1. Identify and define the three main measures of variability:
Answers
The three main measures of variability are range, variance, and standard deviation.
What is variability?
Variability refers to the degree of dispersion or spread of a set of data points or observations around a central value, such as the mean or median.
The three main measures of variability are:
1) Range: The range is the simplest measure of variability and is calculated by subtracting the smallest value from the largest value in a data set. The range provides information about the spread of the data from the minimum to the maximum value.
2) Variance: Variance is a measure of the spread of the data around the mean. It is calculated by taking the average of the squared differences of each value from the mean. Variance provides a measure of the extent to which individual values deviate from the mean of the data.
3) Standard deviation: Standard deviation is the square root of the variance and is a commonly used measure of variability. It provides a measure of the spread of the data in terms of the number of standard deviations from the mean. Standard deviation is preferred over variance because it has the same unit of measurement as the data, making it easier to interpret.
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Related Questions
Write the equation of the line (in slope-intercept form) that has an x-intercept at -6 and a y-intercept at 2. Provide a rough sketch of the line indicating the given points. [1 mark]. Exercise 2. For the polynomial f(x) = −3x² + 6x, determine the following: (A) State the degree and leading coefficient and use it to determine the graph's end behavior. [2 marks]. (B) State the zeros. [2 marks]. (C) State the x- and y-intercepts as points [3 marks]. (C) Determine algebraically whether the polynomial is even, odd, or neither.
Answers
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
To write the equation of the line with an x-intercept at -6 and a y-intercept at 2, we can use the slope-intercept form of a line, y = mx + b, where m is the slope and b is the y-intercept.
In this case, the y-intercept is given as 2, so the equation becomes y = mx + 2. To find the slope, we can use the formula (y2 - y1) / (x2 - x1) with the given points (-6, 0) and (0, 2). We find that the slope is 1/3. Thus, the equation of the line is y = (1/3)x + 2.
For the polynomial f(x) = -3x² + 6x, the degree is 2 and the leading coefficient is -3. The end behavior of the graph is determined by the degree and leading coefficient. Since the leading coefficient is negative, the graph will be "downward" or "concave down" as x approaches positive or negative infinity.
To find the zeros, we set the polynomial equal to zero and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two solutions: x = 0 and x = 2.
The x-intercept is the point where the graph intersects the x-axis, and since it occurs when y = 0, we substitute y = 0 into the polynomial and solve for x. -3x² + 6x = 0. Factoring out x, we get x(-3x + 6) = 0. This gives us two x-intercepts: (0, 0) and (2, 0).
To determine if the polynomial is even, odd, or neither, we substitute -x for x in the polynomial and simplify. -3(-x)² + 6(-x) = -3x² - 6x. Since the polynomial is not equal to its negation, it is neither even nor odd.
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I need help with this
Answers
1. Since triangle ABC and DEF are congruent, the value of x is -3
2. length AB = 24
length DE = 24
What are congruent triangles?If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
Since triangle ABC is congruent to triangle DEF , then we can say that line AB is equal to line DE
therefore;
12- 4x = 15-3x
collect like terms
12 -15 = -3x +4x
x = -3
therefore the value of x is -3 and
AB = 12 - 4x
AB = 12 -4( -3)
AB = 12 +12 = 24
DE = 15-3x
= 15-3(-3)
= 15 + 9
= 24
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What is the median of 68, 69, 71, 71, 71, 73, 74, 75, 75, 78
Answers
Answer:
72
Step-by-step explanation:
cross out 4 from left to right, right to left, you get 71 and 73, the mean of those two numbers is 72
A grocery store sells 25 crates of peaches for $125. How much does 1 crate cost?
Answers
Answer: One crate of peaches is $5
Step-by-step explanation:
All you do for this question is divide 125 by 25 gives us 5
Answer:
5
Step-by-step explanation:
Just decide 125 by 25 and get the answer :)
evaluate the triple integral. 16y dv, where e is bounded by the planes x = 0, y = 0, z = 0, and 2x 2y z = 4 e
Answers
The value of the triple integral is -16.
Triple integral is a mathematical concept used in calculus to calculate the volume of three-dimensional objects. It extends the concept of a single integral to functions of three variables and integrates over a region in three-dimensional space.
The triple integral of a function f(x, y, z) over a region E in three-dimensional space is denoted by:
∭E f(x, y, z) dV
We can set up the triple integral as follows:
∫∫∫ 16y dV
Where the limits of integration are:
0 ≤ x ≤ 2
0 ≤ y ≤ (2- \(x^2\)z)/(2y)
0 ≤ z ≤ 2/\(x^{2y\)
Note that the upper bound of integration for y is not a constant, but depends on both x and z.
Integrating with respect to y first, we get:
∫∫∫ 16y dV = ∫0^2 ∫\(0^(2-x^2z)/(2x)\)∫\(0^(2/x^2y) 16y dz dy dx\)
= ∫\(0^2\) ∫\(0^(2-x^2z)/(2x) 32/x dx dz\)
= ∫\(0^2\) [16(\(2-x^2z)/x^2\)] dz
= ∫\(0^2 (32/x^2 - 16z)\) dz
= 32∫\(0^2 x^-2 dx - 16\)∫\(0^2\)z dz
= 16 - 16(2)
= -16
Therefore, the value of the triple integral is -16.
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2) Janelle is making crumb cake. The recipe makes three cakes, but she
only wants one, so she will only use one-third of the ingredients. If the
recipe calls for 1 cups of sugar, how much sugar will Jancolle need to
make one-third of the recipe?
Answers
Answer:
1.5 cups per cup. cups/cake
6 cups/ 4 cakes
= 1.5 cups per cake
Step-by-step explanation:
hope I help I ma a noob so can I have brainliest pls
Answer:
Janelle will need 1/3 cups of sugar to make 1 cake.Step-by-step explanation:
To answer this question, I am going to multiply the total cups of sugar said in recipe by 1/3. This will tell me how much sugar is required for 1/3 of recipe.
=> 1 x 1/3 => 1/3 cups of sugarHence, Janelle will need 1/3 cups of sugar to make 1 cake.
Hoped this helped.
\(BrainiacUser1357\)
if a bag contains 5 blue marbles, 4 red marbles, and 3 green marbles, what is the probability that a marble randomly picked from the bag will be red
Answers
Answer:
4/12
Step-by-step explanation:
What would be the answer?
Answers
Answer:
6
Step-by-step explanation:
To breakeven means that you made exactly as much money as you spent, so if you spent $50 to make lemonade, you would need to make $50 in profits from selling to break even
first subtract the cost of making each horse from the price of selling each horse (you do this to find out how much profits he makes from one horse):
125 - 75 = 50
now divide 300 by 50 to find out how many horses need to be made to break even:
300 ÷ 50 = 6
2,000x + 6,000 = 3,500x - 39,000
Answers
Dr. Brown is conducting a study in which participants have been randomly assigned to either the treatment condition or a comparison treatment condition and they measured the participants' symptoms before treatment, during treatment, and now 3-months post-treatment. Which type of research design did Dr. Brown use
Answers
Dr. Brown used a randomized controlled trial (RCT) research design.
A randomized controlled trial (RCT) is a type of scientific experiment in which two or more groups of patients are subjected to various clinical treatments, interventions, or exposures. In an RCT, subjects are randomly allocated to either a treatment group or a control group, and the treatment group receives the new intervention being tested, while the control group receives the standard intervention or placebo.
Therefore, Dr. Brown used a randomized controlled trial (RCT) research design in which participants were randomly assigned to either the treatment condition or a comparison treatment condition, and their symptoms were measured before treatment, during treatment, and now 3-months post-treatment.
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onsider the data shown below.
25, 110, 74, 68, 94, 85, 115, 70, 105, 46, 37, 93, 40, 62, 38, 95, 47, 48, 27, 82, 25, 110, 68, 94, 37, 105, 38, 40, 27
complete the table given below.
Interval
0-29
30-59
60-89
90-119
Frequency
Answers
To complete the table, we need to count how many numbers fall within each interval.
For the interval 0-29, we have the following numbers: 25, 27, 25, 27. This means we have 4 numbers that fall within this interval.
For the interval 30-59, we have the following numbers: 46, 37, 40, 38, 47, 48. This means we have 6 numbers that fall within this interval.
For the interval 60-89, we have the following numbers: 74, 68, 85, 62, 82, 68. This means we have 6 numbers that fall within this interval.
For the interval 90-119, we have the following numbers: 94, 115, 105, 93, 95, 110, 94, 105, 110. This means we have 9 numbers that fall within this interval.
Therefore, the completed table would be:
Interval | Frequency
-------------------------
0-29 | 4
30-59 | 6
60-89 | 6
90-119 | 9
Hello! I'd be happy to help you complete the frequency table for the given data.
Interval: Frequency:
0-29 5
30-59 8
60-89 6
90-119 10
Your completed frequency table is as follows:
Interval Frequency
0-29 5
30-59 8
60-89 6
90-119 10
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Use the Pythagorean Theorem to find the length of the leg in the triangle below.25Provide your answer below:b=
Answers
Given the picture attached, we can use the Pythagorean Theorem to solve it:
\(a^2+b^2=c^2\)Where a and b are the legs on the right triangle and c hypotenuse.
Hence:
\(\begin{gathered} b^2=c^2-a^2 \\ b=\sqrt{c^2-a^2} \\ b=\sqrt{25^2-7^2} \\ b=24 \end{gathered}\)ANSWER
b = 24
Use the ratio table to solve the percent problem. What percent is 32 out of 80? 4% 32% 40% 80%)
a.(Use the grid to create a model to solve the percent problem. 21 is 70% of what number? Enter your answer in the box.)
b..(Use the grid to create a model to solve the percent problem. What is 30% of 70? 9 12 19 21)
c.(Use the ratio table to solve the percent problem. Part Whole ? 90 20 100 What is 20% of 90? Enter your answer in the box.)
d.(In each box, 40% of the total candies are lemon flavored. In a box of 35 candies, how many are lemon flavored? Enter the missing value in the box to complete the ratio table. Part Whole 35 40 100)
Answers
a. To find what number 21 is 70% of, we can set up the equation: 70% of x = 21. To solve for x, we divide both sides of the equation by 70% (or 0.70):
x = 21 / 0.70
x ≈ 30
Therefore, 21 is 70% of 30.
b. To find 30% of 70, we can set up the equation: 30% of 70 = x. To solve for x, we multiply 30% (or 0.30) by 70:
x = 0.30 * 70
x = 21
Therefore, 30% of 70 is 21.
c. To find 20% of 90, we can set up the equation: 20% of 90 = x. To solve for x, we multiply 20% (or 0.20) by 90:
x = 0.20 * 90
x = 18
Therefore, 20% of 90 is 18.
d. In the ratio table, we are given that 40% of the total candies are lemon flavored. We need to find the number of candies that are lemon flavored in a box of 35 candies.
To find the number of lemon-flavored candies, we multiply 40% (or 0.40) by the total number of candies:
Number of lemon-flavored candies = 0.40 * 35
Number of lemon-flavored candies = 14
Therefore, in a box of 35 candies, 14 are lemon flavored.
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Can someone tell me the answer to this please?????
Answers
Answer:
A
Step-by-step explanation:
The triangle NLM has corresponding angles with triangle LND
The chief of security for the Mall of the Dakotas directed a study of theft. He selected a sample of 200 boxes that had been tampered with and ascertained that for 80 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 45 boxes, employees had stolen the goods, and for the remaining 75 boxes, he blamed poor inventory control. In his report to the mall management, can he say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the 0.10 significance level.
H0: The proportions are as stated. H1: The proportions are not as stated.
1. State the decision rule using 0.10 significance level. (Round your answer to 3 decimal places.)
2. Compute the value of chi-square. (Round your answer to 3 decimal places.)
Answers
The chief of security for the Mall of the Dakotas directed a study of theft. He selected a sample of 200 boxes that had been tampered with and ascertained that for 80 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 45 boxes, employees had stolen the goods, and for the remaining 75 boxes, he blamed poor inventory control.
In his report to the mall management, can he say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the 0.10 significance level. H0: The proportions are as stated. H1: The proportions are not as stated. The decision rule using a 0.10 significance level is: Reject H0 if the computed chi-square value is greater than 4.605. Compute the value of chi-square as follows: Observed Frequencies: Shoplifting: 80 Employee theft: 45 Poor inventory control: 75 Total: 200 Expected Frequencies: Shoplifting: (80+45+75) x (80/200) = 80. Employee theft: (80+45+75) x (45/200) = 36. Poor inventory control: (80+45+75) x (75/200) = 84. Total: 200The formula for chi-square is: χ2=∑((Oi−Ei)2/Ei). Using the observed and expected frequencies from above, we get: χ2 = [(80 - 80)²/80] + [(45 - 36)²/36] + [(75 - 84)²/84] = 2.4. The value of chi-square is 2.4, which is less than 4.605. Therefore, we fail to reject H0. Hence, the chief of security for the Mall of the Dakotas cannot say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely at a 0.10 significance level.
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Which of the following best describes the least squares criterion?
it minimizes the sum of the absolute distances from the line
the best fitting line minimizes the sum of the horizontal distances from the line
none of these
it identifies the best fitting line as the line that minimizes the sum of the squared vertical distances of points from the line
Answers
The best answer that describes the least squares criterion is that it identifies the best fitting line as the line that minimizes the sum of the squared vertical distances of points from the line. Therefore, the correct option is: It identifies the best fitting line as the line that minimizes the sum of the squared vertical distances of points from the line.
What is least squares criterion?The least squares criterion is a statistical approach that aims to find the best-fitting line for a set of data points. It works by minimizing the sum of the squares of the residuals, where a residual is the difference between the observed value and the predicted value of the dependent variable.
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Which of the following graphs shows a line with a negative slope
Answers
Answer: B
Step-by-step explanation: As slope is "rise over run", and only B has a decreasing rise (y-value), it must be the only one with a negative slope.
Please help no matter how much math I do I can’t figure this out
Answers
Answer:
8 student tickets and 2 adult
Step-by-step explanation:
$12 for popcorn
$12 for drink
12+12=24
9x8=72
24+72=96
12x2=24
96+24=120
I gotchu homie
Step-by-step explanation:
4×3 =12 (the drinks)
6+6=12 (popcorn)
even if they purchased 12 student tickets for the cheapest price of 9$ it will be a total of 108...and just with the food and drinks which would add another 24 to it?
how is this possible?
If the drinks and snacks arent added on it would work such as
4 adults ($12 each) = $48
8 student tickets ($9 each) = $72
total price = $120
17% of students in a class have brown hair. If 6 students are chosen at random, what is the probability that exactly 3 have brown hair? (Write your answer as a percentage rounded to the nearest tenth.)
Answers
Answer:
6.8%
Step-by-step explanation:
the question has no information about class size (no. of student in class)
assume no. of student is infinite
P(3brown out of 6) = 6C3 * P(brown)^3 * P(not brown)^3
= 20 * 0.004913 * 0.695789
= 0.06837
A manager at a theater needs to order 267 new seats if the seats are sold only in groups of 10 what is the least number of seats that the manager should order
Answers
The least number of seats the manger could order to 270 seats
How to find the least number of seats the manger could orderThe information that the the seats are sold only in groups of 10 will help to know that the order will be in a multiple of 10.
The manager wants to order 267 seats and this is not a multiple of 10 the nearest multiple of 10 is 270.
This is because, 260 will be short of want the manager want however ordering for 270 will be in excess with three seats.
Hence the manager will order 270 and heave 3 extra seats
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what types of numbers are used for different generations in a pedigree?
Answers
Answer:
Roman numerals
Step-by-step explanation:
In a pedigree, Roman numerals are used to represent different generations, while Arabic numerals are used to represent individuals within each generation. For example, the first generation would be represented by Roman numeral I, the second generation by Roman numeral II, and so on. Within each generation, individuals are numbered sequentially using Arabic numerals, starting with 1 for the first individual in the generation.
A square has a perimeter of 24 inches. What is the area of the Square?
Answers
Answer:
36 inches squared
Step-by-step explanation:
24/4= 6
6*6=36
please hallllllllp!!!!!
Answers
Answer:
A, $20
Step-by-step explanation:
5. A, b, c plsssssss rn
Answers
5a. a° = 128°
5b. b° = 1.3°
5c. c° = 341°
How to determine the unknown sides5a
a° = 128°
This is because parallel angles are equal and angles a° and 128° are parallel to each other
5b
Angles (4b-10)° and (2b - 2)° are equal.
This is because alternate angles are equal and they are alternate to each other
To find b , equate both angles
4b - 10 = 2b - 2
collect like terms
4b + 2b = -2 + 10
6b = 8
Make 'b' subject of formula
b = 8/6
b = 1.3°
5c.
c° is at angle at a point.
19° is alternate to the other part of the point
We have, c° + 19° = 360° (angle at a point)
c° + 19° = 360°
Make 'c' subject of formula
c° = 360° - 19°
c° = 341°
Thus, the unknown angles are given as a = 128°, b = 1.3°, c = 341°
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Multiply and simplify if possible. (2sqrt3x -2)(3sqrt3x +5)
show work
Answers
The expression is simplified to give 2(9x + 2√3x - 5)
How to determine the valueFirst, we need to know that surds are mathematical forms that can no longer be simplified to smaller forms
From the information given, we have that;
(2√3x - 2)(3√3x + 5)
expand the bracket, we get;
6√9x² + 5(2√3x) - 6√3x - 10
Find the square root factor
6(3x) + 10√3x - 6√3x - 10
collect the like terms, we have;
18x + 4√3x - 10
Factorize the expression, we have;
2(9x + 2√3x - 5)
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Find the measure of the missing angle.
45 degree angle
X=-8
Answers
Answer:
47238
Step-by-step explanation:
CAN SOMEONE HELP WITH THESE 2 questions please!! Reposting cause someone said too !!! Will mark u brainlist and give u points!!!
Answers
Answer:
do u need help with the whole page?
Step-by-step explanation:
Helppppppppppppp this is due tonight at 8:00
Answers
Knowing this, you subtract both the 30 and the 24 to get the missing angle.
90 - 30 - 24 = 36 degrees.
The answer is 36 degrees.
katlin bought 14 pencils, it costs her $3.50. how much did each pencil cost?
Answers
Answer: 0.25$ or a quarter
Step-by-step explanation:
Katlin bought 14 pencils, which cost her $3.50. So all you have to do is divide the amount ($) by the number of pencils.
3.50/14 = 0.25$
3.50 divided by 14
Each pencil cost a quarter
A parobola has the equation y=x²+2x-3
What are the coordinates of the turning point of the parabola? what is the equation of the axis of symmetry for this parabola?
Answers
Answer:
(-1,-4) is the vertex
x = -1 is the equation of symmetry;
Step-by-step explanation:
See attached image.
Answer:
(- 1, - 4 ) and x = - 1
Step-by-step explanation:
given a parabola in standard form
y = ax² + bx + c ( ax≠ 0 )
then the x- coordinate of the vertex is
x = - \(\frac{b}{2a}\)
y = x² + 2x - 3 ← is in standard form
with a = 1, b = 2 , then
x = - \(\frac{2}{2}\) = - 1
substitute x = - 1 into the equation for corresponding y- coordinate
y = (- 1)² + 2(- 1) - 3 = 1 - 2 - 3 = - 4
vertex = (- 1, - 4 )
this is an upward opening parabola ( a > 0 )
the axis of symmetry is a vertical line passing through the vertex with equation
x = c ( c is the value of the x- coordinate of the vertex ), then equation is
x = - 1