Given:
[tex]\sigma_A=3[/tex]
[tex]n_A=6[/tex]
[tex]\sigma_B=5[/tex]
[tex]n_B=4[/tex]
[tex]\overline{x}_A=\overline{x}_B[/tex]
To find:
The variance. of combined set.
Solution:
Formula for variance is
[tex]\sigma^2=\dfrac{\sum (x_i-\overline{x})^2}{n}[/tex] ...(i)
Using (i), we get
[tex]\sigma_A^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{n_A}[/tex]
[tex](3)^2=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}[/tex]
[tex]9=\dfrac{\sum (x_i-\overline{x}_A)^2}{6}[/tex]
[tex]54=\sum (x_i-\overline{x}_A)^2[/tex]
Similarly,
[tex]\sigma_B^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{n_B}[/tex]
[tex](5)^2=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}[/tex]
[tex]25=\dfrac{\sum (x_i-\overline{x}_B)^2}{4}[/tex]
[tex]100=\sum (x_i-\overline{x}_B)^2[/tex]
Now, after combining both sets, we get
[tex]\sigma^2=\dfrac{\sum (x_i-\overline{x}_A)^2+\sum (x_i-\overline{x}_B)^2}{n_A+n_B}[/tex]
[tex]\sigma^2=\dfrac{54+100}{6+4}[/tex]
[tex]\sigma^2=\dfrac{154}{10}[/tex]
[tex]\sigma^2=15.4[/tex]
Therefore, the variance of combined set is 15.4.
I will mark brainliest thanks
Answer:
B
Step-by-step explanation: it All Becomes Negative if it is Reflected
The surface area for a rectangular prism is given by the formula SA = 2ab + 2bc + 2ac, where a, b, and c are the lengths of the prism. If the surface area of a rectangular prism with side c measuring 12 meters is 434 square meters and length of side a measuring the same length as side b, then what is the length of side a of the rectangular prism?
Answer:
We are given
We are also given and , which allows us to rewrite the equation as
(I substituted every "b" with "a" and every "c" with "9").
The solutions to this quadratic equation are -25 and 7. We discard -25 because a side with negative length would make no sense.
The required measure of side a of the rectangular prism is a = 9.3 meters.
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Here,
SA = 2ab + 2bc + 2ac
434 = 2a² + 14a + 14a
434 = 2a² + 28a
2a² + 28a - 434 = 0
a² + 14a - 217 = 0
a² + 14a + 49 - 49 - 217 = 0
(a + 7)² = 266
a = 9.3 or a = -23.3
Since the negative measure of length can be neglected.
a = 9.3 = b
Thus, the required measure of side a of the rectangular prism is a = 9.3 meters.
Learn more about the surface area here: https://brainly.com/question/2835293
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If a = -3, find the value of 3a²
Step-by-step explanation:
given
a = - 3
3a² = 3 * ( -3) ²
= 3 * 9
= 27
The value of 3a² is 27.
What it 12/14<9=
I really need help on this :
Answer:
This isn't a real question... but i can explain what you gave. 12/14 is less than 1, so it is less than 9.
The lines AB and CB intersect at B
(a) Find the co-ordinates of the midpoint of AB
(b) Find the equation of the line CB
Step-by-step explanation:
Soln
given,
from the figure
coordinate of B is (5,3),
A(7,0) and C(0,4)
A. solution
let, M(x,y) be the mid point of AB
A(7,0) = (x1,y1)
B(5,3) = (x2,y2)
we know
x = (x2+x1)/2
or, x = (5+7)/2
or, x = 12/2
or, x = 6
and for y
y = (y2+y1)/2
or, y = (3+0)/2
or, y = 3/2
therefore M(x,y) = (6,3/2)
B. solution
let,
C(0,4) = (x1,y1)
B(5,3) = (x2,y2)
equation of line is ;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
or, (y - 4)/(x -0) = (3 - 4)/(5 - 0)
or, (y - 4)/(x - 0) = -1 / 5
by cross multiply
or, 5×(y - 4) = -1×(x)
or, 5y - 20 = -x
or, x + 5y = 20 is the required equation.
One report said that it rained 3 inches in two days. It actually rained 1.05 inches and 1.8 inches. How far off was the report? Explain your answer.
Answer:
Step-by-step explanation:
1.80 + 1.05 = 2.85
3.00 - 2.85 = .15 inches
Can someone help me please!
Answer:
divide the numerator by the denominator
Pls help me with this question.
Answer:
x=1Step-by-step explanation:
[tex] \frac{5(x + 6) - 15(2 - x)}{3x - 1} = 10 \\ [/tex]
[tex] = > 5(x + 6) - 15(2 - x) = 10(3x - 1)[/tex]
[tex]5x + 30 - 30 + 15x = 30x - 10[/tex]
[tex] = > 20x = 30x - 10 \\ = > 20x - 30x = - 10 \\ = > - 10x = - 10 \\ = > x = 1[/tex]
hope it helps:)
find what x=______
show work pleae
Answer:
Use pythogoras theorem
a^2+b^2=c^2
x^2=c^2-a^2
x^2=15^2-12^2
x^2=81
x= square root of 81
x=9
Step-by-step explanation:
if g(x) =x -7, what if the value of x when g(x) =6
Answer:
x=13
Step-by-step explanation:
1. Place 6 in
6=x-7
2. Evaluate
x=6+7
x=13
WILL MARK YOU BRAINLIEST HURRY PLZ IM ON A TIME LIMIT
Answer:
Angle Y < Angle Z
Step-by-step explanation:
Answer:
angle X < angle Y
Step-by-step explanation:
........
Using the formula Distance = rate . time, find the distance covered by an airplane flying at 300 mph for 3 hours.
is a hotdog a taco or a sandwitch?
Answer:
Step-by-step explanation:
None of them
A market research survey has 15 questions and will be sent to 500 people. What is the total cost to conduct the survey if it has a $1,000 base fee plus $5 per question and $2 per person surveyed?
Answer:
Total cost to conduct survey = $2075
Step-by-step explanation:
Given that:
Number of questions on survey = 15
Number of people = 500
Base fee = $1000
Per question charge = $5
Per person surveyed = $2
Let,
q be the number of questions
p be the number of people
Total cost = Base fee + 5q + 2p
Total cost = 1000 + 5(15) + 2(500)
Total cost = 1000 + 75 + 1000
Total cost = $2075
Hence,
Total cost to conduct survey = $2075
If bricks are each 3 inches × 4 inches × 8 inches, how many bricks can be fit into a space which is 1 foot × 4 feet × 8 feet?
A 1 to 250
B 251 to 500
C 501 to 750
D 751 to 1000
E >1000
Answer:
The correct option is B.
Step-by-step explanation:
Consider the provided information.
The dimensions of bricks are in inches so convert foot into inches.
1 foot = 12 in
4 feet = 48 in
8 feet = 96 in
To calculate the number of bricks that fit into space we divide the space's volume by the volume of 1 brick.
[tex]\text{Number of bricks in space}=\dfrac{12\times 48 \times96}{3\times 4 \times8}[/tex]
[tex]\text{Number of bricks in space}=576[/tex]
Hence, 576 bricks can be fit into a space.
Therefore the correct option is B.
Please help.
Mary is currently 14 years older than her friend Courtney. In 5 years she will be 2 times as old as Courtney. Let x be Courtney’s age and solve for both of their ages.
How old is Courtney?
Answer:
x = 19
Step-by-step explanation:
x = Courtney's current age
14+x = Mary's current age
Mary's current age: 14 + 19 = 33
14 + x + 5 = 2x
19 = x
SOMEONE PLEASE HELP ME IM STRESSED OUT ILL GIVE OUT BRAINLIEST PLEASE DON’T ANSWER IF YOU DON’T KNOW THANK YOU
Answer:
$88
Step-by-step explanation:
first, you find 20% of 57 which = 11.4
then subract it with 57 which looks like 57-11.4 = 45.6
= 45.6
first, you find 20% of 53 which = 10.6
then subract it with 53 which looks like 53-10.6 = 42.7
= 42.4
then you add them both which = 45.6+ 42.4= 88
Mr.Klein's class is selling candy for a fundraiser. The class has a goal of raising $450 for selling (c) boxes of candy. Each box of candy costs $3.75.
Answer:
so since their goal is to get $450 and each candy box is $3.75, what you do is divide $3.75 by $450 you will get $120, soooooooooooooooooooooooooooo you times $3.75 by $120 you will get $450.
Step- by-step explanation:
A bag contains 3 red marbles and 5 blue marbles.
Find the probability of drawing a blue marble,
keeping it, and drawing another blue marble. Write
the probability as a fraction in simplest form.
Evaluate y=−4x+3, for x=4.
Answer:
y = -13
Step-by-step explanation:
Given
x = 4
y = - 4 * 4 + 3
= - 16 + 3
= - 13
Hope it will help :)
What are the x- and y-intercepts of the following Standard Form Equation:
- 2x + 5y = 0
Answer:
X-Intercept: [tex]x=-\frac{5}{2}y[/tex]
Y-Intercept: [tex]y=-\frac{2}{5}x[/tex]
Step-by-step explanation:
X-Intercept-
2x+5y=0 - Move the variable to the right-hand side and change its sign
2x=-5y - Divide both side of the equation by 2
x=-5/27 - Write the solution x in parametric form
x=-5/2y, y∈R
Y-Intercept-
2x+5y=0 - Move the variable to the right hand side and change its sign
5y=-2x Divide both sides of the equation by 5
y=-2/5x Write the solution y in parametric form
y=-2/5x, x∈R
6 boy students make up 24% of the total class how many total students are in class
Answer:
There are 25 students in the class.
Step-by-step explanation:
1. Set up an equation. The equation would be 6 = 24/100x.
2. Solve the equation. You can solve this by multiplying both sides by 100/24, and 100/24 * 6 = 25. You would then get that x = 25, which means that the number is 25.
Answer:
25 students
Step-by-step explanation:
25 x 0.24 = 6
3n^2 + 8n + 16 = 2n^2
Answer:
=11n+2+8n+16+2n+2 simplification is 11n+20+2N
Step-by-step explanation:
evaluate 1/6t + 5/18 when t = 1/3
1/6(__)+5/18=_/_+5/18
Answer:
[tex] \frac{1}{6} t + \frac{5}{18} \\ (\frac{1}{6} \times \frac{1}{3} ) + \frac{5}{18} \\ \frac{1}{18} + \frac{5}{18} = \frac{(1 + 5)}{18} \\ \frac{6}{18} = \frac{1}{3} [/tex]
1/3 is the right value of the given equation.I need help, I’ve been trying to figure out answers and I’m not getting anywhere is there anyone who could help me with (work shown)
Help pleasee! Thank uu
Answer:
The answer is the 2nd option
Step-by-step explanation:
Solve for b in the equation 4(b + 2) = 16
Answer:
b=2
Step-by-step explanation:
What do 5a represent in f(x)=5ax
Answer:
[tex]y = mx + c \\ f(x) = 5ax[/tex]
By comparing both the equation we get that,
5a represent a slope in f(x)In a standard deck of cards, what is the probability of drawing a face card?
Answer (round) to the hundredth place value.
Reasoning:
There are 12 face cards since there are 3 face cards in any suit, and 4 suits. So 3*4 = 12.
There are 52 cards total.
Dividing the values leads to 12/52 = 0.230769 which rounds to 0.23
please help (picture above)
Answer:
y= 45
x=9
Step-by-step explanation:
plug 5x into y since y=5x:
5x=4x+9
-4. -4
x=9
5(9)=45
Answer:
x=9 y=45
Step-by-step explanation:
y=4x + 9.......(1)
y= 5x.........(2)
Substitute 5x for y in equation 1.
5x= 4x + 9
5x - 4x = 9 (Collect like terms 5 and 4 have x in common if +4 crossover it changes to -4)
x = 9
substitute 9 for x in equation 2.
y = 5(9)
y = 5 x 9(multiplication)
y = 45