How do you evaluate 1.5x + 120 ≥ 270

Nandini makes 'halwa' one evening and divides it into four equal portions for her family of four. However, just as they are abou

wel

Answer:

5%

Step-by-step explanation:

Total 'halwa' made = 1

Divided into four equal portion = 1/4

Arrival of an unexpected guest = 1/5

By what percentage has each family member's share been reduced:

Change in the sharing proportion:

Previous share ratio - new sharing ratio

(1/4 - 1/5) = (5 - 4) / 20 = 1/20

That means total reduction in the sharing = 1/ 20

Since each member comes contributed equally:

Reduction in each family member's share ;

(1 / 20) ÷ 4

(1 / 20) * 1/4 = 1/ 80

Percentage reduction:

(Reduction / original share) * 100%

[(1/80) ÷ (1/4)] * 100

(1/80 * 4/1) * 100%

(1/20) * 100%

= 5%

Reduction in each family members share = 5%

3 0

1 year ago

You are traveling down a country road at a rate of 95 feet/sec when you see a large cow 300 feet in front of you and directly in

emmainna [20.7K]

Answer:

1) You can rely solely on your brakes because when doing so the car will just travel 250ft from the point you hit your brakes till the point the car stopped completely, leaving you 50ft away from the cow.

2) See attached picture.

j(t) represents the distance from the point you hit the brake t seconds after you hit it in feet

j'(t) represents the velocity of the car t seconds after the brakes have been hit in ft/s.

j"(t) represents the acceleration of the car t seconds after the brakes have been hit in $ft/s^{2}$

3) yes, any time after t=5.28 will not accurately model the path of the car since at that exact time the car will reach a velocity of 0ft/s and unless another force is applied to the car, then the car will not move after that time.

4) $j(t)=\left \{ {{95t-9t^{2}; 0\le t$

$j'(t)=\left \{ {{95-18t; 0\leq t$

(see attached picture for graph)

Step-by-step explanation:

1) In this part of the problem we need to find the time when the speed of the car is 0. Gets to a complete stop. For this we will need to take the derivative of the position function so we get:

$j(t)=95t-9t^2$

$j'(t)=95-18t$

and we set the first derivative equal to zero so we get:

95-18t=0

and solve for t

-18t=-95

$t=\frac{95}{18}$

t=5.28s

so now we calculate the position of the car after 5.28 seconds, so we get:

$j(5.28)=95(5.28)-9(5.28)^{2}$

$j(5.28)=250.69ft$

so we have that the car will stop 250.69ft after he hit the brakes, so there will be about 50ft between the car and the cow when the car stops completely, so he can rely just on the breaks.

2) For answer 2 I take the second derivative of the function so I get:

$j(t)=95t-9t^{2}$

$j'(t)=95-18t$

j"(t)=-18

and then we graph them. (See attached picture)

j(t) represents the distance from the point you hit the brake t seconds after you hit it in feet

j'(t) represents the velocity of the car t seconds after the brakes have been hit in ft/s.

j"(t) represents the acceleration of the car t seconds after the brakes have been hit in $ft/s^{2}$

3) yes, any time after t=5.28 will not accurately model the path of the car since at that exact time the car will reach a velocity of 0ft/s and unless another force is applied to the car, then the car will not move after that time.

4) $j(t)=\left \{ {{95t-9t^{2}; 0\le t$

$j'(t)=\left \{ {{95-18t; 0\leq t$

(see attached picture for graph)

5 0

1 year ago

REASONING An even integer can be represented by the expression $2n$ , where $n$ is any integer. Find three consecutive even inte

san4es73 [151]

Answer:

First Integer = 16

Second Integer = 18

Third integer = 20

Step-by-step explanation:

An even integer is represented by 2n

Where n is any integer

Let :

First Integer = 2n - 2

Second Integer = 2n

Third integer = 2n + 2

The sum of three even consecutive numbers = 2n - 2 + 2n + 2n + 2

= 2n + 2n + 2n - 2 + 2 = 54

= 6n = 54

n = 54/6

n = 9

First Integer = 2n - 2 = 2(9) - 2

= 16

Second Integer = 2n = 2(9)

= 18

Third integer = 2n + 2 = 2(9) + 2

= 20

8 0

2 years ago

To pass inspection, a machine part from a factory must be no thinner than 4.225 centimeter and no thicker than 4.233 centimeters

Mrrafil [7]

Machine should abide by te following:

4.225<Machine<4.233 The margin of acceptance
:

4.233-4.225 = 0.008cm.

Any thickness greater than 4.233+0.008 or smaller than 4.225-0.008

or <4.233cm & >4.217

6 0

2 years ago

Jeff saved $500 from his summer job so he would have spending money during the school year. He withdraws $12 from his account ea

Alex Ar [27]

Jeff Lucy Goethe licky

4 0

1 year ago