1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Nezavi [6.7K]
3 years ago
6

Tasty Donut Shack charges $4.00 for 6 donuts. At this rate, what is the charge for 4 dozen donuts?

Mathematics
1 answer:
ElenaW [278]3 years ago
3 0
$4.00 for 6 donuts would mean $1.50 per donut. There are 48 donuts in 4 dozen. $1.50 times 48 is $72. The correct answer is $72.
Hope this helped!
You might be interested in
It takes 5 men 12 days ro complete a job how many days does it take 3 men to complete the job
ss7ja [257]

Answer:

5=12

3=? then Criss cross it and you will get 12*3 divided by 5 then you get 7.2

so the answer will be 7 days

5 0
3 years ago
Solve these recurrence relations together with the initial conditions given. a) an= an−1+6an−2 for n ≥ 2, a0= 3, a1= 6 b) an= 7a
8_murik_8 [283]

Answer:

  • a) 3/5·((-2)^n + 4·3^n)
  • b) 3·2^n - 5^n
  • c) 3·2^n + 4^n
  • d) 4 - 3 n
  • e) 2 + 3·(-1)^n
  • f) (-3)^n·(3 - 2n)
  • g) ((-2 - √19)^n·(-6 + √19) + (-2 + √19)^n·(6 + √19))/√19

Step-by-step explanation:

These homogeneous recurrence relations of degree 2 have one of two solutions. Problems a, b, c, e, g have one solution; problems d and f have a slightly different solution. The solution method is similar, up to a point.

If there is a solution of the form a[n]=r^n, then it will satisfy ...

  r^n=c_1\cdot r^{n-1}+c_2\cdot r^{n-2}

Rearranging and dividing by r^{n-2}, we get the quadratic ...

  r^2-c_1r-c_2=0

The quadratic formula tells us values of r that satisfy this are ...

  r=\dfrac{c_1\pm\sqrt{c_1^2+4c_2}}{2}

We can call these values of r by the names r₁ and r₂.

Then, for some coefficients p and q, the solution to the recurrence relation is ...

  a[n]=pr_1^n+qr_2^n

We can find p and q by solving the initial condition equations:

\left[\begin{array}{cc}1&1\\r_1&r_2\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]

These have the solution ...

p=\dfrac{a[0]r_2-a[1]}{r_2-r_1}\\\\q=\dfrac{a[1]-a[0]r_1}{r_2-r_1}

_____

Using these formulas on the first recurrence relation, we get ...

a)

c_1=1,\ c_2=6,\ a[0]=3,\ a[1]=6\\\\r_1=\dfrac{1+\sqrt{1^2+4\cdot 6}}{2}=3,\ r_2=\dfrac{1-\sqrt{1^2+4\cdot 6}}{2}=-2\\\\p=\dfrac{3(-2)-6}{-5}=\dfrac{12}{5},\ q=\dfrac{6-3(3)}{-5}=\dfrac{3}{5}\\\\a[n]=\dfrac{3}{5}(-2)^n+\dfrac{12}{5}3^n

__

The rest of (b), (c), (e), (g) are solved in exactly the same way. A spreadsheet or graphing calculator can ease the process of finding the roots and coefficients for the given recurrence constants. (It's a matter of plugging in the numbers and doing the arithmetic.)

_____

For problems (d) and (f), the quadratic has one root with multiplicity 2. So, the formulas for p and q don't work and we must do something different. The generic solution in this case is ...

  a[n]=(p+qn)r^n

The initial condition equations are now ...

\left[\begin{array}{cc}1&0\\r&r\end{array}\right] \left[\begin{array}{c}p\\q\end{array}\right] =\left[\begin{array}{c}a[0]\\a[1]\end{array}\right]

and the solutions for p and q are ...

p=a[0]\\\\q=\dfrac{a[1]-a[0]r}{r}

__

Using these formulas on problem (d), we get ...

d)

c_1=2,\ c_2=-1,\ a[0]=4,\ a[1]=1\\\\r=\dfrac{2+\sqrt{2^2+4(-1)}}{2}=1\\\\p=4,\ q=\dfrac{1-4(1)}{1}=-3\\\\a[n]=4-3n

__

And for problem (f), we get ...

f)

c_1=-6,\ c_2=-9,\ a[0]=3,\ a[1]=-3\\\\r=\dfrac{-6+\sqrt{6^2+4(-9)}}{2}=-3\\\\p=3,\ q=\dfrac{-3-3(-3)}{-3}=-2\\\\a[n]=(3-2n)(-3)^n

_____

<em>Comment on problem g</em>

Yes, the bases of the exponential terms are conjugate irrational numbers. When the terms are evaluated, they do resolve to rational numbers.

6 0
3 years ago
Which value is equivalent to 12 + 24 ÷ 3? A) 8 B) 12 C) 20 D) 36
Montano1993 [528]

Answer:

c.20

Step-by-step explanation:

first step:24÷3=8

final step: 12+8=20

5 0
3 years ago
Read 2 more answers
Use =, &lt;, or &gt; signs (ratios)
oksano4ka [1.4K]

Answer:

< > > I am pretty sure that is it

5 0
3 years ago
Please give me correct answer this is major
MA_775_DIABLO [31]

Answer:

d

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Other questions:
  • Use an algebraic rule to describe a translation right 4 units and down 2 units.
    12·1 answer
  • The larger of two numbers is 3 less than the smaller number. If the sum of the numbers is 57. What are the two numbers?
    7·1 answer
  • According to the graph, what is the value of the constant in the equation
    7·1 answer
  • Worker A earns $9.50 per widget produced, produces 7 widgets per day, and works 5 hours per day. Worker B earns $8.80 per widget
    15·2 answers
  • What is the difference between -7 and 8?<br><br> 15<br> -15<br> 1<br> -1
    9·2 answers
  • Determine the smallest 6 digit number which is exactly divisible by 8,15,and21
    13·1 answer
  • Which statement must be true?
    14·1 answer
  • Find the distance between (4,5) and (-5,2).
    12·2 answers
  • Please answer these for me !
    9·1 answer
  • Hi please help me out
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!