Robert is looking to buy a deep fryer. He has narrowed his search down to two models. The following table gives the details of the prices, cost per use in electricity and oil, and lifespan of the two models Robert is considering to purchase. Brand Brand P Brand Q Price $144. 00 $37. 50 Avg. Cost/Use $0. 49 $0. 75 Lifespan 6 years 2 years Robert plans on using his deep fryer about eight times per month. After six years, which brand will have the lower lifetime cost, and by how much? Hint: Assume that either deep fryer can be repurchased at the same price, if needed to provide the desired length of service. A. Brand P will be $118. 26 cheaper than Brand Q. B. Brand P will be $149. 76 cheaper than Brand Q. C. Brand Q will be $184. 50 cheaper than Brand P. D. Brand Q will be $31. 50 cheaper than Brand P.

Answer:

153

Step-by-step explanation:

i = square root of -1

i = √-1

(3+12√-1) (3-12√-1)

√a times √b = √ab

a√b times c√d = (a times c) √ (b times d)

9 - (36√-1) + (36√-1) - (144(√-1)^2) =

9 - 0 - (144 * -1) =

9 - 0 - (-144) =

9 - (-144) =

9 + 144 =

153

*** funny thing is if you put

(3+12i) (3-12i)  

in a calculator

it works!

it gives you the answer 153

another way:

Expand the expression using

(a-b) (a+b) =

a²-b² :

3²-(12i)²

Simplify using exponent rule with same exponent

(a*b)^n =

a^n*b^n:

3²-12²* i²

Calculate the power:

9-144* i²

Rewrite by definition

i²=-1:

9–144×(−1)

Calculate the product or quotient: 9+144

Calculate the sum or difference: 153

Answer: 153

gathmath

The 41th term of the arithmetic sequence is 66.

Arithmetic sequences are those that contain these patterns. The difference between successive terms in an arithmetic series is constant. Because the difference between consecutive words is always two, the sequence 3, 5, 7, and 9 is an example of arithmetic.

[tex]a_{n}=a_{1}+(n-1)d[/tex]

[tex]a_n[/tex] =   the nᵗʰ term in the sequence.

[tex]a_1[/tex] =  the first term in the sequence.

d    =   the common difference between terms.

Finding arithmetic sequence for the nth term:

aₙ = a₁ + (n-1)d

d = the common difference

a₇ = a₁ + (7-1)d

34 = 5 + 6d

29 = 6d

d = 29/6

Now ,

Finding the  41st term of the arithmetic sequence.

a₄₁ = a₁ + (n-1)d

   = 5 + (41-1)d

   = 5 + 40d

   = 5 + 40(29/6)

   = (198)* 1/3

  =  66

The 41th term of the arithmetic sequence is 66.

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The total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape

The two cubes are stacked upon one another, so they form a composite figure.

The side lengths of the cubes are given as

Cube 1 = 4p

Cube 2 = 2q^2

The volume of each cube is calculated as:

Volume = Side length^3

So, the total volume is

Total = (4p)^3 + (2q^2)^3

Evaluate the exponents

Total = 64p^3 + 8q^6

Using the sum of cubes, we have the factored form to be

Total = (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

Hence, the total volume of the cubes in factored form is  (4p + 2q^2)(16p^2 -  8pq^2 + 4q^4)

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Complete question

A cube with side length 4p is stacked on another cube with side length 2q^2. What is the total volume of the cubes in factored form?

The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11

As a general rule, we have:

f⁻¹(f(x)) = x

Substitute 58 for x

So, we have:

f⁻¹(f(58)) = 58

Hence, the value of f⁻¹(f(58)) is 58

Also, we have:

f(f(5))

From the table, we have:

f(5) = 9

So, we have:

f(f(5)) = f(9)

From the table, we have:

f(9) = 11

So, we have:

f(f(5)) = 11

Hence, the value of the function f(f(5)) is 11

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Answer:

2x - 3

Step-by-step explanation:

10x²-23x+ 12 ÷ 5x-4

Answer:

2x - 3

Step-by-step explanation:

[tex](5x-4)(2x-3)=10x^{2} -23x+12[/tex]

Hope this helps

The volume of the cone based on the figure illustrated wil be 196cm³.

The information is incomplete and the complete question wast found online. An overview will be given.

Let's assume that the height is 4cm and the radius of the cone is 7cm. The volume of the cone will be:

= 1/3πr²h

= 1/3 × 3.14 × 7² × 4

= 196cm³

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In the graph, the constant of proportionality is 40

From the question, we are to determine the constant of proportionality

The constant of proportionality = [tex]\frac{y}{x}[/tex]

From the graph, a point on the line is (1, 40)

That is,

When x = 1 and y = 40

Thus,

The constant of proportionality = [tex]\frac{40}{1}[/tex]

Constant of proportionality = 40

Hence, the constant of proportionality is 40

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Answer:

40

Step-by-step explanation:

The constant of proportionality is 40/1 which equals 40.

Answer:

By 3.

Step-by-step explanation:

-12-3=-15

Hope this helps!

Answer:

-12 exceeds -15 by 3

Step-by-step explanation:

To find out by how much a exceeds b, subtract a - b.

For example, by how much does 8 exceed 6?

Here, a = 8 and b = 6.

a - b = 8 - 6 = 2

2 is correct since we know that 8 is 2 greater than 6.

Now we do this problem.

By how much does -12 exceed -15?

a = -12; b = -15

a - b = -12 - (-15) = -12 + 15 = 3

Answer: -12 exceeds -15 by 3

Since the given lines a and b are neither parallel, nor do they intersect each other. Also, they lie on two different planes, P and Q respectively, and thus, are co-planar. hence, a and b can be called skew lines.

Definition of Skew Lines

Skew lines in 3D geometry, are, by definition, a pair of lines that are neither parallel nor intersect each other. Such lines are therefore not coplanar, according to the conclusion.

Skew lines tend to occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet. Skew lines go on forever in both directions.

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Answer:

Step-by-step explanation:

Skew lines are noncoplanar and do not intersect. Line a lies in plane Q and line b lies in plane R, so the lines are not coplanar. No other plane can be drawn through the lines, so they are not parallel. So, a and b are skew.

Direct Variation; k=3 best describes the function on the graph

Option A)

Direct variation is a linear function defined by an equation of the form y = kx when x is not equal to zero. Inverse variation is a nonlinear function defined by an equation of the form xy = k when x is not equal to zero and k is a nonzero real number constant. In direct variation, as one number increases, so does the other. This is also called direct proportion: they're the same thing. An example of this is relationship between age and height. As the age in years of a child increases, the height will also increase. In inverse variation, it's exactly the opposite: as one number increases, the other decreases. This is also called inverse proportion. An example would be the relationship between time spent goofing off in class and your grade on the midterm. The more you goof off, the lower your score on the test

The given equation is a Straight line with equation y = 3x.

Thus the given graph is direct Variation graph with k=3.

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The exact values of sin θ/2 and tan θ/2 given below as:

Given that tan θ = -5/12 and θ lies between 90° and 180°, the values of sin θ/2 and tan θ/2 can be found as follows:

tan θ = -5/12

θ =  180 -tan⁻¹-(5/12)

θ = 157.38

sin θ/2  = sin 157.38/2

sin θ/2 = 0.9806

tan θ/2 = tan 157.38/2

tan θ/2 = 4.99

In conclusion, the values of the sine and tangent are found from the given values.

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The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet

An equation is an expression that shows the relationship between two or more variables and numbers.

The clock reads 12 hours (720). The angle if the tip travels from 6:00pm to 6:20pm (20 minutes) is:

Ф = (20/720) * 360 = 10°

The length of the arc is given as:

Length of arc = (Ф/360) * 2π * length of hand = (10/360) * 2π(3) = 0.52 feet

The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet

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[tex] {\qquad\quad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 34[/tex]

[ add 2 on both sides ]

[tex]\qquad \sf  \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 = 34 + 2[/tex]

[ form identity : a² + b² + 2ab ]

[tex]\qquad \sf  \dashrightarrow \: {(x)}^{2} + { \bigg(\cfrac{1}{ {x}^{} } \bigg) }^{2} + 2 \sdot(x) \sdot \bigg(\cfrac{1}{x} \bigg) = 36[/tex]

[ a² + b² + 2ab = (a + b)² ]

[tex]\qquad \sf  \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{2} = 36[/tex]

[tex]\qquad \sf  \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{} = \sqrt{ 36}[/tex]

[tex]\qquad \sf  \dashrightarrow \: x + \cfrac{1}{x} = \pm 6[/tex]

so, the value of required expression is 6

[usually positive value is considered, but if asked the value can be either positive or negative]

The parents could have 3 boys and 3 girls in 400 ways

The given parameters are

Children, n = 6

Boys, r = 3

Girls, r =3

The number of combination is:

[tex]Ways = ^nC_{r1} *^nC_{r2}[/tex]

So, we have:

[tex]Ways = ^6C_3 *^6C_3[/tex]

Apply the combination formula

[tex]Ways = \frac{6!}{3!3!} *\frac{6!}{3!3!}[/tex]

This gives

Ways = 400

Hence, the parents could have 3 boys and 3 girls in 400 ways

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Answer:

3 elements

Step-by-step explanation:

Let A = solution set of x²-4

B = solution set of x²-3x+2

First, find the solution of each sets:

[tex]\displaystyle{x^2-4=0}\\\\\displaystyle{(x+2)(x-2)=0}\\\\\displaystyle{x=2,-2}[/tex]

Set B:

[tex]\displaystyle{x^2-3x+2=0}\\\\\displaystyle{(x-2)(x-1)=0}\\\\\displaystyle{x=1,2}[/tex]

Now we can write new set as:

A = {2, -2}

B = {1, 2}

The union of A and B means combine both sets together:

A ∪ B = {2, -2, 1, 2}

However, in a set, we do not write duplicate elements, so the union set will be:

A ∪ B = {2, -2, 1}

Hence, there are 3 elements in A ∪ B.

46.5 is higher than 5.2

Note that:

The larger the magnitude(value) of the heights given the larger the heights

Units are not added to the values representing each height

By carefully considering the heights given:

5.2 is a lesser value than 46.5

Since 46.6 > 5.2, we can conclude that 46.5 is higher than 5.2

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Multiplicative rule's probability is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

According to the statement

we have to explain about the those law which is used when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

So, For this purpose we know that the

According to multiplicative rule of probability ,

If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B) In case of dependent events , the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B | A)

and we see that these conditions are fulfilled by the definition of the multiplicative rule.

So, Multiplicative rule is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

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Answer:

Step-by-step explanation:

hello :

P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6

Answer:

x = 19.1

Step-by-step explanation:

Because this is a right triangle, we can use trigonometry.

Thus, we must use either sine (opposite / hypotenuse), cosine (adjacent / hypotenuse), or tangent (opposite / adjacent).

If we use 33 as the reference angle, the side measuring 16 is the adjacent side and x is the hypotenuse.

Thus, we can use cosine:

[tex]cos 33=\frac{16}{x} \\x*cos33=16\\x=19.0778=19.1[/tex]

The system of linear equations that represent the given situation is:

5x + 10y = 1750 and 1/3x + 1/2y = 100.

A linear equation is an equation with the highest degree of the variable is one. There may be one or more variables but their degree must be 1 to become a linear equation.

The general form of a linear equation is y = mx + c.

In the given situation,

Consider x as the number of short-sleeved shirts ordered and y as the number of long-sleeved shirts ordered.

It is given that,

Price for short-sleeved shirts = $5

Price long-sleeved shirts =$10

The total price for 100 shirts ordered = $1,750

So, we can write the linear equation as

5x + 10y = 1750  ...(i)

It is given that,

After the first week, they sold 1/3 of the short-sleeved shirts and 1/2 of the long-sleeved shirts. I.e.,

1/3x + 1/2y = 100  ...(ii)

Thus, from equations (i) and (ii), the system of linear equations that represent the given situation is

5x + 10y = 1750

1/3x + 1/2y = 100

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Disclaimer: The given question is incomplete. Here is the complete question.

Question:

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of shirts ordered, and to earn a total of $1,750. After the first week of the fundraiser, they sold 1/3 of the short-sleeved shirts and 1/2 of the long-sleeved shirts, for a total of 100 shirts.

Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered. which system of linear equations represents the situation?

Answer:

c

Step-by-step explanation:

The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.

Expression consists of terms and factors. The terms are separated by the mathematical signs.

Given the expression below

ab+cd+ef+gh

The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.

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Answer:

y = 120

x = 10.6

Step-by-step explanation:

Given polygons are parallelograms.

In parallelograms, consecutive angles are supplementary which means their sum is equal to 180.

Since two parallelograms are similar:

60 + y = 180 subtract 60 from both sides

y = 120

To find the value of x:

side lengths are proportional because these are similar polygons

[tex]\frac{x+4}{22} = \frac{12}{18}[/tex] cross multiply fractions

18x + 72 = 264 subtract 72 from both sides

18x = 192 divide both sides by 18

x = 10.6 approximately

Answer: 480

Step-by-step explanation:

20(12)(2) = 480

Answer:

Step-by-step explanation:

hello :

The graph of y =-3x+4 is the line

Answer:

Step-by-step explanation:

the answer is D

Answer:

Obtuse, scalene.

Step-by-step explanation:

In ΔSVU, one angle is 120° which is obtuse angle.

So, ΔSVU is a obtuse triangle.

All the sides  have different measurements. So, It is a Scalene triangle.

Answer:

1+2√2

a = 1 b= 2

See the attached page, I've shown the calculation over there.

The derivative of the natural logarithm function is given by:

[tex]f^{\prime\prime}(x) = \cotg{x}[/tex]

Suppose we have a composite natural logarithm function given as follows:

[tex]f(x) = \ln{g(x)}[/tex]

The derivative of the function is given as follows:

[tex]f^{\prime}(x) = \frac{g^{\prime}(x)}{g(x)}[/tex]

In this problem, the function, which is already a first derivative, it given by:

[tex]f^{\prime}(x) = \ln{|\sin{x}|} + 3[/tex]

The derivative of a constant is of zero, and the derivative of sin(x) is cos(x), hence the derivative of the entire function is given as follows:

[tex]f^{\prime\prime}(x) = \frac{\cos{x}}{\sin{x}} = \cotg{x}[/tex]

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The given exponential function exists [tex]f(x)=3(1/3)^x[/tex] . The growth value of the function is 1/3.

An exponential function exists a mathematical function of the following form: [tex]f ( x ) = a^ x[/tex].

where x exists a variable, and a exists a constant named the base of the function.

An exponential function exists of the form [tex]f(x)=ab^x[/tex]

where a ≠ 0, b > 0, b ≠1, and x exists any real number.

when b > 1, the graph increases.

when 0 < b < 1, the graph decreases.

a = initial value

r = growth or decay rate

x = number of time.

The given exponential function exists [tex]f(x)=3(1/3)^x[/tex]

The function exists a stretch of the function [tex]f(x)= (1/3)^x.[/tex]

Therefore, the correct answer is the growth value of the function is 1/3.

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The value of s is 45 and the value of BC is 434

The given parameters are:

AB = 9s + 29

DC = 10s - 16

Opposite sides of rhombus are equal.

So, we have:

9s + 29 = 10s - 16

Evaluate the like terms

s = 45

Substitute s = 45 in AB = 9s + 29

AB = 9 * 45 + 29

Evaluate

AB = 434

This means that

BC = AB = 434

Hence, the value of s is 45 and the value of BC is 434

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