A magic square is a square array of numbers arranged so that the numbers in all rows, all columns, and the two diagonals have the same sum. Use the properties of a magic square to fill in the missing numbers in the magic square on the right. CO. 16 24 Use the figure with the letters below to give the missing numbers. CO A= B= C= B 16 D= E= E 24 ​

The equation for the line in slope-intercept form y=-4x+5

1. We will, first of all, Determine the slope by counting down and over from one place to another. Let's start at (-2,13) and work our way down (0,5)

If at all you are concerned about miscounting, you can use the slope formula, which is y2-y1/x2-x1.

5-13/0--2 \s = -8/2

The gradient is -4.

2. Determine where the line intersects the y-axis to obtain the y-intercept. It crosses it at 5 here.

3. Write the equation in slope-intercept form, y=mx+b, where mx is the slope and b is the y-intercept.

y=-4x+5

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The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer:

x=63/2

Step-by-step explanation:

x/7=9/2

x=63/2

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Draw the given table

STEP 2: Explain how to get the relative frequency

The relative frequency is derived by dividing the columns by the total frequency.

STEP 3: Complete the table

STEP 4; Draw the complete table

STEP 5: Calculate the relative Frequency

STEP 6: Calculate the percentage of customers without smartphones

Hence, the percentage of customers without smartphones is 34%

The missing sides and angles of the triangles are:

1) ∠L = 53°

LA = 23.145 ft

AB = 18.9 ft

2) ∠S = 57.31°

SA = 98.57 cm

SW = 69.12 cm

3) B = 30.71°

C = 99.29°

The law of cosine formula is expressed as:

c² = a² + b² - 2ab cos C

The Law of sines is expressed as:

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

Thus:

1) ∠L = 180 - (102 + 25)

∠L = 53°

LA/sin 102 = 10/sin 25

LA = 23.145 ft

AB = 10 * sin 53/sin 25

AB = 18.9 ft

2) ∠S = 180 - (79 + 43.69)

∠S = 57.31°

84.5/sin 57.3 = SA/sin 79

SA = 98.57 cm

SW/sin 43.69 = 84.5/sin 57.3

SW = 69.12 cm

3) 15/sin 50 = 10/sin B

sin B = (10 sin 50)/15

sin B = 0.5107

B = sin⁻¹0.5107

B = 30.71°

C = 180 - (50 + 30.71)

C = 99.29°

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Answer

y = f(x) = 3x - 1

Explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

Two lines that are parallel to each other have the same slope.

If the equation of a straight line is written in the form of y = 3x - 6,

,The slope and y-intercept form of the equation of a straight line is given as

y = mx + c

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

c = y-intercept of the line.

So, in y = 3x - 6, the slope = m = 3

So, using the point-slope form,

y - y₁ = m (x - x₁)

m = 3

(x₁, y₁) = (2, 5)

x₁ = 2, y₁ = 5

y - y₁ = m (x - x₁)

y - 5 = 3 (x - 2)

y - 5 = 3x - 6

y = 3x - 6 + 5

y = 3x - 1

In function notation, y = f(x)

So, the equation of the line required is

y = f(x) = 3x - 1

Hope this Helps!!!

The two points are B'=(-6,-8).

To plot the points:

Plot a new point that is 8 units down and also has the same x coordinate.

Given - Point B = ( -6, 0 )

Represent the new point with B':

In Point B = ( -6, 0 )  

\(x=-6,y=0\)

This means that B' has an x coordinate of -6.

Next, is to determine the y coordinate:

If a point (x,y) is translated b units down, the new point is (x, y, -b)

In this case:

The y coordinate of B is 0 and b = 8.

So, the new y coordinate is 0 - 8 = -8

So, we have B'=(-6,-8).

Therefore, the two points are B'=(-6,-8).

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Answer:

Step-by-step explanation:

\(6.25\times (0.74)^{5}=\)

Answer:

The answer is 1.38687914 but if you round it to the nearest tenth then it is 1.4

Step-by-step explanation:

The given matrix is nilpotent of index 3. If matrix A is nilpotent, then its transpose AT is also nilpotent. Nilpotent matrices are not invertible, and as a consequence, the identity matrix minus a nilpotent matrix is always invertible.

(a) To determine the index of the given matrix A, we need to find the smallest positive integer k such that \(A^{k}\) = 0. Computing the powers of A, we have \(A^{2}\) = \(\left[\begin{array}{ccc}0&1&2\\1&0&0\\2&1&0\end{array}\right] t\), \(A^{3}\) = 0, where 0 represents the zero matrix. Therefore, the index of matrix A is 3.

(b) If A is nilpotent, it means that there exists a positive integer k such that \(A^{k}\)= 0. Taking the transpose of both sides, we have (\(A^{k}\))T = 0. Since the transpose of a matrix raised to a power is the same as the transpose of the matrix raised to that power, we have\((A^T)^k\) = 0. Hence, AT is also nilpotent.

(c) Nilpotent matrices are not invertible. To see why, consider a nilpotent matrix A of index k. If A was invertible, there would exist a matrix B such that AB = BA = I, where I is the identity matrix. However, multiplying \(A^{k}\)with B yields (\(A^{k}\)B = 0, contradicting the fact that AB = I. Therefore, nilpotent matrices are not invertible.

(d) If A is nilpotent, then the identity matrix minus A, denoted as I - A, is invertible. To prove this, suppose there exists a matrix B such that (I - A)B = I. Expanding the left side, we get IB - AB = I. Simplifying, we have B - AB = I. Rearranging the terms, we get B = I + AB. Now, multiplying both sides by A, we have AB = A + \(A^2\)B. Since \(A^2\)B is nilpotent,\(A^2\)B = 0. Therefore, B = I + 0 = I. This shows that there exists a unique matrix B such that (I - A)B = I, confirming that I - A is invertible.

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Answer:

Step-by-step explanation:

-9r - 73 = -10

-9r = 63

r = -7

Answer:

87.12

Step-by-step explanation:

Answer:

12.5

Step-by-step explanation:

Answer:a=4

Step-by-step explanation:

Answer:

a = 4

Step-by-step explanation:

16 × a = 32 × 2

16a = 64

dividing both sides of the equation by 16 gives

16a/16 = 64 /16

a = 4

The probability of either of the two die landing on 4 is 1/36.

To calculate the probability of either of the two dice landing on 4 when rolling two regular dice, we need to determine the favorable outcomes and the total possible outcomes.

Favorable outcomes: There are three ways to get a 4 with two dice: (1, 3), (3, 1), and (2, 2).

Total possible outcomes: Each die has 6 sides, so there are 6 possible outcomes for the first die and 6 possible outcomes for the second die.

Therefore, the total possible outcomes are 6 x 6 = 36.

Probability = Favorable outcomes / Total possible outcomes

Probability = 1/6 x 1/6

Probability = 1/36

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Answer:

This is not a function as -5 has relationship with more than 1 elements

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The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.

In the context of consumption, the Euler equation can be expressed as:

u'(Ct) = β * u'(Ct+1)

where:

- u'(Ct) represents the marginal utility of consumption in the current period,

- Ct represents current-period consumption,

- β is the discount factor representing the individual's time preference,

- u'(Ct+1) represents the marginal utility of consumption in the future period.

This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.

Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.

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Answer:

8x³ + 6x² + 5x

Step-by-step explanation:

Let's simplify step-by-step.

−x^3 + 5x + 7x^2 + 8x^3 − ( −x^3 + x )

Distribute the Negative Sign:

= −x^3 + 5x + 7x^2 + 8x^3 + −1 ( −x^3 + x )

= −x^3 + 5x + 7x^2 + 8x^3 + −1 ( −x^3 ) + −1x

= −x^3 + 5x + 7x^2 + 8x^3 + x^3 + −x

Combine Like Terms:

= −x^3 + 5x + 7x^2 + 8x^3 + x^3 + −x

= ( −x^3 + 8x^3 + x^3 ) + ( 7x^2 ) + ( 5x + −x )

= 8x^3 + 7x^2 + 4x

Answer:

= 8x^3 + 7x^2 + 4x

Answer:

the radius would be 88cm

Sososos

Step-by-step explanation:

Saeng's third race is between race 2 and race 3.

Ascending order: Arranging the numbers from lowest number to highest number.

Descending order: Arranging the numbers from highest number to lowest number.

The times for 5 races are given in the table  

  Race       timings

      1              -1.2

      2             \(+1\frac{1}{10}=1.1\)    

      3              \(-1\frac{1}{4}=-1.25\)

      4              - 1.4

      5               \(+1\frac{1}{2}=1.5\)

Arranging the timings in ascending order we get,

-1.4,-1.25,-1.2,1.1,1.5

Hence third race is -1.2 it lies between race 2 and race 3.

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Answer:

\(v = \frac{1}{3} \times 15 \times 7 \\ 5 \times 7 \\ = 35\)

Answer:

There would be 950 cm of thread left on the reel

Step-by-step explanation:

Here in this question, we are interested in knowing the amount of thread left on the reel.

To answer this question properly, we shall need to be consistent in using our units.

Thus, we need to convert the length of thread on the reel to cm.

Mathematically;

100cm = 1 m

let x cm = 15.25 m

x = 15.25 * 100 = 1525 m

Since 575 cm has been used for a project, the amount of thread in cm left on the reel will be;

1525 cm - 575 cm = 950 cm

Step-by-step explanation:

log54 = log(2×3³)

= log2 + log3³

= log2 + 3log3

Answer:

Step-by-step explanation:

Since none of the answer choices match the drawing of the gardener, we assume the question is referring to the drawing of the partner.

The gardener's drawing is 1/4 of actual size. So, in terms of the gardener's drawing, actual size is ...

  gardener's drawing = (1/4)actual size

  actual size = 4(gardener's drawing)

__

The partner's drawing is 1/20 of actual size, so is ...

  partner's drawing = actual size/20 = (4(gardener's drawing))/20

  partner's drawing = (4/20)(gardener's drawing)

  partner's drawing = (gardener's drawing)/5

__

Then the {length, width} of the partner's drawing are ...

  partner's drawing {length, width} = {15 in, 10 in}/5 = {3 in, 2 in}

The partner's drawing has a length of 3 inches and a width of 2 inches.

The answer is Quadrant II. First, we need to understand what csc and cos represent in trigonometry. Csc (cosecant) is the reciprocal of sine, meaning it is equal to 1/sin.

Cos (cosine) represents the ratio of the adjacent side of a right triangle to its hypotenuse.
Now, let's look at the given statements. csc 0 > 0 means that the sine of 0 is positive. Since sine is positive in Quadrants I and II, we know that 0 lies in either of those two quadrants.
Next, cos 0 < 0 means that the cosine of 0 is negative. Since cosine is negative in Quadrants II and III, we can eliminate Quadrant I as a possibility and conclude that 0 must lie in Quadrant II.

Based on the given conditions, csc θ > 0 and cos θ < 0, θ lies in Quadrant II.
Explanation:
csc θ is positive when sin θ is positive. Sin θ is positive in Quadrant I and II.
cos θ is negative in Quadrant II and III.
The only common quadrant is Quadrant II.

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Answer:

Step-by-step explanation:

You want the area of a 16-unit circle using different values for pi.

The formula for the area of a circle is ...

  A = πr² . . . . . . where r is half the diameter

For the different values of pi, this will be (in square units) ...

  π(8²) = 64π . . . . exact

  3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low

  22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high

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Answer: factor...

Step-by-step explanation:  If we divide a polynomial f(x) by (x - c), and (x - c) is a factor of the polynomial f(x), then the remainder of that division is simply equal to 0. Thus, according to this theorem, if the remainder of a division like those described above equals zero, (x - c) must be a factor.