find the total service area of this cone. leave your answer in terms of pi.
r=10in h=24in

Answer:

Box dimensions:

L = 3 ft

D = 6 ft

H = 1 ft

Volume  V = 18 ft³

Step-by-step explanation:

a) Each side of the future box is

L = 5 - 2*x     D = 8 - 2*x  

height of the box is   x

Then the volume of the box as function of x is:

V(x) =  ( 5 - 2*x ) * ( 8  - 2*x ) * x

V(x) = ( 40 - 10*x - 16*x + 4*x² ) * x

V(x) = 40*x - 26*x² + 4*x³

Tacking derivatives on both sides of the equation:

V´(x) = 40 - 52*x + 12x²     or     V´(x) = 20 - 26*x + 6*x²

If V´(x) = 0

6*x² - 26*x + 20  = 0

Solving for x

x₁,₂  = (-b ± √ b² - 4*a*c  ] /2*a

x₁,₂  = ( 26  ±  √ 676  - 480  ) / 12

x₁,₂  =  (26 ± 14 )/ 12

x₁  = 1

x₂ = 3,33        ( we dismiss this solution since is not feasible according to cardboard dimensions )

Then the sides of the box are:

L = 5 -2*x      L  =  5 - 2*1     L = 3 ft

D = 8 - 2*x    D  = 8 - 2*1     D = 6 ft

H = x = 1 ft

And the volume is    V = 6*3*1 = 18 ft³

Let X be a random variable denoting pulse rates of females as described, with mean µ = 74.0 bpm and standard deviation σ = 12.5 bpm. Then

P(70 < X < 78) = P((70 - µ)/σ < (X - µ)/σ < (78 - µ)/σ)

… = P(-0.32 < Z < 0.32)

… = P(Z < 0.32) - P(Z < -0.32)

… ≈ 0.6255 - 0.3745

… ≈ 0.2510

where Z is normally distributed with mean 0 and s.d. 1.

• • •

Next, you sample 25 females from the population and want to find the probability that their average falls between 70 and 78 bpm. Let [tex]X_i[/tex] denote the pulse rate of the i-th woman from the sample, and let Y be the random variable for the sample mean; that is,

[tex]Y=\displaystyle\sum_{i=1}^{25}\frac{X_i}{25}[/tex]

Recall that a sample of size n taken from a normal distribution with mean µ and s.d. σ has a mean that is also normally distributed with mean µ and s.d. σ/√n.

The mean stays the same, µ = 74.0, but now the s.d. is σ/√n = σ/5 = 2.5. So we have

P(70 < Y < 78) = P((70 - µ)/(σ/5) < (Y - µ)/(σ/5) < (78 - µ)/(σ/5))

… = P(-1.6 < Z < 1.6)

… = P(Z < 1.6) - P(Z < -1.6)

… ≈ 0.9452 - 0.0548

… ≈ 0.8904

Answer:

a) 16

b) 100

c) 64

d) [tex]\frac{81}{4}[/tex][/tex]

Step-by-step explanation:

Perfect square trinomial:

A perfect square trinomial has the following format:

[tex](x \pm a)^2 = x^2 \pm 2ax + a^2[/tex]

a.

x² – 8x

[tex]x^2 - 8x = x^2 - 2ax[/tex]

So 2a = 8, a = 4. Then

[tex]a^2 = 4^2 = 16[/tex]

The perfect square trinomial is [tex]x^2 - 8x + 16[/tex]

b. x2 + 20x +

2a = 20, so a = 10

[tex]a^2 = 10^2 = 100[/tex]

The perfect square trinomial is [tex]x^2 + 20x + 100[/tex]

C.

x² – 16x +

2a = -16, so a = -8.

[tex]a^2 = (-8)^2 = 64[/tex]

The perfect square trinomial is [tex]x^2 - 16x + 64[/tex]

d. x2 + 9x +

[tex]2a = 9[/tex], so [tex]a = \frac{9}{2}[/tex]

[tex]a^2 = (\frac{9}{2})^2 = \frac{81}{4}[/tex]

The perfect square trinomial is [tex]x^2 + 9x + \frac{81}{4}[/tex][/tex]

Answer:

.......

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Take half of b (6/2=3)

Square it (3^2=9)

9514 1404 393

Answer:

  (x, y) = (4, 5)

Step-by-step explanation:

The solution to the matrix equation ...

  [tex]\left[\begin{array}{cc}3&-2\\6&-5\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}2\\-1\end{array}\right][/tex]

is shown in the attachment. It is found by multiplying the equation on the left by the inverse of the coefficient matrix.

  [tex]\left[\begin{array}{c}x\\y\end{array}\right] =\left[\begin{array}{c}4\\5\end{array}\right][/tex]

Answer:

588000

Step-by-step explanation:

if i am wrong pls tell me cause i think there's a different answer gl g

Answer:

$103,421.88

Step-by-step explanation:

Given:

P = 70000

r = 0.05

n = 1

t = 8

Work:

[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=70000(1+\frac{0.05}{1} )^{1*8}\\\\A=70000(1.05)^8\\\\A=103421.88[/tex]

Answer:

√193

Step-by-step explanation:

pathagorus theorem:

[tex]( {hyp})^{2} = ( {base)}^{2} + ( {perp)}^{2} [/tex]

hyp=x , base= 12 , perp= 7

subtitles all values in formula:

we get

x^2 = 12^2 + 7^2

x^2 = 144 +49

x= √193

The missing side of this right triangle is, 13.90 units.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

The base of the triangle = 12

The perpendicular distance of the triangle = 7

Now, We know that;

Pythagoras theorem stated as;

⇒ Hypotenuse² = Base² + Perpendicular²

⇒ x² = 12² + 7²

⇒ x² = 144 + 49

⇒ x² = 193

⇒ x = √193

⇒ x = 13.90

Thus, The missing side of this right triangle is, 13.90 units.

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Answer:

Step-by-step explanation:

h = 4.2 in

Volume = 3.6  cubic inches

[tex]\frac{1}{3}\pi r^{2}h = 3.6\\\\\frac{1}{3}*3.14*r^{2}*4.2 = 3.6\\\\r^{2}= \frac{3.6*3}{3.14*4.2}\\\\ = 0.81\\r=\sqrt{0.81}\\\\[/tex]

r = 0.9 in

Answer:

.... ..................

Answer:

It's Positive

Step-by-step explanation:

Answer:

D. Parallelogram

Step-by-step explanation:

Answer:

The answer is Parallelgram(D)

two pairs of parallel sides in a quadrilateral

hope it helps...

Answer:

2/8

Step-by-step explanation:

freshman=4/8

1/8 soph    1/8 jr

add all together u get 6/8

the rest is seniors so its 2/8

Answer:

Step-by-step explanation:

x/3 + 6 = 17

Bringing like terms on one side

x/3 = 17 - 6

x/3 = 11

Dividing by 3 on both sides

x = 11/3

Answer:

Step-by-step explanation:

we will find the area of the inner circle and then the area of the outer circle and see what the ratio is between those 2

area of a circle = [tex]\pi[/tex][tex]r^{2}[/tex]  (where r is the radius, NOT the diameter, easy to confuse)

the radius of the inner circle is 2.5. which  is half of the diameter of 5

inner circle = [tex]\pi[/tex]*(2.5)^2

inner circle =  19.6349...

outer circle = [tex]\pi[/tex]*(10^2)

outer circle = 314.1592...

the ratio is    19.6349... /  314.1592...  = 0.0625

0.0625 = 6.25%

= 6% ( rounded to nearest whole number )

Answer:

A

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

8(4) + 11 -2(2)

32 + 11 - 4

43 - 4

39

The similarity ratio of two similar triangles is equal to the ratio of their corresponding sides :

Similarity ratio = BA / GF = BC / GH = CA / HF

Similarity ratio = 18 / 9 = 14 / 7 = x / 6

x / 6 = 2

multiple sides by 6

6 × x / 6 = 6 × 2

simplification

x = 12

Answer:

The company manufactures about 350 canoes, obtaining $ 28,000 after selling them all.

Step-by-step explanation:

Given that a company that manufactures small canoes has a fixed cost of $ 14,000, and it cost $ 40 to produce each canoe while the selling price is $ 80 per canoe, to determine the number of canoes that the company produces and the amount of money it makes after selling them, the following calculation must be carried out:

14/000 / 40 = X

350 = X

350 x 80 = 28,000

Thus, the company manufactures about 350 canoes, obtaining $ 28,000 after selling them all.

Answer:

x=10

Step-by-step explanation:

Because of the two parallel lines, the ratio between the sides must be the same.  Since the bottom is 12 to 18 (a ration of two to three) we know that x and x+5 would have the same ratio.  Logically, x would have to equal 10 so that x+5 would equal 15 and a ratio of two to three would exist there too.  If you go to solve a problem and the answer isn’t obvious, jut set up a ratio.

12/18=x/(x+5)

then cross multiply and solve

12(x+5)=18x

12x+60=18x

60=18x-12x

60=6x

10=x

Answer:

x=10

Step-by-step explanation:

You can set it up as a proportion, since the lines are parallel, the sections are proportionate to each other.

[tex]\frac{x}{12} = \frac{x+5}{18} \\18x=12(x+5)\\18x=12x+60\\6x=60\\x=10[/tex]

Answer:

[tex]y = 56.6208[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find y

To find y, we make use of the relationship between sides lengths 44 & y and angle 39

The relationship is:

[tex]cos(39) = \frac{44}{y}[/tex]

i.e.

[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

Make y the subject

[tex]y = \frac{44}{cos(39)}[/tex]

[tex]y = \frac{44}{0.7771}[/tex]

[tex]y = 56.6208[/tex] -- approximated

Answer:

m<H = 62°

Step-by-step explanation:

If FG is congruent to HF, it means their opposite angles are also congruent to each other. This implies that, <H = <G. Thus, ∆FGH is an isosceles triangle with base angles <F and <G.

Given that m<F = 56°, therefore:

56° + 2(m<H) = 180° (sum of triangle)

2(m<H) = 180° - 56°

2(m<H) = 124°

m<H = 124/2

m<H = 62°

Answer:

Hey mate......

Step-by-step explanation:

This is ur answer.....

= 90 - 18

= 72

--> 72° is the complement angle of 18°

Hope it helps!

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Follow me!

Answer:

1/5%

Step-by-step explanation:

The percentage of the model shaded green will be 20.

Suppose a number is 'a'

Suppose another number is 'b'

We want to know how much percent of 'b' is 'a'.

Then, it is calculated as:

[tex]\dfrac{a}{b} \times 100[/tex]

(in percentage)

The total number of the box in the figure is 100.

The total number of shaded green = 20

So,

[tex]\dfrac{20}{100} \times 100[/tex]

20%

Therefore, The percentage of the model shaded green will be 20.

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Answer:

The problem is telling you to find g ( f ( x ) )

Since we know that f(x) is square root of x, we can put the function this way.

g(√x)

Then, we use  √x as our x in our g(x) function.

You plug in  √x for x and you solve.

(√x ) ^2 is just x.

Finally the answer is

x-3

hope this helps :)

Step-by-step explanation:

Answer:they pay by yeezys

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

85/100*x=51

Step-by-step explanation:

85x=5100

Answer:

w = 1/2

Step-by-step explanation:

One of the ways to solve problems using log is to use these two equations that use the same variables and plug in numbers.

log b (a) = c

b^c = a

By plugging in the numbers we get this:

log 16 (4) = w

16^w = 4

w = 1/2

Answer:

y = 4

Step-by-step explanation:

Given that,

RS= 4y+2, ST = 3y+8, and RT = 38

We need to find the value of y.

As,

RT = RS+ST

Put all the values,

38 = 4y+2+3y+8

38-2-8 = 4y+3y

28 = 7y

y = 4

So, the value of y is equal to 4.