To find out how fast a tree grows, you can measure its trunk. A giant red oak's diameter was 248 inches in 1965. The tree's diameter had grown to 251 inches in 2005. Find the average rate of change in the diameter of the tree per year.

Answer:

Option 4). Machine with $8 per hour operating cost, producing 14 pounds of candy per hour.

Step-by-step explanation:

We have to find the most profitable investment for a candy shop that earns $1 per pound of candy.

We will take up each option one by one.

Option 1).

Producing eight pounds of candy per hours means profit = $1×8 = $8

But workers take $10 per hours so expenditure = $8 - $10 = -$2

There is a loss of $2 in this investment.

Option 2).

Production of 16 pounds candy per hour will make the profit = $1 × 16 = $16

But workers take $12 per hour so profit earned = 16 - 12 = $4

Option 3).

Machine produces 10 pound of candy per hour so profit will be = $1 ×10 = $10

Operating cost of the machine = $5 per hour

So profit generated = profit - Operating cost of machine

                                 = 10 - 5 = $5

Option 4).

Profit earned by production of 14 pounds of candy per hour = $1 × 14 = $14

Operating cost of the machine = $8 per hour

Therefore, Total profit per hour = 14 - 8 = $6

Finally we can say that the maximum profit will be generated in option 4.

Therefore, Option 4) will be the best option to invest.

Final answer:

The most profitable investment for a candy shop is the machine with an $8 per hour operating cost, producing 14 pounds of candy per hour, yielding a net profit of $6 per hour.

Explanation:

The task is to determine the most profitable investment for a candy shop that makes $1 profit per pound of candy. To calculate the profitability of each option, we need to figure out the net profit per hour for each.

Worker at $10 per hour, producing eight pounds of candy per hour:

Profit = 8 pounds * $1 profit per pound - $10 wage per hour = $8 - $10 = -$2 per hour.

Worker at $12 per hour, producing 16 pounds of candy per hour:

Profit = 16 pounds * $1 profit per pound - $12 wage per hour = $16 - $12 = $4 per hour.

Machine with $5 per hour operating cost, producing 10 pounds of candy per hour:

Profit = 10 pounds * $1 profit per pound - $5 operating cost per hour = $10 - $5 = $5 per hour.

Machine with $8 per hour operating cost, producing 14 pounds of candy per hour:

Profit = 14 pounds * $1 profit per pound - $8 operating cost per hour = $14 - $8 = $6 per hour.

Comparing the net profit per hour for each option, the Machine with $8 per hour operating cost, producing 14 pounds of candy per hour, is the most profitable investment.

y=mx+b
4y=5x-12
y=5/4x-3
so you change your y intercept (-3) to your other y intercept (15)
y=5/4x+15

You can use both to prove the triangle is congruent.

So either ASA or AAS Theorem.

Hope this helped! :D

The length of the rectangle is 10 cm and the width of the rectangle is 5 cm because 2(10)+2(5)=30

I hope this helps you




p^2+13p-30=0


p +15


p -2


(p+15)(p-2)=0


p= -15


p=2

Answer:

The correct option is D.

Step-by-step explanation:

The given quadratic equation is

[tex]p^2+13p-30=0[/tex]

First find two numbers whose sum is 13 and whose product is -30.

The two numbers are 15 and -2.

[tex]p^2+(15-2)p-30=0[/tex]

[tex]p^2+15p-2p-30=0[/tex]

[tex]p(p+15)-2(p+15)=0[/tex]

[tex](p+15)(p-2)=0[/tex]

By using zero product property, equate each factor equal to 0.

[tex]p+15=0[/tex]

[tex]p=-15[/tex]

[tex]p-2=0[/tex]

[tex]p=2[/tex]

Therefore the values of p are -15 and 2. Option D is correct.

Answer:

Ques 1)

The student whose measurement might be in centimeters is:

                         Jim

Ques 2)

                 C.   5,000

Step-by-step explanation:

Ques 1)

We know that the standard unit centimeters or meters is used to represent the length of some object.

Here Jim measured an object's length.

Hence, he would represent his measurement in centimeters.

Ques 2)

We know that  1 m=100 cm

and 1 km=1000 m

Hence,

1 km=100000 cm

Hence,

0.05 km=0.05×100000 cm

Hence, we have:

0.05 km=5000 cm.

Hence, the correct answer is: Option: C

Answer:

#1. d. ann's

#2. 5,000

Step-by-step explanation:

x - y

4 - 5 = -1

The difference between x and y is -1.

8 - 1 = 7

The answer for when y = 8, x = 7.

y = kx,,5=4k,,k=5/4,,8=(5/4)x,,x=6.4

A = P(1+rt)
A (Future) = 450(2) = 900
P (Principal) = 450
R (Rate) = 14% = .14
T (Time) = Unknown

Create the equation:
900=450(1+.14t)

Distribute the 450:
900=450 + 450(.14t)

Multiply the 450(.14t)
900=450 + 63t

Subtract the 450:
450 = 63t

Divide by 63:
t=7.142857

Answer:
It will take 7.1 years.

2p=p(1+0.14t),,2=1+0.14t,,1=0.14t,,t==7.14 years or 7 years

The following statement is true about the 2 (two) triangles shown in the image:
_________________________________________________
Triangle ABC is similar to Triangle FDE because:

AB  =   AC 
FD       FE
_________________________________________________

Answer:

171 degrees

Step-by-step explanation:

40-sided polygon has an interior angle equal to:

(40 - 2) (180) /40 = 171 degrees

306!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

LCM of 9,17 and 51 is 153

The function n^3/1000 - 100n^2 - 100n + 3. The big-Theta notation represents a function that can sandwich the given function for sufficiently large n. Formally, Theta(g(n): k1*g(n) < f(n) < k2*g(n). Sometimes, it is just as easy as removing the lower order terms and dropping the coefficient of the highest degree term. Thus, the function can be represented as Theta(n^3).

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

Answer:

a.  The inequality will be:  [tex]\frac{3}{4}x\geq 10[/tex]

b.  Solving the inequality:  [tex]x\geq 13.333...[/tex]

c.  Jeanette should buy 14 tiles to form one row.

Step-by-step explanation:

Suppose, the number of tiles needed to make one row [tex]=x[/tex]

Each square tiles measure [tex]\frac{3}{4}[/tex] ft on each side.

So, the total length of [tex]x[/tex] number of tiles [tex]=\frac{3}{4}x\ ft[/tex]

Given that, the room is 10 ft wide.

So, the inequality will be:  [tex]\frac{3}{4}x\geq 10[/tex]

Solving the above inequality.....

[tex]\frac{3}{4}x\geq 10\\ \\ 3x\geq 4(10)\\ \\ 3x\geq 40\\ \\ x\geq \frac{40}{3}\\ \\ x\geq 13.333...\\ \\ x\approx 14[/tex]

So, Jeanette should buy 14 tiles to form one row.

I hope this helps you




y=2/3x+7.3/3.1


y=2x+21/3


3y=2x+21


3y-2x=21

The answer is: [A]: -2x + 3y = 21 .
___________________
Note that "standard form" refers to:
_______________________________
→  Ax +By =C ;
      in which "x" and "y" are variables; "A" and "B" represent the coefficients before those variables, respectively; and "C" is a number (not a variable).
_______________________________
I shall demonstrate 2 (two) methods to convert the equation given:
________________________________________
→  y = (⅔) x + 7 ;   to "standard form".).
_____________________ 
Method 1:
_______________________
→ Given: y = (⅔)x + 7 ; 
______________________
→ Subtract "y" from EACH SIDE of the equation; and subtract "7" from EACH SIDE of the equation. Doing so: 1) puts the "x" and "y' values on one side of the equation; 2) removes a numeric value from the side of the equation with the "x" and "y" values; and 3) puts a numeric value on a side of the equation that does not have any "x" or "y" values — all three of which help to convert to equation to "standard form"—that is, " Ax + By = C " ;
____________
→ y = (⅔)x + 7 ;  → y − y − 7 = (⅔)x + 7 − y − 7 ; To get:
____________
→  -7 = (⅔)x − y  ↔ Rewrite as: (⅔)x − y = -7 ;
________________________
Note:  While this very would could be an answer in"standard form"; 
 "Ax + By = C", in which A = ⅔ , B = -1; and C = -7; 
                     (Note: There is an implied "1" before the "y", since  "1*y = y; 
                                    since: y*1 = y; (anything * 1 = said number); 
                                     and the coefficient is "-1" (NEGATIVE 1); since the                                               "standard form" is: "Ax + By = C; and we have: 

                                                                             (⅔)x − y = -7 ; so the:
"− y" functions as a: PLUS "negative 1y"; in this circumstance.
_________________________________________________
However, this equation—as written—does NOT match any of the answer choices given.
___________________
→So, now we should multiply our ENTIRE equation (BOTH SIDES) by "-3"; for the sake of:  
___________________
1) getting an answer choice that matches one of the answer choices given;
AND: 
2) for the general sake of simplicity—which would include getting the "-7" changed to a "positive 21" ;
_______________________.
 → {Note: A non-zero, negative integer, when multiplied by another non-zero, negative integer; will result in a non-zero POSITIVE integer.
 As such: -7 *-3 = 21}.
_________________
We have:  (⅔)x − y = -7 ; We shall multiply EACH SIDE of the equation by "-3";     → -3 * {(⅔)x − y = -7} ;
______________________
→  Note: Start with:
   →"(-3 * (⅔)x =  -3 * ⅔ * x ;
   →   -3 * ⅔  = [tex] \frac{-3}{1} [/tex] * [tex] \frac{2}{3} [/tex]  =(-3*2)/(1*3)
= -6 / 3 = -2 ;  → Don't forget to bring down the "x":  -2 * x = -2x ; 
→ So: - 3 *(⅔)x = - 2x ;
_________________
The next term: -3 *-1y = +3y ; (Note: -3 *-1y = (-3* -1)*y = 3*y = +3y ;
____________________
The next term: -3*(-7) = +21 ;
_______________________________________
→ to get:  → -2x + 3y = 21 ; which is: 'Answer choice: [A]'.
___________________________________________________________
Method 2:
____________
Given: y = (⅔)x + 7 ; write in standard form:
_________________________
 →  Given:    y = (⅔)x + 7 ; Multiply EACH SIDE of the equation by "3", to get rid of the fraction, "(⅔)" ; 
___________________________
 → 3* { y = (⅔)x + 7 } ;  to get:
____________________________
First term: 3*y  = 3y;  

Second term: 3*((⅔)x)) = 3 * (⅔) * x ;  3 * (⅔) = (3/1)*(2/3) =(3*2)/(1*3) =
6/3 = 2; → Don't forget the "x" → 2 * x
    = 2x;
___________________
Third term: 3*7 = 21;
__________________
→To get: → 3y = 2x + 21 ; 
____________________________
 → Now, subtract "3y" and subtract "21" from EACH SIDE of the equation:
____________________________
→ 3y = 2x + 21 ;   →  3y − 21 − 3y = 2x + 21 − 3y − 21 ;
_____________________________________________
to get: →  -21 = 2x − 3y ; → Rewrite as: → 2x − 3y = -21 ;

______________________________
Note:  This would appear in "standard form" equation; "Ax + By = C"; 
                       in which A = 2; B = 3; C = -21;
___________________________________________
However,  " 2x − 3y = -21 " ;  is NOT an answer choice given.
______________________________
However, there are answer choices given with "21" {note: "positive 21"} representing the number for "C" within the "standard form" equation: 
________
→ "Ax + By = C"
_________________
 So, given our equation:
________________________
→ 2x − 3y = -21 ;
          → We can multiply the ENTIRE equation (BOTH sides) by "-1" ; to                 change the "-21" value to "21" (positive 21); and see if the equation matches any of the answer choices:
______________
→  -1 * {2x − 3y = -21} ; 
______________
First term:  -1* 2x = -2x ; 

Second term: -1 * -3y = -1 * -3 * y = +3y ; 

Third term: -1 * -21 = + 21
___________________________
→  -2x + 3y = 21 ; which is:   'Answer choice: [A]'.

The apparent solution is (1,2) because it moves over 1 on the x axis and 2 up on the y axis.

Solution for system of 2 equations of lines is coordinates of point at which those 2 lines intercept. The reason for is that those coordinates fit in both equations. IF you implement coordinates of that point in either of those equations of 2 lines you will see that left side is equal to right side which means that that point belongs to that line. 

This method here is graphical method of solving system of equations. Other method is, of course, solving system of equations using math...

Answer is (1,2)

y = log x / x
y ` = (( log x )` * x - (x)` * log x) / x²=
= (1/x * x - 1 * log x ) / x² =
= ( 1 - log x ) / x²
y ` = 0;
1 - log x = 0
log x = 1
x = e
The maximum value:
y max = log e / e = 1 / e

So here is how you determine the values of x that cause the polynomial function to be positive. 
Set each one greater than zero:x+2>0x+1>0x−5>0

Then, solve for x on all three:
 x > -2 x > -1 x > 5
 so in order for the polynomial to be positive the answer is x > 5.
Hope this is the answer that you are looking for. 

20.833333 is 20 5/6 and 20.8 is basically 20.80000000 and since 3 is larger than zero 20 5/6 is larger 20 5/6 > 20.8 

20 5/6 is larger than 20.8

the number 5 is prime

Answer:

5

It's easy.

5 has only 2 factors: 1 and itself.

Therefore, it is prime:)

Step-by-step explanation:

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y = 7x - 4x² 

7x - 4x² = 0 

x(7 - 4x) = 0 

x = 0, 7/4 

Find the area of the bounded region... 

A = ∫ 7x - 4x² dx |(0 to 7/4) 

A = 7/2 x² - 4/3 x³ |(0 to 7/4) 

A = 7/2(7/4)² - 4/3(7/4)³ - 0 = 3.573 

Half of this area is 1.786, now set up an integral that is equal to this area but bounded by the parabola and the line going through the origin... 

y = mx + c 

c = 0 since it goes through the origin 

The point where the line intersects the parabola we shall call (a, b) 

y = mx ===> b = m(a) 

Slope = m = b/a 

Now we need to integrate from 0 to a to find the area bounded by the parabola and the line... 

1.786 = ∫ 7x - 4x² - (b/a)x dx |(0 to a) 

1.786 = (7/2)x² - (4/3)x³ - (b/2a)x² |(0 to a) 

1.786 = (7/2)a² - (4/3)a³ - (b/2a)a² - 0 

1.786 = (7/2)a² - (4/3)a³ - b(a/2) 

Remember that (a, b) is also a point on the parabola so y = 7x - 4x² ==> b = 7a - 4a² 
Substitute... 

1.786 = (7/2)a² - (4/3)a³ - (7a - 4a²)(a/2) 

1.786 = (7/2)a² - (4/3)a³ - (7/2)a² + 2a³ 

(2/3)a³ = 1.786 

a = ∛[(3/2)(1.786)] 

a = 1.39 

b = 7(1.39) - 4(1.39)² = 2.00 

Slope = m = b/a = 2.00 / 1.39 = 1.44

Final answer:

The slope of the line that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area is -2.

Explanation:

To find the slope of the line that divides the region bounded by the parabola y=2x-4x^2 and the x-axis into two regions with equal area, we need to set up an integral to find the area under the parabola. The equation of the line will be in the form y = mx, where m is the slope we need to find. Setting up the integral, we get:

Solve the integral to find:

Substituting the limits of integration and solving, we get:

Therefore, the slope of the line that divides the region into two equal areas is -2.

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The Factor theorem states that  for any polynomial f(x) if f(c)=0 then x-c is a factor of the polynomial f(x).

If any polynomial f(x) is divided by x-a and remainder is 0 that means f(a)= 0 .In other words we can say x-a is a factor of the polynomial f(x).So the statement :If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial is True.

It is true that (x -a) is a factor of the polynomial.

How to determine the true statement?

Let the polynomial function be f(x)

When divided by x -a, we have:

f(x)/(x - a) = Some polynomial remainder 0

The above can be represented as

f(a) = 0

This means that it is true that (x -a) is a factor of the polynomial.

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Each year has 12 months so you just need to use the formula 12 * 4 = x to get the answer. The answer is 48

i know this is late but the answer is 8 because your doing common factors so you you so 16 over 24 and see what number can go into both of those numbers which is 8 because 8 times 2=16 and 8 times 3= 24 so the answer is 8 again sorry i was late

Answer:

Maximum number of packets made = 8

Step-by-step explanation:

Number of pencils Rosy has = 16

Number of erasers Rosy has = 24

Now, it is given all the packets made contain equal number of pencils and erasers in each packet.

Therefore, to find the maximum number of packets : We find the HCF of both 16 and 24

16 = 2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 3

Common factors are : 2, 2 and 2

⇒ HCF = 2 × 2 × 2

            = 8

So, 8 packets can be made from 16 pencils and 24 erasers so that each packet will contain 2 pencils and 3 erasers each.

Hence, Maximum number of packets made = 8

1. A. (-1,2) 
2. Sorry but i cant help you with this one
3. C. (3,2)

Hope this help! Need anything else just ask! :)

P=a+b+c. Sub in what we know: 29=a+a+(a+5). Combine like terms: 29=3a+5. Subtract 5 from both sides: 24=3a. Divide by 3: 8=a. Short sides: A=8m, b=8m, long side: c=13m. :)

The answer to this is 36.

Let t = initial number of trees "remove 5 trees at the start of the season"  means     (t    - 5)     remain "each remaining tree made 210 oranges for a total of 41,790 oranges"    means         ( t   - 5)           *        210                  = 41790 Now, you can solve for t:        (t-5)(210) = 41790                     [just re-writing]        210t - 1050 = 41790                    [distribute]        210t = 42840                            [add 1050 to each side]          t = 204                                  [divide each side by 210] There were initially 204 trees.  After 5 were removed, the remaining 199 produced 210 oranges each for a total of 199*210 = 41790 oranges.

Answer:

Equations: f(t) = 210(t-5)

Initial number of trees(t) = 204

Step-by-step explanation:

Let  t represents the initial number of trees and f(t) represents the total number of oranges.

"Remove 5 orange trees from his farm" means (t-5)

" Each of the remaining trees produced 210 oranges" means [tex]210\cdot (t-5)[/tex]

so, the equation become [tex]f(t) = 210 \cdot (t-5)[/tex]

Also, it is given that total harvest of, 41790 oranges.

⇒f(t) = 41790

Substitute this in the above equation to get t;

[tex]41790 = 210(t-5)[/tex]

Divide both sides by 210 we get;

[tex]199 = t-5[/tex]

Add 5 both sides of an equation we get;

199 + 5 = t-5 + 5

Simplify:

204 = t

Therefore, there were initially 204 orange trees

The correct answer is $6000.00

The original cost of the mink coats was $6,000. This is determined by dividing the markup amount of $3,000 by the markup percentage, which is 50% or 0.50 in decimal form.

A 50% markup on cost means that the extra amount added to the cost price of the coats is 50% of that original cost price. Since the markup on the mink coats is given as $3,000, we can set up the equation as follows to find the original cost price (C):

Markup = 50% of Cost
3000 = 0.50  imes C

To find the cost (C), we divide the markup by the percentage, which in decimal form is 0.50:

C = $3,000 / 0.50
C = $6,000

Hence, the original cost of the mink coats was $6,000.

Here is an analogy comparing between unwrapping a present and unwrapping an equation. Both actions do require following a process. You cannot just skip one step in order to arrive at the answer. Just like unwrapping a present, you need to do it in order. First, you take off the ribbon, then you start to unwrap the wrapper until you see the actual gift. On the other hand, when you are unwrapping an equation, you also follow a certain step. You are given a certain formula and values. What you need to do next is to substitute, do the solution, until it is simplified. And lastly, there you have it. You can now see the actual answer. Hope this answer helps.

Final answer:

Solving an equation is likened to unwrapping a present because in both cases, you aim to uncover what's within by dealing with the outer layers systematically. Through an inverse process, you isolate the equation's variable and solve for it, just as the step-by-step unwrapping of layers reveals the gift within the package.

Explanation:

Unwrapping a present is a great way to understand the process of solving an equation. If you consider the equation itself as being 'wrapped' in different operations such as multiplication, division, addition, and subtraction, you can begin to 'unwrap' it by systematically dealing with these operations in reverse from the order of operations. This would be like when you unpack the present by undoing the tape, then the paper, then the box, or whatever other layers might be present.

To use a direct example, let's consider the equation 3x + 7 = 22. You start unwrapping by isolating for the term with the variable. This means you handle the operation that does not involve the variable first. So, subtract 7 from both sides of the equation to get 3x = 15. Next, you handle the multiplication operation by dividing both sides by 3 and solving for x, which would be 5 in this case. Just like unwrapping a present, we aim to get to the 'inside' or the root of the equation.

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the distance between any 2 points on a number line when the 2 points are x and y is
|x-y|

|-2-3|=|-5|=5
the distance is 5

or
it take 2 units to get to 0 from -2
it takes 3 units to get from 0 to 3
2+3=5