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2 years ago

A rectangular prism is 3 units high, 2 units wide, and 5 units long. What is its surface area

Mathematics

1 answer:

andrew11 [14]2 years ago

8 0

Answer:

62 square units

Step-by-step explanation:

Surface area of a rectangular prism = 2 ( wl + hl + hw)

Where,

w = width = 2 units

h = height = 3 units

l = length = 5 units

Surface area of a rectangular prism = 2 ( wl + hl + hw)

= 2 (2*5 + 3*5 + 3*2)

= 2 (10 + 15 + 6)

= 2 (31)

= 62 square units

Surface area of the rectangular prism = 62 square units

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Jeanne wants to start collecting coins and orders a coin collection starter kit. The kit comes with three coins chosen at random

lesya692 [45]

Conditional probability is a measure of the probability of an event given that another event has occurred. If the event of interest is A and the event B is known or assumed to have occurred, "the conditional probability of A given B", or "the probability of A under the condition B", is usually written as P(A|B), or sometimes $P_B(A)$ .

The conditional probability of event A happening, given that event B has happened, written as P(A|B) is given by
$P(A|B)= \frac{P(A \cap B)}{P(B)}$

In the question, we were told that there are three randomly selected coins which can be a nickel, a dime or a quarter.

The probability of selecting one coin is $\frac{1}{3}$

Part A:
To find the probability that all three coins are quarters if the first two envelopes Jeanne opens each contain a quarter, let the event that all three coins are quarters be A and the event that the first two envelopes Jeanne opens each contain a quarter be B.

P(A) means that the first envelope contains a quarter AND the second envelope contains a quarter AND the third envelope contains a quarter.

Thus $P(A)= \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} = \frac{1}{27}$

P(B) means that the first envelope contains a quarter AND the second envelope contains a quarter

Thus $P(B)= \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

Therefore, $P(A|B)=\left( \frac{ \frac{1}{27} }{ \frac{1}{9} } \right)= \frac{1}{3}$

Part B:
To find the probability that all three coins are different if the first envelope Jeanne opens contains a dime, let the event that all three coins are different be C and the event that the first envelope Jeanne opens contains a dime be D.

$P(C)= \frac{3}{3} \times \frac{2}{3} \times \frac{1}{3} = \frac{6}{27} = \frac{2}{9}$

 $P(D)= \frac{1}{3}$ 

Therefore, $P(C|D)=\left( \frac{ \frac{2}{9} }{ \frac{1}{3} } \right)= \frac{2}{3}$

3 0

2 years ago

Ford Motor Company sells the Fusion SES for $24,400. The Fusion Hybrid sells for $29,975. What is the percentage increase in pri

Lubov Fominskaja [6]

Percent increase is:
Change/original * 100
(29975-24400)/24400
5575/24400= .228 * 100=
22.8%

6 0

2 years ago

Read 2 more answers

Triangle ABE is similar to triangle ACD. AED and ABC are straight lines. EB and DC are parallel. AE = 5 cm, BC = 4.5 cm, BE = 4

lianna [129]

Answer:

y = 16x/65

Step-by-step explanation:

Given:

Triangle ABE is similar to triangle ACD. AED and ABC are straight lines

EB and DC are parallel

The area of quadrilateral BCDE = xcm²

The area of triangle ABE = ycm²

Find attached the diagram from the above information.

In similar triangles, the ratio of their corresponding angles are equal.

Also, the ratio of the area of the two triangles = square of ratio of the corresponding sides of the two triangles.

Area ∆ACD/area of ∆ABE = (DC/EB)²

Area ∆ACD/area of ∆ABE = [(area of quadrilateral BCDE +

area of ∆ABE)]/(area of ∆ABE)

(x+y)/y = (DC/EB)²

(x+y)/y = (9/4)²

x+y = (81/16)y

x = (81/16)y - y

x = (81y - 16y)/16

x = 65y/16

Making y subject of formula

16x = 65y

y = 16x/65

An expression for y in terms of x:

y = 16x/65

3 0

1 year ago

A number x, rounded to 1 decimal place is 12.3 write down the error interval for x

icang [17]

We know that
A number x, rounded to 1 decimal place is 12.3
so
x>=12.25
and
x < 12.35

the error interval for x is the interval [12.25,12.35)

the answer is
[12.25,12.35)

3 0

2 years ago

Mark and Sofia walk together down a long, straight road. They walk without stopping for 4 miles. At this point Sofia says their

Marina CMI [18]

Answer:

Sofia is correct.

Step-by-step explanation:

Mark's statement depends on the starting point. He can be correct if they started at the 0 mile, but in this case we don't know where they started. They could had started at the 12 mile and their current position after the walking would be 16 miles.

On the other hand, Sofia's statement doesn't depend on where they started. She refers to how much they walked, not to where they are after the walking. Since they stopped after 4 non-stopping miles, their displacement was exactly 4 miles. So Sofia is correct.

5 0

2 years ago