Andrés is 35 years old, Carlos is 31 years old, and Rodolfo is 24 years old based on the sum is given.
Let's assume the age of Andrés is x years.
According to the problem, Carlos' age is (x - 4) years and Rodolfo's age is (x - 11) years.
Now, we know that the sum of their ages is 90, so we write an equation:
x + (x - 4) + (x - 11) = 90
Simplify following equation:
3x - 15 = 90
Adding 15 to both sides, we get:
3x = 105
Dividing by 3, we get:
x = 35
So Andrés' age is 35 years.
Carlos' age is (x - 4) = 31 years.
Rodolfo's age is (x - 11) = 24 years.
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Translation: The sum of the ages of Andrés, Carlos and Rodolfo is 90 years. Andrew's age exceeds Carlos' age by 4 years and Rodolfo's by 11. Determine the ages of all three
Find the difference
Answer:
Step-by-step explanation:
425 - 59 is 366
:)
Answer:
366.
Step-by-step explanation:
Identify the area of a regular pentagon with side length 21
in.
rounded to the nearest tenth.
The area of regular pentagon is 758.7 square in.(rounded to the nearest tenth.)
What is pentagon?A pentagon is a specific type of polygon with 5 sides and 5 angles. The word “pentagon” is constructed of two words, namely Penta and Gonia, which defines five angles. So in a simplified way it can be said that pentagon is a polygon having 5 sides.
Here is a regular pentagon with side length 21 in.
Area of regular pentagon (A)= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} a^{2}[/tex]
Here a= 21 in
So Area = [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} (21)^{2}[/tex] square in.
= [tex]\frac{1}{4} \sqrt{5(5+2\sqrt{5} )} 441[/tex] "
≈758.73053 square in
= 758.7 square in. ( rounded to the nearest tenth).
Hence the area of regular pentagon is 758.7 square in.
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calculate (5)^-2+3 giving your answers to two decimal places
Answer: 3.04
Step-by-step explanation:
3.04
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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how can you use the unit circle to define the trigonometric functions of any angle
By following these steps, you can use the unit circle to define the trigonometric functions of any angle.
Steps: Draw a unit circle, place the angle, Identify the point of intersection, Define the trigonometric functions.
To use the unit circle to define the trigonometric functions of any angle, follow these steps:
1. Draw a unit circle: This is a circle with a radius of 1, centered at the origin (0, 0) of the coordinate plane.
2. Place the angle: Position the angle in standard position, which means that the initial side (starting side) of the angle is along the positive x-axis and the terminal side (ending side) is formed by rotating the initial side counterclockwise to a certain position.
3. Identify the point of intersection:
Determine the point where the terminal side of the angle intersects the unit circle.
This point will have coordinates (x, y).
4. Define the trigonometric functions:
Using the coordinates (x, y), define the six trigonometric functions as follows:
- Sine (sin): sin(angle) = y
- Cosine (cos): cos(angle) = x
- Tangent (tan): tan(angle) = y/x
- Cosecant (csc): csc(angle) = 1/y
- Secant (sec): sec(angle) = 1/x
- Cotangent (cot): cot(angle) = x/y.
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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:
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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The difference between the tens digit and ones digit of a two-digit number is 2. The number is 27 greater than the number created when the digits are reversed. What is the two-digit number?
Thus, the two digits are 9 and 11.
What is the Two-Variable Equations?
Two-variable equations are algebraic equations that involve two variables, typically x and y, and describe a relationship between them.
Let's call the tens digit "T" and the ones digit "O". Based on the problem, we know that:
T - O = 2 (the difference between the tens and ones digit is 2)10T + O = 10O + T + 27 (the number is 27 greater than the number created when the digits are reversed)T = 2 + O
Then substitute this equation in 10T + O = 10O + T + 27 i.e.
10T + O = 10O + T + 27
10T - T = 10O - O + 27
9T = 9O + 27
9(2 + O) = 8O + 27
9(2 + O) = 8O + 27
18 + 9O = 8O + 27
9O - 8O = 27 - 18
O = 9
Then,
T = 2 + 9
T = 2 + 9
T = 11
Thus, the two digits are 9 and 11.
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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:
Which angle(s) below is/are supplementary?
A. X and Y
B. Z
C. V
D. W and U
Answer:
Only Z
Step-by-step explanation:
Supplementary angles are angles whose sum up to 180 degrees.
Tamara earns her living as a salary plus commission employee. Her annual salary is $48,000, and she earns 4% commission on all sales she makes. If Tamara wants to make a total of $6,000 this month, how much in sales does she need to have?
a.
$30,000
b.
$50,000
c.
$100,000
d.
$150,000
Please select the best answer from the choices provided
A
B
C
D
Answer:
B. $50,000
Explanation:
4%=.04
50,000 x .04=2000
48000/12=4000
She makes $4000 off of her salary each month. Then because she only gets 4% of her commissions you multiply the 50000 by .04 and you get 2000. So she gets $2000 in commissions and $4000 off of her salary.
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.
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).
Can someone please help me?
Answer:
2) x = 3√5; y = 6;
3) x = 12√2; y = 12;
4) x = 45∘; y = 45∘;
5) x = 60∘; y = 30∘
Step-by-step explanation:
2) Use trigonometry:
[tex] \cos(60∘) = \frac{3}{y} [/tex]
Use the property of the proportion to find y:
[tex]y = \frac{3}{ \cos(60∘) } = \frac{3}{1} \div \frac{1}{2} = \frac{3}{1} \times \frac{2}{1} = 6[/tex]
Use the Pythagorean theorem to find x:
[tex] {x}^{2} = {y}^{2} + {3}^{2} = {6}^{2} + {3}^{2} = 36 + 9 = 45[/tex]
[tex]x > 0[/tex]
[tex]x = \sqrt{45} = 3 \sqrt{5} [/tex]
3) Use trigonometry:
[tex] \sin(45∘) = \frac{12}{x} [/tex]
Use the property of the proportion to find x:
[tex]x = \frac{12}{ \sin(45∘) } = \frac{12}{1} \div \frac{ \sqrt{2} }{2} = \frac{12}{1} \times \frac{2}{ \sqrt{2} } = 12 \sqrt{2} [/tex]
Use trigonometry:
[tex] \tan(45∘) = \frac{12}{y} [/tex]
Use the property of the proportion to find y:
[tex]y = \frac{12}{ \tan(45∘) } = \frac{12}{1} = 12[/tex]
4) Use trigonometry:
[tex] \tan(x∘) = \frac{3}{3} = 1[/tex]
x = 45∘
[tex] \tan(y∘) = \frac{3}{3} = 1[/tex]
y = 45∘
5) Use trigonometry:
[tex] \cos(x∘) = \frac{4}{8} = \frac{1}{2} = 0.5[/tex]
x = 60∘
[tex]x = \sin(y∘) = \frac{4}{8} = \frac{1}{2} = 0.5[/tex]
y = 30∘
someone help me with this
The gallons of gas that Aubrey would need to travel 111.54 miles is 7.8 gallons.
What is a direct proportion?In Mathematics, a direct proportion simply refers to a mathematical equation which is typically used to represent the equality of two (2) ratios.
By applying direct proportion to the given information, we have the following mathematical equation:
15 gallons of gasoline = 214.5 miles
X gallons of gasoline = 111.54 miles
By cross-multiplying, we have the following:
214.5x = 15 × 111.54
x = 1,673.1/214.5
x = 7.8 gallons of gasoline.
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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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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.)"--
what is most likely true about melting these two types of chocolate?
Dark chocolate usually takes longer to melt than milk chocolate, as shown by the fact that the median melting time for dark chocolate is higher than the median melting time for milk chocolate.
What is the role of median?Based on the given box plots, it is most likely true that after 64 seconds, about half of the brands of milk chocolate are likely to melt, and none of the brands of dark chocolate are likely to melt.
After 259 seconds, none of the brands of milk chocolate are likely to melt, and about a quarter of the brands of dark chocolate are likely to melt.
This conclusion is based on the fact that the box plot for milk chocolate shows a wider spread of melting times, indicating more variation in melting times among the different brands.
while, the box plot for dark chocolate shows a narrower spread of melting times, indicating less variation in melting times among the different brands.
Therefore, Additionally, the median melting time for dark chocolate is higher than the median melting time for milk chocolate, indicating that dark chocolate generally takes longer to melt.
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suppose you have two data sets, a and b, with means of 20 and 30, respectively, and the same standard deviation of 5. which data set is more spread out?
Assuming that we have two data sets, a and b, with means of 20 and 30, respectively, and the same standard deviation of 5, we can conclude that neither data set is more spread out than the other.
What do we understand by sparse data set?Suppose you have two data sets A and B, with means of 20 and 30, respectively, and the same standard deviation of 5. To determine which data set is more spread out, we need to compare the variance of the two data sets. Since the variance is the square of the standard deviation, we can compare the variances of the two data sets. Using the formula, Var = s², we can calculate the variances of data set A and B.
[tex]Var(A) = (5)^2 = 25\\Var(B) = (5)^2 = 25[/tex]
Both data sets have the same variance, indicating that they have the same amount of spread, or convergence. Therefore, we can conclude that no data set is more spread out than the other.
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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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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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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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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?
Paul gets $5 every week for doing his chores. He is saving his money to buy a skateboard that costs $85. He has already saved $25.
Which equation describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard?
Let x be the number of weeks it will take Paul to save enough money to buy the skateboard.
In one week, Paul earns $5, so in x weeks he will earn 5x dollars.
Since he already has $25 saved, the total amount of money he will have after x weeks is:
5x + 25
To be able to buy the skateboard that costs $85, Paul needs to save up an additional:
85 - 25 = 60
Therefore, we can set up the following equation to find the number of weeks it will take Paul to save up enough money:
5x + 25 = 60
Simplifying and solving for x:
5x = 35
x = 7
Therefore, it will take Paul 7 weeks to save up enough money to buy the skateboard.
The equation that describes the number of weeks (w) that it will take Paul to save enough money to buy the skateboard is:
5w + 25 = 85
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
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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Tina and carl share a 20 ounce bucket of clay 3/10 and 3/5
Tina and Carl will use 6 and 12 ounces of clay, respectively. Tina uses 3/10 of the 20-ounce bucket and Carl uses 3/5 of the 20-ounce bucket.
To determine how much clay Tina and Carl will use, we need to first find the total amount of clay they will use together.
If 3/10 of the clay is used by Tina and 3/5 of the clay is used by Carl, we can find the total amount of clay used by adding these fractions:
3/10 + 3/5 = (3/10 * 1/2) + (3/5 * 1/2) (we multiply by 1/2 to find the common denominator of 10)
= 3/20 + 6/20
= 9/20
Therefore, Tina and Carl will use a total of 9/20 of the 20-ounce bucket of clay.
To find how much each of them will use, we can multiply the total amount of clay by each person's fraction:
Tina: (3/10) x 20 ounces = 6 ounces
Carl: (3/5) x 20 ounces = 12 ounces
Therefore, Tina will use 6 ounces of clay, while Carl will use 12 ounces of clay.
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Tina and carl share a 20 ounce bucket of clay 3/10 and 3/5, how much of the clay each of them will use?
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The expressions, when written as products , would be:
81a² + 6bc - 9b² - c² ⇒ (9a - c)(9a + c) + 6bcb²c² - 4bc - b² - c² + 1 ⇒ (b² - 1)(c² - 4c + 1)1 - 25x² + 10xy - y² ⇒ (1 - 5x + y)(1 + 5x + y)How to write as products?To factor this expression, let's first rearrange the terms:
(81a² - c²) + (6bc - 9b²)
Now, we can see that the first part is a difference of squares, which can be factored as:
(9a - c)(9a + c)
However, the second part (6bc - 9b²) cannot be factored further as a product of binomials. So the expression can be written as:
(9a - c)(9a + c) + 6bc
1 - 25x² + 10xy - y²
This expression remains:
(1 - 5x + y)(1 + 5x + y)
Using the same rule as above.
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