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maw [93]
1 year ago
15

Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The vo

lume of the box is 10{,}00010,00010, comma, 000 cm^3 3 cubed. The base of the box is 252525 cm by 101010 cm
Mathematics
1 answer:
Mashcka [7]1 year ago
8 0

Complete question:

Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is 10,000 cm^3 cubed. The base of the box is 25cm by 10cm.

How tall is the box of cereal?

Answer: 40cm

Step-by-step explanation:

Given the following :

Volume = 10,000cm^3

Base of box = 25cm by 10cm,

Base of box = Length × width

Therefore:

Length = 25cm, Width = 10cm

Volume = Lengh × Width × Height

10,000cm^3 = 25cm × 10cm × Height

10,000cm^3 = 250cm^2 × Height

Height = 10,000cm^3 ÷ 250cm^2

Height = 40cm

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Four speed skaters, Marco, Naim, Oliver, and Pedro, compete in a relay race where they all agree that Naim will be the last
Romashka [77]

Answer:

<em>A = {MOPN. MPON, PMON, POMN)</em>

Step-by-step explanation:

<u>Complete Question</u>

<em>Four speed skaters, Marco, Naim, Oliver, and Pedro, compete in a relay race where they all agree that Naim will be the last  skater. Then, they try to decide whether or not Oliver should be the first skater in the race. </em>

<em>Which subset, A, of the sample space shows the complement of the event in which Oliver is the first skater in the race? </em>

<em>A = {MOPN, PMON} </em>

<em>A = {OPMN, OMPN) </em>

<em>A = {MOPN,MPON, OPMN, POMN) </em>

<em>A = {MOPN. MPON, PMON, POMN)</em>

<em />

So,

Naim would be last, that means, "N" must come last in all the sets. All of them have this, so that's good.

Now, they want "COMPLEMENT" of the set where Oliver is 1st. Complement is the "opposite" event, not in set/subset. So we disregard anyone where there is "O" in first place.

1st set have only 2 possibilities, so that's out.

2nd set have same, so that's out.

3rd set has "O" at first place in third sub, so that's out.

4th set DOESN'T have "O" in first place and has 4 subs, so this is the correct answer.

<em>A = {MOPN. MPON, PMON, POMN)  -- correct</em>

6 0
2 years ago
Read 2 more answers
Coordinates, gradient and tangent work (see image).
Ivenika [448]

Answer:

a) P(x,2x^2-5),\ Q(x+h,2(x+h)^2-5)

b) 4x+2h

c) 4x

Step-by-step explanation:

Given the curve

y=2x^2-5

a) If the x-coordinate of P is x, then the y-coordinate is 2x^2-5, so point P has coordinates (x,2x^2-5)

If the x-coordinate of Q is x+h, then the y-coordinate is 2(x+h)^2-5 so point Q has coordinates (x+h,2(x+h)^2-5)

b) The gradient of the secant RQ is

\dfrac{y_Q-y_P}{x_Q-x_P}\\ \\=\dfrac{(2(x+h)^2-5)-(2x^2-5)}{(x+h)-x}\\ \\=\dfrac{2(x+h)^2-5-x^2+5}{x+h-x}\\ \\=\dfrac{2(x+h)^2-2x^2}{h}\\ \\=\dfrac{2x^2+4xh+2h^2-2x^2}{h}\\ \\=\dfrac{4xh+2h^2}{h}\\ \\=4x+2h

c) If h\rightarrow 0, then the gradient 4x+2h\rightarrow 4x

5 0
1 year ago
What is the constant of proportionality in the equation y = StartFraction x over 9 EndFraction? 0 StartFraction 1 over 9 EndFrac
Sonja [21]

Answer:

The answer is C.

Step-by-step explanation:

You only need the answer.

8 0
1 year ago
Read 2 more answers
If f (x) = 5 x minus 25 and g (x) = one-fifth x + 5, which expression could be used to verify g(x) is the inverse of f(x)?
Vinil7 [7]

Answer:

The expression used to represent g(x) as inverse of f(x) is \frac{1}{5}(5x-25)+5

Option B is correct.

Step-by-step explanation:

We are given:

f(x)= 5x-25\\g(x)=\frac{1}{5}x+5

We need to find the expression that could be used to verify g(x) is the inverse of f(x).

We know that g(f(x))=x is inverse of function

So placing value of f(x) in g(x)

g(f(x))=\frac{1}{5}(5x-25)+5

So, the expression used to represent g(x) as inverse of f(x) is \frac{1}{5}(5x-25)+5

Option B is correct.

We can also solve to prove that g(f(x))=x

g(f(x))=\frac{1}{5}(5x-25)+5\\g(f(x))=\frac{5}{5}(x-5)+5\\g(f(x))=x-5+5\\g(f(x))=x

5 0
1 year ago
Read 2 more answers
An equivalent expression for 16x − 8 is _____ . The _____ Property is used to generate this expression.
Anvisha [2.4K]
16x - 8 can be 8(2x - 1)

The distributive property

hope this helps
8 0
2 years ago
Read 2 more answers
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