The total Messages that Tammy, Felipe, and David sent are 30, 50, and 45 messages respectively.
Let's denote the number of text messages sent by Tammy as x, Felipe as y, and David as z. Based on the information given, we have:
y < x and z = 3y.
The total number of messages they sent is x + y + z = x + y + 3y = 4y + x.
Since the total number of messages sent is not specified, we can choose an arbitrary value for the total number of messages. Let's choose 90 messages. Then, we have:
4y + x = 90
x = 90 - 4y.
Substituting z = 3y into x = 90 - 4y, we get:
3y = 90 - 4y
7y = 90
y = 90/7 = 15.
Plugging y = 15 into x = 90 - 4y, we get:
x = 90 - 4 * 15 = 30.
Therefore, Tammy sent 30 messages, Felipe sent 15 messages, and David sent 45 messages.
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An arithmetic sequence has a common difference of 125,000. A geometric
sequence has a common ratio of 4. In both sequences, a(1) = 10. Compare the
sequences. How will a(n) compare for both sequences as n increases without bound?
The nth term in the given AP is given by aₙ = 125000n - 124990 and the nth term in the given GP is given by aₙ = 5×4ⁿ/2
What is arithmetic sequence and geometric sequence?An arithmetic sequence has a constant difference between each consecutive pair of terms. This is similar to the linear functions that have the form y=mx+b. A geometric sequence has a constant ratio between each pair of consecutive terms. This would create the effect of a constant multiplier.
Given that, an arithmetic sequence has a common difference of 125,000. A geometric sequence has a common ratio of 4. In both sequences, a(1) = 10. We asked to compare the sequences,
The formula for AP =
aₙ = a + (n-1)d, d = common difference, a = first term, n = number of terms and aₙ = nth term
The formula for GP =
aₙ = arⁿ⁻¹, r = common ratio, a = first term, n = number of terms and aₙ = nth term
The common difference and first term are, 125000 and 10 respectively,
aₙ = 10 + (n-1)125000
aₙ = 10+1245000n-125000
aₙ = 125000n - 124990
Therefore, nth term in the given AP is given by aₙ = 125000n - 124990
The common ratio and the first term are, 4 and 10 respectively,
aₙ = 10×4ⁿ⁻¹
aₙ = 10×4ⁿ / 4
aₙ = 5×4ⁿ/2
Therefore, nth term in the given GP is given by aₙ = 5×4ⁿ/2
In the AP, nth term will be multiplied to 125000 and the product will be subtracted from 124990, and GP nth term will increase by product of 2.5 and 4ⁿ,
Hence, the nth term in the given AP is given by aₙ = 125000n - 124990 and the nth term in the given GP is given by aₙ = 5×4ⁿ/2
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Describe what moves you could use to create
the transformation of the original image shown
below.
original
Answer:
Reflection , Reflection
Step-by-step explanation:
when the triangle reflects off the x axis and then reflects along the y axis.
A graduated cylinder that is 24 cm tall can hold 1 L of water.What is the radius of the cylinder?What is the height of the 500 ml mark? The 250 ml mark?Recall that 1 liter(L) is equal to 1,000 milililiters (ml) nad that 1 liter (L) is equal to 1,000 cm cubed.
The radius of the cylinder will be equal to 112.8 cm.
What is volume?The capacity of an object is measured by its volume. For instance, a cup's volume is said to be 100 ml if it can hold 100 ml of water in its brim. The amount of space occupied by a three-dimensional object can also be used to define volume.
Given that a graduated cylinder that is 24 cm tall can hold 1 L of water. The radius of the cylinder will be calculated as:-
Volume = 1 L
Volume = 1000000 cm³
πr²l = 1000000 cm³
r² = ( 1000000 / π x 25 )
r² = 12732.4
r = √12732.4
r = 112.8 cm
Therefore, the radius of the cylinder will be 112.8 cm.
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stem-and-leaf displays can be used to multiple select question. observe individual data points. analyze qualitative data. determine central tendency and dispersion. analyze the shape of the data.
A stem-and-leaf display is a statistical tool used for organizing and displaying data.
It is especially useful for analyzing small data sets and can be used for a variety of purposes. With stem-and-leaf displays, individual data points can be easily observed and analyzed, which is particularly useful for answering multiple-choice questions.
Additionally, stem-and-leaf displays can be used to analyze qualitative data by observing patterns and relationships between data points. By determining the central tendency and dispersion of the data, a stem-and-leaf display can help to provide a clearer understanding of the data set as a whole.
Furthermore, the shape of the data can be analyzed through the use of a stem-and-leaf display, which can be helpful in identifying outliers and skewness. In conclusion, stem-and-leaf displays are a useful tool for organizing and analyzing data and can provide valuable insights into data sets.
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1/√4+√5 + 1/√5+√6 + 1/√6+√7 + 1/√7+√8 + 1/√8+√9 =1
Hello,
Answer:
We can start by rationalizing the denominators of each fraction.
For the first fraction, we multiply the numerator and denominator by the conjugate of the denominator, which is √4 - √5:
1/√4+√5 = 1/√4+√5 × (√4 - √5)/(√4 - √5)
= (√4 - √5)/(4 - 5)
= (√4 - √5)/(-1)
For the second fraction, we multiply the numerator and denominator by √5 - √6:
1/√5+√6 = 1/√5+√6 × (√5 - √6)/(√5 - √6)
= (√5 - √6)/(5 - 6)
= (√5 - √6)/(-1)
We can do the same for the remaining fractions:
1/√6+√7 = (√6 - √7)/(-1)
1/√7+√8 = (√7 - √8)/(-1)
1/√8+√9 = (√8 - √9)/(-1)
Now we can simplify the expression:
1/√4+√5 + 1/√5+√6 + 1/√6+√7 + 1/√7+√8 + 1/√8+√9
= (√4 - √5)/(-1) + (√5 - √6)/(-1) + (√6 - √7)/(-1) + (√7 - √8)/(-1) + (√8 - √9)/(-1)
= (√4 - √5 + √5 - √6 + √6 - √7 + √7 - √8 + √8 - √9)/(-1)
= (√4 - √9)/(-1)
= √9 - √4
= 3 - 2
= 1
Therefore, the expression simplifies to 1, which is equal to the right-hand side of the equation.
Good luck
Juan went to the store to buy a plant for his mother, but forgot to ask which kind to get. Out of 30 plants, six of them are a kind that his mother would want. If Juan chooses one randomly, what is the probability that he will choose a kind that his mother would want? You will need to change your probability to a decimal and then to a percent.
The probability that Juan will choose a kind of plant his mother would want is 6/30, which is equal to 0.2 or 20%
To calculate the probability that Juan will choose a kind of plant his mother would want, out of 30 plants, six of them are a kind that his mother would want, first divide the number of plants his mother would want (6) by the total number of plants (30). This will give you a decimal, 0.2. To turn this decimal into a percent, multiply it by 100. This will give you 20%, or a 20% chance of Juan choosing a kind of plant his mother would want. To summarize, therefore, the probability that Juan will choose a kind of plant his mother would want is 0.2 or 20%.
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Clue #8
In a group of middle school students:
.
●
●
.
21 students play tennis
16 students play soccer
19 students play volleyball
3 students play soccer & tennis
5 students play volleyball & tennis
4 students play volleyball & soccer
1 student plays all 3 sports
13 students do not play volleyball, tennis,
or soccer
Based on this information, what values are
missing from the Venn diagram shown?
Soccer
X
3
2
1
Z
Volleyball
Tennis
4
y
W
Step-by-step explanation:
To determine the missing values in the Venn diagram, we can use the information from the problem to set up a system of equations. Let's assign variables to each section of the diagram:
X = number of students who play tennis only
Y = number of students who play soccer only
Z = number of students who play volleyball only
W = number of students who play tennis and soccer only
y = number of students who play tennis and volleyball only
Using the information from the problem, we can set up the following equations:
X + W + 3 = 21 (21 students play tennis)
Y + W + 4 = 16 (16 students play soccer)
Z + y + 5 = 19 (19 students play volleyball)
W + 3 = 3 (3 students play soccer and tennis)
y + 5 = 5 (5 students play volleyball and tennis)
Solving for one variable in terms of the others, we can substitute into the other equations:
X = 21 - W - 3
Y = 16 - W - 4
Z = 19 - y - 5
Substituting into the equation for W, we find:
W + 3 = 3
W = 0
Substituting W = 0 into the equations for X and Y:
X = 21 - 0 - 3 = 18
Y = 16 - 0 - 4 = 12
Finally, we can substitute X, Y, and W into the equation for Z to find:
Z = 19 - y - 5
Z = 19 - 5 - 5 = 9
So the missing values in the Venn diagram are:
Soccer: 12 students
Volleyball: 9 students
Tennis: 18 students
Soccer & Tennis: 0 students
Volleyball & Tennis: 5 students
Volleyball & Soccer: 4 students
Note that the number of students who play none of the three sports is not explicitly stated in the problem, but it can be calculated as:
13 = total number of students - (X + Y + Z + W + y)
13 = total number of students - (18 + 12 + 9 + 0 + 5)
13 = total number of students - 44
So there are 57 total middle school students
Question 6
10 pts
During a football play, Odell Beckham Jr. Runs a straight route 40 yards up the sideline before
turning around and catching a pass thrown by Eli Manning. On the opposing team, a
defender who started 20 yards across the field from Beckham saw the play setup and ran a
slant towards Beckham What was the distance the defender had to run to get to the spot
where Beckham caught the ball?
The distance the defender had to run to get to the spot where Beckham caught the ball is 34.6 yards.
Let's call the distance the defender had to run to get to the spot where Beckham caught the ball "d".
Since the defender was running aslant towards Beckham, we can use the Pythagorean theorem to find the distance he had to run. The theorem states that in a right triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse (the longest side).
If we call the sideline 40 yards, we can set up the equation as follows:
d² + 20² = 40²
Expanding and simplifying:
d² + 400 = 1600
d² = 1600 - 400 = 1200
d = √(1200)
= √(300 * 4)
= √(300) * √(4)
= √(300) * 2
= 10 √(3) * 2
= 20 √3
Rounding to the nearest tenth, we have:
d ≈ 34.6 yards
So, the defender had to run approximately 34.6 yards to get to the spot where Beckham caught the ball.
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PIC BELOW
PLEASE HELP!! ITS JUST FINDING THE AREA!
Answer question one please
Drag the red and blue dots along the x-axis and y-axis to graph
−4+6=24
See the attached image for the plotted graph
What is a Graph?The graph of a function f in mathematics is the collection of ordered pairs where f(x)=y.
These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
4x -4y = 24
x - y= 6
y= x-6
Slope= 1, pass through (6,0), (0, -6)
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Consider the function g(x)=−(x+1)3−2.
Which ordered pair lies on the inverse of the function?
The ordered pair that lies on the inverse of the function is (6, -3)
Which ordered pair lies on the inverse of the function?From the question, we have the following parameters that can be used in our computation:
g(x)=−(x+1)3−2.
Rewrite as
g(x) = −(x + 1)³ − 2
Next, we test the options
Set x = -3
So, we have the following representation
g(-3) = −(-3 + 1)³ − 2
Evaluate the expression
g(-3) = 6
As an ordered pair, we have (6, -3)
So, the ordered pair of the inverse is (6, -3)
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I moves on from last one, pls help: 33 first-year teachers and 42 experienced teachers attended a school staff meeting
meeting. What percentage of the teachers in the meeting were Trst-year teachers?
(0) Write your answer using a percent sign (%).
You have prizes to r
Video
Answer:
44%
Step-by-step explanation:
33 first-year teachers
42 experienced teachers
What % of the teachers in the meeting were Trst-year teachers?
33/(33+42)= 44%
one fruit punch has fruit juice and another is fruit juice. how much of the punch should be mixed with of the punch to create fruit punch that is fruit juice?
The below calculation allows us to determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.
To create a fruit punch that is entirely fruit juice, we must calculate the ratio of fruit juice to total punch. To do this, we will use the following formula:
Fruit Juice Ratio = (Fruit Juice / (Fruit Juice + Punch)) x 100
For example, if we have 10 ounces of fruit juice and 10 ounces of fruit punch, the ratio of fruit juice to total punch is 50%. Therefore, we need to mix 50% fruit juice with 50% punch to create a fruit punch that is entirely fruit juice.
To calculate this for any given amount of fruit juice and punch, we simply plug the numbers into the formula. For instance, if we have 20 ounces of fruit juice and 60 ounces of punch, the ratio of fruit juice to total punch is 25%. Therefore, we need to mix 25% fruit juice with 75% punch to create a fruit punch that is entirely fruit juice.
By using this formula, we can easily determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.
We can use the formula Fruit Juice Ratio = (Fruit Juice / (Fruit Juice + Punch)) x 100 to calculate the ratio of fruit juice to total punch. This allows us to determine the amount of fruit juice and punch needed to create a fruit punch that is entirely fruit juice.
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Express the function graphed on the axes below as a piecewise function.
Answer:
Step-by-step explanation:
[tex]y=\left \{ {({1/2)x+6, x > 4} \atop {6x,} x\geq 1} \right.[/tex]
Help write an expression that represent the voltage
On solving the provided question, we can say that the equation, we have is [tex]t^2 +5t +6.[/tex]
Which equation is this?Two assertions in a mathematical equation are joined by the equal sign (=), which stands for equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The connection between the two sentences on either side of a letter is explained by a mathematical formula. Typically, there is only one variable, which also serves as the symbol. In this case, 2x4=2.
the equation, we have is V = P/I
[tex]V = \frac{t^3 +9t^2 +26t +24}{t + 4}[/tex]
on dividing
the answer will be [tex]x^3+9x^2+26x +24=t^2 + 5t + 6[/tex]
x = -4
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8TH GRADE MATH HELP ASAP
RSTU and VXYZ are quadrilaterals. Given RSTU and VXYZ , describe a sequence of rigid motions followed by a dilation with center (0,0) that maps RSTU to VXYZ
The area is 93.6 and the width is 13 cm what is the height
The width of the rectangle is 7.2 cm because if you divide 93.6 cm by 13 cm you will get 7.2 cm.
Brainliest please that would be nice of you(:
Pls help 20 points hurry plssss I’m begging u
Answer:
Step-by-step explanation:
1. B
2.D
3.2
4.A,C,D
Answer:
1=b
Step-by-step explanation:
go to the comments for other answers
What's the lateral area of the drawing
A. 284m²
B. 232m²
C. 294m²
D. 588m²
294 cm² is the lateral area of the drawing .
Describe Area?
The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies. Area is the amount of surface a two-dimensional shape can cover, measured in square units. The SI unit of area is the square meter (m2), which is a derived unit.
the lateral surface are square of each side .
= 7 cm
lateral area = 6 * (7)² = 294 cm²
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A chemistry class has learned how to read a sensitive high-caliber balance scale (this is not a digital scale). Since most students are very good at reading the scale, the instructor decides it’s time to test their skills. The instructor asks each student to weigh the same 1. 6 ounce bag of Peanut M&Ms, and then records each student’s reading of the balance scale. Which histogram shows the distribution of the students’ balance-scale readings?
a. Histogram I
b. Histogram II
c. Histogram III
d. Histogram IV
The Histogram shows the distribution of the students’ balance-scale readings is Histogram II.
The distribution of numerical data is roughly shown by a histogram. Karl Pearson was the one who initially coined the phrase. The first stage in creating a histogram is to "bin" (or "bucket") the range of values, or split it into a series of intervals, and then count the number of values that fall into each interval.
The bins are often defined as a series of discrete intervals that don't overlap. The bins (intervals) must be close together and frequently, but not always, have the same size.
When the mean and median are equal, a histogram is said to be symmetrical. A symmetric histogram will be split into two equal halves if we draw a line through its centre. The two parts will be exact replicas of one another.
Therefore, The Histogram shows the distribution of the students’ balance-scale readings is Histogram II.
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Please answer the table
Answer:
*diameter=radius ×2
6cm×2=12cm
*diameter=10 ×2=30cm
*radius=diameter÷2
140cm÷2=70cm
*radius
250cm÷2=125cm
*diameter
2.5m×2=5m
*radius
3.6m÷2=1.8m
Help please, i need to turn in today
Answer:
two plus two equals five
Step-by-step explanation:
If a1 = 3 and an = 5an-1 + 1 then find the value of a5.
Consequently, when a1 is provided as 3 and the expression for the following term is a = 5an-1 + 1, the value of a5 is 2031.
what is arithmetic progression ?An algebraic progression is when there is a continual difference between terms that follow each other in an series. For illustration, the decimal number 5, 7, 9, 11, 13, and 15 is an example of an algebraic expression with a tolerance of two. A advance with a set tolerance among any two consecutive numbers is referred to as a "arithmetic progression" (A.P.). Two types of algebraic progression are plausible: series in mathematics with a finite length A finite geometric evolution is a series with just a finite number of terms. The early, late, allowance, and frequency of terms may all be calculated using the terms in the series.
given
a1 = 3
a2 = 5 * 3 + 1 = 16
a3 = 5 * 16 + 1 = 81
a4 = 5* 81 + 1 = 406
a5 = 5* 406 + 1 = 2031
Consequently, when a1 is provided as 3 and the expression for the following term is a = 5an-1 + 1, the value of a5 is 2031.
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Nelly owns farm land that has an area of 4.2 × 102 acres. Each year, the farm produces 6.72 × 104 bushels of corn. What is the average amount of corn produced per acre represented in scientific notation?
A.
2.82 × 107 bushels per acre
B.
1.6 × 102 bushels per acre
C.
1.6 × 103 bushels per acre
D.
2.82 × 106 bushels per acre
E.
1.6 × 101 bushels per acre
The average amount of corn produced per acre represented in scientific notation is, 1.6 × 10² bushels per acre.
What is Scientific notation?Scientific notation is a way of writing a very large or very small numbers. For example; 230,000,000 can be written in scientific notation as 2.3 x 10⁸.
Given that;
Nelly owns farm land that has an area of 4.2 × 10² acres. Each year, the farm produces 6.72 × 10⁴ bushels of corn.
Hence, The average amount of corn produced per acre is,
⇒ 6.72 × 10⁴ ÷ 4.2 × 10²
⇒ 6.72 × 10⁴ / 4.2 × 10²
⇒ 1.6 × 10²
Thus, The average amount of corn produced per acre represented in scientific notation is, 1.6 × 10² bushels per acre.
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[tex](x^(2)-xy)/(9y^(2))/(2x)/(3y)[/tex]
The given expression [tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]is equivalent to (x - y)/18y².
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the expression as -
[tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]
The given expression is -
[tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]
We can solve further as -
{(x² - xy)/9y²} x {3y/2x}
{x(x - y)/9y²} x {3y/2x}
(x - y)/18y²
Therefore, the given expression [tex]$\frac{\frac{(x^{2} -xy)}{9y^{2} } }{\frac{2x}{3y} }[/tex]is equivalent to (x - y)/18y².
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if rooms revenue is $75,884 and the total number of rooms sold is 662, then the average daily rate is: group of answer choices $114.63 $125.00 $118.75 $136.50
The average daily rate is calculated by dividing the total rooms revenue by the total number of rooms sold. In this case, the average daily rate is (option) $114.63.
The average daily rate is a measure of the average amount of money that a hotel is able to generate per room per day. It is calculated by dividing the total rooms revenue by the total number of rooms sold. In this case, the total rooms' revenue was $75,884 and the total number of rooms sold was 662, which gives us an average daily rate of $114.63. This is a useful measure for hotels to gauge the performance of their business and to set pricing accordingly. It also helps hotels identify opportunities for increasing revenue, such as offering discounts or promotions to attract more customers.
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There are 3 right triangles in the drawing below. They are all similar. Chose the correct
similarity statement.
The correct similarity of the triangles are JMK ~ LMK ~ JLM (option D)
What is similarity?Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.
Given that, there are 3 right triangles in the drawing given. They are all similar. we need to identify the correct similarity,
So, from the figure, if we separate each triangle,
We will get,
Triangles JLM, JMK and LMK
If we check,
They are showing true similarity by their figure (refer to diagram attached)
Hence, the correct similarity of the triangles are JMK ~ LMK ~ JLM (correct option is D)
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a tank contains 1000 l of brine with 15 kg of dissolved salt. pure water enters the tank at a rate of 10 lymin. the solution is kept thoroughly mixed and drains from the tank at the same rate. how much salt is in the tank (a) after t minutes and (b) after 20 minutes?
The salt is in the tank (a) after t minutes is 20 minutes and (b) after 20 minutes there are 150 kg of salt.
Salt in Brine Tank CalculationLet's call the amount of salt in the tank after t minutes "S(t)".Since pure water is entering the tank and brine is leaving at the same rate, the volume of the solution in the tank remains constant at 1000 liters.However, the concentration of salt in the solution is changing over time. At any given time, the amount of salt in the tank can be found by multiplying the volume of the solution by its concentration, which we can call "C(t)".So, we have:S(t) = C(t) * 1000
The rate of change of salt in the tank is equal to the rate at which salt is entering the tank (from the dissolved salt in the brine that is leaving the tank) minus the rate at which salt is leaving the tank (from the brine that is leaving).dS(t)/dt = (C(0) - C(t)) * 10
where C(0) is the initial concentration of salt in the
brine (15 kg / 1000 liters = 0.015 kg/liter).
We can solve this differential equation to find the concentration of salt in the tank as a function of time. However, this can be a bit complicated, so let's just consider the answer for the specific times asked:(a) After 20 minutes, we have:C(20) = C(0) - (S(20) / 1000 - S(0)) / 10
= 0.015 - (S(20) / 1000) / 10
And (b) the amount of salt in the tank after 20 minutes is:S(20) = C(20) * 1000
Plugging in the value of C(20) from part (a), we get:S(20) = (0.015 - S(20) / 1000 / 10) * 1000
S(20) = 15 - S(20) / 10
S(20) = 150
So, after 20 minutes, there are 150 kg of salt in the tank.Learn more about Salt in Brine Tank Calculation here:
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is it possible to obtain a negative value of ss (sum of squares), variance, and standard deviation? why?
No, it is not possible to obtain a negative value for the ss, variance, or standard deviation. They represent the amount of spread in data, and the values are always positive or zero.
Sum of squares (SS) measures the deviation of each data point from the mean of the set, squared. The formula for SS is:
SS = Σ (X - μ)^2
Variance is the average of the sum of squares, and it is calculated by dividing the SS by the degrees of freedom (n-1), where n is the number of data points in the set:
Variance = SS / (n - 1)
Standard deviation is the square root of variance and it is a measure of how far each data point is from the mean of the set:
Standard deviation = √Variance
Since both variance and standard deviation are based on the sum of squares, which is always non-negative, variance and standard deviation are also always non-negative.
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Since the equation for both triangles have a2+b2, you can think of two equations for c2 and n2 as in a system of equations. Substitute what a2+b2 equals for the first equation for a2+ b2 give me second equation. After you substitute what equation do you get
The equation by substituting first equation in the second equation:
[tex]n^2 - c^2 =0[/tex]
Triangle:A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
The equation for both triangles have :
[tex]c^2 = a^2 + b^2\\n^2 = a^2 + b^2[/tex]
To write the equation by substituting first equation in the second equation.
Now consider,
[tex]c^2 = a^2 + b^2-------(1)\\n^2 = a^2 + b^2-------(2)[/tex]
Now, Plug the value of equation(2) in (1), we get
[tex]n^2 = c^2[/tex]
[tex]n^2 - c^2 =0[/tex]
Hence, the equation by substituting first equation in the second equation:
[tex]n^2 - c^2 =0[/tex]
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