find the height of a cylinder with a volume of 1215pi mm and a radius of 9mm

Answer:

s = 1.5

Step-by-step explanation:

10 + 2.375 = 12.375 = 8.85

12.375/8.25 = 8.25s/8.25

s = 1.5

Answer:

The profit will be [tex]\$22.31[/tex]

Step-by-step explanation:

we know that

To find the profit subtract the cost of the case of bottled water from the sell of all the bottles of water  

Let

x-----> the profit

[tex]x=36*0.75-4.69=\$22.31[/tex]

Answer:

Step-by-step explanation:

The question is not biased.  It doesn't push the participants to answer one way or another.

However, the sample is biased.  It does not represent the population.

The first and fourth options are correct.

Answer:

2500

Step-by-step explanation:

Let the first square number be [tex]x^2[/tex] then the next square number is [tex](x+1)^2[/tex].

The difference between these two consecutive numbers is 99.

This implies that:

[tex](x+1)^2-x^2=99[/tex]

We expand to get:

[tex]x^2+2x+1-x^2=99[/tex]

Simplify:

[tex]2x=99-1[/tex]

[tex]2x=98[/tex]

Divide both sides by 2

[tex]x=49[/tex]

Therefore the value of the larger perfect number is

[tex](49+1)^2=50^2=2500[/tex].

Using law of sines:

Sin(angle) = opposite leg (height) / hypotenuse ( length of ladder)

Sin(70) = 25/x

x = 25 * sin(70)

x = 26.6 feet

Answer:

The first answer is the one you want

Step-by-step explanation:

The rate of change is the slope.  Here it is represented by the dollar value/number of tickets sold.  This will give you the 1:1 ratio, meaning it will give you the number of dollars generated by the sale of 1 ticket.  That's what rate of change is.

Use the slope formula and 2 points on the table.  I chose the points (225, 250) and (200, 0):

[tex]\frac{0-250}{200-225} =\frac{-250}{-25} =10[/tex]

That translates to $10 per ticket.

look up a video on the internet and it will show you

To find the angle of depression, we can use trigonometry. The elevation of the North Rim and the campground, along with the line of sight distance, can be used to calculate the angle using the tangent function.

To find the angle of depression of the man's line of sight to the campground, we can use trigonometry. The angle of depression is the angle between the line of sight and a horizontal line. In this case, the elevation of the North Rim is 5389 ft and the elevation of the campground is 2405 ft. The line of sight distance to the campground is 3044 ft.

We can use the tangent function to find the angle of depression. Tangent(theta) = opposite/adjacent. The opposite side is the difference in elevation between the North Rim and the campground (5389 ft - 2405 ft) and the adjacent side is the line of sight distance (3044 ft). So, tangent(theta) = (5389 ft - 2405 ft) / 3044 ft.

Using a scientific calculator, we can find the value of theta by taking the inverse tangent (or arctan) of the ratio: theta = arctan((5389 ft - 2405 ft) / 3044 ft). The answer is approximately 57.38 degrees.

Answer:

Let l = length and w = width of the rectangular garden

=> w < 30

and 2(l + w) ≤ 180

=> l + w ≤ 90

=> 0 < w < 30 and 60 ≤ l < 90.

Step-by-step explanation:

Answer:

  1. predicted attendance: 141.35

  2. residual: 18.65

Step-by-step explanation:

1. Predicted attendance is ...

  y = -5.9·5 +170.85 = 141.35

__

2. As the problem statement tells you, ...

  actual value - predicted value = residual

  160 - 141.35 = 18.65 . . . the residual

Answer:

The surface area of the sphere is [tex]529\pi\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The surface area of a sphere is equal to

[tex]SA=4\pi r^{2}[/tex]

we have

[tex]r=23/2=11.5\ ft[/tex] ----> the radius is half the diameter

substitute

[tex]SA=4\pi (11.5)^{2}[/tex]

[tex]SA=529\pi\ ft^{2}[/tex]

Answer:

[tex](n+6)(5u+x)[/tex]

Step-by-step explanation:

The given expression is;

[tex]5u(n+6)+x(n+6)[/tex]

The greatest common factor is (n+6).

Let us factor the GCF to obtain:

[tex](n+6)(5u+x)[/tex]

Therefore the completely factored form of

[tex]5u(n+6)+x(n+6)[/tex]

is

[tex](n+6)(5u+x)[/tex]

f(-1) means the x value is -1 and you need to find what the Y value is.

Find -1 in the set of parenthesis and see what the Y value is.

When x = -1, y = 3

The answer would be 3.

The area of a triangle is half the multiplication of the base and the height.

So, if the smaller triangle has height 6 cm and base 2 cm, its are is

[tex]\dfrac{6\times 2}{2}=6[/tex]

Similarly, if the height of the larger triangle is 9 cm, and its base is 3 cm, its area is

[tex]\dfrac{9\times 3}{2}=\dfrac{27}{2}[/tex]

So, the total area is

[tex]6+\dfrac{27}{2} = \dfrac{12}{2}+\dfrac{27}{2}=\dfrac{39}{2}[/tex]

The total area of the two triangles that need to be painted is 19.5 cm².

The total area of the two triangles that need to be painted can be found by adding the area of the smaller triangle and the area of the larger triangle. The formula to calculate the area of a triangle is:

Area = (base * height) / 2

For the smaller triangle, the base is 2 cm and the height is 6 cm. Substituting these values into the formula, we get:

Area of smaller triangle = (2 cm * 6 cm) / 2 = 6 cm²

For the larger triangle, the base is 3 cm and the height is 9 cm. Substituting these values into the formula, we get:

Area of larger triangle = (3 cm * 9 cm) / 2 = 13.5 cm²

To find the total area, we add the areas of the two triangles:

Total area = area of smaller triangle + area of larger triangle = 6 cm² + 13.5 cm² = 19.5 cm²

Answer:

D. (2.4, -1).

Step-by-step explanation:

The midpoint  of the line segment with endpoints (x1,y1) and (x2,y2) is

[(x1+x2) / 2 , (y1+y1)/2 ].

So here we have : [  (3.2+1.6)/ 2 (2.5 - 4.5)/2)

= (2.4, -1) answer.

The midpoint of the line segment with endpoints (3.2, 2.5) and (1.6, -4.5) is (2.4, -1).

To find the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂), you can use the midpoint formula:

Midpoint (M) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

For the given endpoints (3.2, 2.5) and (1.6, -4.5), we can calculate the midpoint as follows:

Midpoint (M) = ((3.2 + 1.6) / 2, (2.5 + (-4.5)) / 2)

= (4.8 / 2, -2 / 2)

= (2.4, -1)

Therefore, the midpoint of the line segment with endpoints (3.2, 2.5) and (1.6, -4.5) is (2.4, -1).

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Answer:

d. arc BCE

Step-by-step explanation:

BE is a diameter which means it cuts the circle in half therefore arc BCE is a semicircle

Answer:

A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36

Step-by-step explanation:

We have two sides of the triangle and we have an angle.

A = 32 °, a = 19, b = 14

We use the sine theorem to find the angle B.

We know that according to the sine theorem it is true that:

[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]

[tex]\frac{sin(32\°)}{19}=\frac{sin(B)}{14}[/tex]

[tex]sin(B)=14*\frac{sin(32\°)}{19}\\\\B=Arcsin(14*\frac{sin(32\°)}{19})\\\\B=22.98\°[/tex]

We know that the sum of the internal angles of a triangle is always equal to 180.

So:

[tex]C=180-32-22.98\\\\C=125.02\°[/tex]

Finally we find the c side

[tex]\frac{sin(A)}{a}=\frac{sin(C)}{c}[/tex]

[tex]\frac{sin(32\°)}{19}=\frac{sin(125.02)}{c}[/tex]

[tex]0.02789=\frac{sin(125.02)}{c}[/tex]

[tex]c=\frac{sin(125.02)}{0.02789}\\\\c=29.36[/tex]

Answer:  [tex]\bold{D)\quad h^{-1}(x)=\dfrac{1}{6}(x-1)}[/tex]

Step-by-step explanation:

Inverse is when you swap the x's and y's and then solve for y

y = 6x + 1

x = 6y + 1          swapped the x's and y's

x - 1 = 6y           subtracted 1 from both sides

[tex]\dfrac{1}{6}[/tex] (x - 1) = y         divided both sides by 6

Answer:

a)

The equation of variation is;

N = 80000*S

b)

14400000

Step-by-step explanation:

We are informed that the number of instructions N performed per second by a computer varies directly as the speed S of the​ computer's internal processor. This means that N and S are directly proportional;

N∝S

Introducing a constant of proportionality, k;

N=k*S

We shall find the value of k by using the information given;

N = 1600000

S = 20

k = 1600000/20

  = 80000

a)

The equation of variation is thus;

N = 80000*S

b)

We are required to find N when S = 180

Using the equation of variation obtained above;

N = 80000 (180)

   = 14400000

Answer:

The length of the lot is [tex]105.6\ ft[/tex]

Step-by-step explanation:

Remember that

[tex]1\ acre=43,560\ ft^{2}[/tex]

In this problem the area of the lot  is equal to

[tex]\frac{2}{3} (43,560)=29,040\ ft^{2}[/tex]

Let

x-----> the length of the lot

y ----> the deep of the lot

The area of the lot is

[tex]A=xy[/tex]

we have

[tex]A=29,040\ ft^{2}[/tex]

[tex]y=275\ ft[/tex]

substitute and solve for x

[tex]29,040=x(275)[/tex]

[tex]x=29,040/(275)=105.6\ ft[/tex]

[tex]\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \log_{3x+4}(4096)=4\implies \stackrel{\textit{exponential form}}{(3x+4)^4=4096}\implies (3x+4)^4=2^{12} \\\\\\ \stackrel{~\hfill \textit{same exponents, the bases must be the same}}{(3x+4)^4=2^{3\cdot 4}\implies (3x+4)^4=(2^3)^4}\implies 3x+4=2^3\implies 3x+4=8 \\\\\\ 3x=4\implies x=\cfrac{4}{3}[/tex]

Answer:

5*B=C

Step-by-step explanation:

Five cookies times the number of boxes will give you the total number of cookies

Answer:

80

Step-by-step explanation:

let w = the width of the rectangles

then

12w = the area of one rectangle

8w = the area of other

:

12w - 8w = 320

4w = 320

w = 320/4

w = 80 units wide

;

:

Check

12 * 80 = 960

8 * 80 = 640

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

difference: 320

We know that both rectangles have the same width, which is 80 units.

We know that both rectangles have the same width, so we can say that both have the width W.

One of the rectangles has a length of 12 units, and the other of 8 units, so the areas are:

A = 12*W

A' = 8*W

And the largest area is 320 square units more than the other area, so we have:

12*W = 8*W + 320

Solving for W we get:

12*W - 8*W = 320

4*W = 320

W = 320/4 = 80

Then the width of each rectangle is 80 units.

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Answer:

Domain is all real numbers; Range is all numbers less than or equal to 0

Step-by-step explanation:

Domain covers x values, range covers y values.  The domain of an x^2 parabola, which is what this is, has a domain of all real numbers.  Meaning that while the branches of the function keep going up and up and up or down and down and down, the values of x will never stop growing.

The range here is indicative of the lowest y value to the highest that the function covers.  In this case, since the parabola is upside down, we have the highest to the lowest.  The highest that the function goes up the y axis is right at the origin, where y = 0.  Then it drops down into forever.  So the range is all values of y less than or equal to 0

The Domain of [tex]f(x)[/tex] is all the real numbers, and

The Range of [tex]f(x)[/tex] is  [tex]y\le0[/tex] or [tex]f(x)\le0[/tex]

The diagram shows the graph of the quadratic function

[tex]f(x)=-x^2[/tex]

The domain of [tex]f(x)[/tex] is all the real numbers, since the function has defined values for all real values of [tex]x[/tex].

The range of [tex]f(x)[/tex] is the set of values that [tex]f(x)[/tex] can assume. The square function has a range

[tex]\{y \text{ }|\text{ }y=x^2\text{ and }y\ge0\}[/tex] or the half-open interval [tex][0,\infty)[/tex].

This means that the negative of the square function will have the range

[tex]\{y \text{ }|\text{ }y=-x^2\text{ and }y\le0\}[/tex] or the half-open interval [tex](-\infty,0][/tex].

So, the domain of [tex]f(x)[/tex] is the open interval [tex](-\infty,\infty)[/tex] (all the real numbers), and the range of [tex]f(x)[/tex] is the half-open interval [tex](-\infty,0][/tex] (or, [tex]y\le0[/tex])

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Answer:

arc NO has measure 48

Step-by-step explanation:

We assume all measures are in consistent units (degrees or something similar). The two inscribed angles intercept the same arc, so are congruent:

9x -3 = 4x +12

5x = 15 . . . . . . . add 3-4x

x = 3 . . . . . . . . . divide by 5

The measure of the inscribed angle is then ...

4x +12 = 4(3) +12 = 24

That is half the measure of the arc, so the measure of arc NO is ...

arc NO = 2·24 = 48

Answer:

48°

Step-by-step explanation:

I'm actually just assuming that you mean arc NO.  Proceeding with that...

Angle NMO is an inscribed angle which intercepts arc NO.  Angle NPO is also an inscribed angle that intercepts arc NO.  Because they both intercept the same arc, both inscribed angles have the same measure.  Therefore,

9x - 3 = 4x + 12

Solving for x:

5x = 15

x = 3.  Plug 3 in for x in either one of the equations to get that angles NMO and NPO measure

9(3) - 3 = 24°

The rule is that inscribed angles measure HALF of the arcs they intercept, so the measure of arc NO is 48°

Answer:

48 people

Step-by-step explanation:

1. 4/50 = x/600  do 4x600 and 50 times x

2.50x=2400

3. divide both sides by 50 to get a result of x=48.

Answer:

This is the alternate exterior angle theorem

Step-by-step explanation:

This is because angle 2 and angle 7 are in the outer part of each side of opposite lines

Answer:

2) First option

3) Second option

Step-by-step explanation:

5² = 625

13 × 8 × 5 = 520

For this case we must find an expression equivalent to:

[tex]216 ^ {\frac {1} {3}[/tex]

So, we can rewrite the 216:

[tex]216 = 6 * 6 * 6 = 6 ^ 3[/tex]

Rewriting the expression:

[tex](6 ^ 3) ^ {\frac {1} {3}=[/tex]

By definition of power properties we have:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

So:

[tex]6 ^ {\frac {3} {3}} =\\6 ^ 1 =\\6[/tex]

Answer:

[tex]216 ^ {\frac {1} {3}}= 6[/tex]

The equivalent expression of [tex]216^{1/3}[/tex] is determined as 6.

Simplification refers to the process of reducing an expression, equation, or fraction into its simplest or most concise form.

The equivalent expression is determined by converting the exponents into roots as follows.

The given expression;

[tex]216^{1/3}[/tex]

This expression is simplified as follows;

     [tex]216^{1/3}[/tex] = ∛ 216

The final expression becomes;

6³ = 216

So 6 is the answer

Thus, the equivalent expression of [tex]216^{1/3}[/tex] is determined as 6.

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Answer:

Second choice