Determine whether the graphs of the given equations are parallel, perpendicular, or neither.
y = -5 x=3​

The pairs of function which are linearly independent are f(x) = 2cos x + 3 sin x and g(x) = 3cox x - 2 sin x.

We need to determine the pairs of functions are linearly independent or linearly dependent on the real line

f(x) = 2cos x + 3 sin x

g(x) = 3cox x - 2 sin x

Let c₁f(x) and c₂g(x) = 0

using wornkskin method

w(f, y) = [tex]\left[\begin{array}{cc}f(x)&g(x)\\f'(x)&g'(x)\\\end{array}\right] \\\left[\begin{array}{cc}2cosx + 3sin x&3cos x - 2 sin x\\-2sin x + 3 cos x&-3sin x - 2 cos x\\\end{array}\right][/tex]

= - (2cos x + 3sin x) (3 sinx + 2 cos x) - (3cos x - 2sin x) (3cos x - 2sin x)

= - (9sin²x + 4cos² x + 12cos x sin x) + 9cos² x + 4 sin² x - 12 sin x cos x

= - (13 sin² x + 13 cos² x )

= - 13

since,

w(f , g) ≠ 0

f, g are linearly independent

Therefore, the function  f(x) = 2cos x + 3 sin x and g(x) = 3cox x - 2 sin x are linearly independent.

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The same trip will be 8 hours long if you traveled at 10 mph

Variation is a concept that deals with variability or change in mathematics. Variation is defined as any change in some quantity due to a change in another

Given: The time T it takes to travel some distance varies inversely with the rate r of travel. This implies:

T α 1/r

T = k/r    where k is the constant of proportionality

if it takes 2 hours to get somewhere traveling 40 mph. Then:

2 = k/40

k = 2 x 40 = 80

How long would the same trip take you instead if you traveled 10 mph will be:

T = k/r

T = 80/10

T = 8 hours

Therefore, the same trip take you 8 hours if you traveled 10 mph

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The vertex of the function is transformed from (-4,0) to (4,0). The expression will be transformed from f(x) = −2|x + 4| to h(-x) = -2|-x + 4|.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the absolute function is f(x) = −2|x + 4|. The transformed function is calculated as,

f(x) = −2|x + 4|

h(-x) = −2|-x + 4|

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There is significant relation between price and overall score.

Given that,

Following are details on the cost ($) and final rating for the six stereo headphones that Consumer Reports examined. ($) brand price Score: Bose 180, 72 Scullcandy 150, 78 Koss, 96, 54 Phillips/O'Neill, 72, 42 Denon, 48, 24.

a) t =3.54

The P value is less than 0.2

There is significant relation between price and overall score.

P value is between 0.01 and 0.025.

Because p value is less than or equal to 0.05 , we reject H₀ : β₁ is equal to zero.

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Answer: 26%

Step-by-step explanation:

23 + 52 + 34 + 61 + 30 = 200

do 52/200 because theres 52 gumballs and times it by 100

52/200 x 100 = 26% on calculator

Answer: none of the above

Explanation: as it's - -8/-4 it means the answer is negative which none of the answers provided are so it's none of the above

Answer: 36

Step-by-step explanation:

Since all triangle angles add up to 180 we just add up both the angle measure we know and then subtract by 180.

54+90=144

180-144=36

The acute angle measure is 36 degrees.

answer:

36 degrees

step-by-step explanation:

all the angles of a triangle add up to be 180 degrees. so subtract 90 and 54 degrees to get the answer. hope that helps!

The probability that at least one of them is a 1 is 0.2778 when a fair set of dice is thrown and the total of the numbers falling above them is even.

Given that,

A fair set of dice is thrown.

We have to find given that the total of the numbers falling above them is even, what is the probability that at least one of them is a 1.

We know that,

A fair set of dice is thrown.

The total of the numbers falling above them is even.

The probability that at least one of them is a 1 is

(5/36)/(8/36)

5/18

0.2778

Therefore, The probability that at least one of them is a 1 is 0.2778 when a fair set of dice is thrown and the total of the numbers falling above them is even.

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Answer:

(2) 3 pages in 1 hour

Step-by-step explanation: Simply dividing 9/3 we get, 3/1 by unitary method this is the right answer.

The three stages of an annealing process in the sequence is  recovery, recrystallisation, and gain growth.

Sequence:

In math, a series is defined as the sum of the elements of a sequence.

Given,

Here we need to find the are the three stages during annealing when  an annealing process is provided for the sample after cold work.

In order to find the stages of the annealing process, first we have to know the definition of annealing process,

A process which is used to enhance ductility and counter the increase in hardness by cold working is known as annealing.

This one is to deal with residual stresses we first can reheat the glass to a high temperature known as annealing point and let it cool slowly so that the outside and inside cool at about the same rate.

And the resultant will have little to no residual stresses making annealed glass.

In the first stage recovery stage of annealing recovers the physical properties of the metals.

Second stage is recrystallisation, and gain growth.

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The original Price of a case of scented candles was 8.5

A percent increase refers to how much a percentage has gone up over time.

In order to reach this number, you would need to find the difference between the original value and the final value, subtracting to find the exact total of the decrease.

The formula for calculating Percentage increase is:

(ΔPrice/Original price) × 100

change in price (new price - original price)/original price) × 100

From the question:

Percentage increase = 110%

New price = 17.85

Original price = X

so it  we can substitute in the formula

((17.85 - X)/X) * 100 = 110%

Opening brackets

(17.85*100 - X*100)/ X =110

1785 - 100X = 110X (we balance the equation)

(we collect like terms)

1785 = 210X

to find X we divide both sides by 210

1785/210 = X

8.5

The original Price was $8.5

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the sample proportion under probability has a mean sampling distribution of 82.

The population percentage is the major variable in the sampling distribution of this proportion, which has a quarter-um normal distribution. Variants include population proportion times one and population proportion divided by sample size. Additionally, we are aware that the population proportion is under the null hypothesis. 200 is the sample soil. When we enter the value of P into this calculation without normalisation, we can obtain the standing ovation as the variance's root. 025 in excess. The probability that we got a sample result of 188/58 or less is then calculated. We simply need to determine this left tail probability after that.

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Answer:

(-15x^3 -12x^2 -5x-3)

Step-by-step explanation:

You can't add/subtract numbers that have different exponent numbers so you have to stick with the ones that have the same number

So then the coefficients would be:

x^3 : -9 - 6 = -15

x^2 : -7 -5 = -12
x: -3 -2 =-5
0: -1 - 2 = -3

A certain bacteria strain needs 4 hours to double its population. If in the beginning there are 45 bacteria, after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.

The problem can be solved using the exponential growth model.

In the given problem, the formula for the growth model is given, that is:

f(x) = 45 (64)^(x)

Where:

f(x) = total number of bacteria present after x days

To find f(x) for 1 day, 2 days, and 3 says, substitute x = 1, x = 2, and x = 3 into the formula.

f(1) = 45 (64)¹ = 2,880

f(2) = 45 (64)² = 184,320

f(3) = 45 (64)³ = 11,796,480

Hence,

after 1 day, the number of bacteria present is 2,880, after 2 days, the number of bacteria is 184,320, after 3 days, the number of bacteria is 11,796,480.

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Crickets must have been introduced at the lambda = 2 is 20.

Given:

you observe 40 crickets on an island after crickets were first introduced 2 years ago ,  at the lambda = 2 how many number of crickets must have been introduced .

Let x be the crickets must have to been introduced.

Number of crickets = observed crickets / lambda value

we know that,

Observed crickets = 40

lambda value = 2

substitute these values

Number of crickets = observed crickets / lambda value

= 40 / 2

= 20 crickets.

Therefore Crickets must have been introduced at the lambda = 2 is 20.

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Full question:

you observe 40 crickets on an island after crickets were first introduced 2 years ago. at lambda = 2 how many crickets must have been introduced?

Answer:

-2x + 8

Step-by-step explanation:

(2x - 6) is subtracted from (7 - 5).

First term that into an equation.

Because our first term is being subtracted from our second one, our equation is written as:

(7 - 5) - (2x - 6).

Simplify the first term by subtracting:

7 - 5 = 2

Now simplify the second term by multiplying 2x - 6 by -1 to get them out of the parenthesis. We do this because there is a negative sign in front of it.

-1 (2x - 6)

-2x + 6

Now our equation is:

2 - 2x + 6

Combine like terms:

2 + 6 = 8

So -2x + 8

(2x - 6) subtracted from (7 - 5) is -2x+8

Answer:

5/6

Step-by-step explanation:

1. Line up the fractions

  1/6

+ 2/3

_____

2. Find the common denominator

  1/6 x 1/1

+ 2/3 x 2/2

_____

Thus, we get:

  1/6

+ 4/6

_____

3. Add

  1/6

+ 4/6

_____

  5/6

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Answer:

5/6 which is also 0.833

Step-by-step explanation:

(The whiteboard below)

Using for loop we can get the syntax in order to calculate this arithmetic series n is A = 0.9999.

An arithmetic collection is the sum of the phrases in an mathematics collection with a specific range of phrases. Following is a easy system for locating the sum: Formula 1: If S n represents the sum of an mathematics collection with phrases.

This system calls for the values of the primary and ultimate phrases and the range of phrases. Finite Sequence- Finite sequences have countable phrases and do now no longer cross as much as infinity. An instance of a finite mathematics collection is 2, 4, 6, 8. Infinite Sequence- Infinite arithmetic collection is the collection wherein phrases cross as much as infinity.

using while

A=0; n=1; while n<=10000     A=A+(1/(n*(n+1)));     n=n+1; end A

output

A =      0.9999

using  for loop

A=0; for n=1:10000     A=A+(1/(n*(n+1))); end A

output

A = 0.9999.

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Correct Question:

The following series can be written with a shorthand form of sigma notation (A). Use while syntax to calculate this arithmetic series:

1/(1x2) + 1/(2x3) + 1/(3x4) + ... + 1/(n x (n+1)) ......1

A = ∈ 1/(n x (n+1)); n=[1:10000]

Oliver and his little brother will have an additional shot of 11shots and they both have 38points

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 and 4x − 4y = 4.

Represent the number of additional shot made by the brothers as x and the common point made by both of them be y

therefore,

16+2x=y equation 1

27+x= y equation 2

subtract equation 1 from 2

11-x= 0

therefore x= 11

substitute 11 for x in equation 2

y = 27+ 11

y= 38

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The simplest form expression for the addition of the fractions given using the lowest common multiple of the denominator is 2/3.

A fraction is a numerical value that is a part of a whole. It is evaluated by dividing a whole into a number of parts.In Mathematics, a fraction is defined as a part of the whole thing.  For example, ½ represents half of a whole number or a thing

Given the fractions :

1/4 + 5/12

The lowest common multiple of the denominator ;

A lowest common multiple of 4 and 12 = 12

1/4 + 5/12 = (3 + 5) / 12

1/4 + 5/12 = 8/12

Expressing in simplest form :

8/12 = 2/3

Therefore, the simplest form expression of the addition is 2/3

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For the function that is locate any absolute extreme points over the given interval  h (x) - x 3 - 5x2 - 6x, 10 a we get absolute maximum for x and y  (-0.380, 0.488) (10, 350) and  absolute minimum for x and y (-2, -22) and (4.38, -52.924)

Both critical point lies in domain -2 [tex]\leq[/tex] n [tex]\leq[/tex] 10. We know that h (n) is not define at both side of interval end point so n = -2 and n = 10 are critical point,

The critical point are point where f(n) is defined and its derivative is zero or undefined.

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Answer:3

Step-by-step explanation:

20-9.50=11-3.50

On #1, you used the side of 18 twice.

You should have had

      [tex]\dfrac{40.5}{18}=\dfrac{49.5}{22}=\dfrac{54}{\boldsymbol{24}}[/tex]

with 24 in that last denominator.  And with 24 in the last denominator, they're all equal to 2.25.

On #2, you should have compared 90 to 40 and then 81 to 36:

    [tex]\dfrac{90}{40}=\dfrac{81}{36}[/tex]

Those are both equivalent to 9/4.

[tex]\cfrac{x^2-4x-45}{x+6}\div\cfrac{x^2-3x-40}{x+6}\implies \cfrac{x^2-4x-45}{~~\begin{matrix} x+6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{~~\begin{matrix} x+6 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{x^2-3x-40} \\\\\\ \cfrac{x^2-4x-45}{x^2-3x-40}\implies \cfrac{(x-9)~~\begin{matrix} (x+5) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{(x-8)~~\begin{matrix} (x+5) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x-9}{x-8}[/tex]

The mathematical program will help the user to provide the data on the Excel sheet and solve accordingly.

The mathematical program to minimize the total cost of constructing the wastewater treatment plants can be expressed as follows:

Minimize z = 50x1 + 100x2 + 100x3 + 50x4 + 50x5 + 100x6 + 100x7

Subject to:

x1 + x2 + x3 + x4 + x5 + x6 + x7 <= 4 (1)

x1 + x2 + x3 + x4 + x5 + x6 + x7 >= 1 (2)

x1 + x4 <= 1 (3)

x2 + x4 <= 1 (4)

x3 + x4 <= 1 (5)

x4 + x5 <= 1 (6)

x4 + x6 <= 1 (7)

x4 + x7 <= 1 (8)

x1, x2, x3, x4, x5, x6, x7 are binary variables (i.e. they can only take on the values 0 or 1)

The objective function (1) minimizes the total cost of constructing the wastewater treatment plants, where the cost of constructing a plant in each city is given in the table. The constraints (2)-(8) ensure that at most four wastewater treatment plants are constructed and that each city is served by at most one wastewater treatment plant.

To solve this problem with Excel, we can create a spreadsheet with columns for the names of the cities, the corresponding costs of constructing a wastewater treatment plant, and the binary variables x1, x2, x3, x4, x5, x6, x7. We can then use Excel's solver tool to minimize the objective function subject to the constraints. The solver tool can be found under the Data tab in the Analyze group.

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The function which defines the total sales done by Samantha in 'x' number of weeks is: f(x) = 475 + 5x/100.

As per the stated question-

Weekly pay of Samantha = $475.

Sales percentage = 5% of the sales.

Let 'x' be the sales done for the week.

Then, function models for the pay of the week.

f(x) = 475 + 5%x

f(x) = 475 + 5x/100

Thus, the function which defines the total sales done by Samantha in 'x' number of weeks is: f(x) = 475 + 5x/100.

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Answer:

C

Step-by-step explanation:

length = 17 + width/2

2×length = 34 + width

width = 2×length - 34

area of a rectangle

length × width = length × (2×length - 34) =

= 2×length² - 34×length

which is the answer option C.

The inequality that can be used to represent the number of miles, x, Jaime could bicycle on the 4th week to meet his goal is 240 + 310 + 320 + x ≥ 4 (280).

What is inequality?

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other.

For the next four weeks, Jaime wants to log at least 280 miles per week on average. Jamie's objective can be graphically expressed by the inequality: T4, or alternatively T 4 if T is the total number of miles he will pedal his bicycle for four weeks (280).

The sum of the distances Jamie has covered and has yet to cover is the total number of miles Jamie will cycle during this time. Hence,  T = 240 + 310 + 320 + x. Replacing this term into the inequality T ≥ 4(280) gives 240 + 310 + 320 + x ≥ 4(280). Therefore, choice D is the correct answer.

Thus, the correct answer is  240 + 310 + 320 + x ≥ 4 (280).

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