. Evaluate
11! 11!
24!
.
The evaluations are:
i. 11! = 39916800
ii. 24! = 2.045 x 10^37
What is expansion by factorial?Expansion by factorial is a method of expanding a given number from 1 to the number given. An example is given thus;
5! = 5 x 4 x 3 x 2 x 1!
= 120
To evaluate the given expressions;
a. 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1!
= 39916800
Also,
b. 24! = 24 x 23 x 22 x 20 x ........ x 5 x 4 x 3 x 2 x 1!
= 204484017332398 x 10 ^23
= 2.045 x 10^37
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(3d). Mary decided to open a uniform cleaning service at GTUC. When she started the business she had to purchase an Ironing Board for $15 and an Iron for $35. Also, she figured it would cost $1.25 in cleaning products for each uniform, so she decided she was going to charge $3.25 for cleaning and pressing one entire uniform i. Write a system of equations that would represent the above scenario. ii. How many uniforms does Mary have to clean in order to break even?
she needs to clean 15 uniforms to break even
for the first question the answer choice is 35, 45, 145, 155,
the second question is a true or false answer
for the first question answer is 35 , which we can clearly see its pointing 35 degree in the protractor .second question is incomplete
what is protractor ?
To measure an angle using a protractor instrument, follow these steps:
Place the protractor on the angle: Place the flat side of the protractor on one of the angle's sides, making sure that the vertex (the point where the two sides of the angle meet) is at the center of the protractor.Align the protractor with the angle: Make sure the protractor is aligned with the angle you want to measure. The zero-degree mark on
In the given question,
for the first question answer is 35 , which we can clearly see in the protractor
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Need help in this question, with explanation please.
Answer:
a) (1/2)(5)(CD) = 20 cm^2
5CD = 40, so CD = 8 cm
b) (1/2)(12)(8) = 48 cm^2
Which sequence below would best model the description? 50 points!
In a lottery game, a player picks six numbers from 1 to 22. If the player matches all six numbers, they win 40,000 dollars. Otherwise, they lose $1.
To find the probability of winning the lottery game, we can use the formula for combinations:
nCk = n! / (k! * (n - k)!)
where n is the total number of choices (22 in this case) and k is the number of choices we make (6 in this case).
So, the number of possible combinations of six numbers from 22 is:
22C6 = 22! / (6! * 16!) = 13,983,816
Therefore, the probability of winning the lottery game is 1 in 13,983,816.
The expected value of playing the lottery game can be calculated as follows:
Expected value = (Probability of winning * Amount won) - (Probability of losing * Amount lost)
Expected value = (1/13,983,816 * $40,000) - (13,983,815/13,983,816 * $1)
Expected value = $0.5709
This means that on average, the player can expect to win about 57 cents per game played. However, it is important to note that this is just an average and the actual outcome of any single game can vary widely.
An employee at a department store is stocking cell phone cases. He has a box of 80 cases. Among the 80 cases, 40 are black, 10 are white, and 30 are pink. If he reaches into the bag randomly and removes one at a time, what is the probability that the first three cases are all pink? Please help I have no clue how to do this at all. I listen in math class but this is hard!
The probability of drawing a pink case on the first draw is 30/80.
What is probability?Probability is a branch of mathematics that deals with the measurement and analysis of random phenomena. It is the study of the likelihood or chance of an event occurring. It involves analyzing and predicting the likelihood of certain outcomes based on the available information and the rules of probability theory. Probability is used extensively in various fields, including statistics, physics, finance, engineering, and computer science, among others.
In the given question,
The probability of drawing a pink case on the first draw is 30/80. Since the cases are not replaced, the probability of drawing a pink case on the second draw is 29/79 (there are now 29 pink cases left out of 79 total cases). Similarly, the probability of drawing a pink case on the third draw is 28/78. Therefore, the probability of drawing three pink cases in a row is:
(30/80) * (29/79) * (28/78) = 0.0412 or about 4.12%.
So, the probability that the first three cases are all pink is 0.0412 or about 4.12%.
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solution set of the following inequality 4x-1>15 is ........*
Answer:
4x - 1 > 15
4x > 16
x > 4
The solution set is all numbers greater than 4.
use logb28
PLEASE HELP SOLVE!! 30 PTS!!
Answer:
logb28 ≈ 1.634.
Step-by-step explanation:
logb28 = (log428)/(log47)
We can then substitute the given values for logb4 and logb7:
logb28 = (log428)/(log47) = (log28)/(log24 + log27) = (log28)/(1.386 + 1.946)
1.386+1.946=3.332
logb28/3.332
logb28 ≈ 1.634.
Answer:
[tex]log_b28=3.332[/tex]--------------------
Given:
[tex]log_b 4 = 1.386\ and\ bog_b7=1.946[/tex]Use the following identity to find [tex]log_b28[/tex]:
[tex]log_a(bc)=log_ab+log_ac[/tex]Apply the identity to the given:
[tex]log_b28=log_b(4*7)=log_b4+log_b7=1.386+1.946=3.332[/tex]Watch help video Triangle QRS is formed by connecting the midpoints of the side of triangle NOP. The lengths of the sides of triangle QRS are shown. Find the perimeter of triangle NOP. Figures not necessarily drawn to scale. N S 6 5 P 7 R
Since Q is the midpoint of NP, we know that NQ = QP. Similarly, we know that RS is the midpoint of OP, so we have RS = SO.
Let's label the length of QS as x. Then, we know that QR = 2x and SR = 3x.
To find the perimeter of triangle NOP, we need to find the lengths of NO, OP, and NP.
Using the Pythagorean Theorem, we can find that:
NO^2 = NQ^2 + OQ^2
NO^2 = (QP)^2 + (SO)^2
NO^2 = (x)^2 + (2x)^2
NO^2 = 5x^2
NO = x√5
Similarly, we can find that:
OP^2 = OQ^2 + PQ^2
OP^2 = (SO)^2 + (QP)^2
OP^2 = (3x)^2 + (x)^2
OP^2 = 10x^2
OP = x√10
Finally, we know that NP = NO + OP, so:
NP = x√5 + x√10
NP = x(√5 + √10)
To find the perimeter of NOP, we add up the three sides:
Perimeter of NOP = NO + OP + NP
Perimeter of NOP = x√5 + x√10 + x(√5 + √10)
Perimeter of NOP = x(2√5 + 2√10)
Perimeter of NOP = 2x(√5 + √10)
We can substitute the value we found for QS, which is x, to get:
Perimeter of NOP = 2(5 + 2√10)
Perimeter of NOP = 10 + 4√10
Therefore, the perimeter of triangle NOP is 10 + 4√10 units.
Find the surface area of the rectangular prism.
Answer: 64
Step-by-step explanation:
multiple all of them
Use words to describe the relationship between the number of miles and each corresponding number of gallons.
10 gallons 300 miles.
The unit rate that relates the two quantities of distance and volume of gas is:
U = 30 miles per gallon.
How to describe this relation?To do so, we can find the unit rate.
This would say how many gallons are consumed to drive a unit of distance, or which distance can you drive with one gallon.
Here we have the values:
10 gallons and 300 miles.
Then the unit rate is the quotient between these:
300miles/10 gallons = 30 miles per gallon
This says that with one gallon of gas you can travel 30 miles.
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Please answer this please you will not understand how much this means 25 points
The solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.
Understanding Trigonometric Function(a) For f(x) = 0
We set the function equal to zero and solve for x:
f(0) = sec²x - 1 = 0
sec² x = 1
Taking the square root of both sides, we get:
sec x = ±1
Recall that sec x = 1/cos x = cos⁻¹ x
Therefore
x = cos⁻¹ (1) = 0 (using calculator or table)
x = cos⁻¹(-1) = pi
Therefore, the solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.
(b) For f(x) > 0
To get the positive values of x, we can start by factoring f(x):
f(x) = sec²x - 1 = (sec x + 1)(sec x - 1)
Since the square of the secant function is always positive, we have:
f(x) > 0 if and only if (sec x + 1)(sec x - 1) > 0
There are two cases to consider:
sec x + 1 > 0 and sec x - 1 > 0
sec x + 1 < 0 and sec x - 1 < 0
For case 1, we have:
sec x > -1 and sec x > 1
Since secant is always positive, we have sec x > 1.
For case 2, we have:
sec x < -1 and sec x < 1 (This is not possible)
(c) For f(x) < 0
By using the factored form of f(x) from part (b), we can find the values of x where f(x) is negative.
f(x) < 0 if and only if (sec x + 1)(sec x - 1) < 0
There are two cases to consider:
sec x + 1 > 0 and sec x - 1 < 0
sec x + 1 < 0 and sec x - 1 > 0
For case 1, we have:
sec x > 1 and sec x < -1 (not possible)
For case 2, we have:
sec x < -1 and sec x > 1
Since secant is always positive, this case is not possible either.
Therefore, there are no solutions to f(x) < 0 over the interval [0, 2pi).
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Commutative property
Answer:
Commutative property of addition: Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4. Associative property of addition: Changing the grouping of addends does not change the sum
Find f(−3), f(0) and f(1) for the following function.
f(x)=2x
Answer:
-6, 0, 2Step-by-step explanation:
f(x)=2x
note: putting anything in the f(x) parentheses replaces x in the function with that value
so,
f(-3) = 2(-3) = -6
f(0) = 2*0 = 0
f(2) = 2(2) = 4
What is the product? -4x [8 -1 -5 g]
The resulting matrix after the product is given as follows:
[-32 4 20].
What happens when a matrix is multiplied by a constant?When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.
The parameters for this problem are given as follows:
Constant of -4.Matrix [8 -1 -5].Hence the products are:
-4 x 8 = -32.-4 x -1 = 4.-4 x -5 = 20.Then the resulting matrix after the product is given as follows:
[-32 4 20].
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cos(0) = 2 ar
sin(8) = ?
- 2
**
2
√√2
2
√√2
DONE
,and
3
<
< 0 < 21, evaluate sin(0) and tan(0)
tan(8)=L
DONE
Using trigonometric identities when cosθ = √2/2 and 3π/2 < θ < 2π
sinθ = -√2/2 tanθ = - 1What are trigonometric identities?Trigonometric identities are mathematical equations that contain tigonometric ratios
Since cosθ = √2/2 and 3π/2 < θ < 2π, we desire to find sinθ and tanθ. We proceed as follows
a. To find sinθ, using the trigonometric identity
sin²θ = 1 - cos²θ
⇒ sinθ = ±√(1 - cos²θ)
So, substituting the value of cosθ into the equation, we have that
sinθ = ±√(1 - cos²θ)
sinθ = ±√(1 - (√2/2)²)
= ±√(1 - 2/4)
= ±√[(4 - 2)/4]
= ±√[2/4]
= ±√2/2
Since 3π/2 < θ < 2π, which is the fourth quadrant, we take the negative answer.
So, sinθ = -√2/2
b. To find tannθ, using the trigonometric identity
tan²θ = sec²θ - 1
⇒ tanθ = ±√(sec²θ - 1)
= ±√(1/cos²θ - 1)
So, substituting the value of cosθ into the equation, we have that
tanθ = ±√(1/cos²θ - 1)
tannθ = ±√(1/(√2/2)² - 1)
= ±√(1/2/4 - 1)
= ±√(4/2 - 1)
= ±√[2 - 1]
= ±√1
Since 3π/2 < θ < 2π, which is the fourth quadrant, we take the negative answer.
So, tanθ = -1
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HELP FAST!!! EASY ALEGRA 2!
log base 16, 32 can be written as log₂⁴ 2₅.
Evaluate with logₐx, write a and x as powers of same.
a) log₁₆ 64
= log₂⁴=2⁶
b) log₈₁ 27
= log₃⁴ 3³
c) log₁₆ 32
= log₂⁴ 2₅
d) log₂₇ 243
= log₃³ 3₅
Therefore, log base 16, 32 can be written as log₂⁴ 2₅.
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HELPPPP !!
Mr. Olaffsen opened a sandwich shop and a smoothie stand in his neighborhood.
The following table and equation show function f, representing Mr. Olaffsen's profit, in dollars, x months since opening the sandwich shop.
__________________________________________________________________
x 1 2 3 4 5 6 7
f(x) 12,000 15,500 18,000 19,500 20,000 19,500 18,000
__________________________________________________________________
The following table and equation show function g, representing Mr. Olaffsen's profit, in dollars, x months since opening the smoothie stand.
__________________________________________________________________
x 1 2 3 4 5 6 7
g(x) 9,300 12,000 14,100 15,600 16,500 16,800 16,500
__________________________________________________________________
Select the true statement.
A.) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,000.
B.) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,500.
C. ) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,200.
D. ) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700.
The true statement is that the difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700. (option d).
To determine the maximum profit earned by each business, we need to find the vertex of each quadratic function. The vertex of a quadratic function of the form ax² + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the maximum value of the function.
The equations for the two functions are:
f(x) = -500x² + 9000x + 7500 g(x) = -500x² + 7500x + 4200
To find the vertex of f(x), we need to first rewrite the function in standard form:
f(x) = -500(x² - 18x - 15)
Completing the square, we get:
f(x) = -500(x - 9)² + 12000
So the vertex of f(x) is (9, 12000), which represents the maximum profit earned by the sandwich shop.
Similarly, to find the vertex of g(x), we rewrite the function in standard form:
g(x) = -500(x² - 15x - 8.4)
Completing the square, we get:
g(x) = -500(x - 7.5)² + 14100
So the vertex of g(x) is (7.5, 14100), which represents the maximum profit earned by the smoothie stand.
Finally, we can calculate the difference between the maximum profits earned by both businesses as:
12000 - 14100 = -2700
Therefore, the correct answer is option (d).
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ASAP PLEASE
The histogram shows data collected about the number of passengers using city bus transportation at a specific time of day.
A histogram titled City Bus Transportation. The x-axis is labeled Number Of Passengers and has intervals of 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50. The y-axis is labeled Frequency and starts at 0 with tick marks every 1 units up to 9. There is a shaded bar for 1 to 10 that stops at 2, for 11 to 20 that stops at 4, for 21 to 30 that stops at 5, for 31 to 40 that stops at 6, and for 42 to 50 that stops at 3.
Which of the following data sets best represents what is displayed in the histogram?
1 (4, 5, 7, 8, 10, 12, 13, 15, 18, 21, 23, 28, 32, 34, 36, 40, 41, 41, 42, 42)
2 (4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)
3 (4, 5, 7, 8, 12, 13, 15, 18, 19, 21, 24, 25, 26, 28, 29, 30, 32, 33, 35, 42)
4 (4, 6, 11, 12, 16, 18, 21, 24, 25, 26, 28, 29, 30, 32, 35, 36, 38, 41, 41, 42)
Answer:
Step-by-step explanation:
After organizing the data, the researcher must present them so they can be understood by those who will benefit from reading the study. The most useful method of presenting the data is by constructing statistical charts and graphs. There are many different types of charts and graphs, and each one has a specific purpose.
This chapter explains how to organize data by constructing frequency distributions
and how to present the data by constructing charts and graphs. The charts and graphs
illustrated here are histograms, frequency polygons, ogives, pie graphs, Pareto charts,
and time series graphs. A graph that combines the characteristics of a frequency distribution and a histogram, called a stem and leaf plot, is also explained.
Section 2–2 Organizing Data 35
2–3
Objective
Organize data using
frequency
distributions.
1
2–2 Organizing Data
Suppose a researcher wished to do a study on the number of miles that the
employees of a large department store traveled to work each day. The researcher
first would have to collect the data by asking each employee the approximate distance the
store is from his or her home. When data are collected in original form, they are called
raw data. In this case, the data are
1 2 6 7 12 13 2 6 9 5
18 7 3 15 15 4 17 1 14 5
4 16 4 5 8 6 5 18 5 2
9 11 12 1 9 2 10 11 4 10
9 18 8 8 4 14 7 3 2 6
Since little information can be obtained from looking at raw data, the research
Answer:
c
Step-by-step explanation:
its ez
find area of the triangle help please
The calculated area of the triangle is 7.5 square inches
Finding the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle with the following dimensions
base = 6 inches
height = 2.5 inches
Using the above as a guide, we have the following:
Area = 1/2 * base * height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 6 * 2.5
Evaluate
Area = 7.5
Hence, the area of the triangle is 7.5 square inches
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Using the net below, find the surface area
of the pyramid.
7\in.
4 in.
4 in.
Surface Area = [?] in.2
The surface area of the pyramid is approximately 74.24 square inches.
What is a pyramid?
A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a single point called the apex. The most common type of pyramid is a square pyramid, which has a square base and four triangular faces.
To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base, and then add them up.
The area of each triangular face can be found using the formula:
Area = (1/2) * base * height
where the base is one of the sides of the square base and the height is the slant height of the pyramid.
The slant height of the pyramid can be found using the Pythagorean theorem:
slant height² = height² + (1/2 * base)²
where the height is the height of the pyramid, which is given as 7 inches, and the base is 4 inches.
height = 7 in.
base = 4 in.
slant height² = 7² + (1/2 * 4)² = 49 + 4 = 53
slant height = √53 ≈ 7.28 in.
Now we can find the area of each triangular face:
Area = (1/2) * base * height = (1/2) * 4 * 7.28 ≈ 14.56 in^2
There are four triangular faces, so the total area of the triangular faces is:
4 * 14.56 = 58.24 in²
The area of the square base is:
Area = side² = 4² = 16 in²
Finally, we can find the surface area of the pyramid by adding up the area of the triangular faces and the area of the square base:
Surface Area = 58.24 + 16 = 74.24 in²
Therefore, the surface area of the pyramid is approximately 74.24 square inches.
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A $162,000 trust is to be invested in bonds paying 9%, CDs paying 7%, and mortgages paying 10%. The sum of the bond and CD investment must equal the mortgage investment. To earn an $14,650 annual income from the investments, how much should the bank invest in bonds? (It's okay to use your calculator to solve the system you set up on this problem.
The bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
How to solve for the amount(162,000 - 2x) is invested in mortgages.
The annual income earned from the bond investment is:
0.09x
The annual income earned from the CD investment is:
0.07x
The annual income earned from the mortgage investment is:
0.10(162,000 - 2x) = 16,200 - 0.20x
The total annual income earned from the investments is:
0.09x + 0.07x + 16,200 - 0.20x = 14,650
Simplifying and solving for x, we get:
-0.04x + 16,200 = 14,650
-0.04x = -1,550
x = 38,750
Therefore, the bank should invest $38,750 in bonds to earn an annual income of $14,650 from the investments.
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Colin put some buttons on a table. There were 4 blue buttons, 5 red buttons, 7 tan buttons, and 8 white buttons.
Colin's cat jumped up and knocked 2 buttons onto the floor. What is the probability that the button on the floor was blue or red? Show or explain your work to justify your answer.
There are 4 + 5 + 7 + 8 = 24 buttons in total.
After the cat knocks 2 buttons onto the floor, there are 22 buttons remaining on the table. The probability that the first button knocked onto the floor is blue or red can be calculated as follows:
P(blue or red) = P(blue) + P(red)
P(blue or red) = 4/24 + 5/24
P(blue or red) = 9/24
P(blue or red) = 3/8
Therefore, the probability that the button on the floor was blue or red is 3/8 or 0.375.Answer:
Step-by-step explanation:
The Blue Whale is the largest animal to have ever lived. As an adult it is as long as three school buses added together. A 170,000 kg Blue Whale cruises along at a modest pace. If it has 890,000 Joules of kinetic energy, what is its cruising speed?
the cruising speed of the blue whale is approximately 3.16 meters per second.
What are velocity?
a velocity is a unit of measurement for the Distance an object travels in a
the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by
dividing the total Distance traveled by the journey time.
In this case, we know the mass of the blue whale (m = 170,000 kg) and its kinetic energy (KE = 890,000 J), but we need to solve for its velocity (v).
Rearranging the formula, we get:
v = √(2 * KE / m)
Plugging in the values we know, we get:
v = √(2 * 890000 J / 170000 kg)
Simplifying this expression, we get:
v = √10 = 3.16 m/s
Therefore, the cruising speed of the blue whale is approximately 3.16 meters per second.
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The mean monthly salary of female employees of a company is 3750 Birr, while the mean monthly salary of male employees is 4500 Birr. It is known that the mean monthly salary of male and female employees combined is 4000 Birr. a) What is the ratio of the number of female employees to male employees? b) What percentage of employees are females?
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 15 square feet use 3.14 for pi
The distance from which the sprinkler can spread water is 4.37 feet
How to determine the valueTo determine the value, we need to know the area of the circle.
The formula for the area of a circle is expressed as;
A = πr²
Given that the parameters are;
A is the area of the circler is the radius of the circleSubstitute the values, we have;
15 = 3.14r²
Divide both sides by the coefficient, we get;
r² = 4. 77
find the square root of both sides, we get;
r = 2. 19 feet
But note that the formula for diameter is given as;
Diameter = 2radius
Diameter = 2(2.19)
multiply the values
Diameter = 4.37 feet
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HELPPPPPPPPPP... please help i don't get this whatsoever and my teacher doesn't really help. i dont get none of it at all. please help asap !
Answer:
I can tell
Step-by-step explanation:
Ok so to help you understand it do you see the button that says video? Yeah, click it. A video will pop up and explain it to you! :)
QUESTION 6·1 POINT
A medical experiment on tumor growth gives the following data table.
x y
81 25
90 36
92 41
103 59
151 60
The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 914.8 and the sum of squares of regression (SSR) was 568.5. Calculate R2, rounded to three decimal places.
Provide your answer below:
The calculated R2 value is 0.621, indicating that 62.1% of the variability in tumor growth can be explained by the linear regression model.
In statistics, the coefficient of determination, denoted by R2, is a measure of how well the regression line fits the data. It represents the proportion of the variance in the dependent variable (y) that is predictable from the independent variable (x).
To calculate R2, we use the formula R2 = SSR/SST, where SSR is the sum of squares of regression and SST is the total sum of squares.
From the given data, SSR = 568.5 and SST = 914.8. Thus, R2 = 568.5/914.8 = 0.621, rounded to three decimal places.
This means that 62.1% of the variability in the tumor growth can be explained by the linear regression model. The remaining 37.9% of the variability is unexplained and may be due to other factors not included in the model.
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Workers in a Certain Company are require to pay 5.5% of their salary into a social Security fund. Mr. Mensah has monthly salary of Gld 4500.00 How much Will he pays each month to the Social Security fund.
Mr. Mensah will pay 247.5 each month to the social security fund because 5.5% of 4500 is 247.5.
The total monthly salary of Mr. Mensah is 4500.
He is required to pay 5.5% of his salary into a social security fund.
Now, we have to find the amount he has to pay each month into the social security fund.
To find that, we need to find the value of 5.5 percent of 4500.
4500 ×5.5/100
45×5.5
247.5
Therefore, 5.5% of 4500 is 247.5.
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