24 and 1 fifth minus negative 14 and one third

A tap can fill a bucket in 6 hours. After half the bucket is filled, three more similar taps are opened. What is the total time

Masja [62]

The total time taken to fill the bucket completely is 3 hours and 45 minutes.

<h3>What is Division?</h3>

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

Let the volume of the bucket be represented by x. Then the rate at which the complete bucket can be filled is,

Rate = Total volume/ Time taken to fill the bucket

Rate = x / 6

Now, the time it will take for the half bucket, therefore, x/2 bucket to fill,

Rate = Volume / Time

x/6 = (x/2) / Time

Time = (x/2) / (x/6)

Time = 3 hours

Now, since three more such taps are opened, therefore, the rate of filling the bucket will be,

Rate = 4 × Rate of a single tap

= 4 × (x/6)

= 4x / 6

= 2x / 3

Further, the time it will take for the four taps to fill the half bucket is,

Rate = Volume / Time

2x/3 = (x/2) / Time

Time = (x/2) / (2x/3)

Time = 3/4 hours

Furthermore, the total time taken to fill the bucket completely is,

Total time = 3 hours + 3/4 hours

= 3 3/4 hours

= 3.75 hours

= 3 hours and 45 minutes

Hence, the total time taken to fill the bucket completely is 3 hours and 45 minutes.

Learn more about Division here:

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7 0

1 year ago

Plz help!!! I need the answer quickly

MaRussiya [10]

Hamburger cheeseburger big Mac whopper

3 0

3 years ago

Read 2 more answers

Is the relationship shown by the data linear? If so, model the data with an equation. x= -7, -5, -3 ,-1 , y = 5, 9, 13, 17

PIT_PIT [208]

First we take the two points (-7,5) and (-5,9).
Compute the slope: $\frac{9-5}{-5+7}=2$
Then the linear relation may be in the following form $y=2x+b$
Since the point (-7,5) is on the line, then $5=-7(2)+b\text{ then }b=19.$
The relation is then $y=2x+19$ .
We check that the other point are on the above line:
$2(-3)+19=13 \text{ OK}\\2(-1)+19=17 \text{ OK}$
We have then a linear relation.

3 0

3 years ago

June and Stella can each create six floral arrangements in one hour. If they take in 372 Valentineâs Day orders, how many hours

sesenic [268]

Answer:

31 hours

Step-by-step explanation:

June and Stella can create 6 floral arrangements in one hour.

They take in 372 Valentine's Day order

No of hours = orders / (June's rate + Stella's rate)

June's rate = 6 arrangements / hour

Stella's rate = 6 arrangements / hour

June's rate + Stella's rate = 2(6 arrangements /hour)

= 12 arrangements / hour

No of hours = 372 arrangements / 12 arrangements / hour

= 31 hours

June and Stella have 31 hours to fulfill the 372 Valentine's Day order

8 0

3 years ago

Dylan Rieder is a statistics student investigating whether athletes have better balance than non-athletes for a thesis project.

Kobotan [32]

Answer:

$t=\frac{(3.7-4.1)-0}{\sqrt{\frac{1.1^2}{32}+\frac{1.3^2}{45}}}}=-1.457$

$p_v =P(t_{75}$

Comparing the p value with a significance level for example $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the population mean for the athletes is significantly lower than the population mean for non athletes.

Step-by-step explanation:

Data given and notation

$\bar X_{A}=3.7$ represent the mean for athletes

$\bar X_{NA}=4.1$ represent the mean for non athletes

$s_{A}=1.1$ represent the sample standard deviation for athletes

$s_{NA}=1.3$ represent the sample standard deviation for non athletes

$n_{A}=32$ sample size for the group 2

$n_{NA}=45$ sample size for the group 2

$\alpha=0.01$ Significance level provided

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the population mean for athletes is lower than the population mean for non athletes, the system of hypothesis would be:

Null hypothesis: $\mu_{A}-\mu_{NA}\geq 0$

Alternative hypothesis: $\mu_{A} - \mu_{NA}< 0$

We don't have the population standard deviation's, we can apply a t test to compare means, and the statistic is given by:

$t=\frac{(\bar X_{A}-\bar X_{NA})-\Delta}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{NA}}{n_{NA}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

With the info given we can replace in formula (1) like this:

$t=\frac{(3.7-4.1)-0}{\sqrt{\frac{1.1^2}{32}+\frac{1.3^2}{45}}}}=-1.457$

P value

We need to find first the degrees of freedom given by:

$df=n_A +n_{NA}-2=32+45-2=75$

Since is a one left tailed test the p value would be:

$p_v =P(t_{75}$

Comparing the p value with a significance level for example $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the population mean for the athletes is significantly lower than the population mean for non athletes.

5 0

3 years ago