What is the sum of 17.25 and 1.725 , to the nearest integer?

The half-life of a radioactive material is the time it takes for half of its atoms to decay. The half-life of the given radioactive material is approximately 4.5 hours.

To calculate the half-life of the given radioactive material, we need to use the formula:
Nt = N0 \((1/2)^{(t/T)}\)
Where Nt is the number of radioactive atoms at time t, N0 is the initial number of radioactive atoms, T is the half-life of the material, and t is the time elapsed since the initial measurement.
Using the given data, we can set up two equations:
1450 = N0 \((1/2)^{(0/T)}\)
380 = N0 \((1/2)^{(8/T)}\)
Dividing the second equation by the first equation, we get:
380/1450 = \((1/2)^{(8/T)} / (1/2)^{(0/T)}\)
Simplifying this expression, we get:
380/1450 = \((1/2)^{(8/T)}\)
Taking the natural logarithm of both sides, we get:
ln(380/1450) = ln\((1/2)^{(8/T)}\)
Simplifying this expression, we get:
T = -8ln(380/1450)/ln(1/2) ≈ 4.5 hours

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1.because sample is random and (130)

(0.923) and (130)(0.077) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.923 and q=1-0.923=0.077

np = 130 x 0.923

np = 120 ≥ 10

nq = 130 × 0.077

nq = 10 = 10

Hence, Yes, because sample is random and

(130)(0.923) and (130)(0.077) are both at least 10. This means the normal model is a good fit for the sampling distribution.

2.because sample is random and (130)

(0.919) and (130)(0.081) are both at least 10.

This means the normal model is a good fit for the sampling distribution.

Consider the provided information.

130 randomly selected flights and find that

120 of the flights arrived on time.

n=130

The on-time arrival performance was 91.9%

p=0.919 and q=1-0.919=0.081

np = 130 x 0.919

np = 119.5 ≥ 10

nq = 130 × 0.081

nq = 10.5 ≥ 10

Hence, Yes, because sample is random and

(130)(0.919) and (130)(0.081) are both at least 10. This means the normal model is a good fit for the sampling distribution.

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Answer:

D) is the correct answer

Step-by-step explanation:

To define a function, so one x can only corresponding to one y.

Then for A) we have x = -5, but y can be 1 and 4, so it is to a function,

for B) x =1, y = -1 or -4, so not. For C) x =0, y = -3 or 0, so wrong. Then left with D) which each x only corresponding to one y, so D) is correct.

If it is helpful, plz give me Brainliest.

Answer:

Step-by-step explanation:

a) Side ratios in the smaller triangle are 3:4:6. In the larger triangle, they are 5:6:9. These are not equivalent ratios, so the triangles are not similar.

__

b) The missing angle in the left triangle is 90° -55° = 35°. This matches the acute angle shown in the right triangle, so the right triangles are similar by the AA similarity criterion. The given triangle JKL starts with the largest acute angle, then the right angle, so the similarity statement must be ...

  ΔJKL ~ ΔHIG

__

c) All we know for sure is that the vertical angles are congruent. We need information about a pair of sides or of another angle before any similarity can be claimed. The triangles are not necessarily similar.

Without additional information, it is not possible to identify the correct statement describing φ for the given SHM in figure (a).

The parameter φ represents the phase angle or phase shift of the harmonic motion. It determines the initial position or displacement of the oscillating object at t = 0. It is the angle by which the cosine function is shifted horizontally.

From the options provided, we need to identify the statement that correctly describes φ in Figure (a).

The statement that describes φ for the given SHM x(t) = a cos(wt + φ) can be determined by analyzing the position of the oscillating object at t = 0. If the object is at its maximum positive displacement, φ is 0 degrees or 0 radians. If the object is at its maximum negative displacement, φ is 180 degrees or π radians. If the object is at the equilibrium position (zero displacements) at t = 0, φ is 90 degrees or π/2 radians.

Since figure (a) is not provided in the question, we cannot directly determine the exact position at t = 0. Therefore, without additional information, it is not possible to identify the correct statement describing φ for the given SHM in Figure (a).

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

5.33

It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.

Given solution to t²y'' - 4ty' + 6y = 0 is

y₁(t) = t²

Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,

y₂ = vt²

y₂' = 2vt + t²v'

y₂'' = 2v + 2tv' + 2tv' + t²v''

y₂'' = 2v + 4tv' + t²v''

Substituting this

t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0

t⁴v'' = 0

v'' = 0

v' = c, c is a constant

v = ct

Therefore, y₂(t) = ct×t²

y₂ (t) = ct³

Therefore general solution will be y(t) = c₁t² + c₂t³

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Answer:

\(Fraction = \frac{23}{125}\)

Step-by-step explanation:

Given

\(Total = 125\)

\(Chocolate = 102\)

Required

Determine fraction who do not drink chocolate

First, we need to determine the number of those who do not drink chocolate

\(No\ Chocolate = 125 - 102\)

\(No\ Chocolate = 23\)

Their fraction is calculated as thus

\(Fraction = \frac{No\ Chocolate}{Total}\)

\(Fraction = \frac{23}{125}\)

Answer:

la respuesta correcta es $123.222per mile

Answer: T he number of miles in a day at which the rental costs for Company A and Company B are the same is when x = 160miles.

Step-by-step explanation:

Step 1

Let us  write the rental cost with each company:

Company A , they will charge =$160 +$ 0.40x

Company B, They will charge = $80 + $0.90x

Where x =number of miles travelled

Step 2

we then find the number of miles in a day at which the rental costs for Company A and Company B will be  the same by equating both equations and solving for x

160 + 0.40x= 80 + 0.90x

160-80 = 0.90x-0.40x

80= 0.50x

x= 80/0.5

x= 160

Therefore t he number of miles in a day at which the rental costs for Company A and Company B are the same is when x = 160 miles.

Answer:

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

Given system of inequalities:

Plot the inequality and the given points to determine which of them fall into solution area.

See attached.

As we see only two points fall in the solution area, brown zone on the bottom: (6, −2), (6, 0.5).

(Answer:

(6, 5)

Step-by-step explanation:

For this question, there are not two correct choices.

Given systems:

y ≤ 2/3x + 1

y > -1/4x + 2

For the first equation, the y-intercept is 1, and the rate of change is 2/3 (rise over run). The inequality symbol is less than or equal to (≤), meaning this will be a solid line and the area shaded will be below the line.

For the second equation, the y-intercept is 2, and the rate of change is -1/4 (this means it is decreasing in number, therefore the line is going down). The inequality symbol is greater than (>), meaning this will be a dashed line and the area shaded will be above the line.

the area overlapped is where the solution will be. The answer is (6, 5) because it lies on the solid line of the first inequality, indicating it does satisfy the first inequality. Any point on the solid line satisfies the inequality. The point also lies above the second inequality, meaning it is a solution to the system.

Also, if you plug it into the system of inequalities, all the outcomes will make sense.

The function takes a different value (7) at u = 1, causing a sudden jump in the function's behavior at that point.

To determine if a function is continuous at a given point, we need to check three conditions: existence of the function at that point, existence of the limit of the function as x approaches the given point, and equivalence of the function value and the limit at that point. If any of these conditions fail, the function is discontinuous. The type of discontinuity can be identified based on the behavior of the function at the point. For the three given functions, the first function is continuous at x = 1, the second function has a removable discontinuity at x = π, and the third function has a jump discontinuity at u = 1/7.

The function f(x) = 2x² - 5x + 3 is a polynomial, and polynomials are continuous everywhere. Therefore, the function is continuous at x = 1.

The function h(x) = sin(8) - cos(0) tan(6) involves trigonometric functions. At x = 0, sin(8) and cos(0) are constant values, and tan(6) is also a constant value. Thus, the function h(x) is also continuous at x = 0, as it is a composition of continuous functions.

The function g(u) is defined as (6u² + u - 2)/(24 - 1) if u ≠ 1 and g(u) = 7 if u = 1. The function is defined differently depending on the value of u. At u = 1, the function has a jump discontinuity since the limit of g(u) as u approaches 1 does not exist. The function takes a different value (7) at u = 1, causing a sudden jump in the function's behavior at that point.

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Answer:

3

Step-by-step explanation:

A function cannot have two y values for any value of x

answer three has two y values for x =1

The solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.

The equation 4x^2 - 20x + 25 = 10 can be rewritten as 4x^2 - 20x + 15 = 0. To find the solutions to this equation, we can factor it or use the quadratic formula.

The equation factors as (2x - 5)(2x - 3) = 0. Setting each factor equal to zero, we get 2x - 5 = 0 and 2x - 3 = 0. Solving these equations, we find x = 5/2 and x = 3/2.

Using the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by x = (-b ± sqrt(b^2 - 4ac)) / 2a, we can determine the solutions.

In this case, a = 4, b = -20, and c = 15. Substituting these values into the quadratic formula, we get x = (-(-20) ± sqrt((-20)^2 - 4 * 4 * 15)) / (2 * 4), which simplifies to x = (20 ± sqrt(400 - 240)) / 8.

Simplifying further, we have x = (20 ± sqrt(160)) / 8, which becomes x = (20 ± 4sqrt(10)) / 8. Finally, simplifying again, we obtain x = 5/2 ± sqrt(10)/2, which gives us the same solutions as before: x = 5/2 and x = 3/2.

Therefore, the solutions to the equation 4x^2 - 20x + 25 = 10 are x = 5/2 and x = 3/2.

To find the solutions to the equation, we can either factor it or use the quadratic formula. In this case, factoring and using the quadratic formula both yield the same solutions: x = 5/2 and x = 3/2. These values of x satisfy the equation 4x^2 - 20x + 25 = 10 when substituted back into the equation.

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Answer:

6,16,25,27,33,39,45 are the composite numbers.

Answer:

the answer is D

Step-by-step explanation:

The centripetal force is the force that acts on an object moving in a circular path, directing it towards the center of the circle. option a.

When a car is driving around a curve, the centripetal force is provided by the frictional force between the tires and the road. This force acts inwards, towards the center of the circle, and is responsible for keeping the car moving in a circular path.

The centripetal force is always perpendicular to the direction of motion, so option (b) and (d) can be eliminated.

Additionally, there is no force that acts away from the center of the circle, so option (c) can also be eliminated. Option (e) is not applicable since the question is asking about the direction of the force, not its orientation.

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In terms of pi means to include pi in your answer. In other words, don't use 3.14 or 22/7 for pi.

Answer:

x = 9.7    y = 11.4

Step-by-step explanation:

tan 45 = x/6

x = tan 45 (6)

= 9.7

c² = a² + b²

c² = 9.7² + 6²

= 94.09 + 36

= 130.09

= 11.4

Answer:

That equals 99.9

Step-by-step explanation:

Answer:

I’m answering so the other peep can get brainliest she’s correct I think I’m pretty sure I think so thx for points have a great day byee

Step-by-step explanation:

To compare the two options, we need to calculate the total earnings for each option over the 4-year period.

Option 1: Earning an additional $500 each year

The total earnings for this option will be:

Year 1: $15,000

Year 2: $15,500 ($15,000 + $500)

Year 3: $16,000 ($15,500 + $500)

Year 4: $16,500 ($16,000 + $500)

Total earnings over 4 years = $15,000 + $15,500 + $16,000 + $16,500 = $63,000

Option 2: Earning 2% of current salary

To calculate the earnings for this option, we need to find the salary for each year using the formula:

salary = $15,000 + 2% × (previous year's salary)

Year 1: salary = $15,000

Year 2: salary = $15,300 ($15,000 + 2% × $15,000)

Year 3: salary = $15,606 ($15,300 + 2% × $15,300)

Year 4: salary = $15,924.12 ($15,606 + 2% × $15,606)

Total earnings over 4 years = $15,000 + $15,300 + $15,606 + $15,924.12 = $61,830.12

Therefore, the first option of earning an additional $500 each year results in higher total earnings of $63,000 over 4 years, compared to earning 2% of the current salary, which results in total earnings of $61,830.12. Hence, the first option of earning an additional $500 each year is the better choice.

Answer:

(5, -18)

Brainliest, please!

Step-by-step explanation:

(12, -9)(19, 0)

x distance: 7, y distance: 9

To get the other endpoint, we must apply the opposite.

x distance: -7, y distance: -9

(12, -9)

12 - 7 = 5, -9 - 9 = -18

(5, -18)

Circular equations are typically organized like this:

\((x-h)^2+(y-k)^2=r^2\)

We're given:

Plug the given information into the formula:

\((x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-1)^2=(\sqrt{14})^2\\(x+5)^2+(y-1)^2=14\)

\((x+5)^2+(y-1)^2=14\)

Answer:

C = -4

Step-by-step explanation:

Answer:

c = -4

Step-by-step explanation:

;)

Step-by-step explanation:

M = L + rL

a.

L = $63.80

M = $121.80

need to find r

121.80 = 63.80 + r×63.80

58 = r×63.80

r = 58/63.80 = 0.91 = 91%

b.

L = $65

M = $146.25

need to find r

146.25 = 65 + r×65

81.25 = r×65

r = 81.25/65 = 1.25 = 125%

a )The equation of the new parallel line is   x - y = 3

b ) The equation of the new perpendicular line is   x + y = -1

The given line passes through the points (0, 3 ) and (-3, 0).

Here,

\((x _{1}, y _{1}) = (-3, 0)\\\\(x _{2}, y _{2}) = (0, 3)\)

The slope of the line = m

\(m =\frac{y_{2}- y _{1}}{x _{2}- x_{1}} \\\\m = \frac{3-0}{0+3} \\\\m = \frac{3}{3} = 1\)

The slope of the given line is 1

a ) The new line passes through the point (1, -2) and is parallel to the given line .

           \(y- y_{1} = m (x- x_{1}) -- (1)\)

          y + 2 = 1 (x -1 )

          y  +2 = x - 1

           x - y -1 -2 = 0

           x - y - 3 =0

           x - y = 3

The equation of the new parallel line is   x - y = 3

b ) The new line passes through the point (1, -2) and is perpendicular to the given line .

           \(y- y_{1} = m (x- x_{1}) -- (1)\)

          y + 2 = -1 (x -1 )

          y  +2 = - x + 1

           x + y -1 +2 = 0

           x + y + 1 = 0

           x + y = -1

The equation of the new perpendicular line is   x + y = -1

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