The average rate of change over the interval is 10 and it tells us about the slope
How to determine the average rate of changeThe definition of the function is given as
f(x) = 2.5xsquared + 3
Rewrite the function properly
So, we have the following equation
f(x) = 2.5x² + 3
The interval to calculate the average rate of change is given a
0 ≤ x ≤ 4
This can be represented as
[0, 4]
Further, rewrite as
[a, b] = [0, 4]
Where a = 0 and b = 4
Calculate f(a) and f(b)
So, we have
f(0) = 2.5(0)² + 3 = 3
f(4) = 2.5(4)² + 3 = 43
The average rate of change is then calculated as
Average rate = [f(b) - f(a)]/[b - a]
Substitute the known values in the above equation
So, we have
Average rate = [43 - 3]/[4 - 0]
Evaluate
Average rate = 10
What the average rate tells usThe average rate is the slope of the function
This means that it represents the amount of change in the function with respect to the change in the input variables
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The sum of three times x and 4 is 25. Find x.
Answer: X=7
Equation: 3x+4=25
Subtract 25-4=21
Divide 21 by 3, which equals 7
Therefore, x=7
imagine that a researcher is interested in whether residents in his local area have higher levels of well-being than the national average. what would be an appropriate alternate hypothesis for a one-tailed or directional z-test for this test? group of answer choices
The alternate hypothesis for the directional z-test is:
Local resident's average > National average
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.
One of the ideas put out in the hypothesis test is the alternate hypothesis.
A researcher wants to know if people in his neighborhood have a better well-being than people nationwide.
The appropriate hypothesis for a one-tailed or directional z test for the test will be that the average local residents are higher than the national average.
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Select the correct answer. Which statement correctly compares functions f and g? function f function g An exponential function passes through (minus 1, 5), and (2, minus 1.5) intercepts axis at (1, 0), and (0, 2) Function g is a decreasing exponential function with a y-intercept of 5 and no x-intercept. A. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. B. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. D. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞.
Ans just ad it to your profile
Step-by-step explanation:
insert "c" or "g" in the blank to make it true {1,3,5} ____ {x|x is an odd counting number}
The correct sentence regarding the sets is given as follows:
{1,3,5} C {x|x is an odd counting number}.
Counting numbers and odd numbersThe set of counting numbers is composed by the non-negative numbers that are not decimals, hence they are given as follows:
{0, 1, 2, 3, 4, ...}
The set of odd numbers is composed by the numbers that are not divisible by 2, hence numbers that finish with digits 1, 3, 5, 7 or 9.
A set A is contained into another set B when it is a subset of the set B, that is, all of the elements of A belong to B. The symbol that represents if a set is contained into another is given by letter c.
In the context of this problem, we have that the elements 1, 3 and 5 are:
Odd numbers, as they are not divisible by 2.Counting numbers, as they are non-negative and non-decimal.Hence the set is contained, and the correct sentence is:
{1,3,5} C {x|x is an odd counting number}.
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I need the answers to this assignment it’s one questions but multiple steps
Solution;
[tex]\begin{gathered} D=305-50P \\ \end{gathered}[/tex][tex]\begin{gathered} Solving\text{ for P;} \\ 50P=305-D \\ P=\frac{305}{50}-\frac{D}{50} \\ P=\frac{61}{10}-\frac{D}{50} \end{gathered}[/tex][tex]\begin{gathered} When\text{ D=240 pints;} \\ P=6.1-\frac{240}{50} \\ P=\text{ \$}1.3 \end{gathered}[/tex]||
Finding the dimensions of a rectangle given its perimeter and a...
The length of a rectangle is five times its width.
If the perimeter of the rectangle is 120 in, find its length and width.
length: 111
width: in
X
E
S
Answer:
Width = 10 in
Length = 50 in
Step-by-step explanation:
Define the variables
Let x be the width of the rectangle.If the length is five times its width, then the length of the rectangle is 5x.Given the perimeter is 120 in:
[tex]\begin{aligned}\textsf{Perimeter of a rectangle} & = 2(\sf width + length)\\120 & = 2(x + 5x)\\120 & = 2(6x)\\120 & = 12x\\\dfrac{12x}{12}&=\dfrac{120}{12}\\\implies x&=10\end{aligned}[/tex]
Solution:
Width = 10 inLength = 5 × 10 in = 50 in40 students and 24 staff members how many is on the same team with same number of students and staff
The number on same team with same number of students and staff is 8.
What is a factor?A factor of a number simply means a number that divides another number without having a reminder.
In this case, there are 40 students and 24 staff members. Therefore, to have same team, we have to find the highest common factor for the numbers.
The highest common factor for 24 and 40 will be:
24 = 2, 3, 4, 6, 8, 12 and 24
40 = 2, 4, 5, 8, 10, 20 and 40
The highest factor is 8 which is the correct answer regarding the question.
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PLS HELP ASAP!!!!!!!
Triangle ABC is congruent to triangle XYZ. Side
BC corresponds to what side in triangle XYZ?
Insert brackets to make this answer correct: 9 +32 x 10÷2=90
Answer:
the answer is not 90 its 169
Step-by-step explanation:
(-r²s) (-3rs³) (-s²)
Answer: -3r³s⁶
Step-by-step explanation:
[tex](-r^2s)(-3rs^3)(-s^2)=\\\\(-3)(-r^2)(r)(s)(s^3)(-s^2)=\\\\-3(-r^{2+1})(-s^{1+3+2})=\\\\-3(-r^3)(-s^6)=\\\\-3r^3s^6[/tex]
a square has an area of 169 mm2 what is the side of the length area
The side of the square with area 169 mm² is 13 mm.
The side of the square and it's area are related to each other by the following relation -
Area = side². According to the known fact, all the sides of the square are same..
Keep the value of area in formula to find the value of the length of the side of the square
169 = side²
Side = ✓169
Taking square root of the value of area to find the value of the length of the side of the square
Side = 13 mm
Therefore, the length of the side of the square is 13 mm.
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A shelf storage center has many storage rooms that are 6 feet wide, 10 feet deep, and 12 feet high. What is the volume of the room?
We need to find the volume of a rectangular prism with dimensions 6 ft, 10 ft, and 12 ft:
• The volume of a rectangular prism is given by the product of its dimensions.
Thus, the volume V of the room is given by:
[tex]\begin{gathered} V=6ft\cdot10ft\cdot12ft \\ \\ V=6\cdot10\cdot12(ft\cdot ft\cdot ft) \\ \\ V=720ft^{3} \end{gathered}[/tex]Therefore, that volume is 720 cubic feet.
What is the domain of the function??
Answer:
Domain is permissible values of x.
Set notation: { x | -1 ≤ x < 6, x ∈ R}
Interval notation: [-2,6)
Hope that helps
A group of 23 friends are at the theater but can't agree on which movie to see. some of the group decides to see lightyear which is playing for $4 per ticket and the rest of the group decides to see jurassic park which is playing for $9 per ticket. altogether the group spends $172, how many of them saw lightyear?
The number of people who watched light year are 7.
Let x= number of friends that watches light year
and y= number of friends that watches jurassic park.
Let the equations be
All together total cost => 4x+9y=172 ------> 1
And total number of people=> x + y=23 ------> 2
By multiplying both equations by 1 and 4 respectively we can get,
By Solving above two equations we get, x=7 and y=16
As X represents number of friends that watches light year, the answer is 7
Therefore, number of people that watches light year will be 7.
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Parvatis group brought in pizzas but is buying drinks at the concession stand. How many medium sellers can provide a group by the 20 bucks make a table to show your answer at the concession stand medium sodas cost $1.25.
i think the answer is 16 im not to sure tho sorry
please answer it...... Question:
[tex]if 3 (X - 1) - 5 (x - 4) = 8 find the value of x -5 \times \frac{1}{2} [/tex]
Answer:
.........................
Write as a monomial in standard form.
The monomial in standard form will be written as 5y³x².
A Monomial may be defined as a type of polynomial which contains only one term. For example, 3x², 5x and 6x are called monomials. When written in standard form it is the product of one or more factors which can be a constant coefficient and one factor for each variable in the expression. While writing in standard form the terms having the highest power is written first and then the succeeding powers are written. Here, the expression given is 5x²y³ which is not in standard form. The terms having highest power is y³ so it should be written before the term x² as 5y³x² which will be the required standard form.
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Mary is four years older than Sue. If the sum of their ages is 16, how old are Mary and Sue?
Answer: Mary 10 Sue 6
Step-by-step explanation:
Answer:
Sue is 6 and Mary is 10
Step-by-step explanation:
let Sue's age be x then Mary is x + 4 and the sum of their ages is
x + x + 4 = 16
2x + 4 = 16 ( subtract 4 from both sides )
2x = 12 ( divide both sides by 2 )
x = 6
x + 4 = 6 + 4 = 10
then Mary is 10 and Sue is 6
a) The sum of the three dimensions of a cuboid is 48 cm and the ratio among the lengths of its dimensions is 5: 4:3, Find its area. (grade 6)
Answer:
588 cm
Step-by-step explanation:
What is the 12th term of the geometric sequence if T10 = -6 and r = 3?
The 12th term of the sequence is:
[tex]T_{12} = T_{11}*r = -18*3 = -54[/tex]
How to find the 12th term of the sequence?For a geometric sequence with a common ratio r and a first term T₁, the equation for the n-th term is:
[tex]T_n = T_1*(r)^{n-1} = T_{n-1}*r[/tex]
Such that the second formula (the right one) is called the recursive formula or recursive relation for the sequence.
We know that r = 3, and T₁₀ = -6, then we can use the recursive relation:
T_{11} = T_{10}*r = -6*3 = -18
T_{12} = T_{11}*r = -18*3 = -54
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Name a pair of vertical angles.Vert
The pair of vertically opposite angles are ∠1 and ∠3 and ∠4 and ∠2.
What is vertically opposite angles?Vertical angles are a pair of non-adjacent angles formed by the intersection of two straight lines and are opposite to each other.
Vertically opposite angles share the same vertex point.
In other words, vertically opposite angles are angles that are opposite one another at a specific vertex and are created by two straight intersecting lines
Vertically opposite angles are congruent to each other.
Therefore, the pair of vertical angles are as follows:
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Determine which integer will make the inequality 2(n + 2) < 5(n − 1) true.
S:{10}
S:{3}
S:{2}
S:{0}
Answer:
10
Step-by-step explanation:
if you replace n with 10 you will get
2(10+2)<5(10-1)
2(12)<5(9)
24<45
which is a true statement if you replace n with any other number you will get a incorrect statement and if you replace n with 3 though they are equal it's not a ≤ it's only <
4−32⋅(−0.25)−12÷1/3 help
Answer:
Your answer is 8.
Answer:
Step-by-step explanation:
-24
Directions: Determine whether each equation represents a direct variation. If yes, identify the
constant of variation.
Y - 6 =2(x-3)
Answer:
Yes, this equation represents a direct variation equation
constant of variation = 2
=========================================================
Explanation:
Let's solve for y
y - 6 = 2(x-3)
y - 6 = 2x - 6
y - 6+6 = 2x - 6+6
y + 0 = 2x + 0
y = 2x
The equation is in the form y = kx which fits a direct variation equation. The constant of variation is k = 2.
Tori uses the greatest common factor and the distributive property to rewrite this sum:
24 + 84
What expression does Tori write?
Responses
4(6+21)
, 4 left parentheses 6 plus 21 right parentheses,
12(2+7)
, 12 left parentheses 2 plus 7 right parentheses,
2(24+42)
, 2 left parentheses 24 plus 42 right parentheses,
24(1+4)
, 24 left parentheses 1 plus 4 right parentheses,
Skip to navigation
Answer:
12·(2 + 7)
Step-by-step explanation:
24 + 84
= 12·2 + 12·7
= 12·(2 + 7)
………………………………………………..
Answer:
A coma is placed where there is a pause in a sentence, or a list of things. Therefor the commas will be placed as shown.
I pledge allegiance to the red, white, and blue flag.
My brother slowly picked up the spooky, wooden box with gold, silver, and copper inlay.
Step-by-step explanation:
Hope it helps! =D
7. The volume of a cylinder is represented by the formula V = r² h.
Find each missing height and show your reasoning.
volume (cubic inches) radius (inches) height (inches)
96. 4
31.25. 2.5
V. r
Based on the calculations, each missing height of this cylinder is; 6 and 5 inches.
How to calculate the volume of a cylinder?Mathematically, the volume of a cylinder can be calculated by using this formula:
V = πr²h
Where:
V is the volume of a cylinder. h is the height of a cylinder. r is the radius of a cylinder.
Now h the subject of formula, we have:
h = V/πr²
When V = 96π and r = 4, the volume of this cylinder is;
h = V/πr²
h = 96π/π(4)²
h = 96/16
Height, h = 6.
When V = 31.25π and r = 2.5, then the volume of this cylinder is;
h = V/πr²
h = 31.25π/π(2.5)²
h = 31.25/6.25
Height, h = 5.
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A city advertises that the average number of runners over the past two decades in their annual road race is 800.
The difference between the average number of runners and the greatest number of runners is the same as the difference between the average number of runners and the least number of runners. The greatest number of runners in a race was 920.
What absolute value equation can be written to determine the least number of runners, and what is this value?
Enter your answers in the boxes.
Absolute value equation: |x- ___| = ___
The least number of runners in a race was ___
Step-by-step explanation:
Absolute value equation:
[tex] |x - 120| = 920[/tex]
least no of runners = 800 - ( 920 - 800) = 680
-14a-(-48a) Please help me and show the work
Write y=-2x in standard form. Then graph the function.
The equation y = -2x in the standard form is 2x + y = 0 and the graph of the function is shown below .
In the question ,
it is given that
the equation is y = -2x
The equation in standard form is represented as ax + by = c
to write the equation y = -2x in the standard form
taking all the terms to LHS , we get
2x + y = 0
hence y = -2x in standard form is 2x + y = 0 .
the graph is shown below .
Therefore , The equation y = -2x in the standard form is 2x + y = 0 and the graph of the function is shown below .
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