A prisoner is planning to escape from prison! The prison s gate consists of horizontal and vertical bars that are spaced one unit apart so the area of each hole between the bars is 1 x 1. The prisoner manages to remove certain bars to make some bigger holes. Determine the area of the largest hole in the gate after the bars are removed in java

Answer:

B. hexagon

Step-by-step explanation:

Answer:

an = 40 - 3n

Read down to get the alternate answer.

Step-by-step explanation:

an = a1 + (n - 1)*d

a2 = a1 + (2 - 1)d

34 = a1 + d

a7 = a1 + 6*d

19 = a1 + 6d

34= a1 + d                Subtract

-15 = 5d                   Divide by 5

d = - 3

Now use the first equation to find a2

a1 + d = 34

a1 -3 = 34                 Add 3

a1 = 34 + 3

a1 = 37

The formula you want is

an = 37 + (n - 1)*-3   You could reduce it further. Remove the brackets

an = 37  - 3n + 3

an = 40 - 3n

Does it work? Try a7

19 = 40 - 3*7

19 = 40 - 21

19 = 19

Yes it works.

[tex]\\ \rm\longmapsto Length(Breadth)=Area[/tex]

[tex]\\ \rm\longmapsto Length(7)=672[/tex]

[tex]\\ \rm\longmapsto Length=\dfrac{672}{7}[/tex]

[tex]\\ \rm\longmapsto Length=96m[/tex]

Answer:

x=60

Step-by-step explanation:

x=180-120

Answer:

The sum of three times a number and twelve is fewer than twenty translates into an inequality

3x+12 < 20

Step-by-step explanation:

it's not the perfect answer of your question but it's kind of similar to it

Step-by-step explanation:

here,

let MP be x then,

SP=x-20%of X

=x - 20x/100

=x- 0.2x

=0.8x

CP= x- 30% of x

= x- 30x/100

=x- 0.3x

=0.7x

now,profit (P) = SP -CP

= 0.8x-0.7x

=0.1x

so,

P%=( P\CP ) ×100%

= (0.1x/0.7x) ×100%

= 14.28 %

Answer:

68 blue marbles are there.

Answer:

Blue marbles are 100.

Step-by-step explanation:

Number of red marbles=252 × 2/7

Number of red marbles=72

Remaining marbles=252-72

Remaining marbles=180

Now,

Number of green marbles=180×4/9

Number of green marbles=80

Reaminng marbles which are blue=100-80

=100

If you have any questions about it let me know.

Answer:

Answer:

If:   153  words = 3  minutes  :

Then:  1 minute =  153 3 =  51 words

10 minutes is:

10 × 51 = 510

Ben can type 510 words in 10 minutes

Answer:

infinite solutions

Step-by-step explanation:

-9(x+3) +12 = -3(2x+5)-3x

Distribute

-9x-27 +12 = -6x-15-3x

Combine like terms

-9x -15 = -9x-15

Add 9x to each side

-9x-15+9x = -9x-15+9x

-15 = -15

This is a true statement so it is true for all x

please mark this answer as brainlist

Answer:

It is 36 cm

Step-by-step explanation:

In equilateral triangle, all sides are equal.

[tex]{ \sf{perimeter = side + side + side}}[/tex]

but side = 12 cm

[tex] { \sf{p = (12 + 12 + 12)}} \\ { \sf{p = 36 \: cm}}[/tex]

Answer: Perimeter = 36 cm

Concept:

Here, we need to know how to find the perimeter of an equilateral triangle.

An equilateral triangle is a triangle in which all three sides have the same length.

Perimeter (equilateral triangle) = 3s

s = side length

Solve:

Given information

Side length = 12 cm

Given expression

Perimeter = 3s

Substitute values into the expression

Perimeter = 3 (12)

Simplify by multiplication

Perimeter= [tex]\boxed{36cm}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Step-by-step explanation:

According to the quotient rule of differentiation, if [tex]y(x) = u(x)/v(x),[/tex] then its derivative is given by

[tex]\dfrac{dy}{dx} = \dfrac{v\dfrac{du}{dx} - u\dfrac{dv}{dx}}{v^2}\:\:\:\:\:\:\:\:\:(1)[/tex]

We can see that

[tex]u(x) = \ln (4x^2 + 1)[/tex]

[tex]\dfrac{du}{dx} = \dfrac{8x}{4x^2 + 1}[/tex]

[tex]v(x) = 2x - 3[/tex]

[tex]\dfrac{dv}{dx} = 2[/tex]

Plugging the above expressions into Eqn(1), we find that the derivative is

[tex]\dfrac{dy}{dx} = \dfrac{\dfrac{8x(2x - 3)}{(4x^2 + 1)} - 2\ln (4x^2 + 1)}{(2x - 3)^2}[/tex]

[tex]\:\:\:\:\:\:\:= \dfrac{8x}{(4x^2 + 1)(2x - 3)} - \dfrac{2\ln (4x^2 + 1)}{(2x - 3)^2}[/tex]

Answer:

it is 5000 in my guess . to you can ask me anytime

Answer:

you can check the picture, i tried to make it as simple as possible. so I answered by the format.

Answer:

8.5 × 10^5

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

[tex]\\ \rm\Rrightarrow (2.5\times 10^3)^3\times 4\times 10^2[/tex]

[tex]\\ \rm\Rrightarrow 2.5\times 3.4 10^3 \times 10^2[/tex]

[tex]\\ \rm\Rrightarrow 8.5\times 10^{3+2}[/tex]

[tex]\\ \rm\Rrightarrow 8.5\times 10^5[/tex]

Answer:

Step-by-step explanation:

5 bulbs in 30-day month will consume electricity:

The total cost is:

Total electricity consumed per day

Consumed in 30days

For 5bulbs

Cost

Step-by-step explanation:

The speed of sound has nothing to do with "sea level" and sound pressure and without the medium air there is no speed of sound. In SI units with dry air at 20°C (68°F), the speed of sound c is 343 meters per second (m/s). This also equates to 1235 km/h, 767 mph, 1125 feet per second (ft/s), or 666 knots.

Answer:

Step-by-step explanation:

The fifth root of -243 = - 3

If you now square  - 3, you get (-3)(-3) = 9

Answer:

x+x+5=10

Step-by-step explanation:

ya

Answer:

x+3+x+2

X+x+3+2

2x+5

Step-by-step explanation:

mark me as brainliest

Answer:

$12.5 dollars

Step-by-step explanation:

cc

Proteins consist of monomers of glucose bonded together in a variety of ways and can function as energy, enzymes, and transport. Proteins function as storage, movement, and defense and are diverse due to the arrangement of the nucleic acids.

Answer:

The correct answer to the question is, proteins are made of amino acids bonded together in a variety of ways and can function as enzymes, transport, and structure.

One of the abundant organic molecules in living systems is the proteins. Proteins have the most various ranges of functions of all macromolecules.

Further Explanation

They may be regulatory, contractile, structural or protective. They serve in membranes, transport or storage. In a living system, each cell may have thousands of different proteins and performs different functions.  Proteins function and structures differ. However, all proteins are polymers of amino acid which are arranged in linear sequence.

Proteins perform a lot of functions and this is because there are 20 chemically distinct amino acids which constitute the long chains and the amino can take different order. For instance, proteins can function as hormones or enzymes. Living cells produced enzymes and are catalyst in chemical reaction. They are usually proteins. Enzymes can function to rearrange bond, to break bonds, or formation of new bonds. One of the examples of enzymes is salivary amylase, which is a component of starch. Hormones are usually proteins or steroids, which are secreted by a group of endocrine cells that control physiological process such as metabolism, reproduction and growth.

The monomers comprises of proteins are called amino acid and each amino acid has structures that make up of central carbon atom bonded into amino group.  

KEYWORDS:

amino acid

proteins

enzymes

transport

hormones

I'll only look at (37) here, since

• (38) was addressed in 24438105

• (39) was addressed in 24434477

• (40) and (41) were both addressed in 24434541

In both parts, we're considering the line integral

[tex]\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy[/tex]

and I assume C has a positive orientation in both cases

(a) It looks like the region has the curves y = x and y = x ² as its boundary***, so that the interior of C is the set D given by

[tex]D = \left\{(x,y) \mid 0\le x\le1 \text{ and }x^2\le y\le x\right\}[/tex]

• Compute the line integral directly by splitting up C into two component curves,

C₁ : x = t and y = t ² with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = 1 - t with 0 ≤ t ≤ 1

Then

[tex]\displaystyle \int_C = \int_{C_1} + \int_{C_2} \\\\ = \int_0^1 \left((3t^2-8t^4)+(4t^2-6t^3)(2t))\right)\,\mathrm dt \\+ \int_0^1 \left((-5(1-t)^2)(-1)+(4(1-t)-6(1-t)^2)(-1)\right)\,\mathrm dt \\\\ = \int_0^1 (7-18t+14t^2+8t^3-20t^4)\,\mathrm dt = \boxed{\frac23}[/tex]

*** Obviously this interpretation is incorrect if the solution is supposed to be 3/2, so make the appropriate adjustment when you work this out for yourself.

• Compute the same integral using Green's theorem:

[tex]\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dy = \iint_D \frac{\partial(4y-6xy)}{\partial x} - \frac{\partial(3x^2-8y^2)}{\partial y}\,\mathrm dx\,\mathrm dy \\\\ = \int_0^1\int_{x^2}^x 10y\,\mathrm dy\,\mathrm dx = \boxed{\frac23}[/tex]

(b) C is the boundary of the region

[tex]D = \left\{(x,y) \mid 0\le x\le 1\text{ and }0\le y\le1-x\right\}[/tex]

• Compute the line integral directly, splitting up C into 3 components,

C₁ : x = t and y = 0 with 0 ≤ t ≤ 1

C₂ : x = 1 - t and y = t with 0 ≤ t ≤ 1

C₃ : x = 0 and y = 1 - t with 0 ≤ t ≤ 1

Then

[tex]\displaystyle \int_C = \int_{C_1} + \int_{C_2} + \int_{C_3} \\\\ = \int_0^1 3t^2\,\mathrm dt + \int_0^1 (11t^2+4t-3)\,\mathrm dt + \int_0^1(4t-4)\,\mathrm dt \\\\ = \int_0^1 (14t^2+8t-7)\,\mathrm dt = \boxed{\frac53}[/tex]

• Using Green's theorem:

[tex]\displaystyle \int_C (3x^2-8y^2)\,\mathrm dx + (4y-6xy)\,\mathrm dx = \int_0^1\int_0^{1-x}10y\,\mathrm dy\,\mathrm dx = \boxed{\frac53}[/tex]

Answer:

y = -30

Step-by-step explanation:

Set the ratio: [tex]\frac{x_1}{y_1} = \frac{x_2}{y_2}[/tex]

Let:

[tex](x_1 , y_1) = (-4 , 10)\\(x_2 , y_2) = (12 , y)\\[/tex]

Plug in the corresponding terms to the corresponding variables:

[tex]\frac{-4}{10} = \frac{12}{y}[/tex]

First, cross multiply.

[tex](-4 * y) = (10 * 12)\\-4y = 10 * 12\\-4y = 120[/tex]

Next, isolate the variable, y. Divide -4 from both sides of the equation:

[tex]\frac{-4y}{-4} = \frac{120}{-4}\\y = \frac{120}{-4}\\y = -30[/tex]

-30 is your answer for y.

Using proportions, it is found that the Big Board market had the largest fraction.

------------------------

Big board:

The proportion that rose is:

[tex]p_B = \frac{1788}{3154} = 0.5669[/tex]

------------------------

NASDAQ:

The proportion that rose is:

[tex]p_N = \frac{2068}{3655} = 0.5658[/tex]

[tex]p_B > p_N[/tex], thus, the Big Board market had the largest fraction.

A similar problem is given at https://brainly.com/question/19905617

9514 1404 393

Answer:

  next: ←, ↑, →, ↓, ←

Step-by-step explanation:

It appears you want to identify a rule describing the sequence, then provide several additional elements in the sequence.

It looks to me like each successive element has been rotated 90° CW from the previous one.

Continuing that pattern, the arrows will point left, up, right, down, left.

Probabilities are used to determine the chance of an event. The following are the summary of the solution.

Given that:

[tex]n = 8[/tex]

[tex]G = 6[/tex] --- Green

[tex]Y = 2[/tex] --- Yellow

(a) Probability that the two cellphones are green (without replacement).

Since the cellphone is not replaced, the probability is calculated as follows:

[tex]Pr = \frac Gn \times \frac{G - 1}{n-1}[/tex]

So, we have:

[tex]Pr = \frac 68 \times \frac{6 - 1}{8-1}[/tex]

[tex]Pr = \frac 68 \times \frac 57[/tex]

[tex]Pr = \frac{30}{56}[/tex]

[tex]Pr = \frac{15}{28}[/tex]

Hence, the probability that the two cellphones are green (without replacement) is 15/28

(b) Probability that one green and one yellow is selected (without replacement).

Since the cellphone is not replaced, the probability is calculated as follows:

[tex]Pr = \frac Gn \times \frac{Y}{n-1} + \frac Yn \times \frac{G}{n-1}[/tex]  ---- The subtraction means the cellphones are not replaced

This gives

[tex]Pr = \frac 68 \times \frac{2}{8-1} + \frac 28 \times \frac{6}{8-1}[/tex]

[tex]Pr = \frac 34 \times \frac{2}{7} + \frac 14 \times \frac{6}{7}[/tex]

[tex]Pr = \frac 32 \times \frac17 + \frac 12 \times \frac 37[/tex]

[tex]Pr = \frac{3}{14} + \frac{3}{14}[/tex]

Take LCM

[tex]Pr = \frac{3+3}{14}[/tex]

[tex]Pr = \frac{6}{14}[/tex]

[tex]Pr = \frac{3}{7}[/tex]

Hence, the probability that one green and one yellow is selected (without replacement) is 3/7

(c) Probability that the all three cellphones are yellow (with replacement).

Since the cellphone is replaced, the probability is calculated as follows:

[tex]Pr = \frac Yn \times \frac Yn \times \frac Yn[/tex]

So, we have:

[tex]Pr = \frac 28 \times \frac 28 \times \frac 28[/tex]

[tex]Pr = \frac 14 \times \frac 14 \times \frac 14[/tex]

[tex]Pr = \frac 1{64}[/tex]

Hence, the probability that all three cellphones are yellow (with replacement) is 1/64

(d1) Probability that the two cellphones are green (with replacement).

Since the cellphone is replaced, the probability is calculated as follows:

[tex]Pr = \frac Gn \times \frac{G}{n}[/tex]

So, we have:

[tex]Pr = \frac 68 \times \frac{6}{8}[/tex]

[tex]Pr = \frac 34 \times \frac{3}{4}[/tex]

[tex]Pr = \frac{9}{16}[/tex]

Hence, the probability that the two cellphones are green (with replacement) is 9/16

(d2) Probability that one green and one yellow is selected (with replacement).

Since the cellphone is replaced, the probability is calculated as follows:

So, we have:

[tex]Pr = \frac Gn \times \frac{Y}{n} + \frac Yn \times \frac{G}{n}[/tex]

This gives

[tex]Pr = \frac 68 \times \frac{2}{8} + \frac 28 \times \frac{6}{8}[/tex]

[tex]Pr = \frac 34 \times \frac{1}{4} + \frac 14 \times \frac{3}{4}[/tex]

[tex]Pr = \frac 3{16} + \frac{3}{16}[/tex]

Take LCM

[tex]Pr = \frac {3+3}{16}[/tex]

[tex]Pr = \frac {6}{16}[/tex]

[tex]Pr = \frac {3}{8}[/tex]

Hence, the probability that one green and one yellow is selected (with replacement) is 3/8

Read more about probabilities at:

https://brainly.com/question/795909

Answer:

a. 8.75

b. 0.72

c. 9.31

d. 23.04

e. 6.98

Step-by-step explanation:

a.

in this number 8.7495980

the digit in the hundredth place is 4

the digit in the thousandth  place is 9

Since 9 ≥ 5 ,then 8.7495980 rounded to nearest hundredth is :

8,75

b.

in this number 0.72091

the digit in the hundredth place is 2

the digit in the thousandth  place is 0

Since 0 < 5 ,then  0.72091 rounded to nearest hundredth is :

0.72

c.

in this number 9.3113

the digit in the hundredth place is 1

the digit in the thousandth  place is 1

Since 1 < 5 ,then  9.3113 rounded to nearest hundredth is :

9.31

d.

in this number 23.0368

the digit in the hundredth place is 3

the digit in the thousandth  place is 6

Since 6 ≥ 5 ,then 23.0368 rounded to nearest hundredth is :

23.04

e.

in this number 6.9788

the digit in the hundredth place is 7

the digit in the thousandth  place is 8

Since 8 ≥ 5 ,then 6.9788 rounded to nearest hundredth is :

6.98

Answer:

Step-by-step explanation: