A regular octagon has an apothem of 11.6 inches and a perimeter of 87.2 inches. What is the area of the octagon

Answer:

x = -8/2

Step-by-step explanation:

To make the equation easier to work with, our first step will be to make all of our fractions have a common denominator. Both 2 and 4 are factors of 8, so that will be our common denominator.

Old Equation: 1/4x - 1/8 = 7/8 + 1/2x

New Equation (with common denominators): 2/8x - 1/8 = 7/8 + 4/8x

Now, we're going to begin to isolate the x variable. First, we're going to subtract 2/8x from both sides, eliminating the first variable term on one side completely.

2/8x - 1/8 = 7/8 + 4/8x

-2/8x                    -2/8x

__________________

-1/8 = 7/8 + 2/8x

We're one step closer to our x variable being isolated. Next, we're going to move the constants to the left side of the equation. To do this, we must subtract by 7/8 on both sides.

-1/8 = 7/8 + 2/8x

- 7/8  -7/8

______________

-1 = 2/8x

Our last step is to multiply 2/8x by its reciprocal in order to get the x coefficient to be 1. This means multiply both sides by 8/2.

(8/2)  -1 = 2/8x (8/2)

The 2/8 and 8/2 cancel out, and you're left with:

-8/2 = x

I hope this helps!

Answer:

75

Step-by-step explanation:

Given:

mAB =105

The minor arc given mAB is 105. Subtract that from 360 to get the measure of the major arc mACB

<=> mACB = 360 - 105 = 255

As we know, the measure of an angle formed by two tangents intersesting outside the circle can be found by one haft of the difference between the mearsure of two intercepted arcs

=> the measure of ∠P is:

= (mACB - mAB)/ 2

= (255 - 105)/2

= 75

Answer:

3kg

Step-by-step explanation

kg is heavier

Answer: 980 tickets

Step-by-step explanation:

A band sold out a concert that has 4,200 seats. A random sample of 120 ticket buyers was surveyed, and 28 buyers were found to have made their purchase on the first day the tickets were being sold. This means (28/120) = 7/30 of the 120 ticket were purchased on the first day.

To get the number of first day tickets purchased when 4,200 tickets are likely to have been purchased will be the fraction gotten multiplied by 4200. This will be:

= 7/30 × 4200

= 29400/30

= 980 tickets

Answer:

The equation x = y-8

The equation  (y-8) y = 240

The first number x = 12 and second number y =20

Step-by-step explanation:

Explanation:-

Step(l):-

Let 'x' be the first number and 'y' be the second number

Given the product of two numbers is 240

Given  data        x y = 240 …(l)

Given data the first number is 8 less than the second number.

                       x = y-8...(ll)

Substitute (ll) in equation (l) , we get

                           (y-8) y = 240

                           [tex]y^{2} -8y -240 =0[/tex]

                            [tex]y^{2} -20y+12y -240 =0[/tex]

                           [tex]y(y -20)+12(y -20) =0[/tex]

                           [tex](y +12)(y -20) =0[/tex]

                          y = -12 and y = 20

              Y= -12 is not satisfied

              we can choose y = 20

Step(ll):-

Given data x =y-8

  substitute value y = 20 in x = y -8

                                             x = 20-8 = 12

Final answer:-

The first number x = 12 and second number y =20

Answer:

  $2700

Step-by-step explanation:

Using Heron's formula, we can find the area of the triangle to be ...

  A = √(s(s -a)(s -b)(s -c)) . . . . where s=(a+b+c)/2 and a, b, c are the sides

Here, we have ...

  s = (50 +75 +100)/2 = 225/2 = 112.5

  A = √(112.5 · 62.5 · 37.5 · 12.5) ≈ 1815.461 . . . square yards

Then the profit is expected to be ...

  (1815.451 yd²)($1.50/yd²) = $2723.19 ≈ $2700

The farmer expects a profit of about $2700 from that crop.

Answer:

1,852.5 in³

Step-by-step explanation:

Volume of a rectangular prism:

Length × width × height (depth)

19 × 13 × 7½

1852.5 inches³

Answer:

Newton discovered that sunlight has many colors when it passes through a prism.

Answer:

x= -1/2y +2

Step-by-step explanation:

Answer:

The dimensions of the box are 5.67 cm by 5.67 cm by 8.51 cm.

The total minimum cost = 28.97 cents.

Step-by-step explanation:

Let the base dimensions are a cm by a cm and the height is h cm.

So, a²h = 274 ............. (1)

And, total cost, C = 0.3a² + 0.1 × 4ah = 0.3a² + 0.4ah

C = 0.3a² + 0.4 × (274/a) ................. (2)

Now, for minimum total cost, the condition is [tex]\frac{dC}{da} = 0 = 0.6a - \frac{0.4 \times 274}{a^{2} }[/tex]

⇒ [tex]a^{3} = \frac{0.4 \times 274}{0.6} = 182.67[/tex]

⇒ a = 5.67 cm

So, [tex]h = \frac{274}{a^{2}} = 8.51[/tex] cm.

Therefore, the dimensions of the box are 5.67 cm by 5.67 cm by 8.51 cm.

And the total minimum cost = [tex]C_{min} = 0.3 (5.67)^{2} + 0.4 \times \frac{274}{5.67} = 28.97[/tex] cents. (Answer)

Answer:

0.29

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

h(3)=h(1)*h(2)=

(-10)*(-2)=

20

Answer:

[tex]A(t)=(0.902)^t \cdot 1500[/tex] [tex][km^2][/tex]

Step-by-step explanation:

In this problem, the initial area of the  forest at time t = 0 is

[tex]A_0 = 1500 km^2[/tex]

After every year, the area of the forest decreases by 9.8%: this means that the area of the forest every year is (100%-9.8%=90.2%) of the area of the previous year.

So for instance, after 1 year, the area is

[tex]A_1 = A_0 \cdot \frac{90.2}{100}=0.902 A_0[/tex]

After 2 years,

[tex]A_2=0.902 A_1 = 0.902(0.902A_0)=(0.902)^2 A_0[/tex]

And so on. So, after t years, the area of the forest will be

[tex]A(t)=(0.902)^t A_0[/tex]

And by substituting the value of A0, we can find an explicit expression:

[tex]A(t)=(0.902)^t \cdot 1500[/tex] [tex][km^2][/tex]

Answer:

3 * 5 = 15

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

[tex]5a = 15\\\frac{5a}{5} = \frac{15}{5} \\a = 3[/tex]

5 * 3 = 15

Answer:

Question 1: The hours that will pass between two consecutive times, when the water is at its maximum height is π hours

Question 2: Sin of the angle is -0.8

Step-by-step explanation:

Question 1: Here we have h(t) = 4·cos(t) + 10

The maximum water level can be found by differentiating h(t) and equating the result to zero as follows;

[tex]\frac{\mathrm{d} h(t)}{\mathrm{d} t} = \frac{\mathrm{d} \left (4cos(t) + 10 \right )}{\mathrm{d} t} = 0[/tex]

[tex]\frac{\mathrm{d} h(t)}{\mathrm{d} t} = - 4 \times sin(t) = 0[/tex]

∴ sin(t) = 0

t = 0, π, 2π

Therefore, the hours that will pass between two consecutive times, when the water is at its maximum height = π hours.

Question 2:

B = (3, -4)

Equation of circle = x² + y² = 25

Here we have

Distance moved along x coordinate = 3

Distance moved along y coordinate = -4

Therefore, we have;

[tex]Tan \theta = \frac{Distance \ moved \ along \ y \ coordinate}{Distance \ moved \ along \ x \ coordinate} = \frac{-4}{3}[/tex]

[tex]\therefore \theta = Tan^{-1}(\frac{-4}{3}) = -53.13^{\circ}[/tex]

Sinθ = sin(-53.13) = -0.799≈ -0.8.

Answer:

The correct answer is 9 m per [tex]second^{2}[/tex]

Step-by-step explanation:

Force is defined by mass of an object times it's acceleration.

Let the mass of the object be m kilograms.

When a force of 30 N acts on a certain object the acceleration of the object is 5 m per [tex]second^{2}[/tex]

∴ 30 = m × 5

⇒ m = 6.

If the force is changed to 54 N, let the acceleration of the object be x  m per [tex]second^{2}[/tex].

∴ 54 = m × x

⇒ x = [tex]\frac{54}{6}[/tex] = 9

Thus when the force is 54 N, the acceleration of the object is 9 m per [tex]second^{2}[/tex].

Answer:

Step-by-step explanation:

The roll of nickels forms a cylinder

cylinder area includes the sides and the round areas

round areas  = pi r^2   there is two   so    2 pi r^2

                                                                    = 2 pi (.835/2)^2

and the side area  pi x d x h

                               pi x .835 ( .077 x 40)     (there are 40 nickels in $ 2

Add the areas to get the total ......

To find the total surface area of a $2 roll of nickels, we calculate the surface area of one nickel and then multiply by 40 (the number of nickels in a $2 roll), resulting in an approximate surface area of 47.84 in² when rounded to the nearest hundredth.

To calculate the approximate surface area of a $2 roll of nickels, we must first determine how many nickels are in a $2 roll. Knowing that each nickel is worth 5 cents, a $2 roll would contain 40 nickels ($2.00 / $0.05 = 40). The surface area of a nickel includes the area of the circles on both sides and the area of the edge. The formula for the area of a circle is πr² (where r is the radius) and the formula for the area of the side (cylinder height) is 2πrh (where h is the width).

The diameter of a nickel is 0.835 inches, so the radius is half of that or 0.4175 inches. Using these measurements:

Therefore, the total approximate surface area for a $2 roll of 40 nickels = 40 * 1.196 in² = 47.84 in².

Rounded to the nearest hundredth, the surface area is 47.84 in².

Answer:

b is the correct answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

the correct answer is B

Answer:

25 stones will be needed to trade for 10 bricks

Answer:

25 stones see needed

Step-by-step explanation:

Since 1 brick=10 logs

10 bricks= 100 logs

Since1 stone=4 logs

X=100 logs

X=100/4

X=25 stones.

Answer:

36p³-46p-24

Step-by-step explanation:

Its the second one

All we need to do is distribute

to do this, we need to multiple 6p by everything in the parenthesis

and then multiply -8 by everything in the parenthesis

If we do this, we get

36p³ + 48p² + 18p - 48p² - 64p - 24

Now we combine like terms for our final answer

the 48p² and -48p² cancel out

The FINAL answer is ...

The second option:    36p³ - 46p - 24

Answer:

(a) The meaning of W'(8) is the rate of change of the depth of the water at time t = 8 hours is -0.8 ft/hr

(b) The tangent line equation is Y = 0.79×t +6.143

Therefore, W(3.5) ≤ 9 as 0.79×3.5 +6.143 = 8.908 < 9

(c) [tex]\lim_{t \to 2 }\frac{W(t) - t^3 + \frac{1}{4} }{t -2}[/tex] is [tex]\frac{\sqrt{3} \pi -96 }{8}[/tex]

Step-by-step explanation:

Here we have

[tex]W(t) = \begin{cases}\frac{17}{2}-\frac{3}{2}\cos \left (\frac{\pi t}{6} \right ) & \text{ if } 0\leq t\leq 6 \\ 10-\frac{1}{5}\left (t-6 \right )^{2} & \text{ if } 6< t\leq 10 \end{cases}[/tex]

(a) To find W'(8) we have

W(8) = [tex]10-\frac{1}{5}\left (8-6 \right )^{2}[/tex]

Therefore, W'(8) given by the following relation;

[tex]W'(t) = \frac{\mathrm{d} \left (10-\frac{1}{5}\left (t-6 \right )^{2} \right )}{\mathrm{d} t} = - \frac{2t-12}{5}[/tex]

∴[tex]W'(8) =- \frac{2\times 8-12}{5} = -0.8 \ ft/hr[/tex]

The meaning of W'(8) is the rate of change of the depth of the water at time t = 8 hours = -0.8 ft/hr

b) Here we have the line tangent is given by the slope of the graph at the point t = 3, therefore we have

W'(t), t = 3 = [tex]\frac{\pi \sin(\frac{\pi t}{6} )}{4}[/tex]

The tangent line equation is Y = 0.79×t +6.143

Therefore, W(3.5) ≤ 9 as 0.79×3.5 +6.143 = 8.908 < 9

c) [tex]\lim_{t \to 2 }\frac{W(t) - t^3 + \frac{1}{4} }{t -2}[/tex] where W(t) = [tex]\frac{17}{2}-\frac{3}{2}\cos \left (\frac{\pi t}{6} \right )[/tex]

[tex]\lim_{t \to 2 }\frac{W(t) - t^3 + \frac{1}{4} }{t -2}[/tex]  = [tex]\frac{\sqrt{3} \pi -96 }{8}[/tex].

Answer:

The equation that represents the battery charge in Sanchez's phone as a percentage t hours after he left his house is B(t) = 30 - 3*t.

Step-by-step explanation:

The initial state of the battery on Sanchez's phone is 30% so in time t equals zero the battery should be at that value and as time progresses the battery should lose battery charge at a rate of 3% for each hour. We can write this in an equation form by taking the initial state and subtract it by the rate multiplied by the value of time. We have:

B(t) = 30 - 3*t

The equation that represents the battery charge in Sanchez's phone as a percentage t hours after he left his house is B(t) = 30 - 3*t.

x<-5

Step-by-step explanation:

-3x<12+3

3x>15 divide both sides with ÷3

x<-5

XE(-œ,-5)

Answer: 48

Step-by-step explanation: If each cube is 1/2 in length, then its volume is .25. If you divide 6/.25 it's 48

Answer:

from the looks of it, all you have to do is, for f(x), is plug it in as an exponent. in order (top to bottom), it should be: 64, 2048, 4096, 8192.

g(x) is being squared and then multiplied, so it should be (from top to bottom): 720, 2420, 2880, 3380

Step-by-step explanation:

the approximate percentage of light bulb replacement requests numbering between 40 and 47 is 34% .

Step-by-step explanation:

Step 1: Sketch the curve.

The probability that 40<X<47 is equal to the blue area under the curve.

Step 2:

Since μ=40 and σ=7 we have:

P ( 40<X<47 ) = P ( 40−40 < X−μ < 47−40 )=P ( 40−40/7< X−μ/σ < 47−40/7)

Since Z = x−μ/σ , 40−40/7 = 0 and 47−40/7 = 1 we have:

P ( 40<X<47 )=P ( 0<Z<1 )

Step 3: Use the standard normal table to conclude that:

P ( 0<Z<1 )=0.3413

Percentage = 0.3413(100)=34.13%

Therefore , the approximate percentage of light bulb replacement requests numbering between 40 and 47 is 34% .

Answer:

0.625

Step-by-step explanation:

turn it into a percentage

This is an example of a percent change question. The formula to solve this type of question is (new price - old cost / new cost). Solve the formula with the given values. 207.20-129.50/129.50 → 77.70/129.50 → 0.6. Turn the decimal into a percentage by multiply 0.6 * 100%. This gives us 60%. So, Amazon marked up this item by 60%.

~Good Luck!

Answer:

C

Step-by-step explanation:

Answer:

it's C because the answer looks like C

Answer:

27%

Step-by-step explanation:

50+61=111

111÷4=27

4 is the number of roles

Answer:

60%

Step-by-step explanation:

50 + 61 = 111 (amount of female 11th and 12th graders)

42 + 31 + 111 = 184 (amount of female at school)

111/184 = 60%

Answer:

5x10=50

Step-by-step explanation:

baba booey