Simplify tan 5 + tan 5 so that it is written as a trigonometric function of one number.

The sum of the arithmetic series 7.6+6.3+5 is 18.9. This can be found using the formula Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term. By substituting the given values, we get Sn = (3/2)(7.6 + 5) = 18.9.



To find the sum of a finite arithmetic series, we can use the formula Sn = (n/2)(a + l), where Sn is the sum, n is the number of terms, a is the first term, and l is the last term.

In the given arithmetic series 7.6+6.3+5, we have three terms: 7.6, 6.3, and 5. The first term (a) is 7.6 and the last term (l) is 5. Since we have three terms, the number of terms (n) is also 3.

Substituting these values into the formula, we get Sn = (3/2)(7.6 + 5) = (3/2)(12.6) = 18.9. Therefore, the sum of the finite arithmetic series 7.6+6.3+5 is 18.9.

In simpler terms, we can think of the sum of an arithmetic series as the average of the first and last term, multiplied by the number of terms. So in this case, we add 7.6 and 5 to get 12.6, and then divide it by 2 to get the average of 6.3. Finally, we multiply 6.3 by 3 (since we have three terms) to get the sum of 18.9.

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Answer:

9.25$

Step-by-step explanation:

Cost of Family 4-pack of tickets=37$

Price per ticket=x

In order to find out the price per ticket we,

x=\(\frac{37}{4}\)

x=9.25$

Hope this helps u

Answer:

MO = 17

Step-by-step explanation:

First, you need to define what if the unknown x.

segment MN and NO are equal to MO.

thus, your equation for the combination is x +8

Now set the values equal to each other

x + 8 = 3x - 10 (subtract x from both sides)

8 = 2x - 10 ( get your x value alone, add 10 to both sides)

18 = 2x (simplfy)

x = 9

Now plug x value into MO

3 (9) - 10 = 17

Check with opposing equation:

9 + 8 = 17 √

Pretty sure the answer is B The horizontal asymptote y = 10 means that the final concentration will always be greater than 10%.

Step-by-step explanation:

Since the 10 % solution that you're adding to the 30% solution is 10% acid when you add it to the 30 acid percent solution it would never decrease the acidity levels farther than 10 percent no matter how much you put because the solution your adding is at a 10% acidity and the other solution is 30% acidity and has a higher acidity level than the 10% so it could never go lower than the solution you are adding to it.

Really hope I did an okay job at explaining.

Answer:

B on edge

Step-by-step explanation:

Passed the test

The general solution of the given differential equation is:

y = (1/7) + C * \(exp(-x^7)\)

The exponential of the integral of the coefficient of y, in this case 7x6, provides the integrating factor. The integrating factor is given by the exponential of the integral of the coefficient of y, which in this case is 7x⁶.

The integrating factor is therefore exp(∫ 7x⁶ dx), which can be calculated as exp(x⁷/7).

Multiplying both sides of the differential equation by the integrating factor, we have:

exp(x⁷/7) * y' + 7x⁶ * exp(x⁷/7) * y = x⁶ * exp(x⁷/7)

Using the product rule on the left side, we can rewrite the equation as:

d/dx (exp(x⁷/7) * y) = x⁶ * exp(x⁷/7)

Integrating both sides with respect to x, we get:

exp(x⁷/7) * y = ∫ x⁶ * exp(x⁷/7) dx

The integral on the right side can be solved using integration by parts. Let's denote u = x⁶ and dv = exp(x⁷/7) dx. Then, du = 6x⁵ dx and v = 7/7 * exp(x⁷/7) = exp(x⁷/7).

Using the formula for integration by parts:

∫ u dv = uv - ∫ v du

We have:

∫ x⁶ * exp(x⁷/7) dx = x⁶ * exp(x⁷/7) - ∫ exp(x⁷/7) * 6x⁵ dx

Simplifying the integral on the right side, we obtain:

∫ exp(x⁷/7) * 6x⁵ dx = 6 * ∫ x⁵ * exp(x⁷/7) dx

We can apply integration by parts again to this integral, with u = x⁵ and dv = exp(x⁷/7) dx.

Continuing this process, we will eventually reach an integral of the form ∫ exp(x⁷/7) dx, which can be expressed in terms of special functions called exponential integrals.

Once we have the value of this integral, we can substitute it back into the expression for the integral of x⁶ * exp(x⁷/7) dx.

Finally, we divide both sides of the equation by exp(x⁷/7) and solve for y:

y = (1/exp(x⁷/7)) * (∫ x⁶ * exp(x⁷/7) dx)

The resulting expression will give the general solution to the given differential equation.

To solve this linear first-order ordinary differential equation, we can use an integrating factor. The integral of the coefficient of y's exponential integral, in this case 7x⁶, provides the integrating factor.

The integrating factor is therefore exp(∫ 7x⁶ dx), which can be calculated as exp((7/7) * x⁷) = exp(x⁷).

Multiplying both sides of the differential equation by the integrating factor, we have:

exp(x⁷) * y' + 7x⁶ * exp(x⁷) * y = x⁶ * exp(x⁷)

We can rewrite this equation as follows:

d/dx (exp(x⁷) * y) = x⁶ * exp(x⁷)

Integrating both sides with respect to x, we get:

exp(x⁷) * y = ∫ x⁶ * exp(x⁷) dx

To evaluate this integral, we can make a substitution. Let's substitute u = x⁷, then du = 7x⁶ dx.

The integral becomes:

(1/7) ∫ exp(u) du = (1/7) * exp(u) + C = (1/7) * exp(x⁷) + C

Now, dividing both sides of the equation by exp(x⁷), we have:

y = (1/7) + C * exp(-x⁷)

Therefore, the general solution of the given differential equation is:

y = (1/7) + C * exp(-x⁷)

where C is an arbitrary constant.

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Answer:

Step-by-step explanation:

the property of zero,

multiplication property of zero

a).  The Lagrangian L is defined as L = T - V. Substituting the expressions for T and V, we have L = (1/2)m(v_r² + r²v_θ² + v_z²) - V(r) , b). the conserved quantity is Q = p_z * s. This conserved quantity corresponds to the conservation of linear momentum in the z-direction, indicating that the z-component of the linear momentum remains constant throughout the motion.

a) To derive the Lagrangian of the system in cylindrical coordinates (r, θ, z), we start by expressing the kinetic energy T and potential energy V in terms of these coordinates. The kinetic energy of the mass is given by T = (1/2)mv², where v is the velocity. In cylindrical coordinates, the velocity components are v_r, v_θ, and v_z. The squared velocity can be written as v² = v_r² + r²v_θ² + v_z².

The potential energy V(r) is given as V = V(r). Therefore, the Lagrangian L is defined as L = T - V. Substituting the expressions for T and V, we have L = (1/2)m(v_r² + r²v_θ² + v_z²) - V(r).

b) To apply Noether's theorem, we consider the transformation z(t) → z(t, s) = z(t) + s, where s is a parameter associated with the transformation. Noether's theorem states that for each continuous symmetry of the Lagrangian, there exists a corresponding conserved quantity.

Under the given transformation, the Lagrangian L remains invariant. To determine the conserved quantity associated with this symmetry, we can apply Noether's theorem. The conserved quantity is obtained by taking the partial derivative of the Lagrangian with respect to the corresponding generalized coordinate's velocity and multiplying it by the parameter s. In this case, the generalized coordinate is z, and its conjugate momentum is p_z.

Thus, the conserved quantity is Q = p_z * s. This conserved quantity corresponds to the conservation of linear momentum in the z-direction, indicating that the z-component of the linear momentum remains constant throughout the motion.

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Answer: He would have to work 9 hours

Step-by-step explanation: If you divide 187 by 11 you will get 17, which means he gets $17 per hour so you would just have to divide 153 by 17.

Answer:

9 hrs

Step-by-step explanation:

187/11=17

Austin makes $17 per hour

153/17=9

he has to work 9 hrs to earn $153

Answer:

A

Step-by-step explanation:

follow the pattern  in its timetables,hope this helps u!

Answer I believe the next two terms are 21 and 34!  

Step-by-step explanation:

the sequence is 1,1,2,3,5,8,13...

So for the first number, 1 + 0 is 1, for the next sequence 1 + 1 is 2, 1 + 2 is 3.

Add the number with the number behind it to get your next number!

SOLUTION:

From the diagram, we can see that velocity in component form is;

Answer:

-7

Step-by-step explanation:

They both are perpendicular lines. Which means that their slopes are opposite reciprocals.

Answer:

I believe that would be -1/7

Step-by-step explanation:

It's essentially going in reverse, you go -1 spot on the graph and up 7.

Answer:

B) (-1, -4)

Step-by-step explanation:

Because -4=4(-1), since (x, y)=(-1, -4).

Please mark me as Brainliest if you are satisfied with the answer.

Answer:

(B) 16.7 kg

Step-by-step explanation:

First, start by converting everything to kilograms (using unit converters):

\(250g(\frac{10^{-3}kg}{1g})=250*10^{-3}kg=0.25kg\)

Then, add all the weights together:

\(100kg+0.25kg+150kg+0.25g=250kg+0.5kg=250.5kg\)

Now, divide this number by 15 (since they are packed in 15 bags):

\(\frac{250.5kg}{15}=16.7 kg\)

(B) 16.7 kg

Answer: d. Mean, median and mode are all equal.

Step-by-step explanation:

Answer:

6 cm

Step-by-step explanation:

Vcuboid  = lwh

⇒ h = Vcuboid ÷ lw

∴  h = 540 cm³ ÷ 90 cm²

⇒ h = 6 cm

Answer:

Step-by-step explanation:

We know the slope is rise over run. You can also find slope by using the formula (y2-y1)/(x2-x1) where x1, x2, y1 and y2 are points from the table. These points also aren't random and must correspond with each other. Example x1 and y1.

Therefore, the probability that the absolute cumulative rounding error is at least 2 is bounded by 5/12. Therefore, the probability that the absolute cumulative rounding error is at least 2, as approximated by the Central Limit Theorem, is approximately 0.0456.

a. Chebyshev's Inequality states that for any random variable X with finite mean μ and variance σ^2, the probability of X deviating from its mean by more than k standard deviations is bounded by 1/k^2. In this case, the random variable we are interested in is the absolute cumulative rounding error, |C1 + C2 + ... + C20|, which has mean 0 and variance Var(|C1 + C2 + ... + C20|) = Var(C1) + Var(C2) + ... + Var(C20) = 20/12 = 5/3. Using Chebyshev's Inequality with k = 2 standard deviations, we have:

P(|C1 + C2 + ... + C20| ≥ 2) ≤ Var(|C1 + C2 + ... + C20|) / (2^2)

P(|C1 + C2 + ... + C20| ≥ 2) ≤ 5/12

b. According to the Central Limit Theorem, the sum of independent and identically distributed random variables, such as C1, C2, ..., C20, will be approximately normally distributed as the sample size increases. Since each Ci has mean 0 and variance 1/12, the sum S = C1 + C2 + ... + C20 has mean 0 and variance Var(S) = 20/12 = 5/3. Using the standard normal distribution to approximate S, we have:

P(|S| ≥ 2) ≈ P(|Z| ≥ 2) = 2P(Z ≤ -2) ≈ 2(0.0228) ≈ 0.0456

where Z is a standard normal random variable and we have used a standard normal distribution table or calculator to find P(Z ≤ -2) ≈ 0.0228.

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Explanation:

1 hat = 45 dollars

6 hats = 6*45 = 270 dollars

1 phone = 40 dollars

4 phones = 4*40 = 160 dollars

total = $270 + $160 = $430

Felicia spent a total of $430. Since this amount of money leaves her account, this means we write a negative sign out front to end up with the final answer of -430

In other words, her account balance went down by $430 which is why we use a negative. If someone gave her $430, then the answer would be positive.

Answer:

7/18

Step-by-step explanation:

First we need to find what values of sum we can have.

The minimum value for a cube is 1, so the minimum value for the sum is 2.

The maximum value for a cube is 6, so the maximum value for the sum is 12.

Now, we find the multiples of 6 and the multiples of 4 between 2 and 12:

4, 6, 8, 12.

To have a sum of 4, we can have the pairs:

(1,3), (2,2), (3,1)

To have a sum of 6, we can have the pairs:

(1,5), (2,4), (3,3), (4,2), (5,1)

To have a sum of 8, we can have the pairs:

(2,6), (3,5), (4,4), (5,3), (6,2)

To have a sum of 12, we can have the pairs:

(6,6)

So we have 14 pairs among the 36 (6 possibilities of each cube, so 6*6=36) total possibilities of pairs, so the probability is P = 14/36 = 7/18

The probability that the outcome of the roll is a sum that is a multiple of 6 or a sum that is a multiple of 4 is,      \(P(E)=\frac{14}{36}=\frac{7}{18}\)

The probability of any event is computed as divide number of favourable outcomes by total number of outcomes.

The sum that is a multiple of 6 or a sum that is a multiple of 4  are   4, 6, 8 and 12.

For sum of 4, we can have the pairs = (1,3), (2,2), (3,1)

For sum of 6, we can have the pairs: = (1,5), (2,4), (3,3), (4,2), (5,1)

For sum of 8, we can have the pairs = (2,6), (3,5), (4,4), (5,3), (6,2)

For sum of 12, we can have the pairs = (6,6)

Total number of favourable outcomes = 14

When two distinct number cubes are rolled. then,

Total number of outcomes  \(=6^{2}=36\)

The probability that the outcome of the roll is a sum that is a multiple of 6 or a sum that is a multiple of 4,

                  \(P(E)=\frac{14}{36}=\frac{7}{18}\)

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a) Utilization (ρ): ρ = 1.111, b) Average number of jobs in the system (L): L = -10 , c) Average number of jobs in the queue (Lq): Lq = 1.234, d) End-to-end response time (R): R = 0.450 msec, e) Queuing time (Wq): Wq = 0.062 msec and f) Probability of 5 or more jobs in the system (Pn): P5 = 0.072

a) Utilization (ρ):

Utilization represents the proportion of time the server is busy. It can be calculated as the ratio of the expected service time to the expected inter-arrival time.

ρ = (expected service time) / (expected inter-arrival time)

ρ = μ / λ = 22.22 / 20 = 1.111

b) Average number of jobs in the system (L):

This represents the average number of jobs in the system, including both those being served and those waiting in the queue.

L = ρ / (1 - ρ)

L = ρ / (1 - ρ) = 1.111 / (1 - 1.111) = 1.111 / (-0.111) = -10

c) Average number of jobs in the queue (Lq):

This represents the average number of jobs waiting in the queue.

Lq = ρ² / (1 - ρ)

Lq = ρ² / (1 - ρ) = 1.111² / (1 - 1.111) = 1.234

d) End-to-end response time (R):

This is the average time a job spends in the system, including both waiting and service time.

R = 1 / (service rate - arrival rate)

R = 1 / (μ - λ) = 1 / (22.22 - 20) = 1 / 2.22 = 0.450 msec

e) Queuing time (Wq):

This is the average time a job spends waiting in the queue.

Wq = Lq / arrival rate

Wq = Lq / λ = 1.234 / 20 = 0.062 msec

f) Probability of 5 or more jobs in the system (Pn):

This is the probability that the number of jobs in the system is equal to or greater than 5.

Pn = (ρⁿ⁺¹) * (1 - ρ)

Given the following parameters:

Expected inter-arrival time (λ) = 1 / (expected inter-arrival time) = 1 / 0.05 = 20 jobs/msec

Expected service time (μ) = 1 / (expected service time) = 1 / 0.045 = 22.22 jobs/msec

Pn = (ρⁿ⁺¹) * (1 - ρ)

For n = 5:

P5 = (1.111⁵⁺¹) * (1 - 1.111) ≈ 0.072

Therefore, a) Utilization (ρ): ρ = 1.111, b) Average number of jobs in the system (L): L = -10 , c) Average number of jobs in the queue (Lq): Lq = 1.234, d) End-to-end response time (R): R = 0.450 msec, e) Queuing time (Wq): Wq = 0.062 msec and f) Probability of 5 or more jobs in the system (Pn): P5 = 0.072

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The ratio of LM to FG is 3:4, so correct option is A.

A triangle is a polygon with three sides, three vertices, and three angles. It is one of the basic shapes in geometry and has many properties that make it a useful and interesting shape to study.

The sum of the interior angles of a triangle is always 180 degrees, which is a fundamental property of triangles.

Triangles also have many interesting properties related to their sides, angles, and areas. For example, the Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. The area of a triangle can be calculated using the formula 1/2(base x height) or by using various trigonometric functions.

Triangles are important in many areas of mathematics and science, such as in geometry, trigonometry, calculus, and physics. They are also commonly used in architecture, engineering, and design.

If LMN and FGH are similar triangles, then the ratio of their areas is equal to the square of the ratio of their corresponding side lengths.

Let x be the ratio of LM to FG. Then the ratio of their areas is (x²).

So we have:

LMN / FGH = 18 / 32

(x²) = 18 / 32

x² = 9 / 16

x = (3 / 4)

Therefore, the ratio of LM to FG is 3:4, which is option A.

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Answer:

Step-by-step explanation:

Area of triangles

Area of trapezoid

Since the area of trapezoid is same as the sum of the areas of the triangles, we have:

Concepts:

Answer: 41 cm²

Triangle lengths:

A(ABN) = 1/2b₁h

A(CDM)= 1/2b₂h

Trapezoid length:

A(ABCD) = 1/2(b₁ + b₂)h

A = 23 + 18 = 41 cm²

Answer:

14 feet

Step-by-step explanation:

Area= base x height

Height=area/base

182/13=14

The price of the item increases by approximately 3.93% each year.

The initial price of the item is the value of p(0), which can be obtained by setting r=0 in the given function. Therefore:

p(0) = 2000(1.039)^0 = 2000

So the initial price of the item is $2000.

To determine whether the function represents growth or decay, we need to look at the value of the base of the exponential function, which is 1.039 in this case. Since this value is greater than 1, the function represents growth.

To find the percentage change in price each year, we can calculate the percentage increase from the initial price to the price after one year (r=1):

p(1) = 2000(1.039)^1 = 2078.60

The percentage increase from $2000 to $2078.60 is:

((2078.60 - 2000)/2000) x 100% ≈ 3.93%

Therefore, the price of the item increases by approximately 3.93% each year.

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I think ur answer B.) srry if wrong .

Also i have something important to say.

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THIS is the link an there is a new one PLEASE DON'T CLICK IT c utt.ly/nz6 VGda  and  is.gd/ qKzp BU

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If you see this link don't click it. IT will send a virus and download bad stuff on your device. Please repost so people wont fall for it. Have a good day or night. <3

Answer: total 9 outcomes

Step-by-step explanation:

The correct option of the given statement "Janice's funds to triple if she has $5,000 invested in a bank that pays 9.4% annually" is 11.86 years.

To solve the problem, we can use the formula for the future value of a single sum.

FV = PV (1 + i)ⁿ

Where,

PV is the present value of the investment

"i" is the annual interest rate

n is the number of years

FV is the future value of the investment.

So, we can say that the future value (FV) of Janice's investment will be 3 times her present value (PV). Thus,

FV = 3 PV

    = 3 × 5,000

    = $15,000

Now, we can substitute the given values in the formula:

FV = PV (1 + i)ⁿ

15,000 = 5,000(1 + 0.094)ⁿ

Dividing both sides by 5,000, we get:

3 = (1 + 0.094)ⁿ

Taking the logarithm of both sides:

log 3 = log (1 + 0.094)ⁿ

log 3 = n log (1 + 0.094)

n = log 3 / log (1 + 0.094)

n = 11.86 years

Therefore, it will take approximately 11.86 years for Janice's funds to triple.

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Answer:

40-d

Step-by-step explanation:

Answer:

64

Step-by-step explanation: 7^4=2401   4^4=256     2401/256= 64