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2 years ago

If a bag contains 12 quarters, 6 dimes, and 18 nickles, what is the part-to-whole ratio of nickles to all coins?

Mathematics

1 answer:

zepelin [54]2 years ago

3 0

Answer:

18/36 or 1/2

Step-by-step explanation:

There are 18 nickels, which is the numerator.

You add all the numbers together to get the denominator, which is 12+6+18=36.

Then, you put the two values in a fraction - 18/36

and simplify, to get you 1/2.

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Find the coordinates of the circumcenter of △PQR with vertices P(−2,5), Q(4,1), and R(−2,−3).

mel-nik [20]

Answer: (1/3,2)

Step-by-step explanation:

Let O(x,y) be the circumference of the triangle PQR,

Thus, by the property of circumcenter all the vertices of the triangle are at same distance from this circumcenter.

Thus, PO = QO

By the distance formula,

$(x+2)^2+(y-5)^2 = (x-4)^2+(y-1)^2$

$\impliesx^2+ 4x + 4 + y^2+ 25 - 10 y = x^2+16 - 8 x + y^2+1 - 2y$

$\implies 4x + 4 + 25 - 10 y = 16 - 8 x + 1 - 2y$

$\implies 4x +8x-10y+2y = 16 + 1 -25-4$

$\implies 12x - 8y = 17 - 29$

$\implies 12 x - 8 y = - 12$ ---------(1)

Similarly, QO = RO

$\implies (x-4)^2 + (y-1)^2 = (x+2)^2+(y+3)^2$

$\implies x^2 + 16 - 8x + y^2+ 1 - 2y = x^2+ 4 + 4 x +y^2+ 9 + 6 y$

$\implies 16 - 8x + 1 - 2y = 4 + 4 x + 9 + 6 y$

$\implies - 8x -4x-2y-6y=4+9-16-1$

$\implies -12 x - 8 y = 13 - 17$

$\implies 12 x + 8 y = 4$ ------------(2)

By adding equation (1) and (2),

24 x = - 8

x = 1/3

By putting this value in equation (1),

We get,

Thus, 4 - 8 y = -12

8 y = 16

y = 2

7 0

2 years ago

Determine whether the statement is always, sometimes, or never true: Two points A and B determine a line. *

alisha [4.7K]

Answer:

sometimes

Step-by-step explanation:

8 0

2 years ago

Solve 2y-3 = 4y + 6.<br> y=?

valentinak56 [21]

y= 3/8 OR 0.375

Step-by-step explanation:

yes

5 0

2 years ago

Read 2 more answers

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

BARSIC [14]

Total handshakes will be $\\2^{n} = 2^{66}$

4 0

2 years ago

Use the compound interest formula to determine the final value of the following amount. $1900 at 10.4% compounded monthly for 4.

nikklg [1K]

Answer:

$3027.80

Explanation:

The compound interest formula is the following.

$A=P(1+\frac{r}{n})^{nt}$

where

A = final amount

P = principle amount

r = interest rate / 100

n = number of compounds per interval

t = time interval

Now in our case,

A = unknown

P = $1900

r = 10.4/100

n = 12 months / year ( because the interest is compounded monthly)

t = 4.5 yrs

Therefore, the compound interest formula gives

$A=1900(1+\frac{10.4/100}{12})^{12*4.5}$

Using a calculator, we evaluate the above to get

$\boxed{A=\$3027.80}$

which is our answer!

8 0

10 months ago