The Fibonacci sequence is defined as follows: F0 = 0, F1 = 1 and for n larger than 1, FN+1 = FN + FN-1. Set up a spreadsheet to compute the Fibonacci sequence. Show that for large N, the ratio of successive Fibonacci numbers approaches the Golden Ratio (1.61).

Answer:

3, 1/2

Step-by-step explanation:

x + 2y = 4

2x - 2y = 5

_______________ +

2x + x + 2y + (-2y) = 4 + 5

3x + 0 = 9

3x = 9

x = 9/3

x = 3

if you want to find the value of y, you just have to choose one of the equation. I will choose x + 2y = 4, even if you choose 2x - 2y = 5 the result remains same

x + 2y = 4

3 + 2y = 4

2y = 4 - 3

y = 1/2

x, y = 3, 1/2

i'm sorry, i'm not good at english ^^

Answer:

$15

Step-by-step explanation:

107% is the price of $16.05

so, 107% = $16.05

Divide both sides by 107:

1% = $0.15

Multiply both sides by 100:

100% = $15.00

Answer:

B. 11

Step-by-step explanation:

The 50th percentile represents the halfway point of a data set and therefore, it is simply another name for the median.

We can use the following steps to find the median:

Step 1:  Arrange the numbers in ascending numerical order:

10, 10, 11, 12, 13.

Step 2:  Find the middle of the numbers:

Since there are 5 numbers, the median will have two numbers to the left and right of it.  11 satisfies this requirement so it is the median and thus the 50th percentile of the numbers.

Answer:

7 m

Step-by-step explanation:

you divide the volume by the radius I'm pretty sure. that's what I did and I got 7

Answer:

It is A

Step-by-step explanation:

If the y2 get subtracted by the 8 then itll be 8

Number of meters Joe jogged is 123.43 meters. Therefore, the correct answer is option C.

Given that, the distance between bases on a baseball field is 27.43 meters.

Joe has jogged from one base to the next 4.5 times.

Number of meters Joe jogged = Distance between bases on a baseball field × Number of times Joe jogged

= 27.43 × 4.5

= 123.43 meters

Therefore, the correct answer is option C.

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The general solution of the differential equation y" - 4y' + 5y = 16 cos (1) using determinant coefficients is given by y =

yh + yp = c1 e^(2x) cos(x) + c2 e^(2x) sin(x) + 16/((5^2 + 1)√26) cos(1).

In order to find the solution using determinant coefficients, first, we solve the homogeneous equation y" - 4y' + 5y = 0. The characteristic equation is given by r^2 - 4r + 5 = 0, which has roots r = 2 ± i. Therefore, the general solution of the homogeneous equation is yh = c1 e^(2x) cos(x) + c2 e^(2x) sin(x).

Next, we find the particular solution of the non-homogeneous equation using the method of undetermined coefficients. Since the forcing function is cos(1), we assume the particular solution to be of the form yp = a cos(1). Substituting this into the differential equation, we get -a + 4a + 5a cos(1) = 0, which implies a = 16/(5^2 + 1). Hence, the particular solution is yp = 16/((5^2 + 1)√26) cos(1).

Therefore, the general solution of the given differential equation is y = yh + yp = c1 e^(2x) cos(x) + c2 e^(2x) sin(x) + 16/((5^2 + 1)√26) cos(1).

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Answer:

x >12

Step-by-step explanation:

2 + 5(x-3) > 3x + 11

Distribute

2 + 5x - 15 > 3x+11

Combine like terms

5x -13 > 3x+11

Subtract 3x from each side

5x-13-3x> 3x+11-3x

2x-13 > 11

Add 13 to each side

3x-13+13> 11+13

2x> 24

Divide by 2

2x/2 > 24/2

x >12

Answer:

What is it love ?

Step-by-step explanation:

a) Formal explanation of risk aversion An agent with utility function u is more risk averse than an agent with utility function ˜u if the former has a higher marginal utility of consumption and a diminishing marginal utility of consumption.

The marginal utility of consumption is defined as the amount of utility gained from an additional unit of consumption.

b) Show that an agent with utility function u(x) = log x is more risk averse than an agent with utility function ˜u(x) = √ x. An agent with utility function u(x) = log x is more risk averse than an agent with utility function ˜u(x) = √ x. To show this, we need to find the Arrow-Pratt coefficient of risk aversion, also known as the coefficient of relative risk aversion. The Arrow-Pratt coefficient of risk aversion is given by :-u''(x)/u'(x)Where u'(x) is the first derivative of u with respect to x and u''(x) is the second derivative of u with respect to x.

The Arrow-Pratt coefficient of risk aversion measures the curvature of the utility function. A higher value of the Arrow-Pratt coefficient of risk aversion indicates greater risk aversion. Let us calculate the Arrow-Pratt coefficient of risk aversion for both functions:-For u(x) = log x, u'(x) = 1/x, and u''(x) = -1/x². Therefore, the Arrow-Pratt coefficient of risk aversion for u(x) is given by:-u''(x)/u'(x) = -1/x² ÷ (1/x) = -x For ˜u(x) = √ x, ˜u'(x) = 1/2√ x, and ˜u''(x) = -1/4x^(3/2). Therefore, the Arrow-Pratt coefficient of risk aversion for ˜u(x) is given by:-˜u''(x)/˜u'(x) = -1/4x^(3/2) ÷ (1/2√ x) = -1/2√ x

Therefore, since -x < -1/2√ x, the agent with the utility function u(x) = log x is more risk averse than the agent with the utility function ˜u(x) = √ x.

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Answer:

b

Step-by-step explanation:

Answer:

20, 18, 14, and 24 are all not perfect squares

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

they both equal 5x=1 where x = 1/5

Answer:

1 7/10

Step-by-step explanation:

Given that:

Weight of bag 1 = 2/5 pounds

Weight of bag 2 = 7/10 pounds

Weight of bag 3 = 3/5 pounds

Total weight of the three bags :

2/5 + 7/10 + 3/5

Take the lcm of 5 and 10

Lcm of 5 and 10 = 10

(4 + 7 + 6) / 10

17 /10

= 1 7/10

Answer:

Question 7 = $2

Question 8 = $16

Answer:

hi

Step-by-step explanation:

hope it helps

have a nice day

Answer:

3.14, 5.8, 0.3, negative 2

Step-by-step explanation:

3.14 is found bn 2 and 3 but very close to 3 u can just take 3.1 and for 5.8 it's bn 5 and 6 very close to 6 but not six , and we'll negative 2 is right on negative 2

Answer:

522

Step-by-step explanation:

Answer:

k = 192

Step-by-step explanation:

Given that,

y varies inversely with x. It can be written as :

[tex]y=\dfrac{k}{x}[/tex]

Where

k is the constant of variation

Put x = 16 and y = 12 in the above formula.

[tex]k=yx\\\\k=16\times 12\\\\k=192[/tex]

So, the value of the constant of variation is equal to 192.

Answer:

No solution

Step-by-step explanation:

The easiest approach here is to divide the second equation by 2:  x + 2y = -4.

Comparing the first equation with this result, we see that the the two lines never intersect, and thus that there is no solution.

It is proved here that an integer is divisible by 9 if and only if the sum of its decimal digits is divisible by 9. This is known as divisibility test for 9.

How to test divisibility for 9?

To show that an integer is divisible by 9 if and only if the sum of its decimal digits is divisible by 9, we can use the concept of congruence.

Let's start by representing an integer as the sum of its decimal digits. Consider an integer n expressed in decimal notation as:

[tex]n = d_k * 10^k + d_(k-1) * 10^(k-1) + ... + d_2 * 10^2 + d_1 * 10^1 + d_0 * 10^0[/tex],

where [tex]d_i[/tex] represents the i-th decimal digit of n, and k is the number of digits in n (k >= 0).

We want to prove that n is divisible by 9 if and only if the sum of its decimal digits, [tex]d_k + d_(k-1) + ... + d_2 + d_1 + d_0[/tex], is divisible by 9.

1. If n is divisible by 9:

Assume n is divisible by 9, which means there exists an integer q such that n = 9q. We can express n as:

[tex]n = (d_k * 10^k + d_(k-1) * 10^(k-1) + ... + d_2 * 10^2 + d_1 * 10^1 + d_0 * 10^0) = 9q[/tex]

Since 10 is congruent to 1 modulo 9 (10 ≡ 1 (mod 9)), we can rewrite the above equation as:

[tex](d_k + d_{(k-1)} + ... + d_2 + d_1 + d_0)[/tex]  ≡ [tex]9q (mod\ 9)[/tex].

The left-hand side of the congruence represents the sum of the decimal digits, and the right-hand side is a multiple of 9. Therefore, the sum of the decimal digits is divisible by 9.

2. If the sum of the decimal digits is divisible by 9:

Assume the sum of the decimal digits is divisible by 9, which means there exists an integer p such that [tex](d_k + d_{(k-1)} + ... + d_2 + d_1 + d_0) = 9p.[/tex]

We can express n as:

[tex]n = (d_k * 10^k + d_{(k-1)} * 10^{(k-1)} + ... + d_2 * 10^2 + d_1 * 10^1 + d_0 * 10^0) = (9p + d_k * 10^k + d_{(k-1)} * 10^{(k-1)} + ... + d_2 * 10^2 + d_1 * 10^1 + d_0).[/tex]

Since 10 is congruent to 1 modulo 9 (10 ≡ 1 (mod 9)), we can rewrite the above equation as:

n ≡ [tex](9p + d_k + d_{(k-1)} + ... + d_2 + d_1 + d_0)[/tex] ≡ 0 (mod 9).

This shows that n is congruent to 0 modulo 9, or in other words, n is divisible by 9.

Therefore, we have shown that an integer is divisible by 9 if and only if the sum of its decimal digits is divisible by 9.

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A)The probability that the yield strength is greater than 60 is approximately 0.0003.

B)The yield strength value that separates the strongest 75% from the others is approximately 45.3725 ksi.

What is probability?

Probability is a fundamental concept in mathematics and statistics that quantifies the likelihood or chance of an event occurring. It provides a numerical measure of uncertainty or the relative frequency with which an event is expected to happen. In simpler terms, probability is a way of expressing how likely it is for a particular outcome or event to take place.

(a) The probability that yield strength is at most 39:

Using the standard normal distribution, we can calculate the z-score as follows:

[tex]\[ z = \frac{{39 - 42}}{{5.0}} = -0.6 \][/tex]

The cumulative probability associated with a z-score of -0.6 represents the probability of obtaining a value less than or equal to 39. Using a standard normal distribution table or a calculator, we find that this cumulative probability is approximately 0.2743.

Therefore, the probability that the yield strength is at most 39 is approximately 0.2743.

The probability that yield strength is greater than 60:

Converting 60 to a z-score:

[tex]\[ z = \frac{{60 - 42}}{{5.0}} = 3.6 \][/tex]

The cumulative probability associated with a z-score of 3.6 represents the probability of obtaining a value greater than 60. Using a standard normal distribution table or a calculator, we find that this cumulative probability is approximately 0.9997.

Since we want the probability of a value greater than 60, we subtract this cumulative probability from 1:

[tex]\[ P(\text{{yield strength}} > 60) = 1 - 0.9997 = 0.0003 \][/tex]

Therefore, the probability that the yield strength is greater than 60 is approximately 0.0003.

(b) The yield strength value that separates the strongest 75% from the others:

To find the yield strength value that separates the strongest 75% from the others, we need to find the z-score corresponding to the cumulative probability of 0.75. Using a standard normal distribution table or a calculator, we find that the z-score associated with a cumulative probability of 0.75 is approximately 0.6745.

Next, we can use the z-score formula to find the yield strength value:

[tex]\[ z = \frac{{x - \mu}}{{\sigma}} \][/tex]

Rearranging the formula to solve for x:

[tex]\[ x = \mu + (z \times \sigma) \][/tex]

Substituting the values into the formula:

[tex]\[ x = 42 + (0.6745 \times 5.0) = 45.3725 \][/tex]

Therefore, the yield strength value that separates the strongest 75% from the others is approximately 45.3725 ksi.

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Answer:

7.5 in.

Step-by-step explanation:

Answer:

7.5 in

Step-by-step explanation:

using pythagorean theorem

Hyp²= Opp² + Adj ²

where 9= hyp

5= adj

and x = opp

9²=x²+5²

81=x² + 25

collect like terms

81-25=X²

56=X²

since we're looking for X and not X²

we square root both sides

√x²=√56

x=7.483 approximately 7.5

The probability is equal to 0 for the option "a) Less than 5.0."Explanation:Given, the mean of the normal distribution, μ = 7.5 and the standard deviation of the normal distribution, σ = 2.5 The formula to find the Z-score, z is given by;z = (x - μ)/σwhere x is the value of the random variable under consideration.

a) To find the probability of the random variable being less than 5, we find the Z-score;z = (5 - 7.5)/2.5 = -1 Therefore, P(X < 5) = P(Z < -1)Using the standard normal table, the probability corresponding to the Z-score -1 is 0.1587.Therefore, the probability of the random variable being less than 5 is 0.1587.

b) To find the probability of the random variable being between 4.0 and 10.0, we find the Z-score corresponding to each value and calculate the difference in their probability. The probability required will be the absolute value of this difference. z 1 = (4 - 7.5)/2.5 = -1.4 z 2 = (10 - 7.5)/2.5 = 1 Therefore, P(4 < X < 10) = P(-1.4 < Z < 1) = P(Z < 1) - P(Z < -1.4) = 0.8413 - 0.0808 = 0.7605

c ).To find the probability of the random variable being greater than 9.0, we find the Z-score;z = (9 - 7.5)/2.5 = 0.6 Therefore, P(X > 9) = P(Z > 0.6)Using the standard normal table, the probability corresponding to the Z-score 0.6 is 0.2743.Therefore, the probability of the random variable being greater than 9.0 is 0.2743

d) To find the probability of the random variable being between 6.0 and 8.0, we find the Z-score corresponding to each value and calculate the difference in their probability. The probability required will be the absolute value of this difference. z 1 = (6 - 7.5)/2.5 = -0.6z2 = (8 - 7.5)/2.5 = 0.2Therefore, P(6 < X < 8) = P(-0.6 < Z < 0.2) = P(Z < 0.2) - P(Z < -0.6) = 0.5793 - 0.2743 = 0.305Therefore, the probability is equal to 0 for the option "a) Less than 5.0."

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A random variable has a normal distribution with mean 7.5 and standard deviation 2.5. The following is the probability equal to 0.

Option a) Less than 5.0 is correct.

Note that the normal distribution is symmetrical. So, the probabilities of events occurring are equal on either side of the mean.

The probability is zero when the range of events is beyond the limits of the standard normal distribution, which is from -3 to +3. Now let's standardize the values below:

a. less than 5.0: The formula to standardize is

[tex]z = (x - \mu) / \sigma[/tex]

z = (5 - 7.5) / 2.5

z = -1

Thus, the area of the left side of the standard normal distribution is zero, indicating that the probability of less than 5 is zero. Therefore, option a) is correct.

Other options are: b. Between 4.0 and 10.0: The probability that the values fall between 4 and 10 is 0.974 c. Greater than 9.0: The probability that the values are greater than 9 is 0.080 d. Between 6.0 and 8.0: The probability that the values fall between 6 and 8 is 0.329.

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Answer:

-1.25, -1/4, -1/8, 0.125

Step-by-step explanation:

Answer:-1.25, -1/4, -1/8, 0.125

Step-by-step explanation:

Answer:

where is the table lol

Answer:

La razón entre el número de gallinas y el total de animales es: [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

La razón es una comparación entre dos magnitudes comparables.

En otras palabras, la razón es el cociente entre dos números o dos cantidades comparables entre sí, expresado como fracción.

En este caso, la cantidad total de animales es la suma de la cantidad de conejos y la cantidad de gallinas:

2 conejos + 5 gallinas= 7 animales

Entonces la razón entre el número de gallinas y el total de animales es: [tex]\frac{5}{7}[/tex]

Answer:

its 9 signs

Step-by-step explanation:

in order to find number of  signs you gonna divide total distance by distance of a small sign

3/4  ÷ 1/12  

= 3/4 × 12/1 = 3 × 3

therefore, the answer is 9 sign

Answer:

27

Step-by-step explanation:

Length * width * height to find the volume so it is 3*3*3=27

Answer:

63°

Step-by-step explanation:

1) Examing that right triangle, we can find the value of the angle x starting by using a trig ratio and then its reciprocal. Like this:

sin( x ) = 81/91

x = arcsin (81/91)

x = 62.88 = 63

Notice we have the opposite leg and the hypotenuse, so we started with the sine. And to find the value of the angle the arcsin.

2) So, that angle x is 63° (rounding off to the nearest degree)

The value of det(3A^-2B^T) + 1, given det(A) = 1 and B is a singular matrix, is :

1

To find the determinant of the given expression, let's break it down step by step.

Matrix A is 4x4 with det(A) = 1.

Matrix B is a singular matrix.

Find the inverse of matrix A.

Since A is given to be a 4x4 matrix with det(A) = 1, we know that A is invertible. Therefore, A^-1 exists.

Find the determinant of the expression 3A^-2B^T.

Let's calculate the determinant of 3A^-2B^T:

det(3A^-2B^T) = det(3) * det(A^-2) * det(B^T)

We know that det(A^-2) = (det(A))^(-2) = 1^(-2) = 1.

Also, det(B^T) = det(B) because the determinant of a transpose is the same as the determinant of the original matrix.

So, det(3A^-2B^T) = 3 * 1 * det(B) = 3 * det(B)

Determine the value of det(3A^-2B^T) + 1.

Since B is given to be a singular matrix, its determinant is 0.

Therefore, det(3A^-2B^T) + 1 = 3 * det(B) + 1 = 3 * 0 + 1 = 1.

So, the value of det(3A^-2B^T) + 1 is 1.

Therefore, the correct answer is 1.

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