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BigorU [14]
2 years ago
3

Last saturday, there were 1,486 people at the cineplex. there were about the same people in each of the 6 theaters. which is the

best estimate of the number of people in each theater? use compatible numbers to find two estimates the the quotient is between.
Mathematics
2 answers:
satela [25.4K]2 years ago
7 0
8,916 I think! I'm not sure because I'm in sixth grade, but I just wrote it down on a piece of paper. 1,486 times 6 = 8,916


Drupady [299]2 years ago
5 0
1,486 ÷ 6 = 247 \frac{2}{3}. That would be an estimate of between 200 and 300.
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A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.
Reika [66]

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 cm^{3}

The function that represents the area of the cardboard without a lid is given by

f (x,y,z) = xy + 2xz + 2yz ------  (1)

Volume of the cardboard with sides x, y & z is

xyz = 16384

z =  \frac{16384}{xy}

Put this value of z in equation (1) we get

f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )

f (x,y,z) = xy + \frac{32768}{y}  + 2y(\frac{32768}{x} )

Differentiate above equation with respect to x & y we get

f_{x}  = y - \frac{32768}{x^{2} }

f_{y}  = x - \frac{32768}{y^{2} }

Take f_{x}  = 0 \ and  \ f_{y} = 0

y - \frac{32768}{x^{2} } = 0

y = 32768 \ x^{-2}  ------ (2)

x - \frac{32768}{y^{2} } = 0

x = 32768 \ y^{-2}  ------- (3)

By solving equation (2) & (3) we get

x^{3} = 32768

x = 31 cm

From equation 2

y = 32768 \ x^{-2}

y = 32768 (31^{-2})

y = 34 cm

z =  \frac{16384}{xy}

z =  \frac{16384}{(34)(31)}

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm ,  y = 34 cm & Z = 15.54 cm

6 0
2 years ago
3. A balloon with a small leak loses 0.5% of its volume each day. If it originally contained 40 liters of gas, what is the volum
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Given the frequency table, what percentage of the students in grades 9–10 like country music? Round to the nearest whole percent
motikmotik

Answer:

b: 44%

Step-by-step explanation:

From grades 9-10 there are 55 students who like country music.

While there are 125 grades 9-10 students in total.

This gives us a percentage of (55/125) *100% = 44%

8 0
2 years ago
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Answer:3

Step-by-step explanation:

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A football player kicks a football downfield. The height of the football increases until it reaches a maximum height of 15 yards
tino4ka555 [31]

Answer:

kick 1 has travelled 15 + 15 = 30 yards before hitting the ground

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards  

Step-by-step explanation:

1st kick travelled 15 yards to reach maximum height of 8 yards

so, it has travelled 15 + 15 = 30 yards before hitting the ground

2nd kick is given by the equation

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and maximum height is

y = 1.6(25) - 0.032 (25)^2

y = 20

so kick 2 travels 25 + 25 = 50 yards before hitting the ground

first kick reached 8 yards and 2nd kick reached 20 yards  

6 0
2 years ago
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