Four pencils are held together with a band.
the figure on the right shows the bottom end of the pencils and the band.
each of the pencils has a diameter of 10mm
find the length of the band in this position.
give your answer in terms of pi.
Answers
Answer: (40+10π) mm.
Step-by-step explanation: Given diameter of the circle = 10mm.
Radius of the circle = 10/2 = 5 mm.
From the figure, we can see that each or the four corners makes a quarter of the circle.
And four corners would make the complete circle with radius 5mm.
Therefore, circumference of the four quarters of a circle = 2 π r
= 2 π (5) = 10 π.
Now, we can see that each side 10 mm of band also there.
So, the length of straight band on all four sides = 4 × 10 = 40 mm.
Total length of the band = (40+10π) mm
The length of the band is the number of units it covers
The actual length of the band is: [tex]\mathbf{40 + 10\pi}[/tex]
The diameter of 1 pencil is given as:
[tex]\mathbf{d = 10}[/tex]
The circumference of 1 pencil is:
[tex]\mathbf{C = \pi d}[/tex]
So, we have:
[tex]\mathbf{C = 10\pi }[/tex]
Multiply by 4, to calculate the circumference of all pencils
[tex]\mathbf{4C =4 \times 10\pi }[/tex]
[tex]\mathbf{4C =40\pi }[/tex]
The rubber band covers a quarter of the 4 pencils.
So, we divide by 4
[tex]\mathbf{C = 10\pi }[/tex]
The length of the band on one pencil is:
[tex]\mathbf{L = 10}[/tex]
Multiply by 4, for the 4 pencils
[tex]\mathbf{L = 40}[/tex]
So, the actual length of the band is:
[tex]\mathbf{Length = 40 + 10\pi}[/tex]
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Related Questions
which of the following is equal to the rational expression when x does not equal to 5 or -1
(x-7)(x+1)/(x+1)(x-5)
a- x+1/x-5
b-x-7/x+1
c- x+1/x-7
d- x-7/x-5
Answers
The expression that is equal to the rational expression when x does not equal to 5 or -1 is; (x - 7)/(x -5)
How to simplify Algebraic Expressions?
We want to simplify the algebraic expression;
(x - 7)(x + 1)/(x + 1)(x - 5)
Now, looking at the given expression, we see that (x + 1 ) is common to both numerator and denominator and as such they will cancel out to leave us with;
(x - 7)/(x -5)
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Write each of the following expressions without using absolute value. |z−7|−|z−9|, if z<7
Answers
[tex]\left\{ \begin{array}{rcl}-2&\mbox{for}&z < 7\\2(z-8)&\mbox{for}&7\le z\le9\\2&\mbox{for}&9 < z\end{array}\right\,[/tex]
Nadine has 3 yard of ribbon to wrap birthday party favors if each favor use 1/5 yards of ribbon how many favors can nadine wrap
Answers
a _____ is a list of things where each thing appears only once and Order matters
Answers
Answer: Permutation
Permutation is a way, in which a set or number of things can be ordered or arranged. It is a listing where order matters and each thing in the list of things appears only once.
In Mathematics, permutation is the action of changing the arrangement of a set of items. .It is also called an "arrangement number" or "order
Corey drew 8 shapes. Four are squares, two are triangles, and the rest are parallelogram. Write two fractions that name the part of the shapes that are quadrilaterals
Answers
6(4 squares and 2 parallelograms) out of 8
6/8 = 3/4
The two fractions are 6/8 and 3/4.
Nina wants to put color tiles on a square three color tiles fit across the top of the square how many rows and Columns of the squares will Nina need how many color tiles will she use in all
Answers
Hope that helped
Randy worked 18 hours each week for four weeks. for each of the next four weeks, he worked 1/3 fewer hours as the previous four weeks. what was the total number of hours he worked for the eight weeks
Answers
from 5th week to 8th week: 18 x 1/3 x 4 = 48 hours
72 + 48 = 120 hours
Given a mean of 24.5 and a standard deviation of 1.7, within how many standard deviations of the mean do the values 24, 23, 28, 23, 24, and 25 fall?
Answers
Given mean = 24.5 and standard deviation = 1.7
Within 1 standard deviations, x ∈ [24.5 - 1.7 , 24.5 + 1.7] or [22.8 , 26.2].
Within 2 standard deviations, x ∈ [24.5 - 2(1.7) , 24.5 + 2(1.7)] or [21.1 , 27.9].
Within 3 standard deviations, x ∈ [24.5 - 3(1.7) , 24.5 + 3(1.7)] or [19.4 , 29.6].
Given values are 24, 23, 28, 23, 24, and 25.
So {24, 23, 23, 24, 25} fall within 1 standard deviation and {28} falls within 3 standard deviations.
Find the length of CE
Answers
CE=CD+DE
in the right triangle EDF
cos 38°=EF/DE-----> DE=EF/cos 38°-----> DE=17/cos 38°----> DE=21.57 units
∠FDE=90-38----> 52°
∠BDC=∠FDE------> vertical angles
so
∠BDC=52°
in the right triangle BDC
cos 52°=BD/CD-------> CD=BD/cos 52°----> CD=10/cos 52°---> CD=16.24
CE=CD+DE----> CE=16.24+21.57----> CE=37.81 units
the answer is
the length of CE is 37.81 units
A combination lock requires 4 selections of numbers, each from 1 to 20. • how many different combinations are there? • suppose that the lock is constructed in such a way that no number maybe used twice. how many different combinations are possible?
Answers
Answer: 116 280
mean median mode range on 83 75 74 40 85 64 23 68
Answers
In the given set, the mean is 64, the median is 66, there is no mode, and the range is 62.
To find the mean, median, mode, and range of the given set of numbers: 83, 75, 74, 40, 85, 64, 23, 68.
1. Mean:
[tex]\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}} \][/tex]
[tex]\[ \text{Mean} = \frac{83 + 75 + 74 + 40 + 85 + 64 + 23 + 68}{8} \][/tex]
[tex]\[ \text{Mean} = \frac{512}{8} \][/tex]
[tex]\[ \text{Mean} = 64 \][/tex]
2. Median:
The median is the middle number when the numbers are arranged in ascending order.
Arranging the numbers in ascending order: 23, 40, 64, 68, 74, 75, 83, 85
Since there are 8 numbers, the median is the average of the two middle numbers:
[tex]\[ \text{Median} = \frac{64 + 68}{2} \][/tex]
[tex]\[ \text{Median} = 66 \][/tex]
3. Mode:
The mode is the number that appears most frequently.
In this set, there is no number that appears more than once.
So, there is no mode.
4. Range:
The range is the difference between the largest and smallest numbers.
[tex]\[ \text{Range} = \text{Largest number} - \text{Smallest number} \][/tex]
[tex]\[ \text{Range} = 85 - 23 \][/tex]
[tex]\[ \text{Range} = 62 \][/tex]
So, for the given set of numbers, the mean is 64, the median is 66, there is no mode, and the range is 62.
find the range for the given data in 115, 534, 122, 599, 417, 289 A) 534 B) 167 C)115 D)484
Answers
Find the volume of the given prism round it to the nearest tenth, 6 cm, 3.9 cm, 13.2 cm
Answers
(6 cm)*(3.9 cm)*(13.2 cm) ≈ 308.9 cm³
write the ratio 41 to 100 as a percent
Answers
Answer:
[tex]41\%[/tex]
Step-by-step explanation:
we have the ratio
[tex]\frac{41}{100}[/tex]
To write as percent, multiply the ratio by 100
so
[tex]\frac{41}{100}*100=41*100/100=41\%[/tex]
G a family has five children. if it is just as likely to have a boy as a girl, what is the probability that 3 of the children are girls and 2 are boys?
Answers
Find the perimeter and the area of a rectangle measuring 8 1/4 yd long by 4 1/8 yd wide
Answers
perimeter = 2 * 8.25 + 2 * 4.125 =
16.50 + 8.25 =
24.75 yards
Arnob may want to borrow his cousin’s tent, which is shown below. He needs to determine x, the center height of the tent, to determine if it will be large enough for his camping trip. (Picture below)
What is the center height of this tent, to the nearest tenth of a foot?
4.1 feet
8.1 feet
9.8 feet
12.0 feet
Answers
In this question, we will use Pythagoras theorem in order to find the height of the tent.
The center height of tent is 8.1 feet.
What is right triangle?Right triangle is defined as a triangle which one angle is a right angle or two sides are perpendicular.
What is Pythagoras theorem?A right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
perpendicular² + base² = hypotenuse²
Given,
Side length of each triangle = 4 feet
Hypotenuse of each triangle = 9 feet
Shared side = x
Given the triangles are right angled,
According to Pythagoras theorem,
a² + b² = c²
Here, a = 4 , b = x , c= 9
Substitute the values in Pythagoras theorem,
4² + x² = 9²
16 + x² = 81
x² = 81 - 16
x² = 65
Taking square root on both sides
x = √65
x = 8.062
x = 8.1 (Rounding nearest tenth)
Hence, the center height of tent is 8.1 feet.
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Sunny's garden has 9 tomato plants, 5 pepper plants, 3 squash plants, and 6 pumpkin plants. For every 3 tomato plants in Sunny's garden, there is 1 ____ plant.
Answers
from the list of plants there are 3 squash plants
3 squash plants x 3 tomato plants = 9 total tomato plants
the answer is Squash Plants
Answer: Squash plant is the right answer to fill the blank.
Step-by-step explanation:
Since we have given that
Number of tomato plants = 9
Number of pepper plants = 5
Number of squash plants = 3
Number of pumpkin plants = 6
Since the ratio of tomato plants to squash plants is 9 : 3 = 3 : 1.
So, for every 3 tomato plants in Sunny's garden, there is 1 squash plant.
Hence, Squash plant is the right answer to fill the blank.
HELP
Given right triangle ABC.
In the given right triangle, find the length of the hypotenuse, AB, if BC = 6 and AC = 5.
A.5
B.√36
C.√61
D.√11
Answers
A²+B²=C²
6²+5²=C²
36+25=C²
61=C²
√61=C
So the answer is C.
Answer:
Correct answer is option C (√61)
Step-by-step explanation:
in this question we have given a right triangle in which
∠C=[tex]90^{0}[/tex]
BC = 6 and AC = 5
we have to find the length of the hypotenuse, AB=?
To find the the hypotenuse we will apply Pythagoras theorem (According to Pythagoras theorem, "in a right angle triangle, square of hypotenuse is equal to the sum of square of other two sides")
In ΔABC by Pythagoras theorem
[tex]AB^{2}=AC^{2}+BC^{2}[/tex]...................(1)
put values of BC and AC in equation 1
[tex]AB^{2}=5^{2}+6^{2}[/tex]
[tex]AB^{2}=25+36[/tex]
[tex]AB^{2}=61[/tex]
AB=√61
what is 0.0003840 expressed in scientific notation
Answers
0.0003840 = 0.003840/10 = 0.03840/100 = 0.3840/1000 = 3.840/10000
The one we're interested in is the last one, which has one non-zero digit to the left of the decimal point. The power of 10 in the denominator is the 4th power (the number of zeros is 4). 10^4 in the denominator is equivalent to multiplying by 10^(-4) in the numerator.
Expressed in scientific notation,
[tex]0.0003840=3.840 \cdot 10^{-4}[/tex]
0.0003840
Written in scientific notation!
Move the decimal point.
.00384 x 10^1
.0384 x 10^2
.384 x 10^3
3.84 x 10^4
38.4 x 10^5
Hey can you please help me posted picture of question
Answers
C. G(x)=x-6
The explanation is shown below:
You have that the patern function of the linear function is: F(x)=x. By definition, the patern function is the most basic function in the families of functions. If you have the linear function f(x)=x and you shifted it 6 units down, the function will be: f(x)=x-6, which inficates the it moves 6 units on the –y axis. Therefore, as you can see, the correct answer is the option mentioned above (The option C).
hello can you please help me posted picture of question
Answers
The favorable outcomes in this case are the numbers divisible by 3. So the numerator lists the numbers that are divisible by 3, which are the favorable outcomes.
So, the answer to this question is option C
The scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. if the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? give the answer that is closest to the exact number.
Answers
the z-score is given by:
z=(x-μ)/σ
where:
σ-standard deviation
μ- mean
we are required to evaluate for x, given that P(x<X)=0.05
The value of z that corresponds to 5% will be:
z=-1.65
thus plugging our values we obtain:
-1.65=(x-62)/11
solving for x we get:
-18.15=x-62
thus
x=-18.15+62
x=43.85
x~44
Thus the lowest score is 44
The lowest marks that a student can have and still be awarded a passing grade is 44.
Step-by-step explanation:
Given :
Mean, [tex]\mu = 62[/tex]
Standard Deviation, [tex]\sigma = 11[/tex]
Calculation :
z score is given by,
[tex]z = \dfrac{x-\mu }{\sigma}[/tex] ----- (1)
Value of z corresponds to 5% is,
[tex]z =-1.65[/tex]
from equation (1) we get,
[tex]-1.65=\dfrac{x-62}{11}[/tex]
[tex]x=43.85[/tex]
[tex]\rm x = 44 \;\;(Approx)[/tex]
The lowest marks that a student can have and still be awarded a passing grade is 44.
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Two urns contain white balls and yellow balls. The first urn contains 5 white balls and 8 yellow balls and the second urn contains 9 white balls and 2 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?
Answers
This is because you have to start with the probability of each urn. The first urn has 13 total balls (5 white and 8 yellow). Since 5 of them are white, the odds of pulling a white ball are 5/13. Then find the same for the second urn (9 white and 2 yellow). Therefore there are 11 total balls and 9/11 chance of getting a white one. After finding both, multiply them together to get the answer.
[tex] \frac{5}{13} [/tex] * [tex] \frac{9}{11} [/tex] = [tex] \frac{45}{143} [/tex] = 31.5%
p(white ball) = 5/13
For the second urn:
p(white ball) = 9/11
Since the two drawings are independent events, the probability of both happening is the product of the individual probabilities.
p(drawing two white balls) = 5/13 * 9/11 = 45/143
Q # 15 please solve
Answers
The slope of a parallel line is always 0, and the equation of the horizontal line can be expressed as:
y = c
where c is the x-intercept.
So 2nd option is the correct answer
Which of the following statements is true? If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are proportional. If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. If two polygons are similar, then the corresponding sides are congruent and the corresponding angles are proportional. None of the choices are correct.
Answers
The correct statement is that if two polygons are similar, their corresponding sides are proportional while their corresponding angles are congruent. Similar polygons have the same shape but can have different sizes, and this applies across various geometrical figures and principles, like the Pythagorean theorem in the context of right triangles.
Explanation:The correct statement among the given options is: If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. When polygons are similar, this means their shapes are geometrically the same but they may differ in size. The ratios of the lengths of corresponding sides of similar polygons are equal, which is true for any pairs of similar polygons, not just triangles. The corresponding angles, on the other hand, are congruent, which means they have the same measure in both polygons.
To explain this concept, we use different examples in geometry. For instance, in similar triangles, not only are the three angles in one triangle congruent to the three angles in the other, but also the sides are proportional, which can be expressed as the ratio of any two corresponding sides in the two triangles being equal. This proportional relationship is a key characteristic of similarity in geometry.
Moreover, a statement like the Pythagorean theorem applies to right triangles, stating that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is connected to similarity because one can generate a family of similar right triangles by scaling a single right triangle.
kirsten has an area of 70 square feet for a flower garden she plants 5 varieties of flowers equally in her garden which ratio shows the square feet per flower type
Answers
The Ratio of the square feet to the per flower type is 14 : 1.
What is Ratio?A Ratio shows the relative size of two or more value.
According to the question,
Area of a flower garden = 70 square feet
Number of flower plants varieties = 5
Formula for Perimeter of square = 4a where 'a' is sides of a square
4(a) = 70
a=70/4
a=15
To find the Ratio of the square feet to the per flower type
70 : 5
14 : 1.
Hence, the Ratio of the square feet to the per flower type is 14:1
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hey can you please help me posted picture of question
Answers
The function and its inverse are reflected about the line y=x. This means that the x and y values are replaced.
So, if a function has a point (2,3) the same point on its inverse will moved be (3,2). This happens for all the points.
Therefore, the statement is false.
list all the possible whole number length and width of rectangles that darla can cut from the 400 square inch piece of paper
Answers
400 = 1 x 400
400 = 2 x 200
400 = 4 x 100
400 = 5 x 80
400 = 8 x 50
400 = 10 x 40
400 = 16 x 25
400 = 20 x 20
How would you solve 1/8 divided by 6
Answers
The required 1/8 divided by 6 is equal to 1/48.
To solve 1/8 divided by 6, we can rewrite it as a fraction. The reciprocal of 6 is 1/6, so the division problem becomes (1/8) * (1/6). To multiply fractions, we multiply the numerators together and the denominators together.
Step 1 is given as:
= (1/8) * (1/6)
Step 2(simplification) is given as:
= 1 * 1 / 8 * 6
= 1/48
Therefore, the required 1/8 divided by 6 is equal to 1/48.
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