Tammy is at the dentist's office waiting on her appointment. She notices that the 6-inch-long minute hand is rotating around the clock and marking off time like degrees on a unit circle. Part 1: How many radians does the minute hand move from 1:20 to 1:55? (Hint: Find the number of degrees per minute first.)

Answers

Answer 1
There are 12 five minutes in one hour and 1 hour correspond to 360°, then each 5 minutes represents 360/12 = 30°

From 1:20 to 1: 55 we have 35 minutes or 7 x 5 minutes or

7 x 30° = 210° 

To convert degree into radian, we apply the following formula:

degree/180° = radian/π

210/180 = r/π or (cross multiplication) →Radian = (π x 210/180

→ Radian = 7π/6 (simplify by 30)

Answer 2

Answer:

Part 1:

In order to find how many radians the minute hand moves from 1:20 to 1:55, we need to remember that there are 60 minutes in an hour (clock) and there are 360 degrees in the clock since the clock is a circle. After dividing 360 by 60, we find that each minute is equal to 6 degrees. After that, we can subtract the times, which tells us that there are 35 minutes between 1:20 and 1:55. Using this we can just multiply this out, to get 35 times 6, which is equal to 210 degrees. We can get our final answer by converting this into degrees. Since one 1 degree is about 0.0174, we can set up a proportion. After solving, we will get that the minutes hand moves 3.555 radians in total.


Related Questions

Candidates for employment at a city fire department are required to take a written aptitude test. scores on this test are normally distributed with a mean of 280 and a standard deviation of 60. a random sample of nine test scores was taken.

Answers

Final answer:

The question asks for statistical analysis of aptitude test scores for firefighters, requiring an understanding of probability, statistics, normal distribution, and sample observations.

Explanation:

The question concerns the statistical analysis of employment test scores, specifically discussing aptitude tests for a firefighter position. These tests are normally distributed with a given mean and standard deviation. Understanding this concept is an application of probability and statistics, which involves analyzing data to make inferences about a population based on sample observations. Knowledge of the normal distribution and its properties is key to answering questions about what proportion of test scores fall within certain intervals, or to calculate probabilistic outcomes such as percentile ranks or cutoff scores.

An accepted relationship between stopping distance, d in feet, and the speed of a car, in mph, is d(v)=1.1v+0.06v^2 on dry, level concrete.

a) how many feet will it take a car traveling 45 mph to stop on dry, level concrete?
b) if an accident occurs 200 feet ahead, what is the maximum speed at which one can travel to avoid being involved in the accident?

Answers

Final answer:

The distance it will take a car traveling at 45 mph to stop on dry, level concrete is 171 feet. If an accident occurs 200 feet ahead, one can travel at a maximum speed of approximately 58.4 mph to avoid the accident. The answers were calculated using the given equation for stopping distance and the speed of the car.

Explanation:

To address this question, we first need to make use of the equation d(v)=1.1v+0.06v²

First, let's answer part a): to find how many feet it will take a car traveling at 45 mph to stop, we simply substitute v with 45 in the equation, resulting in d = 1.1(45) + 0.06(45)² = 49.5 + 121.5 = 171 feet.

For part b), we need to solve the equation for v when d is equal to 200 feet. This is a quadratic equation (1.1v + 0.06v^2 = 200) and can be solved using the quadratic formula, or a method such as factoring or completing the square. Using the quadratic formula, we find that v ≈ 58.4 mph.

Therefore, if an accident happens 200 feet ahead, the maximum speed at which one can travel to avoid being involved in the accident is approximately 58.4 mph.

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a) At 45 mph, stopping distance is 171 feet. b) To avoid a 200-ft accident, max speed is 48.33 mph.

a) To find the stopping distance when the car is traveling at 45 mph, substitute v = 45 into the equation:

d(45) = 1.1(45) + 0.06(45)^2

= 49.5 + 121.5

= 171 feet

b) To find the maximum speed to avoid a 200 feet accident, set d(v) = 200 and solve for v:

1.1v + 0.06v^2 = 200

0.06v^2 + 1.1v - 200 = 0

Using the quadratic formula:

v = [-b ± √(b^2 - 4ac)] / (2a)

v = [-1.1 ± √(1.1^2 - 4(0.06)(-200))] / (2 * 0.06)

v ≈ [-1.1 ± √(1.21 + 48)] / 0.12

v ≈ [-1.1 ± √49.21] / 0.12

Now, solve for v:

v ≈ [-1.1 ± 7] / 0.12

This gives two solutions:

v ≈ (-1.1 + 7) / 0.12 ≈ 48.33 mph (Approx.)

v ≈ (-1.1 - 7) / 0.12 ≈ -63.33 mph (Not applicable)

Therefore, the maximum speed to avoid the accident is approximately 48.33 mph.

round 26,891 to the nearest ten-thousands place

Answers

30,000
I hope this helps.

Laura sends an average of 27 text messages per month to each of f friends. Her cell phone provider charges her a flat rate of $3.50 per month and $0.04 per text message. The function t(f) gives the total number of text messages Laura sends each month to f friends, and g(t) gives the amount Laura is charged by her cell phone provider for t text messages.
find t(f) and g(t)

Answers

t(f) = 27*f

g(t) = $0.04*27*f

without the value for f (the number of friends) that is the farthest this can be solved.

A manufacturing company has developed a cost model, C(X)= 0.15x^3 + 0.01x^2 +2x +120, where X is the number of item sold thousand. The sales price can be modeled by S(x) + 30- 0.01x. Therefore revenues are modeled by R(x)= x*S(x).
The company's profit, P(x) = R(x)-C(x) could be modeled by
1. 0.15x^3+ 0.02x^2- 28x+120
2. -0.15x^3-0.02x^2+28x-120
3. -0.15x^3+0.01x^2-2.01x-120
4. -0.15x^3+32x+120

Answers

Profit is calculated by subtracting the total cost from the total revenue as expressed in the equation given above as,
    P(x) = R(x) - C(x)

If we are to substitute the given expression for each of the terms, we have, 
   P(x) = x(S(x)) - C(x)
Substituting,
   P(x) = x(30 - 0.01x) - (0.15x³ + 0.01x² + 2x + 120)

Simplifying,
   P(x) = 30x - 0.01x² - 0.15x³ - 0.01x² - 2x - 120

Combining like terms,
   P(x) = -0.15x³ - 0.02x² + 28x - 120

The answer to this item is the second among the choice, number 2. 

tiffany and Adele sold cookies and brownies to raise money for their school. They sold a total of 25 sweets. If each cookie costs 1$ and the brownies cost a 1.50 each and they made a total of 32$, how many did each sell?

Answers

By setting up a system of equations based on the total number of sweets sold and the total amount of money made, we find that Tiffany and Adele sold 11 cookies and 14 brownies.

To determine how many cookies and brownies Tiffany and Adele sold, we can set up a system of equations. Let's define the number of cookies sold as x and the number of brownies sold as y.

The first equation comes from the total number of sweets sold: x + y = 25. The second equation is based on the total amount of money made: 1*x + 1.50*y = 32.

Solving this system of equations will give us the number of each type of sweet sold.

To solve the system of equations, we can use substitution or elimination. I'll use substitution:

From the first equation, we can express y as y = 25 - x.Next, we substitute y in the second equation: 1*x + 1.50*(25 - x) = 32.Simplify and solve for x: X + 37.50 - 1.50x = 32, which simplifies further to 0.50x = 5.50. Divide both sides by 0.50 to find x = 11.Now that we have the value for x, substitute it back into the equation for y: y = 25 - 11 = 14.

Tiffany and Adele sold 11 cookies and 14 brownies.

On a bike trip, Erika rides 5 miles in the first 30 minutes and 13 miles in the next hour. What is her average rate of speed?

Answers

Her average speed was 12 miles per hour. Total distance over total time.

Answer:

12 miles per hour

Step-by-step explanation:

Speed is the ratio of distance travelled to the time used.

The total distance covered = (5 + 13) miles

                                             = 18 miles

The whole journey took 1 hour + 30 minutes = 1.5 hours

                    Average rate of speed = [tex]\frac{total distance covered}{total time taken}[/tex]

                                                           = [tex]\frac{18 miles}{1.5 hours}[/tex]

                                                           = 12 miles per hour

Therefore, her average rate of speed is 12 miles per hour.

Line F passes through the points (7, 13) and (9, -3). What is the slope of a line parallel to line F?


A) -8

B) -1/8

C) 1/8

D) 8

Answers

13+3/7-9
16/-2
-8
A) -8

a bicycle costs $198.99. If the sales tax is 8%, what will be the final cost of the bicycle including tax (in dollars)?

Answers

If the sales tax is 8%, then you multiply the previous cost by (1 + 0.08).

198.99 x (1.08) = 214.91.

Final Cost: $214.91.

what is 15% of 60 using a model to prove your answer

Answers

To find this out, the first step would be to turn the percent into a decimal:

15% -----> .15 (Divide by 100)

Then multiply the number by .15:

60 x .15 = 9 

So 15% of 60 is 9.

Hope this helps!
15% of 60  is calculated by converting 15% into the decimal fraction 0.15 and then mult. 60 by this 0.15:  9.

15% of 60 is 9.

Note that 10% of 60 is 6; 20% of 60 is 12; so 15% of 60 is 9 and this makes sense.

The shorter leg of a 30°- 60°- 90° right triangle is 12.5 inches. How long are the longer leg and the hypotenuse?

Answers

if u know the short leg...which we do, it is 12.5......to find the hypotenuse, double it......so the hypotenuse is : 12.5 * 2 = 25 inches.....and to find the longer leg, multiply shorter leg by square root of 3.....12.5 * sqrt 3 = 21.65 (thats rounded)
A right angle with angles 30° - 60° - 90° is cut from an equilateral triangle, for example as shown below in triangle ABC

The shorter leg would be the side BD (or CD) since D is the midpoint of side BC

We are to find the length of side AD (which is the height of the triangle ABC) and the hypotenuse AB (or AC ⇒ depends on which right angle triangle that you'd want to work with)

Since we know the three angles in the right angle triangle ABD, we can use the trigonometry ratio

Side AD is the opposite of the angle 60° and we know the length of side that is adjacent to 60° so we'll use the tangent ratio

tan (x°) = opposite ÷ adjacent
tan (60°) = AD ÷ 12.5
√3 = AD ÷ 12.5
AD = 12.5 × √3
AD = 21.65

We can then use the Pythagoras theorem to work out AB

AB² = AD² + BD²
AB² = 12.5² + 21.65²
AB² = 624.9725
AB = √624.9725
AB = 25 (rounded to 2 significant figures)



Ummmmmmmmmmmm. What is 90% of 550?

Answers

550 *0.9 = 495 Does this make sense? Do you need any further explanation?
To do this problem you would set up an equation, x/550=90/100. You would then multiply 550 by 90 and then divide that answer by 100. This would get you the answer 495.

$720, 4.25%, 3 months

Answers

Final answer:

The interest earned on $720 at a rate of 4.25% over a period of 3 months is $30.60.

Explanation:

The question is asking about $720, at an interest rate of 4.25%, over a period of 3 months.

To calculate the interest earned, we multiply the principal amount ($720) by the interest rate (4.25%) and divide by 100:

Interest = ($720 * 4.25) / 100 = $30.60

Therefore, the interest earned on $720 at a rate of 4.25% over a period of 3 months is $30.60.

20 yards for $30.00
35 yards for $45.00
50 yards for $70.00
65 yards for $85.00

You work for a dress makers. Your boss sends you to the fabric store to buy blue fabric. She tells you to buy the best deal. What is the savings per unit between the best deal and worst deal?


A) $55.00
B) $27.00
C) 2 cents
D) 21 cents

Answers

A) $55.00
65 yards for $85.00 subtract
20 yards for $30.00
85-30=55

Answer:

D) 21 cents

Step-by-step explanation:

Best deal: $45.00/35 = 1.29 each

Worst deal: $30.00/20 = 1.50 each

1.50 - 1.29 = 21 cents

A fisherman drops his net to a depth of -8 feet below the surface of the water. How far does he need to raise the net to bring it back to the surface of the water?

Answers

It has to be positive 8 feet.

The function d(x) = 1375 − 110x represents the distance (in miles) a high-speed
train is from its destination after x hours. (Section 3.3)
a. How far is the train from its destination after 8 hours?
b. How long does the train travel before reaching its destination?

Answers

We are given the function:

d (x) = 1375 – 110 x

 

A. To solve for the distance between the train and its destination after 8 hours, we simply have to plug in, x = 8 into the equation. That is:

d (x) = 1375 – 110 * 8

d (x) = 495 miles

Therefore the train is now only 495 miles away from the destination.

 

B. To solve for the total time needed to reach its destination, we must set d = 0 and find for the value of x:

0 = 1375 – 110 x

110 x = 1375

x = 12.5 hours

Therefore it takes 12.5 hours for the train to reach its destination.

A group of 48 friends meets for lunch. They greet each other by exchanging fist bumps. How many fist bumps are exchanged if each friend must bump with each of the 47 ​others?

Answers

2256 fist bumps. 47 fist bumps x 48 friends is 2256 fist bumps.

Answer:

The correct answer is 1128 fist bumps exchanged.

Step-by-step explanation:

Each friend exchanges 47 fist bumps, one for each friend on the group.  

If the group is made up of 48 friends, and each exchange is done by 2 friends, you have to divide by 2 each interaction:

(48 friends * 47 first bumps) / 2 friends = (2256 friends per first bumps exchanged) / 2 friends = 1128 fist bumps exchanged.

How do you find absolute extrema for a function?
f(x)= (8+x)/(8-x); Interval of [4,6]

Answers

[tex]\bf f(x)=\cfrac{8+x}{8-x}\implies \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{1(8-x)-(8+x)(-1)}{(8-x)^2}}\implies \cfrac{dy}{dx}=\cfrac{16}{(8-x)^2}[/tex]

now, we get critical points from zeroing out the derivative, and also from zeroing out the denominator, but those at the denominator are critical points where the function is not differentiable, namely a sharp spike or cusp or an asymptote.

so, from zeroing out the derivative we get no critical points there, from the denominator we get x = 8, but can't use it because f(x) is undefined.

therefore, we settle for the endpoints, 4 and 6,

f(4) =3    and      f(6) = 7

doing a first-derivative test, we see the slope just goes up at both points and in between, but the highest is f(6), so the absolute maximum is there, while we can take say f(4) as the only minimum and therefore the absolute minumum as well.

a country's people consume 7.7 billion pounds of candy per year Express this quantity in terms of pounds per person per month. note that the population of the country is 303 million

Answers

Ratio: 303 million to 7.7 billion. Divide 303 million by 7.7 billion ?...

A square with an area of 49 in2 is rotated to form a cylinder. What is the volume of the cylinder

Answers

343 pi in^3 ; exact volume 1078 in^3 ; Approximate volume Since it's not specified, I will assume the axis of rotation will be one edge of the square. With that in mind, here's the solution. Since the shape specified is a square with an area of 49 in^2, the length of any edge will be sqrt(49) = 7 inches. Since we're rotating along one edge, we will create a cylinder with a radius of 7 inches and a height of 7 inches. The volume will be the area of a circle with a 7 inch radius multiplied by the height of the cylinder. So V = pi*h*r^2 V = pi*7*7^2 V = pi*7*49 V = pi*343 V = 343pi V = 1077.56628; approximately. So the exact volume is 343pi in^3 and an approximate volume is 1078 in^3

Use what you know about compound statements to determine if "A piece of paper is an object that can be drawn on " would be considered a good definition. Explain.

Answers

 The statement would not be considered a good definition. The statement is a biconditional statement that can be written as the conjunction of a conditional statement and its converse. We can write it as "If an object is a piece of paper, then it can be drawn on, and if an object can be drawn on, then it is a piece of paper.” The conditional statement is true, but its converse is not. A counterexample would be that you can draw on a marker board. A good definition requires that both the conditional statement and its converse are true.

A compound statement can be represented in symbolic logic as p ∧ q

The statement "A piece of paper is an object that can be drawn on" is not a compound statement

Reason:

A compound statement is a statement that consists of two simple statements combined into one statement

The given statement is "A piece of paper is an object that can be drawn on"

The given statement is made up of just one subject which is 'a piece of paper'. The statement also has just one predicate, which is 'is an object that can be drawn on'

Therefore;

The given statement is a simple statement and not a compound statement

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Solve using the standard algorithm 232 * 4 =

Answers

It's = to 928 you just have to multiply 232 * 4
what is (),., * and x are multiplication sings
HOPE THIS HELPS

can someone help me please

Answers

to convert feet to miles you would use a ratio of feet over miles

 so the answer would be B

an electric generator can power 3550 watts of electricity. write and solve an equation to find how many 75 watt light bulbs a generator could power.

Answers

3550/75=47+1/3 
your generator can power 47 light bulbs

The generator can power up to 47 light bulbs of 75 watts each. This is calculated by dividing the total power output of the generator by the power rating of a single light bulb.

To solve this question, let's set up the equation:

Total power of generator = Number of bulbs * Power rating of each bulb

Given the generator can produce 3550 watts and each light bulb consumes 75 watts, we need to find the number of bulbs (N) the generator can power. So the equation will be:

3550 = N * 75

To find N, we can rearrange the equation and solve for N:

N = 3550 / 75

Calculating this gives:

N = 47.33

Since the number of light bulbs must be a whole number, the generator can power up to 47 light bulbs.

Summary

The generator can power up to 47 light bulbs of 75 watts each.

Which data set is represented by the box plot below?

A. 10, 10, 10, 14, 23, 25, 26, 28, 30, 31, 34, 34, 44, 50, 50
B. 10, 10, 11, 12, 14, 18, 18, 18, 19, 20, 22, 26, 36, 42, 50
C. 10, 14, 18, 18, 19, 22, 31, 32, 33, 34, 40, 42, 43, 46, 50
D. 10, 14, 17, 24, 27, 32, 34, 34, 37, 38, 39, 39, 40, 43, 50

Answers

Reading the box plot, we have

The lowest value = 10
The highest value = 50
The middle value (median) = 28

The data set that gives the box plot value is set A


Describe the transformation of the graph from f(x) to g(x)

1) f(x)=2x+1
g(x)=2x+4

2) f(x)=x+3
g(x)=-x+1

3) f(x)=x^2
g(x)=(x-1)^2 +3

Answers

Final answer:

Transformations of the functions include a vertical shift, reflection and vertical shift, and a horizontal and vertical shift for three different pairs respectively. Specific (x, y) data pairs demonstrate these transformations on the graphs.

Explanation:

We have three functions, f(x) and g(x), and we will describe the transformation from f(x) to g(x) for each:

Vertical Shift: For the functions f(x)=2x+1 and g(x)=2x+4, g(x) represents a vertical shift up by 3 units from f(x).Reflection and Vertical Shift: For f(x)=x+3 and g(x)=-x+1, g(x) is f(x) reflected across the x-axis (due to the negative sign before x) and then a vertical shift down by 2 units.Horizontal Shift and Vertical Shift: Lastly, from f(x)=x^2 to g(x)=(x-1)^2+3, the graph of g(x) is the graph of f(x) shifted to the right by 1 unit and then up by 3 units.

The transformations can be sketched by plotting specific (x, y) data pairs and shifting the graphs accordingly.

Which are zeros of the following polynomial?

6x 2 - 11x - 10 = 0

A x = 6, x = 10
B x = ; x =
C x = -2; x = 5
D x = ; x =

Answers

Answer:

x = -2/3; x = 5/2.

Step-by-step explanation:

6x 2 - 11x - 10 = 0

Use the 'ac' method:

6 * -10 = -60. We need 2 numbers whose product is -60 and whose sum is -11.

That would be -15 and +4.  So we write:

6x^2 - 15x + 4x - 10 = 0      Factor by grouping:

3x(2x - 5) + 2(2x - 5) = 0

(3x + 2)(2x - 5) = 0

x = -2/3; x = 5/2.

Suppose that f(t) is continuous and twice-differentiable for t≥0. Further suppose f″(t)≥9 for all t≥0 and f(0)=f′(0)=0. Using the Racetrack Principle, what linear function g(t) can we prove is less than or equal to f′(t) (for t≥0)?

Answers

The linear function g(t) = 9t satisfies the condition g(t) ≤ f′(t) for t ≥ 0, as guaranteed by the Racetrack Principle.

What linear function g(t) satisfies g(t) ≤ f′(t) for t ≥ 0?

Racetrack principle is a mathematical concept that involves bounding a function based on its second derivative and initial conditions.

Given data:

f(t) is continuous and twice-differentiable for t ≥ 0.f″(t) ≥ 9 for all t ≥ 0.f(0) = f′(0) = 0.

We want to find a linear function g(t) that satisfies g(t) ≤ f′(t) for t ≥ 0.

Since f″(t) ≥ 9 for all t ≥ 0, we will use Racetrack Principle to establish an upper bound for f(t) based on its second derivative:

= f(t) ≤ (1/2) * 9 * t^2

= 4.5t^2

Now, we need to find a linear function g(t) such that g(t) ≤ f′(t) for t ≥ 0. To do this, we differentiate the upper bound we found for f(t):

= f′(t) ≤ 9t

So, we can see that g(t) = 9t satisfies g(t) ≤ f′(t) for t ≥ 0.

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Final answer:

The Racetrack Principle can be used to find a linear function that is less than or equal to f'(t). We can prove this by comparing the initial conditions and the second derivative of the functions.

Explanation:

The Racetrack Principle states that if two objects are traveling at the same initial and final velocities, but one of them has a greater magnitude of acceleration, then the object with the greater acceleration will overtake the other or be ahead of it at some point in time.



In this case, since f''(t) = 9 and f(0) = f'(0) = 0, we can use the Racetrack Principle to find a linear function g(t) that is less than or equal to f'(t).



Let g(t) = 3t (since 3 is the square root of 9). We can prove that g(t) is less than or equal to f'(t) by showing that g(0) = f'(0) and g''(t) ≥ f''(t) for all t ≥ 0.

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1.5(−2.4+(−5.3)) ​please hurry

Answers

1.5(-2.4+(-5.3))
1.5(-7.7)

Your answer is...
-11.55
1.5(-2.4+(5.3))
=1.5(-2.4-5.3)
=1.5(-7.7)
=-11.55

Daniel is completing a home project. He needs 13 pieces of wood, each 112 feet long, to complete the project. How much wood does Daniel need to complete his home project? 823 ft

Answers

Answer:

its a

Step-by-step explanation:

Answer:

19 1/2 ft

Step-by-step explanation:

hope this helped

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