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3 years ago

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A piggy bank contains only quarters and nickels, and there is a total of 60 coins. The total value of coins in the bank is 7.40.

How many quarters are in the piggy bank? HELP

1 answer:

Eduardwww [97]3 years ago

8 0

There are 22 quarters in the bank

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SVEN [57.7K]

Answer:

1)

1st Error: In going from Step 3 to Step 3.

Reason: Negative sign is not distributed inside the brackets.

2nd Error: In going from Step 5 to Step 6

Reason: Sign of the number is not changed while moving to other side of inequality,

2)

a) 12=-4(-6x-3) and x+5=-5x+5

b) -(7-4x)=9 and 5x+34=-2(1-7x) and -8=-(x+4)

Step-by-step explanation:

Question 1)

The given inequality is:

$\frac{5}{12}-\frac{x-3}{6} \leq \frac{x-2}{3}$

<u>Step 1: Making the denominators common for all fractions</u>

$\frac{5}{12}-\frac{2}{2} \times \frac{x-3}{6} \leq \frac{4}{4} \times \frac{x-2}{3}$

This step is done correctly in the given solution.

<u>Step 2: Simplifying </u>

$\frac{5}{12}-\frac{2x-6}{12}\leq \frac{4x-8}{12}$

This step is done correctly in the given solution

<u>Step 3: Multiplying both sides by 12, and simplifying.</u>

$5-(2x-6)\leq 4x-8\\\\ 5-2x+6\leq 4x-8$

First error is made in this step. While opening the brackets, the negative sign should be distributed inside the bracket, which will change the signs.

<u>Step 4: Simplification:</u>

$11-2x\leq 4x-8$

<u>Step 5: Moving Common terms to one side and simplifying</u>

$-2x-4x\leq -8-11\\\\ -6x\leq -19$

Error was made in this step. When a number is moved to other side, its sign will be changed.

<u>Step 6: Dividing both sides by -6</u>

$x\geq \frac{19}{6}$

Conclusion:

1st Error: In going from Step 3 to Step 3.

Reason: Negative sign is not distributed inside the brackets.

2nd Error: In going from Step 5 to Step 6

Reason: Sign of the number is not changed while moving to other side of inequality,

Question 2:

In the Equation 2: 12=-4(-6x-3), when -4 will be multiplied inside the brackets, the 12 on eft hand side will cancel the 12 that will appear on right hand side, giving a result that will lead to x = 0.

Same is the case with Equation 6: x+5=-5x+5, 5 on both sides will cancel out leaving x = 0.

So, 2nd and 6th equations will have the same solution.

In Equation 1, on expanding the bracket and moving 7 to other side, we get a relation: 4x = 16

In Equation 3, on simplifying the right hand side, and carrying common terms to one side, we get the relation: - 9x = -36

In Equation 5, on expanding the bracket and simplifying the relation is reduced to 4 = x

It can be observed that all these 3 equations have the same solution i.e. x = 4

So, the following set of Equations have the same solution:

a) 12=-4(-6x-3) and x+5=-5x+5

b) -(7-4x)=9 and 5x+34=-2(1-7x) and -8=-(x+4)

6 0

3 years ago

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An object falls freely in a straight line and experiences air resistance proportional to its? speed; this means its acceleration

KiRa [710]

Answer:

t = 1.068 s

Step-by-step explanation:

given,

a(t) =- k v(t)

speed of the object decreases from 800 ft/s to 700 ft/s

distance = 1400 ft

time for deceleration = ?

a(t) =- k v(t)

$\dfrac{dv}{dt}= - kv$

$\dfrac{dv}{v}= - kdt$

integrating both side

$\int_{800}^{700}\dfrac{dv}{v}= - k\int dt$

$ln(\dfrac{7}{8})=-kt$

$t = -\dfrac{1}{k}ln(\dfrac{7}{8})$ ..........(1)

since,

$v = v_1e^{-kt}$

$\dfrac{ds}{dt} = 800e^{-kt}$

$\int ds= 800\int_0^t e^{-kt}dt$

$1400= -\dfrac{800}{k}[e^{-kt}-e^0]$

from equation 1

$k= -\dfrac{8}{14}[\dfrac{7}{8}-1]$

$k= \dfrac{1}{8}$

putting value of k in equation (1)

$t = -8ln(\dfrac{7}{8})$

t = 1.068 s

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3 years ago

The number of days, d, of snow is not 7

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3 years ago

(3^6)^-2/(6^-9*-2^10)

kaheart [24]

$\frac{(3^{6})^{-2}}{(6^{-9}*-2^{10})}\\
\frac{3^{-12}}{(6^{-9}*-2^{10})}\\
\frac{6^{9}}{(3^{12}*-2^{10})}\\
\frac{10077696}{531441*-1024}=-0.0185185$

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3 years ago

Molly can bake 3 cakes in 2 hours. How many cakes can she bake per hour?

just olya [345]

Answer: 1.5 cakes per hour

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3 years ago

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