The DVD stack is shown below consists of 100 disks. The diameter of each disk is 120 millimeters, the diameter of the hollow center of the disk is 15 millimeters, and the thickness is 1.2 millimeters. What is the volume of the stack in terms of LaTeX: \pi π ?

Answer:

$ 38,824

Step-by-step explanation:

Total Area of land that was bought = [tex]4\frac{2}{8}[/tex] acres

Total Cost of this area = $ 165,000

We have to find the cost of 1 acre of land.

Cost of [tex]4\frac{2}{8}[/tex] acres of land = $ 165,000

Dividing both sides by [tex]4\frac{2}{8}[/tex], we get:

Cost of 1 acre of land = $ 165,000 ÷ [tex]4\frac{2}{8}[/tex]

= $ 38,824

Thus the cost of each acre of land  is $ 38,824 (rounded to nearest dollar)

Answer: $38,824

Step-by-step explanation:

Convert the mixed number [tex]4\ \frac{2}{8}[/tex] as a decimal number.

Divide the numerator by the denominator and add it to the whole number 4. Then:

[tex]4+0.25=4.25acres[/tex]

Then, knowing that 4.25 acres cost $165,000 , divide this amount by 4.25 acres to find the cost of each acre.

Therefore, you get that the cost of each acre rounded to nearest dollar is:

[tex]cost=\frac{\$165,000}{4.25}\\cost=\$38,824[/tex]

Answer:

y=1/2x+5 or d

Step-by-step explanation:

Answer is D

Step-by-step explanation:

Answer:

56 cm

Step-by-step explanation:

The tangents from the 90° angle will form a square with the radii that has a side length of 4. If we call the length of the short side of the right triangle "x", then the tangent lengths are ...

on the short side of the triangle: 4, x-4

on the hypotenuse side of the triangle: x-4, 24-(x-4) = 28-x

on the long side of the triangle: 4, 28-x

The perimeter is twice the sum of the unique tangent lengths:

P = 2(4 + (x-4) + (28-x)) = 2·28

P = 56 . . . . . the perimeter is 56 cm.

_____

Using the Pythagorean theorem on side lengths x and 32-x and hypotenuse 24, we find x = 16-4√2 ≈ 10.34, the length of the short side (in cm).

g(4)=2×4_1

8-1

=9

hence the answer is 9

hope it helps you!!!!!!!!!

Answer:

g(4) = 7

Step-by-step explanation:

To evaluate g(4) substitute x = 4 into g(x), that is

g(4) = (2 × 4) - 1 = 8 - 1 = 7

Answer:

The height of the next door building is 41.7 feet

Step-by-step explanation:

* Lets study the situation in the problem

- The man standing on the roof of a building 64.0 feet high

- The angle of depression to roof of the next door building is 34.7°

- The angle of depression to the bottom of the next door building

  is 63.3°

- We need to find the height of the next door building

* Lets consider the height of the man building and the horizontal

 distance between the two building formed a right triangle and the

 angle of depression is opposite to the side which represented the

 height of the building

- Let the horizontal distance between the two buildings called x

# In the triangle

∵ The length of the side opposite to the angle of depression (63.3°)

  is 64.0

∵ The length of the horizontal distance is x which is adjacent to the

  angle of depression (63.3°)

- Use the trigonometry function tanФ = opposite/adjacent

∴ tan 63.3° = 64.0/x ⇒ use cross multiplication

∴ x (tan 63.3°) = 64 ⇒ divide both sides by (tan 63.3°)

∴ x = 64.0/(tan 63.3°)

∴ x = 32.1886 feet

- Lets use this horizontal distance to find the vertical distance between

  the roofs of the two buildings

* Lets consider the height of the vertical distance between the roofs

 of the two buildings  and the horizontal distance between the two

 building formed a right triangle and the

 angle of depression is opposite to the side which represented the

 vertical distance between the roofs of the two buildings

- Let the vertical distance between the roofs of the two buildings

 called y

# In the triangle

∵ The vertical distance between the roofs of the two buildings is y

   and opposite to the angle of depression (34.7°)

∵ The horizontal distance x is adjacent to the angle of

   depression (34.7°)

∴ tan (34.7°) = y/x

∵ x = 32.1886

∴ tan 34.7° = y/32.1886 ⇒ use the cross multiplication

∴ y = 32.1886 (tan 34.7°)

∴ y = 22.2884 ≅ 22.3 feet

∴ The vertical distance between the roofs of the two

   buildings is 22.3 feet

- The height of the next door building is the difference between the

  height of the man building and the vertical distance between the

  roofs of the two buildings

∴ The height of the next door building = 64.0 - 22.3 = 41.7 feet

Final answer:

This answer explains how to calculate the height of a building using trigonometry based on given angles of depression.

Explanation:

To determine the height of the building next door, we need to use trigonometric functions. Specifically, the tangent of an angle in a right triangle relates the angle to the ratio of the opposite side to the adjacent side.

The total height of the building next door will be H + D.

From the top of the 64.0 feet building, looking down with an angle of depression of 34.7° to the roof of the building next door gives us:

Tan(34.7°) = D/Distance

Similarly, looking down with an angle of depression of 63.3° to the bottom of the building next door gives us:

Tan(63.3°) = (H + D)/Distance

By creating a right triangle for each angle, we can establish the relationships to find the height, which turns out to be around 52.0 feet.

Answer:

x intercept= 3

y=-2

Step-by-step explanation:

the intercept is the point when the line crosses the axis

you cannot show too much "work"

basically, you remove what is common to all of the factors, and then put brackets, as it will be multiplied back in, remember that when you multiply exponents with the same base, its same as adding them, so subtract to remove...

you can seperate two of the variables , then factor, then subtract the last one from those two, because it cannot be factored out , as in part2 #2

Answer: P=8s

Perimeter of octagon=8sides(unit value of side)

Answer:

P=8s

Step-by-step explanation:

we know that

The perimeter of a regular figure is equal to multiply the number of sides by the length of one side

In this problem

A regular octagon has 8 sides

Let

s-----> the length of one side

The perimeter is equal to

P=8s

Answer:

4a. About 54 times NOT INCLUDING THE FIRST TRIAL

4b. About 60 times NOT INCLUDING THE FIRST TRIAL

Step-by-step explanation:

I say about because we don't know if it's ALWAYS going to be the same results.

4a. Also 12*4 because it's 20 times so 20*4=80 then you add half of it to become 90 and you get 54

4b. 12*5 because 100/5=20 for the 20 trials of them

Answer:

The discriminant D=0

Step-by-step explanation:

For the duadratic polynomial [tex]ax^2+bx+c[/tex] the discriminant is

[tex]D=b^2-4ac.[/tex]

In your case, for the polynomial [tex]4x^2-20x+25,[/tex]

Answer:

The answer is 0 D

Answer:

  (x, f(x)) ≈ (5.5, 4)

Step-by-step explanation:

You can go to the trouble to find the point where the second derivative is zero (the derivative has a maximum), or you can realize the function is symmetrical about y=4, which is where the point of inflection is. The x-value there is ...

  4 = 8/(1 +3e^(-0.2x))

  1 +3e^(-0.2x) = 8/4 = 2

  e^(-0.2x) = 1/3

  x = ln(1/3)/-0.2 = 5ln(3) ≈ 5.493 ≈ 5.5

We already know the value of f(x) is 4 there.

The point of maximum growth is about (5.5, 4).

Answer:

23) option c

    JL ≈ 9.3

25) option c

      y ≈ 9.6

Step-by-step explanation:

Given in the question that,

cos(21°) = 9 / y

y = 9/cos(21°)

y = 9.64

y ≈ 9.6(nearest tenth)

Given in the question that the hypotenuse of right angle triangle = 12

To find,

height of the right angle triangle

angle k = 39°

so by using trigonometry identity

cos(39) = opp/hypo

cos(39) = JL / KL

JL = cos(39)(12)

JL = 9.32

JL ≈ 9.3

Answer:

Q 23.  Last option 7.6

Q 25 Third option

Step-by-step explanation:

To solve Q 23

From the figure we can write,

Sin 39 = Opposite side/Adjacent side

 = JL/KL

 = JL/12

JL= 12 * Sin 39

 = 12 * 0.629  = 7.55

 = 7.6

To solve Q 25

Cos 21 = 9/y

y = 9/Cos 21 = 9/0.9335

= 9.64

 = 9.6

Answer:

  (x, y) = (-6, -7)

Step-by-step explanation:

Substitute for y:

  2x +5 = 3x +11 . . . . . use the first expression for y in the second equation

  0 = x +6 . . . . . . . . . . subtract 2x+5

  -6 = x . . . . . . . . . . . . add -6

  y = 2(-6) +5 = -7 . . . .substitute for x

The solution is x = -6, y = -7.

Answer:

E. 44 meters

Step-by-step explanation:

The function that models the distance covered by the object is

[tex]s(t)=t^2+5t[/tex]

where s(t) is in meters and t is in seconds.

The distance covered by the object after 1 second is

[tex]s(1)=1^2+5(1)=6m[/tex]

The distance covered by the object after 1 second is

[tex]s(1)=5^2+5(5)=50m[/tex]

The distance covered between 1 second and 5 seconds is

50-6=44m

Answer:

person above is right

Step-by-step explanation:

right on plato

Answer:

15 inches

Step-by-step explanation:

The longest side of the right triangular window frame is 39 inches

The height is 36 inches

Let the base of the window frame be x inches

So according to Pythagoras theorem,

x² + 36² = 39²

x² = 39² - 36² = 225

x = [tex]\sqrt{225}[/tex] = 15 inches

The third side of the window frame is therefore equal to 15 inches.

The length of the third side of the window frame will be 15 inches. Then the correct option is A.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The longest side has a length labeled as 39 inches. The height of the frame is labeled as 36 inches.

Let x be the length of the third side of the window frame. Then we have

39² = x² + 36²

 x² = 39² - 36²

 x² = 1521 - 1296

 x² = 225

  x = 15 inches

Then the correct option is A.

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ2

Answer:

The equation of the line into point slope form is [tex]y-32=3(x-10)[/tex]

Step-by-step explanation:

we know that

The equation of the line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

In this problem we have

[tex]m=3[/tex]

[tex](x1,y1)=(10,32)[/tex]

substitute

[tex]y-32=3(x-10)[/tex] ---> equation of the line into point slope form

[tex]y=3x-30+32[/tex]

[tex]y=3x+2[/tex] ---> equation of the line into slope intercept form

Answer:

[tex]4800+183x\geq 8000[/tex]

She must sell at least 18 policies to make an annual income of at least $8,000

Step-by-step explanation:

Let [tex]x[/tex] be the number of policies Mrs. Robinson must sell

We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:

[tex]\frac{3*6,100}{100} =183[/tex]

Now we know that she makes $183 per policy sold. Since [tex]x[/tex] is the number of policies sold, [tex]183x[/tex] is her total commission for selling [tex]x[/tex] policies.

We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:

[tex]4800+183x[/tex]

Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:

[tex]4800+183x\geq 8000[/tex]

Let's solve the inequality:

1. Subtract 4800 from both sides

[tex]4800-4800+183x\geq 8000-4800[/tex]

[tex]183x\geq 3200[/tex]

2. Divide both sides by 183

[tex]\frac{183x}{183} \geq \frac{3200}{183}[/tex]

[tex]x\geq 17.48[/tex]

Since she can't sell a fraction of a policy, we must round the result to the next integer:

[tex]x\geq 18[/tex]

We can conclude that she must sell 18 policies to make an annual income of at least $8,000.

[tex]\bf ~~~~~~\textit{initial velocity} \\\\ \begin{array}{llll} ~~~~~~\textit{in feet} \\\\ h(t) = -16t^2+v_ot+h_o \end{array} \quad \begin{cases} v_o=\stackrel{}{\textit{initial velocity of the object}}\\\\ h_o=\stackrel{}{\textit{initial height of the object}}\\\\ h=\stackrel{}{\textit{height of the object at "t" seconds}} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ h(t)=-16t^2+\stackrel{\stackrel{v_o}{\downarrow }}{19}t+110~\hspace{10em}19~\frac{ft}{sec}[/tex]

The initial velocity of the rock when thrown from the cliff is represented by the coefficient of the t term in the quadratic equation, which is 19 feet per second.

The equation h(t) = -16t² + 19t + 110 describes the height of a rock in feet, as a function of time in seconds after it is thrown from a cliff. To find the initial velocity of the rock when it is thrown, we look at the coefficient of the linear term in this equation, which represents the initial velocity in feet per second (since the equation is quadratic and the coefficient of the t2 term corresponds to half the acceleration due to gravity in feet per second squared).

The initial velocity of the rock is given by the coefficient of the t term, which is 19 feet per second.

Answer:

40 (cm)

Step-by-step explanation:

0. make up a new picture with additional elements (radius of the inscribed circle, it's 'x'; and some elements as shown in the attached picture);

1. the formula of the required perimeter is P=a+b+c, where c- hypotenuse.

2. apply the Pythagorean theorem: a²+b²=c², where c - hypotenuse, then calculate value of 'x' (attention! x>0, the length is positive value !)

3. substitute 'x' into the formula of the required perimeter. The result is 40.

PS. All the details are in the attached picture, answer is marked with red colour.

Answer:

  none of the above

Step-by-step explanation:

The transformation ...

  g(x) = k·f(x -a) +b

vertically stretches the function f(x) by a factor of "k", translates it to the right by "a" units and up by "b" units. There won't be any reflection across the x-axis unless the stretch factor (k) is negative.

You have k=2, a=2, b=-2, so the function is stretched by a factor of 2, then translated to the right and down by 2 units each.

_____

The stretch is done first. If it is done last, then the translation factor(s) are also stretched. All the answer choices given in your problem statement list the stretch last, so none is correct. (You are probably expected to choose d.)

ANSWER

The correct choice is A

EXPLANATION

The given inequality is

y < -|x|

We substitute each point into the inequality to determine which one is a solution.

Option A

-2 < -|1|

-2 < -1.

This statement is true.

Hence (1,-2) is a solution.

Option B.

-1 < -|1|

-1 < -1.

This statement is false.

Option C

0 < -|1|

0 < -1.

This statement is also false.

Answer:

  338 in

Step-by-step explanation:

If each of the measures shown is the measure from the vertex to the point of tangency, then that measure contributes twice to the perimeter (once for each leg from the vertex to a point of tangency).

  2(22 in + 27 in + 22 in + 98 in) = 2(169 in) = 338 in

Answer:

According to the given question if one of the angle of the triangle is 75 degree and the other two sides are of length 2 and 3 units respectively then option C is correct. Only One triangle can be formed where Angle B will be 40 degree. You can figure it out from the steps mentioned below first of all draw an Arc with the length either 3cm or 2 cm that will be the base of a triangle and then from the ending point again cut an arc then after from the starting point that is the point draw  an angle of 75 degree with the help of protactor and extend it to meet the Arc finally you can get the 40 degree.

Hope this helps. Name me brainliest please

Answer:

Option C is correct.

Step-by-step explanation:

The equation used to represent the slop-intercept form is

y= mx + b

where m is the slope

and b is the y-intercept.

So, in the given question y-intercept = (0,8)

b= 8 and

slope =m= 1/2

the equation will be:

y = mx + b

y= (1/2)x + 8

So, Option C is correct.

Answer:

• domain: x ≥ 0

• range: y ≥ 0

Step-by-step explanation:

The graph shows a ray that starts at the origin and extends to infinity in both the +x and +y directions. The domain (horizontal extent) is [0, ∞), as is the range (vertical extent).

Answer:

y = -3

Step-by-step explanation:

Following the directions, we have ...

y = 2·(-1) -1 = -2-1 . . . . . . put -1 where x is in the equation

y = -3

Answer:

㏒3(14) = 2.402 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise some rules of the logarithmic functions

- log(a^n) = n log(a)

-  log(a) + log(b) = log(ab) ⇒ vice versa

- log(a) - log(b) = log(a/b)  ⇒ vice versa

* Lets solve the problem

- We have the value of ㏒3(2) and ㏒3(7)

- We must change the problem to these logarithm to solve

∵ 14 = 2 × 7

∴ We can write ㏒3(14) as ㏒3(2 × 7)

∴ ㏒3(14) = ㏒3(2 × 7)

* Now lets use the rules above

∵  log(ab) = log(a) + log(b)

∴ ㏒3(2 × 7) = ㏒3(2) + ㏒3(7)

∵ ㏒3(2) = 0.631 and ㏒3(7) = 1.771

∴ ㏒3(2 × 7) = 0.631 + 1.771 = 2.402

* ㏒3(14) = 2.402

Answer:

x^3 -6x^2 +18x-10

Step-by-step explanation:

f-g (x) = f(x) -g(x)

f(x) = x^3 -2x^2 +12x-6

g(x)  =4x^2 -6x +4

f(x) -g(x) =x^3 -2x^2 +12x-6 - (4x^2 -6x +4)

Distribute the minus sign

            x^3 -2x^2 +12x-6 - 4x^2 +6x -4

Combine like terms

           x^3 -2x^2- 4x^2 +12x+6x-6  -4

            x^3 -6x^2 +18x-10

I think it’s C sorry if I’m wrong

For this case we have a system of sos equations with two unknowns:

[tex]x-5y = -3\\-7x + 8y = -33[/tex]

We clear "x" from the first equation:

[tex]x = -3 + 5y[/tex]

We substitute in the second equation:

[tex]-7 (-3 + 5y) + 8y = -33\\21-35y + 8y = -33\\-27y = -33-21\\-27y = -54\\y = \frac {-54} {- 27}\\y = 2[/tex]

We find the value of "x":

[tex]x = -3 + 5 (2)\\x = -3 + 10\\x = 7[/tex]

ANswer:

(7,2)

Option C

Answer:

A and C are correct because the farther its is to 1 the stronger it is

Answer:

The answer is A and C

Step-by-step explanation: