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3 years ago

Find the volume of the L shaped composite prism, show clearly how you got your answers

Mathematics

1 answer:

ruslelena [56]3 years ago

3 0

9514 1404 393

Answer:

510 cm³

Step-by-step explanation:

The overall height of the front face is 9+2 = 11 cm.

The overall width of the front face is 6+4 = 10 cm.

Out of that 11 cm by 10 cm rectangle, a cutout is made in the upper right corner. The area of that cutout (in the plane of the front face) is 2 cm high by 4 cm wide.

Then the area of the front face is ...

(11 cm)(10 cm) -(2 cm)(4 cm) = 110 cm² -8 cm² = 102 cm²

The volume of the prism can be found using the formula ...

V = Bh

where B is the area of the "base" of the prism, and h is its height. Here, the "base" is the front face, and the height is the dimension marked 5 cm. The volume is ...

V = (102 cm²)(5 cm) = 510 cm³

The volume of the prism is 510 cm³.

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3 years ago

Is 40/8 an integer or no

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2 years ago

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A professional basketball team made 37.9% of its three-point field goals in one season. If 80 three-point field goal attempts ar

kompoz [17]

Answer:

The probability that more than 35 were made is 0.14686.

Step-by-step explanation:

We are given that a professional basketball team made 37.9% of its three-point field goals in one season.

80 three-point field goal attempts are randomly selected from the season.

Let $\hat p$ = <em>sample proportion of three-point field goals made in one season.</em>

The z-score probability distribution for the sample proportion is given by;

Z = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }$ ~ N(0,1)

where, p = population proprotion of three-point field goals = 37.9% = 0.379

n = sample of three-point field goal attempts = 80

$\hat p$ = sample proportion of three-point field goals = $\frac{35}{80}$ = 0.4375

Now, if 80 three-point field goal attempts are randomly selected from the season, the probability that more than 35 were made is given by = P( $\hat p$ > 0.4375)

P( $\hat p$ > 0.4375) = P( $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }$ > $\frac{0.4375-0.379}{\sqrt{\frac{0.4375(1-0.4375)}{80}} }$ ) = P(Z > 1.05) = 1 - P(Z $\leq$ 1.05)

= 1 - 0.85314 = <u>0.14686</u>

The above probability is calculated by looking at the value of x = 1.05 in the z table which has an area of 0.85314.

4 0

3 years ago