The length of the minute hand is 150% of the length of the hour hand.
In one hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Round your answer to the nearest tenth.
Answers
[tex]s=r\cdot\theta[/tex]
where [tex]\theta[/tex] is the central angle in radians
In one hour, the hour hand makes 1/12 of a revolution (2π radians), so travels ...
[tex]s_{h}=(30\,mm) \times \frac{1}{12}\cdot 2\pi=5\pi\,mm[/tex]
In one hour, the minute hand makes 1 full revolution, so travels
[tex]s_{m}=(1.5 \cdot 30\,mm) \times 2\pi = 90\pi\,mm[/tex]
The difference in distance traveled is ...
[tex]s_{m}-s_{h}=(90\pi-5\pi)\,mm=85\pi\,mm \approx 267.0\,mm[/tex]
In an hour, the minute hand, which is 1.5 units long, travels a full revolution or approximately 9.4 units, while the hour hand, 1 unit long, covers one-twelfth, or about 0.5 units. Therefore, the minute hand travels approximately 7.9 units more than the hour hand.
Explanation:This question can be solved by first examining the distance each hand travels. In an hour, the minute hand completes a full revolution around the clock face, moving a distance equal to the clock's circumference. If we call the length of the minute hand 1.5 units, then its distance traveled is 2π(1.5).
In contrast, the hour hand moves onto the next hour, covering on-twelfth of the clock's face, or 2π(1/12) using a length of 1 unit for the hour hand. Substract the second measure from the first to find the difference. Thus, the minute hand travels about 7.9 units farther than the hour hand.
Learn more about Circumference here:https://brainly.com/question/37011717
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Related Questions
A tortoise travels 11 feet in one hour. In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour. How far does this tortoise travel in 6 hours?
Answers
The distance that a tortoise will cover in 6 hours is:
16.47735 feet.
Step-by-step explanation:It is given that :
A tortoise travels 11 feet in one hour.
In each subsequent hour, the tortoise travels one-third the distance it traveled in the previous hour.
This means that in 2 hours it travels a total of:[tex]11+\dfrac{1}{3}\times 11\ feet[/tex]
which is equal to:
[tex]11\times \dfrac{4}{3}\ feet=\dfrac{44}{3}\ feet[/tex]
in the 3 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11\ feet[/tex]
In 4 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11\ feet[/tex]
In 5 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11\ feet[/tex]
In 6 hours it will travel a total of:[tex]=11+\dfrac{1}{3}\times 11+\dfrac{1}{3^2}\times 11+\dfrac{1}{3^3}\times 11+\dfrac{1}{3^4}\times 11+\dfrac{1}{3^5}\times 11\ feet=16.47735\ feet[/tex]
Hence, the answer is:
16.47735 feet
If jeremy gives his horse 12 gallons of water each day. How many one quart pails of water is that
Answers
4 quarts= 1 gallon
= 12 gallons * 4 quarts in 1 gallon
= 48 quarts
ANSWER: He would use 48 quart pails of water per day to give his horse 12 gallons of water.
Hope this helps! :)
Sara got 88, 90, 75, 78, 100, 54, 90, 100, 45, and 60 on her English tests. Lee got 77, 67, 99, 79, 100, 65, 79, 89, 58, and 67 on his English tests. What is the mean of Sara's English tests? What is the mean of Lee's English tests? please answer both questions
Answers
Sara's mean: 78
Lee's mean: 78
88, 90, 75, 78, 100, 54, 90, 100, 45 and 60
add them all up which is 780
then divide by the number of test results you have which is 10
780/10
Sara's mean is 78 on her test scores.
Lee:
77, 67, 99, 79, 100, 65, 79, 89, 58, 67
add them all up which is 780
divide by the number of test results 10
780/10
Lee's mean is 78 on her test scores.
Morgan bought a pair of shoes at a sale of 25%. If the amount she paid was $1000, find the marked price.
Answers
250=the discount on the product
1000-250= 750$
Your answer would be 750$
The marked price of the shoes that Morgan bought at a 25% discount for $1000 is $1333.33. The calculation was done by dividing the discounted price by (1 minus the discount percentage in decimal form).
The question involves finding the marked price of an item given the discounted price and the discount percentage. Morgan paid $1000 for a pair of shoes after getting a 25% discount. To find the original marked price, we can use the formula:
Discounted Price = Marked Price × (1 - Discount Percentage)
Here, the Discounted Price is $1000, and the Discount Percentage is 25%, which is equivalent to 0.25 in decimal form.
By rearranging the formula to solve for the Marked Price, we get:
Marked Price = Discounted Price ÷ (1 - Discount Percentage)
Now we can calculate:
Marked Price = $1000 ÷ (1 - 0.25) = $1000 ÷ 0.75 = $1333.33
Therefore, the marked price of the shoes was $1333.33.
Matt has a rectangular garden that is 10 ft wide and 24 Ft long . He wants to build a fence from one corner to the opposite corner . How many feet of fence does Matt need ???
Answers
The length of the fence Matt needs is 26 ft.
Explanation:To find the length of the fence, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the width of the garden is one side of the right triangle, the length of the garden is the other side, and the fence is the hypotenuse.
So, we can calculate the length of the fence as follows:
Length of the fence = √((Width)^2 + (Length)^2)
Substituting the given values, we get:
Length of the fence = √((10 ft)^2 + (24 ft)^2)
Length of the fence = √(100 ft^2 + 576 ft^2)
Length of the fence = √676 ft^2
Length of the fence = 26 ft
Final answer:
To calculate the length of fence needed for Matt's garden, the Pythagorean theorem is used, resulting in needing a fence that is 26 feet long.
Explanation:
Calculating the Fence Length Across a Rectangular Garden
Matt has a rectangular garden with dimensions of 10 feet in width and 24 feet in length. To find the length of the fence that Matt needs to build from one corner of the garden to the opposite corner, we will use the Pythagorean theorem, since the corners of the garden and the fence form a right triangle.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The formula is c² = a² + b².
For Matt's garden, the length is 'a' = 24 ft and the width is 'b' = 10 ft. Plugging these values into the formula, we get:
c² = 24² + 10²
c² = 576 + 100
c² = 676
We then take the square root of both sides to solve for 'c':
c = √676
c = 26 ft
Therefore, Matt needs 26 feet of fence to reach from one corner of the garden to the opposite corner.
i need help
Fundraising your school raised 125% of its fundraising goal the school raised $6750.what was the goal
Answers
6750 = 1.25 * 100%
6750/1.25 = 100%
5400 = 100%
Polygon ABCD is the result of a translation of polygon EFGH . AB¯¯¯¯¯ is parallel to DC¯¯¯¯¯ in the pre-image. Drag the answers to the boxes to correctly complete the statement about this image. The corresponding segments and in the image are
Answers
Answer: The corresponding segments in the in the figure and the image are :
AB and EF,
AD and EH,
CD and HG,
BC and FG,
Step-by-step explanation:
Given: Polygon ABCD is the result of a translation of polygon EFGH .
AB is parallel to DC in the pre-image.
We know that a translation is a rigid transformation which produces congruent images such that the corresponding segments have equal lengths.
So from the given statements the corresponding segments in the figure and the image are :
AB and EF,
AD and EH,
CD and HG,
BC and FG,
The family room floor in Zacks home has a rectangular area rug that measures 6.5 feet by 9 feet the floor is rectangular and measures 10 feet by 12 feet What area of the floor is not covered by the rug
Answers
The area of a rectangle can be found using the formula:
A = L × W = length × width
The area of the floor is
12 × 10 = 120 square feet.
The area of the rug is
6.5 × 9 = 58.5 square feet.
The area of the floor that is not covered by rug is
120 square feet - 58.5 square feet =
61.5 square feet.
The answer is 61.5 square feet.
~ Hope this helps you!
Final answer:
To find the area of the floor not covered by the rug, calculate the total floor area (120 square feet), subtract the rug's area (58.5 square feet), resulting in 61.5 square feet of uncovered floor.
Explanation:
To find the area of the floor that is not covered by the area rug, we first need to calculate the area of the entire floor and then subtract the area of the rug.
The area of the floor is calculated by multiplying its length and width. So for a floor that measures 10 feet by 12 feet, the area is 10 feet × 12 feet = 120 square feet.
The area rug measures 6.5 feet by 9 feet, which means its area is 6.5 feet × 9 feet = 58.5 square feet.
Now, subtract the area of the rug from the area of the entire floor to find the part of the floor not covered by the rug:
120 square feet - 58.5 square feet = 61.5 square feet.
Therefore, the area of the floor not covered by the rug is 61.5 square feet.
you plan to leave a 15% tip and your dinner bill is $45(tax included). How much total should you leave
Answers
Caitlin creates an architectural blueprint of a rectangular dining room. The area of the actual dining room is 900 times as large as the area of the dining room on the blueprint. The length of the dining room on the blueprint is 4 inches. What is the length of the actual dining room?
Answers
In week 3 the two athletes concentrate on biking. Minh's goal is to bike 125 1/2 miles. At the end of the week he found that he actually biked 125 1/6 miles. PJ's Goal was to bike 120 1/4 miles. At the end of the week he found that he actually biked 120 miles. Which athlete was closer to making their goal? Explain
Answers
subtract what was actually biked from his goal
= 125 1/2 - 125 1/6
convert to like denominators
= 125 3/6 - 125 1/6
= 2/6
simplify
= 1/3 or 0.3333333
PJ:
= 120 1/4 - 120
= 1/4 or 0.25
ANSWER: PJ came closer to his goal because 1/4 (or 0.25) is closer to zero which makes it a smaller number than 1/3 (or 0.33).
Hope this helps! :)
Which data set is represented by the modified box plot?
•85, 70, 80, 108, 46, 66, 68, 82, 70, 68
•85, 78, 80, 108, 46, 66, 68, 80, 72, 68
•85, 78, 80, 108, 46, 66, 68, 82, 72, 80
•85, 78, 80, 108, 46, 66, 68, 82, 72, 68
Answers
They all have a minimum of 46 and maximum of 108. The median is 75 and since there's 10 numbers in each set, you would have to find the middle of two numbers.
First set:
Let's put them in order.
46, 66, 68, 68, 70, 70, 80, 82, 85, 108
The median of that set is 70, not 75.
Second Set:
Let's put them in order.
46, 66, 68, 68, 72, 78, 80, 80, 85, 108
Right away, I can tell the median of the set is 75. We should still check the other sets.
Third set:
Let's put them in order.
46, 66, 68, 72, 78, 80, 80, 82, 85, 108
Fourth set:
Let's put them in order.
46, 66, 68, 68, 72, 78, 80, 82, 85, 108
So, the fourth and second set both have a median of 75. We need to find their third quartile. On the graph, it is about 82 or 83.
Second Set's third quartile: 80
Fourth Set's third quartile: 82
So the box plot represents the last set of numbers.
According to the table, what is the mode of the average high temperatures for states listed in the chart? A) no mode B) 55° F C) 81° F D) 88° F
please explain how to do this type of math I need help ;-;
Answers
Answer:no mode
Step-by-step explanation:
Why was the country of Australia created
Answers
Steven earns extra money babysitting. He charges $31.00 for 4 hours and $54.25 for 7 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Steven babysits and y represent the amount he charges.
The equation is y =
PLEASE HELP WILL GIVE BRANLIEST!!!!!!!!!
Answers
Maria’s math test had 25 questions. She got 84% correct. How many problems did she get wrong
Answers
Therefore, Maria got 21 correct out of the 25.
Do 25 - 21 (25 for the 25 questions and 21 for the ones she got correct)
25 - 21
=4
So, Maria got 4 problems wrong.
[tex] \frac{Number Wrong}{Total Problems} = \frac{Percentage of Questions Wrong}{Total Percentage of Questions} \\ \frac{x}{25} = \frac{16}{100} \\ x= \frac{16}{4} \\ x=4 [/tex]
So Maria got 4 questions wrong.
What is 0.24 ̅ (4 is repeating) expressed as a fraction in simplest form?
Show your work please
Answers
10x=2.44
10x - x = 2.44- 0.24
9x=2.2
2.2/9 =22/90
Here, we need to find express 0.2444... as a fraction in simplest form.
Let the fraction be expressed as x
Now,
x = 0.2444....
Since, x is recurring in 1 decimal places, we multiply it by 10.
10x = 2.4444....
From left hand-side, x is subtracted and from 0.24444... from right hand side
10x - x = 2.4444.... - 0.24444....
So now,
9x = 2.2
x = [tex] \frac{2.2}{9} [/tex]
x = [tex] \frac{22}{90} [/tex]
x = [tex] \frac{11}{45} [/tex]
Thus, fraction as simplest form = [tex] \frac{11}{45} [/tex]
The height of a triangle is twice the length of its base. The area of the triangle is 50m^2. Find the height and base to the nearest tenth of a meter
Answers
Given: The height of a triangle is twice the length of its base
so h = 2b
so
A = 1/2 (b)(2b)
A = b^2
area of the triangle is 50m^2
b^2 = 50
b = √50
b = 7.1
h = 2b = 50
answer
the height = 14.2 m
and
the base = 7.1 m
Find the volume of the triangular prism. Round to the nearest cubic unit.
•288 cm^3
•144 cm^3
•576 cm^3
•71 cm^3
Answers
Answer:
114 cm∧3
Step-by-step explanation:
V= area of base x height
1) calculate the area of the base with formula: 1/2 bh
B=1/2 (8) (6)=24 then Multiply to get the area: Bh
2) (24) (6)= 144cm∧3
hope this helps.
PLEASE HELP!!!!!!
Of all students, calculate the relative frequency for males who carpool.
0.204
9
33
0.088
Answers
Answer:
It's 0.088.
Step-by-step explanation:
So the males who carpool is 9 right? Well relative frequency is the frequency divided by the total. So we must divide 9 by 102.
9÷102 = 0.088
what type of figure is quadrilateral fxyh
Answers
Answer: Quadrilateral fxyh is a trapezoid
Step-by-step explanation: Hi, the correct answer is trapezoid.
A trapezoid is a Quadrilateral ( a polygon with four sides) with a pair of opposite sides parallel. These parallel sides are called the bases of the trapezoid, and the other non-parallel sides are known as the "legs" of the trapezoid.
Feel free to ask for more if it´s necessary or if you did not understand something.
180 miles in 3 hours in fraction form and in word form
Answers
60 miles per hour
Or
60/1
which expression represents the perimeter of the model shown below? PLEASE HELP
Answers
P = 2(4x+3) + 2(2x)
answer
B. 2(4x+3) + 2(2x)
P = 2(4x+3) + 2(2x)
Answer :
B. 2(4x+3) + 2(2x)
Give me 5 stars :)
What is the overlap of Data Set 1 and Data Set 2?
A. High
B. Moderate
C. Low
D. None
Answers
20 POINT FOR ONE QUESTIONS PLEASE HELP THANK YOU!!! I WILL MARK BRAINLIEST
1. What is the value of z?
Answers
Sum of the corners should be 180°, so
39+102+5z+4=180 => 5z = 180-145 => z=35/5=7°
my previous answer of 29 was indeed wrong!!!
sorry for that!!
so 180 - 78 = 102
sum of interior angles in a triangle = 180
102 + 39 + 5z + 4 = 180
5z + 145 = 180
5z = 35
z = 7
answer
x = 7
A quadratic equation is shown below: 10x2 − 3x − 1 = 0 Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points) Part B: Solve 16x2 − 2x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)
Answers
For this case we have the following equation:
10x2 - 3x - 1 = 0
The radicand of the equation is:
root (b ^ 2 - 4 * a * c)
Substituting values:
root ((- 3) ^ 2 - 4 * (10) * (- 1))
root (9 + 40)
root (49)
49> 0
Therefore, the function has two real roots.
Part B:
For this case we have the following equation:
16x2 - 2x - 5 = 0
Factoring we have:
(2x + 1) * (8x-5) = 0
The solutions are:
x = -1/2
x = 5/8
The method of factoring is usually faster when solving quadratic equations.
A) Consider the equation [tex]10x^2-3x-1=0[/tex]
We have to describe the solutions to this equation.
We will determine the radicand = [tex]b^2-4ac[/tex]
= [tex](-3)^2 - 4(10)(-1) = 9+ 40 = 49[/tex] which is greater than zero,
Therefore, the given equation ha real roots.
B) Consider the equation [tex]16x^2-2x-5=0[/tex]
We will use middle splitting term method to solve this equation.
[tex]16x^2+8x-10x-5 =0[/tex]
[tex]8x(2x+1) -5(2x+1)=0[/tex]
[tex](2x+1)(8x-5)=0[/tex]
So, [tex]2x+1=0[/tex]
[tex]x = \frac{-1}{2}[/tex] and [tex]x = \frac{5}{8}[/tex]
I chose this method, because this is more easier and takes less time.
How many liters equal 1258 cm3
Answers
The 1258 cm³ is equal to 1.258 liters.
To convert 1258 cm³ to liters, you can use the fact that 1 liter is equal to 1000 cm³. Therefore, the conversion from cubic centimeters to liters is straightforward.
Identify the given volume: 1258 cm³.
Know the conversion factor: 1 liter = 1000 cm³.
Perform the conversion:
[tex]1258 \ cm^3 \times \left( \frac{1 \ liter}{1000 \ cm^3} \right) = 1.258 \ liters[/tex]
Hey guys I need help with this THANKS!
Answers
The second digit can be one of 4
The third digit can be one of 4
For example, all of these would work
111
221
144
331
123
124
And many more.
The total number of ways is 4*4*4 = 64 <<<<<Answer
C <<<<< Answer.
Answer: c
Step-by-step explanation: hope this helps
The surface area of a triangular prism is 60 square centimeters. What is the surface area of a similar prism that is smaller by a scale factor of 1 5th
Answers
The surface area of the smaller prism is
(60 cm²)*(1/25) = 2.4 cm²
The smaller triangular prism's surface area is calculated by squaring the scale factor of 1/5 (which is 1/25) and then multiplying it by the surface area of the larger prism. The result is 2.4 square centimeters.
The question asks about the surface area of a similar but smaller triangular prism given that the larger prism has a surface area of 60 square centimeters and the scale factor of the smaller prism is 1/5. When the size of an object changes by a scale factor, the surface area changes by the square of that scale factor. For the smaller triangular prism, the surface area will be the square of 1/5, which is 1/25, times the surface area of the larger prism.
To calculate it:
Take the surface area of the larger prism, which is 60 square centimeters.Multiply this area by the square of the scale factor, (1/5)², which is 1/25.The result will give us the surface area of the smaller prism: 60 cm2 * 1/25 = 2.4 cm².Therefore, the surface area of the similar smaller triangular prism by the given scale factor is 2.4 square centimeters.
enter the missing value into the box to complete the ratio comparing 500 meters to 3 kilometers
Answers
So, if 1 kilometer equals 1,000 meters, that means 3 kilometers equal 3,000 meters.
So the ratio is 500:3000
But let's shrink it down:
= 1:3000/500
= 1:6