Determine the angular velocity in radians per second of 4.9 revolutions in 5 seconds. Use 3.14 for pi.
a) 89 miles per hour
b) 117 miles per hour
c) 149 miles per hour
d) 129 miles per hour

If the coordinate B is reflected over x-axis, the resulting coordinate will be (5, -9)

If an image is reflected over the x-axis, the resulting coordinate will be (x, -y). The reflections shows the mirror image of a figure.

Given the coordinate B before reflection as (5, 9)> If the coordinate is reflected over x-axis, the resulting coordinate will be (5, -9)

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d = dimes

q = quarters

d=10+q

0.25q +0.10d = 3.45

0.25q + 0.10(10+q) = 3.45

0.25q + 1 +0.10q =3.45

0.35q=2.45

q = 2.45/0.35 = 7

d = 10+7 =17

0.25*7=1.75, 17*0.10 = 1.70, 1.75+1.70 = 3.45

she has 7 quarters and 17 dimes for a total of 24 coins

Final answer:

The correct answer is a ratio of 4 to 7, representing the ratio of female penguins to the total number of penguins in the zoo.

Explanation:

We're given that there are 3 male penguins for every 4 female penguins in a zoo.

To find the ratio of females to the total number of penguins, we first have to add up the total number of penguins, which is 3 males + 4 females = 7 penguins in total.

Now, we can express the ratio of females to the total number of penguins. There are 4 females out of 7 total penguins, so the ratio is 4 females to 7 penguins in total.

Therefore, the correct answer to the student's question is 4 to 7.

Answer:

3(x+12)

-----------

10

(three times x plus twelve OVER ten)

Step-by-step explanation:

To determine if a relation is a function, check for repeated x-values. The relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.

In order for a relation to represent a function, each input (x-value) must correspond to exactly one output (y-value). We can determine if a relation is a function by checking for any repeated x-values. If there are no repeated x-values, then the relation is a function. Let's apply this to the given relations:

The relation {(1,-3),(-2,0),(1,4)} represents a function because each x-value is unique.

The relation {(-2,0),(3,0),(-2,1)} does not represent a function because there is a repeated x-value (-2).

The relation {(3,-8),(-2,0),(4,1)} represents a function because each x-value is unique.

The relation {(4,12),(4,13),(-4,14)} does not represent a function because there is a repeated x-value (4).

So, the relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.

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Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.

The total central angle around the wheel is 2π.

Therefore the central angle between two cars is

(2π)/16 = π/8 = 0.39 radians (nearest hundredth)

The arc length between two cars is

s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)

The area of a sector formed by two cars is

(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)

Answers: (to the nearest hundredth)

Between two cars,

Central angle = 0.39 radians (or 71.4°)

Arc length = 7.85 ft

Area of a sector = 78.54 ft²

Answer:

b edge

Step-by-step explanation:

Answer:

Maria purchased total 8 CDs.

Step-by-step explanation:

At a particular music store, CDs are on sale at $13.00 for the first one purchased and $10.00 for each additional disc purchased.

Maria spends = $83.00

She purchased her first CD for = $13.00

Now balance of her charge = 83.00 - 13.00 = $70.00

other CDs are purchased for $10.00

Therefore, 70.00 ÷ 10.00 = 7 CDs

Total CDs = 7 + 1 = 8 CDs

Maria purchased total 8 CDs.

Answer:

Volume of the cone = 7 unit³

Step-by-step explanation:

Soda can has the shape of a cylinder.

Volume of soda can = πr²h

where r = [tex]\frac{6}{2}=3[/tex] units

and volume = 21 unit³

We put the values in the formula to get the value of h.

21 = πr²h

[tex]h=\frac{21}{\pi r^{2} }[/tex]

Now If we fit a cone inside the can, radius of the cone will be equal to the radius of the cylinder and height of the cylinder will be equal to the height of the cone fit inside.

By the formula of volume of cone

Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]

= [tex]\frac{1}{3}\pi r^{2}( \frac{21}{\pi r^{2} })[/tex]

= [tex]\frac{21}{3}=7[/tex] units³

Volume of the cone is 7 unit³

since the 6th comic will be last you need to know how many different ways to schedule 5 comics

5x4x3x2 = 120

 there are 120 different ways.

Using trigonometric functions, specifically the tangent function, we create two equations corresponding to two right triangles formed by the lines of sight from the ground floor and from 60 feet high in the elevator. Solving those equations simultaneously, we can calculate that the height of the building across the street is approximately 149 feet.

This is a trigonometry problem where we're going to establish two right triangles with the elevator as one side, the building across the street as another (the one we're trying to find), and the line of sight as the hypotenuse. From the ground, we form a triangle with the angle of elevation of 51 degrees. Then from 60 feet above the ground, we form another triangle with an angle of elevation of 34 degrees.

Here, we apply tangent of an angle which equals the opposite over adjacent sides in a right triangle. So, we get tan(51) = h/x and tan(34) = (h-60)/x. We have two unknowns here: 'h' which is the height of the building and 'x' the distance from the elevator to the building. Solving these equations simultaneously, we can find 'h'.

If we solve these equations, we'll get 'h' equals approximately 149 feet (rounding to the nearest foot). So, the building across the street is around 149 feet tall.

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The set of outcomes is {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}. The total number is 8.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

All outcomes in flipping 3 coins then the number of samples will be:-

Sample space of all outcomes

Sample space = {HHH,THH, HTH, HHT, TTT, HTT, THT, TTH} = 8 =All possible outcomes.

Sample space of all favorable outcomes (more tails than heads)

Favourable outcomes= {TTT, HTT, THT, TTH} = 4 = All favorable outcome.

Therefore, the set of outcomes is {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}. The total number is 8.

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The solution would be like this for this specific problem:

Area = L * W = 600 
Length = W + 25

Substitute and solve for "W":
(W + 25)W = 600

w^2 + 25w - 500 = 0
(w - 15) (w + 40) = 0
Positive solution:
Width = 15 meters
Length = 15 + 25 = 40 meters

To add, the minimum number of coordinates needed to specify any point within it is the informal definition of the dimension of a mathematical space.

The cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]

In triangle ABC, where angle ABC is a right angle (90 degrees) and sides AB, BC, and AC are given as 6, 8, and 10 units respectively, we can use the cosine and cotangent functions to find the cotangent of angle ABC.

The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.

In this case,[tex]\(\cos(\angle ABC) = \frac{BC}{AC} = \frac{8}{10} = \frac{4}{5}\).[/tex]

The cotangent [tex](\(\cot\))[/tex] of an angle is the reciprocal of the tangent (tan).

The tangent is the ratio of the opposite side to the adjacent side.

Therefore,[tex]\(\cot(\angle ABC) = \frac{1}{\tan(\angle ABC)}\).[/tex]

Since [tex]\(\tan(\angle ABC) = \frac{AB}{BC} = \frac{6}{8} = \frac{3}{4}\)[/tex], we can find the cotangent:

[tex]\[ \cot(\angle ABC) = \frac{1}{\tan(\angle ABC)} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \][/tex]

Therefore, the cotangent of the angle is [tex]\(\frac{4}{3}\).[/tex]

The probable question may be:

The cosine of a certain angle is 4/5. What is the cotangent of the angle?

In triangle ABC , Angle ABC=90 degree, AB=6, BC=8 AC=10

Final answer:

The cosine of an angle being 4/5 means that the ratio of the adjacent side to the hypotenuse in a right triangle is 4/5.

Explanation:

The given question states that the cosine of an angle is 4/5. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. So, if we have a right triangle with an angle A, and the cosine of A is 4/5, it means that the ratio of the length of the adjacent side to the hypotenuse is 4/5.

Thus, we can say that if the length of the adjacent side is 4 units, then the length of the hypotenuse would be 5 units, assuming the units are consistent. This relationship holds true for any right triangle with an angle whose cosine is 4/5.

For example, if we have a right triangle with an adjacent side of 8 units, then the hypotenuse would be 10 units.

Final answer:

To determine the distance from the ends of the couch to the nearest wall, convert all measurements to inches, find the difference between the room and couch lengths, and divide by two. The ends of the couch will be 0.75 feet or 9 inches from the nearest wall.

Explanation:

The question involves determining the distance from the ends of a couch to the nearest wall when the couch is centered in a 12 feet by 12 feet room. The couch is 10 feet and 6 inches long.

To solve this, first convert the couch length to inches. 10 feet is 120 inches, and adding 6 inches gives us a total of 126 inches for the couch length. Since 1 foot equals 12 inches, the room's length in inches is 12 feet times 12 inches per foot, which equals 144 inches.

Now, to find the distance from each end of the couch to the nearest wall, we subtract the couch length from the room's length:

Divide the difference by 2 to get the distance from each end of the couch to the wall:

Finally, convert this distance back to feet:

Therefore, each end of the couch will be 0.75 feet, or 9 inches, from the nearest wall when the couch is centered in the room.

the figure is an equilateral triangle, which all angles are 60 degrees

 angle 3 divides a 60 degree angle in half so angle 3 = 30 degrees

 the base is a right triangle which is 90 degrees

 90+30 = 120

180-120 = 60

 Angle 2 is 60 degrees