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elena-s [515]
2 years ago
14

How many zeroes are at the end of $42!$ (42 factorial)? (Reminder: The number $n!$ is the product of the integers from 1 to $n$.

For example, $5!=5\cdot 4\cdot3\cdot2\cdot 1= 120$.)
Mathematics
1 answer:
Dovator [93]2 years ago
4 0

Answer:

47 zeros

Step-by-step explanation:

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According to the Rational Root Theorem, which statement about f(x) = 66x4 – 2x3 + 11x2 + 35 is true? Any rational root of f(x) i
Kamila [148]

Answer:

The correct option is Any rational root of f(x) is a factor of 35 divided by a factor of 66....

Step-by-step explanation:

According to the rational root theorem:

if a_{0} and a_{n} are non zero then each rational solution x will be:

x= +/- Factors of a_{0} / Factors of  a_{n}

In the given polynomial we have:

66x4 – 2x3 + 11x2 + 35

a_{0} = 35

a_{n} = 66

Therefore,

x= +/- Factors of 35/ Factors of 66.

Thus the correct option is Any rational root of f(x) is a factor of 35 divided by a factor of 66....

3 0
2 years ago
Read 2 more answers
A train is leaving in 11 minutes and you are one mile from the station. Assuming you can walk at 4mph and run at 8mph, how much
ddd [48]

7 minutes is the time can you afford to walk

<em><u>Solution:</u></em>

Given that, train is leaving in 11 minutes and you are one mile from the station

Let "x" represent how much time can you afford to walk

Then, (11 - x) is the time you run

You can walk at 4mph and run at 8mph

<em><u>Convert to miles per minute</u></em>

1 hour = 60 minutes

4\ mph = 4 \times \frac{1}{60} \text{ miles per minute } = \frac{1}{15} \text{ miles per minute }\\\\8\ mph = 8 \times \frac{1}{60}\ \text{ miles per minute } = \frac{2}{15} \text{ miles per minute }

We know that,

Distance = speed \times time

Given that, you are one mile from the station

Therefore,

1 mile = distance walk + distance run

1 = x \times \frac{1}{15} + (11-x) \times \frac{2}{15}\\\\1 = \frac{1}{15}(x + 2(11-x))\\\\1 = \frac{1}{15}(x + 22 - 2x)\\\\x + 22 - 2x = 15\\\\x = 22 - 15\\\\x = 7

Thus, 7 minutes is the time can you afford to walk

6 0
2 years ago
Jake is the kicker on the football team and has an amazing kick during the game. The path of the football can be measured by the
xeze [42]
The height of the ball when it is 5 meters away from Jake to the nearest whole number is 160 meters:
h=-.625*5(5-56)=159.375 meters exact.
3 0
2 years ago
Bentley is working two summer jobs, making $18 per hour lifeguarding and making $8 per hour clearing tables. In a given week, he
Mariulka [41]

Answer:

8 hours

Step-by-step explanation:

First, let's find how much Bentley gets from clearing tables.

5 hours • $8 per hour = $40 total

We can take $40 off his $180 total, leaving the rest for when we figure out how much he needs to work lifeguarding.

$180 needed - $40 earned = $140 left to earn

We know that Bentley makes $18 an hour lifeguarding, so in order to get the number of hours he would need to work in order to make $140, we can divide it by $18.

$140 needed ÷ $18 per hour = 7.77...

We need to convert this to a whole number because we're talking about hours worked, so Bentley would need to work 8 hours lifeguarding to make $140 more. He can only work 15 hours total, so let's check if this exceeds his limit.

5 hours clearing tables + 8 hours lifeguarding = 13 hours < 15 hours max

It is possible to make $180 total from this work schedule, so your answer would be 8 hours.

8 0
1 year ago
Which of the following graphs matches the circle defined by this equation ? (x - 3) ^ 2 + (y + 1) ^ 2 = 25
tiny-mole [99]

Answer:

2x^2+10x-12=0

Step-by-step explanation:

6 0
1 year ago
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