Answer:
(1) Variance = 4.5 and Standard deviation = 2.121.
(2) Variance = 4.5 and Standard deviation = 2.121.
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged.
Step-by-step explanation:
We are given with the following set of data below;
X [tex]X-\bar X[/tex] [tex](X-\bar X)^{2}[/tex]
5 5 - 8 = -3 9
5 5 - 8 = -3 9
8 8 - 8 = 0 0
10 10 - 8 = 2 4
10 10 - 8 = 2 4
10 10 - 8 = 2 4
9 9 - 8 = 1 1
9 9 - 8 = 1 1
6 6 - 8 = -2 4
Total 72 36
Firstly, the mean of the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{72}{9}[/tex] = 8
(1)Now, the variance of the given data is;
Variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]
= [tex]\frac{36}{9-1}[/tex] = 4.5
So, the standard deviation, (S.D.) = [tex]\sqrt{\text{Variance}}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.12
(2) Now, each value is added by 2; so the new data set is given by;
X [tex]X-\bar X[/tex] [tex](X-\bar X)^{2}[/tex]
7 7 - 10 = -3 9
7 7 - 10 = -3 9
10 10 - 10 = 0 0
12 12 - 10 = 2 4
12 12 - 10 = 2 4
12 12 - 10 = 2 4
11 11 - 10 = 1 1
11 11 - 10 = 1 1
8 8 - 10 = -2 4
Total 90 36
Firstly, the mean of the above data is given by;
Mean, [tex]\bar X[/tex] = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{90}{9}[/tex] = 10
(1)Now, the variance of the given data is;
Variance = [tex]\frac{\sum (X-\bar X)^{2} }{n-1}[/tex]
= [tex]\frac{36}{9-1}[/tex] = 4.5
So, the new standard deviation, (S.D.) = [tex]\sqrt{\text{Variance}}[/tex]
= [tex]\sqrt{4.5}[/tex] = 2.12
(3) The effect on the measure of dispersion if each value is changed uniformly is that it remains unchanged as we see in the case of variance or standard deviation.
WILL MARK BRAINLIEST!!! PLZ HELP! The following graph describes function 1, and the equation below it describes function 2. Determine which function has a greater maximum value, and provide the ordered pair. Function 1 Function 2 f(x) = −x2 + 4x + 1 Function 1 has the larger maximum at (4, 1). Function 1 has the larger maximum at (1, 4). Function 2 has the larger maximum at (2, 5). Function 2 has the larger maximum at (3, 2).
Answer:
C: Function 2 has the larger maximum at (2, 5).
Step-by-step explanation:
We are given two functions, with Function 1 being described by the graph and Function 2 given by the function:
[tex]f(x)=-x^2+4x+1[/tex]
Notice that the leading coefficient of Function 2 is negative. The graph of Function 1 is curving downwards. So, both functions will have maximum values.
Recall that for a parobala, the maximum (or minimum) values is the y-value of the vertex point. So, let's find the vertex for each function.
For Function 1, we can see that the vertex is at (4,1). Thus, its maximum value is y = 1.
For Function 2, we will need to work out the vertex. Recall that the vertex is given by:
[tex]\displaystyle \left(-\frac{b}{2a},f\left(-\frac{b}{2a}\right)\right)[/tex]
Function 2 is defined by:
[tex]f(x)=-x^2+4x+1[/tex]
Therefore, a = -1, b = 4, and c = 1.
Find the x-coorindate of the vertex:
[tex]\displaystyle x=-\frac{(4)}{2(-1)}=2[/tex]
Substitute this back into the function to find the y-coordinate.
[tex]f(2)=-(2)^2+4(2)+1=5[/tex]
So, the vertex of Function 2 is (2,5). Therefore, the maximum value of Function 2 is y = 5.
Since 5 is greater than 1, the maximum value of Function 2 is greater.
The answer is choice C.
Please help solve this, I solved it on my own but I think my calculations are wrong. here is the problem,
b-(b+a×4c÷4); use; a=-6, b=1, and c=2?
Hi there! Hopefully this helps!
----------------------------------------------------------------------------------------------------------
Answer: 12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~First we need to substitute the value of the variable into the expression and simplify.
b-(b+a×4c÷4) = 1 - (1 + -6 × 4(2) ÷ 4).
Now we need to solve 1 - (1 + -6 × 4(2) ÷ 4).
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1 - (1 + -6 × 4(2) ÷ 4)
|
| First, we cancel out 4 and 4.
\/
1 - (1 - 6 × 2)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Next, we multiply -6 and 2 to get -12.
1 - (1 - 12)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Then we subtract 12 from 1 to get -11.
1 - (-11)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The opposite of -11 is 11.
1 + 11.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Add 1 and 11 to get, you guessed it, 12!Answer:
Answer: 12
Hope this helps
Translate into an equation: Five times the sum of a number and six is 48
Hey there! I'm happy to help!
When building equations, the word "is" means "equals".
First, we have the sum of a number and six. You can use any letter to represent the number. I will use n.
(n+6)
We see that this is multiplied by 5. We can just put the 5 next to the parentheses. This shows multiplication.
5(n+6)
Is 48
5(n+6)=48
Have a wonderful day! :D
Pens cost 15 pence each.
Rulers cost 20 pence each.
A school buys 150 pens and 90 rulers.
The total cost is reduced by 1/5
How much does the school pay?
Answer:
The amount the school pays is £32.40
Step-by-step explanation:
The cost of each pen = 15 pence
The cost of each ruler = 20 pence
The number of pens bought by the school = 150
The number of rulers bought by the school = 90
The cost reduction (discount) on the items bought = 1/5
Therefore, we have;
The total cost of the pens bought by the school = 150 × 15 = 2250 = £22.50
The total cost of the rulers bought by the school = 90 × 20 = 1800 = £18.00
The total cost of the writing materials (rulers and pens) bought by the school = £22.50 + £18.00 = £40.50
The discount = 1/5 total cost reduction = 1/5×£40.50 = $8.10
The amount the school pays = The total cost of the writing materials - The discount
The amount the school pays = £40.50 - $8.10 = £32.40
The amount the school pays = £32.40.
Plz help me. what is 4.9 * 10^-5 +.0005
Answer:
It should be 490000.0005
Step-by-step explanation:
4.9*10^5+.0005
10^5=100000
4.9*100000=490000
490000+.0005=490000.0005
Answer:
Step-by-step explanation:
[tex]10^{-5}=\frac{1}{10^{5}}=\frac{1}{100,000}=0.00001\\\\[/tex]
4.9* 10^-5 +0.0005 = 4.9 * 0.00001 + 0.0005
= 0.000049 + 0.0005
= 0.000549
8 less than half of n
Answer:
n/2>8
Step-by-step explanation:
Half of N is N/2
And if 8 is less that half of N or N/2
then
N/2 has to be greater than 8
N/2>8
Find the missing probability. P(A)=720,P(B)=35,P(A∩B)=21100 ,P(A∪B)=?
The missing probability P(A∪B) will be 37/50.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Given information;
P(A)= 7/20,
P(B)=3/5,
P(A∩B) =21/100 ,
We need to find the missing probability P(A∪B).
We know that
P(A∪B)= P(A) + P(B) + P(A∩B)
P(A∪B) = 7/20 + 3/5 + 21/100
P (A U B) = 37/50
Therefore, the missing probability P(A∪B) will be 37/50.
Learn more about probability here;
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Which of the following describe an angle with a vertex at A?
Check all that apply.
OA. ZABC
B. ZCAB
C. ZACB
D. ZBAC
Answer:
D) BAC is the correct answer as A is at the middle.
All of the options describe an angle with a vertex at A.
What is a vertex?In geometry, a vertex is a point where two or more lines, curves, or edges meet to form an angle or a corner.
It is the common endpoint of two or more rays, line segments, or sides of a polygon.
We have,
All of the options describe an angle with a vertex at A.
In each option, A is the vertex of the angle.
The letters that come before and after A indicate the other two points that form the angle. So:
∠ABC is an angle with vertex A and points B and C on either side.
∠CAB is an angle with vertex A and points C and B on either side. (Note that the order of the letters is reversed from option A.)
∠ACB is an angle with vertex A and points C and B on either side. (Note that the order of the letters is reversed from option B.)
∠BAC is an angle with vertex A and points B and C on either side. (Note that the letters are in a different order than option A.)
Thus,
All of the options describe an angle with a vertex at A.
Learn more about vertex here:
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what is an equivalent expression for (6^4 *8^-7)^-9
Answer:
(6⁴ * 8⁻⁷) ⁻⁹
equivalent expressión is:
1 / (6⁴ * 8⁻⁷)⁹
Step-by-step explanation:
(6⁴ * 8⁻⁷) ⁻⁹
= 1 / (6⁴ * 8⁻⁷)⁹
Which of the following points lie in the solution set to the following system of inequalities? y < −3x + 3 y < x + 2 (1, −5) (1, 5) (5, 1) (−1, 5)
Answer: (1, −5)
Step-by-step explanation:
Plot the given inequalities on coordinate plane.
For y < −3x + 3, plot y =−3x + 3
At x=0, y= 3
At y =0, 0=-3x+3
⇒ x= 1
so, plot points (0,3) and (1,0) and join to get y =−3x + 3, since inequality has '<' sign, so shade( in red) below line area and line should be dotted.
For y < x + 2, plot y = x + 2
At x=0, y= 2
At y =0, x=-2
so, plot points (0,2) and (-2,0) and join to get y = x + 2, since inequality has '<' sign, so shade( in orange) below line area and line should be dotted.
Now, plot all given points (1, −5) (1, 5) (5, 1) (−1, 5), we can clearly observe that (1, −5) lies in the solution set. (in common shaded region)
Answer:
The correct answer is 1, -5
Step-by-step explanation:
A spinner contains 3 equal sections: one red, one yellow, and one blue. The possible results of two spins are shown in the tree diagram below. What is P(red, then yellow)?
1/9
3 x 3 = 9 (since it is spun twice)
1/9
----------------------------------------------------------------------------
Answer:
1/9
Step-by-step explanation:
Probability of spinning a red = 1/3
Probability of spinning a yellow = 1/3
So Probability of getting red and then yellow = 1/3 x 1/3 = 1/9
Use distributive property to evaluate the expression 5(4/1/5)
Answer:
21
Step-by-step explanation:
4[tex]\frac{1}{5}[/tex] = [tex]\frac{21}{5}[/tex]
5 × [tex]\frac{21}{5}[/tex] = (5×21)/5
[tex]\frac{105}{5}[/tex] = 21
A man bought a car for 5500 cedis and sold it for 6500 cedis .find the percentage gain
Answer:
Around 18.18%
Step-by-step explanation:
We can use the percentage increase formula to find the gain here. The formula goes:
[tex]\frac{new-original}{original}\cdot100[/tex].
We know that the new value is 6500, and the old value is 5500, so we can substitute inside the equation.
[tex]\frac{6500-5500}{5500}\cdot100\\\\\frac{1000}{5500}\cdot100 \\\\0.\overline{18} \cdot100\\\\18.\overline{18}[/tex]
Which rounds to 18.18%.
Hope this helped!
resolver la siguiente ecuación por eliminación o sustitución: a-8b= -9 a-2b= -7
Answer: Solution: [tex]a=\dfrac{-19}{3}[/tex] and [tex]b=\dfrac{1}{3}[/tex] .
Step-by-step explanation:
The given pair of equations:
[tex]a-8b= -9\ ...(i)\\\\ a-2b= -7\ ...(ii)[/tex]
Eliminate equation (i) from (ii) , we get
[tex]-2b-(-8b)=-7-(-9)\\\\\Rightarrow\ -2b+8b=-7+9\\\\\Rightarrow\ 6b=2\\\\\Rightarrow\ b=\dfrac{1}{3}[/tex]
Put value of b in (ii) , we get
[tex]a-2\times\dfrac{1}{3}=-7\\\\\Rightarrow\ a=-7+\dfrac{2}{3}\\\\\Rightarrow\ a=\dfrac{-21+2}{3}\\\\\Rightarrow\ a=\dfrac{-19}{3}[/tex]
Solution: [tex]a=\dfrac{-19}{3}[/tex] and [tex]b=\dfrac{1}{3}[/tex] .
Find the decimal number exactly halfway between 1.01 and 1.02.
please help
Answer:
1.015
Step-by-step explanation:
just find their average, which is adding them up and dividing by 2
(1.01 + 1.02)/2 = 1.015
The decimal number exactly halfway between 1.01 and 1.02 is 1.015.
What are decimals?A decimal numeral system is the standard system for denoting integer and non-integer numbers. The way of denoting numbers in the decimal system is often referred to as decimal notation.
The given numbers are,
1.01 and 1.02
Now to find the halfway between the number we need to find their sum first and then the half of the sum.
So, the sum of number,
1.01 + 1.02 = 1.03
Now for half way divide the sum by 2
1.03/2 = 1.015
Hence, The decimal number exactly halfway between 1.01 and 1.02 is 1.015.
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A number if that number and the number b sum to 40.
Answer:
40-b
Step-by-step explanation:
x is the unknown number
x+b = 40
We want to find x
Subtract b from each side
x+b-b = 40 -b
x = 40-b
The unknown number is 40-b
Answer:
[tex]\huge \boxed{40-b}[/tex]
Step-by-step explanation:
[tex]\sf Let \ x \ be \ that \ number.[/tex]
[tex]x+b=40[/tex]
[tex]\sf Solve \ for \ x.[/tex]
[tex]\sf Subtract \ b \ from \ both \ sides.[/tex]
[tex]x+b-b=40-b[/tex]
[tex]\sf Simplify \ the \ equation.[/tex]
[tex]x=40-b[/tex]
PLEASE HELP! Find the coordinates of the vertices of the figure after the given transformation: T<2,3>
A. N′(−1,0),U′(1,5),L′(3,2),H′(1,−2)
B. N′(1,0),U′(3,5),L′(5,2),H′(3,−2)
C. N′(0,−2),U′(2,3),L′(4,0),H′(2,−4
D. N′(1,−1),U′(3,4),L′(5,1),H′(3,−3)
Answer:
The correct option is;
B. N'(1, 0), U'(3, 5), L'(5, 2), H'(3, -2)
Step-by-step explanation:
The coordinates of the pre-image are given as follows;
H(1, -5), N(-1, -3), U(1, 2), and L(3, -1)
The required transformation is T₍₂, ₃₎,which is a translation of (two) 2 units right and an additional translation of (three) 3 units up, which gives the coordinates of the image as follows;
N(-1, -3) transformed by N(-1 + 2, -3 + 3) [tex]\overset{T_{(2,\, 3)}}{\rightarrow}[/tex] N'(1, 0)
U(1, 2) transformed by U(1 + 2, 2 + 3) [tex]\overset{T_{(2,\, 3)}}{\rightarrow}[/tex] U'(3, 5)
L(3, -1) transformed by L(3 + 2, -1 + 3) [tex]\overset{T_{(2,\, 3)}}{\rightarrow}[/tex] L'(5, 2)
H(1, -5) transformed by H(1 + 2, -5 + 3) [tex]\overset{T_{(2,\, 3)}}{\rightarrow}[/tex] H'(3, -2)
The coordinates of the vertices of the given figure after the given transformation, T₍₂, ₃₎, are N'(1, 0), U'(3, 5), L'(5, 2), and H'(3, -2).
Therefore, the correct option is N'(1, 0), U'(3, 5), L'(5, 2), H'(3, -2).
Find the midpoints of the points (-3,-2) and (1,-4)
Answer: (-1,-3)
Step-by-step explanation:
midpoint formula [tex]\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-3,\:-2\right),\:\left(x_2,\:y_2\right)=\left(1,\:-4\right)[/tex]
[tex]\left(\frac{1-3}{2},\:\frac{-4-2}{2}\right)[/tex]
[tex](\frac{-2}{2},\frac{-6}{2})[/tex]
-2/2=-1
-6/2=-3
So the midpoint is (-1,-3)
Please mark brainliest
look at picture and solve
Answer:
79°
Step-by-step explanation:
PQO is straight angle with measure of 180°
the given angles' sum makes 101° and we need 79 to complete it to 180° therefore the angle STQ = 79°
Calvin has 80 meters of fencing to enclose his rectangular garden. He wants the garden’s length to be 12 meters greater then its width. Find the length and width of the garden.
a) 12m x 28m
b) 14m x 26m
c) 12m x 24m
d) 18m x 22m
Pls help!
Answer:
a
Step-by-step explanation:
a because when you divide 80 by 12 you get 28, so then it is 12 x 28m. :/
Answer:
Width W = 14 m
Length L = 26 m
Step-by-step explanation:
Perimeter of a rectangle = 80 m = 2L + 2W
L = 12 + W
80 = 2L + 2W
80 = 2(12 + W) + 2W
80 = 24 + 2W + 2W
80 - 24 = 4W
56 = 4W
W = 56 / 4
W = 14 m
L = 12 + W
L = 12 + 14
L = 26 m
check:
80 = 2L + 2W
80 = 2(26) + 2(14)
80 = 52 + 28
80 = 80 ---- OK
1 minus tan square A by 2 by tan + square A by 2 equals to Cos A
Answer:
trerjyhtrwgfdfeqrtgfnerwqdfgfgrqwefgn
Step-by-step explanation:
The Gonzalez family drove from 10:38 am to 2:05 pm. How long did they drive?
Answer:
3 hours and 27 minutes
Step-by-step explanation:
2:05 pm = 14:05 hours
1 hour = 60 minutes
14:05 = 13 hours + 60 minutes + 5 minutes = 13 hours + 65 minutes
then:
13h 65m
- 10h 38m
= 3h 27m
they drive:
3 hours and 27 minutes
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice. Write an equation for the number of minutes you swim, yyy, when your friend swims xxx number of minutes.
Answer:
y = x + 15
Step-by-step explanation:
My friend swims x minutes.
I swim 15 minutes more than my friends, so I swim x + 15 minutes.
I swim y minutes, so y equals x + 15
Answer: y = x + 15
what is the same number like 0.07
Answer:
we need more information
Step-by-step explanation:
Shawn wanted to model the number 13,450 using 13,450 using base-ten blocks how many large cubes, flats, and longs does he need to model the number
Answer:
See attached
Step-by-step explanation:
13450 = 13000 + 400 + 50
13*1000 = 13 large cubes4*100 = 4 flats5*10 = 5 longsWhich of the following can be used to express the total area of a figure?
A. (5)(4x)(3x)
B. 12x^2 + 15x
C. (3x + 4x) (5)
D. 3x (4x + 5)
Answer:
The answer is option BStep-by-step explanation:
The figure above is a rectangle
Area of a rectangle = length × width
From the question
The total length of the rectangle = 3x
The total width of the rectangle = 4x + 5
So the area of the figure is
A = 3x( 4x + 5)
Expand
We have the final answer as
A = 12x² + 15xHope this helps you
how to write x divided by 16 in algebraic expression
Answer:
x/16 the line means your dividing the x by 16
Step-by-step explanation:
1. Calculate the amount of gallons needed to fill the pool shown below.
Answer:
25,070 gal
Step-by-step explanation:
will make it simple and short.
vol = ( a + b ) * h/2 times the depth
vol = (8 + 3.5) x (35/2) x 20 = 4025 cu. ft. ---------->>> then convert to gal.
6.2288 gal
vol = 4025 cu.ft. x ----------------- = 25,070 gal
1 cu.ft.
There are 2 Rectangles, a red one and a blue one.The Blue rectangle has the perimeter of 250 km. If the area of the red rectangle is 2,500 square kilometers, what are its dimensions?
(Both of the rectangles have the same perimeter)
Answer:a
Step-by-step explanation:
Answer:
length = 100
width = 25
Step-by-step explanation:
Let L = length of red rectangle
Let H = height of red rectangle
Equation1: L+H=125 : we know the perimeter is 250 so L+H is 125
Equation2: L*H=2,500 : we know the area is 2,500
Equation3: L=125-H : subtracted H from both sides of Equation1
Equation4: (125-H)*H=2,500 : substituted "125-H" for L into Equation2
Solve equation4:
(125-H)*H=2,500 multiple terms on left side of equation
125H - H^2 = 2,500 rearrange into standard form
H^2 - 125H + 2,500 = 0
At this point you can "brute force" the answer with the quadratic formula:
H = (125 ± SQRT(125^2 - 4*1*2500) ) / 2
H = 100 or H = 25 : actually these are L and H
You could also factor the equation:
(H - 100) * (H - 25) = 0 : gives same answe
Vince went on a 333 day hiking trip. Each day, he walked 3\4 the distance that he walked the day before. He walked 83.2583, point, 25 kilometers total in the trip.
Answer:
x= 36 km
Step-by-step explanation:
Vince went on a 3 day hiking trip. Each day, he walked 3/4 the distance that he walked the day before. He walked 83.25 kilometers total in the trip. How far did Vince walk on the 1st day of the trip?
Assume vince walked x km on the first day .
The following equation can be formed
x + 3/4 x + (3/4)^2 x = 83.25
x + 0.75x + 0.5625x = 83.25
Add the like terms
2.3125x = 83.25
Divide both sides by 2.3125
x = 36 km.
Answer:
36
Step-by-step explanation: