Solve c = ab? for b.

The area and perimeter of each of the given polygons are a) 12+2√3+√34 units, 32 units² and b) 27 units and 46 units²

A polygon is a two-dimensional geometric figure that has a finite number of sides.

Given that, two polygons, we need to calculate the area and perimeter of each of the following polygons.

1) Calculating the lengths of the side by using Pythagoras theorem,

Sides = 2√3, √34, 5, 5 and 2

Therefore, perimeter = 12+2√3+√34 units

Area =

The polygon is divided into a trapezium and a triangle,

Therefore,

Area = 1/2(8x3)+4/2(8+2) = 12+20 = 32 units²

2) Perimeter = 1+1+2+2+2+3+3+4+4+5 = 27 units

Area = (2x1)+(3x1)+(3x5)+(3x2)+(5x4) = 2+3+15+6+20 = 46 units²

Hence, the area and perimeter of each of the given polygons are a) 12+2√3+√34 units, 32 units² and b) 27 units and 46 units²

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To find p(b/), we need to use the formula for conditional probability:

p(b/a) = p(a and b) / p(a)

We already know that p(a and b) = 0.2, but we need to find p(a) first.

p(a) = p(a and b) + p(a and b/) = 0.2 + p(a0)*p(b0/) = 0.2 + 0.4*0.5 = 0.4

Now we can substitute these values into the formula:

p(b/a) = 0.2 / 0.4 = 0.5

This means that the probability of b occurring given that a has occurred is 0.5. To find the probability of b occurring without any knowledge of a, we use the law of total probability:

p(b) = p(a)*p(b/a) + p(a/)*p(b/a/) = 0.4*0.5 + 0.6*p(b0/) = 0.2 + 0.6*p(b0/)

We don't know p(b0/), but we can use the fact that probabilities must add up to 1:

p(b) = 0.2 + 0.6*(1-p(b))

Solving for p(b), we get:

p(b) = 0.5

So the probability of b occurring is 0.5, whether or not we know whether a has occurred.

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Answer:

\(\huge\boxed{\sf y = 100.4}\)

Step-by-step explanation:

Given equation is:

53 = y - 47.4

Add 47.4 to both sides

53 + 47.4 = y

100.4 = y

OR

y = 100.4

\(\rule[225]{225}{2}\)

Hope this helped!

Hello there!

\(\sf \longmapsto53=y - 47.4\)

This is a equation. We need to find the value of variable y.

\(\sf \longmapsto53=y- 47.4\)

To Solve further,we need to overturn the equation.

That is :-

\(\sf \longmapsto \: y - 47.4 = 53\)

Then, Add +47.4 to two sides:-

\(\sf \longmapsto \: y - 47.4 + 47.4 = 53 + 47.4\)

On Simplification:-

Note that (-) and (+) equals to (-). So it would be 47.4 - 47.4 . Which results to 0.

\(\sf \longmapsto \: y - 0 = 100.4\)

\(\sf \longmapsto \: y = 100.4( Ans.)\)

Answer as a mixed fraction:-

\(\sf \longmapsto 100\dfrac{2}{5}\)

Answer as a fraction:-

\(\sf\longmapsto 502/5\)

______________________________________

Henceforth, the value of y is :-

\(\bf \: y = 100.4\)

Or as a mixed fraction:-

\(\bf y = 100\dfrac{2}{5}\)

Or as a fraction:-

\(\bf y = 502/5\)

________________________________

I hope this helps!

Please let me know if you have any questions.

The equatiion where C is the constant of integration.To evaluate the indefinite integral ∫(3e^x + 4x^5 - x^3/4 + 1)dx, we can integrate each term separately.

∫3e^x dx = 3∫e^x dx = 3e^x + C₁

∫4x^5 dx = 4∫x^5 dx = 4 * (1/6)x^6 + C₂ = (2/3)x^6 + C₂

∫-x^3/4 dx = (-1/4)∫x^3 dx = (-1/4) * (1/4)x^4 + C₃ = (-1/16)x^4 + C₃

∫1 dx = x + C₄

Now, we can combine these results to obtain the final answer:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

Therefore, the indefinite integral of (3e^x + 4x^5 - x^3/4 + 1)dx is:

∫(3e^x + 4x^5 - x^3/4 + 1)dx = 3e^x + (2/3)x^6 - (1/16)x^4 + x + C

where C is the constant of integration.

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No solution because everything cancels out

Answer: 0.796 meters

Step-by-step explanation:

Circumference of circle = \(2\pi r\) , where r=radius

Here, Circumference of loop = 2.5 meters

i.e. \(2\pi r=2.5\)

\(\Rightarrow\ r=\dfrac{2.5}{2\pi}\)

\(\Rightarrow\ r=\dfrac{2.5}{2\times\dfrac{22}{7}}\\\\\Rightarrow\ r=\dfrac{2.5\times7}{2\times22}\\\\\Righttarrow\ r=0.398\ m\)

Diameter = 2r = 2(0.398) = 0.796 meters

Hence, The diameter of Taiga's exercise hoop = 0.796 meters

Answer:

The correct option is;

Because Boomer has a larger standardized score, he did better relative to his division than Paulina

Step-by-step explanation:

The standard score of Boomer in the junior division = -0.23

The standard score of Paulina in the senior division = -0.28

We note that the standard score is the same as the z-score which is given as follows;

\(Z=\dfrac{x-\mu }{\sigma }\)

Where;

μ = The mean or average score (average speed of the runners in a division)

x = The recorded score (the speed recorded by a given runner)

σ = The standard deviation of the data set (of the division)

Therefore, given that we have;

The standard score of Boomer in the junior division = -0.23

The standard score of Paulina in the senior division = -0.28

Therefore, since -0.23 > -0.28, we have;

The standard score of Boomer > The standard score of Paulina

Which gives;

Because Boomer has a larger standardized score, he did better relative to his division than Paulina

Answer:

Because Boomer has a larger standardized score, he did better relative to his division than Paulina.

Explanation:

On the z-table, Boomers score is 59.10% and Paulina’s score is 38.97%. Boomer’s score is larger.

Answer:

9 x 10 to the power of 8 meters in 3 seconds

Step-by-step explanation:

Answer:

how many of each color are in the dresser?

Step-by-step explanation:

Answer:19 for first answer. Second answer is subtract 16 from both sides

Step-by-step explanation:76/4 first answer

Answer:

The difference would be 1/12.

Step-by-step explanation:

2/3 is 8/12.

a)There are three possible outcomes for two tosses:HT, TH, and TT.

b)Therefore, the number of different outcomes with exactly four heads is 495.

c)Therefore, the number of outcomes that have at least two heads is equal to:2¹² – 13 = 4,083

d)The complement principle, the number of outcomes with at most eight heads is equal to 2¹² – 1 = 4,095

Let us assume that there are only two possible outcomes for each toss. In this case, we can make a simple list of all possible outcomes that are possible. One outcome, for example, would be heads or tails, which could be written as HT or TH.

There are three possible outcomes for two tosses:HT, TH, and TT.

There are four possible outcomes for three tosses:HHH, HHT, HTH, and THH.

Therefore, in the case of twelve coin tosses, there are a total of 2¹² or 4,096 possible outcomes.  

b)Four heads must occur in one of the twelve coin tosses for there to be exactly four heads.

There are 12 possible places for the four heads to occur. The other eight spots must be tails.

The total number of ways to choose four spots from twelve spots is equal to 12C4.

Therefore, the number of different outcomes with exactly four heads is 495.  

c)To determine how many different outcomes have at least two heads, we can use the complement principle.

To begin with, we must determine the number of outcomes in which zero or one heads occur.

There is only one possibility for zero heads: TTTTTTTTTTTT. There are twelve possibilities for one head.

This one head can be in one of twelve positions, and the other eleven positions must be tails.

Therefore, there are 12 + 1 or 13 possible outcomes that contain zero or one head.  

The total number of possible outcomes is 2¹², as we have previously stated.  

Therefore, the number of outcomes that have at least two heads is equal to:2¹² – 13 = 4,083  

d)There are two possible methods for counting the number of different outcomes with at most eight heads, depending on whether we are interested in finding the actual outcomes or simply the number of outcomes.

The number of different outcomes is 2¹² or 4,096, as we have previously stated.

The number of outcomes with at least nine heads is one, since there must be nine heads in one of the twelve coin tosses.

Using the complement principle, the number of outcomes with at most eight heads is equal to 2¹² – 1 = 4,095

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Answer:

1/4 or 0.25 of a lemon is being used per cup

Step-by-step explanation:

Answer:

2x -3

Step-by-step explanation:

Answer:

2x-3 isn't monomial. hope u like it

Answer:

2428.57mg

Step-by-step explanation:

170 mg of sodium =7%

170/7% = 2428.57mg

Answer:

A group of five people are at a restaurant, the bill comes and is $50, the bill is split evenly amongst the five people, each person pays $10 which is the same as gaining -$10 which is the answer to the expression

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

A: 600=1.05x

B: 600=1.06x

Step-by-step explanation:

:-)

The slope of the tangent at theta = Phi/2 is: dy/dx = (dy/dtheta) / (dx/dtheta) = (4/0) = undefined

To find the slope of the tangent to the curve r = -8 + 4 cos theta at the value Theta = Phi/2, we need to take the derivative of the polar equation with respect to theta, then plug in theta = Phi/2 and evaluate.

The derivative of r with respect to theta is given by:

dr/dtheta = -4 sin theta

At theta = Phi/2, we have:

dr/dtheta|theta=Phi/2 = -4 sin(Phi/2)

Now we need to find the slope of the tangent, which is given by:

dy/dx = (dy/dtheta) / (dx/dtheta)

To find dy/dtheta and dx/dtheta, we use the formulas:

x = r cos theta
y = r sin theta

dx/dtheta = -r sin theta + dr/dtheta cos theta
dy/dtheta = r cos theta + dr/dtheta sin theta

Plugging in r = -8 + 4 cos theta and dr/dtheta = -4 sin theta, we get:

dx/dtheta = -(4 cos theta)(-4 sin Phi/2) + (-8 + 4 cos theta)(-sin theta)
dy/dtheta = (4 cos theta)(cos Phi/2) + (-8 + 4 cos theta)(cos theta)

At theta = Phi/2, we have:

dx/dtheta|theta=Phi/2 = 0
dy/dtheta|theta=Phi/2 = 4

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Answer:

\(26\)

Step-by-step explanation:

\((-4a - 6) + a2\)

\(a=8\)

Let's Substitute a with 8:

\(-4\times \:8-6+8^2\)

\(26\)

Answer:

x = 2.

Step-by-step explanation:

Let the number be x.

Write it as an equation :-

6x - 3 = -1x + 11

6x + 1x = 11 + 3

7x = 14

x = 2.

Answer:

c

Step-by-step explanation:

y=2(2)2-8(2)+3

=8-16+3

=-8+3

=-5

Answer:

c

Step-by-step explanation:

i did the prep

Answer:

30 students they are including the students that are also planning to participate in other sports to.

Answer:

the answer is 11.

Step-by-step explanation:

To find the number of integers divisible by 6 between -30 and 39, we need to find how many multiples of 6 are in this range.

The first multiple of 6 greater than -30 is -24 (which is 6 times -4), and the last multiple of 6 less than 39 is 36 (which is 6 times 6).

So, we need to count the number of integers between -4 and 6 (inclusive), because each of these integers multiplied by 6 will give us an integer in the range -30 to 39 that is divisible by 6.

There are a total of (6 - (-4) + 1) = 11 integers between -4 and 6 inclusive, so there are also 11 integers between -30 and 39 that are divisible by 6.

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This equation is written in slope-intercept form, which looks like so:-

\(\bigstar{\boxed{y=mx+b}\)

where

m is the slope

b is the y-intercept

Now, what is the slope?

Hint:- The slope is the coefficient of x, and the y-intercept is the constant.

That's right! The slope is 3, and the y-intercept is -4.

=========================================================

Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

To find the volume of the smallest cube-shaped box that can contain the pyramid, we need to first determine the length of the smallest edge of the box. Since the base of the pyramid is a square, the smallest edge of the box will be the diagonal of the square base of the pyramid.

Using the Pythagorean theorem, we find that the diagonal is:√(10² + 10²) = √200 = 10√2 inches Thus, the length of each edge of the smallest cube-shaped box that can contain the pyramid will be 10√2 inches. The volume of a cube is given by the formula

V = s³, where s is the length of one of its edges. Therefore, the volume of the box will be:(10√2)³ = 1000√8 cubic inches To simplify this expression, we can use the fact that √8 = √(4 · 2) = 2√2. Thus, the volume of the box is:1000√8 = 1000 · 2√2 = 2000√2 cubic inches Therefore, the volume of the smallest cube-shaped box that can contain Eric's pyramid is 2000√2 cubic inches, or approximately 2827.43 cubic inches to two decimal places.

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