The notations correctly describe the end behavior of the polynomial graphed is,
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
What is end behavior of polynomial?
The polynomial function's leading term can be used to determine the end behavior. The behavior of the leading term will dominate the graph because it has the highest power, which means it will grow significantly faster than the other terms as x gets very large or very small.
From the graph we know that the vertex of this parabola is V(0, 8).
This is a maximum y-value. We also know that the parabola opens downward, so the leading coefficient is negative.
Given that the function is even and the leading coefficient is negative, it follows that the graph falls to the left and right.
In a mathematical language this is:
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
Hence, the notations correctly describe the end behavior of the polynomial graphed is,
x → -∞ ⇒ f(x) → -∞
x → ∞ ⇒ f(x) → -∞
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(a). Mr. and Mrs. Jones have a large family. They want to take all their children on a vacation. When they discussed where to go on their vacation, they discovered that of all their children; (1). 8 refused to go to the family cottage. (ii). 7 refused a resort spot on the ocean. (iii). 9 refused a camping trip. (iv). 3 will go neither to the family cottage nor the resort. (v). 4 will go neither to the resort nor on a camping trip. (vi). 6 will go neither to the family cottage nor on a camping trip. (vii). 2 will not go to the family cottage, the resort spot on the ocean or the camping trip. (viii). No child will agree to go to all the 3 places. How many children do the Jones have?
The total number of children Mr. and Mrs. Jones are having is 13 children.
What is a set ?A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.
In set theory, the set containing every element in a collection is the union of all its sets. It is one of the fundamental operations that allows sets to be joined together and connected to one another. A union of zero sets is referred to as a nullary union, because it is by definition equivalent to the empty set.
The symbol "∩" can be used to represent the intersection of sets. According to the definition given above, the intersection of two sets A and B is the collection of all the items that are shared by both sets.
8 refused to go to the family cottage = set A
7 refused a resort spot on the ocean. = Set B
9 refused a camping trip. = Set C
3 will go neither to the family cottage nor the resort = A∩B
4 will go neither to the resort nor on a camping trip = B∩C
6 will go neither to the family cottage nor on a camping trip = A∩C
2 will not go to the family cottage, the resort spot on the ocean or the camping trip = A∩B∩C
The total number of children = A + C - (A∩B + B∩C + A∩C) + A∩B∩C
= 8+7+9 -(3+4+6) + 2 = 13
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0.333, 0.323, 0.3 least to greatest
Answer:
0.3, 0.323, 0.333
Step-by-step explanation:
Answer:
0.3,0.323,0.333
Hope it helps!
given two points, (3,2) and (7,18), determine both the linear and quadratic equations crossing both points. let f(x) and f(k) be the linear and quadratic equation respectively. write both in standard form. write the function in terms of function notation.
The linear equation passing through both points is:
f(x) = 8x - 14 ,the quadratic equation passing through both points is:
[tex]f(k) = -1/28k^2 + 17/14k - 36/7[/tex]
Linear Equation:
f(x) = mx + b
Where, m is the slope and b is the y-intercept.
Calculation:
By substituting the two points (3,2) and (7,18) in the equation, we get:
2 = 3m + b
18 = 7m + b
Solving the equation we get:
m = 8
b = -14
Therefore, the linear equation passing through both points is:
f(x) = 8x - 14
Quadratic Equation:
f(k) = ax^2 + bx + c
Where, a, b and c are constants.
Calculation:
Substituting the two points (3,2) and (7,18) in the equation, we get:
2 = a(3)^2 + b(3) + c
18 = a(7)^2 + b(7) + c
Solving the equation we get:
a = -1/28
b = 17/14
c = -36/7
Therefore, the quadratic equation passing through both points is:
f(k) = -1/28k^2 + 17/14k - 36/7
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please help with 4, 5 and 6 pleasee someone
The respective answers are 1/3π r² h, πr²h, (4 ⁄ 3) π r³
What is the area and volume of a right circular cone?For a right circular cone of radius 'r', height 'h', and slant height 'l', we have; Curved surface area of the right circular cone = π r l. The total surface area of a right circular cone = π(r + l) r. The volume of a right circular cone = 1/3π r² h.
Given:
Volume of cone =1/3π r² h.
Volume of a cylinder= πr²h.
Volume of a sphere=(4 ⁄ 3) π r³
Volume of the ice cream cone≈100.53
Volume of the basket ball≈268.08
Volume of the cylindrical can=42.41
Hence, The respective answers are 1/3π r² h, πr²h, (4 ⁄ 3) π r³
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the eifell tower 324 m tall. the height was halved repeatedly to make a model around 30 cm. what power of 2 was the height divided by?
Answer:
n=3
Step-by-step explanation:
324/2^ n. = 30
324/30 = 2^n
Log 324/30 = Log 2^n = n x Log2
n = Log 324/30 ÷ Log 2
n = 3.43...
as n musg be an integer, thus
take n=3. or 4 will makd the midel height cliase to 30m
A machine wheel spins at a rate of 500 revolutions per minute. if the wheel had a diameter of 80 centimeters, what is the angular speed of the wheel, in radians per second? round your answer to the nearest hundredth. ______ rad/sec
The angular speed of the wheel, in radians per second is equal to 52.37 rad/sec.
What is an angular speed?In Mathematics, an angular speed can be defined as the rate of change of angular displacement of a physical object with respect to time. This ultimately implies that, angular speed is a measure of how fast and quickly a physical object revolves or rotates relative to another point or how its angular position changes with respect to time.
Mathematically, the angular speed of a physical object can be calculated by using this formula:
ω = 2πF or ω = Δθ/Δt
Where:
ω represents the angular speed.F is the frequency.π is equal to 3.142Δt is the change in time.Substituting the given parameters into the angular speed formula, we have;
Angular speed of the wheel, ω = 2 × 3.142 × 500
Angular speed of the wheel, ω = 3142 rad/min
In rad/sec, we would divide by 60;
Angular speed of the wheel, ω = 3142/60
Angular speed of the wheel, ω = 52.37 rad/sec.
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There are 32 Year 12 pupils in a music club, out of a total of 85 pupils.
Write this proportion as a percentage.
Give your answer correct to 1 decimal place when appropriate.
Answer:To write a proportion as a percentage, you first convert it to a decimal and then multiply it by 100.
The proportion of Year 12 pupils in the music club is 32/85.
To convert to a decimal, divide 32 by 85:
32/85 = 0.376
To convert this decimal to a percentage, multiply by 100:
0.376 * 100 = 37.6
So, the proportion of Year 12 pupils in the music club as a percentage is 37.6%.
To convert a proportion to a percentage, you can multiply it by 100.
The proportion of Year 12 pupils in the music club can be represented as 32/85.
Multiplying by 100, we get:
(32/85) * 100 = 37.65
So, 37.65% of the pupils in the school are Year 12 pupils in the music club.
Rounded to 1 decimal place, the answer is 37.7%.
average rate of change of polynomials f(x)=x^2+10 Over which interval does f have a positive average rate of change?
answers are
[−3,1]
[−1,2]
[−4,−1]
[−3,3]
Answer:
Step-by-step explanation:
The answer is [−3,3]. The average rate of change of f(x)=x^2+10 over an interval [a,b] is given by (f(b)-f(a))/(b-a). Since f(x)=x^2+10 is a polynomial of degree two, it is always increasing, and so its average rate of change is always positive. Thus, the average rate of change of f(x) over any interval [a,b] where a<b is positive, so the answer is [−3,3].
what conclusion is appropriate if a chi-square test produces a chi-square statistic near zero?
a. the researcher made a mistake because chi-square can never be close to zero
b. there is a large discrepancy between the sample data and the null hypothesis
c. all of the expected frequencies must also be close to zero
d. there is a good fit between the sample data and the null hypothesis
On solving the provided question, we can say that when the test statistic is chi-squared distributed under the null hypothesis, a statistical hypothesis test known as a chi-squared test
What is null hypothesis?A null hypothesis is a kind of statistical hypothesis that asserts that a specific set of observations has no statistical significance. Using sample data, hypotheses are tested to determine their viability. Sometimes known as "zero" and symbolized by H0. Researchers start off with the presumption that there is a link between the variables. In contrast, the null hypothesis claims that there is no such association. Although the null hypothesis may not appear noteworthy, it is a crucial component of research.
When the test statistic is chi-squared distributed under the null hypothesis, a statistical hypothesis test known as a chi-squared test—more specifically, Pearson's chi-squared test and its variations—is valid to execute.
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Connie keeps her sports card collection in a 54-page book. each page has 9 slots for cards.
football cards take up the first 18 pages of the book. use the drop-down menus to describe
how many slots in the book may be filled with baseball cards.
click the arrows to choose an answer from each menu.
the inequality choose...
can be used to represent the number of slots in the book that
may be filled with baseball cards....plss help i will give brainly:((((
A line would be drawn on the graph for x 324 and tinted also on left side of the line until x = 0.
What does inequality mean to you?Social justice theories are based on the concept of unequal, namely the notion that individuals are not similar, particularly in terms of position, rights, and showed that the type. It is susceptible to misinterpretation in public conversation, nevertheless, as it typically has distinct meanings to different people. However, some characteristics apply to everyone.
54 total pages
Football card pages = 18
Pages remaining = 54 - 18 Equals 36
As a result, the remaining 36 pages may each hold 9 cards.
Therefore, the remaining spaces are 36 * 9 = 324.
Inequality: 324 spots available
A line would be drawn on the graph for x 324 and tinted also on left side of the line until x = 0.
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Daryl spent half of his weekly allowance on clothes, To earn more money his parents let him clean the oven for $10. What is his weekly allowance if he ended with $25?
Daryl's weekly allowance, given the amount he ended with and the amount spent on clothes, is $ 30
How to find the weekly allowance ?To find the weekly allowance, first find the amount that Daryl had after he had spend half his allowance on clothes. This amount can be found by the formula:
= Amount Daryl ended with - Amount gotten from cleaning oven
= 25 - 10
= $ 15
The amount of $ 15 is the amount out of Daryl's weekly allowance that he had after he had spent on clothes. The $15 is therefore half of the weekly allowance which means that the weekly allowance is:
= 15 x 2
= $ 30
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Bonjour, qui pourrait me donner la réponse de cette exercice s’il vous plaît c’est pour mon DM de maths.
Merci d’avance pour la personne qui me donnera la réponse.
Answer:
Bonjour, qui pourrait me donner la réponse de cette exercice s’il vous plaît c’est pour mon DM de maths.
Step-by-step explanation:
=========================================================
Explanation:
Break the 3D figure into two pieces:
A cylinder on top.A cone on the bottom.The relevant formulas we need are:
V = pi*r^2*h = volume of a cylinderV = (1/3)*pi*r^2*h = volume of a conewhere r and h are the radius and height respectively.
The cylinder has radius r = 5 and height h = 17.8
V = pi*r^2*h
V = pi*5^2*17.8
V = 445pi
The cone has the same radius, but the height is h = 24-17.8 = 6.2
V = (1/3)*pi*r^2*h
V = (1/3)*pi*5^2*6.2
V = (155/3)pi
The total volume is then,
445pi+(155/3)pi
(1335/3)pi + (155/3)pi
(1335/3 + 155/3)pi
(1490/3)pi
That's the exact volume of this pencil-shaped figure. This exact volume is in terms of pi.
----------
Now to compute the approximate volume.
If you were to use pi = 3.14, then the approximate volume is
(1490/3)pi = (1490/3)*3.14 = 1559.5333 cubic cm
Here's what my calculator shows when computing the expression.
(1490/3)pi = 1560.32435128293
The calculator has a stored version of pi with more digits for better accuracy.
Both of those results round to 1560 cubic cm when rounding to the nearest cubic centimeter.
Find the volume of this shape
Answer:
Step-by-step explanation:
The volume on the shape on top is 10x3x8=240
The volume of the shape is 3x5x6=90
The bottom shape is 8x5x2=80
the total volume is 240+90+80=410
What are the 3 steps for solving an absolute value equation?
There are three main steps for solving an absolute value equation isolate the absolute value expression, split the equation into two cases and solve the case.
Isolate the absolute value expression: Start by isolating the absolute value expression on one side of the equation. This can be done by adding or subtracting a constant from both sides of the equation, or by dividing or multiplying both sides of the equation by a constant.
Split the equation into two cases: Once the absolute value expression is isolated, you need to split the equation into two cases: one for when the absolute value is equal to the positive value of the expression inside it, and one for when it is equal to the negative value.
Solve each case: For each case, you will have an equation. Solve it like any other equation and find the solutions.
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Is absolute value always positive on a graph?
On a graph, the absolute value of a number is always non-negative.
The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.
This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.
It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.
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The function has one local minimum and one local maximum. Use a graph of the function to estimate these local extrema. Round to the nearest whole number.
There are two types of relative extremas for a function, described as follows:
Local minimum: function changes from decreasing to increasing.Local maximum: functions changes from increasing to decreasing.On the graph, these relative extremas of a function are the turning points of the function.
The function for this problem is defined as follows:
f(x) = 2x³ - 39x² + 180x + 4.
For the function defined in this problem, the graph is given by the image presented at the end of the answer, with the points representing the relative extremas marked.
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Need some help here asap
Answer:
The y-intercept is 450, and it represents how much money he has in his account when he starts out with 0 essays proofread
Step-by-step explanation:
Looking at the standard slope-intercept equation, we see:
y = mx + b
Where b is the y-intercept. In our equation, our b is replaced by 450:
y = 15x + 450
So, the y-intercept is 450, and it represents how much money he has in his account when he starts out with 0 essays proofread.
Hope this helped!
the length of the shadow of a bulding.is 15m. the distance from the top of the building to the tip of the shadow is 25m find the height of the building if nessesart round your answer to the nearest tenth
So on solving the provided question we can say that in the equation 15x - y = 25; x = 24/15
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here,
15x - y = 25
so from provided data we have y = 1
15x - 1 = 25
15x = 24
x = 24/15
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8. There are 4 red balls, 5 blue balls and 3 green balls in a bag
A ball is to be taken at random and not replaced.
A second ball is then to be taken at random.
a) Complete the tree diagram below;
b) Use the tree diagram to calculate the probability that both balls taken will be
(iii)Calculate the probability that exactly one of the balls taken will be red
So on solving the provided question we cans say that probability that we got red balls is - P(R) = 1/3
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
given,
red balls = 4
blue balls = 5
green balls = 3
Probability that we got red balls is -
P(R) = 4/12 = 1/3
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Ians car can go 296 miles on 8 gallons of gas. During a drive last weekend, ians used 7 gallons of gas. How far did he drive?
Answer:
259 miles
Step-by-step explanation:
To find this, we need to multiply his 8 gallons by [tex]\frac{7}{8}[/tex] since he only uses 7 gallons of gas. In turn, we also need to multiply 296 by [tex]\frac{7}{8}[/tex]. We get:
[tex]296 * \frac{7}{8} = 37 * 7 = 259[/tex]
So, Ian drove 259 miles last weekend.
Hope this helped!
Two buildings on level ground are 120 m and
85 m tall respectively. given that the angle of
elevation of the top of the taller building from
the top of the shorter building is 33.99, find the
distance between the two buildings.
Therefore , the solution of the given problem of trigonometry comes out to be 52.1 m separates the two buildings.
What does trigonometry mean exactly?When it comes to trigonometry, the relationship between squares spline and The field is believed to have originated in the late 1700s, more likely beginning with in third century BC, through the fusion of astronomical and mathematical sciences. Numerous geometric equations or their possible uses in calculations are covered by precise mathematical techniques. The subject of trigonometric are the six basic trigonometric operations.
Here,
=> tan 33.9° = adjacent / opposite
=>Tan 33.9 = 35 / adj
=>0.6719=35/adj
=>adj=35/0.6719
=> adj=52.1 m
Consequently, 52.1 m separates the two buildings.
Therefore , the solution of the given problem of trigonometry comes out to be 52.1 m separates the two buildings.
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a combination of three or more tones is called a(n) group of answer choices interval. scale. chord. octave.
A chord is a combination of three or more tones (notes) played together.
To determine the notes in a chord, we need to calculate the intervals between the notes. An interval is the distance between two notes. Intervals are measured in half steps (or semitones). A half step corresponds to the interval between two adjacent keys of a piano.
In a major chord, the formula for determining the intervals is 1-3-5. This means the root note (1st note) is a major third (4 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.
For example, if the root note is C, the 3rd note is E and the 5th note is G. The intervals in this chord are C to E (4 half steps) and C to G (7 half steps). Therefore, the chord is a C major chord.
In a minor chord, the formula for determining the intervals is 1-b3-5. This means the root note is a minor third (3 half steps) away from the 3rd note and a perfect fifth (7 half steps) away from the 5th note.
For example, if the root note is F, the 3rd note is Ab and the 5th note is C. The intervals in this chord are F to Ab (3 half steps) and F to C (7 half steps). Therefore, the chord is a F minor chord.
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17. If theta is an angle in standard position and its terminal
side passes through the point (-9,4), find the exact value of
cot(theta) in simplest radical form.
Therefore , the solution of the given problem of trigonometry comes out to be cot(θ) = 9/5.
What does trigonometry actually mean?The link between the squares spline and trigonometric The field is thought to have been created with in late 1700s, however it probably got its start in the third century BC through the union of the astronomical & mathematical sciences. Precise mathematical approaches can be used to solve a wide variety of geometric equations or to calculate things that they might be used in. The six fundamental trigonometric operations are what trigonometry is all about.
Here,
Given : tan(θ) = y/x
Given that the termination side in this instance traverses (-9, -5), the tangent is as follows:
tan(θ) = -5/-9 = 5/9
The cotangent is hence the tangent's inverse:
=> cot(θ) = 1/tan(θ) = 9/5.
Therefore , the solution of the given problem of trigonometry comes out to be cot(θ) = 9/5.
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In the diagram alongside, circles O and M intersect at S. RST is a straight line segment such that RST | OM. If OM- 7 cm. determine the length of RT.
Answer:
Step-by-step explanation:
Since the line segment RST is perpendicular to OM, the length of RT can be determined by using the Pythagorean Theorem.
Let RT = x
We know that:
OS = OM - OS = 7 cm
Using the Pythagorean Theorem, we can solve for x:
x^2 = OS^2 + RT^2
x^2 = (7 cm)^2 + x^2
2x^2 = 49 cm^2
x^2 = 24.5 cm^2
x = √24.5 cm = 4.94 cm
Therefore, the length of RT = 4.94 cm
What is the formula to get height of triangle?
Step-by-step explanation:
that depends on the type of triangle and what other pieces of information you have about the triangle.
I think you might aim for the geometric mean theorem.
it is the relation between the height on the hypotenuse in a right triangle and the two line segments (p, q) it creates on the hypotenuse (= p + q).
height = sqrt(p×q)
how will the solution of the system y > 2x and y < 2x change if the inequality sign on both inequalities is reversed to y < 2x and y > 2x ?
The solution will remain the system since the same two inequalities still make up the system.
question initially, 40 bacteria are placed in a petri dish. it is observed that the bacteria triple in population every 11 hours. how can this information be interpreted? select true or false for each statement.
The information can be interpreted as,
y = 40 x [tex]3^{x/11}[/tex].
Where y is the number of bacteria and x is the number of hours.
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,
Number of bacteria initially = 40
The number of bacteria triples every 11 hours.
Now,
The number of bacteria after x hours.
= 40 x [tex]3^{x/11}[/tex]
Where x is the number of hours.
Thus,
The expression for the number of bacteria in x hours is 40 x [tex]3^{x/11}[/tex].
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Find the simple interest paid for 10 years on a 17,000 loan at 7%
The simple interest on 17,000 loan for 10 years will be 11,900
Solution:
As we know, simple interest is the interest amount for a particular principal amount of money at some rate of interest.
Here given ,
Principle (P) = 17,000
Rate of interest (R) = 7%
Time (T)= 10 years
Simple Interest = (RxRxT)/100
Therefore,
S.I. = ( 17,000 x 7 x 10 ) / 100
= 11,900
Hence,
The simple interest at the end of 10 years will be 11,900
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Point Q'(3,2) (3,2) is the image of Q (6,4) under a translation.
The translation applied to the point Q is:
T(-3, -2)
(decreases by 3 the x-value and decreases by 2 the y-value)
Which translation is applied to point Q?A general translation T(a, b) (that can be applied to a point (x, y)) is defined as:
T(a, b)[ (x, y)] = (x + a, y + b)
So, in this case we know that we apply a translation T(a, b) to our point Q (6, 4), and the image that we get is Q' (3, 2)
So we can write the equation:
T(a, b)[ (6, 4)] = (6 + a, 4 + b) = (3, 2)
Now we can solve that to get the values of a and b.
6 + a = 3
a = 3 - 6 = -3
And:
4 + b = 2
b = 2 - 4 = -2
Then the translation in this case is:
T(-3, -2)
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The average of the first 3 weights was 20 pounds. the average of the next twelve was 25 pounds. what was the overall average of the weights
Answer: The overall average of the weights is 24 pounds.
Step-by-step explanation:
To find the overall average of the weights, we need to calculate the weighted mean. A weighted mean is a type of average that takes into account the number of items or observations in each group.
In this case, we know that the average of the first 3 weights is 20 pounds and the average of the next 12 weights is 25 pounds.
To find the overall average, we will use the following formula:
( (number of items in first group * average of first group) + (number of items in second group * average of second group) ) / (number of items in first group + number of items in second group)
The formula can be applied as:
( (3 * 20) + (12 * 25) ) / (3 + 12) = (60 + 300) / 15 = 360 / 15 = 24
- C
