8, 10, 11, 12, 16, 20, 24, 28, 32, 33, 37
Using Statkey or other technology, find the following values for the above data. Click here to access StatKey.
The mean and the standard deviation. Round your answers to one decimal place.
mean = ____________ standard deviation = ________
Answers
Answer:
Mean = 21.0
Standard deviation = 9.9
Step-by-step explanation:
I used my TI-84 Plus CE calculator to find the mean and the standard deviation of your data. However, I will explain how to find the mean and standard deviation
First, I'll provide the steps to find the mean:
Mean:
Step 1: Find the sum of the data:
The sum of the data is given by:
8 + 10 + 11 + 12 + 16 + 20 + 24 + 28 + 32 + 33 + 37 = 231
Step 2: Divide this sum by the total number of data points:
There are 11 data points in your data set. Thus, we can find the mean by dividing 231 by 11:
Mean = 231 / 11
Mean = 21.0
Thus, the mean of the data is 21.0.
Now, I'll provide the steps to find the standard deviation:
Standard Deviation:
Step 1: Find the mean:
We've already determined that the mean of the data set is 21.0.
Step 2: Subtract the mean from each data point. Then, square the result:
(8 - 21.0)^2 = (-13)^2 = 169
(10 - 21.0)^2 = (-11)^2 = 121
(11 - 21.0)^2 = (-10)^2 = 100
(12 - 21.0)^2 = (-9)^2 = 81
(16 - 21.0)^2 = (-5)^2 = 25
(20 - 21.0)^2 = (-1)^2 = 1
(24 - 21.0)^2 = (3)^2 = 9
(28 - 21.0)^2 = (7)^2 = 49
(32 - 21.0)^2 = (11)^2 = 121
(33 - 21.0)^2 = (12)^2 = 144
(37 - 21.0)^2 = (16)^2 = 256
Step 3: Find the variance by finding the average of these squared differences:
Mean = (169 + 121 + 100 + 81 + 25 + 1 + 9 + 49 + 121 + 144 + 256) / 11
Mean = (1076) / 11
Mean = 97.81818182 (Let's not round at the intermediate step and round at the end).
Step 4: Take the square root of the variance to find the standard deviation:
Standard deviation = √(97.81818182)
Standard deviation = 9.890307468
Standard deviation = 9.9
Thus, the standard deviation of the data set is 9.9
Related Questions
at a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 20 cubic feet per minute. the diameter of the base of the cone is approximately three times the altitude. at what rate (in ft/min) is the height of the pile changing when the pile is 22 feet high? (hint: the formula for the volume of a cone is v
Answers
When the pile is 22 feet high, the height of the pile changes to 20/1089π.
Given (dV)/(dt) = 20, h = 22 feet , dh /dt =?
The volume of cone is V = 1/3 * pi * r ^ 2 * h
d=3h
2r = 3h
r = (3h)/2
V = 1/3 * pi * r ^ 2 * h
= 1/3 * pi * ((3h)/2) ^ 2 * h
= 1/3 * pi((9 * H ^ 2 )/4) * h
= (9pi)/12 * h ^ 3
Differentiate w.r.to t
(dV)/(dt) = (3pi)/4 * (3h * h^ 2) * (dh)/(dt)
(dV)/(dt) = (9pi)/4 * (h ^ 2) * (dh)/(dt)
(dV)/(dt)=20, h=22 feet
20 = (9pi)/4 * (22 ^ 2) * (dh)/(dt)
(dh)/(dt) = 80/ (9pi * (22^ 2))
h^ t = 20/ 1089 *pi ft / min
Therefore, The height of the pile changing when the pile is 22 feet high is 20/1089π
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A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?
m less-than-or-equal-to 17
m greater-than-or-equal-to 17
m less-than-or-equal-to 20.3
m greater-than-or-equal-to 20.3
Answers
Answer:
less than or equal to 17
Step-by-step explanation:
14=1.25+0.75x
12.75/0.75=x
x=17
17 is the maximum
Q/A: A taxi service charges a flat fee of $1.25 and $0.75 per mile. If Henri has $14.00, which of the following shows the number of miles he can afford to ride in the taxi?
a. m less-than-or-equal-to 17
b. m greater-than-or-equal-to 17
c. m less-than-or-equal-to 20.3
d. m greater-than-or-equal-to 20.3
CC ALGEBRA 2A ED20
how many times smaller is the surface area of a cube if the side length is multiplied 1/2
Answers
Answer:
1/4, or 4 times smaller
Step-by-step explanation:
Since the surface area of a cube is just the combination of the area of all of the square sides, and the formula for those is s^2, if the side length was decreased by 1/2 then the surface area would decrease by (1/2)^2=1/4. Hope this helps!
The NBA regulations require the basketball court to be 132 feet long how many meters is the length of the court
Answers
Answer:
40.2336 meters
Step-by-step explanation:
Answer:
40.2336 meters
Step-by-step explanation:
Danny Metzger's parents invested $1600 when he was born. This money is to be used for Danny's college education and is to be withdrawn in four equal annual payments beginning when Danny is age 19. Find the amount that will be available each year, if money is worth 7%, compounded annually. (Round your answer to the nearest cent.)
Answers
Answer:
\(\begin{array}{ccl}Year&&End \ of \ year \ balance\\1&&\$4,483.18\\2&& \$3,088.68\\3&&\$1,596.57\\4&&0\end{array}\)
Step-by-step explanation:
The initial amount invested, P = $1,600
Danny's age at which the amount, A, is to be used for his college, t = 19 years
The number of equal annual payments, m, to be withdrawn from the amount = 4
The compound interest on the account, r = 7% = 0.07
Let, A, represent the amount at the year the annual withdrawals starts to be made, we have;
\(A = P \times \left(1+\dfrac{r}{n} \right)^{n \times t}\)
n = The number of times the interest is applied annually = 1
Therefore;
\(A = 1,600 \times \left(1+\dfrac{0.07}{1} \right)^{1 \times 19} \approx 5,786.444\)
The amount, m, is withdrawn at start of Danny's first year in college to give the amount in the account = A - m
The amount in the account at the end of the first year with compound interest, r = (A - m)×(1 + r)¹ = (A - m)×(1 + r)
At the stat of the second year, the second withdrawal is made to give the starting amount = (A - m)×(1 + r) - m
The amount in the account at the end of the second year = ((A - m)×(1 + r) - m)×(1 + r)
At the start of the third year, the amount in the account = ((A - m)×(1 + r) - m)×(1 + r) - m
At the end of the third year, we have the amount in the account = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r)
At the start of the forth year, the last yearly installment is withdrawn from the account and we have 0 balance in the account.
Therefore, on the fourth year, we have the amount in the account = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r) - m = 0
(A - m)×(1 + r)³ - m×(1 + r)² - m × (1 + r) - m = 0
A×(1 + r)³ - m×(1 + r)³ - m×(1 + r)² - m × (1 + r) - m = 0
A×(1 + r)³ = m×(1 + r)³ + m×(1 + r)² + m×(1 + r) + m = m × ((1 + r)³ + (1 + r)² + (1 + r) + 1)
A×(1 + r)³ = m × ((1 + r)³ + (1 + r)² + (1 + r) + 1)
m = A×(1 + r)³/((1 + r)³ + (1 + r)² + (1 + r) + 1)
∴ m = 5,786.444×(1 + 0.07)³/((1 + 0.07)³ + (1 + 0.07)² + (1 + 0.07) + 1) ≈ 1,596.56
The amount withdrawn annually, m ≈ $1,596.56
The amount in the account at the end of the each year is given as follows;
First year = (A - m)×(1 + r) = (5,786.444 - 1,596.56)×(1 + 0.07) ≈ 4,483.17588
Second year = ((A - m)×(1 + r) - m)×(1 + r) = ((5,786.444 - 1,596.56)×(1 + 0.07) - 1,596.56)×(1 + 0.07) = 3,088.68
Third year = (((A - m)×(1 + r) - m)×(1 + r) - m) × (1 + r) = (((5,786.444 - 1,596.56)×(1 + 0.07) - 1,596.56)×(1 + 0.07) - 1,596.56) × (1 + 0.07) = 1,596.57
At the end of the first year, we have $4,483.17588
At the end of the second year, we have $3,088.68
At the end of the third year, we have $1,596.57
At the end of the fourth year, we have 0
solve (-t-5)/3= (t-3)/5
Answers
Answer & Step-by-step explanation:
\(\frac{-t-5}{3}=\frac{t-3}{5}\)
Cross multiply.
\(-5t-25=3t-9\)
Subtract -3 on both sides.
\(-8t-25=-9\)
Add 25 on both sides.
\(-8t=16\)
Divide -8 on both sides.
\(t=-2\)
250 pounds = how many tons
Answers
The metric unit from pounds to tons is 250 pounds = 0.125 tons
Converting the metric unit from pounds to tonsFrom the question, we have the following parameters that can be used in our computation:
250 pounds = how many tons
As a general rule, we have
1 pound = 0.0005 tons
Multiply both sides of the equation by 250
So, we have
250 * 1 pound = 0.0005 tons * 250
Evaluate the products
250 pounds = 0.125 tons
Hence, the conversion is 250 pounds = 0.125 tons
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0. 3, 0. 5, 0. 9, 1. 1What are those numbers put in order?
Answers
Answer:
0,0,0,1,3,5,9 I put it in order
Find the equivalent 13÷ 325
Answers
Answer:
Step-by-step explanation:
13/325 as a Decimal Expansion
13/325 = 0.04
or
3/325 is a given fraction,
The decimal expansion of 13/325 is 0.04
ExplainingThe given fraction 13/325 can't be represented as a mixed number since the numerator 13 of the given fraction is smaller than the denominator 325
how many lists of length 3 can be made from the letters u, v, w, x, y, z if repetitions are not allowed, and each list has a w or u in the second entry?
Answers
If repeats are forbidden, the provided letters u, v, w, x, y, and z can be used to create 8 lists of length 3, each of which has a w or u in the second entry.
We can apply the inclusion-exclusion concept to resolve this issue.
First, let's determine how many total lists of length three can be created using the provided letters without any limitations. There are six options for the first submission, five for the second (since it must be either w or u), and four for the third (since no characters can be repeated). Thus, there are a total of the following lists:
6 × 5 × 4 = 120
Next, let's count the number of lists of length 3 that do not have a w or u in the second entry. We have 6 choices for the first entry, 4 choices for the second entry (since we can't choose w or u), and 4 choices for the third entry (since we can't repeat any letters). Thus, the total number of such lists is:
6 × 4 × 4 = 96
Similarly, we can tally the number of lists of length 3 lacking a w or u in the first entry as well as the number of lists of length 3 lacking a w or u in either the first or second entry. Which are:
4 × 5 × 4 = 80 (no w or u in first entry)
4 × 4 × 4 = 64 (no w or u in first or second entry)
Finally, we can use the principle of inclusion-exclusion to count the number of lists that have a w or u in the second entry. This is:
120 - 96 - 80 + 64 = 8
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1 A protected wilderness area in the shape of a rectangle is 5 kilometers long and$12,000 per mile to construct. What will it cost to install the trail? Note that 1 milIt will cost $ to install the trail.(Type an integer or a decimal.)
Answers
Explanation
We are asked to find the cost that will be used to install the trail
Thus, for the question, we will first have to find the perimeter of the wilderness
The first step will be to convert the dimensions to mile
\(\begin{gathered} 5km=\frac{5}{1.6}miles \\ \\ 3.8km=\frac{3.8}{1.6}miles \end{gathered}\)So the perimeter will be
\(\frac{5}{1.6}+\frac{3.8}{1.6}+\frac{5}{1.6}+\frac{3.8}{1.6}=11\text{ miles}\)Next, we will find the Amount by multiplying by the unit cost
\(11\times\text{ \$12,000=\$132,000}\)Therefore, it will cost $132,000 to install the trail
This data set represents the lengths in inches of pieces of ribbon used in a project. What is the mean of this data set? {14, 113, 23, 14, 12} Enter your answer as a fraction
Answers
The mean of the data set is 176/5.
What is mean?Mean can be defined as the average of a statistical distribution.
To calculate the mean of the distribution, we use the formula below.
Formula:
Mean = ∑x/∑n............ Equation 1Where:
∑x = Summation of the data∑N = Total number of data.From the question,
Given the data set
{14,113,23,14,12}∑X = 14+113+23+14+12 = 176∑N = 5Substitute these values into equation 1
Mean = 176/5Mean = 176/5Hence, the mean of the data set is 176/5.
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2x+3y=6 and 2x+y=-2 solved by elimination
Answers
-2/3X+2= -2X-2
Add 2X to both sides
Subtract 2 from both sides
Divide both sides by 4/3
You get X=-3
Plug in 3 to one of the equations and you’ll see that y= 4
Complete the equation for a line through point A(-3, 3) and perpendicular to the line passing through (0, -2) and (4, 1).
Answers
Answer: Zeli shan tel
Step-by-step explanation:
what is 0=2x^2+4x-6 when finding the zeros
Answers
Answer:
zeroes of the equations are x= 1 , -3
Step-by-step explanation:
firstly divide both sides by 2 so new equation will be
x^2+2x-3=0
you can use quadratic formula or simply factor it
its factors will be
x^2 +3x - x -3=0
(x+3)(x-1)=0
are two factors
so
either
x+3=0 or x-1=0
x=-3 and x=1
so zeroes of the equations are x= 1 , -3
by the way you can also use quadratic formula which is
[-b+-(b^2 -4ac)]/2a
where a is coefficient of x^2 and b is coefficient of x
and c is constant term
8.F. 2
5) Function F is described by the equation y= -8x +3
Function G is represented by the table below.
X
у
1
-13
O
5
Which statement about the two functions is true?
A. The slope off is greater than the slope of g
B. The slope of g is greater than the slope off
C. Function F has a positive slope.
D. Function G has a positive slope.
Answers
Answer:
I don't know. Make your question clearer, please.
Step-by-step explanation:
1. In the expression x2, 2 is what we call
A. Base
B. Exponent
C. Multiple
Answers
Answer:
hello! if you're talking about x², then 2 is what we call: B. Exponent.
HELP ASAP LINEAR EQUATIONS!!
Answers
Answer:
y = 4/3x - 10.
Step-by-step explanation:
3x + 4y = 12
4y = -3x + 12
y = -3/4x + 3
If a line is perpendicular to another, the line has a slope that is the negative reciprocal of the other line. Since the given line has a slope of -3/4, the line perpendicular to that line will have a slope of 4/3.
So far, for the equation of the line, we have an equation of y = 4/3x + b.
To find b, simply substitute the coordinates (6, -2) for x and y.
-2 = 4/3(6) + b
b + 4/3(6) = -2
b + 8 = -2
b = -10
So, the equation of the line will be y = 4/3x - 10.
Check your work...
-2 = (4/3)(6) - 10
-2 = 8 - 10
-2 = -2
Hope this helps!
Answer: C) \(y = \frac{4}{3} x-10\)
Step-by-step explanation:
First change this equation into slope-intercept form(y = mx + b). y = -3/4x + 3.
For a line to be perpendicular to another line, it must have an opposite reciprocal slope. The opposite reciprocal of -3/4 is 4/3. Thus, the answer is NOT B. Then, attempt to plug in 6, -2 into each equation. The only one where it works is C.
Hope it helps <3
Two angles from a liner pair. The measure of one angle is 4 times the measure of the other angle. Find the measure of each angle
Answers
Answer:
x = 36 degrees, the smaller angle.
4(36) = 144 degrees, The larger angle.
36 + 144 = 180 degrees.
Cleomenius.
Answer:
x = 36 degrees, the smaller angle.4(36) = 144 degrees, The larger angle.36 + 144 = 180 degrees.
Step-by-step explanation:
(1)adjacent- two non-overlapping angles that share a common vertex and a common side
(2)the non-common sides are opposite rays.
(3)adds up to 180
Write an inequality that describes the graph
Answers
Answer:
x<4
Step-by-step explanation:
The arrow is facing left, making it less than. Next, the open circle on 4 means that it does not include 4, therefore the inequality is x<4.
The inequality that represents this situation is - ∞ ≤ x < 4.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Assuming the number line is represented by x.
An open circle on the right-hand side of the line at 4 represents it is less than 4.
We can also observe that the line is going infinitely in the direction of negative infinity.
So, this situation can be represented by an inequality of the form
- ∞ ≤ x < 4.
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NEED HELP ASAP
Complete the next equation to show the relationship between the number of ounces of oil and vinegar in the recipe.
Answers
Answer:
3!
Step-by-step explanation:
its 3, 8x3 would equal 24.
Answer: is x3
Step-by-step explanation:
Because it equals 24
Someone pls help me with this question pls it will help me so much thank you !:)
Answers
Answer:
50%
Step-by-step explanation:
Percent change is (final - initial) / initial
(120 - 80)/80 = 40/80 = 0.5 = 50%
explain why 1/12 + 1/2= 7/12
Answers
Answer:
1/12 + 1/2 = 1/12 + 6/12 - 1+6/12 = 7/12
Step-by-step explanation:
hope this makes sense
Step-by-step explanation:
1/2 of 12/12 is 6/12.
So, this means: 1/12 + 1/2 = 7/12
is
1/12 + 6/12 = 7/12
The percent increase from 18 to 26 is find the percent of change
Answers
Answer:
10 percent
Step-by-step explanation:
hope this helps!!! mark me brainliest please
Please help me I need to finish this :)
Answers
let f(x)=2x3 3x2−36x. where does the inflection points of f occur?
Answers
When x < 1/2, the second derivative is negative (e.g., f''(-1) = -12), and when x > 1/2, the second derivative is positive (e.g., f''(2) = 18).
To find the inflection points of the function f(x) = 2x^3 - 3x^2 - 36x, we need to determine where the concavity of the function changes. Inflection points occur when the second derivative of the function changes sign.
First, let's find the first derivative of f(x) by taking the derivative of each term:
f'(x) = 6x^2 - 6x - 36
Next, let's find the second derivative by taking the derivative of f'(x):
f''(x) = 12x - 6
To find the inflection points, we need to solve the equation f''(x) = 0:
12x - 6 = 0
12x = 6
x = 6/12
x = 1/2
Therefore, the inflection point of f(x) occurs at x = 1/2.
It's important to note that an inflection point does not guarantee a change in concavity; it simply indicates a potential change in concavity. To confirm the concavity change, we can evaluate the sign of the second derivative on either side of the inflection point. If the sign changes, then the inflection point is confirmed.
This confirms that the concavity changes at x = 1/2, making it an inflection point for the function f(x) = 2x^3 - 3x^2 - 36x.
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A minimum element is deleted from a (min) binary heap with N elements. The running time worst case of this operation is
a. O(N)
b. O(N2)
c. O(logN)
d. O(NlogN)
Answers
The running time wοrst case οf deleting a minimum element frοm a (min) binary heap with N elements is O(lοgN). Therefοre, the cοrrect answer is c. O(lοgN).
What happens when deleting minimum element?When deleting the minimum element frοm a binary heap, the heap needs tο be restructured tο maintain its heap prοperty. This restructuring prοcess invοlves mοving elements within the heap and pοtentially swapping elements tο maintain the heap's structure and οrdering.
Since a binary heap is a cοmplete binary tree and has a height οf lοgN, the wοrst-case running time fοr deleting the minimum element is prοpοrtiοnal tο the height οf the heap, which is O(lοgN). This is because the number οf cοmparisοns and swaps required during the restructuring prοcess is dependent οn the height οf the heap.
Therefοre, the cοrrect answer is c. O(lοgN).
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Solve for the variable
2x + 10 = 30
Answers
Answer:
x=10
Step-by-step explanation:
30-10=20
20/2=10
2(10)+10=30
Answer:
x=10
Don’t hold me up on this but, I think this is the answer.
the half-life of palladium-100 is 4 days. after 12 days a sample of palladium-100 has been reduced to a mass of 4 mg. what was the initial mass (in mg) of the sample? what is the mass (in mg) 7 weeks after the start? you may enter the exact value or round to 4 decimal places.
Answers
Using the half life of palladium, mass seven weeks after start was 0.7931 gm.
The half-life is the amount of time it takes for a quantity (of material) to fall to the cost. In nuclear physics, the phrase usually refers to how rapidly neutrons become radioactive atoms or how long stable atoms survive.
The term can also refer to any sort of hyperbolic (or, in rare situations, non-exponential) decay.
The half life of palladium 100 = 4 days
after 24 days sample has reduced to a mass of 5mg
standard exponential function is
\(P = P_o e^{kt}\)
plugging P = P₀ /2
\(P_o/2 = P_o e^{4k }\)
\(1/2 = e^{4k }\)
ln (1/2) = 4k
k = -0.1733
function becomes
\(P = P_o e^{- 0.1733 t }\)
plugging P = 5 and t = 24
\(5 = P_o e^{( - .1733\times 24 ) }\)
P₀ = 320.10
In the medical sciences, for example, the biological half of drugs and other chemicals in the human body is referred to. The flipside of half-life is doubling time in exponential growth.
For the second part of the problem:
7 weeks = 5 × 7 =49 days
plugging t = 49
\(P = 320.10 e^{(-.1733 * 35 ) }\)
mass 7 weeks after = 0.7431 mg
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How do you simplify-2-8
Answers
Answer:
-10
Step-by-step explanation: