the value of k such that the line through (6, 4) and (k, 2) is parallel to the line y = 2x is k = 5.
How to solve the question ?
To find the value of k such that the line through (6, 4) and (k, 2) is parallel to the line y = 2x, we need to find the slope of the line y = 2x, which is 2.
Since two lines are parallel if and only if they have the same slope, we know that the line through (6, 4) and (k, 2) must also have a slope of 2.
Using the slope formula:
slope = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) = (6, 4) and (x₂, y₂) = (k, 2), we get:
2 = (2 - 4) / (k - 6)
Multiplying both sides by k - 6 gives:
2(k - 6) = -2
Expanding and simplifying gives:
2k - 12 = -2
Adding 12 to both sides gives:
2k = 10
Dividing both sides by 2 gives:
k = 5
Therefore, the value of k such that the line through (6, 4) and (k, 2) is parallel to the line y = 2x is k = 5.
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A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:
Reason 2:
Reason 3:
Reason 4:
The table shows the multiplication of two linear expressions and the subsequent simplification and standard form conversion. The reasons given are the input expressions, Distributive property, Associative Property, simplification to standard form conversion. So, the correct option answer for reason 1, 2, 3 and 3 are B, C, A and D respectively.
The table shows the multiplication of two linear expressions is
Step Step
1 (1/4)x(5x-1)
2 (1/4)x(5x)+(1/4)x(-1)
3 (1/4)(5x^2)+(-1/4)x
4 (5/4)x^2+(-1/4)x
Reason 1: The multiplication of two linear expressions is given in the first column for each step.
Reason 2: The given linear expressions are rearranged in the second column for each step. It is Distributive Property.
Reason 3: The rearranged expressions in the second column are simplified using algebraic operations. It is Associative Property.
Reason 4: The simplified expressions in the second column are written in the standard form of a quadratic polynomial.
So, the correct order of options for reason 1, 2, 3 and 3 are B, C, A and D respectively.
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_____The given question is incomplete, the complete question is given below:
A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:
Reason 2:
Reason 3:
Reason 4:
(A)associative property of multiplication
(B)multiplication
(C)Distributive property
(D) simplify
a 1-ounce letter costs $0.50 to mail through the postal service. a 3-ounce letter costs $0.92 to mail through the postal service. the postal services calculates the weight to the whole ounce. what functions represent the total cost f(x) to send a letter that is x ounces? select all that apply. a f(x)
The function that represents the total cost f(x) to send a letter that is x ounces can be calculated as follows:
$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$
Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$
The total cost to send a letter that is 1 ounce is $0.50, and the total cost to send a letter that is 3 ounces is $0.92. Since the postal service calculates the weight to the whole ounce, if we send a 2-ounce letter, we can consider it as sending two 1-ounce letters.
Therefore, the total cost of sending a 2-ounce letter will be twice the cost of sending a 1-ounce letter.
Let f(x) be the total cost to send a letter that is x ounces.
Then,f(1) = 0.50f(2) = 2f(1) = 2(0.50) = 1.00f(3) = f(2) + 0.42 = 1.00 + 0.42 = 1.42
Hence, we can represent the function as follows:
$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$
Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$
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Need the answer to this math question pls
Answer:
B
Step-by-step explanation:
1. Add the nine over on the k side. So it will be 9+k
2. Divide both sides by 4.
4x-9=k
4x=9+k
x=k+9/4
:)
pelcentile A cumulative frequency curve; the value that would be sampled 95 out of 100 times A frequency polygon; the value in the dataset that is most likely to occur Which would be a uniform probability distribution? The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO A time period in which it rained 25% of the time and did not rain 75% of the time The probabilities of drawing any individual card in a deck with one draw Flipping a coin two times and recording whether heads or tails
The uniform probability distribution is option (c) The probabilities of drawing any individual card in a deck with one draw
The uniform probability distribution is a probability distribution where all outcomes are equally likely. Out of the options provided, (c) The probabilities of drawing any individual card in a deck with one draw is an example of a uniform probability distribution. This is because each card in a deck is equally likely to be drawn, assuming that the deck is well-shuffled.
The other options are not examples of a uniform probability distribution.
(a) The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO is not a uniform distribution because the probability of reaching 75F is not the same throughout the year, and is influenced by many factors like seasonal variation, climate changes, etc.
(b) A time period in which it rained 25% of the time and did not rain 75% of the time is not a uniform distribution since the probability of rain is not equally likely across the time period.
(d) Flipping a coin two times and recording whether heads or tails is also not a uniform distribution as the probability of getting heads or tails is not the same, it is 0.5 for each individual flip, but the probability of getting two heads, two tails or one head and one tail are different.
Therefore, the correct option is (c) The probabilities of drawing any individual card in a deck with one draw
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The given question is incomplete, the complete question is:
Which would be a uniform probability distribution? a) The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO b) A time period in which it rained 25% of the time and did not rain 75% of the time c) The probabilities of drawing any individual card in a deck with one draw d) Flipping a coin two times and recording whether heads or tails
in order to identify all the prime numbers less than 200, a person writes each number from 1 to 200, and eliminates all the multiples of 2, then all the multiples of 3. to complete this task, the person will have to eliminate the multiples of which additional numbers?
In order to identify all the prime numbers less than 200, a person will have to eliminate the multiples of 2, Multiples of 3, Multiples of 5, Multiples of 7, Multiples of 11, and Multiples of 13.
What are multiples?
Multiples are products that result from multiplying any given number by whole numbers. They are obtained by multiplying a whole number by another whole number. Prime numbers are natural numbers that are greater than 1 and have no positive divisors other than 1 and the number itself.
The number 1 is not considered a prime number. In order to identify all the prime numbers less than 200, the person will have to eliminate the multiples of the following additional numbers: Multiples of 2, Multiples of 3, Multiples of 5, Multiples of 7, Multiples of 11, and Multiples of 13
The person will have to eliminate the multiples of all these numbers to complete the task of identifying all the prime numbers less than 200.
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Simplify each expression.
We can conclude after answering the provided question that Therefore, expression the final answer is [tex]-2x^3 + x + 1.[/tex]
what is expression ?An expression in mathematics is a collection of representations, digits, and transnational corporations that depict a significant correlation or regimen. A real number, a mutable, or a combo of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, polarisation, and exponentiation. Arithmetic, arithmetic, and shape all make full use of manifestations. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
[tex]1/x - 1 = (1 - x)/x\\1/x + 1 = (1 + x)/x\\(x^2 - 1) [(1 - x)/x - (1 + x)/x + 1]\\(x^2 - 1) [(-2x)/x + 1]\\(x^2 - 1) (1 - 2x)\\x^2 - 2x^3 - 1 + 2x\\-2x^3 + x + 1\\[/tex]
Therefore, the final answer is [tex]-2x^3 + x + 1.[/tex]
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Which graph shows the solution to the system of linear equations?
y equals one third times x
x + 3y = −6
(coordinate plane with one line that passes through the points 0 comma negative 4 and 2 comma negative 5 and another line that passes through the points 0 comma 0 and 2 comma 1)
(coordinate plane with one line that passes through the points 0 comma 2 and negative 3 comma 3 and another line that passes through the points 0 comma 0 and negative 3 comma negative 1)
(coordinate plane with one line that passes through the points 3 comma negative 3 and 0 comma negative 2 and another line that passes through the points 0 comma 0 and 3 comma 1)
(coordinate plane with one line that passes through the points 0 comma 4 and negative 1 comma 1 and another line that passes through the points 0 comma 0 and 1 comma 3)
Answer:
the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).
Step-by-step explanation:
The system of linear equations can be written as:
y = (1/3)x
x + 3y = -6
To graph the system, we can graph each equation and find the point of intersection of the two lines.
The first equation y = (1/3)x has a slope of 1/3 and passes through the origin (0,0).
The second equation can be written as:
y = (-1/3)x - 2
This has a slope of -1/3 and y-intercept of -2.
To graph the system, we can plot the points (0,0) and (-6,-2) and draw a line through them. This is the graph of the second equation.
To graph the first equation, we can plot the point (3,1) and use the slope of 1/3 to draw a line passing through the origin.
The graphs of the two equations intersect at the point (-3,-1).
Therefore, the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).
Triangle RST has the coordinates R (-2, 2), S (2, 7), and T (6, 2). Which of the following sets of points represents a dilation from the origin of triangle RST?
(D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.
What is dilation?Dilation means changing the size of an object without changing its shape.
The size of the object can be increased or decreased based on the scaling factor.
In mathematics, a dilation is a function f from a metric space M to itself that satisfies the identity d = rd for every point x,y \ in M.
Where d is the distance from x to y and r is a positive real number. In Euclidean space, such extensions are spatial similarities.
So, stretching from the origin is the same as multiplying all coordinates by a number.
Only D satisfies this. We know that we multiply all the coordinates by 3 to create this set of points.
Therefore, (D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.
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Complete question:
Triangle RST has the coordinates R(1, 1), S(3, 8), and T(5, 1). Which of the following sets of points represents a dilation from the origin of triangle RST?
A. R’(3, 1), S’(3, 24), T’(15, 1)
B. R’(4, 4), S’(6, 11), T’(8, 4)
C. R’(3, 1), S’(9, 8), T’(15, 1)
D. R’(3, 3), S’(9, 24), T’(15, 3)
MODELING REAL LIFE After earning interest, the balance of an account is $420. The new balance is 7/6 of the original balance. How much interest did it earn?
Answer:
It earned $60 in interest
Step-by-step explanation:
Please show working out
There are 54 people on a coach trip to a theme park.
There are 30 adults on the coach trip.
A child's ticket costs £25 less than an adult's.
The total cost of the tickets is £1560.
How much is a child's ticket for the trip?
The cost of each Child ticket is £ 15
Total number of people = 54
Number of adults = 30
Number of Children = Total number of people - Number of adults
= 54 - 30 = 24
Cost of each adult ticket =£ x
Cost of each Child ticket = £x-25
Total Cost of tickets = £1560
The total cost of tickets =( Number of adults * Cost of each adult ticket) + (Number of Children*Cost of each Child ticket)
1560 = (30*x) + (24*(x-25))
1560 = 30x + 24 x - 600
1560 + 600 = 54x
2160 = 54x
40 = x
Therefore,
The cost of each adult ticket is £ 40
The cost of each Child ticket is £(x - 25) = £ 15
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HELP DRIVERS ED
both questions pls
20 points BOTH QUESTIONS
Answer: i can answer the first one but the second one i might get wrong
Step-by-step explanation:
for the first question answer B because external lights do not help unless it is dark, you need your battery to start the car and your fluids to keep the car running, your windshield's keep the raid and weather from entering your car as well as stopping you from flying out the window. Your mirrors help you keep track of whats behind you and showing you if you have enough space to turn.
now for the second question i would say in the manual of your car because every car has a manual to read on how to work the car/fix it
5x-4y=61 and 3x+y=23
Answer:
-14
Step-by-step explanation:
Move 4y to the right side making the equation 5x=61+4y
Then divide both sides by 5 making the equation
5x/5 = 61/5 + 4y/5
x = 61 + 4y/5
Multiply both sides by 5 making the equation 61 + 4y = 5
Move 61 to the right side making it negative which makes the equation
4y = 5-61
Divide -56 by 4 because we moved the 4 to the right side
Answer for #1 will be -14
The other one I have no idea am sorry
The solution of the Equation is x= 9 and y= -3.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have Equation,
5x - 4y = 61
and, 3x + y= 23
Now, solving the above equation we get
5x + 12x = 61 + 92
17x = 153
x= 9
and, y = 23- 27 = -4
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Which day did Walker read the fastest?
a) Day 1 - 20 pages in 35 minutes
b) Day 2 - 80 pages in 15 minutes
c) 46 pages in 65 minutes
d) 35 pages in 26 minutes
Show your work
Answer:
B.
Step-by-step explanation:
Divide ( x number of pages) by (x number of minutes) for all answers.
Day 1: 20 divided by 35= around 0.57 pg per minute
Day 2: 80 divided by 15= 5.3 pg per minute
Day 3: 46 divided by 65= around 0.70 pg per minute
Day 4: 35 divided by 26= 1.34 pg per minute.
Therefore, B is your answer!
Crown me brainliest pls!
consider the number of months since a patient had the last medical examination. this is a random variable that varies across patients. at a given point in time, this distribution can be assumed to be uniform between 4 and 20 months. consider 150 patients randomly chosen. what is the probability that the average number of months since the last examination in this random sample is 14 or larger?
The probability that the average number of months since the last examination in a sample of 150 patients is 14 or larger is practically 0, which means it is highly unlikely to occur by chance.
Now that we know the mean and standard deviation of the distribution of the sample mean, we can standardize the variable using the standard normal distribution formula:
Z = (x - μ) / (σ/√n)
where Z is the standard normal variable, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.
Substituting the values we obtained, we get:
Z = (14 - 12) / (0.237)
Z = 8.43
To find the probability that the sample mean is 14 or larger, we need to find the area under the standard normal distribution curve to the right of Z = 8.43.
This can be done using a standard normal distribution table or a calculator. The probability turns out to be practically 0.
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The Tesla electrical company charges $25 per hour to do electrical work plus a fee of $50 for the estimate on the proposed work. AC-DC electrical charges $50 per hour. Write equations to model each relationship. Let x represent the number of hours and let y represent the total cost.
Answer:
tesla: y = 25x + 50
acdc: y = 50x
Step-by-step explanation:
help with both pls and provide explanation
1) the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.
2) the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.
What is the explanation for the above response?Since f is an increasing function over its domain, if a < b, then f(a) < f(b).
We are given the inequality:
f(4x-3) ≥ f(2-x²)
Since f is increasing, this is equivalent to:
4x-3 ≤2-x²
Simplifying, we get:
x² + 4x - 5 ≥ 0
We can factor this inequality as:
(x + 5)(x - 1) ≥ 0
The solutions are x ≤ -5 or x >= 1.
However, we need to ensure that these solutions are within the domain of the function, which is given as (-8, 4).
The solution x ≤ -5 is not within the domain, so we can discard it. Therefore, the solution to the inequality is:
x ≥ 1
To summarize:
f(4x-3) ≥ f(2-x²) is equivalent to x² + 4x - 5 ≥ 0
The solution to x² + 4x - 5 ≥ 0 is x ≥ 1.
Therefore, the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.
2)
Since g is a decreasing function over its domain, if a < b, then g(a) > g(b).
We are given the inequality:
g(3² - 2x) ≥ g(3x - 2)
Since g is decreasing, this is equivalent to:
3² - 2x ≤ 3x - 2
Simplifying, we get:
11 ≤ 5x
The solution is x ≥ 11/5.
To summarize:
g(3² - 2x) ≥ g(3x - 2) is equivalent to 11 ≤ 5x.
The solution to 11 ≤ 5x is x ≥ 11/5.
Therefore, the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.
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Use the figure below to answer the following questions. NOT TO SCALE!
10
12
POSSIBLE POINTS A
a. Give the perimeter of the figure,
b. Give the area of the figure.
Juris
c. If the figure above was a yard measured in feet, and sod cost $2.99 per square foot, how much would it cost to sod the yard.
units
d. If the figure above was a garden measured in feet, and you wanted to put up edging that cost $8.87 per 6 foot piece, how much would it cost to
edge the garden? (you cannot by part of a piece) $
The required perimeter of the given figure is 68 units.
What do we mean by the perimeter?A boundary is a closed path that encloses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length.
The circumference of a circle or ellipse is called the perimeter.
Perimeter calculations have several practical applications.
Perimeter is the distance around the object.
For example, your house has a fenced garden.
The perimeter is the length of the fence.
If the yard is 50 feet by 50 feet, the fence length will be 200 feet.
So, the perimeter of the given figure:
= 10 + 4 + 2 + 12 + 6 + 6 + 6 + 2 + 12 + 4 + 4
= 68 units
Therefore, the required perimeter of the given figure is 68 units.
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Complete question:
Use the figure below to answer the following questions. NOT TO SCALE!
10
12
POSSIBLE POINTS A
Give the perimeter of the figure.
If
�
1
=
8
a
1
=8 and
�
�
=
−
3
�
�
−
1
−
2
a
n
=−3a
n−1
−2 then find the value of
�
5
a
5
.
The value of a₅ is 688. The problem provides us with a recursive formula that relates each term of the sequence to the previous term.
We can use this formula to find the value of any term in the sequence, given the value of the previous term.
The recursive formula is:
aₙ = -3aₙ₋₁ - 2
This formula tells us that to find the value of aₙ, we need to take the previous term aₙ₋₁, multiply it by -3, and then subtract 2.
The problem also provides us with the value of the first term a₁, which is 8. Using the recursive formula, we can find the value of the second term a₂:
a₂ = -3a₁ - 2 = -3(8) - 2 = -26
We can repeat this process to find the value of the third term a₃:
a₃ = -3a₂ - 2 = -3(-26) - 2 = 76
Continuing in this manner, we can find the values of a₄ and a₅:
a₄ = -3a₃ - 2 = -3(76) - 2 = -230
a₅ = -3a₄ - 2 = -3(-230) - 2 = 688
Therefore, the value of a₅ is 688.
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If a₁ = 8 and aₙ = -3aₙ₋₁ - 2, then what is the value of a₅?
Abama Math-5th Grade 1. James is starting a new business in Sitka, AK. He will need to fly from his home in Montgomery to Sitka and back 15 times in the next year. The trip is 2,856 miles one-way. How many miles will James be flying in the next year? (multiplication) Megan's aquarium measuron miles
James will be flying a total of 85,680 miles in the next year.
To find out how many miles James will be flying in the next year, we need to multiply the distance of one round trip by the number of round trips he will make in a year.
The distance of one round trip is twice the one-way distance, so:
2 x 2,856 miles = 5,712 miles per round trip
Since James will make 15 round trips in a year, we can multiply the distance of one round trip by 15:
5,712 miles/round trip x 15 round trips = 85,680 miles
Therefore, James will be flying a total of 85,680 miles in the next year.
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after many (approaching infinity) battles, what is the steady-state probability distribution of kecleon type? (your answer should be three numbers that sum to one.)
Probability distribution after two battles: Dark 1/3, Psychic 1/3, Fighting 1/3 Steady-state probability distribution: Dark 1/3, Psychic 1/3, Fighting 1/3. Probability distribution after two battles: Dark 1/4, Psychic 1/4, Fighting 1/4, Ghost 1/4. Steady-state probability distribution: Dark 1/6, Psychic 1/6, Fighting 1/2, Ghost 1/6
If Kecleon starts as the Fighting type and battles twice, the probability distribution of Kecleon's type is (1/3, 1/3, 1/3).
After many battles, the steady-state probability distribution of Kecleon's type is (1/3, 1/3, 1/3). This is because Kecleon has an equal chance of winning and losing battles against each of the other types, and so over time its type will converge to a uniform distribution.
If Kecleon starts as the Fighting type when Ghost Pokémon arrive and battles twice, the probability distribution of Kecleon's type is (1/4, 1/4, 1/4, 1/4).
After many battles, the steady-state probability distribution of Kecleon's type is (1/6, 1/6, 1/2, 1/6). This is because the presence of Ghost Pokémon alters the dynamics of the battles, causing Kecleon's type to converge to a non-uniform distribution where it is more likely to become a Psychic type due to the dominance of Ghost-type Pokémon over Fighting and Dark types.
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--The given question is incomplete, the complete question is given
" In a particular region of the Pokémon world, there are just three types of Pokémon: Dark, Psychic, and Fighting. Kecleon, the Color Change Pokémon, has the ability to change its type to blend into its surroundings. Its goal is to become the best type. It seeks to accomplish this goal by choosing a type of Pokémon to battle uniformly at random; it may choose a Pokémon of its own type. If it wins the battle, it will keep its old type. If it loses, it will take on the type of the Pokémon that defeated it. It continues this process indefinitely. For all questions assume that Dark Pokémon always defeat Psychic Pokémon, Psy- chic Pokémon always defeat Fighting Pokémon, and Fighting Pokémon always defeat Dark Pokémon. If two Pokémon of the same type battle, each has an equal chance of winning. a) Suppose that Kecleon starts as the Fighting type. After two battles, what is the probability distribution of Kecleon's type? (Your answer should be three numbers that sum to one.) b) After many (approaching infinity) battles, what is the steady-state probability distribution of Kecleon's type? (Your answer should be three numbers that sum to one.) A nearby graveyard is haunted! Ghost-type Pokemon invade the population. Assume that Ghost Pokémon always lose to Dark Pokémon, and always win against Psychic Pokémon and Fighting Pokémon. c) Suppose that Kecleon starts as the Fighting type when the Ghost Pokémon arrive. After two battles, what is the probability distribution of Kecleon's type? (Your answer should be four numbers that sum to one.) d) After many (approaching infinity) battles, what is the steady-state probability distribution of Kecleon's type? (Your answer should be four numbers that sum to one.)"--
Which one is the correct answer?
The statements that describe the graph of f function are A) Asx → ∞, f(x) → -4 and C) The y-intercept is (0, -3).
How to analyze a graphical expression?Let's analyze the given function:
f(x) = 9(1/3)ˣ⁺² - 4
Now, let's analyze the properties of the graph:
A) As x → ∞, f(x) → -4.
As x → ∞, the exponential term ((1/3)ˣ⁺²) approaches 0, so f(x) = 9(0) - 4 = -4. This statement is correct.
B) As x → -∞, f(x) → -∞.
As x → -∞, the exponential term (1/3)ˣ⁺² approaches ∞, so f(x) = 9(∞) - 4 → ∞, not -∞. This statement is incorrect.
C) The y-intercept is (0, -3).
To find the y-intercept, we can plug x = 0 into the function:
f(0) = 9(1/3)ˣ⁺² - 4 = 9(1/9) - 4 = 1 - 4 = -3
The y-intercept is (0, -3), so this statement is correct.
D) The domain is {x | x > -2}
This is incorrect. The domain of the given function is all real numbers because there is no restriction on the value of x.
E) The range is the set of real numbers.
This is incorrect. The range of the given function is {y | y > -4} since the function approaches -4 as x goes to ∞, but never reaches -4, and it increases as x goes to -∞.
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Image transcribed:
Identify the statements which describe the graph of f(x) = 9(1/3)ˣ⁺² - 4.
Select all that apply.
A) Asx → ∞, f(x) → -4.
B) Asx → -∞, f(x) →-∞.
C) The y-intercept is (0, -3).
D) The domain is {xlx > -2}
E) The range is the set of real numbers.
A box is 21 centimeters tall how tall would the box measure in meters
Answer: Correct me if I'm wrong but it should be about 1/4th of a meter
Help with geeomtry with trapezoids. IJKL is a trapezoid with bases LK and IJ. If m < JKL = 71 degrees and m < IJL = 42 degrees, find m < LJK.
7. Write the equation of a line passing through the points (4,-3) and (16, 6). Show all of your work.
15 is the distance of the equation of a line passing through the points.
What is distance ?
Distance is the separation between two objects. Moreover, it serves as a gauge for the distance between two objects. It is measurable along any route. So even though his position does not change, a person who circles about has moved a certain amount of distance.
the points (4,-3) and (16, 6)
D = √(x₂ - x₁)² + (y₂ - y₁)²
= √(16 - 4)² + (6 -(-3)²
= √(12)² + (9)²
= √144 + 81
= √225
= 15
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Emily bought some ice cream cones for noche buena which costs 24 she paid M and got back 6 of change. Find M
Emily paid M = 30 for the ice cream cones.
To find the amount Emily paid (M), we can set up an equation using the given information.
1. The cost of the ice cream cones is 24.
2. She got back 6 in change.
Using these facts, we can write the equation:
M - 24 = 6
Now, let's solve for M:
Step 1: Add 24 to both sides of the equation.
M - 24 + 24 = 6 + 24
Step 2: Simplify.
M = 30.
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help please !!!
solve for x. x/8 =
The value of x in the right triangle is 4√2 units.
How to find the sides of similar triangles?Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.
Therefore, the triangles are similar. Let's use this similarity to find the value of x in the triangles.
Hence, using proportion,
x / 8 = 4 / x
cross multiply
x² = 8 × 4
x² = 32
square root both sides of the equation
x = √32
x = √16 × 2
x = 4√2 units
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how do u do these and how to show ur work
Answer: 1. 37.5%,
Step-by-step explanation:
1. we can solve this using a proportion, 10/13.75 = 100/x
a. using cross multiplication we get 10x = 1375
b. when you simplify you get x= 137.5, the percent it was of the whole
c. then subtract the original 137.5-100, and you get 37.5%
The rest of the problems follow a similar fashion
the serum cholesterol levels of a population of 12 to 14-year-olds follow a normal distribution with mean 155 mg/dl and standard deviation 27 mg/dl. suppose we were to choose at random from the population nine 12- to 14-year-olds. what is the probability that the sample mean cholesterol value be between 145 and 165 mg/dl? (round to four decimal places)
The probability that the sample mean cholesterol value be between 145 and 165 mg/dl is 0.288893452 or 28.89% .
What is probability?
Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.
We first get the z score for the two values. As z =[tex]\frac{x-\mu}{\sigma}[/tex] , then as
x1 = lower bound = 145
x2 = upper bound = 165
μ= mean = 155
σ = standard deviation = 27
Thus, the two z scores are
=> [tex]z_1[/tex] = lower =>z score = [tex]\frac{X_1-\mu}{\sigma}[/tex] = -0.37037037
=> [tex]z_2[/tex]= upper => z score = [tex]\frac{X_2-\mu}{\sigma}[/tex] = 0.37037037
Using table/technology, the left tailed areas between these z scores is
=>P(z < z1) = 0.355553274
=>P(z < z2) = 0.644446726
Thus, the area between them, by subtracting these areas, is
=>P(z1 < z < z2) = 0.288893452 or 28.89%.
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Question 12(Multiple Choice Worth 2 points)
(Laws of Exponents with Integer Exponents MC)
Which expression is equivalent to (10-2.45)-22
104
410
104
410
104
43
104
Answer:
a) 10^4/4^10
Step-by-step explanation:
10^-2 = 1/10^2
4^5 x 1/10^2 = 4^5/10^2
(4^5/10^2)^-2 = (10^2/4^5)^2 = 10^4/4^10
On Saturday morning, Wendy watched one and a half hours of her favorite shows on television. During the shows there were 18 commercials. What is the unit rate of commercials per hour?
12 commercials per hour
14 hours per commercial
16 commercials per hour
18 commercials per hour
Unit rate of commercials per hour is 12 commercials per hour based on division in mathematics.
We must divide the number of ads by the number of hours in order to determine the unit rate of commercials per hour.
Wendy watched her favourite television programmes for an hour or an hour and a half. There were 18 advertisements running at this time.
So, the unit rate of commercials per hour can be calculated as:
18 commercials ÷ 1.5 hours = 12 commercials per hour
So, it is possible to compute the number of ads each hour as follows: 18 commercials divided by 1.5 hours equals 12 commercials every hour.
Consequently, 12 commercials are broadcast each hour as the unit rate of commercials.
This indicates that while viewing her favorite television programes, Wendy saw 12 adverts every hour on average.
It's crucial to remember that unit rate come in handy when comparing two quantities that are measured using various units. In this instance, we were comparing two different units of measurement: the quantity of advertising and the amount of time in hours. By providing the rate at which the quantity is changing per unit of time, the unit rate enables us to meaningfully compare them.
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