Emmanuel wants to tile his rectangular floor. he has 2 kinds of tiles to choose from, one of which is larger than the other. a. What area will be covered by the 8" x 8" tile? 16 by 16 tile? b. if the rectangular floor has dimensions of 74" by 128", how many small square tiles are needed to cover it?

Answers

Answer 1

Answer: $Area\ of\ rectangular\ floor:\n\n A_f=74*128=9472\n\n Area\ of\ small\ tile:\n\n A_s=8*8=64\ Small\ tile\ will\ cover\ 64''^2 \n\n Area\ of\ big\ tile:\n\n A_b=16*16=256\ Big\ tile\ will\ cover 256''^2\n\n A_f:A_s=9472:64=148\n\n A_f:A_b=9472:148=64\n\n\ To\ cover\ the \ floor\ 148\ small\ tiles\ are \ needed.$

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Sophia drew a scale drawing of the elementary school. The scale of the drawing was 1 centimeter : 4 meters. The schoolyard is 52 meters wide in real life. How wide is the schoolyard in the drawing
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Simplify the complex fraction: 4/(x+3)/(1/x+3) A. 12x+4/x^2+3x. B. 4x/3x+9. C. 4x/3x^2+10x+3. D. None of these

Answers

The answer is C. 4x/3x^2+10x+3

$( (4)/(x+3))/( (1)/(x) +3) = ( (4)/(x+3))/( (1)/(x)+ (3x)/(x)) =( (4)/(x+3))/( (1+3x)/(x) ) = (4)/(x+3)* (x)/(1+3x)= (4x)/((x+3)(1+3x)) = (4x)/(x+3 x^(2) +3+9x)$ $= (4x)/(3 x^(2) +10x+3)$

Answer:

The correct option is C.

Step-by-step explanation:

The given expression is

$((4)/(x+3))/(((1)/(x)+3))$

$((4)/(x+3))/(((1)/(x)+3))=((4)/(x+3))/((1+3x)/(x))$

The complex faction can be simplified as

$(((a)/(b)))/(((c)/(d)))=(a)/(b)* (d)/(c)$

$((4)/(x+3))/(((1)/(x)+3))=(4)/(x+3)* (x)/(1+3x)$

$((4)/(x+3))/(((1)/(x)+3))=(4x)/((x+3)(1+3x))$

$((4)/(x+3))/(((1)/(x)+3))=(4x)/(x(1+3x)+3(1+3x))$

$((4)/(x+3))/(((1)/(x)+3))=(4x)/(x+3x^2+3+9x)$

$((4)/(x+3))/(((1)/(x)+3))=(4x)/(3x^2+10x+3)$

Therefore the correct option is C.

trisha standford earns $300 a week plus a 15% commission only on sales she makes after her first $1,000 in sales if ms standfords sales for one week are $2,500 what is her gross pay for that week

Answers

Answer:

Her gross pay for that week=$525

Step-by-step explanation:

Step 1: Express the gross pay

The gross pay can be expressed as follows;

A=F+(R×T)

where;

A=the gross pay per week

F=fixed income per week

R=commission rate

T=total commission sales

In our case;

F=$300 a week

R=15%=15/100=0.15

T=(2,500-1,000)=$1,500

replacing;

A=300+(15% of 1,500)

A=300+(0.15×1,500)

A=300+225=525

A=$525

Her gross pay for that week=$525

Find dy/dx if y= (1+x)e^x^2

Answers

$y=(1+x)e^(x^2)\ny'=(1+x)'\cdot e^(x^2)+(1+x)\cdot(e^(x^2))'\ny'=1\cdot e^(x^2)+(1+x)\cdot e^(x^2)\cdot (x^2)'\ny'=e^(x^2)+(1+x)e^(x^2)\cdot2x\ny'=e^(x^2)(1+(1+x)\cdot2x)\ny'=e^(x^2)(1+2x+2x^2)\ny'=e^(x^2)(2x^2+2x+1)\n$

You first need to know that:

$If\quad y=u\cdot v\n \n \frac { dy }{ dx } =u\frac { dv }{ dx } +v\frac { du }{ dx } \n \n$

Knowing that u is a function of x and that v is a function of x.

So:

$y=\left( 1+x \right) { e }^{ { x }^( 2 ) }=u\cdot v\n \n u=1+x,\n \n \therefore \quad \frac { du }{ dx } =1$

$\n \n v={ e }^{ { x }^( 2 ) }={ e }^( p )\n \n \therefore \quad \frac { dv }{ dp } ={ e }^( p )={ e }^{ { x }^( 2 ) }\n \n p={ x }^( 2 )\n \n \n \therefore \quad \frac { dp }{ dx } =2x$

$\n \n \therefore \quad \frac { dv }{ dp } \cdot \frac { dp }{ dx } =2x{ e }^{ { x }^( 2 ) }=\frac { dv }{ dx }$

And this means that:

$\frac { dy }{ dx } =\left( 1+x \right) \cdot 2x{ e }^{ { x }^( 2 ) }+{ e }^{ { x }^( 2 ) }\cdot 1\n \n =2x{ e }^{ { x }^( 2 ) }\left( 1+x \right) +{ e }^{ { x }^( 2 ) }$

$\n \n ={ e }^{ { x }^( 2 ) }\left( 2x\left( 1+x \right) +1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2x+2{ x }^( 2 )+1 \right) \n \n ={ e }^{ { x }^( 2 ) }\left( 2{ x }^( 2 )+2x+1 \right)$

What number should be added to the expression x^2 + 14x to change it into a perfect square trinomial? Can you help me with this?

Answers

x^2+14x

To make it as perfect square binomial first divide the numerical coefficient of 14 by 2 which is 7. Then square the result[7] which is 49 and add it to the equation
x^2+14x+49
After that think of a number that has a square root of 49 then when u multiply the second term in the perfect square by the first and 2 it results to 14. So the answer is
[x+7]^2

A fair was attended by 834,009 people. Round the number to the nearest ten thousand.

Answers

A fair was attended by 834,009 people

Rounding up this number of people to nearest ten thousand.

9 has a 'ones' value

Going to the right from left:

Second last zero has a 'tens' value.

Third from last zero has a 'thousands' value

4 has 'ten thousands' value

Round up 4 and because it is less than five it converts to zero

This gives an answer of 830,000.

The Hawaiian language has 12 letters: five vowels and seven consonants. Each of the 12 Hawaiian letters are written on a slip of paper and placed in the bag. A letter is randomly chosen from the bag and then replaced. Then, a second letter is randomly chosen from the bag. What is the probability that two vowels are chosen?

Answers

12 total letters...5 vowels and 7 consonants.

probability of 1st letter being a vowel is 5/12
after replacing ...
probability of 2nd letter being a vowel is 5/12

probability of both occurring is (5/12 * 5/12) = 25/144 <===

To solve the problem, the concept of replacement must be considered.

A letter is randomly chosen from the bag and then replaced. Then, a second letter is randomly chosen from the bag.

The probability of the two vowels chosen is 25/144.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

Given

The Hawaiian language has 12 letters.

Five vowels and seven consonants.

To find

The probability of two vowels is chosen.

1. Probability of first letter being vowel.

Total event = 12

Favorable event = 5

Then

$\rm P_1 = (5)/(12)$