Part A
To find the mean, we add up the values and divide by n = 8 since there are 8 values in this set.
Adding the values gets us
28+45+12+34+36+45+19+20 = 239
Dividing this over 8 then leads to 239/8 = 29.875
Answer: 29.875============================================================
Part B
We'll subtract each data value from the mean. We apply absolute value to ensure the result is never negative.
|28 - 29.875| = 1.875 |45 - 29.875| = 15.125 |12 - 29.875| = 17.875 |34 - 29.875| = 4.125 |36 - 29.875| = 6.125 |45 - 29.875| = 15.125 |19 - 29.875| = 10.875 |20 - 29.875| = 9.875The list of results we get so far is:
1.875, 15.125, 17.875, 4.125, 6.125, 15.125, 10.875, 9.875
This represents the distance each value is from the mean.
Add these values up and divide by n = 8
1.875+15.125+17.875+4.125+6.125+15.125+10.875+9.875 = 81
81/8 = 10.125
Answer: 10.125============================================================
Part C
The result of part A is one way to measure the center of the distribution of values. It's the average value, which can more or less represent the entire group. Think of it being like how people vote in a senator to represent them in congress. Ideally, this senator is a supposed "average" person to represent everyone.
The result of part B builds on what part A found. The result of part B is the average distance each value is from the center. This is because each time we subtracted and applied absolute value, we found the distance that item was from the mean.
Example: The calculation |28 - 29.875| = 1.875 shows that 28 is exactly 1.875 units from the mean 29.875
By adding up those results and dividing by 8, we are finding the average distance from the mean. Effectively, it tells us how spread out the data set is. The mean absolute deviation (MAD) is a measure of spread in a similar fashion that the standard deviation is, or in a more looser sense, the range is as well.
---------------
In short, the result of part A is a measure of center while the result of part B is a measure of spread. I use "a" instead of "the" because there are other measures of center and other measures of spread.
find csc theta and sin theta if tan theta = 7/4 and sin theta less than 0
9514 1404 393
Answer:
sin(θ) = (-7√65)/65
csc(θ) = (-√65)/7
Step-by-step explanation:
The angle will have the given characteristics if its terminal ray passes through the 3rd-quadrant point (-4, -7). The distance from the origin to that point is ...
d = √((-4)² +(-7)²) = √65
The sine of the angle is the ratio of the y-coordinate to this value:
sin(θ) = -7/√65
sin(θ) = (-7√65)/65
The cosecant is the inverse of the sine
csc(θ) = (-√65)/7
Hi, hiw do we do this question?
[tex]\displaystyle \int\sec x\:dx = \ln |\sec x + \tan x| + C[/tex]
Step-by-step explanation:
[tex]\displaystyle \int\sec x\:dx=\int\sec x\left(\frac{\sec x+ \tan x}{\sec x + \tan x}\right)dx[/tex]
[tex]\displaystyle = \int \left(\dfrac{\sec x\tan x + \sec^2x}{\sec x + \tan x} \right)dx[/tex]
Let [tex]u = \sec x + \tan x[/tex]
[tex]\:\:\:\:\:\:du = (\sec x\tan x + \sec^2x)dx[/tex]
where
[tex]d(\sec x) = \sec x\tan x\:dx[/tex]
[tex]d(\tan x) = \sec^2x\:dx[/tex]
[tex]\displaystyle \Rightarrow \int \left(\frac{\sec x\tan x + \sec^2x}{\sec x + \tan x}\right)\:dx = \int \dfrac{du}{u}[/tex]
[tex]= \ln |u| + C = \ln |\sec x + \tan x| + C[/tex]
When an individual inherits two identical alleles for the brown eyed gene (BB)which type of individual is this?
Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 22.8 minutes. How many employees must be included in a sample to create a 99 percent confidence interval for the average commute time with a confidence interval width of no more than 12 minutes
Answer:
96 employees
Step-by-step explanation:
Given that the standard deviation = 22.8
The width in the question = 12
We solve for the margin of error E.
E = width / 2
= 12/2 = 6
At 99%
Alpha = 1-0.99
= 0.01
Alpha/2 = 0.01/2 = 0.005
Z0.005 = 2.576
Sample size n
= ((2.576x22.8)/2)²
= 95.8
= 96
The number of employees is 96
Thank you!
The measure of ∠1 is 39°. What is the measure of ∠2?
Answer:
141
Step-by-step explanation:
if the sum of the two angles equals 180 subtract 39 from 180 to get the remainder of 141 which is angle 2
!!!HELPPP PLEASEEE!!! For this problem I thought it meant to subtract 0.1492 - 0.1515 = -0.0023 however my answer was incorrect. How do I solve this problem then? Help Please!
Answer:
0.1492-0.1515= -0.0023
Find the total surface area of this square based pyramid. 10ft 10ft (in the image)
Not sure whether the answer is 9 or -11, so please help
Which proportion correctly shows the equivalence of two fractions?
A)
19∕95 = 57∕76
B)
32∕116 = 9∕29
C)
18∕36 = 72∕144
D)
18∕36 = 144∕72
Answer:
32/166=9/29 if two ratio are equivalent to other
Suppose that the length of a side of a cube X is uniformly distributed in the interval 9
Answer:
[tex]f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.[/tex]
Step-by-step explanation:
Given
[tex]9 < x < 10[/tex] --- interval
Required
The probability density of the volume of the cube
The volume of a cube is:
[tex]v = x^3[/tex]
For a uniform distribution, we have:
[tex]x \to U(a,b)[/tex]
and
[tex]f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.[/tex]
[tex]9 < x < 10[/tex] implies that:
[tex](a,b) = (9,10)[/tex]
So, we have:
[tex]f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]
Solve
[tex]f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]
[tex]f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]
Recall that:
[tex]v = x^3[/tex]
Make x the subject
[tex]x = v^\frac{1}{3}[/tex]
So, the cumulative density is:
[tex]F(x) = P(x < v^\frac{1}{3})[/tex]
[tex]f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex] becomes
[tex]f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.[/tex]
The CDF is:
[tex]F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx[/tex]
Integrate
[tex]F(x) = [v]\limits^{v^\frac{1}{3}}_9[/tex]
Expand
[tex]F(x) = v^\frac{1}{3} - 9[/tex]
The density function of the volume F(v) is:
[tex]F(v) = F'(x)[/tex]
Differentiate F(x) to give:
[tex]F(x) = v^\frac{1}{3} - 9[/tex]
[tex]F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}[/tex]
[tex]F'(x) = \frac{1}{3}v^{-\frac{2}{3}}[/tex]
[tex]F(v) = \frac{1}{3}v^{-\frac{2}{3}}[/tex]
So:
[tex]f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.[/tex]
Nick nas cup of syrup. He uses cup of syrup to make a bont of granota
PartA: How many bow's or granola can Nick make with cup of syrup? (4 points)
Part 8: on your own paper, draw a fraction model that shows the total number of bouts of granola that Nick can make with cup of syrup. Make sure to label the model seks
explain your model in detail to descnbe how this model visually shows the solution for Part A. (6 points). I’ll make u brainless if u help
Answer:
Step-by-step explanation:
its easyk
If one root of the quadratic equation is 2x2 +kx -6= 0 is 2
find the value of k
This is ur answer plz mark brainliest
What is the length of BD Round to one decimal place. Thanks!
Answer:
2.7
Step-by-step explanation:
ratios help
2.5 : 5.8 :: x : 6.2
2.5/5.8 = x/6.2
solve for x :
x = approx. 2.7
If someone earns $10 every 15 minutes, how much do they earn in an hour?
Answer: 40
Step-by-step explanation:
You multiple 15X4=60
And now multiple 10x4=40
Answer:
40$
Step-by-step explanation:
There are 60 minutes in an hour so if we break it down:
$10 = 15 minutes
$10 = 15 minutes
$10 = 15 minutes
$10 = 15 minutes
-------------------------
Add them together and we get:
$40 = 60 minutes or 1 hour
Meaning they would make 40$ in 1 hour.
factor 9-x^2 completely
Answer:
-(x + 3)(x - 3)
Step-by-step explanation:
Using the difference of squares we can factor this expression.
[tex](9 - x^2)\\= (3^2 - x^2)\\= (3 + x)(3 - x)\\= -(3 + x)(-3 + x)\\= -(x + 3)(x - 3)[/tex]
CAN SOMEONE PLEASE ANSWER MY QUESTION?!
Answer:
0.02 m/sec
Step-by-step explanation:
26/30=0.89 —> 0.89 min —> 53.4 sec
42/50=0.84 meters
speed=0.84 / 53.4 = 0.015 m/sec = 0.02 m/sec
does anyone know the answer
Answer:
For some reason I cannot open the photo you have provided.
Step-by-step explanation:
Please try to re-upload?
Answer:
upper left...
there are zeros at (x)(x+3) (x-2)
Step-by-step explanation:
In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments. The following information is provided.
SSTR = 200 (Sum Square Between Treatments)
SST = 800 (Total Sum Square)
The mean square within treatments (MSE) is _____.
a. 10
b. 600
c. 50
d. 200
Answer:
[tex]MSE = 10[/tex]
Step-by-step explanation:
Given
[tex]SSTR = 200[/tex]
[tex]SST = 800[/tex]
Required
Determine MSE
This is calculated as:
[tex]MSE = \frac{1}{ddf} * SSE[/tex]
Where:
[tex]SSE = SST - SSTR[/tex]
[tex]ddf \to[/tex] denominator df
So, we have:
[tex]SSE = 800 - 200[/tex]
[tex]SSE = 600[/tex]
To calculate the df, we have:
[tex]r = 13[/tex] --- observations
[tex]n = 5[/tex] treatments
So:
[tex]ddf = Total\ df - Numerator\ df[/tex]
[tex]Total = n*r-1 = 5*13 -1 = 64[/tex]
[tex]Numerator =n - 1 = 5 - 1 =4[/tex]
[tex]ddf =64-4=60[/tex]
So, we have:
[tex]MSE = \frac{1}{ddf} * SSE[/tex]
[tex]MSE = \frac{1}{60} * 600[/tex]
[tex]MSE = 10[/tex]
C = ſa²+b² Please describe the Mathematical order of Operation
Step-by-step explanation:
C + ſa6+b5 bescribe the Mathematical order of Operation
Find the missing side length, and enter your answer in the box below. If
necessary, round your answer to 2 decimal places.
6
8
The missing side length is 10 unit.
What is Pythagoras theorem?The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.
We have,
Perpendicular = 6
Base = 8
Using Pythagoras theorem
c² = P² + B²
c² = 6² + 8²
c²= 36 + 64
c² = 100
c= 10 unit.
Thus, the missing length is 10 unit.
Learn more about Pythagoras theorem here:
https://brainly.com/question/343682
#SPJ7
Which function below has the following domain and range?
Domain: {-7, - 5,2, 6, 7}
Range: {0, 1,8}
Answer:
{(2,0),(-5,1),(7,8),(6,0),(-7,1)
Write an equation of the line that passes through the pair of points (5, 8) and
(9, 16).
Answer:
D: y = 2x - 2
Step-by-step explanation:
1. [tex]\frac{16-8}{9-5}[/tex] = 2
2. y = 2x + b
3. Insert the points into the equation: 8 = 10 + b
4. b = -2
5. y = 2x - 2
=======================================================
Explanation:
Apply the slope formula
m = (y2-y1)/(x2-x1)
m = (16-8)/(9-5)
m = 8/4
m = 2
Then use this slope, along with another point such as (x,y) = (5,8) to find b
y = mx+b
8 = 2*5+b
8 = 10+b
8-10 = b
-2 = b
b = -2
Or you could use the other point (x,y) = (9,16)
y = mx+b
16 = 2*9+b
16 = 18+b
16-18 = b
-2 = b
b = -2
Either way, we get the same y intercept.
So because m = 2 is the slope and b = -2 is the y intercept, we go from y = mx+b to y = 2x-2
-------------------
To help verify the answer, note how plugging x = 5 leads us to...
y = 2x-2
y = 2*5 - 2
y = 10-2
y = 8
So x = 5 and y = 8 pair up together. This verifies (5,8) is on the line.
Through similar steps, you should find that the input x = 9 leads to the output y = 16. So that would confirm (9,16) is also on the line, and fully confirm the answer.
Given the following formula, solve for y.
Answer:
b) y=x -2(w+z)
Step-by-step explanation:
multiply both sides, move the terms and write on parametric form
Clarissa has abudget of 1,200$ amonth to spend for rent n food she already spent 928 this month which inequality represents the amount she can still spend this month
Answer:
272$
Step-by-step explanation:
You really should be clearer with your questions, but if your looking for the balance she has 272$
Multiply the following and combine terms where possible. -a(a-b-3)
Answer:
-a^2 +ab +3a
Step-by-step explanation:
-a(a-b-3)
Distribute
-a*a -a*(-b) -a *(-3)
-a^2 +ab +3a
help with number 6 please. thank you.
Answer:
See Below.
Step-by-step explanation:
We are given that:
[tex]\displaystyle \frac{dT}{dt} = -k(T - T_0)[/tex]
And we want to show that:
[tex]\displaystyle T = T_0+Ae^{-kt}[/tex]
From the original equation, divide both sides by (T - T₀) and multiply both sides by dt. Hence:
[tex]\displaystyle \frac{dT}{T-T_0}= -k\, dt[/tex]
Take the integral of both sides:
[tex]\displaystyle \int \frac{dT}{T- T_0} = \int -k \, dt[/tex]
Integrate. For the left integral, we can use u-substitution. Note that T₀ is simply a constant. Hence:
[tex]\displaystyle \ln\left|T - T_0\right| = -kt+C[/tex]
Raise both sides to e:
[tex]\displaystyle e^{\ln\left|T-T_0\right|} = e^{-kt+C}[/tex]
Simplify:
[tex]\displaystyle \begin{aligned} \left| T- T_0\right| &= e^{-kt} \cdot e^C \\ \\ &= e^C\left(e^{-kt}\right) \\ \\ &=Ae^{-kt} & \text{Let $e^C = A$}\end{aligned}[/tex]
Since the temperature T will always be greater than or equal to the surrounding medium T₀, we can remove the absolute value. Hence:
[tex]\left(T - T_0\right) = Ae^{-kt}[/tex]
Therefore:
[tex]\displaystyle T = T_0+Ae^{-kt}[/tex]
Mandatory minimum character count of 20.
You are dividing a rectangular garden into 2 equal sections by
placing a wooden plank diagonally across it, from one corner to
the opposite comer. The garden measures 4 feet by 6 feet. What
length diagonal plank should you buy, and why?
Diagonal planks are available in 1-foot increments (you can
buy a 1-foot board, or a 2-foot board, or a 3-foot board, and
so on...)
• You can cut the plank down from the size you buy to the
exact size, but you want to waste as little wood as possible.
Answer:
You can cut the plank down from the size you buy to the
exact size, but you want to waste as little wood as possible.
3-6÷12
simplyfication
Lakisha wants to buy some bitcoins. The exchange rate is $1 USD to 0.004 bitcoin. How many bitcoins can she buy with $400?
Answer:
1.6 Bitcoins
Step-by-step explanation:
Given data
We have the rate as
$1 USD to 0.004
Hence $400 will buy x bitcoins
Cross multiply to find the value of x
1*x= 400*0.004
x=1.6
Hence $400 will get you 1.6 Bitcoins
What system of equations is shown on the graph below
Answer:
A.
Step-by-step explanation:
x-2y=4 has a x-intercept of 4, a slope of 1/2, and a y-intercept of -2. 2x+y=4 has a x-intercept of -2, a slope of 2, and a y-intercept of -4.
