Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Length of remnant fabric = 9.7m
Number of 0.85m length needed for patio = 12
Total length needed = (0.85 * 12) = 10.2m
The length of fabric needed is more than the length of remnant fabric found ;
10.2 m - 9.7m = 0.5m
Hence, Alex will need 0.5m more fabric
Kadeesha bought snacks for her team's practice. She bought a bag of popcorn for $ 1.59 and a 5-pack of juice bottles. The total cost before tax was $13.34. Which equation or tape diagram could be used to represent the context if j represents each bottle of juice costs?
A
5 j=1.59-13.34
C
1.59 j=13.34-5
The equation or tape diagram could be used to represent the context if j represents each bottle of juice costs is; Option D tape diagram
How to Represent Algebraic equations?We are told that;
1 bag of popcorn costs $1.59
She bought a 5-pack of juice bottles
Total cost before tax = $13.34
Now, we are told that j represents each bottle of juice costs. Thus;
Cost of the 5 packs of juice = 5j
Thus, the equation of the total cost before tax is;
1.59 + 5j = 13.34
Looking at the options, only the tape diagram in option D correctly represents the required equation.
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I need help ASAp Ive been stuck on this for a long time
Answer:
Step-by-step explanation:
Write the following expression without negative exponents and without parentheses. (7x)^{-2} (7x) −2
[tex]\frac{1}{(7x)^2}[/tex] is the expression without negative exponents.
What are exponents and indices?
Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
An index, or power, is the small floating number that appears after a number or letter. The plural of index is indices.
According to the given question:
(7x)^{-2} is the given indices expression
To expression without negative exponent, the expression
can be written as
[tex](7x)^{-2} = \frac{1}{(7x)^2}[/tex]
Since the exponent -2 is on the whole 7x term. So, the whole term moves to denominator to make the exponent positive.
Therefore [tex]\frac{1}{(7x)^2}[/tex] is the expression without negative exponents
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Perform the following mathematical operation, and report the answer to the appropriate number of significant figures.
1204.2 + 4.72613 = [?]
The answer is not 1208.92613
Answer
Step-by-step explanation:
A. A random sample of 50 interns has a mean earnings of $6520 with a population standard deviation of $927 over the summer months. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval.
B. In a random sample of 50 designer outfits, the average cost was $350 with a standard deviation of $50. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume the distribution of weekly food expenses is normally shaped.
We determined that normal distribution should be used to construct a confidence interval for these two statistical data.
What is t distribution and normal distribution?In statistics, the t-distribution is a system of describing a set of data where most of the data fall close to the mean value and the remaining data adjust the tail on both sides.
The normal distribution is one of the systems of describing a set of data that implies data close to the mean value are more probable to occurrence than the other data.
When does t-distribution and normal distribution used in statistics?In the statistics, we use t- distribution when the number of samples is less than 30 and the population standard deviation is unknown to us.
we use normal distribution when the sample size is greater than 30 and the population standard deviation is known.
We are given two set of statistical data and for both case population standard deviation is given, and the size of sample is greater than 30.
hence, we will use normal distribution for both cases.
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a histogram showing u.s. household income is highly skewed right. which of following statistics would best describe the center of the distribution? question 10 options: 1) median 2) variance 3) mean 4) mode
......,,........,.....-.......
The median would best describe the centre of the distribution for a highly skewed right histogram of US household income. The correct option is A.
What is the median?The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.
Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.
The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.
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Which solids have more than five planes of symmetry? Check all that apply. cylinders cubes rectangular prisms square pyramids cones regular triangular prisms
Sphere, right cylinder and cube have more than five planes of symmetry.
Define symmetry.Symmetry in mathematics means that when one shape is moved, rotated, or flipped, it looks exactly like the other shape. A symmetrical likeness between two halves of an object, when one half is the mirror image of the other, is defined as being proportionate and balanced. As an illustration, many shapes such as square, rectangle, and circle are symmetric along their respective lines of symmetry.
Given,
Sphere and right cylinder have more than five planes of symmetry.
The number of symmetry planes depends on each solid by definition (a figure of three dimensions). The solid is split into two congruent, mirror-imaged parts by the plane of symmetry.
A cube has nine planes of symmetry, a square pyramid has four, hexagonal prims have thirteen, and spheres and cylinders have an infinite number of planes of symmetry, according to the information presented above.
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Answer nah the correct answer is cylinders cubes and cones
Step-by-step explanation:
seen it irl on edgennuitiy
Solve the quadratic equation numerically (using tables of x- and y- values).
x squared minus 3 = 2 x
a.
x = -1 or x = 3
c.
x = -3 or x = -3
b.
x = 2 or x = -3
d.
x =1 or x = -1
The quadratic equation numerically (using tables of x- and y- values).
Correct option: (a). The value of x are x = -1 and x = 3.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x with the formula; ax² + bx + c = 0, where a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.
The given quadratic equation is:
x² - 3 = 2x
or, x² - 2x - 3 = 0
or, x² - 3x + x - 3 = 0
or, x (x - 3) +1 (x - 3) = 0
or, (x - 3) ( x +1 ) = 0
or, x = +3 , -1
The value of x are x = -1 and x = 3.
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Mason used a 30% coupon to buy a new computer. After the discount, the cost of the computer was $728. Determine the original price of the computer. Show your work.Calculate how much money Mason saved by using the coupon. Show your work.
The original price is $1049 and the amount saved is $321
How to determine the original price?From the question, we have the following parameters that can be used in our computation:
Cost after discount = $728
Discount = 30% off
The original price is calculated as
Cost after discount = Original price * (1 - Discount)
So, we have
Original price = Cost after discount/(1 - Discount)
This gives
Original price = 728/(1 - 30%)
Evaluate
Original price = 1049
The amount savedHere, we have
Amount saved = Original price - Cost after discount
So, we have
Amount saved = 1049 - 728
Evaluate
Amount saved = 321
Hence, the amount saved is $321
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A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 5 child bikes and 15 adult bikes in a week? (1 point)
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
The company can build 5 child bikes and 15 adult bikes in a week.
The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".
Linear Equations:Linear Equations are mathematical statements, which can be used to find an unknown quantity or any value in a given problem. Here we use variables like x, y .. etc. to represent unknown values.
Here we will use Linear Equations to solve the equations.
Here we have
One child bike requires 4 hours to build and 4 hours to test
Number of hours to build 'c' number of child bikes = 4c
Number of hours to test 'c' number of child bikes = 4c
One adult bike requires 6 hours to build and 4 hours to test.
Number of hours to build 'a' number of adult bikes = 6a
Number of hours to test 'a' number of adult bikes = 4a
Number of hours taken to build bikes in one week = 120
=> 4c + 6a ≤ 120 --- (1)
Number of hours taken to test the bikes in one week = 100
=> 4c + 4a ≤ 100 --- (2)
Assume that
The company can build 5 child bikes and 15 adult bikes in a week
Substitute c = 5 and a = 15 in (1) and (2)
(1) => 4(5) + 6(15) ≤ 120
=> 110 ≤ 120 [ which can be true ]
(2) => 4(5) + 4(15) ≤ 100
=> 80 ≤ 100 [ which can be true ]
From the above calculations,
Both (1) and (2) are satisfied
Therefore,
The company can build 5 child bikes and 15 adult bikes in a week.
The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".
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Two fair dice are rolled. Find the joint probability mass function of x
and y
, when x
is the largest value obtained on any die and y
is the sum of the values.
a) P(X = x₀, Y = 2x₀) = 1/36
P(X = x₀, Y = k) = 1/18 for k between x₀+1 and 2x₀-1 inclusive
Every other event has probability 0. x₀ is any number between 1 and 6 inclusive.
b) P(X = x₀, Y = x₀) = x₀/36
P(X = x₀, Y = k) = 1/36 for k between x₀+1 and 6 inclusive.
x₀ is between 1 and 6 inclusive. Every other event has probability 0.
c) P(X = x₀, Y = x₀) = 1/36
P(X = x₀, Y = k) = 1/18 with k between x₀+1 and 6 inclusive
x₀ between 1 and 6 inclusive. Any other event has probability 0.
What is a joint probability?Joint probability is the probability of two events happening simultaneously.
Let P(A) = probability that event A takes place and P(B) = probability that event B takes place. Then, probability of event A and B happening together i.e. P(A and B) is called joint probability.
What is the Calculation of joint probability?(1) When A and B are independent events: When event A has no impact on event B or vice versa, the two events are said to be independent. For independent events, formula for joint probability is:
P(A and B) = P(A) × P(B)
Example: I am performing two acts at a time (i) tossing a coin and (ii) throwing a dice. What is the probability that the coin shows up “head” and the dice shows up “3”?
There is no doubt that getting “head” on coin and getting “3” on dice are independent events.
Probability of the coin showing up “head” = 1/2
Probability of the dice showing up “3” = 1/6
Therefore, probability of getting “head” on coin and “3” on dice = (1/2)×(1/6) = 1/12
(2) When A and B are dependent events: If event A and event B cannot be considered independent, calculation of joint probability requires knowledge of conditional probability. For dependent events, formula for joint probability is:
P(A and B) = P(A) × P(B, given A) = P(B) × P(A, given B).
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Solve.(Refer to the picture)
Answer:
[tex]y=2.182[/tex]
Step-by-step explanation:
Solve for y.
[tex]3.082=y+\frac{9}{10}[/tex]
Move all terms not containing [tex]y[/tex] to the right side of the equation.
[tex]y=3.082-\frac{9}{10}[/tex]
Write [tex]\frac{9}{10}[/tex] as a decimal.
[tex]y=3.082-0.9[/tex]
[tex]y=2.182[/tex]
Fill in the blank to make the two fractions equivalent. ?/27= 4/9
Answer:
12/27 = 4/9
Step-by-step explanation:
Solve for ?:
?/27 = 4/9
Multiply both sides of ?/27 = 4/9 by 27:
(27 ?)/27 = 27×4/9
27×4/9 = (27×4)/9:
(27 ?)/27 = (27×4)/9
(27 ?)/27 = 27/27×? = ?:
? = (27×4)/9
27/9 = (9×3)/9 = 3:
? = 3×4
3×4 = 12:
Answer: ? = 12
Answer:
12/27 = 4/9
Step-by-step explanation:
To get from one fraction to the other, you must find out what the denominator of the fraction we know (4/9) is being multiplied by to get the denominator of ?/27.
We divide 27 by 9 to get 3 then multiply the numerator (4) by 3 as well to get 12, your answer.
PLEASE HELP ME! Does anyone understand this at all?
The trigonometric function -cos(-x) will be not equal to cosx thus option (C) will be correct.
What is a trigonometric function?The trigonometric functions found in the four quadrants, as well as their graphs, domains, and differentiation and integration, will all be understood.
The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.
It is known that, by cosine function property,
cos(-x) = cosx
So, -cos(-x) = -(cosx)
-(cosx) ≠ cosx
Hence "Cos(-x) will not equal cosx in the trigonometric function".
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Clare would like to buy a video game that costs at least $130. She has saved $48 so far and plans on saving $5 of her allowance each week. Write an inequality to find out the number of weeks it will take until she has enough money to buy the game.
Answer:
To determine how many weeks it will take Clare to save enough money to buy the video game, we need to find the number of weeks it will take for her to save at least $130. Let w be the number of weeks it will take for Clare to save enough money. We can set up the following inequality to represent this situation:
$48 + $5w >= $130
To solve this inequality, we can first add $48 to both sides to get rid of the constant on the left side:
$48 + $48 + $5w >= $130
This simplifies to $96 + $5w >= $130. Subtracting $96 from both sides gives us $5w >= $34. Dividing both sides by $5 gives us w >= 6.8. Since w represents the number of weeks, the solution must be a whole number. Therefore, Clare will need to save for at least 7 weeks in order to have enough money to buy the video game.
Natalie takes a car to a title loan business to borrow some money. Natalie is given $3,200.00. She must pay back the $3,200.00 in addition to a $1,000.00 fee in 4 months.
What simple interest rate is she being
charged?
Round to the nearest tenth of a percent and don't forget to include a percent sign, %, in your answer.
Natalie is being charged a simply interest rate of ______.
Answer:
7.8125%
Step-by-step explanation:
(4200/3200-1)/4 the difference for every month
so this would result to 7.8125% every month
Answer:
Rate = (Percentage/Base)/Time
Rate =(1 000/3 200)/4
Rate = 0.3125/4
Rate = 0.078125 (convert to percent)
Rate = 7.9% (nearest tenth)
Therefore, Natalie will pay 7.9% interest per month
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Alex learned 80 new vocabulary words for his English exam. The following function gives the number of words he remembers after t days: W(t) = 80(1 - 0.1t)^3 What is the instantaneous rate of change of the number of words Alex remembers after 5 days? Choose 1 answer: A. 10 days B. 10 words per day C. -6 days D. -6 words per day
The instantaneous rate of change is -6 words per day,
the number of words Alex remembers after 5 days, option (D).
What is the instantaneous rate of change ?
An instantaneous rate is the rate at some instant in time. An instantaneous rate is a differential rate: -d[reactant]/dt or d[product]/dt. We determine an instantaneous rate at time t: by calculating the negative of the slope of the curve of concentration of a reactant versus time at time t.
Have given,
Alex learned 80 new vocabulary words
and after t days he learned,
W(t) = [tex]80 (1-0.1t)^{3}[/tex]
differentiate respect of t
W'(t) = [tex]80 \frac{d}{dt} (1-0.1t)^{3}[/tex]
W'(t) = [tex]80 * 3(1-0.1t)^{2} \frac{d}{dt}(1-0.1t)[/tex]
W'(t) = [tex]240(1-0.1*5)^{2} (0.1)[/tex]
W'(t) = 6
That's mean , the instantaneous rate of change is -6 words per day.
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on Monday Therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If Thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
Therease should take her 7th dose on Friday at 9:00AM
What is time ?
Time can be described in mathematics as an ongoing and continuous series of events that take place one after another, from the past through the present, and into the future. The duration of events or the gaps between them can be measured, compared, or even ordered using time.
Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.
Time is defined by physicists as the flow of events from the past through the present and into the future. In essence, a system is timeless if it is unchanging. When describing events that take place in three-dimensional space, time can be thought of as the fourth dimension of reality.
The doctor told her to take a dose of 4.8 ml every 12 hours for 7 days.
If Theresa took her first dose at 9:00 AM on Monday,
Simply add 12 hours every time up to the 7th dose,
First dose ----> 9:00 AM on Monday,
Second dose ----> 9:00 PM on Monday,
Third dose ----> 9:00 AM on Tuesday,
Fourth dose ----> 9:00 PM on Tuesday,
Fifth dose ----> 9:00 AM on Thursday,
Sixth dose ----> 9:00 PM on Thursday,
Seventh dose ----> 9:00 AM on Friday,
Hence, Theresa should take her 7th dose at 9:00 AM on Friday.
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8 identically sized pieces of timber are x cm long when put together .how long is each individual piece
The length of each individual piece is x/8
How to determine the length of each piece?From the question, we have the following parameters that can be used in our computation:
Number of pieces = 8
Length of timber put together = x
The length of each piece of timber is calculated as
The length of each piece = Length of timber put together/Number of pieces
Substitute the known values in the above equation, so, we have the following representation
The length of each piece = x/8
Hence, the length of each piece is x/8
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How many 1/2 cup servings are in a package of cheese that contains 5 1/4 cups altogether?
There are 10.5 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether.
How to calculate the number of cups?A ratio is the relationship or comparison between two numbers belonging to the same unit in order to determine how much larger one number is than the other.Because the numerator is a decimal value, the ratio 10.2/34 isn't one. This number can be expressed as a ratio by multiplying the numerator and denominator by the appropriate power of ten to get rid of the decimal point.To find the number of 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether, we first need to convert the total amount of cheese in cups to a number of 1/2 cup servings.
We can do this by dividing the total amount of cheese by the size of a 1/2 cup serving.
First, we need to convert the amount of cheese in cups to a decimal number. Since there are two 1/2 cups in a cup, the decimal equivalent of 1/2 cup is 0.5. Therefore, the decimal equivalent of 5 1/4 cups is 5.25 cups.
Next, we need to divide the total amount of cheese in cups by the size of a 1/2 cup serving. Since the size of a 1/2 cup serving is 0.5 cups,
we can divide 5.25 cups by 0.5 cups to find the number of 1/2 cup servings as follows:
5.25 cups / 0.5 cups = 10.5
Therefore, there are 10.5 1/2 cup servings in a package of cheese that contains 5 1/4 cups altogether.
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Jolie is buying a shirt and a hat at the mall. The shirt costs $34.67, and the hat costs $19.48. If she gave the sales clerk $100.00, how much change should she receive?
Answer:
Jolie will get 45.85 change
Step-by-step explanation:
34.67+19.48=54.48
100.00-54.15=45.85
May I require assisstant?
Answer: the answer to a is 50% chance the answer to b is also 50% chance
Step-by-step explanation:
Function f is a linear function and function g is defined by g(x)=f(x)+k t . If the value of k is 7 , how does the graph of g compare with the graph of P?
The graph of g is the graph of f
Choose...
translated up 7 units translated left 7 units translated right 7 units translated down 7 units stretched vertically by a scale factor of 7 stretched horizontally by a scale factor of 7
The graph of g is the graph of f translated up 7 units
How to determine the equation of the graph of the function g(x)?From the question, we have the following parameters that can be used in our computation:
g(x) = f(x) + k
Also, we have the value of k to be
k = 7
From the question, we can interpret g(x) = f(x) + k as f(x) is shifted up by k units
This means that
g(x) = f(x) + k
So, we have
g(x) = f(x) + 7
Hence, the transformation is (a) translated up 7 units
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Belinda is thinking about buying a house for $286,000. The table below shows the projected value of two different houses for three years:
Number of years 1 2 3
House 1 (value in dollars) 294,580 303,417.40 312,519.92
House 2 (value in dollars) 295,000 304,000 313,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer.
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years.
Part C: Belinda wants to purchase a house that would have the greatest value in 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years.
a) The type of function for each case is given as follows:
House 1: Exponential.House 2: Linear.b) The functions for each house are given as follows:
House 1: 294580(1.03)^x.House 2: 295000 + 9000x.c) The value of each house after 25 years is given as follows:
House 1: $616,785.10.House 2: $520,000.There is a significant difference in these valuations, as an exponential function increases faster than a linear function.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
Hence House 1 is an exponential function, as:
312519.92/303417.40 = 303417.40/294580 = 1.03.
And the definition is given as follows:
294580(1.03)^x.
The value of the house after 25 years is given as follows:
294580(1.03)^25 = $616,785.10.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
Hence House 2 is a linear function, as each year, the value of the house is increased by 9000.
Then the definition is given as follows;
295000 + 9000x.
The value of the house after 25 years is given as follows:
295000 + 9000(25) = $520,000.
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The value of car decreases at the rate of 10% per year. If the current price of the car is 245000 calculate it’s price after 3 years
Answer:
year 1: 90% × 245000 = 220500
year 2: 90% × 220500 = 198450
year 3: 90% × 198450 = 178605
∴ the car price after 3 years is 178605
explanation:
the value of car decreases 10%. that means the car price is 90%
The price of the car after 3 years will be 178605
We can calculate the value in the following way
Rate of decrease in car's price: 10%
Current price of the car: 245000
Value after 1 year, say value1= current value-10% of current value
[tex]value1=245000-\frac{10*245000}{100}[/tex]
=245000-24500
=220500
After 1 year, the next decrement in the price will be based on the value of the car in that year. In other words, we calculate the value after the second year by decreasing by 10% of value1.
Value of car after 2 years, say value2= value1- 10% of value1
[tex]value2=220500- (\frac{10*220500}{100})[/tex]
=220500-22050
=198450
Similarly,
Value of car after 3 years, say value3= value2- 10% of value2
[tex]value3=198450- (\frac{10*198450}{100})[/tex]
=198450-19845
=178605
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Convert loo percent to a decimal
DUE SOON! REAL ANSWERS ONLY!!!
Answer:
A.) The sum will be an even integer.
Step-by-step explanation:
The conjecture that can be made about the sum of two even integers and one odd integer is that the sum will be an even integer. This is because even integers are numbers that are divisible by 2, and odd integers are numbers that are not divisible by 2.
For example, consider the sum of the even integer 6 and the odd integer 7. The sum of these two numbers is [tex]6 + 7 = 13[/tex], which is an odd integer. However, if we add another even integer to the sum, such as 4, the resulting sum is [tex]13 + 4 = 17[/tex], which is an even integer. This shows that the sum of two even integers and one odd integer is always an even integer.
This conjecture can be proven using mathematical induction. We can start by showing that the sum of any two even integers and one odd integer is always an even integer. Then, we can assume that the sum of any n even integers and one odd integer is also an even integer. Finally, we can show that the sum of n+1 even integers and one odd integer is also an even integer, using the assumption that the sum of n even integers and one odd integer is even. This will prove that the conjecture is always true.
a candy distributor needs to mix a 10% fat content chocolate with a 30% fat content chocolate to create 100 kg of at 18% fat content chocolate. how many kilograms of each kind of chocolate must they use?
Solving a system of equations we will see that they need to use:
40 kg of the 30% fat content chocolate.60 kg of the 10% fat content chocolate.How many kilograms of each kind of chocolate must they use?Let's define the variables:
x = kilograms of the 10% fat-content chocolate.
y = kilograms of the 30% fat-content chocolate.
We know that they want to create 100kg, then:
x + y =100
And the fat content must be 18%, then we can write the concentration equation:
0.1*x + 0.3*y = 0.18*100 = 18
The coefficients are the percentages in decimal form.
Now we have a little system of equations:
x + y =100
0.1*x + 0.3*y = 18
Isolating x on the first one we get:
x = 100 - y
Replacing that in the other equation we get:
0.1*(100 - y) + 0.3*y = 18
10 + 0.2*y = 18
0.2*y = 18 - 10 = 8
y = 8/0.2 = 40
They need to use 40kg of the 30% chocolate and 60kg of the 10% chocolate.
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In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path allows only moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.8 C 88 C M C 8C M A M C8 C M C 88 C 8(A) 8(B) 9(C) 12(D) 24(E) 36
In the arrangement of letters and numericals, the total number of different paths can one spell AMC8 are 24 in count.
What is counting principle?A basic counting principle is that if there are p ways to do one thing and q ways to do another, then there are p × q ways to do both. Possible results of experiments. The counting principle can be extended to situations where there are two or more alternatives.
We have, the arrangement of letters and numericals in above figure such that
Beginning at the A in middle M a path allows only moves from one letter to an adjacent either above, below, left, or right, but not diagonal letter.There are three different kinds of paths that are on the above diagram to get the required pattern. The first kind is when you directly count A, M, C in a straight line. The second is when you count A, turn left or right to get M, then go up or down to count 8 and C. The third is the one where you start with A, move up or down to count M, turn left or right to count C, then move straight again to get 8.
There are 8 paths for each kind of path, making for 8×3= 24 paths.
Hence, the required paths are 24 in count.
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Can I get help with this quick check
The common difference of the sequence is 70, the slope of the 1st and 2nd lines is 70, the slope of the 3rd and 4th points is 70, and the slope is constant.
What is the slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. Y and x are the net changes in the y and x coordinates, respectively.
Given:
Time in minutes and jumping jack table, coordinates of lines (1, 70) and (2, 140)
(a)
Consider 70, 140, 210, and 280 as an arithmetic sequence then the common difference will be,
Common difference = 140 - 70 = 70
(b)
Calculate the slope of the line as shown below,
[tex]m = (y_2-y_1) / (x_2 - x_1)[/tex]
m = (140 - 70) / (2 - 1)
m = 70 / 1
m = 70
(c)
Calculate the slope for 3rd and 4th points,
m = (280 - 210) / (4 - 3)
m = 70 / 1
m = 70
(d)
As you can, the slope is constant, and the common difference is also constant.
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