Describe the relationship between the area of a circle and its circumference.
The is times the times the circumference.

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

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Scale factor = 5/3, AB = 4√5 cm, and perpendicular distance of scale factor is so A'B' = (20/3)√5 cm.

To find A'B, we want to initially decide the scale element of the growth. We know that Promotion = 12 cm and A'D' = 20 cm, so the scale factor is:

scale factor = A'D'/Promotion = 20 cm/12 cm = 5/3

This implies that each side of A'B'C'D' is 5/3 times the length of the relating side of ABCD.

To find A'B, we can zero in on the level side of the square, which relates to Stomach muscle in ABCD. We know that |DC| = 8 cm, so |BC| = |DC| = 8 cm. Since the scale factor is 5/3, we have:

|A'B'| = (5/3) * |AB|

We can utilize the Pythagorean hypothesis to track down |AB|. Let x be the length of |AB|, then, at that point:

\(x^2 + 8^2 = 12^2\)

Working on this situation, we get:

\(x^2 = 144 - 64 = 80\)

Taking the square base of the two sides, we get:

x = √80 = 4√5

Hence:

|A'B'| = (5/3) * |AB| = (5/3) * 4√5 = (20/3)√5

So the length of A'B' is (20/3)√5 cm.

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Answer:

Cost of game after discount = 72 - 20% of 72 = $57.6

Cost after tax = 57.6 + 7.5% of 57.6 = $61.92

So, the required cost is $61.92.

To attain your target of $15,000 in five years if you can invest in an account that pays 5.25 percent compounded quarterly, you will have to invest $11,557 today.

Since interest is compounded quarterly, we need to calculate the quarterly interest rate and the quarterly time period. The quarterly interest rate will be 1/4th of the annual interest rate and the quarterly time period will be 1/4th of the time period.

Quarterly interest rate, r = 5.25/4 = 1.3125% = 0.013125

Quarterly time period, n = 4*5 = 20

A = P(1 + r/n)^(nt)

15,000 = x(1 + 0.013125)²⁰

By using the above formula, we get:

x = 11,556.96 ≈ $11,557

Therefore, the amount you will have to invest today to attain your target of $15,000 in five years is $11,557.

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Answer: x+42x-2

Step-by-step explanation:

Answer: Part A: 4x    Part B: 4x

Step-by-step explanation: you have to add them

Answer:

Step-by-step explanation:

You want to know the amount borrowed at 10%, 12%, and 14% if the total borrowed was $21000, the total interest was $2580, and the total of amounts borrowed at 10% and 14% was double the amount borrowed at 12%.

The relations give rise to three equations. If we let x, y, z represent the respective amounts borrowed at 10%, 12%, and 14%, we have ...

  x + y + z = 21000 . . . . . . total borrowed

  0.10x +0.12y +0.14z = 2580 . . . . . . total interest

  x + y = 2z . . . . . . . . . . . relationship between amounts

Writing the last equation as ...

  x -2y +z = 0

we can formulate the problem as a matrix equation and use a solver to find the solution. We have done that in the attachment. It tells us the amounts borrowed are ...

__

Additional comment

Recognizing that the amount at 12% is 1/3 of the total, we can use that fact to rewrite the other two equations. The interest on the $7000 at 12% is $840, so we have ...

These two equations have the solution shown above. (It is usually convenient to solve them by substituting for x in the second equation.)

<95141404393>

Answer:

To solve the given system of equations using the substitution method, we need to solve one equation for one variable and then substitute that expression into the other equation for that same variable. Let's solve the second equation for y.

-x + y = 4

y = x + 4

Now we can substitute this expression for y into the first equation and solve for x.

-2x + 2(x + 4) = 7

-2x + 2x + 8 = 7

8 = 7

The equation 8 = 7 is not true, which means the system of equations has no solution. We can see this visually by graphing the two lines. They are parallel and will never intersect, which means there is no point that satisfies both equations.

Therefore, the solution to the system of equations is "No solution."

Note: Please be sure to double-check your work to avoid mistakes.

Step-by-step explanation:

Hope this helps you!! Have a wonderful day/night!!

There are 360 black counters and 306 white counter in 20:17 ratio.

Let's denote the number of black counters by B and the number of white counters by W. We know that the ratio of black to white counters is 20:17, which means that:

B/W = 20/17

We also know that there are 54 more black counters than white counters, which means that:

B = W + 54

We can use substitution to solve for B. Substituting the second equation into the first equation, we get:

(W + 54)/W = 20/17

Cross-multiplying, we get:

17(W + 54) = 20W

Expanding the left side, we get:

17W + 918 = 20W

Subtracting 17W from both sides, we get:

918 = 3W

Dividing both sides by 3, we get:

W = 306

Now we can use the second equation to find B:

B = W + 54 = 306 + 54 = 360

Therefore, there are 360 black counters in the bag.

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Answer:

Quantity of rice cooked in October = 71.3 kg

Step-by-step explanation:

Given:

Quantity of rice cooked per week = 16.1 kg

Number of days in a week = 7

Number of days in October = 31

Find:

Quantity of rice cooked in October

Computation:

Quantity of rice cooked in October = [Number of days in October / Number of days in a week] Quantity of rice cooked per week

Quantity of rice cooked in October = [31 / 7]16.1

Quantity of rice cooked in October = 71.3 kg

The objective function is to minimize the number of calories, subject to the constraints that the total vitamins should be at least 25 milligrams and the total protein should be at least 27 grams.

The objective function is to minimize the number of calories, denoted as C. The constraints are as follows:

- The total vitamins consumed, represented by the variable z, should be at least 25 milligrams: z ≥ 25.

- The total protein consumed, also represented by z, should be at least 27 grams: z ≥ 27.

- The number of servings of casserole, x, and salad, y, should be greater than or equal to 0: x ≥ 0, y ≥ 0.

- The total calories, C, is a linear combination of the calories from casserole (300x) and salad (45y): C = 300x + 45y.

- Additional constraints are given:

  - 3x + y ≥ 60 (ensuring minimum vitamins)

  - 4x + 3y ≥ 120 (ensuring minimum protein)

  - 2x + 4y ≥ 80 (ensuring a balanced diet)

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Answer:

Slope = 6

Step-by-step explanation:

Reading your description carefully, the equation of line has been given to be

When we compare this with the standard form of a straight line

We immediately see that the slope or gradient m = 6.

Alternatively, when we consider the coordinates of the points mentioned, we have

(1, 5)    ;     (0, -1)     ;     (-1, -7)

We can take any two points out of these three and calculate the slope using the formula

For example, let us consider the points (1, 5) and (-1, -7)

Here x₁ = 1; x₂ = -1 and y₁ = 5; y₂ = -7

Plugging the numbers in the above formula, we have

This agrees with what we calculated directly from the equation of the line!

Hence, slope of the line on the graph = 6

The slope of the line in simplified form is -1

Find the required diagram attached.

The formula for calculating the slope of a line is expressed as:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Using the coordinate points (0, -2) and (-2, 0)

Substitute the given coordinates into the formula:

\(m=\frac{0-(-2)}{-2-0}\\m=\frac{0+2}{-2}\\m=\frac{-2}{2}\\m=-1\)

Hence the slope of the line in simplified form is -1

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⟹Answer:

\(x = -10\)

⟹Step-by-step explanation:

Lets Solve!

⟹The first thing we must do is define our variables. Lets look at the problem again:

"The sum of a number and 7 is multiplied by 4. The result is equal to -12."

We can make x the number that is being added to 7.

The sum of x and 7 is multiplied by 4. This expression equals -12.

\(4(x+7) = -12\)

⟹Now we use distribute 4 amongst (x+7)

\(4(x+7) = -12\)

\(4x+28 = -12\)

Next we subtract 28 from both sides.

\(4x+28 = -12\)

\(4x = -40\)

Last we divide 4 on both sides.

\(\frac{4x}{4} = \frac{-40}{4}\)

➧ \(x = -10\)

Woohoo! Brainliest Appreciated! Hope I helped!

It's not entirely clear what is meant by "5 Apples in 6 rows," so I will provide a general answer that could apply to a few different interpretations of the question.

If Johnny has 5 apples and places them in 6 rows, the answer to how many apples he will have left depends on how many apples are in each row and what Johnny does with them. For example, if he eats one apple from each row, he will be left with 5 - 6 = -1 apples, which doesn't make sense. If instead he rearranges the apples into one row, he will still have 5 apples. If he gives away 2 apples, he will have 3 apples left.

In summary, the number of apples Johnny will have left depends on the details of the scenario, including how many apples are in each row and what Johnny does with them.

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Answer:

137

Step-by-step explanation:

3*4=12

12^2=144

-2*4=-8

144-8+1

144-7

137

To prove that the matrix AB is nonsingular when A and B are both n x n nonsingular matrices, we need to show that AB has an inverse.

Let's assume A and B are nonsingular matrices, which means they have inverses, denoted as A^(-1) and B^(-1), respectively. Now, let's consider the product of A^(-1) and B^(-1), denoted as (AB)^(-1). We can show that (AB)(AB)^(-1) is equal to the identity matrix I, which has ones along the main diagonal and zeros elsewhere. (AB)(AB)^(-1) = A(BB^(-1))A^(-1) = AI(A^(-1)) = AA^(-1) = I. This demonstrates that (AB)^(-1) exists, as the product of AB and (AB)^(-1) yields the identity matrix. Since (AB)^(-1) exists, it means that AB is also nonsingular, as it has an inverse (AB)^(-1).

Therefore, if A and B are both n x n nonsingular matrices, the product AB is also a nonsingular matrix.

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Answer:

Inverse of a 3 by 3 Matrix

MM-1 = M-1 M = I.

Step 1: The first step while finding the inverse matrix is to check whether the given matrix is invertible. ...

Step 2: Calculate the determinant of 2 × 2 minor matrices.

Step 3: Formulate the cofactor matrix.

Step-by-step explanation:

The inverse matrix formula, A-¹ = (1/|A|) Adj A, is used to determine the inverse of a 3×3 matrix.

The multiplicative identity is obtained by multiplying the provided matrix by the other matrix which serves as the inverse of a matrix. A matrix's inverse is A-1, since the I is the identity matrix, A A-1 = A-1 A = I.

The formula A-1 = (adj A)/(det A), where det A is in the denominator, is used to determine the inverse of a 3x3 matrix A. 

• adj A = The adjoint matrix of A

• det A = determinant of A

dAs a result, det A should not be 0 for A-1 to exist. i.e.,

• A-1 exists when det A ≠ 0 (i.e., when A is nonsingular)

• A-1 does not exist when det A = 0 (i.e., when A is singular).

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Answer:

what?

Step-by-step explanation:

The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.

The proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips can be determined by finding the area under the normal distribution curve to the right of the mean.

To find this proportion, we can use the z-score formula:
z = (x - mean) / standard deviation

In this case, we want to find the proportion of bags that contain more than 12 ounces, so x = 12 ounces.

z = (12 - 12.5) / 0.2
z = -2.5 / 0.2
z = -12.5

Next, we need to find the cumulative probability associated with the z-score. We can use a standard normal distribution table or a calculator to find this probability.

Looking up the z-score of -12.5 in the table or using a calculator, we find that the cumulative probability is approximately 0.

Therefore, the proportion of 12-ounce bags that contain more than the advertised 12 ounces of chips is 0.

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The best estimate for the deer population on the island is 500.

1. The veterinary doctors marked 30 deer on the island.

2. Later on, they counted 150 deer in total.

3. Out of the 150 deer, 12 had marks.

4. To find the best estimate for the deer population on the island, we can set up a proportion.

5. Let "x" represent the total deer population.

6. The proportion can be set up as: 30/x = 12/150.

7. Cross-multiplying gives us: 12x = 30 * 150.

8. Solving for x, we get: x = (30 * 150) / 12.

9. Evaluating the expression, we find: x = 375.

10. Rounding to the nearest whole number, the best estimate for the deer population on the island is 500.

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The wavelength of the photon emitted when a hydrogen electron transitions from the n=3 to the n=2 energy level is approximately -7.854 x 10⁻⁸ meters..

The wavelength of the photon emitted when a hydrogen electron transitions from the n=3 to the n=2 energy level can be calculated using the Rydberg formula.

The Rydberg formula is given by:

1/λ = R(1/n₁² - 1/n₂²)

Where λ is the wavelength of the photon, R is the Rydberg constant (approximately 1.097 x 10⁷ m⁻¹), n₁ is the initial energy level, and n₂ is the final energy level.

In this case, the initial energy level (n₁) is 3 and the final energy level (n₂) is 2.

Plugging these values into the formula, we get:

1/λ = R(1/3² - 1/2²)

Simplifying further:

1/λ = R(1/9 - 1/4)

1/λ = R(4/36 - 9/36)

1/λ = R(-5/36)

To find the value of λ, we take the reciprocal of both sides:

λ = -36/5R

Substituting the value of R (1.097 x 10⁷ m⁻¹), we get:

λ ≈ -36/5(1.097 x 10⁷ m⁻¹)

Calculating this value, we find:

λ ≈ -7.854 x 10⁻⁸ m.

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The wavelength of the photon emitted when a hydrogen electron transitions from the n1 to the n2 energy level can be calculated using the Rydberg formula: 1/λ = R((1/n1^2) - (1/n2^2)), where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the initial and final energy levels, respectively.

When a hydrogen electron transitions from one energy level to another, it emits or absorbs a photon of specific energy. This energy can be related to the wavelength of the photon using the equation E = hc/λ, where E is the energy, h is Planck's constant, c is the speed of light, and λ is the wavelength.

In the case of a hydrogen atom, the energy levels are quantized and given by the equation E = -13.6 eV/n^2, where n is the principal quantum number. The initial energy level, n1, is usually a higher value than the final energy level, n2.

Using the Rydberg formula, we can determine the wavelength of the emitted photon. By substituting the values of n1 and n2 into the equation, we can calculate the wavelength.

For example, if the electron transitions from n=3 to n=2, the Rydberg formula becomes 1/λ = R((1/3^2) - (1/2^2)). Solving for λ will give us the wavelength of the emitted photon.

Please note that the Rydberg formula is specifically applicable to hydrogen atoms or hydrogen-like ions.

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Answer:

15 inches

Step-by-step explanation:

1. Use the Pythagorean Theorem: a^2+b^2=c^2

You are already given c (the longest side) and one of the legs which could be a or b.

2. Plug the numbers into the formula and square them.

a^2 + 36^2 = 39^2

Squaring the numbers gives you: a^2 + 1,296 = 1,521

3. Subtract 1,296 from both sides and take the square root of the result.

a^2 = 225

\(\sqrt{225}\) = 15

Answer: 15

Step-by-step explanation:

Answer:

14°

Step-by-step explanation:

4x + 32 + 64 = 180 => x = 14 (°)

Answer:

£2250

Step-by-step explanation:

Interest= p×r×t÷100

Interest= 5000×7.5×6÷100

Interest= 225000÷100

Interest= £2250

Answer:

See explanation

Step-by-step explanation:

a) 200,000 x .0288 x 7 = 40,320 interest

b) 240,320/84 = $2860.95

Answer:

subtracting a negititive is the same as adding so -66.1+55.6

Hope This Helps!!!

Answer:

The answer should be 25% off

Step-by-step explanation:

sorry if wrong

a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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