Most of the heat loss for outdoor swimming pools is due to surface
evaporation. So, the greater the area of the surface of the pool, the greater
the heat loss. For a given perimeter, which surface shape would be more
efficient at retaining heat: a circle or a rectangle? Justify your answer.

We have,

[tex]a:b=3:6,a+b=96[/tex]

Introduce variable [tex]x[/tex] such that [tex]a=3x,b=6x[/tex]

The sum [tex]a+b=96[/tex] is therefore [tex]9x=96\implies x=10.\overline{6}[/tex]

So,

[tex]a=3\cdot10.\overline{6}=\boxed{32}[/tex] (sadia's age)

[tex]b=6\cdot10.\overline{6}=\boxed{64}[/tex] (father's age)

Hope this helps :)

Using the shell method, the volume integral would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx[/tex]

That is, each shell has a radius of x (the distance from a given x in the interval [0, 2] to the axis of revolution, x = 0) and a height equal to the difference between the boundary curves y = x ⁸ and y = 256. Each shell contributes an infinitesimal volume of 2π (radius) (height) (thickness), so the total volume of the overall solid would be obtained by integrating over [0, 2].

The volume itself would be

[tex]\displaystyle 2\pi \int_0^2 x(256-x^8)\,\mathrm dx = 2\pi \left(128x^2-\frac1{10}x^{10}\right)\bigg|_{x=0}^{x=2} = \boxed{\frac{4096\pi}5}[/tex]

Using the disk method, the integral for volume would be

[tex]\displaystyle \pi \int_0^{256} \left(\sqrt[8]{y}\right)^2\,\mathrm dy = \pi \int_0^{256} \sqrt[4]{y}\,\mathrm dy[/tex]

where each disk would have a radius of x = ⁸√y (which comes from solving y = x ⁸ for x) and an infinitesimal height, such that each disk contributes an infinitesimal volume of π (radius)² (height). You would end up with the same volume, 4096π/5.

The volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have a function:

[tex]\rm y = x^8[/tex]   or

[tex]x = \sqrt[8]{y}[/tex]

And  y = 256

By using the vertical axis of rotation method to evaluate the volume of the solid formed by revolving the region bounded by the curves.

[tex]\rm V = \pi \int\limits^a_b {x^2} \, dy[/tex]

Here a = 256, b = 0, and [tex]x = \sqrt[8]{y}[/tex]

[tex]\rm V = \pi \int\limits^{256}_0 {(\sqrt[8]{y}^2) } \, dy[/tex]

After solving definite integration, we will get:

[tex]\rm V = \pi(\frac{4096}{5} )[/tex]  or

[tex]\rm V =\frac{4096}{5}\pi[/tex] cubic unit

Thus, the volume of the solid formed by revolving the region bounded by y=x^8 and y = 256 in the first quadrant about the y-axis is 4096π/5 cubic units.

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Answer:

  9

Step-by-step explanation:

If x is the number of 10-inch stones, then (x-1) is the number of 5-inch stones, and the total width is ...

  10x +5(x-1) = 130

  15x -5 = 130 . . . . . . . eliminate parentheses

  15x = 135 . . . . . . add 5

  x = 9 . . . . . . . divide by 15

Wesley will need 9 10-inch stones for one row.

Answer:

35 lbs is the final weight

Step-by-step explanation:

20 +23 = 43 lbs

Then they had to remove 8 lbs

43 - 8 =35

35 lbs is the final weight

9514 1404 393

Answer:

  43

Step-by-step explanation:

Put the value where t is and do the arithmetic.

  h = 50 -t/5

  h = 50 -35/5 = 50 -7 = 43

The output, h, is 43 when the input is 35.

Answer:

43

Step-by-step explanation:

The answer is 43 on Khan :)

Answer:

Hello,

Answer : 1400 and 1575

Step-by-step explanation:

Let's say a and b the ywo numbers

[tex]HCF(a,b)=a\vee b=175=5^2*7\\LCM(a,b)=a\wedge b=12600\\\\a*b=(a\vee b)*(a\wedge b)=(2^3*3^2*5^2*7)*(5^2*7)=2^3*3^2*(5^2*7^2)^2\\\\Both\ numbers\ are\ greater\ than\ their HCF\\a=175*k_1\\b=175*k_2\\\\k_1=2^3\ and\ k_2=3^2\\\\a=175*2^3=1400\\b=175*3^2=1575\\\\[/tex]

Answer:

This depends whether you want to make the fraction bigger or smaller.

Step-by-step explanation:

If you want to the the fraction into something smaller than it already is, you would use division because when you divide something, you get a smaller number.

However, if you want to make the fraction bigger, then you would multiply.

Hope this helps! :)

Answer:

Because 7 is a prime number which means it can only divide by itself and one so you cannot divide seven but you can divide 15.

Step-by-step explanation:

Answer:

(m-6+2root3)(m-6-2root3)

Step-by-step explanation:

m^2 - 12m +36 -12

= (m-6)^2 - 12

= (m-6+2root3)(m-6-2root3)[root 12 = 2root3]

Answer:

Step-by-step explanation:

a) Probability-Above 30 min = 5.72% = .0572

b) Probability-Above 15 min =  99.11% = .9911

c) *Probability-Between  1 - 59.49% = .4051

d) 19.136 minutes  z = -1.28

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

What do you mean by normal distribution ?

A probability distribution known as a "normal distribution" shows that data are more likely to occur when they are close to the mean than when they are far from the mean.

Let assume the time taken for a one way trip be x .

x ⇒ N( μ , σ ²)

x  ⇒ N( 24 , 3.8 ²)

a)

The probability that trip will take at least 1/2 hour or 30 minutes will be :

P ( x ≥ 30)

= P [ (x - μ) / σ ≥ (30 - μ) / σ ]

We know that , (x - μ) / σ = z.

= P [ z ≥ (30 - 24) / 3.8)]

= P [ z ≥ 1.578 ]

= 1 - P [  z ≤ 1.578 ]

Now , using the standard normal table :

P ( x ≥ 30)

= 1 - 0.9394

= 0.0606

b)

The percentage of the time the lawyer is late for work will be :

P ( x  ≥ 15)

= P [ z ≥ -2.368 ]

= P [  z ≤ 2.368]

= 0.9918

or

99.18%

c)

The probability that lawyer misses coffee :

P ( 15 < x < 25 ) = P ( x < 25 ) - P ( x < 15)

= P [  z < 0.263] - P ( z < -2.368)

or

= 0.3659

d)

The length of time above which we find the slowest 10​% of trips :

P( x ≥ X ) ≤ 0.10

=  0.5438

e)

Let's assume that y represents the number of trips that takes at least half hour.

y ⇒ B ( n , p)

y ⇒ B ( 3 , 0.0606)

So , the probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is :

P ( Y = 2 )

= 3C2 × (0.0606)² × ( 1 - 0.0606)

= 0.0103

Therefore , the answers are :

a) The probability that trip will take at least 1/2 hour will be 0.0606.

b) The percentage of time the lawyer is late for work will be 99.18%.

c) The probability that lawyer misses coffee will be 0.3659.

d) The length of time above which we find the slowest 10​% of trips will be 0.5438.

e) The probability that exactly 2 out of 3 trips will take at least one half

1/2 hour is 0.0103.

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Step-by-step explanation:

2., 3., 4., 5.

yes, you had the right idea to calculate the half distances between the coordinates. just create the absolute values of the full distance before cutting it in half.

you need to remember : we have to go this half distance from one point to the other (meaning adding our subtracting the half distance to/from the starting point).

2.

(-4, 6) to (10, -10)

in x the distance is 10 - -4 = 14. half is 7.

in y the distance is |-10 - 6| = |-16| = 16. half is 8.

so the midpoint is

(-4 + 7, 6 - 8) = (3, -2)

remember, to go the half distance in the direction towards the second point (so we have to choose properly, when to use "+" and "-" depending on the change of the coordinate : from -4 to 10 we have to add, from 6 to -10 we have to subtract, of course).

3.

(-3, -8) to (-6.5, -4.5)

in x distance : -3 - -6.5 = 3.5. half is 1.75

in y distance : -8 - -4.5 = |-3.5| = 3.5. half is 1.75

midpoint is

(-3 - 1.75, -8 + 1.75) = (-4.75, -6.25)

4.

(3, 7) to (-8, -10)

x : 3 - -8 = 11. half is 5.5

y : 7 - -10 = 17. half is 8.5

midpoint is

(3 - 5.5, 7 - 8.5) = (-2.5, -1.5)

5.

(-6, -13) to (-6.4, -3.8)

x : -6 - -6.4 = 0.4. half is 0.2

y : -13 - -3.8 = |-9.2| = 9.2. half is 4.6

midpoint is

(-6 - 0.2, -13 + 4.6) = (-6.2, -8.4)

6.

(-1, 7) to (5, 1)

x : -1 - 5 = |-6| = 6. 1/3 is 2.

y : 7 - 1 = 6. 1/3 is 2.

1/3 from C to D

(-1 + 2, 7 - 2) = (1, 5)

7.

2/3 of the way from D to C is the same point as in 6. (1/3 from C to D).

again

(1, 5)

8.

2/3 of the way from C to D.

so, we need to double what we added in 6.

(-1 + 4, 7 - 4) = (3, 3)

9.

1/3 of the way from D to C is the same point as in 8. (2/3 of the way from C to D).

again

(3, 3)

10.

exactly. Pythagoras.

the square root of the sum of the squares of the coordinate differences.

distance = sqrt((x1 - x2)² + (y1 - y2)²)

11.

(6, 8) to (-1, 8)

distance = sqrt((6 - -1)² + (8 - 8)²) = sqrt(49) = 7

12.

(5, -6) to (5, 6)

sqrt((5-5)² + (-6-6)²) = sqrt(144) = 12

13.

(-2, 0) to (11, 0)

sqrt((-2 - 11)² + (0-0)²) = sqrt(169) = 13

14.

(1, -5) to (9, 1)

sqrt((1-9)² + (-5 - 1)²) = sqrt(64 + 36) = sqrt(100) = 10

15.

ST and MT are basically the same equation.

MT is half of ST.

ST equation based on 2 points :

y – yS={(yT – yS)/(xT – xS)}(x – xS)

M = (xS + (xT - xS)/2, yS +(yT - yS)/2)

so, let's put that into the general equation :

y - yM={(yT - yM)/(xT - xM)}(x - xM)

y - (yS +(yT - yS)/2) = {(yT - (yS +(yT - yS)/2))/(xT - (xS + (xT - xS)/2))}(x - (xS + (xT - xS)/2))

16.

the two corners farthest away are (5, 10) and (9, 6).

what distance from (0, 0) is now bigger ?

since it is (0, 0), we can skip the 0s and just sum up the squares of the coordinates.

5² + 10² = 125

9² + 6² = 117

so, the corner (5, 10) is the farthest away.

Answer:

x1 = 3

Step-by-step explanation:

first set up the proportion (write as fractions):

(y1/x1) = (y2/x2)

then fill in the variables:

4/x1 = 8/6

now cross multiply:

8 • x1 = 6 • 4

simple algebra:

8 • x1 = 24

x1 = 24/8

x1 = 3

If y1 = 4, x2 = 6, and y2 = 8, then the value of x1 is 3 which we can solve using ratios.

In a directly proportional relationship, the ratios between the corresponding values of two variables remain constant. This constant ratio is often referred to as the "proportionality constant."

In this problem, you have two pairs of values: (x1, y1) and (x2, y2). We're given that the ratios are directly proportional, which means:

x1 / y1 = x2 / y2

Plugging in the given values:

x1 / 4 = 6 / 8

Now, cross-multiply to solve for x1:

x1 * 8 = 4 * 6

x1 = 24 / 8

x1 = 3

Therefore, the value of x1 is 3.

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Answer:

x = 1

y = 2

Step-by-step explanation:

5x + 2y = 9

-5x + 4y = 3

==> 6y = 12 ==> y = 12/6 ==> y = 2.

we replace y by its value in the first or the second equation, so will have:

5x + 2×2 = 9

5x + 4 = 9

5x = 5

x = 1

Answer:

The Bison is faster by 10 miles per hour.

Step-by-step explanation:

The Bison runs at 3520 ft / min

= 3520/ 5280 miles / minute

= (3520/ 5280) * 60 miles per hour

= 40 miles per hour

The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.

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

To solve this question, we need to find the confidence interval for the amount of time it takes the students to get the degree.

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

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

The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 80 - 1 = 79

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

95% confidence interval

Standard level of confidence, we have to find a value of T, which is found looking at the t table, with 79 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 1.9905.

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

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 1.9905\frac{2.2}{\sqrt{80}} = 0.5[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

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

The lower end of the interval is the sample mean subtracted by M. So it is 4.8 - 0.3 = 4.3 years.

The upper end of the interval is the sample mean added to M. So it is 4.8 + 0.3 = 5.3 years.

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

The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.

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Answer:

...

Step-by-step explanation:

seeee the above picture

Answer:

76 natural number not including the first

Hope this helps <3 Comment if you want more thanks and be sure to give brainliest (4 left) <3

There are 78 natural numbers between 68 and 145.

The Natural numbers are defined as it used for counting and are a component of the number system, which includes all positive integers from 1 to infinity. It does not include zero (0).

The set of natural numbers includes only the positive integers, i.e., 1, 2, 3, 4, 5, 6, ……….∞.

Sum of natural numbers are n(n+1)/2

Sn = n(n+1)/2

Hence, this is the formula to calculate sum of 'n' natural numbers.

Given that numbers are 68 and 145

We will start counting from 68 to 144

Number of natural numbers between 68 and 145 = (144 - 67)+1

Number of natural numbers between 68 and 145= 77 +1

Number of natural numbers between 68 and 145 = 78

Hence, there are 78 natural numbers between 68 and 145.

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Answer:

Step-by-step explanation:

The reduced side ratios, shortest to longest are ...

  AC : AT : CT = 8 : 9 : 15

  OD : OG : DG = 5 : 6 : 10

These are different ratios, so the triangles are not similar.

Step-by-step explanation:

Hey there!

From the given figure;

Angle FVT = 43°

VT = 53

Taking Angle FVT as reference angle we get;

Perpendicular (p) = FT = ?

Base (b) = VT = 53

Taking the of tan;

[tex] \tan( \alpha ) = \frac{p}{b} [/tex]

Keep all values and simplify it;

[tex] \tan(43) = \frac{ft}{53} [/tex]

0.932515*53 = FT

Therefore, FT= 49.423.

Hope it helps!

Answer:

A. 49.42

Step-by-step explanation:

tan 43 = FT ÷ VT

0.932515086 = FT ÷ 53

49.42 = FT

You're looking for a number w such that the numbers

{1 + w, 7 + w, 15 + w}

form a geometric sequence, which in turn means there is a constant r for which

7 + w = r (1 + w)

15 + w = r (7 + w)

Solving for r, we get

r = (7 + w) / (1 + w) = (15 + w) / (7 + w)

Solve this for w :

(7 + w)² = (15 + w) (1 + w)

49 + 14w + w ² = 15 + 16w + w ²

2w = 34

w = 17

Then the three terms in the sequence are

{18, 24, 32}

and indeed we have 24/18 = 4/3 and 32/24 = 4/3.

Answer:

D. [tex]3x\sqrt{2x}[/tex]

Step-by-step explanation:

The problem gives on the following equation:

[tex]\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}[/tex]

Alongside the information that ([tex]x\geq0[/tex]).

One must bear in mind that the operation ([tex]\sqrt[/tex]) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,

[tex]\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}[/tex]

Now remove the duplicate factors from underneath the radical,

[tex]2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}[/tex]

Simplify,

[tex]4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}[/tex]

[tex]3x\sqrt{2x}[/tex]

Answer:

c.) in the correct answer

Answer:

D. 3

Step-by-step explanation:

A triangle can be defined as a two-dimensional shape that comprises three (3) sides, three (3) vertices and three (3) angles.

Simply stated, any polygon with three (3) lengths of sides is a triangle.

In Geometry, a triangle is considered to be the most important shape.

Generally, there are three (3) main types of triangle based on the length of their sides and these include;

I. Equilateral triangle: it has all of its three (3) sides and interior angles equal.

II. Isosceles triangle: it has two (2) of its sides equal in length and two (2) equal angles.

III. Scalene triangle: it has all of its three (3) sides and interior angles different in length and size respectively.

In Geometry, an acute angle can be defined as any angle that has its size less than ninety (90) degrees.

Hence, we can deduce that the greatest number of acute angles that a triangle can contain is three (3) because the sum of all the interior angles of a triangle is 180 degrees.

Answer:

7/12

Step-by-step explanation:

There are 12 roses - 5 white = 7 pink

7 pink / 12 total

Answer:

x = 150°

Step-by-step explanation:

Interior angle of a hexagon = 120° and interior angle of a square = 90°

so remaining angle, 360-120-90 = 150°

Answer:

brown

Step-by-step explanation:

it might be brown because it compelled

9514 1404 393

Answer:

Step-by-step explanation:

The linear speed 12 mi/h translates to inches per minute as follows:

  (12 mi/h) × (5820 ft/mi) × (12 in/ft) ÷ (60 min/h) = 12,672 in/min

The relationship between arc length and angle is ...

  s = rθ

For a constant radius, the relationship between linear speed and angular speed is ...

  s' = rθ'

  θ' = s'/r = (12,672 in/min)/(12 in) = 1056 rad/min

There are 2π radians in one revolution, so this is ...

  (1056 rad/min) ÷ (2π rad/rev) = 168.068 rev/min

90/-10

= 9/-1

= -9

So, -9 is the quotient.