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3 years ago

An oblique square prism is shown. Which expression represents the volume of the prism?

Mathematics

2 answers:

ad-work [718]3 years ago

7 0

Answer:

Step-by-step explanation:

Furkat [3]3 years ago

3 0

Answer:

C. $x^2*(x-2)\text{ Cubic units}$

Step-by-step explanation:

We have been given a diagram of an oblique prism and we are asked to choose the expression that represents the volume of the prism.

Since we know that an oblique prism is a prism in which the bases are parallel, but the faces are not directly one over the other.

The volume of an oblique prism is base area multiplied by the height.

$\text{Volume of an oblique prism}=\text{Base area* Height of the prism}$

We can see from our diagram that our prism has an square base as each side of base equals x units.

$\text{Base area of prism}=x\text{ units}*x\text{ units}$

$\text{Base area of prism}=x^2\text{ units}^2$

We can also see from our given diagram that it has a height of (x-2) units and slant height of (x+1) units.

Since volume of oblique prism is base area times by the height (not slant height). So upon substituting the height and base area of our given prism in volume formula we will get,

$\text{Volume of an oblique prism}=x^2\text{ units}^2*(x-2)\text{ units}$

$\text{Volume of an oblique prism}=x^2*(x-2)\text{ units}^3$

Therefore, the volume of our given prism is $x^2*(x-2)\text{ Cubic units}$ and option C is the correct choice.

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3 years ago

A coin is tossed twice. What is the probability of getting a tail in the first toss and a tail in the second toss?

skelet666 [1.2K]

Answer:

<h2>1/4 Chances</h2><h2>25% Chances</h2><h2>0.25 Chances (out of 1)</h2>

Step-by-step explanation:

Two methods to answer the question.

Here are presented to show the advantage in using the product rule given above.

<h2>Method 1:Using the sample space</h2>

The sample space S of the experiment of tossing a coin twice is given by the tree diagram shown below

The first toss gives two possible outcomes: T or H ( in blue)

The second toss gives two possible outcomes: T or H (in red)

From the three diagrams, we can deduce the sample space S set as follows

S={(H,H),(H,T),(T,H),(T,T)}

with n(S)=4 where n(S) is the number of elements in the set S

tree diagram in tossing a coin twice

The event E : " tossing a coin twice and getting two tails " as a set is given by

E={(T,T)}

with n(E)=1 where n(E) is the number of elements in the set E

Use the classical probability formula to find P(E) as:

P(E)=n(E)n(S)=14

<h2>Method 2: Use the product rule of two independent event</h2>

Event E " tossing a coin twice and getting a tail in each toss " may be considered as two events

Event A " toss a coin once and get a tail " and event B "toss the coin a second time and get a tail "

with the probabilities of each event A and B given by

P(A)=12 and P(B)=12

Event E occurring may now be considered as events A and B occurring. Events A and B are independent and therefore the product rule may be used as follows

P(E)=P(A and B)=P(A∩B)=P(A)⋅P(B)=12⋅12=14

NOTE If you toss a coin a large number of times, the sample space will have a large number of elements and therefore method 2 is much more practical to use than method 1 where you have a large number of outcomes.

We now present more examples and questions on how the product rule of independent events is used to solve probability questions.

8 0

3 years ago

Read 2 more answers

Ben, Shaneeka, and Phil live on the same street. Ben lives 6/11 mile north of Phil, and 1/3 mile north of Shaneeka. How far does

Norma-Jean [14]

Answer:

Shaneeka live from Phil 7/33 mile far.

Step-by-step explanation:

Given:

Ben lives 6/11 mile north of Phil, and 1/3 mile north of Shaneeka.

Now, to get how far does Shaneeka live from Phil.