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2 years ago

9

the mean age of 5 people ina room is 32 years. A person enters the room.The mean age is now 34.What is the age of the person who

entered the room?

1 answer:

astraxan [27]2 years ago

8 0

Answer:

32

Step-by-step explanation:

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(15.) A toy is in the shape of a cone mounted on a hemisphere of same base

lisov135 [29]

Given:

Volume of toy=231 cm³

Diameter of a hemisphere= 7 cm

cone and hemisphere have equal radius.

radius of hemisphere = radius of cone = 3.5 cm

Height of hemisphere= radius of hemisphere= 3.5 cm

Let H be the height of toy

H= height of cone+ height of hemisphere

H = h + r , ( h = height of cone)

H = h + 3.5

volume of toy = volume of cone + volume of hemisphere

Volume of toy= 1/3πr²h + 2/3πr³

Volume of toy=πr²/3(h+2r)

231 = (22/7)×(3.5)² ×(1/3)(h+2×3.5)

231×3 =( 22×3.5×3.5)/7 (h+7)

h+7 = (231×3×7)/(3.5×3.5×22)

h+7 = (3×3)/(.5×.5×2)

h+7= 900 /50= 90/5= 18

h+7= 18

h=18-7

h= 11 cm

Height of toy = h+r

Height of toy = 11+3.5= 14.5

Height of toy =14.5 cm

Hence, the height of the toy = 13.5 cm

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3 years ago

Beverly is painting a mural on a 1-square-meter section of a wall. She has completed a rectangular part of the mural that's is 5

yawa3891 [41]

Answer:

0.21 square meter

Step-by-step explanation:

Area of the section of wall = 1 square meter

Dimension of part of mural completed = $\frac{1}{4}$ meter by $\frac{5}{6}$ meter

Part of the mural completed = Area of the rectangular part of mural completed

But,

Area of a rectangle = length x width

So that,

Part of the mural completed = length x width

= $\frac{1}{4}$ x $\frac{5}{6}$

= $\frac{5}{24}$

= 0.2083

Part of the mural completed = 0.21 square meter

The part of the mural that has been completed by Beverly is 0.21 square meter.

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3 years ago

Solve the proportion

mario62 [17]

Answer:

$\boxed{\sf x = 5}$

Step-by-step explanation:

$\sf Solve \: for \: x \: over \: the \: real \: numbers: \\ \sf \implies \frac{2}{x - 3} = \frac{5}{x} \\ \\ \sf Take \: the \: reciprocal \: of \: both \: sides: \\ \sf \implies \frac{x - 3}{2} = \frac{x}{5} \\ \\ \sf Expand \: out \: terms \: of \: the \: left \: hand \: side: \\ \\ \sf \implies \frac{x}{2} - \frac{3}{2} = \frac{x}{5} \\ \\ \sf Subtract \: \frac{x}{5} - \frac{3}{2} \: from \: both \: sides: \\ \sf \implies \frac{x}{2} - \frac{3}{2} - ( \frac{x}{5} - \frac{3}{2} ) = \frac{x}{5} - ( \frac{x}{5} - \frac{3}{2} ) \\ \\ \sf \implies \frac{x}{2} - \frac{3}{2} - \frac{x}{5} + \frac{3}{2} = \frac{x}{5} - \frac{x}{5} + \frac{3}{2} \\ \\ \sf \frac{x}{5} - \frac{x}{5} = 0 : \\ \sf \implies \frac{x}{2} - \frac{x}{5} - \frac{3}{2} + \frac{3}{2} = \frac{3}{2} \\ \\ \sf \frac{3}{2} - \frac{3}{2} = 0: \\ \sf \implies \frac{x}{2} - \frac{x}{5} = \frac{3}{2} \\ \\ \sf \frac{x}{2} - \frac{x}{5} = \frac{5x - 2x}{10} = \frac{3x}{10} : \\ \sf \implies \frac{3x}{10} = \frac{3}{2} \\ \\ \sf Multiply \: both \: sides \: by \: \frac{10}{3} : \\ \sf \implies \frac{3x}{10} \times \frac{10}{3} = \frac{3}{2 } \times \frac{10}{3} \\ \\ \sf \frac{3x}{10} \times \frac{10}{3} = \cancel{\frac{3}{10} } \times( x) \times \cancel{ \frac{10}{3} } = x : \\ \sf \implies x = \frac{3}{2} \times \frac{10}{3} \\ \\ \sf \frac{3}{2} \times \frac{10}{3} = \cancel{ \frac{3}{2} } \times \cancel{ \frac{3}{2} } \times 5 : \\ \sf \implies x = 5$

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3 years ago