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alexandr1967 [171]
3 years ago
5

A carton has a length of 2 2/3 feet, width of 1 1/3 feet, and a height of 1 1/2. What is the volume of the carton? A( 4 cubic fe

et ) B( 5 1/3 ) C( 6 cubic feet ) D( 6 1/3 )
Mathematics
1 answer:
notsponge [240]3 years ago
8 0

Answer:

The volume of the carton is 5 1/3 cubic feet

Step-by-step explanation:

A carton has a length of 2 2/3 feet, width of 1 1/3 feet, and a height of 1 1/2.

The dimensions can be rewritten as

Length of carton =2 2/3 = 8/3 converting to improper fraction).

width of 1 1/3 feet = 4/3 feet

and a height of 1 1/2= 3/2 ,feet

volume of the carton = length of the carton × width of the carton × height of the carton

Volume of carton = 8/3 ×4/3 × 3/2

= 96/18 cubic feet

Converting to mixed fractions, we have

96/18= 5 1/3 cubic feet

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5 0
3 years ago
Find the rate of change and initial value. Y=mx+b
tekilochka [14]
Y= 4/5 x + 24
To find the rate of change you find the difference in each of the numbers on the graph. For example, 36-32 is 4. So 28-4 is 24 and that would be the next number down. It would also match x to be 0 because since the rate of change for x was 5, if you subtract 5 from 5 you get 0. So from this we know that the coordinates would be 0,5.
From this info, the slope would be 4/5 and the y intercept or initial value would be 24
4 0
3 years ago
If the smallest angle of a triangle is 20° and it is included between sides of 4 and 7, then (to the nearest tenth) the smallest
lawyer [7]

Answer:

3.5

Step-by-step explanation:

The smallest side of a triangle is formed by the smallest angle in the triangle.

To find the side opposite (formed by) the 20 degree angle, we can use the Law of Cosines. The Law of Cosines states that for any triangle, c^2=a^2+b^2-ab\cos \gamma, where a, b, and c are the three sides of the triangle and \gamma is the angle opposite to c.

Let c be the side opposite to the 20 degree angle.

Assign variables:

  • a\implies 4
  • b\implies 7
  • \gamma \implies 20^{\circ}

Substituting these variables, we get:

c^2=4^2+7^2-2(4)(7)\cos 20^{\circ},\\c^2=16+49-56\cos 20^{\circ},\\c^2=12.377213236,\\c=\sqrt{12.377213236}=3.51812638147\approx \boxed{3.5}

Therefore, the shortest side of this triangle is 3.5.

5 0
3 years ago
If there are 17 green marbles in a jar of 65 marbles, what is the probability of drawing 2 green marbles at random without repla
erastovalidia [21]

Answer:

Option b) \frac{17}{260}

Step-by-step explanation:

We are given the following information in the question:

Total number of marbles = 65

Number of green marbles = 17

We have to find the probability of drawing 2 green marbles at random without replacement.

Formula:

Probability = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}

\text{P(Drawing 2 green marbles at random without replacement)} = \\\text{Probability of drawing }1^{st} \text{ green marble}\times \text{Probability of drawing }2^{nd} \text{ green marble}

\text{Probability of drawing }1^{st} \text{ green marble} = \displaystyle\frac{17}{65}\\\\\text{Probability of drawing }2^{nd} \text{ green marble} = \displaystyle\frac{16}{64}

\text{P(Drawing 2 green marbles at random without replacement)} =\displaystyle\frac{17}{65}\times \frac{16}{64}=\frac{17}{260}

Option b) \frac{17}{260}

5 0
3 years ago
Write three ratios equal to 5/40
AnnZ [28]
The answer is

<span>A. 2/14, 3/21, 4/28

B. 1/8, 2/16, 3/24

C. 1/9, 2/18, 3/27

D. 5/40, 5/45, 5/50</span>

7 0
3 years ago
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