Using the probabilities the variance of x represented by Var(x) is equal to var(X) = E(X²) – [E(X)]² , where E(x) represents the expected value of x.
Given the probabilities of the random variable given by x₁ , x₂ , x₃ ,... has the probabilities of P₁ , P₂ , P₃ ...
We know that Variance is given by the formula:
[tex]Var(x) = \sigma^2=\sum_{i=1} ^n (x_i-\mu)^2px_i)\\\\=\sum_{i=1} ^n(x_i^2-2x_i+\mu^2)\\\\=E(x^2)-[E(x^2)][/tex]
We know that expected value is denoted by E(x) .
Hence the variance is denoted by var(X) = E(X²) – [E(X)]² .
In probability theory and statistics, variance is the predicted squared deviation of a random variable from its population mean or sample mean.
The scattering, or how far apart from the mean a bunch of data are from one another, is measured by variance. A few ideas that involve variance are descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling.
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Use the commutative law of addition to match the original expression on the left with its rewritten expression on the right.
35+82
9-6=15
7-3
15-9=6
27+13=40
3-7
13+27= 40
27+ 40 = 13
82 +35
cannot be rewritten
The commutative law of addition makes the expressions as,
35 + 82 → 82 + 35
7 + (-3) → (-3) + 7
15 - 9 = 6 → -9 + 15 = 6
27 + 13 = 40 → 13 + 27 = 40
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The commutative law of addition states that,
a + b = b + a
Now,
Using the commutative law we get,
35 + 82 = 82 + 35
7 - 3:
7 + (-3) = (-3) + 7
15 - 9 = 6
15 + (-9) = 6
(-9) + 15 = 6
-9 + 15 = 6
27 + 13 = 40
13 + 27 = 40
Thus,
The commutative law of addition makes the expressions as,
35 + 82 → 82 + 35
7 + (-3) → (-3) + 7
15 - 9 = 6 → -9 + 15 = 6
27 + 13 = 40 → 13 + 27 = 40
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out of 270 racers who started the marathon, 243 completed the race, 19 gave up, and 8 were disqualified. what percentage did not complete the marathon? %
The percentage is 10% who did not complete the marathon. It can be calculted using the formula of percentage.
What is percentage?
It is way of writting any number as a fraction of 100. Its symbol is % . It is a dimention less qunatity.
Total participants = 270
Number of participants completed the marathon = 243
Number of participants gave up = 19
Number of participnats disqualified = 8
Total number of participants who did not completed the merathon is the sum of participants who gave up and who did not qualified = 19 + 8 =27
Now, percentage of participants who did not complete the marathon is,
[tex]\frac{\text{Number of participants did not complete}}{\text{Total participants}}\times100\\=\frac{27}{270}\times100\\=10\%[/tex]
Hence, 10% did not complete the marathon.
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What is an equation of the line that passes through the point (8, 0) and is parallel to
the line x + y = 5?
Answer:
y = -x + 8
Step-by-step explanation:
x + y = 5
y = -x + 5
y = -x + b
0 = -(8) + b
b = 8
y = -x + 8
Could you please give me brainliest for this? Thank you!
What is the length of the midsegment AB? Type only the numerical answer.
Answer:
A is (3,4) B. is 18,4
Step-by-step explanation:
Check the picture below.
please hurry im about to run out of time
Answer: Quadrant 1, y-axis
Step-by-step explanation:
Morgan is making accsessories for the soccer team. she uses 574.35 inches of fabric on headbands for 32 players and 3 coaches. she also uses 276.16 of fabric on wristbands for just the players. how much fabric was used on a headband and wristband for each player?
Answer:
Step-by-step explanation:
574.35/35=16.41
276.16/32=8.63
16.41 + 8.63 = 25.04
7+8=8+7 identity property
Answer:The property used in 7 + 8 = 8 + 7 is Commutative property under addition
Step-by-step explanation:
Answer:
The identity property is a=a, so it is identity property
Step-by-step explanation:
???
The area of a rectangle is given by 2x-x-7x+9x+6cm
Answer: =3x+6
Step-by-step explanation:
Please help with this question. I need help this is too hard for my friend and I do not have time.
The frequency table formed using tally marks can be analyzed by using the numbers indicated by the tally marks as follows;
The true statements are as follows;
Twice as many students prefer green than purpleTwo more students prefer blue than purpleThe same number of students prefer yellow or purple as the number who prefer blueWhat are tally marks in a frequency table?Tally marks makes use of vertical lines to represent data, in which the fifth count is represented by a diagonal line across four vertical lines;
The data in the table are as follows
The number of students that prefer red = 5 + 1 = 6
The number of students that prefer yellow = 2
The number of students that prefer Blue = 5
The number of students that prefer purple = 3
The number of students that prefer Green = 6
Therefore;
Twice as many students prefer green than purpleTwo more students prefer blue than purpleThe same number of students prefer yellow or purple as the number who prefer blueLearn more about frequency tables in statistics here:
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Sort the following polygons in order of increasing area.
The area of the polygons arranged in order of increasing Area is:
Rectangle = 4Triangle = 12Square = 13What is a polygon?A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.
The area of the triangle is given as:
[Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By)]/2
Where Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.
Hence given:
A(-4-3), B(1, -3), C(-1,2)
we have
[-4(-3-2) + (1(2-(-3)) + (-1(-2-(-3))]/2
= 24/2
= 12
Hence the area of the triangle is 12.
To calculate the area of the rectangle, we use the distance formula. The equation for this is given as:
d² = (x₂ - x₁)² + (y₂-y₁)²
Where (x₁, x₂) are the coordinates of the first point and
(y₁, y₂) are the coordinates of the second point.
Assuming that the vertices are labeled as follows:
A (7,9), B(6,9), C(6,5), D(7,5), then
AB² = (6-7)² + (9-9)²
AB² = 1 + 0
AB = 1
BC² = (6-6)² + (5-9)²
BC² = 0² + -4²
BC = 4
CD² = (7-6)² +(5-5)²
CD² = 1² + 0²
CD = 1
DA² = (7-7)² + (9-5)²
DA² = 0² +4²
DA = 4
From the above, we can tell as is typical of a rectangle, that AB = CDand BC = DA
Since the Area of the rectangle is AB x CD OR BC x DA
The area of the rectangle =
4 x 1 = 4
Using the distance methods we can also arrive at the length of the sides of the square.
Since the area of a square is given as L² we only need the lenght one one side.
Hence,
AB = 3.60555
Hence the area of the square =
3.60555²
= 12.9999908025
Area of the square [tex]\approx[/tex] 13.
Thus the polygons arranged in order of increasing area are:
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Dolores is making a music video using a drone. She sets the drone on a
platform 1 meter above the ground. Then she uses the controls to make it
rise at a constant rate. The drone reaches a height of 16 meters in 5 seconds.
What is the equation for the drone's height, y, as a function of time, x?
Jm
Answer: y=3x-1
Step-by-step explanation:
1st subtract 1 from 16 so 15 then do 15/5 to get 3 seconds
Denise works for a company where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes. What type of IT funding model is the company deploying?
chargeback
The company is deploying chargeback type of IT funding model where the IT department charges her department for actual usage of a SharePoint server, determining how often users log in and how much storage space her department consumes.
What is IT funding model?A financing model is a planned, institutionalized strategy for creating a steady income stream to sustain an organization's core services and operations. Nonprofits need funding because it enables them to make investments in their operations and increase their overall effect. Securing funding is crucial to keeping your organization operational because nonprofits frequently rely on grants to assist with operational costs. Grants of all kinds are available to nonprofit organizations.
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PLSSSS help I will mark brainliest
The total distance a freely falling body covers in time, t, is given by the equation d(t)=1/2 gt 2 , where g is constant at 10 m/s 2 . Show, in terms of n, the distance a falling body covers in t = n seconds of movement.
Show, in terms of n, the distance a falling body covers in t = n - 1 seconds of movement.
The distance a freely falling body covers in the nth second is given by s (n) =d (n) -d(n-1). Show s (n)in terms of g, in simplified form.
In a hypothesis test for population proportion, you calculated the p-value is 0. 01 for the test statistic, which is a correct statement of the p-value?.
For the correct statement of the p-value, we would reject the null hypothesis.
There are two main methods for interpreting the statistical significance of a hypothesis test;
1) compare the p-value to the level of significance or
2) compare test statistics to a critical value.
Either method is acceptable, and is chosen by the researcher based upon which one is most typical in their field of research.
Under a hypothesis test we reject the null hypothesis if our p-value is less than the level of significance (p<α), and fail to reject the null hypothesis otherwise. Under the question, we are given a level of significance of 0.05 and a p-value of 0.01, where
p = 0.01 <α = 0.05
hence we would reject the null hypothesis. Thus the statement is TRUE.
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when conducting a one-way independent anova with three levels on the independent variable, an f-ratio that is large enough to be statistically significant tells us:
One or more of the mean differences are statistically significant, but not the precise location of the group differences.
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. A variable that is independent is precisely what it sounds like. It is a stand-alone variable that is unaffected by the other variables you are attempting to assess. Age, for instance, might be an independent variable.
Dependent variables are so-called because, during an experiment, their values are examined on the assumption or presumption that they are governed by the values of other variables.
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help pls by pst sunday december 4, 2022 12:00 images below
what is the difference between a convex set and a convex function with respect to linear programming?
A linear problem is always convex, because anything linear is convex.
What is linear programming?
A mathematical model whose requirements are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming.
A convex function is a real-valued function defined on an interval with the property that its epigraph (the set of points on or above the graph of the function) is a convex set. Convex minimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.
Every linear function has a concave shape. However, only convex polygons (possible sets of linear programs) exist.
A linear problem is always convex, because anything linear is convex.
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11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession. what is the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball? a) 0.2333 b) 0.5376 c) 0.5600 d) 0.2567 e) 0.3033 f) none of the above.
The probability for the given condition is, 0.56.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given:
11 black balls and 14 white balls are placed in an urn. two balls are then drawn in succession.
We have to find the probability that the second ball drawn is a white ball if the second ball is drawn without replacing the first ball.
P(white ball) = 14 / (11 + 14) = 14 / 25
P(2nd ball is white) = P(first ball is white)*P(2nd ball is white) + P(first ball is black)*P(2nd ball is white)
= (14 / 25) * (13 / 24) + (11 / 25) * (14 / 24)
=0.56
Hence, the probability for the given condition is, 0.56.
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A single die is rolled twice. Find the probability of rolling a 6 the first time and a 1 the second time.
Answer: I believe it is 2/12. tell me if I am wrong.
Step-by-step explanation: Hope this helps!
what is the equation of a line Parallel to -3x + 2y = 6
and through the point (4, -4)?
if the expression $(12-x)\div(3x)$ represents a non-negative integer, what is the largest possible integer value of $x$?
The largest possible value of the expression (12 - x)/3x is 3.
Expression
In algebra, expression is the combination of variables, numbers and constants.
Given,
Here we have the expression (12 - x)/3x.
Now we have to find the largest possible integer value.
As we have given in the question that the x takes only the non negative integer, then the values must be 1, 2, 3, ….
So, we have to apply the values on the given expression ,
Then we get the values,
=> x = 1 = > (12 - 1)/3(1) = 11/3 = 3.6
=> x = 2 => (12 - 2) / 3(2) = 10/6 = 1.6
=> x = 3 => (12 - 3) / 3(3) = 9/9 = 1
Therefore, the resulting value is 3.
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pls help im really slow and dont know how to do this
Answer:
2 1/6 more cups
Step-by-step explanation:
Answer: 2 1/6
Step-by-step explanation:
2 1/6
the wall thickness of 21 randomly selected glass 2-liter bottles was measured by a quality-control engineer. the wall thickness of those glass 2-liter bottles follows a normally distribution with unknown variance. the sample mean and the sample standard deviation of those 21 selected bottales was found to 4.15 millimeters and 0.09 millimeter, respectively. which of the following is the correct 90% two-sided confidence interval for the mean wall thickness?
The 90 % Prediction interval on the wall thickness of next bottle tested is (4.41, 4.99).
What is meant by Prediction Interval?A prediction interval is a form of confidence interval (CI) used with regression analysis predictions; it is a range of values that forecasts the value of a new observation based on your existing model.
Confidence intervals and predictions are frequently used interchangeably. They are not exactly the same thing, though.
A confidence interval is a set of values connected to a population parameter. the population's mean, as an illustration.
Where you anticipate an upcoming number to fall is called a prediction interval.
The Interval Uncertainties
It doesn't imply that you can forecast with confidence where a single number will fall, just like with most things in statistics.
Confidence intervals are usually accompanied with a confidence level, which represents the amount of uncertainty.
How to solve?
X=4.7
s=0.7
n=25
The tabulated value of t at 24 degree of freedom is 2.06
t24=2.064
The 90 % Prediction interval on the wall thickness of next bottle tested is given by:
=(4.7±t24×0.7√25)
=(4.7−2.064×0.75,4.7+2.064×0.75)
=(4.7−0.28896,4.7+0.28896)
=(4.41,4.99)
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The Wood family bought 6 crates of eggs last week. Each crate had 12 eggs. Since then, they have eaten 27 of the eggs. How many eggs are left?
Answer:
45 eggs
Step-by-step explanation:
You want to know the number of eggs left after 27 have been eaten from a supply of 6 crates having 12 eggs each.
Egg purchaseIf each of 6 crates had 12 eggs, the number of eggs bought was ...
(6 crates) × (12 eggs/crate) = 72 eggs
Eggs remainingIf 27 of those 72 were eaten, the number remaining is ...
72 -27 = 45
45 eggs are left.
xyz dV where T is the solid tetrahedron with vertices (0,0,0), (1,0,0), (1,1,0), and (1,0,1)
The volume of the solid tetrahedron is [tex]\frac{1}{144}[/tex] cubic units.
T's base is a triangle in the xy-plane (z= 0), with one edge being the line y=x, z= 0; the front side is a triangle in the vertical plane x= 1; the left side is a triangle in the xz-plane (y= 0); and the top is the plane xyz= 0 (this plane contains the three points (0,0,0), (1,1,0), (1,0,1).
The equation must be ax+by+cz+d=0 and must be satisfied by the three points as well as the edge (x=y, z=0).
T is thus described as 0≤z≤(xy), 0≤y≤x, 0≤x≤1.
for which it is suitable to used V=dzdydx.
[tex]\int\limits\int\ \int\limits{xyz} \, dV=\int\limits^1_0 \int\limits^x_0 \int\limits^{x-y}_0 {xyz} \, dxdydz\\ \\ =\int\limits^1_0 \int\limits^x_0[\frac{1}{2}xyz^2]\limits^{x-y}_0 dydx\\\\=\frac{1}{2}\int\limits^1_0 \int\limits^x_0(x^3y-2x^2y^2+xy^3)dydx\\\\=\frac{1}{2}\int\limits^1_0 [\frac{1}{2}x^3y^2-\frac{2}{3}x^2y^3+\frac{1}{4}xy^4]\limits^x_0dx\\\\=\frac{1}{2}\int\limits^1_0\frac{1}{12}x^5dx\\\\=\frac{1}{2}[\frac{1}{72}x^6]\limits^1_0\\\\=\frac{1}{144}[/tex]
Thus, the volume of the solid tetrahedron is [tex]\frac{1}{144}[/tex] cubic units.
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Question 1-4
A punch bowl contained 4 liters of soda, 5 liters of orange juice, and 2 liters of raspberry juice.
Select the statements that are true.
The ratio of the entire punch bowl to the juices is 9: 11.
The ratio of the entire punch bowl to the orange juice is 11 to 5.
The ratio of orange juice to soda is 4 to 5.
4
The ratio of soda to the entire punch bowl is
11
The ratio of orange juice to raspberry juice is 5 : 2.
Answer:
Its the second one
Step-by-step explanation:
.
a ferris wheel is 16 meters in diameter and makes one revolution every 7 minutes. for how many minutes of any revolution will your seat be above 12 meters?
After 1.67 minutes, the Ferris wheel will be higher than 12 meters.
Given,
The Ferris wheel has a 16-meter diameter.
The circumference of a circle with a diameter of 16 meters, which is calculated as follows, is the distance travelled by the Ferris wheel in one rotation; 16π meter
The Ferris wheel makes one revolution in 7 minutes, hence the following is true:
16π meter = 7 minutes
1 meter = (7/16π) minutes
12 meters = (7 ×12)/16π minutes
12 meters = 1.67 minutes
Therefore,
The Ferris wheel will be above 12 meters after 1.67 minutes.
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this chart shows the changes in value of one share of a stock at the end of each day. the value of stock on mondag morning was 28.42$ a share. sam owns 12 shares a stock what is the total value of sams stocksl at the end of Friday
Using mathematical operation, the value of stock on Friday is $341.04
The value of Share on FridayTo find the value of the stock on Friday, the value of the stock on Monday is $24.42. Since he own 12 shares, we can multiply 12 by $24.42.
This can be done using a mathematical operation called multiplication.
Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.
The value of the stock is 12 * 28.42 = 341.04
The stock value on Friday will $341.04
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what is a good half a mile time? today i ran it in 5:43. how can i improve that? i'm a 14 year old girl.
A good half a mile time is totally good, if a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile.
In the given question, we have to explain, what is a good half a mile time.
First, some background is required for 5:43 for half a mile. When did you start running? Was that time calculated using a full effort, or was it only the distance covered without walking? Don't worry about if it's good if you're spanking new. Use it as a foundation.
Second, like with most things in life, practise makes perfect, and running performance is no exception. If a half mile is the longest distance you've ever run, try a 3/4 mile run the next time. After a few successful attempts at that distance, increase it to a mile. The goal is to gradually push your boundaries until you consistently cross that threshold and then push your limits even farther.
Your body will be encouraged to adapt to the challenge, grow to it, and become prepared for when the challenge gets harder.
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design a rectangular milk carton box of width w, length l, and height h which holds 512 cm3 of milk. the sides of the box cost 1 cent/cm2 and the top and bottom cost 2 cent/cm2. find the dimensions of the box that minimize the total cost of materials used.
The dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
What is the rectangular dimension?
Two dimensions make up a rectangle: the length and, perpendicular to that, the breadth. A triangle's or an oval's interior likewise has two dimensions.
We have,
volume L* W * H = 512 cm³
sides of the box cost = 1 cent/cm²
top and bottom cost 2 cent/cm²
to find out
dimensions of the box that minimize the total cost of material use
we know here,
L* W * H = 512 cm³
where,
L is length and W is width and H is the height
so when we minimize the cost function
C( L, W, H ) = (1) 1 H ( L + W ) + (2) 1 L W
so put here H
substitute [tex]H = \frac{512}{LW}[/tex] we get,
C(L, W) = 512([tex]\frac{1}{l}, \frac{1}{W}[/tex]) + 2LW
so
minimum cost will be when the two partial derivatives is 0
dC/dL = 2W - 512/L² = 0
so
dC/dW = 2L - 512/W² = 0
L = 256/W²
so
by solving the above equation we get
L = W = (256)⁻³ = 16cm
and
H = 512/16 = 32
H = 32 cm
Hence, the dimensions of the box that minimize the total cost of materials used are:
L = W = 16 cm
H = 32 cm
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