It is true that the variance is the simplest measure of dispersion and is computed as the difference between the maximum value and the minimum value in the data set.
What is variance?Variance is a measure of dispersion that, in contrast to range and interquartile range, accounts for the spread of all data points in a data collection. Along with the standard deviation, which is just the square root of the variance, it is the measure of dispersion that is most frequently employed. The statistical assessment of the variation in numbers within a data collection is known as variance. In more detail, variance assesses how far apart each number in the collection is from the mean (average) and, consequently, from each other.
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Using the Pythagorean Theorem, determine the distance from point (8, −6) to the origin
Pls help asap
Step-by-step explanation:
a point on a coordinate grid always creates a right-angled triangle.
the straight distance from the origin (0, 0) is the Hypotenuse (the side opposite of the 90° angle).
the coordinate distances in x and y directions are the 2 legs.
Pythagoras :
c² = a² + b²
c being the Hypotenuse, a and b being the legs.
so,
(distance from origin)² = x² + y²
because the x, y coordinates are the coordinate distances from the origin in x and in y direction.
distance² = 8² + (-6)² = 64 + 36 = 100
distance = sqrt(100) = 10
the point is 10 units apart from the origin.
What number is 150% of 90
Answer: 135
Step-by-step explanation:
Answer: 145
Step-by-step explanation:
100% of 90 is, welll 90, and 50% of 90 is 45, so 150% of 90 is 145
why should nulls in a relation be avoided as much as possible? discuss the problem of spurious tuples and how we may prevent it.
Nulls in a relationship should be avoided as much as possible because of the following reasons:-
• Memory space will be wasted at the storage level
• When aggregate operations such as SUM, AVG etc. are performed on the attribute which has
null value, the result will be incorrect
• When JOIN operation involves an attribute with null values, the result may be unpredictable
• The NULL value has a different meaning. It may be unknown, not applicable or absent
Spurious tuples are generated as the result of bad design or improper decomposition of the base
table.
• Spurious tuples are the tuples generated when a JOIN operation is performed on badly
designed relations. The resultant will have more tuples than the original set of tuples
• The main problem with spurious tuples is that they are considered invalid as they do not
appear in the base tables.
Spurious tuples can be avoided by taking care while designing relation schemas:
• The relations should be designed in such a way that when a JOIN operation is performed, the
attributes involved in the JOIN operation must be a primary key in one table and a foreign key in
another table
• While decomposing a base table into two tables, the tables must have a common attribute. The
the common attribute must be the primary key in one table and the foreign key in another table.
Hence the answer is given.
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randy wants to attach a 20 foot string of lights to the top of the 19 foot mast of his sailboat. how far from the base of the mast should he attach the end of the light string? round your answer to two decimal places.
The distance between the base of the string and the base of the mast of the sailboat is 6.24.
Here we have to find the distance from the base of the mast that should be attached to the end of the light string.
Data given:
length of the string = 20 foot
length of the mast of the sailboat = 19 foot
Distance between the base of the mast and the light string = [tex]\sqrt{20^{2} - 19^{2} }[/tex]
= [tex]\sqrt{400 - 361}[/tex]
= √39
= 6.245
Therefore the distance between the string and the mast is 6.24.
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Point 8 in the graph below is reflected through the line y=-x.
Iy
++
-6-4-2
6-
2-
-2.
-6
B.
2 46. x
I
What are the coordinates of Point B', the image of Point B?
Answer:
[tex](-4,-5)[/tex]
Step-by-step explanation:
When reflecting over [tex]y=-x[/tex], [tex](x,y) \longrightarrow (-y, -x)[/tex].
13. Amelia has similar cake pans. The
first pan is 10 inches long and 8 inches
wide. The second pan is 14 inches
Tong. How wide is the second pan?
11.2 inches
B.
11 inches
C. 10.8 inches
D. 10.6 inches
A.11.2
B.11 inches
Width of second pan become 11.2 inches
What do you mean by similar figures?
Two figures are said to be similar if they share the same shape. Congruent objects are those that are precisely the same size and shape.
The term "similar figures" refers to two figures that share the same shape but differ in size.
When two figures are comparable, the sign ‘∼’ is used to indicate that they are.
It is given that Amelia has similar cake pans. The first pan is 10 inches long and 8 inches wide. The second pan is 14 inches long.
We know that the ratio of the sides of the similar figures is always equal,
So , [tex]\frac{10}{8}=\frac{14}{x}[/tex]
where x is the width of second pan.
Solve the above equation using cross multiplication we get,
x = [tex]\frac{14 \times 8}{10} = \frac{112}{10}=11.2[/tex]
Hence, width of second pan become 11.2 inches
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a farmer is making a circular pen for his sheep. he has 213.52 yards of fencing to use. what should the diameter of the circle pen be?
The diameter of the circle pen for the sheep of the farmer is 68 yards.
Explain the term circumference of the circle?The distance along a circle's perimeter is referred to as its circumference. In other words, the circumference of a circle is equal to the length of a straight line formed by opening up the circle.The space around a circle is known as its circumference. By calculating the distance required to walk around the globe, we may determine the size of the earth's circumference.The total length of the fencing used for the preparation of the fencing for sheep is 213.52 yards.
Thus,
circumference = 213.52 yards
The formula for the calculation of the circumference of circle is,
circumference = 2πr,
In which,
π = 3.14 and radius r.
Thus,
213.52 = 2πr
r = 213.52 / 2π
r = 34
Diameter = 2 x radius
Diameter = 2 x 34
Diameter = 68 yards.
Thus, the diameter of the circle pen for the sheep of the farmer is 68 yards.
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first, we form a riemann sum with n rectangles (or subintervals). (i) what is the width of each rectangle? (ii) list the right-hand endpoints of each rectangle. (iii) list the heights of each rectangle. (iv) list the areas of each rectangle. (v) what is the riemann sum with n rectangles? you may use summation notation, but you do not need to.
The Reimann sum with n rectangle will be given as [tex]\sum^{n-1}_{i = 0} f{(x_i)} \Delta x[/tex]
Let us suppose that f is a non-negative function, defined over a closed interval represented by [a, b].
The integral of f with respect to x signifies the area between the graph of f and X-axis. This area would be called definite integral of a function f from a to b. Then Riemannian method of determining this area is:
“if the area is divided into n rectangles of very small breadth, then it would be simpler to calculate the area of such rectangles and then we can add them up
(i ) The width of each rectangle will be denoted as Δx
Δx = b-a/n,
where , a is lower bound
b is upper bound of the integral
(ii) The right-hand endpoints of each rectangle are refer as [tex]x_i[/tex] and we can find the right endpoints by [tex]x_i[/tex] = a + Δx.i
(iii) The height of each rectangle is the value of the function at the upper point of the interval.
a + (b-a)/n for the first rectangle , a + 2(b-a)/n for the second rectangle and so on
(iv) The area of the each rectangle will be
Area = Width × height
=> A = (b-a)/2 × a + i(b-a)/2
(v) The Riemann sum with n rectangles is
Area of rectangle = [tex]\sum^{n-1}_{i = 0} f{(x_i)} \Delta x[/tex]
Which is also known as Reimann sum
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The parking garage at the airport has 625 parking spaces. 92% of the spaces are empty. How
many empty spaces are there in the parking garage?
Answer:
575 empty spaces
Step-by-step explanation:
If 625 --> 100% then
X --> 92%
X= (625 * 92)/100
X= 575
if sam has 100 apples and Jante steals 36 from sam how many does sam have left
Answer:
the answer to that is 65.
Step-by-step explanation:
maths
Equivalent Ratios: Liam practiced piano 24 times in 4 weeks. His brother practiced 12 times in 2 weeks. Are the rates at which each brother practiced equivalent?
(1): Yes, they are equivalent.
(2): No, they are not equivalent.
Answer:
The rates are equivalent.
Step-by-step explanation:
Liam practiced piano 24 times in 4 weeks. 1 week = 7 days. 4 weeks = 28 days.
y= 5x the table for it
Answer:
The left side represents x, and the right side is y
Step-by-step explanation:
This table is simply going up by 5
two polygons are similar, and the ratio s1/s2? of their corresponding sides is 8/7. find the ratio of their areas, a1/a2.
Two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7 then the ratio of their areas, a1/a2 = 64/49.
In the given question, two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7.
We have to find the ratio of their areas, a1/a2.
As we know that, the measurement of the area that a polygon encloses serves as its definition. The area of a polygon is the space that it takes up in a two-dimensional plane since polygons are closed plane structures.
As given that, two polygons are similar.
The ratio of their corresponding sides are
s1/s2 = 8/7
According to properties of similar polygon, the ratio of the areas of the two polygons is the square of the ratio of the sides. Hence,
a1/a2 = (s1/s2)^2
a1/a2 = (8/7)^2
a1/a2 = 64/49
Hence, two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7 then the ratio of their areas, a1/a2 = 64/49.
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tion for y: 2x + 3y = -6. Then, answer the questions that follow.
formed equation, what is the slope of the linear equation 2x + 3y = -6?
to find solutions to the linear equation.
x
Lesson 17 Problem Se
Transformed Linear Equation:
y
Answer:
The slope is -2/3
Step-by-step explanation:
2x + 3y = -6
We want to find the slope, so we need to get the equation in slope intercept form y = mx+b where m is the slope and b is the y intercept
Subtract 2x from each side
3y = -2x+6
Divide each side by 3
y = -2/3x +2
The slope is -2/3
ar chie and bijan share some money in the ratio 7 : 11. bijan gets £132. how much money does archie get?
Archie will get $84.
We have given that,
archie and bijjan share some money in the ratio 7:11 and bijjan get $132.
We have to find how much money will archie get.
Let us consider x as a money
i.e. 7x:11x
bijjan gets $132
means 11x = 132
x = [tex]\frac{132}{11}[/tex]
x = 12
Therefore archie's money,
7x=7(12) = 84
Hence archie get $84.
A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. The concept of ratio defines us to compare two quantities while the proportion is an equation that shows that two ratios are equivalent.
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a gasoline tank is in the shape of a right circular cylinder (lying on its side) of length 10 ft and radius 4 ft. set up an integral that represents the volume of the gas in the tank if it is filled to a depth of 6 ft
The required integral for the gasoline tank is [tex]V = \int\limits_{ - 5}^3 {20 \cdot \sqrt {16 - {x^2}} } dx[/tex]
For the given circular cylinder, the desired limit is determined by the depth and radius of the cylinder. And, the integral function is obtained by employing a Pythagoras theorem. The final set-up must be in the form of [tex]{eq}\int\limits_a^b {f\left( x \right)dx}[/tex]
Let x be the vertical distance up from the centre line of the tank.
The radius of the right circular cylinder is 4 ft
The length of the right circular cylinder is 10 ft
The volume of the strip is determined by the front view of the right circular cylinder as follows:
dV=(L+L)dx×14
=2L×10dx
=20Ldx
The front view of the right circular cylinder is
x^2 + L^2 = 4^2
[tex]L = \sqrt{16 - x^2}[/tex]
Substitute the value of L in the equation of dV.
[tex]dV = 20 \cdot \sqrt {16 - {x^2}} dx[/tex]
The integral required to set up the volume at a depth of 6 ft will be given by taking integrals limits from -5 to 3
[tex]V = \int\limits_{ - 5}^3 {20 \cdot \sqrt {16 - {x^2}} } dx[/tex]
This is the required integral
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Shown below are the steps used to solve an equation.
5 - 3 (x - 1) = 4 - 7x
5 - 3x + 3 = 4 - 7x
8 - 3x = 4 - 7x
8 = 4 - 4x
x= -1
Explain what is happening to the equation during each step in the solution.
5 - 3 (x - 1) = 4 - 7x, initial equation
5 - 3x + 3 = 4 - 7x, distributing 3 (x - 1) to get 3x + 3
8 - 3x = 4 - 7x, adding 3 to 5 to get 8
8 = 4 - 4x, subtracting 3x from both sides of the equation
x= -1, substituting x for the only possible value to make the equation true.
if the growth rate r of a population is positive and remains constant, the number of people added to the population:
The number of persons added to the population rises annually if the population's growth rate, r, is positive and stable.
Given statement,
If the growth rate r of a population is positive and remains constant, the number of people added to the population,
In the given case the solution will be the number of people added to the population " increases each year ".
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a researcher developing a regression equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3). educational status is a dummy variable with 0
36% of the variability equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).
Given:
Correlation value: 0.6
The amount of variation in the dependent variable that can be predicted from the independent variable is shown by the coefficient of determination.
The correlation coefficient is equal to;
Since the correlation in this instance is equal to 0.6, our coefficient is 0.36. Therefore, the age of the home can account for 36% of the variation in equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).
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two boats leave a dock at the same time. one boat travels south at and the other travels east at . after half an hour, how fast is the distance between the boats increasing?
After half an hour the two boats will be at a distance of 68 mph
Given,
Both boats are moving in a direction that creates a right angle triangle. The lengths of the triangle's legs are the distances that both boats travelled going straight south and straight east. The hypotenuse of a right angle triangle is the distance between them after t hours.
Let x stand for the length of the triangle's shorter south leg.
Let y stand for the length of the right angle triangle's longer (east) leg.
Assume that z is the hypotenuse.
Using the Pythagorean theorem
Hypotenuse² = opposite side² + adjacent side²
Therefore
z² = x² + y²
We would discriminate with regard to t in order to ascertain the speed of the distances' alterations.
It develops,
2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1
One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that
dx/dt = 32
dy/dt = 60
Distance = speed × time
Since t = 0.5 hour, then
x = 32 × 0.5 = 16 miles
y = 60 × 0.5 = 30 miles
z² = 16² + 30² = 256 + 900
z = √1156z = 34 miles
Substituting these values into equation 1, it becomes
2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60
68dz/dt = 1024 + 3600
68dz/dt = 4624
dz/dt = 4624/68
dz/dt = 68 mph
Therefore,
The distance between the boats after half an hour is 68 mph
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Completed question is given below with missing parts.
Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60 mi divided by hr60 mi/hr. After half an hour, how fast is the distance between the boats increasing?
using the following information. coefficients intercept −12.8094 independent variable 2.1794 anova df ss ms f regression 1 12,323.56 12,323.56 90.0481 residual 8 1,094.842 136.8553 total 9 13,418.4 what is the standard error of the estimate? multiple choice 136.8552 1,094.842 11.6985 13,418.4
The Standard error of the estimate is 11.6985
The standard error of estimate is the measure of variation of an observation made around around the regression line
Simply, It is used to check the accuracy of prediction made with the regression line. A standard deviation which measures the variation in the set of data from its mean, the standard error of estimate also measured the variation in actual values of Y from the computed values of Y on the regression line.
Given in the question,
coefficient of y-intercept = -12.8094
Coefficient of x = 2.1794
N-1 = 9
=> N = 10
SSE = 1094.842
Standard error of estimate = √SSE(N-2)
where , SSE is sum of square of error
S.E = √(1094.842)/ (10-2)
=> √(1094.842)/8
=> √136,855
=> 11.6985 is standard error
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What is the equation of this line in slope intercept form?
−x −5y=10
A y=−1/5x+10y
B y=5x−2y
C y=−1/5x−2y
D y=1/5x+10
C
Step-by-step explanation:
add x on both sides
-5y=10+x
divide both sides by -5
y=-1/5x-2
Please help asap now !!!!!
Answer:
220.25
Step-by-step explanation:
881 divided by 4 is 220.25
The circumference of a circle is 22pi cm. What is the area, in square centimeters?
Answer:
Area = 121pi sq cm
Step-by-step explanation:
Circumference is the distance around the circle. The formula for circumference is:
C = pi•d
The question has the info in it that the circumference is 22pi.
C = 22pi
remember,
C = pi•d this means that the circle has a diameter (the d in the formula is diameter) 22cm.
The radius is half the diameter. The diameter is 22cm, so the radius is 11cm.
The formula for the area is:
Area = pi•r^2
= pi•11^2
= pi•121
= 121pi
The area is 121pi sq cm.
which graph represents the peicewise function ?
Graph option B is the correct answer.
What is graphical representation?Graphical representation refers to the use of charts and graphs to visually display, analyse, clarify, and interpret numerical data, functions, and other qualitative structures.
Given are function,
y = x+1 ≤0 and y = 3x
The best demonstration of these functions can be seen in graph 2.
Hence, Graph option B is the correct answer.
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solve 4 6/8 - 2 3/5
A. 1 6/13
B. 1 3/40
C. 2 6/40
D. 2 3/13
Giving Brainliest!!!!!
Answer:
C
Step-by-step explanation:
1. Change to improper fractions
4 6/8 -> Multiply 4 and 8. Add 6. = 38/8
2 3/5 -> Multiply 2 and 5. Add 3. 13/5
Denominators are different so we have to make the same.
38/8 = 190/40
13/5 = 104/40
190/40-104/40 = 86/40 -> 2 6/40
to sample the class you split the class into guys and girls. you then select at random 3 guys and 3 girls. what type of sampling did you do?
The type of sampling used to sample the class split into girls and boys is stratified sampling.
As given in the question,
Sample the class to split into guys and girls
Select at random 3 guys and 3 girls.
Types of sampling :
A simple random : Chances of selection is equally likely. Randomly choose the data.
False
B systematic: Samples are collected from large data so that it can systematically arranged.
False
C convenience : In this sample or data collection is done as per convenience.
False
D cluster : It divides the group into multiple group or clusters.
False
E stratified : This represents the division of heterogeneous group into fairly homogeneous group in form of strata.
True.
Therefore, the stratified sampling represents the splitting of class into guys and girls.
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Use Green's theorem and find the work that the force F performs when acting along the complete trajectory counterclockwise. The dimensions of the region R are b = 3 and d3 in ft. The force F is: F = [ay-cx ] lb; use a=2 and c=2. C, RC 0 c, d x
The work that the force F performs is -36.
How to calculate work using Green's Theorem?F = [ay - cx]
a = 2
b = 3
c = 2
d = 3
Green's theorem is theorem about the relationship between a integral line on a simple closed curve C and a double integral of a plane D bounded by C. So, from Green's Theorem we get,
∫Pdx + Qdy = ∫∫([tex]\frac{\partial Q}{\partial x}[/tex]-[tex]\frac{\partial P}{\partial y}[/tex])dA
Put the a and c value into force F equation. So,
F = [2y - 2x]
From this, we get
P = 2y
Q = -2x
[tex]\frac{\partial P}{\partial y}[/tex] = 2
[tex]\frac{\partial Q}{\partial x}[/tex] = -2
So, the integral formula become
∫∫([tex]\frac{\partial Q}{\partial x}[/tex]-[tex]\frac{\partial P}{\partial y}[/tex])dA = ∫∫(-2-2)dA
= -4 dA
Next, we calculate the work
Work = -4 × b × d
= -4 × 3 × 3
= -36
Thus, the work is -36 for the force F performs.
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If a circle has the diameter of 37in, what is the area?
Answer:
A = pi (r)^2, so first you have to find the radius. The radius = 18.5 since its diameter/2. So if you plug it in, its A = pi (18.5)^2 and your answer would be A = 1075.21. Hope I helped :))
Step-by-step explanation:
given any set of seven integers, must there be at least two that have the same remainder when divided by 6?
Given any set of seven numbers that should be at least 2 that must have the same remainder when divided by 6
What are the factors?A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product since the product is divisible by them.
How do you find factors?Step 1: factor the provided number into primes, or describe it as the product of primes.
Step 2: Write the prime factorization in exponent form in step three.
Step 3: Increase each exponent by one.
Step 4: Multiply each of the results.
There can only be a maximum of six different remainders when dividing by six: 0, 1, 2, 3, 4, and 5.
In any set of seven integers, two must have the same remainder when divided by seven according to the pigeon hole principle.
b) Consider set of integers 0, 1 ,2, 3, 4, 5 and 66. All these have different remainders upon division by 8 and hence the answer is no.
The interpretation is yes
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