Find the volume of the cone. Use u = 3.14. Round to the nearest hundredth.

785.0 cm
7850.0 cm
2616.67 cm
261.67cm

Answer:

Good day! Use trigonometry to define the formula.

Step-by-step explanation:

The height of the tree that the sun appears just over it top is 12 meters

The situation forms a right angle triangle.

The height of the tree is the opposite side of the triangle.

His distance away from the base of the tree is the adjacent side of the right angle triangle.

Therefore,

Using trigonometric ratio,

tan 32 = opposite / adjacent

tan 32 = h / 20

cross multiply

height of the tree = 20 tan 32

height of the tree = 20 × 0.6248693519

height of the tree = 12.4973870382

height of the tree ≈ 12 meters

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Answer:

The area of the walls is [tex]2,160\ ft^{2}[/tex]

Step-by-step explanation:

we know that

The area of the walls is equal to the perimeter of the conference room multiplied by the height of the ceiling

so

[tex]A=2[40+50](12)=2,160\ ft^{2}[/tex]

Both triangles have 2 side lengths labeled and a common angle ( shown by the curved lines).

You could use the SAS Similarity theorem.

Answer:

Step-by-step explanation:

This was the answer that was right for me, I just did this question :) Hope this helps!

Answer is: 213, 278 , 108, 213, 157

213 is repeated 2 times; more than any other number.

A number that appears most often is the mode.

Answer:

213, 278, 108, 213, 157

Step-by-step explanation:

The mode is the number with the highest frequency in a given list of data. Simply, it is the number with most occurrence.

Now, let us chart the frequency of each numbers in the list provided:

1........ 111, 108, 213, 198, 205

Arrange in ascending order

108, 111, 198, 205 and 213

Numbers Frequency

108 1

111 1

198 1

205 1

213 1

No modal value

2..... 212, 215, 213, 211, 220

Arranging in ascending order:

211, 212, 213, 215 and 220

Numbers Frequency

211 1

212 1

213 1

215 1

220 1

No modal value

3......213, 278, 108, 213, 157

Arranging in ascending order:

108, 157, 213 and 278

Numbers Frequency

108 1

157 1

213 2

278 1

The mode here is 213. It has a frequency of 2 compared to other numbers whose mode is 1

4........ 210, 200, 213, 221, 221

Arranging in ascending order:

200, 210, 213, 221

Numbers Frequency

200 1

210 1

213 1

221 2

The mode here is 221

Answer: 500*20%=100-50=50

Step-by-step explanation:

500*20%=100-50=50

Answer:

15.6

Step-by-step explanation:

40% × 39 = 15.6

Hope this helps

12w-27=-34+14w

Add 34 to each side:

12w + 7 = 14w

Subtract 12w from each side:

7 = 2w

Divide both sides by 2:

w = 7/2 ( depending on how you need to write the answer it could also be written as 3 1/2 or 3.5)

Answer:

w=7/2

Step-by-step explanation:

12w-27=-34+14w

12w-27+27=-34+14w+27

12w=14w-7

12w-14w=14w-7-14w

-2w=-7

w=7/2

If you need a decimal divide 7 by 2

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Answer:

[tex]0.46\pi\ radians[/tex]

Step-by-step explanation:

step 1

Find the circumference

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ units[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]C=2(3.14)(5)=31.4\ units[/tex]

step 2

Find  the measure in radians for the central angle of a circle whose radius is 5 and intercepted arc length is 7.2 units

Remember that

The circumference of [tex]31.4\ units[/tex] subtends a central angle of [tex]2\pi \ radians[/tex]

so

using proportion

Let

x-----> the central angle in radians

[tex]\frac{2\pi}{31.4}=\frac{x}{7.2} \\ \\x=2\pi (7.2)/31.4\\ \\x=0.46\pi\ radians[/tex]

Answer:

The equation would be:

(X+1)^2 + (y-1)^2 = 9

This is the equation of the circle in general form.  

[tex]\[ x^2 + y^2 + 2x - 2y - 7 = 0 \][/tex]

or

[tex]\[ (x + 1)^2 + (y - 1)^2 = 9 \][/tex]

To write the equation of a circle in general form, you start with the standard form of the circle's equation, which is:

[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]

where \( (h, k) \) is the center of the circle and \( r \) is the radius.

From the information provided:

- The center of the circle is \( (-1, 1) \)

- The radius of the circle is \( 3 \) units

Let's substitute these values into the standard form:

[tex]\[ (x - (-1))^2 + (y - 1)^2 = 3^2 \][/tex]

[tex]\[ (x + 1)^2 + (y - 1)^2 = 9 \][/tex]

Now, to write it in general form, you'll expand the equation and combine like terms:

Step 1: Expand the squares

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

[tex]\[ (y - 1)^2 = y^2 - 2y(1) + 1^2 \][/tex]

Step 2: Write the expanded form

[tex]\[ x^2 + 2x + 1 + y^2 - 2y + 1 = 9 \][/tex]

Step 3: Combine like terms

[tex]\[ x^2 + y^2 + 2x - 2y + 1 + 1 = 9 \][/tex]

Step 4: Move the constant to the right side

[tex]\[ x^2 + y^2 + 2x - 2y = 9 - 2 \][/tex]

Step 5: Final general form

[tex]\[ x^2 + y^2 + 2x - 2y - 7 = 0 \][/tex]

This is the equation of the circle in general form.

Answer:

The graph is a parabola with vertex (0 , -2)

Equation: y = x² -2

For x = -2, y = (-2)² -2 ⇒  y = 4 - 2  ⇒  y = 2

For x = -1, y = (-1)² -2 ⇒  y = 1 - 2  ⇒  y = -1

For x = 0, y = (0)² -2 ⇒  y = 0 - 2  ⇒  y = -2

For x = 1, y = (1)² -2 ⇒  y = 1 - 2  ⇒  y = -1

For x = 2, y = (2)² -2 ⇒  y = 4 - 2  ⇒  y = 2

B) dilation

this transformation changes the shape's size (making it smaller/larger) whilst the others keep the shape congruent (same shape, same size)

When two shapes are similar but not congruent, it means the transformations performed on the shapes is non-rigid. The transformation that Michael can use to obtain a non-congruent triangle for is (b) dilation.

A non-rigid transformation is such that changes the side lengths of a shape. An example is dilation.

Because the resulting triangle [tex]\triangle A'B'C'[/tex] must not be congruent, then, Michael can dilate the original [tex]\triangle ABC[/tex] to give the new triangle [tex]\triangle A'B'C'[/tex]

See attachment for an illustration of dilation

Hence, (b) is correct

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Answer:

5

Step-by-step explanation:

40/(32/4)

40/8

5

Answer:

[tex]{\huge \boxed{5}}[/tex]

Step-by-step explanation:

Parenthesis

Exponent

Multiply

Divide

Add

Subtract

Do divide from left to right, to find the answer.

[tex]40\div32\div4[/tex]

[tex]32\div4=8[/tex]

[tex]40\div8=5[/tex]

5 is the correct answer.

Answer:

[tex]\large\boxed{-8x^2-(8x-6x^2-8x)-[7-(-8x-7)]=-2x^2-8x-14}[/tex]

Step-by-step explanation:

[tex]-8x^2-(8x-6x^2-8x)-[7-(-8x-7)]\\\\=-8x^2-8x-(-6x^2)-(-8x)-[7-(-8x)-(-7)]\\\\=-8x^2-8x+6x^2+8x-(7+8x+7)\\\\=-8x^2-8x+6x^2+8x-7-8x-7\qquad\text{combine like terms}\\\\=(-8x^2+6x^2)+(-8x+8x-8x)+(-7-7)\\\\=-2x^2-8x-14[/tex]

Answer:

2940

Step-by-step explanation:

Hello There!

To Solve This Equation, I Would Not Use Addition Till The Very End.

Remember, 42 + Something Equals 2,982.

That is The Same As Subtracting 42 From 2,982

2,940 Is Your Answer.

In the given geometric series, the common ratio is 5. The value of n, which indicates the term number, is found to be 4 by setting up and solving an equation based on the general formula for the nth term in a geometric series.

The series presented is a geometric series. In a geometric series, each term is multiplied by a common ratio to get the next term. In this case, the common ratio is 5 because each term is obtained by multiplying the previous term by 5.

In a geometric series, the general formula for the nth term is a * r^(n-1), where a is the first term and r is the common ratio. Hence, let's set up the nth term equation and solve for n.

500 = 4 * 5^(n-1)

When we solve the equation, we find that the value of n is 4.

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Answer:

The measure of angle FGH is m∠FGH=48°

Step-by-step explanation:

step 1

Find the measure of arc FG in terms of x

we know that

The inscribed angle measures half that of the arc comprising

m∠FHG=(1/2)[arc FG]

substitute the given values

(28x−3°)=(1/2)[arc FG]

arc FG=(56x−6°)

step 2

Find the value of x

we know that

arc FG+arc FH+arc GH=360° -----> by complete circle

substitute the values

(56x−6°)+(31x+3°)+ (33x+3°)=360°

120x=360°

x=3°

step 3

Find the measure of angle m∠FGH

we know that

The inscribed angle measures half that of the arc comprising

m∠FGH=(1/2)[arc FH]

substitute the given values

m∠FGH=(1/2)[31x+3°]

m∠FGH=(1/2)[31(3)+3°]

m∠FGH=48°

Answer:

On the left is a 30 60 90 triangle so the height = 10 / 2 = 5 feet

Area of triangle = (5 * 8.7) / 2 = 21.75 sq feet

Area of Rectangle = 12 * 5 = 60 sq feet

TOTAL Area = 21.75 + 60 = 81.75 square feet

Step-by-step explanation:

Answer:

13.2 ft.

Step-by-step explanation:

In the given ΔABC

tanA = [tex]\frac{Height}{Base}[/tex] = [tex]\frac{BC}{AB}[/tex]

tan 31° =[tex]\frac{x}{22}[/tex]

x = 22 tan 31°

  = 22 × (0.6009)

  = 13.22 ≈ 13.2 ft.

Answer:

[tex]x_1=4.158[/tex]

[tex]x_2=0.8416[/tex]

Step-by-step explanation:

For an equation of the form [tex]ax^2 +bx +c[/tex]

The quadratic formula is

[tex]\frac{-b\±\sqrt{b^2 -4ac}}{2a}[/tex]

In this case the equation is:

[tex]2x^2 - 10x + 7 = 0[/tex]

Then

[tex]a= 2\\b= -10\\c= 7[/tex]

Therefore, using the quadratic formula we have:

[tex]x=\frac{-(-10)\±\sqrt{(-10)^2 -4(2(7)}}{2(2)}[/tex]

[tex]x=\frac{5\±\sqrt{11}}{2}[/tex]

[tex]x_1=4.158[/tex]

[tex]x_2=0.8416[/tex]

ANSWER

[tex]x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2} [/tex]

EXPLANATION

The given quadratic equation is:

[tex] 2{x}^{2} - 10x + 7 = 0[/tex]

Comparing this equation to

[tex] a{x}^{2} + bx + c = 0[/tex]

we have

a=2, b=-10 and c=7.

The solution is given by the quadratic formula;

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

We plug in the values to get,

[tex]x = \frac{ - - 10 \pm \sqrt{ {( - 10)}^{2} - 4(2)(7) } }{2(2)} [/tex]

This implies that

[tex]x = \frac{ 10 \pm \sqrt{ {100} - 56 } }{4} [/tex]

[tex]x = \frac{ 10 \pm \sqrt {44 } }{4} [/tex]

[tex]x = \frac{ 10 \pm 2\sqrt {11 } }{4} [/tex]

[tex]x = \frac{ 5 \pm \sqrt {11 } }{2}[/tex]

[tex]x = \frac{ 5 }{2} - \frac{\sqrt {11} } {2} \: or \: x = \frac{ 5 }{2} + \frac{\sqrt {11} } {2} [/tex]

ANSWER

D.

[tex]x = \frac{ - ( - 9 )\pm \sqrt{ {( - 9)}^{2} - 4(2)(4)} }{2(2)} [/tex]

EXPLANATION

The given equation is

[tex]2 {x}^{2} - 9x + 4 = 0[/tex]

When we compare this to:

[tex]a{x}^{2} + bx + c = 0[/tex]

we have a=2, b=-9, and c=4.

The quadratic formula is given by,

[tex]x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]

We substitute the values into the formula to get,

[tex]x = \frac{ - ( - 9 )\pm \sqrt{ {( - 9)}^{2} - 4(2)(4)} }{2(2)} [/tex]

The correct choice is D

Answer:

D)y-intercept of f(x) is greater than the y-intercept of g(x)

Step-by-step explanation:

Y-intercept is the point y-coordinate value on graph where graph line intersects the y-axis and the value of x coordinate on x-axis is zero at that point.

From the given graph of f(x), it can be seen that

y-intercept of f(x) is 2

For the given function g(x)

finding y-intercept

when x=0

y=-3

because g(x) = 3 for 1<x≤3

As 2>-3

hence y-intercept of f(x)>g(x) !

Answer:

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Step-by-step explanation:

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Linear relationship always produces a straight line and are without exponential.

Lets check all the given options:

1. the total area, in square meters, y, of a square garden if the side length is x meters.

The area of a square is [tex](side)^{2}[/tex]

Here, side is 'x' and area 'y' will be [tex]x^{2}[/tex].

This is not linear.

2. the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

The equation forms:

[tex]y=6+0.2x[/tex]

When x = 1

[tex]y=6.2[/tex]

When x = 2

[tex]y=6+0.2(2)[/tex]

=> [tex]y=6.4[/tex]

When x = 3

[tex]y=6+0.2(3)[/tex]

=> [tex]y=6.6[/tex]

This is a linear relation.

3. the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

The equation forms:

[tex]y=15+8x[/tex]

When x = 1

[tex]y=15+8=23[/tex]

When x = 2

[tex]y=15+8(2)[/tex]

=> [tex]y=31[/tex]

When x = 3

[tex]y=15+8(3)[/tex]

=> [tex]y=39[/tex]

This is also linear.

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

The equation forms:

[tex]y=62x[/tex]

When x = 1

[tex]y=62[/tex]

When x = 2

[tex]y=62(2)[/tex]

=> [tex]y=124[/tex]

When y = 3

[tex]y=62(3)[/tex]

=> [tex]y=186[/tex]

This is also linear in nature.

Answer:

Perfect positive association

Step-by-step explanation:

Definition: A perfect positive association means that a relationship appears to exist between two variables, and that relationship is positive 100% of the time. Two variables have a positive association when the values of one variable tend to increase as the values of the other variable increase. (+1 indicates a perfect positive linear relationship)

Definition: A perfect negative association means that a relationship appears to exist between two variables, and that relationship is negative 100% of the time. Two variables have negative association when the values of one variable tend to decrease as the values of the other variable increase. (-1 indicates a perfect negative linear relationship)

Values between 0.3 and 0.7 (-0.3 and -0.7) indicate a moderate positive (negative) linear relationship.

From the graph we can see that this relationship shows perfect positive association (both variables increase and we can plot the straight line which will include all points)

Answer:

perfect positive

Step-by-step explanation:

For this case we have that by definition, the Pythagorean theorem states that:

[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]

Where:

a, b: Are the legs

c: It is the hypotenuse

According to the figure we have to:

[tex]a = 20\\b = 21[/tex]

Substituting in the formula we have:

[tex]c = \sqrt {(20) ^ 2 + (21) ^ 2}\\c = \sqrt {400 + 441}\\c = \sqrt {841}\\c = 29[/tex]

Answer:

Option D

Answer:

841

Step-by-step explanation:

hope this helps

Answer:

x = 14

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value of sin45°

sin45° = [tex]\frac{\sqrt{2} }{2}[/tex]

Hence

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{7\sqrt{2} }{x}[/tex]

Multiply both sides by x

x × sin45° = 7[tex]\sqrt{2}[/tex] ( divide both sides by sin45° )

x = [tex]\frac{7\sqrt{2} }{sin45}[/tex]

  = [tex]\frac{7\sqrt{2} }{\frac{\sqrt{2} }{2} }[/tex]

  = 7[tex]\sqrt{2}[/tex] × [tex]\frac{2}{\sqrt{2} }[/tex] = 7 × 2 = 14

The expression -4x^2(3x - 7) simplifies to -12x^3 + 28x^2 after distributing -4x^2 across the parentheses and performing the necessary multiplications.

The expression to be simplified is -4x^2(3x - 7).

To simplify the expression, you need to distribute the term -4x^2 across the parentheses. This involves two multiplication steps:

Multiply -4x^2 by -7 to get +28x^2.

After performing these multiplications, the expression simplifies to -12x^3 + 28x^2.

Answer:

y = 23

Step-by-step explanation:

The diagonals of a rhombus are perpendicular bisectors of each other, thus

∠1 = 90° and ∠1 = 4y - 2, so equating gives

4y - 2 = 90 ( add 2 to both sides )

4y = 92 ( divide both sides by 4 )

y = 23

Answer:

the answer is 126!

Step-by-step explanation:

i worked it out myself, and got it correct! have a great day :)

There are 126 ways can a committee of 4 be chosen from a group of 9 people, the correct option is B.

The solution is obtained through a combination where we choose "r of n", where r is the amount of things we choose and n the total number of things that can be chosen.

The combinations form uses factorial numbers. This is the formula:

[tex]\rm ^nC_r=\dfrac{n!}{(n-r)!r!}[/tex]

Where the value of n is 9 and r is 4.

The number of ways can a committee of 4 be chosen from a group of 9 people is;

[tex]\rm ^nC_r=\dfrac{n!}{(n-r)!r!}\\\\\rm ^9C_4=\dfrac{9!}{(9-4)!4!}\\\\ ^9C_4=\dfrac{9!}{5!4!}\\\\ ^9C_4=\dfrac{9\times 8 \times 7 \times 6 \times 5!}{5!\times 4\times 3\times 2\times 1}\\\\ ^9C_4=\dfrac{3024}{24}\\\\ ^9C_4=126[/tex]

Hence, there are 126 ways can a committee of 4 be chosen from a group of 9 people, the correct option is B.

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Step-by-step explanation:

Area of a parallelogram is the base times the height.

A = bh

A = (13 cm) (3 cm)

A = 39 cm²

Answer:

The area is 39 square cm.

Step-by-step explanation:

The area of a parallelogram is given as :

[tex]A=base\times height[/tex]

Given is:

base = 13 cm

height = 3 cm

So, area of the parallelogram becomes:

[tex]A=13\times3[/tex]

[tex]A=39[/tex] square cm.

Therefore, the area of the parallelogram is 39 square centimeters.