Ask question

Ask question

All categories

3 years ago

7

Sam is trying to make 12 packs of rice. She packed 2 1/2 kg of rice in each of the first 4 packs & 2 3/4 kg of rice in each

of the remaining 8 packs. How many kgs of rice did she pack?

1 answer:

Lina20 [59]3 years ago

8 0

Answer:

32 kg

Step-by-step explanation:

1. Convert the fractions to decimals:

2 1/2 = 2.5

2 3/4 = 2.75

2. Set up the equation to show 4 packs of 2.5 kg and 8 packs of 2.75 kg:

4*(2.5) + 8*(2.75)

3. Solve the equation using PEMDAS:

4(2.5) + 8(2.75)

10 + 8(2.75)

10 + 22

32

You might be interested in

horrorfan [7]

Answer:

p= $\frac{181}{301}$

Step-by-step explanation:

30100 have dogs, 18100 have cats.

The question simply asks for a union scenario thus the law of AND & OR is applicable.

Therefore:-Those who have both cats and dogs partially have cats.

$P(X=both \ cat \ and \ dog)=\frac{18100}{30100}\\p=\frac{181}{301}$

8 0

3 years ago

Read 2 more answers

Bryan and Jadyn had barbeque potato chips and soda at a football party. Bryan ate 5 oz of chips and drank 1 cup of soda for a

MaRussiya [10]

Answer:

1 oz of chips has 120mg of sodium, while in 1 cup of soda there are 50mg of sodium.

Step-by-step explanation:

This question can be solved by a system of equations.

I am going to say that:

x is the number of mg of sodium in 1 oz of chips.

y is the number of mg of sodium in a cup of soda.

Bryan ate 5 oz of chips and drank 1 cup of soda for a total of 650 mg of sodium.

This means that:

$5x + y = 650$

Jadyn ate 1 oz of chips and drank 5 cups of soda for a total of 250 mg of sodium.

This means that:

$x + 5y = 250$

From the first equation:

$y = 650 - 5x$

Replacing in the second

$x + 5(650 - 5x) = 250$

$x + 3250 - 25x = 250$

$25x = 3000$

$x = \frac{3000}{25}$

$x = 120$

$y = 650 - 5x = 650 - 5*120 = 650 - 600 = 50$

1 oz of chips has 120mg of sodium, while in 1 cup of soda there are 50mg of sodium.

5 0

3 years ago

Distance between two ships At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots (naut

frozen [14]

Answer:

a) $\sqrt{144-288t+208t^2}$ b.) -12knots, 8 knots c) No e) $4\sqrt{13}$

Step-by-step explanation:

We know that the initial distance between ships A and B was 12 nautical miles. Ship A moves at 12 knots(nautical miles per hour) south. Ship B moves at 8 knots east.

a)

We know that at time t , the ship A has moved $12\dot t (n.m)$ and ship B has moved $8\dot t (n.m)$ . We also know that the ship A moves closer to the line of the movement of B and that ship B moves further on its line.

Using Pythagorean theorem, we can write the distance s as:

$\sqrt{(12-12\dot t)^2 + (8\dot t)^2}\\s=\sqrt{144-288t+144t^2+64t^2}\\s=\sqrt{144-288t+208t^2}$

b)

We want to find $\frac{ds}{dt}$ for t=0 and t=1

$\sqrt{144-288t+208t^2}|\frac{d}{dt}\\\\\frac{ds}{dt}=\frac{1}{2\sqrt{144-288t+208t^2}}\dot (-288+416t)\\\\\frac{ds}{dt}=\frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\\frac{ds}{dt}(0)=\frac{208\dot 0-144}{\sqrt{144-288\dot 0 + 209\dot 0^2}}=-12knots\\\\\frac{ds}{dt}(1)=\frac{208\dot 1-144}{\sqrt{144-288\dot 1 + 209\dot 1^2}}=8knots$

c)

We know that the visibility was 5n.m. We want to see whether the distance s was under 5 miles at any point.

Ships have seen each other = $s\leq 5\\\\\sqrt{144-288t+208t^2}\leq 5\\\\144-288t+208t^2\leq 25\\\\199-288t+208t^2\leq 0$

Since function $f(x)=199-288x+208x^2$ is quadratic, concave up and has no real roots, we know that $199-288x+208x^2>0$ for every t. So, the ships haven't seen each other.

d)

Attachedis the graph of s(red) and ds/dt(blue). We can see that our results from parts b and c were correct.

e)

Function ds/dt has a horizontal asympote in the first quadrant if

$\lim_{t \to \infty} \frac{ds}{dt}$

So, lets check this limit:

$\lim_{t \to \infty} \frac{ds}{dt}=\lim_{t \to \infty} \frac{208t-144}{\sqrt{144-288t+208t^2}}\\\\=\lim_{t \to \infty} \frac{208-\frac{144}{t}}{\sqrt{\frac{144}{t^2}-\frac{288}{t}+208}}\\\\=\frac{208-0}{\sqrt{0-0+208}}\\\\=\frac{208}{\sqrt{208}}\\\\=4\sqrt{13}$

Notice that:

$4\sqrt{13}=\sqrt{12^2+5^2}$ =√(speed of ship A² + speed of ship B²)

5 0

3 years ago

Simplify 2x - 8x - 6y + 9 -14 + x + 11y.

raketka [301]

We can see that 2x - 8x + x = -5x
and -6y + 11y = 5y
and 9 - 14 = -5
so simplified, it is -5x + 5y - 5

8 0

2 years ago

Read 2 more answers

A. y=1/2x-2 <br> b. y=-1/2x+3<br> c. y=2x+1<br> d. y= -2x+4

Lyrx [107]

d. y=-2x+4

this is because in the formula used y=mx+b, b is represented as the the "y" intersept, which is 4. the slope, which is -2, is represented as x in this formula. therefore, D. y=-2x+4 is the correct answer

7 0

3 years ago