The letters of the word "MOBILE" are arranged at random. Find
the probability that the word so formed i) starts with M ii) starts
with M and ends with E. ​

Answer:

124.6

Explanation:

Let the number be x.

Thus, we have that: 13% of x =16.2

Next, solve for x by cross-multiplying.

Divide both sides by 13.

Thus, 16.2 is 13% of 124.6 (rounded to the nearest tenth).

Answer:

Step-by-step explanation:

We all know that the volume of a cube can be shown as:

V=s^3

now the volume of nine cubes is:

V=9*s^3

now, we know that the edge length is 0.5 ft, thus, lets find the volume of the figure:

V=9*s^3

V=9*0.5^3

V=9*0.125

V=1.125

Hence, the answer is 1.125 ft^3

The volume of the given figure is 1.125 cubic feet.

The volume of a cube is defined as the total number of cubic units occupied by the cube completely. A cube is a three-dimensional solid figure, having 6 square faces. Volume is nothing but the total space occupied by an object.

Given that, a figure is built out of 9 cubes as shown the edge length of each cube is 1/2 foot.

Volume of one cube = (1/2)³

= 1/8

= 0.125 cubic feet

Volume of 9 cubes = 9×0.125

= 1.125 cubic feet

Therefore, the volume of the given figure is 1.125 cubic feet.

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Answer:

sin (330)

csc (60)

cos (390)

Step-by-step explanation:

Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions

Answer:

2³ +2³= 12.

13¹ + 2² = 17

Step-by-step explanation:

2 x 3 is 6 and 6 + 6 is twelve and 13 x 1 is 13 and 2 x 2 is 4 making it 17 hope this helps

A differential equation is a mathematical equation that relates a function to its derivatives. It involves the unknown function and one or more of its derivative. The solution to the differential equation -

xy' − 2y = x^2, x > 0

is y = (1/4)x^3 + C/x.

To solve the differential equation, we will use the method of integrating factors.

The differential equation is: xy' - 2y = x^2

We can rearrange it in the standard form: y' - (2/x)y = x

The integrating factor (IF) is defined as e^∫(2/x) dx. Integrating 2/x with respect to x gives us 2ln|x|.

Therefore, the integrating factor is IF = e^(2ln|x|) = e^(ln(x^2)) = x^2.

Now, multiply the entire equation by the integrating factor x^2:

x^2(y' - (2/x)y) = x^2(x)

x^2y' - 2xy = x^3

Next, we recognize that the left-hand side is the derivative of (xy) with respect to x. Applying this, we get:

d/dx(xy) = x^3

Integrating both sides with respect to x:

∫d(xy) = ∫x^3 dx

xy = (1/4)x^4 + C

Finally, divide both sides by x:

y = (1/4)x^3 + C/x

where C is the constant of integration.

So, the solution to the given differential equation is y = (1/4)x^3 + C/x.

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Answer:

B

Step-by-step explanation:

11x - 6x + 20

combine like terms:

5x + 20

Answer:

Explanation:

Given a quadratic function of the form:

In order to solve for x, we use the quadratic formula:

Comparing this with the given application:

From the given options, the equation that can be solved with the given formula is:

This is because it simplifies to:

The correct option is A.

Answer:

y = \(\frac{6-3x}{2}\)

Step-by-step explanation:

Given

3x + 2y = 6 ( subtract 3x from both sides )

2y = 6 - 3x ( divide both sides by 2 )

y = \(\frac{6-3x}{2}\)

Answer:

No solution

Step-by-step explanation:

1. Combine like terms: -14x -2 = -14x -4

2. Add 2 on both sides to isolate x: -14x = -14x -2

3. Add 14x on both sides: 0 = -2

There is no solution because 0 does not equal to -2.

Answer:

.27 or 27/100

Step-by-step explanation:

each tenth is equal to 10 one hundredths

Answer:

(0,-5/3)  ( this is the best i could probably do sorry gurl)

Answer:

i think it is the control group sorry if i am wrong

Step-by-step explanation:

1. The minimum number of chickens you should purchase to be 95% confident you will have enough food for a night is 44 chickens

2. The probability of running out of food by the end of the night is approximately P(X > 40) ≈ 0.000000000007

To be 95% confident that you will have enough food for a night, you need to calculate the 95% confidence interval for the number of customers that will arrive.

The 95% confidence interval for the number of customers that will arrive is given by

CI = x ± zα/2 * σ/√n

where

x is the sample mean,

zα/2 is the critical value of the standard normal distribution for the desired confidence level (z0.025 = 1.96 for 95% confidence),

σ is the standard deviation of the Poisson distribution (σ = sqrt(λ) = sqrt(40) ≈ 6.325), and

n is the sample size.

Substitute the values

CI = 40 ± 1.96 * 6.325/√40 ≈ 40 ± 3.95

Thus, the minimum number of chickens you should purchase to be 95% confident you will have enough food for a night is 44 chickens.

If you have 10 chickens, the number of customers you can serve is limited to 40 (since each customer requires 4 chickens).

Therefore, the probability of running out of food by the end of the night is given by

P(X > 40) = 1 - P(X ≤ 40)

where X is the number of customers that arrive.

Using the Poisson distribution, we can calculate:

\(P(X \leq 40) = e^-\lambda* \sum(\lambda^k / k!)\)

for k = 0, 1, 2, ..., 40.

P(X ≤ 40) = \(e^-40\) * Σ(\(40^k\) / k!) ≈ 0.999999999993

Therefore, the probability of running out of food by the end of the night is approximately P(X > 40) ≈ 0.000000000007

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Question is incomplete, find the complete question below

Question 2 You are operating a Fried Chicken restaurant named "Chapman's Second Best Chicken and Waffles" In a given night you are open to customers from 5pm to 9pm When you are open, customers arrive at an average rate of 5 people every 30 minutes. Individuals are equally likely to arrive at any point in time, and previous arrivals do not impact the probability of additional arrivals. You can handle a maximum of 100 customers a night. On any given night, the amount that guests on average spend at your restaurant is uniformly distributed between $10 and $30 (to be clear, it is the overall average level of spending per guest which is uniformly distributed, not the spending of each individual guest) The distribution of spending per-person is statistically independent of the number of guests that arrive on a given night. 2.1 For every customer you need to purchase 4 chickens. What is the minimum amount of chickens should you purchase to be 95% confident you will have enough food for a night? (note, you can only purchase a whole number of chickens) 2.2 If you have 10 chickens, what is the probability that you will run out of food by the end of the night?

Answer:

32 degrees

Step-by-step explanation:

32 degrees is the below freezing point

Answer: The answer is 131 ft.

Step-by-step explanation:

The gazebo staying in the centre of the circular lawn forms an sector with the two paths that are 75 degrees to each other. The formula for length of an arc of a sector which is the distance between the two paths is \frac{angle}{360} * 2\pi * radius\\radius = \frac{diameter}{2} = \frac{200}{2} = 100 ft\\ angle = 75 degrees.\\

Inserting these we have \frac{75}{360} * 2\pi * 100 = 130.8996 = 131 ft.

~Adrianna

To find the total differential of the function w = e^y * cos(x) * z^2, we can take the partial derivatives with respect to each variable (x, y, and z) and multiply them by the corresponding differentials (dx, dy, and dz).

The total differential can be expressed as:

dw = (∂w/∂x) dx + (∂w/∂y) dy + (∂w/∂z) dz

Let's calculate the partial derivatives:

∂w/∂x =   \(-e^{y} * sin(x) * z^{2}\)

∂w/∂y =  \(e^{y} * cos(x) * z^{2}\)

∂w/∂z =  \(2e^{y} *cos (x)* z\)

Now, let's substitute these partial derivatives into the total differential expression:

\(dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y}* cos(x) * z^{2} ) dy + 2e^{y} *cos (x)*z) dz\)

Therefore, the total differential of the function w = e^y * cos(x) * z^2 is given by:

\(dw = (-e^{y} * sin(x) * z^{2} ) dx + (e^{y} * cos(x) * z^{2} ) dy + ( 2e^{y} * cos(x) * z) dz\)

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Answer:

LCM=1078

Step-by-step explanation:

49=7×7

154=7×11×2

LCM=7×7×11×2

=1078

Answer:

\( \boxed{ \huge{ \bold{ \boxed{ \sf{1078}}}}}\)

Step-by-step explanation:

The L.C.M of any numbers can be obtained by using two methods and they are :

I am going to find the L.C.M of 154 and 49 by using these two methods :

1. Prime factorization method:

\( \sf{154 \: and \: 49}\)

First of all , find the prime factors of each numbers.

\( \sf{154 =2 \times 7 \times 11}\)

\( \sf{49 \: = \: 7 \times 7}\)

Take out common prime factor i.e 7

Thenafter, also take out the other remaining prime factors : 2 , 11 and 7

L.C.M = Common factors × Remaining factors

= 7 × 2 × 11 × 7

= 1078

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

Next method :

2. Division method

\( \sf{154 \: and \: 49}\)

Steps :

⇒ Arranging the given numbers in horizontal position.

⇒Thus, arranged numbers should be divided by a prime number. During this process that prime numbers should divide any two or more given numbers.

⇒Repeat the process till you get prime number as quotient for each number.

⇒The product of all prime factors and last quotients is L.C.M

( see attached picture )

Hope I helped!

Best regards!!

The derivative of y = cosh - 3x) is equal to:

dy/dx = sinh(u) * (-3).substituting u = -3x back into the equation, we get:

dy/dx = sinh(-3x) * (-3).

the derivative of y = cosh(-3x) can be found using the chain rule. let's denote u = -3x. then, y = cosh(u). the derivative of y with respect to x is given by:

dy/dx = dy/du * du/dx.

the derivative of cosh(u) with respect to u is sinh(u), and the derivative of u = -3x with respect to x is -3. none of the provided options (a, b, c, d, e) matches the correct derivative, which is -3sinh(-3x).

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K'(-2, 1) is the coordinate of the image of point K, found by multiplying the original x-coordinate of the point K (2) by -1. To reflect the triangle over the y-axis, the x-coordinate of each point is multiplied by -1.

Triangle is a three-sided geometric shape which has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The coordinate of the image of point K is K’(-2, 1). This means that the x-coordinate of the point is -2 and the y-coordinate of the point is 1. This can be found by multiplying the original x-coordinate of the point K (2) by -1. The y-coordinate of point K remains the same, so the y-coordinate of the image of point K is 1.

Therefore, the coordinate of the image of point K is K’(-2, 1).

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Answer:

It would be B: $39.00!

Step-by-step explanation:

Sry can't explain now.

But the answer is correct.

$39.00

The exponential function for the population is P(t) = 4.0 * (1 + 0.035)^t. The population in 2024 is estimated to be approximately 5.89 million. The estimated doubling time for this region's population is approximately 19.81 years.

To find an exponential function for the population of the region at any time t, we can use the formula for exponential growth:

P(t) = P₀ * (1 + r)^t,

where P(t) represents the population at time t, P₀ is the initial population, r is the growth rate, and t is the time in years.

Given that the initial population in 2006 (t = 0) is 4.0 million and the annual growth rate is 3.5% (or 0.035), the exponential function for the population becomes:

P(t) = 4.0 * (1 + 0.035)^t.

To find the population in 2024, we need to calculate the value of P(t) when t = 18 (since 2024 is 18 years after 2006):

P(18) = 4.0 * (1 + 0.035)^18.

Using a calculator or computer, we can evaluate this expression:

P(18) ≈ 4.0 * (1.035)^18 ≈ 5.89 million.

Therefore, the population in 2024 is estimated to be approximately 5.89 million.

To estimate the doubling time for the region's population, we can use the concept of the doubling time formula for exponential growth:

Doubling Time = ln(2) / ln(1 + r),

where r is the growth rate. In this case, the growth rate is 0.035.

Doubling Time = ln(2) / ln(1 + 0.035).

Using a calculator or computer, we can evaluate this expression:

Doubling Time ≈ ln(2) / ln(1.035) ≈ 19.81 years.

Therefore, the estimated doubling time for this region's population is approximately 19.81 years.

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Answer: Acute- (2,3,3.5) Right-(2.5,6,6.5) obtuse- (7,8,12), (7,9,14)

Step-by-step explanation:

Answer:

#CarryOnLearning

Answer:

13.) A(-6, -2), B(7, -4), C(4, 2), D(-1, 2)

14.) AB = 10

15.) MN = 5√2

Step-by-step explanation:

Formulae:

Distance formula: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\)

Calculations:

\(AB=\sqrt{(10-2)^2+(9-3)^2}\\AB=\sqrt{(8)^2+(6)^2}\\AB=\sqrt{64+36}\\AB=\sqrt{100}\\AB=10\)

\(MN=\sqrt{(5-4)^2+(5-(-2))^2}\\MN=\sqrt{(1)^2+(7)^2}\\MN=\sqrt{1+49}\\MN=\sqrt{50}\\MN=5\sqrt{2}\)

Answer:

im so confused tooo

Step-by-step explanation:

Answer:

none of your options are right

Step-by-step explanation:

three : 3, less than : (-), seven : 7, times : (multiplication symbol), a number : (x)

the answer is : 3 - 7 (x)

                       : 3-7x

Simplifying the equation gives

c = (a * √3) / (2 * sin(A))

To solve for c using the Law of Sines, we need to have at least one side-length and its corresponding angle measurement. In this case, we have the angle 60° and we need to find the length of side c.

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant:

a/sin(A) = b/sin(B) = c/sin(C)

Here, a, b, and c are the side lengths of the triangle, and A, B, and C are the opposite angles, respectively.

Given the angle C = 60°, we can set up the equation as follows:

c/sin(C) = a/sin(A)

Substituting the values into the equation:

c/sin(60°) = a/sin(A)

Since sin(60°) is √3/2, the equation becomes:

c/(√3/2) = a/sin(A)

Simplifying further:

c = (a * √3) / (2 * sin(A))

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The value of the volume of the cone is 3240π

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hope it helps! :)

Answer: Dude its B

Step-by-step explanation: Dont even need to do the math lol

The statement which is true is the slopes are all positive in quadrant I.

Given the differential equation is dy/dx=2x-2y

A differential equation is an equation that contains at least one derivative of an unknown function, either a normal differential equation or a partial differential equation.

Given dy/dx=2x-2y

now slope=2x-2y

Along x-axis, y=0.

So, slope=2x≠0.

Since it depends upon x hence the slope along the y-axis are not horizontal.

Along y-axis, x=0.

So, slope=-2y≠0.

Since the slope along the x-axis are also not horizontal.

In quadrant I

x,y≥0

So, dy/dx≥0

Hence the slopes are all positive in quadrant I.

In quadrant IV,

x≥0,y≤0

so, dy/dx is  not always positive.

This, the slope are not all positive in quadrant IV.

Hence, the slope are all positive in quadrant I for the differential equation dy/dx=2x-2y.

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