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3 years ago

a hose fills a hot tub at a rate of 4.78 gallons per minute. How many hours will it take to fill a 309 gallon tub?

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

7 0

You just have to divide 309 by 4.78 so it would =64.6443

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Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

3 years ago

suppose you are in your last semester of college and have a 2.75 GPA after 105 credit hours if you are taking 15 credit hours in

Valentin [98]

Answer:

The overall CGPA would be 2.90 so it is not possible for hum to secure a CGPA of 3 for graduation.

Step-by-step explanation:

Given,

CGPA = 2.75

Credit hours = 105

Last semester GPA = 4

Last semester credit hours = 15

CGPA = $\frac{sum of (Credit hours of each subject * GPA of each subject)}{Total credit hours}$ credit hours * gpa

in our case, it would be:

CGPA = $\frac{(2.75*105)+(4*15}{105+15}$

=> $\frac{(288.75)+(60)}{120}$

=> $\frac{348.75}{120}$

=> 2.90

The overall CGPA would be 2.90 so it is not possible for hum to secure a CGPA of 3 for graduation.

7 0

3 years ago

A research company desires to know the mean consumption of meat per week among people over age 23. A sample of 164 people over a

Elan Coil [88]

Answer:

The 80% confidence interval for the mean consumption of meat among people over age 23 is between 4 and 4.2 pounds.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.8}{2} = 0.1$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.1 = 0.9$ , so $z = 1.28$

Now, find M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.28*\frac{0.7}{\sqrt{164}} = 0.07$

The lower end of the interval is the mean subtracted by M. So it is 4.1 - 0.07 = 4.03 pounds

The upper end of the interval is the mean added to M. So it is 4.1 + 0.07 = 4.17 pounds

Rounded to one decimal place

The 80% confidence interval for the mean consumption of meat among people over age 23 is between 4 and 4.2 pounds.

8 0

3 years ago

Can u pls help me with this thanks

aleksandrvk [35]

Hey!!!

<a and <b are complementary angles.

Those angles which are exactly 90 degree are called complementary angles.

hope it helps..

7 0

3 years ago

Which answer choice is a solution to the inequality 1.5x + 3.75 greater than or equal to 5.5

irga5000 [103]

Answer:

x≥ $\frac{7}{6}$

Step-by-step explanation:

given 1.5x+3.75≥5.5

→ 1.5x≥5.5-3.75

→ 1.5x≥1.75

→ x≥ $\frac{1.75}{1.5}$

→ x≥ $\frac{7}{6}$

8 0

3 years ago

Read 2 more answers