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diamong [38]
3 years ago
7

zachary has coins of the coins 3/6 are nickles, 2/6 dimes, rest are quarters. What is the ratio of zacharies nickles, to dimes t

o quarters?
Mathematics
1 answer:
lesya692 [45]3 years ago
8 0

Answer:

The ratio of zacharies nickels to dimes to quarters is <u>3 : 2 : 1</u>.

Step-by-step explanation:

Given:

Zachary has coins of the coins 3/6 are nickels, 2/6 dimes, rest are quarters.

Now, to get the ratio of zacharies nickels, to dimes to quarters.

So, as given dimes and nickels we find the quarters to get the ratio:

\frac{3}{6} -\frac{2}{6}=\frac{3-2}{6} =\frac{1}{6}.

Thus, the quarters are 1/6.

Now, getting the ratio of the coins:

Nickels = 3/6 × 6 = 3

Dimes = 2/6 × 6 = 2

Quarters = 1/6  × 6 = 1

<em>Nickels : Dimes : Quarters = 3 : 2 : 1.</em>

Therefore, the ratio of zacharies nickels to dimes to quarters is 3 : 2 : 1.

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Use the following information for problems 1 – 3. Suppose you sign a contract for an annual salary of $50,000 with a guaranteed
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Initial salary =  $50,000 .

Rate of raise = 5% each year.

Therefore, each next year salary would be 105% that is 1.05 times.

5% of 50,000 = 0.05 × 50000 = 2500.

Therefore raise is $2500 each year.

According to geometric sequence first term 50000 and common ratio 1.05.

Applying geometric sequence formula

a_n = ar^{n-1}

1) a_n = 50000(1.05)^{n-1}

2) In order to find salary in 5 years we need to plug n=5, we get

a_5 = 50000(1.05)^{5-1}= 50000(1.05)^4

= 50000(1.21550625)

<h3>=$60775.3125.</h3>

3) In order to find the total salary in 10 years we need to apply sum of 10 terms formula of a geometric sequence.

S_n = \frac{a(1-r^n}{1-r}

Plugging n=10, a = 50000 and r= 1.05.

S_10 = \frac{50000(1-(1.05)^{10}}{1-1.05}

S_10 = \frac{50000(0.050)^{10}}{0.05}

= 628894.62678.

<h3>Therefore , you will have earned $ 628894.62678 in total salary by the end of your 10th year.</h3>



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Step-by-step explanation:

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If the coordinates of point a are -3 and 2 and the coordinates of point B are 7 and 6 the x-intercept of CD is what
AveGali [126]

Answer:

The x-intercept of CD is -19/5

Step-by-step explanation:

If the coordinates of the first point is (-3, 2) and the coordinates of the point B are (7, 6) then we need first to find the equation of the line CD:

We know that the general equation of the line is:

y-y0 = m(x-x0) where (x0, y0) represents a point that belongs to the line and m, is the slope which can be calculated by using the following formula:

m = (x1 - x0) / (y1 - y0)

In this case:

(x1, y1) = (7, 6)

(x0, y0) = (-3, 2)

Then:

m = (7 - (-3))/(6-2) = 10/4 = 5/2.

Then, the equation of the line is:

y-y0 = m(x-x0)

y - 2 = 5/2 (x -(-3))

y = 5/2(x+3) + 2

To find the x intercept we make y=0.

Then y = 5/2(x+3) + 2 = 0

Then:

x = -4/5 - 3 = -19/5

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