At Supply World, 4 pens cost $10.00. How much do 3 pens cost if the price per pen is the same

The cube root of -2i,

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

We can represent -2i in polar form as,

r(cosθ + i sinθ)

by computing its magnitude and angle.

The magnitude of -2i is 2

Since the absolute value of any imaginary number is equal to its magnitude.

To find the angle θ,

We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case,

The opposite side is -2 and the adjacent side is 0.

Therefore, we have tanθ = -2/0, which is undefined.

However,

We can use the fact that the cube root of a complex number is equal to the cube root of its magnitude times exp(iθ/3) to find the cube root of -2i.

So, the cube root of -2i is equal to the cube root of 2 times exp(iθ/3).

Now, we need to find the value of θ/3. Since θ is undefined,

we will represent it as π/2 + 2πn,

where n is any integer.

So, θ/3 = (π/2 + 2πn)/3 = π/6 + 2πn/3.

Therefore, the cube root of -2i is equal to

⇒  ∛2 [ cos(π/6 + 2πn/3) + i sin(π/6 + 2πn/3) ]

Now put n = 0

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

This is the final form of the cube root of -2i in the required form.

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Answer:

-1/4xy+y=0

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Parallel lines are the lines that do not intersect or meet each other at any point in a plane. They are always parallel and are at equidistant from each other. Parallel lines are non-intersecting lines. We can also say Parallel lines meet at infinity.

In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle. A line is said to be perpendicular to another line if the two lines intersect at a right angle or 90 degrees.

Answer:

The total weight is 10 tons

Step-by-step explanation:

Answer:

70%

Step-by-step explanation:

Answer:

The probability of rolling a number greater than 2 two times in a row is arond 0.44

Step-by-step explanation:

Divide the number of events by the number of possible outcomes. This will give us the probability of a single event occurring. In the case of rolling a 3 on a die, the number of events is 1 (there's only a single 3 on each die), and the number of outcomes is 6.

Probability formula is the ratio of number of favorable outcomes to the total number of possible outcomes. Measures the likelihood of an event in the following way: - If P(A) > P(B) then event A is more likely to occur than event B. - If P(A) = P(B) then events A and B are equally likely to occur.

Answer:

The cost price of 250 grams of super mix cocoa is Kshs.650/1.3=Kshs.500.

The cost price of 1 kg of super mix cocoa is Kshs.500*4=Kshs.2000.

If x kg of cocoa A is mixed with (1-x) kg of cocoa B, then the cost price of the mixture is Kshs.1800x+Kshs.2400(1-x).

Therefore, Kshs.1800x+Kshs.2400(1-x)=Kshs.2000.

Solving for x, we get x=2/3.

Therefore, the cocoa types A and B are mixed in the proportion 2:1.

Answer:

D

Step-by-step explanation:

8×16=128

2×4=8

128+8=136m^2

answer: D

Therefore, the price of the stock based on the dividend discount model is $16.77.

A discount is a reduction in the price of a product or service that is typically offered to customers in order to encourage them to make a purchase. Discounts are usually expressed as a percentage off the original price, and can be offered for a variety of reasons, such as to clear out inventory, reward customer loyalty, or attract new customers.

Given by the question.

Using the dividend discount model, we can find the price of the stock based on the information given:

P0 = D1 / (rs - g)

Where:

D0 = $1.19 (the dividend just paid)

g = 5.87% (the constant annual growth rate in dividends)

rs = 15.14% (the required rate of return)

First, we need to find D1, the dividend expected one year from now:

D1 = D0 * (1 + g) = $1.19 * (1 + 0.0587) = $1.26

Now we can use the formula to find P0:

P0 = $1.26 / (0.1514 - 0.0587) = $16.77

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Answer:

See below!

Step-by-step explanation:

Let the two numbers be x and y

x + y = 66 ----------------(1)

2x = y + 15

2x - y = 15 ---------------(2)

Add both equations

x + y + 2x - y = 66 + 15

x + 2x = 66 + 15

3x = 81

Divide both sides by 3

Put x = 27 in Eq. 1

27 + y = 66

Subtract 27 to both sides

y = 66 - 27

\(\rule[225]{225}{2}\)

For the information given in the statement you have

Then

That is, to find the nth term, use the immediately previous term already found

Therefore, the sixth term of the sequence is

Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

Answer:

2

Step-by-step explanation:

Answer:

x = 10

Step-by-step explanation:

The hypotenuse of  each of the triangles have to be equal

7x -5 = 4x+25

Subtract 4x from each side

7x -4x-5 = 4x+25-4x

3x -5 = 25

Add 5 to each side

3x-5+5 = 25+5

3x= 30

Divide by 3

3x/3 = 30/3

x = 10

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer:

For this case we know that the random variable of interest would be X and the distribution for X is given by:

\( X \sim Bin (n,p)\)

And by properties of this distribution the expected value for this case is:

\( E(X)= np\)

And the variance :

\( Var(X)= np(1-p)\)

Step-by-step explanation:

For this case we know that the random variable of interest would be X and the distribution for X is given by:

\( X \sim Bin (n,p)\)

And by properties of this the expected value for this case is:

\( E(X)= np\)

And the variance :

\( Var(X)= np(1-p)\)

The inequality value that would be able to show/x/ ≤ 5 is option A

In mathematics, inequality refers to a mathematical statement that expresses a relationship between two quantities, indicating that one quantity is greater than, less than, or not equal to the other.

The symbol that we have  is telling us that the value of the x would be less than  or it would be seen to be equal to five.

We can see that /x/ ≤ 5 would exclude the negative values and this can be seen in the option that is marked option A

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It has taken me 32 minutes to drive 48 km. If the total length of my journey is 146 km and I maintain the same speed,  then you can estimate that you will be driving for approximately 65.344 minutes longer to complete the remaining 98 km of your journey.

To estimate how much longer you will be driving for, we can use the concept of proportionality. We know that the time taken to drive 48 km is 32 minutes. Let's use this information to find the time it would take to drive 146 km.

We can set up a proportion to find the time:

(time taken for 48 km) / (48 km) = (time taken for 146 km) / (146 km)

Let's solve for the time taken for 146 km:

(time taken for 146 km) = (time taken for 48 km) * (146 km / 48 km)

Substituting the given values:

(time taken for 146 km) = 32 minutes * (146 km / 48 km)

Calculating the value:

(time taken for 146 km) ≈ 32 minutes * 3.042

(time taken for 146 km) ≈ 97.344 minutes

Therefore, it would take approximately 97.344 minutes to drive 146 km at the same speed.

To estimate how much longer you will be driving for, we can subtract the initial time of 32 minutes from the estimated time of 97.344 minutes:

Additional time = 97.344 minutes - 32 minutes

Additional time ≈ 65.344 minutes

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Answer:

9 13/28

Step-by-step explanation:

Add whole numbers

Change bottom number of fraction to common factor

add

figure out how much is leftover

done!

Answer: 9 13/28

Step-by-step explanation:

First turn your mixed numbers into improper fractions. 6 3/4 becomes 27/4 and 2 5/7 becomes 19/7. Now we need to make the denominators match. The least common multiple of 7 and 4 is 28. 27/4 becomes 189/28 and 19/7 becomes 76/28. We can now add these to get 265/28. This improper fraction can now be turned back into a mixed number. 28 will go into 265 evenly 9 times with 13 left over. Answer is 9 13/28

The linear function that describes the distance (in miles) is therefore y = 65x + 80

We have to find the slope and the intercept in other to get the linear function

The data points are:

(1, 145) and (3, 275).

m = (y2 - y1) / (x2 - x1)

fixing the data points we have

m = (275 - 145) / (3 - 1)

= 130 / 2

= 65

y = mx + b

(1, 145):

145 = 65(1) + b

b = 145 - 65

= 80

y intercept is 80

The linear function is therefore y = 65x + 80

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The characteristic polynomial  x³ - 7x² + 16x - 12  The characteristic polynomial of a square matrix in linear algebra is a polynomial that is invariant under matrix similarity and has the eigenvalues as roots.

Its coefficients include the determinant and the trace of the matrix.

Characteristic polynomial of a 3×3 matrix A is given by ; x³ - trace(A)x² + (A​​​​​​11 + A​​​​​​22 + A​​​​​​33 )x - determinant(A)

Where A​​​​​​ii is the determinant of the matrix obtained by deleting i​​​​​​ th row and i th column.

Here trace(A) = sum of the diagonals = 12 - 7 + 2 = 7

A​​​​​​11 = -7 × 2 = -14

A​​​​​​22 = 2 × 12 = 24

A​​​​​​33 = ( 12×-7) - (-10×9) = 6

Determinant(A) = 12(-7×2 - 0) + 10(2×9 - 0) = 12

Substituting these values in above equation , we obtain;

x³ - 7x² + (-14 + 24 + 6)x - 12 = x³ - 7x² + 16x - 12.

Hence x³ - 7x² + 16x - 12 is the characteristic polynomial of A.

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Answer: X + 3

Step-by-step explanation:

Sum hints as to an addition statement and it specifies a variable X and the number 3 so the expression would be X + 3.

SUM MEANS ADDITION

HERE IT MEANS THE ADDITION OF x and 3

written as

\(x + 3\)

HOPE THIS HELPS

The coordinates of the vertices of a quadrilateral RFGH E (1, 2), F (1, -1),

G (-2,-2), and H (-2, 2) after being translated 5 units to the right and then 5 units down to create quadrilateral E'F'G'H', now are E' (6, 7), F' (6, 4), G' (3, 3) and H' (3, 7).

To solve this question, we will need to have basic idea about coordinate geometry quadrants, i.e.,

If a point is translated 5 units to the right, its distance from the y-axis will increase by 5 but its distance from the x-axis will remain the same.

And If a point is translated 5 units downwards, its distance from the y-axis will remain same but its distance from the x-axis decrease by 5.

Using the above fundaments, we will individually find out the new positions of all the four vertice points of the quadrilateral.

E (1, 2) after being translated 5 units to the right will become [(1+5), 2] or (6,2) and further being translated 5 units downwards will become

[6, (2+5)] or, (6, 7). Therefore, E' will be (6, 7).

F (1, -1) after being translated 5 units to the right will become [(1+5), -1] or (6,-1) and further being translated 5 units downwards will become

[6, (-1+5)] or, (6, 4). Therefore, F' will be (6, 4).

G (-2, -2) after being translated 5 units to the right will become [(-2+5), -2] or (3, -2) and further being translated 5 units downwards will become

[3, (-2+5)] or, (3, 3). Therefore, G' will be (3, 3).

H (-2, 2) after being translated 5 units to the right will become [(-2+5), 2] or (3, 2) and further being translated 5 units downwards will become

[3, (2+5)] or, (3, 7). Therefore, H' will be (3, 7).

Hence, The coordinates of the vertices of a quadrilateral RFGH E (1, 2), F (1, -1), G (-2,-2), and H (-2, 2) after being translated 5 units to the right and then 5 units down to create quadrilateral E'F'G'H', now are E' (6, 7), F' (6, 4), G' (3, 3) and H' (3, 7).

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The applied overhead cost for job 201 is $36,000 and total cost for job 201 under direct materials cost as allocation base is $86,000.

Allocation base is a technique utilized in accounting to designate the cost of something to its use or product to recognize the price of the finished product.

Example provides the total overhead cost at $120,000 for the period, the base data of $100,000 direct material cost and 500 direct labor hours. The base data are used to calculate the predetermined factory overhead rate, which is used to apply overhead costs to work in progress.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the base data. The predetermined factory overhead rate is multiplied by the actual activity in the allocation base to obtain the applied overhead cost.

Direct materials cost as allocation base $30,000 is the actual direct material cost used in job 201. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct material cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $30,000*120% = $36,000.

Total cost for job 201 under direct materials cost as allocation base is $30,000+$20,000+$36,000 = $86,000.

-Direct labor cost as allocation base:

The actual direct labor cost used in job 201 is $20,000. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $20,000*120% = $24,000.

Total cost for job 201 under direct labor cost as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Direct labor hours as allocation base:

The actual direct labor hours used in job 201 is 400 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor hours, which is $120,000/500 hours = $240 per hour.The applied overhead cost for job 201 is $240*400 hours = $96,000.

Total cost for job 201 under direct labor hours as allocation base is $30,000+$20,000+$96,000 = $146,000.

-Physical output as allocation base: The actual output in units completed for job 201 is 2,000 shirts.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the output in units, which is $120,000/10,000 units = $12 per unit.

The applied overhead cost for job 201 is $12*2,000 units = $24,000.Total cost for job 201 under physical output as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Machine hours as allocation base: The actual machine hours used in job 201 is 240 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the machine hours, which is $120,000/5,000 hours = $24 per hour.

The applied overhead cost for job 201 is $24*240 hours = $5,760.

Total cost for job 201 under machine hours as allocation base is $30,000+$20,000+$5,760 = $55,760.

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The height of the larger cone is 71.13 meters

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

Using the above as a guide, we have the following:

Scale factor = h1/h2

So, we have

h1/h2 = √(1883/7352)

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

36/h2 = √(1883/7352)

So, we have

h2 = 36 * √(7352/1883)

Evaluate

h2 = 71.13

Hence, teh height is 71.13

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Answer:

The length of the hypotenuse is 100.

Step-by-step explanation:

To find the length of the hypotenuse, we use the following formula:

c=\(\sqrt{a^2+b^2}\)

c=\(\sqrt{28^2+96^2}\)

c=\(\sqrt{10,000}\)

c=100

Therefore, the length of the hypotenuse is 100.

Answer:

2.7

Step-by-step explanation:

2.7 is the answer

You are welcome

The equation y² - y²x = 6  can be describe as a function of x as:

y = √(6/(x - x)).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

y² - y²x = 6

Taking y² as common.

y²(1 - x) = 6

Divide both sides with (1 - x).

y² = 6/(1 - x)

Square root on both sides.

y = √(6/(x - x))

This is a function of x.

Thus,

y = √(6/(x - x)) is a function of x.

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Answer:

infinitely many solutions.

Step-by-step explanation: