An interval to estimate the true average tip is (14.84,13.76).
What is standard deviation?The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the deviation of each data point from the mean, the standard deviation may be determined as the square root of variance.
confidence interval = sample mean ± standard deviation /(n)^1/2
substitute the values in it then
confidence interval = 14.3 ± 2.7/(25)^1/2
confidence interval = 14.3 ± 2.7/5
confidence interval = 14.3 ± 0.54
confidence interval = 14.3 + 0.54 , confidence interval = 14.3 - 0.54
confidence interval = (14.84,13.76)
So, an interval to estimate the true average tip is (14.84,13.76).
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Review of logarithms (logs)
For each of the following equations, write down the
name of the operation that occurs in the equation and
the name of the inverse operation that helps you
solve the equation.
Equation
x+10=25
2x=28
4²=64
Name of operation
Name of inverse
operation
The operations, along with their inverses are given as follows:
x + 10 = 25: Operation of addition, the inverse is of subtraction.2x = 28: Operation of multiplication, the inverse is the division.4^x = 64: The operation is the exponential, the inverse is the logarithm.How to solve the operations?The operations are solved applying the inverse operations.
The first operation is solved as follows:
x + 10 = 25
x = 25 - 10
x = 15.
Hence the addition operation was solved applying the subtraction operation, which is the inverse operation of the addition.
The second operation is solved as follows:
2x = 28
x = 28/2
x = 14.
Hence the multiplication operation was solved applying the division operation, which is the inverse operation of the multiplication.
The third operation is given as follows:
4^x = 64.
log4(4^x) = log4(64)
x = 3. (as 4³ = 64, hence log4(64) = 3).
Hence the exponential operation was solved applying the logarithm operation, which is the inverse operation of the exponential.
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19
Select the correct answer.
You work for a carpet company. You sell carpets at these prices: 100 square feet for $67, 200 square feet for $130, 400 square feet for $240, and 800 square feet for $504.
What is the best deal for buying carpet?
A.
B.
C.
D.
100 square feet of carpet for $67
200 square feet of carpet for $130
400 square feet of carpet for $240
800 square feet of carpet for $504
400 square feet of carpet area for $240 is the best deal among the given option.
What is Area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina. Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat. It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).
Detailed explanation:The carpets were sold for the following prices:
1) $67 for 100 square feet.
2) $130 for 200 square feet.
3) $240 for 400 square feet
4) $504 for 800 square feet.
Calculation:
For each of them, we would calculate the unit cost per square foot. It develops
1) The price per square foot is 67÷100 = $0.67
2) The price per square foot is 130÷200 = $0.65.
3) The price per square foot is 240÷400 = $0.6.
4) The price per square foot is 504÷800 = $0.63.
Comparing the unit costs per square foot the best deal costs $0.6 per square foot per unit, which is 400 square feet of carpet for $240.
400 square feet of carpet area for $240 is the best deal among the given option.
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The price of an item has been reduced by 95%. The original price was $65
The new price of the item is equivalent to $3.25.
What is percentage?In mathematics, a percentage is a number or ratio that represents a fraction of 100. A percentage is a dimensionless number i.e. it has no unit of measurement.Given is that the price of an item has been reduced by 95%. The original price was $65
Assume the new price to be $[x]. So, we can write -
x = 65 - {95% of 65}
x = 65 - {(95/100) x 65}
x = 65 - {6175/100}
x = 65 - 61.75
x = 3.25
Therefore, the new price of the item is equivalent to $3.25.
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tara has 5/8 gallons of glue. She uses 2/5 of the glue to make blue slime, 1/5 of the glue to make green slime, and the rest of the glue to make purple slime. How many gallons of glue does tara use to make purple slime
Answer:
We can say that he used a total of 5/8 gallons of glue
let x - glue to make purple slime
5/8 = 2/5 + 1/5 + x
5/8 = 3/5 + x (LCD of 5 and 8 is 40)
25/40 = 24/40 + x
25/40 - 24/40 = 24/40 - 24/40 + x (subtract 24/40 both sides)
x = 1/40
CHECKING:
5/8 = 2/5 + 1/5 + 1/40
5/8 = 3/5 + 1/40
25/40 = 24/40 + 1/40
25/40 = 25/40
Therefore, the glue to make purple slime is 1/40 gallons.
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Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Let X1,82 be independent random variables representing lifetimes (in hours) of two key components of a device that fails when and only when both components fail. Say each Xi has an exponential distribution with mean 1000. Let Y1 = min(X1,X2) and Y2 = max(X1,X2), so that the space of Y1,Y2 is 0 < y1 < y2 <. (a) Find G(y1, y2) = P(Y1 = 71,Y2 = y2).
To find the probability that Y1 = 71 and Y2 = y2, we can write G(y1, y2) = P(Y1 = 71, Y2 = y2).
To find the probability that Y1 = 71 and Y2 = y2, we need to consider the possible values of X1 and X2 that could lead to these values of Y1 and Y2. The probability density functions (PDFs) of an exponential distribution with mean 1000 is f(x) = 1/1000 * e^(-x/1000). Therefore, the probability of this event is
P(X1 = 71, X2 = y2) = f(71) * f(y2) = 1/1000 * e^(-71/1000) * 1/1000 * e^(-y2/1000).Another possibility is that X1 = y2 and X2 = 71. The probability of this event is
P(X1 = y2, X2 = 71) = f(y2) * f(71) = 1/1000 * e^(-y2/1000) * 1/1000 * e^(-71/1000).Since these two events are mutually exclusive and exhaust all possible ways that Y1 can equal 71 and Y2 can equal y2, the probability of these events occurring is the sum of these probabilities. Therefore,
G(y1, y2) = P(Y1 = 71, Y2 = y2) = P(X1 = 71, X2 = y2) + P(X1 = y2, X2 = 71) = (1/1000 * e^(-71/1000) * 1/1000 * e^(-y2/1000)) + (1/1000 * e^(-y2/1000) * 1/1000 * e^(-71/1000)) = 2/1000^2 * e^(-(71 + y2)/1000).Note that this expression is only valid when 0 < 71 < y2 < ∞ since these are the conditions under which Y1 can equal 71 and Y2 can equal y2.
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assume the series can be integrated term by term. use this fact and the result from part a) to find the fourier cosine series of the function f(x)
To find the Fourier cosine series of the function f(x), we first need to find the Fourier coefficients of f(x).
The Fourier coefficients of f(x) are given by:
a0 = (2/L) * integral of f(x) from x=0 to x=L
an = (2/L) * integral of f(x) * cos(npix/L) from x=0 to x=L
bn = (2/L) * integral of f(x) * sin(npix/L) from x=0 to x=L
Using the result from part a) and the fact that the series can be integrated term by term, we can find the Fourier cosine series of f(x) as follows:
F(x) = a0/2 + sum from n=1 to infinity of an * cos(npix/L)
Therefore, the Fourier cosine series of the function f(x) is:
F(x) = (1/L) * integral of f(x) from x=0 to x=L + sum from n=1 to infinity of (2/L) * integral of f(x) * cos(npix/L) from x=0 to x=L
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Use the pair of functions to find f(g(x)) and g(f(x)) . Simplify your answers.
f(x)=sqrt(x)+8 , g(x)=x^2+1
f(g(x))=
g(f(x))=
The solution to the given composite functions are;
f(g(x)) = √(x² + 1) + 8
g(f(x)) = [√(x) + 8]² + 1
How to solve composite functions?
Composite functions are usually formed when one function is used as the input of another function.
We are given the functions;
f(x) = √(x) + 8
g(x) = x² + 1
1) f(g(x)); This simply means we will put the entire g(x) function for x in f(x) to get;
f(g(x)) = √(x² + 1) + 8
2) g(f(x)); This simply means we will put the entire f(x) function for x in g(x) to get; g(f(x)) = [√(x) + 8]² + 1
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What is the value of x?
Enter your answer in the box
___units
The triangle ΔRCD is similar to the triangle ΔRAP. Then the value of the variable 'x' is 28 units.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
The triangle ΔRCD is similar to the triangle ΔRAP. Then the equation is given as,
RC / CA = RD / DP
x / 10 = 42 / 15
x / 2 = 14
x = 2 (14)
x = 28
The triangle ΔRCD is similar to the triangle ΔRAP. Then the value of the variable 'x' is 28 units.
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Answer:
x = 28 units
Step-by-step explanation:
As AP is parallel to CD (indicated by the arrows on the line segment), triangle APR is similar to triangle CDR.
In similar triangles, corresponding sides are always in the same ratio.
[tex]\implies \sf AP:CD=PR:DR=AR:CR[/tex]
Given
PR = 15 + 42 = 57DR = 42AR = 10 + xCR = xTherefore:
[tex]\implies \sf PR:DR=AR:CR[/tex]
[tex]\implies \sf 57:42=10+x:x[/tex]
[tex]\implies \sf \dfrac{57}{42}=\dfrac{10+x}{x}[/tex]
[tex]\implies \sf 57x=42(10+x)[/tex]
[tex]\implies \sf 57x=420+42x[/tex]
[tex]\implies \sf 15x=420[/tex]
[tex]\implies \sf x=28[/tex]
Last year the depth of the river was 4.2 feet deep. This year it dropped 24%. Find the depth of the river this year to cross it.
The depth of the river is 3.192 feet.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.
Since last year the depth of the river was 4.2 feet deep and year it dropped 24%. The depth will be:
= 4.2 - (24% × 4.2)
= 4.2 - 1.008
= 3.192 feet
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If you flip three coins, the probability of getting three heads is 0.125. Which of the following statements follows from this?
answer choices
O If you flip three coins 1000 times, you will get three heads exactly 125 times.
O If you flip 3 coins 10 times and never get three heads, the probability of getting three heads in the next set of 10 flips is slightly greater than 0.125.
O If you have 20 sets of three coin flips, then at least one set of flips will be three heads.
O If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
O If you get 3 heads two times in a row, the probability of getting 3 heads again on the next toss of 3 coins is nearly zero.
Using the given provided probability value of getting three heads, The statement which best follow the given condition is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close to 12.5%.
What do you mean by probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
According to the given question:
Assume you have a fair coin, which means it will likely land tails up 50% of the time and heads up 50% of the time. Let's say you flip it three times, each time independently. What is the likelihood that it will land heads up first, followed by a tails up landing?
The solution is 1/8, or 12.5%.
coin flipped = 3 times.
probability of getting three heads = 0.125
Since, This probability explains the chances of landing three heads which is 0.125 which in terms of percentage is 12.5% .
So, The statement is If you flip 3 coins 5000 times, the percentage of time you get three heads will be very close 12.5%.
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y-2x=4 please help i’m
stuck
Answer:
To find x and y intercept .... y = 4, and x = -2
Step-by-step explanation:
y-2x=4
y = 4
-2x=4
-2x/-2 = 4/-2
x = -2
Is this equation for solving y and x
A rock falls from a tower that is 352 feet high. As it is falling, its height is given by the formula h=352-16t^(2). How many seconds (in tenths ) will it take for the rock to hit the ground (h)=(0)?
The rock will take 10.25 seconds to hit the ground, as the amount determined by the formula h=352-16t^(2).
The given equation is h=352-16t^(2). This equation can be used to calculate the time it will take for a rock to hit the ground after it has been dropped from a tower that is 352 feet high. The equation states that the rock's height (h) is equal to 352 minus 16 times the square of the time (t). To find the time it will take for the rock to hit the ground (h=0), we can rearrange the equation to solve for t. The rearranged equation is t=sqrt((352-0)/16), which simplifies to t=10.25. This means that the rock will take 10.25 seconds to hit the ground. This can also be expressed in tenths of a second as 102.5, which is the same as 10.25 seconds.
t= sqrt((352-0)/16)
t= sqrt(22)/4
t= 10.25
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-3x^2-6x+24 factor this equation by any means
Step-by-step explanation:
-3x² - 6x + 24
this is an expression, not an equation.
for an equation this would have to look like e.g.
-3x² - 6x + 24 = 0
anyway, yes, we can factor this expression :
-3x² - 6x + 24 = -3(x² + 2x - 8) = -3(x + 4)(x - 2)
why ?
x² + 2x - 8 corresponds to
(x + a)(x + b) = x² + (a+b)x + ab
so which factors a and b multiply to ab = -8 and add to (a+b) = 2 ?
-8 has the factors
4, -2
-4, 2
8, -1
-8, 1
only (4, -2) covers the both criteria.
therefore, the correct factorization is
-3(x + 4)(x - 2)
What is the equation of this function after it is reflected over the x-axis?
Answer:
Below
Step-by-step explanation:
Multiplying the equation by -1 will flip it around the x - axis
so 3(x-2)^3
A marina is in the shape of a coordinate grid. Boat A is docked at (4.2, −2) and Boat B is docked at (−5.2, −2). The boats are ____ units apart. (3 points)
6.2
7.2
9.4
13.4
Answer:
so (-5.2,-2) and (4.2,-2) are 9.4 units apart away from each other
Step-by-step explanation:
so (4.2,-2) and (-5.2,-2) add together and get 9.4
in non-degenerate cases of the logistic regression model, the maximum likelihood estimator always exists and is always unique. assume the design matrix is of full rank.
For regression and classification predictive modeling, the Maximum Likelihood Estimation framework can be used as a foundation for estimating the parameters of numerous machine learning models.
The logistic regression model is a part of this.
Is MLE always present?For species distribution models, maximum likelihood is a common parameter estimation method. A popular species distribution model, the Poisson point process, does not always have maximum likelihood estimates.
In logistic regression, how is the maximum likelihood determined?At the end of the day, the most extreme probability gauge for p is the mean of the y variable from the N draws. According to the result, p=n1/N=y is the value of p that maximizes the above log-likelihood function.
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How to add mixed numbers with unlike denominators
Answer:
you multiply to find common denominators. in the example below you multiply the denominators by themselves, and then individually. 1/2 and 1/3 are the fractions your working with. (2x3)=6 and then (1x3)=3 and (1x2)=2 (2+3)=5 and so (5/6)
Step-by-step explanation:
example: 1½+1⅓=2⅚
Answer: You have to find a common denominator.
Step-by-step explanation: Look at this attachment to understand: (Directions included)
I hoped this helped! If you can, may you PLEASE mark me brainliest?
Jessica puts away $200 a month for 20 years. How much will she have if she puts it into an annuity paying 6% interest compounded monthly? How much interest does she earn?
The amount after 20 years is $662.04.
The interest does she earn is $240.
What is compound interest?
Compound interest, also known as interest on principal and interest, is the addition of interest to the loan or deposit principal.
One plus the annual interest rate raised to the number of compound periods minus one is multiplied by the initial loan amount, or principal, to determine compound interest.
Given:
Jessica puts away $200 a month for 20 years.
P = $200
t = 20 years
r = 6% = 0.06
n = 12 (compounded monthly)
Consider the compound interest formula,
[tex]A = P(1+\frac{r}{n})^n^t[/tex]
Plug the values of P, r, n and t in the above equation.
⇒
[tex]A = 200(1+\frac{0.06}{12})^1^2^*^2^0\\ A = 200(1+0.005)^2^4^0\\A = 200(1.005)^2^4^0\\A = 662.04089\\A = 662.04[/tex]
Hence, the amount after 20 years is $662.04.
Now to find the interest does she earn.
Interest = Principle x time x rate
= 200 x 20 x 0.06
Interest = $240
Hence, the interest does she earn is $240.
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Question 1 of 10
For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value. What type of function is it?
A. Increasing linear
B. Decreasing linear
C. Exponential growth
D. Exponential decay
The type of function is it is C . Exponential growth .
Given :
For the x-values 1,2,3, and so on, the y-values of a function form a geometric sequence that increases in value .
If for values of x values of y increases and forms a geometric sequence then it would be an exponential growth function because geometric sequence is an exponential function and since, it is increasing hence, an exponential growth.
Option B is incorrect because because y is not decreasing
Option C and D are incorrect because geometric sequence can never be linear since, it gives common ratio.
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Please help will mark Brainly
Answer:
120 children
Step-by-step explanation:
c=children
a=adults
c+a=237
1.75c+2a=444
(c+a=237)*2 ==> make a in the equation equal to 2a
2c+2a=474
- (1.75c+2a=444) ==> eliminate a from the equation
2c-1.75c + 2a-2a = 474-444
2.00c-1.75c = 30
0.25c = 30
4 * 0.25c = 4 * 30 ==> remove decimals by multiplying each side by 4
c = 120 children
Find the volume of the composite solid (STEP BY STEP PLEASE) 25 POINTS
The volume of the composite solid that is made up of hemisphere and cylinder will be 7,121.52 cubic feet.
What is the volume?Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.
The shape is the combination of the hemisphere and cylinder. Then the volume of the composite solid is calculated as,
V = Volume of hemisphere + Volume of cylinder
V = (2/3) πr³ + πr²h
Simplify the equation, then we have
V = (2/3) π(9)³ + π(9)²(22)
V = 486π + 1782π
V = 2268 x 3.14
V = 7,121.52 cubic feet
The volume of the composite solid will be 7,121.52 cubic feet.
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the ration of hugs to kisses at the family reunion was 4:1 if there were 148 hugs how many kisses were there
There were 37 kisses at the family reunion. Probability is used to make predictions and inform decision-making.
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.
To find the number of kisses at the family reunion, you can set up the ratio 4 hugs : 1 kiss as a proportion and solve for the number of kisses. Here's how you can do this:
First, cross-multiply to find the total number of hugs and kisses:
4 hugs * 1 kiss = 148 hugs
4 kisses = 148 hugs
Then, divide both sides of the equation by 4 to find the number of kisses:
4 kisses / 4 = 148 hugs / 4
1 kiss = 37 hugs
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A worker has 3 bags of pebbles to use in a garden. The mass of each bag is
9 kilograms. What is the total mass, in kilograms, of all of the bags of pebbles?
Answer:
D). 27
Step-by-step explanation:
The mass of each bag is 9 kilograms
We have 3 bags
Let's add the mass of all 3 bags to find our answer.
9 kilograms + 9 kilograms + 9 kilograms = 27 kilograms
The solution is, D). 27 is the total mass, in kilograms, of all of the bags of pebbles.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
given that,
A worker has 3 bags of pebbles to use in a garden. The mass of each bag is 9 kilograms.
so, we have,
The mass of each bag is 9 kilograms
We have 3 bags
i.e. total mass = 9 * 3 =27
here, we have to multiply 9 by 3 we get the total mass,
i,e. 27 kg.
similarly, we have,
Let's add the mass of all 3 bags to find our answer.
9 kilograms + 9 kilograms + 9 kilograms = 27 kilograms
Hence, The solution is, D). 27 is the total mass, in kilograms, of all of the bags of pebbles.
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Solve the following equation for x
You bought 12 red apples and 15 green apples to make some pies.
What is the ratio of the number of red apples to the total number of apples?
Answer:
4.9
Step-by-step explanation:
. construct a finite-state machine that models an oldfashioned soda machine that accepts nickels, dimes, and quarters. the soda machine accepts change until 35 cents has been put in. it gives change back for any amount greater than 35 cents. then the customer can push buttons to receive either a cola, a root beer, or a ginger ale.
We may use the instructions provided to build a finite-state machine that simulates a vintage soda machine and can carry out the specified work.
Nickels (5 cents), dimes (10 cents), and quarters are all accepted by the machine (25 cents).
The states should be s, s1, s2, s3, s4, etc.
If we add a nickel to the machine, we move from state s to state s+1 and so on, and the process is the same for a dime and a quarter.
We can build the necessary finite-state machine to simulate an antique soda machine that takes nickels, dimes, and quarters by using x as the input button for soda pop.
A mathematical model of computation is called a finite-state machine (FSM), often known as a finite automaton or just a state machine.
It is an abstract machine that has a limited number of states that it can only be in at any given time. The FSM can change from one state to another in response to some inputs; this change is known as a transition. A set of states, an initial state, and the inputs that trigger each transition comprise an FSM.
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an fda representative randomly selects 8 packages of ground chuck from a grocery store and measures the fat content (as a percent) of each package. assume that the fat contents have an approximately normal distribution. the resulting measurements are given below.fat contents (%)12 15 16 1315 13 15 13step 1 of 2 : calculate the sample mean and the sample standard deviation of the fat contents. round your answers to two decimal places, if necessary.
We calculated sample mean 14 and standard deviation 1.32
What is sample mean?A sample mean refers to the average of all values included in the data list.
How to calculate sample mean and standard deviation from the list of data?When we have a list of data set, we can calculate the mean value of the data set by adding all the values and divided by the amount of data.
We are given, 8 packages of ground chuck
number of samples, N = 8
fat contents (%) for 8 packages, X= 12, 15, 16, 13, 15, 13, 15, 13
Sum of X= ∑X= 112
sample mean= sum of all data values/ number of data items in the sample
X= ∑X/N
sample mean X = 112/8 =14
we calculate X² for 8 sample = 144, 225, 256, 169, 225, 169, 225, 169
∑X² = 1582
standard deviation is calculated by using the formula bellow
√[∑X²/N-(∑X/N)²] = √[1582/8-(112/8)²]
standard deviation = 1.32
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Let Sn be the number of lattice paths in the Cartesian plane that start at (0,0), end at (n,n), contain no points above the line y = x, and are composed only of steps (0, 1), (1,0), and (1, 1), i.e. 1, +, and /. So = 1. Consider the generating function S(x):=∑_(n=0)^[infinity]▒〖SnX^n〗. Prove that 1 + (x – 1)S(x) + xS(x)2 = 0.
A formal power series that encodes the coefficients of a sequence of numbers is a generating function.
Here, the coefficients of the sequence {Sₙ} are encoded by the generating function S(x). where Sₙ is the number of lattice paths as described above.
Here we will use the fact that the generating function for a sequence satisfies a functional equation that relates the generating function to the sequence itself to prove that 1 + (x – 1)S(x) + xS(x)² = 0,
Here, the functional equation is
S(x) = 1 + xS(x) + xS(x)²
This equation implies that
The term 1 on the right-hand side corresponds to the fact that to reach the point (0,0) (the starting point), there is exactly one way which is to stay at the starting point.
The term xS(x) corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-1, n-1) we can reach any point (n,n)
The term xS(x)² corresponds to the fact that by taking a step in the positive x-direction and then following a path to (n-2, n-2), and then taking another step in the positive x-direction and following a path to (n-1, n-1) we can reach any point (n,n)
Thus, 1 + (x – 1)S(x) + xS(x)² = 0. Hence proved.
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in triangle pqr pq equals 39 inches, pr equals 17 inches, and hte altitude pn equals 15 inches. find ar. consider all cases, two answers
In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 in.
How did we figure this out?Solution:[tex]\boxed{\bold{= > (39)^2=(15)^2+(QN^2}}\\\boxed{= > QN=\bold{\sqrt{(39)^2-(15)^2}} }\\\boxed{= > QN=\bold{36}}[/tex]
Now we have to determine the side RN.
Side PR = 17Side PN = 15Now put all the values in the above expression, we get the value of side RN.
[tex]\boxed{\bold{= > (17)^2}=(15)^2+(RN)^2}\\\boxed{= > RN=\bold{\sqrt{(17)^2-(15)^2} }}\\\boxed{= > RN=\bold{8}}[/tex]
Side QR = 36 + 8Side QR = 44Therefore, In triangle PQR PQ equals 39 inches, PR equals 17 inches, and HTE altitude PN equals 15 inches. The correct answer is QR is, 44 inches.
[tex]\text{The correct answer is QR is, 44 in.}[/tex]
Using Pythagoras theorem in ΔPNQ:
[tex]\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PQ)^2=(PN)^2+(QN)^2}}[/tex]
PQ = 39PN = 15[tex]\boxed{(39)^2=(15)^2+(QN)^2}\\\boxed{\bold{QN=\sqrt{(39)^2-(15)^2} }}\\\boxed{QN=\bold{36}}[/tex]
[tex]\boxed{(Hypotenuse)^2=(Perpendicular)^2+(Base)^2}\\\boxed{\bold{(PR)^2=(PN)^2+(QN)^2}}[/tex]
PR = 17PN = 15[tex]\boxed{\bold{(17)^2=(15)^2+(RN)^2}}\\\boxed{\bold{RN=\sqrt{(17)^2-(15)^2} }}\\\boxed{RN=\bold{8}}}[/tex]
Adding the numbers:
36 + 8 = 44
[tex]\text{Hence, The correct answer is QR is, 44 in.}[/tex]
Type the correct answer in each box. Use numerals instead of words.
If x>0, what values of c and d make the equations true?
Equation A √448 x⁽=8 x³ √7 x
Equation B ∛576 xᵃ=4 x ∛9 x²
In equation A, c is
In equation B, d is
The value of c in the equation A is 7 and the value of d in the equation B is 5
The first equation is
[tex]\sqrt{448x^c}=8x^3\sqrt{7x}[/tex]
Move the term 8x^3 inside the square root
[tex]\sqrt{448x^c}=\sqrt{7x(8x^3)^2}[/tex]
Multiply the terms in the equation
[tex]\sqrt{448x^c} = \sqrt{448x^7}[/tex]
Here the both terms are equal. Therefore the value of x^c and the x^7 will be equal.
Then the value of c = 7
Part 2
The second equation is
[tex]\sqrt[3]{576x^d}=4x \sqrt[3]{9x^2}[/tex]
Move the term 4x inside the square root
[tex]\sqrt[3]{576x^d}=\sqrt[3]{9x^2(4x)^3}[/tex]
Multiply the terms in the equation
[tex]\sqrt[3]{576x^d}=\sqrt[3]{576x^3}[/tex]
Here the both terms are equal. Therefore the value of x^d and the x^5 will be equal
Then the value of d = 5
Therefore, the value of c = 7 and the value of d = 5
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