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.
Right answer gets brainlist
Answer:
50
Step-by-step explanation:
Victory Theater offers matinee tickets that are 35% cheaper than the tickets for the
evening shows. If an evening ticket costs $8.00, how much does a matinee ticket
cost?
A. $2.80
B. $5.20
C. $7.65
D. $10.80

Answer:
B
Step-by-step explanation:
35% off of $8.00 is equal to $5.20
✧brainliest appreciated✧
a rectangle has a width that is 1/2 its length the perimeter of this rectangle is 42 inches what is the width of the rectangle...what is the width of the rectangle
Answer:
w = 7 inches
Step-by-step explanation:
length = n
width = n/2
Perimeter = 2n + 2(n/2)
42 = 2n + n
42 = 3n
n = 14
width = 14/2 = 7
Sketch a graph of the polynomial function f(x) =x3− 2x2. Use it to complete the following:
f is------ on the intervals (−∞, 0) and (0, 2).
f is------ on the interval (2,∞).f is on the interval (0, 4__3).
f is------ on the intervals (−∞, 0) and(4__3, ∞).
Answer:
We have the function:
f(x) = x^3 - 2*x^2
To sketch this, we need to graph some points, and then just draw a line that passes through the points.
The graph of this equation is shown below.
Now we can complete the question.
If the graph is below the x-axis in some interval, the function is negative in that interval
If the graph is above the x-axis in some interval, the function is positive in that interval.
If the graph goes up in a interval, then the function is increasing in that interval
If the graph goes down on an interval, then the function is decreasing in that interval.
Then:
1) f is------ on the intervals (−∞, 0) and (0, 2).
Here we can see that the graph is below the x-axis in those intervals, then here we have:
f is negative on the intervals (−∞, 0) and (0, 2).
2) f is------ on the interval (2,∞)
Here the answer is positive:
f is positive on the interval (2,∞)
3) fi is ------ on the interval (0, 4/3)
In the graph, you can see that the graph goes down in that interval, then the correct answer here is:
f is decreasing on the interval (0, 4/3)
4) f is------ on the intervals (−∞, 0) and (4/3, ∞).
In this case, we can see that the graph goes up in these intervals, then the correct answer here is:
f is increasing on the intervals (−∞, 0) and (4/3, ∞).
2x + 6 = 6x - 22
Infinite Solutions
O No Solution
One Solution
O No answer text provided.
Answer:
it would be only one solution
Step-by-step explanation:
Which is the correct reason why (x+y)^2 is not equal to x^2+y^2
Answer:
Step-by-step explanation:
It would be easier to just show you.
Because we're using variables, I'm going to plug in a random set of numbers to stand for x and y.
(x+y)^2
(2+4)^2=36
vs.
x^2+y^2
2^2+4^2=20
The difference is because, following the order of operations, in the first situation you must first take care of what is in the parenthesis, which means you add x and y together-then you multiply that combined number by the 2nd power. Whereas in the second situation, you multiply x and y by the 2nd power separately, and then add the product of that together. So opposite order. In the first situation you add, then multiply. In the second, you multiply then add.
Express each of the following fractions as a mixed number (the sum of a whole number and the remaining fractional units).
8 over 5=
13 over 12= pleas awnser this im 10 and this is giveing me a hard time to figer out
8/5 = 1 3/5
(5 x 1 = 5 + 3 = 8, to get 8/5)
13/12 = 1 1/12 (12 x 1 = 12 + 1 = 13, to get 13/12)
Hope this helped! :D
A triangle has a base of LaTeX: 3\frac{2}{5}3 2 5 inches and an area of LaTeX: 5\frac{1}{10}5 1 10 square inches. Find the height of the triangle (in inches).
Answer:
For instance, there's the basic formula that the area of a triangle is half the base times the height. This formula only works, of course, when you know what the height of the triangle is. ... That is to say, the area of a triangle is half the product of two sides times the sine of the included angle.
Step-by-step explanation:
Find the unit rate for 72 oz. for 12 servings.
72 servings
12 servings
6 oz. per serving
12 oz. per serving
Answer:
6 onuces per serving
Step-by-step explanation:
In ΔWXY,
m
∠
W
=
(
2
x
−
12
)
∘
m∠W=(2x−12)
∘
,
m
∠
X
=
(
2
x
+
17
)
∘
m∠X=(2x+17)
∘
, and
m
∠
Y
=
(
9
x
−
7
)
∘
m∠Y=(9x−7)
∘
. Find
m
∠
X
.
m∠X.
WHAT IS THAT ? THX
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Find - 5+(-3) + 5.
0) Which pair of addends has a sum of O?
-3 and 5
-5 and 5
-5 and -3
Answer: -5 and 5
Step-by-step explanation:
-5 plus 5 added has a sum of 0
can somebody help me ?
Answer:
I believe the answer is A and D.
6.2.24
Que
In the figure, PQ = QR = RS. Find TU.
w
s
U
2.3
Y
12 R
VO
2.8 x
P Р
The length of TU is
Answer:
TU = 8.4
Step-by-step explanation:
The geometric figure consists of the following segments;
1) 4 parallel lines, WS, YR, XQ, and, VP
2) Three transversals, VW, PS, and, TU
The given parameters are;
PQ = QR = RS
Therefore, given that the transversal, PS, makes equal intercept with the 4 given parallel lines, by equal intercept theorem, the transversal TU will make equal intercepts with the given parallel lines
Therefore;
TX = 2.8 = XZ = ZU
From which we have, by segment addition postulate;
TU = TX + XZ + ZU
∴ TU = 2.8 + 2.8 + 2.8 = 8.4
TU = 8.4.
how to solve this?????????????
Answer: 6.25 cm
Step-by-step explanation:
Area of parallelogram [tex]A=base\times height[/tex]
Using base as AB and height as DE
[tex]Area=8\times 5[/tex]
Now, using base BC and height as DF
[tex]Area=6.4\times x[/tex]
Equating area
[tex]8\times5=6.4\times x\\x=6.25\ cm[/tex]
The grocery store sells 2 pounds of potatoes for $1.50. At this price, how much do 5 pounds of potatoes cost? What is the unit rate?
Answer:
5 pounds of potatoes is $3.75 1 pound is .75 cents
Step-by-step explanation:
I NEED HELP
what is the equation of the line in slope intercept form that passes through (-2,5) and (-1,1)
Answer:
y=4/3x+7/3
Step-by-step explanation:
I don't know if this is right.
A bottle of 150 vitamins costs $5.25. If the cost varies directly with the number of vitamins in the bottle, what should a bottle of 250 vitamins cost?
Answer:
$8.75
Step-by-step explanation:
Set up a proportion where x is the cost of a bottle with 250 vitamins:
[tex]\frac{150}{5.25}[/tex] = [tex]\frac{250}{x}[/tex]
Cross multiply and solve for x
150x = 1312.5
x = 8.75
So, it will cost $8.75 for a bottle with 250 vitamins
circular swimming pool has a diameter of 30 feet and a depth of 5 feet. Which equation can be used to find V, the volume of the swimming pool, in cubic feet?
Answer:
V = hπr^2
V = 5 X π X 15^2
V = 3534.29173
V = 3534.2 cubic feet
The equation that can be used to find the volume V of the swimming pool is πr²h
The swimming pool is circular and has a diameter of 30 feet and a depth of 5 feet.
This simply means the swimming pool follows the shape of a cylinder. The
two bases are circular and has a height of 5 feet.
Therefore, the volume of the swimming pool in cubic feet is the volume of a cylinder.
volume = πr²h
where
r = radius = 30 / 2 = 15 feet
h = 5 feet
volume = 3.14159 × 15² × 5 = 3.14159 × 225 × 5 = 3534.28875 = 3534.3 ft³
learn more about cylinders here: https://brainly.com/question/20766511?referrer=searchResults
can i get help on question 2 please
Answer:
last option is the answer
Step-by-step explanation:
the answer cannot be the two middle options because you can see the y-intercept is 2 so the equation must end with that
now you have to determine if the slope of the line is -5 or -1
you can find the slope by selecting two points on the line; for example, (0,2) and (1,1) and using formula: difference of y-values 2 - 1
difference of x-values 0 - 1
the slope is -1
What’s the distance between the points! round to the nearest tenth i need to show work please help i’m failing!
Answer:
[tex]\sqrt{109}[/tex]
Step-by-step explanation:
using pythagorean theorem
height:3
length=10
a^2+b^2=c^2
a=height=3
b=length=10
9+100=c^2
c=[tex]\sqrt{109}[/tex]
-4(2 + 8g)=
Pleaseee
Answer:
Well when simplified your answer would be
-8-32g
Step-by-step explanation:
So distribute -4 to each number in the parentheses
-4*2= -8
-4*8g= -32g
Now the answer is
-8-32g
A linear model for the data in the table is shown in the scatter plot.
X Y
1 2
2 6
5 6
6 9
7 11
9 10
10 13
(A) which two points should you use to find the equation for the model?
(B) what is the slope of the linear model? Show your work.
(C) what is the equation of the linear model in point slope form?
(D) what is the slope-intercept form of the equation you wrote in part (c). Show your work.
(E) what is the equation for the least squares regression line? Round the values for a and b to three decimal places)
Please be detailed! I really need help!
a) The two points that should be used to find the equation are given as follows: (6,9) and (10,13).
b) The slope of the linear model is of 1.
c) The point-slope form of the linear model is given as follows: y - 9 = (x - 6).
d) The slope-intercept form of the equation you wrote in part (c) is given as follows: y = x + 3.
e) The least squares regression line is given as follows: y = 1.028x + 2.271.
What is the slope-intercept definition of a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope.b is the y-intercept.Two points from the line are defined as follows:
(6,9) and (10,13).
These points were chosen as they have the least residual, that is, these points are the closest to the line of best fit.
Given two points, the slope is calculated as the change in y divided by the change in x, hence:
m = (13 - 9)/(10 - 6) = 1.
Considering point (6,9), the point-slope equation is given as follows:
y - 9 = (x - 6).
Hence the slope-intercept definition of the linear function is given as follows:
y - 9 = x - 6
y = x + 3.
The points from the scatter plot are given as follows:
(1,2), (2,6), (5,6), (6,9), (7,11), (9,10), (10,13).
Inserting these points into a linear regression calculator, the regression line is given as follows:
y = 1.028x + 2.271.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
Which equation has all real numbers as solutions?
A 3y = 3y + 1
B 3y = 3
C 3y = 0
D 3y + 1 = 3y + 1
Find N and explain how
Answer:
The value of n is 5
Step-by-step explanation:
Here, we want to get the value of n
To get this, we will need to use the appropriate trigonometric identity
As we can see, n represents the opposite as it the side that faces the angle given
m is the hypotenuse as it is the side that faces the right angle
The last side is called the adjacent
The trigonometric identity we want to use is that which connects the opposite to the adjacent
The appropriate trigonometric identity to use in this case is the tan
Thus;
Mathematically, the tan is the ratio of the opposite to the adjacent
hence;
tan 30 = n/ 5 √3
n = 5 √3 * 1/ √3
n = 5
Find the difference.
5 1/8 - 2 3/4
Answer:2 3/ 8
Step-by-step explanation: 5 1/8 - 2 3/4
= 41/ 8 - 11/4
= 41/8 - 22/8
=19/8
=2 3/ 8
Change to improper fraction .Then make the denominator the same ,make both denominator to 8 . Now you have 41/8 and 22/8 ,you can subtract it and it gives you 19/8.Lastly you make the improper fraction to mixed numbers which is 2 3/ 8 .
A man finds that the angle of elevationof a building is 22º. After walking 20 m towards the building, he finds that the angle of elevation is 33º. Find the height of the
building?
Answer:
The height of the building is 21.38 m
Step-by-step explanation:
Trigonometric Ratios
The ratios of the sides of a right triangle are called trigonometric ratios.
The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.
It's required to find the height of the building H.
The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:
[tex]\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]
[tex]\displaystyle \tan 22^\circ=\frac{H}{D+B}[/tex]
Multiplying by D+B:
[tex]\tan 22^\circ(D+B)=H[/tex]
Dividing by tan 22°
[tex]\displaystyle D+B=\frac{H}{\tan 22^\circ}[/tex]
Subtracting B:
[tex]\displaystyle D=\frac{H}{\tan 22^\circ}-B\qquad\qquad[1][/tex]
Applying to the smaller triangle:
[tex]\displaystyle \tan 33^\circ=\frac{H}{D}[/tex]
Multiplying by D:
[tex]\tan 33^\circ D=H[/tex]
Substituting from [1]:
[tex]\displaystyle \tan 33^\circ \left(\frac{H}{\tan 22^\circ}-B\right)=H[/tex]
Substituting values:
[tex]\displaystyle 0.6494 \left(\frac{H}{0.4040}-20\right)=H[/tex]
Operating:
[tex]1.6074H-12.988=H[/tex]
[tex]1.6074H-H=12.988[/tex]
[tex]0.6074H=12.988[/tex]
[tex]H = 12.988/0.6074[/tex]
H = 21.38 m
The height of the building is 21.38 m
Help GIVING BRAINLISTTTT
Answer:
12 x 3 = 36
Step-by-step explanation:
This is a Multiplication problem Because the Factory can produce 12 shoelaces in 3 minutes so take 12 and multiply it by 3 and your answer is 36. So the factory made 36 shoelaces in that time.
Answer:
12*3=36
Step-by-step explanation:
Help me if you are smart in math!
Answer:
10th number in the sequence is 786432
n = 4
Step-by-step explanation:
Multiply the following number by 4 (starting at #4) until you reach the 10th number in the sequence
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:)
Ok I need help solving this...
A. 105
B. 120
C. 50
D. 125
Answer:
A - 105
Step-by-step explanation:
since the two measurements are supplements, you do x+82+x+112=180. then you get x=-7. then you do 112-7=105
Answer:
105°
Step-by-step explanation:
A line equals 180, so take the two expressions and set them equal to 180:
x+82+x+112=180
simplify:
2x+194=180
2x=-14
x=-7
now plug the x value into the bolded expression
x+112
-7+112 = 105°