Answer:
The value is \(\sigma = 1.0954\)
Step-by-step explanation:
From the question we are told that
The proportion of people that remember the ad is p = 0.40
The sample size is n = 5
Generally this study of number of web surfers who view online pop up ads and remember them follow binomial distribution in that the outcome is two (which either they remember them or not) , the number of trial is finite , each the two outcome is consistent throughout the study.
Generally the standard deviation in the number that will remember the ad is mathematically represented as
\(\sigma = \sqrt{n * p * (1- p)}\)
=> \(\sigma = \sqrt{ 5 * 0.40 * (1- 0.40)}\)
=> \(\sigma = 1.0954\)
Sunset Lake is stocked with 2800 rainbow trout and after 1 year the population has grown to 7000. Assuming logistic growth with a carrying capacity of 28000, find the growth constant kk, and determine when the population will increase to 14600.
The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.
How to find the increase of population?The increase of population can be found by using the logistic equation. It is
\(P(t) = \frac{K}{1 + Ae^{-kt} }\)
Where
P(t) = population at time t (in years)K = carrying capacityA = (K- P₀)/P₀k = growth constant of proportionalityt = time (in years)Sunset Lake is stocked with the rainbow trout. We have
P₀ = 2800P(1) = 7000K = 28000Find the growth constant k and time t when P(t) = 14600!
A = (K - P₀)/P₀
A = (28000 - 2800)/2800
A = 25200/2800
A = 9
After 1 year, we have 7000 rainbow trout. The growth constant is
\(7000 = \frac{28000}{1 + 9e^{-k(1)} }\)
\(1 + 9e^{-k} = 4\)
\(9e^{-k} = 3\)
\(e^{-k} = \frac{1}{3}\)
k = - ln (1/3)
k = 1.0986
Use k value to find the time when the population will increase to 14600!
\(14600 = \frac{28000}{1 + 9e^{-1.0986t} }\)
\(1.9178 = 1 + 9e^{-1.0986t}\)
\(0.9178 = 9e^{-1.0986t}\)
\(\frac{0.9178 }{9} = e^{-1.0986t}\)
\(t = \frac{ln \: 0.10198}{-1.0986}\)
t = 2.078
t ≈ 2.1 years
It is in another 1.1 years after t = 1.
Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.
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A XYZ is translated left 4 units to form the image A X'Y'Z'.
What are the coordinates of the vertices of A X'Y'Z' ?
Enter your answer by filling in the boxes.
Plz Help
Answer:
y(1,6) x(-4,6) z(1,1)
Step-by-step explanation:
Answer:
X(-8,6)Y(-3,6)Z(-3,1)
Step-by-step explanation:
just moving the coordinate over to the left 4 times
Ms. Tanja Umstead is 46 years old and lives in Richmond, British Columbia. She is in good health
and works in the sales department of a large publicly traded company.
Employment Information
1. Tanja's 2022 salary is $93,500. In addition, she was awarded a year-end bonus of $12,000, all
of which is payable in January 2023.
2.
Tanja's employer sponsors a defined benefit RPP. In 2022, Tanja and her employer each
contribute $4,150 to the plan. In addition, her employer withheld maximum El contributions of
$953 and maximum CPP contributions of $3,500.
3. Her employer offers to pay the tuition for employees taking foreign language courses. Tanja is
taking an intensive course in spoken Chinese at a British Columbia university. The course is
a course of personal interest and is not related to Tanja's employment. The tuition fee for the
course is $3,600, all of which is paid for by her employer. The duration of the course is eight
months.
4. Tanja is provided with disability insurance by an employer-sponsored plan. In 2022, as a
consequence of an automobile accident, she was unable to go to work for one month and
receives benefits of $6,500. Starting in 2020, Tanja has contributed $340 per year for the plan's
coverage. Her employer made a matching contribution in each year.
5. Tanja's employer provides her with an automobile that was purchased several years ago at
a cost of $39,500. In 2022, the car is driven 41,000 kilometres, 34,000 of which were for
employment purposes and 7,000 for personal use. Tanja is required to pay her own operating
costs, which for 2022 totalled $7,240. Except for the one month that she was off from work,
the car was available to Tanja throughout the year. During the one month that she was off, the
car was left in her employer's garage as required by her employer's policy.
6.
Tanja's employer provides all of its employees with financial counselling services. The cost to
the company of the services provided to Tanja was $450.
7.
As a result of winning a sales contest, Tanja received a one-week trip to Las Vegas. The value
of this trip in Canadian dollars was $5,620.
8.
In 2020, Tanja received options to acquire 250 shares of her employer's common stock at a
price of $25 per share. When the options were granted, the shares were trading at $25 per
share. In 2022, Tanja exercises all of the options. On the exercise date, the shares are trading
at $32 per share. Tanja still owns the shares on December 31, 2022.
Required: Calculate Tanja's 2022 minimum taxable income
Ignore any GST/HST & PST considerations.
To calculate the exact minimum taxable income, we need the missing information regarding the standby charge and the stock options exercise.
To calculate Tanja's 2022 minimum taxable income, we need to consider her various income sources and deductions. Let's break it down:
Salary: $93,500
Year-end bonus: $12,000
Defined benefit RPP contributions: Tanja's and her employer's contributions are not taxable income.
Employment Insurance (EI) contributions withheld: $953
Canada Pension Plan (CPP) contributions withheld: $3,500
Tuition fee for Chinese course paid by employer: $3,600 (not taxable)
Disability insurance benefits: $6,500 (taxable as it is a replacement for employment income)
Employer-provided automobile: We need to calculate the standby charge and operating cost benefit.
Standby charge: The standby charge is calculated based on the original cost of the car and the number of personal use kilometers. Since the car was left in the employer's garage for one month, the standby charge is reduced. We need additional information to calculate this.
Operating cost benefit: $7,240 (taxable as it is a personal use benefit)
Financial counseling services provided by the employer: $450 (not taxable)
Value of the Las Vegas trip: $5,620 (taxable as a non-cash prize)
Stock options exercise: We need additional information to calculate the taxable benefit.
To calculate the exact minimum taxable income, we need the missing information regarding the standby charge and the stock options exercise. Once we have those details, we can calculate Tanja's 2022 minimum taxable income by adding up the taxable components mentioned above and subtracting any applicable deductions or credits.
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2. You and your coworkers each bought scooters to get to work that costs $550. If 1
out of 20 people break their scooters or have them stolen, and you work with 40
people, how much will each member need to pay if you all form an insurance company
for your scooters?
The amount each member needs to pay is $27.50
To solve this problemIf 1 in 20 people has their scooters stolen or broken, that means 2 people will need to file a claim for their scooters (1/20 * 40).
We multiply the number of claims by the price of each scooter to determine the total amount of insurance required: 2 * $550 = $1100.
The cost of the insurance will be covered by equal contributions from each of the 40 participants.
Therefore, the amount each member needs to pay is $1100 / 40 = $27.50.
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Last week the Stock A increased by 0.35%. If it had been selling for $150.00, how much did it increase? (round to the nearest penny)
Answer:
5;
Step-by-step explanation:
thyhertbfdhfdvsd
witch is an equation in point slope form the given point and slope point (1, 9) point 5
The formula for equation of line pasing through point (x_1,y_1) with slope m is,
\(y-y_1=m(x-x_1)\)Substitute point and slope in the equation to obtain the equation of line.
\(\begin{gathered} y-9=5(x-1) \\ y-9=5x-5 \\ y=5x+4 \end{gathered}\)So equation of line is y=5x+4.
One store has two family DVDs packaged
together for $5.00.
How much is one DVD?
A certain rectangular prism has a length that is 8 inches more than the width and a height that is 1 inch less than the length. The largest possible width for this rectangular prism is 20 inches. The volume of a rectangular prism is V=lwh.
Write a function V(x) that represents the volume of the rectangular prism in terms of the width.
The function V(w) that represents the volume of the rectangular prism in terms of the width is V(w) = (8 + w)w(7 + w)
How to write a function V(x) that represents the volume of the rectangular prism in terms of the width?The given parameters are:
Length = 8 inches more than the width
Height = 1 inch less than the length
The above means that
l = 8 + w
h = l - 1
The volume of a rectangular prism is calculated as
V = lwh
Substitute l = 8 + w in the equation V = lwh
So, we have
V = (8 + w)wh
Substitute h = l - 1 in the equation V = (8 + w)wh
So, we have
V = (8 + w)w(l - 1)
Substitute l = 8 + w in the equation V = (8 + w)w(l - 1)
So, we have
V = (8 + w)w(8 + w - 1)
Evaluate the like terms
So, we have
V(w) = (8 + w)w(7 + w)
Hence, the function V(w) that represents the volume of the rectangular prism in terms of the width is V(w) = (8 + w)w(7 + w)
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Durant and Westbrook are playing a three-point challenge game to improve long
distance shooting. Each time each of them makes a basket, 3 points are added to
their respective scores. Durant has 18 points and Westbrook has 12 points.
Which of the following options has the pair of explicit formulas that represents the
number of points for each player as an arithmetic sequence?
A: Durant: 18 +(n-1)(3)
B: Durant: 18-(n-1)(3)
C: Durant 18+(n-3)
D: Durant 18+3n
Answer:
I THINK ITS A
Step-by-step explan I TOOK THE TEST TODAY I DONT NOW NOTHING
Determine whether the underlined number is a statistic or a parameter A sample of seniors is selected and it is found that 25% own a computer Choose the correct statement below
A. Parameter because the value is a numerical measurement describing a characteristic of a sample
B. Statistic because the value is a numerical measurement describing a characteristic of a population
C. Statistic because the value is a numerical measurement describing a characteristic of a sample
D. Parameter because the value is a numerical measurement describing a characteristic of a population urses
Answer:
C. Statistic because the value is a numerical measurement describing a characteristic of a sample
helpppppppppppppppppppppp
Please may you enlarge the image, I can't read it.
6(x1.5)+30<48 I need help with this Help
The solution to given linear inequality, 6(x1.5) + 30 < 48, is x < 2
Solving linear inequalitiesFrom the question, we are to solve the given linear inequality
The given linear inequality is
6(x1.5) + 30 < 48
First, we will write this inequality properly.
The inequality can be properly written as
6(1.5x) + 30 < 48
Now, we will solve the linear inequality
6(1.5x) + 30 < 48
Subtract 30 from both sides of the equation
6(1.5x) + 30 - 30 < 48 - 30
6(1.5x) < 18
Divide both sides of the inequality by 6
6(1.5x)/6 < 18/6
(1.5x) < 3
1.5x < 3
Divide both sides of the inequality by 1.5
1.5x/1.5 < 3/1.5
x < 2
Hence, the solution is x < 2
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You pick a card at random, put it back, and then pick another card at random. 5 6 7 8 What is the probability of picking a prime number and then picking a prime number? Simplify your answer and write it as a fraction or whole number.
In fraction form, the answer is 1/4, which represents the simplified probability of the given event occurring.
To find the probability of picking a prime number and then picking another prime number, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
Given the four numbers: 5, 6, 7, and 8, we can see that there are two prime numbers (5 and 7) and two non-prime numbers (6 and 8).
The total number of possible outcomes is 4 since there are four cards to choose from.
Now, let's consider the favorable outcomes, which are picking a prime number and then picking another prime number.
The probability of picking a prime number on the first draw is 2/4, as there are two prime numbers out of the four total cards.
Since we replace the card before the second draw, the probability of picking a prime number on the second draw is also 2/4.
To find the probability of both events occurring, we multiply the individual probabilities:
(2/4) * (2/4) = 4/16 = 1/4
Therefore, the probability of picking a prime number and then picking another prime number is 1/4.
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The line segment joining the points P(-3,2) and Q(5,7) is divided by the y-axis in the ratio:
Answer:
Step-by-step explanation:
The line segment joining two points P and Q can be represented by the equation of a straight line in the form y = mx + b, where m is the slope and b is the y-intercept.
To find the equation of the line, we need to find the slope, which can be calculated using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the points P and Q, respectively.
In this case, the coordinates are:
P = (-3, 2) and Q = (5, 7)
So, the slope is:
m = (7 - 2) / (5 - (-3)) = 5 / 8
Next, we can use either of the points to find the y-intercept. Let's use point P:
b = y - mx, where y and x are the y and x coordinate of the point, respectively.
In this case,
b = 2 - m * (-3) = 2 - (5/8) * (-3) = 2 + 15/8 = 89/8
So, the equation of the line joining the points P and Q is:
y = (5/8)x + 89/8
Now, to find the point where the line crosses the y-axis, we need to find the x-coordinate of the point where y = 0.
So, we have:
0 = (5/8)x + 89/8
Solving for x, we get:
x = -(89/8) / (5/8) = -89 / 5
This means that the line crosses the y-axis at the point (-89/5, 0). To find the ratio in which the line segment is divided by the y-axis, we need to find the ratio of the distance from the y-axis to point P to the distance from the y-axis to point Q.
Let's call the point of intersection with the y-axis R. The distances are then:
PR = (3, 2) and QR = (5 - (-89/5), 7)
The ratio of the distances is then:
PR / QR = (3, 2) / (5 - (-89/5), 7) = 3 / (5 + 89/5) = 3 / (94/5) = 15/47
So, the line segment joining the points P and Q is divided by the y-axis in the ratio 15:47.
Harasti was inspired to build his hotels after he saw seahorses living in old fishing traps. What is the volume of a fishing trap that is 2 feet wide, 5 feet long, and 3 feet tall?
HELP ME DO THIS !!!!
Answer:
volume of rectangular prism = 30 ft³
Step-by-step explanation:
The fishing trap he wants to build to house sea houses are mostly rectangular prism. The traps are mostly glass like. The volume of the fishing trap will be the volume of the rectangular prism.
volume of rectangular prism = LWH
where
L = length
W = width
H = height
volume of rectangular prism = LWH
Length = 5 ft
width = 2 ft
Height = 3 ft
volume of rectangular prism = 5 × 2 × 3
volume of rectangular prism = 10 × 3
volume of rectangular prism = 30 ft³
if I have 10 apples and I take 2 away how many will I have
Answer:
8 apples.
Step-by-step explanation:
Answer:
8 apples
Step-by-step explanation:
Have a nice day
x + y + z = -6 -2x – 2y – 2z = 12 5x + 5y + 5z = -30 find x y and z please
Answer:
x = s, y = t, z = -6 -s -t
Step-by-step explanation:
These are dependent equations. For some values s and t, the solution is ...
x = s, y = t, z = -6 -s -t
HELPPP PLSSS!!
Complete the two-column proof below. The ‘reasons’ are already given, so only the mathematical ‘statements’ need to be completed.
Given: A and B are complementary angles. B and C are complementary angles. Prove: A C
The required statements are;
Given; <A and <B and <B and <C are complementaryDefinition of complementary angles; <A = 180° - <B and <B= 180° - <CSubstitution property of equality; <A = 180° - (180° - <C)Subtraction property of equality; <A = 180° - 180° + <CAngles that gave Equal measures are congruent since, <A = <B.Congruent angles and complementary anglesBy definition, two angles are considered congruent if they have equal angle measures.
Additionally, two angles are said to be complementary if the sum of their angle measures equals 180°.
Hence it follows that A and B are complementary if; <A = 180 - <B.
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Answer:
The answer is actually Vertical angles, Corresponding Angles Theorem, and the last one is Transitive property.
Step-by-step explanation:
Got it right on edge 2023.
Help meee!!!!!!!!!!!!!!
Answer:
perimeter=48
area=144
Step-by-step explanation:
2(3)+3(2)=12
2[(3)(2)]=12
12×4=48
12×12=144
Use Newton’s Method to find the solution to x^3+1=2x+3 use x_1=2 and find x_4 accurate to six decimal places. Hint use x^3-2x-2=0 as your equation.
Let \(f(x) = x^3 - 2x - 2\). Then differentiating, we get
\(f'(x) = 3x^2 - 2\)
We approximate \(f(x)\) at \(x_1=2\) with the tangent line,
\(f(x) \approx f(x_1) + f'(x_1) (x - x_1) = 10x - 18\)
The \(x\)-intercept for this approximation will be our next approximation for the root,
\(10x - 18 = 0 \implies x_2 = \dfrac95\)
Repeat this process. Approximate \(f(x)\) at \(x_2 = \frac95\).
\(f(x) \approx f(x_2) + f'(x_2) (x-x_2) = \dfrac{193}{25}x - \dfrac{1708}{125}\)
Then
\(\dfrac{193}{25}x - \dfrac{1708}{125} = 0 \implies x_3 = \dfrac{1708}{965}\)
Once more. Approximate \(f(x)\) at \(x_3\).
\(f(x) \approx f(x_3) + f'(x_3) (x - x_3) = \dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125}\)
Then
\(\dfrac{6,889,342}{931,225}x - \dfrac{11,762,638,074}{898,632,125} = 0 \\\\ \implies x_4 = \dfrac{5,881,319,037}{3,324,107,515} \approx 1.769292663 \approx \boxed{1.769293}\)
Compare this to the actual root of \(f(x)\), which is approximately 1.769292354, matching up to the first 5 digits after the decimal place.
5a. find the value of a.
The logarithmic function f(x) = a·log₃(x - 4), passing through the points (13, 7), has the values;
5 a. The value of a is 3.5
b. Please find attached the graph of the function, f(x) = 3.5·log₃(x - 4), created with MS Excel
What is a logarithmic function?A logarithmic function is a function that contain and involves logarithm operation and it is the inverse of an exponential function
The function is f(x) = a·log₃(x - 4),
x > 4 and a > 0
The coordinates of a point on the graph of the function, f is A(13, 7)
5 a. The value of a can be found by plugging in the value of (13, 7) = (x, f(x)), as follows
f(13) = 7 = a·log₃(13 - 4) = a·log₃9 = a·log₃3²
7 = a·log₃3²
7 = 2·a·log₃3 = 2·a·1 = 2·a
2·a = 7
a = 7 ÷ 2 = 3.5
a = 3.5
5 b. The coordinates of the x-intercept of the graph = (5, 0)
The equation of the function is;
f(x) = 3.5·log₃(x - 4)
A third point on the graph is given when f(x) = 14 as follows;
f(x) = 14 = 3.5·log₃(x - 4)
log₃(x - 4) = 14 ÷ 3.5 = 4
3⁴ = x - 4
x = 3⁴ + 4 = 85
Which gives the point, (85, 14)
Similarly, we have the point (31, 10.5), (7, 3.5)
Please find attached the graph of f(x) created with MS Excel
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A closet in Shivani's house is 2 yards by 1 yard. How much would it cost to put a new floor in the closet if the flooring costs $38.00 per square yard?
The amount it would cost to put a new floor in the closet is $76.00
Calculating how much it would cost to put a new floor in the closetFrom the question, we are to calculate how much it would cost to put a new floor in the closet
From the given information,
A closet in the house is 2 yards by 1 yard.
To determine how much it would cost to put a new floor in the closet,
First,
We calculate the area of the closet
Area of the closet = 2 yard × 1 yard
Area of the closet = 2 square yards
Now,
From the given information,
The flooring costs $38.00 per square yard
Thus,
The amount it would cost to put a new floor in the closet is
2 × $38.00
= $76.00
Hence,
The amount it would cost is $76.00
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A paper describes a study of the use of MRI (Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was to determine if MRI exams do a better job than mammograms of determining if women who have recently been diagnosed with cancer In one breast have cancer in the other breast. The study participants were 980 women who had been diagnosed with cancer in one breast and for whom a mammogram did not detect cancer in the other breast.
These women had an MRI exam of the other breast, and 131 of those exams indicated possible cancer. After undergoing biopsies, it was determined that 40 of the 131 did in fact have cancer in the other breast, whereas 91 did not. The women were all followed for one year, and two of the women for whom the MRI exam did not indicate cancer in the other breast were subsequently diagnosed with cancer that the MRI did not detect.
Suppose that for women recently diagnosed with cancer In only one breast, the MRI is used to decide between the two "hypotheses.
H0: woman has cancer in the other breast
Ha: woman does not have cancer In the other breast
(Although these are not hypotheses about a population characteristic, this exercise illustrates the definitions of Type I and Type II errors.)
A) One possible error would be deciding that a woman who does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?
B) There Is a second type of error that is possible In this setting. Describe this error.
A Type II error would be coming to the conclusion that the woman_______cancer in the other breast when in fact she_______cancer in the other breast.
Answer:
Step-by-step explanation:
A type I error occurs when the null hypothesis is rejected in favor of the alternative hypothesis when the null hypothesis is actually true.
A type II error occurs when the researcher fails to reject the null hypothesis when the null is false.
H0: woman has cancer in the other breast
Ha: woman does not have cancer In the other breast
A) One possible error would be deciding that a woman who does have cancer in the other breast Is cancer-free. Is this a Type 1 or a Type II error?
This error is a type I error as the patient does have cancer which should warrant failing to reject the null but the null was rejected in favour of the alternative.
A Type II error would be coming to the conclusion that the woman does have cancer in the other breast when in fact she does not have cancer in the other breast.
This is a second type of error that can occur and it is a type II error: failing to reject the null when not true.
What is cos(tan^-1(-2/3))=
cos(tan^(-1)(-2/3)) simplifies to 3√13 / 13.
To evaluate the expression cos(tan^(-1)(-2/3)), we can use the trigonometric identity:
cos(tan^(-1)(x)) = 1 / √(1 + x^2)
In this case, x is -2/3. Substituting the value into the identity:
cos(tan^(-1)(-2/3)) = 1 / √(1 + (-2/3)^2)
Now, let's calculate the value:
cos(tan^(-1)(-2/3)) = 1 / √(1 + 4/9)
= 1 / √(13/9)
= 1 / (√13/3)
= 3 / √13
= 3√13 / 13
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Given a binomial experiment with the probability of success on a single trial p = 0.80, find the probability that the first success occurs on trial number n = 3. (Round your answer to three decimal places.)
The probability that the first success occurs on trial number n = 3 is 0.032
How to find the probability that the first success occurs on trial number n = 3?Given:
probability of success on a single trial p = 0.80
trial number, n = 3
Recall the formula for the Geometric Probability Distribution
P(n) = p(1 - p)ⁿ⁻¹
where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial
P(n) = p(1 - p)ⁿ⁻¹
P(3) = 0.8(1-0.8)³⁻¹
P(3) = 0.8(0.2)²
P(3) = 0.032
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Mr. Hudson has a starting balance of $4,500 in his savings account. He withdraws $150each week for expenses.Write the expression that represents this situation.
To answer this, let t=number of weeks gone by; B= balance left.
Mr. Husdon's balance that will be left after every week of withdrawal will be:
\(B(t)=4500-150t\)Which of the columns in the table below is categorical data? Name Position Goals Bob Goal 0 Cindy Wing 5 Maurice Center 10 Luke Center 15 A. Name B. Goals C. Position
The categorical data in the table is column C, Position.
What is table?In mathematics and statistics, a table is a way of presenting data in a structured manner, typically with columns and rows. Tables are commonly used to organize and present large amounts of data in a clear and concise way, making it easier to read and analyze. Tables can be used to display numerical data, as well as categorical data, such as names, dates, and labels. They can also be used to summarize data and display relationships between different variables. Tables are often used in scientific research, business, finance, and other fields where data analysis is important.
Here,
In the table given, the only column that contains categories or groups is the "Position" column. It contains categorical data as it lists the positions of the players - Goal, Wing, and Center. On the other hand, "Name" and "Goals" columns contain individual values and numerical data, respectively, and are not considered categorical data.
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Will give Brainliest. Amoli and Ella are converting measurements between inches and feet. Amoli says that the constant of proportionality is 12. Ella says it is 1/12. Who do you agree with? Explain your thinking.
please help me with this question
Answer:
6.6 °C
Step-by-step explanation:
Alabama temperature in Celsius:
F= 1.8C + 32
Put F = 112 in the above equation
112 = 1.8C + 32
112 - 32 = 1.8C
80 = 1.8C
80/1.8 =C
C = 44.4°C
Difference = 44.4 - 37.8 = 6.6 °C
find two ordered pairs for x-4y=2
Answer:
x-4y=2 can be written as y=(x-2)/4
(2,0) when x=2, y=0 and (6,1) when x=6, y=1