Answer:
a) 24.09 minutes
b) 0.8%
Step-by-step explanation:
This week a very large running race 5K occurred in Denver the times were normally distributed with a mean of 23.92 minutes and the standard deviation of 3.4 minutes what time in minutes is the cut off for the fastest 51.99%
Z score for 51.99% = 0.05
z = (x-μ)/σ,
where x is the raw score = ? minutes
μ is the population mean = 23.92 minutes
σ is the population standard deviation = 3.4 minutes
0.05 = x - 23.92/3.4
Cross Multiply
0.05 × 3.4= x - 23.92
0.17 = x - 23.92
0.17 + 23.92 = x
x = 24.09 minutes
What percent of runners took more than 32.128 minutes to complete the race
= z score
z = (x-μ)/σ,
where x is the raw score = 32.128 minutes
μ is the population mean = 23.92 minutes
σ is the population standard deviation = 3.4 minutes
z = 32.128 - 23.92/3.4
z = 2.41412
P-value from Z-Table:
P(x<32.128) = 0.99211
P(x>32.128) = 1 - P(x<32.128) = 0.0078867
Approximately =0.008
Converting to percentage = 0.008 × 100
= 0.8%
Using the normal distribution, it is found that:
The cut off for the fastest 51.99% of times is of 24.09 minutes.0.25% of runners took more than 32.128 minutes to complete the race.Normal Probability DistributionIn a normal distribution 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]
It 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, which is the percentile of X.In this problem, we have that the mean and the standard deviation are, respectively, [tex]\mu = 23.92, \sigma = 3.4[/tex].
The cut off for the fastest 51.99% is the lowest 51.99% of times, that is, the 51.99th percentile, which is X when Z = 0.05.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.05 = \frac{X - 23.92}{3.4}[/tex]
[tex]X - 23.92 = 0.05(3.4)[/tex]
[tex]X = 24.09[/tex]
The cut off for the fastest 51.99% of times is of 24.09 minutes.
The proportion of runners who took more than 32.128 minutes to complete the race is 1 subtracted by the p-value of Z when X = 32.128, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32.198 - 23.92}{3.4}[/tex]
[tex]Z = 2.43[/tex]
[tex]Z = 2.43[/tex] has a p-value of 0.9925.
1 - 0.9925 = 0.0025.
0.0025 = 0.25% of runners took more than 32.128 minutes to complete the race.
More can be learned about the normal distribution at https://brainly.com/question/24663213
Determine the unit rate: 2 dozen tennis balls for $36
Answer:
It is $1.50 or $18 per dozen tennis balls
Step-by-step explanation:
1. Divide the total price by the number of tennis balls.
36/24= 1.50
So it cost $1.50 per tennis ball.
2. Then solve by dividing the total price by the number of tennis balls:
36/2= $18
"So it cost $18 per dozen tennis balls"
It is $1.50 or $18 per dozen tennis balls
solve the following
(a) 5+(-5)=?
(b) 5-(-5)=?
(c) 5-(5)=?
(d) 5-/-5/=?
Answer:
A) 0
B) 10
C) 0
D) I dont understand that one
Step-by-step explanation:
~~—☆☆☆——☆☆☆——☆☆☆——☆☆☆——☆☆☆—~~
Answer:
Hello! I hope I’m correct!! :)
Step-by-step explanation:
Solving a:
Remove the parentheses And now you subtract→ 5 - 5
→ = 0
___________________________
Solving b:
Remove the parentheses Simplfiy (or add/subtract the number)→ 5 + 5
→ = 10
____________________________
Solving c:
Remove the parentheses Now you subtract→ 5 - 5
→ = 0
_____________________________
For d, there is no answer since you can’t really solve it
Answers: 0,10,0 and the last one you can’t solve.Hope this helps! If you have any questions about this, feel free to ask! Have a wonderful day! ^-^
#Thank you so much for using brainly!
Best regard! :D
~By, BrainlyAnime~
~~—☆☆☆——☆☆☆——☆☆☆——☆☆☆——☆☆☆—~~
Steve has 54 stamps in his collection of 13 cent, 29 cent, and 45 cent stamps, totaling a value of $15.98. If the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80. Find the number of each type of stamp in his collection.
Answer:
Number of 13 cents stamp = 14
Number of 29 cents stamp = 24
Number of 45 cents stamp = 16
Step-by-step explanation:
We are told he has 54 stamps in total.
These stamps are;13 cent, 29 cent, and 45 cent stamps.
Let's call number of 13 cent($0.13) stamp A
Call number of 29 cent($0.29) stamp B
Call number of 45 cent($0.45) stamp C
Thus;
A + B + C = 54
We are told the total value of the 3 stamps are $15.98.
Thus;
0.13A + 0.29B + 0.45C = $15.98 - - - (eq2)
Now we are told that if the number of 13 cent stamps is doubled, the new total value of his stamp collection would be $17.80.
Thus;
2(0.13A) + 0.29B + 0.45C = 17.8
0.26A + 0.29B + 0.45C = 17.8 - - - (eq 3)
Solving the 3 equations simultaneously, we have;
A = 14
B = 24
C = 16
We have;
Number of 13 cents stamp = 14
Number of 29 cents stamp = 24
Number of 45 cents stamp = 16
Find the z-score such that: a. The area under the standard normal curve to its left is 0.5 b. The area under the standard normal curve to its left is 0.9826 c. The area under the standard normal curve to its right is 0.1423 z
Answer:
The answer is below
Step-by-step explanation:
The z score is used to determine by how many standard deviations the mean is above or below the raw score. If the z score is positive then the raw score is above the mean while if the z score is negative then the raw score is below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}\\ \\\mu=mean, \sigma=standard\ deviation[/tex]
a)
From the normal distribution, 0.5 corresponds to a z score of 0.
z = 0.
b) From the normal distribution, an area of 0.9826 to the left corresponds to a z score of 2.11.
c) An area to the right of 0.1423 = an area of 0.8577 ( 1- 0.1423) to the left. From the normal distribution, an area of 0.8577 to the left corresponds to a z score of 1.07
Soda cans A machine that fills cans with soda fills according to a Normal model with mean 12.1 ounces and standard deviation 0.05 ounces. a. If the cans claim to have 12 ounces of soda each, what percent of cans are under-filled
Answer:
The percentage is [tex]p = 4.55\%[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 12.1 \ ounce[/tex]
The standard deviation is [tex]\sigma = 0.05 \ ounce[/tex]
The value of soda each can claims to have is [tex]X = 12 \ ounce[/tex]
Generally the z-score is mathematically represented as
[tex]z = \frac{ X- \mu }{\sigma }[/tex]
=> [tex]z = \frac{ 12-12.1 }{0.05}[/tex]
=> [tex]z = -2[/tex]
From the z table the area under the normal curve representing the proportion of under filled cans is
[tex]P(x <-2 \ or\ x > 2)= 0.0455[/tex]
Converting to percentage
[tex]p = 0.0455 *100[/tex]
=> [tex]p = 4.55\%[/tex]
Marisa is making a scale drawing of her house. Her
house is 49 feet wide. On her drawing, the house is 7
inches wide. What is the scale of Marisa's drawing?
The scale is
Answer:
7 ft per in
Step-by-step explanation:
If she has a scale where 49 feet is represented by 7 inches, then the ratio is:
49 feet to 7 inches which can be written as:49 ft /7 in = 7 ft / in
So the scale is 7 feet per inch
Can someone please help me? I've been trying to figure this out for days. I don't understand how to construct a confidence interval.
I know that the red box has a mean value of 15.11 and the blue box's mean is 16.83. The difference of sample means is 1.74. The red standard deviation is 3.868 and the blue one is 2.933. the standard deviation of the sample mean differences is 0.69. How do I use all this to construct the interval with no difference between the population means.
Step-by-step explanation:
Confidence interval is:
CI = x ± CV · SE
where x is the mean, CV is the critical value, and SE is the standard error.
There is no difference between the population means, so x = 0.
The confidence level is 95%, so CV = 1.96.
SE = 0.69.
So the confidence interval is:
CI = 0 ± (1.96) (0.69)
CI = (-1.35, 1.35)
1.74 is outside of the confidence interval, so it is statistically significant.
Answer:
Step-by-step explanation:
same i need help
Vx+2 = 5
Find the solutions
Answer:
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
x
=
3
V
Answer:
Vx = 3
Step-by-step explanation:
The answer below is because you move all terms not containing Vx to the right side of the equation.
Khloe drove 204 miles in 4Hours
Answer:
She was driving 51 miles per hour.
Step-by-step explanation:
51 x 4 = 204
204 / 4 = 51
Sydney drove 117 miles in 3 hours. If she continued at the same rate, how far would she travel in 19 hours?i
Answer:
741 miles in 19 hours
Step-by-step explanation:
PLZ HELP
A train travels at an average speed of 67.5 miles per hour. At this speed, how far could the train travel in 3.25 hours?
Answer:
219.375 miles
Step-by-step explanation:
1 hour the train can go for 67.5 miles
so multiply the 67.5 with 3.25 and then you will get 219.375
Four cats and five mice enter a race. In how many ways can they finish with a mouse placing first, second, and third
The requried, there are 240 possible ways the race can finish with a mouse placing first, second, and third.
To find the number of ways the race can finish with a mouse placing first, second, and third, we can use the concept of permutations.
Since the mouse is guaranteed to finish first, there are 5 mice to choose from for the first position.
Once the first place is determined, there are 4 mice left for the second position.
After the first two positions are filled, there are 3 mice left for the third position.
Now, we need to determine the order of the cats. There are 4 cats to choose from for the fourth position.
The total number of ways the race can finish with a mouse placing first, second, and third is given by the product of these choices:
Number of ways = 5 (for first place) * 4 (for second place) * 3 (for third place) * 4 (for fourth place)
Number of ways = 5 * 4 * 3 * 4
Number of ways = 240
There are 240 possible ways the race can finish with a mouse placing first, second, and third.
Learn more about permutation here:
https://brainly.com/question/33149025
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can someone help asap
Domain is the set of all input values, while range is the set of all:
a independent variables
c. relations
b. output values
d. functions
Please select the best answer from the choices provided
Answer:
The answer that would best complete the given statement above would be option B.
Assume that when adults with smartphones are randomly selected, 39% use them in meetings or classes. If 30 adult smartphone users are randomly selected, find the probability that exactly 24 of the use their smartphones in
meetings or classes
The probability is .
(Round to four decimal places as needed)
Answer:
n = 10
p = 0.56
Step-by-step explanation:
What is the sum of the integers less than 100 that have both 6 and 9 as divisors?
Answer:
The sum of the integers less than 100 that have both 6 and 9 as divisors is 270
Step-by-step explanation:
To determine the integers less than 100 that have both 6 and 9 as divisors,
First, we will list the multiples of 6 and 9 that are less than 100, and the common multiples will give the integers less than 100 that have both 6 and 9 as divisors.
Multiples of 6 less than 100 are:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96.
Multiples of 9 less than 100 are:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90, and 99.
Hence, the integers less than 100 that have both 6 and 9 as divisors are 18, 36, 54, 72 and 90.
Then, the sum of the integers less than 100 that have both 6 and 9 as divisors is
18 + 36 + 54 + 72 + 90 = 270
Hence, the sum of the integers less than 100 that have both 6 and 9 as divisors is 270.
Triangle GHJ is shown below.
12 in.
H
16 in.
What is the perimeter, in inches, of Triangle GHJ
Answer:
the perimeter of triangle abc is 56.4 and the perimeter of triangle GHJ is 14.1 cm the perimeter of triangle DEF
Step-by-step explanation:
Question 12
Which expression is equivalent to –6 (
-6 (- 1)?
A little confused by this question. Does anyone know how to do this?
Thank you !
Answer:
[tex]if \: {i}^{k} = 1. \: \iff\:then \: k = 0 .\\ if \: {i}^{k} = i. \: \iff\: then \: k = 1. \\ if \: {i}^{k} = - 1. \: \iff\: then \: k = 0 \: and \:i = - 1 . \\ if \: {i}^{k} = - i. \: \iff \:then \: k = 1 \: and \: i = - i.[/tex]
Step-by-step explanation:
♨Rage♨
Evaluate the expression 263 + 5 when b= 3.
Answer:
59
Step-by-step explanation:
2b^3+5 when b=3
Plug in the value of b
2*3^3+5 = 2*27+5 = 54+5 = 59
Jim earned $95 after working days. At this rate how many days will it take him to earn $285?
Answer:
It will take him 3 days if every day he earns $95.
95 * 3 = 285
285/95 = 3
Step-by-step explanation:
Hope this helped you! <3
Corrected, the answer is 15.
Evaluate the expression for x = 0.1
1.2x
Answer:
0.12
Step-by-step explanation:
This is the answer because:
1) First, rewrite the expression including the x value
1.2(0.1)
2) Next, we know 1.2 x 1 is 1.2, but since we have one decimal point in 0.1, we have to move the decimal point in 1.2 once to the left. This will make the answer 0.12
Hope this helps! :D
One beehive produces 64 pounds of honey per year. How many
beehives does it take to produce 5,504 pounds of honey?
Answer:
86 beehives, Hope I helped!
Step-by-step explanation:
I'm to lazy :P
Find the percentage of area under a normal curve between the mean and the given number of standard deviations from the mean.1.68
Answer:
0.4532
Step-by-step explanation:
Given the question :
Find the percentage of area under a normal curve between the mean and the given number of standard deviations from the mean.1.68
Number of standard deviations from the mean = 1.68
I. 68 standard deviations below the mean :
Mean = 0(normal distribution)
P(Z < 0) = 0.5
1.68 standard deviations above the mean = + 1.68
P(Z < 1.68) = 0.95352
P(0 < x < Z) = (0.95352 - 0.5) = 0.4532
The factorization of 12x + 15 is
how to subtract 1/4 minus 1/8
Answer:
You would multiply 1/4 by 2/2 in order to get a common demoninator. The answer is 1/8.
Step-by-step explanation:
A grid model with 100 squares. 73 squares are shaded.
What percent of the model is shaded? |_____|
What is the equivalent ratio? |____|
What is the equivalent decimal? |____|
What is the equivalent fraction? |____|
Answer:
Step-by-step explanation:
73% is shaded
Equivalent ratio 73/100 times 2
146/200 is the ratio
0.73 is the decimal
73/100 is the fraction
Answer:
73%
Step-by-step explanation:
in 3/5 ÷ 3= 1/5 the quotient is greater than or less than the dividend
Answer:
quotient less than the dividend
Step-by-step explanation:
In this equation:
Dividend = 3/5
Divisor = 3 and
Quotient = 1/5
The question asks you to compare 3/5 to 1/5 and 3/5 is larger therefore the quotient less than the dividend.
Sean and his crew operate a fishing charter company. They caught a blue
marlin and an amberjack. The weight of the blue marlin was 12 times as
great as the weight of the amberjack. The combined weight of both fish was
1,014 pounds. How much did each fish weigh?
Determine the unit rate: 24 tickets for $480
Answer: 20 dollars per ticket
Step-by-step explanation:
Divide the number 480 by 24.
480 ÷ 24 = 20
The answer is 20. Hope this helps!
Step-by-step explanation:
If 24 tickets cost $480 the cost of 1 is:
Let the unit be u
480 ÷ 24= u
[tex] \frac{480}{24} = u[/tex]
[tex]20 = u[/tex]
[tex]u = 20[/tex]
Hope this helps....
Hence the unit = 20
