Answer:
No
It could be purely due to chance.
Step-by-step explanation:
A population is defined as the whole group which has the same characteristics. For example a population of the college belongs to the same college . But a sample may be an element of a population.
So it is not necessary for a population to have the same characteristics as the sample.
But it is essential for the sample to have at least one same characteristics as the population.
So we would not be correct in inferring that such a relationship also exists in the population.
It is a hypothesis which can be true or false due to certain conditions or limitations as the case maybe.
For example in a population of smokers some may be in the habit of taking cocaine. But a sample of cocaine users does not mean the whole population uses it.
It could be purely due to chance if we find out that there is a relationship between parents’ and children’s party identification in the population.
Assume that random guesses are made for multiple-choice questions on a test with choices for each question, so that there are n trials, each with probability of success (correct) given by p. Find the probability of no correct answers
Complete Question
Assume that random guesses are made for 7 multiple-choice questions on a test with 5 choices for each question, so that there are n=7 trials, each with probability of success (correct) given by p=0.20. Find the probability of no correct answers.
Answer:
The probability is [tex]P(X = 0 ) = 0.210[/tex]
Step-by-step explanation:
From the question we are told that
The number of trial is n = 7
The probability of success is p = 0.20
Generally the probability of failure is
[tex]q = 1- 0.20[/tex]
[tex]q = 0.80[/tex]
Given that this choices follow a binomial distribution as there is only two probabilities i.e success or failure
Then the probability is mathematically represented as
[tex]P(X = 0 ) = \left n} \atop {}} \right. C_0 * p^{0} * q^{n- 0}[/tex]
[tex]P(X = 0 ) = \left 7} \atop {}} \right. C_0 * (0.2)^{0} * (0.8)^{7- 0}[/tex]
Here [tex]\left 7} \atop {}} \right. C_0 = 1[/tex]
=> [tex]P(X = 0 ) = 1 * 1* (0.8)^{7- 0}[/tex]
=> [tex]P(X = 0 ) = 0.210[/tex]
Can someone please help me?
Negative Integers are :
Less than zeroTo the left of zero on a number line.FIND THE VALUE OF NT
PLEASE HELP ASAP :(
Answer:
NT = 14 units
Step-by-step explanation:
In this question we will apply the theorem of intersecting chords.
Two chords MY and TN are intersecting each other inside a circle at a point H.
Theorem states,
MH × HY = TH × HN
12(x) = 8(x + 2)
12x = 8x + 16
12x - 8x = 16
4x = 16
x = 4
Therefore, measure of chord NT = NH + HT
= 8 + (x + 2)
= x + 10
= 4 + 10
= 14 units
In a local university, 10% of the students live in the dormitories. A random sample of 100 students is selected for a particular study. Carry answer to the nearest ten-thousandths. (Bonus Question)
a. What is the probability that the sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178?
b. What is the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025?
Answer:
a
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
b
[tex]P( X >0.025 ) = 0.99379[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.10[/tex]
The sample size is [tex]n = 100[/tex]
Generally the standard error is mathematically represented as
[tex]SE = \sqrt{\frac{ p (1 - p )}{n} }[/tex]
=> [tex]SE = \sqrt{\frac{ 0.10 (1 - 0.10 )}{100} }[/tex]
=> [tex]SE =0.03[/tex]
The sample proportion (the proportion living in the dormitories) is between 0.172 and 0.178
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} < \frac{ X - 0.10}{SE} < \frac{ 0.178 - 0.10}{0.03} )[/tex]
Generally [tex]\frac{ X - 0.10}{SE} = Z (The \ standardized \ value \ of X )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (\frac{ 0.172 - 0.10}{0.03} <Z < \frac{ 0.178 - 0.10}{0.03} )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P (2.4 <Z < 2.6 )[/tex]
[tex]P( 0.172 < X < 0.178 ) = P(Z < 2.6 ) - P (Z < 2.4 )[/tex]
From the z-table
[tex]P(Z < 2.6 ) = 0.99534[/tex]
[tex]P(Z < 2.4 ) = 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) =0.99534 - 0.9918[/tex]
[tex]P( 0.172 < X < 0.178 ) = 0.00354[/tex]
the probability that the sample proportion (the proportion living in the dormitories) is greater than 0.025 is mathematically evaluated as
[tex]P( X >0.025 ) = P (\frac{ X - 0.10}{SE} > \frac{ 0.0025- 0.10}{0.03} )[/tex]
[tex]P( X >0.025 ) = P (Z > -2.5 )[/tex]
From the z-table
[tex]P (Z > -2.5 ) = 0.99379[/tex]
Thus
[tex]P( X >0.025 ) = P (Z > -2.5 ) = 0.99379[/tex]
Find the values of x which satisfy the following inequation:
x3 – x² <12x
Answer:
x< -3 and 0 < x < 4
Step-by-step explanation:
x^3 – x² <12x
Subtract 12x from each side
x^3 -x^2 - 12x< 0
Factor
x( x^2 -x-12) <0
Factor
x( x-4) ( x+3) < 0
Using the zero product property
x=0 x=4 x=-3
We have to check the signs regions
x < -3
-( -) (-) < 0 True
-3 to 0
-( -) (+) < 0 False
0 to 4
+( -) (+) < 0 True
x>4
+( +) (+) < 0 False
The regions this is valid is
x< -3 and 0 < x < 4
Simplify the following expression.X^1/3 * X^1/5
Answer:
[tex] X^{\frac{8}{15}} [/tex]
Step-by-step explanation:
[tex] X^\frac{1}{3} \times X^\frac{1}{5} = [/tex]
To multiply two powers with the same base, write the base and add the exponents.
[tex] = X^{\frac{1}{3} + \frac{1}{5}} [/tex]
[tex] = X^{\frac{5}{15} + \frac{3}{15}} [/tex]
[tex] = X^{\frac{8}{15}} [/tex]
(x+1)(x−1)(x−5)=0 HELP
Answer:
x³ - 5x² - x + 5
Step-by-step explanation:
(x+1)(x-1)(x-5) = 0
fisrt step:
(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1
then:
(x+1)(x-1)(x-5) = (x²-1)(x-5)
(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5
Assume that females have pulse rates that are normally distributed with a mean of μ=73.0 beats per minute and a standard deviation of σ=12.5 beats per minute. Complete parts (a) through (c) below.a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 76 beats per minute.b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?A. Since the mean pulse rate exceeds 30, the distribution of sample means is a normal distribution for any sample size.B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size.C. Since the distribution is of sample means, not individuals, the distribution is a normal distribution for any sample size.D. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
Answer:
a. the probability that her pulse rate is less than 76 beats per minute is 0.5948
b. If 25 adult females are randomly selected, the probability that they have pulse rates with a mean less than 76 beats per minute is 0.8849
c. D. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
Step-by-step explanation:
Given that:
Mean μ =73.0
Standard deviation σ =12.5
a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 76 beats per minute.
Let X represent the random variable that is normally distributed with a mean of 73.0 beats per minute and a standard deviation of 12.5 beats per minute.
Then : X [tex]\sim[/tex] N ( μ = 73.0 , σ = 12.5)
The probability that her pulse rate is less than 76 beats per minute can be computed as:
[tex]P(X < 76) = P(\dfrac{X-\mu}{\sigma}< \dfrac{X-\mu}{\sigma})[/tex]
[tex]P(X < 76) = P(\dfrac{76-\mu}{\sigma}< \dfrac{76-73}{12.5})[/tex]
[tex]P(X < 76) = P(Z< \dfrac{3}{12.5})[/tex]
[tex]P(X < 76) = P(Z< 0.24)[/tex]
From the standard normal distribution tables,
[tex]P(X < 76) = 0.5948[/tex]
Therefore , the probability that her pulse rate is less than 76 beats per minute is 0.5948
b. If 25 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute.
now; we have a sample size n = 25
The probability can now be calculated as follows:
[tex]P(\overline X < 76) = P(\dfrac{\overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{ \overline X-\mu}{\dfrac{\sigma}{\sqrt{n}}})[/tex]
[tex]P( \overline X < 76) = P(\dfrac{76-\mu}{\dfrac{\sigma}{\sqrt{n}}}< \dfrac{76-73}{\dfrac{12.5}{\sqrt{25}}})[/tex]
[tex]P( \overline X < 76) = P(Z< \dfrac{3}{\dfrac{12.5}{5}})[/tex]
[tex]P( \overline X < 76) = P(Z< 1.2)[/tex]
From the standard normal distribution tables,
[tex]P(\overline X < 76) = 0.8849[/tex]
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
In order to determine the probability in part (b); the normal distribution is perfect to be used here even when the sample size does not exceed 30.
Therefore option D is correct.
Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
5. What is the solution of the following linear system?
y= 3x + 1
2y = 6x + 2
O A. (5,-2)
OB. (34)
C. Infinitely many solutions
D. No solution
Answer:
C. Infinitely many solutions
Step-by-step explanation:
First, simplify the second equation by dividing it by 2
2y = 6x + 2
y = 3x + 1
Now, we can see that both equations are the same, both y = 3x + 1.
Since they are the same line, this means that there are infinitely many solutions.
So, the correct answer is C.
f(x) = x^2 + 2x + 1, then for what values of x, f(x)=f(x+2) step by step plz
Answer:
x = -2
Step-by-step explanation:
given f(x) = x² + 2x + 1
f(x+2) = (x+2)² + 2(x+2) + 1
= x² 4x+4+2x+4+1
= x² + 6x + 9
for f(x) = f(x+2), simply equate the two expressions and solve for x
f(x) = f(x+2)
x² + 2x + 1 = x² + 6x + 9 (x² terms cancel out)
2x + 1 = 6x + 9 (subtract 1 from both sides)
2x = 6x + 9 - 1
2x = 6x + 8 (subtract 6x from both sides)
2x - 6x = 8
-4x = 8 (divide both sides by -4)
x = 8 / (-4)
x = -2
Consider the following sample data: 12, 13, 7, 5, 15, 18. Which one of the following represents the value of the standard deviation?
A. 11.67
B. 4.89
C. 2.52
D. 23.87
Answer:
Standard deviation= 4.46
B) 4.89 is the nearest answer
Step-by-step explanation:
Standard deviation √variance
Variance= (summation (x-mean)²)/n
Mean= summation of numbers/total
Mean =( 12+13+ 7+5+15 18)/6
Mean= 70/6
Mean= 11.67
Variance=(( 12-11.67)²+(13-11.67)²+ (7-11.67)²+(5-11.67)²+(15-11.67)²+ (18-11.67)²)/6
Variance= (0.1089+1.7689+21.8089+44.4889+11.0889+40.0689)/6
Variance= 119.3334/6
Variance= 19.8889
Standard deviation= √variance
Standard deviation= √19.8889
Standard deviation= 4.46
Select the correct graph.
Answer:
Graph 1
Step-by-step explanation:
The only graph that could be possible would be graph 1.
As you can see the function x = 2t - 4 is linear, and the only graph that consists of a linear line would be the first graph.
Use the following cell phone airport data speeds (Mbps) from a particular network. Find the percentile corresponding to the data speed 4.9 Mbps.
0.2 0.8 2.3 6.4 12.3 0.2 0.8 2.3 6.9 12.7 0.2 0.8 2.6 7.5 12.9 0.3 0.9 2.8 7.9 13.8
0.6 1.5 0.1 0.7 2.2 6.1 12.1 0.6 1.9 5.5 11.9 27.5 0.6 1.7 3.3 8.3 13.8 1.3 3.5 9.8
14.6 10.1 14.7 11.8 14.8
Answer:
Thus percentile lies between 53.3% and 55.6 %
Step-by-step explanation:
First we arrange the data in ascending order . Then find the number of the values corresponding to the given value. Then equate it with the number of observations and x and then multiply it to get the percentile. n= P/100 *N
where n is the ordinal rank of the given value
N is the number of values in ascending order.
The data in ascending order is
0.1 0.2 0.2 0.2 0.3 0.6 0.6 0.6 0.7 0.8 0.8 0.8 0.9 1.3
1.5 1.7 1.9 2.2 2.3 2.3 2.6 2.8 3.3 3.5 5.5 6.1 6.4 6.9 7.5 7.9 8.3 9.8 10.1 11.8 11.9 12.1 12.3 12.7 12.9 13.8 13.8 14.6 14.7 14.8 27.5
Number of observation = 45
4.9 lies between 3.3 and 5.5
x*n = 24 observation x*n = 25 observation
x*45= 24 x*45= 25
x= 0.533 x= 0.556
Thus percentile lies between 53.3% and 55.6 %
will rate you brainliest
Answer:
A
Step-by-step explanation:
f(x)→g(x)
(0, 0) → (3, -4)
Therefore it increases it x-axis from 0 to 3
And decreases in y-axis from 0 to -4
Please help. I’ll mark you as brainliest if correct!
Answer: x= -1, z=2, y= -4
Step-by-step explanation:
System of equations:
-5x - 4y - 3z= 15 +
-10x + 4y + 6z= 6
-15x + 3z = 21 ------> 3 (-5x + z) = 7.3
-5x + z = 7
now,
-10x + 4y + 6z= 6
2(-5x + z) + 4y + 4z = 6
14 + 4y + 4z = 6
7 + 2y + 2z = 3
2y + 2z= -4
y+z=-2
Now we were using the equation: 20x + 4y + 4z = -28
20x + 4(y+z) = 20x -8= - 28
20 x = -20
x= -1
With this we can find y and z
X=-1
-5x + z = 7
z= 2
y+z=-2
y=-4
Finally we have: x= -1, z=2, y= -4
I hope this can help you.
Thank you
34% of working mothers do not have enough money to cover their health insurance deductibles. You randomly select six working mothers and ask them whether they have enough money to cover their health insurance deductibles. The random variable represents the number of working mothers who do not have enough money to cover their health insurance deductibles.
Required:
Construct a binomial distribution using n= 0.6 and p=0.34
Answer:
solution below
Step-by-step explanation:
The question says 6 working mother's were selected so n = 6 not 0.6
We are expected to find
P(X = 0,1,2,3,4,4,6)
1. When x = 0
6C0*(0.34)⁰*(0.66)⁶
= 1 *1* 0.827
= 0.0827
2. When X = 1
6C1*(0.34)¹*(0.66)⁵
= 6 x 0.34 x 0.252
= 0.2555
3. When X = 2
6C2*(0.34)²*(0.66)⁴
= 15 x 0.1156 x 0.1897
= 0.3289
4. When x = 3
6C3*(0.34)³*(0.66)³
20 x 0.039304 x 0.2875
= 0.2599
5. When X = 4
6C4*(0.34)⁴*(0.66)²
= 15 x 0.01336 x 0.4356
= 0.8729
6. When x = 5
6C5*(0.34)⁵*(0.66)¹
= 6 x 0.0045 x 0.66
= 0.01782
7. When x = 6
6C6*(0.34)⁶*(0.66)⁰
1 x 0.0015 x 1
= 0.0015
1. Which word best describes how you feel when working on a math assessment? ( point)
bored
excited
anxious
confident
Answer:
math is really a difficult subject for me. sometimes i feel confident when i get my answers correct, but sometimes i feel bored when i dnt get my answer. Sometimes i feel anxious , sometimes i feel excited to solve the problems.
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Original price of a soda: $800 tax 7% selling price: $
Answer:
$856
Step-by-step explanation:
Find 7% of $800 and then add it to $800
[tex]4x - 2x = [/tex]
Answer:
2x
Step-by-step explanation:
These are like terms so we can combine them
4x-2x
2x
Answer:
2x
Explanation:
Since both terms in this equation are common, we can simply subtract them.
4x - 2x = ?
4x - 2x = 2x
Therefore, the correct answer should be 2x.
Point A is at (2, -8) and point C is at (-4, 7).
Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.
Answer:
(-2, 2)
Step-by-step explanation:
Given:
Point A is at (2, -8) and point C is at (-4, 7)Difference of coordinates:
Δx = 2 - (-4) = 6Δy = - 8 - 7 = - 15The ratio of AB to AC is 2:1. So:
AB = 2*AC/3 and BC = AC/3Then coordinates of point B should be 2/3 from the point A:
x = 2- 6*2/3 = 2 - 4 = -2y = - 8 - (-15)*2/3 = -8 + 10 = 2So point B has coordinates of (-2, 2)
Which of the following statements is TRUE about the stepwise selection procedure?
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
B. Backward stepwise procedure and forward stepwise procedure would end up with the same "best" model.
C. The "best" model determined by the stepwise selection method is the same model as what would be selected by complete search but stepwise method is usually faster.
D. Different choices of alpha limits for variable selection may end up with different final models.
Answer:
A. The stepwise selection procedure uses Adjusted R-square as the "best" model criterion.
Step-by-step explanation:
Stepwise regression is a model which uses variables in step by step manner. The procedure involves removal or inclusion of independent variables one by one. It adds the most significant independent variable and removes the less significant independent variable. Usually stepwise selection uses R-square or Mallows Cp for picking the best fit.
I will rate you brainliest Select the best description of what the LCM of a set of polynomials is. a.It is the quotient of all the factors of the polynomials. b.It is the common numerator of a rational expression. c. It is the product of the prime factors that are either unique to or shared by the polynomials. d. It is all the polynomials in the set.
Answer:
C. It is the product of the prime factors that are either unique to or shared by the polynomials.
Step-by-step explanation:
LCM of polynomials is:
=> Finding the factors of all the numbers and variable in the expression
=> Next, we multiply the unique numbers and the variable of the expression to find the LCM.
So, C is the correct answer.
The LCM of a set of polynomials is the product of the prime factors that are either unique to or shared by the polynomials.
What is LCM of polynomial?To find the lowest common multiple (L.C.M.) of polynomials, we first find the factors of polynomials by the method of factorization and then adopt the same process of finding L.C.M.
Example : The L.C.M. of 4a2 - 25b2 and 6a2 + 15ab.
Factorizing 4a2 - 25b2 we get,
(2a)2 - (5b)2, by using the identity a2 - b2.
= (2a + 5b) (2a - 5b)
Also, factorizing 6a2 + 15ab by taking the common factor '3a', we get
= 3a(2a + 5b)
L.C.M. is 3a(2a + 5b) (2a - 5b)
According to the question
The LCM of a set of polynomials is
is the product of the prime factors that are either unique to or shared by the polynomials.
(from above example we can see that )
Hence, It is the product of the prime factors that are either unique to or shared by the polynomials.
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ASAP Two points ___________ create a line. A. sometimes B. always C. never D. not enough information
Answer: B. Always
Explanation:
Two points always create a line. The correct answer is option B.
What is a line?
A line has length but no width, making it a one-dimensional figure. A line is made up of a collection of points that can be stretched indefinitely in opposing directions.
If there are two points A(x₁,y₁) and B(x₂,y₂) then the distance between the two points will be the length of the line. The formula to calculate the distance is given as below:-
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Therefore, the two points always create a line. The correct answer is option B.
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Jake’s dad is 6 more than 3 times Jake’s age. The sum of their ages is 42 . Find their ages. Use whole numbers.
Answer: Jake is 9 and his dad is 33.
Step-by-step explanation: 9x3=27+6=33 9+33=42
Answer:
Jake is 9 and Jake's dad is 33
Step-by-step explanation:
To solve this we need to create a equation where D is the age of Jake's dad and J is the age of Jake
J+D=42
3J+6=D
Solve by substitution
The number of weekly hours spent on a smart device varies inversely with the person's age. If a 20-year-old person spends 52 hours on their smart device each week, how many hours does a 50-year-old person spend on their smart device?
Answer:
20.8 hours
Step-by-step explanation:
Given that hours (h) varies inversely with age (a) then the equation relating them is
h = [tex]\frac{k}{a}[/tex] ← k is the constant of variation
To find k use the condition h = 52 when a = 20, thus
52 = [tex]\frac{k}{20}[/tex] ( multiply both sides by 20 )
1040 = k
h = [tex]\frac{1040}{a}[/tex] ← equation of variation
When a = 50, then
h = [tex]\frac{1040}{50}[/tex] = 20.8 hours
Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded. (a) Find the probability of the event that exactly one of the colors that appears face up is red.
Answer:
12/27
Step-by-step explanation:
Step 1
We find all the total number of possible outcomes of rolling two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow.
Where
R = Red
B = Blue
Y = Yellow
RRR, BBB, YYY, RBY, RYB, YBR, YRB, BRY, BYR, BBY, BBR, YYB, RRY, RRB, BYB, BRB, YRY, YBY, RYR, RBR,YRR, BRR, RBB, RYY, BYY,YBB, YYR
We have 27 Total outcomes for this 6 faced die
Step 2
The event that exactly one of the colors that appears face up is red.
RBY, RYB, YBR, YRB, RBB, RYY, BBR,
BRB, BRY, YRY, BYR, YYR
Total number of Possible outcomes where EXACTLY one of the colours that appears face up is red = 12
The probability of the event that exactly one of the colors that appears face up is red = Number of possible outcomes/ Total number of outcomes
= 12/27
PLS HELP:Find the side length, C.
Round to the nearest tenth.
Answer:
[tex]\huge\boxed{c = 14.9}[/tex]
Step-by-step explanation:
Using Cosine Rule
[tex]c^2 = a^2 + b^2 -2abCosC[/tex]
Where a = 11 , b = 7 and C = 110
[tex]c^2 = (11)^2+(7)^2-2(11)(7)Cos 110[/tex]
[tex]c^2 = 121+49-154 (-0.34)\\c^2 = 170+52.7\\c^2 = 222.7[/tex]
Taking sqrt on both sides
c = 14.9
PLEASE SOLVE THE ABOVE PROBLEM you’ll get 43 POINTS
heya friend
0.2
0.2**10/10
=2/10
in 2/10 2 and 10 are integers
and 10 is not zero
so it is sacrificed
hope this helps u
Answer:
0.2
0.2**10/10
=2/10
in 2/10 2 and 10 are integers
10 is not 0
Step-by-step explanation:
Reading a Tape Measure
Measure the green bar using the provided image of a tape measure
Answer:
3 inches
Step-by-step explanation:
The green bar reaches all the way to the 3 on the ruler, and each number represents an inch.
On a map 1 cm represents 4.5km. What is the actual distance between two towns which are 4cm apart on the map?
Answer:
18km
Step-by-step explanation:
1cm:4.5km/4cm then get the answer as 18km
1 cm represents [tex]4.5[/tex] km. To find the actual distance between two towns that are 4 cm apart on the map, we can use the scale ratio.
Since 1 cm represents [tex]4.5[/tex] km, we can calculate the actual distance by multiplying the map distance with the scale ratio. Map distance: 4 cm Scale ratio: 1 cm represents [tex]4.5[/tex] km Actual distance = Map distance × Scale ratio Actual distance[tex]= 4 cm × 4.5[/tex] km/cm Actual distance[tex]= 18 km[/tex]
Therefore, the actual distance between the two towns is18 [tex]18[/tex] km. Using the given scale, 1 cm on the map corresponds to[tex]4.5[/tex]km in reality. As the towns are represented as 4 cm apart on the map, the actual distance between them is [tex]18[/tex]km.
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