EASY 5 POINTS!!!!! You have a 1-gallon paint can in the shape of a cylinder. One gallon is 231 cubic inches. The radius of the can is 3 inches. What is the approximate height of the paint can? Use 3.14 for pi.

A.) 5 inches
B.) 25 inches
C.) 8 inches
D.) 26 inches

We first found sin θ using the Pythagorean identity, then found tan θ, and finally used the double-angle formula for tan to find tan 2θ.

To find the value of tan 2θ when cos θ = 8/17 and θ is in Quadrant I, you need first to find the value of sin θ. Since we are in Quadrant I, both cos and sin are positive. You can use the Pythagorean Identity for sin, cos, and tan, which states sin² θ + cos² θ = 1, to find sin θ. Substituting the given value of cos θ in this identity, we can find that sin θ = sqrt(1 - (8/17)²) = 15/17.

With sin and cos known, we can now find tan θ using the formula tan θ = sin θ/cos θ which gives tan θ = (15/17)/(8/17) = 15/8.

Finally, to find tan 2θ, use the Double-Angle formula for the tangent, which states tan 2θ = 2 tan θ / (1 - tan² θ). Substituting tan θ = 15/8 into this formula, we get tan 2θ = 2 * (15/8) / (1 - (15/8)²).

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To find tan 2θ, given cos θ is 8/17 and θ is in the first quadrant, first find sin θ using the Pythagorean identity, then use the double-angle formula where tan 2θ equals 2 tan θ divided by 1 minus tan squared θ, yielding -2.

To find tan 2θ given that cos θ is 8/17 and θ is in the first quadrant, we first need to find the value of sin θ. Since θ is in the first quadrant, all trigonometric functions are positive. Using the Pythagorean identity, we have:

sin θ = √(1 - cos² θ)

Substituting cos θ = 8/17:

sin θ = √(1 - (8/17)²) = √(1 - 64/289) = √(225/289) = 15/17.

Next, we use the double-angle formula for tangent:

tan 2θ = (2 tan θ) / (1 - tan² θ)

To find tan θ, we use:

tan θ = sin θ / cos θ = (15/17) / (8/17) = 15/8

Now, substitute tan θ into the double-angle formula:

tan 2θ = (2 × 15/8) / (1 - (15/8)²)

= (30/8) / (1 - 225/64)

= (30/8) / (-161/64) = -1920/1288 = -15/7.5 = -2

The complete question is :

Given that [tex]\(\cos \theta = \frac{8}{17}\)[/tex] with [tex]\(\theta\)[/tex] in the first quadrant, determine [tex]\(\tan 2\theta\).[/tex]

c = 14h

this would give you the total cost by multiplying 14 by the number of hours

The Taylor series for [tex]\( \sin(x) \)[/tex] centered at [tex]\( a = \pi \)[/tex] is:[tex]\[ \sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]

The radius of convergence of this Taylor series is infinite, meaning it converges for all values of ( x ).

To find the Taylor series for [tex]\( f(x) = \sin(x) \)[/tex] centered at [tex]\( a = \pi \),[/tex] we first need to find the derivatives of \( \sin(x) \) and evaluate them at \( x = \pi \). Then, we'll write out the Taylor series using the formula:

[tex]\[ f(x) = f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + \cdots \][/tex]

Let's find the derivatives of [tex]\( \sin(x) \)[/tex] and evaluate them at [tex]\( x = \pi \):[/tex]

1. [tex]\( f(x) = \sin(x) \)[/tex]

2. [tex]\( f' (x) = \cos(x) \)[/tex]

3.[tex]\( f''(x) = -\sin(x) \)[/tex]

4.[tex]\( f'''(x) = -\cos(x) \)[/tex]

Now, evaluate these derivatives at \( x = \pi \):

1. [tex]\( f(\pi) = \sin(\pi) = 0 \)[/tex]

2. [tex]\( f'(\pi) = \cos(\pi) = -1 \)[/tex]

3.[tex]\( f''(\pi) = -\sin(\pi) = 0 \)[/tex]

4. [tex]\( f'''(\pi) = -\cos(\pi) = 1 \)[/tex]

Now, plug these values into the Taylor series formula:

[tex]\[ \sin(x) = 0 - 1(x - \pi) + \frac{0}{2!}(x - \pi)^2 + \frac{1}{3!}(x - \pi)^3 + \cdots \][/tex]

Simplify:

[tex]\[ \sin(x) = -\sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]

So, the Taylor series for [tex]\( \sin(x) \)[/tex] centered at [tex]\( a = \pi \)[/tex] is:

[tex]\[ \sin(x) = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n + 1)!}(x - \pi)^{2n + 1} \][/tex]

The radius of convergence of this Taylor series is infinite, meaning it converges for all values of ( x ).

The cube root of -27 is -3, which cannot be graphed in the first quadrant of the complex plane. When considering complex roots, the angles of these roots do not lie in the first quadrant either, contradicting the given requirement.

The cube root of -27 that graphs in the first quadrant in complex form can be represented as 3(cos Θ + i sin Θ), where Θ is the angle in degrees. To find a cube root that lies in the first quadrant, we look for an angle Θ whose cosine is positive and sine is positive, which corresponds to angles between 0° and 90°. However, the cube root of -27 is actually a negative real number, which is -3.

Since we cannot graph a negative real number (-3) in the first quadrant of the complex plane, which only contains positive real and imaginary numbers, the question seems to be a bit contradictory. Nonetheless, if we interpret the cube root in terms of complex numbers, we find that the complex roots of -27 are -3, 3ε², and 3ε⁴, where ε² = e²πi/3 and ε⁴ = e⁴πi/3, correspond to angles of 120° and 240° respectively, which do not lie in the first quadrant.

Answer:

The mean is  

✔ 89

The median is  

✔ 92

The mean of Miriam's test scores is 89 and the median is 92.

"It is the average of a data set. "

"It is the middle value in a list ordered from smallest to largest."

For given question,

Total number of test scores = 9

The sum of all the test scores would be,

96 + 81 + 82 + 99 + 94 + 92 + 95 + 82 + 80 = 801

So, the mean would be,

[tex]\bar{X}=\frac{801}{9} \\\\\bar{X}=89[/tex]

So, the mean of Miriam's test scores is 89.

If we arrange the test scores in ascending order then it would be,

80, 81, 82, 82, 92, 94, 95, 96, 99

The middle value is 92

So, the median is 92.

Therefore, the mean of Miriam's test scores is 89 and the median is 92.

Learn more about the mean and median here:

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Answer:

Number of cars needed=3

Step-by-step explanation:

Ethel is arranging rides for 27 members.

If 12 can go in the van and 5 can go in each car.

Let c cars are needed

Then, 12+5c=27

5c=27-12

5c= 15

c= 15/5

c=3

Hence, number of cars needed equals:

3

Answer:

[tex]\displaystyle b = 11[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Functions

Calculus

Integration

Integration Rule [Reverse Power Rule]:                                                               [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:                                     [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:                                                         [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Area of a Region Formula:                                                                                     [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]

Step-by-step explanation:

Step 1: Define

Identify

g(x) = 4x

Interval [1, b]

A = 240

Step 2: Solve for b

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

Answer: a-b+c+d =4

Step-by-step explanation:

The given system of equation is

[tex]2x+8y=7\\4x-2y=9[/tex]

from this we have the following matrices

[tex]A_1 =\begin{bmatrix}\\2 &8 \\ \\4&2 \\\end{bmatrix}\ ,X=\begin{bmatrix}\\x\\ \\y\\\end{bmatrix}\text{and}\ C=\begin{bmatrix}\\7\\ \\9\\\end{bmatrix}[/tex]

the given matrix A =[tex]\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}[/tex]

On comparing Matrix  [tex]A_1[/tex] with Matrix A

[tex]\begin{bmatrix}\\a &c \\ \\b &d \\\end{bmatrix}=\begin{bmatrix}\\2&8 \\ \\4 &-2 \\\end{bmatrix}[/tex]

we have the following values

a=2 ,b=4,c=8,d=-2

Thus a-b+c+d =2-4+8+(-2)=4

The only time you can be so certain that you have picked 2 brown socks is when there are no more white socks and black socks. This means that to be 100% sure that you have picked 2 brown socks, you must pick all 12 white socks and all 18 black socks and only then you can pick 2 brown socks without looking. Therefore the total number of socks that should be picked is:

Total number of socks = 12 white socks + 18 black socks + 2 brown socks

Total number of socks = 32 socks

A total picking of 32 socks is required to be certain without looking that 2 brown have already been chosen.

Answer:

46 2/3% of 28 is 13.06

Step-by-step explanation:

Hello,

thank you very much for asking this here in brainly, I think I can help you with this one

Let's remember

[tex]a\frac{b}{c} =\frac{(a*c)+b}{c}\\[/tex]

Step 1

[tex]46\frac{2}{3} =\frac{(46*3)+2}{3} =\frac{140}{3} =46.67[/tex]

so 46 2/3% =46.67%

Step 2

using a rule of three

define the relationships

if

28⇒ 100%

x?  ⇒46.67%

[tex]\frac{28}{100}=\frac{x}{46.67} \\[/tex]

isolating x

[tex]\frac{28}{100}=\frac{x}{46.67}  \\x=\frac{28*46.67}{100}\\x=\frac{1306.67}{100} \\x=13.06[/tex]

46 2/3% of 28 is 13.06

I hope it helps, have a great day

The average temperature range in Newport, Oregon is between 45 and 65 degrees.

The average yearly temperature T in degrees for Newport, Oregon is given by: |T−55|≤10. This means that the temperature T is within 10 degrees of 55 degrees. To find the average temperature range, we consider the range between 55+10 = 65 degrees and 55-10 = 45 degrees.

Therefore, the average temperature range in Newport, Oregon is 45 to 65 degrees.

3x3 = 9

2x6 = 12

12+9 = 21+1 =22

 score would be 22 points

Answer:

The Giants' score will be 22 points.

Step-by-step explanation:

Consider the provided information.

It is given that tom predicted that the Giants would score three 3-point field goals. Which can be written as:

3 × 3 = 9

Total score by field goals is 9 points.

If he score two 6-point touchdowns, this can be written as:

2 × 6 = 12

Total score by touchdown is 6 points.

And 1 extra point.

Now add all the points as shown below:

Total score is: 9 + 12 + 1 = 22 points

Hence, the Giants' score will be 22 points.

to turn a percent into a decimal, move the decimal point 2 places to the left

84.3% = 0.843

a. Rate law expression: [tex]\(\text{rate} = kxyz\)[/tex]

b. [tex]\[ \text{Rate factor} \approx 3.16 \times 10^3 \][/tex]

**Part A: Rate Law Expression**

Given that the reaction is first order in [tex]\( (IO_3)^- \)[/tex], first order in [tex]\( (SO_3)^{2-} \)[/tex], and first order in [tex]\( H^+ \)[/tex], the rate law for the reaction can be expressed as:

[tex]\[ \text{rate} = k \cdot [(IO_3)^-]^1 \cdot [(SO_3)^{2-}]^1 \cdot [H^+]^1 \][/tex]

Simplifying this, we get:

[tex]\[ \text{rate} = kxyz \][/tex]

Here, [tex]\( x \), \( y \), and \( z \)[/tex] are the concentrations of [tex]\( (IO_3)^- \), \( (SO_3)^{2-} \), and \( H^+ \)[/tex], respectively. [tex]\( k \)[/tex] is the rate constant.

**Part B: Rate Change with pH**

The pH of a solution is a measure of its hydrogen ion concentration [tex](\( [H^+] \))[/tex]. As the reaction is first order in [tex]\( H^+ \)[/tex], a change in pH will directly impact the rate. The relationship between pH and [tex]\( [H^+] \)[/tex] is logarithmic:

[tex]\[ \text{pH} = -\log[H^+] \][/tex]

To calculate the rate change factor when the pH decreases from 5.50 to 2.00, we need to consider the relationship between pH and [tex]\( [H^+] \)[/tex]:

[tex]\[ \text{pH} = -\log[H^+] \][/tex]

1. **At pH 5.50:**

  [tex]\[ [H^+] = 10^{-\text{pH}} = 10^{-5.50} \][/tex]

2. **At pH 2.00:**

  [tex]\[ [H^+] = 10^{-\text{pH}} = 10^{-2.00} \][/tex]

Now, calculate the rate factor:

[tex]\[ \text{Rate factor} = \frac{\text{rate at pH 2.00}}{\text{rate at pH 5.50}} = \frac{[H^+]_{\text{pH 2.00}}}{[H^+]_{\text{pH 5.50}}}\][/tex]

[tex]\[ \text{Rate factor} = \frac{10^{-2.00}}{10^{-5.50}} \][/tex]

[tex]\[ \text{Rate factor} \approx \frac{0.01}{3.16 \times 10^{-6}} \][/tex]

[tex]\[ \text{Rate factor} \approx 3.16 \times 10^3 \][/tex]

Expressing the answer numerically using two significant figures, the rate change factor is approximately [tex]\(3.2 \times 10^3\).[/tex]

The question probable maybe:

Part A:

The reaction is found to be first order in [tex](IO_3)^-[/tex], first order in [tex](SO_3)^2^-[/tex], and first order in H^+.
If [[tex](IO_3)^-[/tex]] = x, [[tex](SO_3)^2^-[/tex]] = y and [[tex]H^+[/tex]]=z, what is the rate law for the reaction in terms of x, y, and z and the rate constant k?
Express the rate in terms of k, x, y, and (e.g., kxy^3z^2).

▸ View Available Hint(s)

rate= kx^1y^1z

Part B:

By what factor will the rate of the reaction change if the ph decreases from 5.50 to 2.00? express your answer numerically using two significant figures.

Answer:

[tex]12\frac{3}{16} \text{inches}[/tex]

Step-by-step explanation:

Given : The city is [tex]2 \frac{7}{16}[/tex] inches across on the map

To Find:On the map, what is the distance across the actual city?

Solution:

Distance on map = [tex]2 \frac{7}{16}=\frac{39}{16} inches[/tex]

Scale: 1 inch = 5 miles

So, [tex]\frac{39}{16} inches=\frac{39}{16} \times 5[/tex]

[tex]\frac{39}{16} inches=\frac{195}{16} =12\frac{3}{16} [/tex]

Thus ,the distance across the actual city is [tex]12\frac{3}{16} inches[/tex]

So, option C is correct.

x=heavy equipment

y= general labor

x+y=38

x=38-y

134x + 92y=4756

134(38-y)+92y =4756

5092-134y+92y=4756

-42y = -336

y = -336/-42 = 8

x=38-8=30

check 30*134 =4020

8*92 = 736

4020+736 = 4756

 8 general laborers

30 heavy equipment operators

x+y=29

y=29-x

x+2y=45

x+2(29-x)=45

x+58-2x=45

-1x=-13

x=13

y=29-13=16

x+y = 13+16 = 29

x+2y= 13 + 2(16) = 13+32 = 45

so the numbers are 13 & 16