There are 5 ways to tile a 2 x 6 checkerboard using L-shaped tiles of size 2 x 1.
We can approach this problem using recursion. Let T(n) be the number of ways to tile a rectangular checkerboard of size 2 x n using L-shaped tiles of size 2 x 1. We can analyze the possible tiles that can be placed in the last column of the checkerboard, and then use recursion to count the total number of ways to tile the remaining (2 x (n-1)) board.
Consider the last column of the checkerboard. We can place either a vertical tile, or two horizontal tiles in the column.
Case 1: Last column has a vertical tile
In this case, we can place a horizontal tile in the second-to-last column, and then we are left with a (2 x (n-2)) checkerboard to tile. So the number of ways to tile the (2 x n) checkerboard in this case is T(n-2).
Case 2: Last column has two horizontal tiles
In this case, we must also have two horizontal tiles in the second-to-last column, and then we are left with a (2 x (n-4)) checkerboard to tile. So the number of ways to tile the (2 x n) checkerboard in this case is T(n-4).
Therefore, the recursive formula for T(n) is:
T(n) = T(n-2) + T(n-4)
with the base cases:
T(0) = 1 (there is only one way to tile an empty checkerboard)
T(1) = 1 (there is only one way to tile a 2 x 1 checkerboard)
T(2) = 2 (there are two ways to tile a 2 x 2 checkerboard)
Using this formula, we can calculate T(6):
T(3) = T(1) + T(-1) = 1 (since T(-1) = 0)
T(4) = T(2) + T(0) = 3
T(5) = T(3) + T(1) = 2
T(6) = T(4) + T(2) = 5
So there are 5 ways to tile a 2 x 6 checkerboard using L-shaped tiles of size 2 x 1.
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Noah brought $30 to the county fair. He paid $6 for parking. Ride tickets cost $2 each.
a. Write an inequality to find the possible numbers of ride tickets he can purchase after he pays for parking. Use x to represent the number of ride tickets.
b. Use the inequality from part A to find the possible numbers of tickets Noah can purchase. For questions 15 – 16, solve each literal equation for x.
The inequality to find the possible numbers of tickets Noah can purchase is 6 + 2x ≤ 30
InequalityAmount with Noah = $30Amount paid for packing = $6Amount per each ride tickets = $2Number of ride tickets = x6 + 2x ≤ 30
2x ≤ 30 - 6
2x ≤ 24
x ≤ 24/2
x ≤ 12
The possible number of ride tickets Noah can purchase is x ≤ 12
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14. Which value of c makes the inequality 4 + 3c > 10 true?
Answer:
C=6
Step-by-step explanation:
3x2 is 6 and 6+4= 10.
This question can be answered using trial and error.
Hi student, let me help you out!
............................................................................................................
Which value of c makes the inequality 4+3c>10 true? We can quickly find it if we follow these steps:
Subtract 4 from both sides.Solve for c.Step 1. Subtract 4 from both sides: \(\mathrm{3c > 10-4}\).
Upon simplifying, we get \(\mathrm{3c > 6}\).
Step 2. Solve for c by dividing both sides by 3: \(\mathrm{c > 2}\)
So the values that make this inequality true are greater than 2.
Hope it helped you out, ask in comments if any queries arise. :)
19. Helen has 2 more than twice as many stamps as Gail. If Gail
buys 10 more stamps, she and Helen will have the same
number of stamps. How many stamps does each person have
now?
Answer:
x(Gail)=8 and y(Helen)=18
Step-by-step explanation:
2x+2=y and x+10=y
Plug y in and solve for x
2x+2=(x+10)
2x-x=10-2
x=8
Plug x in and solve for y
(8)+10=y
y=18
People use water to cook, clean, and drink every day. An estimate of 19.8% of the water used each day is for cooking. If a family uses 69.3 gallons of water a day for cooking, how many gallons do they use every day?
Answer: 350 gallon
Step-by-step explanation:
If 19.8% is 69.3gallons
1% is 69.3/19.8
100% used is 69.3/19.8 × 100/1
Combine any like terms in the expression. If there are no like terms, rewrite the expression. 10f + 6 + 5-8
The expression when evaluated is 10f + 3
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
10f + 6 + 5-8
Collect the like terms
So, we have the following representation
10f + 6 + 5-8 = 10f + 6 + 5-8
Evaluate the like terms in the expression
So, we have the following representation
10f + 6 + 5-8 = 10f + 3
Hence, teh expression is 10f + 3
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PLEASE HELPPPPP, what is the meaning of 1.5 terms context?
Answer: #2 that's an absolute anser i am not sure if there are more or if this is just a multiple choice question
Step-by-step explanation:
4. If the train travels at a constant speed of 460 kilometers per hour 1 for hour, how far does the train travel? 5 5. If the train traveled at a constant rate of its top speed for 6 kilometers, what is the approximate amount of time the train would have traveled? A train reaches rates up to 480 km per hour
4)
Given data:
The given speed is s=460 km/h.
The given time is t= 1/5 h.
The expression for distance is,
\(d=s\times t\)Substitute the given values in the above expression.
\(\begin{gathered} d=(460\text{ km/h)(}\frac{1}{5}\text{ h)} \\ =92\text{ km} \end{gathered}\)Thus, the distance traveled is 92 km.
5)
Given data:
The given speed is s= 480 km/h.
The given distance is d= 6 km.
The expression for the time is,
\(\begin{gathered} t=\frac{d}{s} \\ =\frac{6\text{ km}}{480\text{ km/h}} \\ =0.0125\text{ h} \\ =0.75\text{ min} \\ =45\text{ seconds} \end{gathered}\)Thus, the value of time is 45 seconds.
Answer: 1/80
Step-by-step explanation: The train traveled for about 1/80 hours. (simplified)
What is the surface area of this shape??? Help please!
The area of the composite figure is equal to 216 square inches
How to calculate for the area of the figureThe composite figure can be observed to be made up of six identical squares, so we shall calculate for the area of one square and then multiply the result by six to get the total area of the composite figure as follows:
area of a square = length²
area of the one square = 6 in × 6 in
area of the one square = 36 in²
total area of the composite figure = 36 in² × 6
total area of the composite figure = 216 in²
Therefore, the area of the composite figure is equal to 216 square inches.
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Most interesting way to write 6 billion is...? Why?
Answer:
Its 6 bill because people think its flashy
Step-by-step explanation:
please answer :,)
What is the median of this data set?
The line graph is titled Amount of Rainfall. The Y axis is labeled inches. The X axis is labeled weeks. Week 1 has a dot at 2 inches. Week 2 has a dot at 3 inches. Week 3 has a dot at 1 inch. Week 4 has a dot at 3 inches. Week 5 has a dot at 5 inches. Week 6 has a dot at 4 inches. The dots are connected one to the next by a line to show a change in the amount of rainfall.
4
3
2
1
Answer: 2.5 is the answer. To find median you make a list of numbers from least to greatest then simply find the middle number if theres two in the middle add them both together then divide by two thats your answer.
Step-by-step explanation:
Tran is making fasnachts (deep-fried German doughnuts) to sell the
Tuesday before Ash Wednesday, her bakery's biggest fasnacht day of
the calendar year. She has 8 pounds of butter and her recipe calls for
1/4 cup of butter per 2 dozen
fasnachts. If 1 pound of butter is 2 cups,
then how many individual fasnacht doughnuts will Tran be able to
make?
Answer:
1,536
Step-by-step explanation:
1 pound equals 2 cups, so 8 pounds will be 16 cups.
\(\frac{16}{\frac{1}{4} }\) = 16 x 4 = 64
She can make 64 2 dozen fasnachts. There are 24 fasnachts in 2 dozen.
64 x 24 = 1536 individual fasnachts doughnuts.
HELP PLS HELPP egrhsdjtkfylkfjhtrgthynbvrshtndgvrehtbgd
Answer:
126
Step-by-step explanation:
The area of the top triangle is (6)(6)/2 = 18 square meters.
The area of the bottom rectangle is (9)(12)=108 square meters.
Adding these, we get the total area to be 126 square meters.
What is the difference between Glasgow and Copenhagen. (Glasgow= -7.8 Copenhagen=-3.8)
Answer:
Step-by-step explanation:
The difference of the two values is 4 as calculated by subtraction.
An arithmetic operation called subtraction is the process of deleting or removing items from a collection. The negative symbol (-) denotes subtraction.
Subtraction can mean eliminating or lowering physical and abstract quantities utilizing a variety of things, such as fractions, matrices, vectors, irrational numbers, decimals, functions, and however negative integers. it is typically linked with natural numbers in mathematics.There are several significant patterns in subtraction. It is anticommutative, which means that altering the sequence alters the answer's sign. Additionally, it is not associative, which means that when subtracting more than two numbers, the method used matters. 0 is the additive identity, hence subtracting it has no effect on a number. In relation to related operations like addition and multiplication, subtraction also abides by predictable principles.The given values for Glasgow and Copenhagen are given as -7.8 and -3.8 .
Therefore difference = -3.8 - (-7.8) = -3.8 +7.8 = 4
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ILL BRAINLIEST YOU
PLEASE HELP ME
Answer:
From greatest to least: AB, AC, BC
The grade of a road is the slope of a road. In the u. S. , grade is often expressed as a percent by finding the product 100(slope). Approximate the grade of a road that has a rise of 950 ft over 3 mi.
A road's grade can be thought of as its slope. In the US, grades are frequently reported as percentages by dividing the result by 100. (slope). A road with a rise of 950 feet over three miles is roughly 3% grade.
The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line. Slope is usually represented with the letter m; the rationale for this is unclear, although O'Brien (1844) stated the equation for a straight line as "y = mx + b," which is the first recorded use of the letter in English. It was also written as "y = mx + c" by Todhunter in 1888. The ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line is used to calculate slope.
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What is 7 didved 5436
Solution:
The exact form of the given expression would be \(\frac{7}{5436}\).
Hope this helps! If not, feel free to comment below on what else I can do to better assist you. Other than that, I wish you the best of luck on your studies!
the sum of three consecutive numbers is 45. what is the lowest
Answer:
Step-by-step explanation:
5,1, 9
Answer:
5,1 and 9 like said above sksksk
Step-by-step explanation:
What is the x-intercept ?
Answer:
-3
Step-by-step explanation:
2.5 kg cost £1.40
work out the cost of 4.25kg
Calculating the cost of 4.25 kilogram(kg) is £2.38, by multiplying it by 4.25 kg by 1 kg.
CostCosts are the expenses incurred in the manufacture, marketing, or preparation of a good or asset for regular use. In other terms, it's the cost incurred to produce a good, buy inventories, sell goods, or prepare equipment for use in a commercial activity.
Given,
2.5 kg cost £1.40 i.e,
2.5 kg = £1.40
For 1 kg= \(\frac{1.40}{2.5}\)
= £0.56
To find the cost of 4.25 kg:
Then,
1 kg = £0.56
4.25 kg = 0.56 x 4.25
= £2.38
£2.38 is the cost of 4.25kg after calculating it.
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A painter charges a flat fee and then an additional hourly fee for his work. The table below shows the amount of money the painter ears and the number of hours he works. Create an equation to match the table
of value
1. y - 50x + 25 2. y=100x + 25
3. y=30x + 65
4. y=1502 - 25
Answer:
1. y = 50x + 25
Step-by-step explanation:
See attached image.
a kindergarten teacher has 14 books about a holiday. in how many ways can she select 4 of the books to read to her class in the week before the holiday?
she selects 4 of the books to read to her class in the week before the holiday= \(^{14}C_{4}\)
Permutation and combination are methods for representing a collection of objects by selecting them from a set and forming subsets. It specifies the various ways to arrange a specific set of data. Permutations are when we select data or objects from a specific group, whereas combinations are the order in which they are represented.
The combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. In smaller cases, it is possible to count the number of combinations. Combination refers to the combination of n things taken k at a time without repetition. To refer to combinations in which repetition is allowed, the terms k-selection or k-combination with repetition are often used.
A kindergarten teacher has 14 books about a holiday. in how many ways can she select 4 of the books to read to her class in the week before the holiday,
he can select \(^{14}C_{4}\)
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what is the slope between the points (-3,-4) & (7,6)
Answer:
The slope is 1 I believe.
Answer:
The Slope is 1
Step-by-step explanation:
Slope (m) =
ΔY
ΔX
=
1
1
= 1
θ =
arctan( ΔY )
ΔX
= 45° =
1
4
π
ΔX = 7 – -3 = 10
ΔY = 6 – -4 = 10
Distance (d) = √ΔX2 + ΔY2 = √200 = 14.142135623731
Equation of the line:
y = x – 1
When x=0, y = -1
When y=0, x = 1
there are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, how many have sprinkles or filling?
There are 6 donut with sprinkles and 7 with filling. if there are 3 donut that have both sprinkles and filling, 10 have sprinkles or filling
What is Venn Diagram ?Circles that overlap or do not overlap each other are used in a Venn diagram to illustrate similarities and distinctions between objects or groups of objects.Objects that share characteristics are represented as overlapping circles, whereas objects that are unique stand alone.Venn diagrams are currently utilized in many academic and business settings as demonstrations.Let S represent the set for donut with Sprinklers.
Let F represent the set for donut with Filling.
To find :- How many have sprinkles or filling?
i.e. n ( S ∪ F )
Formula,
n ( S ∪ F ) = n ( S ) + n ( F ) + n ( S ∩ F )
Given,
n ( S ) = 6
n ( F ) = 7
n ( S ∩ F ) = 3
Putting in formula
n ( S ∪ F ) = n ( S ) + n ( F ) - n ( S ∩ F )
= 6 + 7 - 3
= 10
Donuts with Sprinklers or Filling = 10
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an spc chart shows that a process has an overall average measurement of 12.5 and an average moving range of 0.5. what are the control limits for the x chart? a ucl
The Upper Control Limit (UCL) for the X-chart is approximately 14.028.
To calculate the control limits for the X-chart (also known as the process mean chart) in a Statistical Process Control (SPC) chart, we need the average moving range (MR-bar).
The control limits for the X-chart can be determined using the following formulas:
\(Upper $ Control Limit (UCL) = X-double-bar + A2 \times MR-bar\)
\(Lower $ Control Limit (LCL) = X-double-bar - A2 \times MR-bar\)
In these formulas:
X-double-bar represents the overall average measurement.
MR-bar represents the average moving range.
A2 is a constant that depends on the sample size.
The value of A2 can be obtained from statistical tables or calculated using the following formula for sample sizes greater than or equal to 2:
\(A2 = 3.267 - (0.15 \times \sqrt{(N)} )\)
In your case, the overall average measurement is 12.5, and the average moving range is 0.5.
Assuming you have a sample size greater than or equal to 2, we can calculate the value of A2 as follows:
\(A2 = 3.267 - (0.15 \times \sqrt{(N)} )\)
\(= 3.267 - (0.15 \times \sqrt{(2)} ) (assuming N = 2, the $ minimum sample size)\)
\(\approx 3.267 - (0.15 \times 1.414)\)
≈ 3.267 - 0.2121
≈ 3.0559
Now, we can calculate the control limits for the X-chart:
\(UCL = X-double-bar + A2 \times MR-bar\)
\(= 12.5 + 3.0559 \times 0.5\)
= 12.5 + 1.52795
≈ 14.028
Therefore, the Upper Control Limit (UCL) for the X-chart is approximately 14.028.
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The diagrams below show two cereal boxes of different sizes and prices. (a) big box 500 g $8.00 small box 300 g $5.40 Which of the boxes is better value for money? Show your workings.
Answer: Small box has the lowest amount when divided, that box has the best value.
Step-by-step explanation:
Given data,
Big box = 500 g
It cost is $8.00
Small box = 300 g
It cost is $ 5.40
First switch the box that's in kilograms into grams.
One kilogram=1000 grams.
Then, Big box = 500 g = $ 8.00
Small box = 300 g = $ 5.40
Next divide the amount in each box by the cost of each box.
Big box = 500/8
Big box = 62.5
Small box = 300/540
Small box = 0.5555
Therefore,
So, since small box has the lowest amount when divided, that box has the best value.
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9.4. During the course of a normal workday, Sandra and Bob interact with each other more than they do with anyone else. Bob works more closely with Gloria than he does with Joe. Sandra does not work much with Joe but she does work somewhat more with Gloria. If the offices of these individuals were arranged in a linear fashion, one following the other and Sandra's office was first, in what order should they be arranged for maximum communication efficiency?
(1 Point) A. Sandra-Bob-Joe-Gloria B.Sandra-Gloria-Bob-Joe C. Sandra-Gloria-Joe-Bob D.Sandra-Bob-Gloria-loe
10. Reason (2 points)
The ordering that will be important to illustrate maximum communication efficiency is D. Sandra-Bob-Gloria-loe.
What is communication?It should be noted that communication simply means the passing of information from the sender to the receiver.
In this case, ordering that will be important to illustrate maximum communication efficiency is Sandra-Bob-Gloria-loe. This is because Sandra communicates more with Bob than anyone else.
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NI (Factonal of an integer number N) is aperoximated using Stirling s approximation wing the function given below. F(∄)= 2mn
( e
n
) n
Write this fanction in C+1
The given function is: F(∄) = \(2mn e^(n)\) n, which is to be written in C++.Here's the solution to this question:
In C++, we can use the pow() function from the math library to implement exponents.
So, the given function can be written in C++ as:
#include <iostream>
#include <cmath>
using namespace std;
double stirlingApproximation(int n) {
double pi = 3.14159;
double numerator = pow(2 * pi * n, 0.5);
double denominator = pow(n, n) * exp(-n);
double result = numerator / denominator;
return result;
}
int main() {
int n = 5;
double result = stirlingApproximation(n);
cout << "The value of the function F(" << n << ") is: " << result << endl;
return 0;
}
The above code will return the value of the function F(5) using Stirling's Approximation.
Note that we can change the value of n in the main() function to get the value of the function for a different value of n.
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HELP ASAPPPPpppppppp
Answer:
1/12
Step-by-step explanation:
Answer:
1/12
Step-by-step explanation:
1 x 1 = 1
3 x 4 = 12
a survey asks a simple random sample of 500 adults in ohio if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. let denote the proportion in the sample who say they support the increase. suppose that 53% of all adults in ohio support the increase. what is the probability that less than half the sample will say they support the increase? use your calculator. do not round any answer until your final answer. that answer should be rounded to exactly 3 decimal places.
The probability that less than half of the sample will say that they support the increase is given as follows:
0.0885 = 8.85%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by \(\mu\) and standard deviation symbolized by \(\sigma\) is obtained by the rule presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1 - p)}{n}}\), as long as \(np \geq 10\) and \(n(1 - p) \geq 10\).The parameters for this problem are given as follows:
n = 500, p = 0.53.
Hence the mean and the standard error are given as follows:
\(\mu = 0.53\)\(s = \sqrt{\frac{0.53(0.47)}{500}} = 0.0223\)Hence the probability of less than half is the p-value of Z when X = 0.5, hence:
\(Z = \frac{X - \mu}{\sigma}\)
By the Central Limit Theorem
\(Z = \frac{X - \mu}{s}\)
Z = (0.5 - 0.53)/0.0223
Z = -1.35
Z = -1.35 has a p-value of 0.0885.
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Accumulation Functions and FTC 1: Problem 6 (8 points) The curve C is the graph of y = Som t2 -3t+6 dt. Determine x-interval(s) on which the curve is concave downward. C is concave downward on: ___
The curve C is concave downward on the x-interval (-∞, 3/2).
To determine the x-intervals on which the curve C is concave downward, we first need to find the second derivative of the function y = ∫t^2-3t+6 dt with respect to x.
Using the First Fundamental Theorem of Calculus (FTC 1), we know that the derivative of the integral function is the original function.
Therefore, we have:
dy/dx = d/dx [∫t^2-3t+6 dt]
dy/dx = t^2-3t+6
Now, to find the second derivative, we differentiate again with respect to x:
d^2y/dx^2 = d/dx [t^2-3t+6]
d^2y/dx^2 = 2t-3
To determine the concavity of curve C, we need to find where the second derivative is negative (i.e., concave downward).
Setting d^2y/dx^2 < 0, we have:
2t-3 < 0
2t < 3
t < 3/2
Therefore, the curve C is concave downward on the x-interval (-∞, 3/2).
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