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Colt1911 [192]
3 years ago
14

Frank purchased a new ice box having 2kg capacity. He wants it to be full with ice cubes. He measured the ice cubes to be 3.5 cm

by 3.5 cm by 3.5 cm and have a density of 0.914 g/ml. How many cubes can he put in the box?
Mathematics
1 answer:
salantis [7]3 years ago
5 0

Answer:

Frank can put 5 cubes in the box.

Step-by-step explanation:

Formula:

Mass = Volume × density.

1 cubic centimetre = 0.001 liter= 1 millilitre

Given that,

Frank purchase a new ice box having 2 kg capacity.

So,the mass of the cubes is 2 kg.

Each ice cubes measured 3.5 cm by 3.5 cm by 3.5 cm.

The volume of a cube is = Side ^3

The volume of a each ice cubes is =3.5^3 cm³

                                                        = 42.875 ml

The ice cubes have a density of 0.914 g/ml

The mass of each cubes are

=volume of each ice cubes × density

=42.875 ml ×0.914 g/ml

=39.18775 gram.

Let x number of ice cubes he can put in the box.

The mass of x cubes is = 39.18775x grams.

2 kg= 2,000 gram [ since 1 kg= 1000 gram]

According to the problem,

39.18775x=2,000

\Rightarrow x=\frac{2000}{39.18775}

\Rightarrow x\approx 51

Frank can put 5 cubes in the box.

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3 years ago
Which statements are true about ΔJKL and ΔLMN? Select all that apply.
svp [43]

Answer:

A. ΔJKL and ΔLMN have only one pair of angles that are congruent

C. ΔJKL has angles that measure 50^o,60^o,70^o

Step-by-step explanation:

step 1

Find the value of x

we know that

m\angle KLJ=m\angle MLN ----> by vertical angles

substitute the given values

(6x-2)^o=(5x+10)^o

solve for x

6x-5x=10+2\\x=12

step 2

Find the measure of the interior angles of triangle JKL

we have

m\angle KLJ=(6(12)-2)=70^o

m\angle KJL=(5(12))=60^o

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

m\angle JKL=180^o-130^o=50^o

therefore

Triangle JKL has angles that measure 50^o,60^o,70^o

step 3

Find the measure of the interior angles of triangle LMN

we have

m\angle MLN=(5(12)+10)=70^o

m\angle LMN=(6(12)-7)=65^o

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

m\angle LNM=180^o-135^o=45^o

Triangle LMN has angles that measure 45^o,65^o,70^o

we know that

If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

The corresponding angles of triangle JKL and LMN are not congruent

therefore

The triangles are not similar

<u><em>Verify each statement</em></u>

Part a) ΔJKL and ΔLMN have only one pair of angles that are congruent

The statement is true (see the explanation)

Part b) ΔJKL and ΔLMN have two pairs of angles that are congruent

The statement is false

Because have only one pair of angles that are congruent

Part c) ΔJKL has angles that measure 50^o,60^o,70^o

The statement is true  (see the explanation)

Part d) ΔLMN has angles that measure 50^o,60^o,70^o

The statement is false

Because, Triangle LMN has angles that measure 45^o,65^o,70^o

Part e) ΔJKL and ΔLMN are similar

The statement is false

Because, the corresponding angles are not congruent

6 0
3 years ago
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