Total score: ____ of 20 points A marching band performs on the football field at half-time. As they perform, the members of the band stand in the shape of a sinusoidal function. While playing, they move, but still maintain the sinusoidal function, transforming it in different ways. Darla is a member of the marching band. As the band begins to play she is positioned in the exact center of the field. The person closest to her on the same horizontal line, stands 10 yards away. The sinusoidal function extends to the ends of the playing field. The playing area of football field measure 300 feet by 160 feet. Place the playing area of a football field on the coordinate plane such that the origin is the lower left corner of the football field. (Score for Question 1: ___ of 2 points) 1. What is the period and the amplitude of the sine function representing the position of the band members as they begin to play? Answer: (Score for Question 2: ___ of 6 points) 2. Edna is sitting in the stands and is facing Darla. Edna observes that sine curve begins by increasing at the far left of the field. What is the equation of the sine function representing the position of band members as they begin to play? Answer: (Score for Question 3: ___ of 4 points) 3. As the band begins to play, band members move away from the edges, and the curve reverses so that the function begins at the far left by decreasing. Darla does not move. The sine curve is now half as tall as it was originally. What is the equation of the sine curve representing the position of the band members after these changes? Answer: (Score for Question 4: ___ of 3 points) 4. Next, the entire band moves closer to the edge of the football field so that the sine curve is in the lower half of the football field from Edna’s vantage point. What is the equation of the sine curve representing the position of the band members after these changes? Answer: (Score for Question 5: ___ of 5 points) 5. At the end of the performance, the band marches off the field to the right, moving the entire sine curve. Asa grabs his camera to takes a picture of the entire football field. At the instant he takes the picture, the first person forming the curve now stands at the 5 yard line. What is the equation of the sine curve representing the position of the band members in Asa’s picture? Answer: Please help me explain step-by-step thank you
Answers
Answer:
1) Amplitude; A = 80 ft
Period = 60 ft
2)y = 80 sin ((π/30)x - 5π) + 80
3)y = 40 sin ((π/30)x - 5π) + 80
4)y = 40 sin ((π/30)x - 5π) + 40
5)y = -65sin ((π/30)x - 5π) + 80
Step-by-step explanation:
The general formula for sinusoidal wave equation is given by;
y = A sin (Bx - C) + D
Where;
A is amplitude = D_max or D_min
Period = 2π/B
So; B = 2π/Period
Phase Shift = C/B
So; C = B · Phase Shift
D: center
We are Given:
Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft
Thus; A = 80 ft
The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft
Thus; B = 2π/60 = π/30
Field is 300 ft wide and so the center is 300/2 = 150 ft
Thus; Phase Shift = 150.
C = B × Phase Shift = π/30 · 150 = 5π
1) From the calculations above,
Amplitude; A = 80 ft
Period = 60 ft
2) As they begin to play, from the calculations above and y = A sin (Bx - C) + D, equation of the sine function is now;
y = 80 sin ((π/30)x - 5π) + 80
3) In this, since the sine wave is half as tall, then after the changes, we have;
y = 40 sin ((π/30)x - 5π) + 80
4) since they have moved closer, then equation is now;
y = 40 sin ((π/30)x - 5π) + 40
5) We are Given:
Height of the field is 160 ft and so the center is at y = 80. Thus; D = 80 ft
Since the first person forming the curve now stands at the 5 yard line, the minimum is at 5 yds (15 ft). Thus;
D_min = 80 - 15 = 65. Thus; A = 65 ft
The person closest to Darla on the same horizontal line, stands 10 yards(30 ft) Thus, period = 2 × 30 = 60 ft
Thus; B = 2π/60 = π/30
Field is 300 ft wide and so the center is 300/2 = 150 ft
Thus; Phase Shift = 150.
C = B × Phase Shift = π/30 · 150 = 5π
The band ends down (at 15 feet) and thus A is negative
The equation is;
y = -65sin ((π/30)x - 5π) + 80
Part(1): The required values are,
Amplitude=[tex]80 ft[/tex] and Period: [tex]60 sec[/tex]
Part(2):
The equation of the sine function is
[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80[/tex]
Part(3):
The equation of the sine curve is,
[tex]y=40cos(\frac{\pi x}{30})+80[/tex]
Part(4):
The equation of the sine curve representing the position of the band members after these changes is [tex]y=40cos(\frac{\pi x}{30})+40[/tex]
Part(5):
The required graph is attached below,
Simple harmonic motion:Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position
Part(1):
Amplitude=[tex]\frac{1}{2} width=80ft[/tex]
Period=[tex]2\times 30=60 sec[/tex]
Part(2):
Let the equation be,
[tex]y=80 cos(\frac{\pi x}{30}+\pi)+80\\ y'=-\frac{8\pi}{3} sin((\frac{\pi x}{30}+\pi))[/tex]
Darla is at the point [tex]D(150,80)[/tex] which is on the graph at [tex]x=0[/tex] then,
[tex]80=80 cos(5\pi+\pi)=0\\y=-80 cos (\frac{\pi x}{30} )+80[/tex]
Part(3):
Since the wave is now [tex]\frac{160}{2} =80 ft[/tex] then,
Amplitude=40 ft
[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80\\y=40cos(\frac{\pi x}{30})+80[/tex]
Part(4):
The graph shifts downward 40 ft then,
[tex]y=-4 cos (\frac{\pi x}{30} -\pi)+80-40\\y=40cos(\frac{\pi x}{30})+40[/tex]
Part(5):
Start at:[tex]Y(x)=80sin (\frac{2\pi x}{60} )+80\\[/tex]
End at: [tex]Z(x)=80sin[ (\frac{2\pi }{60}(x-15) )]+80\\[/tex]
The graph is attached below:
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Related Questions
Gena wants to estimate the quotient of –21.87 divided by 4.79. Which expression shows the best expression to estimate the quotient using front-end estimation? Negative 21 divided by 4 Negative 21 divided by 5 Negative 20 divided by 4 Negative 20 divided by 5
Answers
Answer:
-21/5 = -4.2
Step-by-step explanation:
-21.87 / 4.79 = -4.5657.....
So, the quotients is -4
Now, Let's see who's quotient is equal to think one:
-21/4 = -5.25
-21/5 = -4.2
-40/4 = -5
-20/5 = 4
Answer:
-21/5 = -4.2
Step-by-step explanation:
A new soft drink is being market tested. It is estimated that 60% of consumers will like the new drink. A sample of 96 taste tested the new drink. a) Determine the standard error of the proportion b) What is the probability that more than 75% of consumers will indicate they like the drink
Answers
Answer:
a
[tex]S.E = 0.05[/tex]
b
[tex]P(P > 0.75) = 0.0013499[/tex]
Step-by-step explanation:
From the question we are told that
The population [tex]p = 0.60[/tex]
The sample size is [tex]n = 96[/tex]
The sample proportion is [tex]\r p = 0.75[/tex]
Generally the standard error is mathematically represented as
[tex]S.E = \sqrt{ \frac{p(1-p)}{n } }[/tex]
substituting values
[tex]S.E = \sqrt{ \frac{0.60 (1-0.60 )}{96 } }[/tex]
[tex]S.E = 0.05[/tex]
The probability that more than 75% of consumers will indicate they like the drink is mathematically represented as
[tex]P(P > 0.75) = P(\frac{\r P - p }{\sqrt{\frac{p(1-p)}{n} } } > \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n} } } )[/tex]
The z-score is evaluated as
[tex]z = \frac{\r p - p }{\sqrt{\frac{p(1-p)}{n} } }[/tex]
So
[tex]P(P > 0.75) = P(Z > \frac{0.75 - 0.60 }{0.05} )[/tex]
[tex]P(P > 0.75) = P(Z > 3)[/tex]
[tex]P(P > 0.75) = 0.0013499[/tex]
This value above is obtained from the z-table
Consider a sample with a mean of 60 and a standard deviation of 5. Use Chebyshev's theorem to determine the percentage of the data within each of the following ranges (to the nearest whole number).
a. 50 to 70, at least %
b. 35 to 85, at least %
c. 51 to 69, at least %
d. 47 to 73, at least %
e. 43 to 77, at least %
Answers
Answer:
a)75%
b)96%
c)69.4%
d)85.2%
e)91.3%
Step by step explanation:
Given:
Mean=60
Standard deviation= 5
We were told to use chebyshev's theorem.to determine the percentage of the above given data within each of the following ranges
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION.
Triangle XYZ is isosceles. Angle Y measures a°. Triangle X Y Z is shown. The lengths of sides Y X and Z X are congruent. Angle X Y Z is a degrees. What expression represents the measure of angle X? 2a StartFraction a Over 2 EndFraction 90 a 180 2a
Answers
Answer:
the answer is D.
Step-by-step explanation:
correct on edge
The expression which represents the measure of angle X is therefore; The angle x =180 - 2a.
Isosceles triangleAccording to the question;
Triangle XYZ is isosceles and Angle Y measures a°.The lengths of sides Y X and Z X are congruent.From the given information;
The measures of angle Y and Z = a.
The expression represents the measure of angle X is therefore; The angle x =180 - 2a.
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Question
Given that cot(0)= -1/2
and O is in Quadrant II, what is sin(0)? Write your answer in exact form. Do not round.
Provide your answer below:
Answers
Answer:
sin(O) = 2/sqrt(5) or 2sqrt(1/5)
Step-by-step explanation:
using 1+cot^2(x) = csc^2(x)
we have, taking reciprocal on both sides,
sin(x) = 1/sqrt(1+cot^2(x)
= 1/sqrt(1+(-1/2)^2)
= 1/sqrt(5/4)
= 2/sqrt(5) or 2sqrt(1/5)
Since angle x is in the second quadrant, sin(x) is positive.
Suppose we want to choose 5 letters, without replacement, from 10 distinct letters. How many ways can this be done, if the order of the choices is relevant? How many ways can this be done, if the order of the choices is not relevant?
Answers
Step-by-step explanation:
If the order is relevant, the number of permutations is:
₁₀P₅ = 30,240
If the order is not relevant, the number of combinations is:
₁₀C₅ = 252
The number of ways to choose 5 letters among 10 without replacement will be 252 and with replacements will be 30240.
What are permutation and combination?When the order of the arrangements counts, a permutation is a numerical approach that establishes the total number of alternative arrangements in a collection.
The number of alternative configurations in a collection of things when the order of the selection is irrelevant is determined by combination.
The number of ways to choose r quantity among n without replacement is given as nCr = n!/(r!(n - 1)!)
n = 10 and r = 5
10C5 = 252
The number of ways to choose r quantity among n with replacement is given as, nPr = n!/(n - r)!
n = 40 and r = 5
10P5 = 10!/(10 - 5)! = 30240
Hence "The number of ways to choose 5 letters among 10 without replacement will be 252 and with replacements will be 30240".
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Jenna drives on average 46 miles per day with a standard deviation of 5.3 miles per day. Suppose Jenna's miles driven per day are normally distributed. Let X = the number of miles driven in a given day. Then X - N(46, 5.3). If necessary, round to three decimal places.
Provide your answer below:
Suppose Jenna drives 41 miles on Monday. The Z-score when x - 41 is______ . The mean is________ This z-score tells you that x = 41 is________ standard deviations to the left of the mean.
Answers
Answer:
Suppose Jenna drives 41 miles on Monday. The Z-score when x - 41 is [tex]-0.943[/tex]. The mean is [tex]46[/tex] This z-score tells you that x = 41 is [tex]0.94[/tex] standard deviations to the left of the mean.
Step-by-step explanation:
From the question we are told that
The mean is [tex]\= x = 46\ miles / day[/tex]
The standard deviation is [tex]\sigma = 5.3 \ miles \ per \ day[/tex]
The value of = 41
Generally the z-score is mathematically represented as
[tex]z = \frac{x-\= x}{\sigma }[/tex]
substituting values
[tex]z = \frac{41-46}{5.3}[/tex]
[tex]z = - 0.943[/tex]
Which is the equation of the line for the points in the given table
Answers
Answer:
A...............................
PLEASE DO THIS !!!!!!!!!!!!!!!!!!!!!!!!! IN THE PIC VERY EASY I GUESS PLEASEEEEEE ANSWER IT!!!!!! NO COPYING FROM ANY SOURCE THOUGH PLZZZZZZZZ! I WILL MARK BRAINLY CROWN THING IF UR ANSWER IS GOOD AND EXPLANATIONAL THANK YOUUUUU
Answers
Answer:
D. (the last one)
Step-by-step explanation:
The horizontal row lists the 3 outcomes of the spinner.
The vertial column lists the 2 outcomes of the card selection.
In the resulting sample space of 2x3=6, each table cell should contain the combination of the row value and the column value.
So in the "Orange" column, all cells below it should start with Orange. Same for the other columns.
In the Purple row, each cell should end with Purple.
Only that way, each table cell represents a possible outcome.
A potato chip company makes potato chips in two flavors, Regular and Salt & Vinegar. Riley is a production manager for the company who is trying to ensure that each bag contains about the same number of chips, regardless of flavor. He collects two random samples of 10 bags of chips of each flavor and counts the number of chips in each bag. Assume that the population variances of the number of chips per bag for both flavors are equal and that the number of chips per bag for both flavors are normally distributed. Let the Regular chips be the first sample, and let the Salt & Vinegar chips be the second sample. Riley conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence that both flavors have the same number of chips in each bag. (a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test. (b) t≈1.44 , p-value is approximately 0.167 (c) Which of the following are appropriate conclusions for this hypothesis test? Select all that apply. Select all that apply:
Answers
Answer:
(a) H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.
Step-by-step explanation:
We formulate the
H0: μ1=μ2; null hypothesis that the two means are equal and alternate hypothesis that the two mean are not equal.
Ha:μ1≠μ2 Two tailed test
Test statistic used is
t= x1`-x2` / s√n as the variances are equal and sample size is same
T value for 9 degrees of freedom for two tailed test at α = 0.05 is 2.26
P- value for t test for 9 degrees of freedom is 0.125 from the table.
Hence only a is correct .
How many ways can 3 boys and 2 girls stand in a row so that the two girls are not next to each other?
Answers
Answer:
3 ways← key b=boy g=girlStep-by-step explanation:
b g b gg b b gg b g bgive brainllest please °∩°
Hope it helps
Please mark my answer as BRAINLIEST
(6/22 + 5/77) ^2 equalviant to in fraction form
Answers
Answer:
676/5929
Step-by-step explanation:
A rectangular cardboard has dimensions as shown. The length of the cardboard can be found by dividing its area by its width. What is the length of
the cardboard in inches?
Area = 36 - square inches
4
width = 4 inches
length = ?
8 7 7
Og
11
O 32
20
O 154
7
20
Answers
Answer:
9 inchesStep-by-step explanation:
Area of the rectangular cardboard = Length * Width ... 1
Given the area of the cardboard = 36-square inches
If the length of the cardboard can be found by dividing its area by its width, then Length = Area/Width ... 2
Given the width to be 4 inches
Length = 36 in²/4 in
Length of the cardboard = 9 inches
Find the zeros of g(x) = x3 + x2 – 9x – 9
Answers
Answer: The zeros are -1,-3, and 3
Hope this helps
Answer:
let g[x]=0
then0=x3−x2-9x+9
rewrite it as x3−x2−9x+9=0
by factorising it becomes
(x−1)(x+3)(x−3)=0
therefore
either x-1=0 OR x+3=0 OR x-3=0
which becomes
x=1 OR x=-ve3 OR x=3
are the zeroes of the polynomial
hope this helps
When josh borrowed money, he originally agreed to repay the loan by making three equal payments of $1500, with a payment due now, another payment due two years from now, and the final payment due four years from now. Instead of the original payments, he plans to pay off the loan by making a single payment of 5010. If interest is 10%, compounded annually, when will he make the single payment?
Answers
Answer:
5 years
Step-by-step explanation:
Principal Amount to be paid=$4500
Interest rate = 2%
Number if Times compounded= number of years
Number of years = x
Among total= $5010
A= p(1+r/n)^(nt)
But n= t =x
A= p(1+r/x)^(x²)
5010=4500(1+0.02/x)^(x²)
5010/4500 = (1+0.02/x)^(x²)
1.11333=( 1+0.02/x)^(x²)
Using trial and error method the number of years maximum to give approximately $5010 is 5 years
Help !! Please I don’t know lol
Answers
G(x) or any letter is the same thing as Y.
Please answer this correctly without making mistakes
Answers
Answer:
The distance between the art gallery and the office supply store is 42 miles
Step-by-step explanation:
Notice that the segment that joins the office store with the art gallery, has a length that equal the distance between the art gallery and the bank, plus the distance between the bank and the office supply store. That is;
32.1 mi + 9.9 mi = 42 mi
Explain
Art to bank
Art: 32.1
Bank: 9.9
Add them together
32.1+9.9
Which equal to 42
Hopefully this help you :)
You can look the picture below
What are the solutions to the system of equations graphed below?
Answers
Answer:
Its B and D
Step-by-step explanation:
Because thats where the points intersects/meet.
Alex : Hey Bob, I think this coin is biased; I flipped it a few times and it always lends Tail. I think p, the probability of landing Head, must be less than 5%. Can you take a look?
Bob: Seriously? I bet it's fair, that is I think p = 1/2. Let me flip it three times and count the number of Heads. If the number of Heads is smaller than some threshold t, then I will buy you dinner. Otherwise, you will buy me dinner.
Alex: Wow Bob, okay! I will go ahead and reserve a fancy restaurant.
Bob: One last thing, though, just to make things fair: pick any t you want, but let's keep the proba- bility that I buy you dinner even if I'm right (that is, even if the truth is p= 1/2) below 10% please.
Alex: Go away, Bob! Stop wasting my time!
Question: why did Alex get mad?
Answers
Answer:
See below
Step-by-step explanation:
Alex finally understands how Bob was trying to trick him into winning the bet because of how he puts in the condition for probability being less than 10%. Whichever way the outcome of the coin toss turns out to be, it will be in Bob's favor and Alex will lose the bet. If the coin is flipped 3 times, the probability of having heads exactly twice is [tex]\frac{4}{9}[/tex]
In a survey, 29 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $41 and standard deviation of $8. Construct a confidence interval at a 99% confidence level.
Give your answers to one decimal place.
Answers
Answer:
The 99% confidence interval is
[tex]37.167< \= x < 44.833[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 29[/tex]
The sample mean is [tex]\= x =[/tex]$41
The sample standard deviation is [tex]\sigma =[/tex]$8
The level of confidence is [tex]C =[/tex]99%
Given that the confidence level id 99% the level of confidence is evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1[/tex]%
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table which is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason we are obtaining values for is because is the area under the normal distribution curve for both the left and right tail where the 99% interval did not cover while is the area under the normal distribution curve for just one tail and we need the value for one tail in order to calculate the confidence interval
Next we evaluate the margin of error which is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \frac{8 }{\sqrt{29} }[/tex]
[tex]MOE = 3.8328[/tex]
The 99% confidence level is constructed as follows
[tex]\= x - MOE < \= x < \= x + MOE[/tex]
substituting values
[tex]41 - 3.8328 < \= x < 41 + 3.8328[/tex]
[tex]37.167< \= x < 44.833[/tex]
g Given p, q, and r three propositional variables, how many different ways are for the propositional logic formula (p -> q) ^ (q -> r) ^ p to be evaluated to FALSE
Answers
Answer:
There are 7 ways in which the formula can be evaluated to False.
Step-by-step explanation:
In order to solve this problem we will need to build a truth table. In order to build the truth table, we must start by setting the possible truth values combinations. In total there must be 8 rows, which you can see on the first three columns of the attached table.
Next, it is advisable that you divide the formula in little chunks of information that will be easier to evaluate. One column can be (p->q).
Let's evaluate that first column. In general, that column can only be false if p=T -> q=F. Which happens only on the 3dr and 4th rows of the table. The rest of the statements are true.
The next column will be (q->r). The same condition is met here, but this time you take into account the values given on the q and r columns. The false values will happen only on the 2nd and 6th rows. The rest of the rows for that collumn should be true.
Finally you can test for the whole formula. the first, 4th and 5th columns must be true for the formula to be true as well, which will happen only on the first row. The rest of the rows will have at least one false statement which makes the whole row false. So the rest of the rows are false.
(see attached picture for the whole truth table)
40.) Decompose 7/8 into the sum of unit fractions.
Answers
Answer:
7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8
7/8 = 1/8 + 6/8
7/8 = 4/8 + 3/8
7/8 = 5/8 + 2/8
Step-by-step explanation:
Hope it helps!
The fraction 7/8 can be written as the sum of unit fraction i.e;
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.
What is unit fraction?A unit fraction can be defined as a fraction whose numerator is 1.
Given fraction 7/8
can be written as the sum of the unit fraction i.e;
7/8=1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8
Hence,7/8 can be decomposed into sum of unit fraction as
1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.
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8mi 200 yds - 2 mi 528 yds =
Answers
Answer:
5 mi 1432 yds
Step-by-step explanation:
8mi 200 yds
- 2 mi 528 yds
---------------------------
We have to borrow 1 mile and convert to yards
1 mile = 1760 yds
7mi 200+1760 yds
- 2 mi 528 yds
---------------------------
7mi 1960 yds
- 2 mi 528 yds
---------------------------
5 mi 1432 yds
Answer:
8mi 200yds - 2mi 528yds
= 5mi 1432yds
Step-by-step explanation:
1 mile = 1760 yards
8 miles = 7miles + 1 mile = 7 miles + 1760 miles = 7 miles 1760 yards
8miles 200 yards = 7miles + 1760 yards + 200 yards = 7miles + 1960 yards
then:
8mi 200 yds - 2 mi 528 yds = 7mi 1960yds - 2mi 528yds
7mi 1960yds
- 2mi 528yds
= 5mi 1432yds
6th grade math, help me please.
Answers
Answer:
B Kim rode 3 more miles per week than Eric rode.
E={a,c,f}
A={a,c,j}
find the intersection of E and A.
find the union of E and A
write your answer using set notation (in roster form)
Answers
Answer:
i. E ∩ A = { a , c }ii. E ∪ A = { a , c , f , j }Step-by-step explanation:
Given
E = { a , c , f }
A = { a , c , j }
i) Let's find the intersection of E and A
E ∩ A = { a , c , f } ∩ { a , c , j }
In the case of intersection , we have to list the elements which are common in both sets:
E ∩ A = { a , c }
ii) Let's find the union of E and A
E ∪ A = ( a , c , f } { a , c , j }
In the case of Union, we have to list all the elements which are present in both sets.
E ∪ A = { a , c , f , j }
Hope this helps..
Best regards!!
all summer olympics championship distamces in the triple jump from 1896 through 2012 avereged 16.38 meters, with standard deviation of 1.34 meters. what is the probability that a randomly selected distance from the distribution would fall into each of the following intervals 16.8 meters and 17.9 meters?
Answers
Answer: 0.2487
Step-by-step explanation:
Given: Mean: [tex]\mu=16.38[/tex] meters
Standard deviation: [tex]\sigma= 1.34[/tex] meters
Let X denote the distance in the triple jump.
The probability that a randomly selected distance from the distribution would fall into interval 16.8 meters and 17.9 meters = [tex]P(16.8<X<17.9)=P(\dfrac{16.8-16.38}{1.34}<\dfrac{X-\mu}{\sigma}<\dfrac{17.9-16.38}{1.34})[/tex]
[tex]=P(0.3134<Z<1.1343)\ \ \ [Z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<1.1343)-P(Z<0.3134)\\\\=0.8717- 0.6230\ [\text{By z-table}]\\\\=0.2487[/tex]
Hence, the probability that a randomly selected distance from the distribution would fall into interval 16.8 meters and 17.9 meters= 0.2487
expand (x+2y)^2 plzzzzzzzz
Answers
(x + 2y) (x + 2y)
x^2 + 2xy + 2xy + 4y^2
= x^2 + 4xy + 4y^2
A consumer magazine wants to compare lifetimes of ballpoint pens of three different types. The magazine takes a random sample of pens of each time and records the lifetimes (in minutes) in the table below. Do the data indicate that there is a difference in the mean lifetime for the three brands of ballpoint pens?
Answers
Answer:
The first step would be to look at the average for each brand.
The average can be calculated as:
A = (a1 + a2 + .... + an)/N
where a1 is the first lifetime, a2 is the second one, etc. And N is the total number of data points.
So, for Brand 1 we have:
A1 = (260 + 218 + 184 + 219)/4 = 220.25
Brand 2:
A2 = (181 + 240 + 162 + 218)/4 = 200.25
Brand 3:
A3 = (238 + 257 + 241 + 213)/4 = 237.25
So only from this, we can see that Brand 3 has the larger lifetime, then comes Brand 1 and last comes Brand 2.
Compare the following two sets of data by using box-and-whisker plots. Explain the similarities and differences between the two data sets. Set A = {56, 62, 71, 82, 92, 101, 106, 103, 97, 84, 68, 57} Set B = {36, 42, 48, 56, 63, 72, 78, 75, 69, 58, 46, 37}
Answers
Answer:
After graphing you can see that There are many differences between the sets. In general for A, values are much higher, the mean median for the set A is above 80 whereas the median for B is below 60, the maximum of A is above 100 and the maximum for B is about 80.
Step-by-step explanation:
With python you can use this code to see the graph.
import pandas as pd
import seaborn as sns
dfA = pd.DataFrame()
dfB = pd.DataFrame()
dfA['Value'] = pd.Series([56, 62, 71, 82, 92, 101, 106, 103, 97, 84, 68, 57])
dfA['Letter'] = 'A'
dfB['Value'] = pd.Series([36, 42, 48, 56, 63, 72, 78, 75, 69, 58, 46, 37])
dfB['Letter'] = 'B'
df = pd.concat([dfA,dfB],axis = 0).reset_index(drop = True)
sns.boxplot(x = 'Letter', y = 'Value', data = df)
After graphing you can see that There are many differences between the sets. In general for A, values are much higher, the mean median for the set A is above 80 whereas the median for B is below 60, the maximum of A is above 100 and the maximum for B is about 80.
Answer:
A values are higher, above 80 and max 100.
B values are lower than 60 and max 80.
The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology. In
how many ways can she select 7 workshops if more than 4 must be about anthropology?
Answers
Answer: She can select 7 workshops if more than 4 must be about anthropology in 1716 ways.
Step-by-step explanation:
Given, The organizer of a conference is selecting workshops to include. She will select from 9 workshops about anthropology and 5 workshops about psychology.
If he select 7 workshops if more than 4 must be about anthropology, the possible combinations = (5 anthropology, 2 psychology), ( 6 anthropology, 1 psychology), (7 anthropology, 0 psychology)
Number of possible combinations = [tex]^9C_5\times ^5C_2+^9C_6\times ^5C_1+^9C_7\times ^5C_0[/tex]
[tex]=\dfrac{9!}{5!4!}\times\dfrac{5!}{2!3!}+\dfrac{9!}{6!3!}\times(5)+\dfrac{9!}{7!2!}\times (1)\\\\=\dfrac{9\times8\times7\times6}{4\times3\times2\times1}\times\dfrac{5\times4}{2}+\dfrac{9\times8\times7}{3\times2\times1}\times5+\dfrac{9\times8}{2}\\\\=1260+420+36\\\\=1716[/tex] [using formula for combinations [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
Hence, she can select 7 workshops if more than 4 must be about anthropology in 1716 ways.