The optimal speed for the delivery minivan to minimize the cost of an 80 mile delivery for the gift shop considering only the cost of fuel and wages is approximately 126 mph.
Let's first determine the total cost of the delivery as a function of the speed of the minivan. The cost consists of two parts: the cost of fuel and the cost of the driver's wages. Since the driver's rate is $20 per hour and the delivery is 80 miles, the cost of the driver's wages is:
W = $20 × (80/V) = $1600/V
The cost of fuel is given by the formula C = [tex]0.005V^2[/tex], where V is the speed of the minivan in mph. The total cost of the delivery is therefore:
C(V) = [tex]0.005V^2 + 1600/V[/tex]
To find the speed that minimizes the cost of the delivery, we need to find the value of V that makes the derivative of C(V) equal to zero:
C'(V) = [tex]0.01V - 1600/V^2[/tex]
0 = [tex]0.01V - 1600/V^2[/tex]
0 = [tex]V^3 - 160000[/tex]
[tex]V^3[/tex] = 160000
V = cuberoot(160000) = 40√10
The exact speed that minimizes the cost of the delivery is V = 40√10 mph. Rounded to the nearest whole number, the answer is 126 mph (since 40√10 ≈ 126.49).
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What is the answer to this problem -2-(-9)-(-2)
the value of the expression -2-(-9)-(-2) is 9.
To solve the expression -2-(-9)-(-2), we can simplify it using the rules of arithmetic:
A double negative becomes a positive. So, -(-9) becomes +9.
Subtracting a negative is the same as adding the positive. So, -(-2) becomes +2.
Using these rules, we can simplify the expression as follows:
-2 - (-9) - (-2) = -2 + 9 + 2
= 9
Therefore, the value of the expression -2-(-9)-(-2) is 9.
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Work out the value of u in the equation below. Give your answer to 1 d.p.
tan 34° = 9/u
Answer:
u ≈ 13.3
Step-by-step explanation:
tan34° = [tex]\frac{9}{u}[/tex] ( multiply both sides by u )
u × tan34° = 9 ( divide both sides by tan34° )
u = [tex]\frac{9}{tan34}[/tex] ≈ 13.3 ( to 1 decimal place )
A moving truck claims to hold 300 cubic feet of boxes. The truck is 25 feet in length and 8 feet in height. What is the width of the moving truck?
Answer: Width of the moving truck is 1.5 ft.
Step-by-step explanation:
Step 1: Volume of the moving truck = 300 ft³, length = 25 ft and height = 8ft. Since the truck is in the shape of a cuboid, use the formula of volume of the cuboid to find width.
⇒ Volume of truck = length × width × height
⇒ 300 = 25 × width × 8
⇒ 300 = 200 × width
⇒ width = 300/200 = 3/2 = 1.5 ft
The trampoline park charges $50 to reseve the place and then $9 per person
The expression to represent the cost for any number of people is $50 + ($9 × x)
The trampoline park charges a fee of $50 to reserve the place. This means that, no matter how many people are going to visit the park, you will have to pay this flat fee of $50 to reserve the place. This fee is fixed and doesn't change with the number of people who will be visiting the park.
In addition to the reservation fee, the park charges $9 per person. So, if there is only one person visiting the park, you will have to pay $50 + $9 = $59. If there are two people visiting the park, you will have to pay $50 + ($9 × 2) = $68. If there are three people visiting the park, you will have to pay $50 + ($9 × 3) = $77, and so on.
To represent the total cost for any number of people, we can use the variable "x" to represent the number of people visiting the park. Then, we can express the total cost as:
Total Cost = Reservation Fee + (Cost per person × Number of people)
Total Cost = $50 + ($9 × x)
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The given question is incomplete, the complete question is:
The trampoline park charges for $50 to reserve the place and then $9 per person. Write an expression to represent the cost for any number of people.
Is positive numbers closest to 0 than negative numbers that is like -3,-1,-2?
|||
Calculator
3.05 Quiz: Volumes of Cones
What is the approximate volume of a cone with a height of 12 in. and radius of 9 in.?
Use 3.14 to approximate pi, and express your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
in³
Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.
How do we find volume of cone ?To find the volume of a cone, we use the following formula:
V = 1/3 * π * r² * h
where V is the volume of the cone, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base of the cone, and h is the height of the cone.
To use the formula, we simply substitute the given values for r and h into the formula and simplify. Make sure that the radius and height are measured in the same units. The resulting volume will be in cubic units.
The formula for the volume of a cone is:
V = 1/3 * π * r² * h
where π is pi (approximately 3.14), r is the radius of the base of the cone, and h is the height of the cone.
Substituting the given values, we get:
V = 1/3 * 3.14 * 9² * 12
= 1/3 * 3.14 * 81 * 12
= 3.14 * 324
= 1017.36
Rounding to the nearest hundredth, the approximate volume of the cone is 1017.36 cubic inches.
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Can someone please help me!!
Answer: 240°
Step-by-step explanation:
The sum of the angles in a circle adds up to 360°, and the central angles are congruent to its arcs, so what we have is arcGFE + arcGHE = 360°, but we know arcGHE adds up to 120°. This makes our equation arcGFE + 120° = 360°, which means arcGHE = 240°
#9: If the mean value test score in a math class was an 82%
and there were 25 students in the class, how much would the
mean score increase if another student scored a 100%?
After answering the provided question, we can conclude that As a result, equation if another student achieved 100%, the mean score would rise by 0.35%.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. In the equation "x2 + 2x - 3 = 0," for example, the variable x is raised to the second power. Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.
You can use the following formula to compute the new mean score:
(Old Sum of Scores + New Score) / (Old Number of Scores + 1) = New Mean
Where:
Old Score Sum = Mean x Number of Scores
Number of old scores = 25 (the original number of students)
The new score is 100.
Then, compute the previous score sum:
Old Score Sum = Mean x Number of Scores = 0.82 x 25 = 20.5
New Total Scores = Old Total Scores + New Score = 20.5 + 100 = 120.5
Finally, compute the new mean score as follows:
New Mean = New Score Sum / (Old Score Sum + 1) = 120.5 / 26 = 4.6346 or 46.35% (rounded to two decimal places)
As a result, if another student achieved 100%, the mean score would rise by 0.35%.
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the equation
-8x-y=3
8x+y=-3
have the same/different what slopes and the same/different what y-intercepts?
Answer:
same for both ; slope = -8 and y-intercept is (0, -3)
Step-by-step explanation:
First, lets write both of these in slope-intercept form!
-8x-y=3 is the same as -y = 8x+3, which is the same as y = -8x-3.
8x+y=-3 is the same as y = -8x-3.
As you can see, these equations are the same, which means that they have the same slopes and y-intercepts.
Since the equation for slope intercept form is y= mx + b where m is the slope and b is the y-intercept, this means that the slope is -8 and the y-intercept is (0, -3).
line segment wx is the radius of circle x, and line segment zy is the radius of circle y. points w, x, c, y, and z are all on line segment wz. what is the area of circle c, which passes though points w and z? 81 164 324 1296
The area of circle C, which passes though points W and Z is 324π square meters.
The center of the outer circle, Point D, is where we want to calculate the area of the circle has a WZ diameter and WC and CZ radii.
That YZ = YD = 10 cm is known.
Let DC = x and CY = 10 - x
The outer circle's radius can be expressed as 8 + 8 + x or 10 + 10 - x, which we can equate to determine its value of x
8 + 8 + x = 10 + 10 - x
Simplify
16 + x = 20 - x
Subtract 16 on both side, we get
x = 4 - x
Add x on both side, we get
2x = 4
Divide by 2 on both side, we get
x = 2
As a result, the circle's radius is
= 8 + 8 + x
= 16 + x
= 16 + 2
= 18 cm
The area of circle = πr²
The area of circle = π(18)²
The area of circle = 324π
Thus, the circle's area is 324π square meters.
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The complete question is:
Line segment WX is the radius of circle X, and line segment ZY is the radius of circle Y. Points W, X, C, Y, and Z are all on line segment WZ.
What is the area of circle C, which passes though points W and Z?
A. 81
B. 164
C. 324
D. 1296
Determine whether the function is a polynomial function. Check by setting in standard from, identifying leading coefficient, constant, Highest degree, and type of function
The given function f(x) = 43 + 5x² - x + 7x³ is a polynomial function.
Standard form: f(x) = 7x³ + 5x² - x + 43; Leading coefficient = 7; constant = 43; degree = 3; type - cubic polynomial.
Explain about the polynomial function?In mathematics, there are many different kinds of functions. When studying functions as well as their applications, it's critical to be consistent with the names we use for various kinds of functions. A form of function is frequently described by more than one phrase.
A quadratic, cubic, quartic, and other functions involving purely non-negative integer powers of x are examples of polynomial functions. We can define a polynomial's degree and provide a generic definition for it.
Given polynomial:
f(x) = 43 + 5x² - x + 7x³
Arrange in standard form: ax³ + bx² + cx + d
Thus,
Standard form: f(x) = 7x³ + 5x² - x + 43;
Leading coefficient = 7;
constant = 43;
degree = 3;
type - cubic polynomial.
Thus, the given function f(x) = 43 + 5x² - x + 7x³ is a polynomial function.
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What is the height of the trapezoid? 3 units 5 units 10 units 12 units
In a trapezoid, the height is the perpendicular distance between the two parallel bases. It is usually denoted as "h".
In order to determine the height of a trapezoid, we need to know the lengths of the two parallel bases or have additional information about the trapezoid's dimensions.
The lengths of the bases of a trapezoid are crucial for calculating the height using various formulas. Without the lengths of the bases or any other relevant information, we cannot determine the height of the trapezoid.
To determine the height of a trapezoid, we need more information. The height of a trapezoid is typically defined as the perpendicular distance between the two parallel bases. In this case, we would need to know the lengths of the two parallel bases or have additional information about the trapezoid's dimensions. Without that information, we cannot determine the height of the trapezoid.
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Answer: 5 units
Step-by-step explanation:
a sports magazine prints 12 issues per year, and a technology magazine prints 10 issues per year. the total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. which system of equations can be used to find s, the number of pages in each issue of the sports magazine, and t, the number of pages in each issue of the technology magazine?
The number of pages in each issue of the technology magazine is 74 pages.
The number of pages in each issue of the sports magazine is s and the number of pages in each issue of the technology magazine is t.
To solve this problem, we have to write a system of equations using the given information. We have to find s and t.
System of equations can be used to find s and t; 12s = 10t + 32 and t = s + 18
The given sports magazine prints 12 issues per year and the technology magazine prints 10 issues per year.
The total number of pages in all the issues of the sports magazine for one year is 32 more than the total number of pages in all the issues of the technology magazine for one year. That means we can write an equation based on the information given for the number of pages in all the issues of the sports magazine and the technology magazine.
12s = 10t + 32
We also know that each issue of the sports magazine has 18 fewer pages than each issue of the technology magazine. That means we can write another equation based on the information given for the number of pages in each issue of the sports magazine and the technology magazine.
t = s + 18
Now, we can solve for s and t by substituting t = s + 18 in the first equation: 12s = 10(s + 18) + 32
12s = 10s + 180 + 32
12s - 10s = 180 + 32s = 56
So, the number of pages in each issue of the sports magazine is 56 pages. And, the number of pages in each issue of the technology magazine is: t = s + 18t = 56 + 18t = 74 pages.
So, each issue of the technology magazine contains 74 pages.
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In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values collected by the manager.
{15, 0, 26, 15, 20, 15, 34, 11, 20, 39, 31, 20, 23, 20, 39, 5}
Which of the following stem-and-leaf plots correctly graphs the data set?
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5
2 0 3 6
3 1 4 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
1 1 5 5 5
2 0 0 0 0 3 6
3 0 1 4 9 9
Key 1|1 = 11
2021 Riverside Red Dragon Football Season Points
0 0 5
1 1 5 5 5
2 0 0 0 0 3 6
3 1 4 9 9
Key 1|1 = 11
Not answer but helpful:
The required stem-and-leaf plot shown below that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s.
What is stem-and-leaf plots?
A stem-and-leaf plot is a type of data display that helps to show the distribution of a set of numerical data.
here,
For the given data set:
Stem Leaf
0 4
1 1, 3, 3
2 0, 0, 0, 6, 7
3 0, 0, 0, 7
The stem-and-leaf plot shows that the majority of the scores fall in the 20s and 30s, with some scores in the teens and low 20s. The plot makes it easier to see the distribution of the data, rather than just looking at the raw values.
cual es la respuesta
Answer:
48
Step-by-step explanation:
a² - 16
a = 8
8² - 16 = 64 - 16 = 48
So, the answer is 48
physics graduate student laura van ertia has conducted a complete randomized design with a single factor, hoping to solve the mystery of the unified theory and complete her dissertation. the results of this experiment are summarized in the following anova display: source df ss ms f factor ? ? 14.18 ? error ? 37.75 ? total 23 108.63 answer the following questions about this experiment. (a) the sum of squares for the factor is? (b) the number of degrees of freedom for the single factor in the experiment is? (c) the number of degrees of freedom for the error is? (d) the mean square for error is? (e) the value of the test statistic is? (f) if the significance level is 0.05, your conclusions are not to reject the null hypothesis. yes or no (g) the p-value for the test statistic is? (i) laura used how many levels of the factor in this experiment? (j) laura replicated this experiment how many times?
The experiment has not been repeated.
The answer to the question:1. (a) The sum of squares for the factor is 14.18.2. (b) The number of degrees of freedom for the single factor in the experiment is 1.3. (c) The number of degrees of freedom for the error is 23.4. (d) The mean square for error is 1.64.5. (e) The value of the test statistic is 8.63.6. (f) If the significance level is 0.05, the conclusion is to reject the null hypothesis. Yes.7. (g) The p-value for the test statistic is 0.0086.8. (i) Laura used how many levels of the factor in this experiment? One.9. (j) Laura replicated this experiment how many times? The experiment has not been repeated.A complete randomized design with a single factor was conducted by physics graduate student Laura van Iertia. She is hoping to solve the mystery of the unified theory and complete her dissertation with the results of this experiment. The results of this experiment are summarized in the following ANOVA display:Source df SS MS F Factor 1 14.18 14.18 8.63 Error 23 37.75 1.64 - Total 24 52.93 - The questions and answers based on this experiment are given below:(a) The sum of squares for the factor is 14.18.(b) The number of degrees of freedom for the single factor in the experiment is 1.(c) The number of degrees of freedom for the error is 23.(d) The mean square for error is 1.64.(e) The value of the test statistic is 8.63.(f) If the significance level is 0.05, the conclusion is to reject the null hypothesis. Yes.(g) The p-value for the test statistic is 0.0086.(i) Laura used how many levels of the factor in this experiment? One.(j) Laura replicated this experiment how many times? The experiment has not been repeated.
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Sam is a school leader. She wants to decide whether makeup should be allowed in school or not? She collected random samples of 100 females regarding make up preference. Make at least two inferences based on the results. How many prefer lipstick out of 375 people?
The two inference we can make from this data is the proportion of females who prefer makeup and the significant difference in makeup preference between different groups of female.
What are the inference from the data?Based on the sample of 100 females regarding makeup preference, Sam could make the following inferences:
1. The proportion of females who prefer makeup can be estimated. Sam can calculate the proportion of females in her sample who preferred makeup and use that as an estimate of the proportion in the population. For example, if 70 out of the 100 females in the sample preferred makeup, then Sam could estimate that 70% of females in the population prefer makeup.
2. Sam could also determine if there is a significant difference in makeup preference between different groups of females. For example, she could compare the proportion of females who prefer makeup in different age groups or different ethnic groups.
To find out how many out of 375 people prefer lipstick, we need to know the proportion of people in the sample who prefer lipstick. If this information is not available, we cannot accurately determine the number of people who prefer lipstick out of 375.
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Draw the line of reflection that reflects Triangle ABC on Triangle A'B'C'.
Answer:
Step-by-step explanation:
The corresponding points of each triangle are equal distance from the line y = -2
The width of a rectangle measures ( 9.5 c + 6.2 d ) (9.5c+6.2d) centimeters, and its length measures ( 5.1 c − 3.4 d ) (5.1c−3.4d) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The expression that represents the perimeter, in centimeters, of the rectangle is 29.2c + 5.6d.
The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the rectangle has two sides with a length (9.5c+6.2d) and two sides with a length (5.1c−3.4d).
Therefore, the perimeter can be calculated by adding the lengths of all four sides:
Perimeter = (9.5c+6.2d) + (9.5c+6.2d) + (5.1c−3.4d) + (5.1c−3.4d)
Simplifying and combining like terms, we get:
Perimeter = 2(9.5c+6.2d) + 2(5.1c−3.4d)
Perimeter = 19c + 12.4d + 10.2c − 6.8d
Perimeter = 29.2c + 5.6d
Therefore, the expression that represents the perimeter, in centimeters, of the rectangle is 29.2c + 5.6d.
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A tabletop in the shape of a trapezoid has an area of 6,350 square centimeters. Its longer base measures 115 centimeters, and the shorter base is 85 centimeters. What is the height?
The height of the trapezoid can be found by dividing the area (6,350 cm2) by the average of the two bases (100 cm). The height is 63.5 cm.
The formula used to find the area of a trapezoid is A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the two bases and h is the height. We are given the area (A) and the lengths of both bases (b1 and b2). All we need to do is solve for h.
To do this, we first need to find the average of the two bases. The average of the two bases is the sum of the two bases divided by two. In this case, the longer base (b1) is 115 cm and the shorter base (b2) is 85 cm, so we can calculate the average as (115 + 85) ÷ 2 = 100 cm.
We can now substitute this value into the area formula and solve for h. A = (1/2)(100)h, so h = A ÷ (1/2)(100). Plugging in the area given (6,350 cm2), we get h = 6,350 ÷ (1/2)(100) = 63.5 cm. The height of the trapezoid is 63.5 cm.
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13. A savings account earns 10% simple
interest. How much interest does an $800
deposit earn in four years?
14. a. Greg deposits $800 into a savings
account that earns 10% interest
compounded
annually. What is Greg's
balance after four years?
b. How much interest did Greg's
account earn?
Answer:
Greg's account earned 80$ because 0.10×800=80 80+800=880 total
The table below shows Nicole's earnings on the job.
Time (hours)
Time (hours)
Earnings (dollars)
Earnings (dollars)
10
10
$
296
$296
22
22
$
651.20
$651.20
24
24
$
710.40
$710.40
What is Nicole’s rate of pay, in dollars per hour?
What is Nicole’s rate of pay, in dollars per hour?
Thus, pay of Nicole per hour for his job in dollars per hour is $29.6.
Explain about the unit value?The appraisal of a single item or constituent within a group is known as unit value. The concept of unit value is applicable in a variety of contexts, including building, inventory control, sales, and stock trading.
The unit value is typically the result of dividing the price or worth of a set of things by the total number of items. Doing unit value calculations is crucial since it enables experts to comprehend the price associated with producing each unit.
For the given question: Nicole's earnings
Time (hours) 10 22 24
Earnings (dollars) $296 $651.20 $710.40
10 hours ----> $296
1 hour ------> $296 / 10
1 hour ------> $29.6
Thus, pay of Nicole per hour for his job in dollars per hour is $29.6.
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Complete questions:
The table below shows Nicole's earnings on the job.
Time (hours) 10 22 24
Earnings (dollars) $296 $651.20 $710.40
What is Nicole’s rate of pay, in dollars per hour?
[tex]306^{2} +270^2[/tex]
for her phone service, jenny pays a monthly fee of $24, and she pays an additional $0.06 per minute of use. the least she has been charged in a month is .what are the possible numbers of minutes she has used her phone in a month?use for the number of minutes, and solve your inequality for $96.36.
Jenny must have used at least 1600 minutes of her phone service to incur a minimum monthly fee of $96.36. This can be calculated by solving the inequality $24 + 0.06x ≥ $96.36 where x is the number of minutes.
Rearranging this equation to 0.06x ≥ $72.36 and solving for x gives us the result x ≥ 1600.
Given that, For her phone service, Jenny pays a monthly fee of $24, and she pays an additional $0.06 per minute of use. The least she has been charged in a month is $96.36.To find the possible numbers of minutes she has used her phone in a month.
Inequality for $96.36 is(0.06m + 24) ≥ 96.36where m is the number of minutes used. In order to solve the above inequality, we will simplify it first(0.06m + 24) ≥ 96.360.06m + 24 - 24 ≥ 96.36 - 24.060.06m ≥ 72.36m ≥ 72.36/0.06m ≥ 1206So, the possible numbers of minutes she has used her phone in a month is greater than or equal to 1206 minutes. Answer: $\boxed{m≥1206}$
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Please answer this :(
Answer:
a = 4, b = 5
Step-by-step explanation:
we need to complete the square to get it in that form.
x^2 - 8x + 21
= x^2 - 8x + 16 + 5
= (x-4)^2 + 5
a = 4, b = 5
The teacher has 1 apple she gives 1 apple to tommy how many apples does she have now
Number of apples that teacher has now is zero
Subtraction is a mathematical operation that involves taking away one quantity from another. It is one of the four basic arithmetic operations, along with addition, multiplication, and division. Subtraction is usually represented using the "-" symbol.
If the teacher had 1 apple and gave 1 apple to Tommy, then the total number of apples the teacher has now can be calculated using subtraction
Teacher's apples after giving one to Tommy = Teacher's apples before - Apples given to Tommy
Teacher's apples after giving one to Tommy = 1 - 1
Teacher's apples after giving one to Tommy = 0
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Jeremiah's ice cream was 23.9 ounces when he checked out at the store. He ate 11.38 ounces before leaving, how many ounces did he take home as leftovers?
Answer:
12.52 ounces
Step-by-step explanation:
Leftovers= 23.9-11.38
=12.52 ounces
x = 30° is a zero for y = tan 3(x +30°). True or False with justification
Answer: true
Step-by-step explanation:
true
Please ANSWER THIS AND CORRECTLY IT'S DUE IN 30 minutes
Question 1
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Sunny Town is skewed
IQR, because Desert Landing is symmetric
Range, because Sunny Town is skewed
Range, because Desert Landing is symmetric
Question 2
The data given represents the number of gallons of coffee sold per hour at two different coffee shops.
Coffee Ground
1.5 20 3.5
12 2 5
11 7 2.5
9.5 3 5
Wide Awake
2.5 10 4
18 4 3
3 6.5 15
6 5 2.5
Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain.
Wide Awake, with a median value of 4.5 gallons
Wide Awake, with a mean value of about 4.5 gallons
Coffee Ground, with a mean value of about 5 gallons
Coffee Ground, with a median value of 5 gallons
Question 3
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru is able to estimate their wait time more consistently and why?
Burger Quick, because it has a smaller IQR
Burger Quick, because it has a smaller range
Super Fast Food, because it has a smaller IQR
Super Fast Food, because it has a smaller range
Question 4(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.
Bus 47, with an IQR of 8
Bus 14, with an IQR of 6
Bus 47, with a range of 8
Bus 14, with a range of 6
Question 5(Multiple Choice Worth 2 points)
(Comparing Data MC)
The data given represents the height of basketball players, in inches, on two different girls' teams.
Allstars
73 62 60
63 72 65
69 68 71
66 70 67
60 70 71
Champs
62 69 65
68 60 70
70 58 67
66 75 70
69 67 60
Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer.
The Allstars, with a mean of about 67.1 inches
The Champs, with a mean of about 66.4 inches
The Allstars, with a median of about 68 inches
The Champs, with a median of about 67 inches
Question 6 (Essay Worth 4 points)
(Comparing Data HC)
The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.
Bay Side School Seaside School
8, 6, 5 0 5, 8
8, 6, 5, 4, 2, 0 1 0, 1, 2, 5, 6, 8
5, 3, 2, 0, 0 2 5, 5, 7, 7, 8
3 0, 6
2 4
Key: 2 | 1 | 0 means 12 for Bay Side and 10 for Seaside
Part A: Calculate the measures of center. Show all work. (2 points)
Part B: Calculate the measures of variability. Show all work. (1 point)
Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
Answer:
Answer below :)
Step-by-step explanation:
Question 1:
When comparing the two sets of data in the histograms to determine the location with the most consistent temperature, we should use IQR as the measure of variability. The reason for this is that IQR is a robust measure of dispersion that is not affected by outliers and is especially useful when the data is skewed. In this case, the data in Sunny Town is skewed, and therefore the range may not be the best measure of variability. IQR is not affected by the shape of the data and provides a better measure of variability in both symmetric and skewed datasets.
Therefore, the correct answer is: IQR, because Sunny Town is skewed.
Question 2:
To determine which coffee shop typically sells the most amount of coffee per hour, we need to find the measure of center that best represents the data. Both the mean and the median can be used as measures of center, but the appropriate one depends on the distribution of the data. If the data is skewed, the median is more appropriate, and if it is symmetric, the mean is more appropriate.
Comparing the data from the two coffee shops, we find that Coffee Ground has a mean value of about 5 gallons, while Wide Awake has a median value of 4.5 gallons. The mean value for Coffee Ground is higher, but since the data is not given, it is not possible to determine the distribution of the data. Therefore, we should use the median as the measure of center for both coffee shops. In this case, we find that the median for Coffee Ground is 5 gallons, while the median for Wide Awake is 4.5 gallons.
Therefore, the correct answer is: Coffee Ground, with a median value of 5 gallons.
Question 3:
To determine which drive-thru is able to estimate their wait time more consistently, we need to compare the variability of the wait times between the two drive-thrus. We can use either the range or IQR as a measure of variability. The smaller the range or IQR, the more consistent the wait times.
Comparing the box plots for Super Fast Food and Burger Quick, we find that Super Fast Food has a smaller IQR of 4.5 (15.5 - 12), while Burger Quick has an IQR of 14.5 (24 - 9.5). Therefore, Super Fast Food has a more consistent wait time.
Therefore, the correct answer is: Super Fast Food, because it has a smaller IQR.
Question 4:
To determine which bus has the most consistent travel times, we need to compare the variability of the travel times between Bus 47 and Bus 14. We can use either the range or IQR as a measure of variability. The smaller the range or IQR, the more consistent the travel times.
Comparing the line plots for Bus 47 and Bus 14, we find that Bus 14 has a smaller IQR of 6 (18 - 12), while Bus 47 has an IQR of 8 (22 - 14). Therefore, Bus 14 has more consistent travel times.
Therefore, the correct answer is: Bus 14, with an IQR of 6.
Question 5:
To determine which girls' basketball team typically has the tallest players, we need to find the measure of center that best represents the data. Both the mean and the median can be used as measures of center, but the appropriate one depends on the distribution of the data. If the data is skewed, the median is more appropriate, and if it is symmetric, the mean is more appropriate.
Comparing the data from the two girls' basketball teams, we find that the Allstars have a median height of 68 inches, while the Champs have a median height of 67
the local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. there are three appetizers, four soups, three main courses, and three desserts. your diet restricts you to choosing between a dessert and an appetizer. (you cannot have both.) given this restriction, how many three-course meals are possible? choices
The possible combination for three-course meals to be chosen from given the restriction is equal to 16.
The restriction that can only choose either a dessert or an appetizer,
Have two choices for the first course.
For the second course,
Have 4 choices for the soup.
For the third course,
Have 3 choices for the main course,
And since can only choose one of the remaining two categories (dessert or appetizer),
Have 2 choices for the third course.
Using the multiplication principle of counting,
The total combinations of number of three-course meals possible under these conditions by multiplying the number of choices for each course,
= Number of choices for the first course × Number of choices for the second course × Number of choices for the third course
= 2 × 4 × 2
= 16
Therefore, there are 16 possible combination for three-course meals that can be chosen.
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