Which sequences are arithmetic
-5,5,-5,5…
96,48,24,12,6
18,5.5,-7,-19.5,-32
-1,-3,-9,-27,-81
16,32,48,64,80
Check all that apply

The ratio of dividends to the average number of common shares outstanding is known as the dividend yield. It is a measure of the return on an investment in the form of dividends received relative to the number of shares held.

To calculate the dividend yield, you need to divide the annual dividends per share by the average number of common shares outstanding during a specific period. The annual dividends per share can be obtained by dividing the total dividends paid by the number of outstanding shares. The average number of common shares outstanding can be calculated by adding the beginning and ending shares outstanding and dividing by 2.

For example, let's say a company paid total dividends of $10,000 and had 1,000 common shares outstanding at the beginning of the year and 1,500 shares at the end. The average number of common shares outstanding would be (1,000 + 1,500) / 2 = 1,250. If the annual dividends per share is $2, the dividend yield would be $2 / 1,250 = 0.0016 or 0.16%.

In summary, the ratio of dividends to the average number of common shares outstanding is the dividend yield, which measures the return on an investment in terms of dividends received per share held.

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This is an example of a sample survey or a sampling method.

Sampling techniques in a statistical study refer to how participants are chosen from the population to participate in the study. If a sample isn't chosen at random, it will likely be skewed in some way, and the results might not be generalizable.

In the given scenario, you are conducting a sample survey to determine the proportion of each color of Peanut Butter M&Ms. A sample survey is a method used to collect data from a subset of a larger population in order to make inferences about the entire population.

Instead of counting every single Peanut Butter M&M in existence, which would be impractical and time-consuming, you decide to take a smaller representative sample. You purchase 10 packages of Peanut Butter M&Ms, each weighing 1.69 ounces, and count the number of M&Ms of each color in those packages.

By analyzing the data collected from this sample, you can estimate the proportion of each color of Peanut Butter M&Ms in the larger population. This approach is more feasible and provides a reasonable approximation of the overall distribution of colors without having to examine every individual item.

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There are 4,651,200 different committees that can be formed with 3 managers and 6 engineers selected without replacement from a pool of 10 managers and 20 engineers.

To determine the number of different committees that can be formed, we need to calculate the combination of managers and engineers that can be selected.

The number of ways to select 3 managers from 10 managers can be calculated using the combination formula:

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

where n is the total number of managers and r is the number of managers to be selected.

In this case, we have n = 10 and r = 3, so the number of ways to select 3 managers from 10 is:

C(10, 3) = 10! / (3!(10 - 3)!) = 10! / (3!7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.

Similarly, the number of ways to select 6 engineers from 20 engineers can be calculated as:

C(20, 6) = 20! / (6!(20 - 6)!) = 20! / (6!14!) = (20 * 19 * 18 * 17 * 16 * 15) / (6 * 5 * 4 * 3 * 2 * 1) = 38,760.

To find the total number of different committees possible, we multiply the number of ways to select managers and engineers:

Total number of committees = C(10, 3) * C(20, 6) = 120 * 38,760 = 4,651,200.

Therefore, there are 4,651,200 different committees that can be formed with 3 managers and 6 engineers selected without replacement from a pool of 10 managers and 20 engineers.

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Answer:

AB + BC + CA

Step-by-step explanation:

12b-8 + 12b- 8 + 9b+8

33b - 8

9514 1404 393

Answer:

  53°

Step-by-step explanation:

The names of the triangles indicate that angle B corresponds to angle Y. Translation does not affect side lengths or angle measures, so angle Y is the same measure as angle B.

  m∠Y = 53°

Answer: 53

Step-by-step explanation:

Answer:

\(x=\frac{4\sqrt{3}}{3}\)

Step-by-step explanation:

From the figure attached,

ΔABC is an equilateral triangle.

Therefore, by the property of the equilateral triangle,

Measure of each angle = 60°

By applying tangent rule in the right triangle ADC,

\(\text{tan}(60^{\circ})=\frac{\text{Opposite side}}{\text{Adjacent side}}\)

\(\sqrt{3}=\frac{4}{x}\)

\(x=\frac{4}{\sqrt{3}}\)

\(x=\frac{4}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3} }\)

\(x=\frac{4\sqrt{3}}{3}\)

Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

Complement of set A is the set of all elements in the universal set that are not in the set .

If there is a subset of the universal set (U) called A, then the complement of set A, denoted by the symbol A', is different from the elements of set A and contains the elements of the universal set but not the elements of set A.

In this case, A' = x U: x A.

In other words, the complement of a set A is the difference between the universal set and set A.

For example: U = {1, 2, 3, 5, 7, 9, 15 ,14, 13}, A = {1, 2, 3, 5,7,9}, find the complement of A.

A' = U - A = {1, 2, 3, 5, 7, 9, 15,14,13} - {1, 2, 3, 5,7,9} = {15,14, 13}

A set that contains items from all related sets, without any repetition of elements, is known as a universal set (often symbolised by the letter U). If A and B are two sets, for example, A = 1, 2, 3 and B = 1, a, b, c, then U = 1, 2, 3, a, b, c is the universal set that these two sets belong to.

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Answer:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. \(42^\circ\)

5. 16.73 m

Step-by-step explanation:

Solution 1.

Reading of map scale = 1cm:5km

i.e. 1 cm is equivalent to 5 km

Measurement of map  = 7 cm

Actual distance = Measurement of map \(\times 5\)

Actual distance = 7 \(\times 5\) = 35 km

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

Solution 2.

Length of dining hall = 35 m

Measurement of map = 7 cm

Scale = Measurement of map : Length of dining hall (i.e. ratio)

Scale = 7 cm :35 m = 1 cm : 5 m

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

Solution 3.

Length of building = 30 m

Scale = 1 cm to 5m

5 m is equivalent to 1 cm on scale

1 m is equivalent to \(\frac{1}{5}\) cm on scale

30m is equivalent to \(\frac{1}{5} \times 30\) = 6 cm on scale

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

Solution 4.

Angle of elevation of A from B = \(42^\circ\)

Angle of depression of B from A = ?

Please refer to the image attached, we can clearly observe that both the angles (i.e. angle of elevation from A to B and angle of depression from B to A )will be equal.

Angle of depression of B from A = \(42^\circ\)

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

Solution 5.

Given that:

String length, or hypotenuse of triangle BC= 25 m

Angle of string with horizontal, \(\angle B = 42^\circ\)

Please refer to the attached image for the clear understanding of the situation.

To find:

Height, AC = ?

We can use trigonometric identity:

\(sin\theta = \dfrac{Perpendicular}{Hypotenuse}\)

OR

\(sinB = \dfrac{AC}{BC}\\\Rightarrow sin42^\circ = \dfrac{AC}{25}\\\Rightarrow AC = 25 \times 0.67\\\Rightarrow AC = 16.73 m\)

============

So, the answers are:

1. 35 km

2. 1 cm to 5m

3. 6 cm

4. \(42^\circ\)

5. 16.73 m

In a unit vector notation, the net force on the loop is (3.2×10⁻³ N)​​

Vector:

In math vector is the object containing both magnitude and direction

Given,

In the figure, a long straight wire carries a current i1​=30A  and a rectangular loop carries current i2​=20A. Take the dimensions to be a=1 cm, b = 8cm and L = 30cm.

Here we need to find the unit-vector notation for the net force on the loop due to i1​.

Here let's divide the loop into 4 parts i.e, they are witten as,

=> 1−2 , 2−3 , 3−4 , and 4−1

Then the force F on a wire of length L carrying current I in magnetic field of strength B (constant) is written as,

=> F=L(I×B)

Now, the force on part  2−3  and  4−1  is equal but opposite , hence cancelled, so the remaining are

⟹F2−3​+F4−1​=0

Therefore, Fnet​=F1−2​+F3−4​

Then the value of the net force is

=> (3.2×10⁻³ N)​​

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As the function f is defined piecewise with different rules on different intervals, we need to check the continuity of f at each point of its domain.

In order for a function to be continuous, it needs to be defined and have no breaks, jumps, or holes in its graph. Let's consider the function f with a positive constant k.

The function f can be written as:

f(x) = {

kx^2, if x < 2,

4k - 3x, if x >= 2

}

To determine the value of k for which f is continuous, we need to ensure that the two cases defined for f match at the point x = 2.

When x < 2, the function is defined as kx^2. At x = 2, this becomes k(2)^2 = 4k.

When x >= 2, the function is defined as 4k - 3x. At x = 2, this becomes 4k - 3(2) = 4k - 6.

For the function f to be continuous, the values of 4k and 4k - 6 must be equal at x = 2. Therefore, we have the equation 4k = 4k - 6.

Simplifying the equation, we find that -6 = 0, which is not true for any value of k.

Since the equation has no solution, it means that there is no specific value of k for which f is continuous. However, we can note that for all positive values of k, the function will still be defined in both cases and continuous within each individual case. Therefore, the function f will be continuous for all positive values of k.

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Answer:

6 units

Step-by-step explanation:

Maximum = n/n+1 and Minimum = 1/n+1

What is the uniform distribution?

Probability distributions with uniform distributions have outcomes that are all equitably likely. Results are discrete and have the same probability in a discrete uniform distribution. Results are continuous and infinite in a continuous uniform distribution. Data near the mean occur more frequently in a normal distribution.

Here, we have

Given: X1, X2,..., Xn is independent and identically distributed random variables having uniform distributions over (0,1).

a) Z = max{X₁, X₂....Xₙ}

Since Z is maximum so it is greater than X1, X2...Xn so cdf of Z will be

F(Z) = P(Z≤z) = P(X₁, X₂....Xₙ≤z) = P(X₁≤z, X₂≤z.....Xₙ≤z)

= P(X₁≤z)P(X₂≤z)....P(Xₙ≤z) = Fₓ(z)Fₓ(z).....Fₓ(z)

F(Z) = zⁿ

So pdf of Z is

F(z) = F'(z) = nzⁿ⁻¹

Expectation of Z is

F(Z) = \(\int\limits^0_1 {zf_Z(z)} \, dz\) = \(n\int\limits^0_1 {} \,\)zⁿdz

= n[zⁿ⁺¹/n+1]₀¹ = n/n+1

b) Let Y = min{X₁, X₂....Xₙ}

Since Y is the minimum so it is less than X1, X2...Xn so the cdf of Y will be

F(Y) = P(Y≤y) = 1 - P(Y>y) = 1- P(X₁, X₂....Xₙ≤z) = 1- P(X₁≤z, X₂≤z.....Xₙ>y)

= 1- P(X₁>y)P(X₂>y)....P(Xₙ>y) = 1- Fₓ(y)Fₓ(y).....Fₓ(y)

= 1 - [1-y]ⁿ

So pdf of Y is

F(y) = F'(y) = n[1-y]ⁿ⁻¹

The expectation of Y is

E(Y) = \(\int\limits^0_1 {yf_Y(y)} \, dy\) = ∫₀¹ yn(1-y)ⁿ⁻¹dy = 1/n+1

Hence, Maximum = n/n+1 and Minimum = 1/n+1

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By treating the,, >, or sign as a = sign, the inequality can be shown graphically. Make a dotted line graph of the equation if the inequality is either or.

For a 125-pound individual, a 30-minute hard stationary bike workout burns roughly 315 calories, 378 calories for a 155-pound individual, and 441 calories for a 185-pound someone. You will burn even more calories if your weight is higher.

According to the American Council on Exercise (ACE), you should cycle for at least 30 minutes at a time at a moderately strenuous intensity if you want to lose weight. You'll want to pedal for longer to burn even more calories. The ACE also advises combining two exercises into one cross-training session to speed up weight loss.

Treat the,, >, or sign as a = sign when graphing an inequality, and then graph the equation. The equation should be plotted as a dotted line if the inequality is either or.

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Answer:

−3 < −1

−3 ≤ −1

Step-by-step explanation:

Symbol explanation

A negative number is any number that is less than zero.

On the number line the negative numbers are to the left of the zero.

-3 is less than -1 because -3 lies to the left of -1 on the number line.

Therefore, the only given inequalities that are true statements are:

16% of students use the internet for longer than 402 minutes per day.

Standard Deviation: A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out. Consider the data set: 2, 1, 3, 2, 4. The mean and the sum of squares of deviations of the observations from the mean will be 2.4 and 5.2, respectively. Thus, the standard deviation will be √(5.2/5) = 1.01.

The majority of people (68%) are within one standard deviation of the mean.

The median is within two standard deviations of 95% of the population.

The median and three standard deviations are shared by 99.7% of the population.

The percentage will be shown as follows:

P(X > 402) = P(X > 30 + 1 × 102)

= (1-0.68) / 2

= 0.32/2

= 16%

16% of students use the internet for longer than 402 minutes per day.

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The resistance of the automotive service is 2.4 ohms

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

Voltage: 120 v

Current: 50 amps

Rewrite properly as

V = 120 volts

I= 50 Amps

The value of the resistance can be calculated using the following voltage equation

V = IR

Where R is the resistance

Male R the subject

R = V/I

Substitute the known values in the above equation, so, we have the following representation

R = 120/50

Evaluate

R =  2.4 ohms

Hence, the value of R is 2.4 ohms

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Answer:

Option D!

Step-by-step explanation:

The volume of the solid obtained by revolving the region enclosed by x = sqrt(y) and y = 2x about the y-axis is (32π/5) cubic units.

To find the volume of the solid, we can use the method of cylindrical shells. We consider an infinitesimally thin strip of width dy along the y-axis. As we revolve this strip around the y-axis, it forms a cylindrical shell with radius x and height 2x.

The range of y-values that encloses the region can be determined by setting the equations x = sqrt(y) and y = 2x equal to each other. Solving for y, we get y = 4.

Now, we need to express the radius and height of the cylindrical shell in terms of y. From the equation x = sqrt(y), we can rearrange it to get x = \(y^(^1^/^2^)\). Therefore, the radius of the cylindrical shell is \(y^(^1^/^2^)\), and the height is \(2y^(^1^/^2^)\).

The volume of each cylindrical shell is given by the formula V = 2πrh, where r is the radius and h is the height. Substituting the values, we have V = 2π\((y^(^1^/^2^)\))(\(2y^(^1^/^2^)\)) = 4πy.

To find the total volume of the solid, we integrate the volume expression over the range of y-values, which is from 0 to 4. Thus, the integral becomes ∫(0 to 4) 4πy dy.

Evaluating the integral, we have [2π\(y^2\)] from 0 to 4, which equals 2π(\(4^2\)) - 2π(\(0^2\)) = 32π.

Therefore, the volume of the solid is (32π/5) cubic units.

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Answer:

-3x³ + 26x² + 2x - 12

Step-by-step explanation:

(3x−2)(−x^2+8x+6)

= -3x³ + 24x² + 18x + 2x² - 16x - 12

= -3x³ + 26x² + 2x - 12

So, the answer is -3x³ + 26x² + 2x - 12

True. Periodic functions can indeed be represented by a harmonically related series of sines and cosines. This representation is known as the Fourier series, which expresses a periodic function as a sum of sine and cosine functions with different frequencies and amplitudes. By appropriately choosing the coefficients of these sine and cosine terms, a periodic function can be accurately approximated or represented.

Periodic functions can be represented by a harmonically related series of sines and cosines, known as the Fourier series. This mathematical representation expresses a periodic function as a sum of sine and cosine functions with different frequencies and amplitudes. By adjusting the coefficients of these harmonically related terms, the Fourier series can accurately approximate or represent the original periodic function. This concept is widely used in various fields, including mathematics, physics, signal processing, and engineering, as it allows for the analysis, manipulation, and synthesis of periodic phenomena. The Fourier series provides a powerful tool for understanding and working with periodic functions, enabling the decomposition of complex periodic signals into simpler harmonic components.

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The given matrix is a 2x2 matrix. The indicated element is 3A, which is located in the first row and second column of the matrix.

The given matrix has two rows and two columns, which means it is a 2x2 matrix. Each entry in the matrix is separated by a comma, and each row is separated by a semicolon. The matrix is written in the standard form [a11, a12; a21, a22], where a11 represents the element in the first row and first column, a12 represents the element in the first row and second column, a21 represents the element in the second row and first column, and a22 represents the element in the second row and second column.

The indicated element is 3A, which means that there is a variable A being multiplied by 3. This element is located in the first row and second column of the matrix, which means that it corresponds to the entry a12. Therefore, we can write the matrix as [9, 3A; 0, 5], where A is some unknown value.

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Answer:

b

Step-by-step explanation:

180 minus 82

$13.35 rougly around that

Answer: $51.48

Step-by-step explanation:

If a $52 item is marked up by 10%, its new price will be:

$52 + 10% of $52 = $52 + $5.20 = $57.20

Then, if this new price is marked down by 10%, the final price will be:

$57.20 - 10% of $57.20 = $57.20 - $5.72 = $51.48

Therefore, the final price of the item after the markup and markdown is $51.48.

Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

To determine which planks Amanda should use to build the triangular-shaped kennel:

Therefore, Amanda would use 3 planks of lengths 3 feet, 5 feet, and 6 feet.

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Answer:

hope I help

hope I help hope I help hope I help hope I help

Answer:

143 over 428

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of a line which passes through (x₁, y₁) and with slope of m in point-slope form:

                            y - y₁ = m(x - x₁)

m = -5

(-2, 7)    ⇒   x₁ = -2,  y₁ = 7

y - 7 = -5(x - (-2))

y - 7 = -5(x + 2)            

(a, 2)   ⇒   2 - 7 = -5(a + 2)

                   -5 = -5a - 10

                   5a = 5 - 10

                     5a = -5

                       a = -1

Answer:

58 square units

Step-by-step explanation:

Take the shaded figure as a full larger rectangle minus the rectangular part which is not shaded.

Area of the full larger rectangle:

Area = length × width

Length = |12 - 2| = 10 units

Width = |8 - 1| = 7 units

Area = 10 × 7 = 70 units²

Area of the unshaded small rectangle:

Length = |10 - 4| = 6 units

Width = |3 - 1| = 2 units

Area = 6 × 2 = 12 units²

Area of the shaded figure = 70 - 12 = 58 square units