a) The number of microstates associated with tossing a coin N times and having it come up H times heads and T times tails is given by the binomial coefficient "N choose H" (or "N choose T", as H+T=N), which is equal to N!/(H! * T!)
b) For a series of 1000 tosses, with 50% heads and 50% tails, there are a total of "1000 choose 500" microstates. This is approximately 2.07*10²⁵ microstates.
c) The probability of getting a specific outcome when tossing a coin is given by the binomial probability mass function. The probability of getting 40% heads and 60% tails in 1000 tosses is given by (1000 choose 400)(0.4⁴⁰⁰)(0.6⁶⁰⁰) which is very less probable.
Coin Toss Microstates Probabilitya) The number of microstates associated with a coin flip can be determined using combinatorics. The coin flip can have two possible outcomes: heads or tails. To calculate the number of microstates for N coin flips with H heads and T tails, we use the binomial coefficient formula "N choose H" (or "N choose T", as H+T=N), which is equal to N!/(H! * T!) where ! denotes factorial. This formula gives the number of ways to choose H heads out of N coin flips.
b) To calculate the total number of microstates for a series of 1000 tosses with 50% heads and 50% tails, we use the binomial coefficient formula "1000 choose 500". This is equivalent to (1000!/(500!500!)) which is approximately 2.0710²⁵ microstates.
c) The probability of getting a specific outcome when tossing a coin is given by the binomial probability mass function. The probability of getting 40% heads and 60% tails in 1000 tosses is given by (1000 choose 400)(0.4⁴⁰⁰)(0.6⁶⁰⁰) which is very less probable. We can calculate this using the binomial probability mass function which is ( n choose k ) * p^k * (1-p)^(n-k) where n is the number of trials, k is the number of successful outcomes, p is the probability of success in one trial, 1-p is the probability of failure in one trial.
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umb
1 MP Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 1/8 pounds of soil
and a box with 1 3/4pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
No, she does not have enough soil as she needs 4 pounds of soil.
What is meant by soil?
A mixture of organic material, minerals, gases, liquids, and living things make up soil, often known as earth or dirt, and they work together to support life. Certain scientific definitions separate dirt from soil by limiting the former term to just displaced soil.The field of edaphology investigates how soils affect living beings.The study of how soils are formed, described (morphology), and categorized in their natural environments is known as pedology.In engineering, the term "soil" is used to refer to loose material that is present on the Moon and other celestial bodies, as well as other loose material that is found above the bedrock.she as = 2 1/8 + 1 3/4
= 17/8 + 7/4
= 17+ 7 × 2 / 8
= 17 + 14 / 8
= 31/8
= 3 7/8 pounds
≤ 4 pounds.
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the distance around a standard tennis court is 228 feet. if the length of the court is 30 feet more than twice the width, find the dimensions of the tennis court
The dimensions of the tennis court are 42 feet by 114 feet.
Let the width of the tennis court be x feet.
We can use the formula for perimeter to solve this problem. The perimeter of a rectangle is equal to 2 times the length plus 2 times the width.
2(2x + 30) + 2x = 228
4x + 60 = 228
4x = 168
x = 42
The length of the tennis court is 2x + 30 = 2(42) + 30 = 114 feet.
The dimensions of the tennis court are 42 feet by 114 feet.
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TUESDAY 1. Allison had one string that was 10 meters long. She used 5.834 meters for her project. What is the length of the string in meters Allison had left?
Each cut piece measures 6.25 meters in length.
What is dividing?One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.
One of the fundamental mathematical operations is division, in which a bigger number is divided into smaller groups with the same number of components.
Given
The thread was divided into 4 equal pieces after being cut at 25 meters.
= 25/4 \s = 6.25.
The thread was divided into 4 equal pieces after being cut at 25 meters.
= 25/4 \s = 6.25.
Each cut piece measures 6.25 meters in length.
The complete question is,
A 25 meter distance. Cindy cut the string into four equal pieces. each component's quality.
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Can you please explain step by step more brought and clearly that how 2x^3-x^2-2x+1 becomes (x-1)(2x^2+x-1)
i am not able to understand please answer Asap
I will make you Brainiest
Answer:
Step-by-step explanation:
it is simply factorized.
as we have 2x³-x²-2x+1
we will take common number and variable from it
So as we can see that in this polynomial we can take x-1 common
we will take x-1 common and write the rest polynomial
As we will multiply x-1 with 2x²+x-1
it will give the previous answer or nmber
The mean is calculated for for 551 respondents and the result is 1.5
The level of measurement of the data can be given as follows:
Interval or ratio.
How to obtain the levels of measurement of the data?There are four levels of measurement for the data, given as follows:
Nominal.Ordinal.Interval.Ratios.The measures of central tendency for each level are given as follows:
Nominal: ModeOrdinal: Mode and median.Interval: Arithmetic mean, mode and median.Ratios: Arithmetic mean, geometric mean, mode and median.For this problem, we have the arithmetic mean, meaning that the level of measurement can be either interval or ratio.
Missing InformationThe problem asks for the level of measurement of the data.
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Assume that K and M are two unlinked genes that affect hearing. The dominant K allele is necessary for hearing, and the dominant M allele causes deafness regardless of the other genes present. What fraction of the offspring of parents with the genotypes KkMm and Kkmm will most likely be deaf?
**Please draw the punnet sqaure and explain the answer in detail.
a) 1/4
b) 3/8
c) 1/2
d) 5/8
The dominant K allele is necessary for hearing, and the dominant M allele causes deafness regardless of the other genes present. What fraction of the offspring of parents with the genotypes KkMm and Kkmm will most likely be deafi is 1/2 so c option is correct
The percentage that the offspring will be deaf is 75%. Two punnet squares are needed each for km and Kkmm individuals. In punnet square 1, half of the genotypes are Km and km while half are Mm and kk in punnet square 2. The two punnet squares are then combined to form a final one where a quarter of the offspring is deaf.
What does genotype mean?
In a wide sense, the word"genotype" refers to the genetic makeup of an organism; it defines an organism's complete set of genes. In a more thin sense, the term can be used to guide the alleles, or variant forms of a gene, that are carried by an organism.
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Triangle A C B is cut by line segment E D. Line segment E D goes from side B C to side A C. The length of B A is 4 x minus 6 and the length of E D is x + 2. The length of B E is x. Sides B E and E C are congruent. Sides A D and D C are congruent.
What is the length of BC?
From the markings on the diagram, we can tell E is the midpoint of BC and
D
is the midpoint of AC
We can apply the
theorem: ED = One-halfBA.
Substituting in the expressions for the lengths and solving for x, we get x =
.
Now, since BE = x, then BC =
.
Applying the Midsegment Theorem, the length of BC is: 10.
What is the Midsegment Theorem?The Triangle Midsegment Theorem states that in a triangle, a line segment connecting the midpoints of two sides is parallel to the third side and is half as long.
From the information given we know that:
E is the midpoint of BC and D is the midpoint of AC.
Thus, applying the Midsegment Theorem, we have:
ED = 1/2(BA)
Substituting the values not expressive, we would get:
x + 2 = 1/2(4x - 6)
2(x + 2) = 4x - 6
2x + 4 = 4x - 6
2x - 4x = -4 - 6
-2x = -10
x = 5
BE = x = 5
Therefore, BC = 2(5) = 10.
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the sum of 6 and the square of 12
the quotient of 30 and the sum of 5 and 7
the difference of 4 cubed and 25
5 more than the product of 12 and 8
The solutions are 150, 2.5, 39 and 101. The solutions have been obtained using the arithmetic operations.
What are arithmetic operations?
In all, there are four basic mathematical operations which are applicable for all the real number. The operations are as follows:
1.Addition(‘+’) operation which gives the sum of the numbers.
2.Subtraction(‘-’) operation which gives the difference of the numbers.
3.Multiplication(‘×’) operation which gives the product of the numbers.
4.Division(‘÷’) operation which gives the quotient of the numbers.
1. The sum of 6 and the square of 12
The square of 12 = 12*12 = 144
Sum of 6 and 144 = 6 + 144 = 150
2. The quotient of 30 and the sum of 5 and 7
The sum of 5 and 7 = 5 + 7 = 12
The quotient of 30 and 12 = 30 ÷ 12 = 2.5
3. The difference of 4 cubed and 25
The cube of 4 = 4*4*4 = 64
The difference of 64 and 25 = 64 - 25 = 39
4. 5 more than the product of 12 and 8
The product of 12 and 8 = 12*8 = 96
5 more than 96 = 5 + 96 = 101
Hence, the solutions are 150, 2.5, 39 and 101.
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What is the answer to the equation
Z - 2/5=1/3
Answer:
To solve the equation Z - 2/5=1/3, we need to get Z alone on one side of the equation.
First we add 2/5 to both sides of the equation to get
Z - 2/5 + 2/5 = 1/3 + 2/5
Z = 1/3 + 2/5
To combine the fractions on the right side of the equation, we need to find a common denominator.
The common denominator of 1/3 and 2/5 is 15
So we can convert 2/5 to 9/15
Z = 1/3 + 9/15
Now we can add the fractions
Z = 12/15 + 9/15
Z = 21/15
So the solution to the equation is Z = 21/15
Step-by-step explanation:
Please help me I don’t know
Note that in the above problem where a marine biologist uses the triangles shown in the diagram to measure the width of an oil spill in the bay from a safe distance on shore, note that the width of the oil spill is 20m. See the proof below.
What is the rationale for the above response?In ΔABC and ΔDEC, Note that since
DC = BC; and
EC = AC
It means that ∠DCE = ∠ACB (Diagonal Equality)
⇒ ΔABC ≅ ΔDEC
Therefore:
DE = AB
Since AB = 20m,
DE is also = 20m.
Thus, it is correct to state that the width of the oil spill is 20m.
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The picture shows six equal squares. The total is 54ft2. What is the perimeter?
Answer:
72ft
Step-by-step explanation:
Area of one square = 54ft^2/6 = 9ft^2
The side of the square is the square root of the area, so the side length of one square is
√9ft^2 = 3ft.
each square has a perimeter of
4*3ft = 12ft.
So the perimeter of all six squares is
12ft * 6 = 72ft
A bag of m & m is dumped on the table and you count 82 blue pieces.approximately how many m&ms do you expect to be in the entire bag based on the entire class. Round to the nearest whole m&m
Answer: Based on the information provided, we can use the proportion of blue m&ms found in the sample (82 out of some larger total number of m&ms) to estimate the total number of m&ms in the entire bag.
If we let x be the total number of m&ms in the bag, we can set up the proportion:
82/x = blue m&ms / total m&ms
To solve for x, we can cross-multiply and divide by 82:
x = 82 * total m&ms / blue m&ms
x = 82 * 1
x ≈ 82
Therefore, based on the sample, we expect there to be approximately 82 m&ms in the entire bag, rounded to the nearest whole m&m.
It's worth noting that this is an estimation, and the actual number of m&ms in the bag may be different.
Step-by-step explanation:
1. If SW = 25 and ST = 24, find the area of rectangle RSTW.
2. If SZ = 25 and WT = 14, what is ST?
1. Using the Pythagoras theorem, the area of the rectangle RSTW is 168 units².
2. Using the Pythagoras theorem, the measure of line segment ST is 48 units.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The diagonal SW measures = 25 units
The breadth ST measures = 24 units.
Applying the Pythagoras theorem -
(Hypotenuse)² = (Base)² + (Perpendicular)²
Substituting the values in the equation -
(SW)² = (ST)² + (WT)²
(25)² = (24)² + (WT)²
(WT)² = (25)² - (24)²
(WT)² = 625 - 576
(WT)² = 49
WT = √49
WT = 7 units
The length WT measures = 7 units
The formula for the area of the rectangle is -
Area = Length × Breadth
Area = WT × ST
Area = 7 × 24
Area = 168 units²
Therefore, the area of the rectangle is obtained as 168 units².
The line segment SZ measures = 25 units
According to the properties of rectangle the diagonals bisect each other.
So, the measure of SW = 2(SZ) = 50 units
The length WT measures = 14 units
Applying the Pythagoras theorem -
(Hypotenuse)² = (Base)² + (Perpendicular)²
Substituting the values in the equation -
(SW)² = (ST)² + (WT)²
(50)² = (ST)² + (14)²
(ST)² = (50)² - (14)²
(ST)² = 2500 - 196
(ST)² = 2304
ST = √2304
ST = 48 units
Therefore, the breadth ST measures = 48 units.
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Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. y = 5 3√x , y = 0, x = 1
The volume of the cylinder is
V = 2πr ∫ x h(x) dx.
Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.
The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
I first found what x=1 would be in terms of y.
y=(2)3=8
And in terms of y, the original equation becomes:
y=x3x=y13
See the image as the answer is given in the image down below.
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The volume of the cylinder is V = 2πr ∫ x h(x) dx.
Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness.
The formula sums the volume of a cylindrical shell over the radius of the cylinder, and the volume of a cylinder is given by V=2πrh V = 2 π r h where r is the radius and h is the height.
I first found what x=1 would be in terms of y.
y=(2)3=8
And in terms of y, the original equation becomes:
y=x3x=y13
See the image as the answer is given in the image down below.
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In the figure below, suppose that m∠PSQ=(5x−12)∘ and m∠QSR=(10x−3)∘. What is the value of x?
Please and thank you!!!
Considering the figure, the value of x is calculated using adjacent angles concept and it is solved to be
7How to solve for xThe angle at PSR is 90 degrees
Also, angle PSQ and angle QSR are adjacent angles hence
angle PSQ + angle QSR = angle PSR = 90
90 = (5x − 12)∘ + (10x − 3)
opening the parenthesis
90 = 5x − 12 + 10x − 3
collecting like terms
90 + 12 + 3 = 5x + 10x
105 = 15x
isolating x by dividing through by 15
15x / 15 = 105 / 15
x = 7
hence the value of x is 7
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Ivan's company makes solid spherical balls out of scrap metal for various industrial uses. A large order just came in to make lead balls with a radius of 3in. If Ivan uses, on average, 28,260in3 of lead each day making these balls, how many balls does he make, on average, each day?
If necessary, refer to the list of geometry formulas.
For your calculations, do not round any intermediate steps, and use the π button on the ALEKS calculator. Round your answer to the nearest hundredth.
balls
Answer: To find the number of balls Ivan makes each day, we need to divide the total volume of lead used each day by the volume of one ball.
The formula for the volume of a sphere is:
V = (4/3) * π * r^3
Where V is the volume, π is pi and r is the radius of the sphere.
We know the radius of the sphere is 3 inches so we can use this information to find the volume of one ball.
V = (4/3) * π * 3^3
V = (4/3) * π * 27
V = 36 * π
Now we know the volume of one ball is 36π cubic inches, we can divide the total volume of lead used per day by the volume of one ball to find the number of balls made per day.
28,260 in^3 / 36π in^3/ball = 785.833 balls/day
Rounding to the nearest hundredth, Ivan on average makes 785.83 balls/day.
Step-by-step explanation:
F(x)=4x^3+7x^2+8x and g(x)=7x^2-7x, find (f-g)(x) and (f-g)(0)
Answer:
(f-g)x is the same as f(x)-g(x)
(f-g)x= 4x^3+7x^2+8x-(7x^2-7x)
= 4x^3+7x^2-7x^2+8x+7x
=4x^3+0+15
=4x^3+15
(f-g)0= 4(0)^3+15
=0+15
=15
Please solve ASAP.
Will give brainliest!!
Thank you!
Answer:
Step-by-step explanation:
5
The angle of depression from the top of a cliff to a nearby town is 10 degrees.
If the top of the cliff is 354 feet above the town, how far is the town from the base of the cliff?
The distance of the town from the base of the cliff is; 62.42 ft
How to use trigonometric ratios?The 6 trigonometric ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/ adjacent
sec θ = 1/cos θ
cosec θ = 1/sin θ
cot θ = 1/cot θ
We are given the angle of depression as 10 degrees. By definition of alternate angles, the angle the hypotenuse formed will make with the base of the town is 10 degrees.
Since the height from the cliff to the town is 354 ft, then we can use trigonometric ratio to find the distance of the town from the base of the cliff as;
354/adjacent = tan 10
adjacent = 354 * tan 10
adjacent = 62.42 ft
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What is the arc of WY
The angle ∠G will be 140° for the given curve.
What is the arc of the circle?An arc is a section of a circle's or curve's boundary in mathematics. It is additionally known as an open curve. The circumference also referred to as the perimeter, is the measurement around a circle that defines its edge.
Given that the angle ∠I is equal to 70°. The value of angle G will be calculated by the angle of the arc theorem.
One-half the size of the central angle is the size of an angle that is inscribed in a circle. Congruent inscribed angles are those that intersect the same arc.
∠I = ( 1 / 2 ) x ∠G
∠G = 2 x ∠I
∠G = 2 x 70
∠G = 140
Hence, the angle ∠G will be 140.
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lucy is five years older than linus. four years ago, eight times linus' age equaled three times lucy's age.
Answer: 3
Step-by-step explanation:
2/3 4/6
A restaurant server believes the distribution of their tips has a model that is slightly skewed to the left, with a mean of $10.70 and a standard deviation of $6.70. They
usually wait on about 60 parties over a weekend of work.
a) Estimate the probability that they will earn at least $800 in tips.
b) How much do they earn on the best 10% of such weekends?
Answer:
a) To estimate the probability that the server will earn at least $800 in tips, we need to use the cumulative distribution function (CDF) of the normal distribution, since the mean and standard deviation of the tips are given. The CDF of the normal distribution with mean μ and standard deviation σ is given by F(x) = P(X <= x) = (1/2)(1 + erf((x-μ)/(σ * sqrt(2)))
We can use this formula to find the probability that the server will earn at least $800 in tips. We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the CDF of the normal distribution with μ = $10.70 and σ = $6.70.
P(X >= 800) = 1 - P(X <= 800) = 1 - F(800)
b) To find out how much the server earns on the best 10% of such weekends, we need to find out what the 90th percentile of the distribution is. We can use the inverse cumulative distribution function (ICDF) of the normal distribution to find this. The ICDF of the normal distribution with mean μ and standard deviation σ is given by x = μ + σ * sqrt(2) * erf^-1(2F(x) - 1)
We know that the mean of the tips is $10.70, and the standard deviation is $6.70. Therefore, we can calculate the ICDF of the normal distribution with μ = $10.70 and σ = $6.70.
Then we can find the 90th percentile: x = $10.70 + $6.70 * sqrt(2) * erf^-1(2*0.1 - 1)
Please note that the above calculation required erf^-1(inverse error function) which is not a standard function on most calculators, you may need to use a software/programming language to find it.
square corners, 5 units on a side, are removed from a 20 unit by 30 unit rectangular sheet of cardboard. the sides are then folded to form an open box. the surface area, in square units, of the interior of the box is
The surface area of the interior of the box is the total area of the interior walls of the box.
This can be calculated by subtracting the area of the 5 unit square removed from the total area of the original 20 by 30 unit rectangular sheet of cardboard. This gives us an area of 450 units. To calculate the area of the interior walls, we need to multiply the length and width of the remaining rectangle. This gives us a length of 15 units and a width of 25 units, which gives us a total area of 375 units. Therefore, the surface area of the interior of the box is 375 square units. We can calculate this using the formula A = L x W, where A represents the area, L represents the length and W represents the width.
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help me slove this math please
By Linear Function f(x) = -4 + 2 and g(x) = x - 3 this we get the Value -2.
How to Find a Linear Function?The slope-intercept form or the point-slope form are used to find a linear function.
With the aid of an example, the procedure for determining a linear function is the same as determining a line's equation.
When "m" and "b" are real numbers, then a function has the form f(x) = mx + b.
Examples :
f(x) = -4 + 2,g(x) = x - 3: -2
Steps
Find f ° g given f(x) = -4 + 2, g(x) = x - 3
f ° g = f(g (x))
Constant function results in a constant
f (x ) = -4 + 2
-4 + 2 = -2
Answer = -2.
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Select all ratios equivalent to 12:6.
10:5 18:9 11:2
The ratios that are equivalent to 12:6 are (a) 10 : 5 and (b) 18 : 9
How to determine the equivalent ratioFrom the question, we have the following parameters that can be used in our computation:
Ratio = 12 : 6
Divide both sides of this ratio by 6
So, we have the following representation
Ratio = 2 : 1
Multiply the ratio by 9
Ratio = 18 : 9
Multiply the ratio by 5
Ratio = 10 : 5
Hence, the equivalent ratios are 10:5 and 18:9
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in a flight simulation test, a particular pilot among a group of pilots receives a very low score. however, when he takes the test after six months, he performs considerably better and his scores are closer to the average of the group. which of the following is most likely to account for the higher scores?
Regression toward the mean is most likely to account for the higher scores. So the option 2 is correct.
The answer to this query is based on a long-term investigation. An observational study that tracks the same people across time, sometimes from birth to death, is called a longitudinal study.
The right response is regression to the mean. When a sample point for a random variable is extreme, regression toward the mean is the phenomena that results, with subsequent measurements, in a point that is closer to the mean or average.
This is your response with justification. You can find me in the comments section if you have any questions or doubts about the question or the answer, though.
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The complete question is:
In a flight simulation test, a particular pilot among a group of pilots receives a very low score. However, when he takes the test after six months, he performs considerably better and his scores are closer to the average of the group. Which of the following is most likely to account for the higher scores?
1. instrument decay
2. regression toward the mean
3. carryover effects
4. fatigue effects
The function f(x)=x is translated 4 units left and 3 units up. Which function represents the transformation?
A function that represents the transformation include the following: B. g(x) = (x + 4) + 3.
What is a translation?In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image or function.
Conversely, the translation a geometric figure or graph upward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image or function.
By translating the pre-image vertically upward by 3 units and horizontally left by 4 units, the function becomes;
f(x) = x
f(x) → g(x) = (x + 4) + 3.
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Plot the image of point QQQ under the translation (x,y)\to(x+1,y+2)(x,y)→(x+1,y+2)left parenthesis, x, comma, y, right parenthesis, \to, left parenthesis, x, plus, 1, comma, y, plus, 2, right parenthesis.
The coordinates of the image of the point Q is Q'(3, 6).
What is Geometric Transformation?Transformation of geometrical figures or points is the manipulation of a given figure to some other way.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
From the given graph, we have point Q(-4, 4).
Here the point is translated.
After translation, the original figure is shifted from a place to another place without affecting it's size.
The rule of translation is given as the point (x, y) is translated as (x + 1, y + 2).
So the given point is (-4, 4).
(-4, 4) after translation becomes by the definition (-4 + 1, 4 + 2).
So the required point is (-3, 6).
Hence the image of point Q is (-3, 6).
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Your question is incomplete, Probably, the correct graph for the question is given below.
What is the ratio of red apples to all apples in the basket?
What is the ratio of red apples to green apples?
Answer: a) 8:6
b) 8:14
Step-by-step explanation:
You got the answer correct for a but you have to switch the numbers around because the ratio of red apple to green apples is 8:6
Write the following set as an interval using interval notation.
{x|−7
Answer: The set {x|−7 < x} can be written in interval notation as (-infinity, -7) < x.
This set represents all real numbers greater than -7. The interval notation uses the less-than symbol (<) to represent that all values of x greater than -7 are included in the set. The interval notation uses the infinity symbol to represent the fact that there are no limits on the lower end of the interval.
It's important to note that the interval notation includes the endpoint values when it is in the form of (a,b) or [a,b) but it does not include endpoint values when it is in the form of (a,b] or [a,b].
Step-by-step explanation: