To put it simply, any outlier with a high or low value has the same impact on the data set. The standard deviation goes down when the outlier is taken out.
What is outlier?Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater).
The standard deviation increases when the outlier's value is higher than the average of the data, compared to when it doesn't exist. When the outlier is eliminated, the mean decreases if the outlier was lower than the majority of the data, and the standard deviation is once more higher than it would be without the outlier. What makes it different is that, as opposed to a fall in the mean, the removal of the outlier would cause an increase.
To put it simply, any outlier with a high or low value has the same impact on the data set. The standard deviation goes down when the outlier is taken out.
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a researcher is interested in the relationship between caffeine consumption and activity level for elementary school children. a sample of 20 children is obtained and each child is interviewed to determine a level of caffeine consumption. the researcher then records the level of activity for each child during a 30-minute session on the playground. is this an experimental or correlational study? explain your answer.
This is an experimental study, as the researcher is manipulating the independent variable (caffeine consumption) to measure the dependent variable (activity level) in a controlled environment.
This is an experimental study, as the researcher is manipulating the independent variable (caffeine consumption) to measure the dependent variable (activity level) in a controlled environment. In an experimental study, the researcher has control over the independent variable and is able to measure the results of the manipulation on the dependent variable. In this study, the researcher is measuring the activity level of the children based on their caffeine consumption, which the researcher can control. The researcher is also measuring the activity level in a controlled environment, the playground, which provides a consistent setting for the experiment. This type of study is designed to test the researcher's hypothesis and determine whether there is a relationship between caffeine consumption and activity level.
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The member of the pedal
pushers bike club have traveled
134.8 miles of a 200 mile trip.
how many more miles do they
have to go?
Let x equal the age, in human years, for a dog that is 2 years old or older. For each of your chosen breeds, write an expression to model its age in dog years. (Hint: Use (x - 2) in each expression.)
These are the dog years:
2yrs: 23 yrs old
3yrs: 27 yrs old
4yrs: 31 yrs old
5yrs: 35 yrs old
75 yrs: ............
find out what's the expression/answer for 75 years.
Therefore , the solution of the given problem of expression comes out to be 15 years: 75 years
what is expression ?In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.
Here,
an expression to represent a dog's age in dog years for a dog that is at least two years old in order to respond to the inquiry above. if x represents human age
then the dog is 2 years older
X = human years
x + 2 = is for the dog age
For 75 years
15 years: 75 years
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7 of 9 The graph shows the speed (m/s) of a car for 40 seconds. By using a single appropriate trapezium, estimate the distance travelled by the car in those 40 seconds. 20 T Speed (m/s) 15 10 LO 5 0 0 5 10 15 20 Time (seconds) 30 35 40 +25
Therefore , the solution of the given problem of speed comes out to be the average distance travelled is 225 meters.
What exactly is speed?We can determine how fast that anything is traveling by looking at it from a distance. The amount of distance an object can go in a given length of time depends on its speed. Velocity is calculated using the formula velocity = distance/time. The three most used units of speed are meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) (mph).
Here,
Given :
Time = 40 seconds.
To find the distance:
We use speed and time formula
=> distance = speed * time
=> distance = 15 * 30
=> distance = 225 meters.
Therefore , the solution of the given problem of speed comes out to be the average distance travelled is 225 meters.
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The Funny Book has its pages numbered the following way:
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5 ... That is, there is one 1, two 2s, three 3s, four 4s, five 5s, and so on.
What is the greatest number of pages that the Funny Book can have if it contains a page that is
numbered “20” but not any that are numbered “21”?
Answer: We can use the formula for the sum of an arithmetic series to find the number of pages in the Funny Book. The formula is:
S = n/2 (2a + (n-1)d)
Where S is the sum of the series, n is the number of terms, a is the first term, and d is the common difference.
In this case, the series is the page numbers, a = 1, d = 1, and we know that there is no page numbered "21" but the page numbered "20" is there.
The number of pages numbered 20 is 20, and the number of pages numbered 19 is 19. So n = 20 + 19 = 39
By substituting the values into the formula
S = 39/2 (2*1 + (39-1)1) = 3920 = 780
The greatest number of pages that the Funny Book can have if it contains a page numbered 20 but not any that are numbered 21 is 780.
Step-by-step explanation:
Determine the savings for each group price. Both the unit price and the group price
are given: 1 bookshelf for $14.95 or 6 for $85.00
By taking a difference, we will see that you can save $4.70 if you buy the pack.
How to find the savings on the group price?To find the savings, we need to take the difference between the cost of the 6 times the cost of 1 bookshelf, and the cost of the 6 bookshelves.
The cost of 1 bookshelf is $14.95, and the cost of 6 together is $85.00, then the savings is given by:
S = 6*$14.95 - $85.00
S = $89.70 - $85.00
S = $4.70
You save $4.70 in total if you buy the pack.
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Write the rule for the linear function. Remember a function rule is written using using f(x). X -10 0 10 y -1 1 3
About 10000 children were asked what their favourite school subject was. The bar chart shows the results for the most popular subjects. % 30 20 10 Art History Maths Subject P.E. a) Which subject was the third most popular? b) About what percentage of the students chose Maths? Submit Answer
a) Maths was the third most popular subject, according to the chart showing the results for the most popular subjects using their percentages.
b) About 10 percent of the students chose Maths.
What is the percentage?The percentage is the ratio of one variable or value compared to another.
Percentages are proportional values. They are obtained as the quotient of one value (the numerator) divided by another value (the denominator) before being multiplied by 100.
Subject Percentage
Art 30%
History 20%
Maths 10%
Thus, based on the percentage of popular subjects, 10% chose Maths as the third most popular subject.
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A room 9m ×7. 5 m i covered with tile. Ize of each tile i 25 cm by 20cm. Find the cot of tile at the rate of ₹45per tile
The price to tile the room is $3,240.
We must figure out how many tiles are required to cover the floor before multiplying that number by the cost per tile to get the cost of tiling the room.
To begin, we must change the room's measurements from meters to centimeters in order to make them consistent with the tile's size. Multiplying 9 by 100 and 7.5 by 100 will yield the results we need: 9m x 100cm/m = 900cm, and 7.5m x 100cm/m = 750cm
Since the room and tile dimensions are now both expressed in centimeters, we can calculate the number of tiles required to cover the space by dividing its size by the tile's area:
25 cm × 20 cm / 36000 cm / 500 cm = (900 cm x 750 cm) / 72
In order to cover the room, 72 tiles are required. We must multiply the quantity of tiles by the price per tile in order to determine the cost:
72 tiles x 45 cents each tile = 3,240
Therefore, the price to tile the room is $3,240.
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WILL GIVE BRAINLY PLS HELP
The value of sin(π/6) is 0.50.
What are trigonometric functions?Trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given the triangle DEF
and ∠E = π/6
converting the radian to the degree,
for conversion put π = 180°
π/6 = 180/6
π/6 = 30°
to find sin(π/6)
sin(π/6) = sin30 = 1/2
sin(π/6) = 0.50
Hence value for the condition is 0.50.
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a square pavement has a side length of 50 m. how many square tiles, each of side length 5 m, are needed to tile the pavement?
The required number of tiles required is 100
as per detail stated above,
the length of the side of the square tile is (s) = 5m
the length of the side of the square pavement (S) is 50m
the area of square tile whose side length is 5 m is
area = side (s) times side (s)
area = 5 x 5
area = 25
now the second area
the area of the square pavement whose side length is 50m is
area = side (s) times side (s)
area = 50 x 50
area = 2500[tex]m^2[/tex]
now to find
the required number of tiles = area of the square pavement by the area of the square tile
therefore
the required number of tiles are =
=> 2500/25
=> 100
therefore the required number of tiles are 100.
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Express sin T as a fraction in simplest terms.
sin T as a fraction in simplest terms is 7/17
How to express sin T as a fraction in simplest terms?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
Sin T = opposite/ hypotenuse
The opposite is where the angle T is facing. That is opposite = 7.
The hypotenuse is where the right angle is facing. That is hypotenuse = 17
Thus, Sin T = 7/17
We cannot further simply sin T.
Therefore, the value of sin T as a fraction in simplest terms is 7/17
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partial quotients, 5,166÷.42?
4,200
5,000
840
420
This is the answer hope you understand it
Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.) Radius r Central Angle θ 16 inches 240°Find the length of the arc on a circle of radius r intercepted by a central angle θ. (Round your answer to two decimal places.)Radius r Central Angle θ
16 inches 240°
The length of the arc intercepted by the central angle of 240 degrees on a circle with a radius of 16 inches would be 67 inches (rounded to two decimal places)
To find the length of an arc on a circle intercepted by a central angle, we can use the formula: arc length = (θ / 360) * (2 * π * r)
where θ is the measure of the central angle in degrees, π is approximately 3.14, and r is the radius of the circle.
In this case, we are given a circle with a radius 16 inches and a central angle of 240 degrees. Plugging these values into the formula, we get:
arc length = (240 / 360) * (2 * 3.14 * 16) = (2/3) * 100.48 = 67 inches
So the length of the arc intercepted by the central angle of 240 degrees on a circle with a radius of 16 inches would be 67 inches (rounded to two decimal places)
Therefore, the length of the arc would be 67 inches.
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Arah mailed her computer to store b for repairs. her bill was: total cost of computer repair = $1,444.50 shipping = 2 percent of total cost if sarah wanted to include a 15 percent gratuity, based on the total cost of the computer repair, excluding shipping, how would you find her new total cost? arah mailed her computer to store b for repairs. her bill was: total cost of computer repair = $1,444.50 shipping = 2 percent of total cost if sarah wanted to include a 15 percent gratuity, based on the total cost of the computer repair, excluding shipping, how would you find her new total cost?
Sarah's new total cost will be $1,685.73 including 15% gratuity.
To find the new total cost, we can first calculate the cost of shipping, which is 2% of the total cost of the computer repair.
Shipping = 2% * 1,444.50 = 28.89
We can then subtract the shipping cost from the original total cost to find the cost of the computer repair, excluding shipping.
Computer repair cost (excluding shipping) = 1,444.50 - 28.89 = 1,415.61
Now we can add the 15% gratuity to the cost of the computer repair, excluding shipping:
Gratuity = 15% * 1,415.61 = 212.34
Finally, we can add the gratuity and shipping cost back to the original cost of the computer repair to find the new total cost:
New total cost = 1,444.50 + 28.89 + 212.34 = $1,685.73
So, Sarah's new total cost will be $1,685.73 including 15% gratuity.
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20 children lineup to ride go carts.The go cart operator collects two dollars from each child in order from the first to the 20th in line. do the ordered pairs (child number, amount paid) represent a function? explain your reasoning.
Yes, the ordered pairs (child number, amount paid) represent a function.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Number of children = 20
Cost per children = $2
Now,
The ordered pairs are:
(1, 2), (2, 4), (3, 6), (4, 8), (5, 10), (6, 12), (7, 14), (8, 16), (9, 18), (10, 20),
(11, 22), (12, 24), (13, 26), (14, 28), (15, 30), (16, 32), (17, 34), (18, 36), (19, 38), (20, 40)
The ordered pairs are a function.
A function can be one-to-one or many-to-one but not one-to-many.
We see that the ordered pairs are one-to-one.
Thus,
The ordered pairs are functions.
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Construct the following quadrilateral
Rhombus BEND
BN = 5.6 cm
DE = 6.5 cm
Answer:
Step-by-step explanation:
To construct this rhombus, we will need a compass and a straightedge.
Step 1: Using the compass, draw two arcs intersecting at point E with the radius of 5.6 cm from B and D respectively.
Step 2: With the same radius, draw two more arcs intersecting at point N from both sides of point E.
Step 3: Draw a straight line from D to E and from E to N.
Step 4: Now draw a line from B to N with the same radius used in Step 2.
The resulting shape is the rhombus BEND with side lengths of 5.6 cm and 6.5 cm.
a person jogs eight complete laps around a quarter-mile track in a total time of 12.5 min. determine the total distance in meter (1 mile
8 laps time 1/4 mile is 2 miles .
Average speed in miles per hour:
2 mi / 12.5 min * 60 min/hour = 9.6 mph
Average velocity is zero, since velocity is directional and the person jogged around a track. [I mention that in case this was set up as a trick question.]
But if we're really looking for average speed in m/s we can easily convert:
A mile is about 1.6 km, so it's about 1600 m.
(2 mi * 1600 m/mi) / (12.5 min * 60 s/min) = 1800 / 750 = 2.4 m/s
The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.
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9.1 Exercises Listing the terms of a sequence In exercises 1-6 write the first five terms answer key
The first five terms of the sequence [tex]a_n = 3n/(n+4)[/tex] are:
3/5, 3/4, 9/7, 3/2, 15/9.
What is a sequence?
A sequence in A.P stands for "Arithmetic Progression" which is a sequence of numbers in which each term is the sum of the previous term and a constant called the common difference.
Now the given expression is
To find the first five terms of the sequence [tex]a_n = 3n/(n+4),[/tex] we need to substitute the values of n from 1 to 5 and solve for [tex]a_n[/tex].
a1 = 3*1/(1+4) = 3/5
a2 = 3*2/(2+4) = 3/4
a3 = 3*3/(3+4) = 9/7
a4 = 3*4/(4+4) = 12/8 = 3/2
a5 = 3*5/(5+4) = 15/9
Hence, the first five terms of the sequence [tex]a_n = 3n/(n+4)[/tex] are:
3/5, 3/4, 9/7, 3/2, 15/9.
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What is the solution of this system in point/coordinate-form? Y=3x-27, x-1/3y=9
Unfortunately not multiple choice.
The solution to the system of equations for this problem is given as follows:
(x, 3x - 27).
How to solve the system of equations?The system of equations for this problem is defined by these two equations presented as follows:
y = 3x - 27.x - y/3 = 9.The first equation can be simplified as follows:
y = 3x - 27 = 3(x - 9).
Hence, substituting y = 3(x - 9) into the second equation, the solution for x can be obtained as follows:
x - 3(x - 9)/3 = 9.
x - x + 9 = 9
0x = 0.
As the system has the format 0x = 0, and considering that the division of 0 by 0 can assume any result different of zero, the system has an infinite number of solutions, in the following format:
(x, 3x - 27).
Meaning that the independent variable x is the free variable and the dependent variable y depends on the value of x.
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This is a parallelogram. y = ___
The value of y in the parallelogram is 120^o.
Properties of a parallelogram.A parallelogram is a plane figure which has opposite sides to be equal. Some of its properties are:
i. Opposite sides are equal in length
ii. It has two diagonals
iii. Sum of adjacent angles is 180^o
The value of y in the diagram can be determined as;
m<ADC + m<DCB = 180^o (sum of adjacent angles is 180^o)
(x + 8) + 3x = 180
4x = 180 - 8
= 172
x = 172/ 4
= 43
x = 43^o
So that;
m<ADC = x + 8
= 43 + 8
= 51^o
Therefore,
m<ADC + m<DAB = 180^o
51^o + (y + 9) = 180^o
y + 60 = 180
y = 180 - 60
= 120
y = 120^o
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What is 30x30 Divided by 0
Answer: Undefined
Step-by-step explanation: any number divided by 0 gives no solution and therefore it is undefined, if u need more explanation then comment
Answer:
Undefined
Step-by-step explanation:
The length of a rectangle is shown below:
On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. Point A is on ordered pair 1, 3, and point B is on ordered pair negative 1, 3. A straight line joins points A and B.
If the area of the rectangle to be drawn is 10 square units, where should points C and D be located if they lie vertically below the line that connects B and A, to make this rectangle? (5 points)
( the image is attach below)
C(−1, 1), D(1, 1)
C(−1, −2), D(1, −2)
C(−1, 5), D(1, 5)
C(−1, −7), D(1, −7)
The coordinates of the points C and D are:
C = (1, -2), D = (-1, -2).
What is cartesian coordinate system?
A Cartesian coordinate system in a plane is a system of coordinates that uniquely identifies each point by a pair of numerical coordinates. These numerical coordinates are the signed distances from two fixed perpendicular oriented lines to the point, measured in the same unit of length.
Given:
The coordinates of A and B are A(1, 3) and b(-1, 3).
We have to find the coordinates of point C and D.
We know that C and D are directly below A and B respectively. So the x-values must coincide.
Then we can say that:
C = (1, y)
D = (-1, y)
Now, remember that for a rectangle of length L and width W the area is:
A = W*L
In this case, the length is AB, then:
L = 1 - (-1) = 2
And the area is 10 square units, so:
10 = W*2
10/2 = W = 5
This means that:
AC = BD = 5
So the difference between the y-component of A and the y-component of C is 5 units
3 - y = 5
3 - 5 = y = -2
Hence, the coordinates of the points C and D are:
C = (1, -2), D = (-1, -2)
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Using a base of 3 and solutions (y values) of 3,9,27,81,243 only, prove: (where log3y)
a. product property for logarithms:
b. quotient property for logarithms:
c. power property for logarithms:
a. To prove the product property for logarithms using a base of 3 and solutions of 3, 9, 27, 81, and 243, we can start with the equation: log3(xy) = log3x + log3y
Let's say we want to find log3(81 * 27)
We know that log3(81) = 4, and log3(27) = 3
So, log3(81 * 27) = log3(81) + log3(27) = 4 + 3 = 7
We can verify this by using the fact that we know the solution of log3(81*27) is 243, and 3^7 = 243.
b. To prove the quotient property for logarithms using a base of 3 and solutions of 3, 9, 27, 81, and 243, we can start with the equation: log3(x/y) = log3x - log3y
Let's say we want to find log3(81 / 27)
We know that log3(81) = 4, and log3(27) = 3
So, log3(81 / 27) = log3(81) - log3(27) = 4 - 3 = 1
We can verify this by using the fact that we know the solution of log3(81/27) is 9, and 3^1 = 9.
c. To prove the power property for logarithms using a base of 3 and solutions of 3, 9, 27, 81, and 243, we can start with the equation: log3(x^n) = n*log3x
Let's say we want to find log3(81^3)
We know that log3(81) = 4
So, log3(81^3) = 3 * log3(81) = 3 * 4 = 12
We can verify this by using the fact that we know the solution of log3(81^3) is 243, and 3^12 = 243.
In all the above examples, we can see that the properties are upheld, and we can use the log3(y) values of 3, 9, 27, 81, and 243 to prove the Product, Quotient and Power property of logarithms with base 3.
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At what point do the curves
r1(t) = t, 3 − t, 48 + t2 and
r2(s) = 8 − s, s − 5, s2
intersect? (x, y, z)=
AND Find their angle of intersection, θ, correct to the nearest degree.
θ =
At point, the parametric curve cross (4, 1, 32).
What are parametric functions?t functions expressed as x = f(y) = y = f(x) = (some function of the variable x) (some function of the variable y).
It is frequently more easier to view functions of two or more variables (although we'll keep it at two here) as parametric functions, particularly in physical science.
The introduction of the idea of time makes parametric functions the most simple to understand.
Imagine tracing a parabola-like function from left to right as time passes.
Then, it is simple to begin considering how the x-coordinate and the y-coordinate change as a function of time: x = f(t), y = g. (t). In this sense, time is actually referred to as the parameter.
We will investigate functions for which a point exists in this section.
Hence, At point, the parametric curves cross (4, 1, 32).
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in a research study to test a new drug on patients with brain cancer, patients were divided into 2 groups randomly. one group received the drug and the other group did not receive the drug. after 6 weeks, the measured results showed reduction in symptoms among the first group who received the drug. is this an example of an observational study or experimental study? if it is an experiment, what is the controlled factor?
This study is an example of an experimental study. The controlled factor is the group of patients.
The collection of data is gathered and chosen from a statistical population with the use of some prescribed techniques in both statistics and quantitative methodology. Data sets may be divided into two categories: sample and population.
All the components of the data set are included in the population, which also contains quantifiable qualities like mean and standard deviation.
A sample is made up of one or more observations that are taken from the population, and a statistic is what makes a sample quantifiable. The act of sampling is the selection of a sample from a population.
Complete question:
In a research study to test a new drug on patients with brain cancer, patients were divided into 2 groups randomly. One group received the drug and the other group did not receive the drug. After 6 weeks, the measured results showed reduction in symptoms among the first group who received the drug. Is this an example of an observational study or experimental study? If it is an experiment, what is the controlled factor?
Select the correct answer below:
The study is an observational study.
The study is an experiment.
The controlled factor is the symptoms of the disease.
The controlled factor is the group of patients.
The controlled factor is the type of drug given to each group.
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Three types of beverage were served at a wedding dinner. 2 persons shared a can of beer. 3 persons shared a jar of fruit punch. 4 persons shared a bottle of wine. 78 cans of beverange were served altogether. How many guests were at the dinner?
Therefore , the solution of fraction problem is number of guests in the dinner were 72.
What is fraction with an example from real life?A fraction is referred to as the portion of a whole in mathematics. For instance, if a pizza is cut into four equal pieces, each one is represented by a quarter. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.
Here,
Given :
Let the number of guests be x,
2 persons shared a can of beer. 3 persons shared a jar of fruit punch. 4 persons shared a bottle of wine ++78
12+8x+6x 24
26x = 1872
x = 72
= 78
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Solomon has some electronics his parents said he could recycle, marcus has permission to recycle some small
household appliances, they looked online and discovered that the local recycling center offers $0.60 per pound
for the appliances and $1.50 per pound for the electronics. but there is a $27 hazardous waste fee that has to
be paid to recycle electronics, no matter how much you recycle.
The pounds that they would have to each recycle so that they earned the same amount of money from the recycle center is 30 pounds.
Equations that depict the revenue from recycling electronics and appliances are:
The following calculation can be used to calculate how much money Solomon can make by recycling appliances:
p = $0.60a
Solomon's potential earnings from recycling electronics are represented by the equation p = $1.50e - $27.
Here,
p = amount earned
a = pounds of appliances recycled
e = number of electronics recycled
The equation that depicts Solomon's earnings when he makes the same amount of money would be the same as the equation that describes his earnings when recycling gadgets.
$1.50e - $27 = $0.60e
To determine the number of pounds:
Combine and add similar terms
$1.50e - 0.60e = $27
$0.90 = $27
Dividing both sides of the equation by 0.9, we get
$27/ 0.9 = 30 pounds
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The complete question is:
"After reading about earning money by recycling, Solomon and Marcus are excited to do some recycling themselves. Solomon has some electronics his parents said he could recycle. Marcus has permission to recycle some small household appliances. They looked online and discovered that the local recycling center offers $0.60 per pound for the appliances and $1.50 per pound for the electronics. But there is a $27 hazardous waste fee that has to be paid to recycle electronics, no matter how much you recycle.
Write one equation that represents how much Solomon would earn by recycling electronics. Write another equation that represents Marcus earns from recycling appliances. How many pounds would they have to each recycle so that they earned the same amount of money from the recycle center?"
An infinite geometric series has first term -3/2 and sums to twice the common ratio. Find the sum of all possible values for the common ratio.
The sum of all possible values for the common ratio is -1/2.
The formula for a convergent infinite geometric series is: Sum = a / (1 - r)
where a = first term and r = common ratio.
Given that,
The first term = -3/2 => a = -3/2
Since it sums to twice the common ratio, Sum = 2r.
Putting these together ---> 2r = (-3/2) / (1 - r)
multiplying both sides by 1 - r:
2r(1 - r) = -3/2
multiplying both sides by 2:
4r(1 - r) = -3
multiplying out the left-hand side:
4r - 4r2 = -3
rearranging the terms:
0 = 4r2 - 4r - 3
factor:
0 = (2r - 3)(2r + 1)
Either r = 3/2 or r = -1/2
Since an infinite geometric series converges only when -1 < r < r, the possible answer 3/2 must be rejected.
Thus, r = -1/2
Therefore, the sum of all possible values for the common ratio is -1/2.
To know more about ratio visit: brainly.com/question/13419413
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the figure above shows the inside dimensions, in feet, of a certain room. an architect made a scale model of the room that had a floor and four walls, but not a ceiling. what was the scale of the model, in inches per foot, if the inside of the model had a total surface area of 2,304 square inches?
The scale of the model is 0.00017 ft/in, or in inches per foot.
To determine the scale of the model, we need to find the ratio of the size of the model to the size of the real room. We can use the information provided about the total surface area of the model to find this ratio.
The total surface area of the model is given as 2,304 square inches. We can find the total surface area of the real room by multiplying the lengths of the four walls and the floor.
The inside dimensions of the room are given as 8 ft x 12 ft x 8 ft x 12 ft x 8 ft = 8 x 12 x 8 x 12 x 8 = 92,160 sq ft
Now we can find the ratio of the size of the model to the size of the real room by dividing the surface area of the model by the surface area of the real room and converting it to inches per foot.
2,304 sq in / 92,160 sq ft = 0.025 sq in/ sq ft
To convert square inches to square feet we divide by 144, so 0.025 sq in/ sq ft = 0.025/144 = 0.00017 ft/in
So, the scale of the model is 0.00017 ft/in, or in inches per foot.
To learn more about the surface area, refer to the link:brainly.com/question/29011883
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