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.

Answer:

y=12xO+b(i think)

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Answer:

34 minutes: 22\(\frac{2}{3}\) miles   1 hour: 40 miles

Step-by-step explanation:

First, find how far it will travel in 1 minute. This will make it easier to find the other distances. Use cross multiplication.

2\(\frac{1}{3}\) miles   3\(\frac{1}{2}\) minutes

 ? miles    1  minute

? = 2\(\frac{1}{3}\) × 1 ÷ 3\(\frac{1}{2}\)

  = 2/3 miles in 1 minute

34 minutes?

2/3 × 34 = 22\(\frac{2}{3}\) miles

1 hour (60 minutes)?

2/3 × 60 = 40 miles

Answer:

3:7 < 7:11

Step-by-step explanation:

3:7 is less than 7:11.

Explanation- Both ratios are in there simplest form so there is no dividing needed to be done, there for we can move on straight to comparing there values. We know that 7:11 is greater than 3:7 because, 7+11= 18 and 3+7= 10, and 18 > 10.

I hope this was helpful and accurate. Have a wonderful rest of your day! I'm so very sorry that the last version of my answer was incomplete, and I hope this version was completed correctly. Again I apoligize for my past mistake.

The child's percentile rank is 84.13%.

To determine the percentile rank of a score, you need to know the mean and standard deviation of the test, as well as the score in question. In this case, the mean is 120 and the standard deviation is 8.

To convert the child's score of 128 to a percentile rank, you would first convert it to a z-score using the formula (score - mean) / standard deviation = z-score.

In this case:

(128 - 120) / 8 = 1

This z-score of 1 represents the number of standard deviations above the mean the child's score is. To convert this z-score to a percentile rank, you can use a table of the standard normal distribution, which shows the proportion of values that are less than or equal to a given z-score.

A z-score of 1 corresponds to a percentile rank of 84.13%

So, the fifth grader who scored 128 on a standardized achievement test has a percentile rank of 84.13%. This means that 84.13% of students scored lower than the child on this test.

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The rational function graphed in this problem is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator, hence they are given as follows:

x= -4 and x = 1.

Hence the denominator of the function is given as follows:

(x + 4)(x - 1).

The intercept is given as follows:

x = 0.

Hence the numerator is:

x.

Thus the function is given as follows:

D. F(x) = x/[(x + 4)(x - 1)]

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Answer:

2 < x < 4

Step-by-step explanation:

Answer:

x = 64 weeks

Step-by-step explanation:

Based on the quantity of water in the tanks and the leakage rate, the two tanks will be equal after 64 weeks.

The first tank has 256 gallons and is leaking at 3 gallons per week. Assuming the number of weeks is x, the expression is:

= Water in tank - (Gallons leaking per week x No. of weeks)

= 256 - (3 × x)

= 256 - 3x

The second tank:

= 384 - 5x

To find the number of weeks they would be equal, equate both tanks:

384 - 5x = 256 - 3x

384 - 256 = -3x + 5x

128 = 2x

x = 128 / 2

========================================================

Explanation:

The angle 945 degrees is not between 0 and 360. We need to adjust it so that we find a coterminal angle in this range. To do this, subtract off 360 repeatedly until we get into the right range

945 - 360 = 585, not in range, so subtract again

585 - 350 = 225, we're in range now

Since 945 and 225 are coterminal angles, this means cos(945) = cos(225)

From here, we use the unit circle. Your unit circle should show the angle 225 in quadrant 3, which is the lower left quadrant. The terminal point here at this angle is \(\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)\)

The x coordinate of this terminal point is the value of cos(theta). Therefore  \(\cos(225^{\circ}) = -\frac{\sqrt{2}}{2}\) and this is also the value of cos(945) as well

Using the periodic property of cos function, you can evaluate the value of cos(945°).

The value of cos(945°) is given by:

\(cos(945^\circ) = -\dfrac{1}{\sqrt{2}}\)

A function returning to same value at regular intervals of specific length(called period of that function).

It is \(2\pi\)

Thus, we have:

\(cos(x) = cos(2\pi +x) \: \forall \: x \in \mathbb R\)

\(cos(945^\circ) = cos(2 \times 360^\circ + 225^\circ) = cos(2\pi + 2\pi + 225)\\ cos(945^\circ) = cos(2\pi) + 225) = cos(225^\circ)\)

\(cos(\pi + \theta) = -cos(\theta)\)

Thus:

\(cos(945^\circ) = cos(225^\circ) = cos(180^\circ + 45^\circ) = -cos(45^\circ) = -\dfrac{1}{\sqrt{2}}\\ cos(945^\circ) = -\dfrac{1}{\sqrt{2}}\)

Note that wherever i have used \(\pi\), it refers to \(\pi ^ \circ\) (in degrees).

Thus, the value of cos(945°) is given by:

\(cos(945^\circ) = -\dfrac{1}{\sqrt{2}}\)

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*I've tried looking up to see if I can find what the part B and c of this question is, but unfortunately, I can't find them. However, I have tried answering this question by answering part a, and also going ahead to answer how to state and explain the secrets of winning the game. I'm pretty sure most of the questions would be answered in the process.

Answer/Step-by-sep explanation:

Using an equation, in slope-intercept form, we can derive an equation that models the relationship of the height of each basket and the number of balls it contains.

The slope-intercept form is given as: \( y = mx + b \), where,

m = slope/rate of change

b = y-intercept/strating value/height of the basket when it's empty.

✍️Baseball Equation:

Using two pairs, (0, 54) and (5, 39) from the given table of values,

Slope/rate of change (m) = \( \frac{y_2 - y_1}{x_2 - x_1} = \frac{39 - 54}{5 - 0} = \frac{-15}{5} = -3 \).

y-intercept, b, = the starting value, or the value of y when x = 0. Therefore, b = 54

This means that the baseball basket was at a height of 54 units when it was empty.

m = -3, means the baseball basket kept reducing at an average rate of -3 units in height as each ball was added.

To derive the baseball equation, substitute m = -3, and b = 54 into \( y = mx + b \).

✅Thus, base ball equation would be:

\( y = -3x + 54 \)

✍️Golf Ball Equation:

Using two pairs, (0, 45) and (5, 35) from the given table of values,

Slope/rate of change (m) = \( \frac{y_2 - y_1}{x_2 - x_1} = \frac{35 - 45}{5 - 0} = \frac{-10}{5} = -2 \).

y-intercept, b, = the starting value, or the value of y when x = 0. Therefore, b = 45

This means that the golf ball basket was at a height of 45 units when it was empty.

m = -2, means the golf ball basket kept reducing at an average rate of -2 units in height as each ball was added.

To derive the baseball equation, substitute m = -2, and b = 45 into \( y = mx + b \).

✅Thus, golf ball equation would be:

\( y = -2x + 45 \)

Now, to win the game, we have to find out how many number of exact balls (x) we need to add in each basket equally, for both baskets to be at the same height.

To do this, set the equation of the baseball equal to that of the golf ball.

Thus:

\( -3x + 54 = -2x + 45 \)

Collect like terms

\( -3x + 2x = -54 + 45 \)

\( -x = -9 \)

Divide both sides by -1

\( x = 9 \)

✅To win the game, add 9 balls each to both basket to make the height of both baskets equal.

Let's check to see if both baskets will yield the same height if we add 9 balls each basket.

✍️Height (y) of Golf ball basket if we add 9 balls (x):

Substitute x = 9 into \( y = -2x + 45 \)

\( y = -2(9) + 45 = -18 + 45 \)

\( y = 27 units \)

✍️Height (y) of Baseball basket if we add 9 balls (x):

Substitute x = 9 into \( y = -3x + 54 \)

\( y = -3(9) + 54 = -27 + 54 \)

\( y = 27 units \)

✅As we can see, both baskets will be at the same height of 27 units when we add 9 balls to each basket.

The game will be won if we do this.

To raise the amount of $500 each member has to raise $50.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the 10 members of the Photography Club want to raise $500, so they will hold a raffle with donated prizes. Jesse proposes that to reach their goal, each member should sell 50 raffle tickets. Alexis proposes that each member should raise $50.

The amount for each person will be,

Amount = 500/10

Amount = $50

Therefore, to raise the amount of $500 each member has to raise $50.

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We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot.

A statistical test is required to determine whether the length of the left foot is greater than the length of the right foot. The null hypothesis states that there is no difference in average length between the left and right feet. The alternative hypothesis is that the left foot's average length is greater than the right foot's average length.

This hypothesis is one-tailed, as we are only interested in whether the left foot is longer than the right foot. We are not considering the possibility that the right foot could be longer than the left foot.

A t-test can be used to determine whether the difference in average length between the left and right feet is statistically significant. We can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis that the left foot is longer than the right foot if the p-value of the t-test is less than the chosen significance level (e.g., 0.05).

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Answer:

2 1/3 I believe

Step-by-step explanation:

The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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Answer:

\(\frac{19}{6} =3\frac{1}{6}\)

Step-by-step explanation:

Answer:

The answer is 3 1/6

Step-by-step explanation:

Answer:

-2<=y<=-7

Step-by-step explanation:

Answer: 283.3333333% (283.3%)

Step-by-step explanation:

First, lets turn 2 5/6 into and improper fraction. It becomes 17/6.

Now, we divide 17/6

17/6 = 2.833333333

Now, to turn it into a percent, we multiply it by 100, or move the decimal point 2 places to the right. That gives us 283.3333333% (283.3%)

Hope this helps!

Answer:

x = 1/8

Step-by-step explanation:

The value of x is 1/8.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

64x = 8

Solve for x.

64x = 8

Divide both sides with 64.

x = 8/64

x = 1/8

Thus,

The value of x is 1/8.

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Answer:

8 cents

Step-by-step explanation:

i'm going to assume you mean the value the store gets from selling the apples

33 - 25 =8

Answer:

100

Step-by-step explanation:

n(u)=120  total people in survey

n(c)=97     people carrying cell phone

n(t)=12     people carrying tablet

n(c∩t)=9  people carrying both tablet and cell phone

n(c∪t)=?   people carrying cell phone or tablet

now,

n(c∪t)= n(c)+n(t) - n(c∩t)

         = 97+12-9

          =109-9

          =100

there fore the number of people carrying cell phone or tablet = 100

Answer:  Option C

Step-by-step explanation: To compare the rates at which the pipes are leaking, we can find the amount of water each pipe leaks per minute.

For Pipe A:

3/4 gallon ÷ 30 minutes = 1/40 gallon per minute

For Pipe B:

1 1/4 gallon ÷ 45 minutes = 5/36 gallon per minute

For Pipe C:

1/2 gallon ÷ 20 minutes = 1/40 gallon per minute

Therefore, Pipes A and C are leaking at the same rate, which means option C is true. Option A and D are false, as Pipe B has the fastest leak rate. Option B is false, as both Pipe A and Pipe C are leaking at the same rate.

The detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is-

"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".

The pyrοlysis prοcess is the thermal decοmpοsitiοn οf materials at elevated temperatures, οften in an inert atmοsphere.

Given is that an engineer at an envirοnmentally minded technοlοgy cοmpany has cοme up with a prοcess tο cοnvert tire waste frοm the autοmοbile industry intο clean energy.

The detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is -

"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".

Therefοre, the detail that best suppοrts the inference that the autο manufacturing industry suppοrts green sοlutiοns is -

"Pyrοlysis generates lοw-cοst energy that can be used in the autοmοbile manufacturing industry".

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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The Centroid of a triangle is the point of intersection of the medians of a triangle.

To find the centroid of a triangle

Explanation

To find the rate of change, we will have to identify the months

The table below shows the months required

We will find the change in the inflation by dividing by the change in inflation by the change in month

The rate of change from February and April will be

The rate of change from February and April is 0.3% per month

The rate of change between July and October will be

The rate of change between July and October will be - 0.1 % per month

A. The following are sets A and B:

A = {2, 3, 5, 7, 11}

B = {1, 2, 3, 4, 6, 12}

C. Elements not in A or A' = ∅

B. The Venn diagram is attached

A universal set is a set which consists of all elements related to the given sets. It is denoted by U.

A. Set A:

A = {2, 3, 5, 7, 11}

Set B:

B = {1, 2, 3, 4, 6, 12}

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A' = {1, 4, 6, 8, 9, 10, 12}

C. Elements not in A or A' = ∅

Complement of set A is refers to a set that contains the elements present in the universal set but not in set A.

Hence, the Venn diagram of sets A, B and U has been attached.

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There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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Answer:

try dividing 161616 with 7 but I don't know what to do with the 6 sorry

Answer:

y=−1.5x−7

Step-by-step explanation:

mr. mole is descending as a constant rate, which means a linear equation. So, we must put it into slope-intercept form: y=mx + b, with m being slope or constant rate, and b being y-intercept

The correct answer is Option C. The graph represents the function f (x) = StartFraction 1 Over x EndFraction minus 1 is On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrant 1, and the other curve opens down and to the left in quadrant 3. A vertical asymptote is at x = negative 1, and the horizontal asymptote is at y = 0.

On a coordinate plane, the graph of a hyperbola is shown.

In quadrant 1, one curve opens up and to the right, while in quadrant 3, the other curve opens down and to the left.

The vertical asymptote is at x = -1, and the horizontal asymptote is at y = 0. This hyperbola is symmetrical across both the x and y axes.

The function f(x) = 1/x - 1 has a vertical asymptote at x = 0 because the denominator approaches zero as x approaches zero.

A fraction with a denominator of zero cannot exist.

The horizontal asymptote of this function is y = -1 because as x approaches infinity or negative infinity, f(x) approaches -1.

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