f(1) = 1

f(2) = 2

f(n) = f(n − 2) + f(n − 1)

f(3)

The volume of the prism with an equilateral triangular base of side S and altitude h is (S * h^2 * sqrt(3))/4.

To find the volume of a prism with an equilateral triangular base using integration, we can divide the prism into infinitesimally small slices parallel to the base and integrate their volumes.

Consider an infinitesimally thin slice located at a distance "y" from the base. The length of this slice is equal to the length of the base, S. The width of the slice at distance "y" can be determined by considering the height of the equilateral triangle at that distance, which is given by h - (h/S) * y.

The volume of this slice is then given by the product of its length, width, and infinitesimal thickness dy, which is S * [h - (h/S) * y] * dy.

To find the total volume, we integrate this expression from y = 0 to y = h:

V = ∫[0,h] S * [h - (h/S) * y] dy.

Evaluating this integral gives us the volume of the prism:

V = S * [h * y - (h/S) * (y^2/2)] evaluated from y = 0 to y = h.

Simplifying this expression yields:

V = (S * h^2 * sqrt(3))/4.

Therefore, the volume of the prism with an equilateral triangular base of side S and altitude h is (S * h^2 * sqrt(3))/4.

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The general solution to the given differential equation, (x³+ ye^xy) dx + (xe^xy-sin3y) = 0, involves two steps: identifying an integrating factor and then integrating the resulting equation. The integrating factor is found to be e^(3xy).  We find F(x, y) = ∫(e^(x^4/4 + ye^xy) (x³+ ye^xy)) dx + g(y),

To solve the given differential equation, we first determine an integrating factor. Since the coefficient of dx, x³ + ye^xy, is a function of x and y only, we can identify the integrating factor as e^(∫(x³ + ye^xy) dx). Evaluating the integral, we obtain e^(x^4/4 + y∫e^xy dx). Simplifying further, the integrating factor is found to be e^(x^4/4 + ye^xy).

Next, we multiply the entire differential equation by this integrating factor. This step transforms the equation into an exact differential equation, which is easier to solve. Multiplying through, we have e^(x^4/4 + ye^xy) (x³+ ye^xy) dx + e^(x^4/4 + ye^xy) (xe^xy-sin3y) = 0.

After multiplying, we can observe that the left-hand side of the equation is now the total derivative of a function F(x, y). By integrating with respect to x, we find F(x, y) = ∫(e^(x^4/4 + ye^xy) (x³+ ye^xy)) dx + g(y), where g(y) is the constant of integration with respect to x. Finally, the general solution is obtained by solving for y in terms of x and the constant g(y).

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Answer:

Circumference = 2(pi)r

C = 2*3.14*4.0= 25.12 round 25.10 m

Step-by-step explanation:

Answer:

20.25

Step-by-step explanation:

Just multiply the base and height then divide the results in half.

Hope this helps!

The length function f(w) of a string w = w₁w₂...W), where n ∈ N and Vi ∈ W: € 9, is equal to n.

The length function f(w) is defined recursively based on the structure of the string w. In the base case, if w is an empty string (ε), the length is defined as 0. In the recursive case, if w can be written as au, where a is a character from the alphabet and u is a string over the alphabet Σ, then the length is defined as 1 plus the length of u.

To prove that for any string w =w₁w₂...wy, where n ∈ N and Vi ∈ W: € 9, the length function f(w) is equal to n, we will use a proof by induction.

For w = ε (an empty string), we have f(ε) = 0, which satisfies the condition when n = 0.

Assume that for any string w = w₁w₂...wn, where n ∈ N and Vi ∈ W: € 9, the length function f(w) = n.

Now, consider a string w' = w₁w₂...wn+1. By the recursive definition, we can write w' as au, where a is the last character wn+1 and u is the string w₁w₂...wn. From our assumption, we know that f(u) = n.

Therefore, f(w') = 1 + f(u) = 1 + n = n + 1.

Since we have established that for any string w = w₁w₂...wy, where n ∈ N and Vi ∈ W: € 9, the length function f(w) = n, we can conclude that f(w) = n.

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a) The probability of finding   a meter stick with a length of more than 100.04cm is 0.44013.

b) The probability of finding a group of 42 meter sticks with a mean length of less than 99.82 cm is 0.65866.

c) The probability of finding a group of 50 meter sticks with a mean length of more than 99.87 cm is 0.44013.

d) The probability of finding   a group of 28 meter sticks with a mean length of between 99.82and 99.86 cm is 0.11974.

e) The mean length that would be at the 92nd percentile for a random sample of 32 meter sticks is 99.89714 cm.

a) The probability of finding a meter stick   with a length of more than 100.04cm is

P(X >   100.04 ) =1 - P(X <= 100.04)

= 1- Φ((100.04   - 99.84) / 0.2)

= 1 - Φ(0.12)

= 1 - 0.55987

= 0.44013

b) The probability of finding a group of 42 meter sticks with a mean length of less than 99.82 cm is

P(¯X < 99.82) = 1 - P(X >= 99.82)

= 1 - Φ((99.82 - 99.84) / 0.2 / √42)

= 1 - Φ(-0.1)

= 1 - 0.34134

= 0.65866

c) The probability of finding a group of 50 meter sticks with a mean length of more than 99.87 cm is

P(X > 99.87) = 1 - P(X <= 99.87)

= 1 - Φ((99.87 - 99.84) / 0.2 / √50)

= 1 - Φ(0.15)

= 0.44013

d) The   probability of finding a group of 28 meter sticks with a mean length of between 99.82 and 99.86 cm    is

P(99.82 < X  < 99.86) = Φ  ((99.86 - 99.84)/ 0.2 / √28) - Φ((99.82 - 99.84) / 0.2/ √28)

= Φ(0.15) - Φ(0.12)

= 0.55987 - 0.44013

= 0.11974

e) The mean length that would be at the 92nd percentile for a random sample of 32-meter sticks is

X₉₂ = μ + z₉₂ σ / √n

= 99.84 + z₉₂ (0.2) / √32

= 99.84 + 1.85 (0.2) / √32

= 99.84 + 0.05714

= 99.89714

Therefore, the mean length that would be at the 92nd percentile for a random sample of 32 meter sticks is 99.89714 cm.

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To determine the standard error of the estimated slope coefficient and its statistical significance, more information is needed, such as the t-statistic or the p-value associated with the estimated slope coefficient. The options provided do not include the necessary details to make a conclusion.

The standard error of the estimated slope coefficient measures the precision or variability of the estimated coefficient. It provides information about how much the estimated slope coefficient could vary across different samples.

The t-statistic and the p-value, on the other hand, are used to assess the statistical significance of the estimated slope coefficient. The t-statistic measures the number of standard errors the estimated coefficient is away from zero, while the p-value indicates the probability of observing a coefficient as extreme as the estimated one under the null hypothesis that the true coefficient is zero.

Without the t-statistic or p-value, it is not possible to determine the statistical significance of the estimated slope coefficient at the 5% level.

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Answer:

am not sure but

Step-by-step explanation:

since they are similar they must have similar ratio

so 12/4 =3/1

so 3:1

4*3=12

for other sides I think

9*3 =27

and

6*3=18

y=27

x=18

Answer:

(x,y) = (-1,3)

Step-by-step explanation:

hope this helps!

Answer:

14

Step-by-step explanation:

separate the figure into two  shapes. On the little one is 2x1 which the answer is 2 then on the larger shape is 6x2 which is 12 then you add 12+2 and then you get your answer

Answer:

13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Hello There!

We can calculate the distance between two points using the distance formula

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

where the x and y values are derived from the coordinates in which you are trying to find the distance between

The points we need to find the distance between is (3,-8) and (8,4)

So we plug the x values and y values into the formula

[tex]d=\sqrt{(8-3)^2+(4-(-8)^2} \\8-3=5\\4-(-8)=12\\d=\sqrt{5^2+12^2} \\5^2=25\\12^2=144\\144+25=169\\\sqrt{169} =13[/tex]

so we can conclude that the distance between the two points is 13 units

Answer:

1.202

Step-by-step explanation:

Answer:

$2,725

Step-by-step explanation:

The maximum number of days is 7.

The cost per days is $375.

The cost for 7 days is 7 * $375 = $2,625.

The owner applies a $100 fee for cleaning which must be added to the cost of the days.

$2,625 + $100 = $2,725

The greatest value for the range is the greatest cost there can be which is $2,725.

a) The proportion of male Internet users who use social networking is approximately 0.6747, and the proportion of female Internet users who use social networking is approximately 0.7358.

b) The difference in proportions is approximately -0.0611.

c) The standard error of the difference is approximately 0.0181.

d) The 95% confidence interval for the difference between these proportions is (-0.096, -0.026).

To calculate the standard error of the difference and find a 95% confidence interval for the difference between the proportions, we can use the formulas for proportions and their differences.

Let [tex]p_1[/tex] be the proportion of male Internet users who use social networking, and [tex]p_2[/tex] be the proportion of female Internet users who use social networking.

a) Proportion for male Internet users: [tex]p_1[/tex] = 517/766 = 0.6747

Proportion for female Internet users: [tex]p_2[/tex] = 692/941 = 0.7358

b) Difference in proportions: [tex]p_1 - p_2[/tex] = 0.6747 - 0.7358 = -0.0611

c) The standard error of the difference (SE) can be calculated using the formula:

[tex]SE = \sqrt{(p_1(1-p_1)/n_1) + (p_2(1-p_2)/n_2)}[/tex]

Where [tex]n_1[/tex] and [tex]n_2[/tex] are the sample sizes for male and female Internet users, respectively.

For male Internet users: [tex]n_1[/tex] = 766

For female Internet users: [tex]n_2[/tex] = 941

Plugging in the values, we have:

[tex]SE = \sqrt{(0.6747(1-0.6747)/766) + (0.7358(1-0.7358)/941)}[/tex]

d) To find the 95% confidence interval for the difference between these proportions, we can use the formula:

[tex]CI = (p_1 - p_2) \± (Z * SE)[/tex]

Where Z is the critical value corresponding to a 95% confidence level. For a large sample size, Z is approximately 1.96.

CI = (-0.0611) ± (1.96 * SE)

CI = -0.0611 ± 0.0355

CI = (-0.096, -0.026)

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Answer:

The difference between the absolute values of these two temperatures is 19°F.

Step-by-step explanation:

|-13| = 13

|6| = 6

13 + 6 = 19°F

Answer:

19

Explanation:

an absolute value is the value of a number without considering its sign.

thus, we can calculate the difference as such:

6 - (- 13) = 6 + 13 = 19

the difference between the absolute values of these two temperatures is 19.

i hope this helps! :D

(a) There are 840 distinguishable permutations of the letters in the word "initial." (b) There are 180 distinguishable permutations of the letters in the word "Hawaii." (c) There are 420 distinguishable permutations of the letters in the word "decreed."

(a) For the word "initial," we have a total of 7 letters, with 2 "I"s, and 1 occurrence of each of the remaining letters. Applying the formula, we get:

n! / (3!1!1!1!1!) = 7! / (3!1!1!1!1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / (3 × 2 × 1 ×1 × 1 × 1 × 1) = 840

(b) For the word "Hawaii," we have a total of 6 letters, with 1 "H," 2 "A"s, and 2 "I"s. Applying the formula, we get:

n! / (1!2!1!2!) = 6! / (1!2!1!2!) = (6 × 5 × 4 × 3 × 2 × 1) / (1 × 2 × 1 × 2 × 1 × 1) = 180

(c) For the word "decreed," we have a total of 7 letters, with 2 "E"s, 3 "D"s, and 1 occurrence of each of the remaining letters. Applying the formula, we get:

n! / (2!3!1!1!) = 7! / (2!3!1!1!) = (7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1 × 3 × 2 × 1 × 1 × 1) = 420

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By applying the the FOIL method, which stands for First, Outer, Inner, Last  we obtained the result -84 + 80i for (4 + 10i)^2.

To calculate (4 + 10i)^2, we can:

First, we multiply the first terms of each binomial:

(4 + 10i) * (4 + 10i) = 16 + 40i

Next, we multiply the outer terms of each binomial:

(4 + 10i) * (4 + 10i) = 16 + 40i

Then, we multiply the inner terms of each binomial:

(4 + 10i) * (4 + 10i) = 16 + 40i

Finally, we multiply the last terms of each binomial:

(4 + 10i) * (4 + 10i) = 100i^2

We know that i^2 is equal to -1, so we can substitute that in:

100(-1) = -100

Putting it all together, we get:

(4 + 10i)^2 = 16 + 40i + 40i + (-100)

= -84+80i

Therefore, by applying this method for squaring a complex number, we obtained the result -84 + 80i for (4 + 10i)^2.

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Answer:

The equation of the line that passes through the given points is ;

7y = -x + 12

Step-by-step explanation:

Here, we want to get the equation of the line that passes through the given points

The general equation form

is;

y = mx + b

where m is the slope and b is the y-intercept

Now, let us substitute the x and y coordinate values of each of the points;

for (-2,2); we have

2 = -2m + b

b = 2m + 2 •••••(i)

for F;

1 = 5m + b

b = 1-5m ••••••(ii)

Equate both b

1-5m = 2m + 2

1-2 = 2m + 5m

7m = -1

m = -1/7

Recall;

b = 2m + 2

b = 2(-1/7) + 2

b = -2/7 + 2

b = (-2 + 14)/7 = 12/7

The equation of the line is thus;

y = -1/7x + 12/7

Multiply through by 7

7y = -x + 12

The probability that the sample mean body temperature will be between 36.5° and 37.10° can be determined using the z-score and the standard normal distribution table.

First, we need to calculate the z-scores for both temperatures using the formula:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the standard deviation, and n is the sample size.

For the lower temperature of 36.5°:

z1 = (36.5 - 36.8) / (0.62 / √19)

For the higher temperature of 37.10°:

z2 = (37.10 - 36.8) / (0.62 / √19)

Next, we look up the corresponding probabilities associated with these z-scores in the standard normal distribution table. Subtracting the probability of the lower z-score from the probability of the higher z-score will give us the probability of the sample mean body temperature falling between the two values.

Let's calculate the z-scores:

z1 = (36.5 - 36.8) / (0.62 / √19) ≈ -1.350

z2 = (37.10 - 36.8) / (0.62 / √19) ≈ 0.775

Now, we look up the probabilities associated with these z-scores in the standard normal distribution table. The probability corresponding to z1 is approximately 0.0885, and the probability corresponding to z2 is approximately 0.7794.

Finally, we subtract the lower probability from the higher probability:

P(36.5° ≤ sample mean ≤ 37.10°) = 0.7794 - 0.0885 ≈ 0.6909

Therefore, the probability that the sample mean body temperature will be between 36.5° and 37.10° for a sample size of 19 people is approximately 0.6909.

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Answer:

31 degrees

Step-by-step explanation:

1. since angle x and angle y are congruent, and segment xw and segment yw are congruent, you can assume that angle xzw and angle wzy are also congruent.

2. set angle xzw and angle wzy equal to each other

8x-1 = 5x+11

3. combine like terms

3x = 12

4. simplify to find the value of x

x = 4

5. plug x into the equation to find the degree of angle wzy

5(4)+11

20+11

=31 degrees

{{{ THE BOLDED CHARACTERS SHOULD BE SMALL. }}}

A sequence can be generated by using an = a(n-1) - 5, where a1 = 100 and n is a whole number greater than 1.

a1 = 100 (given)

a2 = a1 - 5 = 100 - 5 = 95

a3 = a2 - 5 = 95 - 5 = 90

a4 = a3 - 5  = 90 - 5 = 85

a5 = a4 - 5 = 85 - 5 = 80

ANSWER for PART (a): 100, 95, 90, 85, 80

-----------------------------------------------------------------------------

an = a1 + d(n - 1)

an = 100 + -5(n - 1)

an = 100 + -5n + 5

an = 105 - 5n

ANSWER for PART (b): an = 105 - 5n

Answer:

I agree with the person above me and here give him brainliest

Step-by-step explanation:

what? bro I am confused is this a question?

Answer:

x = 27.2 or 27 1/5

Step-by-step explanation:

cos 54° = 16/x

x = 27.2 or 27 1/5

Answer:

2a°+2a°=180°[opposite angle of cyclic quadrilateralis 180°]

4a°=180

a=180°/4

a=45°

4b+2b=180°[similarly]

6b=180°

b=180°/6

b=30

Answer:

James will spend $119.94

Step-by-step explanation:

Multiply $19.99 by 6.

$19.99 x 6 = $119.94

The length M is 12

The measure of the angle BEC is 102

The measure of the arc AB is 128

The length PQ is 18.3

The length M can be calculated using

M² = 8 * (8 + 10)

So, we have

M² = 144

Take the square roots

M = 12

The measure of the angle BEC can be calculated using

BEC = 1/2 * (BC + AD)

So, we have

BEC = 1/2 * (156 + 48)

Evaluate

BEC = 102

The measure of the arc ABcan be calculated using

AB = 180 - 2 * BC

So, we have

AB = 180 - 2 * 26

Evaluate

AB = 128

The length PQ can be calculated using

x² = (12 + 8)² - 8²

So, we have

x² = 336

Take the square roots

x = 18.3

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To verify that a matrix A satisfies the conditions A € M2x2(R), A = [a b; c d], and det(A) = 0, we can use the formula for the determinant of a 2x2 matrix:

det(A) = ad - bc

In this case, since det(A) = 0, we have:

ad - bc = 0

This formula allows us to check whether a given matrix satisfies the given conditions.

To find three matrices A when a = 5 and det(A) = 27, we can use the formula:

ad - bc = 27

Let's assume b = 1, c = 0, and d = 27/a.

Substituting these values into the formula, we get:

5 * (27/a) - 1 * 0 = 27

135/a = 27

a = 135/27

a = 5

Therefore, one possible matrix A that satisfies the conditions is:

A = [5 1; 0 27/5]

Similarly, we can find two more matrices by choosing different values for b, c, and d, as long as the determinant condition is satisfied.

Now, let's suppose B is a matrix such that det(B) = det(A):

B = [p q; r s]

To show that det(B) = det(A), we can equate their determinants:

det(B) = det(A)

ps - qr = ad - bc

Since we already know that ad - bc = 0, we can conclude that:

ps - qr = 0

This equation shows that the determinant of B is also zero, satisfying the condition det(B) = 0.

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