1.) What is the domain and range of the function in the graph?
2.) What is the average rate of change over the interval [1, 0]?
Answers
Answer:
Domain → (-∞, ∞)
Range → (-2, ∞)
Step-by-step explanation:
1). Domain of a function is defined by the input values (set of x-values) and Range of the function is defined by the output values (set of y-values).
From the graph attached,
Function is defined for all real values of x.
Therefore, domain of the function will be (-∞, ∞).
On y-axis values of the function vary from -2 (excluding 2) to positive infinity.
Therefore, range of the function will be (-2, ∞).
2). Average rate of change of a function in the interval (a, b) is defined by,
Average rate of change = [tex]\frac{f(b)-f(a)}{b-a}[/tex]
By using this expression we can find the average rate of change in the given interval.
Please give the correct interval for which the average rate of change is to be calculated.
Related Questions
Find the slope of the line that passes through (9, 6) and (5, 5).
Answers
Answer:
slope = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
Calculate the slope using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (9, 6) and (x₃, y₃ ) = (5, 5)
m = [tex]\frac{5-6}{5-9}[/tex] = [tex]\frac{-1}{-4}[/tex] = [tex]\frac{1}{4}[/tex]
---------please help asap---- ---------------
Answers
Answer:
Question 1:
SAT average divided by budget per student and
SAT average divided by teachers per student
Question 2:
Yes. According to both definitions, school A has the higher SAT average relative to the resources invested per student.
x/3 + 8 = 23 . Find the value of x
Answers
Answer:
45
Step-by-step explanation:
x/3 + 8 =23
=> x/3 = 23-8
=> x/3 = 15
=> x = 15 x 3
x = 45
Answer:
x=45
Step-by-step explanation:
To find x isolate the variables by using the properties of equality. First, subtract 8 from both sides, [tex]\frac{x}{3} = 15[/tex]. Then multiply both sides by 3, [tex]x=45[/tex]. Finally, to check you can plug 45 back into the equation, [tex]\frac{45}{3} +8=23[/tex]. Next, solve this equation and get 23=23, since this is a true statement 45 is correct.
Someone help me with these math problems please
Please
Answers
Answer:
a = 15
34.8 + b = 54.6
Step-by-step explanation:
First one:
5a - 10b = 45 (b = 3)
5a - 10(3) = 45
5a - 30 = 45
5a = 75
a = 15
Second one
b + a + 3a = 54.6
b + 4a = 54.6 ( a = 8.7)
b + 4(8.7) = 54.6
b + 34.8 = 54.6
34.8 + b = 54.6
Answer:
a=15 26.1 + b =54.6
Step-by-step explanation:
for the second question we first multiply 8.7 by 3 which gives us 26.1 and since there is only one answer with 26.1 it's it.
The difference between $500.02 - $79.3 add explanation if possible
Answers
Answer:
420.72
Step-by-step explanation:
Find the sum of the Arithmetic series
2+5+8+............20th term
Answers
What is the next step for this construction?
Connect points A' to C.
A. Connect points A’C
B. Draw another arc
C. Erase BC
D. Connect points C’ and B’
Answers
Solve for x. Round to the nearest tenth of a degree, if necessary
Answers
Step-by-step explanation:
here's the answer to your question
4a+b+16a^2-b^2 how to factorize this can u plz solve it
Answers
Answer:
(4a+b)(1+4a-b)
Step-by-step explanation:
4a+b+16a²-b²4a+b+(4a)²-(b)²4a+b+(4a+b)(4a-b)(4a+b)(1+4a-b)hope it helps
stay safe healthy and happy.Answer:
(4a + b)( 1 + 4a - b )
Step-by-step explanation:
4a + b + 16a² - b²
Step 1 :- Use a² - b² = ( a - b ) ( a + b ) to factor the expression.
4a + b + ( 4a - b ) ( 4a + b ).
Step 2 :- Factor out 4a + b from the expression.
(4a + b)( 1 + 4a - b )
In a carnival game called Spot the Spot, the player has to drop five disks onto a red circle. The disks must cover it completely for the player to win. The probability that a skilled player can drop one of the disks onto the exact place on the red circle that it must occupy is about 1/3. What is the probability that such a player will be able to drop
Answers
Answer:
See explanation
Step-by-step explanation:
Given
[tex]n=5[/tex] --- disks
[tex]p = \frac{1}{3}[/tex] --- success probability
Required
The question is incomplete, as the required probability is not stated.
However, the question follows binomial distribution and the probability is calculated using:
[tex]P(x) = ^nC_x * p^x * (1 - p)^{n-x}[/tex]
Assume the question requires that we calculate the probability that he's able to drop 2 disks, the probability will be:
[tex]P(x = 2) = ^5C_2 * (\frac{1}{3})^2 * (1 - \frac{1}{3})^{5-2}[/tex]
[tex]P(x = 2) = ^5C_2 * (\frac{1}{3})^2 * (\frac{2}{3})^{3}[/tex]
[tex]P(x = 2) = 10 * \frac{1}{9}* \frac{8}{27}[/tex]
[tex]P(x = 2) = \frac{80}{243}[/tex]
Apply the formula to the complete question
Please help me with this one I seriously suck at math
Answers
Answer:
6×5+8×6+6×7+2×1/2×4×8
= 152 in^2
○●○●○●○●○●○
☆Hope it helps...
use the order of operations -5 + 3(7.2 - 3.2)
Answers
Answer:
-5 + 3(7.2 - 3.2) equals 7.
Step-by-step explanation:
The order of operations states the order in which different mathematical operations should be done first, you can use the mnemonic PEMDAS to remember the order to complete each operation. PEMDAS states that the order must be followed as Parenthesis, Exponents, Multiplication/Division, and Addition/Subtraction. In the expression -5 + 3(7.2 - 3.2), the three mathematical operations being used are subtraction, multiplication, and parenthesis, so based on PEMDAS, the order to complete them is parenthesis, multiplication, and subtraction. -5 + 3(7.2 - 3.2) = -5 + 3(4) = -5 + 12 = 7, so that is your final answer.
[tex]\displaystyle\bf -5+3(7.2-3.2)=7\\\\1)\:7.2-3.2=4\\\\2)\:4\cdot3=12\\\\3)\:12-5=7[/tex]
At the city museum, child admission is 6.30 and adult admission is 9.50. On Saturday, three times as many adult tickets as child tickets were sold for total sales of $1113.60 . How many child tickets were sold that day?
Answers
Answer:
15child tickets
Step-by-step explanation:
$113.60÷4=28.4
28.4×3=85.2
113.60-85.2=100:6.3=15
Can someone help with questions 9-16
Answers
10) 5,814
11) 5,765,760
12) 20
13) 742,560
14) 116,280
15) 110
16) 303,600
A group of 80 frogs was observed. The mean distance of their hops is 69 inches with a standard deviation of 3.5 inches. How many frogs would you expect to jump more than 72.5 inches?
Answers
Hello,
[tex]z=\dfrac{X-69}{3.5} \\\\For\ X=72.5, \\\\z=\dfrac{72.5-69}{3.5} =1\\[/tex]
Using table of a normal reduced law:
p(z≤1)=0.8413
Thus p(z≥1)=1-0.8413=0.1587
There are 80*0.1587=12.696 ≈13 (frogs)
Answer:
12 frogs
Step-by-step explanation:
Hello,
Using table of a normal reduced law:
p(z≤1)=0.8413
Thus p(z≥1)=1-0.8413=0.1587
There are 80*0.1587=12.696 ≈12 (frogs) you don't round up because you cant have .7 percent of a frog.
ps. I copy and pasted caylus's response but corrected their answer because it was correct except the rounding up part.
If each of the n production workers in a factory assembles one instrument every t minutes, how many instruments does the factory assemble in 7.5 hours of production
Answers
Answer:
The number of instruments assembled in 7.5 hours are 450 n/t.
Step-by-step explanation:
The number of instruments assembled in t minutes = n
the number of instruments assembled in 1 minute = n / t
Total time = 7.5 hours = 7.5 x 60 = 450 minutes
So, the number of instruments assembled in 450 minutes are
[tex]\frac{n}{t}\times 450\\\\\frac{450 n}{t}[/tex]
Find the area of the parallelogram
Answers
Answer:
32
Step-by-step explanation:
8x4=32
Answer:need more time to solve-
Step-by-step explanation: A= b x h
Find the value of x if A, B, and C are collinear points and B is between A and C. AB=x,BC=x+2,AC=14
Answers
Answer:
x=6
Step-by-step explanation:
( x) +(x+2)=14
(2x+2)=14
(2x)=12
x=6
What is the first step in solving the quadratic equation -5x^2+8=133?
taking the square root of both sides of the equation
subtracting 8 from both sides of the equation
squaring both sides of the equation
adding 8 to both sides of the equation
Answers
Answer:
Step-by-step explanation:
-5x²+8=133
-5x²=133-8
-5x²=125
x²=-25 ........... dividing 125 by -5
x=√-25..........Taking square root of -25
x=±5
Hope this might help you...
The first step in solving the quadratic equation -5x²+8=133 is subtracting 8 from both sides of the equation.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is -5x²+8=133
Minus five times of x square plus eight equal to one hundred thirty three.
x is the variable in the equation.
We have to solve for x
-5x²+8=133
The first step is to isolate the variable x to do this we have to subtract 8 from both sides
-5x² = 125
Divide both sides by 5
x² = -125/5
x² =-25
Hence, first step in solving the quadratic equation -5x²+8=133 is subtracting 8 from both sides of the equation.
To learn more on Equation:
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There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
7/12
There are 84 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.
Answers
Answer:
49
Step-by-step explanation:
The probability of choosing a red marble is equal to the number of red marbles over the number of total marbles there are.
Therefore, let the number of red marbles be [tex]x[/tex].
We have the following equation:
[tex]\frac{x}{84}=\frac{7}{12}[/tex]
Cross-multiplying, we get:
[tex]12x=7\cdot 84,\\x=\frac{84\cdot 7}{12},\\x=\boxed{49}[/tex]
Therefore, there are 49 red marbles in the bag.
Complete the remainder of the table for the given function rule: y= x/4 + 7
Answers
Let's replace x with -4 and simplify
y = (x/4) + 7
y = (-4/4) + 7
y = -1 + 7
y = 6
This means x = -4 and y = 6 pair up together.
So 6 goes in the box under the -4
----------------------------------------------------------
Repeat those steps for x = 0
y = (x/4) + 7
y = (0/4) + 7
y = 0 + 7
y = 7
So 7 goes in the box under the 0
----------------------------------------------------------
Let's repeat those steps for x = 4
y = (x/4) + 7
y = (4/4) + 7
y = 1 + 7
y = 8
So 8 goes in the box under the 4
----------------------------------------------------------
Lastly, for x = 8, we get
y = (x/4) + 7
y = (8/4) + 7
y = 2 + 7
y = 9
9 goes in the box under the 8
----------------------------------------------------------
The y outputs we got were: 6, 7, 8, 9
Notice how each time y increases by 1, x goes up by 4.
This means slope = rise/run = 1/4
We can think of x/4 as (1/4)x to help see that the slope is 1/4.
A function assigns the values. The value of the y in the given table should be 6, 7, 8, and 9, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The function of the x and y is given y=(x/4)+7, use this function to find the value of y for the given values of x. Thus,
x = -4
y = (-4/4)+7
y = -1+7
y = 6
x = 0
y = (0/4)+7
y = 7
x = 4
y = (4/4)+7
y = 8
x = 8
y=(8/4)+7
y = 9
Hence, the value of the y in the given table should be 6, 7, 8, and 9, respectively.
Learn more about Function:
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Kenneth ran a marathon (26.2) miles) in 5.5 hours. What was Kenneth’s average speed? (Round your answer to the nearest tenth.)
Answers
Answer:
4.8 miles per hour.
Step-by-step explanation:
Average speed=Total distance/Time taken
=26.2miles/5.5hour
=4.8 miles per hour
How do I write 7^2 (4 - 15x) in written form?
Answers
Answer:
square of 7 times 4-15xhope it helps
stay safe healthy and happy...Write an
equivalent expression by distributing the "_" sign outside the parentheses:
-(2h + 9.6k) + 1
Answers
Answer:
On distributing the - sign outside the parenthesis we get,
-2h - 9.6k + 1
If a flexible air-filled container has a volume of 40 cu ft on the surface, what would the volume be at 99 feet in sea water
Answers
Answer:
50 cu ft
Step-by-step explanation:
The volume of flexible air filled container at 99 feet in sea water is 10 cu.ft.
What is Boyle's law?Boyle's Law states that If the temperature is constant, the volume of a gas is inversely proportional to the absolute pressure.
V 1/V2 =P2/P1
V2 = P1 x V1 /P2
Substitute 60 psi for P2, 14.7 psi for P1 and 40cu.ft for V1, we get the volume V2
V2 = 40 x 14.7 / 60
V2 = 9.8 cu.ft
Volume is approximately 10 cu.ft.
Thus, the volume of flexible air filled container at 99 feet in sea water is 10 cu.ft.
Learn more about Boyles law.
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I have another question I need help with. How do I solve for the missing angle?
Answers
Answer:
The angle measures approximately 18.19°.
Step-by-step explanation:
Since we want to find the angle and we are given the side adjacent to the angle and the hypotenuse, we can use the cosine ratio. Recall that:
[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]
The adjacent side is 19 and the hypotenuse is 20. Substitute:
[tex]\displaystyle \cos \theta = \frac{19}{20}[/tex]
We can take the inverse cosine of both sides:
[tex]\displaystyle \theta = \cos^{-1}\frac{19}{20}[/tex]
Use a calculator (make sure you're in Degrees Mode!). Hence:
[tex]\theta \approx 18.19^\circ[/tex]
The angle measures approximately 18.19°.
What is the value if X?
A) 16
B) 30
C) 8
D) 15
A step by step analysis would be greatly appreciated but a simple answer will do as well.
Answers
Answer:
[tex] \large{ \tt{ \bigstar \: {EXPLANATION : }}}[/tex]
Q. What do you mean by circumference ?
Ans : The perimeter of a circle is called its circumference. It is the total length of the curved line of the circle.
Q. What do you mean by chord ?
Ans : The line segment that joins any two points on the circumference of a circle is called the chord of the circle. In the figure , BA and DC are any two chords of the circle.
[ See the attached picture ] Observe the figure , you can see AB = 30 & CD = 15 + 15 = 30 which means chord BA and DC are equal. We know : Equal chords of a circle are equidistant from the centre. Hence, PO = OQ = 16 .[tex] \large{ \boxed{ \boxed{ \tt{✺ \: OUR \: FINAL \: ANSWER : \boxed{16}}}}}[/tex]
Hope I helped! Let me know if you have any queries regarding my answer and also , Notify me if you need any help! ツ
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Elana runs for 28 seconds and finishes at 250 meters .what is her velocity
Answers
Answer:
8.9m/s
Step-by-step explanation:
Time= 28s
Displacement= 250m
Velocity=?
Velocity (v) = displacement (d)/ Time (t)
V= 250/28
V=8.9m/s
OR YOU CAN APPROXIMATE IT
V=8.928
YOU CAN APPROXIMATE IT TO
V=8.93m/s
At a party there are 30 students over the age of 21 and 15 under the age of 21. You select a representative sample of 5to interview about attitude towards alcohol. Explain your method and select ypur sample
Answers
Answer:
Stratified sampling
Step-by-step explanation:
Given
[tex]30 \to 21\ and\ above[/tex]
[tex]15 \to Under\ 21[/tex]
Required
The type of sampling method
From the question, we understand that, the sample are divided into two categories. This means that each person in each person do not have the same probability of being selected.
Such method is a stratified sampling
In parallelogram BCDE if m
C
B
70
50°
E
Answers
Answer:
[tex]x=130[/tex]
Step-by-step explanation:
Opposite angles of a parallelogram are equal
EBC = 50° while, CDE = 50° too
Area of a parallelogram is 360°
Suppose, BCD to be x too, & form an equation:
[tex]50+50+x+x=360[/tex]
[tex]100+2x=360[/tex]
[tex]2x=360-100[/tex]
[tex]2x=260[/tex]
[tex]x=260/2[/tex]
[tex]x=130[/tex]
{CHECK: [tex]130+130+50+50=360^{o}[/tex]}
Answer:
m∠DEB = 130°
Step-by-step explanation:
Key: Only two angles are congruent because of the parallelogram
Since m∠EBC = 50° m∠CDE = 50°
Then we are missing m∠BCD and m∠DEB
50 + 50 + m∠BCD + m∠DEB = 360°
100 + m∠BCD + m∠DEB = 360°
m∠BCD + m∠DEB = 360 - 100
m∠BCD + m∠DEB = 260
m∠BCD + m∠DEB = 260/2
m∠BCD + m∠DEB = 130°
m∠BCD and m∠DEB = 130°
