Using it's concept, the average rate of change is given as follows for the intervals:
a) -6 millions of dollars per year.
b) -18 millions of dollars per year.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For item a, we have that:
In 2003, the amount is of 372 million sales.In 2004, the amount is of 366 million sales.Hence:
r = (366 - 372)/1 = -6 millions of dollars per year.
For item b, we have that:
In 2003, the amount is of 372 million sales.In 2006, the amount is of 318 million sales.Hence:
r = (318 - 372)/3 = -18 millions of dollars per year.
More can be learned about the average rate of change of a function at https://brainly.com/question/11627203
#SPJ1
A stack of 9 cups measures 194 mm. Another stack of 22 of the same cups measures 272 mm.
1.) Find the height of one cup.
2.) How tall would a stack of n cups measure?
The result for the stack of cups are shown below;
The height of the one cup is found to be 6 mm,The height formed by the stack of n cups is 6n.What is defined as unitary method?The term unitary refers to a single or unique unit. As a result, the goal of this method is to determine values are related to a single unit.
The Unitary Method is the method in which we first find the value of one unit and then calculate the value of the necessary number of units.For example, if a car travels 44 kilometres on two litres of gasoline, we can employ the unitary method to calculate how far it will travel on one litre of gasoline.Now, as per the given question.
Part 1: The height of one cup;
The stack of 9 cups form the height 194 mm.
Similarly, the height of the 22 of the same cups measures 272 mm.
For the calculation of height of one cup;
Difference in the total height = 272 - 194 = 78.
Difference in the number of cups = 22 - 9 = 13.
Thus, the height of one cup = 78/13 = 6
The height of the one cup is found to be 6 mm.
Part 2: The height of n stack of cups;
The height of one cup is estimated as 6 mm.
There are total n number of cups.
Thus, the height of the n cups will be 6×n mm.
To know more about the unitary method, here
https://brainly.com/question/23423168
#SPJ9
p and q are both prime numbers with p < q.
They are each less than 18
Give an example where p + q is odd but not prime.
The value of p is 2 and q is either 7 or 13 and their sum is either 9 or 15.
It is given that the value of p and q is a prime number, and p<q.
But it is also given that the value of both should be less than 18 as well as a prime number.
Therefore the value of both should be 2, 3, 5, 7, 11, 13, and 17.
And it is also given that p<q.
Now we have to find the value of p + q which is odd but not a prime number.
To have a sum as an odd number one number should be even and as it is given that p<q, therefore p=2, and q = 3, 5, 7, 11, 13, 17.
So
p + q = 2 + 5 = 7, which is odd but it is prime
Now again, q = 7
p + q = 2 + 7 = 9 , which is odd as well as not prime.
Again take q = 11
p + q = 2 + 11 = 13, which is odd but prime
Now take q = 13
p + q = 2 + 13 = 15, which is odd as well as not prime.
Now take q = 17
p + q = 2 + 17 = 19, which is odd and prime.
Therefore we have p =2 and q = 7 or 13 and sum p + q =9 or 15 which is odd but not prime.
To know more about the prime number refer to the link given below:
https://brainly.com/question/792663
#SPJ1
of the 35 flavors of ice cream at an ice cream parlor, 25 flavors contain some sort of nuts, 12 are fat-free, and 8 both fat-free and contain nuts. how many of the flavors at the ice cream parlor neither are fat-free nor contain nuts?
The number of ice creams according to the probability, Neither contain nuts nor are fat free is 6.
According to the statement
We have to find that the ice creams that neither are fat-free nor contain nuts.
So, For this purpose, we know that the
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur.
From the given information:
There are 35 flavors of ice cream at an ice cream parlor, 25 flavors contained ice creams.
Contain nuts = 25
Are fat free = 12
Are both = 8
Then
Contain nuts or are fat free = 25+12-8 = 29
Total = 35
Neither contain nuts nor are fat free = 35-29 = 6.
So, The number of ice creams according to the probability, Neither contain nuts nor are fat free is 6.
Learn more about Probability here
https://brainly.com/question/9385303
#SPJ4
The temperature at 3:00 p.m. was 7F. By 9.00 p.m. the temperature had dropped by 12 degrees. What was the temperature at 9.00 p.m.?
Answer: The answer is -5
Step-by-step explanation: According to the question it stated that the temperature was 7 degrees at 3pm and by 9pm it dropped 12 degrees so from my answer it would -5 degrees
researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. the researchers attend political debates and record how frequently each candidate displays positive facial expressions. which research method are the researchers using? a. random sample b. case study c. naturalistic observation d. survey
researchers are interested in finding out if winning congressional candidates display more positive facial expressions than losing candidates. c. naturalistic observation
What is naturalistic observation?A study technique called naturalistic observation includes watching participants in their natural settings. Many psychologists and other social scientists employ this strategy. It is an approach to qualitative research that emphasizes gathering, analyzing, and describing non-numerical data.
When performing lab research would be impractical, expensive, or would adversely influence the subject's behavior, it may be helpful. Naturalistic observation is to capture behavior as it happens in its natural environment without intervention or efforts to change any of the factors. In a lab context, people frequently act differently than they would in the wild. Sometimes, researchers wish to watch their subject's behavior "in the wild".
To know more about naturalistic observation, visit;
https://brainly.com/question/28041973
#SPJ4
Make x the subject of the formula
√a=x−b^2/2c
Answer:
x = [tex]\sqrt{a}[/tex] + [tex]\frac{b^2}{2c}[/tex]
Step-by-step explanation:
[tex]\sqrt{a}[/tex] = x - [tex]\frac{b^2}{2c}[/tex] ( add [tex]\frac{b^2}{2c}[/tex] to both sides )
[tex]\sqrt{a}[/tex] + [tex]\frac{b^2}{2c}[/tex] = x
Solve the inequality 34q−23q<512q−112 and write the solution in interval notation.
Answer: [tex]q=\frac{112}{501}[/tex]
Step-by-step explanation:
1) Add similar elements: 11q < 512q - 112
2) Subtract 512q from both sides: 11q - 512q < 512q - 112 - 512q
3) Simplify: -501q < -112
4) Multiply both sides by -1 to reverse the inequality: (-501q)(-1) > (-112)(-1)
5) Simplify: 501q > 112
6) Divide both sides by 501: [tex]\frac{501q}{501} > \frac{112}{501}[/tex]
7) Simplify: [tex]q=\frac{112}{501}[/tex]
Name the segment in the scaled copy that corresponds to segment AD
Segment PS in the scaled copy corresponds to segment AD in polygon ABCD in polygon PQRS. They are similar in appearance and appear in the same location.
What is a polygon?A polygon is a two-dimensional flat shape with straight, fully closed sides. Straight, not curved, sides are required. Polygons, on the other hand, can have any number of sides.
Polygon is derived from the Greek word "polugonos." It has evolved into the term "polygon" over time. The term "polygon" means "many" and "gon" means "angled." This is due to the fact that a polygon has numerous angles and corners within its shape.
The Greeks may have been the first to recognize polygons, as there are numerous examples of them recognizing polygons such as the pentagram in their ancient art and writings.
Learn more about polygons
https://brainly.com/question/17424269
#SPJ9
WILL CHOOSE THE BRAINLIEST!
The measure of x, that is, the angle OBA is equal to 22.5°.
What is the measure of the missing angle in geometrical system?
Herein we find a geometric system formed by a circle, a diameter and a chord. In the image attached below we present all the possible angles of the geometric system, formed by two isosceles triangles.
According to Euclidean geometry, an isosceles triangle has two sides and two angles of equal length. Then, the sum of the internal angles of the triangle AOB is equal to:
m ∠ AOB + m ∠ OBA + m ∠ OAB = 180°
135° + 2 · m ∠ OBA = 180°
2 · m ∠ OBA = 45°
m ∠ OBA = 22.5°
By taking advantage of the properties of isosceles triangles, the measure of x, that is, the angle OBA is equal to 22.5°.
To learn more on inscribed triangles: https://brainly.com/question/17228959
#SPJ1
is james scored a 40 on a test with a mean of 38 and the standard deviation was for whataburger z-score be
The value of z-score for James is 0.2
Step-by-step explanation:
From the formula of z-score we know that
z-score = individual score - mean / standard deviation
Given
James score = 40
Mean = 38
Standard deviation = 10 (missing in question)
To find
z-score =?
Let's put the values in the formula
z-score = 40-38/ 10
z-score = 0.2
You can learn more about z-score from
https://brainly.com/question/25638875
#SPJ4
Find the surface area of a cylinder with a height of 8 inches and base diameyer of 6 inches i need help badly
The surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches
How to find the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches?The given parameters are
Height, h = 8 inches
Diameter, d = 6 inches
The radius is calculated as
r = d/2
So, we have
r = 6/2
r = 3
The surface area of a cylinder is calculated as
S = 2πr(r + h)
So, we have
S = 2 * 3.14 * 3 * (3 + 8)
Evaluate
S = 207.24
Hence, the surface area of a cylinder with a height of 8 inches and base diameter of 6 inches is 207.24 square inches
Read more about surface area a
https://brainly.com/question/22744289
#SPJ1
Calculate the electric potential energy in a capacitor that stores 1.0 x 10^-10 C
of charge at 100.0 V. Use PE = 1/2QAV.
OA. 1.0 x 10-8 J
OB. 1.0 x 102 J
O C. 5.0 × 10¹ J
OD. 5.0 × 10-9 J
The electric potential energy is 5.0 × 10^(-9) J
How to calculate the electric potential energy?
The formula to calculate the electric potential energy in a capacitor is;
E = 1/2 * C * V²
Where;
E = electric potential energy
C = capacitance = charge
V = voltage applied
We are given;
Voltage applied; V = 100 V
Capacitance (Charge) = 1 × 10⁻¹⁰ C
Plugging in the relevant values gives
E = 1/2 * 1 × 10⁻¹⁰ * 100
E = 1/2 * 1 × 10⁻⁸
E = 0.5 × 0⁻⁸ volts
E = 5.0 × 10^(-9) J
Thus, we conclude that the electric potential energy is 5.0 × 10^(-9) J
Read more about electric potential energy at; https://brainly.com/question/27879133
#SPJ1
a cell phone carrier charges a monthly fee of $20 and also charges customers $0.05 per text message. the function c(t) = 0.05t +20 represents the cost, c, per month based on t text messages in a month. which best describes the domain of the function?
The best description of the domain of the function is t >= 0
How to determine which best describes the domain of the function?The equation of the function is given as
C(t) = 0.05t + 20
The above equation is a linear function, and the variable t represent the number of text messages in a month
The number of text messages in a month cannot be negative
This means that
t >= 0
Hence, the best description of the domain of the function is t >= 0
Read more about domain at
https://brainly.com/question/2264373
#SPJ1
Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?
l ≤ 12
2l + 2w < 30
l > 12
2l + 2w < 30
l ≤ 12
l + w < 30
l > 12
l + w < 30
The system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30
How to determine the system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?The given parameters are
Length = Not more than 12 inches
Perimeter = Less than 30 inches
"Not more than" means less than or equal to
So, we have
l ≤ 12
The perimeter of a rectangle is
P = 2l + 2w
So, we have
2l + 2w = Less than 30 inches
"Less than" is represented with <
So, we have
2l + 2w < 30
Hence, the system of inequalities represents the possible length, l, and the possible width, w, that her frame could have is l ≤ 12 and 2l + 2w < 30
Read more about system of inequalities at
https://brainly.com/question/9290436
#SPJ1
Answer:
a. I ≤ 12
2l + 2w < 30
Step-by-step explanation:
i got it right on edge.
I need help ASAPPPPPPPPP
Answer:
C) 3/8 < 1/2 good luck
Step-by-step explanation:
brainliest please
marilyn is going on a class outing to an amusement park. she has $40 to spend. the admission price is $20. she plans to buy a sandwich for $5. a cup of lemonade costs $3.00. write an inequality to show how many cups of lemonade, c, she can buy.
The inequality for the number of cups of lemonade she can buy is :
0 < c < 5.
Marilyn has $40 to spend in the amusement park.
Admission price = $20
So money left = 40 - 20 = $20
Now she plans to buy a sandwich for $5.
So the money left now will be = 20 - 5 = $15
Price of a cup of lemonade = $3
Marilyn can buy at most $15/3 = 5 cups of lemonade.
She can either choose to not buy a cup of lemonade or can buy at most 5 cups of lemonade.
So the inequality for the number of cups of lemonade she can buy will be
0 < c < 5 , where 'c' denotes the number of cups of lemonade.
Learn more about inequalities at https://brainly.com/question/25275758
#SPJ4
Mrs. Figueroa made a spaghetti dinner for the cheerleaders after practice. She purchased four and three fourths pounds of beef for $3.99 per pound. How much money did she spend on the beef for the spaghetti?
$7.25
$8.87
$9.98
$18.95
Answer:
$18.95
Step-by-step explanation:
Amy and Myra each walked from their houses to the mall. Amy walked one
half a mile and Myra walked two-thirds of a mile. How far did the girls walk all
together?
Answer:
C
Step-by-step explanation:
just do 1/2+2/3
Common denominators
3/6+4/6=7/6=1+1/6
C
At Cheng's Bike Rentals, it costs $46 to rent a bike for 9 hours. How many hours of bike use does a customer get per dollar? Answer each part. If necessary, round your answers to the nearest hundredth.
Answer:
0.20 hours
Step-by-step explanation:
Bike rental is $46 for 9 hours.
We want to find hours per dollar, so divide time by cost:
9 hours / 46 dollars = 0.19565217... hours/dollar
Rounded to nearest hundredth:
0.20 hours
Tallie wants to buy a new iPhone. The iPhone costs
$850. She has saved $325 to put down as an initial
payment and will pay another $75 each month until
the phone is paid off. How many months will it take
for Tallie to pay for her new iPhone?
Answer:
7 months to pay it off.
Step-by-step explanation:
see attached for details.
What is the measure of x?
3/2(8w-6)
can I get the answer in simplest form
Answer: 12w-9
Step-by-step explanation:
please help me answer this with solution
Answer:
Question 1:
[tex]{ \tt{f(x) = {x}^{2} - 10x + 25}}[/tex]
when f(x) is f(10), we substitute for x as 10; x = 10
[tex]{ \tt{f(10) = {10}^{2} - 10(10) + 25 }} \\ { \tt{f(10) = 100 - 100 + 25}} \\ { \boxed{ \tt{ \: f(10) = 25 \: }}}[/tex]
Question 2:
[tex]{ \tt{f(x) = \frac{2 {x}^{3} - 7 }{10} }} \\ [/tex]
when f(x) is f(-1), we substitute for x as -1; x = -1
[tex]{ \tt{f( - 1) = \frac{2 {( - 1)}^{3} - 7 }{10} }} \\ \\ { \tt{f( - 1) = \frac{ - 2 - 7}{10} }} \\ \\ { \boxed{ \tt{ \: f( - 1) = - \frac{9}{10} \: }}}[/tex]
Help with all answers
The value of m∠1 is 158° as the two line x and y are parallel.
Two lines are said to be parallel if they do not meet at any point and the perpendicular distance between them is always the same.
A straight line intersecting both the parallel lines is called a transversal.The alternate interior or exterior angles formed are always equal.The corresponding angles are equal.The co-interior angles are supplementary.In the given figure it is given that x║y and m∠2 = 22°.
Now let us use the above principles to solve the value of the other angles.
m∠2+m∠1 = 180°(linear pair)
or, m∠1= 180°-22°
or, m∠1=158°
m∠2+m∠3 = 180°(co-interior angles are supplementary)
or,m∠3=158°
m∠2=m∠4(Corresponding angles are equal)
or, m∠4=22°
m∠2=m∠5 (vertically opposite angles are equal)
or, m∠5=22°
m∠6=m∠1 (vertically opposite angles are equal)
or, m∠6=158°
m∠2=m∠7(alternate angles are equal)
or, m∠7=22°
m∠3=m∠8 (vertically opposite angles are equal)
or, m∠8=158°
Hence all the above angles are calculated using the properties of parallel lines.
To learn more about parallel lines visit:
https://brainly.com/question/24607467
#SPJ9
What is the slope of the line that passes through the points (10, 8) and (7, 14)?
Write your answer in simplest form.
Answer:
-0.2667
Step-by-step explanation:
m =y2 - y1
x2 - x1
=14 - (10)
-7 - (8)
=14 - 10
-7 - 8
=4
-15
Given: B is midpoint if AC
C is the midpoint if BD
Prove: AB is congruent to CD
Answer:
See proof below
Step-by-step explanation:
If B is the midpoint of AC, then AB = BC
If C is the midpoint of BD then BC = CD
Using the transitive property of equality, if a = b and b = c then a =c
We apply this to the above line segments and get
If AB = BC and BC = CD then AB=CD
For two line segments to be congruent they must have the same length
So AB is congruent to CD
How many boxes of cereal can you buy with $42 if one box costs $5.25? As Equation Review
Answer:
8
Step-by-step explanation:
$ 42 / 5.25 $ / box = x = 8 boxes
what are corresponding angles
the limit of f(x) as xa describes what happens to f(x) when x is near, but not equal to, the value a.
If x is near but not equal to, the value an is that f(a) then the function will not continue.
What is the limit?Limit, a nearness in mathematical notion, is largely used to give values to some functions at locations that were usually not given or defined, in a manner consistent with neighboring values.
In another word, limit is a mathematical concept in which we find out the value of any function at a point by its adjacent very close point.
If a function f(x) is defined near to x = a but not a then there will be no continuity of that function at that point.
To exist a limit at x = a
LHL = RHL
But for continuity
LHL = RHL = f(a)
Hence "If x is near but not equal to, the value an is that f(a) then the function will not continue".
For more about limits,
https://brainly.com/question/12207558
#SPJ4
What is an undefined term?
Answer : Undefined terms are those terms that don’t require a formal definition. The four terms are point line plane and set
Step-by-step explanation: