Answer:
The answer is "0.68".
Step-by-step explanation:
Given value:
[tex]X_i \sim \frac{G_1}{2}[/tex]
[tex]E(X_i)=2 \\[/tex]
[tex]Var (X_i)= \frac{1- \frac{1}{2}}{(\frac{1}{2})^2}\\[/tex]
[tex]= \frac{ \frac{2-1}{2}}{\frac{1}{4}}\\\\= \frac{ \frac{1}{2}}{\frac{1}{4}}\\\\= \frac{1}{2} \times \frac{4}{1}\\\\= \frac{4}{2}\\\\=2[/tex]
Now we calculate the [tex]\bar X \sim N(2, \sqrt{\frac{2}{n}})\\[/tex]
[tex]\to \frac{\bar X - 2}{\sqrt{\frac{2}{n}}} \sim N(0, 1)\\[/tex]
[tex]\to \sum^n_{i=1} \frac{X_i - 2}{n} \times\sqrt{\frac{n}{2}}} \sim N(0, 1)\\\\\to \sum^n_{i=1} \frac{X_i - 2}{\sqrt{2n}} \sim N(0, 1)\\[/tex]
[tex]\to Z_n = \frac{1}{\sqrt{n}} \sum^n_{i=1} (X_i -2) \sim N(0, 2)\\[/tex]
[tex]\to P(-1 \leq X_n \leq 2) = P(Z_n \leq Z) -P(Z_n \leq -1) \\\\[/tex]
[tex]= 0.92 -0.24\\\\= 0.68[/tex]
Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet. What is the probability that a carpet that is 8 feet by 14 feet contains no flaws
Answer:
The probability that it contains no flaws=0.585
Step-by-step explanation:
Flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet.
One = 270 ft²
8*14= 112 ft²
Probability of containing flaws
So if 270 ft² = 1
112 ft² = 112/270
112ft² = 0.415
The probability that it contains no flaws= 1- probability that it contains
The probability that it contains no flaws= 1-0.415
The probability that it contains no flaws=0.585
Find the cost of 4 tubes of oil paint and 2 canvases
Answer:
You have to put in the whole word problem
Step-by-step explanation:
A truck traveled 205 miles in 3 1/2 hours. The distance is the product of the rate and the time. To the nearest tenth, what is the average speed of the delivery truck? Enter your answer in the box. ____ miles per hour
Answer:
58.6 miles / hour
Step-by-step explanation:
The formula is
d= rt where d is the distance, r is the rate ( speed) and t is the time
205 miles = r * 3.5 hours
Divide each side by 3.5
205 miles/ 3.5 hours = r
58.57142857 miles / hour = r
To the nearest tenth
58.6 miles / hour
Answer:
58.6
Step-by-step explanation:
So the truck traveled 205 miles in 3.5 hours.
As given, the distance is the product of the rate and the time. In other words:
[tex]d\text{ mi}=r\cdot t\text{ hours}[/tex]
Substitute 205 for d and 3.5 for t. Thus:
[tex]205\text{ mi} =r\cdot (3.5)\text{hours}[/tex]
Divide both sides by 3.5 hours. Thus:
[tex]r=\frac{205\text{ mi}}{3.5\text{ hours}}[/tex]
Divide 205 and 3.5:
[tex]r\approx58.6\text{ mi/hr}[/tex]
The face of a cat is symmetrical, with the bridge of the nose falling on the line of symmetry directly between the eyes. If a cat’s right eye is 3 inches from the bridge of its nose, how far is the cat’s left eye from its right eye?
Answer:
6
Step-by-step explanation:
The cat's bridge of its nose lines up directly on the line of symmetry, so let's say it's (0,0). If the cat's right eye is 3 inches away from its nose, then that point is (3, 0). The cat's left eye is also 3 inches away from the bridge of its nose, so that point is (-3, 0). How do you go from -3 to 3? You must add 6!
What expression converts 100 inches per minute to feet per minute?
1 foot= 12 inches.
To convert you must have "2 fractions" to multiply.
Your first fraction must be 100in/1min. (100 inches per 1 minute).
The second should serve to convert inches to feet. It should be 1 foot/ 12 inches. (1 foot per 12 inches).
Your product should be 100ft/12 which equals 8.3 repeating or 25/3 (8 1/3) feet.
Which of the following is a monomial ? 9/x 11x2 20x9-7x 20x -14
Answer: 11x^2
Step-by-step explanation:
I suppose that the options are:
a) 9/x
b) 11x^2
c) 20x^9-7x
d) 20x -14
First, a polynomial is something like:
aₙx^n + .... + a₂*x^2 + a₁*x^1 + a₀*x^0
Where n is the degree of the polynomial, the therms a are the coefficients, and aₙ is the leading coefficient.
Depending on the number of terms of the polynomial, it takes different names.
If we have only one term, it is called a monomial, if it has two terms, it is called a binomial, and so on.
So if we want to find a monomial, then we need to look at the options with only one term.
The options with only one term are options a and b.
But option a is a quotient (we have a negative power of x: 9/x = 9*x^-1)
So this is not a polynomial, then the correct option is option b.
What is the reciprocal of 100
Answer:
0.01
Steps:
The definition of "reciprocal" is simple. To find the reciprocal of any number, just calculate "1 ÷ (that number)." For a fraction, the reciprocal is just a different fraction, with the numbers "flipped" upside down (inverted). For instance, the reciprocal of 3/4 is 4/3
Answer:
It is 100
Step-by-step explanation: A reciprocal is is obtained by inverting a fraction.
100 is the same as 100/1
So the reciprocal of 100 is 1/100
Part A) What is the cost of 14.6 gallons of gasoline at $2.70 per gallon? Part B) Explain the steps you would take to solve this problem.
Answer:
$39.42
Step-by-step explanation:
SImply multiply 14.6 with 2.70 which will give us 39.42.
Price:-
[tex]\\ \tt\hookrightarrow 14.6(2.7)[/tex]
[tex]\\ \tt\hookrightarrow 39.42\$[/tex]
What is the value of (-3/4)-4
Answer: -19/4
Step-by-step explanation:
Answer:
-4.75
Step-by-step explanation:
-3+16/4
= -19/4
= -4.75
Forty percent of all Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway. Suppose a random sample of n=25 Americans who travel by car are asked how they determine where to stop for food and gas. Let x be the number in the sample who respond that they look for gas stations and food outlets that are close to or visible from the highway.
a. What are the mean and variance of x?
b. Calculate the interval μ±2σμ±2σ. What values of the binomial random variable x fall into this interval?
c. Find P(6≤≤x$\leq$14). How does this compare with the fraction in the interval μ±2σμ±2σ for any distribution? For mound-shaped distributions?
Answer:
Explained below.
Step-by-step explanation:
Let the random variable X be defined as the number of Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway.
The probability of the random variable X is: p = 0.40.
A random sample of n =25 Americans who travel by car are selected.
The events are independent of each other, since not everybody look for gas stations and food outlets that are close to or visible from the highway.
The random variable X follows a Binomial distribution with parameters n = 25 and p = 0.40.
(a)
The mean and variance of X are:
[tex]\mu=np=25\times 0.40=10\\\\\sigma^{2}=np(1-p)-25\times0.40\times(1-0.40)=6[/tex]
Thus, the mean and variance of X are 10 and 6 respectively.
(b)
Compute the values of the interval μ ± 2σ as follows:
[tex]\mu\pm 2\sigma=(\mu-2\sigma, \mu+ 2\sigma)[/tex]
[tex]=(10-2\cdot\sqrt{6},\ 10+2\cdot\sqrt{6})\\\\=(5.101, 14.899)\\\\\approx (5, 15)[/tex]
Compute the probability of P (5 ≤ X ≤ 15) as follows:
[tex]P(5\leq X\leq 15)=\sum\limits^{15}_{x=5}{{25\choose x}(0.40)^{x}(1-0.40)^{25-x}}[/tex]
[tex]=0.0199+0.0442+0.0799+0.1199+0.1511+0.1612\\+0.1465+0.1140+0.0759+0.0434+0.0212\\\\=0.9772[/tex]
Thus, 97.72% values of the binomial random variable x fall into this interval.
(c)
Compute the value of P (6 ≤ X ≤ 14) as follows:
[tex]P(6\leq X\leq 14)=\sum\limits^{14}_{x=6}{{25\choose x}(0.40)^{x}(1-0.40)^{25-x}}[/tex]
[tex]=0.0442+0.0799+0.1199+0.1511+0.1612\\+0.1465+0.1140+0.0759+0.0434\\\\=0.9361\\\\\approx P(5\leq X\leq 15)[/tex]
The value of P (6 ≤ X ≤ 14) is 0.9361.
According to the Tchebysheff's theorem, for any distribution 75% of the data falls within μ ± 2σ values.
The proportion 0.9361 is very large compared to the other distributions.
Whereas for a mound-shaped distributions, 95% of the data falls within μ ± 2σ values. The proportion 0.9361 is slightly less when compared to the mound-shaped distribution.
Probabilities are used to determine the chance of an event.
[tex]\mathbf{Mean = 10}[/tex] and [tex]\mathbf{Variance = 6}[/tex].97.72% values of the binomial random variable x fall into the interval [tex]\mathbf{\mu \pm 2\sigma}[/tex].93.61% values of the binomial random variable x fall into the interval 6 to 14The given parameters are:
[tex]\mathbf{n = 25}[/tex]
[tex]\mathbf{p = 40\%}[/tex]
(a) Mean and variance
The mean is calculated as follows:
[tex]\mathbf{Mean = np}[/tex]
[tex]\mathbf{Mean = 25 \times 40\%}[/tex]
[tex]\mathbf{Mean = 10}[/tex]
The variance is calculated as follows:
[tex]\mathbf{Variance = np(1 - p)}[/tex]
So, we have:
[tex]\mathbf{Variance = 25 \times 40\%(1 - 40\%)}[/tex]
[tex]\mathbf{Variance = 6}[/tex]
(b) The interval [tex]\mathbf{\mu \pm 2\sigma}[/tex]
First, we calculate the standard deviation
[tex]\mathbf{\sigma = \sqrt{Variance}}[/tex]
[tex]\mathbf{\sigma = \sqrt{6}}[/tex]
[tex]\mathbf{\sigma = 2.45}[/tex]
So, we have:
[tex]\mathbf{\mu \pm 2\sigma = 10 \pm 2 \times 2.45}[/tex]
[tex]\mathbf{\mu \pm 2\sigma = 10 \pm 4.90}[/tex]
Split
[tex]\mathbf{\mu \pm 2\sigma = 10 + 4.90\ or\ 10 - 4.90}[/tex]
[tex]\mathbf{\mu \pm 2\sigma = 14.90\ or\ 5.10}[/tex]
Approximate
[tex]\mathbf{\mu \pm 2\sigma = 15\ or\ 5}[/tex]
So, we have:
[tex]\mathbf{\mu \pm 2\sigma = (5,15)}[/tex]
The binomial probability is then calculated as:
[tex]\mathbf{P = ^nC_x p^x \times (1 - p)^{n - x}}[/tex]
This gives
[tex]\mathbf{P = ^{25}C_5 \times (0.4)^5 \times (1 - 0.6)^{25 - 5} + ...... +^{25}C_{15} \times (0.4)^{15} \times (1 - 0.6)^{25 - 15}}[/tex]
[tex]\mathbf{P = 0.0199 + ..... + 0.0434 + 0.0212}[/tex]
[tex]\mathbf{P = 0.9772}[/tex]
Express as percentage
[tex]\mathbf{P = 97.72\%}[/tex]
This means that; 97.72% values of the binomial random variable x fall into the interval [tex]\mathbf{\mu \pm 2\sigma}[/tex]
[tex]\mathbf{(c)\ P(6 \le x \le 14)}[/tex]
The binomial probability is then calculated as:
[tex]\mathbf{P = ^nC_x p^x \times (1 - p)^{n - x}}[/tex]
So, we have:
[tex]\mathbf{P = ^{25}C_6 \times (0.4)^6 \times (1 - 0.4)^{25 - 6} + ...... +^{25}C_{14} \times (0.4)^{14} \times (1 - 0.4)^{25 - 14}}[/tex]
[tex]\mathbf{P = 0.0422 +.............+0.0759 + 0.0434}[/tex]
[tex]\mathbf{P = 0.9361}[/tex]
This means that:
93.61% values of the binomial random variable x fall into the interval 6 to 14
By comparison, 93.61% is very large compared to the other distributions., and the proportion 93.61 is slightly less when compared to the mound-shaped distribution.
Read more about binomial probability at:
https://brainly.com/question/19578146
Which set of ordered pairs could represent the same function as y = x2 ?
A (1, 1), (2, 4), (3,6)
B (1,1),(3,9), (7,49)
© (1,2), (4,16), (8, 64)
D (4,8), (5, 25), (6,36)
Answer:
B (1, 1),(3, 9), (7, 49)
Step-by-step explanation:
Given function:
y = x²Let's verify which set of pairs are same with the given function:
A....................
(1, 1) - yes(2, 4) - yes(3, 6) - no, 6≠ 3²B....................
(1, 1) - yes(3, 9) - yes(7, 49) - yesC....................
(1, 2)- no, 2≠ 1²(4, 16) - yes(8, 64) - yesD....................
(4, 8) - no, 8 ≠ 4²(5, 25) - yes(6, 36) - yesWhat is the probability that a randomly chosen student admitted in the hospital is between 11 and 14 years
Answer:
convert 13.025 to base 10
5. 2x + 5 - 7x = 15
6.
X=
Help me
Answer:
-2
Step-by-step explanation:
2x+5-7x=15
Combine like terms
-5x+5=15
Subtract 5 from both sides
-5x=10
Divide -5 from both sides
x=-2
Answer:
2x+5-7x=15
-5x+5=15
5-15 =5x
-10 =5x
10/5=x
x= -2
Suppose that the functions g and h are defined for all real numbers x as follows.
g(x) = 3x-6
h(x) = 5x
Write the expressions for (g-h)(x) and (g+h)(x) and evaluate (g-h)(-1)
Answer:
See Below.
Step-by-step explanation:
We are given the two functions:
[tex]\displaystyle g(x) = 3x - 6 \text{ and } h(x) = 5x[/tex]
Part A)
Recall that:
[tex](g\cdot h)(x)=g(x)\cdot h(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned} (g\cdot h)(x) & = (3x-6)\cdot(5x) \\ \\ &=5x(3x)-5x(6) \\ \\&=15x^2-30x \end{aligned}[/tex]
Part B)
Recall that:
[tex](g+h)(x)=g(x)+h(x)[/tex]
Substitute and simplify:
[tex]\displaystyle \begin{aligned} g(x) + h(x) & = (3x-6) + (5x) \\ \\ & = 8x- 6 \end{aligned}[/tex]
Part C)
Recall that:
[tex]\displaystyle (g-h)(x) = g(x) - h(x)[/tex]
Hence:
[tex]\displaystyle \begin{aligned} (g-h)(-1) & = g(-1) - h(-1) \\ \\ & = (3(-1)-6) - (5(-1)) \\ \\ & = (-9) + (5) \\ \\ & = -4\end{aligned}[/tex]
Find the area of a triangle whose vertices are P(1,3,2) Q(2,-1, 1) R(-1,2,3)
Answer:
5199
Step-by-step explanation:
Because
in training for a swim meet Logan swim 750 meters in 1/3 of an hour his swimming partner Milo swam 2/3 of Logan's distance in 1/4 of an hour.Compare mila's and logan's swimming speeds.
Answer:
speed of Logan is 37.5 m/minutes
speed of Milo is 33.33 meters per minutes
Speed of Logan is greater than speed of Milo
difference in speed = 37.5 - 33.33 = 4.17 meters per minutes
Step-by-step explanation:
we will calculate speed in meters per minutes
we know 1 hour = 60 minutes and
1 minutes = 60 seconds
speed = distance/time
____________________________________
For Logan
distance = 750 meters
time = 1/3 of hour = 1/3 *60 minutes = 20 minutes
speed = 750/20 = 37.5 meters per minute
__________________________________________________
For milo
distance = 2/3 of Logan's distance = 2/3 * 750 meters = 500 meters
time = 1/4 of hour = 1/4 *60 minutes =15 minutes
speed = 500/15 = 33.33 meters per minute
Thus, speed of Logan is 37.5 m/minutes
speed of Milo is 33.33 meters per minutes
Speed of Logan is greater than speed of Milo
difference in speed = 37.5 - 33.33 = 4.17 meters per minutes
how many lines are symmetry has an isosceles triangle
The amount of a chemical solution is measured to be 2 liters. What is the percent error of the measurement? 2.55% 25% 50%
Answer:
2.55 percent
Step-by-step explanation:
A company finds that the rate at which the quantity of a product that consumers demand changes with respect to price is given by the marginal-demand function Upper D prime (x )equals negative StartFraction 4000 Over x squared EndFraction where x is the price per unit, in dollars. Find the demand function if it is known that 1002 units of the product are demanded by consumers when the price is $4 per unit.
Answer:
D(x) = 4000 / x + 2
Step-by-step explanation:
Given:
marginal-demand function = d /dx[D(x )] = D'(x)= -4000/x²
Quantity of product demanded = 1002 units
Price of product per unit = $4
To find:
demand function D(x)
Solution:
D'(x)= -4000/x²
= -4000/x² dx
= -4000 x⁻² dx
D(x) = -4000 x⁻¹ + C
D(x) = -4000/x + C
Since we know that the quantity of product is 1002 and price per unit is $4 so,
D(4) = 1002 = 4000/4 + C
1002 = 4000/4 + C
1002 = 1000 + C
1002 - 1000 = C
C = 2
Hence the demand function is:
D(x) = 4000 / x + 2
Let (8,−3) be a point on the terminal side of θ. Find the exact values of cosθ, cscθ, and tanθ.
Answer:
[tex]\text{Cos}\theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}[/tex]
[tex]\text{Csc}\theta=-\frac{\sqrt{73}}{3}[/tex]
[tex]\text{tan}\theta =\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}[/tex]
Step-by-step explanation:
From the picture attached,
(8, -3) is a point on the terminal side of angle θ.
Therefore, distance 'R' from the origin will be,
R = [tex]\sqrt{x^{2}+y^{2}}[/tex]
R = [tex]\sqrt{8^{2}+(-3)^2}[/tex]
= [tex]\sqrt{64+9}[/tex]
= [tex]\sqrt{73}[/tex]
Therefore, Cosθ = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}=\frac{x}{R}=\frac{8}{\sqrt{73}}[/tex]
Sinθ = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}=\frac{y}{R}=\frac{-3}{\sqrt{73} }[/tex]
tanθ = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}=\frac{y}{x}=\frac{-3}{8}[/tex]
Cscθ = [tex]\frac{1}{\text{Sin}\theta}=\frac{R}{y}=-\frac{\sqrt{73}}{3}[/tex]
Square root of 136161
by
long
division
Answer:
369
Step-by-step explanation:
Hello. If we write this number as square root of (41)^2 x 9^2, 41 and 9 will exit in the root. So, 41 x 9 = 369.
36,815 to the nearest hundred
Answer:
36,800
Step-by-step explanation:
If x < 5, we round down.
If x ≥ 5, we round up.
We are specifically looking at 8 and 1 in 36,815.
1 < 5, so we round down:
36,800
What is the slope of the line?
A. −1/2
B. 2
C. −2
D. 1/2
Answer:
[tex]\frac{2}{1}[/tex]
Step-by-step explanation:
Hello!
To find the slope of a line we divide how many times it goes over by the number of times it goes up
The line goes over 4 and up 2 which is shown like
[tex]\frac{4}{2}[/tex]
We can simplify this
[tex]\frac{2}{1}[/tex]
The answer is [tex]\frac{2}{1}[/tex]
Hope this helps!
who was the first president of unitate state America
Answer:
George Washington
Step-by-step explanation:
[tex] 👋 [/tex] Hello! ☺️
R- George Washington
[tex]<marquee direction="left" scrollamount="2" height="100" width="150">Mynea04</marquee>[/tex]
On a tree farm, a forester wants to estimate the total number of trees with diameters exceeding 12 inches. A map of the farm is available. Discuss the problem of choosing appropriate sampling units and an appropriate frame.
Answer:
The problems associated with choosing appropriate sampling units and frame are given below;
Step-by-step explanation:
1. The only aid available to the forester or researcher is a map of the farm.
2. Appropriate sampling units will be hard to choose because farm trees are only characterized by attributes such as
- type of crop/plant (as all trees of a certain crop are much likely to have similar width or diameter)
- height of tree (as height is closely related to width)
- location of tree on the farm (e.g. North on the map, East on the map, South on the map, West on the map)
- age of tree (as older trees are more likely to have diameters exceeding 12 inches, than the younger trees)
- etcetera.
3. Appropriate frame (size) of sample will be hard to choose because a number of trees cannot just be selected from the total number of trees, if the categorization for sampling units is uncertain.
The distribution of the weights of a sample of 140 cargo containers is symmetric and bell-shaped, with a mean of 500 pounds and a standard deviation of 20 pounds. What percentage of the cargo containers will weigh between 460 pounds and 540 pounds?
a. 95%
b. Can't tell-there is not enough information
c. 67%
d. 99%
Answer:
a. 95%
Step-by-step explanation:
We solve this question, using z score formula.
Z score formula = (x - μ)/σ/√n
where x is the raw score
μ is the population mean
σ is the population standard deviation.
n is number of samples
For z1, where x1 = 460, μ = 500, σ = 20, n = 140
z score formula = (460 - 500)/ 20
= -40/20
= -2
We find the probability of the z score using the z score table.
P(x = 460) = P(z = -2)
= 0.02275
For z2, where x2 = 540, μ = 500, σ = 20
z score formula = (540 - 500)/20
= 40/20
= 2
We find the probability of the z score using the z score table.
P(x = 540) = P(z = 2)
= 0.97725
The probability that the cargo containers will weigh between 460 pounds and 540 pounds is calculated as:
= 460 < x < 540
= P(z = 2) - P(z = -2)
= 0.97725 - 0.02275
= 0.9545
Converting to percentage
0.9545 × 100
= 95.45%
Therefore,the percentage of the cargo containers will weigh between 460 pounds and 540 pounds is 95%
Identify the LCD of the rational expressions in the equation.
[tex]\frac{x}{x+3} + \frac{1}{x} = \frac{3}{x}[/tex]
Answer: okay so i did the equation for you to find the least common denominator. hope that helps!
1. A research team wants to investigate the usefulness of relaxation training for reducing levels of anxiety in individuals experiencing stress. They identify 30 people at random from a group of 100 who have "high stress" jobs. The 30 people are divided into two groups. One group acts as the control group - they receive no training. The second group of 15 receive the relaxation training. The subjects in each group are then given an anxiety inventory. The summarized results appear below where higher scores indicate greater anxiety. Evaluate using the criteria of p < .05. Assume it is a two tailed test.
Answer:
a. H0:u1=u2
Ha:u1>u2
b. T-critical value =1.7011
c. We can conclude that relaxation training has reduced stress levels based on evidence gathered from statistical calculations
Step-by-step explanation:
Please find attachment
Find the volume of the cylinder either enter an exact answer in terms of pi or use 3.14 for pi
1/2πr^2h.
1/2×3.142×3^2×2=
1/2×56.556=28.278~ 28.
Answer:
18pi
Step-by-step explanation:
I just got it right on Khan Academy
1. When bisecting a line segment, why must you find the intersection points of the arcs both above and below the line segment? A. To make sure that you get a straight line to bisect the line segment. B. The intersection point above the line segment overestimates the midpoint, while the intersection point below the line segment underestimates the midpoint. C. Finding both intersection points helps if the line segment is not completely vertical or horizontal. D. Only one intersection point is needed to find the midpoint, but finding both points allows you to check your work. 2. A line segment has a length of approximately 10 cm. If a compass is set to a width of 9 cm, will it still be possible to bisect the line segment? Explain. A. No, it is not possible. The compass should be just a little bit wider than half of the length of the line segment, which in this case is 5 cm. B. Yes, it is still possible. The width of the compass in respect to the length of the line segment does not matter. C. No, it is not possible. The width of the compass should be exactly half of the length of the line segment, which in this case is 5 cm. D. Yes, it is still possible. So long as the compass is wider than half the length of the line segment and still intersects the line segment, it is possible to bisect the line segment.
Answer:
A)Option A - To make sure that you get a straight line to bisect the line segment
B) Option D - Yes, it is still possible. So long as the compass is wider than half the length of the line segment and still intersects the line segment, it is possible to bisect the line segment.
Step-by-step explanation:
1) In bisection of a line segment, we seek to divide the line into 2 equal parts. Now, when using the bisection points of an arc, it's important to have two intersection points above and below the line segment so that we can draw a straight line that will pass through the horizontal line segment we are bisecting to make the bisected parts equal in length.
So option A is correct.
2) When bisecting a horizontal line segment using compass, usually we place one leg of the compass at one endpoint of the line and open the other leg of the compass to a length that's more than half of the horizontal line segment. Thereafter, we draw our arc from top to bottom. Without changing the distance of the opened compass, we put one of the legs at the 2nd endpoint and now draw another arc to intersect the previously drawn one.
Now, from the question we are told that the line segment has a length of approximately 10 cm and the compass is set to a width of 9 cm. Now, since 9cm is more than half of the line segment and provided this width of 9cm is maintained when moving the leg to the second endpoint, then it is possible.
Option D is correct.