Mathematical Modeling. (a) Solve the given recurrence relation an an-1 + an-2, ao = 1, a₁ = 1 = (b) Find the fixed point for the equation 5+5=10 Marks Xn-Xn-1e¹*n-1, r is a constant and test stability. =

Answer:

7

Step-by-step explanation:

rate of change of function not necessary mean linear, it can be the slope of a tangent line.

a: y=8x+3    slope = 8

b: rate of change: 1

8-1=7

I wish this is true...

Answer:

93.33 miles

Step-by-step explanation:

60 min/ 20 min = 3

280/3 = 93.333333

Answer:

93.3 miles

Step-by-step explanation:

Since there are 60 minutes in an hour and 20/60 = 1/3, you can divide 280 by 3 to get the amount of miles travelled in 20 minutes.

The equivalence of the remainder following the division of 17 and 30 by N indicates that the largest value N can have is 30

The remainder term in a division of one value by a second value is the value which is less than the divisor, remaining after the divisor divides the dividend by a number of times indicated by the quotient.

The remainder following the division of 17 and 30 by the number N are the same.

Let R represent the remainder following the division of the integers 17 and 30 and let b represent the number of times N divides 30 than 17. Using the long division formula, we get;

17/N = Q + R/17

30/N = b·Q + R/17

30/N - 17/N = 13/N

The substitution property indicates that we get the following equation;

30/N - 17/N = b·Q + R/17 - (Q + R/17) = b·Q - Q

30/N - 17/N = b·Q - Q

13/N = b·Q - Q = (b - 1)·Q

13/N = (b - 1)·Q

The fraction 13/N which is equivalent to the product of (b - 1) and Q indicates that N is a factor of 13

13 is a prime number, therefore, the factors of 13 are 13 and N

Therefore, the possible values of N are 13 and 1

The largest value N can have is therefore, 13

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Answer:

15

Step-by-step explanation:

7x+9=5x+39

7x-5x=39-9

2x=30

30/2=x

x=15

Hi there!!

  If you need  X to be solved then the answer is X=Y over 5+3 and if your looking for the answer for Y then the answer is Y=5x−15

When you are solving for X you will need to use the distributive property so you can multiply 5 by X-3.

Y=5x-15. Once you've done that then you need to swap sides so all of the variables are on the same side as each other  (they need to be on the left side) 5x-15=Y.

Then you need to add 15 to both of the sides to make it look like this     ->5x=Y+15

When that's done you then need to divide both sides by 5 so it then looks like this when done.

5x over 5= Y+15 over 5

When you divide this by 5, it then undoes the multiplication by 5.

X= Y+15 over 5

Finally, you need to divide Y+15 by 5

X=Y over 5 plus 3

When solving for Y, all you will need to do is use the distributive property to multiply 5 by X-3.

I REALLY HOPE THIS HELPED YOU OUT AND THAT I DIDN'T WASTE YOUR TIME WITH A WRONG ANSWER . BUT IF THIS WAS CORRECT THEN YOU ARE VERY WELCOME

Answer:

x = 17

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

(x+7) * 7 = ( 13+8) *8

(x+7) * 7 = ( 21) *8

Divide each side by 7

x+7 = 21/7 *8

x+7 = 3*8

x+7 = 24

Subtract 7

x = 17

Answer:

The answer is x = 17

Though I think the other guy explained it better

Answer:

Angle 4 = 135, angle 5 = 45

Step-by-step explanation:

Consecutive interior angles are supplementary, therefore angle 5 + angle 8 = 180 degrees. Since the complement of 5 is the supplement of 4, we can write the system of equations.

180 - x = 90 - y or -x + y - 90 - 180 or -x + y = -90 or x - y = 90

x + y = 180

x - y = 90

Where angle 4 is x and angle 5 is y.

y = 180 - x

x - (180 - x) = 90

x - 180 + x =90

x + x = 270

2x = 270

x = 135

By plugging that in to an equation we can solve for y.

y = 45

Answer:

Step-by-step explanation:

ABC

B= 65

C= 25

AC=9

AB=10

DEF

E=75

F= 75

DF=13

DE=13

GHI

H=105

I= 45

GI=14

GH=10

The correct answer is option B. In an analysis of variance, differences caused by treatment effects contribute to both between-treatments variance and within-treatments variance. This is because the overall variance in the data can be attributed to both differences between the treatment groups (between-treatments variance) and differences within each treatment group (within-treatments variance).

Using multiple t tests increases the risk of a type I error, which is rejecting the null hypothesis when it is actually true. This is because the more tests that are run, the more likely it is that one will result in a false positive. On the other hand, the analysis of variance is more likely to detect statistical significance because it takes into account the overall variance in the data and can determine if the differences between groups are larger than would be expected by chance alone.

In a three-group comparison, at least one of the three population means is different from another population mean. This is the minimum requirement for there to be a significant difference between the groups. However, it is also possible for all three of the population means to be different from each other.

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Answer:

sqrt66

Step-by-step explanation:

Area of a square is

A = s^2

Here, the area is 66.

66 = s^2

Squareroot both sides to solve.

sqrt66 = s

The side of the square is sqrt66 ft.

This number, sqrt66 is not a rational number because 66 is not a perfect square. Sqrt64 is 8, sqrt81 is 9. But sqrt66 is 8.1240384046 (continuing, neverending, never repeating decimal)

That is not rational.

Answer:

Step-by-step explanation:

(-12 - 13)/(-1 - 4)= -25/-5 = 5

y - 13 = 5(x - 4)

y - 13 = 5x - 20

y = 5x - 7

True, Logarithms were used extensively for complicated calculations before the electronic calculator became widely available. A logarithm is a mathematical function that helps simplify complex arithmetic operations by converting multiplication and division into addition and subtraction, respectively.

By using logarithms, complex calculations could be broken down into simpler steps and performed more easily. Logarithms were particularly useful in fields such as astronomy, physics, and engineering, where large numbers and complicated formulas were common. However, with the advent of electronic calculators, the use of logarithms for everyday calculations declined. Today, logarithms are still used in certain fields and for specific applications, but they are no longer the primary tool for carrying out complicated calculations.

Before the electronic calculator became widely available, logarithms were used to carry out complicated calculations. Logarithms simplified complex calculations by turning multiplication and division operations into addition and subtraction.

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Answer: \(x=\frac{-3}{k}\)

Step-by-step explanation:

To solve for x, you need to get x alone. In this problem, k is a constant.

\(kx=-3\)

\(x=\frac{-3}{k}\)

Answer:

yes is the 3rt answer

Step-by-step explanation:

Answer: 15,712.15 ft^3 ;)

Answer:15712.2

Step-by-step explanation:

In parallelogram LMNP the side RM= SP. The proof of the question is given below.

Since LR || MP and NS || MP, we have ∠LMP = ∠RMP and ∠MNP = ∠SNP by alternate interior angles.

Also, since LMNP is a parallelogram, we have LM || NP and LP || MN.

Therefore, we have ∠MLN = ∠MNP and ∠PLN = ∠LMP by alternate interior angles.

Adding these two angles, we get:

∠MLN + ∠PLN = ∠MNP + ∠LMP

2∠PLN = 180° (since LMNP is a parallelogram)

∠PLN = 90°

Similarly, we can show that ∠MLN = 90°.

Therefore, LMNP is a rectangle.

Since MP is a diagonal of the rectangle, we have RM = SP by the property of diagonals of rectangles.

Hence, we have proved that RM = SP.

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The image of the correct question is given in the attachment.

Answer:

She has $225 dollars so far.

Step-by-step explanation:

To determin the answer, its pretty simple:

take 250 and subtract 25 from 250 (250 - 25).

This would give you $225 dollars. To check, add 25 to $225 and you would get $250. $225 is your final answer.

Answer:

x≈7.5

Step-by-step explanation:

Part A:

Let's call the missing side of x:

5²+x²=9²

25+x²=81

x²=56

x= square root of 56

x≈7.5

Part B:

The sum of the internal angles of a triangle is always 180°, and the square in the top angle means that it is 90°, so:

90°+21°+y=180°

y=180°-90°-21°

y=69°

Answer:

0.44x10^3

Step-by-step explanation:

The number has to be from 1 to 10, not below 1, like 0.44 does.

The statistical question that will have the least variability is A. How many pets does each sixth grade student own? Therefore, option A, which asks about the number of pets, is likely to have the least variability among the given options

Variability refers to the spread or dispersion of data. In this case, we are comparing the variability of different statistical questions related to sixth grade students.

Option A asks about the number of pets each sixth grade student owns. This question is likely to have the least variability because the number of pets a student owns tends to be relatively small and limited. The range of possible values is typically smaller compared to the other options.

Options B, C, and D ask about the number of movies seen, songs downloaded, and hours spent playing video games, respectively. These activities can vary significantly among students. Some students may have seen a few movies, while others may have seen many. Similarly, the number of songs downloaded and hours spent playing video games can vary greatly, leading to higher variability in the data.

Therefore, option A, which asks about the number of pets, is likely to have the least variability among the given options.

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The length is x is √(1/2) * √2/√2 is √2/2. So, the missing side length(s) in the triangle is √2/2 inches.

In a 45°-45°-90° triangle, the side opposite the 45° angles are congruent.

Let's call this side length x.

The hypotenuse is given as 1 inch.

Using the Pythagorean theorem, we can find the missing side length(s). The theorem states that the sum of the squares of the two legs is equal to the square of the hypotenuse.

\(So, x^2 + x^2 = 1^2.\)

Simplifying this equation, we get

\(2x^2 = 1.\)

Dividing both sides by 2, we find

\(x^2 = 1/2.\)

Taking the square root of both sides, we get

x = √(1/2).

To rationalize the denominator, we multiply the numerator and denominator by √2. Therefore,

x = √(1/2) * √2/√2

= √2/2.

So, the missing side length(s) in the triangle is √2/2 inches.

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Answer: where is the picture show it to me so that there’s none

Step-by-step explanation:

Answer:

You can buy a maximum number of 11 boxes

Step-by-step explanation:

The first step is to calculate the number of boxes that you can afford with the $150 without the discount. This can simply be done by dividing $150 by $15

= 10 boxes.

The next step is to calculate the effect of the discount on the total of $150. The $25 discount will increase your average sum to $175.  This extra $ 25  can afford you one more box. bringing the total number of boxes to 11.

You can buy a maximum number of 11 boxes

Answer:

About 20.63 feet

Step-by-step explanation:

The tangent of an angle in a right triangle is the length of the opposite side divided by the length of the adjacent side. In this case:

\(\tan 38= \dfrac{T}{20}\\\\T=\tan 38 \cdot 20 \approx 15.63\)

Adding this to your height at eye level, you get a total height of the tree of about 20.63 feet. Hope this helps!

Given that f'(x) = cos x and g'(x) = 1, and both f(0) = g(0) = 0, we can find the limit as x approaches 0 of f(x)/g(x).
First, we can integrate the derivatives to find f(x) and g(x):
f(x) = ∫cos x dx = sin x + C₁
g(x) = ∫1 dx = x + C₂
Since f(0) = 0 and g(0) = 0, we know that C₁ = 0 and C₂ = 0. Therefore, f(x) = sin x and g(x) = x.
Now, we can find the limit:
lim(x→0) [f(x) / g(x)] = lim(x→0) [sin x / x]
Applying L'Hôpital's Rule (since it's an indeterminate form 0/0):
lim(x→0) [f'(x) / g'(x)] = lim(x→0) [cos x / 1]
Now, evaluate the limit as x approaches 0:
lim(x→0) [cos x] = cos(0) = 1
So, the correct answer is B: 1.

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Answer:

A

Step-by-step explanation:

Getting closer together means that both are becoming more accurate.

A valid model is such model whose calculated value approximates to the actual value. If it doesn't approximate to the actual value, it must be close to the actual value.

The model is valid if the results from the survey are close enough, together.

Given that:

\(p_1 = 75\%\) -- the actual estimation of satisfied students

\(p_2 = 70\%\) -- the second estimation of satisfied students

For a model to be valid, the calculated value must be close to the actual value.

If after Mateo's survey of more students, the result of satisfied or very satisfied students is still close to 75%, then Mateo's model is valid.

If otherwise, then the model is invalid.

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Answer: It is not a real expression there is no answer

Step-by-step explanation: