find a recurrence relation an that counts the number of ways to climb n stairs if you can take either 1 star or 3 strais at a time

Answer:

2

Step-by-step explanation:

4p-3+2p+5=6p-3+5=6p+2

(6p+2)/(3p+1)=2(3p+1)/(3p+1)=2

Answer:

C

Step-by-step explanation:

Answer:

x = - 1

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

the denominator of the rational function cannot be zero as this would make it undefined. Equating the denominator to zero and solving gives the value that x cannot be.

x + 1 = 0 ( subtract 1 from both sides )

x = - 1

P is undefined when x = - 1

The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)

1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)

2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).

3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).

4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)

5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)

6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)

7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)

8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)

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Answer:

A. Substitution

Step-by-step explanation:

You have already gotten what y is in x terms, so you could plug that into the first equation and find out what y and x are

The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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In the quadrilateral ABCD and LBNM the corresponding angles and line segments are as follow,

∠A = ∠L, ∠D =∠M , ∠C = ∠N , and

AB = LB , CD = NM ,  DA = ML.

Quadrilateral ABCD rotates 180 degrees around point B,

New quadrilateral formed named LBMN

The corresponding angle after rotation of 180 degrees around B is equals to,

B remain at same position.

A rotates and point L take the position of A.

D rotates and point M take the position of D.

C rotates and point N take the position of C.

Corresponding angle to A is angle L.

Corresponding angle to D is angle M.

Corresponding angle to C is angle N.

Similarly corresponding segments are of ABCD and LBNM are

Line segment AB corresponds to line segment LB.

Line segment CD corresponds to line segment NM

Line segment DA corresponds to line segment ML.

Therefore, in the quadrilateral the corresponding angles and line segments are ∠A = ∠L, ∠D =∠M , ∠C = ∠N , AB = LB , CD = NM , and DA = ML.

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Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

The required probability is 3 √7 / 32.

Given, a square with sides of length 4 units and a red-shaded triangle with sides 3 units, 3 units and 4 units. We need to find the probability that a randomly selected point within the square falls in the red-shaded triangle.To find the probability, we need to divide the area of the red-shaded triangle by the area of the square. So, Area of square = 4 × 4 = 16 square units. Area of triangle = 1/2 × base × height.

Using Pythagorean theorem, the height of the triangle is found as: h = √(4² − 3²) = √7

The area of the triangle is: A = 1/2 × base × height= 1/2 × 3 × √7= 3/2 √7 square units. So, the probability that a randomly selected point within the square falls in the red-shaded triangle is:  P = Area of triangle/Area of square= (3/2 √7) / 16= 3 √7 / 32.

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Answer:

b

Step-by-step explanation:

in a right triangle as the one in the image above, you can find the value of any of the sides or the angles with the next trigonometric functions:

You have the value of:

o = 50ft

h= 75ft

You use the frist function:

Answer:

Area = 12a m²

Step-by-step explanation:

Given information,

→ Length = 4a m

→ Width = 3a m

Now we have to,

→ find the area of rectangular park.

Formula we use,

→ Area = L × W

Then the area of rectangle is,

→ L × W

→ 4a × 3a

→ (4 × 3)a

→ 12a m²

Therefore, the area is 12a m².

The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

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Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.

Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).

Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.

Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.

Q3 or upper quartile for the data 2,4,6,8,10,12 is 10

Q3 or upper quartile is an statistical term that separates the highest 25 percent data from lowest 75 percent data.

For finding quartile first arrange the given data into ascending order.

Find the median of the data then the median divides the data into two potions . the median of the upper half of data is the upper quartile.

Or if the total no of terms are n then Quartile formula for upper quartile is  

  = (n+1)3/4   term

Given data is 2,4,6,8,10,12 which is already arranged in ascending order and no of terms are n=6

Median of this data = ( 3rd term + 4th term)/2 =(6+8)/2=7

7 divides the data into two halves 2,4,6 and 8,10,12

Upper half is 8,10, 12 as this data has odd terms thus median will be the middle term

Median is middle term of 8,10,12 that is 10

Therefore, Q3 or the upper quartile of the given data is 10

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Answer:

\(dy \ = \ 0.1\)

Step-by-step explanation:

Considering the Leibniz notation to represent the derivative of \(y\) with respect to \(x\), suppose \(y \ = \ f\left(x\right)\) is a differentiable function, let \(dx\) be the independent variable such that it can be designated with any nonzero real number, and define the dependent variable \(dy\) as

                                                  \(dy \ = \ f'\left(x\right) \ dx\),

where \(dy\) is the function of both \(x\) and \(dx\). Hence, the terms \(dy\) and \(dx\) are known as differentials

Dividing both sides of the equation by \(dy\), yield the familiar expression

                                                         \(\displaystyle\frac{dy}{dx} \ = \ f'\left(x\right)\).

Given that \(f\left(x\right) \ = \ x\) and \(dx \ = \ 64.1 \ - \ 64 \ = \ 0.1\), hence

                                                 \(f'\left(x\right) \ = \ 1\).

Subsequently,

                                               \(dy \ = \ f'\left(64\right) \ \times \ 0.1 \\ \\ dy \ = \ 1 \ \times \ 0.1 \\ \\ dy \ = \ 0.1\).

Answer:

five almost 6 weeks

Step-by-step explanation:

brady is saving up to 245 but he already has 98 which means he needs to save 147 more dollars. Brady is making 25 a week so if you divide 147 by 25 you get 5.88 so in 6 weeks he can have a new skateboard with a couple extra doll hairs.

Answer:

Step-by-step explanation:

11 years

Using the compound interest formula. :

Final amount, A = 41000 or more

Rate, r = 7% = 0.07

Loan amount, P = 20,000

Number of compounding times per period = 1

A = P(1 + r/n)^nt

41000 = 20000(1 + 0.07)^t

41000/20000 = 1.07^t

2.05 = 1.07^t

t = log(2.05) / log(1.07)

t = 10.609727

t = 11 years

Answer:

20 dollars

Step-by-step explanation:

Because there is 3 people according to where it said the amount of names there are and they each had to pay 6 dollars. 6 x 3 is 18. That is the price after discount. The coupon is 2 dollars so 18 + 2 is 20 dollars. That is the final price.

Answer:

\(B(t) = 1150*(2)^{t}\)

After 10 hours: 1,177,600

Step-by-step explanation:

The number of bacteria after b hours is given by the following equation:

\(B(t) = B(0)(1+r)^{t}\)

In which B(0) is the initial number of bacteria and r is the rate that it increases.

The initial number of bacteria in the dish was 1,150. The amount of bacteria doubles at the end of each hour.

This means that \(B(0) = 1150, B(1) = 2*1150\)

So

\(B(t) = B(0)(1+r)^{t}\)

\(2*1150 = 1150(1+r)^{1}\)

\(1 + r = 2\)

\(r = 1\)

So

\(B(t) = 1150*(2)^{t}\)

After 10 hours:

\(B(10) = 1150*(2)^{10} = 1177600\)

1,177,600 bacteria after 10 hours.

The probabilities that they are all different, All fruit drops, All the same, All not fruit drops are 2.22%, 7.03%, 11.2%, and 18.96%, respectively.

Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,

Probability= Desired Outcomes / Total Number of outcomes possible

Given that the bag of mixed sweets contains 20 fruit drops, 15 chewing gum and 12 toffees. Therefore, the probabilities can be written as,

Probability of getting a fruit drop = 20/47

Probability of not getting a fruit drop = 1 - (20/47) = 0.574468

Probability of getting a chewing gum = 15/47

Probability of getting a toffee = 12/47

Now, we can write the following probabilities as,

a.) Probability of getting All different

        = (20/47) × (15/46) × (12/45)

= 0.2553 × 0.326 × 0.2667

= 0.02219

= 2.22%

b.) Probability of getting all fruit drops,

        = (20/47) × (19/46) × (18/45)

= 6840 / 97290

= 0.0703

= 7.03%

c.) Probability of getting all the same

= Probability of getting all fruit drops + Probability of getting all chewing gum + Probability of getting all toffee

= [(20/47) × (19/46) × (18/45)] + [(15/47) × (14/46) × (13/45)] + [(12/47) × (11/46) × (10/45)]

= (6840/97290) + (2730/97290) + (1320/97290)

= 0.112

= 11.2%

d.) Probability of getting all not fruit drops

= (Probability of not getting a fruit drop)³

= 0.574468³

= 0.189582

= 18.96%

Hence, the probabilities are calculated for different cases as shown above.

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To subtract 47.96 from 320.041, you can align the decimal points and then subtract each digit from right to left.

First, write the numbers with the decimal points aligned:

320.041

- 47.960

Next, subtract the digits in the ones place, which is 1 minus 0, resulting in 1. Then, subtract the digits in the tenths place, which is 4 minus 6. Since 4 is less than 6, you need to borrow 1 from the digit to the left, making the 2 into a 1 and adding 10 to the 4, giving you 14. So, 14 minus 6 equals 8.

Continue subtracting each digit in the same way:

   320.041

-   47.960

= 272.081

Therefore, 320.041 minus 47.96 is equal to 272.081.

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The equation of the line that passes through the point (-3, 7) and has a slope of -5/3 is y - 7 = (-5/3)(x + 3).

We are given the point (-3, 7) and the slope of the line as -5/3.The slope-intercept form of a line is y = mx + b where m is the slope and b is the y-intercept.

To obtain the equation of the line, we need to substitute the values of slope and point in the slope-intercept form and solve for b.(7) = (-5/3)(-3) + b 21/3 = b.

Now we have the value of b, and we can substitute the values of m and b in the slope-intercept form.y = (-5/3)x + 21/3 is the equation of the line in slope-intercept form.

To obtain the equation in the standard form Ax + By = C, we multiply each term by 3.3y = -5x + 7Add 5x to both sides5x + 3y = 7.

This is the equation of the line in standard form.

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1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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The Answer is:

2/5

Simple math.

The proportion of people with IQs above 130 is 2.3%.

Normal distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Here the mean is 100 and a standard deviation of 15.

µ = 100, σ = 15

P(X > 130) =

= P( (X-µ)/σ > (130-100)/15)

= P(z > 2)

= 1 - P(z < 2)

Using excel function:

= 1 - NORM.S.DIST(2, 1)

= 0.023 = 2.3%

The value is 2.3%.

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Answer:

The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.

Step-by-step explanation:

To compare the intensities, we first need to convert the magnitudes to intensities using the log formula. Then we will set up a ratio to compare the intensities.

Convert the magnitudes to intensities and write them in exponential form.

R=logI

2011 earthquake:

9.1I=logI=109.1

2003 earthquake:

8.3I=logI=108.3

Form a ratio of the intensities.

intensity for 2011intensity for 2003

Substitute in the values and divide by subtracting the exponents to find

109.1108.3100.8≈6.

The intensity of the 2011 earthquake was about 6 times the intensity of the 2003 earthquake.

Your answer:

The intensity of the 2011 earthquake was about 15 times the intensity of the 2003 earthquake.

The intensities of the two earthquakes will be 6.3095.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

In 2011, Japan encountered a serious quake with an extent of 9.1 on the Richter scale. In 2003, Japan encountered another extraordinary seismic tremor that deliberate 8.3 on the Richter scale.

The intensity of the earthquake is given as,

㏒ (I₁ / I₂) = M₁ - M₂

㏒ (I₁ / I₂) = 9.1 - 8.3

Simplify the equation, then we have

㏒ (I₁ / I₂) = 9.1 - 8.3

㏒ (I₁ / I₂) = 0.8

Take anti log, then we have

(I₁ / I₂) = 6.3095

The intensities of the two earthquakes will be 6.3095.

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Answer:

25

Step-by-step explanation:

25 times 3=75-10=65

Answer:

743

Step-by-step explanation:

23+23=46

789-46=743

Answer:

743

Step-by-step explanation:

The in this case, the distance covered by the car would be 120 miles. The equation Distance = Speed * Time allows us to determine the distance covered by an object when the speed and time taken are known.

To determine distance, we can rearrange the formula for speed:

Speed = Distance / Time. By multiplying both sides of the equation by Time, we can isolate Distance.

Distance = Speed * Time

The formula indicates that distance is equal to the product of speed and time. By multiplying the rate at which an object moves (speed) by the duration of travel (time), we can determine the total distance covered during that period.

The equation Distance = Speed * Time represents the relationship between distance, speed, and time.

It states that the distance covered is equal to the product of the speed at which an object is moving and the time it takes to travel that distance.

For example, if a car is traveling at a constant speed of 60 miles per hour for 2 hours, the distance it would cover can be calculated as follows:

Distance = 60 miles/hour * 2 hours = 120 miles.

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