Answer:
Josh: 20 messages
Kira: 25 messages
Sam: 40 messages
Suppose that a category of world-class runners are known to run a marathon in an average of 147 minutes with a standard deviation of 12 minutes. Consider 49 of the races. Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons. (Round your answer to two decimal places.)
Answer:
0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Average of 147 minutes with a standard deviation of 12 minutes.
This means that [tex]\mu = 147, \sigma = 12[/tex]
Consider 49 of the races.
This means that [tex]n = 49, s = \frac{12}{\sqrt{49}} = \frac{12}{7} = 1.7143[/tex]
Find the probability that the runner will average between 146 and 150 minutes in these 49 marathons.
This is the p-value of Z when X = 150 subtracted by the p-value of Z when X = 146. So
X = 150
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{150 - 147}{1.7143}[/tex]
[tex]Z = 1.75[/tex]
[tex]Z = 1.75[/tex] has a p-value of 0.9599
X = 146
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{146 - 147}{1.7143}[/tex]
[tex]Z = -0.583[/tex]
[tex]Z = -0.583[/tex] has a p-value of 0.3075.
0.9599 - 0.3075 = 0.6524.
0.6524 = 65.24% probability that the runner will average between 146 and 150 minutes in these 49 marathons.
Probability of picking a blue marble and a yellow marble when 2 marbles are picked (without replacement) from a bag containing 4 blue and 4 yellow marbles
Answer:
9/49
Step-by-step explanation:
that is the procedure above
Which points are also part of this set of equivalent ratios? Select all that apply.
a. (3, 2)
b. (4, 2)
c. (4, 8)
d. (8, 4)
e. (12, 6)
Answer:
Option b, (4,2)
Option d, (8,4)
Option e, (12,6)
Answered by GAUTHMATH
Answer:
Option b, (4,2)
Option d, (8,4)
Option e, (12,6)
Step-by-step explanation:
the person above me is correct
A sample of 4 children was drawn from a population of rural Indian children aged 12 to 60 months. The sample mean of mid-upper arm circumference was 150 mm with a standard deviation of 6.73. What is a 95% confidence interval for the mean of mid-upper arm circumference based on your sample
Answer:
The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 4 - 1 = 3
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 3 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 3.1824
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 3.1824\frac{6.73}{\sqrt{4}} = 10.71[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 150 - 10.71 = 139.29 mm
The upper end of the interval is the sample mean added to M. So it is 150 + 10.71 = 160.71 mm
The 95% confidence interval for the mean of mid-upper arm circumference based on your sample is between 139.29 mm and 160.71 mm.
How many numbers multiple of 3 are in the range [2,2000]?
Answer:
There are 666 numbers multiple of 3 in the interval.
Step-by-step explanation:
Multiples of 3:
A number is a multiple of 3 if the sum of it's digits is a multiple of 3.
Range [2,2000]:
First multiple of 3 in the interval: 3
Last: 1998
How many:
[tex]1 + \frac{1998 - 3}{3} = 1 + 665 = 666[/tex]
There are 666 numbers multiple of 3 in the interval.
A rectangle has a length of 7 in. and a width of 2 in. if the rectangle is enlarged using a scale factor of 1.5, what will be the perimeter of the new rectangle
Answer:
27 inch
Step-by-step explanation:
Current perimeter=18
New perimeter=18*1.5=27 in
Make x the subject
5y + 2x = 25
Answer:
x = -5/2 y +25/2
Step-by-step explanation:
5y + 2x = 25
Subtract 5y from each side
5y + 2x -5y= -5y+25
2x = -5y +25
Divide by 2
2x/2 = -5y/2 +25/2
x = -5/2 y +25/2
All of the following are equivalent except
x-7
X-(-7)
-7+x
x+(-7)
Answer:
X-(-7)
Step-by-step explanation:
If you are subtract by a negative number it turns it into a positive. It would look like this: X+(+7)
Estimating Mean SAT Math Score
Type numbers in the boxes.
aby Part 1: 5 points
The SAT is the most widely used college admission exam. (Most community
aby Part 2: 5 points
colleges do not require students to take this exam.) The mean SAT math score
varies by state and by year, so the value of u depends on the state and the year. 10 points
But let's assume that the shape and spread of the distribution of individual SAT math scores in each
state is the same each year. More specifically, assume that individual SAT math scores consistently
have a normal distribution with a standard deviation of 100. An educational researcher wants to
estimate the mean SAT math score (u) for his state this year. The researcher chooses a random
sample of 661 exams in his state. The sample mean for the test is 494.
Find the 99% confidence interval to estimate the mean SAT math score in this state for this year.
(Note: The critical z-value to use, zc, is: 2.576.)
Your answer should be rounded to 3 decimal places.
Answer:
(483.981 ; 504.019)
Step-by-step explanation:
Given :
σ = 100
Sample size, n = 661
xbar = 494
We use the Z distribution since we are working with the population standard deviation ;
C.I = xbar ± (Zcritical * σ/√n)
Zcritical at 99% = 2.576
C.I = 494 ± (2.576 * 100/√661)
C.I = 494 ± 10.019
Lower boundary = (494−10.019) = 483.981
Upper boundary = (494+10.019) = 504.019
C.I = (483.981 ; 504.019)
A triangle has base of 7 1/8 feet and height 6 1/4 feet. Find the area of a triangle as a mixed number.
Answer: The area is 22 17/64.
Step-by-step explanation:
base = 7 1/8 = 57/8
height = 6 1/4 = 25/4
area = 1/2*b*h
= 1/2*57/8*25/4
= 1425/64
= 22 17/64
Pls solve this for me ryt now wai abeg
...The first three terms of an arithmetic progression (A.P) are (x+1),(4x-2) and(6x-3) respectively .If the last term is 18,find the
a.Value of x b.Sum of the terms of the progression
Answer:
[tex]x = 2[/tex]
[tex]S_n = 63[/tex]
Step-by-step explanation:
Given
[tex]a_1 = x + 1[/tex]
[tex]a_2 = 4x -2[/tex]
[tex]a_3 = 6x -3[/tex]
[tex]a_n = 18[/tex]
Solving (a): x
To do this, we make use of common difference (d)
[tex]d = a_2 - a_1[/tex]
[tex]d = a_3 - a_2[/tex]
So, we have:
[tex]a_3 - a_2 = a_2 - a_1[/tex]
Substitute known values
[tex](6x - 3) - (4x - 2) = (4x - 2) - (x + 1)[/tex]
Remove brackets
[tex]6x - 3 - 4x + 2 = 4x - 2 - x - 1[/tex]
Collect like terms
[tex]6x - 4x- 3 + 2 = 4x - x- 2 - 1[/tex]
[tex]2x- 1 = 3x- 3[/tex]
Collect like terms
[tex]2x - 3x = 1 - 3[/tex]
[tex]-x = -2[/tex]
[tex]x = 2[/tex]
Solving (b): Sum of progression
First, we calculate the first term
[tex]a_1 = x + 1[/tex]
[tex]a_1 = 2 + 1 = 3[/tex]
Next, calculate d
[tex]d = a_2 - a_1[/tex]
[tex]d = (4x - 2) - (x +1)[/tex]
[tex]d = (4*2 - 2) - (2 +1)[/tex]
[tex]d = 6 - 3 = 3[/tex]
Next, we calculate n using:
[tex]a_n = a + (n - 1)d[/tex]
Where:
[tex]a_n = 18[/tex]
[tex]d = 3; a = 3[/tex]
So:
[tex]18 = 3 +(n - 1) * 3[/tex]
Subtract 3 from both sides
[tex]15 = (n - 1) * 3[/tex]
Divide both sides by 3
[tex]5 = n - 1[/tex]
Add 1 to both sides
[tex]6 = n[/tex]
[tex]n = 6[/tex]
The sum of the progression is:
[tex]S_n = \frac{n}{2} * [a + a_n][/tex]
So,, we have:
[tex]S_n = \frac{6}{2} * [3 + 18][/tex]
[tex]S_n = 3 * 21[/tex]
[tex]S_n = 63[/tex]
A cyclist rides his bike at a speed of 15 miles per hour. What is this speed in kilometers per hour? How many kilometers will the cyclist travel in 4 hours? In your computations, assume that 1 mile is equal to 1.6 kilometers. Do not round your answers.
Answer:
Step-by-step explanation:
Speed = (15 mi)/hr × (1.6 km)/mi = (24 km)/hr
:::::
(4 hr) × (24 km)/hr = 96 km
6.(a) A laptop was bought at Canadian $ 770. If the tax of 20% and 13% VAT should be paid, find the least selling price of it in Nepali rupee that prevents the shopkeeper from loss?
The LEAST selling price of the laptop should be ;
$1024.1 in other to avoid loss.
Price of laptop = $770
Tax = 20%
VAT = 13%
TO avoid loss ;
both the VAT percentage and TAX must be added to the price of the laptop:
Total percentage = VAT + TAX = (20 + 13) = 33%
THEREFORE, Least selling price should be :
Price of laptop * (1 + 33%)
770 * 1.33
= $1024.1
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PLEASE HELP!!!!!!!!! DUE ASAP I WILL GIVE BRAINLIEST!!!!!!!!
Explanation:
A = values on the die greater than 1
A = {2,3,4,5,6}
B = values on the die less than 5
B = {1,2,3,4}
Union those two sets together
C = A u B = {1,2,3,4,5,6}
Effectively, we get every possible value on the die. This is due to the "or" keyword. If it was "and", then it would be a difference story.
So the probability of getting anything in set C is 100% or just 1. We have guaranteed certainty we'll have this event happen.
Question 6 of 10
The domain of a function f(x) is x = 0, and the range is ys -1. What are the
domain and range of its inverse function, '(x)?
Answer: y = 0 and x = -1
Last question I need help on
( x + 1 )( x )( x - 5 ) =
( x + 1 )( x - 5 )( x ) =
( x^2 - 4x - 5 )( x ) =
x^3 - 4x^2 - 5x
Step-by-step explanation:
the other answer is basically correct.
as the simplest form you create 3 terms for the three given solutions (= the values for when the equation equals 0).
but maybe you need to add " = 0" for the full equation.
A runner can run 2 miles in 14 minutes. At this rate, how many miles can he run in 70 minutes?
Answer:
The answer is that the runner can run 10 miles in 70 minutes.
Step-by-step explanation:
To solve for the number of miles that the runner can run in 70 minutes, start by setting up the information given from the problem in the form of a proportion.
A proportion is an equation which defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In a proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
The proportion for this problem will look like [tex]\frac{2 miles}{14 minutes}=\frac{x}{70 minutes}[/tex]. (x) will be used as the variable for the number of miles that the runner can run in 70 minutes.
To solve the proportion, start by cross multiplying to form an equation, and the equation will look like [tex](14)(x)=(2)(70)[/tex]. Next, simplify the equation, which will look like [tex](14)(x)=140[/tex]. Then, solve the equation by dividing both sides of the equation by 14, and it will look like [tex]x=10[/tex]. The final answer is that the runner can run 10 miles in 70 minutes.
1% defective parts. 100,00 parts made in total. The number of defects made should equal?
Answer:
1,000 defects
Step-by-step explanation:
Find how many defects that should be made by finding 1% of 100,000:
100,000(0.01)
= 1000
So, there should be 1,000 defects
Solve for f(-7) plz thanks
Answer:
12
Step-by-step explanation:
If f(x) = 5 - x
Then f(-7) = 5 - (-7)
f(-7) = 5 + 7
f(-7) = 12
Instructions: Find the missing length indicated.
Answer:
x = 65
Step-by-step explanation:
x = √(25×(25+144))
x = √(25×169)
x = 5×13
x = 65
Answered by GAUTHMATH
given the recursive formula below, what are the first four terms of the sequence
Answer:
c
Step-by-step explanation:
The first four terms are 17, 15, 13, and 11.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
f(n):
f(1) = 17
f(n) = f(n - 1) - 2 if n > 1
Now,
The first term is 17.
The second term.
f(2) = f(2 - 1) - 2
= f(1) - 2
= 17 - 2
= 15
The third term.
= f(3 - 1) - 2
= f(2) - 2
= 15 - 2
= 13
The fourth term.
f(4) = f(4 - 1) - 2
= f(3) - 2
= 13 - 2
= 11
Thus,
The terms are 17, 15, 13, 11
Learn more about functions here:
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What is the area of the polygon given below?
Answer:
diện tích đa giác trong hình là :
186 cm2
Step-by-step explanation:
hãy tách hình đa giác trên thành 4 hình chữ nhật và tính diện tích từng hình chữ nhật
Assuming boys and girls are equally likely, find the probability of a couple having a baby boy when their third child is born, given that the first two children were both boys
The required probability of a couple having a baby boy when their third child is born is 1/2.
What is probability?probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.
Given:
Assuming boys and girls are equally likely.
The first two children were both boys
According to given question we have
The probability of having a baby girl is an independent probability.
The first two children were both boys
So, it is not related to the previous child.
So required probability = 1/2
Therefore, the required probability of a couple having a baby boy when their third child is born is 1/2.
Learn more details about probability here:
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The lines shown below are parallel. If the green line has a slope of 5, what is a
the slope of the red line?
Answer:
A. 5
Step-by-step explanation:
Parallel lines have the same slope.
Answer:
5
Step-by-step explanation:
Ellicott City Manufacturers, Inc., has sales of $6,344,210, and a gross profit margin of 67.3 percent. What is the firm's cost of goods sold? Round your final answer to the nearest dollar.
Answer:
$3792116
Step-by-step explanation:
that's the answer above
What's the next number in the sequence 16, 4, 1,
Answer:
0.25
Step-by-step explanation:
16/4 = 4
4/4 = 1
1/4 = 0.25
0.25/4 = 0.0625
0.0625/4 = 0.015625
give me brainliest please:)
Question 4 of 16
If the probability of rain today is 35%, what is the probability that it will not rain
today?
A. 100%
B. 65%
C. 35%
D. 50%
Answer:
I think the answer is B. 65%
Lines a and b are perpendicular. If the slope of line a is 3, what is the slope of
line b?
Answer:
-1/3
Step-by-step explanation:
Perpendicular lines have slopes that multiply to -1
a*b = -1
3 * b = -1
b = -1/3
The slope of line b is -1/3
Max has 3 fiction books and 6 nonfiction books to donate to the community center. He wants to package them so that there is an equal number of fiction and nonfiction books in each group. He also wants to have as many packages as possible. How many books are in each group?
Answer:
Each group has 1 fiction book and 2 nonfiction book(s).
Suppose you believe that the true average daily trade volume for General Electric stock is 49,829,719 shares and a standard deviation of 21,059,637 shares. Considering a 95% confidence level: What is the minimum required sample size if you would like your sampling error to be limited to 1,000,000 shares
Answer:
The minimum sample size is 1,704.
Step-by-step explanation:
We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation of 21,059,637 shares
This means that [tex]\sigma = 21059637[/tex]
What is the minimum required sample size if you would like your sampling error to be limited to 1,000,000 shares?
This is n for which [tex]M = 1000000[/tex], so:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1000000 = 1.96\frac{21059637}{\sqrt{n}}[/tex]
[tex]1000000\sqrt{n} = 1.96*21059637[/tex]
[tex]\sqrt{n} = \frac{1.96*21059637}{1000000}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*21059637}{1000000})^2[/tex]
[tex]n = 1703.8[/tex]
Rounding up:
The minimum sample size is 1,704.
