Answer:
Step-by-step explanation:
The table can be computed as:
Advertising Expenses ($ million) Number of companies
25 up to 35 4
35 up to 45 19
45 up to 55 27
55 up to 65 16
65 up to 75 9
TOTAL 75
Let's find the probabilities first:
[tex]P(25 - 35) = P \Big(\dfrac{25-50.93}{10.80}<z< \dfrac{35-50.93}{10.80}\Big) \\ \\ =P \Big(\dfrac{-25.93}{10.80}<z< \dfrac{-15.93}{10.80}\Big) \\ \\ =P(-2.4009<z<-1.475) \\ \\ =(0.0694 -0.0082) \\ \\ =0.0612[/tex]
For 35 up to 45
[tex]P(35 - 45) = P \Big(\dfrac{35-50.93}{10.80}<z< \dfrac{45-50.93}{10.80}\Big)=P \Big(\dfrac{-15.93}{10.80}<z< \dfrac{-5.93}{10.80}\Big) \\ \\ =P(-1.475<z<-0.5491) \\ \\ =(0.2912 -0.0694) \\ \\ =0.2218[/tex]
For 45 up to 55
[tex]P(45 - 55) = P \Big(\dfrac{45-50.93}{10.80}<z< \dfrac{55-50.93}{10.80}\Big)=P \Big(\dfrac{-5.93}{10.80}<z< \dfrac{4.07}{10.80}\Big) \\ \\ =P(-0.5491<z<0.3769) \\ \\ =(0.6480 -0.2912) \\ \\ =0.3568[/tex]
For 55 up to 65
[tex]P(55 - 65) = P \Big(\dfrac{55-50.93}{10.80}<z< \dfrac{65-50.93}{10.80}\Big)=P \Big(\dfrac{4.07}{10.80}<z< \dfrac{14.07}{10.80}\Big) \\ \\=P(0.3768<z<1.3028) \\ \\ =(0.9032-0.6480) \\ \\ =0.2552[/tex]
For 65 up to 75
[tex]P(65 - 75) = P \Big(\dfrac{65-50.93}{10.80}<z< \dfrac{75-50.93}{10.80}\Big)=P \Big(\dfrac{14.07}{10.80}<z< \dfrac{24.07}{10.80}\Big) \\ \\ =P(1.3028<z<2.2287) \\ \\=(0.9871-0.9032) \\ \\ =0.0839[/tex]
Chi-Square Table can be computed as follows:
Expense No of Probabilities(P) Expe [tex](O-E)^2[/tex] [tex]\dfrac{(O-E)^2}{E}[/tex]
compa cted E (n*p)
nies (O)
25-35 4 0.0612 75*0.0612 = 4.59 0.3481 0.0758
35-45 19 0.2218 75*0.2218 = 16.635 5.5932 0.3362
45-55 27 0.3568 75*0.3568 = 26.76 0.0576 0.021
55-65 16 0.2552 75*0.2552 = 19.14 9.8596 0.5151
65-75 9 0.0839 75*0.0839 = 6.2925 7.331 1.1650
[tex]\sum \dfrac{(O-E)^2}{E}= 2.0492[/tex]
Using the Chi-square formula:
[tex]X^2 = \dfrac{(O-E)^2}{E} \\ \\ Chi-square \ X^2 = 2.0942[/tex]
Null hypothesis:
[tex]H_o: \text{The population of advertising expenses follows a normal distribution}[/tex]
Alternative hypothesis:
[tex]H_a: \text{The population of advertising expenses does not follows a normal distribution}[/tex]
Assume that:
[tex]\alpha = 0.02[/tex]
degree of freedom:
= n-1
= 5 -1
= 4
Critical value from [tex]X^2 = 11.667[/tex]
Decision rule: To reject [tex]H_o \ if \ X^2[/tex] test statistics is greater than [tex]X^2[/tex] tabulated.
Conclusion: Since [tex]X^2 = 2.0942[/tex] is less than critical value 11.667. Then we fail to reject [tex]H_o[/tex]
Belinda is thinking about buying a house for $286,000. The table below shows the projected value of two different houses for three years:
Number of years 1 2 3
House 1 (value in dollars) 294,580 303,417.40 312,519.92
House 2 (value in dollars) 295,000 304,000 313,000
Part A: What type of function, linear or exponential, can be used to describe the value of each of the houses after a fixed number of years? Explain your answer.
Part B: Write one function for each house to describe the value of the house f(x), in dollars, after x years.
Part C: Belinda wants to purchase a house that would have the greatest value in 25 years. Will there be any significant difference in the value of either house after 25 years? Explain your answer, and show the value of each house after 25 years.
a) The type of function for each case is given as follows:
House 1: Exponential.House 2: Linear.b) The functions for each house are given as follows:
House 1: 294580(1.03)^x.House 2: 295000 + 9000x.c) The value of each house after 25 years is given as follows:
House 1: $616,785.10.House 2: $520,000.There is a significant difference in these valuations, as an exponential function increases faster than a linear function.
How to classify the functions?A function is classified as exponential if when the input variable is changed by one, the output variable is multiplied by a constant.
Hence House 1 is an exponential function, as:
312519.92/303417.40 = 303417.40/294580 = 1.03.
And the definition is given as follows:
294580(1.03)^x.
The value of the house after 25 years is given as follows:
294580(1.03)^25 = $616,785.10.
A function is classified as linear if when the input variable is changed by one, the output variable is increased/decreased by a constant.
Hence House 2 is a linear function, as each year, the value of the house is increased by 9000.
Then the definition is given as follows;
295000 + 9000x.
The value of the house after 25 years is given as follows:
295000 + 9000(25) = $520,000.
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how do you solve -40 -(-12/5) =
Answer:
Below
Step-by-step explanation:
-40 -(-12/5) = -200/5 + 12/5 = -188/5 = - 37 3/5
Select all terms equivalent to √24.
A: the area of a square with side length 24 units
B: the side length of a square with area 24 units
C: the positive number x, where x - x = 24
D: the positive number y, where y = 24-24
E: the edge length of a cube with volume 24 cubic units
F: the volume of a cube with edge length 24 units
Answer:
B, E
Step-by-step explanation:
is this a function (1, 8.5)(2, 8)(3, 7.5)(4, 7)(5, 6.5)(6, 6)
Yes, because no x values repeat.
What is the missing number, what property did you use? –––=0×5
Answer:
0 is the answer
Step-by-step explanation:
0*5=0
0=0*5 ==> use Zero property of multiplication
This property states that any number multiplied by 0 equals 0.
Clare would like to buy a video game that costs at least $130. She has saved $48 so far and plans on saving $5 of her allowance each week. Write an inequality to find out the number of weeks it will take until she has enough money to buy the game.
Answer:
To determine how many weeks it will take Clare to save enough money to buy the video game, we need to find the number of weeks it will take for her to save at least $130. Let w be the number of weeks it will take for Clare to save enough money. We can set up the following inequality to represent this situation:
$48 + $5w >= $130
To solve this inequality, we can first add $48 to both sides to get rid of the constant on the left side:
$48 + $48 + $5w >= $130
This simplifies to $96 + $5w >= $130. Subtracting $96 from both sides gives us $5w >= $34. Dividing both sides by $5 gives us w >= 6.8. Since w represents the number of weeks, the solution must be a whole number. Therefore, Clare will need to save for at least 7 weeks in order to have enough money to buy the video game.
The cash register receipts each day last week at a coffee shop were $1,846, $1,521, $1,439, $1,439, $1,851, $2,722, and $2,540. (a) Find the mean. (Round your answer to to the nearest cent.)
6. Calculate the number that you need to add to each side of the equation w 2– 3w = 350 to create a perfect square trinomial. Add this number to each side of the equation. Show your work. (3 points)
7. Factor the trinomial. (3 points)
The number that we need to add is 1.5^2 = 2.25, we will get the perfect square trinomial:
(w - 1.5)^2 = 352.25
How to complete squares here?Remember that a perfect square trinomial is:
(a - b)^2 = a^2 - 2ab + b^2
Here we have the quadratic equation:
w^2 - 3w = 350
We can rewrite this as:
w^2 - 2*1.5*w = 350
Then what we need to add and subtract is 1.5^2, then we will get:
w^2 - 2*1.5*w = 350
w^2 - 2*1.5*w + 1.5^2 - 1,5^2 = 350
Grouping the first 3 terms we will get:
(w - 1.5)^2 - 1.5^2 = 350
(w - 1.5)^2 = 350 + 1.5^2
(w - 1.5)^2 = 352.25
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9. Mai rode on a train at a rate of speed of 70 miles per hour for 3 hours. Then she rode in a car at a rate
of speed of 50 miles per hour for 2 hours. What is the difference between the number of miles Mai
rode on the train and the number of miles she rode in the car?
a. 20
b.
60
c.
100
d. 110
The difference between the number of miles travelled on train and car is 110 miles
How to determine the difference between the number of milesFrom the question, we have the following parameters that can be used in our computation:
Distance 1 (train): 70 miles per hour for 3 hoursDistance 2 (car): 50 miles per hour for 2 hoursThe difference between the distance covered can be calculated as
Distance difference = The difference of the product of speed and time
Substitute the known values in the above equation, so, we have the following representation
Distance difference = 70 * 3 - 50 * 2
Evaluate the products
Distance difference = 210 - 100
Evaluate the difference
Distance difference = 110 miles
Hence, the distance difference is 110 miles
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Consider two securities, a and b. security a and b have a correlation coefficient of 0.65. security a has standard deviation of 12, and security b has standard deviation of 25. calculate the covariance between these two securities.
a. 300
b. 461.54
c. 261.54
d. 195
e. 200
The correct answer is option D. The covariance between securities a and b is 195.
To calculate the covariance between securities a and b, we can use the formula:
covariance = correlation coefficient * standard deviation of security a * standard deviation of security b
Plugging in the given values, we get:
covariance = 0.65 * 12 * 25 = 195
Therefore, the answer is (d) 195.
The covariance between two securities measures the extent to which the two securities tend to move together. A positive covariance indicates that the securities tend to move in the same direction, while a negative covariance indicates that the securities tend to move in opposite directions.
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H(x) = -4x - 3, find h (2)
Answer:
h(2) = (-11)
Step-by-step explanation:
h(x) = (-4x - 3), if h(2)
h(2) = (-4(2) - 3)
h(2) = -8 - 3
h(2) = (-11)
Thus, The answer is (-11) if h(2)
a histogram showing u.s. household income is highly skewed right. which of following statistics would best describe the center of the distribution? question 10 options: 1) median 2) variance 3) mean 4) mode
......,,........,.....-.......
The median would best describe the centre of the distribution for a highly skewed right histogram of US household income. The correct option is A.
What is the median?The median is the value that separates the distribution into two equal parts and is less influenced by extreme values than the mean.
Since a highly skewed right distribution has a long tail on the right side, the mean is likely to be pulled towards that tail, making it an unreliable measure of the centre.
The mode, or most frequently occurring value, may not be useful for describing the centre of a skewed distribution. The variance is a measure of the spread or dispersion of the data, not its centre.
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it is expected that 35% of students in a math course offered at northern university will earn an a. using excel to approximate the binomial distribution with a normal distribution, find the probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn an a.
The probability that of 300 randomly selected students enrolled in the course, more than 75 of them will earn is 0.9998..
We have given that,
A data of students in a math course offered at northern university will earn .
Total number of randomly selected students enrolled in the course = 300
i.e total number of trials, n = 300
probability of success, p = 35% = 0.35
probability of failure, q = 1-0.35 = 0.65
np = 300× 0.35 =
n(1-p) = 300×0.65 =
both np and n(1-p) are greater than 10 , so we can use normal approximation here.
We have to calculate probability that more than 75 of them will earn an , P(X>75). Using Binomial Probability distribution, X~ Bin(300, 0.35)
P(X= x) = ⁿCₓ(p)ˣ(q)⁽ⁿ⁻ˣ⁾
Now, P(X>75) = 1 - P(X=<75)
but here data is large, that is n= 300, x = 75 so tough to calculate it by hands , thus we use Excel function to find out the required probability. Excel Command: =BINOM.DIST(number_s,trials,probability_s,cumulative)
where, Number_s (required argument) -->the number of successes in trials,i.e "x" Trials (required argument) --> the number of independent trials i.e , "n" must 0≤ n. Probability_s (required argument) --> the probability of success in each trial.
Cumulative (required argument)-->A logical value that determines the form of the function. It can either be: TRUE--> Uses the cumulative distribution function and FALSE--> Uses the probability mass function. Now, for P(X ≤ 75) , the function is look like as
=BINOM.DIST(75,300, 0.35, TRUE) =0.000126081
=BINOM.DIST(75,300, 0.35, FALSE)
= 5.0305E-05
Now, the required probability, P(X> 75)
= 1 - P(X ≤75)
= 1 - 5.03095E-05 = 0.999949691
or using cumulative distribution function,
P(X>75) = 0.999873919
both are give approx. same results
.So, required probability is 0.9998.
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The ordered pairs model an exponential function, where w is the function name and t is the input variable.
{(1,60),(2,240),(3,960),(4,3840)}
What is the function equation in sequence notation?
wt=
Answer:
The answer is in my screen shot:
Explanation:
It's a geometric sequence with common ratio 3. You can calculate the common ratio by dividing the 240 by 80 or likewise 720 by 240.
Jolie is buying a shirt and a hat at the mall. The shirt costs $34.67, and the hat costs $19.48. If she gave the sales clerk $100.00, how much change should she receive?
Answer:
Jolie will get 45.85 change
Step-by-step explanation:
34.67+19.48=54.48
100.00-54.15=45.85
The above table shows statistics on the ages, in years, of the people who attended a lecture last week. The data are summarized in the boxplot shown.Which of the following statements is supported by the table and boxplot?answer choicesThe range of the distribution is 20 years.There were 43 people who attended the lecture.At least 50% of the people who attended the lecture were 43 years or younger.At least 75% of the people who attended the lecture were age 53 years or younger.At least 25% of the people who attended the lecture were 33 years old.
The boxplot shows that the majority of the people who attended the lecture were age 53 or younger, which means at least 75 percentage of the people were in that range.
The table and boxplot provide information about the ages of the people who attended a lecture last week. The boxplot shows that the majority of the people who attended the lecture were age 53 or younger. This is supported by the table, which shows that the median age is 53 and the interquartile range is between 36 and 53. This indicates that at least 75% of the people who attended the lecture were age 53 years or younger. The range of the distribution is 20 years, with the minimum age being 18 and the maximum age being 38. This suggests that there were at least two people in each age range, from 18 to 38. This also indicates that there were at least 43 people who attended the lecture. The boxplot also shows that at least 25% of the people who attended the lecture were 33 years old. This is supported by the table, which shows the lower quartile is 33.
Interquartile range = Maximum - Minimum
Interquartile range = 53 - 36 = 17
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A 2010 study of 240 randomly-selected residents of a subtropical resort city with 82,000 residents found that 5.4% of them had been exposed to the mosquito-borne virus that causes Dengue fever. Suppose the actual percentage of people in the city who have been exposed to the virus is 3%. Let p^= the proportion of residents who have been exposed in a random sample of 240.
The standard deviation of p^ is approximately...
The standard deviation of p^ is approximately 0.00012.
What do you mean by standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. When the standard deviation is low, the data are concentrated around the mean, and when it is large, the data are widely dispersed.
How to calculate standard deviation?The formula for standard deviation S.D is given below:
By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance. The bigger the deviation within the data collection, the more the data points deviate from the mean; hence, the higher the standard deviation, the more dispersed the data.
Calculation:
The formula for standard deviation S.D is given below:
Here,P = 3% = 0.03 and N = 240
∴ S.D = √0.03(1 - 0.03)/240
∴ S.D = 0.00012.
The standard deviation of p^ is approximately 0.00012.
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3. (8.4B) The graph below shows the relationship
between the number of dollars a worker earns,
and the number of hours worked. What does the slope of the graph represent? HELP PLEASE
The slope of the graph represent d)The number of hours worked to earned dollors
What is Slope of the graph?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, although it may be found in O'Brien's (1844)and Todhunter'sformulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute slope. The ratio can also be written as a quotient ("rise over run"), which provides the same valueTo learn more about Slope of the Graph refer to:
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You are given the figure below as well as following. Explain how a and b are parallel. Explain giving measurements and angels. Angels should be part of your answer.
Answer:
Since angle 9 is 110 degrees, that means that angle 10 must be 70 degrees, because the angle is on a straight line, so the angles must add to be 180 degrees, because they are supplementary angles. Since p ll q (p is parallel to q), that means that angle 1 is 110 degrees and angle 2 is 70 degrees. Because angles 1, 2, 5, and 6 have to add to be 360 degrees and angles 1+2 equals 180 degrees, that means that 5+6 equals 180 degrees as well. Angle 6 equals 110 degrees so that means angle 5 is 70 degrees. On the other side, angle 8 is 70 degrees, and since the two angles are the same, p and q are the same.
The farm's owner wants to increase the income from the sale of strawberries to at least $70,000 per year. What change would you suggest that would allow the farm's owner to meet this goal?
Answer:
Possible changes —
(i) Increase farmland
(ii) Sow healthy strawberry seeds
(iii) Choose a nutrient-rich, suitable plot of land
7. Sylvia went on a trip. The number of shirts she packed was 2 fewer than twice the number of pants
she packed. The total number of pairs of pants and shirts was 16.
A. Let x = the number of pants she packed and let y = the number of shirts she packed. Write a system of
equations to represent the problem.
B. Solve the system of equations using substitution to find the number of shirts and pairs of pants Sylvia
brought.
The system of equations is x + y = 16 and y = 2x - 2
The number of shirts and pairs of pants Sylvia brought are 10 and 6, respectively
How to determine the system of equations?From the question, we have the following parameters that can be used in our computation:
x = the number of pants she packed y = the number of shirts she packedWhen the statements are interpreted, we have the system of equations to be
x + y = 16
y = 2x - 2
The solution of the equationIn (a), we have
x + y = 16
y = 2x - 2
This gives
x + 2x - 2 = 16
Evaluate the like terms
3x = 18
Divide
x = 6
Recall that
y = 2x - 2
So, we have
y = 2 x 6 - 2
y = 10
Hence, the number of shirts she packed is 10
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Im stuck on finding G im wondering if someone can help me
Answer:
G=15-1.25×t
or,G=1.25(12-t)
Answer:
G= 15-t1.25
Step-by-step explanation:
Evaluate the following 14/2+4*4-4
Answer:
14/2+4x4-4= 19
Step-by-step explanation:
calculate
7+19-4
which is 19
(BODMAS rule is used here)
14/2 + 4 × 4 - 4
7 + 4 × 4 - 4
7 + 16 - 4
7 + 12
19
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part 1: 2 airplanes left the same airport at the same time. One is traveling at 422 mph straight east, the other is traveling 384 mph straight west.
How long will it take before they are 6045 miles apart?
part 2: 2 airplanes left the same airport at the same time. One is traveling at 422 mph straight NORTH, the other is traveling 384 mph straight WEST.
How long will it take before they are 1997 miles apart?
The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.
What is speed?Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Time
2 planes left a similar air terminal simultaneously. One is going at 422 mph straight east, the other is voyaging 384 mph straight west.
If the distance between them is 6045 miles. Then the time is calculated as,
T = 6045 / (384 + 422)
T = 6045 / 806
T = 7.5 hours
2 planes left a similar air terminal simultaneously. One is going at 422 mph straight NORTH, the other is voyaging 384 mph straight WEST.
If the distance between them is 1997 miles. Then the time is calculated as,
T = 1997 / (384 + 422)
T = 1997 / 806
T = 2.48 hours
The number of hours taken by plane in cases 1 and 2 will be 7.5 hours and 2.48 hours, respectively.
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the height of a triangle is 2 more than twice the base. the area is 20 square feet. find the quadratic equation that represents this situation if the formula for the area of a triangle is A = 1/2 bh.Select one a. 2b^2 - b - 20 = 0b. b^2 + 2b= 0с. b^2 + b - 20 = 0d. b^2 + 2b + 20 = 0
On solving the provided question we can say - area = 1/2 x b x (2b+2), area = [tex]b^2 + b -20 {[/tex]
What is Triangle?A triangle is a polygon that has three sides and three corners. The spots where the three sides join end to end make up the triangle's corners. Three triangle angles added together equal 180 degrees. A three-sided form is a triangle. Triangles are known by a variety of names. Triangle kinds are determined by the size of the angles and the length of the sides (angles). Depending on how long their sides are, triangles fall into one of three categories. Isosceles, equilateral, and uneven
Let 'b' be the base of the triangle, then
then height is - 2b + 2
area = 1/2 bxh
area = 1/2 x b x (2b+2)
area =
[tex]b^2 + b -20 {[/tex]
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Please give me detailed answer
The values of x, y and z are 5, 18 and 12 using the congruent triangles properties and triangles sum properties.
What are the characteristics of a triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
In congruent triangles all the sides are equal, with respect to the other triangle.
Calculation:Given that ΔUVW≅ΔTSR.
We can see that in TSR triangle the lengths of TR and TS are given as 50 and 53 now the remaining side RS is 5y-33 as we know that both triangles are similar we compare side RS with side VW
i.e..,
5y-33 = 57
5y = 90
y = 18
So we can now compare vertices vertex V is vertex R , vertex W is vertex S and vertex U is vertex T.
So equating the sides of triangles we get,
12x-7 = 53 and 3z+14 = 50
12x = 60 3z = 36
x= 5 z = 12
The values of x, y and z are 5, 18 and 12 using the similar triangles properties and triangles sum properties.
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2
Write the correct answer in the box. Substitute numerical values into the expression for all known variables.
Jeff wants to purchase a television for his first apartment. The television costs $750. He can get a zero-interest loan for the television if he pays $100
per month. At the same time, he puts away $200 per month in savings. To figure out when his savings will equal the remaining amount he owes on
the television, he starts writing a system of equations:
Equation 1: y=200x
Equation 2:
Write the second equation in the system.
y=??????
Answer:
Equation 2: y=750-100x
Step-by-step explanation:
Part A USE A MODEL Express the statement using an inequality involving absolute value. Let x represent the number of students attending the dance. The dance committee expects attendance to number within 25 of last year's 87 students.
Step-by-step explanation:
The dance committee expects attendance to number within 25 of last year's 87 students can be expressed using an inequality involving absolute value as:
|x - 87| <= 25
This inequality states that the absolute difference between the number of students attending the dance (x) and 87, which was the number of students attending last year, must be less than or equal to 25. This means that the number of students attending the dance this year must be within 25 of the number of students attending last year.
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, can the company build 5 child bikes and 15 adult bikes in a week? (1 point)
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
The company can build 5 child bikes and 15 adult bikes in a week.
The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".
Linear Equations:Linear Equations are mathematical statements, which can be used to find an unknown quantity or any value in a given problem. Here we use variables like x, y .. etc. to represent unknown values.
Here we will use Linear Equations to solve the equations.
Here we have
One child bike requires 4 hours to build and 4 hours to test
Number of hours to build 'c' number of child bikes = 4c
Number of hours to test 'c' number of child bikes = 4c
One adult bike requires 6 hours to build and 4 hours to test.
Number of hours to build 'a' number of adult bikes = 6a
Number of hours to test 'a' number of adult bikes = 4a
Number of hours taken to build bikes in one week = 120
=> 4c + 6a ≤ 120 --- (1)
Number of hours taken to test the bikes in one week = 100
=> 4c + 4a ≤ 100 --- (2)
Assume that
The company can build 5 child bikes and 15 adult bikes in a week
Substitute c = 5 and a = 15 in (1) and (2)
(1) => 4(5) + 6(15) ≤ 120
=> 110 ≤ 120 [ which can be true ]
(2) => 4(5) + 4(15) ≤ 100
=> 80 ≤ 100 [ which can be true ]
From the above calculations,
Both (1) and (2) are satisfied
Therefore,
The company can build 5 child bikes and 15 adult bikes in a week.
The answer is "Yes because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100".
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In each of the following scenarios, determine whether the data is paired or not paired.
Part A: Compare pre- (beginning of semester) and post-test (end of semester) scores of students.
Part B: Assess gender-related salary gap by comparing salaries of randomly sampled men and women.
Part C: Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Part D: Assess effectiveness of a diet regimen by comparing the before and after weights of subjects.
Part (A) = Paired, Part (B) = Not Paired, Part (C) = Paired, Part (D) = Paired
Part A:
Compare pre- (beginning of the semester) and post-test (end of the semester) scores of students
Paired, as a subject are the same in both.
Score
A score is a group of 20 (often used in combination with a cardinal number, i.e. fourscore to mean 80), but also often used as an indefinite number.
Part B:
Assess the gender-related salary gap by comparing the salaries of randomly sampled men and women.
Not paired.
Sample
A sample is an outcome of a random experiment. When we sample a random variable, we obtain one specific value out of the set of its possible values. That particular value is called a sample. The possible values and the likelihood of each are determined by the random variable's probability distribution.
Part C:
Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Paired, as a subject are the same in both.
Vitamin E
Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.
Part D:
Assess the effectiveness of a diet regimen by comparing the before and after weights of subjects.
Paired, as a subject are the same in both.
Weight
The weight of an object refers to the force of gravity that is acting on the object. Furthermore, its calculation is mass times the acceleration of gravity, w = mg. The SI unit of weight is the newton because weight is a force.
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Compare artery thicknesses at the beginning of a study and after 2 years of taking Vitamin E for the same group of patients.
Paired, as a subject are the same in both.
Vitamin E
Vitamin E is a fat-soluble vitamin with several forms, but alpha-tocopherol is the only one used by the human body.