To decide which random sample has a higher probability, we need to consider the sample size. As the sample size increases, the sample mean tends to approach the population mean more closely. We can use the properties of the normal distribution and the formula for the standard error of the mean to calculate the probabilities for each random sample size.
Explanation:To decide which has a higher probability, we need to consider the sample size of each random sample. In general, as the sample size increases, the sample mean tends to approach the population mean more closely.
Given that each sample is from a population that is normally distributed with a mean of 100 and a standard deviation of 15, we can use the properties of the normal distribution to calculate the probabilities.
(a) For a random sample of size n = 10, the probability of the sample mean being between 90 and 110 can be calculated using the formula for the standard error of the mean:
Standard error of the mean = standard deviation / sqrt(sample size)
Using this formula, the standard error of the mean for n = 10 is 15 / sqrt(10) = 4.74.
Since the sample mean follows a normal distribution, we can use the properties of the normal distribution to find the probability:
p(90 ≤ sample mean ≤ 110) = p((90 - 100) / 4.74 ≤ (sample mean - 100) / 4.74 ≤ (110 - 100) / 4.74)
We can look up the probabilities for the z-scores using a standard normal distribution table or a calculator to find the probability for the given range.
(b) For a random sample of size n = 20, we can follow the same steps as above to calculate the probability of the sample mean being between 90 and 110.
The standard error of the mean for n = 20 is 15 / sqrt(20) = 3.35.
p(90 ≤ sample mean ≤ 110) = p((90 - 100) / 3.35 ≤ (sample mean - 100) / 3.35 ≤ (110 - 100) / 3.35)
We can again use a standard normal distribution table or a calculator to find the probability for the given range.
What are two items that weigh less than 1 oz
Josef says that the range for the car data is greater than the range for the minivan data because the box in the box plot for the car data is wider. Which explains Josef’s error?
Answer:
its a ik it
Step-by-step explanation:
Will Give 100 points and brainliest!
An image of a rectangular pyramid is shown below: A right rectangular pyramid is shown. Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base. What is the name of the shape created by the cross section? Explain your answer. (5 points) Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex, what would be the shape of the resulting cross section? Explain your answer. (5 points)
The Part A cross section will be rectangle and Part B cross section will be triangle .
What is rectangular pyramid ?A rectangular pyramid is a 3-D object with a base shaped like a rectangle and triangle-shaped faces or sides that correspond to each side of the base. Like the other types of pyramids, a rectangular pyramid also has a point on top of the base of the pyramid that is joined together by bringing the top of all the sides which is known as the apx. A rectangular pyramid has a total of 5 faces, 5 vertices, and 8 edges and is of two types a right pyramid or an oblique pyramid.
According to the question
Part A: A cross section of the rectangular pyramid is cut with a plane parallel to the base.
When we cut a cross section parallel to base of the rectangular pyramid which have rectangular base
The cross section will always be a rectangle.
Part B: If a cross section of the rectangular pyramid is cut perpendicular to the base, passing through the top vertex .
When we cut a cross section perpendicular to the base, passing through the top vertex of the rectangular pyramid
The cross section will always be a Triangle.
As the lateral face of a rectangular pyramid is a triangle, so a cross section that passes through the top vertex and the base is also a triangle.
Hence , The Part A cross section will be rectangle and Part B cross section will be triangle .
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what's a Fibonacci sequence?
find the distance between :(-1,5)( 3,-2)
A self-service car wash charges $4 for the initial 5 minutes plus an additional $0.75 for each minute after that. Nick only has $10 to spend on washing his car. Let m represent the number of minutes Nick spends washing his car.
Nick can spend a total of 13 minutes washing his car at the self-service car wash with his $10 budget, accounting for both the initial charge and the additional cost per minute after the first 5 minutes.
Nick is planning to use a self-service car wash that charges $4 for the initial 5 minutes and an additional $0.75 for each minute after that. With a budget of $10, he wants to calculate the number of minutes (m) he can spend washing his car. The cost for m minutes is given by the equation:
Total Cost = Initial Charge + (Additional Charge per minute * Number of extra minutes)
First, subtract the initial charge from the total amount Nick has:
$10 - $4 = $6
This is the amount remaining for the additional minutes. Next, divide this by the additional charge per minute:
$6 / $0.75 per minute = 8 minutes
Therefore, Nick can spend 8 minutes washing his car after the initial 5 minutes, for a total of 13 minutes.
Which expression is equivalent to (2mn)^4/6m^-4n^-2? Assume m=/0 n=/0.
Dam is rowing a boat away from a dock the graph shows the relationship between the time and sams distance from the dock. Evaluate the function for an input of 9
Answer:
B. After 9 minutes Sam is 80 meters away from the dock.
Step-by-step explanation:
We have been given a graph of function that shows the relationship between the time and Sam's distance from the dock.
Let us see our given options one by one to find the correct choice.
A. After 80 minutes Sam is 9 meters away from the dock.
Upon looking at our graph we can see that y-axis is representing distance in meters and x-axis is representing time in minutes. Range of x is from 0 to 11 So our input cannot be greater than 11.
Therefore, option A is not a correct choice.
B. After 9 minutes Sam is 80 meters away from the dock.
We can clearly see from our given graph that at 9 minutes distance is 80 meters, which means that after 9 minutes Sam is 80 meters away from the dock. Therefore, option B is the correct choice.
C. After 80 minutes Sam is 80 meters away from the dock.
We can see from our graph that range of x is from 0 to 11 minutes, So our input can not be greater than 11. Therefore, option C is not a correct choice.
D. After 9 minutes Sam is 3 meters away from the dock.
We can see from our graph that initial value of our function is 20, which means that at time equals 0 minutes Sam was 20 meters away from dock and this distance is increasing with the time. Therefore, option D is not a correct choice.
Convert the equation 3x + 2y = 14 to slope intercept form
Answer:
Step-by-step explanation:
y=-3/2x+7
Find the coefficient of x 4 in the taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x 2 ).
The coefficient of x4 in the Taylor series expansion of the given function is 0.
Explanation:To find the coefficient of x4 in the Taylor series expansion of the function f(x) = 8 ln(9 + 3x2), we need to compute the fourth derivative of f(x) and evaluate it at x = 0.
The Taylor series expansion for a function centered at the origin is given by:
f(x) = f(0) + f'(0)x + f''(0)x2/2! + f'''(0)x3/3! + f''''(0)x4/4! + ...
In this case, we have:
f'''(x) = 48x/(9 + 3x2)
Evaluating f'''(x) at x = 0 gives:
f'''(0) = 0/9 = 0
Therefore, the coefficient of x4 in the Taylor series expansion centered at the origin for the function f(x) = 8 ln(9 + 3x2) is 0.
What is the correct data set for the box & whisker plot shown above??
Answer: It’s A.
Step-by-step explanation:
for a p e x
You want to have $31,664 in cash to buy a car in 4 years. you expect to earn 11.5% per year on your savings. how much do you need to deposit today if this is the only money you save for this purpose?
You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.
We have,
To determine how much you need to deposit today, we can use the concept of present value (PV).
The present value represents the current value of a future cash flow, accounting for the time value of money and the expected interest rate.
In this case, you want to have $31,664 in cash in 4 years, and you expect to earn an annual interest rate of 11.5%.
Let's calculate the present value using the following formula:
[tex]PV = FV / (1 + r)^n[/tex]
where PV is the present value, FV is the future value, r is the interest rate per period, and n is the number of periods.
Plugging in the values, we have:
[tex]PV = $31,664 / (1 + 0.115)^4[/tex]
Calculating this equation, we find:
[tex]PV = $31,664 / (1.115)^4[/tex]
= $31,664 / 1.530749
PV ≈ $20,701.27
Therefore,
You would need to deposit approximately $20,701.27 today if this is the only money you save for the purpose of buying a car in 4 years, considering an expected annual interest rate of 11.5%.
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check all that apply
Answer:
A, D, E
Step-by-step explanation:
Squaring both sides of the inequality, we get
x < 25 . . . . . with the restriction x ≥ 0
The listed numbers that are in the range [0, 25) are 1, 18, 24.
The sum of 5 consecutive even numbers is 200 what is the fifth term in the sequence
The perimeter of parallelogram ABCD is equal to 10 cm. Find the length of diagonal BD if you know that the perimeter of △ABD is 8 cm.
The length of the diagonal BD is 3 centimeters.
Procedure - Length determination in a parallelogram sideA parallelogram is a quadrilateral where each pair of parallel sides have the same length and can be form by two congruent triangles which share the same side (diagonal).
Expressions for the parallelogramPerimeter equations for the parallelogram are the following:
[tex]AB + BD + AD = 8\,cm[/tex] (1)
[tex]2\cdot AB + 2\cdot AD = 10\,cm[/tex] (2)
Where:
[tex]AB[/tex], [tex]AD[/tex] - Side lengths of the parallelogram, in centimeters. [tex]BD[/tex] - Diagonal length of the parallelogram, in centimeters.Resolution of the systemBy (2) we have the following conclusion:
[tex]AB + AD = 5\,cm[/tex]
And we find the length of the diagonal BD by (1):
[tex]5\,cm + BD = 8\,cm[/tex]
[tex]BD = 3\,cm[/tex]
The length of the diagonal BD is 3 centimeters. [tex]\blacksquare[/tex]
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what is the answer to the system of equations 2x+y=29 and y=1x+2.
explain why, if answer is a random answer you will be reported and lose points.
this is for free and easy points
2x+y = 29
2x+x+2 = 29
3x = 27
x = 9
Hope this helps...
!!!!!GIVING BRAINLIEST!!!!!
Select the graph for the solution of the open sentence. Click until the correct graph appears. 3|x| > 6
Answer:
Given equation,
3|x| > 6 -----(1)
∵ [tex]\frac{1}{3}>0[/tex]
Thus, multiplying both sides of inequality (1) by [tex]\frac{1}{3}[/tex]
We get,
[tex]|x| > 2[/tex]
⇒ 2 < x or 2 < - x
⇒ 2 < x or -2 > x (when a > b where a > 0, b > 0, If c < 0 ⇒ ac < bc),
⇒ (2, ∞ ) ∪ (-∞, -2)
By plotting the above interval in the number line we can get the graph of the given equation ( shown below )
Eliminate the parameter. x = one divided by two t, y = 3t^3 - 1
Answer:
y = 24x3 - 1
Step-by-step explanation:
None needed YW
Which are the solutions of x2 = –5x + 8?
Answer:
The solutions are 1.275 and -6.275
Step-by-step explanation:
Given
x^2 = –5x + 8
First, put all terms in the left side of the equal sign, as follows:
x^2 + 5x - 8 = 0
Then, use the quadratic formula with a = 1 (the coefficient of the quadratic term), b = 5 (the coefficient of the linear term) and c = -8 (the independent term).
[tex]x = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)}[/tex]
[tex]x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-8)}}{2(1)}[/tex]
[tex]x = \frac{-5 \pm \sqrt{57}}{2}[/tex]
[tex]x_1 = \frac{-5 + \sqrt{57}}{2}[/tex]
[tex]x_1 = \frac{-5 + 7.55}{2}[/tex]
[tex]x_1 = 1.275[/tex]
[tex]x_2 = \frac{-5 - \sqrt{57}}{2}[/tex]
[tex]x_2 = \frac{-5 - 7.55}{2}[/tex]
[tex]x_2 = -6.275 [/tex]
library library currently has 125 audiobook the library plan purchase the same number of books each month after 4 months the library has 20 more audiobook which equation can be used to determine t and a total number of audio books the library will have after and months
each picnic table seats 6 people how many picnic tables are needed to seat 24 people?
Final answer:
To seat 24 people at picnic tables that each seat 6, you divide 24 by 6, which equals 4 tables needed.
Explanation:
The question is asking how many picnic tables are needed to seat 24 people, if each table seats 6 people. This is a division problem where we need to divide the total number of people by the number of seats at a single table. You divide 24 (the total number of people) by 6 (the number of seats at one table) to find out the number of tables needed.
Here is the calculation: 24 \/ 6 = 4. Therefore, you would need 4 picnic tables to seat 24 people, assuming each person takes one seat and that there are no empty seats.
I need this equation solved with the work shown please
Alice has a box that is 5 inches long, 5 inches wide, and 5 inches tall. How many 1 inch by 1 inch by 1 inch blocks can Alice fit into the box?
What is the circumference of a circle with a radius of 5.4 inches? Enter your answer as a decimal in the box. Use 3.14 for pi. Round your answer to the nearest tenth. in.
Answer:
33.9
Step-by-step explanation
I got 100% on my test and just wanted everyone to know that it is correct.
Martin put 8 pounds of grapes into a bowl. Four friends each took 2/3 pounds from the bowl. What fraction represents the total amount of grapes removed from the bowl ?
Answer:
-8/3
Step-by-step explanation:
i took the test on edg
How many positive integers between 100 and 999 inclusive are divisible by three or four?
The total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is 450.
Explanation:The problem is looking for positive integers between 100 and 999 inclusive, that are divisible by three or four. First, we find out how many numbers between 100 and 999 are divisible by 3 by using the formula: (Last Numbers - First Number) divided by the number you are dividing + 1. Hence, [tex](999 - 102) / 3 + 1 = 300.[/tex] Similarly, for numbers divisible by 4: (996 - 100) / 4 + 1 = 225. However, we must subtract out the numbers that are counted twice because they are divisible by both 3 and 4 (i.e., divisible by 12). To find this, we do [tex](996 - 108) / 12 + 1 = 75.[/tex]
In conclusion, we add the numbers divisible by 3 and those divisible by 4 and subtract the ones that are divisible by both (12). Hence, the total number of positive integers between 100 and 999 inclusive that are divisible by 3 or 4 is [tex]300 + 225 - 75 = 450.[/tex]
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Complete the comparison: 26 < ? A. 25 B. 54 C. 13 D. 26
A segment has endpoints at (3,−4) and (3,−17) How many units long is the segment?
Answer:
what the other person said
Step-by-step explanation:
how do you reduce 4/8?
what is the variable in this algebraic expression 8+6, 4d-2, 7r-15=6, 11+14=25
For this case we have that by definition, a variable is a symbol that can be replaced or that takes a numerical value in an equation or expression, mathematical in general.
Then we have the following options:
A) [tex]8 + 6[/tex]
It is a sum of two real numbers. There are no variables.
B)[tex]4d-2[/tex]
In this case the variable is "d"
C) [tex]7r-15 = 6[/tex]
In this equation, the variable is represented by "r"
D) [tex]11 + 14 = 25[/tex]
It is a sum of two real numbers. There are no variables.
Answer:
A) There are no variables
B) "d"
C) "r"
D) There are no variables