You may use the unit circle shown below to help you answer this question.



Which of these are true statements about the sine function? Choose all that are correct.

A
For any value of θθ , sin(−θ)=sin(θ)sin(−θ)=sin(θ) .
B
For any value of θθ , sin(−θ)=−sin(θ)sin(−θ)=−sin(θ) .
C
The sine function is an odd function.
D
The sine function is an even function.
E
The sine function has a period of ππ .
F
The sine function has a period of 2π2π .

Answer:

x = 3 ± √5

Step-by-step explanation:

The expression (x - 3)² = 5 doesn't need completing the square to solve (this is the step after you finish completing the square):

Step 1: Square root both sides

x - 3 = ±√5

Step 2: Add 3 to both sides

x = 3 ± √5 = 0.76392, 5.23607

Step-by-step explanation:

There are two ways to solve this equation for x

Either you develop (x-3)^2 and then solve the quadratic equation

Or you can solve it this way :

(X-3)^2= 5

x-3 = + or - root square 5

So x = 3+ or - root square 5

Answer:

Step-by-step explanation:

The given data is

Male female total

Democrat. 600 600 1200

Republican 500 300 800

other 122 100 222

total. 1222 1000 2222

The total number of people (males and females) that voted is 2222. The total number of people that did not vote Republican or Democrat but voted "other" instead is 222

Therefore, the percentage of all voters that did not vote Republican or Democrat but voted "other" instead is

222/2222 × 100 = 9.990990999099

Rounding up to the nearest tenth of a percent, it becomes 10.0

Answer:   A review of voter registration in a small rural town revealed the following:

Refer to the table above. Determine the percent of all voters that did not vote Republican or Democrat but voted "Other" instead.

22%

25%

222%

10% this is right

Step-by-step explanation:

Answer:

Decreases by 2 degrees

Step-by-step explanation:

The expression that describes temperature as a function of latitude is:

[tex]T=110-2(Latitude)[/tex]

This equation represents a linear relationship between latitude and temperature in a way that an increase in latitude causes a decrease in temperature. The magnitude of this decrease is quantified by the slope of the linear equation, which is -2. Therefore, the estimated temperature decreases by 2 degrees when latitude is increased by one.

Complete Question:

You want to install a 1 yd wide walk around a circular swimming pool. The diameter of the pool is 23 yd. What is the area of the​ walk? Use 3.14 for pi π.

Answer:

75.36 square yard

Step-by-step explanation:

From the question,

The diameter of this circular pool inside is 23 yd.

This means that the radius = Diameter/2 = 23yd/2 = 11.5 yd.

The formula for the area of a circle =

A = πr²

A = π(11.5)²

A =3.14 × 11.5²

A = 415.265 yd²

This is the Area of the inner circle.

We were told in the question also that he wants to install a walk of 1 yard

Hence, the radius of outer circle =

radius of inner circle +length of the walk

11.5yard + 1 yard

= 12.5 yard

A = πr²

A = 3.14 × (12.5)²

A = 490.625yd²

Area of the walk = Area of the Outer circle - Area of the inner circle

= (490.625 - 415.265)yd = 75.36 yd²

Therefore, the area of the walk is 75.36 square yards.

Answer:

357 mi²

Step-by-step explanation:

The shape is made of a triangle and a half-square

we will calculate the area of each one

let A1 be the area of the half-circle:

A1= (10²*π)/2 = 50π mi²

Let A2 be the area of the triangle:

A2= 10*20=200 mi²

let At be the total area:

At =A1+A2= 200+50π =357.07≈ 357 mi²

Answer:

The answer is 41%.

Step-by-step explanation:

First, you have to find the total volume of the cylindrical flask using the formula. Then, you have to substitute the following values into the formula :

[tex]v = \pi \times {r}^{2} \times h[/tex]

[tex]let \: \pi = 3.14 \\ let \: r = 3 \\ let \: h = 12[/tex]

[tex]v = 3.14 \times {3}^{2} \times 12[/tex]

[tex]v = 3.14 \times 108[/tex]

[tex]v = 339.12 {cm}^{3} [/tex]

Next, given that 200cm³ of liquid is poured into the cylinder. So in order to find the volume of flask that is not filled by liquid, you have to subtract :

[tex]v = 339.12 - 200 = 139.12 {cm}^{3} [/tex]

Lastly, you have to find the percentage :

[tex] \frac{139.12}{339.12} \times 100 = 41\% \: (near. \: whole \: number)[/tex]

Answer:

Step-by-step explanation:

To solve for c we use the formula for Pythagoras theorem

That's

a² = b² + c²

Where a is the hypotenuse

From the question above

c is the hypotenuse

So we have

c² = 9² + 7²

c ² = 81 + 49

c² = 130

Find the square root of both sides

Hope this helps you

Answer:

c=√130

Step-by-step explanation:

In order to solve this question, you have to know the Pythagorean Theorem. The Pythagorean Theorem uses this equation: a^2 + b^2 = c^2. The letters indicate one side of the triangle, but c is always the longest side of the triangle, or the hypotenuse. In the image, both of the triangles are the same size so we basically just have to solve for one. We plug in 9 for a and 7 for b in our equation we just learned.

a^2 + b^2 = c^2

9^2 + 7^2 = c^2

We have to square the 9 and 7. In order to do that, we just multiply 9 by itself, and 7 by itself (9*9, 7*7), because the small number on the right corner tells you how many times you have to multiply that number.

81 + 49 = c^2

Now we add them together and we get:

81 + 49 = 130

130 is our c^2, and that number goes into the green box in the image. The actual number is very long so we just use this number for your answer! Hope this helps :)

Answer:

P ( 3, - pi/3 + 2 pi n) or P ( -3 , -pi/3 + pi(2 n +1))

Step-by-step explanation:

P ( 3, - pi/3)

We can circle 2pi n around the circle and be back at the same polar coordinate

P ( 3, - pi/3 + 2 pi n)

or we can flip the radius to a negative and add pi to the theta

P ( -3, - pi/3 + pi)

Then we can circle 2pi n around the circle and be back at the same polar coordinate

P ( -3 , -pi/3 + 2 pi n +pi)

P ( -3 , -pi/3 + pi(2 n +1))

Answer:

F distribution test

Step-by-step explanation:

He would use the F distribution test. This test is used in comparing the variances of two categorical variables if they are equal. The null hypothesis is rejected if after carrying out the test the results states otherwise.

Answer: 1,365 possible special pizzas

Step-by-step explanation:

For the first topping, there are 15 possibilities, for the second topping, there are 14 possibilities, for the third topping, there are 13 possibilities, and for the fourth topping, there are 12 possibilities. This is how you find the number of possible ways.

15 * 14 * 13 * 12 = 32,760

Now, you need to divide that by the number of toppings you are allowed to add each time you add a topping.

4 * 3 * 2 * 1 = 24

32,760 / 24 = 1,365

There are 1,365 possible special pizzas

Using the combination principle, the number of special pizzas from which to choose from is 1365

Using Combination :

nCr = [(n! ÷ (n - r)! r!)]

15C4 = [(15! ÷ (15 - 4)! 4!)]

15C4 = [(15! ÷ 11!4!)]

15C4 = (15 × 14 × 13 × 12) ÷ (4 × 3 × 2 × 1)

15C4 = 32760 / 24

15C4 = 1365

Therefore, 1365 different special pizzas can be made.

Learn more : https://brainly.com/question/19120549

Answer:Hk and IJ

Step-by-step explanation:

They are parallel to eachother, hope this helped!

<!> Brainliest is appreciated! <!>

Answer:

the answer is reflection

Step-by-step explanation:

i took edg

The transformation maps the pre- image to image by reflection.

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.

Given:

A transformation of ΔSTV results in ΔUTV.

As, both the triangles are connected to the base and having identical side length and angle measure.

So, here the transformation is refection.

Learn more about transformation here:

https://brainly.com/question/11709244

#SPJ2

Answer:

No of rooms in Hotel G = 280

No of rooms in Hotel H = 145

Step-by-step explanation:

I solved the question using Elimination Method.

Answer:

5

Step-by-step explanation:

(+3 + (+2))

Remove the brackets.

3 + (+2)

3 + 2

Add the numbers.

= 5

Answer:

+5 or 5

Step-by-step explanation:

(+3)+(+2)

=> According to the rule, ( + )( + ) = ( + )

So,

=> +3+2

=> +5

Answer:

7.2

Step-by-step explanation:

Since 72 goes into 10 7 times, we do have 7 point something. We are left with 2/10ths, which is 0.2, so we add them together to get 7.2.

Answer:

[tex]\boxed{4 : 1}[/tex]

Step-by-step explanation:

Colored Fabric = 48 mm

White Fabric = 1.2 cm

Ratio of white fabric to colored fabric is:

48 mm : 1.2 cm

To express any ratio, we need to equalize the units  ( 1 cm = 10 mm)

=> 48 mm : 12 mm

     ÷12           ÷12

=> 4 : 1

Answer:

Ratio of white:coloured = 1 : 4

Step-by-step explanation:

48mm coloured : 1.2 cm white

48mm coloured : 12 mm white

Express the amount of white fabric to coloured fabric as a ratio in its simplest form.

Order is important, so

WHITE : COLOURED

= 12 : 48 ...............................simplify

= 1 : 4

Answer:

not sure if it's 26 or76

Answer:

its 2

Step-by-step explanation:

Answer:

Step-by-step explanation:

x - 1/2 =0

2x = 1

4x = 2

Answer:

x + 3 = 7/2

100x = 50

16/x = 24

Step-by-step explanation:

The value of x is 1/2 in the three equations.

Explanation:

The sample proportion 0.617 is at the exact midpoint of the interval from  0.572 to 0.662

We can confirm this by applying the midpoint formula.

The distance from the center (0.617) to either endpoint will be the margin of error. In other words, it is half the width of the confidence interval

L = lower boundary of confidence interval = 0.572

C = center of confidence interval = 0.617

U = upper boundary of confidence interval = 0.662

We have three methods to find the confidence interval

Each yielding the same result of 0.045

With the third method, you don't need to know the center of the confidence interval.

Answer:

Option C is the correct option

Step-by-step explanation:

The y-intercept is the value of the function where X is 0. For g(X) , y-intercept is 5 while the y-intercept of h(X) is 9.

So, h(X) has a greater y-intercept.

Hope this helps...

Good luck on your assignment..

Answer:

h(x) has a greater y-intercept.

Step-by-step explanation:

Answer: x=5 and 1/2

Step-by-step explanation:

You have to go to a graph and put it simply it, makes it a lot easier, hope this helps!

Steps to solve:

2x^2 + 5 = 11x

~Subtract 11x to both sides

2x^2 - 11x + 5 = 0

~Factor

(2x - 1)(x - 5) = 0

~Solve each factor

2x - 1 = 0

2x = 1

x = 1/2

x - 5 = 0

x = 5

Best of Luck!

Answer:

x ≥ -0.75

Step-by-step explanation:

3.75 - 3x ≤ 6

Subtract 3.75 on both sides.

- 3x ≤ 6 - 3.75

- 3x ≤ 2.25

Divide both sides with -3.

x ≥ 2.25/-3

x ≥ -0.75

Answer:

x [tex]\geq[/tex] -0.75

Step-by-step explanation:

3.75 - 3x [tex]\leq \\[/tex] 6

1. Subtract 3.75 from both sides.

3.75 - 3x - 3.75 [tex]\leq \\[/tex] 6 - 3.75

2. Simplify.

-3x [tex]\leq \\[/tex] 2.25

3. Multiply both sides by -1.

(-3x)(-1) [tex]\geq[/tex] 2.25(-1)

4. Simplify.

3x [tex]\geq[/tex] -2.25

5. Divide both sides by 3.

3x/3 [tex]\geq[/tex] -2.25/3

6. Simply.

x [tex]\geq[/tex] -0.75

Answer:

Vertex: (-3. -8)

Step-by-step explanation:

Quickest and easiest way to do this is to using a graphing calc and graph the function. Once you have done so, trace the graph to the lowest point of the graph. You should be able to see that (-3, -8) is your answer.

Alternatively, you can convert this function into f(x) = a(bx - h)² + k (by Completing the Square) form to find (-h, k) as your vertex.

Answer:

D. -5 <= x < 1

Step-by-step explanation:

the values under the square-root radical must not be negative, AND

the value of the denominator must not be 0 or negative

x+5 >=0  or x >= -5

and 1-x > 0 or x < 1

So the answer is -5 <= x < 1

Answer:

12

Step-by-step explanation:

36= 2 × 2 × 3 × 3

60= 2 × 2 × 3 × 5

HCF(36, 60)= 2 × 2 × 3 = 12

12 is the greatest number that divides 36 and 60 without leaving a remainder​

Answer:

The correct answer is:

The volume of the triangular prism is equal to the volume of the cylinder

Step-by-step explanation:

Given that there are two figures

1. A right triangular prism and

2. Right cylinder

Area of cross section of prism is equal to Area of cross section of cylinder.

Let this value be A.

Also given that Height of prism = Height of cylinder = 6

Volume of a prism is given as:

[tex]V_{Prism} = \text{Area of cross section} \times Height[/tex]

[tex]V_{Prism} = A \times 6 ........ (1)[/tex]

Cross section of cylinder is a circle.

Area of circle is given as: [tex]\pi r^{2}[/tex]

Area of cross section, A = [tex]\pi r^{2}[/tex]

Volume of cylinder is given as:

[tex]V_{Cylinder} = \pi r^{2} h\\\Rightarrow V_{Cylinder} = A \times h\\\Rightarrow V_{Cylinder} = A \times 6 ...... (2)[/tex]

From equations (1) and (2) we can see that

[tex]V_{Prism}=V_{Cylinder}[/tex]

Hence, the correct answer is:

Volume of prism is equal to the volume of cylinder.

Answer:

the answer is C for short

Answer:

  9 ft

Step-by-step explanation:

Let x represent the shortest piece. Then the sum of lengths is ...

  x + (x +25) +3x = 40

  5x = 15

  x = 3

  3x = 9

The third piece is 9 feet long.

_____

Check

The pieces are 3 ft, 28 ft, 9 ft, so total 40 ft, as required.

Answer:

  3, 8, 13, 18, 23

Step-by-step explanation:

The recursive definition tells you the first term is 3, and that each successive term is 5 more than the one before. 5 terms are ...

  3, 8, 13, 18, 23

Answer:

90% confidence interval for the proportion of fans who bought food from the concession stand

(0.5603,0.6529)

Step-by-step explanation:

Step(i):-

Given sample size 'n' =300

Given data  random sample of 300 attendees of a minor league baseball game, 182 said that they bought food from the concession stand.

Given sample proportion

                       [tex]p^{-} = \frac{x}{n} = \frac{182}{300} =0.606[/tex]

level of significance = 90% or 0.10

Z₀.₁₀ = 1.645

90% confidence interval for the proportion is determined by

[tex](p^{-} - Z_{0.10}\sqrt{\frac{p(1-p)}{n} } , p^{-} +Z_{0.10}\sqrt{\frac{p(1-p)}{n} })[/tex]

[tex](0.6066 - 1.645\sqrt{\frac{0.6066(1-0.6066)}{300} } ,0.6066+1.645\sqrt{\frac{0.6066(1-0.6066)}{300} })[/tex]

(0.6066 -  0.0463  ,0.6066 +  0.0463)

(0.5603,0.6529)

final answer:-

90% confidence interval for the proportion of fans who bought food from the concession stand

(0.5603,0.6529)

Answer:

(B)24 Units

Step-by-step explanation:

Triangle MNO is an equilateral triangle with sides  measuring [tex]16\sqrt{3}[/tex] units.

The height divides the base into two equal parts of lengths [tex]8\sqrt{3}[/tex] units.

As seen in the diagram, we have a right triangle where the:

Using Pythagoras Theorem

[tex](16\sqrt{3})^2=(8\sqrt{3})^2+h^2\\16^2*3-8^2*3=h^2\\h^2=576\\h=\sqrt{576}\\ h=24$ units[/tex]

The height of the triangle is 24 Units.

The height of the given equilateral triangle is gotten as;

B: 24 units

Equilateral Triangles

The height of an equilateral triangle starts from the mid - point of the base to the ap ex.

Now, if the sides of the equilateral triangle are 16√3 units, then it means we can use pythagorean theorem to find the height h.

Half of the base will be; ¹/₂ * 16√3 = 8√3

Thus, the height h can be calculated from;

h²= ((16√3)² - (8√3)²)

h² = 3(256 - 64)

h² = 576

h = √576

h = 24 units

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