The function that models the growth of the Bacillus Megaterium over each generation is B. P (n) = 12 + 2n.
Which is a quadratic function having a leading coefficient of 3 and a constant term of –12?
The required quadratic function having a leading coefficient of 3 and a constant term of –12 is f(x) = 3x^2 + bx - 12.
What is the equation?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
A quadratic function can be written in the general form:
f(x) = ax² + bx + c
where a, b, and c are constants.
Given a leading coefficient of 3 and a constant term of -12, we can write the quadratic function as,
f(x) = 3x² + bx - 12
Therefore, a quadratic function having a leading coefficient of 3 and a constant term of –12 is f(x) = 3x^2 + bx - 12.
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Need help???!!!! Please
Explanation:
Here are all of the ways to factor 16 using positive whole numbers
1*162*84*4Which of those add to 10? That would be 2+8 = 10
Now make each of those numbers negative
-2 times -8 = 16-2 plus -8 = -10The order of the -2 and -8 doesn't matter. Use a number line to help see why -2 plus -8 = -10.
How many of the numbers have three digits in monotone (i. E. , non-increasing or non-decreasing) order?
There are a total of 198 numbers with three digits in monotone order.
For non-decreasing order, we can choose any three digits from 0-9, and arrange them in increasing order. The total number of ways to do this is 10 choose 3, which is 120. For non-increasing order, we can choose any three digits from 1-9, and arrange them in decreasing order. The total number of ways to do this is 9 choose 3, which is 84. However, we have double counted the numbers that are all the same digit, such as 111, 222, etc. There are 9 of these numbers, so we need to subtract them from our total.
So the total number of numbers with three digits in monotone order is 120 + 84 - 9 = 198.
Therefore, there are 198 numbers with three digits in monotone order.
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Lelah has budgeted $135
for new clothes. She decides to buy a pair of shoes that cost $35.25,
and then she buys some $18.25
shirts.
Which inequality represents this situation, where s
is the number of shirts she can buy?
The inequality that this situation, where s is the number of shirts she can buy is S>81.5.
What is a solution set to an inequality or an equation?If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.
We are given that;
Budget of lelah for clothes= $135
For shoes= $35.25
For shirts= $18.25
Now,
S+$18.25+35.25>135
S>135-18.25-35.25
S>135-53.5
S>81.5
Therefore, the inequality will be S>81.5.
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Consider the graphs of the following lines.
3x - 5y = 2
3x + 5y = -2
Find the slope m of each line.
3x - 5y = 2
m₁ =
3x + 5y = -2
m2 =
8.6A.
4
Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.
What is slope of the line?The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as
Line slope is a measure of the steepness or direction of a line in the coordinate plane.
m = Δy/Δx
where,m is the slope
Given,
equations of the line
3x - 5y = 2
Moving 3x to RHS
-5y = -3x + 2
y = (3/5)x - 2/5
comparing with slope intercept equation of the line y = mx + c
slope m₁ = 3/5
Now, equation
3x + 5y = -2
moving 3x to RHS
5y = -3x - 2
y = (-3/5)x - 2
comparing with slope intercept equation of the line y = mx + c
slope m₂ = -3/5
Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.
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X/1.2 - 18 - 2 Please help right answer gets brain liest and 15 points.
Answer:
= x-24
Step-by-step explanation:
[tex] \frac{x}{1.2} - 18 - 2 \\ = 1.2 \times \frac{x}{1.2} - 1.2 \times 18 - 1.2 \times 2 \\ = x - 21.6 - 2.4 \\ = x - 24[/tex]
What is the test of nonverbal intelligence?
A test of nonverbal intelligence is a type of cognitive assessment that measures an individual's ability to solve problems and think abstractly without the use of language.
Unlike traditional intelligence tests that rely heavily on verbal abilities such as vocabulary, reading, and verbal reasoning, nonverbal intelligence tests use visual-spatial and abstract reasoning tasks that do not require the use of language.
Nonverbal intelligence tests can be particularly useful for individuals who have language or communication difficulties, such as those with speech and language disorders, or those who are non-native speakers of the language in which the test is administered. They can also be used to assess individuals who have difficulty with traditional tests due to visual or hearing impairments.
Examples of nonverbal intelligence tests include Raven's Progressive Matrices, the Naglieri Nonverbal Ability Test (NNAT), and the Universal Nonverbal Intelligence Test (UNIT). These tests typically involve completing visual pattern recognition and completion tasks, spatial reasoning tasks, and other nonverbal problem-solving tasks.
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solve for x 3x-6 x-2
Answer:
x=46
Step-by-step explanation:
this is how you set up the problem
3x-6+x-2=180
then you combine like terms
4x-6-6=180
then combine like terms again
4x-4=180
then you have to get 4 to the other side
4x-4=180
+4 +4
which leaves you with 4x=184
which you then divide both sides by 4
which leaves you with
x=46
I hope this helps you!!!
Answer:
x=46 =))))))))))))))))))))))))))))))))))(((()((((()()(
If there are roughly 4500 bacterial in a culture, and the number of bacteria doubles each hour, the number N
of bacteria after t
hours can be found using the formula N=4500(2^t)
. About how long will it take the culture to grow to 80,000 bacteria?
To grow 80000 bacteria, it will take 4.152 hours.
What is exponential function?An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
Given,
Initial number of bacteria = 4500
Number of bacteria get doubled each hour
Function for population growth of bacteria is given by
N = 4500(2ˣ)
x is time in hours
Future population is N = 80000
Then
80000 = 4500(2ˣ)
800 = 45 . 2ˣ
taking log on both sides
log 800 = log (45 . 2ˣ)
log(mn) = log m + log n and log mⁿ = nlogm
log800 = log45+ x log2
2.9030 = 1.653 + x . 0.3010
x = (2.9030 - 1.653)/0.3010
x = 4.152
Hence, it will take 4.152 hours to grow 80000 bacteria.
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please help me on this
B. 5/12
B. 5/12
B. 5/12
B. 5/12
B. 5/12
B. 5/12
B. 5/12
Answer: B
Step-by-step explanation:
Here's how to subtract 3/12 from 4/6:
4/6−3/12
Step 1
We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.
So we multiply 4 by 12, and get 48.
Then we multiply 3 by 6, and get 18.
Next we give both terms new denominators -- 6 × 12 = 72.
So now our fractions look like this:
48/72−18/72
Step 2
Since our denominators match, we can subtract the numerators.
48 − 18 = 30
So the answer is:
30/72
Step 3
Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?
To find out, we try dividing it by 2...
Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:
30/72÷ 2 =15/36
Let's try dividing by 2 again...
Nope! So now we try the next greatest prime number, 3...
Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:
15/36÷ 3 =5/12
Let's try dividing by 3 again...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
No good. 7 is larger than 5. So we're done reducing.
There you have it! The final answer is:4.6−3/12=5/12
I am stuck on both of these questions.
1. Draw a vertical y-axis on the left-hand side of your graph and label it. Then draw a horizontal
x-axis at the bottom of your graph. Then label the coordinates of each corner of the sign on your graph. Draw a line on your graph. What is the slope of line a?
2. What is the equation of line a?
I think this is the graph I need to use I am not sure.
PLEASE HELP. ASAP ALMOST DUE?????
A linear function is demonstrated by the line a.
Line a has a slope of one.
Y = x + 2 is the equation for the line a.
How do you calculate a line's slope?
Following points on line a (x,y) = (0,2) and are available in the figure (2,4)
Calculating the slope (m) involves using:
m= y^2-y^1/x^2-x^1
This results
m= 4-2/2-0
Analyze m = 1
Consequently, the line's slope is 1.
The formula for line aThe formula for this is y = m(x - x1) + y1.
We thus have:
y = (x - 0) + 2
y = x + 2: Compare the difference and the result.
Consequently, y = x + 2 is the equation for the line a.
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Tasha is at the top of
sledding hill that has a
run of 300 feet long and a
vertical drop of 128 feet.
what is the angle of
depression of from the top
of the hill to the bottom?
The angle of depression from the top of the hill to the bottom is 23.106°.
What is Angle of Depression?Angle of depression is the angle which is between a horizontal line and the line of sight which is pointed downwards.
The figure representing the situation is given below.
From the figure, we get a right angled triangle ABC, right angle at B.
AB = 300 feet
BC = 128 feet
tan x = BC / AB
tan x = 128 / 300
tan x = 0.4267
x = tan⁻¹ (0.4267)
x = 23.106°
Hence the angle of depression is 23.106°.
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what is the coefficient of x^4y^4 in the expansion of (x+y)8?
The coefficient of the term x⁴y⁴ as required to be determined in the task content is; Choice C; 70.
What is the coefficient of the term x⁴y⁴ in the given expansion.By observation, since the expansion is to the eighth power, it follows that the number of terms in the expansion would be 9.
On this note, the x⁴y⁴ term would be the 5th term whose coefficient would be; ⁸C⁴.
Therefore, the coefficient of the x⁴y⁴ as required would be; 70.
Ultimately, Choice C is correct.
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PLEASE HELP MEEE
find the lateral area of a cone with a radius of 7ft and a slant height of 13ft use 3.14 for and round to the nearest tenth ADD EXPLANATION!!!!
The lateral area of the cone with a radius of 7ft and a slant height of 13ft is 285.7 ft².
What is the lateral area of the cone?A cone is simply a 3-dimensional geometric shape with a flat base and a curved surface pointed towards the top.
The lateral area of a cone is expressed as;
A = π × r × l
Where r is radius and l is slant height.
Given the data in the question;
Radius r = 7ftSlant height h = 13ftLateral area A = ?Plug the given values into the above formula and solve for the lateral area of the cone.
A = π × r × l
A = 3.14 × 7ft × 13ft
A = 285.7 ft²
Therefore, the lateral area is 285.7 square feet.
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Exponential Growth and Exponential Decay
There are 30 bacterial cells on a petri dish. each hour the number of cells doubles. after 5 hours, how many cells are there
a) Identify if it is growth or decay.
b) Write an equation to model the situation
c) Answer the question.
a) This situation represents exponential growth, as the number of bacterial cells is doubling every hour.
b) Let N be the number of bacterial cells on the petri dish at time t in hours. The equation to model the situation is:
N = 30 x 2^t
This equation represents exponential growth, as the number of bacterial cells is doubling every hour. The initial number of bacterial cells is 30 (when t = 0), and the number of bacterial cells at any time t is given by multiplying the initial number by 2 raised to the power of t.
c) After 5 hours, the number of bacterial cells on the petri dish is:
N = 30 x 2⁵ = 30 x 32 = 960
So there are 960 bacterial cells on the petri dish after 5 hours.
The exponential growth and exponential decayThe math subject that is relevant to the case above is exponential growth and exponential decay. These are mathematical concepts that describe the behavior of quantities that increase or decrease at a constant percentage rate over time.
Exponential growth refers to a situation where a quantity grows at a constant percentage rate over time. In the case above, the number of bacterial cells doubles every hour, which is an example of exponential growth.
Exponential decay, on the other hand, refers to a situation where a quantity decreases at a constant percentage rate over time. An example of exponential decay could be the decay of a radioactive substance.
In summary, the case above involves the mathematical concept of exponential growth, which is a key concept in the field of mathematics and has important applications in fields such as biology, economics, and finance.
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What is the area for 5ft 10 1/2 ft
The area of this rectangular figure is equal to 52 1/2 feet.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
Area of rectangular figure = 5 × 10 1/2
Area of rectangular figure = 5 × 21/2
Area of rectangular figure = 105/2
Area of rectangular figure = 52 1/2 feet.
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The base of s is the triangular region with vertices (0, 0), (8, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles.
The volume of the triangular solid is 128/3 cubic units.
The cross-sections of the triangular solid along the y-axis are equilateral triangles with side length equal to the width of the triangular base at that y-coordinate. The width of the triangular base at y = h is equal to 8 - 4h/4. So, the side length of the equilateral triangle at y = h is 8 - 4h/4.
Let's call the height of the equilateral triangle at y = h as "x". Then, using the Pythagorean theorem, we can find the relationship between x and the side length:
x^2 = (8 - 4h/4)^2 - (x/2)^2
Expanding and simplifying the right-hand side:
x^2 = 64 - 16h + h^2/16 - x^2/4
Multiplying both sides by 4:
4x^2 = 256 - 64h + h^2 - x^2
Solving for x^2:
3x^2 = 256 - 64h + h^2
Taking the square root of both sides:
x = √(256 - 64h + h^2)/√3
So, the height of the equilateral triangle at y = h is equal to x = √(256 - 64h + h^2)/√3.
The volume of the triangular solid can be found by integrating the cross-sectional area over the height of the triangular base:
V = (1/3) ∫[0, 4] x^2(y) dy
= (1/3) ∫[0, 4] (√(256 - 64h + h^2)/√3)^2 dh
= (1/3) ∫[0, 4] (256 - 64h + h^2)/3 dh
Evaluating the definite integral:
V = (1/3) * [(256h/3 - 32h^2/2 + h^3/3) |_0^4]
= (1/3) * [(256/3 * 4 - 32/2 * 4^2 + 4^3/3) - (256/3 * 0 - 32/2 * 0^2 + 0^3/3)]
= (1/3) * (256 - 128 + 64/3)
= 128/3.
Correct Question :
The base of s is the triangular region with vertices (0, 0), (8, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles. What is the volume of the triangular solid.
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Do the equations 1/5 + 2= 6 and 1/5(x +2)= 6 represent the same situation? Explain
No, the equations 1/5 + 2 = 6 and 1/5(x + 2) = 6 do not represent the same situation.
About the equationThe first equation, 1/5 + 2 = 6, is a simple arithmetic equation that can be solved to find the value of the variable. The second equation, 1/5(x + 2) = 6, is an algebraic equation that can be solved to find the value of the variable x.To solve the first equation, we can subtract 2 from both sides to get 1/5 = 4, and then multiply both sides by 5 to get 1 = 20.
This equation is not true, so there is no solution. To solve the second equation, we can multiply both sides by 5 to get x + 2 = 30, and then subtract 2 from both sides to get x = 28.
This is the solution to the equation. So, while both equations contain the same numbers and operations, they represent different situations and have different solutions.
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If the prism is surrounded by a fluid, what is the maximum index of refraction of the fluid that will still cause total internal reflection within the prism?.
The maximum index of refraction of the fluid that will still cause total internal reflection within the prism is nf = n/sinΘc.
Total internal reflection is a phenomenon in which light passes through a medium with a higher index of refraction and bounces back into the same medium instead of exiting it. This is possible when the angle of incidence is greater than the critical angle of the material.
In the case of a prism surrounded by a fluid, the maximum index of refraction of the fluid that will still cause total internal reflection within the prism can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two materials.
The critical angle of the prism can be calculated as the angle at which the sine of the angle of refraction becomes equal to 1. The critical angle can be calculated using the equation:
sinΘc = 1/n
where n is the index of refraction of the prism.
The maximum index of refraction of the fluid can then be found by rearranging Snell's law and substituting the critical angle into the equation:
nf = n/sinΘc
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Graph the angle -4pi/3 in standard position
The angle -4π/3 in its standard position is added as an attachment
How to plot the angle in its standard positionFrom the question, we have the following parameters that can be used in our computation:
Angle = -4π/3
The coordinates of this point can be found by using the formula for converting from polar to rectangular coordinates:
x = cos(-4π/3)
y = sin(-4π/3)
So, we have
x = -0.5
y = 0.86
As an ordered pair, we have
(0.86, -0.5)
This means that we plot (0.86, -0.5)
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is it always true (Dm x Dn)(X) = Dmn(X)
Answer:
No
Step-by-step explanation:
is it always true (Dm x Dn)(X) = Dmn(X)?
NO
(Dm x Dn)(x) = D²xmn
what would be the rate of change
The rate of change of the table is $0.8 per pencil
How to determine the rate of changeFrom the question, we have the following parameters that can be used in our computation:
The table of values
Using the above as a guide, we have the following:
Rate of change = Cost/Pencils
Substitute the known values in the above equation, so, we have the following representation
Rate of change = 6.4/8
Evaluate
Rate of change = 0.8
Hence, the Rate of change is $0.8
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What is the percentage of data between 20 - 50?
The percentage of data between 20 and 50 is 25%
How to determine the percentage of dataThe boxplot in the complete question is added as an attachment
From the attached box plot, we have
From the given box plot it is clear that 20 is the median and 50 is the third quartile.
As a general rule:
There are 25% of data values between the median and the third quartile.
Hence, 25% of the data values are between 20 and 50.
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The residents of a city voted on whether to raise property taxes. the ratio of yes votes to no votes was 5to 6. if there were 10,604total votes, how many yes votes were there?
The number of yes votes would be 4,836.
Solution:
Given,
The ratio of yes votes to no votes is 5:6. So, assuming the actual values of yes votes and no votes be 5x and 6x respectively. We can frame an equation as follows,
5x + 6x = 10,640
=> 11x = 10,640
=> x = 967.27272727
So, the number of yes votes would come out to be,
5*967.272727 = 4836.3636
Since the answer can not be a fractional integer,
therefore, we will round it up to 4,836.
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Alonzo borrowed money from a credit union for 2 years and was charged simple interest at an annual rate of 8%. The total interest that he paid was $1120.
How much money did he borrow?
If necessary, refAssignmener to the list of financial formulas.
$1
I need help quick
The money borrowed by Alonzo at a simple interest rate of 8% for a time period of 2 years is $7000.
What is simple interest?
In the fields of finance and economics, interest is the payment made at a set rate by a borrower or deposit-taking financial institution to a lender or depositor in excess of the principal amount (the amount borrowed). It is not the same as a fee that the borrower might pay to the lender or another entity.
Borrowers must pay lenders simple interest as a fee in exchange for a loan. For simple interest calculation, compounding interest is excluded from the calculation and just the original principal is used. Simple interest applies to all loans, not just specific ones. Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.
Given,
Time period = 2 years
Rate of interest = 8%
The simple interest paid at the end of 2 years = $ 1120
The money borrowed or the principal amount is
Simple interest = (Principal amount * rate * time)
1120 = P * 0.08 * 2
P = 1120/0.16 = $7000
Therefore the money borrowed by Alonzo at a simple interest rate of 8% for a time period of 2 years is $7000.
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An employee who receives a weekly salary of $300 and a 4% commission is paid according to the formula y = 0.04s + 300, where s represents the total weekly sales. Make a table to show an employee's weekly salary for weekly sales of $3,000, $2,340, and $4,675.
The weekly salary for weekly sales of $3,000, $2,340, and $4,675 of the employee is $420, $393.6 and $487 respectively.
Table is attached
What is commission?A commission is the extra pay to the person in the form of incentives.
Given that, an employee who receives a weekly salary of $300 and a 4% commission is paid according to the equation y = 0.04s + 300, where s represents the total weekly sales.
We are asked to find and make a table for employee's weekly salary for weekly sales of $3,000, $2,340, and $4,675.
We are given values of s,
so, weekly salary for weekly sales of $3,000
y = 0.04(3000)+300
= $420
Weekly salary for weekly sales of $2,340
y = 0.04(2340)+300
= $393.6
Weekly salary for weekly sales of $4,675
y = 0.04(4675)+300
= $487
Hence, the weekly salary for weekly sales of $3,000, $2,340, and $4,675 of the employee is $420, $393.6 and $487 respectively.
Table is attached
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Sam drive 965 mile from city A to city b ,Rita drive 1,041 mile from city C To city B
Sam travels on the highway for approximately 1.4 hours.
We know that Sam's total travel time is 1.5 hours plus the time he spends on the highway, which we'll call "x" hours. So his total travel time can be represented as:
Total travel time = 1.5 + x
We also know that the total distance he travels is 140 miles. We can use the formula:
distance = rate x time
to set up two equations, one for his travel on city roads and one for his travel on the highway. Let's start with the city roads:
distance = rate x time
distance = 35 mph x 1.5 hours
distance = 52.5 miles
So Sam travels 52.5 miles on city roads, which means he still has to travel:
140 miles - 52.5 miles = 87.5 miles
on the highway. Now we can set up an equation for his travel on the highway:
distance = rate x time
87.5 miles = 65 mph x x hours
Solving for x, we get:
x = 87.5 miles / (65 mph)
x ≈ 1.35 hours
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I have solved the question in general, as the given question is incomplete:
The complete question is:
Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads , on which can he travel an average of 35 mph for a total of 1.5 hours . Sam also takes the highway , on which he travels an average of 65 mph for a total of x hours . approximately how long does Sam travels on the highway , to the nearest tenth of an hour ?
What is the image point of (5,1) after translation right 5 units and down 2 units
The image point after the translation would be (10, - 1).
What is translation of image?The translation of image is the movement of image across the dimensional plane. It can be either horizontally {rightwards or leftwards) or vertically {upwards or downwards}.Given is the coordinate point of (5, 1).
We can write the translation rule as -
(x, y) → (x + 5, y - 2)
We can write the image point as -
(5, 1) → (5 + 5, 1 - 2)
(5, 1) → (10, - 1)
Therefore, the image point after the translation would be (10, - 1).
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which terms are used to describe events that have no outcomes in common?
The term used to describe events that have no outcomes in common is called "Mutually Exclusive."
Probability is a measure of how likely an event is to occur. The probability of an event ranges from 0 to 1, where 0 means that an event will not occur, and 1 means that an event will certainly occur.
In Mutually Exclusive events, the probability of both events happening at the same time is 0, which means that the outcome of one event completely eliminates the possibility of the outcome of the other event. The probability of getting heads and tails at the same time is 0, as it is impossible for the coin to show both heads and tails at the same time.
In mathematical terms, Mutually Exclusive events are represented by
=> P(A) + P(B) = P(A or B),
where P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A or B) represents the probability of either event A or B occurring.
To summarize, Mutually Exclusive events are events that have no outcomes in common and have a probability of 0 of occurring simultaneously.
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