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3 years ago

Are these ratios equivalent?

Mathematics

1 answer:

lianna [129]3 years ago

5 0

Answer:

Yes

Step-by-step explanation:

3:9 in their lowest forms are 1:3 which is the same for 6:18

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The quantity demanded x each month of Russo Espresso Makers is 250 when the unit price p is $138. The quantity demanded each mon

Stells [14]

Answer:

(a) $D(q)=\frac{-1}{25} q+148$

(b) $S(q)=\frac{1}{50}q+58$

Step-by-step explanation:

(a) For the demand equation D(q) we have

P1: 138 Q1: 250

P2: 108 Q2: 1000

We can find m, which is the slope of the demand equation,

$m=\frac{p_{2} -p_{1} }{q_{2} -q_{1} }=\frac{108-38}{1000-250} =\frac{-30}{750}=\frac{-1}{25}$

and then we find b, which is the point where the curve intersects the y axis.

We can do it by plugging one point and the slope into the line equation form:

$y=mx+b\\\\D(q)=mq+b\\\\138=\frac{-1}{25}(250) +b\\\\138=-10+b\\\\138+10=b=148$

With b: 148 and m: -1/25 we can write our demand equation D(q)

$D(q)=\frac{-1}{25} q+148$

(b) to find the supply equation S(q) we have

P1: 102 Q1: 2200

P2: 102 Q2: 700

Similarly we find m, and b

$m=\frac{p_{2} -p_{1} }{q_{2} -q_{1} }=\frac{72-102}{700-2200} =\frac{-30}{-1500}=\frac{1}{50}$

$y=mx+b\\\\D(q)=mq+b\\\\72=\frac{1}{50}(700) +b\\\\72=14+b\\\\72-14=b=58\\$

And we can write our Supply equation S(q):

$S(q)=\frac{1}{50}q+58$

(c) Now we may find the equilibrium quantity q* and the equilibrium price p* by writing D(q)=S(q), which means the demand equals the supply in equilibrium:

$D(q)=S(q)\\\\\frac{-1}{25}q+148=\frac{1}{50}q+58\\\\$

$148-58=\frac{1q}{50} +\frac{1q}{25} \\\\90= \frac{1q}{50} +\frac{2q}{50}\\\\90=\frac{3q}{50}\\ \\q=1500\\\\$

We plug 1500 as q into any equation, in this case S(q) and we get:

$S(q)=\frac{1}{50}q+58\\\\S(1500)=\frac{1}{50}(1500)+58\\\\S(1500)=30+58\\\\S(1500)=88$

Which is the equilibrium price p*.

8 0

3 years ago

Examine the diagram. Parallel lines a and b are crossed by transversal t to create 8 angles. Clockwise from top left, the angles

choli [55]

Answer:

60.25 then 34.5

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

M∠6 is (2x – 5)° and m∠8 is (x + 5)°. What is m∠3?

erastovalidia [21]

I hope this helps you

4 0

3 years ago

Read 2 more answers

What is the value of StartFraction negative 2 (7 minus 15) over 4 EndFraction? –4 –2 2 4

BartSMP [9]

Answer:

The Correct answer is last option i.e 4.

Therefore,

$-2(\dfrac{7-15}{4})=4$

Step-by-step explanation:

Given:

StartFraction negative 2 (7 minus 15) over 4 EndFraction

Means

$-2(\dfrac{7-15}{4})$

$-2(\dfrac{-8}{4})$

$-2(-2)$

Minus sign will enter in it and ( - ) × ( - ) = ( + )

$4$

Therefore,

$-2(\dfrac{7-15}{4})=4$

3 0

3 years ago

Read 2 more answers

Jake opens a credit card with 18% annual interest compounded monthly. If he charges $800 on the card and never pays it off, how

Makovka662 [10]

<h3>Answer: $1,143.60</h3>

Work Shown:

A = P*(1+r/n)^(n*t)

A = 800*(1+0.18/12)^(12*2)

A = 1,143.60224954321

A = 1,143.60

Notes:

P = 800 is the principal. It is the amount loaned to Jake.
r = 0.18 is the decimal form of the 18% interest rate
n = 12 because we're compounding monthly, i.e. 12 times a year
t = 2 = number of years
For more information, check out the compound interest formula.

4 0

2 years ago