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3 years ago

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darrel wants to see how much water is wasted by his leaky facet. he put a 4 gallon bucket under the fausey. after 24 hours the b

ucket was full. if the same amount of water leaks each hour how much water will be in the bucket after 70 hours?

1 answer:

aleksley [76]3 years ago

6 0

Answer:

The quantity of water filled in the bucket after 70 hours is 11.67 gallon .

Step-by-step explanation:

Given as :

The quantity of water filled in the bucket after 24 hours = 4 gallon

Let The quantity of water filled in the bucket after 70 hours = x gallon

So, According to question

<u>Applying unitary method</u>

∵In 24 hours, The quantity of water filled in bucket = 4 gallons

So,In 1 hour, The quantity of water filled in bucket = $\dfrac{4}{24}$ gallon

∴ In 70 hour, The quantity of water filled in bucket = $\dfrac{4}{24}$ × 70 gallon

I.e x = $\frac{4\times 70}{24}$ gallons

Or, x = 11.67 gallons

So,The quantity of water filled in the bucket after 70 hours = x = 11.67 gallon

Hence, The quantity of water filled in the bucket after 70 hours is 11.67 gallon . Answer

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A box has a volume of 308 cm cubed. Its height is 4 cm greater than its length. Its length is 3 cm greater than its width. What

kifflom [539]

Answer:

4 cm.

Step-by-step explanation:

Given:

A box has a volume of 308 cm cubed.

Its height is 4 cm greater than its length.

Its length is 3 cm greater than its width.

Question asked:

What is the width of the box?

<u>Solution</u>:

Let width = $x\ cm$

Length = $x+3\ cm$

Height = $x+3+4=x+7\ cm$

<u>As we know:</u>

<u /> $Volume\ of\ box=length\times width\times height$

$308=(x+3)\times x\times(x+7)\\ \\ 308=(x^{2} +3x)(x+7)\\ \\ 308=x^{2} (x+7)+ 3x(x+7)\\ \\ 308=x^{3} +7x^{2} +3x^{2} +21x\\ \\ 308=x^{3} +10x^{2} +21x\\ \\ Subtract\ 308\ from\ both\ sides\\ \\ x^{3} +10x^{2} +21x-308=0\\ \\ factor\ left\ side\ of\ equation\\ \\ (x-4)(x^{2} +14x+77)=0\\ \\ Set\ factors\ equal\ to\ 0.\\ \\ x-4=0 \ or\ x^{2} +14x+77=0\\ \\ \\$

As width can never be in negative, $x= 4\ cm$

By substituting the value:-

Width = $x\ cm$ = 4 cm

Thus, width of the box is 4 cm.

4 0

3 years ago

An arched drainage culvert can be modelled by the function:

Zanzabum

Substitute 136.5 for y.

$136.5=\frac{x(191-x)}{60}$

$8190=x(191-x)$

$8190=191x-x^{2}$

$x^{2} -191x+8190=0$

Compare this equation with $ax^{2} +bx+c=0$

a = 1, b = - 191, c = 8190

$x=\frac{-b+\sqrt{b^{2}-4ac } }{2}$ or

$x=\frac{-b-\sqrt{b^{2}-4ac } }{2}$

$x=\frac{191+\sqrt{191^{2}-4(1)(8190) } }{2}$ or

$x=\frac{191-\sqrt{191^{2}-4(1)(8190) } }{2}$

$x=\frac{191+\sqrt{36481-32760 } }{2}$ or

$x=\frac{191-\sqrt{36481-32760 } }{2}$

$x=\frac{191+\sqrt{3721 } }{2}$ or

$x=\frac{191-\sqrt{3721 } }{2}$

$x=\frac{191+61}{2}$ or

$x=\frac{191-61}{2}$

$x=\frac{252}{2}$ or

$x=\frac{130}{2}$

x = 126 or x = 65

Hence, the points on the curve are (65, 136.5) and (126, 136.5).

The width of the air space is the distance between these points.

Width = $\sqrt{(x_{2}- x_{1})^{2} +( y_{2}- y_{1}) ^{2}$

= $\sqrt{(126- 65)^{2} +(136.5-136.5) ^{2}$

= 126 - 65

= 61

Hence, width of the air space is 61m.

5 0

3 years ago

Help even tho it’s multiple choice make sure you are correct... I beg you lol

kondaur [170]

Answer:

The equation of the line is:

$y=(-\frac{1}{2})x+1$

Therefore, option a is the correct answer.

Step-by-step explanation:

Given the points

(-2, 2)

(4, -1)

Finding the slope

$\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-2,\:2\right),\:\left(x_2,\:y_2\right)=\left(4,\:-1\right)$

$m=\frac{-1-2}{4-\left(-2\right)}$

$m=-\frac{1}{2}$

As the point-slope form of the equation of the line is

$y-y_1=m\left(x-x_1\right)$

where m is the slope

substituting the values $m=-\frac{1}{2}$ and the point (-2, 2)

$y-y_1=m\left(x-x_1\right)$

$y-2=\frac{-1}{2}\left(x-\left(-2\right)\right)$

$y-2=\frac{-1}{2}\left(x+2\right)$

$y-2=-\frac{1}{2}\left(x+2\right)$ ∵ $\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{b}=-\frac{a}{b}$

Add 2 to both sides

$y-2+2=-\frac{1}{2}\left(x+2\right)+2$

$y=(-\frac{1}{2})x+1$

Hence, the equation of the line is:

$y=(-\frac{1}{2})x+1$

Therefore, option a is the correct answer.

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3 years ago

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Papessa [141]

Answer:

Step-by-step explanation:

3 0

3 years ago

Analyses were run. The following is the (edited) output for the test:

ArbitrLikvidat [17]

Answer: C. The data do not provide sufficient evidence to reject H0; thus, we cannot conclude that the mean point spread fo home games is higher than that of away games.

Step-by-step explanation: In Hypothesis Testing using p-value, after stating the null an alternative hypothesis, you have to compare p-value with level of significance, also known as α. If p-value is less than α, reject null hypothesis and accept alternative. If p-value is bigger, we would fail to reject null hypothesis and not accept the alternative.

In the above testing, P-value is 0.4351. Level of significance is, generally, 0.05. Comparing them, p-value is bigger than α. What it means is there is not enough evidence to support null hypothesis and, consequently, we can't conclude the difference in mean point spread of home games is higher than of the away games.

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3 years ago