What are both of these?

pencils are in packages of 10. Erasers come in packages of 12. Phillip wants to purchase the smallest number of pencils and eras

Sonja [21]

The smallest number of pencils and erasers and 1 eraser per pencil so number of pencils and erasers are equal
*GCD( 12;10) = 60
So Philip buy 60÷12=5 packages of erasers
60÷10=6 packaes of pencils

8 0

3 years ago

In a random sample of 10 residents of the state of Washington, the mean waste recycled per person per day was 2.3 pounds with a

djverab [1.8K]

Answer:

90% confidence interval for the mean waste recycled per person per day for the population of Washington is [2.074 , 2.526].

Step-by-step explanation:

We are given that a a random sample of 10 residents of the state of Washington, the mean waste recycled per person per day was 2.3 pounds with a standard deviation of 0.39 pounds.

Firstly, the pivotal quantity for 90% confidence interval for the mean waste recycled per person per day for the population of Washington is given by;

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

where, $\bar X$ = sample mean waste recycled per person per day = 2.3 pounds

s = sample standard deviation = 0.39 pounds

n = sample of residents = 10

$\mu$ = population mean waste recycled per person per day

Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.833 < $t_9$ < 1.833) = 0.90 {As the critical value of t at 9 degree of

freedom are -1.833 & 1.833 with P = 5%}

P(-1.833 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 1.833) = 0.90

P( $-1.833 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $1.833 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X-1.833 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+1.833 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

90% confidence interval for $\mu$ = [ $\bar X-1.833 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+1.833 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $2.3-1.833 \times {\frac{0.39}{\sqrt{10} } }$ , $2.3-1.833 \times {\frac{0.39}{\sqrt{10} } }$ ]

= [2.074 , 2.526]

Therefore, 90% confidence interval for the mean waste recycled per person per day for the population of Washington is [2.074 , 2.526].

8 0

3 years ago

Maria is monitoring the temperature of two substances in her science lab. Substance A is currently 96.2 and rising 1.4 each minu

lilavasa [31]

It would take 1.045 minutes for both substances to be at the same temperature.

Substance A started at a temperature of 96.2 and is rising at 1.4 every minute. Assuming minutes were denoted as x, the relevant expression would be:

= Starting temperature + (Rate temperature is rising x number of minutes)

= 96.2 + 1.4x

Substance B is reducing in temperature:

= 98.5 - 0.8x

Equate both expressions:

96.2 + 1.4x = 98.5 - 0.8x

1.4x + 0.8x = 98.5 - 96.2

2.2x = 2.3

x = 2.3 / 2.2

= 1.045 minutes

It would therefore take 1.045 minutes for both substances to be at the same temperature.

Find out more at brainly.com/question/12012659.

6 0

2 years ago

Math help. Solve for x

Dafna1 [17]

X=2 $\sqrt{3}$

5 0

3 years ago

What is 12.00 divided by 4.5

Pavel [41]

The answer is 2.6666666667

3 0

3 years ago