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2 years ago

13

Mr. phill stopped to fill his car with gas on the way to New York. It took 1 ¼ minutes to fill a 15 liters of gas in his tank. A

t this rate, how long will it take to fill his 50 liter gas tank?

1 answer:

KatRina [158]2 years ago

4 0

Answer:

4 1/6 min or 4 min 10 sec

Step-by-step explanation:

<u>Filling rate is:</u>

15 ÷ 1 1/4 = 15 ÷ 5/4 = 15 × 4/5 = 12 l/min

<u>Total volume is 50 l, time required to fill is:</u>

50/12 = 4 2/12 = 4 1/6 min or 4 min 10 sec

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Find the area of the largest rectangle (with sides parallel to the coordinate axes) that can be inscribed in the region enclosed

garik1379 [7]

F(x) = 18-x^2 is a parabola having vertex at (0, 18) and opening downwards.
g(x) = 2x^2-9 is a parabola having vertex at (0, -9) and opening upwards.
By symmetry, let the x-coordinates of the vertices of rectangle be x and -x => its width is 2x.
Height of the rectangle is y1 + y2, where y1 is the y-coordinate of the vertex on the parabola f and y2 is that of g.
=> Area, A
= 2x (y1 - y2)
= 2x (18 - x^2 - 2x^2 + 9)
= 2x (27 - 3x^2)
= 54x - 6x^3
For area to be maximum, dA/dx = 0 and d²A/dx² < 0
=> 54 - 18x^2 = 0
=> x = √3 (note: x = - √3 gives the x-coordinate of vertex in second and third quadrants)

d²A/dx² = - 36x < 0 for x = √3
=> maximum area
= 54(√3) - 6(√3)^3
= 54√3 - 18√3
= 36√3.

4 0

3 years ago

The local video store is having a sale on video games. The store is offering a sale pack of 4 video games for $48. What is the p

Alinara [238K]

A single video game would cost $12

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2 years ago

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How long will it take an investment to double in value if the interest rate is 10% compounded continuously? (round your answer t

Varvara68 [4.7K]

Assumed
PW as 100
FW as twice PW as 200

answer is 7.27254 years

manually take the log of both sides and solve for n

8 0

3 years ago

In testing a certain kind of missile, target accuracy is measured by the average distance X at which the missile explodes. The d

3241004551 [841]

Answer:

The answer is c) 761.0

Step-by-step explanation:

Mathematical hope (also known as hope, expected value, population means or simply means) expresses the average value of a random phenomenon and is denoted as E (x). Hope is the sum of the product of the probability of each event by the value of that event. It is then defined as shown in the image, Where x is the value of the event, P the probability of its occurrence, "i" the period in which said event occurs and N the total number of periods or observations.

The variance of a random variable provides an idea of the dispersion of the random variable with respect to its hope. It is then defined as shown in the image.

Then you first calculate E [x] and E [ $x^{2}$ ], and then be able to calculate the variance.

$E[x]=0*\frac{1}{40} +10*\frac{1}{20} +50*\frac{1}{10} +100*\frac{33}{40}$

$E[x]=0+\frac{1}{2} +5+\frac{165}{2}$

E[X]=88

So <em>E[X]²=88²=7744</em>

On the other hand

$E[x^{2} ]=0^{2} *\frac{1}{40} +10^{2} *\frac{1}{20} +50^{2} *\frac{1}{10} +100^{2} *\frac{33}{40}$

E[x²]=0+5+250+8250

<em>E[x²]=8505 </em>

Then the variance will be:

Var[x]=8505-7744

<u><em>Var[x]=761 </em></u>

5 0

3 years ago

5. How long is the diagona of a 12 ft-by-16 ft rectangular garden?

kupik [55]

Answer:

The correct answer is option D, 20ft

Step-by-step explanation:

After drawing the picture below, you can just use pythagorean theorem to solve for the diagonal, or the hypotenuse in this case;

(Length)² + (Width)² = (Diagonal)²

(16)² + (12)² = (Diagonal)²

256 + 144 = (Diagonal)²

400 = (Diagonal)²

$\sqrt{400}$ = $\sqrt{Diagonal^{2} }$

<em>20 = Diagonal</em>

<em>Hope this helps!</em>

7 0

2 years ago

Read 2 more answers