The probability that all 4 selected workers will be from the day shift is, = 0.0198
The probability that all 4 selected workers will be from the same shift is = 0.0278
The probability that at least two different shifts will be represented among the selected workers is = 0.9722
The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257
To solve this question properly, we will need to make use of the concept of combination along with set theory.
What is Combination?In mathematical concept, Combination is the grouping of subsets from a set without taking the order of selection into consideration.
The formula for calculating combination can be expressed as:
[tex]\mathbf{(^n _r) =\dfrac{n!}{r!(n-r)! }}[/tex]
From the parameters given:
Workers employed on the day shift = 10Workers on swing shift = 8Workers on graveyard shift = 6A quality control consultant is to select 4 of these workers for in-depth interviews:
Using the expression for calculating combination:
(a)
The number of selections results in all 4 workers coming from the day shift is :
[tex]\mathbf{(^n _r) = (^{10} _4)}[/tex]
[tex]\mathbf{=\dfrac{(10!)}{4!(10-4)!}}[/tex]
= 210
The probability that all 5 selected workers will be from the day shift is,
[tex]\begin{array}{c}\\P\left( {{\rm{all \ 4 \ selected \ workers\ will \ be \ from \ the \ day \ shift}}} \right) = \dfrac{{\left( \begin{array}{l}\\10\\\\4\\\end{array} \right)}}{{\left( \begin{array}{l}\\24\\\\4\\\end{array} \right)}}\\\end{array}[/tex]
[tex]\mathbf{= \dfrac{210}{10626}} \\ \\ \\ \mathbf{= 0.0198}[/tex]
(b) The probability that all 4 selected workers will be from the same shift is calculated as follows:
P( all 4 selected workers will be) [tex]\mathbf{= \dfrac{ \Big(^{10}_4\Big) }{\Big(^{24}_4\Big)}+\dfrac{ \Big(^{8}_4\Big) }{\Big(^{24}_4\Big)} + \dfrac{ \Big(^{6}_4\Big) }{\Big(^{24}_4\Big)}}[/tex]
where;
[tex]\mathbf{\Big(^{8}_4\Big) = \dfrac{8!}{4!(8-4)!} = 70}[/tex]
[tex]\mathbf{\Big(^{6}_4\Big) = \dfrac{6!}{4!(6-4)!} = 15}[/tex]
P( all 4 selected workers is:)
[tex]\mathbf{=\dfrac{210+70+15}{10626}}[/tex]
The probability that all 4 selected workers will be from the same shift is = 0.0278
(c)
The probability that at least two different shifts will be represented among the selected workers can be computed as:
[tex]= 1-\dfrac{ (^{10}_4) }{(^{24}_4)}+\dfrac{ (^{8}_4) }{(^{24}_4)} + \dfrac{ (^{6}_4) }{(^{24}_4)}[/tex]
[tex]=1 - \dfrac{210+70+15}{10626}[/tex]
= 1 - 0.0278
= 0.9722
The probability that at least two different shifts will be represented among the selected workers is = 0.9722
(d)
The probability that at least one of the shifts will be unrepresented in the sample of workers is:
[tex]P(AUBUC) = \dfrac{(^{6+8}_4)}{(^{24}_4)}+ \dfrac{(^{10+6}_4)}{(^{24}_4)}+ \dfrac{(^{10+8}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]
[tex]P(AUBUC) = \dfrac{(^{14}_4)}{(^{24}_4)}+ \dfrac{(^{16}_4)}{(^{24}_4)}+ \dfrac{(^{18}_4)}{(^{24}_4)}- \dfrac{(^{6}_4)}{(^{24}_4)}-\dfrac{(^{8}_4)}{(^{24}_4)}-\dfrac{(^{10}_4)}{(^{24}_4)}+0[/tex]
[tex]P(AUBUC) = \dfrac{1001}{10626}+ \dfrac{1820}{10626}+ \dfrac{3060}{10626}-\dfrac{15}{10626}-\dfrac{70}{10626}-\dfrac{210}{10626} +0[/tex]
The probability that at least one of the shifts will be unrepresented in the sample of workers is P(A∪B∪C) = 0.5257
Learn more about combination and probability here:
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1. Find the equation of the line passing through the point (2,−4) that is parallel to the line y=3x+2 y= 2. Find the equation of the line passing through the point (1,−5) and perpendicular to y=18x+2 y=
Answer:
Step-by-step explanation:
1) Parallel lines have same slope
y = 3x + 2
m = 3
(2, -4) ; m = 3
equation: y - y1 = m (x - x1)
y - [-4] = 3(x - 2)
y + 4 = 3x - 6
y = 3x - 6 - 4
y = 3x - 10
2) y = 18x + 2
m1 = 18
Slope the line perpendicular to y = 18x + 2, m2 = -1/m1 = -1/18
m2 = -1/18
(1 , -5)
[tex]y-[-5]=\frac{-1/18}(x-1)\\\\y+5=\frac{-1}{18}x + \frac{1}{18}\\\\y=\frac{-1}{18}x+\frac{1}{18}-5\\\\y=\frac{-1}{18}x+\frac{1}{18}-\frac{5*18}{1*18}\\\\y=\frac{-1}{18}x+\frac{1}{18}-\frac{90}{18}\\\\y=\frac{-1}{18}x-\frac{89}{18}\\\\[/tex]
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes with a standard deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. The p-value is
A sports shop sells tennis rackets in 4 different weights, 2 types of string, and 3 grip sizes. How many different rackets
could they sell?
O 32
O 18
0 24
0 9
Answer: C) 24
Step-by-step explanation:
first we take down the information given to us
sports shop sells rackets in
4 different weights
2 types of strings
3 grip sizes
Now to get the number of different rackets they could sell, you simply take the multiplication of the number of racket gripe sizes, the types of strings and different weights they sell
so
4 * 2 * 3 = 24
therefore the sport shop could sell up to 24 different rackets .
Answer:
24
Step-by-step explanation: got it right on my test
The table below shows the number of e-mails received each day by a company employee for two separate weeks. If the data were represented with a comparative dot plot, which day would have more dots for week 2 than week 1
Answer:
C
Step-by-step explanation:
Hope this helps
Answer:
C
Step-by-step explanation:
Wednesday hope this helps!
What is the value of X ?
A-12
B-17
C-23
D-25
Step-by-step explanation:
25 answer by considering
What term should be inserted in
p²-
___+36 to make it a perfect
Square
Answer:
12p
Step-by-step explanation:
the perfect square is form
(p - 6)² = p² - 12p + 36
Answer:
12p
Step-by-step explanation:
p² - ? + 36 = p² - ? + (-6)² = p² -2*6*p + (-6)² = p² - 12p + 36 = (p-6)²
Find the number of ways of arranging the numbers 1,2,3,4,5,6,7, if no two even numbers can be adjacent, and no two odd numbers can be adjacent.
Answer:
24 ways
Step-by-step explanation:
1) In Combinatorics when we arrange a number and the order matter, we call it arrange the possibilities. For this exercise let's not use formulas but reasoning.
2) For this case we need a two figure number. Since we have seven numbers.
Since there is no repetition, all the possibilities are:
[tex]7*6=42[/tex]
3) But there is a restriction it's forbidden adjacent even and odd numbers: These numbers we don't want them:
13 15 17
24 26
31 35 37
42 46
51 53 57
62 66
71 73 75
18 non desirable results
The total arrangements minus the not possible combinations, will match the possible results:
[tex]42-18=24[/tex]
3) Just for checking, we have here the allowed combinations:
12 14 16
21 23 25 27
32 34 36
41 43 45 47
52 54 56
61 63 65 67
72 74 76
A total of 24 possible ways.
what is X:
|4x−1|=3
|x|=−4
Answer:
1
Step-by-step explanation:
Please hurry
On each bounce, a ball dropped from 100 feet rises to the height
from which it has fallen. How high does the ball rise, in feet, on the 10th bounce?
Answer:
D
Step-by-step explanation:
divide 10 times starting with 100.
The answer is 25/256 or 0.09765625
The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the height of the ball after x bounce. Given that the ball rises to the height from which it has fallen, hence:
y = 100(1/2)ˣ
After the 10th bounce:
y = 100(1/2)¹⁰ = 0.09766
The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet.
Find out more on equation at: https://brainly.com/question/2972832
Small sample: During an economic downturn, companies were sampled and asked whether they were planning to increase their workforce. Only of the companies were planning to increase their workforce. Use the small-sample method to construct a confidence interval for the proportion of companies that are planning to increase their workforce. Round the answers to at least three decimal places. A confidence interval for the proportion of companies that are planning to increase their workforce is .
Complete Question
The complete question is shown on the first uploaded image
Answer:
The confidence level interval is [tex]0.016 \le C \le 0.404[/tex]
Step-by-step explanation:
The sample size is [tex]n = 20[/tex]
The number planning to increase workforce is [tex]x = 3[/tex]
The confidence level is [tex]c = 98[/tex]%
The value of proportion for a plus 4 method is
[tex]p = \frac{x+2}{n+4}[/tex]
substituting values
[tex]p = \frac{3+2}{20+4}[/tex]
[tex]p =0.21[/tex]
The z-critical value at confidence level of 98% is
[tex]z_{c}=z_{0.98} = 2.33[/tex]
This values is obtained from the standard normal table
The confidence level interval can be mathematically represented as
[tex]C =p \ \pm z_{c} * \sqrt{\frac{p(1-p)}{n+4} }[/tex]
substituting values
[tex]C = 0.21 \pm 2.33 * \sqrt{\frac{0.21(1- 0.21)}{20 +4} }[/tex]
[tex]C = 0.21 \pm 0.194[/tex]
=> [tex]0.016 \le C \le 0.404[/tex]
The following data show the brand, price , and the overall score for stereo headphones that were tested by Consumer Reports. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from (lowest) to (highest). The estimated regression equation for these data is = 23.194 + 0.318x, where x = price ($) and y = overall score.
Brand Price Score
Bose 180 76
Scullcandy 150 71
Koss 95 62
Phillips/O'Neill 70 57
Denon 70 30
JVC 35 34
Required:
a. Compute SST, SSR, and SSE (to 3 decimals).
b. Compute the coefficient of determination r2.
c. What is the value of the sample correlation coefficient?
Answer:
a. SST = 1816
SSR = 1511.804
SSE = 465.804
b. Coefficient of determination, R² = 0.832491079
c. The correlation coefficient r = 0.8636
Step-by-step explanation:
y = 23.194 + 0.318·x
Where:
x = Price
y = Overall score
The observed data are given as follows;
Brand Price Score
Bose 180 76
Scullcandy 150 71
Koss 95 62
Phillips/O'Neill 70 57
Denon 70 30
JVC 35 34
[tex]SST = \sum \left (y - \bar{y} \right )^{2}[/tex]= 1816
[tex]SSR = \sum \left ({y}'-\bar{y{}'} \right )^{2}[/tex] = 1511.804
[tex]SSE = \sum \left (y - {y}' \right )^{2}[/tex] = 465.804
Coefficient of determination
[tex]Coefficient \, of \, determination = \dfrac{SSR}{SST}[/tex]= 0.832
Coefficient of correlation =
[tex]r = \dfrac{n\left (\sum xy \right )-\left (\sum x \right )\left (\sum y \right )}{\sqrt{\left [n\sum x^{2}-\left (\sum x \right )^{2} \right ]\left [n\sum y^{2}-\left (\sum y \right )^{2} \right ]}}[/tex]
Ʃxy = 37500
Ʃx =600
Ʃy = 330
Ʃx² = 74950
Ʃy² = 19966
[tex]r = \dfrac{6 \left (37500 \right )-\left (600 \right )\left (330 \right )}{\sqrt{\left [6\times 74950-\left (600 \right )^{2} \right ]\left [6 \times 19966-\left (330 \right )^{2} \right ]}} = 0.8636[/tex]
All of the following are examples of quantitative data EXCEPT ________.
a. the amount of sleep normally gotten by the students in a class
b. the number of siblings that students have
c. the cholesterol levels of the students in a class
d. the exam scores for the students in a class
d. the gender of the students in a class
Answer:
e. the gender of the students in a class
Step-by-step explanation:
Quantitative data is measured is numbers. For example 1, 2, 3.5,...
Qualitative data are labels, that is, tall, short, male, female, Brazilian, Colombian,...
In this question:
The only data that is not measured in numbers is the gender of the studens in class, which can be male or female, they do not assume any numeric value. So the answer is e.
The quantitive data example does not include option e. the gender of the students in a class.
Data:Quantitative data is measured in numbers. like 1, 2, 3.5,..While on the other hand, Qualitative data are labels i.e. tall, short, male, female, etc. Based on this, the last option is correct.learn more about the data here: https://brainly.com/question/20296761
The sum of two consecutive integers is −19. Find the integers.
Answer:
-9 and -10
Step-by-step explanation:
x + x+1=-19
2x+1=-19
2x=-19-1
2x=-20
x=-10
x+1
-10+1=-9
Answer:
[tex]-9[/tex]
[tex]-10[/tex]
Step-by-step explanation:
[tex]x+x+1=-19[/tex]
[tex]2x+1=-19[/tex]
[tex]2x=-19-1[/tex]
[tex]2x=-20[/tex]
[tex]x=-20 \div 2[/tex]
[tex]x=-10[/tex]
[tex]x+x+1=-19[/tex]
[tex]x+1=-19-x[/tex]
[tex]-10+1=-19-(-10)[/tex]
[tex]-9=-19+10[/tex]
[tex]-9=-9[/tex]
The people at the party ate 16 chocolate chip cookies and 26 sugar cookies. What percent of the cookies were sugar cookies?
Answer:
61%
Step-by-step explanation:
16/26 x 100 = 61.538461
You have to round it up if the question tells you to round it up.
hope it helps! :)
Answer:
62%
Step-by-step explanation:
42 x 62% = 26.04
I am sorry if you get this wrong. I really hope this helps.
what is 0.84÷3 matggggg
[tex]0.84 \div 3 = 84 \div 300 = 0.28[/tex]
Simplify 1 ∙ x -x/1 .
Answer:
0
Step-by-step explanation:
1x=x
-x/1=-x
x-x=0
Answer:
Brainleist !
Step-by-step explanation:
x - x /1
x - x = nothing or 0
Select the proper inverse operation to check the answer to 25 - 13 = 12.
A. 12 x 13 = 25
B. 12 x 25 = 13
C. 12 = 25 = 13
O D. 12 + 13 =25
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The number of points scored during a basketball game b. The number of free dash throw attempts before the first shot is made c. The response to the survey question "Did you smoke in the last week question mark " d. The number of people in a restaurant that has a capacity of 150 e. The time it takes for a light bulb to burn out f. The height of a randomly selected giraffe a. Is the number of points scored during a basketball game a discrete random variable, a continuous random variable, or not a random variable?
Answer:
a. Discrete random variable
b. Discrete random variable
c. Discrete random variable
d. Discrete random variable
e. Continous random variable
f. Continous random variable
Step-by-step explanation:
a. The number of points scored during a basketball game.
This is a random variable, that only takes integer values, so it is a discrete random variable.
b. The number of free dash throw attempts before the first shot is made.
This is a count, so it is a discrete random variable.
c. The response to the survey question "Did you smoke in the last week question mark".
This is a boolean random variable (only two values), and can be considered discrete.
d. The number of people in a restaurant that has a capacity of 150.
This is a count of people, so it is a discrete random variable.
e. The time it takes for a light bulb to burn out.
Time is continous, so it is a continous random variable.
f. The height of a randomly selected giraffe.
Height, as it is a distance, is also a continous variable, so it is a continous random variable.
Balu and Pumba shared 2/3 of a cake. Balu got to eat three times as much cake as Pumba. What fraction of the whole cake did Balu eat?
Pleas answer help and answer correctly.
Answer:
In fraction, Balu ate 1/2 of the whole cake
Step-by-step explanation:
Balu and Pumba shared 2/3 of a cake.
Balu eats three times as much cake as Pumba.
So let's take the 2/3 they shared as a whole.
Let's Balu share be x
And pumbs share be y
X = 3y
But x + 3y = 2/3
Since x = 3y
Y = x/3
x + x/3 = 2/3
4x/3 = 2/3
X = (2*3)/(4*3)
X = 2/4
X = 1/2
Balu ate half of the whole cake
In fraction, Balu ate 1/2 of the whole cake
Idaho is shaped like a triangle with a base of approximately 320 miles and a height of approximately 520 miles. Calculate the area of Idaho and write the answer in scientific notation
Answer:
8.32 × 10^4
Step-by-step explanation:
The formula for the area of a triangle is 1/2×b×h.
1/2(320)(520) = 83,2000
83,200 in scientific notation is 8.32 × 10^4
Which size would you see on the box for a new television whose screen measures 36 inches wide by 27 inches high? A. 9" B. 45" C. 50" D. 63"
Answer: b) 45"
Step-by-step explanation:
Tv's are measured by their diagonal length.
Use Pythagorean Theorem to find the diagonal of the tv.
a² + b² = c²
36² + 27² = c²
1296 + 729 = c²
2025 = c²
√2025 = c
45 = c
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.
Market
Weekly Gross Revenue
($100s)
Television Advertising
($100s)
Newspaper Advertising
($100s)
Mobile
101.3
5
1.5
Shreveport
51.9
3
3
Jackson
74.8
4
1.5
Birmingham
126.2
4.3
4.3
Little Rock
137.8
3.6
4
Biloxi
101.4
3.5
2.3
New Orleans
237.8
5
8.4
Baton Rouge
219.6
6.9
5.8
(a) Use the data to develop an estimated regression with the amount of television advertising as the independent variable.
Let x represent the amount of television advertising.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x
Test for a significant relationship between television advertising and weekly gross revenue at the 0.05 level of significance. What is the interpretation of this relationship?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(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 x1 represent the amount of television advertising.
Let x2 represent the amount of newspaper advertising.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x1 + x2
Is the overall regression statistically significant at the 0.05 level of significance? If so, then test whether each of the regression parameters β0, β1, and β2 is equal to zero at a 0.05 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(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.
%
(e) Given the results in part (a) and part (c), what should your next step be? Explain.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(f) What are the managerial implications of these results?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
IQ levels: A study investigated whether there are differences between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else. What is the null hypothesis in this case
Answer:
The null hypothesis: there is no difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else.
Step-by-step explanation:The null hypothesis can be a general statement mostly in statistics that proposes no difference or no relationship between 2 phenomena etc
Researchers always carry out a study to test against the null hypothesis ie the opposite of the null hypothesis showing that there is a difference. In this study, the researchers aim is to establish that there is a difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else. This goes against the null which states that
there is no difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else.
A company that manufactures toothpaste is studying five different package designs.Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs (to 2 decimals)
Answer:
The selection probability to be assigned to each of the package designs is 0.20
Step-by-step explanation:
Firstly, we need to assume that one design is just as likely to be selected by a consumer as any other design
so the probability of selecting any of the design is same and that is 1/5 = 0.20
Thus, what we are trying to say is that each of the package designs have an equal selection probability of 0.20
What is the inverse of the function f(x) = 2x + 1?
1
Oh(x) =
Ex-
2
2
O h(x)
1
2
1
2
h(x) =
Ex-
- 3x + 2
h(x) =
X
+
Save and Exit
Next
Mark this and return
Answer:
The inverse function is [tex]f^{-1}(x) = \frac{x-1}{2}[/tex]
Step-by-step explanation:
We have the following function:
y = 2x + 1
Finding the inverse:
Exchange y and x, and then isolate y again. So
y = 2x + 1
Exchange y and x
x = 2y + 1
2y = x - 1
[tex]y = \frac{x-1}{2}[/tex]
So
The inverse function is [tex]f^{-1}(x) = \frac{x-1}{2}[/tex]
Please show how the following equasion Square root of 64+6/-2*-2 I cannot arrive at the answer of 9.5
Answer:
[tex]9.5[/tex]
Step-by-step explanation:
[tex]\sqrt{64}+\frac{6}{-2\left(-2\right)}[/tex]
[tex]\sqrt{64}+\frac{6}{2 \times 2}[/tex]
[tex]8+\frac{6}{4}[/tex]
[tex]\frac{19}{2}[/tex]
[tex]=9.5[/tex]
Answer:
Hello!
I hope that this is the answer you are looking for
=8.09320
That is the rounded answer.
I hope that helped you!
Step-by-step explanation:
Find the coordinates of the other endpoint of the segment, given its midpoint M and one
endpoint Q.
M(c,n), Q(h,s)
The second endpoint is P
Answer:
P(2c - h, 2n - s )
Step-by-step explanation:
If there are two points (x1,y1) and (x2,y2) on the coordinate plane
then midpoint is given by (x1+x2)/2 , (y1+y2)/2
_________________________________________________
in the problem midpoint is m(c,n)
one point is Q(h,s)
let other point be P(x,y)
By using midpoint formula given above
for point P(x,y) and Q(h,s)
midpoint = (x+h)/2, (y+s)/2
also midpoint is m(c,n)
comparing m(c,n) with (x+h)/2, (y+s)/2
c = x+h/2
=> 2c = x+h
=> 2c - h = x
n = (y+s)/2
=> 2n = y+s
=> 2n - s = y
Thus, second endpoint is P(x,y) = P(2c - h, 2n - s )
A field is in the shape of a rectangle 5/6 mile long and 3/4 mile wide. What is the area of the field? *
Area = length x width
Area = 5/6 x 3/4
= (5x3) / (6x4)
= 15/24
= 5/8 square miles
Chris is constructing a diagram for a deck he is restructuring in his backyard. The deck will be in the shape of a square, and he
has labeled a side length with the equation below, where x represents the original deck area.
side length = V1 + 12
Answer:
Increase the area of the deck by 12 square feet.
Step-by-step explanation:
The area of the deck increased by 12 square feet.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
Given that, Chris is constructing a diagram for a deck he is restructuring in his backyard.
The deck will be in the shape of a square, and he has labeled a side length with the equation below, where x represents the original deck area. Side length = V1 + 12
Increase the area of the deck by 12 square feet.
Therefore, the area of the deck increased by 12 square feet.
Learn more about the area here:
https://brainly.com/question/27683633.
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A train is traveling at a constant speed and has traveled 67.5 miles in the last 11 hours.
Which equation shows the proportional relationship between the distance, d, and the time, t,
that the train has traveled?
A.d=45t
B.d=50t
C.d = 690
D.d=67.5t
Answer:
A. d= 45t
Step-by-step explanation:
(assuming that you meant 67.5 in the last 1.5 hours)
67.5 miles = distance
1.5 hours = time
therefore:
[tex]\frac{d}{t\\}[/tex] = 67.5/1.5
making your answer 45
leaving a as your correct answer:
d= 45t
The proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).
What is a proportion relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.
Given that, A train travels at a constant speed and has travelled 67.5 miles in the last 1.5 hours. (assuming that you meant 67.5 in the last 1.5 hours)
67.5 miles = distance
1.5 hours = time
We know that, speed = distance / time
s = 67.5/1.5
s = 45 mph
Now, distance = speed × time
d = 45t
Hence, the proportion relationship between the distance d, and the time t, that the train has travelled is, d = 45t. So the correct option is A).
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