There is a one-sample study to test the null hypothesis that m = 0 versus the alternative that m > 0. Assume that s is 20. Suppose that it would be important to be able to detect the alternative m > 4. What sample size is needed to detect this alternative with power of at least 0.80? Use a 5% significance level.

Answer:

XY = 4.75 cm

Step-by-step explanation:

Δ VXY and Δ VWZ are similar so the ratios of corresponding sides are equal, that is

\(\frac{XY}{WZ}\) = \(\frac{VX}{VW}\) , substitute values

\(\frac{XY}{2.5}\) = \(\frac{4.5+5}{5}\) = \(\frac{9.5}{5}\) ( cross- multiply )

5 XY = 23.75 ( divide both sides by 5 )

XY = 4.75 cm

Answer: X <0

Step-by-step explanation: 2(x+3)<x+6

Use the distributive property to multiply 2 by x+3.

2x+6<x+6

Subtract x from both sides.

2x+6−x<6

Combine 2x and −x to get x.

x+6<6

Subtract 6 from both sides.

x<6−6

Subtract 6 from 6 to get 0.

x<0

The solution to the given initial value problem, obtained using Laplace transforms, is y(x) = 0. This means that the function y(x) is identically zero for all values of x.

To find the solution of the initial value problem using Laplace transforms for the equation d²y/dx² + 9y = 9sin(t)u(t - 3), where y(0) = y'(0) = 0, we can follow these steps:

Take the Laplace transform of the given differential equation.

Applying the Laplace transform to the equation d²y/dx² + 9y = 9sin(t)u(t - 3), we get:

s²Y(s) - sy(0) - y'(0) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Since y(0) = 0 and y'(0) = 0, the Laplace transform simplifies to:

s²Y(s) + 9Y(s) = 9 * (1/s² + 1/(s² + 1))

Solve for Y(s).

Combining like terms, we have:

Y(s) * (s² + 9) = 9 * (1/s² + 1/(s² + 1))

Multiply through by (s² + 1)(s² + 9) to get rid of the denominators:

Y(s) * (s⁴ + 10s² + 9) = 9 * (s² + 1)

Simplifying further, we have:

Y(s) * (s⁴ + 10s² + 9) = 9s² + 9

Divide both sides by (s⁴ + 10s² + 9) to solve for Y(s):

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9)

Partial fraction decomposition.

To proceed, we need to decompose the right side of the equation using partial fraction decomposition:

Y(s) = (9s² + 9)/(s⁴ + 10s² + 9) = A/(s² + 1) + B/(s² + 9)

Multiplying through by (s⁴ + 10s² + 9), we have:

9s² + 9 = A(s² + 9) + B(s² + 1)

Equating the coefficients of like powers of s, we get:

9 = 9A + B

0 = A + B

Solving these equations, we find:

A = 0

B = 0

Therefore, the decomposition becomes:

Y(s) = 0/(s² + 1) + 0/(s² + 9)

Inverse Laplace transform.

Taking the inverse Laplace transform of the decomposed terms, we find:

L^(-1){Y(s)} = L^(-1){0/(s² + 1)} + L^(-1){0/(s² + 9)}

The inverse Laplace transform of 0/(s² + 1) is 0.

The inverse Laplace transform of 0/(s² + 9) is 0.

Combining these terms, we have:

Y(x) = 0 + 0

Therefore, the solution to the initial value problem is:

y(x) = 0

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The values of x and y are 6 and 4, respectively. So, x = 6 and y = 4.

Given equations:

2x + 3y = 24, and

5x - 2y = 22

To find the values of x and y,

we have to solve the equations by using the elimination method.

Here's how:

Step 1:

Multiply equation (1) by 2 and equation (2) by 3.

4x + 6y = 48  (Equation 1 multiplied by 2)

15x - 6y = 66 (Equation 2 multiplied by 3)

Step 2: Add both equations to eliminate y,

4x + 6y = 48

15x - 6y = 66 ___________________________

19x = 114

Step 3: Divide both sides by 19.

x = 6

Step 4: Substitute the value of x in any of the given equations.

2x + 3y = 24

Putting the value of x, we get:

2 (6) + 3y = 24

Simplifying, we get:

12 + 3y = 24

Step 5: Solve for y,

3y = 24 - 12

y = 4

Thus, the values of x and y are 6 and 4, respectively. So, x = 6 and y = 4.

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Answer:

36

Step-by-step explanation:

24+12=36

Answer:

B. √16 × √6

C. √96

Step-by-step explanation:

4√6

4 can be written as a square root.

4 = √16

√16 × √6

The square roots are multiplied, they can be written under one whole square root.

√(16 × 6)

√96

P(|K| ≥ 1) = 1 - P(-1 ≤ K ≤ 1)

To find this probability, we can look up the values in a standard normal distribution table or use a calculator that provides the CDF of the standard normal distribution. The result will give us the probability that the quadratic equation has real solutions.

Using the quadratic formula you provided, x = (-2K ± sqrt((2K)^2 - 4(1)(1))) / (2(1)) simplifies to:

x = -K ± sqrt(K^2 - 1)

For the quadratic equation to have real solutions, the discriminant (K^2 - 1) must be greater than or equal to zero, since the square root of a negative number would result in imaginary solutions.

So, we need to find the range of values for K that satisfy the inequality K^2 - 1 ≥ 0.

Let's solve this inequality:

K^2 - 1 ≥ 0

Adding 1 to both sides:

K^2 ≥ 1

Taking the square root of both sides (note that K^2 is always positive):

|K| ≥ 1

This means that the absolute value of K must be greater than or equal to 1 for the quadratic equation to have real solutions.

Now, since K is Gaussian distributed with a mean of μ = 0 and variance of σ^2 = 1, we can calculate the probability using the standard normal distribution.

Using the properties of the standard normal distribution, the probability that K falls within the range |K| ≥ 1 is equal to 1 minus the cumulative distribution function (CDF) at 1 and -1:

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For the function F(x, y) = x³ + y³ - 3x² - 6y² - 9x ,  the local maximum value is 5 and the local minimum value is -3. The graph is discontinuous, so we cannot locate the saddle points.

In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function.

We have the following function -

F(x, y) = x³ + y³ - 3x² - 6y² - 9x

We will plot the 3 dimensional graph of this function. From the model it can be seen that, the local maximum value is 5 and the local minimum value is -3. Since the graph is discontinuous, we cannot locate the saddle points.

Therefore, for the function F(x, y) = x³ + y³ - 3x² - 6y² - 9x ,  the local maximum value is 5 and the local minimum value is -3. The graph is discontinuous, so we cannot locate the saddle points.

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The approximate increase in area is 1915.86 mm^2.

The area of a circle is given by the formula A = πr^2, where r is the radius.

Initially, the radius is 40 mm, so the area of the colony is:

A1 = π(40)^2 = 1600π mm^2

After the radius increases to 47 mm, the new area of the colony is:

A2 = π(47)^2 = 2209π mm^2

The increase in area is then:

ΔA = A2 - A1 = (2209π - 1600π) mm^2

ΔA = 609π mm^2

Approximating π as 3.14, we get:

ΔA ≈ 1915.86 mm^2

Therefore, the approximate increase in area is 1915.86 mm^2.

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Answer:

B

Step-by-step explanation:

Great circles are the largest possible circles that can be drawn around a sphere and are the lines called in Riemann's spherical geometry.

Answer:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

The radioactive decay of a substance is given by the following formula:

Since the element has a half life of 12 minutes, this means that after this time the mass of the element will be half of it was originally, therefore:

Therefore the mass of the element is given by:

If the initial mass is 760 g and the final mass is 15 g, we have:

The time it'd take for the element to have 15 g of mass is approximately 68 min.

Step-by-step explanation:

Element X take 32.6 minutes to decay to 87 grams.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Element X decays radioactively with a half life of 15 minutes.

And, there are 400 grams of Element X.

Now, By the given information, we can formulate;

⇒ \(y = x (0.5)^{t/h}\)

Substitute all the values we get;

⇒ 400 = 87 × \((0.5)^{t/15}\)

⇒ 400 / 87 =  \((0.5)^{t/15}\)

⇒ 4.6 =  \((0.5)^{t/15}\)

Take log both side,

⇒ ln 4.6 = t/15 (ln 0.5)

⇒ 1.52 = t/15 x 0.7

⇒ t = 32.6 minutes

Thus, Element X take 32.6 minutes to decay to 87 grams.

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The probability of Bob and Joan's fourth child having sickle cell disease, given that their first three children are healthy, is 6.25%.

When Bob and Joan have children, each child has a 25% chance of inheriting two copies of the sickle cell gene and thus developing the disease, a 50% chance of inheriting one copy of the sickle cell gene and being a carrier like their parents, and a 25% chance of inheriting two copies of the normal gene and not carrying the disease.

To understand this probability calculation mathematically, we can use the laws of probability. We can define the probability of the fourth child inheriting the sickle cell gene as P(s), and the probability of the fourth child inheriting the normal gene as P(n).

Since Bob and Joan are each heterozygous carriers for the sickle cell gene, we know that P(s) = 0.25 (25%), and P(n) = 0.75 (75%). We can use the multiplication rule of probability to calculate the probability of their fourth child inheriting two copies of the sickle cell gene, which is:

P(sickle cell disease) = P(s) x P(s) = 0.25 x 0.25 = 0.0625 or 6.25%

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Complete Question:

Bob and Joan know from a blood test that they are each heterozygous (carriers) for the autosomal recessive gene that causes sickle cell disease. If their first three children are healthy, what is the probability that their fourth child will have the disease?

In real life, permutations and combinations can exist in the following examples -

The formula to find the permutation is -

P(n, r) = n!/(n - r)!

Given is to investigate the real life problems on -

Combinations and permutations

Permutations and combinations in real life exist in a lot of different ways such as the arrangement of peoples in a particular order, selection of food from the menu etc.

Therefore, in real life, permutations and combinations can exist in the following examples -

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{QUESTION IN ENGLISH -

Combinations and permutations in daily life?

Answer:

<DCE = 72°

Step-by-step explanation:

If lie AB is perpendicular to each other, then the sum of angle DCE and ECB will be equivalent to 90°.

Given

<DCE = 7x+2

<ECB = x+8

Hence

<DCE + < ECB = 90

7x+2 + x+8 = 90

7x+x+2+8 = 90

8x+10 = 90

8x = 90-10

8x = 80

x = 80/8

x = 10°

Since <DCE = 7x+2, substitute x= 10 into the expression

<DCE = 7(10)+2

<DCE = 70+2

<DCE = 72°

Answer: -24x^2+28x

Step-by-step explanation: -4x*6x-(-4x)*7 to -24x^2+28x

Answer:

x=14

Step-by-step explanation:

2 times x = 2x and 2 time 9 is 18 so the equation is 2x-18=10. then you add 18 to both sides and get 2x=28 then simplify to x=14

Answer:

x=14

Step-by-step explanation:

2(x-9)=10

Step one - Simplify both sides

(2)(x)+(2)(-9)=10 (distribute)

2x+-18=10

2x-18=10

Step two - Add 18 to both sides

2x-18+18=10+18

2x=28

Step three - Divide both sides by 2

2x÷2 = 28÷2

x= 14

Answer:

x=14

The value of x is approximately 369.186.

To solve the equation -0.17 = (x - 390) / 390 + 7.2 / 390 for x, we can simplify the equation and isolate x.

Given:

-0.17 = (x - 390) / 390 + 7.2 / 390

First, let's simplify the right side of the equation by finding a common denominator:

-0.17 = (x - 390 + 7.2) / 390

Combine like terms:

-0.17 = (x - 382.8) / 390

Multiply both sides of the equation by 390 to eliminate the fraction:

-0.17 * 390 = x - 382.8

-66.3 = x - 382.8

Add 382.8 to both sides of the equation:

-66.3 + 382.8 = x

316.5 = x

Therefore, the value of x is approximately 316.5 (rounded to three decimal places).

Note: There seems to be an error in the given equation. The correct equation should be -0.17 = (x - 390) / 390 + 7.2 / 390, not -0.17 = (x - 390) / 390 + 7.2 / 390.

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Answer:

x=-1/9; -1/9; (-1/9,0)

(each one is a different way to write the answer)a

Step-by-step explanation:

Zeros of a function are when the y-value of a point on a graph is equal to 0. Plugging in 0 for y in this equation of the function we get 0=-9x-1, which we can solve by adding 9x to both sides of the equation to get 0+9x=-9x+9x-1, or 9x=-1, and divide both sides by 9 to get x=-1/9

Answer:xy

Step-by-step explanation:

Step-by-step explanation:

We can use trigonometry to solve this problem. Let's draw a diagram:

```

A - observer (1.5 m above ground)

B - base of the clock tower

C - top of the clock tower

D - intersection of AB and the horizontal ground

E - point on the ground directly below C

C

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| x

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

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|

|

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B

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A

```

We want to find the height of the clock tower, which is CE. We have the angle of elevation ACD, which is 19 degrees, and the distance AB, which is 100 m. We can use tangent to find CE:

tan(ACD) = CE / AB

tan(19) = CE / 100

CE = 100 * tan(19)

CE ≈ 34.5 m (rounded to 1 decimal place)

Therefore, the height of the clock tower is approximately 34.5 m.

Answer:

1. 1/20

2. 0.05

3. 5%

Step-by-step explanation:

Hope it helps :)

Have a good day/night

Brainliest pls?

Answer:

its A correct me if im wrong in the comments

The volume of the cereal box(rectangular prism) is 182 cubic in.

What is rectangular prism?

A rectangular prism is a three-dimensional shape that has six faces (two top and bottom and four side faces). All sides of the prism are rectangular in shape. So there are three pairs of identical faces. It is also called cuboid.

Given that the dimensions of the cereal box(rectangular prism) are 2in, 7in, 13in

volume=l× b× h( l= length, b=breadth ,h= height)

             = 2×7×13

             =182

hence the volume is 182 cubic in.

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Answer:

15.7 ft

Step-by-step explanation:

circumference = pi * diameter

c = 3.14 * 5 ft

c = 15.7 ft

Answer: 15.7 ft

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Answer:

The speed of the boat is approximately 0.704 m/s

Step-by-step explanation:

The time it takes the man in the boat to change the angle of elevation from 60° to 45°, t = 2 minutes = 120 seconds

The height of the light house = 200 m

Given that the angle of elevation is reducing, the direction of the man is away from the lighthouse

The initial distance of the man in the boat from the lighthouse = 200 m/(tan(60°)) = (200/√3) m

The final distance of the man in the boat from the lighthouse = 200 m/(tan(45°)) = 200 m

The distance traveled in 2 minutes, d = 200 m - (200/√3) m ≈ 84.53 m

The speed of the boat, v = d/t

∴ v = 84.53 m/(2 min × 60 s/min) ≈ 0.704 m/s

The speed of the boat, v ≈ 0.704 m/s.