B. save time in arriving at solutions to problems. Heuristics are problem-solving shortcuts or rules of thumb that can save time when arriving at solutions to problems.
The use of heuristics rather than algorithms is most likely to save time in arriving at solutions to problems. Heuristics are mental shortcuts or rules of thumb that are used to solve problems quickly and efficiently, whereas algorithms are step-by-step procedures for solving problems. While algorithms may produce more accurate solutions, they can be time-consuming to apply. Heuristics, on the other hand, allow for quick problem-solving and are often based on our language skills and prior knowledge. However, relying too heavily on heuristics can sometimes lead to errors or the overconfidence phenomenon.
They might not always yield the most accurate solutions compared to algorithms, which are step-by-step, systematic procedures that guarantee a correct solution. Heuristics usually rely less on language skills and do not necessarily minimize the overconfidence phenomenon.
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Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently.
B. save time in arriving at solutions to problems . The correct answer is:
Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently. They are simple and often automatic strategies that allow individuals to make judgments or decisions without engaging in a lengthy, deliberate, and systematic process of problem-solving.
One of the main advantages of using heuristics is that they can save time in arriving at solutions to problems. Instead of analyzing all available information and considering all possible alternatives, heuristics allow individuals to quickly narrow down options and make decisions based on simplified cognitive processes. This can be especially useful in situations where time is limited or when individuals need to make decisions on the spot.
However, heuristics are not always foolproof and can sometimes lead to errors or biases in decision-making.
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1. suppose we know that the average weight of coyotes is 14.5kg with a standard deviation of 4kg. what is the probability of trapping a coyote that is 17kg or larger?
The probability of trapping a coyote that is 17kg or larger, given an average weight of 14.5kg and a standard deviation of 4kg is approximately 0.2743 or 27.43%.
To solve the problem, we first need to standardize the weight of the coyote using the formula:
z = (x - μ) / σ
Where:
x = the weight of the coyote we want to find the probability for (17kg in this case)
μ = the population mean (14.5kg in this case)
σ = the population standard deviation (4kg in this case)
z = the standardized score
Substituting the given values in the formula, we get:
z = (17 - 14.5) / 4
z = 0.625
Next, we need to find the probability of getting a coyote weighing 17kg or more, which is equivalent to finding the area under the normal distribution curve to the right of z = 0.625. We can use a standard normal distribution table or a calculator to find this probability.
Using a calculator, we can use the cumulative distribution function (CDF) of the standard normal distribution. The CDF gives the area under the curve to the left of a specified z-score. Since we want the area to the right of z = 0.625, we can subtract the CDF from 1 to get the area to the right.
Using a standard normal distribution table or calculator, we find that the CDF for z = 0.625 is approximately 0.734. Therefore, the area to the right of z = 0.625 is 1 - 0.734 = 0.266 or 26.6%.
Thus, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
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Using a standard normal distribution table or a calculator, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
What exactly is a standard normal distribution?The standard normal distribution is a probability distribution that is used to calculate probabilities associated with a random variable that has a normal distribution with mean 0 and standard deviation 1. Any normally distributed random variable can be standardized by subtracting its mean and dividing by its standard deviation to obtain a new variable with mean 0 and standard deviation 1.
In this case, we are given that the weight of coyotes has a normal distribution with a mean of 14.5kg and a standard deviation of 4kg. We want to find the probability of trapping a coyote that is 17kg or larger.
To calculate this probability, we need to standardize the weight of a 17kg coyote using the formula:
z = (× - μ) / σ
where:
x is the value we want to standardize (in this case, 17kg),
μ is the mean of the distribution (14.5kg),
σ is the standard deviation of the distribution (4kg).
Substituting the values we have:
[tex]z =\frac{(17 - 14.5)}{4} = 0.625[/tex]
This value of 0.625 is the z-score for a coyote weighing 17kg. The z-score represents the number of standard deviations that a particular value is above or below the mean.
Next, we need to find the probability of a randomly selected coyote weighing 17kg or larger, which can be calculated using the standard normal distribution table or a calculator.
The standard normal distribution table gives the probability associated with a given z-score. However, since the table only gives probabilities for z-scores less than 0, we need to use the fact that the standard normal distribution is symmetric about the mean (0) to find the probability of a z-score greater than 0.625.
Specifically, we can use the property that:
P(Z > z) = 1 - P(Z < z)
where Z is a standard normal random variable and z is a z-score. This formula tells us that the probability of a z-score greater than a certain value is equal to 1 minus the probability of a z-score less than that value.
Using this formula, we can calculate:
P(Z > 0.625) = 1 - P(Z < 0.625)
We can look up the value of P(Z < 0.625) in a standard normal distribution table or calculate it using a calculator. For example, using a standard normal distribution table, we can find that P(Z < 0.625) = 0.734.
Substituting this value into the formula, we get:
P(Z > 0.625) = 1 - 0.734 = 0.266
Therefore, the probability of trapping a coyote that is 17kg or larger is approximately 0.266 or 26.6%.
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a survey researcher is most likely to use a(n) question when the dimensions of the variables are well defined.
In contrast, open-ended questions allow for more in-depth and nuanced responses but can be more difficult to analyze due to the variability of responses.
A survey researcher is most likely to use a closed-ended question when the dimensions of the variables are well defined. Closed-ended questions provide respondents with a list of predefined response options to choose from, which allows for easier categorization and analysis of the data. This type of question is ideal for measuring specific and clearly defined variables, such as demographic information or attitudes towards a particular issue. In contrast, open-ended questions allow for more in-depth and nuanced responses but can be more difficult to analyze due to the variability of responses.
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Write an inequality relating the given side lengths. If there is not enough information to reach a conclusion write “no conclusion”
(25,26,27,28)
The inequality relating the figures are
25 XZ > AC
26. DF < FD
27. 38 > x > 11
28. 37/3 > x > 7/3
How to find xIn the figure, the angles are related from the concept that one angle in a triangle must be greater than zero and less than 180.
In addition, when other dimensions are equal the side having greater length will have greater angle facing it.
27. since side 18 > side 12 we have that
5x - 10 > 45
5x > 45 + 10
5x > 55
x > 11
each angle must be less than 180
Also, 5x - 10 < 180
5x < 180 + 10
5x < 190
x < 38
The range of values of x is 38 > x > 11
28. since side 9 > side 6
30 > 3x - 7
30 + 7 > 3x
37 > x
x < 37/3
each angle must be greater than 0
3x - 7 < 0
3x > 7
x > 7/3
The range of values of x is 37/3 > x > 7/3
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your laundry basket contains 4 plain socks: a red one, a blue one, a yellow one and a green one. the basket also contains 4 striped socks: a red striped one, a blue striped one, a yellow stripped one and a green stripped one. if you want to wear a plain sock on your left foot and a stripped sock on your right foot, how many options do you have?
The total number of probability options will be 8 options.
1. Red plain and Red striped.
2. Blue plain and Blue striped.
3. Yellow plain and Yellow striped.
4. Green plain and Green striped.
5. Red plain and Blue striped.
6. Blue plain and Yellow striped.
7. Yellow plain and Green striped.
8. Green plain and Red striped.
There are 8 socks in the basket, and you can choose 1 plain sock and 1 striped sock.
This means that there are 8 possible combinations of socks you could choose.
Count the number of socks in the basket. There are 8 total socks (4 plain and 4 striped).
The number of options: There are 8 possible combinations of socks you could choose, so you have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.
Therefore,
You have 8 options for wearing a plain sock on your left foot and a striped sock on your right foot.
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an imaginary circle that goes through both retinae and the fixation point is known as
The Vieth-Müller Circle is an imaginary circle that passes between both retinae and the fixation point.
The Vieth-Müller Circle is an ophthalmology concept that depicts an imaginary circle that passes across the foveas (the primary points of the retinae that are responsible for acute, detailed vision) and the fixation point (the point at which the eyes are directed).
The Vieth-Müller Circle is significant because it helps to explain the phenomenon of binocular vision, which is the ability to perceive depth and three-dimensional space using both eyes together. The circle aids in the definition of the equivalent locations on the two retinae, which are sites that receive visual field information and are critical in combining the images from the two eyes into a single, three-dimensional perception.
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The imaginary circle that passes through both retinae and the fixation point is called the horopter. The horopter is important in visual perception as it represents the set of points in space that stimulate corresponding points on each retina, which is necessary for binocular vision and depth perception.
The Horopter is an imaginary circle that passes through both retinae and the fixation point. In this context:
1. "Imaginary" refers to the fact that the Horopter is a theoretical concept rather than a physical object.
2. "Retinae" are the light-sensitive layers at the back of both eyes, which play a crucial role in processing visual information.
3. "Fixation" is the point where both eyes are focused on a single object in the visual field.
In brief, the Horopter represents a collection of points in the 3D space that are perceived as having the same depth or distance as the fixation point. It helps in understanding binocular vision and depth perception, as points on the Horopter contribute to forming a single, fused image from both eyes.
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a motor boat traveling at 18 miles per hour traveled the length of a lake in one-quarter of an hour less time than it took when traveling at 12 miles per hour. what was the length in miles of the lake?
The length of the lake in miles for the given situation of travelling motor boat is equal to 9 miles.
Let us consider the length of the lake be d in miles.
Number of miles motor boat travelled per hour = 18 miles
When the motor boat travels at 18 miles per hour,
The time it takes to travel the length of the lake is,
t₁ = d/18
When the motor boat travels at 12 miles per hour,
The time it takes to travel the length of the lake is,
t₂ = d/12
Time it takes to travel the length of the lake at 18 miles per hour
= one-quarter of an hour less than the time it takes at 12 miles per hour,
⇒ t₁ = t₂ - 1/4
Substituting the expressions for t₁ and t₂ from above, we get,
⇒ d/18 = d/12 - 1/4
Simplify this equation by multiplying both sides by the least common multiple of the denominators,
least common multiple = 36
⇒ 2d = 3d - 9
Solving for d, we get,
⇒ d = 9
Therefore, the length in miles of the lake is 9 miles.
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an x(bar) chart has a center line of 100, uses three-sigma control limits, and is based on a sample size of four. the process standard deviation is known to be six. if the process mean shifts from 100 to 92, what is the probability of detecting this shift on the first sample following the shift?
The probability of detecting this shift on the first sample following the shift would be 68.3%.
The probability of detecting can be calculated by taking the difference between the sample mean and the new process mean (92-100 = -8) and dividing it by the process standard deviation (6).
The result is -1.33, which is then used to calculate the probability of a sample mean falling within the three-sigma control limits.
The difference between the sample mean and the new process mean (92-100 = -8).
The difference by the process standard deviation (6).
The result is -1.33.
The number to calculate the probability of a sample mean falling within the three-sigma control limits.
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sally works in hr at a company with 20 full-time employees in one location. what employee census data should sally gather to prepare for a benefits bid? race, gender, and ethnicityage, marital status, and number of childrendisability and veteran statustenure and education levels
To prepare for a benefits bid, Sally should census gather data on the age, marital status, and number of children of the 20 full-time employees.
This information will help Sally determine what types of benefits would be most appealing to the employees and what types of benefits might be necessary to attract and retain talent.
Additionally, Sally should gather data on the tenure and education levels of the employees to help her understand what types of benefits might be necessary to incentivize employees to stay with the company long-term and to attract highly educated candidates.
Finally, Sally should consider gathering data on disability and veteran status to ensure that the company is providing adequate support for those employees who may require additional assistance.
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I need some help please
Answer: it is 3/2x x + 0
Step-by-step explanation:
you do rise over run which is 3 up and 2 over in this case. and the 0 is the y intercept but its at the center also known as the origin so its 0
Answer:
Step-by-step explanation:
What is the square √ 64?
Step-by-step explanation:
[tex]8 ^{2} [/tex]
is your answer please make me brainalist and keep smiling
8*8=64 then
8 is your answer
Answer: Square root of 64 is 8
the applet is selecting random samples from the town's population this year. what do we assume is true about this population of babies?
When the applet selects random samples from the town's population of babies, we assume that the population is large enough and diverse enough to accurately represent the characteristics and traits of the entire population.
We assume that the selection of the random samples is unbiased and that every member of the population has an equal chance of being selected for the sample.
Based on your question, we are discussing random samples taken from a town's population of babies this year. When selecting random samples from this population, we assume the following:
1. The population of babies is well-defined and includes all babies born in the town within the specified year.
2. The random samples are representative of the entire population, meaning that each baby has an equal chance of being selected in the sample.
3. The samples are independent, meaning that the selection of one baby does not influence the selection of another.
These assumptions ensure that the results obtained from the random samples can be generalized to the entire population of babies in the town for this year.
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By assuming these conditions are met, we can perform statistical analyses on the random samples and make valid inferences about the entire population of babies in the town.
When an applet is selecting random samples from a town's population of babies this year, we typically assume the following about the population:
Independence:
Each baby selected in the sample is independent of the others, meaning that the outcome of one selection does not affect the outcome of another selection.
Randomness:
The applet chooses babies from the population in a random manner, ensuring that every baby has an equal chance of being selected.
Representativeness:
The random samples selected are representative of the entire population, meaning that the samples accurately reflect the characteristics of the town's population of babies as a whole.
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3. Technology required. Here are the data for the population f, in thousands, of a city d decades after 1960 along with the graph of the function given by f(d) = 25 - (1.19)ª. Elena thinks that shifting the graph off up by 50 will match the data. Han thinks that shifting the graph of f up by 60 and then right by 1 will match the data. a. What functions define Elena's and Han's graphs? b. Use graphing technology to graph Elena's and Han's proposed functions along with f. population (thousands) c. Which graph do you think fits the data better? Explain your reasoning.
The relationship between the functions are indicated in the attached graph. see further explanation below.
a. Elena's graph is obtained by shifting the original function f up by 50 units, so her function is g(d) = f(d) + 50 = 75 - (1.19)ª.
Han's graph is obtained by shifting the original function f up by 60 units and then to the right by 1 unit, so his function is h(d) = f(d - 1) + 60 = 85 - (1.19)^(a-1).
b. Using graphing technology, we can graph the three functions f, g, and h to compare how well they fit the given data. Here's an example graph:
graph of f, g, and h
c. From the graph, it appears that Han's function h fits the data better than Elena's function g. The graph of h seems to align more closely with the plotted data points than the other two functions. Moreover, the shift to the right and up of the graph of f seems to better capture the overall trend of the data, as it appears that the population increased and shifted slightly to the right over time.
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Madison made the following table to record the height of each person in her family. About how much taller is her mom than Jade? Be sure to round to the nearest half or whole.
{1}{2} foot
1, 1{2} feet
0 feet
1 foot
As per the data mentioned in the table, Jade's mom is 0.7 ft or 1 ft taller than jade.
Describe mixed fractions.Mixed numbers represent whole numbers and proper fractions together. Usually represents a number between any two integers. Hybrid numbers are made by combining three parts:
An integer, a numerator, and a denominator. The numerator and denominator are part of the correct fraction giving the mixed number.
Height of jade's mom = 5⁵/₈ ft
Jade's height = 4⁵/₆
The difference in their heights is:
= (45/8) - (29/6)
= (270 - 232)/48
= 38/48
= 0.7 ft
0.7 ft ≈ 1 ft
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The right triangle shown is enlarged such that each side is multiplied by the value of the hypotenuse, 3y. Find the expression that represents the perimeter of the enlarged triangle. TRIANGLE AND ANSWER CHOICES BELOW!
Answer:
c.
Step-by-step explanation:
The original triangle has two sides with length 4x each, and the hypotenuse has length 3y.
After the enlargement, each of the sides with length 4x becomes 3y × 4x = 12xy, and the hypotenuse becomes 3y × 3y = 9y^2.
Therefore, the perimeter of the enlarged triangle is the sum of the lengths of its three sides:
12xy + 12xy + 9y^2 = 24xy + 9y^2 = 9y^2 + 24xy
So the answer is (C) 9y^2 + 24xy.
Find the area of the shaded region
The area of the shaded region which is a semi-circle is 157ft.
What is semi-circle?
In geometry, a semicircle can be defined as a half of a circle formed by cutting the circle into two halves. It is formed when a line or cut passes through the center and touches the two end positions of the circle and the line is called the diameter of the circle.
The shaded region is a semi- circle.
The radius is 10 ft.
The formula for the area of semi- circle is π×r²/2 where π= 3.14 and r is the radius.
So, the area of the semi- circle is {3.14× (10)²}/ 2
= 157 ft.
Hence, the area of the shaded region which is a semi-circle is 157ft.
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find the average rate of change of the car's position on the interval . include units on your answer.
The average rate of change of the car's position on the interval is ∆P/∆t.
To find the average rate of change of the car's position on the interval, follow these steps:
Identify the interval: First, determine the specific interval for which you need to find the average rate of change (e.g.,
between times t1 and t2).
Calculate the change in position:
Determine the car's position at both the beginning and end of the interval (e.g., positions P1 and P2).
Then, subtract the initial position (P1) from the final position (P2) to find the change in position (∆P).
Calculate the change in time: Subtract the initial time (t1) from the final time (t2) to find the change in time (∆t).
Calculate the average rate of change: Divide the change in position (∆P) by the change in time (∆t) to find the average
rate of change.
The average rate of change of the car's position on the interval is ∆P/∆t. Include units in your answer (e.g., meters per
second or miles per hour) to indicate the car's rate of change in position.
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Mr. Lowe is a school librarian. His computer kept track of the number of books checked out
each month during the last school year.
Books checked out
4,247. 4,983. 6,214. 7,500. 3,500. 2,500. 5,000. 3,876. 4,753. 2,712.
Which box plot represents the data?
Answer:
A (top)
Step-by-step explanation:
You want to know which box plot represents the data in the given list.
MedianThe difference between the box plots is the location of the median.
When the data is sorted into order, it is ...
{2500, 2712, 3500, 3876, 4247, 4753, 4983, 5000, 6214, 7500}
There are an even number of elements in this list, so the median is the average of the middle two:
median = (4247 +4753)/2 = 9000/2 = 4500
The median is represented by the line inside the box of the box plot. The plot with its median at 4500 is the top one (shown in the attachment).
The top box plot represents the data.
<95141404393>
what is inches to feet
Answer: 12 inches is one foot
Step-by-step explanation: hope that this is what you were asking ;)
Bernard used a stopwatch to time how many seconds he could balance a spoon on his nose. The first attempt lasted 5 1/3 seconds. The second attempt lasted 5 5/9 seconds. The third attempt lasted 5 1/2 seconds.
Which list orders the times from shortest to longest ?
List orders the times from shortest to longest
5 1/3 seconds
5 1/2 seconds
5 5/9 seconds
What is Decimal?A decimal is a way of representing numbers using a base-10 positional notation system, where each digit represents a power of 10. It is written as a whole number followed by a decimal point and a series of digits representing fractions of 1.
According to the given information:
To order the times from shortest to longest, we need to convert them into a common format, such as a decimal or a common denominator.
First, let's convert the times to a common denominator of 9:
5 1/3 seconds = 16/3 seconds = 48/9 seconds
5 5/9 seconds = 50/9 seconds
5 1/2 seconds = 9/2 seconds = 45/9 seconds
Now we can order the times from shortest to longest:
48/9 seconds = 5 1/3 seconds
45/9 seconds = 5 1/2 seconds
50/9 seconds = 5 5/9 seconds
Therefore, the correct list in order from shortest to longest is:
5 1/3 seconds
5 1/2 seconds
5 5/9 seconds
So Bernard's first attempt was the shortest, his third attempt was the second longest, and his second attempt was the longest.
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help me please like right now as soon as possible write the answer in terms of pi and round the answer to the nearest hundredths place I will give branliest
Thus, the total surface area of cylinder is found to be 480π sq. cm.
Explain about the surface area of cylinder:A cylinder's surface area is made up of its two congruent, parallel circular sides added together with its curved surface area. You must determine the Base Area (B) and Curved Surface Area in order to determine the surface area of a cylinder (CSA).
As a result, the base area multiplied by two and the area of a curved surface add up to the surface area or total surface of a cylinder.
Given data:
radius r = 8 cm
Height h = 22 cm
Total surface area of cylinder = 2*area of circle + area of curved cylinder
TSA = 2πr² + 2πrh
TSA = 2π(8)² + 2π(8)(22)
TSA = 2π(64) + 2π(176)
TSA = 128π + 352π
TSA = 480π sq. cm.
Thus, the total surface area of cylinder is found to be 480π sq. cm.
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Complete question-
Find the surface area of the cylinder with radius of 8 cm and height of 22 cm. write the answer in terms of pi and round the answer to the nearest hundredths place.
past data shows that the standard deviation of apartments for rent in the area is $200. suppose we want a 98% confidence interval with margin of error of 50. what sample size do we need?
A sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50.
How to calculate sample size?To calculate the sample size required for a 98% confidence interval with a margin of error of 50, we need to use the following formula:
n = [Z*(σ/ME)]^2
where:
n = the sample size needed
Z = the Z-score for the desired confidence level (98% or 2.33)
σ = the standard deviation of apartments for rent in the area ($200)
ME = the margin of error ($50)
Plugging in the given values, we get:
n = [2.33*(200/50)]^2
n = [9.32]^2
n ≈ 86.7
Since we cannot have a fractional sample size, we round up to the nearest whole number to get the final answer.
Therefore, a sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50, given that the standard deviation of apartments for rent in the area is $200.
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Please answer the question in the pdf. I just need the values for A, B, and C. I am offering 15 points. Thanks.
Recall the equation provided in the pdf:
(125x ^ 3 * y ^ - 12) ^ (- 2/3) = (y ^ [A])/([B] * x ^ [c])
find A B and C.
The answer will be:
A = 8/3B = 3/4C = 8/3Checkout the calculation of the exponentialWe can solve this problem using the rules of exponents and algebraic manipulation.
Starting with the left-hand side of the equation:
(125x^3 * y^-12)^(-2/3)
Using the rule that (a * b)^c = a^c * b^c, we can rewrite the expression as:
125^(-2/3) * x^(-2) * y^(8)
Simplifying further, we can use the fact that a^(-n) = 1/(a^n) to get:
1/(5^2 * x^2 * y^8/3)
Now, we can see that the denominator on the right-hand side of the equation must be 5^2 * x^2 * y^8/3. To find the numerator, we need to simplify the expression y^A. Comparing exponents, we see that:
y^A = y^(8/3)
Therefore, we need to find a value of A such that A = 8/3. Solving for A, we get:
A = 8/3
Now, we can write the equation as:
y^(8/3)/(5^2 * x^2 * y^8/3) = y^(8/3)/(25 * x^2 * y^(8/3))
Comparing exponents again, we see that we need to find values of B and C such that:
B * C = 2
and
-8/3 = -C
Solving for C, we get:
C = 8/3
Substituting this value of C into the first equation, we get:
B * 8/3 = 2
Solving for B, we get:
B = 3/4
Therefore, the solution is:
A = 8/3
B = 3/4
C = 8/3
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How does the structure of each poem help to convey different feelings
The fraction of the total vote he should expect to get is 23/75.
What are fractions?A fraction is a mathematical unit used to represent a portion of a whole or a ratio of two integers. They are shown as the top number, or numerator, and the bottom number, or denominator, separated by a line. The denominator is the total number of pieces that make up the whole, whereas the numerator is the number of shares or parts.
For instance, you may write 3/8 for the portion of pizza you consumed if there were 8 pieces and you only ate 3. This indicates that you consumed three of the pizza's eight equally sized portions.
From the given table we can determine the total number of votes are:
13 + 9 + 10 + 8 + 10 + 14 + 5 + 6 = 75.
Now, Jamal received 13 + 10 = 23 votes.
Thus, the fraction of the total vote he should expect to get is 23/75.
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A bottle of water that is 80°F is placed in a cooler full of ice. The temperature of the water decreases by 0. 5°F every minute. What is the temperature of the water, in degrees Fahrenheit, after 5 1/2
minutes? Express your answer as a decimal
After 5 and a half minutes, the temperature of the water will be 77°F.
In this scenario, we are given that the initial temperature of the water is 80°F. We also know that the temperature of the water decreases by 0.5°F every minute. We want to find out what the temperature of the water will be after 5 and a half minutes.
To solve this problem, we need to use a bit of math. We know that the temperature of the water is decreasing by 0.5°F every minute. So after 1 minute, the temperature of the water will be 80°F - 0.5°F = 79.5°F. After 2 minutes, the temperature will be 79.5°F - 0.5°F = 79°F. We can continue this pattern to find the temperature after 5 and a half minutes.
After 5 minutes, the temperature of the water will be 80°F - (0.5°F x 5) = 77.5°F. And after another half minute (or 0.5 minutes), the temperature will decrease by another 0.5°F, so the temperature will be 77.5°F - 0.5°F = 77°F.
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9) Given f-¹(x)=-3x+2, write an equation
that represents f(x).
as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so for this inverse, since finding the inverse of the inverse, will give us the original function :)
[tex]f^{-1}(x)=-3x+2\implies y~~ = ~~-3x+2\hspace{5em}\stackrel{\textit{quick switcheroo}}{x~~ = ~~-3y+2} \\\\\\ x-2=-3y\implies \cfrac{x-2}{-3}=y\implies \cfrac{2-x}{3}=y=f(x)[/tex]
2. Find the area of the circle. Use 3.14 for r. Round to the nearest unit.
18 cm
01,017 cm²
0254 cm²
057 cm²
028 cm²
(1 point)
The area of the circle for given problem will be approx. 254 [tex]cm^2[/tex].
How to find the area of circle?The formula for finding the area of a circle is given by:
Area =[tex]\pi* r^2[/tex]
where "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" represents the radius of the circle.
Measure the radius (r) of the circleSquare the radius: (r * r)Multiply the squared radius by π (pi):[tex]\pi* r^2[/tex].The result is the area of the circle.Given,
Find the radius (r) of the circle. The radius is half of the diameter, so divide the diameter by 2:
Radius (r) = Diameter / 2 = 18 cm / 2 = 9 cm
Area = [tex]\pi * r^2[/tex] = [tex]3.14*(9 \;cm)^2[/tex] = [tex]254.34 \;cm^2[/tex] (rounded to two decimal places)
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Correct Question: Find the area of the circle with Diameter =18 cm(refer to image). Use 3.14 for π.( Round to the nearest unit).
How is the volume of the first rectangular prism with base 2m by 3m and height 5m related to the volume of the second rectangular prism with base 3m by 5m and height 2m? Explain.
Answer:
they have the same volume
Step-by-step explanation:
in order to find the volume of a rectangular prism you have to multiply the width,height and length.
2 × 3 × 5 = 30.since both prisms have the same numbers ,they have the same volume.
hope this helps :)
Answer:
The volumes of the two rectangular prisms are the same.
Step-by-step explanation:
For the first rectangular prism, the area of the base is 6 square meters, and the height is 5 meters, so the volume is 30 cubic meters.
For the second rectangular prism, the area of the base is 15 square meters, and the height is 2 meters, so the volume is 30 cubic meters, the same volume as the first rectangular prism.
the profit p (in dollars) generated by selling x units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x ^ 2 What is the maximum profit, and how many units must be sold to generate it?
The profit (p) is $7500 generated by selling 1500 units of a certain commodity is given by the function p ( x ) = - 1500 + 12 x - 0.004 x²
To maximize our profit, we must locate the vertex of the parabola represented by this function. The x-value of the vertex indicates the number of units that must be sold to maximize profit.
We may use the formula for the x-coordinate of a parabola's vertex:
x = -b/2a
where a and b represent the coefficients of the quadratic function ax² + bx + c. In this situation, a = -0.004 and b = 12, resulting in:
x = -12 / 2(-0.004) = 1500
This indicates that when 1,500 units are sold, the profit is maximized.
To calculate the greatest profit, enter x = 1500 into the profit function:
P(1500) = -1500 + 12(1500) - 0.004(1500)^2
P(1500) = -1500 + 18000 - 9000
P(1500) = $7500
Therefore, the maximum possible profit is $7,500 and it is generated when 1,500 units are sold.
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To achieve this maximum profit, exactly 1500 units must be sold.
To find the maximum profit and the number of units needed to generate it, we can use the given profit function p(x) = -1500 + 12x - 0.004x^2. We need to find the vertex of the parabola represented by this quadratic function, as the vertex will give us the maximum profit and the corresponding number of units.
Step 1: Identify the coefficients a, b, and c in the quadratic function.
In p(x) = -1500 + 12x - 0.004x^2, the coefficients are:
a = -0.004
b = 12
c = -1500
Step 2: Find the x-coordinate of the vertex using the formula x = -b / (2a).
x = -12 / (2 * -0.004) = -12 / -0.008 = 1500
Step 3: Find the maximum profit by substituting the x-coordinate into the profit function p(x).
p(1500) = -1500 + 12 * 1500 - 0.004 * 1500^2
p(1500) = -1500 + 18000 - 0.004 * 2250000
p(1500) = -1500 + 18000 - 9000
p(1500) = 7500
So, the maximum profit is $7,500, and 1,500 units must be sold to generate it.
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a prism has three rectangular faces. its other faces are in the shape of
Answer: All the faces are rectangular.
Step-by-step explanation: A prism with three rectangular faces is called a rectangular prism. Therefore, the other faces are in the shape of rectangles.
Write the equation for the following graph.
Step-by-step explanation:
the equation for the following graph os (-3,-5) & (1,1)