Part a)
We have that,the distribution of finishing time for men was approximately normal with mean 242 minutes and standard deviation 29 minutes.
We want to calculate and interpret the standardized score for Clay's marathon time, if the finishing time for Clay was 289 minutes.
We use the formula:
[tex]z = \frac{x - \bar x}{s} [/tex]
we substitute the values to get:
[tex]z = \frac{289 - 242}{29} [/tex]
[tex]z = 1.62[/tex]
This means Clay's finishing time is 1.62 standard deviation above the mean finishing time.
Part b)
This time, we have that, the distribution of finishing time for women was approximately normal with mean 259 minutes and standard deviation 32 minutes.
We want to find the proportion of women who ran the marathon that had a finishing time less than Kathy if the finishing time for Kathy was 272 minutes.
We first calculate the z-score to get:
[tex]z = \frac{272 - 259}{32} = 0.41[/tex]
From the normal standard distribution table P(z<0.41)=0.6591.
This means 65.91% of women had a finishing time less than Kathy's finishing time.
Part c
The standard deviation of a data set tells us how far away the individual data are from the mean.
If the standard deviation of finishing time is greater for women than men, it means the finishing time for women are farther from the mean finishing time than that of men.
Using the normal distribution, it is found that:
a) His standardized score was of z = 1.6, which means that his finishing time is of 1.6 standard deviations above the mean finishing time for all men.
b) 0.6591 = 65.91% of women who ran the marathon had a finishing time less than Kathy's.
c) The higher standard deviation shows that the finishing times of the women who ran the marathon are more spread out compared to the finishing times of the men who ran the marathon.
In 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.Item a:
For men, mean of 242 minutes, thus [tex]\mu = 242[/tex].Standard deviation of 29 minutes, thus [tex]\sigma = 29[/tex].The z-score is found when X = 289, thus:[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{289 - 242}{29}[/tex]
[tex]Z = 1.6[/tex]
His standardized score was of z = 1.6, which means that his finishing time is of 1.6 standard deviations above the mean finishing time for all men.
Item b:
For women, mean of 259 minutes, thus [tex]\mu = 259[/tex]Standard deviation of 32 minutes, thus [tex]\sigma = 32[/tex].The proportion is the p-value of Z when X = 272, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{272 - 259}{32}[/tex]
[tex]Z = 0.41[/tex]
[tex]Z = 0.41[/tex] has a p-value of 0.6591.
0.6591 = 65.91% of women who ran the marathon had a finishing time less than Kathy's.
Item c:
The higher standard deviation shows that the finishing times of the women who ran the marathon are more spread out compared to the finishing times of the men who ran the marathon.
A similar problem is given at https://brainly.com/question/24855678
Jill needs to cut a piece of string into 20 smaller pieces. How many times will she need to cut the string?
Answer:
She need to cut the string 19 times
Step-by-step explanation:
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
19 cut.
Jill needs to make 19 cuts in the piece of string to have 20 smaller pieces, as each cut adds one additional piece and the first piece does not require a cut.
To determine how many times Jill needs to cut the string to get 20 smaller pieces, we need to understand the relation between cuts and pieces. Imagine having a single piece of string. Once you make a single cut, you now have two pieces.
Therefore, the number of cuts is always one less than the number of pieces you want to have because the first piece does not require a cut.
If Jill wants 20 pieces of string, she will need to make 19 cuts. This is because every cut adds one additional piece to the total count. After the first cut, there are two pieces. After the second cut, assuming she cuts one of those two pieces, there are three pieces, and so on. When she makes the nineteenth cut, she will have twenty pieces.
According to the annual Summer Vacation Survey conducted by Myvesta, a nonprofit consumer education organization, the average summer vacation costs $2252. If $1650 of this amount is charged on a credit card, what percent of the vacation cost is charged?
Answer:
The answer is : 73.3% (to 1 decimal place)
Step-by-step explanation:
The question is asking us to convert the proportion of a certain amount into percentage, and this is done as shown below:
vacation cost = $2252
amount charged = $1650
%of vacation cost that was charged = X%
∴ X% of 2252 = 1650
[tex]\frac{X}{100}[/tex] × 2252 = 1652
[tex]\frac{2252X}{100} =1650[/tex]
2252X = 165000 (dividing both sides by 2252)
[tex]\frac{2252X}{2252}=\frac{165000}{2252}[/tex]
∴ X = 165000 ÷ 2252
X = 73.3%
The perimeter of a triangle is 19 cm. Assume the sides (in order of length from smallest to longest are a, b, c respectively). If the length of the longest side is twice that of the shortest and is 3 cm less than the sum of the lengths of the other two sides, find the lengths of each side.
Answer:
The lengths of each side are:
a = 4 cm.
b = 7 cm.
c = 8 cm.
Step-by-step explanation:
To solve this, we will write the equation out of the word problem given in the question, and this is done as follows;
sides of the triangle from smallest to longest = a, b, c
perimeter of the triangle = a + b + c = 19 cm - - - - - - - - - (1)
Length of the longest side is twice that of shortest side; c = 2a - - - - - - (2)
length of longest side is equal to 3 cm less than the sum of the lengths of the other two sides; c = (a + b) - 3 - - - - - - - (3)
therefore:
a + b + c = 19 - - - - - (1)
c = 2a - - - - - - - - - - (2)
c = (a + b) - 3 - - - - - - - - (3)
putting equation (2) into equation (1)
a + b + (2a) = 19
3a + b = 19 - - - - - - (4)
Substituting for c in equation (3) using equation (2)
c = (a + b) - 3 - - - - - - - - (3) (replacing c with 2a from equation 2)
2a = a + b - 3 (making b the subject)
2a - a = b - 3
∴ b = 2a - a + 3
b = a + 3 - - - - - - -(5)
substituting for the value of b in equation (4), using equation 5
3a + b = 19 - - - - - - (4) ( replacing b with equation 5)
3a + (a + 3) = 19
4a + 3 = 19
4a = 19 - 3 = 16
∴ a = 16 ÷ 4 = 4
since, we know 'a', calculating for b, using equation 5;
b = a + 3 - - - - - - -(5) (where a = 4)
∴ b = 4 + 3 = 7
Finally calculating for c, using equation 2
c = 2a - - - - - - - (2) (where a = 4)
c = 2 × 4 = 8
Therefore:
a = 4; b = 7 ; c = 8
Rashid solved a fraction division problem using the rule "multiply by the reciprocal." His work is shown below. Three-fourths divided by 9. Three-fourths times StartFraction 1 Over 9 EndFraction = StartFraction 3 Over 36 EndFraction or StartFraction 1 Over 12 EndFraction
Answer:
A. Rashid solved the problem correctly.
Step-by-step explanation:
The missing option is given as:
Which is the most accurate description of Rashid’s work?
A. Rashid solved the problem correctly.
B. Rashid multiplied the dividend by the divisor instead of finding the reciprocal.
C. Rashid multiplied the denominators instead of finding a common denominator.
D. Rashid multiplied with the reciprocal of the dividend instead of the reciprocal of the divisor.
Rashid solve the problem correctly as he gave the answer in lowest form.
[tex]\frac{3}{4}[/tex] ÷ [tex]9[/tex]
[tex]\frac{3}{4} *\frac{1}{9} \\\frac{3 * 1}{4 * 9} \\\frac{3}{36} =\frac{1}{12}[/tex]
So, Rashid final answer is correct 3/36 or 1/12
Answer:
Rashid Missed This Step: [tex]\dfrac{3}{4 X 9}[/tex]
Step-by-step explanation:
Rashid solved a fraction division problem using the rule "multiply by the reciprocal."
[tex]\dfrac{3}{4} \div 9\\ =\dfrac{3}{4} X \dfrac{1}{9}\\=\dfrac{3}{36}\\=\dfrac{1}{12}[/tex]
Rashid misses a step which will now be shown below:
[tex]\dfrac{3}{4} \div 9 =\dfrac{3}{4} X \dfrac{1}{9}\\=\dfrac{3}{4 X 9}\\=\dfrac{3}{36}\\=\dfrac{1}{12}[/tex]
I need to know the lengths of MN, NP, and PM
Answer:
MN = 12 units
NP = 16 units
PM = 20 units
Step-by-step explanation:
You can find MN and NP by counting on the graph. To find PM you will need to use the formula a^2 + b^2 = c^2 ( ^ stands for exponent)
MN and NP will be a and b.
Example: 12^2 + 16^2 = c^2
Simplify.
Example:
144 + 256 = c^2
144 + 256 = 400
Then find the square root of 400 which is 20.
To check your work put all of the sides into the formula and it should be true.
find the area of the shape shown below
Answer:
63
Step-by-step explanation:
3x3= 9x7= 63
Compare and contrast pounds and ounces
Out of the two units, ounce is smaller than pound and both have traditionally been used for different purposes. Whereas ounces are used to measure precious metals and spices as they are required in smaller quantities, pounds are used to measure fruits and vegetables, and interestingly, mass of people also.
Mr.smith and mr.Stein We’re driving to a business meeting 100 miles from their office. Mr.smith Drove the first y miles ,then mr. Stein Drove the rest of the way.
Answer:
mrs smith drove 50 miles and mr stein drove 50 mile
Step-by-step explanation:
Please help !! Timed !! *****
Answer:
The answer to your question is 6x
Step-by-step explanation:
Data
f(x) = 3x
g(x) = 2x
(g°f)(x) = ?
Process
1.- To find (g°f)(x) substitute the value of f(x) in g(x) and simplify
-Substitution
(g°f)(x) = 2(3x)
-Simplification
(g°f)(x) = 6x
The third choice is correct
A study was conducted looking at the association between the number of polyps in the colon and mean grams of fiber consumed per day based on a standard food frequency questionnaire. The Pearson correlation coefficient was 0.9 with a p-value of 0.003 and the Spearman correlation coefficient was 0.28 with a p-value of 0.049. Which form of correlation would be more appropriate to report and why?
Answer:
C) The Spearman correlation results should be reported because at least one of the variables does not meet the distribution assumption required to use Pearson correlation.
Explanation:
The following multiple choice responses are provided to complete the question:
A) The Pearson correlation results should be reported because it shows a stronger correlation with a smaller p-value (more significant).
B) The Pearson correlation results should be reported because the two variables are normally distributed.
C) The Spearman correlation results should be reported because at least one of the variables does not meet the distribution assumption required to use Pearson correlation.
D) The Spearman correlation results should be reported because the p-value is closer to 0.0556.
Further Explanation:
A count variable is discrete because it consists of non-negative integers. The number of polyps variable is therefore a count variable and will most likely not be normally distributed. Normality of variables is one of the assumptions required to use Pearson correlation, however, Spearman's correlation does not rest upon an assumption of normality. Therefore, the Spearman correlation would be more appropriate to report because at least one of the variables does not meet the distribution assumption required to use Pearson correlation.
Part A
If you spin the spinner 11 times, what is the prediction for the number of times it will land on red?
Each section is equal in size.(it's talking about the spiner)
Answer:
Part B
What is the probability of green?
A: 3/11
B:4/11
C:1/11
D:7/11
Since all sectors have the same area, the spinner is equaly likely to land on each of them. There are:
3 yellow sectors3 red sectors4 green sectors1 blue sectorObviously, this implies that there are 11 sectors in total.
So, the spinner will land on a certain color with probability
[tex]p=\dfrac{\text{\# of sectors for that color}}{\text{11}}[/tex]
Use this formula to deduce the probability of green.
Finally, you can multiply the probability of red by 11 to get the expected number of reds in 11 spins.
Alejandro ha hecho 3 exámenes. El primero tenía 8 preguntas, el segundo 9 y el tercero 12. Las preguntas correctas de cada uno de ellos han sido 7, 8 y 10, respectivamente. Si en cada examen todas las preguntas tenían la misma calificación ¿en cuál de ellos ha obtenido un mejor resultado?
An object is dropped from 43 feet below the tip of the pinnacle atop a 527-ft tall building. The height h of the object after t seconds is given by the equation h equals negative 16 t squared plus 484. Find how many seconds pass before the object reaches the ground.
Answer:
5.5 seconds
Step-by-step explanation:
The function that gives the height of the object after t seconds falling is:
h = -16t^2 + 484.
To find the time when the object reaches the ground, we just need to use the value of h = 0 in the equation, and then find the value of t:
0 = -16t^2 + 484.
16t^2 = 484
t^2 = 30.25
t = 5.5 seconds
So the object will reach the ground after 5.5 seconds
Answer:
5.5 sec
Step-by-step explanation:
The height h of the object after t seconds is given by the equation
h =- 16 t²+ 484
The height would be zero when the object hits the ground. therefore equating the above equation to zero
0 = - 16 t²+ 484 (solving for t)
16 t²= 484
t² = 484/16
t²= 30.25
taking square root on B.S
t= 5.5 sec
3x + 10 = 22
Solve for x
Answer:
x=4
Step-by-step explanation:
Step 1: Subtract 10 from both sides.
3x+10−10=22−10
3x=12
Step 2: Divide both sides by 3.
3x/3=12/3
x=4
if i can get brainliest that would be great
Jen rode her bike 1/5 of a mile to her friend's house. It took her 5 minutes to get there. What was Jen's speed?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
Jen's speed was 1/25 miles per minute or 2.4 miles per hour. This was found by dividing the distance travelled by the time it took.
Explanation:To find Jen's speed, we need to divide the distance she rode by the time it took her. In this case, Jen rode 1/5 of a mile in 5 minutes. To get her speed in miles per minute, we perform the division:
1/5 mile ÷ 5 minutes = 1/25 miles per minute
This means that Jen's speed was 1/25 miles per minute. You could also convert this to miles per hour if you prefer, by multiplying the result by 60 (since there are 60 minutes in an hour). In that case:
1/25 miles per minute x 60 minutes/hour = 2.4 miles/hour.
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Jen's speed was 1/25 miles per minute, calculated by dividing the distance traveled, 1/5 mile, by the time taken, 5 minutes.
Explanation:To determine Jen's speed, we would divide the distance she traveled by the time it took her to get there. Jen rode her bike for 1/5 of a mile, and it took her 5 minutes. To find her speed in miles per minute, we perform the following calculation:
Speed = Distance ÷ Time
Speed = (1/5) mile ÷ 5 minutes = 1/5 ÷ 1/5 = 1/25 miles per minute.
We don't need to convert the units since we are asked to provide the answer as a proper fraction. Therefore, Jen's speed was 1/25 miles per minute.
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Helppp me please!!!!!
Answer:
3^-2 = 1/3^2 = 1/9
Step-by-step explanation:
3^4 * 3^-6
Using the properties of exponents
We know that a^b * a^c = a^(b+c)
3^4 * 3^-6 = 3^-2
If we only want positive exponents
We know that a^-b = 1/a^b
3^-2 = 1/3^2 = 1/9
We can also look at it
The negative exponent puts the 3's in the denominator
3*3*3*3 * 1/ (3*3*3*3*3*3)
Canceling
1/ (3*3)
1/9
Type an equation for the following pattern
Answer:
y=35x+20
Step-by-step explanation:
The equation for the given pattern of values is y = 85x - 80, found by determining the slope and y-intercept from the provided data.
The task is to find an equation for the pattern given by x = 1, 2, 3, 4, 5, and y = 5, 90, 125, 160, 195, which we can determine by using the equation for a line, y=mx+b.
To find m, the slope, we calculate the change in y divided by the change in x between two data points. Based on the given numbers, m = (90-5)/(2-1) = 85.
Once we have m, we substitute a known point (1, 5) into y=mx+b and solve for b, giving b=5- 85*1 = -80. So, our equation for the given pattern is y = 85x - 80.
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What is a equation using (h) hours and (c) cookies?
Answer:
There are 12 cookies (c). It takes 2 hours (h) to bake 1 cookie. How long will it take to bake 12 cookies?
How do you simplify numbers with exponents
Find the perimeter of the shape
5cm
6cm
17cm
8cm
Perimeter = [perimeter] cm
Hey need help asap :):):):
Answer:
C Option is the right one. (•‿•)(•‿•)(•‿•)(•‿•)
Answer:
Its B
Step-by-step explanation:
Distribute and do not forget the minus in the middle and the 4 is negative
Mr. Patel decided to challenge his Algebra I students by asking them to describe the effect 2f | 1x would have on the
function f(x) = 2. Use your understanding of horizontal and vertical stretches to explain the result.
Answer:
A: The parabola would stretch both vertically and horizontally by a factor of 2.
Answer:
The parabola would stretch both vertically and horizontally by a factor of 2.
Step-by-step explanation:
I just took the quiz on Edg.
If 30% of a number is 45, what is 4/5 of the number?
Answer: 4/5 of 45 is 36
Step-by-step explanation: If you were to divide 45 by 5 you would get 9. 9 is 1/5 of 45 so if you multiplied it by 4 you would 4/5 of 45 which is 36.
The ( 4/5 )th of the number is 120 and the equation is ( 30 / 100 ) N = 45 , where N is the number and N = 150
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number be represented as N
A = 30% of a number is 45
Substituting the values in the equation , we get
( 30/100 ) N = 45 be equation (1)
Multiply by 100 on both sides of the equation , we get
30 N = 4500
Divide by 30 on both sides of the equation , we get
N = 4500 / 30
N = 150
Therefore , the value of N is 150
Now , ( 4/5 )th of the number be calculated as
Let the ( 4/5 ) of the number be = B
So , the equation will be
B = ( 4/5 ) x 150
B = 4 x 30
B = 120
Hence , the number is 150 and ( 4/5 ) th of the number is 120
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simple problem! will mark brainliest!
Answer:
r=1
Step-by-step explanation:
Because the table has the same input and output, the constant of proportionality is 1
On december 1, jonas jewelry wholesale center started with an inventory of 1,000 watches. shipments of 168, 231, and 411 were sent out on january 3, february 8, and march 7, respectively. receipts of 21, 145, and 11 were received on january 8, february 22, and march 18. find the number of watches on hand as of march 18. 1,732 424 367 1,633
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
Total watches in an inventory = 1000
Number of shipments sent out = 168, 231, 411
So, Remaining inventory of watches would be :
[tex]1000-(168+231+411)\\\\=1000-810\\\\=190[/tex]
New receipts = 21, 145 and 11
So, Number of watches on hand becomes :
[tex]190+(21+145+11)\\\\=367[/tex]
Hence, Third option is correct.
A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. The 9898% confidence interval for p is 59 plus or minus 0.08 .59±0.08. Interpret this interval. A. We are 9898% confident that between 5151% and 6767% of the sampled students receive some sort of financial aid. B. We are 9898% confident that the true proportion of all students receiving financial aid is between 0. 51.51 and 0. 67..67. C. 9898% of the students receive between 5151% and 6767% of their tuition in financial aid. D. We are 9898% confident that 59% of the students are on some sort of financial aid.
Answer:
Step-by-step explanation:
Confidence interval is written as
Sample proportion ± margin of error
Margin of error = z × √pq/n
Where
z represents the z score corresponding to the confidence level
p = sample proportion. It also means probability of success
q = probability of failure
q = 1 - p
p = x/n
Where
n represents the number of samples
x represents the number of success
From the information given,
n = 200
x = 118
p = 118/200 = 0.59
q = 1 - 0.59 = 0.41
To determine the z score, we subtract the confidence level from 100% to get α
α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01
This is the area in each tail. Since we want the area in the middle, it becomes
1 - 0.01 = 0.9
The z score corresponding to the area on the z table is 2.326. Thus, confidence level of 98% is 2.326
Therefore, the 98% confidence interval is
0.59 ± 2.326√(0.59)(0.41)/200
= 0.59 ± 0.08
The lower boundary is
0.59 - 0.08 = 0.51
The upper boundary is
0.59 + 0.08 = 0.67
The correct option is
B. We are 98% confident that the true proportion of all students receiving financial aid is between 0. 51 and 0. 67
STVZ~JHGF. Find the value of X
5x - 2y = 30 if 8 = x
Answer:
Y=5
Step-by-step explanation:
If x = 8 then y = 5
Step-by-step explanation:Plug x into the equation and solve
5x - 2y = 30 <- Rewrite
5(8) - 2y = 30 <- Plug x in
40 - 2y = 30 <- Simplify
-40 -40 <- Get y alone
-2y = -10 <- Simplify
y = 5 <- Divide both sides by -2 to get y
There are 16 tables set up for a banquet, of which 4 have red tablecloths.
What is the probability that a randomly selected table will have a red tablecloth?
Write your answer as a fraction or whole number.
The probability that a randomly selected table will have a red tablecloth is 1/4, since there are 4 red tablecloths out of 16 tables.
Explanation:The question asks for the probability that a randomly selected table will have a red tablecloth given that there are 16 tables and 4 have red tablecloths. To find the probability, we use the formula:
Probability (P) of choosing a red tablecloth = (Number of red tablecloths) / (Total number of tables)
Substituting the given numbers:
P(red tablecloth) = 4 / 16 = 1 / 4
Therefore, the probability is 1/4 or 0.25 when expressed as a decimal.
It is important to round answers to relative frequency and probability problems to four decimal places when required, but in this case, the fraction 1/4 is already as simple as it can be.
Scores of two school basketball teams are recorded. The mean of Team A is 68. The mean of Team B is 67. What conclusion can you derive from the random samples?
The conclusions that can be drawn are 3, two of a direct type and the other of an indirect type.
The direct ones are the values. Team A has an average of 68 points per game, which means that it has a good point average and, in the same way, team B, which has an average of 67, which is still a good point average per game.
The hint is the comparison of both teams, and that is that team A is one point above team B, which in terms of points per game makes them better.