a. Use the sample mean for the 10 schools to estimate the population mean annual salary for head basketball coaches at colleges and universities playing NCAA Division 1 basketball (to 2 decimals). b. Use the data to estimate the population standard deviation for the annual salary for head basketball coaches (to 4 decimals). c. What is the 95% confidence interval for the population variance (to 2 decimals)
Answer:
A) x¯ = $1.33 million
B) σ = $0.9508 million
C) CI = ($0.74 million, $1.92 million)
Step-by-step explanation:
We are given the salary data as;
$2.2 million, $1.5 million, $0.5 million, $0.2 million, $2.4 million, $1.5 million, $2.7 million, $0.1 million, $2 million, $0.2 million
A) Population mean annual salary = $(2.2 + 1.5 + 0.5 + 0.2 + 2.4 + 1.5 + 2.7 + 0.1 + 2 + 0.2)/10 in millions
x¯ = $1.33 million
B) Formula for the standard deviation is;
√(Σ(x - x¯)²/n)
Thus, let's first find (x - x¯)² all in millions
>> (2.7 - 1.33)² = 1.37² = 1.8769
>> (2.4 - 1.33)² = 1.07² = 1.1449
>> (2.2 - 1.33)² = 0.87² = 0.7569
>> (2 - 1.33)² = 0.67² = 0.4489
>> (1.5 - 1.33)² = 0.17² = 0.0289
>> (1.5 - 1.33)² = 0.17² = 0.0289
>> (0.5 - 1.33)² = (-0.83)² = 0.6889
>> (0.2 - 1.33)² = (-1.13)² = 1.2769
>> (0.2 - 1.33)² = (-1.13)² = 1.2769
>> (0.1 - 1.33)² = (-1.23)² = 1.5129
Σ(x - x¯)² = 1.8769 + 1.1449 + 0.7569 + 0.4489 + 0.0289 + 0.0289 + 0.6889 + 1.2769 + 1.2769 + 1.5129
Σ(x - x¯)² = $9.041 million
Σ(x - x¯)²/n = $9.041/10 = $0.9041 million
standard deviation = √0.9041
σ = $0.9508 million
C) Critical value at a Confidence level of 95% is z = 1.96
Thus,formula for critical interval is;
CI = x¯ ± z(σ/√n)
CI = 1.33 ± 1.96(0.9508/√10)
CI = ($0.74 million, $1.92 million)
Trenia walked her dog 4 miles on Saturday. On Sunday she walked her dog 35% less than she did on Saturday. How far did Trenia walk on Sunday?
Answer:
2.6 miles
Step-by-step explanation:
Saturday = a = 4 miles
Sunday = a - 35%a = 0.65a = 0.65 x 4 = 2.6 miles
A process that is in control has a mean of 12.5 and a standard deviation of 1.1.
a. Construct the control chart for this process if samples of size are to be used (to 1 decimal).
For N=4
Find the UCL
Find the LCL
b. Repeat part (a) for samples of size and (to 2 decimals).
For N=10
Find the UCL
Find the LCL
For N=15
Find the UCL
Find the LCL
c. What happens to the limits of the control chart as the sample size is increased? Discuss why this is reasonable. and become - Select your answer (closerfarther) together as n increases. If the process is in control, the larger samples should have less variance and should fall - Select your answer (closerfarther) to 12.5
Answer:
1a) UCL = 14.2
LCL = 10.9
b) UCL = 15.63
LCL = 9.37
c) UCL = 16.48
LCL = 8.52
2) The difference between the limits falls close together as n increases
and the difference between the limits falls farther away from 12.5
Step-by-step explanation:
mean ( μ ) = 12.5
std ( б ) = 1.1
UCL = μ + ( n - 1 ) б / √n
LCL = μ - ( n - 1 ) б / √n
1) a) Given n = 4
UCL = 12.5 + ( 3 ) * 1.1 / 2
= 12.5 + 3.3/2 = 14.15 ≈ 14.2
LCL = 12.5 - 3.3/2 = 10.85 ≈ 10.9
b) Given n = 10
UCL = 12.5 + ( 9 ) * 1.1 /√10
= 12.5 + 3.13 = 15.63
LCL = 12.5 - 3.13 = 9.37
c) Given n = 15
UCL = 12.5 + 14 * 1.1 / √15
= 12.5 + 3.98 = 16.48
LCL = 12.5 - 3.98 = 8.52
2) As the sample size increases the difference between the limits of the control chart decreases
Hence the difference falls close together as n increases
and the difference between the limits falls farther away from 12.5
Calculate the area.
Answer:
d. 91.61 cm^2
Step-by-step explanation:
have a nice day :)
Answer:
area of circle=πr²=π×5.4²=91.6cm²
The sales tax for an item was $13.60 and it cost $340 before tax.
Find the sales tax rate. Write your answer as a percentage.
Answer:
4%
Step-by-step explanation:
13.60/340=.04 or 4%
The length of a rectangle is 11 units more than its width. The perimeter of the
rectangle is 182 units. Solve for the dimensions of the rectangle. What is the
area of the rectangle?
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Answer:
width: 40 unitslength: 51 unitsarea: 2040 square unitsStep-by-step explanation:
Let w represent the width of the rectangle. Then w+11 is the length. The perimeter is given by ...
P = 2(L +W)
182 = 2((w+11) +w)
182 = 4w +22 . . . . . simplify
160 = 4w . . . . . . . . . subtract 22
40 = w . . . . . . . . . . . divide by 4
40 +11 = length = 51 . . . . determine length
The dimensions of the rectangle are 40 × 51 units.
__
The area of the rectangle is ...
A = LW
A = (51)(40) = 2040 . . . . square units
The area is 2040 square units.
_____
Additional comment
The perimeter of a rectangle is double the sum of length and width, so that sum is 182/2 = 91 units. Now, this is a "sum and difference" problem, where the sum of length and width is 91, and the difference is 11. The solutions to such a problem are half the sum and half the difference of these numbers. Above, we found the smaller dimension (width) first: (91-11)/2 = 40. We could have found the length as (91+11)/2 = 51. The knowledge of the general solution to "sum and difference" problems often lets you work them with mental arithmetic.
9 divided by 8 is equal to 9 multiplied by _
Answer:
1/8.
Step-by-step explanation:
9/8 = 9x
Cross multiply:
9x * 8 = 9
72x = 9
x = 9/72 = 1/8.
CHECK the answer:
9/8 = 9 * 1/8 = 9/8.
Checks OK.
Write an equation that can be used to find the nth term of the sequence, an.
80, 105, 130, 155, 180, ...
Enter your answer by filling in the boxes.
an = n +
Answer:
an=105-25n is the answer
The filling in the boxes an is equal to 105-25n.
We have given that,
Write an equation that can be used to find the nth term of the sequence, an.
What is the sequence?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members. The number of elements is called the length of the sequence.
The sequence is 80, 105, 130, 155, 180.
We have to determine an term.
To learn more about the sequence visit:
https://brainly.com/question/6561461
#SPJ2
HELP PLEASE IM GIVING BRAINLIEST!!
Answer:
the answer to the problem is b
solve the following inequality: 55-5q > 4 (7-q)
Answer:
27 > q
Step-by-step explanation:
Solving an algebraic inequality is very similar to solving an algebraic equation, one uses inverse operations. One major difference between the two is that when one multiplies or divides an algebraic inequality by a negative number, one must remember to flip the inequality sign.
55 - 5q > 4 ( 7 - q )
Distribute,
55 - 5q > 28 - 4q
Inverse operations,
55 - 5q > 28 - 4q
+5q +5q
55 > 28 + q
-28 -28
27 > q
3. Find the values of the constants in each of the following:
(1) f(x) = ax + b, a and b are constants, f2) = 7,f(1) = -1
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Answer:
a = 8; b = -9
Step-by-step explanation:
Filling in the given values gives you two equations.
7 = a(2) +b
-1 = a(1) +b
Subtracting the second equation from the first gives ...
(7) -(-1) = (2a +b) -(a +b)
8 = a . . . . . simplify
Using this value in the first equation gives ...
7 = (8)(2) +b
b = 7 -16 = -9
The constants are a = 8, b = -9.
Element X is a radioactive isotope such that its mass decreases by 26% every day. If an experiment starts out with 810 grams of Element X, write a function to represent the mass of the sample after tt days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent.
Answer:
The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.
The function to represent the mass of the sample after t days is [tex]A(t) = 810(0.74)^t[/tex]
Step-by-step explanation:
Exponential equation of decay:
The exponential equation for the amount of a substance is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
Hourly rate of change:
Decreases 26% by day. A day has 24 hours. This means that [tex]A(24) = (1-0.26)A(0) = 0.74A(0)[/tex]; We use this to find r.
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]0.74A(0) = A(0)(1-r)^{24}[/tex]
[tex](1-r)^{24} = 0.74[/tex]
[tex]\sqrt[24]{(1-r)^{24}} = \sqrt[24]{0.74}[/tex]
[tex]1 - r = (0.74)^{\frac{1}{24}}[/tex]
[tex]1 - r = 0.9875[/tex]
[tex]r = 1 - 0.9875 = 0.0125[/tex]
The hourly decay rate is of 1.25%, so the hourly rate of change is of -1.25%.
Starts out with 810 grams of Element X
This means that [tex]A(0) = 810[/tex]
Element X is a radioactive isotope such that its mass decreases by 26% every day.
This means that we use, for this equation, r = 0.26.
The equation is:
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]A(t) = 810(1 - 0.26)^t[/tex]
[tex]A(t) = 810(0.74)^t[/tex]
The function to represent the mass of the sample after t days is [tex]A(t) = 810(0.74)^t[/tex]
If sin0=7/25 find csc0
Answer:
7/25 Hope it helps
Step-by-step explanation:
Given sin theta = 7/25;
Cosec of any variable is the reciprocal of sin of the variable. Therefore cosec theta = 1/sin theta
Substituting the value of sim theta given in the formula for cosec theta gives;
Cosec theta = 1/(7/25)
Cosec theta = 1÷7/25
Cosec theta = 1× 25/7
Cosec theta = 25/7
This is about scientific notation. Can someone plzzzz help I’m confused
Answer: Carat
Step-by-step explanation:
It is given that 1 atomic unit is equivalent to
[tex]8.3\times 10^{-24}\ \text{carat}[/tex] and [tex]1.66\times 10^{-21}\ mg[/tex]
Express carat and milligram in the atomic mass unit, that is
[tex]1\ \text{amu}\equiv 8.3\times 10^{-24}\ \text{carat}\\1\ \text{carat}\equiv \dfrac{1}{8.3\times 10^{-24}}=1.204\times 10^{23}\ amu[/tex]
For milligram
[tex]1\ \text{amu}\equiv 1.66\times 10^{-21}\ mg\\1\ mg\equiv \dfrac{1}{1.66\times 10^{-21}}=6.02\times 10^{20}\ \text{amu}[/tex]
clearly, carat is greater than milligram
Parker randomly pulled out a sock that was black form
his drawer. Without replacement, what is the
probability that Parker will randomly pull out a white
sock on his second pull?
Answer:
[tex]Probability\ that\ Parker'd\ pull\ off\ a\ White\ Sock(\ On\ His\ Second\ Pull)=\frac{6}{11}[/tex]
Step-by-step explanation:
[tex]We\ are\ given\ that,\\Total\ number\ of\ Black\ Socks=7\\Total\ number\ of\ White\ Socks=12\\Total\ number\ of\ Navy\ Socks=4\\Hence,\\Total\ number\ of\ Socks\ Parker\ has=12+4+7=23\\We\ know\ that,\\The\ Random\ experiment\ here,\ is\ pulling\ out\ a\ white\ sock,\ after\ pulling\\ a\ black\ sock.\\Hence,\\Since\ the\ Black\ Sock\ had\ been\ removed\ from\ his\ drawer,\ the\\ number\ of\ 'Socks'\ that\ remain\ in\ his\ drawer=23-1=22\\[/tex]
[tex]Hence,\\Total\ elementary\ events\ for\ this\ random\ experiment=22\\Now,\\We\ just\ need\ to\ find\ out\ the\ probability\ of\ pulling\ out\ a\ 'White\ Sock'.\\Hence,\\Number\ of\ White\ socks=12\\Hence,\\Favorable\ number\ of\ elementary\ events\ for\ the\ Random\ Experiment=12[/tex]
[tex]We\ also\ know\ that,\\Probability\ for\ an\ Event\ A=\frac{Favorable\ No.\ of\ Elementary\ Events}{Total\ no.\ of\ elementary\ events}[/tex]
[tex]Hence,\\Probability\ that\ Parker\ would\ pull\ off\ a\ white\ sock\ on\ his\\ second\ pull=\frac{12}{22}=\frac{6}{11}[/tex]
Help? ill give 10 points.
Answer:
it is the first one
Step-by-step explanation:
Find the measure of < 3
t
43
90°
K
43 = [?]
Enter
Answer:
Solution given:
<3+90=180[co interior angle ]
<3=180-90=90°
is your answer
which of the following pairs of functions are inverses of each others
Answer:
(B).
Step-by-step explanation:
(D). f(x) = 2x³ + 9
Solve equation y = 2x³ + 9 for "x"
2x³ = y - 9
x³ = [tex]\frac{y-9}{2}[/tex]
x = [tex]\sqrt[3]{\frac{y-9}{2} }[/tex]
Switch "x" and "y"
y = [tex]\sqrt[3]{\frac{x-9}{2} }[/tex] or g(x) = [tex]\sqrt[3]{\frac{x-9}{2} }[/tex]
(C). y = [tex]\frac{x}{4}[/tex] + 10
[tex]\frac{x}{4}[/tex] = y - 10
x = 4y - 40
g(x) = 4x - 40
(B). y = [tex]\frac{12}{x}[/tex] - 18
[tex]\frac{12}{x}[/tex] = y + 18
x = [tex]\frac{12}{y+18}[/tex]
g(x) = [tex]\frac{12}{x+18}[/tex]
2. Give vector v=< 3,-6 > and w is a vector with a magnitude of 36 and direction 155 degrees.
a. Write the vector v in i, j component form.
b. Find the magnitude and direction of vector v.
c. Find the i, j vector form of w.
d. Find the resultant vector of v+w. This includes its component form, magnitude and direction.
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Answer:
a) v = 3i -6j
b) v ≈ 6.708∠-63.43°
c) w = -32.627i +15.214j
d) v+w = -29.627i +9.214j = 31.027∠162.72°
Step-by-step explanation:
Most graphing calculators and many scientific calculators can do arithmetic with vectors, often in the form of complex numbers or arrays. Of course, the usual conversions can be used:
(r; α) ⇒ (r·cos(α), r·sin(α))
(x, y) ⇒ (√(x²+y²); atan2(x, y))
where atan2(x, y) is arctan(y/x) quadrant-adjusted for the signs of x and y
__
a) v = 3i -6j
b) v ≈ 6.708∠-63.43°
c) w = -32.627i +15.214j
d) v+w = -29.627i +9.214j = 31.027∠162.72°
__
The first attachment shows the vectors and their sum in component form as complex numbers. For your purpose, the translation is ...
a +bi ⇒ ai +bj
The second attachment shows the vectors and their sum in polar form (magnitude and direction). I like the A∠B format. You may translate it to whatever form you need, for example, (A; B), A·cis(B), A(cos(B)i +sin(B)j), Ae^(iB), or any other. (The "semicolon format" is used by at least one app to distinguish between rectangular coordinates (a, b) and polar coordinates (A; B).) The angles here are in degrees (not radians), matching the form in the problem statement.
Do #5 please will mark brainlist
Step-by-step explanation:
12/7 is equal to 14/8 is equal to ab/cd
how many fluid ounces are equal to 26 quartz? i will give brainliest answer.
An arena is hosting a concert. At the most, the arena can hold 8,500 people. If tickets have already been sold to 6,900 people, what is the highest number of tickets that can still be sold?
Answer:
Subtract 6,900 from 8,500 to get the highest number of tickets that can still be sold which is 1,600.
Target has a television on sale 20% off the regular price of $500.00. How much is the price after the markdown?
Answer:
What is 20 percent of 500.? = 100.
Step-by-step explanation:
Answer:
The answer is 100$
Step-by-step explanation:
This is step-by-step explanation : 500:100×20=100
write your answer as a mix number 8 1/2 + 7 2/3 add
Answer:
[tex]15\frac{13}{21}[/tex]
Step-by-step explanation:
[tex]answer[/tex]
Equalizing the denominator
Likening retailers can be done by calculating the frequency from numbered fractions. Based on examples calculated by pec from 4/3 and 5/3 = 34/4
#semogamembantu
1+1-1+1-1 Will choose brainly
Answer:
1
Step-by-step explanation:
Decide whether the equation describes a function.
y= 4x - 5
What is the domain and range?
Answer: The domain is in the picture
Step-by-step explanation:
Colin asked some of his classmates how many minutes they spent working on their math homework last night. He created a dot plot to show his results.
What is the range of the data Colin collected?
20
11
25
5
Answer:
If you can attach it i would be happy to help.
Step-by-step explanation:
*answer will be updated if shown*
Answer:
Step-by-step explanation:
5
The local High School currently has approximately 950 students enrolled. They are anticipating a 12% increase next year. How many students are they anticipating? *
(b) In summer, the zoo increases the prices.
An Adult ticket increases by 20%.
A Child ticket increases by 15%.
How much more does it cost the family to visit in the summer than in the winter?
Find the simplified product: 2 square root 5x^3
Answer:
x Square root 5x
Step-by-step explanation:
A map is drawn to the scale 1:4,000.
(a) The length of a road on the map is
3.5 cm. Find its actual length in meters.
Answer:
Original length of the road = 14,000 meter
Step-by-step explanation:
Given Scale;
1 cm = 4,000 meter
The length of road on map = 3.5 cm
Find:
Computation:
Original length of the road
Original length = Length on drawing x scale factor
Original length of the road = The length of road on map x scale factor
Original length of the road = 4,000 x 3.5
Original length of the road = 14,000 meter