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3 years ago

8

A lottery has a grand prize of 25and 1/2 million dollars. There are 5 people who have winning tickets and they share this prize

equally. How many millions of dollars does each person get? Express the answer as a mixed number.

1 answer:

evablogger [386]3 years ago

7 0

Answer:

5 1/10 million dollars

Step-by-step explanation:

25and 1/2 million dollars = 25 1/2 million dollars

= (25*2) + 1 / 2

= 50+1/2

= 51/2

Total prize = 51/2 million dollars

Number of people with winning ticket = 5

How many millions of dollars does each person get?

Amount of prize each person get = Total prize / Number of people with winning ticket

= 51 / 2 ÷ 5

= 51/2 × 1/5

= (51 * 1) / (2 * 5)

= 51/10

= 5 1/10 million dollars

Amount of prize each person get = 5 1/10 million dollars

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Fernando followed two diagonal paths, Paths 1 and 2, to get from his house, F, to a neighborhood corner store, C, as shown below

aleksandrvk [35]

Answer:

42 meters

Step-by-step explanation:

Given

See attachment for complete question

Required

Calculate distance FC

FC is calculated as:

$FC = Path\ 1 + Path\ 2$

Where

$Path\ 1 = FB$

$Path\ 2 = BC$

Considering $\triangle FEB$ , we have:

$FB^2 = FE^2 + BE^2$ --- Pythagoras theorem

Where

$FE = FD - BA$

$FE = 22m - 15m$

$FE = 7m$

and

$BE = CD - CA$

$BE = 32m - 8m$

$BE = 24m$

So:

$FB^2 = FE^2 + BE^2$

$FB^2 = 7^2 +24^2$

$FB^2 = 49 +576$

$FB^2 = 625$

Take square roots of both sides

$FB = 25$

So:

$Path\ 1 = 25$

Considering $\triangle BAC$ , we have:

$BC^2 = BA^2 + AC^2$ --- Pythagoras theorem

Where:

$BA = 15$ and $AC = 8$

So, we have:

$BC^2 = 15^2 + 8^2$

$BC^2 = 225 + 64$

$BC^2 = 289$

Take square roots of both sides

$BC = 17$

So;

$Path\ 2= 17$

Recall that:

$FC = Path\ 1 + Path\ 2$

$FC = 25 + 17$

$FC = 42$

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3 years ago

What is the following is the solution to the equation 25^(z+2) = 125

maksim [4K]

First, rewrite the equation $25^{z+2} = 125$ with the base equal to 5. Note that:

$25=5^2;$
$125=5^3;$
$25^{z+2}=(5^2)^{z+2}=5^{2\cdot (z+2)}.$

Then

$5^{2\cdot (z+2)}=5^3.$

Since the bases are equal, you have that powers are equal too:

$2\cdot (z+2)=3,\\ \\2z+4=3,\\ \\2z=3-4,\\ \\2z=-1,\\ \\z=-\dfrac{1}{2}.$

Answer: $z=-\dfrac{1}{2}.$

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