4, -4, 0 are examples of-
i. irrational numbers.

ii. natural numbers.

iii. integers.
v. none of these.

The cash flow to stockholders for 1998 is -$4 million.

To calculate the cash flow to stockholders for 1998, follow these steps:

Identify the dividends paid: Brandy's Candies paid $23 million in dividends during 1998.

Determine the net common stock repurchases: Brandy's Candies made net common stock repurchases of $27 million during 1998.

Subtract the net common stock repurchases from the dividends paid: $23 million - $27 million = -$4 million.

The resulting cash flow to stockholders for 1998 is -$4 million, indicating a net outflow of cash from stockholders.

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Answer:

y = 7 when x = -5

Step-by-step explanation:

First go to x = -5

Then go up to where you meet the green line

The y value is 7

y = 7 when x = -5

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

For part (a), we can find a nonzero vector orthogonal to the plane through the points P, Q, and R by constructing a normal vector to the plane using the cross product of two vectors in the plane. The two vectors in the plane are \($\vec{PQ} = (1- (-2), 0-1, 1-3) = (3, -1, -2)$\) and \($\vec{PR} = (1-4, 0-2, 1-5) = (-3, -2, -4)$\). Taking the cross product of the two vectors gives us the normal vector to the plane, \($\vec{n} = \vec{PQ} \times \vec{PR} = (8, -8, 12)$\). Therefore, the vector orthogonal to the plane is \($\vec{n} = (8, -8, 12)$.\)

For part (b), the area of triangle PQR can be found using the formula for Heron's Formula, which states that the area of a triangle with sides a, b,and c is given by

\($A = \sqrt{s(s-a)(s-b)(s-c)}$\)

where \($s = \frac{a+b+c}{2}$\) . In this case, the sides are \($a = \|\vec{PQ}\| = \sqrt{3^2 + (-1)^2 + (-2)^2} = \sqrt{14}$, $b = \|\vec{QR}\| = \sqrt{(-2-4)^2 + (1-2)^2 + (3-5)^2} = \sqrt{14}$\), and\($c = \|\vec{PR}\| = \sqrt{(-3)^2 + (-2)^2 + (-4)^2} = \sqrt{29}$\). Plugging these values into the formula, we get

\(= \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{\frac{7(7-\sqrt{14})(7-\sqrt{14})(7-\sqrt{29})}{4}} = \sqrt{7(7-\sqrt{14})^2(7-\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2(\sqrt{14}+\sqrt{29})} = \sqrt{7(7-\sqrt{14})^2\sqrt{43}} = \sqrt{301}$\)Therefore, the area of triangle PQR is \($\sqrt{301}$\)

The vector orthogonal to the plane through the points P, Q, and R is (8, -8, 12), and the area of triangle PQR is \($\sqrt{301}$\).

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Answer:

$10.90

Step-by-step explanation:

Hmm... this question can be tricky. Don't get caught up! The formula is simple once you know what you're doing. Let's figure it out!

So, from the word problem we can determine that the weight is 2.5 pounds with a price of 4.36 a pound.  

The formula we will be using for this question is \(2.5(4.36)\). This may seem complicated, but all its saying is 2.5x4.36. You may be wondering, why are we using this formula? Well, for every pound of roast he buys, he pays 4.36 dollars. He is buying 2.5 pounds of roast, so we can do 4.36 2 times and 4.36 .5 times, which translates into 2.5 times 4.36. You with me so far? I hope so, because here comes the tricky part. Let's multiply:

4.36

x 2.5

--------

10.9

And there you have it! $10.90.

Please consider giving this response a brainliest. It took plenty of effort and time

Answer:

34, and if 55 was replaced with 33, the new median would be 33.

Step-by-step explanation:

The median is the number that is in the middle of a data set, once the numbers are organized from least to greatest. If we put the numbers in order (18, 22, 24, 32, 34, 39, 55, 57, 59), the number in the middle is 34. If we do the same, but replace 55 with 33, (18, 22, 24, 32, 33, 34, 39, 57, 59), we get 33 as the median.

Answer:

Step-by-step explanation:

To find the explicit formula for the sequence 31, 27, 23, ..., we first need to find the common difference between consecutive terms.

We can see that each term is obtained by subtracting 4 from the previous term. Therefore, the common difference is -4.

Using the general formula for an arithmetic sequence:

an = a1 + (n - 1)d

where a1 is the first term, d is the common difference, and n is the index of the term we want to find.

In this sequence, a1 = 31 and d = -4. So, we have:

an = 31 + (n - 1)(-4)

Simplifying, we get:

an = 35 - 4n

Therefore, the explicit formula for the n-th term of the sequence 31, 27, 23, ... is an = 35 - 4n.

Answer:

The third answer: no, the answer shows that metals only melt at temperatures greater than -38.87 degrees celsius.

Step-by-step explanation:

Zero-point energy is the lowest energy state of a quantum system at absolute zero temperature.

Zero-point energy is the lowest energy state of a quantum system at absolute zero temperature. To calculate the zero-point energy, the energy of the system must first be determined at the lowest temperature that can be achieved in practice, typically close to absolute zero. The energy at this temperature is then subtracted from the energy of the system at higher temperatures. This difference is the zero-point energy. The zero-point energy can be calculated by taking the sum of the energies of all of the quantum states at absolute zero. This sum can be approximated using the uncertainty principle and the Heisenberg Uncertainty Principle. The sum is then multiplied by Planck's constant to get a value for the zero-point energy. Finally, the total zero-point energy is the sum of the individual zero-point energy values of each quantum state. This energy represents the energy of the system at absolute zero and is the lowest energy state possible.

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Answer:

1: Line symmetry. (You can fold the shape in half and the lines match up exactly to be the exact same shape)

Answer:

Kindly check explanation

Step-by-step explanation:

Let number of loaves = nl

Cups of flour = cp

Tablespoonful of water = sw

Teaspoonful of salt = ss

1 loaf of bread calls for :

2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt

1 loaf :

cp = 2 × nl

sw = 12 × nl

ss = 1 × nl = nl

nl - - - - - - cp - - - - - - sw - - - - - - ss

1 - - - - - - - 2 - - - - - - - 12 - - - - - - 1

2 - - - - - - - 4 - - - - - - - 24 - - - - - 2

4 - - - - - - - 8 - - - - - - - 48 - - - - - 4

3 - - - - - - - 6 - - - - - - - 36 - - - - - 3

Number of loaves = cups of flour / 2

Answer: The card is 28 cm by 23 cm

Check out the diagram below

Explanation:

I added 4 cm to each dimension of the "24 x 19". Why 4 instead of 2? Because we're effectively adding two copies of "2 cm" to each of the original length and width. Along the horizontal component, we have the left and right boundaries. Along the vertical component, we have the top and bottom boundaries. The diagram hopefully clears up any confusion you may have.

The t value will be the result that is  58.851995039

The t-statistic for the observed correlation coefficient of 0.951 can be calculated to determine if it is statistically significant. Using the T.INV() spreadsheet function and the appropriate degrees of freedom.

We can test the null hypothesis of no correlation at the 5% significance level. Additionally, the T.DIST() function can be used to calculate the p-value of the t-statistic.

To calculate the t-statistic, we need to know the sample size (n) and the observed correlation coefficient (r). In this case, we have 37 monthly observations and a correlation coefficient of 0.951. The t-statistic can be calculated using the formula t = r x sqrt((n - 2) / (1 - r^2)). Plugging in the values, we find t = 0.951 x sqrt((37 - 2) / (1 - 0.951^2)).

By comparing this t-statistic to the critical value at the desired significance level (5% in this case), we can determine if the null hypothesis of no correlation can be rejected. Additionally, the p-value can be calculated using the T.DIST() function to determine the probability of obtaining a t-statistic as extreme as the observed value. If the p-value is less than the chosen significance level, the null hypothesis can be rejected.

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The formula (kerA)⊥=im(AT) is indeed true.

First, recall that the kernel (or null space) of an n×m matrix A is the set of all vectors x in \(R^m\) such that Ax=0. Geometrically, the kernel of A represents the subspace of \(R^m\) that gets mapped to the origin under the linear transformation represented by A. Similarly, the image (or range) of A is the set of all vectors y in \(R^n\) that can be written as y=Ax for some x in \(R^m\). Geometrically, the image of A represents the subspace of R^n that can be reached by applying the linear transformation represented by A to some vector in \(R^m\).

Now, let W denote the subspace spanned by the kernel of A, that is, W=span{v1, v2, ..., vk} where {v1, v2, ..., vk} is a basis for kerA. By definition, any vector w in W satisfies Aw=0. We want to show that the orthogonal complement of W, denoted by W⊥, is equal to the image of the transpose of A, im(AT). That is, we want to show that any vector y in W⊥ satisfies y=ATx for some x in \(R^m\).

To prove this, let y be an arbitrary vector in W⊥. Then, by definition, y is orthogonal to every vector in W, including the basis vectors {v1, v2, ..., vk}. In other words, we have y⋅vi=0 for all i=1,2,...,k. Now, consider the transpose of A, denoted by AT, which is an m×n matrix. The i-th row of AT is given by the i-th column of A, and the j-th column of AT corresponds to the j-th row of A. Therefore, we have AT=[a1T, a2T, ..., amT], where ajT denotes the transpose of the j-th column of A. Let x be the vector in \(R^m\) given by x=c1a1+c2a2+...+cma m, where {c1, c2, ..., cm} are arbitrary scalars. Then, we have ATx=(c1a1T+c2a2T+...+cmamT)=[c1, c2, ..., cm] [a1T, a2T, ..., amT]=c1v1+c2v2+...+ckvk.

Note that the vector c1v1+c2v2+...+ckvk belongs to the kernel of A, since Aw=0 for any w in the kernel of A. Therefore, we have ATx⋅vi=0 for all i=1,2,...,k. But we also have y⋅vi=0 for all i=1,2,...,k, since y is orthogonal to every vector in W. Therefore, we have (ATx+y)⋅vi=0 for all i=1,2,...,k. Since {v1, v2, ..., vk} is a basis for kerA, this implies that ATx+y is in the kernel of A, that is, A(ATx+y)=0. But this means that ATx+y is orthogonal to every column of A, and hence lies in the orthogonal complement of the image of A.

Therefore, we have shown that any vector y in W⊥ can be written as y=ATx for some x in \(R^m\). This proves that W⊥.

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It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.

The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.

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Answer:

<DCA and <BCF

Step-by-step explanation:

vertical angles are the opposite angles created by intersecting lines and are congruent. Vertical angles share only a vertex

1. Im(z1 + z2) = 2 * Im(z1).

2. Re(z1) = Re(z1 + z2) - Im(z2).

3. arg(z1 z1*) = arctan(Im(z1) / Re(z1)).

4. |z1^z2| = |z1|^Re(z2) * exp(-arg(z1) * Im(z2)).

5. arg(z1 z2) = arg(z1) + arg(z2).

1. The imaginary part of z1 + z2 can be calculated by adding the imaginary parts of z1 and z2. Since z1 and z2 are complex conjugates, their imaginary parts are equal. Therefore, Im(z1 + z2) = 2 * Im(z1).

2. The real part of z1 can be calculated by subtracting the imaginary part of z2 from the real part of z1 + z2. Since z1 and z2 are complex conjugates, their imaginary parts are equal and cancel out when added. Therefore, Re(z1) = Re(z1 + z2) - Im(z2).

3. The argument of z1 z1* can be calculated by taking the arctan of the imaginary part divided by the real part of z1 z1*. Since z1 and z1* are complex conjugates, their imaginary parts are equal and cancel out when subtracted. Therefore, arg(z1 z1*) = arctan(Im(z1) / Re(z1)).

4. The modulus of z1^z2 can be calculated by taking the modulus of z1 and raising it to the power of the real part of z2, multiplied by the exponential of the negative of the argument of z1 multiplied by the imaginary part of z2. Therefore, |z1^z2| = |z1|^Re(z2) * exp(-arg(z1) * Im(z2)).

5. The argument of z1 z2 can be calculated by taking the argument of z1 and adding it to the argument of z2. Therefore, arg(z1 z2) = arg(z1) + arg(z2).

To find the values of the given expressions, we can use the properties of complex numbers and the formulas mentioned above.

For the first expression, we know that z1 and z2 are complex conjugates, so their imaginary parts are equal. Therefore, the imaginary part of z1 + z2 is twice the imaginary part of z1.

For the second expression, we subtract the imaginary part of z2 from the real part of z1 + z2. Since z1 and z2 are complex conjugates, their imaginary parts cancel out when added.

For the third expression, we calculate the argument of z1 z1* by taking the arctan of the ratio of their imaginary part to their real part. Since z1 and z1* are complex conjugates, their imaginary parts cancel out when subtracted.

For the fourth expression, we calculate the modulus of z1^z2 by raising the modulus of z1 to the power of the real part of z2 and multiplying it by the exponential of the negative of the argument of z1 multiplied by the imaginary part of z2.

For the fifth expression, we simply add the arguments of z1 and z2 to obtain the argument of z1 z2.

By applying these calculations, we can find the values of the given expressions for the complex quadratic function.

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We have to find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1.

To find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1, we have to integrate x^(1/2) and x^(1/3) with respect to x. That is, Area = ∫0¹ [x^(1/2) - x^(1/3)] dx= [2/3 x^(3/2) - 3/4 x^(4/3)] from 0 to 1= [2/3 (1)^(3/2) - 3/4 (1)^(4/3)] - [2/3 (0)^(3/2) - 3/4 (0)^(4/3)]= 0.2857 square units

Therefore, the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1 is 0.2857 square units. Note: The question  but the answer has been provided in the format requested.

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Answer:

9231.60 cubic inches

Step-by-step explanation:

V = \(\pi r^{2} h\)

V = \(\pi (14)^{2} (15)\)

V = 9231.60 cubic inches

Given that set A contains 12 elements and set B contains 49 elements, and the total number of elements in either set A or set B is 52, we can determine the number of elements they have in common.

To find the number of elements in common between set A and set B, we subtract the sum of the number of elements in each set from the total number of elements. The total number of elements in either set A or set B is given as 52. Therefore, we have:

Number of elements in common = Total number of elements - (Number of elements in set A + Number of elements in set B)

= 52 - (12 + 49)

= 52 - 61

= -9

Since the result is negative (-9), it indicates that there are no elements in common between set A and set B. In other words, there are no elements that are present in both set A and set B.

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Answer:

Step-by-step explanation:

x = 39

C. 39 Cars

Answer:

396

Step-by-step explanation:

12 × 33

396

Answer:

the angle measurement is 75

Step-by-step explanation:

The results indicate that encountering sales clerks who smile could potentially increase customer purchases.

From the information given, we have that;

The four stores in the smile condition were 36, 40, 36, and 44;

To determine the t-value, we need to first calculate the mean for the control condition, we have;

Mean = 36 + 40 + 36+ 44/4

Mean =126/4

Mean = 32

Mean for the smile condition;

Mean = 39

One can employ a t-test to compare the average values of the two situations in order to scrutinize the outcomes. With a significance level of 0. 05, a two-tailed test with six degrees of freedom would require a critical t-value of around 2. 447

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Answer:

-249/28

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

C=pi×d

C÷pi = Pi×d÷Pi

C/pi=d

Answer:

B

Step-by-step explanation:

Given

C = πd ( isolate d by dividing both sides by π )

\(\frac{C}{\pi }\) = d

Answer:

90.29

Step-by-step explanation:

I did math

Answer:

1a. 58/99

1b. 53/90

1c. 29/50

Step-by-step explanation:

let's start with the easiest one

1.(c)

0.58 = 58/100 = 29/50

that is the simplest possible form, as 29 is a prime number and not a factor of 50.

1.(a)

0.585858585858... = 58×0.0101010101010101...

now, we know that 1/"double digit" (like 1/22) mostly produces a repeating pattern with a period length of 2 after the decimal point.

and we find

1/99 = 0.01010101010101...

so, our solution is

58 × 1/99 = 58/99

that is the simplest possible form, as 58 and 99 do not share any factors.

1.(b)

0.5888888888888... = 0.5 + 0.0888888888888... =

= 0.5 + 8×0.01111111111111... = 0.5 + 8×1/10 × 0.1111111111...

we know how to create 0.11111111111... :

1/9 = 0.111111111111111...

so, our solution is

0.5 + 8 × 1/10 × 1/9 = 0.5 + 8/90 = 5/10 + 8/90 =

= 45/90 + 8/90 = 53/90

this is the simplest possible form, as 53 is already a prime number and not a factor of 90.

Answer:

y=(-5/2)x-4

Step-by-step explanation:

Step 1: Define the equation of a line.

Equation of a line is written in the form y=ax+b where a is the slope and b is the y-intercept.

Step 2: Write the given parameters

(x1,y1)=(-2,1)

m=-5/2

Using the formula y-y1=m(x-x1)

y-1=-5/2(x-(-2))

y-1=-5/2(x+2)

y-1=(-5x-10)/2

By cross multiplication,

2(y-1)=-5x-10

2y-2=-5x-10

2y=-5x-10+2

2y=-5x-8

y=(-5x-8)/2

y=(-5/2)x-4

Answer:

= 16m² - 9

Step-by-step explanation:

(4m+3)(4m-3)

= 4m*4m + 4m*3 + 3*4m + 3*-3

= 16m² + 12m -12m - 9

= 16m² - 9