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allochka39001 [22]
3 years ago
10

The ration of girls to boys is 7:8. If there are 140 girls, how many boys are there?

Mathematics
1 answer:
Triss [41]3 years ago
7 0

Answer:

160

Step-by-step explanation:

140 divided by 7 equals 20, then you times the answer by 8, which you get 160.

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6. The diagram on the right shows the cross-section of a cylindrical pipe with water lying in the bottom. a) If the maximum dept
riadik2000 [5.3K]

Answer:

404 cm³ Anyway... Look down here for my explanation.

Step-by-step explanation:

Let's Draw a line from the center of the circle to one of the ends of the chord (water surface) and another to the point at greatest depth on your paper. A right-angled triangle is formed too. The Length of side to the water-surface is 5 cm, the hospot is 7 cm.

We Calculate the angle θ in the corner of the right-angled triangle by: cos θ = 5/7 ⇒ θ = cos ˉ¹ (5/7)

44.4°, so the angle subtended at the center of the circle by the water surface is roughly 88.8°

The area shaded will then be the area of the sector minus the area of the triangle above the water in your diagram.

Shaded area 88.8/360*area of circle - ½*7*788.8°

= 88.8/360*π*7² - 24.5*sin 88.8°

13.5 cm²

(using area of ∆ = ½.a.b.sin C for the triangle)

Volume of water = cross-sectional area * length

13.5 * 30 cm³

404 cm³

6 0
2 years ago
Use the properties of logarithms to prove log, 1000 = log2 10.
Leto [7]

Given:

Consider the equation is:

\log_81000=\log_210

To prove:

\log_81000=\log_210 by using the properties of logarithms.

Solution:

We have,

\log_81000=\log_210

Taking left hand side (LHS), we get

LHS=\log_81000

LHS=\dfrac{\log 1000}{\log 8}                  \left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right]

LHS=\dfrac{\log (10)^3}{\log 2^3}

LHS=\dfrac{3\log 10}{3\log 2}                   [\because \log x^n=n\log x]

LHS=\dfrac{\log 10}{\log 2}

LHS=\log_210                    \left[\because \log_ab=\dfrac{\log_x a}{\log_x b}\right]

LHS=RHS

Hence proved.

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Answer:

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Step-by-step explanation:

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