In this problem, there are two parts. We will need to find what q is if 18% of q is 27, and what 27% of 2q is.
First, let's set up and solve the equation for 18% of q is 27.
18 / 100 = 27 / q
100q = 486
q = 4.86
Next, we'll find the value of 2q.
2(4.86) = 9.72
Finally, we'll set up a proportion and solve for 27% of 2q.
27 / 100 = x / 9.72
100x = 262.44
x = 2.6244
If 18% of q is 27, then 27% of 2q is 2.6244 (round to tenths/hundredths place as needed).
Hope this helps!! :)
Answer:
81Step-by-step explanation: Let's first find the value of q
[tex]18/100 \times q = 27\\\frac{18q}{100} = \frac{27}{1}\\18q = 2700\\\frac{18q}{18} = \frac{2700}{18} \\q= 150.\\[/tex]
Now we can find 27% of 2q
[tex]27 \% \times 2q = \\27 \% \times 2(150)\\\frac{27}{100} \times 300\\\\= \frac{8100}{100} \\= 81[/tex]
What is 5/7 subtracted by 2/5
Answer:
11/35
Step-by-step explanation:
Usando a fatoração com fator comum em evidência, fatore o seguinte polinômio: x3 + x2 + x
Answer:
x(x^2 + x + 1)
Step-by-step explanation:
x^3 + x^2 + x = x(x^2 + x + 1)
The length and width of a rectangle are in a 3:5 ratio. The perimeter of the rectangle is 64. What are the length and width of the rectangle? The length is? And the width is?
Hey there! I'm happy to help!
We know that the perimeter is 2L+2W. Le'ts plug in the values 3 and 5 from our ratio and see what our perimeter would be with that.
2(3)+2(5)
6+10
16
How can we get this 16 to 64?
64/16=4
So, we need to multiply this length and width by four to get 64 as our perimeter!
3*4=12
5*4=20
We can plug this into our perimeter equation
2(12)+2(20)
24+40
64
Therefore, our length is 12 and our width is 20.
Have a wonderful day! :D
Please answer this now in two minutes
Answer:
[tex] s = 14.1 [/tex]
Step-by-step explanation:
Find s using the Law of Cosines:
m < S = 31°
SR = q = 21
SQ = r = 9
QR = s = ?
Thus,
[tex] s^2 = r^2 + q^2 - 2(r)(q)*cos(S) [/tex]
[tex] s^2 = 9^2 + 21^2 - 2(9)(21)cos(31) [/tex]
[tex] s^2 = 81 + 441 - 378*0.8572 [/tex]
[tex] s^2 = 522 - 324.0216 [/tex]
[tex] s^2 = 197.9784 [/tex]
[tex] s = \sqrt{197.9784} [/tex]
[tex] s = 14.07 [/tex]
[tex] s = 14.1 [/tex] (to the nearest tenth)
i attached the question in the image below
Answer:
45°
Step-by-step explanation:
[tex]tan^{-1}(1)[/tex] = 45°
Answer:
[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]
Step-by-step explanation:
[tex]\tan\theta=1[/tex]
[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]
George walks 1 mile to school. He leaves home at the same time each day, walks at a steady speed of 3 miles per hour, and arrives just as school begins. Today he was distracted by the pleasant weather and walked the first 1/2 mile at a speed of only 2 miles per hour. At how many miles per hour must George run the last 1/2 mile in order to arrive just as school begins today?
Answer:
George must run the last half mile at a speed of 6 miles per hour in order to arrive at school just as school begins today
Step-by-step explanation:
Here, we are interested in calculating the number of hours George must walk to arrive at school the normal time he arrives given that his speed is different from what it used to be.
Let’s first start at looking at how many hours he take per day on a normal day, all things being equal.
Mathematically;
time = distance/speed
He walks 1 mile at 3 miles per hour.
Thus, the total amount of time he spend each normal day would be;
time = 1/3 hour or 20 minutes
Now, let’s look at his split journey today. What we know is that by adding the times taken for each side of the journey, he would arrive at the school the normal time he arrives given that he left home at the time he used to.
Let the unknown speed be x miles/hour
Mathematically;
We shall be using the formula for time by dividing the distance by the speed
1/3 = 1/2/(2) + 1/2/x
1/3 = 1/4 + 1/2x
1/2x = 1/3 - 1/4
1/2x = (4-3)/12
1/2x = 1/12
2x = 12
x = 12/2
x = 6 miles per hour
angle x and y are complementary angles . angle y measure 37 plzz help asap
Answer:
53 degrees
Step-by-step explanation:
Complementary angles add to 90 degrees
a+b = 90
a=37
37+b = 90
Subtract 37 from each side
37+b-37 = 90-37
b =53
Answer: 53 degrees
Step-by-step explanation: We can find the measure of <b by taking 90 minus the measure of <a which is 90 - 37 or 53 degrees.
If some of the omitted variables, which you hope to capture in the changes analysis, in fact change over time within entity, then the FE estimator a. will be unbiased only when allowing for heteroskedastic-robust standard errors. b. may still be biased. c. will only be unbiased in large samples. d. will always be unbiased.
Answer:
d. will always be unbiased.
Step-by-step explanation:
When some of variables are omitted the estimator on indulge charge regressor may still be unbiased. If there is a special case where T = 2 then the FE estimator will be unbiased. Fixed effect regression model has different intercepts.
HIIIIII 2 QUESTIONS IN THE 2 PICS HELP PLS
Answer:
(1)C- Trapezoid
(2)D-20 square feet
Step-by-step explanation:
Question 1
A cross-section of a rectangular pyramid cut perpendicular to the base but not passing through the top will have two parallel sides where one of the sides will be longer. Therefore, the shape which describes the cross-section will be a trapezoid.
Question 2
The base of the Triangle = 5 feet
Height of the Triangle = 8 feet
[tex]\text{Area of a triangle}=\dfrac12 \times $Base \times Height\\=\dfrac12 \times 5 \times 8\\=20 ft^2[/tex]
a football is fired upward with an initial speed of 800 feet per second. It is given that h=-12t^2+360t (h is the height of the football at any given time).what will you set h equal to in the equation to to find how many seconds it takes the football to hit the ground?
Answer:
30 s
Step-by-step explanation:
When the ball hits the ground h=0. To find the time t when this happens we must solve the equation h=0.
●h= 0
● -12t^2+360t =0
● t(-12t +360) = 0
● t = 0 or -12t +360 =0
● t=0 or -12t = -360
● t=0 or 12t =360
● t=0 or t=360/12
● t=0 or t= 30
The equation has two solutions.
The ball was fired with an initial speed of 800 feet per second so it cannot hit the ground at t=0.
So the ball hits the ground after 30 s.
4. The difference between twice a number and
half the number is 30. What is the number?
Help me please
Answer:
20
Step-by-step explanation:
let the number be n then twice the number is 2n and half the number is [tex]\frac{1}{2}[/tex] n
Then the difference is
2n - [tex]\frac{1}{2}[/tex] n = 30 ( multiply through by 2 to clear the fraction )
4n - n = 60, that is
3n = 60 ( divide both sides by 3 )
n = 20
The roots of \[x^2 + 5x + 3 = 0\]are $p$ and $q,$ and the roots of \[x^2 + bx + c = 0\]are $p^2$ and $q^2.$ Find $b + c.$[tex]The roots of\[x^2 + 5x + 3 = 0\]are $p$ and $q,$ and the roots of\[x^2 + bx + c = 0\]are $p^2$ and $q^2.$ Find $b + c.$[/tex]
By the factor theorem, we have
[tex]x^2+5x+3=(x-p)(x-q)\implies\begin{cases}3=pq\\-5=p+q\end{cases}[/tex]
[tex]x^2+bx+c=(x-p^2)(x-q^2)\implies\begin{cases}c=p^2q^2\\-b=p^2+q^2\end{cases}[/tex]
Then
[tex]c=p^2q^2=(pq)^2=3^2=9[/tex]
and
[tex]p+q=-5\implies(p+q)^2=p^2+2pq+q^2=25\implies b=-(p^2+q^2)=-19[/tex]
So we have b + c = -19 + 9 = -10.
The given roots of the equation x² + 5x + 3 = 0 as p and q, and x² + bx + c = 0 as p² and q², gives us the value of b + c = -10.
What are the sum and product of the roots of a quadratic equation?If the quadratic equation ax² + bx + c = 0, has roots as α and β, then:
Sum of the roots, α + β = -b/aProduct of the roots, αβ = c/aHow to solve the given question?In the question, we are informed that the roots of the expression x² + 5x + 3 = 0 are p and q, and the roots of the expression x² + bx + c = 0 are p² and q².
We are asked to find the value of b + c.
Since the roots of the equation x² + 5x + 3 = 0 are given as p and q.
So, we can say that:
Sum of the roots, p + q = -5Product of the roots, pq = 3Now, we are informed that the roots of the equation x² + bx + c = 0 are p² and q². So, we can say that:
Sum of the roots, p² + q² = -b, or, (p + q)² - 2pq = -b, or, (-5)² - 2(3) = -b, or, 25 - 6 = -b, or, 19 = -b, or, b = -19.Product of the roots, p²q² = c, or, (pq)² = c, or, 3² = c, or, c = 9.∴ b + c = -19 + 9 = -10.
∴ The given roots of the equation x² + 5x + 3 = 0 as p and q, and x² + bx + c = 0 as p² and q², gives us the value of b + c = -10.
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An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 634" by 412" on the drawing, how large is the bedroom?
and the answer should be 18 x 27. The answers were reversed.
Step-by-step explanation:
basically you can do (6x4) + 3 = 27
and (4x4) + 2 = 18.
A ratio shows us the number of times a number contains another number. The real size of the bedroom is 2536' by 1648'.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that architectural drawing lists the scale as 1/4" = 1'. Therefore, we can write the scale ratio as,
1/4" = 1'
1" = 4'
Now, given that the bedroom measures 634" by 412" on the drawing. Therefore, the real dimensions of the bedroom are,
634" = 634 × 4' = 2536'
412" = 412× 4' = 1648'
Hence, the real size of the bedroom is 2536' by 1648'.
Learn more about Ratios:
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hey loves!!! PLz help me
Answer:
Hey there!
We must use what we are given, so even though it looks like there might be four isosceles triangles, we are only given CA=CE, so that only allows us to conclude mathematically that there is only 1 isosceles triangle.
Hope this helps :)
Valerie had a jug that contained 128 fl oz of salsa to put into bowls at a restaurant. She filled each bowl with 6 fl oz of salsa until there was not enough salsa left in the jug to completely fill another bowl. How many fluid ounces of salsa were left in the jug?
Answer: 2 fl oz
Step-by-step explanation:
Division with remainders
128/6=21.33333..
[tex]21\cdot 6=126[/tex]
128-126=2
2 fl oz was left in the jug
WILL MARK BRAINLIEST!! PLZ HELP!!
Answer:
The answer is D.
Step-by-step explanation:
When x=0, then y=300, so it has to be more than that.
When x=25, y=300, so it has to be less than that.
how to solve for x?Knowledge and Understanding
Answer:
x = 25°Step-by-step explanation:
The figure above is a quadrilateral
Angles in a quadrilateral add up to 360°
To find x add up all the angles and equate them to 360°
That's
6x + 4x + 3x + x + 10 = 360
14x = 350
Divide both sides by 14
x = 25°
Hope this helps you
2. A vertical stick 10 cm long casts a shadow 8 cm long. At the same time a tower casts a
shadow 30 m long. Determine the height of the tower.
Answer:
The height of the tower is:
24 meters
Step-by-step explanation:
1 meter = 100 centimeters
10 centimeters = 10/100 = 0.1 meters
8 centimeters = 8/100 = 0.08 meters
On a three rule:
0.1 meters is to 0.08 meters
30 meters is to A meters
A = 30*0.08/0.1
A = 24 meters
Related task:
https://brainly.lat/tarea/14821170
Please answer this in two minutes
Answer:
366.6 mm²
Step-by-step explanation:
Step 1: find XY using the Law of sines.
Thus,
[tex] \frac{XY}{sin(W)} = \frac{WY}{sin(X)} [/tex]
m < W = 180 - (70+43) (sum of angles in a triangle)
W = 180 - 113 = 67°
WY = 24 mm
X = 43°
XY = ?
[tex] \frac{XY}{sin(67)} = \frac{24}{sin(43)} [/tex]
Cross multiply:
[tex] XY*sin(43) = 24*sin(67) [/tex]
[tex] XY*0.68 = 24*0.92 [/tex]
Divide both sides by 0.68 to solve for XY
[tex] \frac{XY*0.68}{0.68} = \frac{24*0.92}{0.68} [/tex]
[tex] XY = 32.47 [/tex]
XY ≈ 32.5 mm
Step 2: find the area using the formula, ½*XY*WY*sin(Y).
Area = ½*32.5*24*sin(70)
Area = ½*32.5*24*0.94
= 32.5*12*0.94
Area = 366.6 mm² (nearest tenth)
Please help Asap, will give brainiest only if answer correctly with a good explanation
Answer:
D, or the last option.
Step-by-step explanation:
See how the rotation does not say whether it is Clockwise or Counterclockwise?
Now, what that means, is that it will, default, be CCW. I don't know why, but math teachers are like that.
Now, 80* and 10* add up to 90* (because they are both unmarked and going to the same direction).
So, 90* rotation CCW. Simple! Thus, the last option should be correct.
Hope this helps!
P.S. Stay Safe!
A cake mix calls for these ingredients. 2 cups of sugar 7 cups of flour 3 cups of milk 1 cup of oil Write the ratios of sugar to flour and milk to oil. Which correctly compares the ratios?
Answer:
Ratio of sugar and flour
2:7
Ratio of milk and oil
3:1
Step-by-step explanation:
Here in this question, we shall be writing ratios based on the given number of cups in the question.
We start with ratio of sugar to flour.
We have;2 cups of sugar and 7 cups of flour. Thus we have the ratio of sugar to flour as 2:7
Also we want the ratio of milk and oil
we have 3 cups of milk and 1 cup of oil
So the ratio of milk and oil is 3:1
Answer: TO be short for it its B! :D
A cake mix calls for these ingredients.
2 cups of sugar
7 cups of flour
3 cups of milk
1 cup of oil
Write the ratios of sugar to flour and milk to oil. Which correctly compares the ratios?
3/7 > 2/1
2/7<3/1
7/1<2/3
3/2>1/7
2
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2/7<3/1
with 2 cups of sugar to 7 cups of flour that is a small ratio/ fraction while as
3 cups of milk to 1 cup of oil is a larger ratio/fraction.
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Answer: The correct option is (B).
The ratio of sugar to flour is and the ratio of milk to oil is
Step-by-step explanation: Given that a cake mix calls for the following ingredients:
2 cups of sugar , 7 cups of flour , 3 cups of milk and 1 cup of oil.
We are given to write the ratios of sugar to flour and milk to oil and select the correct comparison of the ratios.
The ratio of sugar to flour is given by
and the ratio of milk to oil is given by
Since
so have
Thus, the ratio of sugar to flour is and the ratio of milk to oil is The correct comparison is
Option (B) is CORRECT.
Step-by-step explanation:
On a coordinate plane, 2 lines are shown. Line H J has points (negative 4, negative 2) and (0, 4). Line F G has points (negative 4, 1) and (0, negative 2). Which statement best explains the relationship between lines FG and HJ? They are perpendicular because their slopes are equal. They are perpendicular because their slopes are negative reciprocals. They are not perpendicular because their slopes are equal. They are not perpendicular because their slopes are not negative reciprocals.
Answer:
They are not perpendicular because their slopes are not negative reciprocals.
Step-by-step explanation:
Well first we need to find slope.
[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]
Line HJ)
(-4,-2) , (0,4)
y2 is 4 y1 is -2, so 4 - -2 = 6
0 - -4 = 4
6/4 -> 3/2
Due to the point (0,4) having no x value 4 is the y intercept.
Hence, y = 3/2x + 4 is the slope of line HJ
Line FG)
(-4,1) , (0,-2)
y2 is -2 y1 is 1, so -2 - 1 = -3
0- -4 = 4
Because (0,-2) is missing an x value -2 is the y intercept,
Equation: y = -3/4x - 2
They are not perpendicular because their slopes are not negative reciprocals.
The slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).
Recall:
Lines that are parallel will have the same slope.Lines that are perpendicular to each other will have slope values that are negative reciprocal of each other.Slope (m) = [tex]\frac{y_2- y_1}{x_2 - x_1}[/tex]Given that lines HJ (blue line) and FG (red line) are on a coordinate plane as shown in the diagram attached below, let's find their slope:
Slope of line HJ:
[tex]Slope (m) = \frac{-2 - 4}{-4 -0} = \frac{-6}{-4} = \frac{3}{2}[/tex]
Slope of HJ is 3/2Slope of line FG:
[tex]Slope (m) = \frac{-2 - 1}{0-(-4)} = \frac{-3}{4} = -\frac{3}{4}[/tex]
Slope of FG is -3/4Therefore, the slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).
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simplify: m–(a–k–b) HElp!
Answer: m-a+k+b
Step-by-step explanation:
m-(a-k-b)= m+-1*(a-k-b). Then, simply use distributive property to simplify the equation into m-a+k+b
Hope it helps <3
StartLayout enlarged left-brace 1st row 4 x minus 5 y = 5 2nd row negative 0.08 x + 0.10 y = 0.10 EndLayout
Answer:
[tex]x = 1.25[/tex]
[tex]y = 0[/tex]
Step-by-step explanation:
Given
[tex]4x - 5y = 5[/tex]
[tex]0.08x + 0.10y = 0.10[/tex]
Required
Determine the solution
Make x the subject of formula in: [tex]4x - 5y = 5[/tex]
[tex]4x = 5 + 5y[/tex]
Divide both sides by 4
[tex]\frac{4x}{4} = \frac{5 + 5y}{4}[/tex]
[tex]x = \frac{5 + 5y}{4}[/tex]
Substitute [tex]x = \frac{5 + 5y}{4}[/tex] in [tex]0.08x + 0.10y = 0.10[/tex]
[tex]0.08(\frac{5 + 5y}{4}) + 0.10y = 0.10[/tex]
Solve the fraction
[tex]0.02(5 + 5y) + 0.10y = 0.10[/tex]
Open the bracket
[tex]0.1 + 0.1y + 0.10y = 0.10[/tex]
[tex]0.1 + 0.2y = 0.10[/tex]
Subtract 0.1 from both sides
[tex]0.1-0.1 + 0.2y = 0.10 - 0.1[/tex]
[tex]0.2y = 0[/tex]
Divide both sides by 0.2
[tex]y =0[/tex]
Substitute 0 for y in [tex]x = \frac{5 + 5y}{4}[/tex]
[tex]x = \frac{5 + 5*0}{4}[/tex]
[tex]x = \frac{5 + 0}{4}[/tex]
[tex]x = \frac{5 }{4}[/tex]
[tex]x = 1.25[/tex]
Please answer this question now only answer if you know the answer
Answer:
v = 10.997
Step-by-step explanation:
For this, simply use the law of cosines.
v^2 = (16)^2 + (6)^2 - 2(16)(6)cos(27)
v^2 = 256 + 36 - 171.073
v^2 = 120.927
v = 10.997
Cheers.
Answer:
[tex]\boxed{11}[/tex] unitsStep-by-step explanation:
To solve the length of UW, you can use the Law of Cosines for a SAS case:
[tex]\boxed{v^2=\sqrt{u^2+w^2-2(uw)cos(V)} }[/tex]
Substitute the values and solve with a calculator:
[tex]\boxed{\sqrt{16^2+6^2-2(16*6)cos(27)} = 10.99666983 \approxeq 11}[/tex]
The length of UW is 11 units.
what is the value of X when f(x)=g(x) ?
Answer:
x=3
Step-by-step explanation:
We want to find the value of x where the two graphs intersect
The graphs intersect at ( 3,8)
The value of x is 3
The television show Lett3rs has been successful for many years. That show recently had a share of 24, meaning that among the TV sets in use, 24% were tuned to Lett3rs. Assume that an advertiser wants to verify that 24% share value by conducting its own survey, and a pilot survey begins with 11 households have TV sets in use at the time of a Lett3rs broadcast.
Find the probability that none of the households are tuned to Lett3rs. P(none) =
Find the probability that at least one household is tuned to Lett3rs. P(at least one) =
Find the probability that at most one household is tuned to Lett3rs. P(at most one) =
If at most one household is tuned to Lett3rs, does it appear that the 24% share value is wrong? (Hint: Is the occurrence of at most one household tuned to Lett3rs unusual?)
Answer:
(a) P(none) = 0.0488
(b) P(at least one) = 0.9512
(c) P(at most one) = 0.2186
(d) No, it doesn't appear that the 24% share value is wrong.
Step-by-step explanation:
We are given that among the TV sets in use, 24% were tuned to Lett3rs.
A pilot survey begins with 11 households have TV sets in use at the time of a Lett3rs broadcast.
Let X = Number of households that are tuned to Lett3rs
The above situation can be represented through binomial distribution;
[tex]P(X = r)=\binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,......[/tex]
where, n = number of samples (trials) taken = 11 households
r = number of success
p = probability of success which in our question is % of
households that were tuned to Lett3rs, i.e; 24%
So, X ~ Binom{n = 11, p = 0.24}
(a) The probability that none of the households are tuned to Lett3rs is given by = P(X = 0)
P(X = 0) = [tex]\binom{11}{0}\times 0.24^{0} \times (1-0.24)^{11-0}[/tex]
= [tex]1\times 1 \times 0.76^{11}[/tex]
= 0.0488
(b) The probability that at least one households are tuned to Lett3rs is given by = P(X [tex]\geq[/tex] 1)
P(X [tex]\geq[/tex] 1) = 1 - P(X = 0)
= 1 - 0.0488
= 0.9512
(b) The probability that at most one households are tuned to Lett3rs is given by = P(X [tex]\leq[/tex] 1)
P(X [tex]\leq[/tex] 1) = P(X = 0) + P(X = 1)
= [tex]\binom{11}{0}\times 0.24^{0} \times (1-0.24)^{11-0}+\binom{11}{1}\times 0.24^{1} \times (1-0.24)^{11-1}[/tex]
= [tex]1\times 1\times 0.76^{11}+11\times 0.24^{1} \times 0.76^{10}[/tex]
= 0.2186
No, it doesn't appear that the 24% share value is wrong because the probability that at most one household is tuned to Lett3rs is somewhere close to 24% and this probability is also not unusual as it is way more than the criteria of more than 5%.
When using a calorimeter, the initial temperature of a metal is 70.4C. The initial temperature of the water is 23.6C. At the end of the experiment, the final equilibrium temperature of the water is 29.8C. What is the final temperature of the metal? C What is the temperature change of the water? C What is the temperature change of the metal? C
Answer:
29.8C6.2C-40.6CStep-by-step explanation:
a) "Equilibrium" means the final temperatures of everything in the calorimeter are the same. The final temperature of the metal is the same as that of the water: 29.8C.
__
b) The temperature change of the water is ...
final temp - initial temp = 29.8C -23.6C = 6.2C
__
c) The temperature change of the metal is ...
final temp - initial temp = 29.8C -70.4C = -40.6C
Answer:
29.8C
6.2C
-40.6C
Step-by-step explanation:
Answer:
????
Step-by-step explanation:
Where is the question????
Find HY if YL=9. nobody has shown me how to do this the last two weeks
Step-by-step explanation:
(a) Your computer may be programmed to allocate borderline cases to the
next group down, or the next group up; and it may or may not manage
to follow this rule consistently, depending on its handling of the numbers
involved. Following a rule which says 'move borderline cases to the next
group up', these are the five classifications.
(i) 1.0-1.2 1.2-1.4 1.4-1.6 1.6-1.8 1.8-2.0 2.0-2.2 2.2-2.4
6 6 4 8 4 3 4
2.4-2.6 2.6-2.8 2.8-3.0 3.0-3.2 3.2-3.4 3.4-3.6 3.6-3.8
6 3 2 2 0 1 1
(ii) 1.0-1.3 1.3-1.6 1.6-1.9 1.9-2.2 2.2-2.5
10 6 10 5 6
2.5-2.8 2.8-3.1 3.1-3.4 3.4-3.7
7 3 1 2
(iii) 0.8-1.1 1.1-1.4 1.4-1.7 1.7-2.0 2.0-2.3
2 10 6 10 7
2.3-2.6 2.6-2.9 2.9-3.2 3.2-3.5 3.5-3.8
6 4 3 1 1
(iv) 0.85-1.15 1.15-1.45 1.45-1.75 1.75-2.05 2.05-2.35
4 9 8 9 5
2.35-2.65 2.65-2.95 2.95-3.25 3.25-3.55 3.55-3.85
7 3 3 1 1
(V) 0.9-1.2 1.2-1.5 1.5-1.8 1.8-2.1 2.1-2.4
6 7 11 7 4
2.4-2.7 2.7-3.0 3.0-3.3 3.3-3.6 3.6-3.9
7 4 2 1 1
(b) Computer graphics: the diagrams are shown in Figures 1.9 to 1.11