Use the graph below to answer the question that follows:
What is the average rate of change between the interval of x = 0 and x = pi/2?
A) 2/pi
B) pi/2
C) pi/4
D) 4/pi
Answers
Answer:
the correct answer is option D.
Step-by-step explanation:
average rate of change in the graph in interval x = 0 and x = pi/2
when we look into the graph between interval x = 0 and x = pi/2
we can see that on y - axis
at x = 0 value of y = 3 and
at x = π/2 value of y = 5
rate of change = [tex]\frac{change\ in y-axis}{change\ in\ x-axis}[/tex]
= [tex]\dfrac{y_2-y_1}{x_2- x_1}[/tex]
=[tex]\dfrac{5-3}{\frac{\pi}{4} - 0}[/tex]
= 4/π
hence, the correct answer comes out to be 4/π
hence, the correct answer is option D.
Related Questions
Find the center, vertices, and foci of the ellipse with equation x squared divided by one hundred plus y squared divided by thirty six = 1.
Answers
(x-h)²/a² + (y-k)²/b², where h, k are the coordinates of the center, a & b represent half of the major & minor axis respectively.
The given equation is:
x²/100 + y²/36 = 1.( a =10 and b = 6)
CENTER: Since h and k = 0, then the center of this ellipse is the origin (0,0)
VERTICES: a² = 100, → a = +10 and a = -10, then the right vertex is (10,0) and the left vertex is (-10,0)
FOCI: The distance "c" from the center to the focus is given by the following:
c² = a² - b²
c² = 100 - 36 = 64 and c = +8 and - 8
The coordinate of the right focus F₁(8,0) and F₂(-8,0) for the left focus
A man paid the bank $4,080 at the end of three years. This was the amount borrowed plus 12% interest for three years. How much money had he borrowed?
Answers
(rounded to the nearest tenth)
The equation =+y3115
is solved in several steps below.
For each step, choose the reason that best justifies it.
Answers
Which should come next at the end of this row of letters: a b d g?
Answers
From a to b, we skip 1 letter.
From b to d, we skip 2 letters.
From d to g, we skip 3 letters.
Inductively, we should skip 4 letters to arrive at the next letter, which is k.
Answer: k
Answer:
Next letter will be k.
Step-by-step explanation:
we have to find the letter which will come next at the end of the row of letters
a b d g.
First we will write the alphabets as below to understand the sequence
a b c d e f g h i j k
Between a and b alphabet skipped = 0
Between b and d alphabets skipped = 1 (c)
Between d and g skipped alphabets = 2 (e and f)
Therefore after g number of alphabets skipped will be = 3 (h i j)
Next alphabet will be k.
what are the discontinuities of the function f(x) =x<2-36/4x-24 ?
Answers
Your class has 30 students. if 1313 of them walk to school, how many students in your class walk to school?
Answers
Answer:10
Step-by-step explanation:
Which equation would best help solve the following problem? Rennie kicks a field goal with an initial vertical velocity of 31 m/s. How long will it take the football to hit the ground?
–4.9t2 + 31t = 0
–4.9t2 – 31t = 0
16t2 + 31t = 0
–16t2+ 31t = 0
Answers
v=⌠a
v=gt+vi
h=⌠v
h=gt^2/2+vit+hi
So height as a function of time is:
h(t)=gt^2/2+vit+hi
g=-9.8m/s^2, vi=31m/s, hi=0 so
h(t)=-4.9t^2+31t
And it will hit the ground when h(t)=0 so
-4.9t^2+31t=0
When 0.3(4x – 8) – 0.5(–2.4x + 4) is simplified, what is the resulting expression?
Answers
The resulting expression for x when the algebraic expression is simplified is 2.4x - 4.4
What is the simplification of an algebraic expression?The simplification of algebraic expressions follows an approach where we aim to solve for the unknown variables of the algebraic expression.
From the given algebraic expression, we have:
0.3(4x – 8) – 0.5(–2.4x + 4)
Open brackets1.2x - 2.4 + 1.2x - 2
Collect like terms1.2x + 1.2x = 2.4 + 2
2.4x = 4.4
2.4x - 4.4
Learn more about algebraic expression here:
https://brainly.com/question/2164351
Answer:
simply d
Step-by-step explanation:
The height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. what is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? round your answer to the nearest thousandths place (3 places).the height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. what is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? round your answer to the nearest thousandths place (3 places).
Answers
The probability of an 18-year-old man selected at random being between 67 and 69 inches tall is approximately 0.261.
Here's how we can calculate this:
Standardize the values: Convert the heights of 67 inches and 69 inches to z-scores using the formula:
z = (x - mean) / standard deviation.
In this case, z for 67 inches is -0.33 and z for 69 inches is 0.33.
Calculate the area between the z-scores: Using a standard normal distribution table or calculator, find the area between -0.33 and 0.33. This represents the probability of an 18-year-old man having a height within that range.
Round the answer: The calculated area is approximately 0.261, which is the probability of a randomly selected man being between 67 and 69 inches tall.
Therefore, the probability of an 18-year-old man selected at random being between 67 and 69 inches tall is approximately 0.261.
The probability that an 18-year-old man selected at random is between 67 and 69 inches tall is approximately 0.259.
To find the probability that an 18-year-old man selected at random is between 67 and 69 inches tall, we first need to standardize the values using the z-score formula:
[tex]\( z = \frac{x - \mu}{\sigma} \)[/tex]
where x is the value
[tex]\( \mu \)[/tex] is the mean, and
[tex]\( \sigma \)[/tex] is the standard deviation.
For x = 67 inches: [tex]\( z = \frac{67 - 68}{3} = -0.333 \)[/tex]
For x = 69 inches: [tex]\( z = \frac{69 - 68}{3} = 0.333 \)[/tex]
Using the standard normal distribution table or calculator, we find the corresponding probabilities:
P(z < -0.333) and P(z < 0.333)
P(z < -0.333) = 0.3707 and P(z < 0.333) = 0.6293
To find the probability between 67 and 69 inches, we subtract the smaller probability from the larger:
0.6293 - 0.3707 = 0.2586
The safety inspector notes that Ray also needs to plan for a vertical ladder through the center of the coaster's parabolic shape for access to the coaster to perform safety repairs. Find the vertex and the equation for the axis of symmetry of the parabola, showing your work, so Ray can include it in his coaster plan.
f(x)= 3x^2+9x+12
Answers
f(x) = 3(x^2 + 3x) + 12 = 3(x+1.5)^2 +5.25
So you can see the vertex is at (0,5.25) when x = -1.5
The axis of symmetry then lies in x = -1.5
Answer with explanation:
Equation of the Parabola is
[tex]f(x)= y=3x^2+9x+12\\\\y=3[x^2+3 x+4]\\\\y=3[(x+\frac{3}{2})^2+4-(\frac{3}{2})^2]\\\\y=3[(x+\frac{3}{2})^2+(\frac{\sqrt 7}{2})^2]\\\\y-\frac{21}{4}=3[(x+\frac{3}{2})^2][/tex]
Vertex of the parabola can be obtained by
[tex]x+\frac{3}{2}=0\\\\ x=\frac{-3}{2}\\\\ y-\frac{21}{4}=0\\\\y=\frac{21}{4}\\\\ Vertex(\frac{-3}{2},\frac{21}{4})[/tex]
Axis is that line of parabola which divides the parabola into two equal halves.
[tex]x+\frac{3}{2}=0\\\\x=-\frac{3}{2}[/tex]
Find the value of x. Express your answer in simplest radical form
Answers
h^2=a^2+b^2 (the hypotenuse squared is equal to the sum of the squared sides)
5^2=x^2+x^2
25=2x^2
2x^2=25
x^2=25/2
x=√(25/2)
x=5/√2 now if we rationalize the denominator...
x=(5√2)/(√2√2)
x=(5√2)/2
Write the converse of the statement. If the converse is true, write true; if not true, provide a counterexample.
If x = 4, then x2 = 16
Answers
It's false, because if [tex]x^2=16[/tex], then [tex]x=4 \vee x=-4[/tex]
Solve the following system by any method. 8x + 9y = –5 –8x – 9y = 5 A. (–10, 3) B. (–3, 10) C. (0,0) D. Infinitely many solutions
Answers
Step 1: Solve for x or y in either of the two equations. I will choose to solve for y in the equation 8x + 9y = -5
8x + 9y = -5
- 8x + 8x
-------------------------
9y = 8x - 5
----- ----- -----
9 9 9
y = 8/9x - 5/9
Step 2: Plug in the value you got for x or y into the equation that you have not worked with yet.
8x - 9(8/9x - 5/9) = 5
8x - 8x + 5 = 5
0x + 5 = 5
5 = 5
This turns out to be a true statement, so the answer to your system will be infinitely many solutions.
A mouse spots an owl flying 10.1 feet over a nearby bush. The mouse is 30 feet away from the bush, and it sees the owl at a certain angle of elevation.
Which trigonometric equation can be used to solve for x, the angle of elevation from the mouse to the owl?
Answers
ANSWER PLEASE
In the figure, sin ∠MQP =
a. cos N and sin R
b. sin R and sin N
c. cos N and sin M
d. cos R and sin N
Answers
sin ∠MQP = sin(56) = 0.829
cos ∠N = cos(56) = 0.559
sin ∠R = sin(34) = 0.559
sin ∠N = sin(56) = 0.829
cos ∠N = cos(56) = 0.559
sin ∠M = sin(90) = 1
cos ∠R = cos(34) = 0.828
Based on these findings, it is obvious that sin ∠MQP is equal to cos ∠R and sin ∠N.
Thus, the correct choice is "d".
Question 1(Multiple Choice Worth 5 points) (07.05 HC)
The work of a student to solve the equation 3(2x − 4) = 8 + 2x + 6 is shown below: Step 1: 3(2x − 4) = 8 + 2x + 6 Step 2: 5x − 7 = 14 + 2x Step 3: 5x − 2x = 14 + 7 Step 4: 3x = 21 Step 5: x = 7 In which step did the student first make an error and what is the correct step?
Step 2; 6x − 12 = 14 + 2x
Step 2; 6x − 7 = 2(6 + x + 4)
Step 3; 5x − 2x = 14 − 7
Step 3; 5x + 2x = 14 + 7
Answers
Step 2: 5x − 7 = 14 + 2x wrong. Must be 6x - 12 = 14 + 2x
Eight people enter a race. If there are no ties, in how many ways can the first two places come out
Answers
The number of ways the first two places can come out is 56.
Permutation and CombinationPermutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nP_r = \dfrac{n!}{(n-r)!},\ \ ^nC_r = \dfrac{n!}{(n-r)!\times r!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given to us,Eight people enter a race, n = 8,
There are no ties, r = 2,
As there is an equal chance of everyone being first and second, but also there will be cases where the first and second positions can be exchanged between the same two people. therefore, there is a particular order in which these 8 people can win. Thus, we will use permutation.
Permutation[tex]^8P_2 = \dfrac{8!}{(8-2)!}=\dfrac{8!}{(6)!} = \dfrac{8\times 7\times 6!}{6!} = 8\times 7 = 56[/tex]
Hence, the number of ways the first two places can come out is 56.
Learn more about Permutation and Combination:
https://brainly.com/question/11732255
A boat makes a 120-mile trip downstream in 3 hours but makes the return trip in 4 hours. If b = the rate of the boat in still water and c = the rate of the current, which of the following equations represents the trip downstream?
3(b - c) = 120
3(b + c) = 120
4(b + c) = 120
Answers
also time downstream = 3 hours
time * rate = distance
3 * (b + c) = 120
so its the second choice.
Which table represents the second piece of the function f(x)
Answers
8-2(1)=6
8-2(2)=4
8-2(3)=2
So it is the third table.
Answer:
Third table represents the second piece of the function f(x)
Step-by-step explanation:
The second piece of the function f(x) is [tex]f(x)=8-2x[/tex]
Now, we substitute some values of x and find the corresponding function values and check which table satisfy the points.
For x = 1
[tex]f(1)=8-2(1)\\f(1)=6[/tex]
For x = 2
[tex]f(2)=8-2(2)\\f(2)=4[/tex]
For x = 3
[tex]f(3)=8-2(3)\\f(3)=6[/tex]
Among the given tables, third tables contains these values.
Third table represents the second piece of the function f(x)
Provide the reasons for the proof:
Given: Trapezoid RIAG with RI = RG = GA
m angle I = m angle NAG
Prove: angle T ≈ angle N
Answers
We know that shape RIAN is a parallelogram with RN || IA and RI || NA
RG is a part of the line RN, so RG is also parallel to IA
-----------------------------------------------------------------------------------------------------------------
m∠TRG = m∠I : Corresponding angle on a transversal
Line TI is a transversal to the parallel lines RN and IA.
m∠TRG and m∠I are corresponding to each other
----------------------------------------------------------------------------------------------------------------
m∠TGR = m∠NGA: Opposite angles on a transversal
Line TA is a transversal on line RN and IA
----------------------------------------------------------------------------------------------------------------
ΔTGR = ΔNGA: Opposite angles property in a parallelogram
Opposite angles on a parallelogram are equal
---------------------------------------------------------------------------------------------------------------
∠T = ∠N: Angle sum of triangle
∠T = 180° - (∠R + ∠G)
∠N = 180° - (∠G + ∠N)
A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows: First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3, 0 Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2 Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3 Which is the best measure of center for second period and why?
A) Mean, because there are no outliers that affect the center.
B) Median, because there is 1 outlier that affects the center.
C) Interquartile range, because there is 1 outlier that affects the center.
D) Standard deviation, because there are no outliers that affect the center
Answers
I believe the answer is D.
Answer:
B) Median, because there is one outlier that affects the center
An 800 gallon swimming pool is being drained. After five hours, 500 gallons have been drained. If the rate of drainage continues, how long will it take to drain the pool?
A) 0.125 hours
B) 5 hours
C) 8 hours
D) 9 hours
Answers
how do you solve this system of linear equation by substitution
x-3y=-12
y=2x+9
Answers
If y=2x+9, substitute y into the equation x-3y=-12.
You will get: x-3(2x+9)=-12
Now, distribute: x-6x-27=-12
Add like terms: -5x-27=-12
Add 27 to both sides: -5x=15
Divide both sides by -5: x=-3
Now, substitute this value of x into the equation to find y: y=2(-3)+9
Multiply: y=-6+9
Add: y=3
Here is the solution: (x,y)=(-3,3)
Hope this explanation helped!
If the ratio between the radii of the two spheres is 5:8, what is the ratio of their volumes?
Answers
Answer: The required ratio of the volumes of two spheres is 125 : 512.
Step-by-step explanation: Given that the ratio between the radii of the two spheres is 5 : 8.
We are to find the ratio of the volumes of the two spheres.
Let, 'r' and 'R' represents the radii of the two spheres, so
r : R = 5 : 8.
The volume of a sphere with radius 'r' units is given by the formula:
[tex]V=\dfrac{4}{3}\pi r^3.[/tex]
Let, V and V' be the volumes of the spheres with radius r and R units respectively.
Then, the ratio of the volumes of the two spheres will be
[tex]\dfrac{V}{V'}=\dfrac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}=\dfrac{r^3}{R^3}=\left(\dfrac{r}{R}\right)^3=\left(\dfrac{5}{8}\right)^3=\dfrac{125}{512}\\\\\\\Rightarrow V:V'=125:512.[/tex]
Thus, the required ratio of the volumes of two spheres is 125 : 512.
Answer: 125:512
Step-by-step explanation:
a p e x
The length of the rectangle is 4 times the height. the area of the triangle is 63 cm2. Find the width. Round to the nearest tenth of an inch
Answers
area = l x h
l=4h
area = 4h x h = 4h^2
4h^2 =63
63/4 = 15.75
h^2 = 15.75
sqrt(15.75)=h
h = 3.968cm
rounded to nearest tenth would be 4.0cm
check L=4(4) = 16 x 4 = 64 ( since it was round 64 is pretty close to 63)
A ball is dropped from the top of a 550 ft. building. The function h(t) = - 16t2 + 50 models the height of the ball, h(t) (in feet), at any given time, t (in seconds).
What is the maximum height of the ball?
550 ft
423 ft
Answers
Help!!!!ASAP PLEASE
Answers
If you add 10 in, plus 10 in below it, then the 6 in, and the 8 in, and 3 in and the other 3 in, you should get 40 in.
What are radians, how do I solve for the measurement of radians in the angle of BAC
Answers
So BAC = 45 degrees, which is 45 / 360 * 2pi = pi/4
What are the difference between polynomial long division and arithmetic long division?
Answers
Answer:
The purpose of long division with polynomials is similar to long division with integers; to find whether the divisor is a factor of the dividend and, if not, the remainder after the divisor is factored into the dividend. The primary difference here is that you are now dividing with variables.
In circle Y, what is m?
59°
67°
71°
118°
Answers
[tex] \frac{arc \ SR+arc \ TU}{2}=63 \\ \\ 55+arc \ TU=63*2 \\ \\55+arc \ TU=126\\\\ \ arc \ TU = 126-55=71^o[/tex]
Answer:
[tex]arc\ TU=71\°[/tex]
Step-by-step explanation:
we know that
The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite
In this problem we have that
[tex]63\° =\frac{1}{2}(arc\ SR+arc\ TU)[/tex]
we have
[tex]arc\ SR=55\°[/tex]
substitute and solve for arc TU
[tex]63\° =\frac{1}{2}(55\°+arc\ TU)[/tex]
[tex]126\° =(55\°+arc\ TU)[/tex]
[tex]arc\ TU=126\°-55\°=71\°[/tex]