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3 years ago

Prove that's the decimal number 9.86 is a rational by finding its fractional form

1 answer:

5 0

9.86 = 9.86/1 = (9.86 x 100) / (1 x 100) = 986/100, GCF of 986 and 100 is 2, (986/2) / (100/2) = 493/50 The fractional form of 9.86 is 943/50.

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Convert each rational number into its decimal form. 1. 1/3 2. 1/6 3. 1/9

stepladder [879]

Answer:

1. 0.33 2. 0.16 3. o.11

Step-by-step explanation:

5 0

3 years ago

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

X+3y=14 y=3x-14 Solving systems using substitution How do i do this?

Free_Kalibri [48]

X + 3y = 14
x + 3(3x - 14) = 14
x + 9x - 42 = 14
10x - 42 = 14
 + 42 + 42
 10x = 56
 10 10
 x = 5.6
5.6 + 3y = 14
- 5.6 - 5.6
 3y = 8.4
 3 3
 y = 2.7
 (x, y) = (2.7, 5.6)

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4 years ago

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What is the reflection across the y-axis?

Allisa [31]

Answer:

Step-by-step explanation:

what ever it is you do the same on the other side

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1 year ago

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A field is 3654 feet long what is the length of the field in yards

charle [14.2K]

Answer:

1,218 yd.

Step-by-step explanation:

3 ft. = 1 yd. 3,654 ÷ 3 = 1,218

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3 years ago