Evaluate this expression. (6x103) ÷ (3x102) express your answer in scientific notation.

The 220 cm (2.2 m) perimeter of the tiles and the 9.6 meter side length of the square floor gives equations with the following solutions;

(a) The dimensions of the tiles are;

Width = 0.3 meters

Length = 0.8 meters

(b) 384 tiles are needed

(c) The fitting cost of the tiles is Kshs 51,000

An equation is a mathematical statement that consists of two expressions connected with an equals sign

Shape of the floor = Square

Shape of the tiles = Rectangular

Perimeter of the tiles = 220 cm = 2.2 m

The number of tiles in each row =  20 + The number of tiles in each column

Length of the floor = 9.6 m

(a) Let w represent the width of the tiles, the length l is found using the equation;

[tex]l = \dfrac{2.2 - 2\cdot x}{2} = 1.1 - x[/tex]

Let n represent the number of tiles in each row, which gives;

The number of tiles in each column = 20 + n

(20+n)·x = n·(1.1 - x)

Which gives;

[tex]x = \dfrac{1.1\cdot n}{2\cdot n+20}[/tex]

The side length of the square floor, s = 9.6

(20+n)·x = n·(1.1 - x) = 9.6

Which gives;

[tex]n\cdot \left(1.1 - \dfrac{1.1\cdot n}{2\cdot n+20}\right) = 9.6[/tex]

Which gives;

0.55·n² - 1.4·n -96 = 0

n = 12 or n ≈ -14.5

The number tiles in each roe, n = 20

Which gives; n·(1.1 - x) = 9.6

20 × (1.1 - x) = 9.6

x = 0.3

The width of each tile, x = 0.3 m

The length of each tiles = 1.1 m - 0.3 m = 0.8 m

(b) The number of tiles in each row, n = 20

The number of tiles in each column = n + 20, which gives;

Number of tiles in each column = 12 + 20 = 32

The number of tiles needed = 12 × 32 = 384

(c) The cost of a dozen tiles = Kshs 1,500

The labour cost = Kshs 3,000

Number of dozens of tiles = 384 ÷ 12 = 32

The cost of the tiles C = Kshs 1500 × 32 = Kshs 48000

The total cost = Kshs 48,000 + Kshs 3,000 = Kshs 51,000

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Step-by-step explanation:

Square has perimeter 4a because every side is equal,

so :

if a=√8 , then 4a = 4*√8 or 11.313708499

and the number is rational

The image of the corresponding to each slope is attached

A line's steepness can be determined by looking at its slope.

Slope is determined mathematically as "rise over run" (change in y divided change in x).

assuming slope is m

m = (y₂ - y₁) / (x₂ - x₁) = change in y / change in x

considering the formula

slope is between 0 and 1 when rise (change in y) is so smaller than run (change in x) hence the line is closer to horizontal

slope is greater than 1 then the rise is more than run, in this case the line is approaching vertical line

numbers less than zero are negative hence slope has a negative value

A horizontal line is a line that has a slope of of zero while vertical lines has its slope as infinity

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From the proportional relationship graphed, it is found that:

A proportional relationship is a special case of a linear function, with slope represented by the constant of proportionality of k and intercept of 0, meaning that the relationship passes through the origin.

When the two variables x and y are direct proportional, the output variable y is obtained multiplying the input variable x by the constant of proportionality k, according to the rule presented follows:

y = kx.

From point (2,16) in this problem, the constant is given as follows:

k = 16/2 = 8.

Hence the equation is:

y = 8x.

Meaning that her rate is of:

8 miles per hour.

If she ran faster, the slope = constant would increase, as it represents the velocity.

The problem is given by the image at the end of the answer.

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According to the given statement the correct option is A.

The researcher did not assign individuals to treatment groups.

Typically, researchers are employed by either university or commercial organizations. To support future research, enlarge the body of academic literature, and enhance decision-making, researchers collect data over the course of a project, evaluate the data, and publish the results.

Researchers have an obligation to share their findings, collaborate with others when needed, and transmit and use information for the good of their employer, the economy, and society at large. In the process of their research, researchers have an obligation to conduct themselves honestly and ethically.

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Two heads in three tosses is 3/8, 3/8x713=267.375. 267.375×41=10,962.375.

5/8x713=445.62, 445.62×29=12,923.125

So 10,962.375-12,923.125=-1960.75

Therefore if you played this game, you would statistically lose $1960.75

Answer:

Step-by-step explanation:

solving 3x+4=2x-4

now 3x-2x=-4-4

⇒ x=-8

(c) x=8 here you have given it as O thank you

Answer:

x= -2, -10

Step-by-step explanation:

(x+6)^2-16=0

(x+6)(x+6)-16=0

x^2+6x+6x+36-16=0

x^2+12x+20=0

10+2=12

10(2)=20

(x+2)=0

(x+10)=0

x= -2, -10

Answer:

Step-by-step explanation:

Answer:

4(67 + 22)

Step-by-step explanation:

1. Find the greatest common factor(in this case it is 4)

2. Divide both 268 and 88 by 4 and you get 67 and 22

3. Put it in the requested format and you are left with 4(67 +22)

Answer:

a = -10

So your answer is a = -10, I hope this helps!

Step-by-step explanation:

a + (-7) is the same as a - 7, so you could rewrite it as

a - 7 = -17

+ 7

Answer:

0.97m : 1.08m

Step-by-step explanation:

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Louie can choose the vessel for exhibition using combination in 3003 ways

information from the question include

Louie is studying ceramics and he is to submit 5 vessels

He has 15 vessels

The problem will be solved using combination

combination is method of choosing or making selection when order does not matter

Louie can choose any 5 of his vessel with no particular order

The formula is ₁₅C₅

₁₅C₅ = 15! / {5!(15 - 5)! )

= 15! / {5! * 10!}

= 3003 ways

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Answer:

y=-2x-5

Step-by-step explanation:

m =-2 and b=-5 so when substituted it will get you y=-2x-5

Answer:

1:commutative

2:distribution

3:3+0=3

4:distributive

5:

a.

A gardener can afford to buy 125 vinca plants and 60 phlox plants. $1.20/plant Vinca $2.50/plant Phlox.

The equation in standard form that models the possible combinations of x vinca plants and y phlox plants the gardener can afford to buy is

⇒ $1.20*x + $2.50*y

b.

An equation that models the possible combinations is

⇒ $1.20*125 + $2.50*60 = 300

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Answer:

Step-by-step explanation:

I think the slope and the y is not 1/x because 2 is not part of the slope, im not sure

According to the solving Probability the value are as follows.

a) P(Blue)= 0/10

b) P(Red)= 5/10

c) P(Red or Yellow)= 9/10

The definition of probability is "How likely something is to happen."

Probability is indeed a number ranging from 0 to 1 that expresses the likelihood that an event will take place as specified.

First, 0 P(E) 1 (where P(E) specifies the probability of an event E) and second, the sum of the probabilities of any collection of mutually and exclusive exhaustive occurrences equals 1 are the two characteristics that define a probability.

We have a Bag of marbles has 4 yellow, 5 red, and 1 purple.

Total balls in a bag= 4+5+1=10 balls.

Something that is IMPOSSIBLE to happen.

P(Blue)= 0/10

Something that is EQUALLY LIKELY to happen.

P(Red)= 5/10

Something that is LIKELY to happen.

P(Red or Yellow)= 9/10

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Differentiation of f(x) is [tex]-8x^{3} sinx^{4}[/tex].

Given,

f(x) = [tex]cos2x^{4}[/tex]

Now, we will differentiate f(x) with respect to x,

[tex]\frac{d}{dx}cos2x^{4} = (\frac{d}{dx}cos2x^{4})(\frac{d}{dx}2x^{4} )[/tex]

              [tex]= (-sin2x^{4})(2*4x^{3})[/tex]

              [tex]= -8x^{3}sin2x^{4}[/tex]

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The concentration of the type of antibiotic after 4 hours is; 11.04 parts per million

We are told that the equation that models the concentration in parts per million of a type of antibiotic in a human's bloodstream after h hours is;

A(h) = -0.06h² + 2h + 4

where h is the time in number of hours after which the concentration is recorded.

Now, we want to find the concentration after 4 hours and as such we will input 4 for h in the equation to get;

A(4) = -0.06(4²) + 2(4) + 4

A(4) = -0.96 + 12

A(4) = 11.04 parts per million

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The plan that fits to Landyn's budget is plan B

What is percentage and how to calculate it?

A percentage is a certain number or part in every hundred. It is a fraction with the denominator 100, and the symbol for it is "%." Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. Two methods exist for calculating a percentage. By adjusting the fraction's denominator to 100 and applying the unitary approach.

We are given that Landyn's current monthly net pay is $560

And he does not wish to spend more than 10% of his current net pay

That means not more that $56

Now we are given 3 choices

Out of which the third one is more than 60 hence this rules out the third option. Now the first option the value is 55+55(0.005) which again is more than $56

Consider the option B)

50 + 50(0.05)

= 52.5

Which is less than $56

Hence, The plan that fits to Landyn's budget is plan B

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Answer:

Infinite solutions

Step-by-step explanation:

The equation is,

→ 8x + 16x - 12 = 24x - 12

Let's solve for the value of x,

→ 8x + 16x - 12 = 24x - 12

→ 24x - 24x = -12 + 12

→ [ 0 = 0 ]

Hence, it has infinite solution. Because, all the real numbers are suitable.

Answer:

infinite number.

Step-by-step explanation:

Comment

There is only the same letter (x) on both sides of the equation. None of the xs are raised to any power. The power is 1 for all of them. That being so, there is only ONE solution.

x^2 + 5x + 6 would give 2 solutions because the x is raised to the second power.

x^3 + x^2 + 4x + 9 would give 3 solutions.

Solution

8x + 16x - 12 = 24x - 12 This equation is a little different. Both sides are exactly the same -- 24x - 12. That means that there is an infinite number of solutions.

For example let x = 10

The right side = 240 - 12 = 228

The left side = 8*10 + 16*10 - 12 = 228

You can't come up with a number that will make the left side unequal to the right side.

Answer: f (x)= -2x + 4

Step-by-step explanation:

"down by one" means that the y values (the function result values) are all decreased by 1.

so, k = -1

Josephine have £3882.9 amount after 2 years and £3994.9 amount after 3 years.

Using the formula of compound interest we can find the amount after t years compounded annually at the r per cent rate.

The formula of compound interest is as follows,

[tex]A=p(1+\frac{r}{100} )^t[/tex]

Where P is the principal value, A is the amount, r is the rate and t is the time.

Here we have a principal value of £3,500 and a rate is 4.5%.

Now, finding the amount after 2 years by putting the values in the formula of compound interest,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^2\\\\A=3500(1+0.045 )^2\\A=3500(1.045)^2\\A=3500\times1.092025\\A=3882.0875[/tex]

So, After 2 years Josephine will have £3882.9.

Now, finding the amount after 3 years,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^3\\\\A=3500(1+0.045 )^3\\A=3500(1.045)^3\\A=3500\times1.141166125\\A=3994.0814375[/tex]

So, After 3 years Josephine will have £3994.9.

Therefore, After 2 years Josephine will have £3882.9 and after 3 years Josephine will have £3994.9 when 4.5% interest is compounded annually.

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Answer:

Step-by-step explanation:

Correct answer is A 5

check your textbook for the remainder theorem, where it states that for a factor (x-5) of f(x) then the remainder will be 0, thus f(5) = 0, what the heck all that means?

well, it means that if we evaluate f(5) our result should be 0, so

[tex]\stackrel{factor}{(x-5)}\hspace{5em}f(5)=(5)^3-7(5)^2+(5)+a=0 \\\\\\ 0=(5)^3-7(5)^2+(5)+a\implies 0=125-175+10+a \\\\\\ 0=-40+a\implies \boxed{40=a}[/tex]

The probability that a simple random sample of 50 unemployed individuals will provide a sample mean within 1 week of the population mean is 0.92

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the avergae number of weeks an individual is unemployed of a population, and for this case we know the distribution for X is given by:

X = N(17.5)

Where μ = 17.5 and σ = 4

Since the distribution for X is normal then, the distribution for the sample mean  is given by:

X = N(17.5, σ/√n)

X =N(17.5.4/√50) = 0.566

We select a sample of n =50 people. And we want to find the following probability

P(16.5 < X < 18.5) = P((16.5 -17.5)/(4/√50) < Z < (16.5 -17.5)/(4/√50) )

And using the normal standard table or excel we find the probability:

P(-1.768 < Z 1.768) = P(Z < 1.768) - P(Z< -1.768) = 0.961 - 0.039 = 0.92

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