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kotykmax [81]
3 years ago
6

A middle school has the fifth and sixth grades. There are 100 fifth-grade boys and 110 fifth-grade girls. There are 7 fewer sixt

h-grade boys than fifth-grade boys, and there are 10 more sixth-grade girls than sixth-grade boys What is the ratio of girls to boys in the middle school? Show your work.
Mathematics
1 answer:
Mama L [17]3 years ago
4 0

The ratio of girls to boys in the middle school = 213 : 193

Number of fifth-grade boys = 100

Number of fifth grade girls = 110

There are 7 fewer sixth-grade boys than fifth-grade boys

Number of sixth-grade boys = 100 - 7

Number of sixth-grade boys = 93

There are 10 more sixth-grade girls than sixth-grade boys

Number of sixth-grade girls = 93 + 10

Number of sixth-grade girls = 103

Total number of girls = Number of sixth-grade girls + Number of fifth-grade girls

Total number of girls = `103 + 110

Total number of girls = 213

Total number of boys = Number of sixth-grade boys + Number of fifth-grade boys

Total number of boys = `93 + 100

Total number of boys = 193

The ratio of girls to boys in the middle school = 213 : 193

Learn more on ratio here: brainly.com/question/25927869

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a toy manufacturer has designed a new piece for use in building models. It is a cube with side lengths 7 mm and has a 3 mm in di
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Given that the cubical piece has side (s) 7 mm, and a cylindrical hole of diameter (d) as 3 mm.

The volume of the piece can be calculated as,

\begin{gathered} \text{Volume of piece}=\text{ Volume of cube}-\text{ Volume of cylinder} \\ V=s^3-\frac{\pi}{4}d^2s \\ V=7^3-\frac{\pi}{4}(3)^2(7) \\ V=343-\frac{63\pi}{4} \\ V\approx293.52mm^3 \\ V\approx293.52\times10^{-9}\text{ }m^3 \end{gathered}

It is mentioned that the material costs $207 per cubic meter, so the cost (c) of 1 piece is calculated as,

\begin{gathered} \text{Cost of 1 piece}=\text{ Cost per unit volume}\times\text{ Volume of 1 piece} \\ c=207\times293.52\times10^{-9} \\ c\approx60758.64\times10^{-9} \end{gathered}

This is the cost (in dollars) for 1 piece.

Given that the manufacturer wants to produce 1,000,000 such pieces, so the total cost (TC) is calculated as,

\begin{gathered} \text{Total Cost}=\text{ Cost per piece}\times\text{ No. of pieces} \\ TC=60758.64\times10^{-9}\times1,000,000 \\ TC=60758.64\times10^{-9}\times10^6 \\ TC=60758.64\times10^{-3} \\ TC=60.75864 \\ TC\approx60.75 \end{gathered}

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7 0
1 year ago
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KengaRu [80]

Answer:

m∠X = 29°

m∠V = 61°

m∠W == 90°⇒given

Step-by-step explanation:

∵ ΔXWV is right angle at W

∴ m∠W = 90°

∴ m∠X + m∠V = 180° - 90° = 90°

∵ m∠X = 2x + 5 and m∠V = 4x +13

∴ 2x + 5 +4x + 13 = 90

∴ 6x + 18 = 90

∴ 6x = 90 - 18 =72

∴ x = 72/6 = 12

∴ m∠X = 2(12) + 5 = 29°

∴ m∠V = 4(12) + 13 = 61°

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