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Marizza181 [45]
3 years ago
7

An open box is to be made from a flat piece of material 19 inches long and 4 inches wide by cutting equal squares of length x fr

om the corners and folding up the sides. Write the volume Vof the box as a function of x. Leave it as a product of factors, do not multiply out the factors. V= If we write the domain of the box as an open interval in the form (a,b), then what is a=? a= and what is b=? b=
Mathematics
1 answer:
Aleksandr [31]3 years ago
7 0

Answer with Step-by-step explanation:

We are given that

Length of flat piece of material =19 inches

Width of flat piece=4 inches

An open box  is to be made from a flat piece by cutting equal squares of length  x from the corners and folding up the sides

Therefore, length of open box=(19-2x) inches

Width of open box=4-2x inches

Height of box=x inches

Volume of box=l\times b\times h

Substitute the values then we get

Volume of box=x(19-2x)(4-2x)

x(19-2x)(4-2x) > 0

Because volume of open box is always greater than  zero.

Then , x >0

Substitute

19-2x > 0

2x-19 < 0

2x < 19 By adding 19 on both sides

Dividing by 2 on both sides

x< \frac{19}{2}=9.5

It means x\in (0,9.5)

Substitute 4-2x> 0

2x-4< 0

Adding 4 on both sides then we get

2x < 4

Dividing by 2 on both sides

x< \frac{4}{2}=2

x

Then, x\in (0,2)

Therefore, domain of the box =(0,2)\cap (0,9.5)=(0,2)

Then ,a=0 and b=2

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Serga [27]

1) If a die is rolled once, determine the probability of rolling a 4: Rolling a 4 is an event with 1 favorable outcome (a roll of 4) and the total number of possible outcomes is 6 (a roll of 1, 2, 3, 4, 5, or 6). Thus, the probability of rolling a 4 is \frac{1}{6}.

If a die is rolled once, determine the probability of rolling at least a 4: Rolling at least 4 is an event with 3 favorable outcomes (a roll of 4, 5, or 6) and the total number of possible outcomes is again 6. Thus, the probability of rolling at least a 4 is \frac{3}{6} = \frac{1}{2}.

<h3>Here are two more examples: </h3>

If a coin is flipped twice, determine the probability that it will land heads both times:

Favorable outcomes: 1 -- HH

Possible outcomes: 4 -- HH, HT, TH, TT

Thus, the probability that the coin will land heads both times is \frac{1}{4}.

If Dan grabs one sock from a drawer containing 3 white socks, 4 blue socks, and 5 yellow socks, what is the probability that he will grab a white sock?

Favorable outcomes: 3 (3 white socks)

Possible outcomes: 12 (3 white socks + 4 blue socks + 5 yellow socks)

Thus, the probability that Dan will grab a white sock is \frac{3}{12} = \frac{1}{4}.

6 0
3 years ago
Elio makes candles that are 14 cm tall. Each candle burns 8 hours before going out. He is wondering how many hours a 21 cm tall
MAXImum [283]
Elio is right in assuming the relationship between the height and the hours it burns is proportional.

Find the unit rate

14 ÷ 8 = 1.75 cm/h

Divide

21 ÷ 1.75 = 12

You can set this up as an algebraic equation to check the answer.

If the candle is 21 cm tall, it will burn for 12 hours.

Hope this helped you! :)
8 0
3 years ago
Josiah want to gp to the movies with his friends. Tickets are $8.50 plus he must play Fangalingo a $3 transaction fee for purcha
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Answer:

The equation that represents the number of tickets that Josiah can buy with $45.50

3 + 8.50x = 45.50

The number of number of tickets that Josiah can buy with $45.50 is 5 ticketa

Step-by-step explanation:

Let the number of tickets be represented by x

Tickets are $8.50 plus he must play Fangalingo a $3 transaction fee for purchasing the tickets online.

The equation that represents the number of tickets that Josiah can buy with $45.50

$3 + $8.50 × x = $45.50

3 + 8.50x = 45.50

Solving further for x

3 + 8.50x = 45.50

8.50x = 45.50 - 3

8.50x = 42.50

x = 42.50/8.50

x = 5

Hence, the number of number of tickets that Josiah can buy with $45.50 is 5 ticketa

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Answer:

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Area of a circle is calculated using the following formula :

πr^2 (r: radius, and π is given as3.14)

the diameter is given as 6 and radius is equal to half of it so :

(3.14)*3^2 = 28.26  ft^2

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you can only choose 4 unique ways Step-by-step explanation:

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