Consider a sequence defined similarly to the Fibonacci, but with a slight twist:

f(n) = f(n-1)-f(n-2) with f(1) = 2 and f (2) = 5

Generate terms f (3), f(4), f(5), f(6), f(7), and f(8). Then, determine the value of f(25). ​

Due to length restrictions, we kindly invite to read the explanation for further details on trigonometric functions of the angle in unit circle.

Herein we find the coordinates of the terminal side of an angle in a unit circle. The values of cos θ and sin θ are determined by numerical methods and the values of the trigonometric functions for π - θ, 2π - θ and π + θ can be found by means of the following expressions: (Note: Angles are measured in radians)

sin (π - θ) = sin π · cos θ - sin θ · cos π

sin (π - θ) = sin θ

cos (π - θ) = cos θ · cos π + sin θ · sin π

cos (π - θ) = - cos θ

sin (2π - θ) = sin 2π · cos θ - sin θ · cos 2π

sin (2π - θ) = sin θ

cos (2π - θ) = cos θ · cos 2π + sin θ · sin 2π

cos (2π - θ) = cos θ

sin (π + θ) = sin π · cos θ + sin θ · cos π

sin (π + θ) = - sin θ

cos (π + θ) = cos θ · cos π - sin θ · sin π  

cos (π + θ) = cos θ

And the sine and cosine of the angle are introduced below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

Now we complete the table:

sin θ = 0.753 / √[(- 0.658)² + 0.753²]

sin θ = 0.753

cos θ = - 0.658 / √[(- 0.658)² + 0.753²]

cos θ = - 0.658

Case 1

sin (π - θ) = sin θ

sin (π - θ) = 0.753

cos (π - θ) = - cos θ

cos (π - θ) = 0.658

sin² (π - θ) + cos² (π - θ) = 0.753² + 0.658²

sin² (π - θ) + cos² (π - θ) = 1

Case 2

sin θ = 0.753

cos θ = - 0.658

sin² θ + cos² θ = 0.753² + (- 0.658)²

sin² θ + cos² θ = 1

Case 3

sin (2π - θ) = sin θ

sin (2π - θ) = 0.753

cos (2π - θ) = cos θ

cos (2π - θ) = - 0.658

sin² θ + cos² θ = 0.753² + (- 0.658)²

sin² θ + cos² θ = 1

Case 4

sin (π + θ) = - sin θ

sin (π + θ) = - 0.753

cos (π + θ) = cos θ

cos (π + θ) = - 0.658

sin² θ + cos² θ = (- 0.753)² + (- 0.658)²

sin² θ + cos² θ = 1

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Answer:

If she bought 2lbs of almonds, she bought 0.4lbs of raisins. If she bought  1lb of almonds, she can buy up to 2.36lbs of raisins. If she bought 0.64lbs of almonds, she can buy up to 1.9lbs of almonds.

Step-by-step explanation:

The total pounds of raisins bought  is 0.47 pounds.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that Priya bought 0.47 pounds of raisins, Almonds cost is $5.20 per pound and Raisins cost $2.75 per pound.

The Total cost of almonds purchased = $5.20a

The Total cost of raisins purchased = $2.75r

Where:

a = total pounds of almonds bought

r = total pounds of raisins bought

The Total amount spent on raisins and almonds;  

5.20a +2.75r = 11.70

If 2 pounds of almonds are bought;

5.20(2) +2.75r = 11.70.

10.40 + 2.75r = 11.70

Combine similar terms;

2.75r = 11.70 - 10.40

2.75r = 1.30

Now Divide both sides of the equation by 2.75

r = 0.47 pounds

Hence, the total pounds of raisins bought  is 0.47 pounds.

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Answer: The shape below is formed from a rectangle measuring 18 cm by 24cm from which a rectangle of length 8.6cm has been removed

Step-by-step explanation:

initial Perimeter of rectangle =  2 (24 + 18)  = 84 cm

After removing rectangle of  length 8.6 cm

two sides of 8.6 cm are added in perimeter

Perimeter of Shape

= 2 (24 + 18)  + 8.6 + 8.6

= 84 + 17.2

= 101.2  cm

perimeter of the shape = 101.2  cm

Answer:

210 degrees

Explanation:

In symmetrical rotation i.e for the polygon to appear to be in the same place

The angle of rotation = 360/number of sides of the polygon

Number of sides=12

Therefore, Angle of rotation = 360/12=30 degrees

For AB to map onto FG, the polygon will have been rotated symmetrically seven times.

Therefore, the angle of rotation such that AB maps onto FG

= 30 x 7

= 210 degrees.

Answer:

A

Step-by-step explanation:

1.5 c flour = 12 cupcake

0.75 c flour = 6 cupcake

1.5 + 1.5 + 0.75 = 3.75 c flour

From the shadow of the flagpole, we can build a right triangle that will allow us to estimate the angle of elevation of the sun.

The shadow on the ground will be one hick of the triangle, and the flagpole will be the other hick. The hypotenuse will be the line connecting the tip of the flagpole and the tip of the shadow. The angle of elevation is the one formed between the ground and the hypotenuse.

With that, the adjacent hick will be the shadow in the ground (22 ft long), and the opposite hick is the flagpole itself (45 ft tall). The tangent of an angle is the ratio of the opposite hick to the adjacent hick. Let's call the angle of elevation α. Then:

To find the value of α we use the function inverse tangent:

Then, the angle of elevation is approximately 63.9°. The correct answer is option A.

Answer:

1400

Step-by-step explanation:

it will be easier to first do 30 times 60, which is 180, then subtract the parts

the left up part is 100, the left bottom is 150, the top right is 150, added together, is 400

1800-400

Answer:

$109.14

Step-by-step explanation:

This is correct!

Answer:

D/ $109.14

Step-by-step explanation:

i did the quiz

Answer:

3/4 a pint

Step-by-step explanation:

1/4 + 2/4 = 3/4

Given that csc(θ) = -19/4 and cos(θ) < 0. Based on the given value of csc(θ), we can determine that sin(θ) = -4/19. Since csc(θ) = 1/sin(θ), we know that θ lies in either the second or fourth quadrant. Furthermore, since cos(θ) < 0, we conclude that θ lies in the second quadrant.

Given that csc(θ) = -19/4 and cos(θ) < 0, we can deduce that sin(θ) = -4/19. The cosecant function, csc(θ), is the reciprocal of the sine function, so csc(θ) = 1/sin(θ). Therefore, we have 1/(-4/19) = -19/4. Since csc(θ) is negative, we know that θ lies in either the second or fourth quadrant.

To determine the specific quadrant, we consider the given information that cos(θ) < 0. In the second quadrant, cosine values are negative. Hence, we can conclude that θ lies in the second quadrant.

With sin(θ) = -4/19 and cos(θ) < 0, we can find the remaining trigonometric ratios. Using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can solve for cos(θ). Substituting the known value of sin(θ), we have (-4/19)^2 + cos^2(θ) = 1, which gives us cos(θ) = -15/19.

Finally, we can use sin(θ) and cos(θ) to find the remaining trigonometric ratios. The tangent function is defined as tan(θ) = sin(θ)/cos(θ), giving us tan(θ) = (-4/19)/(-15/19) = 4/15. The other trigonometric ratios can be determined by taking the reciprocal or applying the appropriate trigonometric identities. For example, cosec(θ) = 1/sin(θ) = -19/4, sec(θ) = 1/cos(θ) = -19/15, and cot(θ) = 1/tan(θ) = 15/4.

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To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

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To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.

Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.

Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.

(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.

Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.

Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.

(3) Show that HK=G.

To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.

Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.

Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.

(4) Show that G is a cyclic group.

Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.

Therefore, G is not a cyclic group.

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The volume of a stack of 9 books is 1368.75 cubic inches.

To find the volume of a stack of 9 books, we first need to find the height of the stack. Since each book is 3/4 inch thick, the height of the stack is 9 times 3/4 inch, which is 6 3/4 inches.

Now we need to find the area of the base of the rectangular prism formed by the stack of books. Since each book has an area of 22 1/2 square inches, the total area of the base of the stack is 9 times 22 1/2 square inches, which is 202 1/2 square inches.

Therefore, the volume of the stack of 9 books is:

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To graph the curve represented by the parametric equations x = 3(−sin(t)) and y = 3(1 − cos(t)), we can use a graphing utility like Desmos or GeoGebra

The direction of the curve can be determined by observing the movement of the parameter t. As t increases, the curve moves in a counterclockwise direction. Similarly, as t decreases, the curve moves in a clockwise direction.

In the graph, the curve starts at the point (0, 0) when t = 0 and continuously moves in a loop, forming the characteristic shape of a cycloid. The curve repeats itself as t increases or decreases.

Please note that the scale of the graph may vary depending on the specific settings of the graphing utility used.

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Answer:

The amount more in interest she will pay if she choose 8 years instead of 5 years loan is approximately $2,665.92

Step-by-step explanation:

The total worth of debt Crystal has. P = $23,000

The options on the number of years for which the loans for consolidation are available, t = 5 and 8 years

n = 12 × t = The number of monthly payment = 12×5 = 60 or 12 × 8 = 96

The annual percentage rate of the loans, r = 6.75% = 0.0675

The monthly payments, 'M', Crystal pays is given as follows;

\(M = \dfrac{P \cdot \left(\dfrac{r}{12} \right )\cdot \left ( 1 + \dfrac{r}{12} \right)^{n} }{\left ( 1 + \dfrac{r}{12} \right)^{n} - 1}\)

When n = 60, we get;

\(M = \dfrac{23,000 \times \left(\dfrac{0.0675}{12} \right )\cdot \left ( 1 + \dfrac{0.0675}{12} \right)^{60} }{\left ( 1 + \dfrac{0.0675}{12} \right)^{60} - 1} \approx 452.72\)

The total amount payed, A = M × n

∴ The total amount payed when n = 60 is, A₅ = 452.72 × 60 = 27163.2

A₅ ≈ $ 27,163.2

The interest on the loan, I₅ = A₅ - P

∴ I₅ = $27,163.2 - $23,000 = $4,163.2

When n = 80, we get;

\(M = \dfrac{23,000 \times \left(\dfrac{0.0675}{12} \right )\cdot \left ( 1 + \dfrac{0.0675}{12} \right)^{96} }{\left ( 1 + \dfrac{0.0675}{12} \right)^{96} - 1} \approx 310.72\)

∴ The total amount payed when n = 80 is, A₈ = 310.72 × 96 = 29,829.12

A₈ = $ 29,829.12

The interest on the loan, I₈ = A₈ - P

∴ The interest on the loan, I₈ = 29,829.12 - 23,000 = 6,829.12

The interest Crystal pays when takes the loan for 8 years, I₈ = $6,829.12

Therefore, the amount more interest she will pay if she choose 8 years instead of 5 years loan, ΔI = I₈ - I₅

ΔI = $6,829.12 - $4,163.2 = $2,665.92

The amount more interest she pays if she choose 8 years instead of 5 years loan, ΔI = $2,665.92.

Answer:

Below

Step-by-step explanation:

The maximum area of land that can be enclosed is a SQUARE

  using the river as one side of the square means there are 3 sides that total 800 ft     800 / 3 = 266 2/3 ft per side

  area would then be L x W =    266 2/3  * 266 2/3 = 71111  1/9 ft^2

The amount shared among the four brothers is 1200. Let the brothers be a, b, c and d. If the eldest is a, then it means a got 100 more than b. This means a got b + 100. Also, b got c + 100, and c got d + 100 and d got d. Therefore;

Answer:

26,000

Step-by-step explanation:

There are 4 places to be filled.

_ _ _ _

Now we put in each place the number of possible characters that can go there.

26 10 10 10

Finally we multiply all the numbers together.

26 * 10 * 10 * 10 = 26,000

Answer: 26,000

Answer:

14

Step-by-step explanation:

 ✩brainliest appreciated✩

Answer: 14 is the common factor

Step-by-step explanation:

Initial size of the culture = 400 , Doubling period = (35 minutes - 10 minutes) / (1900 - 400) = 0.1437 minutes , Population after 60 minutes = 400 * (2^(60/0.1437)) = 10201 and Population will reach 11000 after approx. 74.51 minutes.

The initial size of the culture can be found by substituting t = 0 into the exponential growth formula:

P(t) = P0 * (2^(t/T))

where P(t) is the population at time t, P0 is the initial population, and T is the doubling period. Substituting t = 0, we get:

400 = P0 * (2^(0/T))

Therefore, P0 = 400.

The doubling period can be found by rearranging the exponential growth formula:

T = (t2 - t1) / (ln(P2) - ln(P1))

where t1 and t2 are the time points, and P1 and P2 are the populations at those time points. Substituting t1 = 10, t2 = 35, P1 = 400, and P2 = 1900, we get:

T = (35 - 10) / (ln(1900) - ln(400)) = 0.1437 minutes

The population after 60 minutes can be found by substituting t = 60 into the exponential growth formula:

P(60) = P0 * (2^(60/T))

Substituting P0 = 400 and T = 0.1437, we get:

P(60) = 400 * (2^(60/0.1437)) = 10201

Finally, the population will reach 11000 after approx. 74.51 minutes can be found by setting P(t) = 11000 in the exponential growth formula and solving for t:

11000 = 400 * (2^(t/0.1437))

t/0.1437 = ln(11000/400)

Therefore, t = 0.1437 * ln(11000/400) ≈ 74.51 minutes

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Is valid

a• (b+c) = ab + ac. Its called distributive property

We note here that, are equivalents

a= 2

b= x

c= -y

Then in conclusion , both are the same expression

Answer:

Hey buddy whatsup? All good

Coming to the question fig 1 and 3 aren't functions

Coz.... Reason for fig 1... Every distinct element of domain must have a unique element in codomain, but in this fig the same element has more than two unique elements which is a relation not a function.

Reason for fig 3 every element in domain must have an unique element in codomain but in this fig the element c doesn't have any unique element hence it isn't a function.....

Thank you

Answer:

fig 1 is not function because x-componet (A) has two range

We can drag the particles in mass/grams measurement to the corresponding descriptions as follows:

1.  1.6744 × 10⁻²⁴: Two electrons and 0ne proton

2. 5.021 × 10⁻²⁴: Two protons and one neutron

3. 5.0224 × 10⁻²⁴: One proton and two neutrons

4. 3.3484  × 10⁻²⁴: One electron, one proton, and one neutron

To match the measurements to the descriptions first note that one neutron is 1.6749 × 10⁻²⁴. One proton is equal to  1.6726 × 10⁻²⁴ and one electron is equal to  9.108 × 10⁻²⁸.

To obtain the right combinations, we have to add up the particles to arrive at the constituents. So, for the figure;

1.6744 × 10⁻²⁴, we would

Add 2 electrons and one proton

= 2(9.108 × 10⁻²⁸) + 1.6726 × 10⁻²⁴

= 1.6744 × 10⁻²⁴

The same applies to the other combinations.

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Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Answer:

I think it's between +1 and +2

Step-by-step explanation:

Please follow me on brainy

x = number of people went to movies

equation

6.25x + 12 = 30.75

6.25x = 30.75 - 12

6.25x = 18.75

      x = 18.75 / 6.25

      x = 3

answer

3 people

Answer:

6.25x + 12 = 30.75

3 people

Step-by-step explanation:

Answer: I don’t know how to really read that term but the coefficient in ANY term will be the number directly behind a variable. For example, 2x, the variable is ‘x’ and the coefficient is 2. But in the case 2 (space in between) x , 2 is not a coefficient of x. It’ll be 1 because if a variable is by its self, ‘x’, there is always an invisible 1 because the variable is by itself meaning there is only one. You don’t need to put a 1 behind ‘x’ because it should be known already. The coefficient basically tells you how many unknown values there are and the variable tells you the unknown value (when you eventually solve for it).

Using this information try to find the coefficient for that term or rewrite the term correctly.

I really tried to explain it the best way I could; hoped this helped :)

The coupon give Shanice 75 percent off the original price of the pair of jeans.

At a clothing store, a pair of jeans costs $40. Using a coupon, Shanice is

able to pay $10 less than the original price. Therefore, the percentage off  the original price the coupon represents can be calculated as follows:

Therefore,

Price Shanice bought the jeans = 40 - 10 = 30 dollars

Hence,

let

x = percentage off the original price

Therefore,

x / 100 × 40 = 30

40x / 100 = 30

cross multiply

3000 = 40x

divide both sides by 40

x = 3000 / 40

x = 75%

Therefore,  the coupon gives Shanice 75% off of the original price.

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Answer:

\(\displaystyle y = x + 6\)

Step-by-step explanation:

The line diagonally intersects the y-intercept of \(\displaystyle [0, 6],\)and through every endpoint in its way, therefore the b-value is 6 and the rate of change is 1.

I am joyous to assist you at any time.

Answer:

$1

Step-by-step explanation:

because there is more odd numbers then even

Answer:

One dallar

Step-by-step explanation:

The degrees of freedom (df) for the within-groups scenario is 27.

In the F-test, which is used to compare variances between groups, the degrees of freedom consist of two components: the numerator df and the denominator df. The numerator df corresponds to the number of groups being compared, while the denominator df represents the total number of observations minus the number of groups.

In the given scenario, F(2,27) = 8.80 indicates that the F-test is comparing variances between two groups. The numerator df is 2, representing the number of groups being compared.

To determine the within-groups df, we need to calculate the denominator df. The denominator df is calculated as the total number of observations minus the number of groups. Since the denominator df is given as 27, it implies that the total number of observations is 27 + 2 = 29, considering the two groups being compared.

Therefore, the within-groups df is 27, as it represents the total number of observations minus the number of groups in the F-test.

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