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2 years ago

What is the volume of the prism with the dimensions given below? 2/3m 1 1/8m 3 3/4m

Mathematics

1 answer:

Ad libitum [116K]2 years ago

5 0

answer:

volume = $2.8125$ m³

explanation:

Volume of rectangular prism: length * width * height

Here given the length is $\frac{2}{3}$ , width is $1\frac{1}{8}$ , height is $3\frac{3}{4}$

using the formula:

$\frac{2}{3}$ * $1\frac{1}{8}$ * $3\frac{3}{4}$

$\frac{2}{3} *\frac{9}{8} *\frac{15}{4}$

$\frac{45}{16}$

$2.8125$ m³

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A number cube with faces labeled 1 to 6 is rolled once.

Zepler [3.9K]

Answer:

a) A ∪ B = {2, 4, 5, 6}

b) A ∩ B = {6}

c) $\sf B^c$ = {1, 3, 5}

Step-by-step explanation:

Set notation is used in math to list numbers, objects or outcomes.

It uses curly brackets called "braces". Objects placed within the braces are the elements of the set.

The listing method of set notation simply lists the numbers in the set.

The three dots "..." means it is infinite (goes on forever).

Given:

A number cube with faces labeled 1 to 6.

Therefore the set of all possible outcomes is {1, 2, 3, 4, 5, 6}.

Event A

The number rolled is greater than 4.

Therefore, the set of outcomes for event A is {5, 6}.

Event B

The number rolled is even.

Therefore, the set of outcomes for event B is {2, 4, 6}.

Part (a)
Event "A or B" means the outcomes in A or B or both.

⇒ A ∪ B = {2, 4, 5, 6}

Part (b)

Event "A and B" means the outcomes in both A and B.

⇒ A ∩ B = {6}

Part (c)

The complement of event B means everything that is not in B.

$\sf \implies B^c =$ {1, 3, 5}

Learn more about set notation here:

brainly.com/question/27913822

4 0

1 year ago

The table shows the cost of several bunches of bananas.

Alja [10]

Answer:

c=0.42 pounds

Step-by-step explanation:

You divide one of cost by the pounds to get how much one costs then you plug in the equation Cost= # of pound times 48

6 0

3 years ago

Read 2 more answers

I need help with this

defon

i guess just times them all then divide up by how many numbers you have

3 0

4 years ago

Help!! 50 points and brainliest!

Viktor [21]

Answer:

Second choice:

$x=2t$

$y=4t^2+4t-3$

Fifth choice:

$x=t+1$

$y=t^2+4t$

Step-by-step explanation:

Let's look at choice 1.

$x=t+1$

$y=t^2+2t$

I'm going to subtract 1 on both sides for the first equation giving me $x-1=t$ . I will replace the $t$ in the second equation with this substitution from equation 1.

$y=(x-1)^2+2(x-1)$

Expand using the distributive property and the identity $(u+v)^2=u^2+2uv+v^2$ :

$y=(x^2-2x+1)+(2x-2)$

$y=x^2+(-2x+2x)+(1-2)$

$y=x^2+0+-1$

$y=x^2$

So this not the desired result.

Let's look at choice 2.

$x=2t$

$y=4t^2+4t-3$

Solve the first equation for $t$ by dividing both sides by 2:

$t=\frac{x}{2}$ .

Let's plug this into equation 2:

$y=4(\frac{x}{2})^2+4(\frac{x}{2})-3$

$y=4(\frac{x^2}{4})+2x-3$

$y=x^2+2x-3$

This is the desired result.

Choice 3:

$x=t-3$

$y=t^2+2t$

Solve the first equation for $t$ by adding 3 on both sides:

$x+3=t$ .

Plug into second equation:

$y=(x+3)^2+2(x+3)$

Expanding using the distributive property and the earlier identity mentioned to expand the binomial square:

$y=(x^2+6x+9)+(2x+6)$

$y=(x^2)+(6x+2x)+(9+6)$

$y=x^2+8x+15$

Not the desired result.

Choice 4:

$x=t^2$

$y=2t-3$

I'm going to solve the bottom equation for $t$ since I don't want to deal with square roots.

Add 3 on both sides:

$y+3=2t$

Divide both sides by 2:

$\frac{y+3}{2}=t$

Plug into equation 1:

$x=(\frac{y+3}{2})^2$

This is not the desired result because the $y$ variable will be squared now instead of the $x$ variable.

Choice 5:

$x=t+1$

$y=t^2+4t$

Solve the first equation for $t$ by subtracting 1 on both sides:

$x-1=t$ .

Plug into equation 2:

$y=(x-1)^2+4(x-1)$

Distribute and use the binomial square identity used earlier:

$y=(x^2-2x+1)+(4x-4)$

$y=(x^2)+(-2x+4x)+(1-4)$

$y=x^2+2x+-3$

$y=x^2+2x-3$ .

This is the desired result.

3 0

4 years ago

Read 2 more answers

(3 pt) Marie has $830 in her bank account and withdraws $60 each month. Denise has $970 in her bank account and withdraws $80 ea

Lady bird [3.3K]

The answer is c because if you do 7x60 you'll get 420 and 830-420=410 and 7x80 you'll get 560 and 970-560 is also 410.

3 0

3 years ago

Read 2 more answers