From the combined standard deviation, with the mean, and standard
deviation of the data sets, the required variance can be found.
[tex]\underline{\mathrm{The \ variance \ of \ the \ second \ set \ is} \ 4\dfrac{5}{28}}[/tex]Reasons:
The given data information are;
Mean of the first set of observation, [tex]\overline x_1[/tex] = 9.0
Standard deviation of the the first set, σ₁ = 4.0
Sample size of second observation, n₂ = 20
Mean of second sample, [tex]\overline x_2[/tex] = 10
Standard deviation of the combined set, σ₁₂ = 3.0
Sample size of combined set of observation, n₂ = 35
Solution:
The number of elements in the second sample, n₁ = 35 - 20 = 15
The standard deviation of the combined set is given by the formula;
[tex]{\sigma_{12}} = \mathbf{\sqrt{\dfrac{n_1 \cdot \left ( \sigma^2_{1}-d_1^2 \right ) + n_2 \cdot \left ( \sigma^2_{2}-d_2^2 \right )}{n_{1}+n_{2}}}}[/tex]
Where;
[tex]\overline x_{12} =\mathbf{\dfrac{n_1 \cdot \overline x_1 +n_2 \cdot \overline x_2 }{n_1 + n_2}}[/tex]
Therefore;
[tex]\overline x_{12} =\dfrac{15 \times 9.0 +20 \times10.0 }{15 + 20} = \dfrac{67}{7}[/tex]
d₁ = [tex]\mathbf{\overline x_{12}}[/tex] - [tex]\mathbf{\overline x_1}[/tex]
[tex]d_1 = \dfrac{67}{7} - 9.0 = \dfrac{4}{7}[/tex]
d₂ = [tex]\mathbf{\overline x_{12}}[/tex] - [tex]\mathbf{\overline x_2}[/tex]
[tex]d_2 = \dfrac{67}{7} - 10.0 = -\dfrac{3}{7}[/tex]
Therefore;
[tex]3=\sqrt{\dfrac{15 \times \left ( 4.0^2-\left(\dfrac{4}{7}\right) ^2 \right ) + 20 \cdot \left ( \sigma^2_{2}-\left(-\dfrac{3}{7}\right) ^2 \right )}{15+20}}[/tex]
Solving gives;
[tex]Variance, \ \sigma^2_2 = \mathbf{\dfrac{{117} }{28}}[/tex]
[tex]\mathrm{The \ variance \ of \ the \ second \ set, \ \sigma_2^2} = \dfrac{{117} }{28} = 4\dfrac{5}{28}[/tex]
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Under his cell phone plan, Alonso pays a flat cost of $53.50 per month and $3 per gigabyte. He wants to keep his bill at $59.80 per month. Write and solve an equation which can be used to determine gg, the number of gigabytes of data Alonso can use while staying within his budget.
Answer:
Alonso can use 2.1 gigabytes while staying within his budget.
Step-by-step explanation:
53.50 + 3x = 59.80
3x = 59.80 - 53.50
3x = 6.3
x = 6.3 ÷ 3
x = 2.1
Alonso can use 2.1 gigabytes while staying within his budget.
Tristan is ordering a taxi from an online taxi service. The taxi charges $3 just for the pickup and then an additional $1.50 per mile driven. How much would a taxi ride cost if Tristan is riding for 9 miles? How much would a taxi ride cost that is mm miles long?
Answer:
$ 16.50
y = 1.50m + 3
Step-by-step explanation:
1.50(9) + 3 = $16.50
Determine the equation of the line passing through the point below having the corresponding slope.
Point: ( -20, -34)
Slope: m =9/5
Write your answer as an equation in the form y=mx+b
Answer:
Step-by-step explanation:
-34 = (9/5)(-20) + b
b = -34 + 36 = 2
y = (9/5)x + 2
Sorry its blurry but please answer fast!!!!!
Answer:
i know 14 and 15 are true but not sure about 12 sry
Step-by-step explanation:
can anyone heelp me pls pls
Answer: liquid= lotion capsule= solid suspension=semisolid
Step-by-step explanation:
13 12 28 candy bars and 42 packs of gum were put in gift bags. The same number of candy bars and the same number of packs of gum were put in each bag. What is the greatest number of gift bags that could be made?
Answer:
Step-by-step explanation:
The function
y = 3.5x + 2.8 represents the cost y (in dollars)
of a taxi ride of x miles,
a. Identify the independent and dependent variables
Write the equation of the line with a slope of -3/4 and a y-intercept of 8 in slope
intercept form
Is it fair to give only 5 points for such a big question?
Answer:
No
Step-by-step explanation:
Because you (or whoever asks) shouldn't give only 5 points to such a big question, because whoever answers the question might have worked really hard to answer it while you just gave them only 5 points...its not worth answering of only 5 points. In my opinion at least ♀️
Hope what I said makes sense :)
Solve. −2x−35=87 Enter your answer in the box. x =
Hello there! I am Grace Rosalia (SilentNature), and I hope my answer will help you! :)
-2x-35=-87
-2x=-87+35
-2x=-52
Divide both sides by -2 to isolate x:
x=26
Hope this helps you! :)
~Just a joyful teen
[tex]SilentNature[/tex]
The solution of the given equation is x = -21.
How to solve a linear equation?A linear equation can be solved by equating the LHS and RHS of the equation following some basic rules such as by adding or subtracting the same numbers on both sides and similarly, doing division and multiplication with the same numbers.
The given equation can be solved as follows,
−2x − 35 = 87
=> -2x = -35 + 87
=> -2x = 42
=> x = -42/2
= -21
Hence, the value of x for the given equation is -21.
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What is the maximum, minimum, Midline, amplitude and period of the graph
Answer:
maximum -1 minimum -7 amplitude 6 midline -4
Step-by-step explanation:
What is the value of x in the equation 3x-y = 30, when y = 15?
62663773828hfnmdmsmlap62sjdldleldlb
f
[tex]x=200[/tex]
Explanation:
Okay so we can start by substituting in [tex]y[/tex] as we know what it is already:
[tex](\frac{1}{5} )x-(\frac{2}{3} )(15)=30[/tex]
Now at this stage we could use a calculator to figure out what [tex]\frac{2}{3}[/tex] of [tex]15[/tex] are though a bit of mental math is as easy:
[tex](\frac{15}{3} )[/tex] · [tex]2=[/tex] [tex]5[/tex] · [tex]2[/tex]
okay so now we have:
[tex](\frac{1}{5} )x-10=30[/tex] add 10 to both sides to get rid of the [tex]-10[/tex]
[tex](\frac{1}{5})x=40[/tex] let's get rid of that fraction by multiplying by [tex]5[/tex]
and there's the solution for x
We can check we got this right by substituting it back into the original equation with the known y:
[tex](\frac{1}{5} )(200)-(\frac{2}{3})(15)=30[/tex]
now, and we already know what out of is so :
that means
which is ✓
Therefore we know our solution is right.
helppppppppppppppppppppppppppppppppppppp
Answer:
(m÷3)+2in
Step-by-step explanation:
(m÷3) represents the division of Myron's height and 3
+2 is the extra 2 inches
Hope this helps! :)
What is the value of x in the diagram below? If necessary, round your answer
to the nearest tenth of a unit.
14
х
B
L
D
с
30
O A. 30.1
B. 6.5
C. 14
O D. 16
Answer:
D. 16
Step-by-step explanation:
Don’t answer on this or ur sus
>:)
heheheheheheheherhehehehreh
if 8 ^ x=2 sqrt 2 find the value of x.
Answer:
[tex]{ \rm{ {8}^{x} = \sqrt{2} }} \\ \\ { \rm{ {2}^{3x} = {2}^{ \frac{1}{2} } }} \\ \\ { \rm{3x = \frac{1}{2} }} \\ \\ { \rm{x = \frac{1}{6} }}[/tex]
HELPP
subtract a from 9, double the result, then add 10 to what you have
Answer:
Step-by-step explanation:
9 - a = 9 -a
9 - a + 10 = 19 - a
What is the value of k?
2k+9=7−3k
k=−2
k=−0.4
k = 2
k = 3.2
Answer:
k = -0.4
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
2k + 9 = 7 - 3k
Step 2: Solve for k
[Addition Property of Equality] Add 3k on both sides: 5k + 9 = 7[Subtraction Property of Equality] Subtract 9 on both sides: 5k = -2[Division Property of Equality] Divide 5 on both sides: k = -0.4Which equation describes a line that passes through the points (0, -3)
and (2,7)?
Answer:
y = 5x - 3
Step-by-step explanation:
3. What is 11% of $3,000? • A) $250 e B) $300 • C) $380 • D) $350
Answer:
$330.00
Step-by-step explanation:
Hey there!
The word ‘of’ in math means multiply
And
11% of 3,000
= 11/100 * 3,000
= 11/100 * 3,000/1
= 11(3,000)/100(1)
= 33,000/100
= 33,000 ÷ 100/100 ÷ 100
= 330/1
= 330
Therefore, the answer is most likely: 330
(NONE of the ABOVE)
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
I have more question just don't get it wronge
Answer:
Relfection over the x axis
Step-by-step explanation:
It is the name shape but flipped onto the other side, therefore it is a reflection
(-8r^2s^-8)(-3r^-7s^8)
24r^−5s^0 would be your answer
which one is this a b c d e the thing on the side dosent matter
Answer:
21.5m²
Step-by-step explanation:
Area for a square: LxW = A
10x10=100m²
Area for a circle: pi r² = A
pi(5)²=78.5m²
Find the difference:
100m²-78.5m² = 21.5m²
pls help me with this math
Find the volume of the prism.
3 cm
37 cm
5 cm
What is the y-intercept of the line graphed on the grid?
A) -1
B) 2
C) -2
D) 1
what is the value of p(x)=4x+15 ?
Answer:
The answer is 10x
Step-by-step explanation:
In which quadrant does the point (3 , 19) lie?
A.
Quadrant I
B.
Quadrant II
C.
Quadrant IV
D.
Quadrant III
Answer:
A.
Quadrant I
Step-by-step explanation:
Quadrant I= Both co=ordinates positive.
What is 8 units to the left of (3, -7)
Answer:
(-5,4)
Step-by-step explanation:
Please help I don’t understand it