Use an exponent to write each expression

1. For the carnival, the park rented a dunking booth shaped as a rectangular prism. The booth is 3 1/2 ft wide, 3 1/2 ft long, a

tangare [24]

Answer:

Part a) The total volume is $98\ ft^{3}$

Part b) $84\ ft^{3}$

Step-by-step explanation:

Part a)

Find the total volume

we know that

The volume of a rectangular prism is equal to

$V=LWH$

we have

$L=3\frac{1}{2}\ ft=\frac{3*2+1}{2}=\frac{7}{2}\ ft$

$W=3\frac{1}{2}\ ft=\frac{3*2+1}{2}=\frac{7}{2}\ ft$

$H=8\ ft$

substitute in the formula

$V=(\frac{7}{2})(\frac{7}{2})(8)=98\ ft^{3}$

Part b) If they are only going to fill the dunking booth 6/7 full, how many cubic feet of water will they need?

Multiply the total volume by 6/7

so

$98(6/7)=84\ ft^{3}$

6 0

4 years ago

Can you please try to help me

8090 [49]

Frist of all he traveled

3hours

so 3/4

1/2

so line on the left put 3 hours one one the right put 3/4-1/2

8 0

3 years ago

the speed of light is 1.86×10^5 miles per second.how many miles will light travel in 4,200,000 seconds?

stiks02 [169]

Answer: $7.812*10^{11}\ miles$

Step-by-step explanation:

Let be "x" the amount of miles light will travel in 4,200,000 seconds.

Rewrite 4,200,000 seconds in Scientific notation. Move the decimal point 6 places to the left. Then:

$4,200,000\ seconds=4.2*10^6\ seconds$

According to the exercise, light travels $1.86*10^5$ miles in 1 second.

Therefore, based on this data, you can set up the following proportion:

$\frac{1.86*10^5\ miles}{1\ second}=\frac{x}{4.2*10^6\ seconds}$

And finally, you must solve for "x" in order to find its value.

(Remember the Product of powers property: $a^m*a^n=a^{mn}$ )

Then:

$(4.2*10^6\ seconds)(\frac{1.86*10^5\ miles}{1\ second})=x\\\\x=7.812*10^{11}\ miles$

7 0

3 years ago

How do you know if this equation is true 1/3+1/5=2/8=1/4

raketka [301]

4/16 or 1/4 because 1 + 1 + 2 is 4 & 3 + 5 + 8 is 16 so the fraction will be 4/16 but u can also divide both by 4’s which is 1/4.

7 0

3 years ago

A friend offers to play a game, in which you roll 3 standard 6-sided dice. If all the dice roll

VMariaS [17]

Answer: The expected value is $0.32

Step-by-step explanation:

The expected value can be calculated as:

EV = ∑xₙ*pₙ

Where:

xₙ is the n-th event.

pₙ is the probability of the n-th event.

First, let's see the events in this situation and the probability of each event.

Lossing $1.

This happens when you roll all different numbers.

To calculate the number of combinations where you roll all different values, we first need to count the number of possible options for each roll, this is:

First dice: you have 6 options

Second dice: You have 5 options, because we remove the option that was rolled in the first dice.

Third dice: You have 4 options, because we removed the two outcomes showed in the two previous rolls.

Then the number of combinations is:

c = 6*5*4 = 120.

And the total number of combinations for rolling 3 dice is equal to the product between the number of outcomes for each dice, each dice has 6 possible outcomes, then the total number of outcomes is:

C = 6*6*6 = 216

The probability of rolling all different numbers will be equal to the quotient between the number of combinations where you roll all different values and the total number of combinations:

P₁ = 120/216 = 0.56

In the other case, where you roll at least two equal outcomes, you win $2.

The probability for this case will be the complement of the previous one, then the probability can be calculated as:

P₂ = 1 - P₁ = 1 - 0.56 = 0.44

Then the expected value will be:

EV = -$1*0.56 + $2*0.44 = $0.32

The expected value is $0.32

5 0

3 years ago