The correct answer is option A. "Brand P will be $118.26 cheaper than Brand Q." The brand that will have the lower lifetime cost after six years and by how much are to be determined when Robert plans on using his deep fryer about eight times per month.
Hence, the total number of times the deep fryer will be used for six years is:
8 times/month x 12 months/year x 6 years = 576 times
Firstly, let's calculate the lifetime cost of Brand P:
Cost of Deep Fryer: $144.00
Cost per use: $0.49 (electricity + oil)
Number of uses: 576
Lifetime cost:[tex]$144.00 + ($0.49 x 576) = $417.84[/tex]
Lifetime cost of Brand Q is to be calculated now:
Cost of Deep Fryer: $37.50
Cost per use: $0.75 (electricity + oil)
Number of uses: 576
Lifetime cost: [tex]$37.50 + ($0.75 x 576) = $481.50[/tex]
Therefore, Brand P will have a lifetime cost of $417.84 and Brand Q will have a lifetime cost of $481.50 after six years.
We can find the difference between the two amounts: [tex]481.50 - 417.84 = 63.66[/tex]
The difference between the lifetime cost of Brand P and Brand Q will be $63.66.
However, we have to consider the amount of money saved by purchasing Brand P instead of Brand Q.
Hence, Brand P will be $118.26 cheaper than Brand Q, and thus, option A, "Brand P will be $118.26 cheaper than Brand Q" is the correct answer.
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[tex]\huge\sf\underline{Question}[/tex]
[tex]\sf If \: {x}^{2} + \frac{1}{x ^{2} } = 34[/tex]
[tex]\sf find \: the \: value \: of \: \: \: x + \frac{1}{x} [/tex]
a proper explanation needed :)
Thxx !!
[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]
Please help ASAP!! Thank you :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.
Planes Q and R are parallel. Explain how you know lines a and b are skew. Planes Q and R are parallel. Line a is on plane Q and is diagonal down and to the left. Line b is on plane R and is diagonal up and to the left.
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.
the graph of y =-3x+4 is
Answer:
Step-by-step explanation:
hello :
The graph of y =-3x+4 is the line
Cuantos litros de agua se necesitan para llenar una piscina de 20m de largada, 12m de ancho y 2m de profundidad
Answer: 480
Step-by-step explanation:
20(12)(2) = 480
Which best describes the function on the graph?
A) Direct Variation; k=3
B) Direct Variation; k=1/3
C) Inverse Variation; k=3
D) Inverse Variation; k=1/3
Please answer quickly! <3
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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HELP PLS!!!! i don’t get it
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
Explain how to find the 41st term of the arithmetic sequence where a1 = 5 and a7 = 34.
The 41th term of the arithmetic sequence is 66.
What is arithmetic sequence in math's ?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.
According to the given information: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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compare these heights:
5,2 and 46,5
46.5 is higher than 5.2
Comparison of heightNote 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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Rhombus A B C D is shown. The length of A B is 9 s + 29 and the length of opposite side D C is 10 s minus 16.
What is the value of s and the length of side BC if ABCD is a rhombus?
s =
BC =
units
The value of s is 45 and the value of BC is 434
How to solve for s and BC?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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Can you guys help me with this problem, please I need it right now.
In the graph, the constant of proportionality is 40
Calculating the constant of proportionalityFrom 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.
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? 5x 10y = 100 and 5 x plus 10 y equals 100 and startfraction one-third endfraction x plus startfraction one-half endfraction y equals 1,750.x startfraction one-half endfractiony = 1,750 5x 10y = 1,750 and 5 x plus 10 y equals 1,750 and startfraction one-third endfraction x plus startfraction one-half endfraction y equals 100.x y = 100 x y = 100 and x plus y equals 100 and startfraction one-third endfraction x plus startfraction one-half endfraction y equals 1,750.x y = 1,750 x y = 1,750 and x plus y equals 1,750 and startfraction one-third endfraction x plus startfraction one-half endfraction y equals 100.x y = 100
The system of linear equations that represent the given situation is:
5x + 10y = 1750 and 1/3x + 1/2y = 100.
What is a linear equation?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.
Calculation:
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:
Suppose that tan 0=-5/12 and 90° <0<180°.
Find the exact values of sin
0/2 and
tan
O/2
The exact values of sin θ/2 and tan θ/2 given below as:
sin θ/2 = 0.9806tan θ/2 = 4.99What is the exact values of sin θ/2 and tan θ/2 given that tan θ = -5/12?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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If the clock tower in "Back to the Future" had a big hand length of 3 feet, what would be the length of the arc, in feet, the tip travels from 6:00pm to 6:20pm. Round to the nearest foot.
The length of the arc made by the big hand if the tip travels from 6:00pm to 6:20pm is 0.52 feet
What is an equation?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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Expand (1 + root 2) (3 - root 2)
Give your answer in the form a+b root 2 where a and b are integers.
Answer:
1+2√2
a = 1 b= 2
See the attached page, I've shown the calculation over there.
The binomial 5x – 4 is a factor of 10x^2 – 23x + 12. What is the other factor?
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
he section of paper shown in the pattern below is 1/4 of a circle. It will be wrapped around a cone. The wrapper will then be painted.
The volume of the cone based on the figure illustrated wil be 196cm³.
Host illustrate the information?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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what is the derivative of this
The derivative of the natural logarithm function is given by:
[tex]f^{\prime\prime}(x) = \cotg{x}[/tex]
What is the derivative of the natural logarithm function?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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A cube with side length is stacked on another cube with side length . What is the total volume of the cubes in factored form
The total volume of the cubes in factored form is (4p + 2q^2)(16p^2 - 8pq^2 + 4q^4)
What is the volume of a figure?The volume of a figure or a three dimensional shape is the amount of space inside the figure or the three dimensional shape
How to determine the total volume?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?
Choose the equation that satisfies the data in the table.
Answer:
Step-by-step explanation:
the answer is D
Which rule states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities
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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If a family has 6 children, in how many ways could the parents have 3 boys and 3 girls?
The parents could have 3 boys and 3 girls in 400 ways
How to determine the number of 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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by how much does -12 exceed -15
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
The table below shows some inputs and outputs of the invertible function f with domain all real numbers.
X 5, 3, 1, 18, 0, 9
f(x) 9, -2, -5, -1, 1, 11
Find the following values:
f-1 (f(58))=
f(f (5)) =
The value of f⁻¹(f(58)) is 58 and the value of the function f(f(5)) is 11
How to solve the function values?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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If 4 is the solution set of the equation x² -4 = 0 and B is
the solution set of the equation x²-3x+2=0, how many
elements are in the union of the two sets?
A. 1
C. 3
B. 2
D. 4
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.
WORTH 50 points pls answer.
The two polygons are similar. Find the values of x and y
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
P(A) = 1/2
P(B) = 1/3
If A and B are independent, what is P(A ∩ B)?
Answer:
Step-by-step explanation:
hello :
P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6
Complete the statement to describe the expression ab+cd+ef+gh
The expression consists of __ terms, and each term contains __ factors.
HELP!
The terms of the expression are ab, cd, ef and gh. This shpws that the expression contains 4 terms and 0 factor.
Terms and factors of an expressionExpression 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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Find the missing side. Round your answer to the nearest tenth.
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]
Consider the exponential function f(x)=3(1/3)^x and it’s graph
The given exponential function exists [tex]f(x)=3(1/3)^x[/tex] . The growth value of the function is 1/3.
What is exponential function?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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