Joy Co. allocates overhead expenses to all departments on the basis of floor space (sq. ft.) occupied by each department. This year total overhead expenses were $22,000. Department A. occupied 15,000 sq. ft., Department B. 18,000 sq. ft., and Department C. 9,000 sq. ft. The amount of overhead allocated to Department B is (round to the nearest dollar):
How do you add subtract multiply and divide complex numbers and polynomials
Final answer:
To operate on complex numbers, add or subtract real and imaginary parts separately, multiply using the distributive property, and divide by multiplying by the conjugate of the denominator. Polynomial operations similarly involve combining like terms, using the distributive property, and performing long or synthetic division.
Explanation:
Adding, Subtracting, Multiplying, and Dividing Complex Numbers and Polynomials
To add complex numbers, combine the real parts and the imaginary parts separately. For example, (3 + 2i) + (1 + 4i) = (3 + 1) + (2i + 4i) = 4 + 6i. For subtracting complex numbers, similarly subtract the real and imaginary parts: (3 + 2i) - (1 + 4i) = (3 - 1) + (2i - 4i) = 2 - 2i.
To multiply complex numbers, use the distributive property (FOIL), and remember that i² = -1. For instance, (3 + 2i)(1 + 4i) = 3 + 12i + 2i + 8i² = 3 + 14i - 8 = -5 + 14i.
For dividing complex numbers, multiply the numerator and the denominator by the conjugate of the denominator to rationalize it. For example, (3 + 2i) ÷ (1 + 4i), multiply numerator and denominator by (1 - 4i) to get [(3 + 2i)(1 - 4i)] ÷ [(1 + 4i)(1 - 4i)] = (3 - 12i + 2i - 8i²) ÷ (1 - 16i²) = (11 - 10i) ÷ 17 = (11÷ 17) - (10i÷ 17).
Polynomial operations are similar, but instead of imaginary units, we work with variables. For adding polynomials, combine like terms. For subtracting polynomials, change the sign of each term in the polynomial being subtracted and combine like terms. Multiplying polynomials also requires the distributive property, and for division, you can use either long division or synthetic division depending on the polynomials involved.
Hermina cut a 10" by 15" piece of cardboard down the diagonal
Hermina can calculate the length of the diagonal on her 10" by 15" rectangle of cardboard by using the Pythagorean theorem. The formula states that the square of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides, the length and the width. Thus, by inputting the values into the formula, we get a diagonal length of about 18.03".
Explanation:The question involves calculating the length of the diagonal on a rectangular piece of cardboard. In mathematics, the Pythagorean theorem is used to calculate the length of a diagonal. In this case, the length and width of the rectangle are given as 10" and 15" respectively. We can apply the theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The diagonal here acts as the hypotenuse, with the other two sides being the length and width of the rectangle. Therefore, the length of the diagonal is the square root of the sum of squares of these sides, which would be sqrt(10^2 + 15^2), resulting in approximately 18.03".
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American car makers produce 5,650,000 cars each year. In a report, Ben wrote that Americans made 6,550,000 cars. What mistake did Ben make? How can he fix it? Find the error.
Can someone please help me? person who helps gets brainly
−5r+8r+5
What is the verbal expression of 23f
Multiply (2.4 ⋅ 1014) ⋅ (4 ⋅ 107). Express the answer in scientific notation. 9.6 ⋅ 1021 9.6 ⋅ 1022 96 ⋅ 1021 96 ⋅ 1022
Answer:
9.6 × [tex]10^{21} )[/tex].
Step-by-step explanation:
Given : Multiply [tex](2.4 * 10^{14} ) * ( 4 *10^{7} )[/tex].
To find : Express the answer in scientific notation.
Solution : We have given that
[tex](2.4 * 10^{14} ) * ( 4 *10^{7} )[/tex].
Combine the like terms
(2.4 * 4 )( [tex](10^{14} ) (10^{7} )[/tex].
By the exponent same base rule : if the base of two exponent are same then exponent will be add.
9.6 × [tex]10^{14 + 7} )[/tex].
9.6 × [tex]10^{21} )[/tex].
Therefore, 9.6 × [tex]10^{21} )[/tex].
What is the solution to this system of equations?
a fellow classmate tosses 4 coins and finds that 3 of them come up tails. Which of the following is the best conclusion for her to come to?
A. She needs to keep flipping the coins until she gets a 50% in heads to determine if they are fair.
B. The coins are unfair
C. This could easily happen with a fair coin after only 4 flips
D. If she flips the coins one more, they will all come up heads
Answer:
Option C -This could easily happen with a fair coin after only 4 flips.
Step-by-step explanation:
Given : A fellow classmate tosses 4 coins and finds that 3 of them come up tails.
To find : Which of the following is the best conclusion for her to come to?
Solution :
According to statement,
A fellow classmate tosses 4 coins and finds that 3 of them come up tails.
This could be happen when coin is tossed or flip 4 times and the coin must be fair.
As when we flip 4 coins the possible outcomes were
HHHH THHH HTHH TTHH
HHHT THHT HTHT TTHT
HHTH THTH HTTH TTTH
HHTT THTT HTTT TTTT
So, The best conclusion for her is Option C
This could easily happen with a fair coin after only 4 flips.
Olga saves $15 from every paycheck to save up for a new game system that cost $399. Currently, she has $360 saved. Ignoring the purchase, how many more paychecks does she have until she has enough money saved to buy the game system
Working alone, Ryan can dig a 10 ft by 10 ft hole in five hours. Castel can dig the same hole in six hours. How long will it take them if they worked together?
Explain too please, thanks.
How can you use the number line in picture it to figure out how many miles Tim travels from home to school
PLZ Help
The tables show the cost of different numbers of t-shirts ordered at two different stores, Store A and Store B:
Store A
Number
of T-shirts Cost (in $)
2 $6
4 $12
8 $24
Store B
Number
of T-shirts Cost (in $)
3 $12
6 $24
9 $36
Which of these explains which store has a better buy?
Store A, because the ratio of the number to the cost is 3:1 in Store A and 4:1 in Store B
Store B, because the ratio of the number to the cost is 2:8 in Store A and 3:15 in Store B
Store B, because the ratio of the number to the cost is 8:2 in Store A and 15:3 in Store B
Store A, because the ratio of the number to the cost is 1:3 in Store A and 1:4 in Store B
Answer:
The last one.
Step-by-step explanation:
I tried it and got it right. Bye. If it helped please let me know. Also if u need anymore help try reaching out to me.
NEED HELP FAST!
3.
(08.01 MC)
The graph shows two lines, A and B:
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B? (1 point)
(3, 4) is the solution to both lines A and B.
(3, 4) is the solution to line A but not to line B.
(0, 2) is the solution to both lines A and B.
(0, 2) is the solution to line A but not to line B.
Answer:
(3,4) For both
Both lines meet up at that point. X is the thicker ones in the middle going across the graph while y is upward.
(x,y)
Boundary Peak in Nevada is 13,000 feet high. Guadalupe Peak in Texas is 8,749.75 feet high. How much higher than Guadalupe Peak is Boundary Peak? Round your answer to match the less precise measurement.
Answer:
The Boundary peak is 48.58% higher than Guadalupe peak.Step-by-step explanation:
Givens:
Boundary Peak is 13,000 ft high.Guadalupe Peak is 8,749.75 high.To know how much higher is Boundary Peak than Guadalupe peak, we only need to subtract:
Boundary Peak - Guadalupe peak = 13,000 - 8,749.75 = 4250.25 m.
However, the best way to represent this is to express it in percentage. To do that, we need to use the rule of three. If 100% is 8749.75, what percentage would be 13000:
[tex]13000m\frac{100\%}{8749.75m}=148.58 \%[/tex]
Therefore, the Boundary peak is 48.58% higher than Guadalupe peak.
Hilary wants to fill a mini cake pan with batter to make a mini cake for Phillip's party. The cake pan is 4.0 inches long, 9.0 inches wide, and 2.2 inches deep. What is the volume of the cake pan?
The volume of the cake pan Hilary wants to use is calculated using the formula for the volume of a rectangular prism. With dimensions of 4.0 inches by 9.0 inches by 2.2 inches, the volume is 79.2 cubic inches.
To find the volume of the cake pan that Hilary wants to use for making a mini cake for Phillip's party, we need to use the formula for the volume of a rectangular prism, which is Volume = length × width ×height. Given the dimensions of the cake pan are 4.0 inches long, 9.0 inches wide, and 2.2 inches deep, we can calculate the volume as follows:
Volume = length × width × height
Volume = 4.0 in× 9.0 in × 2.2 in
Volume = 79.2 in³
Therefore, the volume of the cake pan is 79.2 cubic inches.
Write 12c+10 as an equivalent expression with one term
In the polynomial below, what number should replace the question mark to produce a difference of squares?
I need help with this math problem _:5=72:30
i need to fill in the blank
What is the sum of 2/5 and 2/4
An elephant can run one over four mile in 36 seconds. Which of the following correctly shows this rate as miles per hour?
thirty-six seconds over one-fourth mile = 25 miles per hour
one-fourth mile over thirty-six seconds = 144 miles per hour
one-fourth mile over thirty-six seconds = 25 miles per hour
thirty-six seconds over one-fourth mile = 144 miles per hour
Answer:
The answer is 1/4 mile over 36 seconds = 24 miles per hour
Step-by-step explanation: I hope this helps :)
5+ 1/7b = -2
whats be and explanation
(don't get it cause its a fraction)
A regular octagon has side lengths of 11 centimeters. Determine the perimeter of the octagon. 66 cm 77 cm 88 cm 99 cm
an octagon has 8 sides
the perimeter would be 8 x length of side
8x11 = 88 cm
Answer:
8*11 = 88 cm
Step-by-step explanation:
simple
The average number of rainy days in Seattle, Washington is listed below: Month January February March April Rainy days 18 16 17 14 If the data was only accurate to the tens place, which month's rainy day total would be different from the others?
Answer: April's rainy days are different from the others.
Step-by-step explanation:
Since we have given that
Months Rainy days
January 18
February 16
March 17
April. 14
When we round the rainy days to nearest tens then we get that
January has 20 rainy days
February has 20 rainy days.
March has 20 rainy days.
But April has 10 rainy days.
So, April's rainy days is different from others.
b(n)=4−6(n−1) Find the 4th term in the sequence.
Answer:
-14
Step-by-step explanation:
answer on khan
A password is 4 characters long and must consist of 3 letters and 1 of 10 special characters. If letters can be repeated and the special character is at the end of the password, how many possibilities are there? a. 175,760
1st character = 26 possibilities ( 26 letters in the alphabet)
2nd character = 26 possibilities
3rd character = 26 possibilities
4th character = 10 ( 10 special characters)
26 x 26 x 26 x 10 = 175,760 combinations
How to factor a polynomial when the leading coefficient isn't 1
Final answer:
To factor a polynomial with a leading coefficient that isn't 1, use the ac method or factoring by grouping, identify common factors, and check your work by expanding the factors.
Explanation:
When factoring a polynomial with a leading coefficient that isn't 1, you should consider each term, and factor out any common factors first. If the polynomial is a quadratic, for instance, with a leading coefficient greater than 1, you can use techniques such as the ac method or factoring by grouping. The ac method involves finding two numbers which multiply to give you the product of the leading coefficient and the constant term, and add up to the middle term's coefficient. Once you have these numbers, you can rewrite the middle term and then factor by grouping.
Step-by-Step Explanation
Identify the leading coefficient, the constant term, and the middle term's coefficient.Find two numbers that multiply to the product of the leading coefficient and the constant term, and add to the middle term's coefficient.Rewrite the middle term using the two numbers found in step 2, splitting it into two terms.Factor by grouping, which involves pairing off the terms in such a way that they have a common factor, and then factoring out the greatest common factor from each pair.If you have factored correctly, you should be able to factor out an additional term from the resulting expression, resulting in a factored polynomial.Simplify further if possible, and check your answer by expanding the factors to ensure you get the original polynomial.Lily is 14 older than her little brother Ezekiel. In 8 years, Lily will be twice as old as Ezekiel will be then. What is Lily and Ezekiel's combined she?
The combined age of Lily and Ezekiel is 42.
Lily is 14 older than her little brother Ezekiel. In 8 years, Lily will be twice as old as Ezekiel will be then. What is Lily and Ezekiel's combined To be determined.
In mathematics it deals with numbers of operations according to the statements.
Let the age of lily be L and the gare of her brother Ezekiel is E.
Lily is 14 older than her little brother Ezekiel.
L = 14 + E - - - - - -(1)
In 8 years, Lily will be twice as old as Ezekiel will be then.
L = 2(E)
put L in equation 1.
2E = 14 + E
2E - E = 14
E = 14
Now put E in equation 1
L = 14 + 14
L = 28
Combined age of Lily and Ezekiel's = 28 + 14
= 42
Thus, the combined age of Lily and Ezekiel's is 42.
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Round this number to the nearest 1,000 25,386
Round this number to the nearest 100,000 5,370,288
Round this number to the nearest 10,000 7,298,341
Round this number to the nearest 1,000,000 6,289,002
I know thi is a lot but please pretty pleas this is the hardest one:(
identify the following probability as theoretical or empirical. After tossing the same coin 10 times, you are surprised to find that tails has come up 8 times. You therefore conclude that this coin is not fair and that the probability of getting tails with this coin is 0.80. A. Empirical B. Theoretical
Answer:
A. Empirical
Step-by-step explanation:
Theoretical probability is defined as a probability which is based on reasoning. This is written in a ratio form - of the number of favorable outcomes to the number of possible outcomes.
And the empirical probability gives an estimation of an event occurring based on how often that event occurred after collecting the data from large number of trials.
So, based on the definitions, the given scenario is empirical or experimental probability.