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3 years ago

five more than one-fourth of a number is two-thirds of that number. find the number. a. 15 b. 12 c. 13 d. 14

Mathematics

1 answer:

andrew11 [14]3 years ago

3 0

Let the number be x, then 5 + 1/4 x = 2/3 x
2/3 x - 1/4 x = 5
5/12 x = 5
5x = 5(12)
x = 12

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Construct a 99% confidence interval for the population mean, mu. Assume the population has a normal distribution. A group of 1

Zarrin [17]

Answer:

99% confidence interval for the population mean is [19.891 , 24.909].

Step-by-step explanation:

We are given that a group of 19 randomly selected students has a mean age of 22.4 years with a standard deviation of 3.8 years.

Assuming the population has a normal distribution.

Firstly, the pivotal quantity for 99% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean age of selected students = 22.4 years

s = sample standard deviation = 3.8 years

n = sample of students = 19

$\mu$ = population mean

Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 99% confidence interval for the population mean, $\mu$ is ;

P(-2.878 < $t_1_8$ < 2.878) = 0.99 {As the critical value of t at 18 degree of

freedom are -2.878 & 2.878 with P = 0.5%}

P(-2.878 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 2.878) = 0.99

P( $-2.878 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $2.878 \times {\frac{s}{\sqrt{n} } }$ ) = 0.99

P( $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ) = 0.99

99% confidence interval for $\mu$ = [ $\bar X -2.878 \times {\frac{s}{\sqrt{n} }$ , $\bar X +2.878 \times {\frac{s}{\sqrt{n} }$ ]

= [ $22.4 -2.878 \times {\frac{3.8}{\sqrt{19} }$ , $22.4 +2.878 \times {\frac{3.8}{\sqrt{19} }$ ]

= [19.891 , 24.909]

Therefore, 99% confidence interval for the population mean is [19.891 , 24.909].

6 0

3 years ago

The correlation coefficient for the ages of drivers in a driver safety class and the number of traffic violations they have rece

Doss [256]

A correlation coefficient is always a value in between -1 and 1
The closest a coefficient to -1, the correlation is a strong negative correlation
The closest a coefficient to 1, the correlation is a strong positive correlation
The closest a coefficient to 0, there is no correlation at all

The coefficient -0.61 shows a strong negative correlation
This means that the relationship between the age and the violation is an inverse relationship; as age increases, violation decreases

Answer: option C

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3 years ago

Write 4.5 as a mixed number.

Zolol [24]

Answer:

9/2

Step-by-step explanation:

4.5 = 4 1/2 = 9/2

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3 years ago

Read 2 more answers

What's an excuse if you miss a class

diamong [38]

Answer:

Say you ate something bad and you kept throwing up idrk

Step-by-step explanation:

5 0

2 years ago

How would I solve n/5-3n/10=1/5 pls help me I am literally failing math.

otez555 [7]

Answer:

53/5

Step-by-step explanation:

since 10 is the denominator of the denominator we can move it to the numerator, giving us 10n/5-3n = 1/5

multiply all sides by 5-3n, giving us 10n = (5-3n)/5

now multiply by 5 to get rid of the final denomintor, 50n = 5-3n

move 3n to the other side 53n = 5, n = 53/5

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3 years ago