Hello and Good Morning/Afternoon
Let's take this problem step-by-step:
The sum of all angles in a triangle is equal to 180 degrees:
\(\hookrightarrow x + 120 +20 = 180\\\hookrightarrow x + 140 = 180\\\hookrightarrow x =180-140=40\)
∠y and ∠x are on a flat line ⇒ total angle measured between is 180°
\(\hookrightarrow x + y = 180\\\hookrightarrow 40 + y = 180\\\hookrightarrow y = 180-40=140\)
Answer: y = 140°
Hope that helps!
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the
answe says $0.67. why? and how do i solve for that
Find the producer's surplus for the following supply function at the given point. 5) S(x) = x2 + 1; X = 1 =
The producer's surplus for the supply function \(S(x) = x^2 + 1\) at x = 1 is 2 units.
To calculate the producer's surplus, we need to find the area between the supply curve and the price level at the given quantity.
At x = 1, the supply function \(S(x) = (1)^2 + 1 = 2\). Therefore, the price level corresponding to x = 1 is also 2.
To find the producer's surplus, we integrate the supply function from 0 to the given quantity (in this case, from 0 to 1) and subtract the area below the price level curve.
Mathematically, the producer's surplus (PS) is calculated as follows:
PS = ∫[0, x] S(t) dt - P * x
Substituting the values, we have:
PS = ∫[0, 1] (t^2 + 1) dt - 2 * 1
Evaluating the integral, we get:
PS = [1/3 * t^3 + t] [0, 1] - 2
Plugging in the values, we have:
PS = (1/3 * 1^3 + 1) - (1/3 * 0^3 + 0) - 2
Simplifying the expression, we find:
PS = (1/3 + 1) - 2 = (4/3) - 2 = -2/3
Therefore, the producer's surplus for the supply function \(S(x) = x^2 + 1\) at x = 1 is approximately -0.67 units.
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Find the measure of each missing side length. Round to the nearest tenth.
Answer:
x = 24.0
Step-by-step explanation:
We will need to use one of the trigonometric ratios to find x.
If we use 58 as the reference angle, we can use tan to find x, as \(tan=\frac{opposite}{adjacent}\)
\(tan (58)=\frac{x}{15}\\ 15*tan(58)=x\\x=24.005\\x=24.0\)
Solve for x. x+5.39>4.48
Answer:
\(\boxed {x > -0.91}\)
Step-by-step explanation:
Solve for \(x\) :
\(x + 5.39 > 4.48\)
-Subtract \(5.39\) on both sides:
\(x + 5.39 - 5.39 > 4.48 - 5.39\)
\(x > -0.91\)
So, therefore, the final answer is \(\boxed {x > -0.91}\).
(Please state whether the statement is True or False in the
space provided below, and explain the reasoning behind your
answer.
It is possible to get partial grade for explanation, even if
your T/F
Partial grades can be awarded for providing explanations, even if the answer to the True/False statement is straightforward. Hence, the given statement is true.
In many cases, providing a simple True or False answer may not fully demonstrate the depth of understanding or reasoning behind the response. Therefore, instructors or evaluators may award partial grades for explanations that show some level of comprehension, even if the True/False statement itself is correct or incorrect.
In academic or evaluative settings, explanations are often valued as they provide insight into the thought process and understanding of the individual. Even if the answer to a True/False statement is clear-cut, an explanation can demonstrate critical thinking, application of relevant concepts, and an ability to articulate reasoning.
Grading partial credit for explanations encourages students to provide thorough and thoughtful responses, fostering a deeper understanding of the subject matter. It acknowledges that the process of arriving at an answer can be just as important as the answer itself, promoting a more comprehensive evaluation of the individual's knowledge and skills.
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The midpoint of \overline{\text{AB}} AB is M( 2, -7)M(2,−7). If the coordinates of AA are (-2, -8) (−2,−8), what are the coordinates of BB?
Answer:
(6,-6)
Step-by-step explanation:
The required coordinates of B is (6,-6).
What is the line segment?In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line that is between end points.
Now it is given that,
Midpoint M (x,y) = (2,-7)
Coordinates of A( x₁,y₁) = (-2,-8)
Let the coordinates of B be (x₂,y₂)
Since, midpoint of line segment AB is given as,
{[(x₁+x₂ )/2] , [(y₁+y₂ )/2]}
Therefore,
x = (x₁+x₂ )/2
⇒ 2x = (x₁+x₂)
⇒ x₂ = 2x - x₁
Putting the values we get,
x₂ = 2(2) - (-2)
⇒ x₂ = 4 + 2
⇒ x₂ = 6
Similarly,
y₂ = 2y - y₁
Putting the values we get,
y₂ = 2(-7) - (-8)
⇒ y₂ = -14 + 8
⇒ y₂ = -6
so, the coordinates of B is (6,-6)
Thus, the required coordinates of B is (6,-6).
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The ratio of men to women working for a company is 4 to 5. If there are 110 women working for the company, what is the total number of employees?
Answer:
198
Step-by-step explanation:
?/4 110/5
cross-multiply 4*110
440
divide 440/5
88 men
add total employees
110 women + 88 men = 198
Dixie Showtime Movie Theaters, Inc., owns and operates a chain of cinemas in several markets in the southern U.S. The owners would like to estimate weekly gross revenue as a function of advertising expenditures. Data for a sample of eight markets for a recent week follow. Click on the datafile logo to reference the data, DATA file Weekly Gross Revenue Television Advertising Newspaper AdvertisingMarket ($100) ($100) ($100s) Mobile 5.0 1.5 101.3 51.9 3.0 3.0 Shreveport Jackson 74.8 4.0 1.5 Birmingham 126.2 4.3 43 Uttle Rock 137.8 3.6 4.0 Biloxi 101.4 23 3.5 New Orleans 5.0 8.4 237.5 Baton Rouge 219.6 6.9 5.B (a) Use the data to develop an estimated regression equation with the amount of television advertising as the independent variable. Let x represent the amount of television advertising 1' required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a sign before the blank (Example-300) (b) How much of the variation in the sample values of weekly gross revenue does the model in part (a) explain? If required, round your answer to two decimal places. (c) Use the data to develop an estimated regression equation with both television advertising and newspaper advertising as the Independent variables Let xi represent the amount of television advertising Let x2 represent the amount of newspaper advertising If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a sign before the blank (Example: -300) X1 + X2 (d) How much of the variation in the sample values of weekly gross revenue does the model in part (c) explain? If required, round your answer to two decimal places.___ %
(a) a= -45.43 and b = 40.06 and (b) R² = 0.56
(c) the variation in the independent sample values of weekly gross revenue
Y= - 42.57 + 22.40X₁ + 19.50X₂
a) Using X: TV Advertising Volume as the independent variable, you need to test simple linear regression.
The first step is to estimate the regression model
E(Yi) = α + βXi
Then ^Yi = a + bXi
where "a" is the estimate of the intercept and "b" is the estimated slope of the intercept.
Using statistical software, I calculated a simple linear regression as follows:
a= -45.43
b= 40.06
^Yi= -45.43 + 40.06Xi
To test whether there is a significant relationship between TV advertising and total weekly income, one needs to test the population slope of the regression, assuming:
H₁: β ≠ 0
α: 0.05
We have two ways to test if the regression is significant, you can use two-tailed t-test or one-tailed F-test. They are two different distributions and tests, but you can get the same result.
I will use a t-test for this item and an F-test for later tests.
t = b-β/Sb × t(n-2)
\(t_{H0} = \frac{40.06 -0}{14.64} = 2.74\)
The p-value for this test is 0.0339
Using the p-value method, the decision rule is:
If the p-value ≤ α, the decision to reject the hypothesis is .
Decided not to reject the null hypothesis if the value of p > α.
p-value: 0. 0339 is less than α: 0.05, we decide to reject the null hypothesis. conclude that there is a significant relationship between television advertising and the sample total weekly revenue.
Looking at the estimated value of the slope, these two variables can have a direct relationship, namely
With each additional TV advertising volume, the total weekly revenue also increases. (This is just a hypothesis, without proper hypothesis testing you cannot draw any conclusions)
b) To find out what percentage of the change in total weekly income is explained by the model, you need to calculate the coefficient of determination.
For item a), the coefficients are:
R²= 0.56
This means that 56% of the variability in total weekly income is explained by the amount of television advertising according to the estimated model: ^ Yi= -45 .43 + 4.06Xi
c) This time you need to formulate the regression equation with two independent variables, namely:
X₁: Volume of TV ads
X₂: Volume of newspaper ads
The model will be
\(E(yi) = \alpha +\beta _{1} X_1 +\beta _{2} X_2\)
The model is ^Y = -42.57 + 22.40X₁ + 19.50X₂
For this hypothesis test, it is better to use the F-test
1) Intersection
H₀: α = 0
H₁: α ≠ 0
\(t_{H0} =-1.49\)
The p-value is greater than the significance level and it is decided not to reject the null hypothesis.
2) Slope of X₁
H₀: β₁ = 0
H₁: β₁≠0
α: 0.05
\(t_{H0} = 3.16\)
The 4th value is less than the null hypothesis for decision rejection.
Using a 5% significance level, the regression is significant.
3) Slope for X₂
H₀: β₂ = 0
H₁: β₂ ≠ 0
α: 0.05
\(t_{H0} = 5.27\)
e) The number of newspaper advertisements will affect the average weekly gross income.
d) The multivariate regression corresponds to a coefficient of determination of R²= 0.9393% of the variability of the average weekly gross income is explained by the combined volume of TV and newspaper advertisements under the estimated model:
Y= - 42.57 + 22.40X₁ + 19.50X₂
By comparing the results in a) and c), we can say that the two independent variables explain the dependent variable well.
Comparing the R² of the two, it can be said that TV advertising volume alone does not explain the fluctuation in total weekly income very well, but together with newspaper advertising volume, it becomes a good explanatory variable .
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whats 34* 12 i have no idea I'm only 9
Multiply 1 & 2 from 3 and 4 respectively and add to get product.
- BRAINLIEST answerer
Answer:
\(408\)
Step-by-step explanation:
Hey there,
\(34 \\ \times 12 \\ ................. \\ \: \: \: \: \: \: \: 6 8 \\ + 34 0 \\ ............. ... \\ = 40 8\)
Hope this helps you.
Let me know if you have any other questions:-):-)
What is the predetermined overhead rate? \( \$ 10.00 / \mathrm{MH} \) \( \$ 17.50 / \mathrm{MH} \) \( \$ 20.00 \) / MH \( \$ 32.86 / \mathrm{MH} \)
The predetermined overhead rate is the estimated manufacturing overhead cost per unit of a specific allocation base.
In the options, there are four different rates:
1. $10.00 / MH (MH stands for machine hour): This means that the estimated manufacturing overhead cost per machine hour is $10.00.
2. $17.50 / MH: This indicates that the estimated manufacturing overhead cost per machine hour is $17.50.
3. $20.00 / MH: This implies that the estimated manufacturing overhead cost per machine hour is $20.00.
4. $32.86 / MH: This shows that the estimated manufacturing overhead cost per machine hour is $32.86.
Each rate represents the estimated cost of manufacturing overhead per unit of the allocation base (machine hour) and is used to allocate overhead costs to products or services based on their usage of the allocation base.
The specific rate chosen depends on the nature of the business, its cost structure, and the accuracy of the estimated overhead costs.
The correct question is ''What is the predetermined overhead rate?\(\( \$ 10.00 / \mathrm{MH} \) \( \$ 17.50 / \mathrm{MH} \) \( \$ 20.00 \) / MH \( \$ 32.86 / \mathrm{MH} \)\).''
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WORTH MANY POINTS——Please answer this I beg you please. I just need an answer. It’s ok if its wrong. Please show work. And explain how you got parts b and c. Please.
Tip: You seem like you are slightly stuck. That is okay! Don't forget the formulas that can help you solve for the circumference. When you can solve for the circumference, the rest of the answers come a bit easier.
[a] 88 inches
The circumference can be found with C = 2πr, but they tell us to use \(\frac{22}{7}\) instead of pi, so we will do just that.
C = 2 * \(\frac{22}{7}\) * r
C = 2 * \(\frac{22}{7}\) * (14)
C = 88
[b] 176 inches
Again, the circumference can be found with C = 2πr, but they tell us to use \(\frac{22}{7}\) instead of pi, so we will do just that.
C = 2 * \(\frac{22}{7}\) * r
C = 2 * \(\frac{22}{7}\) * (28)
C = 176
[c] When you double the radius, the circumference also doubles.
We will divide the second circumference by the first circumference so we can see how they compare:
176 / 88 = 2
Now we will take the second radius divided by the first radius:
28 / 14 = 2
We could use a longer explanation, but in summary, when the radius is doubled the circumference is also doubled as seen with the value 2.
American ladybugs have an average adult length of 1 cm with a known standard deviation of 0.2 cm. The population of American ladybugs in Raleigh was around 440000 last spring. Assume a normal distribution for the lengths of adult American ladybugs. Your niece asks you what's the probability of a random ladybug in Raleigh being bigger than 1.5 cm. Is it appropriate to calculate this probability? Select one:
a. No, because the population distribution is skewed. b. No, because the sample size is less than 30. c. No, because the empirical rule is violated.
Therefore, probability solution is estimating this likelihood without additional data or analysis is inappropriate correct response is option a.
What exactly does the probability entail?The main goal of the mathematical branch known as statistical inference is to estimate the likelihood that a statement is accurate or that a particular event will take place. Any number among 0 and 1, where 1 typically denotes confidence and 0 typically denotes possibility, can be used to symbolise chance. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
Because of the skewed demographic distribution, the right response is (a).
We could use the normally distributed to compute probabilities because the length of adult American ladybirds is distributed normally with a known standard deviation. The normal distribution may not, however, correctly depict the distribution of ladybird lengths in the population due to the skewed population distribution.
Furthermore, even if the difference between the actual community mean and the assumed mean of 1 cm is tiny, the given size of the population of 440000 could result in a statistically significant outcome.
However, because the assumption of normality may not hold true, this does not imply that we can accurately determine the likelihood of a random ladybird in Raleigh being larger than 1.5 centimetres.
Therefore, estimating this likelihood without additional data or analysis is inappropriate.
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Somebody plz help ASAP (4.5+3 5/6)-0.6
Answer:
Step-by-step explanation:
(4.5+ (35/6))-0.6)
(31/3)-0.6
146/15.. about 9.74
Answer:
5
Step-by-step explanation:
Easy Dubs
Help deadline is soon I'm doing another packet rn tho.
Answer:
Step-by-step explanation:
12. 40h + 100 = 300
40h = 200
h = 5 hours
answer is A
13. 4p - 4 = 48
4p = 52
p = $13
answer is C
14. e + 3e = 24
4e = 24
e = 6
16. 3p + $4.29 = $8.94
3p = $4.65
p = $1.55
answer is B
17. 2x + 2x + x - 6 = 74
5x - 6 = 74
5x = 80
x = 16
2(16) = spearmint gum
answer is D
15. x + 2x + 10 = 76
3x + 10 = 76
3x = 66
x = 22 years old
2(22)= 44 years old
18. 2x + 26 = 54
2x = 28
x = 14
answer is B
How I can answer this question, NO LINKS, if you answer correctly I will give u brainliest!
Answer:
20
Step-by-step explanation:
\(\frac{-8*10^7}{-4*10^6}\\=2*10\\=20\)
Two towns tracked the attendance at their summer fairs in 2016 and 2017. The data for each town and year is shown below. Year Ogdenville North Haverbrook 2016 960 500 2017 1008 540 What was the difference between the percent increases for each town from 2016 to 2017?
Answer:
48 and 5%; 40 and 8%
Step-by-step explanation:
The computation of the difference between the percentage increase for each town from 2016 to 2017 is given below:
Year Ogdenville North Haverbrook
2016 960 500
2017 1008 540
So here the difference would be
For 2016 to 2017
= 1008 - 960
= 48
The percentage increase is
= 48 ÷ 960
= 5%
And,
= 540 - 500
= 40
And, the percentage increase is
= 40 ÷ 500
= 8%
URGENT 50 PTS
In ALMO, Point C is the intersection of the blue and green segments. If CM = 11, QM = 5, PL = 6, RM = 10, CO =9.8, and LC = 2x + 5, solve for X
TRUE/FALSE: there is a basis of rn consisting of eigenvectors of a, then a is diagonalizable. TRUE/FALSE: if a is diagonalizable, then a is invertible.
If Rn has a basis of eigenvectors of A, then A is diagonalizable.
This statement is true.
If A is diagonalizable, then A is invertible.
This statement is false.
What is diagonalizable matrix?
If there is an invertible matrix P and a diagonal matrix D such that P^-1AP=D, or alternatively A=PDP^-1, then the square matrix A is said to be diagonalizable or non-defective in linear algebra.
If Rn has a basis of eigenvectors of A, then A is diagonalizable.
This statement is true.
In this case we can construct an invertible matrix P.
If A is diagonalizable, then A is invertible.
This statement is false.
It’s invertible if it doesn’t have a zero as eigen value but this doesn’t affect diagonalizabilty.
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determine whether the integral is convergent or divergent. [infinity] e−6p dp 2
The given integral is convergent and its value is 0.
Given integral: ∫[0,∞)e⁻⁶ᵖ ᵈᵖ
We can see that the given integral is of the form:
∫[0,∞)e⁻ᵏᵖ ᵈᵖ
Where k is a constant and k > 0.
To determine whether the given integral is convergent or divergent, we use the following rule:
∫[0,∞)e⁻ᵏᵖ ᵈᵖ is convergent if
k > 0∫[0,∞)e⁻ᵏᵖ ᵈᵖ
is divergent if k ≤ 0
Now, comparing with the given integral, we can see that
k = 6.
Since k > 0, the given integral is convergent.
Therefore, the given integral is convergent and its value can be found as follows:
∫[0,∞)e⁻⁶ᵖ ᵈᵖ= [-e⁻⁶ᵖ/6]
from 0 to ∞
= [-e⁰/6] - [-e⁻⁶∞/6]
= [0 - 0]
= 0
Hence, the given integral is convergent and its value is 0.
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1. When simplified, 17a - 14b - 20a - 2b is equal to
Answer:
- 3a -16b
Step-by-step explanation:
1. (a) The sum of two numbers is 17. The difference between twice the larger number and three times the smaller is 4. Find the numbers
Answer:
Denoting 2 desired numbers: x and y, then:
x + y = 17
2x = 3y + 4
<=>
x = 17 - y
2*(17 - y) = 3y + 4
<=>
x = 17 - y
34 - 2y = 3y + 4
<=>
x = 17 - y
5y = 30
<=>
y = 6
x = 17 - 6 = 11
Hope this helps!
:)
Evaluate 2a +7-8a-14+5a
Answer: -a-7
Step-by-step explanation:
Answer:
−a −7
Step-by-step explanation:
group the 'a's. 2a-8a+5a. It is -a. Next, group the numbers and simplify them. 7-14. It is equal to -7. If you put -a and -7 together, you get "-a-7" as an answer.
Ir-11 2-25
A) rs-14: *
-20 -18
-16 -14 -12
B) rz-14 :
+
-20 -18 -16 -14 -12 -10
C) rs 14:
12
16
18
20
25
D) r2-
11
:
-6
-
-2 0 2
Answer:
what's ir but looks like a calculator will help
u need a little better explanation
Step-by-step explanation:
how do i solve this x^2 −12x+36=0
Step-by-step explanation:
x^2-6x-6x+36=0
x(x-6)-6(x-6)=0
(x-6)(x-6)=0
x=6
Seraphina is driving two hours to visit her family. For the first hour, she traveled at a speed of 60 miles per hour. Then, in the second hour, she traveled at a speed of 74 miles per hour. What is the percentage increase of Seraphina's speed? If necessary, round to the nearest tenth of a percent
Seraphina's speed has increased by a factor of around 23% compared to the first hour.
What Is a Change in Percentage?
The ratio of the difference in the amount to its starting value multiplied by 100 is known as the percentage change. When a number's final value is determined by increasing or decreasing a percentage of its starting value, the percentage change of that quantity will always change.
How can you determine the percentage to the closest tenth?
Rounding to the closest tenth entails adding one integer after the decimal point. The number in the thousandths place, or the second number from the right of the decimal, must be considered while rounding. If the amount is five or more, we add one percent to the number in the tenth position.
Percent Change Formula = \(\frac{ (Final value -Initial value)}{ (Initial value)}\)× 100
Percent Change = \(\frac{(74-60)}{60}\)× 100
… = \(\frac{14}{60}\) × 100
... ≈ 0.23333 × 100
Percent Change ≈ 23.33%
The pace of Seraphina increased by around 23% in the second hour compared to the first.
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Partition the interval into equal parts. Label the fractions at 0 and 1. Plot the given fraction on the number line
The fractions between 0 and 1, we have represented on a number line, include 1/4, 2/4, and 3/4. All of these have equal intervals of 0.25.
To plot 1/4, 2/4 and 3/4 on the number line, we need to divide the interval between 0 and 1 into four equal parts. Each part will represent 1/4.
We can label the fractions at 0 and 1 as shown below:
0 1/4 2/4 3/4 1
Now we can plot the given fractions on the number line as shown below:
0 1/4 2/4 3/4 1
o o o
1/4 2/4 3/4
We can divide the fractions to get the difference of intervals. This can be done as follows:
2/4-1/4 = 0.25, also:
3/4-2/4 = 0.25.
Any portion of a whole number that is stated as one number multiplied by another is referred to as a fraction. One-half of something, for instance, is represented by the fraction 1/2. Another approach to represent a portion of a full number is with a decimal.1/2 is same as 0.25 as a decimal.
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i dont now this question
Answer:
x = 1Step-by-step explanation:
3x + 2 = (2x + 13)/3
9x + 6 = 2x + 13
9x - 2x = 13 - 6
7x = 7
x = 7 : 7
x = 1
HELP PLSSSSSS math i suck at it!!!!
Answer:
i can help...
Step-by-step explanation:
from a group of six people, two individuals are to be selected at random. how many selections are possible? group of answer choices 12 36 15 8
There are a total of six people in the group. To select two individuals at random, we can use the formula for combinations, which is nCr = n!/r!(n-r)!, where n is the total number of individuals in the group and r is the number of individuals to be selected. Therefore, the number of selections possible is:
6C2 = 6!/(2!(6-2)!) = 15
The formula for combinations is used to calculate the number of ways we can select r individuals from a total of n individuals. This formula is nCr = n!/r!(n-r)!. In this case, n is 6 (the total number of individuals in the group) and r is 2 (the number of individuals to be selected). Therefore, we substitute n=6 and r=2 into the formula to obtain the number of selections possible.
The number of selections possible from a group of six people, where two individuals are to be selected at random, is 15. This is obtained by using the formula for combinations, which is nCr = n!/r!(n-r)!, where n is the total number of individuals in the group and r is the number of individuals to be selected.
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Match the given point in polar coordinates to the points A,B,C, or D. (2,
13π/6)
The point in polar coordinates (2, 13π/6) can be matched with the point A.
Explanation:
Here, (2, 13π/6) is given in polar coordinates.
So, we need to convert it into rectangular coordinates (x, y) to plot the given point in the cartesian plane.
The relation between polar and rectangular coordinates is given below:
x = r cos θ, y = r sin θ
where r is the distance of the point from the origin, and θ is the angle made by the line joining the point and the origin with the positive x-axis.
Therefore,
we have:
r = 2, θ = 13π/6
Substituting these values in the above equations,
we get:
x = 2 cos (13π/6)
= 2(-√3/2)
= -√3 y
= 2 sin (13π/6)
= 2(-1/2)
= -1
So, the rectangular coordinates of the given point are (-√3, -1).
Now, let's look at the given points A, B, C, and D.
A(-√3, -1) B(√3, 1) C(-√3, 1) D(√3, -1)
The rectangular coordinates of the given point match with point A.
Therefore, the given point in polar coordinates (2, 13π/6) can be matched with the point A.
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Imagine that you lived in a dot on the surface of an expanding balloon, and as you looked to more distant dots, you observed the following: 1. A dot at a distance of 5 centimeters from you is moving away from you at a speed of 1 centimeter per hour (1 cm/hr). 2. A dot at a distance of 10 centimeters from you moving away from you at a speed of 2 centimeters per hour (2 cm/hr). 3. A dot at a distance of 15 centimeters from you moving away from you at a speed of 3 centimeters per hour (3 cm/hr). Which equation below correctly states the relationship between the dot distances and speeds as observed by you? a. dot speed = dot distance / 1 hr b. dot speed = dot distance / 5 hr c. dot speed = dot distance / 5 cm
The correct equation that states the relationship between the dot distances and speeds is dot speed = dot distance / 5 hr. The correct option is (b).
This is because the dots are observed to be moving away from the observer at a constant rate, which is given in units of centimeters per hour.
This equation correctly represents the observed relationship because it implies that the speed at which a dot is moving away from you is directly proportional to its distance from you.
The coefficient of proportionality in this case is 1 cm/hr per 5 cm of distance.
This means that for every 5 centimeters of distance, the dot's speed increases by 1 centimeter per hour. As the distance increases, the speed also increases proportionally.
This is consistent with the information where dots at greater distances have higher speeds.
Therefore, to relate the dot distance (in centimeters) to the dot speed (in centimeters per hour), we need to divide the dot distance by the time taken for the dot to move that distance, which is 5 hours for all dots.
To know more about speed and distance equations, refer here :
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