The expected length of the middle part of the stick is 1/3
We know that the Symmetry Principal,
When n points are drooped on a unit segment, the distributions of lengths of the so obtained n + 1 pieces are all the same.
Let the two points have coordinates x and y. Then the expected value of the middle segment is:
[tex]\int\limits^1_0 \int\limits^1_0 {x-y} \, dx~ dy = \frac{1}{3}[/tex]
Let L be the expected value of the length of the middle part of a stick. Since, according to the Symmetry Principle, the lengths of all three segments have the same distribution, their lengths have the same expected value, viz., L.
But in any experiment, the lengths of the three pieces add up to 1.
⇒ 3L= 1
⇒ L = 1/3
Therefore, the expected length of the middle part of the stick is 1/3
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question 15(multiple choice worth 1 points) (03.02 lc) abcd is a rectangle. what is the value of x? rectangle with length 56 m, width x m, and diagonal 65 m 9 meters 28 meters 33 meters 65 meters
The width of the rectangle is: 33m, by Pythagoras theorem.
What is Pythagoras Theorem?The Pythagorean Theorem describes a fundamental relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.Now,
given:
Length of rectangle = 56m (say, l)Diagonal = 65m (say, d)TO find: Width of rectangle = ? (say, w)
Finding:
BY Pythagoras theorem, in the rectangle ABCD,
For l = AB, w = BC and d = AC,
=> l² + w² = d²
Ob substituting the values, we get: 56² + w² = 65²
=> w² = 65² - 56²
=> w² = 4225 - 3136
=> w² = 1089
=> w = 33m
Hence, for the given values of rectangle, the width of the rectangle is 33m by Pythagoras Theorem.
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CHECK MY ANSWERS
1. How would you write the name of a segment differently than the name of a line. What symbols would you use?
Answer: A line and a line segment may sound quite similar however they are very different. A line, in short, is a line that never ends so it's infinite. It's the same for a line segment except at its end it is indicated by dots rather than arrows
2. How is constructing a perpendicular bisector similar to constructing an angle bisector? How is it different
Answer: A perpendicular bisector and an angle bisector are similar because they both require the need to find where two arcs meet. They are different because angle bisectors split into congruent angles meanwhile a perpendicular bisector splits into congruent segments.
3. Describe a process you would use to create the perpendicular bisector to a segment AB using only an unmarked straightedge and an unmarked compass.
Answer: The first step I will do will be to open the compass and stretch it to a width that will be greater than the length of AB. Then I would place one point of the compass onto the line's segments A, then I would move the compass and draw the arcs above and below the AB line. Next step I would do would be to remove the compass from point A and place it onto point B, then repeat the second step (drawing arcs above and below the line). Then lastly, I will use my straightedge and draw a line that will go vertically through where they connect.
1. A line segment can be written with just naming it by its end points and a bar above it while the name of a line requires an double-headed arrow mark above its name.
2. For constructing both a perpendicular and an angle bisector, we need to construct two arcs using a compass and their intersection point. A perpendicular bisector divided a line segment into two equal parts whereas an angle bisector divides an angle into two equal parts.
3. A perpendicular bisector can be drawn by drawing two arcs each above and below the line segment and joining using an straight edge.
1. A line and a line segment may sound quite similar however they are very different. A line, in short, is a line that never ends so it's infinite. It's the same for a line segment except at its end it is indicated by dots rather than arrows.
This difference can be seen in naming them too. A line segment is named using the initial and terminal points of the segment. Sometimes we put a 'bar' mark above its name. For example, [tex]\bar{AB}[/tex]
For a line of infinite length, it is named simply as 'line A' or 'line B' or sometimes put a double-headed arrow mark above its name.
2. A perpendicular bisector and an angle bisector are similar because they both require the need to find where two arcs meet. They are different because angle bisectors split into congruent angles meanwhile a perpendicular bisector splits into congruent segments.
Constructing a perpendicular bisector is similar in the sense that both are drawn using straight edge and compass and need to find the intersection point of the arcs. But they are different in their use as perpendicular bisector equally divides a line segment and an angle bisector equally divides an angle.
3. We have an unmarked straightedge and a compass. First put the compass at one end point A of the line. Then stretch the compass to a length more than half of the line segment AB to be bisected. In the next step, draw an arc above and one below the line. Next put the compass on the other end B of the line. Then repeat drawing two arcs, each above and below the line and also intersecting with the previous arcs. Finally join the two points got with a line cutting the line segment AB. This will be the perpendicular bisector of the line AB.
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find the quotient 4 4/5 divided by 4/5
Answer:
Step-by-step explanation:
6
help help help help help help help help help help help help help help help
Step-by-step explanation:
11. Is a real numer
12. Is integer
13. Is rational
14. Is whole number
Round 3,487,967 to the nearest ten thousands
Answer:
3,490,000
Step-by-step explanation:
3,487,967 = (87967) The 7 rounds up so the 8 would become 9.
suppose a jar contains 9 red marbles and 14 blue marbles. if you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red. answer should be in fractional form.
The probability that both are red should be 0.1423.
The possibility of picking up x number of balls among n number of balls is ⁿCₓ.
jar contains 9 red marbles and 14 blue marbles. Total number of marbles are 23.
favorable cases of picking two red marbles among 9 red marbles is ⁹C₂
And the total possible cases of picking two marbles among 23 marbles is ²³C₂
Therefore, the probability of picking both red marbles are = ( no. Of favorable cases/no. Of possible cases) = ( ⁹C₂ )/( ²³C₂ ) = 36/253 = 0.1423.
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Maggie has a container in the shape of a right prism. the formula for its surface area is sa = ph 2b. solve for h. h = sa minus two times b over p h = sa plus two times b over p h = sa plus p over two times b h = sa minus p over two times b
The value of the height of the right prism is given by the formula, h = (SA - 2B) / P. It is gained by using the surface area of the right prism.
What is the right prism?
A right prism is a three-dimensional closed figure with 6 faces, 8 corners and 12 edges. It is called a right prism because, in this prism, the angle between the base and the sides is 90 degrees. All the faces of a right prism are rectangular, hence sometimes also called a right rectangular prism.
Calculation of h for the right prism
We know the surface area of the right prism is given by:
SA = Ph + 2B
Ph + 2B = SA
Subtracting 2B from both sides of the above equation, we have,
Ph + 2B - 2B = SA - 2B
Ph = SA - 2B
Dividing both sides of an equation by P, we get,
(Ph) / P = (SA - 2B) / P
h = (SA - 2B) / P
Hence, the value of h can be found using the formula, h = (SA - 2B) / P
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Find the area of a circle with radius 6 in. Use the value 3.14 for π, and do not round your answer.
Step-by-step explanation:
Área of a circle is given as
[tex]\pi \times {r}^{2} [/tex]
Therefore you can substitute the values as follows:
[tex]3.14 \times {6}^{2} = 113.09733552923[/tex]
Answer not rounded to any decimal place and used of 3.14 as said in the instruction
The area is:
113.04 in²Explanation:
To find the circle's area, use the formula [tex]\sf{A=\pi r^2}[/tex].
where:
A = area;
π = 3.14 (pi);
r = radius
Diagram:
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 6\ in}\end{picture}[/tex]
Plug in the data:
[tex]\sf{A=3.14\times6^2}[/tex]
[tex]\sf{A=3.14\times36}[/tex]
[tex]\sf{A=113.04\:in^2}[/tex]
What is the value of x? enter your answer in the box. x = two lines slightly inclined with vertical intersect at the midpoint. the left and right angles made by these lines are obtuse. the right obtuse angle is labeled left square bracket 5 left parenthesis x minus 4 right parenthesis right square bracket degrees. the left obtuse angle is labeled left parenthesis 4 x plus 7 right parenthesis degrees.
The value of 'x' in the given question is 27°.
Obtuse Angle may be defined as an angle that is greater than 90° and less than 180°. It may be also defined as an angle between a right angle and a straight-line angle.
From the question we can conclude that the given angles are vertically opposite to each other, and vertically opposite angles are always equal to each other.
Vertically opposite angles are formed when two lines are intersecting each other and the angles formed on each side of the intersection point are called vertically opposite angles.
Now according to the question:
[5(x-4)]°=(4x+7)°
Rearranging the terms:
(5x-20)°=(4x+7)°
=>x=27°
Therefore, the value of x is 27°.
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Can you pls help me tink u <3
Some sales positions pay a commission only if sales exceed a sales
quota. The salesperson is rewarded only for having sales beyond an
expected amount. Joyce Doyle is a sales trainee. She is paid $1,550 per
month plus a commission of 7.5% on all sales of more than a $20,000
monthly quota. What is Joyce's total pay for a month in which her sales
totaled $22,650?
The sales on which Joyce earns commission is the sale beyond $20,000 which is $2,650. So the total pay for a month for Joyce in which her sales is $22,650 is $1748.75.
Joyce is paid $1,550 per month plus a commission of 7.5% on all sales of more than a $20,000 monthly quota. For the given month her sales is $22,650.
Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. The abbreviations used to represent the percentage are ‘pct’ or ‘pc’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.
Total pay of Joyce = Her pay per month + Commission that she gets
Commission she gets is on the sales beyond $20,000.
Here, commission is on $22,650 - $20,000 = $2,650
She gets 7.5% commission. So, her commission is 7.5% * $2,650
=> 75/1000 * $2,650 = $198.75
So, the total pay of Joyce is $1,550 + $198.75
=> $1748.75 for the month.
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If point P (-1, 4) is translated to the right 4 units and up 2 units, what are the new coordinates.
Answer:
The correct answer should be P(1, 7)
Find the coordinates of the missing endpoint if b is the midpoint of AC. A(-4,2),B(6,-1)
Answer:
Step-by-step explanation:
Answer:(3,2)
Step-by-step explanation:
Draw a scaled copy of polygon with the scaled factor of 2
A scaled copy of polygon with the scaled factor of 2 is Scale factor is defined as
It is a growing organism that falls between (0, infinity). According to the scale factor, an original figure might be either raised or decreased.
Consider two circles that appear to be the same. The word "identical" does not guarantee that both circles are of similar size. They could have various radii. One figure would be the other figure scaled down.
The ideas of ratio and proportion are intimately related to scale considerations. A given amount is multiplied or divided in ratio and proportions to create a new quantity.
A Scaled copy involves multiplying the lengths in the original figure by scale factor.
Here scale factor = 2,
Since the scale factor > 1, so there is an enlargement.
So, the scale copy's sides are 2 times of the sides of figure A.
Take the reference of grid:
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multiply or divide write your answer in simplest form 3/6 x 7/10
Answer:
0.35
Step-by-step explanation:
3/6=1/2
7/10=0.7
1/2=0.5,0.5×0.7
=0.35
Answer: 7/20
Step-by-step explanation:
3/6*7/10= 0.35
First write down the decimal number divided by 1 like this:
0.35
1
As we have 2 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by 102 = 100, so that there is no decimal point in the numerator
0.35 × 100
1 × 100
=
35
100
Since the greatest common factor of 35 and 100 is 5, we can simplify the fraction and show the same amount
35 ÷ 5
100 ÷ 5
=
7
20
Therefore, 0.35 as a fraction is 7/20
A dress has a retail price of $195, but the store is running a sale and is giving 15% off of the retail price on all dresses. The store is located in Los Angeles, CA, which has a sales tax rate of 8%. Note: The 15% discount is applied prior to the item being taxed. You have $180 to spend. Can you afford to buy the dress? How much will it cost you?
Answer:
$179.01
Step-by-step explanation:
(First Step) $195 - 15% = $165.75
(Second Step) $165.75 + 8% = $179.01
HELP !!!
Point (2,6) is 2/3 of the way from A to B. If A has coordinates (-8, 6), what are the coordinates of B?
The coordinates of the point B are (-5, 6)
How to determine the coordinates of the point B?The given parameters are
A = (-8, 6)
Point = (2, 6)
Proportion = 2/3
Because the y coordinates are the same, we can make use of only the x coordinate
So, we have
Point = Proportion * (B - A)
This gives
2 = 2/3 * (B + 8)
Multiply through by 3/2
So, we have
3 = B + 8
Subtract 8 from both sides
B = -5
Hence, the coordinates of the point B are (-5, 6)
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Define a variable and write an inequality to model the given situation. The restaurant can seat at most 154 people. *** If p is the restaurant's capacity, which of the following inequalities models the given situation?
A. p≥ 154
B. p≤ 154
C. p< 154
D. p>154
Answer:
B. p ≤ 154
Hope that helps :)
Step-by-step explanation:
The restaurant can hold 154 people or less than that.
A projectile with an initial velocity of 48 feet per second is launched from a building 190 feet tall. the path of the projectile is modeled using the equation h(t) = â€""16t2 48t 190.approximately when will the projectile hit the ground?1.5 seconds3.2 seconds5.3 seconds6.2 seconds
The time for the projectile to hit the ground from the given position is 1.5 s, which is obtained using the concept of time period and velocity of a projectile.
What is a projectile?
A projectile is defined as an object that has the force of gravity as the only force occurring on it. Acceleration in the projectile motion always acts vertically.
Calculation of the time taken by projectile to hit the ground
The given parameters:
The starting velocity of the projectile, u = 48 ft / s
Height of the projectile, h = 190 ft
Model of the projectile path, h(t) = - 16(t)2 + 48t + 190 —-- 1
When the projectile hits the ground, the final velocity, v = 0
differentiating equation 1 w.r.t t, we get,
(dh(t)) / (dt) = - 32t + 48
Putting dh(t) / dt = 0, we have,
- 32t + 48 = 0
32t = 48
t = 48 / 32
t = 1.5 s
Hence, the time taken by the projectile to hit the ground is 1.5 s.
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the data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. find (a) the number of classes, (b) the class limits for the second class, and (c) the class width.
I need some help with my math please: Triangles ABD and ACE are similar right triangles. Which ratio best explains why the slope of AB is the same as the slope of AC?
Answer:
The second answer is the correct one I believe
Answer:
second one
Step-by-step explanation:
Please Help! Best answer gets Brainliest.
Find P on NM that is the given fractional distance from N to M. Please explain.
Equation:
1/5; N (-3, -2), M (1, 1)
The coordinates of the point P that partitions the Line N, into the ratio 1:5 is; P(x, y) = (-14/6), (-9/6)
How to partition line segment?We are told that the point P partitions the Line N, into the ratio 1:5.
Now, the coordinates of N and M are;
N(-3, -2), M(1, 1)
The formula to find the coordinates that partition a line is;
P(x, y) = (bx1 + ax2)/(a + b), (by1 + ay2)/(a + b)
where the ratio is a:b. Thus;
Thus, the coordinates of point P here are calculated as;
P(x, y) = (5*-3 + 1*1)/(1 + 5), (5*-2 + 1*1)/(1 + 5)
P(x, y) = (-14/6), (-9/6)
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"One subtracted
from the
product of 4 and
a number is Il”
The number will be 3.
How to calculate the value?Let the number be represented by x.
Therefore based on the information, the equation will be:
(x × 4) - 1 = 1
4x - 1 = 11
Collect like terms
4x = 11 + 1
4x = 12
Divide
x = 12/4
x = 3
The number is 3.
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the sum of 17 and 3 times x *
The sum of 17 and 3 times x is given by the algebraic expression "17+3x" .
A mathematical construct called an algebraic expression is made up of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by a rational exponent).
Let us take an expression 4x³+6xy+9 is an algebraic expression. Where
x,y are variables 4 and 6 are co-efficients and 9 is the constant .
In the above statement it is given that the sum of 17 and times x. Here x is a variable.
3 times x equates to 3x and when 17 is added we get the expression 17+3x.
Hence the required algebraic expression is 17+3x
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What percentage of those who were married were obese?
a. 25.6%(331/1293)
b. 44.4% (147/331)
c. 32.8%(424/1293)
d. 34.7% (147/424)
The percentage of those who were married were also obese is: 34.7% (147/424; Option B)
What are percentages?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. A % is a number without dimensions and without a standard measurement.Now,
The percentage of number of married participants who were obese is calculated by: dividing the former (147) by the total number of married participants(424)
=> Percentage of married participants who were obese = 147/424.
Hence, The percentage of those who were married were also obese is: 34.7% (147/424; Option B)
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(COMPLETE QUESTION:
A 2009 study analyzed data from the National Longitudinal Study of Adolescent Health. Participants were followed into adulthood. Each study participant was categorized as to whether they were obese (BMI >30) or not and whether they were dating, cohabiting, or married. The table below summarizes the results.
Dating Cohabiting Married Total
Obese 81 103 147 331
Not Obese 359 326 277 962
Total 440 429 424 1293
What percentage of those who were married were obese? (Round your answer to 1 decimal place.)
A. 32.8% (424/1293)
B. 34.7% (147/424)
C. 25.6% (331/1293)
D. 44.4% (147/331))
a store normally sells windows at $100 each. This week the store is offering one free window for each purchase of 4. Dave needs 7 windows and Doug needs 8. How much money will they save if they purchase together rather than separately?
They will save $100 if they purchase together rather than separately.
If this week, the store is offering one free window for each purchase of 4, then the price of 5 windows will be just equal to the price of 4.
1 window = $100
5 windows = 4 x $100 = $400
If
Dave needs 7 windows
Doug needs 8 windows
total they need together = 7+8 = 15 windows.
Buying at the offer of $400/5 windows,
they should buy 3 sets of 5 windows.
3 x 5 = 15
cost when bought together : 3 x $400
cost when bought together : $1200
If they bought separately,
Dave : 7 = 5 + 2
cost = $400 + 2($100)
cost = $600
Doug : 8 = 5 + 3
cost = $400 + 3($100)
cost = $700
cost when bought separately : $600 + $700
cost when bought separately : $1300
compare the two total costs and to determine how much they will save.
$1300 - $1200 = $100
They will save $100 if they purchase together rather than separately.
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8 as a product of three primes
Answer: 2x2x2 or 2 cubed
Step-by-step explanation: 2x2=4 2x4=8
Write an equation for a cubic function that has been reflected across the x-axis, shifted
right 3 units and shifted up 1 unit.
y = x³
The shaded area of the square is:
14 12 34
Answer:
5902
Step-by-step explanation:
that's what it tells with my calculations
What do you need to add to -6 to get 10? i need helppp
Answer:
16
Step-by-step explanation:
x+(-6)=10 Take (-6) to the other side it becomes (+6).
x= 10 + 6
x=16