A maple syrup producer would like to increase production by 500 gallons per each consecutive year with a goal of producing at least 20,000 gallons of syrup cumulatively for the first five year period of production.
If the first year’s production, in gallons, is given by x, write expressions for each of the other years’ productions.

Year 1 = x Year 2 = Year 3 = Year 4 = Year 5 =



b) Find all possible values of syrup that could be produced the first year to meet the goal of at least 20,000 gallons cumulatively over the five-year period. You must set up a mathematical formula/rule and solve algebraically.

Answer:

  f(x) = -1/3x² -2x

Step-by-step explanation:

For vertex (h, k) and scale factor "a", the vertex form of a quadratic is ...

  y = a(x -h)² +k

For the given vertex, the vertex form function with scale factor "a" is ...

  f(x) = a(x +3)² +3

If that goes through the point (-6, 0), then we have ...

  f(-6) = a(-6 +3)² +3 = 0

  9a = -3 . . . . . . . subtract 3

  a = -1/3 . . . . . . . divide by 9

In standard form, the equation is ...

  f(x) = (-1/3)x² -2x

Answer:

  A.  $16,079

Step-by-step explanation:

You are given the income of a married couple and the tax table applicable to married couples. To find the amount of tax owed, you first find the applicable line in the table, then do the computation it tells you.

The applicable line for an income of $110,000 is the one that says ...

  "77,401 to 165,000"

The left (Tax Rate) column of that line has "22%", and the right (Tax Owed) column tells you the computation you need to make.

You find "the excess over $77,400" by subtracting that amount from the $110,000 income:

  the excess over $77,400 = $110,000 -77,400 = $32,600

__

Then the tax owed is 22% of this amount plus $8907:

  tax owed = $8,907 + 0.22 × 32,600

  = $8,907 + 7,172

  tax owed = $16,079

Answer:

Multicollinearity

Step-by-step explanation:

Answer:

The probability is 0.9993

Step-by-step explanation:

This situation follows a Binomial distribution in which we have:

So, the probability that x of the n elements are success is given by:

[tex]P(x)=nCx*p^{x}*(1-p)^{n-x}[/tex]

That means that the probability that x adults from the 66 use their smartphone in meeting or classes is:

[tex]P(x)=66Cx*0.52^{x}*(1-0.52)^{66-x}[/tex]

Where 66Cx is calculated as:

[tex]66Cx=\frac{66!}{x!(66-x)!}[/tex]

Then, the probability that at least 22 of them use their smartphone in meeting or classes is:

P = P(22) + P(23) + P(24) +... + P(64) + P(65) + P(66)

Therefore, replacing x for each number from 22 to 66 on the equation of P(x), and making a sum with all the probabilities, we get that:

P = 0.9993

Answer:

1,2,3,4,6,9,12,18,36 Is correct one

Answer:

1, 2, 3, 4, 6, 9, 12, 18, 36

Step-by-step explanation:

Answer:

1.28 or 128

Step-by-step explanation:

you would take 32 and divide it by.25

Answer: x= - 3, y = 7

Step-by-step explanation:

Answer: 2 hours

Step-by-step explanation:

Given : Working alone at their respective constant rates, machine A and machine B can fill a certain order in 3 hours and 6 hours, respectively.

Let t be the time taken by both of them working together.

Then, according to the question, we have

[tex]\dfrac{1}{t}=\dfrac{1}{3}+\dfrac{1}{6}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{2+1}{6}\ \ [\because\ L.C.M. (3,6)=6]\\\\\Rightarrow\dfrac{1}{t}=\dfrac{3}{6}=\dfrac{1}{2}\\\\\Rightarrow t=2[/tex]

Hence, it will take 2 hours by the two machines .

The Expression  [tex]\((\frac{p^4q}{p^8})^2\)[/tex] simplifies to [tex]\(\frac{1}{p^8}\)[/tex].

The correct option is D.

To simplify the expression (p⁴q/p⁸)², we can simplify the numerator and denominator separately, and then simplify the exponent:

Numerator: p⁴q

Denominator: p⁸

To simplify the numerator, we divide the exponents of p:

[tex]\(p^4q = \frac{p^4}{p^8}\)[/tex]

Now, we can simplify the expression [tex]\((\frac{p^4}{p^8})^2\)[/tex]:

[tex]\((\frac{p^4}{p^8})^2 = \frac{p^4}{p^8} \cdot \frac{p^4}{p^8} = \frac{p^4 \cdot p^4}{p^8 \cdot p^8}\)[/tex]

Simplifying the numerator and denominator further:

[tex]\(\frac{p^4 \cdot p^4}{p^8 \cdot p^8} = \frac{p^{4+4}}{p^{8+8}} = \frac{p^8}{p^{16}}\)[/tex]

Finally, we can simplify the expression to:

[tex]\(\frac{p^8}{p^{16}} = p^{8-16} = p^{-8} = \frac{1}{p^8}\)[/tex]

Therefore, [tex]\((\frac{p^4q}{p^8})^2\)[/tex] simplifies to [tex]\(\frac{1}{p^8}\)[/tex].

Learn more about Exponents and power here:

https://brainly.com/question/28515493

#SPJ2

The inequality to represent the losing bids can be written as:

b < 17000.

The winning bid for Superman's cape from the 1978 movie was $17,000.

To represent the amounts of all the losing bids, we need to write an inequality that indicates bids that are less than $17,000.

Let "b" represent the amount of a bid.

The inequality to represent the losing bids can be written as:

b < 17000

This inequality states that any bid "b" that is less than $17,000 would be a losing bid. The symbol "<" signifies "less than."

So, any bid amount smaller than $17,000 falls into the category of losing bids.

To learn more on inequality click:

https://brainly.com/question/28841069

#SPJ12

The inequality representing all losing bids for Superman's cape is b < 17,000, where b is the amount of any losing bid. Bidders must consider auction strategies and valuations to avoid overbidding and the winner's curse.

The question involves creating an inequality to represent the losing bids in an auction where Superman's cape was sold for $17,000. The variable b is introduced to represent the amount of any losing bid. The inequality that represents all the losing bids would be b < 17,000. since any bid that is less than $17,000 would not win the auction.

Answer:

  If production is to be maximized, Jerry should build fences and Tom should make dishes.

Step-by-step explanation:

Tom can build more fences per day than Jerry, and Jerry can make more dishes per day than Tom. Each has his special skill, and production will be maximized when that special skill is utilized.

For this case we have that by definition, the equation of a line in the point-slope form is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

[tex](x_ {0}, y_ {0})[/tex]: It is a point through which the line passes

m: It's the slope

We have according to the graph, that the line goes through:

[tex](x_ {1}, y_ {1}): (- 2, -1)\\(x_ {2}, y_ {2}) :( 2,1)[/tex]

We found the slope:

[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {1 - (- 1)} {2 - (- 2)} = \frac {1 +1} {2 + 2} = \frac {2} {4} = \frac {1} {2}[/tex]

Thus, the line is of the form:

[tex](y-y_ {0}) = \frac {1} {2} (x-x_ {0})[/tex]

We substitute a point:

[tex](y-1) = \frac {1} {2} (x-2)[/tex]

Answer:

[tex](y-1) = \frac {1} {2} (x-2)[/tex]

Answer:

The term used to describe this type of survey is - voluntary response sample or self elected sample.

The thing that is wrong with this type of sampling is that only those people will respond who have a strong interest in the particular topic.

Also, it is quite possible that only 38% responses do not reflect the opinions of the whole general population.

Answer:

L=13.715

Step-by-step explanation:

Given that

x=t + cos t

y= t - sin t

0 ≤ t ≤ 3π

[tex]\dfrac{dx}{dt}=1-sin\ t[/tex]

[tex]\dfrac{dy}{dt}=1-cos\ t[/tex]

We know that length of parametric curve given as

[tex]L=\int_{a}^{b}\sqrt{\left(\dfrac{dx}{dt}\right)^2+\left(\dfrac{dy}{dt}\right)^2}dt[/tex]

[tex]\left(\dfrac{dx}{dt}\right)^2=1+sin^2 t-2t\ sint[/tex]

[tex]\left(\dfrac{dy}{dt}\right)^2=1+cos^2 t-2t\ cost[/tex]

Now by putting the values

[tex]L=\int_{0}^{3\pi}\sqrt{3-2sin\ t-2cos\ t}\ dt[/tex]

Now by using calculator

L=13.715

To find the curve length for ( x = t + cos t ) and ( y = t - sin t ) over [tex]\( 0 \le t \le 3\pi \):[/tex]

1. Calculate derivatives:

[tex]\[ \frac{dx}{dt} = 1 - \sin t, \quad \frac{dy}{dt} = 1 - \cos t \][/tex]

2. Set up integral:

 [tex]\[ L = \int_0^{3\pi} \sqrt{(1 - \sin t)^2 + (1 - \cos t)^2} \, dt \][/tex]

3. Simplify integrand:

  [tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]

4. Calculate numerically:

 [tex]\[ L \approx 21.2694 \][/tex]

The curve length is approximately ( 21.2694 ).

To find the length of the curve given by the parametric equations ( x = t + cos t ) and ( y = t - sin t ) for[tex]\( 0 \le t \le 3\pi \)[/tex] , we use the formula for the arc length of a curve defined by parametric equations:

[tex]\[ L = \int_a^b \sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2} \, dt \][/tex]

1. **Find the derivatives of ( x ) and ( y ) with respect to ( t ):**

  For [tex]\( x = t + \cos t \):[/tex]

 [tex]\[ \frac{dx}{dt} = 1 - \sin t \][/tex]

  For[tex]\( y = t - \sin t \):[/tex]

 [tex]\[ \frac{dy}{dt} = 1 - \cos t \][/tex]

2. **Set up the integral for the arc length:**

[tex]\[ L = \int_0^{3\pi} \sqrt{\left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2} \, dt \][/tex]

3. **Simplify the integrand:**

[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 \][/tex]

  Expand both terms:

[tex]\[ \left(1 - \sin t\right)^2 = 1 - 2\sin t + \sin^2 t \][/tex]

  [tex]\[ \left(1 - \cos t\right)^2 = 1 - 2\cos t + \cos^2 t \][/tex]

  Add the expressions together:

[tex]\[ \left(1 - \sin t\right)^2 + \left(1 - \cos t\right)^2 = (1 - 2\sin t + \sin^2 t) + (1 - 2\cos t + \cos^2 t) \][/tex]

[tex]\[ = 1 - 2\sin t + \sin^2 t + 1 - 2\cos t + \cos^2 t \][/tex]

  [tex]\[ = 2 - 2\sin t - 2\cos t + \sin^2 t + \cos^2 t \][/tex]

  Recall that[tex]\( \sin^2 t + \cos^2 t = 1 \):[/tex]

[tex]\[ = 2 - 2\sin t - 2\cos t + 1 \][/tex]

[tex]\[ = 3 - 2(\sin t + \cos t) \][/tex]

  So the integrand becomes:

[tex]\[ \sqrt{3 - 2(\sin t + \cos t)} \][/tex]

4. **Set up the integral for the arc length:**

[tex]\[ L = \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \][/tex]

5. **Calculate the integral:**

  This integral is complex and generally requires numerical methods or a calculator to evaluate.

  Using a calculator:

[tex]\[ L \approx \int_0^{3\pi} \sqrt{3 - 2(\sin t + \cos t)} \, dt \approx 21.2694 \][/tex]

Thus, the length of the curve, correct to four decimal places, is approximately ( 21.2694 ).

There were 100 total students surveyed.

There are 41 freshman students that have an ATM card.

The probability is the number of freshman that have an ATM card over the total number of students.

The probability becomes 41/100

Now divide the fraction to get the decimal answer:

41/100 = 0.410

Answer:

[tex]1.486*10^8[/tex]

[tex]9.118*10^3[/tex]

Step-by-step explanation:

By definition, the form of Scientific notation is:

[tex]a*10^n[/tex]

Where the base is 10, "a" is any number from 1 to 10 but not including 10,  and "n" is an integer.

Therefore to write a number in Scientific notation, the decimal point must be after the first digit and the power "n" must indicate how many places the decimal point is moved.

We know that:

[tex]148.6\ million=148,600,000\ millions[/tex]

Then, we need to move the decimal point 8 places to the left:

[tex]=1.486*10^8[/tex]

To write $9,118 in scientific notation, we need to move the decimal point 3 places to the left:

[tex]=9.118*10^3[/tex]

Answer:

A neuropsychologist​ is most likely to be administering the tests.

Step-by-step explanation:

Mr. Spindero periodically visits a hospital clinic where he takes various paper and pencil tests that document the progression of his dementia.

A neuropsychologist​ is most likely to be administering the tests.

Certain disorders within the brain and nervous system can alter the normal  behavior and cognitive function of a person.

So, a neuropsychologist deals with such patients. He specializes in understanding the relationship between the physical brain and behavior.

Final answer:

Jimmy earned $190 for working on 500 parts. This includes $37.50 for the first 150 parts, $52.50 for the next 150 parts, and $100 for the 200 parts beyond the initial 300.

Explanation:

Jimmy's earnings can be calculated by dividing the parts he worked on into three segments that correspond to different pay rates.

The first 150 parts at $0.25 each.

The next 150 parts (from part 151 to 300) at $0.35 each.

Any parts above 300 at $0.50 each.

So the calculation would be as follows:

First segment: 150 parts × $0.25 = $37.50

Second segment: 150 parts × $0.35 = $52.50

Third segment: 200 parts (500 - 300) × $0.50 = $100.00

Adding these amounts together will give us the total earnings:

$37.50 + $52.50 + $100.00 = $190.00

Therefore, Jimmy earned a total of $190 yesterday.

Answer:

4b - 3s = 40

4b = 40 + 3s

b = 40 - 3s/4

4b - 3s = 40

4b - 40 =3s

4b - 40 /3 = s

The age of the brother b = 40 - 3s/4, and the age of the sister is s = 4b - 40/3

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Let the age of the brother be b and the age of the sister be s

If four times the brother's age is subtracted from three times the sister's age, the difference is 40.

So the equation that represents this statement is:

⇒ 4b - 3s = 40

⇒ 4b = 40 + 3s

Divided by 3 into both sides and solve for b,

⇒ b = 40 - 3s/4

Now solve for b,

⇒ 4b - 3s = 40

⇒ 4b - 40 =3s

Divided by 3 into both sides

⇒ s = 4b - 40/3

Hence, the age of the brother b = 40 - 3s/4, and the age of the sister is s = 4b - 40/3

Learn more about the equation here:

brainly.com/question/10413253

#SPJ2

Answer:

Step-by-step explanation:

1) The greatest common factor of 72 and 112 is 8, so the least common multiple is ... 72×112/8 = 1008.

The least common multiple of 72 and 112 is 1008.

__

2) The house number will be a multiple of 1008 between 3000/1008 = 2.98 and 4000/1008 = 3.96. The only integer in that range is 3, so Peter's house number is ...

  3 × 1008 = 3024

Peter's house number is 3024.

Answer:

There are 795 combinations.

Step-by-step explanation:

The number of ways or combinations in which we can select k element from a group of n elements is given by:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

So, if Miriam want to choose 3 movies with at least two comedies, she have two options: Choose 2 comedies and 1 foreign film or choose 3 comedies.

Then, the number of combinations for every case are:

1. Choose 2 Comedies from the 10 and choose 1 foreign film from 15. This is calculated as:

[tex]10C2*15C1=\frac{10!}{2!(10-8)!}*\frac{15}{1!(15-14)!}[/tex]

[tex]10C2*15C1=675[/tex]

2. Choose 3 Comedies from the 10. This is calculated as:

[tex]10C3=\frac{10!}{3!(10-3)!}=120[/tex]

Therefore, there are 795 combinations and it is calculated as:

675 + 120 = 795

Answer:

They're are all correct.

Step-by-step explanation:

I went each of them carefully. They are all correct.

Answer:7

Step-by-step explanation:

Answer: $61 because you have to do 10 x3 to get 30 then + $1 because $1 is equal to 5 pounds

Answer:

Step-by-step explanation:

For the first two parts, you need to know the number of hours in a day, and the number of days in 30 days (!?). No doubt, these numbers are familiar to you.

Part A.

The distance traveled in 24 hours (1 day) is 24 times the distance traveled in one hour.

  distance per day = (27,600,000 m/h)×(24 h/day) = 662,400,000 m/day

Since you are familiar with place value and powers of 10, you know you can write this as ...

  662,400,000 m/day = 6.624×100,000,000 m/day = 6.624×10⁸ m/day

__

Part B.

Using the result from Part A, we know that 30 days' travel will be 30 times one day's travel:

  distance in 30 days = (30 days)×6.624×10⁸ m/day = 198.72×10⁸ m

     = 1.9872×10¹⁰ m

__

Part C.

Your judgment is required to determine a "suitable unit." I might choose gigameters, abbreviated Gm. "giga-" is a prefix meaning 10⁹, so the distance traveled in 30 days could be written as ...

  1.9872×10¹⁰ m = 19.872×10⁹ m = 19.872 Gm = 1.9872×10¹ Gm

_____

Comment on "suitable unit"

In my engineering career, I would often choose units from the list of SI prefixes, so that exponents were a multiple of 3. That means any given measurement or calculation result ranged from 1 to 999, multiplied by some suitable choice of units. Here, the distance traveled in 30 days would be left as (about) 19.9 Gm. The choice of units is intended to avoid the need for scientific notation.

The meaning of "a more suitable unit in scientific notation" is unclear in this context. I would say a "more suitable unit" is Gm, whose value in scientific notation is 10^9 m or 10^6 km.

Answer:

A. simpson's paradox

Step-by-step explanation:

The Simpson's paradox was named after Edward Simpson, the person who described this paradox for the first time in 1951. In this paradox, you find two contrary patterns. For example, a positive and a negative correlation, depending on how data is analyzed. The differences in the analyses are how data are grouped. This paradox is observed often in social researches. Most of the times, results are affected by the sample on each group or additional information related to the data.

Answer:

x=-y/g

Step-by-step explanation:

m-y=m+gx

m-m-y=gx

-y=gx

x=-y/g

Answer:

The answer to your question is: 800.4 km

Step-by-step explanation:

Data:

111 km to east

444 km to north

555 km to east

How far is from her starting position?

See the picture please

To do this problem, we must to find the hypotenuse of a right triangle where one cathetus is 444 km and the other one is the sum of 111 and 555km.

them the pythagorean theorem says c² = a² + b²

                                                              c² = 444² + (111+555)²

                                                               c² = 444² + 666²

                                                                c² = 197136  + 443556

                                                               c² = 640692

                                                                c = 800.4 km

Answer: 7.211

Step-by-step explanation:

TRUST ME, IF IT"S WRONG YOU CAN GIVE ME 1 STAR, IF YOU GET IT RIGHT PLEASE SUBSCRIBE TO ICONIC COOKING, THANK YOU, LUV YOU

Answer:

  x = ±6

Step-by-step explanation:

The left side is the difference of squares, so factors accordingly:

  (2x -12)(2x +12) = 0

The zero factor property tells you the product will be zero when one or more factors is zero.

  2x -12 = 0

  x -6 = 0 . . . . divide by 2

  x = 6 . . . . . . one solution to the equation

__

  2x +12 = 0

  x + 6 = 0 . . . . divide by 2

  x = -6 . . . . . . . the other solution to the equation

Answer:

No.

Step-by-step explanation:

The equation does not match the form of any conic section.

I hope this helps you out alot, and as always, I am joyous to assist anyone at any time.

Answer:

Step-by-step explanation:

Let's get this in a form we can better recognize.  we'll rearrange it until we have y by itself.

x^2 + xy = 1

xy = 1 - x^2

y = 1/x - x

There, much better.  Now,  just looking at the graph you can tell there's no symmetry along the x or y axis.  If you do not know how to check for symmetry along x=y or origin symmetry let me know.  But checking for those does show that there is no symmetry along y = x but there is origin symmetry.  

To determine that you just make all x and ys negative, and then see if you can get back to the original.  Again, let me know if you don't get determining symmetry through algebra and I'd be happy to explain each of the variations; x ais, y axis, y=x and origin.