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kkurt [141]
3 years ago
9

a leak is slowly draining water from a pool containing 324 gallons of water. How much water is remaining after 8 hours if it lea

ks 7 gallons per hour
Mathematics
1 answer:
sergey [27]3 years ago
3 0
268 gallons are remaining. The equation would be y=324-7x, with x being 8. 7(8) is 56, and then you take away 56 from 324, which then gives you 268 gallons remaining
You might be interested in
Pleaseee answer asap worth 17 pts
bija089 [108]
Speed=distance/time
average speed=(total distance)/(total time)

total distance=203+243=446
total time=3.5+4.5=8

average speed=(446)/(8)=55.75


answer is A
7 0
3 years ago
a scarf is originally priced at $30.00. it is then discounted by 25%. several days later, it is discounted 10% off the new price
jeka94
No. 
a. take 35% off 30 =19.5
b. first take 25% off 30 = 22.5, then take 10% off 22.5 = 20.25
8 0
3 years ago
Which expression should you simplify to find the 90% confidence interval,
bogdanovich [222]

Answer:

0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.2870.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613

we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

Step-by-step explanation:

The estimated proportion of interest is \hat p=0.45

We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025.

And the critical value is:z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the true population proportion is interest is given by this formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Replacing the values provided we got:

0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287\\\\0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613

And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

5 0
3 years ago
The board of directors of a corporation must select a president, a secretary, and a treasurer. In how many possible ways can thi
pentagon [3]

Answer:

9,240 ways possible in which  this can be accomplished if there are 22 members on the board of directors.

Step-by-step explanation:

Total number of available members in the board = 22

The number of posts chosen are a president, a secretary, and a treasurer.

<u>For the Post of President:</u>

The number of available options to choose a president = 22  options

<u>For the Post of Secretary:</u>

As we can not repeat the members because one person CANNOT hold two positions simultaneously.

The number of available options to choose a secretary = 21  options

<u>For the Post of Treasurer:</u>

As we can not repeat the members because two person CANNOT hold three positions simultaneously.

The number of available options to choose a treasure = 20 options

Now, the  possible ways can this whole election be accomplished is the product of all possible options

= 22 option x 21 option x 20 option

= 9,240 ways

Hence, there are 9,240 ways possible in which  this can be accomplished if there are 22 members on the board of directors.

4 0
3 years ago
Consider a data set containing the following values: 70 65 71 78 89 68 50 75 The mean of the preceding values is 70.75. The devi
Leokris [45]

Answer:

If this is the sample data, the sample variance is 125.07 and the sample standard deviation is 11.18

If this is a population data, the population variance is 109.44 and the population standard deviation is 10.46

Step-by-step explanation:

We are given the following data-set:

70, 65, 71, 78, 89, 68, 50, 75

Deviations from the mean

–0.75, –5.75 , 0.25, 7.25, 18.25, –2.75, –20.75, 4.2

Sample size, n = 8

Sample:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

s = \sqrt{\dfrac{875.5}{7}} = 11.18

\text{ Sample variance} = s^2 = 125.07

Population:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.

Sum of squares of differences =

0.5625 + 33.0625 + 0.0625 + 52.5625 + 333.0625 + 7.5625 + 430.5625 + 18.0625 = 875.5

\sigma = \sqrt{\dfrac{875.5}{8}} = 10.46

\text{ Population variance} = \sigma^2 = 109.44

7 0
3 years ago
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