Find the probability that a randomly
selected point within the circle falls
in the red shaded area (square).
r = 4 cm
4 √2 cm
[? ]%
round to the nearest tenth of a percent.

Answer:

2 yards 5 inches will be equivalent to 77 inches

Step-by-step explanation:

Given length -

2 yards 5 inches

One yard has 36 inches

Two yards will have 2*36 = 72 inches

Thus, 2 yards 5 inches will sum up to 72 inches + 5 inches = 77 inches

Hence,  2 yards 5 inches will be equivalent to 77 inches

Answer:

3 yards = 9 feet

77 inches = 2 yards 5 inches

48 inches = 1 yard 1 foot

32 inches = 2 feet 8 inches

I hope this helped!! <3

Thus, we get the final values here as:

a. For Kyd, we are given here the gain and loss probabilities as:

P(X=5) = 3/13 as all the 3 face cards are equally likely as any of the 13 ranks of the cards.

For the losing outcome, we have here:

P(X=-2) = 10/13 as we lose 2 in all the other ranks here.

Therefore the expected value here is computed as:

Summation of X = 15/13 - 20/13 = -5/13 = -0.38

Therefore, -0.38 is the required expected value here.

Every 3 of the 13 ranks are face ranks and thus, the probability for getting a face card is given as:

b) As this is a zero sum game, the expected value for the other person would be the negative of the expected value for  Kyd here. This is computed here as 0.38.

Therefore, 0.38 is the expected value here.

c) Clearly North has an advantage here.

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The reported values have a weighted average of 2.35.

Given the following data:

Value     Weight

2.00      75.0%

3.00      15.0%

4.00      10.0%

The weighted average of these figures is calculated as follows:

First, multiply each value by its corresponding weight in decimal form and then add up the products:

2.00 * 0.75 + 3.00 * 0.15 + 4.00 * 0.10 = 1.50 + 0.45 + 0.40 = 2.35.

dividing the outcome by the weighted average:

2.35 ÷ (0.75 + 0.15 + 0.10) = 2.35 ÷ 1.00 = 2.35.

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Answer:

Step-by-step explanation:

Question 1:  Assumption: This is a 30-60-90 triangle.

Remember that the sides of a 30-60-90 triangle are in the ratio 1:√3:2

The side opposite the 90° angle is 16, so the side opposite the 30° angle is 16/2 =  8

x = 8 units.

:::::

Question 2:  Assumption: This is an isosceles triangle.

Draw the altitude to the vertex angle and you get a 30-60-90 triangle.

The side opposite the 90° angle has length 22, so the side opposite the 30° angle has length 11.

x/2 = 11

x = 22 units

:::::

Question 3:  Assumption: This is a 45-45-90 triangle.

The sides of a 45-45-90 triangle are in the ratio 1:1:√2

The sides opposite the 45° angles are 19 and x.

x = 19

:::::

Question 4:  Assumption: This is an isosceles triangle.

x = 13 units

:::::

Question 5:  Assumption: This is a right triangle.

sin(54°) = x/45

x = 45sin(54°) ≅ 36.4 units

:::::

Question 6:  Assumption: This is a right triangle.

sin(35°) = z/23

z = 23sin(35°) ≅ 13.2 units

They need to put 14.4 grams of onion powder in each bottle.

Given,

The quantity of onion powder in a seasoning blend = 4%

We have to find the quantity of pure onion powder should they include in a 72g bottle to make the final blend have 20% onion powder;

How much is a percentage?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%."

Here,

Let x be the seasoning blend.

Now, 4% of 72=20% of x

⇒ 0.04×72=0.2×x

⇒ 0.2x=2.88

⇒ x=2.88/0.2

⇒ x=14.4 g

Therefore, a container should contain 14.4 grams of onion powder.

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Answer:

(a) \(x\³ - 6x - 6\)

(b) Proved

Step-by-step explanation:

Given

\(r = $\sqrt[3]{2} + \sqrt[3]{4}$\) --- the root

Solving (a): The polynomial

A cubic function is represented as:

\(f = (a + b)^3\)

Expand

\(f = a^3 + 3a^2b + 3ab^2 + b^3\)

Rewrite as:

\(f = a^3 + 3ab(a + b) + b^3\)

The root is represented as:

\(r=a+b\)

By comparison:

\(a = $\sqrt[3]{2}\)

\(b = \sqrt[3]{4}$\)

So, we have:

\(f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3\)

Expand

\(f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

\(f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4\)

Evaluate like terms

\(f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)\)

Recall that: \(r = $\sqrt[3]{2} + \sqrt[3]{4}$\)

So, we have:

\(f = 6 + 6r\)

Equate to 0

\(f - 6 - 6r = 0\)

Rewrite as:

\(f - 6r - 6 = 0\)

Express as a cubic function

\(x^3 - 6x - 6 = 0\)

Hence, the cubic polynomial is:

\(f(x) = x^3 - 6x - 6\)

Solving (b): Prove that r is irrational

The constant term of \(x^3 - 6x - 6 = 0\) is -6

The divisors of -6 are: -6,-3,-2,-1,1,2,3,6

Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values

\(f(-6) = (-6)^3 - 6*-6 - 6 = -186\)

\(f(-3) = (-3)^3 - 6*-3 - 6 = -15\)

\(f(-2) = (-2)^3 - 6*-2 - 6 = -2\)

\(f(-1) = (-1)^3 - 6*-1 - 6 = -1\)

\(f(1) = (1)^3 - 6*1 - 6 = -11\)

\(f(2) = (2)^3 - 6*2 - 6 = -10\)

\(f(3) = (3)^3 - 6*3 - 6 = 3\)

\(f(6) = (6)^3 - 6*6 - 6 = 174\)

For r to be rational;

The divisors of -6 must divide f(x) without remainder

i.e. Any of the above values  must equal 0

Since none equals 0, then r is irrational

According to Chebyshev's theorem, at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.

Chebyshev's theorem states that for any set of data, regardless of its distribution, a certain percentage of the data lies within a certain number of standard deviations from the mean. Specifically, Chebyshev's theorem states that for any data set, at least 1 – 1/k² of the data values will lie within k standard deviations of the mean, where k is any number greater than 1. If k=2, at least 75% of the data values lie within 2 standard deviations of the mean. If k=3, at least 89% of the data values lie within 3 standard deviations of the mean.

Therefore, for a data set with a mean of 63.6 minutes and a standard deviation of 2.5 minutes, we can use Chebyshev's theorem to determine that at least 75% of the employees will have commuting times that fall within 2 standard deviations of the mean, or between 58.6 minutes and 68.6 minutes.

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If an opponent stands less than 10 yards from the ball when a free kick is awarded, and the ball subsequently strikes that opponent, the referee should award an indirect free kick to the opposing team.

This is because the opponent is in violation of the laws of the game, specifically Law 13 - Free kicks which states that at a direct free kick, a player must be at least 10 yards (9.15m) from the ball until it is in play.

The indirect free kick should be taken from the spot where the opponent was when they were struck by the ball.

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Answer:

Given, the annual profit equation is f(n) = 65n - 0.04n².

When the number of pizzas sold, n = 300, the annual profit will be:

f(300) = 65(300) - 0.04(300)²

= 19500 - 0.04(90000)

= 19500 - 3600

= $15,900

Therefore, the annual profit if the pizza maker sells 300 pizzas is $15,900. Answer: D.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve the system of equations algebraically, we need to substitute the second equation into the first equation and solve for x:

y = 4x – 5 (equation 1)

y = -3 (equation 2)

Substitute equation 2 into equation 1:

-3 = 4x – 5

Add 5 to both sides:

2 = 4x

Divide both sides by 4:

x = 1/2

Now, we can substitute this value of x back into either equation to find y:

y = 4(1/2) – 5 = -3

Therefore, the solution to the system of equations is (1/2, -3).

To verify this solution using the graph, we can plot the two equations on the same set of axes:

y = 4x – 5 (red line)

y = -3 (blue line)

The two lines intersect at the point (1/2, -3), confirming our solution.

Therefore, the answer is (B) (1/2, -3).

The label covers 11,936 over 7 square centimeters of the wheel.

The cylindrical-shaped wheel of cheese has a radius of 22 centimeters and a height of 16 centimeters. The label covers the entire wheel except the circular top and bottom. Therefore, the area covered by the label is the lateral surface area of the cylinder.

The lateral surface area of a cylinder can be calculated using the formula 2πrh, where r is the radius of the base, h is the height, and π is approximately equal to 22/7.

Substituting the given values, we get:

Lateral surface area = 2 × (22/7) × 22 × 16

Lateral surface area = (44/7) × 22 × 16

Lateral surface area = 1,936 square centimeters (approx.)

Therefore, the label covers approximately 1,936/7 square centimeters of the wheel. The closest option is (C) 1,936 over 7 square centimeters.

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Using the secant method, the positive root of the equation x³ - 15x² + 62x - 48 is approximately 1.

To find the positive roots of the equation x³ - 15x² + 62x - 48 using the secant method, we need to start with two initial guesses, x₀ and x₁, such that f(x₀) and f(x₁) have opposite signs.

Let's begin the iterations:

1. Choose an initial guess, x₀ = 0, and calculate f(x₀):

  f(x₀) = (0)³ - 15(0)² + 62(0) - 48 = -48

2. Choose a second initial guess, x₁ = 1, and calculate f(x₁):

  f(x₁) = (1)³ - 15(1)² + 62(1) - 48 = 0

3. Calculate the next approximation, x₂, using the formula:

  x₂ = x₁ - f(x₁) * ((x₁ - x₀) / (f(x₁) - f(x₀)))

Substituting the values:

  x₂ = 1 - 0 * ((1 - 0) / (0 - (-48)))

  x₂ = 1

4. Update the values of x₀ and x₁:

  x₀ = x₁

  x₁ = x₂

5. Repeat steps 2-4 until convergence is achieved.

  - Calculate f(x₁):

    f(x₁) = (1)³ - 15(1)² + 62(1) - 48 = 0

Since f(x₁) = 0, we have found a root.

6. Round the root to the nearest whole number:

  x₁ ≈ 1

Therefore, the positive root of the equation x³ - 15x² + 62x - 48 is approximately 1.

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Complete the square to write

ax² + bx + c = a (x + b/(2a))² - (b² - 4ac)/(4a)

The quadratic has a double root at x = -b/(2a) if the constant term (b² - 4ac)/(4a) vanishes, which happens if b² - 4ac = 0.

Let A, B, and C be random variables representing the value of the first, second, and third roll of the die. They are independent and identically distributed with PMF

Pr [X = x] = 1/6

if x ∈ {1, 2, 3, 4, 5, 6}, and 0 otherwise.

We want to find

Pr [B² - 4AC = 0]

Note that

B² - 4AC = 0   ⇒   B² = 4AC   ⇒ (B/2)² = AC

which tells us that B must be even, and also that AC is a perfect square. Then there are 5 possible outcomes that satisfy the conditions:

• If B = 2, then AC = 1   ⇒   A = C = 1

• If B = 4, then AC = 4   ⇒   A = 1, C = 4 or A = C = 2 or A = 4, C = 1

• If B = 6, then AC = 9   ⇒   A = C = 3

and there are 6³ = 216 total possible outcomes in the sample space. So,

Pr [B² - 4AC = 0] = 5/216

Answer:

14.4 i hope it helped you

Answer:

look at image attached, hope this helps :)

Step-by-step explanation:

30 im sure that ia the corect answer

Answer:

30

Step-by-step explanation:

i know this for a fact lmal

Answer:

the answer is -34

Step-by-step explanation:

the answer is n=34

Given the equivalent ratios:

4:12 and 11:x

To get an equivalent ratio, the denominator and numerator of one ratio is multiplied or divided by the same non zero number.

To find the value of x, we have:

The value of x = 33

ANSWER:

33

in our bstnode class the variables left and right, that represent the links of a node, are of class comparable is FALSE.

The variables left and right in the bstnode class represent the links to the left and right subtrees of a node in a binary search tree. These variables are typically of the same type as the bstnode class itself, since they also represent nodes in the tree. They do not need to be of the class Comparable, as that interface is used for objects that can be compared to each other for the purposes of sorting. The bstnode class may contain an instance variable of a comparable type if the nodes are being sorted based on their values, but this is separate from the left and right variables. Conclusion: The variables left and right in the bstnode class are not of class Comparable.

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The midpoint of a segment in the complex plane with endpoints at 6 - 2i and -4 + 6i is 1 + 2i.

To find the midpoint of a segment in the complex plane, we average the coordinates of the endpoints. The first endpoint is 6 - 2i, and the second endpoint is -4 + 6i.

Adding the real parts and the imaginary parts separately, we get (6 + (-4))/2 = 1 for the real part and ((-2) + 6)/2 = 2 for the imaginary part.

Therefore, the midpoint is given by 1 + 2i. This means that the midpoint of the segment lies on the complex plane at the coordinates (1, 2).

It represents the point equidistant from both endpoints, dividing the segment into two equal parts.

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The ordered pairs that is a solution to the system is (1, 2)

(x,y), Is it a solution

(0,-8)  No

(-2,-5) No

(-9,-6) No

(2, 1) No

From the question, we have the following parameters that can be used in our computation:

-4x + 5y = 6

7x - 3y = 1

Make the coefficients of x in the equations equivalent

So, we have

-28x + 35y = 42

28x - 12y = 4

Add the equations

23y = 46

So, we have

y = 2

Next, we have

-4x + 5y = 6

-4x + 5(2) = 6

-4x + 10 = 6

-4x = -4

x = 1

So, the solution is (1, 2)

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Question

For each ordered pair, determine whether it is a solution to the system of equations.

-4x + 5y = 6

7x - 3y = 1

(x,y), Is it a solution? [,Yes ],[No,]

(0,-8)  ___   ____

(-2,-5)  ___   ____

(-9,-6)  ___   ____

(2,1)  ___   ____

Given that none of the provided options directly address the power of the test described, we can conclude that the answer is:

c) None of these.

The power of a test refers to the probability of correctly rejecting the null hypothesis when it is false. It measures the ability of a statistical test to detect a true effect or relationship.

The description of the power of the test cannot be determined based on the given options.

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Answer:

Approximately 67.348 litres can be put in six hemispherical bowl with a diameter of 35 centimetres.

Step-by-step explanation:

The volume of a hemisphere (\(V\)), measured in cubic centimetres, is obtained from this formula:

\(V = \frac{2\pi}{3}\cdot R^{3}\)

Where \(R\) is the radius of the hemisphere, measured in centimetres.

We know that radius is the half of the diameter (\(D\)), measured in centimetres, then:

\(R = 0.5\cdot D\)

(\(D = 35\,cm\))

\(R = 0.5\cdot (35\,cm)\)

\(R = 17.5\,cm\)

Now, we get the volume of each hemispherical bowl:

\(V = \frac{2\pi}{3} \cdot (17.5\,cm)^{3}\)

\(V \approx 11224.649\,cm^{3}\)

The total volume of six hemispherical bowl is:

\(V_{T} = 6\cdot V\)

\(V_{T}= 6\cdot (11224.649\,cm^{3})\)

\(V_{T} = 67347.894\,cm^{3}\)

From Physics we know that 1 litre equals 1000 cubic centimetres. Then:

\(V_{T} = 67.348\,L\)

Approximately 67.348 litres can be put in six hemispherical bowl with a diameter of 35 centimetres.

Using Leibniz's notation for the chain rule  \(\frac{dy}{dx}\)= 540x⁸.

To find ​ \(\frac{dy}{dx}\) using Leibniz's notation for the chain rule, we have:

y=f(u)=5u⁴+2

u=g(x)=3x³u

Let's start by finding \(\frac{dy}{du}\) and \(\frac{du}{dx}\) individually:

1. \(\frac{dy}{du}\):

To find \(\frac{dy}{du}\)​, we differentiate y with respect to u while treating uas the independent variable:

\(\frac{du}{dy}\) ​=d/du​(5u⁴+2) = 20u³

2. \(\frac{du}{dx}\) :

To find \(\frac{du}{dx}\)​ , we differentiate u with respect to x:

\(\frac{du}{dx}\)​​​ = d/dx​(3x³)=9x²

Now, we can apply the chain rule by multiplying  \(\frac{dy}{du}\) and  \(\frac{du}{dx}\) to find  \(\frac{dy}{dx}\)

\(\frac{dy}{dx}\) = \(\frac{dy}{du}\) * \(\frac{du}{dx}\) = (20 u³)* (9x²)

Substituting u=3x³:

\(\frac{dy}{dx}\) = (20(3x³)³)⋅(9x²)

Simplifying:

\(\frac{dy}{dx}\) = 540 x⁸

Therefore, \(\frac{dy}{dx}\)=540x⁸ using Leibniz's notation for the chain rule.

The question should be:

QUESTION 1 · 1 POINT Given y = f(u) and u = g(x), find dy/dx by using Leibniz's notation for the chain rule:

dy/dx = (dy/du)* (du/dx) , y=5u⁴ + 2 , u= 3x³

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The given system of differential equations is:

x'(t) = -95x + 53y - 2xy

y'(t) = -185x - 203y - xy

To solve this system, we can use various methods such as substitution or matrix methods. Let's solve it using the matrix method.

We can rewrite the system of differential equations in matrix form as:

X' = AX

where X = [x y]', X' = [x'(t) y'(t)]', and A is the coefficient matrix:

A = [[-95 53], [-185 -203]]

To find the solutions, we need to find the eigenvalues and eigenvectors of matrix A. The eigenvalues are the roots of the characteristic equation det(A - λI) = 0, where I is the identity matrix. Solving this equation gives us the eigenvalues λ1 = -100 and λ2 = -198.

Next, we find the eigenvectors associated with each eigenvalue. For λ1 = -100, the corresponding eigenvector is [2 1]'. For λ2 = -198, the corresponding eigenvector is [-1 1]'.

Therefore, the general solution of the system of differential equations is:

X(t) = c1e^(-100t)[2 1]' + c2e^(-198t)[-1 1]'

where c1 and c2 are constants determined by initial conditions.

In summary, the solution to the system of differential equations is given by X(t) = c1e^(-100t)[2 1]' + c2e^(-198t)[-1 1]', where c1 and c2 are constants determined by the initial conditions.

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Answer:

16

Step-by-step explanation:

4y = 2.6

y = 0.65

20y + 3

= 20 × 0.65 + 3

= 13 + 3

= 16

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Answer:

1.) .423

2.).602

3.) .675

4.) .375

5.) .259

6.)8.144

7.).839

8.).017

9.) .966

10.).454

11.).978

12.) 57.28996

13.).5299

14.).809

15.).9004

16.).819

17.).788

18.) 1.235

Basically just change your calculator to degree by pressing the mode button then scroll to degree and pressing it. Then type the questions in with the cos tan and. Sin buttons and that’s the answer.

The probability of spinning a 5 or a 4 is 0.2 or 20%.

To find the probability of spinning a 5 or a 4, you'll need to follow these steps:

1. Determine the total number of possible outcomes when spinning. For example, if the spinner has 10 equally spaced sections numbered 1 through 10, there are 10 possible outcomes.

2. Identify the number of successful outcomes, which are the ones with a 5 or a 4. In this case, there are 2 successful outcomes (spinning a 4 or a 5).

3. Calculate the probability by dividing the number of successful outcomes by the total number of possible outcomes. In this example, the probability would be:

Probability = (Number of successful outcomes) / (Total number of possible outcomes) = 2/10

4. To express this probability as a decimal, divide the numerator (2) by the denominator (10). The result is:

Decimal probability = 2 ÷ 10 = 0.2

5. Apply the appropriate rounding rule, if necessary. In this case, the decimal probability (0.2) is already in its simplest form, so no rounding is needed.

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