The height of a cone is twice the radius of its base.
2x
X
What expression represents the volume of the cone, in
cubic units?
O 2x³
O 47x³

The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

1st.) x = 5 /Sin(30°)

x = 10

!) sin(45°) = 4/x

x = 4/sin(45°)

x = 4√2

I) Cos(45°) = √3 / x

x = √3 / Cos(45°)

x = √6

E) Tan(60°) = 3√3 / x

x = 3√3 / 3

W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.

x = 45°

N) x² + x² = (7√2)²

x = 7

V) Tan(60°) = 7 / x

x = 7√3/3

K) x² + x² = (9)²

x = 9/√2

Y) Sin(60°) = 7√3/x

x = 14

M) Sin(30°) = x/11

x = 11/2

T) Sin(45°) = x/√10

x = √5

A) x + 2x + 90° = 180°

x = 30°

O) Sin(45°) = √2 / x

x = 2

R) Tan(30°) = x / 4

x = 4/√3 = 4√3 / 3

S) Sin(60°) = x / (10/3)

x = 5√3 / 3

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Step-by-step explanation:

[tex]\sqrt[4]{81} -2\\=3-2 \\=1[/tex]

If we have a function f(x), f(5) is f(x) but replacing x with 5. The result give us a value of y and a point of the function, (x, y).

[tex]f(5) = \frac{1}{4} ({2})^{5} = \frac{32}{4} = 8[/tex]

ANSWER A

Hello!

Substitute x = 5 to find f(5).

⇒ f(5) = 1/4(2)⁵

⇒ f(5) = 32/4

⇒ f(5) = 8

∴ The correct option is A.

Step-by-step explanation:

f(x) = y = -1/2 × sqrt(x + 3), x >= -3

-2y = sqrt(x + 3)

4y² = x + 3

x = 4y² - 3

and now we need to rename x to y and y to x to make it a "normal" function :

y = 4x² - 3

since in the original function x >= -3, this gave us y <=0.

and therefore (remember the x of the inverse function actually stands for the y of the original function) the limit for the inverse function is x <= 0.

so, again, the full answer is

f^-1(x) = 4x² - 3, x <= 0

Answer:

No this is not a function because the x-values repeat. In a function you can have the the output duplicate but not the input. The input at 3 has duplicates s o this is not a function.

Step-by-step explanation:

Definition

A relation is called to be a function if every domain has an unique range

Here

As

f(3) has 2 corresponding values it's not a function

The percent of time the photographer spent negotiating with the bison greater than the time he spent taking pictures is 500%

Percentage of time negotiating greater than taking pictures = (difference in time) / time to take pictures × 100

= (30 - 5) / 5 × 100

= 25/5 × 100

= 5 × 100

= 500%

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The new employee should choose the second option to make the most money on a typical day. The amount that the new employee will earn 20-day at this rate is $3,100.

Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.

For Option 1,

Receive an hourly rate of $15.25 for 8 hours plus $0.50 per bottle of wax sold to customers. Also, A typical day consists of 12 bottles of wax sold per detailer.

Earning = ($15.25 × 8) + ($0.50×12)

= $122 + $6

= $128

For Option 2,

Receive $38.75 per automobile detailed in a day. Also, 4 automobiles are detailed per employee. Therefore, the earnings are,

Earning = $38.75 × 4

= $155

For Option 3,

Receive $100 per day plus 2% of sales in a day. Also, the average daily sales are $1,500. Therefore, the earnings are,

Earning = $100 + 0.02($1500)

= $130

Hence, The new employee should choose the second option to make the most money on a typical day.

2.)

The amount that the new employee will earn 20-day at this rate is,

Amount earned = $155 × 20 days

                           = $3,100

Hence, The amount that the new employee will earn 20-day at this rate is $3,100.

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Answer:

x ≥ 21.5/19

Step-by-step explanation:

-1.5(4x + 1) ≥ 45 - 25(x + 1)

-6x - 1.5 ≥ 45 - 25x - 25

-6x + 25x ≥ 45 - 25 + 1.5

19x ≥ 21.5

x ≥ 21.5/19

The linear equation is represented by the second table as  y= -2 .5 x-15 and the solution to the system of equations is  (-6, 0).

First, take two point from the table and as such it will be:

P (-4, -5) and Q(-2, -10)

So the two point is used to create a straight line and as such it will be:

y - y₁ = y₂ - y₁/ x₂ - x₁ (x₁-x )

y -(-5) = [tex]\frac{-10-(-5)}{-2-(-4)}[/tex]  (x -(-4))

y + 5 = [tex]\frac{-5}{2}[/tex]  x +4

y + 5 =  [tex]\frac{-5}{2}[/tex]  x - 10

y =  [tex]\frac{-5}{2}[/tex]  x - 15

y= -2 .5 x-15

The linear equation is represented by the second table as  y= -2 .5 x-15 and the solution to the system of equations is  (-6, 0)

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Answer:

1st one option A to lazy to right out location

2nd one -6,0

Step-by-step explanation:

Answer:

151°

Step-by-step explanation:

The above shape is a quadrilateral.

The exterior angles are :

82°, 70°, 62°, and (x -5)°

Therefore,

82 + 70 + 62 + x - 5 = 360

214 -5 + x = 360

209 + x = 360

x = 360 - 209

x = 151°

Answer:

357 mi²

Step-by-step explanation:

A = LW + 0.5πr²

A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²

A = (10 × 20 + 0.5 × 3.14159 × 10²) mi²

A = 357 mi²

The probability that the randomly selected student is female or Physics major is 0.625.

Given Information

Total number of students = 40

Number of Physics major out of the total students, P = 15

Number of females in the class, F = 16

Number of females that are Physics major, (P∩F) = 6

We have to find the probability P(P∪F).

Calculating the Probability

Probability of Physics major students, P(P) = 15/40

= 0.375

Probability of female students, P(F) = 16/40

= 0.4

Probability of female students who are Physics major, P(P∩F) = 6/40

= 0.15

Since, we know that,

P(P∪F) = P(P) + P(F) - P(P∩F)

∴ P(P∪F) = 0.375 + 0.4 - 0.15

P(P∪F) = 0.625

Thus, the probability that the randomly selected student will be a Physics major or a female is 0.625

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According to the central angle theorem, the measure of angle MNP = 114°.

According to the central angle theorem of a circle, the measure of central angle MNP equals the measure of intercepted arc MP.

Measure of arc MP = 114°

Measure of angle MNP = arc MP

Measure of angle MNP = 114° [central angle theorem]

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The probability that exactly 9 buyers would prefer green is 0.1408

We will use the Binomial probability formula to find the answer

The formula is given by ⁿCₓ (p)ˣ (1-p)ⁿ-ˣ

We have

n, the number of trial = 12

x, the sample we aim to try = 9

p, the probability of success = 0.6

Substitute these values into the formula

[tex]P(9)= ^{12}C_{9} (0.6)^{9} (1-0.6)^{12-9}[/tex]

P(9) = 0.1408 (rounded to four decimal places)

Hence, The probability that exactly 9 buyers would prefer green is 0.1408

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To eliminate the biggest common factor, use the distributive property: Solution: 16 + 36 = 4 (4 + 9)

To “distribute” means to divide something or give a share or part of something. According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Due to that,

To remove the most significant common factor, we must use the distributive property.

Given expression:16 + 36

1, 2, 4, 8, and 16 make up the number 16.

1, 2, 3, 4, 6, 9, 12, 18, and 36 make up the number 36.

Then, 4 is the most prevalent component.

distributed property

The formula is ab + bc

subtracting 4 from the supplied expression.

Therefore, the distributive property is used.

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Answer:

6 quarts

Step-by-step explanation:

2 pints = 1 quart

4 cups = 1 quart

• 5 pints of orange juice

5 pints = 5/2 =>2.5 quarts

• 6 cups of grape juice

6 cups = 6/4 => 1.5 quarts

• 8 cups of apple juice

8 cups = 2 quarts

2.5 + 1.5 + 2 = 6 quarts

Answer: Draw a line through (0,5) and (1,2)

The graph is shown below.

=====================================================

Reason:

The equation y = -3x+5 is in the form y = mx+b

m = -3 = slope

b = 5 = y intercept

The y intercept is where the graph crosses the y axis. In this case, it's at (0,5). This is one point needed.

Another point can be found by going down 3 and to the right 1 to arrive at (1,2). The motion "down 3, right 1" is from the slope of -3/1.

Therefore, this line goes through (0,5) and (1,2)

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

Another approach:

Plug in x = 0 to get...

y = -3x+5

y = -3(0) + 5

y = 5

The input x = 0 leads to the output y = 5

This tells us the point (x,y) = (0,5) is on the line.

Repeat for x = 1

y = -3x+5

y = -3(1)+5

y = 2

So (1,2) is another point on the line.

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

Check out the graph below.

Step-by-step explanation:

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

x | 0 | 1 |

y | 5 | 2 |

Shape A was reflected over the y axis and translated 1 unit down to get shape B.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Translation is the movement of a point either up, down, left or right on the coordinate plane.

Shape A was reflected over the y axis and translated 1 unit down to get shape B.

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a) [tex]-3(1)+1=\boxed{-2}[/tex]

b) [tex]4=-3x+1 \longrightarrow -3x=3 \kongrightarrow x=\boxed{-1}[/tex]

The 95% confidence interval of voters not favoring the incumbent is (0.0706, 0.1294).

Sample size, n=400

Sample proportion, p = 40 / 400

= 0.1

We use normal approximation, for this, we check that both np and n(1-p) >5.

Since n*p = 40 > 5 and n*(1-p) = 360 > 5, we can take binomial random variable as normally distributed, with mean = p = 0.1 and standard deviation  = root( p * (1-p) /n )

= 0.015

For constructing Confidence interval,

Margin of Error (ME) =  z x SD = 0.0294

95% confidence interval is given by Sample Mean +/- (Margin of Error)

0.1 +/- 0.0294 = (0.0706 , 0.1294)

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Answer: [tex]120^{\circ}[/tex]

Step-by-step explanation:

[tex]12\pi=2(\pi)(18)\left(\frac{\theta}{360} \right)\\\\12\pi =36\pi \left(\frac{\theta}{360} \right)\\\\\frac{1}{3}=\frac{\theta}{360}\\\\\theta=120^{\circ}[/tex]

Answer:

the answer will be equal to x= 1962 over 7

1.9

Step-by-step explanation:

A = kB/C -----------(1)

A=12

B = 3

C= 2

substitute A, B and C into equation (1).

12 = K × 3/2

12 = 3k/2

12×2 = 3k

3K = 24

dividing bothsides by 3

3K/3 = 24/3

K = 8

substitute K = 8 into equation (1)

A = 8B /C --------------(2)

Equation (2) is the equation connecting

A,B and C.

Finding B when A = 10 and C = 1.5

10 = 8B / 1.5

10× 1.5 = 8B

15 = 8B

Dividing bothsides by 8 :

B = 15/8

B = 1.875

B = 1. 9 ( approximately)

Answer:

The equation of the line that passes through the points (2a, b) and (a, b+1) is [tex]$y=-\frac{1}{a} x+2+b$[/tex].

Step-by-step explanation:

The given points are (2a, b) and (a, b+1).

It is required to find the equation of the line that passes through the points. the slope-intercept form.

Step 1 of 4

Using the given two points, to find the slope.

Given points are (2a, b) and (a, b+1).

Substitute [tex]$x_{1}[/tex]=2a,

[tex]$$\begin{aligned}&y_{1}=b \\&x_{2}=a \text { and } \\&y_{2}=b+1\end{aligned}$$[/tex]

into the formula, [tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

Step 2 of 4

Simplify [tex]$m=\frac{b+1-b}{a-2 a}$[/tex], further

[tex]$$\begin{aligned}m &=\frac{b+1-b}{a-2 a} \\m &=-\frac{1}{a}\end{aligned}$$[/tex]

As a result, the slope is [tex]$m=-\frac{1}{a}$[/tex].

Step 3 of 4

Use the slope [tex]$m=-\frac{1}{a}$[/tex] and the coordinates of one of the points (2a, b) into the point-slope form, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex].

Substitute [tex]$m=-\frac{1}{a}$[/tex],

[tex]x_{1}=2 a$ and$y_{1}=b$[/tex]

into the formula, [tex]$y-y_{1}=m\left(x-x_{1}\right)$[/tex]

[tex]$y-b=-\frac{1}{a}(x-2 a)$[/tex]

[tex]$y-b=-\frac{1}{a} x+2$$[/tex]

Step 4 of 4

Rewrite the above equation as a slope-intercept equation. So, from the above term [tex]$y-b=-\frac{1}{a} x+2$[/tex], Add b on each side.

[tex]$$\begin{aligned}&y-b=-\frac{1}{a} x+2 \\&y=-\frac{1}{a} x+2+b\end{aligned}$$[/tex]

Therefore, the equation of the line that passes through the points is [tex]$y=-\frac{1}{a} x+2+b$[/tex].

Answer:

4

Step-by-step explanation:

348 / 87 = 4

There are 87 Customers. The restauraunt served 348 pancakes. You divide 348 by 87 and conclude that each customer ate 4 pancakes.

Answer:

4

Step-by-step explanation:

348 ÷ 87 = 4

each person ate 4 pancakes

Answer:

B

Step-by-step explanation:

given a quadratic function in standard form

y = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² - 4x + 3 ← is in standard form

with a = 1, b = - 4 , then

x = - [tex]\frac{-4}{2}[/tex] = 2

substitute into the equation for corresponding y- coordinate

y = 2² - 4(2) + 3 = 4 - 8 + 3 = - 1

vertex = (2, - 1 )

Answer: 48

Step-by-step explanation:

By the geometric mean theorem,

[tex]\frac{x}{36}=\frac{64}{x}\\\\x^{2}=36 \cdot 64\\\\x=\sqrt{36 \cdot 64}\\\\x=\sqrt{36} \sqrt{64}=48[/tex]

Using it's vertex, the maximum value of the quadratic function is -3.19.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

Considering the coefficient a, we have that:

In this problem, the equation is:

y + 4 = -x² + 1.8x

In standard format:

y = -x² + 1.8x - 4.

The coefficients are a = -1 < 0, b = 1.8, c = -4, hence the maximum value is:

[tex]y_v = -\frac{1.8^2 - 4(-1)(-4)}{4(-1)} = -3.19[/tex]

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