Answers
The average rate of change of the function for the interval given in first part (a) is equal to -2 and the average rate of change for the second interval (b) is = 5.
What about rate of change?
The rate of change is a mathematical concept that describes the speed at which a quantity is changing over a given period of time. It refers to how quickly or slowly a value is changing with respect to another value or variable. The rate of change can be calculated by finding the difference between two values and dividing that difference by the amount of time it took to achieve that difference.
Define about function:
A function is a relation between two sets of values, where each value in the first set (the domain) is associated with a unique value in the second set (the range). In other words, a function takes an input, performs a specific operation on it, and produces a unique output.
A function can be represented by an equation or a graph, and it can be described using different notations such as f(x) or y = f(x), where x is the input and y is the output.
According to the given information:
As, we know that the rate of change of the given interval is given in the form of (x) = \(\frac{fb) - f (a)}{b-a}\)
So, In first case (A) the value of a = -2 and b = 0
Rate of change is:
\(\frac{f(0) - f(-2)}{0-(-2)} \\\\\frac{-9 - (4-9)}{(0)+2} = -2\)
For the second case (B) the value of a = 2 and b = 3
Rate of change is:
\(\frac{f(3) - f(2)}{3-2} \\\\\frac{(9-9)-(4-9)}{3-2} = 5\)
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Related Questions
Drag each tile to the correct box.
The table shows data on an airline's adherence to scheduled departure times over the weekend at an airport for 300 randomly selected flight
On Time
Total
142
210
56
90
198
300
Domestic Flights
International Flights
um. All rights reserved.
Total
Order the probabilities of the given events from least to greatest.
P(international | on time)
P(delayer domestic)
Delayed
68
34
102
<
P(on time and domestic)
Answers
Answer:
Step-by-step explanation:
P(international | on time)< P(delayed | domestic) <P(on time and domestic)
correct in plato
Use a for loop to calculate (1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3, assigning the result to the variable a2.
Answers
a2 is assigned the sum of \((1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3\) using a for loop variable a2 = 0
for i in range(2, 129, 2):
a2 += 1/i**3 add 1/i^3 to a2 for each iteration
a2 contains the sum of
\((1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3\)
The goal is to calculate
\((1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3\),
and assign the result to the variable a2. To do this, we can use a for loop. First, we need to declare a2 and initialize it to 0. Then, we can use a for loop to iterate over all the numbers from 2 to 128, stepping in increments of 2. For each iteration, we can add the value of\(1/i^3\) to a2. When the loop is finished, the value stored in a2 will be the sum of \((1/2)^3 + (1/4)^3+ (1/6)^3 + ... +(1/128)^3\).
This value can then be used for further calculations or stored for later.
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A grocery store buys organic apples for $0.75 per apple. The grocery store marks up the cost of each apple by 18%. To the nearest cent, how much will one organic apple cost at the grocery store?
Answers
The cost of one organic apple at the grocery store is $0.89.
Cost of one apple = $0.75.Mark up percentage = 18%Therefore, the cost of one organic apple will be calculated thus:
= $0.75 + (18% × $0.75)
= $0.75 + $0.135
= $0.885
= $0.89
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solve the system of linear equations by substitution. x+4y=18 y=-x+9
Answers
Using the substitution method, the solution to the system of linear equations, is: (6, 3).
System of Linear EquationsUsing substitution method, we can make one of the variables the subject of the formula for one of the equations, then find the other variable by substituting.
Given:
x + 4y = 18 --> eqn. 1y = -x+9 --> eqn. 2.Substitute y = -x + 9 into equation 1.
x + 4(-x + 9) = 18
x - 4x + 36 = 18
-3x + 36 = 18
-3x = 18 - 36
-3x = -18
x = 6
Substitute x = 6 into equation 2 to find y
y = -6 + 9
y = 3
Therefore, using the substitution method, the solution to the system of linear equations, is: (6, 3).
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u=(8,-2) and v=(5,-5) what is angle between u and v
Answers
The angle between u and v is approximately 26.6 degrees.
To find the angle between two vectors, u and v, we can use the dot product formula:
u · v = ||u|| ||v|| cosθ
where u · v represents the dot product of u and v, ||u|| and ||v|| represent the magnitudes of u and v respectively, and θ represents the angle between the vectors.
Given that u = (8, -2) and v = (5, -5), we can calculate the dot product as follows:
u · v = (8 * 5) + (-2 * -5) = 40 + 10 = 50
Next, we find the magnitudes of u and v:
||u|| = √(8^2 + (-2)^2) = √(64 + 4) = √68 ≈ 8.246
||v|| = √(5^2 + (-5)^2) = √(25 + 25) = √50 ≈ 7.071
Substituting these values into the dot product formula:
50 = 8.246 * 7.071 * cosθ
Simplifying, we have:
cosθ = 50 / (8.246 * 7.071) ≈ 0.899
Taking the inverse cosine (arccos) of 0.899, we find:
θ ≈ 26.6 degrees
Therefore,To find the angle between two vectors, u and v, we can use the dot product formula:
u · v = ||u|| ||v|| cosθ
where u · v represents the dot product of u and v, ||u|| and ||v|| represent the magnitudes of u and v respectively, and θ represents the angle between the vectors.
Given that u = (8, -2) and v = (5, -5), we can calculate the dot product as follows:
u · v = (8 * 5) + (-2 * -5) = 40 + 10 = 50
Next, we find the magnitudes of u and v:
||u|| = √(8^2 + (-2)^2) = √(64 + 4) = √68 ≈ 8.246
||v|| = √(5^2 + (-5)^2) = √(25 + 25) = √50 ≈ 7.071
Substituting these values into the dot product formula:
50 = 8.246 * 7.071 * cosθ
Simplifying, we have:
cosθ = 50 / (8.246 * 7.071) ≈ 0.899
Taking the inverse cosine (arccos) of 0.899, we find:
θ ≈ 26.6 degrees
Therefore, the angle between u and v is approximately 26.6 degrees.
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The volume, V , of a sphere in terms of its radius, r , is given by V(r)=4/3πr^3 . Express r as a function of V , and find the radius of a sphere with volume of 100 cubic feet.
Round your answer for the radius to two decimal places.
A sphere with volume 100 cubic feet has radius ??
Answers
So the radius of the sphere is approximately 2.88 feet (rounded to two decimal places).
What is volume?Volume is the amount of space occupied by a three-dimensional object as measured in cubic units. It is the measure of the amount of material or substance that a container, object, or shape can hold.
Here,
To express r as a function of V, we can rearrange the equation V = 4/3πr³ to solve for r:
V = 4/3πr³
V / (4/3π) = r³
r = ³√(V / (4/3π))
r = ³√(3V / 4π)
To find the radius of a sphere with volume 100 cubic feet, we can substitute V = 100 into the equation:
r = ³√(3V / 4π)
= ³√(3(100) / (4π))
≈ 2.88 units
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h(x)=-2x-4,find h (-2)
Answers
Answer: -8
Step-by-step explanation:
Plug in -2 in h(x)=2x-4
h(-2)=2(-2)-4
= -4-4
= -8
Of 80 t shirts 10% are white, 30% are blue and the rest are red how many are red ?
Answers
10 % + 30 % = 40 %
100% - 40% = 60%
60% are red
Multiply total shirts by 60%
80 x 0.60 = 48
48 shirts are red
Answer:
48 shirts are red
Step-by-step explanation:
The percents have to add to 100
100 -10 -30 = 60
60% are red
80*60%
80*.6
48
g There are students in a kindergarten class. If each kindergartner can have only one task, in how many ways can the teacher assign out the following tasks: line leader, wipe down the tables, pass out papers, water the plants
Answers
Answer:
1 or as many students as she has
Answer:She can divide the 4 tasks by the amount of students in the class.
Step-by-step explanation:
Help me!
“Average cost of a dozen oranges was $1.72 in October 2020 and $5.59 in October 2021. What is the percent increase in the average cost of a dozen oranges from October 2020 to 2021?”
Answers
Answer:
The percent increase in the average cost of a dozen oranges from October 2020 to October 2021 is approximately 225%.
Step-by-step explanation:
To find the percent increase in the average cost of a dozen oranges from October 2020 to 2021, we need to first calculate the difference in the average cost and then divide it by the original average cost, and finally multiply by 100 to get the percentage increase.
The difference in the average cost of a dozen oranges between October 2020 and October 2021 is:
$5.59 - $1.72 = $3.87
To calculate the percent increase, we need to divide the difference by the original average cost and multiply by 100:
Percent increase = (difference/original average cost) x 100
Percent increase = ($3.87/$1.72) x 100
Percent increase = 224.41%
Therefore, the percent increase in the average cost of a dozen oranges from October 2020 to October 2021 is approximately 224.41%.
Step by step (for more help understanding):
The problem states that the average cost of a dozen oranges was $1.72 in October 2020 and $5.59 in October 2021. We need to find the percent increase in the average cost from October 2020 to October 2021.
Step 1: Find the difference in the average cost
To find the difference in the average cost, we subtract the original average cost from the new average cost.
$5.59 - $1.72 = $3.87
This means that the average cost of a dozen oranges increased by $3.87 from October 2020 to October 2021.
Step 2: Find the ratio of the difference to the original cost
To find the percentage increase, we need to express the difference as a percentage of the original cost. We do this by dividing the difference by the original cost.
$3.87 / $1.72 = 2.25
This means that the new average cost is 2.25 times the original average cost.
Step 3: Convert the ratio to a percentage
To convert the ratio to a percentage, we multiply it by 100.
2.25 x 100 = 225%
Step 4: Round the percentage to one or two decimal places
Finally, we round the percentage to one or two decimal places, depending on the level of accuracy required.
The percent increase in the average cost of a dozen oranges from October 2020 to October 2021 is approximately 225%.
Hope this helps, If not I'm sorry. If you need more help, ask me! :]
What is the mean of 10, 10, 9, 9, 10, 8, 9, 10, 8, 0
Answers
Answer:
83
Step-by-step explanation:
Add them all together and then divide by 10 (which is the number of digits there are)
Answer:9.125
Step-by-step explanation:
what is the value of Y?
Answers
Answer:
y = 3
Step-by-step explanation:
2y + 4 = 10
2y = 6
y = 3
(1 point) Suppose the price of a school lunch at Sunny Elementary School is based on the annual income of a student's family. A student from a family of four whose annual family income is between $ 70000 and $ 75000 will pay $5.00 plus 0.02 % of their family income over $ 70000.
a) Find the price of a school lunch for a child from a family of four whose family income is $ 73500.
$______
b) Find a formula for P(x), the price of a school lunch for a child from a family of four whose annual income is x, where 70000 < x < 75000.
P(x)=____
c) Evaluate P(70000) and select the most appropriate interpretation.
A. It is the price of a school lunch for a child from a family of four whose annual income is 70000.
B. Is it the price of school lunches for a month for a child from a family of four whose annual income is 70000.
C. It is the number of school lunches a child from a family of four whose annual income is 70000 must buy.
Answers
A youngster from a household of four earning $73,500 will therefore spend $5.70 for a school meal.
How to calculate annual income?The term "annual" refers to the typical yearly wage that is distributed over 12 months. The sum of your earnings for the entire year is your yearly income, in contrast. This sum comprises both your wage and other sources of income, such as interest from savings accounts or rent from a property you own. Your yearly take-home pay, minus any deductions, is your annual income. Your yearly income, for instance, would be $45,000 if your base pay were that amount, even though your take-home pay would be less after deductions. Your hourly wage should be multiplied by the number of hours you work each week in order to determine your yearly salary. Then, divide the result by 52.a) The cost of a school lunch for a family making $73,500 can be determined as follows:
Price = $5.00 + 0.02% × ($73,500 - $70,000)
= $5.00 + 0.02% × $3,500
= $5.00 + $0.70
= $5.70
A youngster from a household of four earning $73,500 will therefore spend $5.70 for a school meal.
b) The equation for P(x), which represents the cost of a child's school lunch in a household of four with an annual income of $70,000 x x $75,000, is:
P(x) = $5.00 + 0.02% × (x - $70,000)
c) To evaluate P(70,000), we substitute x = 70,000 in the above formula:
P(70,000) = $5.00 + 0.02% × ($70,000 - $70,000)
= $5.00
As a result, the best interpretation is option A. P(70,000) represents the cost of a child's school meal for a household of four with an annual income of $70,000.
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chad and alison are shopping at a department store
Answers
That’s cool...
Explain:
Is there more to this question?
The system has ___________ solution(s). y = 2x + 6 4y = 8x + 24
Answers
Answer:
Step-by-step explanation:
4(2x + 6) = 8x + 24
8x + 24 = 8x + 24
infinite many solutions
The table shows several points for function f(x).
A 2-column table with 8 rows. Column 1 is labeled x with entries negative 4, negative 2, 0, 2, 4, 6, 8, 10. Column 2 is labeled f (x) with entries 19, 15, 11, negative 6, negative 7, negative 8, negative 10, negative 14.
Which statement correctly identifies a point on the graph of f–1(x)?
A. The point (4, –7) is on the graph of f(x), so the point (7, –4) will be on the graph of f–1(x).
B. The point (–2, 15) is on the graph of f(x), so the point (2, –15) will be on the graph of f–1(x).
C. The point (–4, 19) is on the graph of f(x), so the point (–4, –19) will be on the graph of f–1(x).
D. The point (10, –14) is on the graph of f(x), so the point (–14, 10) will be on the graph of f–1(x).
Answers
Answer:
The answer is D.
Step-by-step explanation:
Just took the test. Got 100%.
Mrs. Buchanan is planning marching routines for the school band. The band has 36 members. Band
members can march in any number of rows as long as each row has the same number of members. The
marching path, however, limits members to 6 per row.
this assignment is worth so much and it’s gonna lock soon so can someone please help?
Answers
Answer:
Down below
Step-by-step explanation:
9 rows - 4 members
6 rows - 6 members
18 rows - 2 members
12 rows - 3 members
36 rows - 1 member
I hope you get it in time!!
help me asap. my exam is tomorrow.
Answers
The total surface area of the doghouse is 1452 ft²
What is surface area?The area occupied by a three-dimensional object by its outer surface is called the surface area.
The dog house has many surfaces including the roofs . The total surface area is the sum of all the area of the surfaces.
area of the roof part = 2( 13×11) + 2( 12× 10)×1/2
= 286 + 720
= 1006 ft²
surface area of the building
= 2( lb + lh + bh) -bh
= 2( 10× 11 + 10×8 + 11×8) - 10×11
= 2( 110+80+88)-110
= 2( 278) -110
= 556 -110
= 446ft²
The total surface area = 1006 + 446
= 1452 ft²
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PLEASE HELP !! ILL GIVE BRAINLIEST !! 100 POINTS
Answers
Answer:
144° and 36°
Step-by-step explanation:
17x-9 and 4x are same side interior angles. This means that they add to 180°.
17x-9+4x=180
21x-9=180
21x=189
x=9
substitute x back into the original angles and you get
17(9)-9=144
and
4(9)=36
Which expression shows the first step in dividing 5x + 3 by x?
o 5x/ + 3/3
o 5x/x + 3/x
o 5x/5 + 3/5x
o 5x/5x + 3/5x
Answers
Answer:
second
Step-by-step explanation:
(5x+3)/x=
5x/x + 3/x=
5+3/x
Which is a solution of x2-x-3/4= 0?
-1/4
1/2
3/2
3/4
Answers
Answer:
3/2
Step-by-step explanation:
Answer:
3/2 because when you multiply it it is equal to ilove you
pls answer all the questions
Answers
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yeaaa free coins
I DONT CARE
Step-by-step explanation:
PLEASE HELP.
3. What is the probability that a randomly selected student from your group is a 9th grader?
4. what is the probability that a randomly selected student from your group prefers comedy.
5. what is the probability that a randomly selected student does not prefer action.
6. what is the probability that a student prefers comedy being in 10th grade.
7. what is the probability that a student prefers comedy being in 12th grade
8. what is the probability that a student does not prefer action being in 9th
----if you can answer please do or you could explain to me how to do them, I would like that thanks for your help will give brainliest.-----
Answers
Answer:
3: 1/4 4:1/2 5: 27/32 6: 1/5 7: 1/6 8: 5/6
Step-by-step explanation:
Matt runs 1500 m in 3 minutes 45 seconds. Find his average speed in m/s. Give your answer as a mixed number.
Answers
6.25
meters per second or
22.5
kilometers per hour
Explanation:
1500
meters in
4
minutes or
240
seconds means
1500
240
=
1500
25
240
4
=
25
4
=
6.25
meters per second (dividing by
60
)
or
6.25
×
3600
=
22500
meters per hour
or
22.5
kilometers per hour.
can someone help me with this?
Answers
Write an expression to represent the product of 6 and the square of a number plus 15. In your expression what is the value of the coefficient? A. 1 B. 6 C. 15 D. 2
Answers
Answer:
B) 6
Step-by-step explanation:
Let the number be x
Product of 6 and square of number plue 15 : (6x²) + 15
Coefficient of x² = 6
4. Two student groups are working on the school yearbook. They printed two batches of pages on a printer in the computer lab. The table below shows the number of pages printed by each group and the time needed to print the pages. Time in Seconds (x) 30 20 Number of Pages (y) 150 130 Write ratios for the two print jobs in the form . Do the data represent a proportional relationship? Explain.
Answers
Answer:
The ratio for the first print job is 150/30 = 5 pages per second.
The ratio for the second print job is 130/20 = 6.5 pages per second.
Since the ratios are different, the data do not represent a proportional relationship. In a proportional relationship, the ratio between two variables remains constant.
Step-by-step explanation:
4. Simplify the algebraic expression: 7x² + 6x - 9x - 6x² + 15.
Answers
Answer:
x² -3x + 15
Step-by-step explanation:
7x² + 6x - 9x - 6x² + 15
x² -3x + 15
Determine the equation of the circle with center (0, -2) containing the point
(√12,-5).
Answers
Answer:
i think its
x^2 + (y + 2)^2 = 21.
Step-by-step explanation:
Question 10 (1 point)
A
33
7 in.
B
C
Answers
The value of AB is,
⇒ AB = 5.9
(rounded to nearest tenth)
We have to given that,
A right triangle ABC is shown.
Now, By trigonometry formula,
we get;
⇒ cos 33° = Base / Hypotenuse
Substitute all the values, we get;
⇒ cos 33° = AB / 7
⇒ 0.84 = AB / 7
⇒ AB = 0.84 × 7
⇒ AB = 5.88
⇒ AB = 5.9
(rounded to nearest tenth)
Thus, We get;
AB = 5.9
(rounded to nearest tenth)
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