Find the surface area of the sphere

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The inequality that represents the number of animals at the shelter for expenses to be at least $1170 a week is x ≥ 70.

To solve this problem, we need to start by setting up an equation that represents the total weekly expenses of the animal shelter. Let's call the number of animals in the shelter "x".

The fixed expenses are $750, and each animal costs an additional $6 per week, so the total weekly expenses can be represented by the equation:

Total Weekly Expenses = $750 + $6x

We also know that during the summer months, the total weekly expenses are at least $1170. So, we can set up an inequality to represent this:

$750 + $6x ≥ $1170

To solve for x, we can start by subtracting $750 from both sides of the inequality:

$6x ≥ $420

Then, we can divide both sides by $6 to isolate x:

x ≥ 70

This means that there must be at least 70 animals in the shelter for the total weekly expenses to be at least $1170.

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The half life of the bacterial culture is 5 hours.

We know that the decay constant tells us how the decay is progressing per unit time.

We know that;

N = Noe^-kt

N = bacteria at time t

No = Bacteria present at the beginning

k = decay constant

t = time taken

20 = 80e^-10k

20/80 = e^-10t

1/4 = e^-10k

ln(0.25) =  -10k

k = ln(0.25)/-10

k = 0.14 hr-1

Then;

Half life = 0.693/k

Half life = 0.693/0.14 hr-1

Half life = 5 hours

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The 20th prize is $4400.

It is a sequence where the difference between each consecutive terms is the same.

Example:

2, 4, 6, 8 is an arithmetic sequence.

We have,

First prize = $12,000

Successive prize worth $400 less than the preceding prize.

Now,

We can make an arithmetic sequence.

12,000, 11,600, 11,200, ...

So,

a = 12,000

d = -400

The nth term of an arithmetic sequence.

= a + (n - 1)d

So,

The 20th prize.

= 12,000 + (20 -1)400

= 12,000 - 19 x 400

= 12,000 - 7600

= 4400

Thus,

20th prize = $4400

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Answer:

to find the value of x u would have to multiply the numbers in the equation and then u will get ur answer.

Step-by-step explanation:

I hope this helps

The determinant of the given matrix A is 0. This means that the correct answer is option (C).

The determinant of the given matrix A = [[1, -3, 1], [0, 2, -1], [0, -4, 2]] needs to be determined.

The determinant of a 3x3 matrix can be found using the cofactor expansion method. In this case, we expand along the first row:

det(A) = 1 * det([[2, -1], [-4, 2]]) - (-3) * det([[0, -1], [0, 2]]) + 1 * det([[0, 2], [0, -4]])

Calculating the determinants of the 2x2 matrices:

det([[2, -1], [-4, 2]]) = (2 * 2) - (-1 * -4) = 4 - 4 = 0

det([[0, -1], [0, 2]]) = (0 * 2) - (-1 * 0) = 0 - 0 = 0

det([[0, 2], [0, -4]]) = (0 * -4) - (2 * 0) = 0 - 0 = 0

Substituting these values back into the cofactor expansion:

det(A) = 1 * 0 - (-3) * 0 + 1 * 0 = 0 + 0 + 0 = 0

Therefore, the determinant of matrix A is 0. The correct answer is (C) 0.

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Answer:

{} {1},{2},{3},{4} {1,2,3,4}

No one can catch the bill without moving their hand downward due to the effects of gravity and human reaction time.

When the bill is released, it will immediately start to fall due to the force of gravity acting on it. The person attempting to catch the bill would need to react quickly and move their hand downward in order to intercept its path. However, human reaction time introduces a delay between perceiving the bill's movement and initiating a response.

Even with a relatively quick reaction time of 0.25 seconds, the bill would have already fallen a significant distance in that time. This is because the acceleration due to gravity is approximately 9.8 meters per second squared. In just 0.25 seconds, the bill would have fallen approximately 1.225 meters (4 feet) assuming no air resistance.

Given that the person's hand is positioned with the center of the bill between their index finger and thumb, they would need to move their hand downward by at least the distance the bill has fallen within that reaction time. However, it would be practically impossible to move their hand downward by such a large distance in such a short amount of time, making it impossible to catch the bill without moving their hand downward.

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The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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Answer:

Step-by-step explanation:

4.2 is rational....and -11/2 as well...I think...

Answer: $2,466.45

Step-by-step explanation:

Hi, to answer this question we have to apply the compounded interest formula:

A = P (1 + r/n) nt

Where:  

A = Future value of investment (principal + interest)  

P = Principal Amount  

r =  Nominal Interest Rate (decimal form, 3.5/100= 0.035)

n=   number of compounding periods in each year (365)

Replacing with the values given

3,500= P (1+ 0.035/365)^365(10)

Solving for P

3,500= P (1.00009589)^3650

3,500/  (1.00009589)^3650 =P

P = $2,466.45

Answer:

yes ur on track

Step-by-step explanation:

Answer:

47.5 minutes

Step-by-step explanation:

40 min = 80

x min = 95

40/80 = x/95

3800 = 80x

x = 47.5

-Chetan K

Answer: 10

Step-by-step explanation: you look at x=1 and go over to x=3 and do rise over run

To solve the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0, we can use algebraic methods and the unit circle to determine the values of x that satisfy the equation.

1. Start by rearranging the equation to a quadratic form: \(6sin^2(x)\) + 6sin(x) + 1 = 0.

2. Notice that the equation resembles a quadratic equation in terms of sin(x). Let's substitute sin(x) with a variable, such as u: \(6u^2\) + 6u + 1 = 0.

3. Solve this quadratic equation for u. You can use the quadratic formula or factorization methods to find the values of u. The solutions are u = (-3 ± √3) / 6.

4. Since sin(x) = u, substitute back the values of u into sin(x) to obtain the values for sin(x): sin(x) = (-3 ± √3) / 6.

5. To find the values of x, we can use the inverse sine function. Take the inverse sine of both sides: x = arcsin[(-3 ± √3) / 6].

6. The arcsin function has a range of [-π/2, π/2], so the values of x lie within that range. Use a calculator to find the approximate values of x based on the values obtained in step 5.

7. Plot the obtained x-values on the graph to show the solutions of the equation \(6sin^2(x)\) + 6sin(x) + 1 = 0. The graph will illustrate the points where the curve intersects the x-axis.

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Answer:

\(x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4\)

Step-by-step explanation:

\(y = x^2-2x+5\\\\6=x^2-2x+5\\\\x^2-2x-1=0\\\\\\\frac{-b+-\sqrt{b^2-4ac} }{2a} = x\\a = 1, b = -2, c = -1\\\\\frac{2+-2\sqrt{2} }{2\\}\\\\x = 1+\sqrt{2} = 2.4\\or\\x= 1-\sqrt{2} = -0.4\)

The value of the x is -0.4 when y = 6 and the graph is drawn on the left.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The quadratic equation,

y = x² – 2x + 5

To find the value of x:

When y = 6.

So,

x² – 2x + 5 = 6

x² – 2x - 1 = 0

Comparing the quadratic equation with standard quadratic equation,

ax²+ bx +c = 0

We get,

a = 1, b = -2 and c = -1

So,

x = {-b ±√(b²-4ac)}/2a

Substituting the values,

x = (2±√8)/2

x = 1 ± √2

x = 2.41421 and x = −0.414214

And the graph is drawn on the left so x = −0.414214 = -0.4 to one decimal place.

Therefore, the value of the x is -0.4.

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The value of Milton Industries with leverage is $131.52 million.

Milton Industries expects free cash flows of $20 million each year.

Milton's corporate tax rate is 22%, and its unlevered cost of capital is 16%.

Milton also has outstanding debt of $26.48 million and it expects to maintain this level of debt permanently.

a. Value of Milton Industries without leverage: Formula to calculate the value of a firm without leverage is; VL = VU + (PV of Tax shield) Where, VL = Value of the firm with leverage VU = Value of the firm without leverage PV of Tax Shield = Present Value of Tax Shield Expected Free Cashflows of Milton Industries = FCF = $20 million

Corporate Tax rate = T = 22%Unlevered

Cost of Capital = Ku = 16%Debt of Milton Industries = D = $26.48 million

Weighted Average Cost of Capital = WACC = Ku (1 - T)PV of Tax Shield = D x T x (1 - T) = $6.52 million VL = VU + PV of Tax Shield VU = FCF / Ku = $125 million VL = $125 + $6.52 = $131.52 million

b. Value of Milton Industries with leverage: VL = VU + PV of Tax Shield PV of Tax Shield = D x T x (1 - T) = $6.52 million VL = VU + PV of Tax Shield VU = FCF / Ku = $125 million VL = VU + PV of Tax Shield = $125 + $6.52 = $131.52 million. Therefore, The value of Milton Industries without leverage is $125 million. The value of Milton Industries with leverage is $131.52 million.

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Therefore, the definite integral of f(x) over the given limits is ∫-3 6 f(x) dx = ∫-3 4 f(x) dx + ∫4 6 f(x) dx= 50 + 8= 58

Hence, the required answer is 58.

We are given a piecewise function and are asked to evaluate its definite integral. The function is defined as:f(x) = {4x if x < 4, if x ≥ 4We need to find the integral of this function over the given limits. Let's evaluate the integral:

∫-3 6 f(x) dx = ∫-3 4 f(x) dx + ∫4 6 f(x) dx

Now, we will evaluate the two integrals one by one:

∫-3 4 f(x) dx = ∫-3 4 4x dx [∵ f(x) = 4x for x < 4]

∫-3 4 f(x) dx = [2x²] from -3 to 4= [2(4)²] - [2(-3)²]∫-3 4 f(x) dx = 32 + 18= 50

Now, let's evaluate the second integral:

∫4 6 f(x) dx = ∫4 6 4 dx [∵ f(x) = 4 for x ≥ 4]∫4 6 f(x) dx = [4x] from 4 to 6= (6 x 4) - (4 x 4)∫4 6 f(x) dx = 8Therefore, the definite integral of f(x) over the given limits is:

∫-3 6 f(x) dx = ∫-3 4 f(x) dx + ∫4 6 f(x) dx= 50 + 8= 58

Hence, the required answer is 58.

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The graph the describes the points x-intercepts: (-35, 0) and (-9, 0); y-intercept: (0, 225) and vertex: (-17, -64)

A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.

The features of the graph are given as:

x-intercepts: -35, -9

y-intercept: 225

Vertex: (-17, -64)

The above points can be properly written as:

x-intercepts: (-35, 0) and (-9, 0)

y-intercept: (0, 225)

Vertex: (-17, -64)

Next, we plot the points on a coordinate plane.

Then, we connect the points

Since the y-intercept is greater than the vertex, then it means that the vertex is a minimum and the graph must not exceed this point

See the attachment for the graph that describes the given points.

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Answer:Answer for the first one is just 7/9, 28/36Second one is 9/14, 3/4For the third one you multiply 12.50 by 5 which gives you 62.5

Step-by-step explanation:

Answer:

B.) 4,096 feet

Step-by-step explanation:

You were given a time, and time in the equation is represented by "t". To find the height, represented by "h", you just need to plug the given value in for "t" and simplify to find "h".

t = (1/4)√x                                         <--- Original equation

16 = (1/4)√x                                      <--- Plug 16 in "t"

64 = √x                                            <--- Divide both sides by (1/4)

4,096 ft = x                                    <--- Square both sides

The object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

The equation is t=1/4 √x , where t is time in seconds and x is height in feet. To determine the height  x at which an object should be dropped to reach the ground in 16 seconds, you can plug in the value of t=16 into the equation:

16 = 1/4 √x

Simplify the equation by multiplying both sides by 4:

4⋅16= √x

64= √x

Now, square both sides to isolate x:

64²=x

4096 = x

Therefore, to have the object reach the ground in 16 seconds, you should drop it from a height of 4096 feet.

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A is not a subset of B, and B is not a subset of A.

(a) A is not a subset of B.

(b) B is not a subset of A.

(a) To determine if A is a subset of B, we need to check if every element in A is also in B. A consists of integers of the form 4r - 1, where r is an integer. On the other hand, B consists of integers of the form 8s + 1, where s is an integer. It is clear that not every element of A can be expressed in the form 8s + 1, as the numbers in A have the form 4r - 1. Therefore, A is not a subset of B.

(b) Similarly, to determine if B is a subset of A, we need to check if every element in B is also in A. B consists of integers of the form 8s + 1, where s is an integer. A consists of integers of the form 4r - 1, where r is an integer. It is clear that not every element of B can be expressed in the form 4r - 1, as the numbers in B have the form 8s + 1. Therefore, B is not a subset of A.

In conclusion, A is not a subset of B, and B is not a subset of A.

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Answer:

\(\huge\boxed{\sf x = 2 }\)

Step-by-step explanation:

\(\sf \frac{3x-1}{5} = \frac{x+1}{3} \\\\Cross \ Multiplying \\\\3(3x-1) = 5(x+1)\\\\9x - 3 = 5x+5\\\\Combining \ like \ terms\\\\9x-5x = 5+3\\\\4x = 8 \\\\Dividing \ both \ sides \ by \ 4\\\\x = \frac{8}{4}\\\\\boxed{\sf x = 2 }\\\\\rule[225]{225}{2}\)

Hope this helped!

it may be permissible to proceed with a hypothesis test even if the assumption of random participant selection is violated, under the conditions of known and accounted for non-random selection or random assignment to treatment groups

Random participant selection is an important assumption in hypothesis testing, as it helps ensure the generalizability of the results to the target population. However, in some situations, it may be impractical or impossible to achieve perfect random selection. In such cases, there are a few conditions under which it may still be permissible to proceed with a hypothesis test despite the violation of this assumption:

Non-random selection is known and accounted for: If the non-random selection process is well-documented and understood, researchers can adjust their analysis or statistical methods to account for potential biases introduced by the non-random selection.

Random assignment to treatment groups: Even if participants are not randomly selected, random assignment to different treatment groups can help mitigate the impact of non-random selection. By randomly assigning participants to treatment groups, the effects of non-random selection are distributed evenly across the groups, allowing for valid comparisons and hypothesis testing.

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Answer:

6s2

= 6(2)2

= 12 × 12

= 144

: The value of the expression is equal to 144

The length of the third side in this triangle is equal to 96 units

Mathematically, the perimeter of a triangle can be calculated by using this mathematical expression:

P = a + b + c

Where:

Substituting the given parameters into the perimeter of a triangle  formula, we have the following;

214 = 118 + c

Third side, c = 214 - 118

Third side, c = 96 units.

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the probability is 5/12

To calculate the probability that the sum of the values on two fair six-sided dice is a prime number, we need to determine the number of favorable outcomes (sums that are prime) and the total number of possible outcomes.

First, let's identify the prime numbers that can be obtained as the sum of two dice:

2 (1+1)

3 (1+2, 2+1)

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

7 (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)

11 (5+6, 6+5)

There are 15 pairs whose sum is prime numbers that can be obtained as the sum of two dice.

Next, let's calculate the total number of possible outcomes when throwing two six-sided dice. Each die has 6 possible outcomes, so the total number of outcomes is 6 * 6 = 36.

Therefore, the probability that the sum of the values on two fair six-sided dice is a prime number is:

Number of favorable outcomes / Total number of possible outcomes

= 15 / 36

= 5/12

Therefore, the probability is 5/12

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Answer:

the answer is (-3,-3)

Step-by-step explanation:

Solve for the first variable in one of the equations, then substitute the result into the other equation.

24 hours takes all five machines to fill the same production order.

Given,

Four machines take 30 hours to fill a certain production order.

\(Rate = \frac{Work}{Time}\)

Let, Total work = 1 unit

The rate of 4 machines = \(\frac{1}{30}\)

We can let the rate of 5 machines be n and create the equation:

\(\frac{4}{\frac{1}{30} }=\frac{5}{n}\)

\(120=\frac{5}{n}\)

\(120n = 5\)

\(n=\frac{5}{120}\)

\(n=\frac{1}{24}\)

Time taken by five machines = \(\frac{1}{\frac{1}{24} }\)

Time is taken by five machines = 24 hours

Hence, 24 hours takes all five machines to fill the same production order.

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