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Arada [10]
3 years ago
8

a bus is full of passengers. if you count them by either twos, threes, or fives, there is one left. if you count them by seven t

here will be none left. find the least number of passengers in the bus?​
Mathematics
1 answer:
devlian [24]3 years ago
3 0

Answer:

91.

Step-by-step explanation:

The least number will be a multiple of 7 while the number - 1 will be a multiple of 2,3 and 5.

2*3*5 = 30  but 31 is not a multiple of 7.

2*2*3*5 = 60 but 61  is not divisible by 7.

2*3*3*5 = 90 and 91 is divisible by 7.

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A random sample of 36 students at a community college showed an average age of 25 years. Assume the ages of all students at the
Pavel [41]

Answer:

98% confidence interval for the average age of all students is [24.302 , 25.698]

Step-by-step explanation:

We are given that a random sample of 36 students at a community college showed an average age of 25 years.

Also, assuming that the ages of all students at the college are normally distributed with a standard deviation of 1.8 years.

So, the pivotal quantity for 98% confidence interval for the average age is given by;

             P.Q. = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \bar X = sample average age = 25 years

            \sigma = population standard deviation = 1.8 years

            n = sample of students = 36

            \mu = population average age

So, 98% confidence interval for the average age, \mu is ;

P(-2.3263 < N(0,1) < 2.3263) = 0.98

P(-2.3263 < \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < 2.3263) = 0.98

P( -2.3263 \times {\frac{\sigma}{\sqrt{n} } < {\bar X - \mu} < 2.3263 \times {\frac{\sigma}{\sqrt{n} } ) = 0.98

P( \bar X - 2.3263 \times {\frac{\sigma}{\sqrt{n} } < \mu < \bar X +2.3263 \times {\frac{\sigma}{\sqrt{n} } ) = 0.98

98% confidence interval for \mu = [ \bar X - 2.3263 \times {\frac{\sigma}{\sqrt{n} } , \bar X +2.3263 \times {\frac{\sigma}{\sqrt{n} } ]

                                                  = [ 25 - 2.3263 \times {\frac{1.8}{\sqrt{36} } , 25 + 2.3263 \times {\frac{1.8}{\sqrt{36} } ]

                                                  = [24.302 , 25.698]

Therefore, 98% confidence interval for the average age of all students at this college is [24.302 , 25.698].

8 0
3 years ago
Simplify the following expression.<br> 2x^2-9-17x^2+10+7x
snow_lady [41]

Answer:

- 15x² + 7x + 1

Step-by-step explanation:

Given

2x² - 9 - 17x² + 10 + 7x ← collect like terms

= (2x² - 17x² ) + 7x + 1

= - 15x² + 7x + 1

5 0
3 years ago
What time 30equals 200
Dovator [93]
The answer is 20/3 first you set a variable x and 30x=200 divid both side by 30 and get the final answer
8 0
3 years ago
Read 2 more answers
What is the probability of getting an odd number 1-10?
Annette [7]

Answer:

1/2 - Half of the numbers are odd

7 0
3 years ago
Need Assistance<br>Show Work​
Evgesh-ka [11]

Answer:

-52, and the opposite of this is 52.

Step-by-step explanation:

If we are losing 52 pounds, then our number is -52 since we are losing 52 pounds (adding a negative number to a positive number is the same as subtracting that number).

The opposite of a number is when we negate the number, or multiply it by -1.

A negative number times a negative number is a positive number.

-52\cdot-1 = 52\cdot1 = 52

Hope this helped!

6 0
3 years ago
Read 2 more answers
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