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weqwewe [10]
3 years ago
15

Two similar solids have a scale factor of 6 : 7. What is the ratio of their volumes, expressed in lowest terms?

Mathematics
2 answers:
Anarel [89]3 years ago
7 0
The ratio of volumes is equal to the ratio of the cubes of the scale factor. Thus,
Volume ratio:
6³ : 7³
216 : 343

creativ13 [48]3 years ago
3 0

Answer:

The ratio of their volumes is equal to \frac{216}{343}  

Step-by-step explanation:

we know that

If two solids are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x/y----> the ratio of its volumes

so

z^{3}=\frac{x}{y}

we have

z=\frac{6}{7}

substitute

(\frac{6}{7})^{3}=\frac{x}{y}

(\frac{216}{343})=\frac{x}{y}

rewrite

\frac{x}{y}=(\frac{216}{343}) -----> the fraction is irreducible

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Answer:

Option 1

Step-by-step explanation:

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3 0
2 years ago
Heights​ (cm) and weights​ (kg) are measured for 100 randomly selected adult​ males, and range from heights of 133 to 193 cm and
yawa3891 [41]

Answer:

The weight of an adult male who is 172 cm tall is 89.36 kg.

Step-by-step explanation:

The regression equation representing the relationship between height and weight of a person is:

\hat y=-105+1.13x

Here

<em>y</em> = weight of a person

<em>x</em> = height of a person

The information provided is:

\bar x=167.90\ cm\\\bar y=81.47\ kg\\r (X, Y) = 0.228\\p-value=0.023\\\alpha =0.05

The hypothesis to test the significance of the correlation between height and weight is:

<em>H₀</em>: There is no relationship between the height and weight, i.e. <em>ρ</em> = 0.

<em>Hₐ</em>: There is a relationship between the height and weight, i.e. <em>ρ </em>≠ 0.

Decision rule:

If the <em>p</em>-value of the test is less than the significance level, then the null hypothesis will be rejected and vice-versa.

According to information provided:

<em>p</em>-value = 0.023 < <em>α</em> = 0.05

The null hypothesis was rejected at 5% level of significance.

Thus, concluding that there is a relationship between the height and weight.

Compute the weight of an adult male with height, <em>x</em> = 172 cm as follows:

\hat y=-105+1.13x

  =-105+(1.13\times 172)\\=-105+194.36\\=89.36

Thus, the weight of an adult male who is 172 cm tall is 89.36 kg.

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Answer:

A function with a positive constant other than 1 raised to a variable exponent.

Step-by-step explanation:

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Step-by-step explanation:

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