The length of a rectangle is 4 ft longer than it’s width. If the perimeter of the rectangle is 28 ft, find it’s area.
The Area of the rectangle is 45 square feet.
What is Perimeter?The perimeter of a form is the space surrounding its edge. To Find the perimeter of various forms by summing the lengths of their sides.
Given, The length of a rectangle is 4 ft longer than its width. If the perimeter of the rectangle is 28 ft.
Let "l" be the length of the perimeter
Thus, width = l - 4
From the general formula of perimeter:
perimeter = 2*(length + width)
In our case
Perimeter = 2* (l + l -4)
Perimeter = 4l - 8
Since the perimeter is given 28 ft
thus,
4l - 8 = 28
4l = 36
l = 9 ft
thus width = 9 - 4 = 5 ft
Since,
Area = Length * width
Area = 9 * 5
Area of rectangle = 45 square feet.
therefore, The Area of the rectangle is 45 square feet.
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The sum of two numbers is x. If one of the numbers is 12, what is the other ?
The sum of two numbers is 38. The larger number is 12 more than the smaller number. What are the numbers?
The smaller number is 13 and the larger number is 25, as determined by solving the given equations.
Let's denote the smaller number as x. According to the given information, the larger number is 12 more than the smaller number, so we can represent the larger number as x + 12.
We are also told that the sum of the two numbers is 38. This can be expressed as the equation x + (x + 12) = 38.
Combining like terms, we simplify the equation to 2x + 12 = 38.
Next, we subtract 12 from both sides to isolate 2x: 2x = 26.
To solve for x, we divide both sides of the equation by 2: x = 13.
So, the smaller number is 13.
To find the larger number, we substitute the value of x into the expression x + 12: 13 + 12 = 25.
Therefore, the larger number is 25.
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And episode of the television show is 60 minutes from when I originally air on activity without commercials the episode is only 41 1/2 minutes out how many 1/2 minutes commercials did the episode include when it originally aired? Write and solve an equation
to justify your answer
Which ordered pairs are solutions to the inequality x+3y≥−8?
Select each correct answer.
Answer:
A. [tex](-1,-2)[/tex]
D. [tex](-6,0)[/tex]
E. [tex](-5,-1)[/tex]
Step-by-step explanation:
We have been given an inequality [tex]x+3y\geq -8[/tex]. We are asked to find the ordered pairs that are solution to the given inequality.
Let us check each ordered pair by substituting in the given inequality.
A. [tex](-1,-2)[/tex]
[tex]-1+3(-2)\geq -8[/tex]
[tex]-1-6\geq -8[/tex]
[tex]-7\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-1,-2)[/tex] is a solution for the inequality.
B. [tex](-16,2)[/tex]
[tex]-16+3(2)\geq -8[/tex]
[tex]-16+6\geq -8[/tex]
[tex]-10\geq -8[/tex]
Since the given inequality is not true, therefore, ordered pair [tex](-16,2)[/tex] is not solution for the inequality.
C. [tex](0,-3)[/tex]
[tex]0+3(-3)\geq -8[/tex]
[tex]0-9\geq -8[/tex]
[tex]-9\geq -8[/tex]
Since the given inequality is not true, therefore, ordered pair [tex](0,-3)[/tex] is not solution for the inequality.
D. [tex](-6,0)[/tex]
[tex]-6+3(0)\geq -8[/tex]
[tex]-6+0\geq -8[/tex]
[tex]-6\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-6,0)[/tex] is a solution for the inequality.
E. [tex](-5,-1)[/tex]
[tex]-5+3(-1)\geq -8[/tex]
[tex]-5-3\geq -8[/tex]
[tex]-8\geq -8[/tex]
Since the given inequality holds true, therefore, ordered pair [tex](-5,-1)[/tex] is a solution for the inequality.
If someone flips switches on the selection in a completely random fashion, what is the probability that the system selected contains at least one sony component? exactly one sony component? (round your answer to three decimal places.) at least one sony component correct: your answer is correct. exactly one sony component
S the square footage of a housesquare footage of a house discrete or continuous?
I have a past due balance of 87.50 and my new charges are $75 I was also charged a late fee of 15% of my past due balance what is my new total
Answer: $175.63.
Step-by-step explanation:
As per given ,
Past due balance = $87.50
New Charge = $75
Late fee charge = (15% ) of ( Past due balance )
= 0.15 x ($87.50)
= $ 13.125 ≈ $ 13.13 [Round off to the nearest cent]
Now , the new total = (Past due balance)+(New Charge )+(Late fee charge)
i.e. New total = ($87.50)+($75)+($13.13)
i.e. New total = $175.63
Hence, the new total is $175.63.
3 pounds fruit salad = how many ounces
Answer: 48 ounces
Step-by-step explanation: To convert 3 pounds into ounces, we first need to identify the conversion factor for pounds and ounces, which is shown below.
16 ounces = 1 pound
We are going from a larger unit, pounds, to a smaller unit, ounces.
When we go from a larger unit to a smaller unit, we multiply.
So here, we multiply 3 lb x 16 which gives us 48 ounces.
Note that I multiplied by the conversion factor.
This means that the fruit salad is 48 ounces.
Harry started a school in the year 2000. The number of students was 500 in the beginning and is increasing at a rate of 13% each year. Use a graph to predict the number of students in the year 2020.
Answer:
The predicted number of students in the year 2020 is 5762.
Step-by-step explanation:
Given,
The initial number of students, P = 500 ( In year 2000),
Also, it is increasing at a rate of 13% each year.
So, the rate of increasing = 13 % = 0.13,
Thus, the number of students after x years since 2000,
[tex]A=P(1+r)^x[/tex]
[tex]=500(1+0.13)^x[/tex]
[tex]=500(1.13)^x[/tex]
Which is an exponential growth function,
Having y-intercept = (0,500),
And, horizontal asymptote x-axis,
By making the graph of the above function we observed that,
It is passes from the point (20, 5761.544 )
Hence, the predicted number of students in the year 2020 is 5762. ( number can not be in decimals )
A submarine cruised below the surface of the water. During training exercise, it made 4 dives, each time descending 45 feet more. Then it rose 112 feet. What is the change in the submarine's position?
Answer:
68 feet
Step-by-step explanation:
A submarine cruised below the surface of the water
During training exercise, each time descending= 45 feet
Number of dives= 4
Total distance he descended= 45×4 feet
Total distance he descended= 180 feet
Then, it rose by= 112 feet
Now , the distance he is at below the surface if water= 180- 112
The distance he is at below the surface if water= 68 feet
Now, he is at 68 feet below the surface of the Earth
Hence, the correct answer is 68 feet
Determine all values of the constant α for which {1 + αx2, 2 + x + x2, 3 + x} is a basis for p2. (enter your answers as a comma-separated list.)
Tony buys a CD that is priced at $13.59. He has a coupon for $1.85 off. He pays with a $20 bill. Which is the best whole number estimate of how much change he gets? $8 $8.26 $9 $9.26
Answer:
I think A
Step-by-step explanation:
As an advertising campaign, a chocolate factory places golden tickets in some of its candy bars, with the promise that a golden ticket is worth a trip through the chocolate factory, and all the chocolate you can eat for life. if the probability of finding a golden ticket is p, find the mean and the variance of the number of candy bars you need to eat to find a ticket
The mean number of candy bars needed to find a golden ticket is 1/p, and the variance is (1-p)/p^2.
Explanation:To find the mean and variance of the number of candy bars you need to eat to find a golden ticket, we need to use the concept of a geometric distribution. The geometric distribution models the number of trials it takes to achieve a success, where each trial has the same probability of success.
The mean of a geometric distribution is given by μ = 1/p, where p is the probability of success. In this case, p represents the probability of finding a golden ticket. Therefore, the mean number of candy bars needed to find a golden ticket is 1/p.
The variance of a geometric distribution is given by σ^2 = (1-p)/p^2. This represents the spread or variability in the distribution. Using the given value of p, you can calculate the variance of the number of candy bars needed to find a golden ticket.
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the graph of y=x^2 is shifted 4 units to the right,
and shifted 7 units downward
Suppose that x is a binomial random variable with n = 10 and p = 0.25 . find p( 4 ). write only a number as your answer. round to 4 decimal places (for example 0.1849). do not write as a percentage.
Final answer:
To determine the probability of obtaining exactly 4 successes in 10 trials with a binomial random variable having p = 0.25, use the binomial probability formula to calculate P(4), resulting in an answer of 0.0881.
Explanation:
To find the probability P(4) for a binomial random variable with n = 10 and p = 0.25, we use the binomial probability formula. In this case, we are calculating the probability of getting exactly 4 successes in 10 trials. Using the binomial probability formula, P(x = k) = (n choose k) * p^k * (1-p)^(n-k), we can calculate P(4) by substituting n = 10, k = 4, and p = 0.25 into the formula. This calculation yields the value of 0.0881 (rounded to 4 decimal places).
What is the greatest common factor of 42a5b3, 35a3b4, and 42ab4?
Answer:
[tex]7ab^3[/tex]
Step-by-step explanation:
the greatest common factor of [tex]42a^5b^3[/tex], [tex]35a^3b^4[/tex], and [tex]42ab^4[/tex]
LEts write the factors for each expression
[tex]42a^5b^3=6*7*a*a*a*a*a*b*b*b[/tex]
[tex]35a^3b^4=5*7*a*a*a*b*b*b*b[/tex]
[tex]42ab^4=6*7*a*b*b*b*b[/tex]
From all the terms we have common factors
7, 'a' and b^3
So GCF is [tex]7ab^3[/tex]
A person plans to invest a total of $140,000 in a CD at 7% annual interest and in a mutual fund that has a three-year average annual interest of 10% by X and Y represent the money in dollars invested in the CD and the mutual fund respectively how much money should be invested in each account to earn a total of $12,200 in one year
Final answer:
The student should invest $60,000 in the CD at 7% annual interest and $80,000 in the mutual fund at 10% to earn a total interest of $12,200 in one year. This is determined by setting up and solving a system of linear equations.
Explanation:
The student asked how much money should be invested in a CD at 7% annual interest and a mutual fund with a three-year average annual interest of 10%, given a total investment of $140,000, to earn a total of $12,200 in one year. We can set up a system of equations to solve for X (the amount invested in the CD) and Y (the amount invested in the mutual fund).
Let X be the amount invested in the CD and Y be the amount invested in the mutual fund. We then have the following system of equations:
X + Y = $140,000 (the total investment)0.07X + 0.10Y = $12,200 (the total interest earned in one year)Solving this system, we subtract the first equation from the second equation multiplied by 0.07:
0.07X + 0.10Y = $12,2000.07X + 0.07Y = $9,800Subtract the second equation from the first we get:
0.03Y = $2,400
Dividing both sides by 0.03 gives:
Y = $80,000
Substitute Y in the first equation:
X + $80,000 = $140,000
X = $140,000 - $80,000 = $60,000
Therefore, $60,000 should be invested in the CD and $80,000 in the mutual fund to obtain a total interest of $12,200 in one year.
wrong answer its the right one above you
How do I solve 3x+5x+10x=16x-6
James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f).
Elapsed Time
(seconds) Distance Traveled
(feet)
1 6.2
2 12.4
3 18.6
4 24.8
Which of the following equations represents the relationship between the distance traveled and the elapsed time?
f = 6.2 + n
n = 6.2 + f
f = 6.2n
n = 6.2f
The graph represents this system of equations. What is the solution to the system of equations? a(–2, 4) b( 3, 4) c (4, –2) d(4, 3)
The solution to the system of equations is (-2,4)
How to determine the solution to the system of equations?The solution to the system of equations is the point of intersection of the lines in the graph
From the figure, the lines intersect at the point:
(x,y) = (-2,4)
Hence, the solution to the system of equations is (-2,4)
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A penny is 0.061 inch thick.What is the value of the 6 in the thickness of a penny
Ed can run a mile in 6 min and 30 sec.Ned can run a kilometer in 4 min.Who runs at a faster rate?Explain.
Ned runs at a faster rate.
What is Measurement unit?
A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.
Given that;
Ed run a mile in 6 min and 30 seconds.
And, Ned run a kilometer in 4 min
Now,
Since, We know that;
1 mile = 1.60 kilometer
So, We get;
Ed run 1.61 km in 6 min and 30 seconds.
So, The time to cover 1 meter = 390 sec / 1600
= 0.23 sec
And, Ned run a kilometer in 4 min
So, The time to cover 1 meter = 240 sec / 1000
= 0.24 sec
Thus, Ned runs at a faster rate.
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a car recently sold for $32,345. if there is a 6% sales tax on automobile sales, how much tax will be added to the price of the car? I got $194.70. is this right?
The speed of a Dragonfly is 6.974
Mark said that the speed of a dragonfly rounded to the nearest tenth was 6.9 meters per second. Is he correct? If not, what is his error?
Multiply using partial products Estimate then record the product 149*5
Consider the problem of constructing (not solving) crossword puzzles: fitting words into a rectangular grid. the grid, which is given as part of the problem, specifies which squares are blank and which are shaded. assume that a list of words (i.e., a dictionary) is provided and that the task is to fill in the blank squares by using any subset of the list. formulate this problem precisely in two ways:
a. as a general search problem. choose an appropriate search algorithm and specify a heuristic function. is it better to fill in the blanks one letter at a time or one word at a time?
b. as a constraint satisfaction problem. should the variables be words or letters?
a. For the general search problem, filling in blanks one word at a time is generally more efficient.
b. For the constraint satisfaction problem, variables such as words might lead to a more structured approach depending on complexity and abstraction preferences.
a. General Search Problem Formulation:
State Space: Each state represents a current configuration of the crossword grid where some squares are filled with letters and some are blank. The goal is to completely fill the grid while adhering to the provided dictionary of words.Initial State: An empty crossword grid with all squares blank.Actions: For each blank square, there is an action to fill it with a letter from the provided dictionary.Transition Model: The transition function takes the current grid configuration and a chosen word from the dictionary and places the word into the grid in a valid way, adhering to the provided constraints. Goal State: The goal is to fill all blank squares with words from the dictionary, creating a complete crossword grid.Path Cost: The cost can be defined as the number of words used to fill the grid. Minimizing the path cost would mean using the fewest words.Heuristic Function: For a heuristic function, you could calculate the number of blank squares that can potentially be filled with valid words from the dictionary. This gives an estimate of progress toward the goal. You could also consider the lengths of the words that can fit in each blank space and choose words that can fill multiple spaces.When it comes to filling in the blanks one letter at a time or one word at a time, it's generally more efficient to fill in one word at a time.
This reduces the branching factor of the search space and allows for better optimization since a complete word placement can be validated more easily than individual letters.
b. Constraint Satisfaction Problem Formulation:
Variables: Each variable represents a blank square in the grid, and the domain of each variable is the set of words that can fit in that square.Constraints: The constraints involve ensuring that the words placed in the grid adhere to the crossword rules, which include words intersecting each other at common letters and fitting into the available grid space.Objective: The objective is to find an assignment of words to the blank squares that satisfies all the constraints.Variable Selection: Variables can be either words or letters. If variables are words, then each variable represents a whole word to be placed in a blank square. If variables are letters, then each variable represents an individual letter to be placed in a blank square. Using variables as words might lead to a more structured approach to fitting the grid.Constraint Propagation: As words are placed in the grid, constraints are applied to ensure they fit correctly with intersecting words. This involves checking for conflicts and adjusting the domain of variables accordingly.Backtracking and Search: Backtracking can be used to explore the possible assignments of words/letters to blank squares while adhering to the constraints. A depth-first search can be employed to traverse the search space.To learn more about the Heuristic function;
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The crossword construction problem can be addressed as a general search problem, utilizing search algorithms like Depth-First or Breadth-First, and filling in words rather than individual letters. Alternatively, it can be approached as a constraint satisfaction problem, where each word is a variable that must fit in the grid and be unique.
Explanation:The problem of constructing crossword puzzles can be defined in the following ways:
a. As a general search problem: This formulation would involve selecting each blank square and iteratively filling it in with a letter from a candidate word. A possible algorithm could be a Depth-First Search or Breadth-First Search algorithm, which would explore all the possible combinations of letters in the blank squares. A heuristic function could be designed to prioritize the filling of squares that belong to both across and down words. It would generally be better to fill in the blanks one word at a time, as one wrong letter in a position could potentially disrupt the arrangement of multiple words.b. As a constraint satisfaction problem: In this case, each word could be considered a variable, and the constraints would be that each word has to fit in the given grid and that all words in the grid are unique. The variables in this case should be the words themselves, not the individual letters. The reasoning behind this is that having large numbers of variables (individual letters) would drastically increase the size of the problem and the complexity of solving it.Learn more about Crossword Construction Algorithm here:https://brainly.com/question/30281402
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.
A mountain climber ascends a mountain to its peak. The peak is 12,740 ft above sea level. The climber then descends 200 ft to meet a fellow climber. Find the climber’s elevation above sea level after meeting the other climber.
–12,540 ft
12,940 ft
10,740 ft
12,540 ft
Assume that a set of test scores is normally distributed with a mean of 70 and a standard deviation of 10. In what percentile is a score of 65?
1. 95th
2. 79th
3. 46th
4. 30th
The score of 65 is in the 70th percentile.
Explanation:To find the percentile of a score of 65 in a normally distributed set of test scores with a mean of 70 and a standard deviation of 10, we can use the standard normal distribution table or a calculator that can find the inverse normal distribution.
Using the inverse normal distribution, the 70th percentile is 65.6. This means that 70 percent of the test scores fall at or below 65.6, and 30 percent fall above.