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3 years ago

8

The back-up generators at the local clinic use 25 gallons of oil in 3 hours and 45 minutes. At this rate, how much oil would the

generators use in 6 hours?

1 answer:

sveticcg [70]3 years ago

4 0

<span>The word problem gives a rate of oil consumption at a rate of 25 gallons per 3 hours and 45 minutes. 3 hours and 45 minutes can be displayed as 3.75 hours. so you can say the generator consumes oil at a rate of 25 gallons per 3.75 hours. The following equation give you the oil consumption on a per hour basis; 25/3.75 and that gives you 6.67 gallons per hour. In 6 hours the generator will consume 40 gallons.</span>

You might be interested in

3/10 divided by -1/3

Snezhnost [94]

Answer:

-9/10

Step-by-step explanation:

Find the LCM of 10 and 3: 30
Alter the numerators to fit the denominators: 3 × 3 = 9, -1 × 10 = -10
Re-write the fractions: 9/30 ÷ -10/30
9/30 ÷ -10/30 = 9/30 × -30/10
9/30 × -30/10 = -270/300
$-\frac{270}{300} = -\frac{9}{10}$

I hope this helps!

8 0

3 years ago

A rectangle is drawn so that the width is 3 feet shorter than the length. The area of the rectangle is 70 square feet. Find the

Vedmedyk [2.9K]

Answer:

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Let 'x' be the length of the rectangle

Given that the width is 3 feet shorter than the length

The width of the rectangle = x -3

Area of the rectangle = length × width

<u><em>Step(ii):-</em></u>

Area of the rectangle = length × width

= x ( x-3)

Given that the area of the rectangle = 70 square feet

x ( x-3) = 70

⇒ x² - 3x - 70 =0

⇒ x² - 10 x + 7 x - 70 =0

⇒ x (x -10) +7( x-10) =0

⇒ ( x+7) ( x-10) = 0

⇒ x =-7 and x=10

<u><em>Final answer:</em></u>-

we choose x=10

The length of the rectangle (l) = 10 cm

The width of the rectangle (w) = 7 cm

8 0

3 years ago

What is the equation of the line perpendicular to –x + y = 7 and passing through (-1, -1)?

Vesna [10]

- x + y = 7
y = x + 7
slope = 1
perpendicular slope = -1

at point (-1, -1),
y = mx + c
-1 = -1 (-1) + c
-1 = 1 + c
c = -1 -1
c = - 2

equation:
y = -x -2
y + x = -2 or - x - y = 2

6 0

3 years ago

Which scatterplot shows a linear association?

algol [13]

A linear association is when the shape of the scatter plot is a straight line.

Therefore, the answer would be C, as you had it, because it is showing the data in a straight line.

4 0

3 years ago

Read 2 more answers

I need help with these. They are hard.<br><br>

iragen [17]

Answer:

Find the explicit from for the sequence $t_n=t_{n-1}+4,t=6$ :

$a_n=4n+2$

This next question I edited a bit. Your question just says find the four terms. I'm assuming they meant the first four. I also changed the c to an $a$ .

Find the first four terms of the sequence given by: $a_n=n a_{n-1}-3,a_1=2$ :

a) 2,1,0.-3

You might want to read that second question again because there is errors in the question or things that don't really make sense. I made my own interpretation of the problem based on my own mathematical experience.

Step-by-step explanation:

So your first question actually says that you can find a term by taking that term's previous term and adding 4.

So more terms of the sequence starting at first term 6 is:

6,10,14,18,....

This is an arithmetic sequence. When thinking of arithmetic sequences you should just really by thinking about equations of lines.

Let's say we have this table for (x,y):

x | y

----------

1 6

2 10

3 14

4 18

So we already know the slope which is the common difference of an arithmetic sequence.

We also know point slope form of a line is $y-y_1=m(x-x_1)$ where m is the slope and $(x_1,y_1)$ is a point on the line. You can use any point on the line. I'm going to use the first point (1,6) with my slope=4.

$y-6=4(x-1)$

$y=6+4(x-1)$ :I added 6 on both sides here.

$y=6+4x-4$ :I distribute here.

$y=4x+2$ :This is what I get after combining like terms.

So $a_n=y$ and $x=n$ so you have:

$a_n=4n+2$

---------------------------------------------------------------------------------------

The first four terms of this sequence will be given by:

$a_1,a_2,a_3,a_4$

$a_1=2$ so it is between choice a, c, and d.

$a_n=na_{n-1}-3$

To find $a_2$ replace n with 2:

$a_2=2a_{1}-3$

$a_2=2(2)-3$

$a_2=4-3$

$a_2=1$

So we have to go another further the only one that has first two terms 2,1 is choice a.

7 0

3 years ago