Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri will need [Blank] glass tiles. The dimentions are...26 , 15, 8.

Answers

Answer 1

Answer:

The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.

What is the Surface Area of a Box?

The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.

What is the Surface Area of a Box?

SA = 2(lw + lh + hw), where:

l = length
w = width
h = height of the box

The image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:

The surface area to be covered = surface area of the box - area of the bottom rectangular face

The surface area to be covered = 2(lw + lh + hw) - (l)(w)

l = 26

w = 15

h = 8

Substitute

The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =

The surface area to be covered = 1436 - 390 = 1,046 cm

Area of one tile = 1 cm square

Number of tiles needed = 1,046/1

Number of tiles needed = 1,046 tiles.

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A bacteria culture is initially 10 grams at t=0 hours and grows at a rate proportional to its size. After an hour the bacteria culture weighs 11 grams. At what time will the bacteria have tripled in size?

Answers

A bacteria culture is initially 10 grams at t=0 hours & grows at a rate proportional to its size , After an hour the bacteria culture weighs 11 grams , The bacteria takes 11.56 hours to have tripled in size.

To find the time of bacteria when increasing the growth to tripled.

Given : when time=0 hours , weight=10 grams.

when time=1 hours , weight=11 grams.

To find: when time= ? hours , weight=30grams.

Here according to question, initial size = 10 grams we have asked for tripled in size i.e. 30 grams.

Now we knows that,

The formula for exponential growth in population or size is

$\rm (P)=P_0e^(rt)$ where,

$\rm P_0=initial\;size\n\nr= rate\;of\;growth\n\nt= time \;period$

Now, we put the value in formula we get,

$\rm P_0=10\;grams \n\nwhen ,\n\;\;t=1\;hour P(t)=11 grams\nThen,\n11=10e^{r(1)\n1.1 =e^r\n\n\rm Taking \;log(natural)\;both\;the\; side \;on \;solving\;we\;get,\nln(1.1)=r\;ln(e)\nr=ln(1.1)\nr=0.953101798043\approx0.095$

Now when the bacteria increase its size to triple

$\rm P(t) = 3 * 10 = 30$

Then, according to the formula we substitute values in the formula,

$\rm 30=10e^(0.095t)\n\n3=e^(0.095t)\n\nAgain \;we \;take\;natural\;log\;on \;both\;the\;sides, we\;get\nln\;3=0.095t\n\nt=(\rm ln\;3)/(0.095)\n\n\n\n\rm t= (1.09861228867)/(0.095) \n\n\ t=approx \; 11.56$

Therefore, The bacteria takes 11.56 hours to have tripled in size.

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Answer: It will take 11.56 hours .

Step-by-step explanation:

Exponential growth in population or size formula :

$P(t)=P_0e^(rt)$

, where $P_0$ = initial size

r= rate of growth

t= time period

As per given , we have

$P_0=10$ grams

At t= 1 , P(t)= 11 grams

Then,

$11=10e^(r(1))\n\n 1.1= e^r\n\n\text{Taking natural log on both sides , we get} \n\n\ln (1.1)=r\ln (e)\n\n r=\ln (1.1)\n\n r=0.0953101798043\approx0.095$

When, the bacteria have tripled in size , P(t) = 3 x10 = 30

Then,

$30=10e^(0.095t)\n\n 3=e^(0.095t)$

$\text{Taking natural log on both sides , we get}\n\n \ln 3=0.095t\n\n t=(\ln3)/(0.095)\n\n t=(1.09861228867)/(0.095)\approx11.56$

Hence, it will take 11.56 hours .

Antonio has a job as a waiter. He is paid $20.00 per day, plus $5.50 per table served, x. On Friday, Antonio earned $157.50. Which equation can be used to determine how many tables Antonio served on Friday?

Answers

The required equation used to determine how many tables Antonio served on Friday is 157.50 = 20 + 5.5x.

What are equation models?

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Antonio has a job as a waiter. He is paid $20.00 per day, plus $5.50 per table served, x.
Let the total earnings of Antonia for a day be y,
According to the question,
y = 20 + 5.5x

Now,
Antonio earned $157.50 on Friday.
157.50 = 20 + 5.5x

Thus, the required equation used to determine how many tables Antonio served on Friday is 157.50 = 20 + 5.5x.

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Answer:

He served 25 tables

Step-by-step explanation:

Do..

£157.50 - £20 (as he gets this daily) = £137.50

£137.50 ÷ £5.50 = number of tables he served = 25 tables

Hope this helped

nixon cuts 5/6 inch sections of wood to make a birdhouse roof . he cut 24 sections. how many inches did he cut

Answers

Answer: 20 inches

Step-by-step explanation: 5/6 x 24 = 20

Answer:20 Inches

Step-by-step explanation:

5/6in*24=20inches

What is the difference, in hours and minutes, between these times?
a)11:25 and 14:10

Answers

Answer:

14:10 is 24 hours clock which only come in after noon that is 12

11:25 is a normal clock with remains normal before 12:00

Which expression can be used to determine the product of -4 and 3 1/4

Answers

Answer:

Possible options:

= -4 * 3 1/4

= -4 * 13/4

= -4 * 3.25

Step-by-step explanation:

Without the options that seemed to go along with this question, it will be difficult to give the exact expression, but here are a few options.

-4 * 3 1/4 = -13

-4 * 13/4 = -13

-4 * 3.25 = -13

Each of these expressions will give the product of -4 and 3 1/4.

Cheers

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