Find the maximum value of P=3x+2y subject to the following constraints:
Please help me!!!

Answer:

  (a)   -3/4

  (b)  -0.75

  (c)  -0.75

Step-by-step explanation:

It's a bit hard to tell what constitutes an "iteration" when using the bisection method to approximate a polynomial root. For the purpose here, we'll say one iteration consists of ...

Thus, the result of the iteration consists of a bracketing interval and the choice of one of the interval's ends as the solution approximation.

__

(a) We observe that the graphs intersect in the interval (-1, 0). For the first iteration, we evaluate f(x)-g(x) at x=-1/2. This tells us the solution is in the interval (-1, -1/2). The x-value closest to the root is x=-1/2.

For the second iteration, we evaluate the function f(x)-g(x) at x=-3/4. This tells us the solution is in the interval (-1, -3/4). The x-value closest to the root is x=-3/4.

For the third iteration, we evaluate the function f(x)-g(x) at x=-7/8. This tells us the solution is in the interval (-7/8, -3/4). The x-value closest to the root is x=-3/4.

__

(b) The graph tells us the solution is approximately 0.7549. Rounded to 2 decimal places, the solution is approximately 0.75.

__

(c) The above solution found after 3 iterations rounded to 2 decimal places is exactly 0.75.

__

See the attached table for function values.

_____

Comment on bisection iteration

Since you cut the interval containing the root in half with each iteration, you gain approximately one decimal place for each 3 iterations. When the function value is very nearly zero at one of the interval endpoints, it can take many more iterations to achieve a better result.

Here, it takes 4 more iterations before an x-value becomes closer to the solution (x≈-97/128). And it takes one more iteration to move the end of the interval away from -3/4. After these 5 more iterations (8 total), the solution is known to lie in the interval (-97/128, -193/256). The corresponding solution approximation is -193/256. It is still only correct to 2 decimal places.

Answer:

(0.5, 2)

Step-by-step explanation:

substitution method is when you substitute a variable for another

so, it is given that y=2x+1 and y=6x-1. so we know the 'y' value is equal since they are the same thing

hence:

y=2x+1

y=6x-1

2x+1=6x-1

4x=2

x=1/2

y=2

Answer:

Odds for = Odds against = 1/2

Step-by-step explanation:

In a fair die, we have {1, 2, 3, 4, 5, 6} and [tex]$ n(S) = 6 $[/tex]

{1, 4, 5} and {2, 3, 6} constitute the entire sample space.

So, Probability of getting a 1 or a 4 or a 5

= Probability of getting a 1 +

Probability of getting a 4 +

Probability of getting a 5

= [tex]$ \frac{1}{6} + \frac{1}{6} + \frac{1}{6} $[/tex]

=[tex]$ \frac{3}{6} = \frac{1}{2} $[/tex]

Therefore, Odds for 1 or 4 or 5 = [tex]$ \frac{1}{2} $[/tex].

Since, Probability of getting a number between 1 and 6 is 1 and Probability of getting a number from 2 or 3 or 6 = [tex]$ \frac{1}{2} $[/tex], we have:

Probability of not getting a 1 or 4 or 5 = 1 - [tex]$ \frac{1}{2} $[/tex]

= [tex]$ \frac{1}{2} $[/tex]

Hence, odds for and odds against = [tex]$ \frac{1}{2} $[/tex]

Answer:

5.

Step-by-step explanation:

3 * 5 = 15

6 * 5 = 30

7*5 = 35

9*5 = 45

So the constant is 5.

Answer:

0.97

Step-by-step explanation: i used a calculator to divide and then rounded to the nearest hundredth.

Answer:

1/3 cup of water.

Step-by-step explanation:

Answer:

2 HOURS

Step-by-step explanation:

The 1st hour of Billys moped shop costs $17. While Julios costs $25. But at the second hour mark it Billy's moped shop charges $34 an hour and Julios also charges $34nfor 2 hours of rental.

Answer:

2

Step-by-step explanation:

Billy's Moped Shop charges $17 per hour for a moped + helmet.  Julio's moped shop charges $9 per hour for a moped + $16 upfront for a helmet.

Let x be hours and p be price,  let's set up an equation for each.

Billy's equation is 17x = p

Julio's equation is 9x + 16 = p

After 1 hour,  Billy's would charge $17 and Julio's would have charged $25.  After 2 hours,  Billy's would charge $34 and Julio's would charge $34.  The answer is 2.

Answer:

a=-4, b=-4. (-4, -4).

Step-by-step explanation:

-3a+7b=-16

-9a+5b=16

-------------------

-3(-3a+7b)=-3(-16)

-9a+5b=16

---------------------------

9a-21b=48

-9a+5b=16

------------------

-16b=64

b=64/-16

b=-4

-3a+7(-4)=-16

-3a-28=-16

-3a=-16+28

-3a=12

a=12/-3

a=-4

Answer:

They both are equal to -4.

Step-by-step explanation:

Just took the test and got it right hope this helps. :)

Answer:

Population: The entire number of students present in town’s high school.

Sample: Identical number of students across various categories of freshers, senior students and juniors.  

Step-by-step explanation:

Population is the large set of the people who are present during the experiment. Sample is a smaller subset from the population who become a part of the experiment. In this question, samples are the students who are either new joiners to the college, the senior students or the juniors. It will help Alan to come to a possible conclusion using the survey

Answer:

Sample Response-bThe population of Alan's survey is all the students at the town's high school. The sample must be representative of the population. A possible sample would be an equal number of freshman, sophomores, juniors, and seniors.

Step-by-step explanation:

Answer:

22%

Step-by-step explanation:

Given: Profit this year= $245000

           Profit last year= $315000

Now, lets find the percentage decrease in profit this year.

Profit percentage= [tex]\frac{\textrm{difference in profit}}{\textrm{last years profit}} \times 100[/tex]

Profit percentage= [tex]\frac{\$ 315000-\$ 245000}{\$ 315000} \times 100[/tex]

⇒ Profit percentage= [tex]\frac{70000}{315000} \times 100[/tex]

⇒ Profit percentage=~[tex]\frac{7000}{315} =  22.22\%[/tex] ≅ 22% (nearest whole percent)

∴ Percent decrease in profit is 22%

Answer:

22%

Step-by-step explanation:

Answer:

req time=2.5 year

Step-by-step explanation:

simple interest=[tex]\frac{P\times R\times T}{100}[/tex]

where P=principle

          R=rate of interest

          T=time

totel amount= principle+simple interest

simple interest=totel amount-principles

simple interest=$575-$500=$75

ac/ques, 75=[tex]\frac{500\times 6\times T}{100}[/tex]

75=[tex]30\timesT[/tex]

T=2.5 year

Answer:

The number of hot dogs sold was 35 and the number of sodas sold  was 52

Step-by-step explanation:

Let

x ----> the number of hot dogs sold

y ----> the number of sodas sold

we know that

[tex]x+y=87[/tex]

[tex]x=87-y[/tex] ----> equation A

[tex]1.50x+0.50y=78.50[/tex] ----> equation B

Solve the system by substitution

substitute equation A in equation B

[tex]1.50(87-y)+0.50y=78.50[/tex]

solve for y

[tex]130.50-1.50y+0.50y=78.50[/tex]

[tex]1.50y-0.50y=130.50-78.50[/tex]

[tex]y=52\ sodas[/tex]

Find the value of x

[tex]x=87-52=35\ hot dogs[/tex]

therefore

The number of hot dogs sold  was 35 and the number of sodas sold  was 52

Answer:

Step-by-step explanation:

Here two equation of straight lines are given.

Two equations can intersect each other at a point.

The given equations are,

Equating both 1 and 2 we get,

[tex]10 - 5x = 3x + 2\\8x = 8\\x = 1[/tex]

Hence, from 1 we get, [tex]y = 3+2 = 5[/tex]

Answer:

The answer is 1.25cm/s

Step-by-step explanation:

I took the 10cm and divided by the 8 seconds the get the proportional relationship.

Answer:

Option C. 4(20-16y): Each side measures 20-16y units.

Step-by-step explanation:

we know that

The perimeter of a square is equal to

[tex]P=4b[/tex]

where

b is the length side of the square

we have

[tex]P=(80-64y)\ units[/tex]

substitute the given value in the formula

[tex](80-64y)=4b[/tex]

solve for b

Divide by 4 both sides

[tex](20-16y)=b[/tex]

Rewrite the expression

[tex]b=(20-16y)\ units[/tex]

Alternative Method

we have

[tex]P=(80-64y)\ units[/tex]

Factor 4

[tex]P=4(20-16y)\ units[/tex]

so

Each side measures (20-16y) units.

Answer:

Two quarters (50 cents)

Two dimes (20 cents)

Four pennies (4 cents)

Step-by-step explanation:

Guess and check.  

Rachel has two quarters (50 cents), two dimes (20 cents) and four pennies (4 cents) that amounts to 74 cents.

Money is any item or medium of exchange that is accepted by people for the payment of goods and services, as well as the repayment of loans.

A current medium of exchange in the form of coins and banknotes.

Given that, Rachel has 8 coins.

The amount of her coins is 74 cents.

Let us split 74 cents into 8 coins as follows

Two quarters (50 cents)

Two dimes (20 cents)

Four pennies (4 cents)

Therefore, Rachel has two quarters (50 cents), two dimes (20 cents) and four pennies (4 cents).

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Answer:

[tex]r_Y=\frac{3}{\pi}[/tex]

Step-by-step explanation:

Circumference has the formula:

C = 2πr,

Where

C is the circumference

and

r is the radius

Given Circle Y has Circumference of 6, we can find the radius:

C = 2πr

6 = 2πr

r = 6/2π

r = 3/π

So, the radius (r_y) of Circle Y is 3/π, the first choice is right.

The exponential expression 3^1/2 can be converted to radical form as √3. This is because the fractional exponent 1/2 equates to a square root and the base of the expression, 3, becomes the number under the square root symbol.

The expression 3^1/2 can be expressed in radical form by understanding that the exponent 1/2 represents a square root, which means the value inside the square root is being multiplied by itself to get the original number. Therefore, we rewrite this exponential term in radical form by placing the base, which is 3, under a square-root symbol, so 3^1/2 can be expressed as √3 in radical form. This is because the root, which corresponds to the denominator of the fractional exponent, is 2 (hence square root), and the radicand, which corresponds to the numerator of the fractional exponent, is 3.

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To convert the expression 3^1/2 to radical form, we need to find the square root of 3, which is represented as √3 or 3^(1/2).

Exponential expressions involve a base raised to an exponent. They are written in the form a^n, where "a" is the base and "n" is the exponent. These expressions represent repeated multiplication, where the base is multiplied by itself "n" times. Exponential functions play a crucial role in various mathematical and scientific contexts.

To convert the expression 3^1/2 to radical form, we need to find the square root of 3.

The square root of a number is a value that, when multiplied by itself, gives the original number.

In this case, the square root of 3 is represented as √3 or 3^(1/2).

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Answer:

8+6n

Step-by-step explanation:

First, distribute the 2 into the parenthesis.

2(6)+2(3n)-4

Then, multiply the numbers.

12+6n-4

Now add(subtract in this case) the common multiples.

12-4= 8

8+6n

Since you can no longer simplify the equation, this is the answer..

8+6n

Answer:

16 children

Step-by-step explanation:

80% of 20 children comes out to 16 children who are of age 5.

If desired, rewrite "80%" as "0.80" and use that 0.80 as the multiplier of 20:

0.80(20 children) = 16 children.

Final answer:

By setting up a proportion using the percentage 80% as the decimal 0.80, and cross multiplying with the total number of children in the class (20), we find that the number of children age 5 in the class is 16, corresponding to option E.

Explanation:

To determine the number of children age 5 in a kindergarten class when 80% of the class is that age, and the total number of children is 20, we can set up a proportion. Since 80% of the class is age 5, we can express this as 0.80 (the decimal equivalent of 80%). Therefore:

0.80 (the percentage as a decimal) = Number of children age 5 / Total number of children in the class

0.80 = x / 20

Now, we can solve for x, which represents the number of children age 5, by cross multiplying:

0.80 * 20 = x

16 = x

Therefore, the number of children aged 5 is 16, which corresponds to option E.

Answer:

N=3/5

Step-by-step explanation:

(1/5)/N=1/3

N=(1/5)/(1/3)

N=(1/5)(3/1)

N=3/5

Answer:

-75x + 45

Step-by-step explanation:

-15(5x - 3)

-75x + 45

Answer: -75x + 45

Step-by-step explanation: Let's simplify this problem using the distributive property.

Let's first change the minus in front of the 3 to plus a negative.

Now we can distribute or multiply this -15 times each of the terms inside the set of parentheses.

So we get -15 (5x) + -15 (-3) and this simplifies to -75x + 45

Answer

20.45pi

Step-by-step explanation:

14/2=7

49pi

49pi/2=20.45pi

Answer:

[tex]f) 120[/tex]

Step-by-step explanation:

1) La règle de simplification des fractions est très simple. Divisez simplement le numérateur et le dénominateur par le même nombre (non nul).

Exemple:

[tex]\frac{6:3}{3:3}=\frac{1}{2}\\[/tex]

2)  Une solution possible à cette question:

[tex]\frac{120}{240}=\frac{120:2=60}{240:2=120}=\frac{60:3=20}{120:3=40}=\frac{20:4=5}{40:4=10}=\frac{5:5=1}{10:5=2}=\frac{1}{2}[/tex]

120 plus petit commun multiple de 2,3,4,5. C'est le principe pour trouver un nombre multiple des nombres 2,3,4 et 5.

Answer: -3/6 (reduced is -1/2)

Step-by-step explanation:

distribute the 6

-18 = 9 + 6y - 24

combine like terms on one side

-18 = -15 + 6y

get all like terms on one side

-3 = 6y

divide by 6

-3/6 = y

if you need to simplify or reduce the answer is -1/2.

Answer:

[tex]\large\boxed{y=-\dfrac{1}{2}=0.5}[/tex]

Step-by-step explanation:

[tex]-18=9+6(y-4)\qquad\text{use the distributive property}\\\\-18=9+6y+(6)(-4)\\\\-18=9+6y-24\qquad\text{combine like terms}\\\\-18=6y+(9-24)\\\\-18=6y-15\qquad\text{add 15 to both sides}\\\\-3=6y\qquad\text{divide both sides by 6}\\\\\dfrac{-3}{6}=\dfrac{6y}{6}\\\\-\dfrac{3:3}{6:3}=y\to y=-\dfrac{1}{2}[/tex]

Answer:

*From what I'm getting, many of the blanks have multiple numbers that would work.*

No Solutions:

First Blank: 7

Second Blank: Any number but 5

One Solution:

First Blank: Any number but 7

Second Blank: Any number

Infinitely Many Solutions:

First Blank: 7

Second Blank: 5

For no solutions, the equation could be 7x + 5 = 7x + 6. For one solution, the equation could be 7x + 5 = 7x + 6. For infinitely many solutions, the equation would be 7x + 5 = 7x + 5.

The given problem is an algebraic expression which needs to be manipulated appropriately to yield No Solutions, One Solution and Infinitely Many Solutions.

Let's simplify the left-hand side expression first: 2x + 5 + 2x + 3x = 7x + 5.

For No Solutions, you would need the constant term on the right-hand side to not be equal to 5, and the coefficient of x not equal to 7, for example, 7x + 6 would yield no solutions, because there's no value of x which would make 7x + 5 equal to 7x + 6.

For One Solution, you need to make sure the right-hand side and left-hand side aren't identical. For example, 7x + 6 = 7x + 5 has one solution, x = -1.

For Infinitely Many Solutions, the equation on the right-hand side should be the same as the left-hand side. So, it would be 7x + 5 = 7x + 5 as for every real number x, these two expressions will be equal.

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Answer:

25x^2

Step-by-step explanation:

Answer:

The interior angle of 12-gon is [tex]150^{\circ}[/tex]  

The exterior angle of 12-gon is [tex]30^{\circ}[/tex]

Step-by-step explanation:

Given as :

A regular 12-gon is a dodecagonal polygon

i.e The number of sides of the polygon = n = 12

Let The exterior angle of 12-gon = x°

And Let The interior angle of 12-gon = y°

Now,

∵ Exterior angle = [tex]\frac{360^{\circ}}{number of sides}[/tex]

So, exterior angle of 12-gon = [tex]\frac{360^{\circ}}{n}[/tex]

Or, x = [tex]\frac{360^{\circ}}{12}[/tex]

∴ x = [tex]30^{\circ}[/tex]

So,The exterior angle of 12-gon = x = [tex]30^{\circ}[/tex]

Again

∵ Interior angle = [tex]180^{\circ}[/tex] - exterior angle

So, interior angle of 12-gon = [tex]180^{\circ}[/tex] - exterior angle

Or, y =  [tex]180^{\circ}[/tex] -  [tex]30^{\circ}[/tex]

∴ y =  [tex]150^{\circ}[/tex]

So,The interior angle of 12-gon = y = [tex]150^{\circ}[/tex]

Hence, The interior angle of 12-gon is [tex]150^{\circ}[/tex] and The exterior angle of 12-gon is [tex]30^{\circ}[/tex] . Answer

Answer:

4

Step-by-step explanation:

The soil is 4 inches deep in the pot, calculated by dividing the volume of soil (48 cubic inches) by the area of the pot's base (length times width).

Ian put 48 cubic inches of soil into a flower pot. The length of the pot is 4 inches, and the width of the pot is 3 inches. To find out how many inches deep the soil is, we can use the formula for the volume of a rectangular prism, which is Volume = length times width times height. In this case, we have the volume and the dimensions for length and width, so we can solve for the height (or depth).

The formula would be:

Therefore, the soil is 4 inches deep in the pot.

Answer:

[tex]2,400\pi[/tex] cubic units

Step-by-step explanation:

Given the cylinder has a base radius of 10 units.

And slant length of 26 units.

The formula for volume of an oblique cylinder is [tex]\pi r^2h[/tex]

Where [tex]r[/tex] is the radius and [tex]h[/tex] is the height of cylinder.

We will now find height of cylinder using following equation.

[tex](slant\ length)^2=(radius)^2+(height)^2[/tex]

[tex]26^2=10^2+(height)^2\\\\676=100+(height)^2\\\\676-100=(height)^2\\\\576=(height)^2\\\\\sqrt{576}=\sqrt{(height)^2}\\ \\24=height[/tex]

Now, the volume of cylinder would be

[tex]=\pi r^2h\\=\pi(10)^2\times24\\=\pi 100\times24\\=2400\pi[/tex]cubic units

The volume of the cylinder is 2,400pi cubic units

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where:

r is the radius = 10units

h is the height

Since the cylinder is oblique, hence:

h² = 26² - 10²

h² = 676 - 100

h² = 576

h = 24 units

V = 22/7(10)² * 24

V = 2400 pi cubic units

Hence the volume of the cylinder is 2,400pi cubic units

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