The length of each side of a metal cube increases at the rate of 0.025cms' when heated. Find the rate of increase in cm²s¯¹ of the total surface area of the cube, when the length of each side is 6cm.
Plssss I really need this submission due tomorrow by 6 am
Answers
Answer:
3.06 cm^2/sec
Step-by-step explanation:
Since the shape is a cube, all sides have equal lengths, 6 cm The rate of increase of 0.025cm/s [Note: I assume the unit should be cm/s, not cms'].
See the attached spreadsheet calculation. Starting at time = 0 sec, the initial area is 36 cm^2. Each second adds 0.025 cm to each side length,.
We can express this change in length as an equation:
Initial Length (6cm) + (x seconds)*(0.025 cm/s)
So for 10 second, l = 6 cm + 0.25cm or 6.25cm
--
The area is also changing with time. At 0 seconds, the area is (6cm)^2 or 36 cm^2. At 10 seconds, the area is (6.25cm)*(6.25cm) or 39.06 cm^2.
The area increased from 36 cm^2 to 39.06 cm^2 in 10 seconds. That is a change rate of ((39.06 - 36 cm^2)/(10 sec):
((39.06 - 36 cm^2)/(10 sec)
((3.06 cm^2)/(10 sec)
3.06 cm^2/sec
Related Questions
why does tangent function have asymptotes when sine and cosine fjnction have none ?
Answers
The tangent function has asymptotes because it is defined as the ratio of the sine and cosine
Why does tangent function have asymptotes?The tangent function has asymptotes because it is defined as the ratio of the sine and cosine functions:
tan(x) = sin(x) / cos(x)
When the cosine function approaches zero, the denominator of the tangent function becomes very small, and the tangent function grows to infinity or negative infinity. Therefore, the tangent function has vertical asymptotes where the cosine function is equal to zero.
In contrast, the sine and cosine functions do not have vertical asymptotes because they are periodic functions that oscillate between -1 and 1. They do have horizontal asymptotes at positive and negative infinity, but these are not vertical asymptotes.
Note that the tangent function is not defined at the points where the cosine function is equal to zero because the division by zero is undefined. This also contributes to the existence of the vertical asymptotes in the tangent function.
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PLEASE HELP ME OUT GUYS
Answers
Answer:
Given as steps.
Step-by-step explanation:
Step 2: Opposite angles of a parallelogram are Equal
Step 4 ( After " Definition of a parallelogram"): Given
Step 5: ASA congruency Property / Therom
Step 6: CPCTC
P.S: It is ASA congruency Therom as both angles are adjacent to the side they are trying to prove.
Hope It Helps!
If the sum of the 2nd and 7th term of an arithmetic progression is 25 and the fifth term is 15 find the common difference
Answers
Answer: Let's call the first term of the arithmetic progression "a" and the common difference "d". Then we can use the following formulas to find the second, fifth, and seventh terms:
- The second term is a + d.
- The fifth term is a + 4d.
- The seventh term is a + 6d.
We are given that the sum of the second and seventh terms is 25:
(a + d) + (a + 6d) = 25
Simplifying this equation, we get:
2a + 7d = 25 ...(1)
We are also given that the fifth term is 15:
a + 4d = 15 ...(2)
Now we can solve for the common difference "d" by using equations (1) and (2) to form a system of two equations in two variables. One way to do this is to solve equation (2) for "a" in terms of "d", and then substitute that expression for "a" into equation (1):
a = 15 - 4d ...(3)
Substituting equation (3) into equation (1), we get:
2(15 - 4d) + 7d = 25
Simplifying this equation, we get:
30 - 8d + 7d = 25
Solving for "d", we get:
d = -5
Therefore, the common difference is -5.
Step-by-step explanation:
can someone pls help me
Answers
Answer:b
Step-by-step explanation:
Since you flip the numerator and denominator to get 8 power 10 over 8 power 4 which then you subtract the powers since you have same base so:10-4=6
8^6
in a given class room the number of girls is greater than the number of boy. If of the number of girls to the number of boys is 7 ratio 5,then find the number of boys with the solution
Answers
Answer:
So the number of girls is 7 times the number of boys. If we want a specific number, we would need to know the total number of students in the class.
Step-by-step explanation:
Let's use algebra to solve the problem:
Let's say the number of boys in the classroom is "b", and the number of girls is "g".
From the problem statement, we know that:
g > b (the number of girls is greater than the number of boys)
g/b = 7/5 (the ratio of girls to boys is 7:5)
We can use the second equation to write g in terms of b:
g/b = 7/5
g = (7/5) * b
Now we can substitute this expression for g into the first equation:
g > b
(7/5) * b > b
Simplifying this inequality:
7b/5 > b
7b > 5b
2b > 0
b > 0
So we know that b is positive.
To find the exact value of b, we can use the fact that the ratio of g to b is 7:5:
g/b = 7/5
(7/5) * b/b = 7/5
7b/5b = 7/5
7/5 = 7/5
This equation is true for any value of b (as long as b is positive), so we don't actually get a unique solution for b. However, we can still make a statement about the relationship between b and g:
g/b = 7/5
g = (7/5) * b
g = (7/5) * 5x
g = 7x
So the number of girls is 7 times the number of boys. If we want a specific number, we would need to know the total number of students in the class.
Answer:
B = (5/7)G where B and G are the numbers of Boys and Girls,
Step-by-step explanation:
The ration of girls to boys is 7/5. If we let G and B represent the numbers of Girls and Boys, we can write:
G/B = 7/5
The problem dioes not tell us the number of either boys or girls, so we cannot calculate the number of boys, as the question seems to ask. If the actual number of girls is provided, then we can calculate the number of boys:
G/B = 7/5
5G = 7B [Multiply both sides by 5B]
7B = 5G and so
B = (5/7)G
If, for example, there were 14 girls, there would be B = (5/7)*(14) or 5 Boys.
A rectangle has side lengths of x cm and (x + y) cm, where x and y are
both positive.
The rectangle has an area of 57 cm² and a perimeter of 44 cm.
Work out the values of x and y.
Answers
The values of x and y are 7 and 6 respectively
What is area and perimeter of a rectangle?The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m².
Perimeter is the distance around the edge of a shape. Learn how to find the perimeter by adding up the side lengths of various shapes.
The area of a rectangle = l× w
The perimeter of rectangle = 2(l+b)
length = x
breadth = x+y
57 = x(x+y)
44 = 2( x+(x+y)
therefore ;
57 = x²+y. equation 1
44 = 4x + 2y equation 2
from equation 2, y = 22-2x
substitute 22-2x for y in equation 1
57 = x²+22-2x
57 -22= x²-2x
x²-2x -35 = 0
(x²-7x)(+5x -35 )= 0
x( x-7) 5( x-7) = 0
x+5 = 0
x-7 = 0
therefore x = -5 or 7
but we are going to take the positive answer for x
57 = 7²+y
y = 55-49
y = 6
therefore the value of x and y are 7 and 6 respectively
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two triangle are similar. rye length of one side of one triangle is 4 times that of the corresponding side of the other determine the ratio of the perimeter the ratio of the areas of the polygon
Answers
The ratios for the similar triangles are given as follows:
The ratio of the perimeter is of 4.The ratio of the area is of 16.What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The length of one side of one triangle is 4 times that of the corresponding side of the other, hence the constant of the proportional relationship for the side lengths is given as follows:
k = 4.
The perimeter is measured in units, just like the side lengths, while the area is measured in units squared, hence the ratios are given as follows:
The ratio of the perimeter is of 4.The ratio of the area is of 4² = 16.More can be learned about similar triangles at brainly.com/question/14285697
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Lupita deposited $5,000 into a savings account that earns 2% interest compounded annually. Rounded to the nearest cent, how much interest will Lupita have earned after 48 months?
Answers
The difference between the total and the initial contribution, which is: Interest [tex]= $5,409.09 - $5,000, I[/tex] nterest $409.09, is the amount of interest earned. Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.
We can use the compound interest calculation to determine how much money Lupita will receive after 48 months:
Where: [tex]A = P(1 + r/n)(nt)[/tex] A represents the whole sum after t years.
P represents the primary sum.
The yearly interest rate is r.
Given that interest is compounded yearly, [tex]P = $5,000, r = 0.02, n = 1,[/tex]and[tex]t = 48/12 = 4[/tex] (since the time is given in months, we need to convert to years by dividing by 12).
Hence, the equation is: [tex]A = $5,000(1 + 0.02/1)^(1*4)[/tex]
[tex]A = $5,000(1.02)^4\sA ≈ $5,409.09[/tex]
The amount that differs between the total and the original deposit that represents interest earned is: Interest equals [tex]$5,000 - $5,409.09$409.09[/tex] in interest
Lupita will have accrued interest of $409.09, rounded to the closest penny, after 48 months.
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write the variable and constant for the expression : 2x+1
Answers
Answer:
Step-by-step explanation:
variable means we can put any value to it.
the variable is 2x
the constant is +1
If the company orders 27 boxed lunches from a deli for $245. 70 and each boxed lunch costs the same amount then the unit cost of each boxed lunched is $9. 1. What is the unit cost of each boxed lunch?
Given that;
27 boxed lunches from a deli cost $245. 70
Cost of 1 box = ?
To determine the unit cost of each
Answers
If the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunch is $9.1.
This example belongs to a word problem.
What is the unit cost of each boxed lunch?
Given that;
27 boxed lunches from a deli cost $245.70
Cost of 1 box =?
To determine the unit cost of each boxed lunch, we say;
Cost of each box = $245.70 ÷ 27
Cost of each box = $9.1
Hence, if the company orders 27 boxed lunches from a deli for $245.70 and each boxed lunch costs the same amount then the unit cost of each boxed lunch is $9.1
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need help with part a part b part c
Answers
Answer:
Part A 4 Part B 20 Part C C
there are total 28 balls. 1 / 7 = 4 balls.
A tamily has 4 children. Assume that each child is as likely to be a boy as it is to be a girl. Find the probability that the family has 4 girls if it is known the family has at least one giri. Answer
Answers
Therefore , the solution of the given problem of probability comes out to be the likelihood that they have four girls is 1/15.
What precisely is probability?The assessment of the probability that a claim is true or that a particular event will happen is the main objective of the constructions inside style known as criteria. Chance can be symbolised by any number between zero and 1, for which 1 typically denotes certainty range and 0 typically denotes possibility. A probability diagram illustrates the likelihood that a particular occurrence will take place. Decimal digits 0, 1, rationals with just 0% and roughly 100%.
Here,
Given that the family has at least one girl, we can use Bayes' theorem to determine the likelihood that they have four girls:
=> P(4 girls | at least one girl) = P(4 girls)
=> Times P(at least one girl | 4 girls) / P. (at least one girl)
Additionally, we are aware that the probability of having at least one female is
=> P(at least one girl = 1 - P(no girls) = 1 - (1/2)4 = 15/16.
The likelihood of not having any females is equal to the likelihood of having four boys,
which is
=> (1/2)4 = 1/16.
Given that all four of the children are female, the likelihood of producing girls is one.
Combining everything, we have:
=> P(4 females | a girl)
=> 1 * (1/16) / (15/16) = 1/15
Given that the household has at least one girl, the likelihood that they have four girls is 1/15.
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What is 10 x 9.2^-13
Answers
Answer:
-4721613632.87 or -4721613632.9 or -4721613633
Step-by-step explanation:
10x9.2^-13 = 10x-472161363.287 = -4721613632.87 or you can round -4721613632.9 or -4721613633
Rewrite 9.2^-13 as 1/(9.2^13), using the rule a^(-n) = 1/(a^n).
Substitute 1/(9.2^13) into the expression 10 x 1/(9.2^13).
Simplify by multiplying 10 by 1/(9.2^13):
10 x 1/(9.2^13) = 10/(9.2^13)
To calculate the numerical value of this expression, we can use a calculator. The result is approximately:
10/(9.2^13) ≈ 1.1082 x 10^9
Therefore, 10 x 9.2^-13 is approximately equal to 1.1082 x 10^9.
In ∆ABC, AB//QR and AP:PB =BR: RC. With reasons, prove that PQ// BC
Answers
In triangle ABC, if AB is parallel to QR and if AP:PB=BR:RC, then PQ is parallel to BC.
Since AB is parallel to QR, we can use the alternate interior angles theorem to conclude that ∠PAB = ∠QBR and ∠PBA = ∠QRB.
Also, since AP:PB=BR:RC, we can let AP=x and PB=y, so that BR=z and RC=w. Then we have:
x/y = z/wCross-multiplying, we get:
xw = yzNow consider triangles ABP and QBR. By the angle-angle similarity theorem, we have that these triangles are similar. So:
AB/PB = QB/BRSubstituting our values for PB and BR, we get:
AB/y = QB/zCross-multiplying, we get:
ABz = QBySimilarly, considering triangles APC and RCB, we can use the angle-angle similarity theorem to conclude that these triangles are also similar. So:
AC/RC = RB/CBSubstituting our values for RC and RB, we get:
AC/w = RB/zCross-multiplying, we get:
ACz = RBwNow, let's consider the ratio of the lengths of PQ and BC. We have:
PQ/BC = (QB + BP)/(RB + BC)Substituting in the values we found earlier for ABz, QBy, ACz, and RBw, we get:
PQ/BC = [(ABz + QBy)/(RBw + ACz)]Using the fact that ABz = QBy and ACz = RBw (which we found earlier), we can simplify this expression to:
PQ/BC = 1This means that PQ and BC are parallel, which is what we wanted to prove.
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A farmer pays $50 to rent a booth at a farmers market. She is selling watermelons for $8 each. At the end of the day, she wants to have earned at. least $200 after she pays to rent the booth. How many watermelons does the farmer need to sell?
Answers
Answer:
Let x be the number of watermelons the farmer needs to sell to earn at least $200.
The amount of money earned from selling x watermelons is 8x dollars.
After paying $50 to rent the booth, the farmer's profit is 8x - 50 dollars.
The problem states that the farmer wants to earn at least $200, so we can set up the following inequality:
8x - 50 ≥ 200
Adding 50 to both sides, we get:
8x ≥ 250
Dividing both sides by 8, we get:
x ≥ 31.25
Since the number of watermelons must be a whole number, the farmer needs to sell at least 32 watermelons to earn at least $200 after paying for the booth.
A cone of radius rcm and height 3rcm is removed from a cone of radius 10 cm and height 30 cm to give a frustum. The volume of the frustum is 2855 cm³ Calculate the value of r. Show all your working.
Answers
If the volume of the frustum is 2855 cm³ and the value of r = 28.4
What is a cone?A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point called the apex or vertex.
Volume of the = (1/3*п*R²*H) + 1/3*п*r²*h
2855 = 1/3*22/7*10*30 + 1/3*22/7*r²*3
2855 = 314.3 + 66r²/21
2540.7 *21= 66r²
53354.7 = 66r²
r² = 808.4
r √808.4
Therefore the value of r = 28.4
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The value for 4/m+1 at m=1
Answers
Answer:
5 is the answer
Step-by-step explanation:
factorise 4px-3my-2pm-6xy
Answers
Answer:
E
Step-by-step explanation:
NO
what percent of 1225 is 147?
Answers
Answer:
12%
Step-by-step explanation:
147/ 1225 x 100/ 1
0.12 x 100 = 12%
Answer:
Therefore, 147 is 12% of 1225.
What is one example of math in mr. Maxs life outside the classroom
Answers
Here some examples of math by using Mr. Maxs life outside the classroom.
Define the examples of math?One example of math in Mr. Max's life outside the classroom could be calculating the amount of gas needed to fill up his car's tank before a road trip. This involves using basic arithmetic operations such as addition, subtraction, multiplication, and division to calculate the total distance he intends to travel, the fuel efficiency of his car, and the capacity of the fuel tank. By doing so, he can estimate the amount of gas needed for the trip and plan accordingly. Additionally, he may also use math to calculate the cost of the gas based on the current price per gallon or liter, and decide on the most cost-effective way to fill up his tank.
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complete question is:
What is one example of math in Mr. Max's life outside the classroom? 10. Is math everywhere, as Bobby believes? Support your answer with evidence.
Adam drove to his grandmother's house 24 miles away.
How many meters did Adam drive?
Answers
Answer:
Step-by-step explanation:
1 mile = 1609 meters
24 miles = 38624 meters
So, Adam drives 38624 meters.
The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x values containing values negative 3, negative 1, 1, 3, and 5 and another circle labeled y values containing values 0, 2, and 5 and arrows from negative 3 to 0, negative 1 to 2, 1 to 0, 3 to 2, and 5 to 5. Is the relation a function? Explain. No, because for each input there is not exactly one output No, because for each output there is not exactly one input Yes, because for each input there is exactly one output Yes, because for each output there is exactly one input
Answers
The relatiοnship in the given diagram is nοt a functiοn, because fοr each input there is nοt exactly οne οutput. Sο Optiοn A is cοrrect
What are functiοns?Functiοn is a relatiοn between a set οf inputs and a set οf οutputs which are permissible. In a functiοn, fοr particular values οf x we will get οnly a single image in y. It is denοted by f(x).
Vertical line test:-
Whenever we want tο check whether a given expressiοn is a functiοn οr nοt we can apply a vertical line test, in this test we check fοr a single image οf x , we are getting a single image οr mοre.
If we get mοre images then it will nοt be a functiοn.
Fοr example, let us take, y² = 4ax
y = ±√4ax
Fοr single value οf x we get twο values οf y
Hence, it will nοt be a functiοn.
Given that,
Values οf x and values οf y
In given diagram,
fοr x = 0,
there are twο values οf y, -4 and -2
but accοrding tο definitiοn οf y, it shοuld give οnly οne value
Hence, it is nοt a functiοn
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The Blacktop Speedway is a supplier of automotive parts. Included in stock are 12 speedometers that are correctly calibrated and two that are not. Three speedometers are randomly selected without replacement. Let the random variable z represent the number that are not correctly calibrated Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.) P(x) N 3 3 Find the mean of this probability distribution. (Appropriate rounding rules apply.) mean = Submit Question
Answers
The mean of the given probability distribution is 0.2007.
The probability distribution table for the given scenario can be completed as follows:
| x | P(x) |
|---|------|
| 0 | 0.8036 |
| 1 | 0.1929 |
| 2 | 0.0036 |
| 3 | 0.0000 |
The probabilities are calculated using the hypergeometric distribution formula:
P(x) = (C(N-K, n-x) * C(K, x)) / C(N, n)
Where N is the total number of items (14), K is the number of items that are not correctly calibrated (2), n is the number of items selected (3), and x is the number of items that are not correctly calibrated in the selection.
For x = 0:
P(x) = (C(14-2, 3-0) * C(2, 0)) / C(14, 3) = (C(12, 3) * C(2, 0)) / C(14, 3) = (220 * 1) / 364 = 0.8036
For x = 1:
P(x) = (C(14-2, 3-1) * C(2, 1)) / C(14, 3) = (C(12, 2) * C(2, 1)) / C(14, 3) = (66 * 2) / 364 = 0.1929
For x = 2:
P(x) = (C(14-2, 3-2) * C(2, 2)) / C(14, 3) = (C(12, 1) * C(2, 2)) / C(14, 3) = (12 * 1) / 364 = 0.0036
For x = 3:
P(x) = (C(14-2, 3-3) * C(2, 3)) / C(14, 3) = (C(12, 0) * C(2, 3)) / C(14, 3) = (1 * 0) / 364 = 0.0000
The mean of this probability distribution can be calculated by multiplying each value of x by its corresponding probability and summing the results:
mean = (0 * 0.8036) + (1 * 0.1929) + (2 * 0.0036) + (3 * 0.0000) = 0.2007
Therefore, the mean of this probability distribution is 0.2007.
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The Martinez family picked 3 1/2 lb of apples. Ana picked 1/4 of those apples.
How many pounds of apples did Ana pick?
Answers
As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.
what is unitary method ?Finding a value of a single unit or the ratio of two values, then using this value to determine the value of a bigger or smaller number, is the unitary method, a problem-solving strategy used in mathematics. The unit method, single unit method, and percentage method are additional names for the unitary approach. The unitary method, which can be used to address issues in a number of disciplines including mathematics, algebra, geometry, and physics, entails using a ratio, proportion, or factor. The approach is founded on the proportionality concept, according to which two ratios or quantities are proportional if they have the same ratio or proportion.
given
Three and a half pounds of apples, which can be expressed as a mixed amount or an incorrect fraction, were harvested by the Martinez family:
3 1/2 = 7/2
Ana selected one-fourth of those apples, so the quantity she selected can be calculated by dividing by the total number of apples selected by the Martinez family:
1/4 × 7/2 = (1 × 7)/(4 × 2) = 7/8
As a result, Ana chose 7/8 of a pound of apples , while the Martinez family chose 3 1/2 pounds.
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sampling refers to a method to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions. a. random b. snowball c. stratified d. convenience
Answers
Random sampling is the correct answer. Which is option (A).
Sampling refers to a method to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is referred to as Random sampling.
What is sampling?
In statistics, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. Sampling is frequently employed in social science research. The method employed to select a subset of individuals for the sample from the population so that each has an equal chance of being assigned to the various study conditions is known as random sampling.
Content-loaded sampling refers to a form of sampling that is more sophisticated than simple random sampling.
In order to form a sample, it involves first determining which variables (or characteristics) are essential to the study, and then choosing people based on those variables, hence the name "content-loaded."On the other hand, in Stratified sampling, the population is divided into subgroups (strata) based on one or more characteristics that are expected to impact the study's outcomes. The proportion of people chosen from each group should reflect the group's percentage of the overall population.
Snowball sampling is a method for selecting a sample of individuals by locating others who share the characteristics being studied and asking them to suggest additional individuals who might participate in the study. Among the given options, (A) random sampling is the correct answer.
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Thank you so much for answering this!!!
If x^7=2.5, then what is x^14?
Answers
Answer:
6.25
Step-by-step explanation:
The equation 2 = (1.01)* models a population that has doubled. What is the rate of increase? What does x represent?
Answers
The rate of increase is 1% and the variable x represents when the population will double
Calculating the rate of increaseThe rate of increase is determined by the value of the exponent x. In this case, x represents the number of years that have passed since the population was at its initial value.
The exponent x increases by 1 for each year that passes, indicating that the population is increasing by a factor of 1.01 each year.
Therefore, the rate of increase is 1%, or 0.01 as a decimal.
What does x represent?The variable x represents when the population will double
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The purpose of this assignment is to apply hypothesis tests to the case of Bayview University. 1. Open the dataset of Bayview University (attached) and read the case in its entirety at the end of Chapter 9
2. Use descriptive statistic to summarize the data and comment on your finding
Answers
The strengths and weaknesses of the data will help to identify the areas that need to be improved.
The steps that are to be taken to apply hypothesis tests to the case of Bayview University are given below:Open the dataset of Bayview University and read the case in its entirety at the end of Chapter 9. After opening the dataset of Bayview University, read the case in its entirety at the end of Chapter 9. It is important to read the case carefully in order to understand it properly. This is the first step that is to be taken in order to apply hypothesis tests to the case of Bayview University.
Use descriptive statistics to summarize the data and comment on your findings. Once the case has been read carefully, descriptive statistics are to be used to summarize the data. Descriptive statistics are statistical techniques that are used to describe and summarize the data. They are used to summarize the data in a way that is meaningful and easy to understand. The descriptive statistics will help to identify the central tendency and the variability of the data. After summarizing the data, comments are to be made on the findings. These comments will help to identify the strengths and weaknesses of the data. The strengths and weaknesses of the data will help to identify the areas that need to be improved.
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Triangle a b c. side a c is 9 units, c b is 9 units, a b is 7 units. dilate triangle abc about point a by a scale factor of 1/3. what is the length of ac'? what is the length of ab'?
Answers
After dilating the triangle abc about point a by a scale factor of 1/3, the length of new side length of ac' is equals to the 3 units.
Dilation is a transformation used to change the size of an object. Dilation is used to make objects larger or smaller. This transformation produces an image of the same shape as the original. For a scale factor k, the algebraic representation of inflation is (x, y) → (kx, ky). Here we have a triangle abc with side length, ac = 9 units
side length, cb = 9 units
side length, ab = 7 units
remove triangle abc around point a, and
factor dilation scale = 1/3
We need to determine the length of the new side ac'. Dimensions of original shape, ac × scale factor = Dimensions of new shape, ac'
=> length of ac' = 9 units × 1/3
=> length of ac' = 3 units
Hence, required length is 3 units.
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what are some issues you must consider when choosing the appropriate number of treatment conditions for your experiment? what does it mean to have conditions that are proportional to each other?
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When selecting the appropriate number of treatment conditions, it is essential to consider factors such as resources, research complexity, and confounding variables.
Having conditions that are proportional to each other means that the level or intensity of each condition varies in direct proportion to the others, such that if one condition is increased or decreased, the others are also adjusted in a corresponding manner.
When choosing the appropriate number of treatment conditions for an experiment, there are several issues to consider. One of these is the ability to distinguish differences between treatment conditions.
A suitable number of treatment conditions for an experiment should be able to identify important differences between them. If there are too few treatment conditions, differences may not be identified, while if there are too many treatment conditions, resources may be wasted, making it difficult to obtain meaningful results.Another factor to consider is the need for replicability. The more treatment conditions that are used, the more difficult it is to replicate the experiment. A suitable number of treatment conditions should allow for replicability, meaning that the experiment can be repeated with similar results.To have proportional treatment conditions means that the levels of the independent variable (the treatment) are proportionate. This means that the differences between the levels of the independent variable are proportional to each other. This is important because it ensures that the treatment conditions are balanced and that the results obtained are valid. If the levels of the independent variable are not proportional, it can be difficult to interpret the results and draw conclusions.Having conditions that are proportional to each other means that the differences between treatment conditions are consistent across all levels of the independent variable. In other words, if the independent variable increases by a certain amount, the difference between the treatment conditions remains constant. This can be important for ensuring that the treatment effects are interpretable and generalizable to other populations.
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