is an important skill not only for mathematics students, but also for professionals in various fields. For example, in engineering, linear equations are used to model physical systems and phenomena, and their resolution is necessary to perform calculations and make informed decisions. In the economy, they are used to analyze the behavior of financial variables and make projections for the future.
Now we solve our exercise:
To solve the equation 11x - 24 = 7x + 76 we need to isolate the variable x on one side of the equation.
First, we can simplify both sides of the equation by combining like terms:
11x - 7x = 76 + 24
Which gives us
4x = 100
Next, we can solve for x by dividing both sides of the equation by 4:
4x/4 = 100/4
x = 25
Therefore, the solution to the equation is x = 25.
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The Volume of a Rectangular prism is given by the expression LWH, What is its volume if L=1.2, W=3, H=2.5?
What solution please
4 times 1/6 in fraction.
Answer:
4/6 or 2/3 simplified
Step-by-step explanation:
4 ⋅ 1/6=4/6
multiply numerators together and denominators together
4/6
simplify
2/3
Hope this helps :)
(Part 2 of 2) Please help there is not much time left (Look at photo)
The rate of change for the function f(x) is 9.5 over the interval.
How I calculated the rate of change for f(x):
f(2) = 12, f(6) = 50
slope = (50 - 12) / (6 - 2) = 9.5
The rate of change for the function g(x) is -2 over the interval.
How I calculated the rate of change for g(x):
g(2) = -10, g(6) = -18
slope = (-18 - (-10)) / (6 - 2) = -2
What is the rate of change of the function?To find the rate of change for a function over an interval, we need to calculate the slope of the secant line that connects the two endpoints of the interval.
The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
For the quadratic function f(x) = (x + 1)² + 8, we can find the values of f(2) and f(6) by substituting x = 2 and x = 6 into the function:
f(2) = (2 + 1)² + 8 = 12
f(6) = (6 + 1)² + 8 = 50
Therefore, the rate of change for f(x) over the interval 2 ≤ x ≤ 6 is:
slope = (f(6) - f(2)) / (6 - 2) = (50 - 12) / 4 = 9.5
So the answer is: The rate of change for f(x) is 9.5 over the interval.
To find the rate of change for the linear function g(x) = -2x - 6, we can use the same formula:
g(2) = -2(2) - 6 = -10
g(6) = -2(6) - 6 = -18
Therefore, the rate of change for g(x) over the interval 2 ≤ x ≤ 6 is:
slope = (g(6) - g(2)) / (6 - 2) = (-18 - (-10)) / 4
slope = -2
So the answer is: The rate of change for g(x) is -2 over the interval.
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Use the following data to answer questions 1-2.
1. Find the median, mean, and range of the elephant ages.
a) Median:.
b) Mean:,
Ages of 10 elephants (in years) living in zoos:
28, 14, 19, 20, 21, 28, 33, 36, 41
c) Range:.
years
years
years
Answer:
median - 28
mean - 26.6 (6 repeating)
range - 27
Step-by-step explanation:
The elephant ages would go in the order of 14, 19, 20, 21, 28, 28, 33, 36, 41. To find the median, you need to look for the center of the numbers, which would be 28, since 28 is the middle number. To find the mean, you add all the numbers up and divide them by however many numbers there are, in this case, they add up to 240, and there is 9 numbers, so you would do 240 divided by 9 = 26.66 (repeating so a line over the 6's after the decimal) and to find the range you subtract the highest number and the lowest, which is 41 and 14 and that would give you 27.
I'M SO SORRY IF THIS DIDN'T MAKE SENSE!
Think of a number. The L C M of this number and 42 is 126. If the number lies between 60 and 70, what is the number
The LCM of 63 and 42 is 126 where 63 is the required number lying in between 60 and 70.
Let the missing number be x.
The number x lies in between 60 and 70.
The LCM ( Least Common Multiple) refers to the least value that is divisible by any two (or more) numbers.
Here LCM of x and 42 is 126.
Simplifying 126 we can write it as,
126 = 2*3*21
Thus, one of the number having 126 is as multiple is 42 (as already given).
The other number, that is x, having 126 as multiple lying between 60 and 70 is,
x = 3*21 = 63
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HELPP
Find the area of this shape:
Answer:
67 [tex]ft^{2}[/tex]
Step-by-step explanation:
Divide the shape into more recognizable shapes.
5*7 = 35
7*4 = 28
35+28
67
PLEASE ANSWER QUICK!!! 20 POINTS!!!!1
Suppose the length of voicemails (in
seconds) is normally distributed with a mean
of 40 seconds and standard deviation of 10
seconds. Find the probability that a given
voicemail is between 20 and 50 seconds.
10
20
30
40
P = [?]%
Hint: use the 68 - 95 - 99.7 rule.
50 60
70
Enter
Answer:
P=9600000000
Step-by-step explanation:
1 point is =0.150119
40x10=400x20=8000x50x400000x10=400000x20=800000x30=240000000x40=9600000000