A music competition on television had five elimination rounds. After each elimination, only half of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition:
x
1
2
3
4
5
f(x)
64
32
16
8
4
Compute the average rate of change of f(x) from x = 3 to x = 5 and describe what it represents
A. −6 contestants per round, and it represents the number of contestants who will reach the final round
B. −28 contestants per round, and it represents the number of contestants who will reach the final round
C. −6 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round
D. −28 contestants per round, and it represents the average rate at which the number of contestants decreased from the third round to the fifth round
Answer:
The correct option is C.
Step-by-step explanation:
The given table represent the number of contestants in each round of the competition.
The average rate of change of f(x) from x = 3 to x = 5.
[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]
[tex]m=\frac{f(5)-f(3)}{5-3}[/tex]
[tex]m=\frac{4-16}{2}[/tex]
[tex]m=\frac{-12}{2}[/tex]
[tex]m=-6[/tex]
The average rate of change of f(x) from x = 3 to x = 5 is -6, it represents the average rate at which the number of contestants decreased from the third round to the fifth round.
Therefore option C is correct.
If u lies on the same line as r and n, what terms describe the relationship the three points must have? (select all that apply.) noncollinear between the points collinear coplanar
Answer:
Collinear, coplanar, and between the points
Step-by-step explanation:
Collinear means that the points are in the same line.
Coplanar means that the points are in the same plane.
Between the points is used when three points are in the same line an you want tro express that one of them is between the others.
So those three relationships can apply for the three points.
noncollinear not apply because it means that the points don't lie in a line.
Solve 3c − 5f = 55 for f. Show your work.
[tex]\(f = \frac{3c - 55}{5}\)[/tex] is the solution for the given expression.
To solve the equation 3c - 5f = 55 for f, you need to isolate the variable f by performing a series of mathematical operations. Let's go step by step:
Start with the equation:
3c - 5f = 55
Add 5f to both sides to move the term involving f to one side of the equation:
3c = 5f + 55
Subtract 55 from both sides to isolate the term with f:
3c - 55 = 5f
Now, divide both sides by 5 to solve for f:
(3c - 55) / 5 = f
f = (3c - 55) / 5
So, [tex]\(f = \frac{3c - 55}{5}\)[/tex] is the solution for (f).
Please i really need help on this one please!!!! :( I need an answer ASAP
Multiply r^2 + 7r + 10 / 3 by 3r - 30 / r^2 - 5r - 50
A. r + 2
B. 7r^2 - 20r - 300 / -5r - 5
C. (r + 5)( r + 2) / (r + 10)
D. 3r + 6 / 2
By factoring and simplifying the given polynomials, we found that the expressions simplify to r + 2. Therefore, the correct answer is option A. This process involves cancelling out common factors from the numerator and the denominator.
Polynomial Multiplication and Simplification
To solve the problem, we need to multiply the given rational expressions and simplify the result. The expressions are:
(r^2 + 7r + 10) / 3 and (3r - 30) / (r^2 - 5r - 50)
First, let's factor the polynomials where possible:
Factor the numerator of the first expression:[tex]r^2 + 7r + 10 = (r + 2)(r + 5)[/tex]Factor the denominator of the second expression: [tex]r^2 - 5r - 50 = (r - 10)(r + 5)[/tex]Now, the problem can be written as:
([tex](r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
Next, we simplify by canceling out the common factors:
[tex]=( (r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]
The (r + 5) terms and the (r - 10) terms can be canceled:
[tex]= (r + 2) / 1[/tex]
So, the simplified answer is r + 2,
The correct option is A. r+2
how do you do number 10?
Calculate population variance from population standard deviation
A swimming pool can be filled by either or both of two pipes of different diameters. it takes the smaller pipe twice the time that the larger pipe takes to fill the pool. if water flows through both pipes it take 213 hours to fill the pool. how long will it take the larger pipe to fill the pool? [hint: let x be the amount of the pool filled by the small pipe in one hour]
Step-by-step explanation:
Let r₁ be the rate of filling of small pipe, r₂ be the rate of filling of large pipe and V be the volume of swimming pool.
[tex]\texttt{Rate of small pipe},r_1=\frac{V}{t_1}\\\\\texttt{Rate of large pipe},r_2=\frac{V}{t_2}=\frac{V}{0.5t_1}=2r_1[/tex]
If both pipes are combined it takes 213 hours, that is
[tex]t=\frac{V}{r_1+r_2}\\\\213=\frac{V}{r_1+2r_1}\\\\V=639r_1[/tex]
Now we need to find how much time it takes to fill the pool by large pipe,
That is
[tex]t_2=\frac{V}{r_2}=\frac{639r_1}{2r_1}=319.5hours[/tex]
By large pipe only it will take 319.5 hours to fill the pool.
What is the smallest integer that is the sum of three different primes, each of which is greater than 10?
cuharra studied Monday and Tuesday for her math test she spent a total of 120 minutes studying. she spend an extra 15 minutes on Tuesday. how long did she study for on Monday and on tuesday
Cuharra studied for 52.5 minutes on Monday and 67.5 minutes on Tuesday.
Explanation:To find out how long Cuharra studied on Monday and Tuesday, we can set up an equation. Let's say C represents the amount of time she studied on Monday. According to the information given, on Tuesday she spent an extra 15 minutes studying, which means she studied for C + 15 minutes. The total time she studied was 120 minutes. So, we can write the equation as C + (C + 15) = 120.
Now, we can solve this equation to find the values of C and C + 15. Combining like terms, we get 2C + 15 = 120. Subtracting 15 from both sides, we get 2C = 105. Divide both sides by 2, and we get C = 52.5.
Therefore, she studied for 52.5 minutes on Monday and 52.5 + 15 = 67.5 minutes on Tuesday.
Final answer:
Cuharra studied for 52.5 minutes on Monday and 67.5 minutes on Tuesday to make a total of 120 minutes of study time over the two days.
Explanation:
The question involves solving for the number of minutes cuharra studied on Monday and Tuesday. Since the total study time for both days is 120 minutes and she studied 15 minutes extra on Tuesday, we can set up two variables to represent the study times on each day. Let x be the number of minutes studied on Monday, then x + 15 will be the number of minutes studied on Tuesday.
To solve for x, we set up the equation x + (x + 15) = 120. Simplifying, we get 2x + 15 = 120. Subtracting 15 from both sides gives us 2x = 105. Dividing both sides by 2, we find that x = 52.5. Therefore, cuharra studied for 52.5 minutes on Monday and 52.5 + 15 = 67.5 minutes on Tuesday.
cosx - 4 = sinx -4
(0,2pi)
Find solutions
Please Help! Will give BRAINLIEST! I don't know how to do this.
Determine the x- and y-intercepts of the graph of y=−1/3x+3 .
Then plot the intercepts to graph the equation.
Answer:
you would graph (0,3) and (9,0)
Step-by-step explanation:
Consider the provided equation.
The x intercepts are the points where y value is zero. Similarly the y intercepts are the points where x values is zero.
In order to find the x intercept substitute y = 0 in the provided equation.
0=-1/3x + 3
-3=-1/3(x)
-9=-x
9=x
Thus, the x intercept is (9,0)
In order to find the y intercept substitute x = 0 in the provided equation.
y=-1/3(0) + 3
y=3
Thus, the y intercept is (0,3)
Now use the x and y intercepts to draw the graph of the equation.
The required graph is shown in figure 1.
Therefore, the x- and y- intercepts is (9,0) and (0,3)
A cyclist rides his bike at a rate of
11
feet per second. What is this rate in miles per hour? How many miles will the cyclist travel in
3
hours? In your computations, use the fact that
1
mile is equal to
5280
feet. Do not round your answers.
the base is 12 the height is 17. and the apothem is 10 inches they are all inches. Triangular pyramid volume
Rachelle can walk 2.5 miles in 40 minutes. At this rate, how far can she walk in 1 hour?
The distance travel Rachelle in 1 hour (60 minutes) will be 3.75 miles.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
Rachelle can walk 2.5 miles in 40 minutes.
Then the speed will be
Speed = 2.5 / 40
Speed = 0.0625 miles per minute
At this rate, distance travel Rachelle in 1 hour (60 minutes) will be
0.0625 = d / 60
d = 3.75 miles
The distance travel Rachelle in 1 hour (60 minutes) will be 3.75 miles.
More about the speed link is given below.
https://brainly.com/question/7359669
#SPJ5
Suppose you have 52 feet of fencing to enclose a rectangular dog pen. The function A = 26x = x2 where x = width, gives you the area of the dog pen in square feet. what width gives you the maximum area? what is the maximum area? round to the nearest tenth if necessary.
maximum area is a square
the side of the square would be 52/4 = 13 feet
area = 13*13 = 169 square feet
Answer:
Width = 13 ft
Maximum Area = 169 ft²
Step-by-step explanation:
Given: A rectangular dog pen whose fencing is 52 feet.
Let length be y and width be x
Fencing = 2(l+b)
52 = 2 (x+y)
x + y = 26
y = 26 - x
Area of rectangular pen = Length x width
= y . x
[tex]A=x(26-x)[/tex]
[tex]A=26x-x^2[/tex]
It is parabolic equation. Maximum/Minimum at vertex.
[tex]x=-\dfrac{b}{2a}[/tex]
where, a=-1, b=26
[tex]x=\dfrac{26}{2}=13[/tex]
Now we put x=13 into A
[tex]A=13(26-13)[/tex]
[tex]A=169[/tex]
Hence, The width is 13 feet and Maximum area is 169 ft²
Tammy takes a job after school to earn money to buy a violin. she knows that the more hours she works, the more money she will make.
a. the number of hours tammy works is a function of the amount of money she makes.
b. the amount of money tammy makes is a function of the number of hours she works.
c. tammy's job is a function of her interest in music.
What is gk can someone solve for gk
Answer:
7
Step-by-step explanation:
12 on the bottom right is 1 up the 11 on the bottom left, so 7 must be the right answer.
Find h(-1), h(0), and h(4) for the given function h(x)=-2x^2-4
You review a lease for a new apartment. The lease requires you pay the first month's rent, last month's rent and a security deposit of one month's rent, at the time of signing. The monthly rent is $500. How much will you need at the time of signing?
Determine if the lines are parallel, perpendicular, or neither x-3y= 15 and y = -3+4
Answer:
Step-by-step explanation:
Liam is setting up folding chairs for a meeting. If he arranges the chairs in 4 rows of the same length, he has 5 chairs left over. If he arranges the chairs in 2 rows of that same length, he has 17 left over. How many chairs does Liam have?
What is the justification for each step in the solution of the equation 3(2x + 7) - 4 = 53 - 3x?
Step 1: 3(2x + 7) - 4 = 53 - 3x
Step 2: 6x + 21 - 4 = 53 - 3x
Step 3: 6x + 17 = 53 - 3x
Step 4: 9x + 17 = 53
Step 5: 9x = 36
Step 6: x = 4
Final answer:
The equation 3(2x + 7) - 4 = 53 - 3x is solved through algebraic processes: distributing, combining like terms, transposing terms, isolating the variable, and dividing to solve for x, resulting in the solution x=4.
Explanation:
The justification for each step in solving the equation 3(2x + 7) - 4 = 53 - 3x involves algebraic manipulation:
Distribute the 3 into the parenthesis: 3(2x) + 3(7) - 4 = 53 - 3x becomes 6x + 21 - 4 = 53 - 3x.Combine like terms on the left side: 6x + 17 = 53 - 3x.Add 3x to both sides to get all x terms on one side: 9x + 17 = 53.Subtract 17 from both sides to isolate the term with x: 9x = 36.Divide both sides by 9 to solve for x: x = 4.Each step is justified by the rules of algebra which allow us to simplify and rearrange equations to isolate the variable. The final step gives us the solution x = 4.
While traveling along a highway a driver slows from 24 m/s to 15 m/s in 12 seconds. What is the automobile’s acceleration? (Remember that a negative value indicates slowing down or deceleration)
We are given that:
vi, initial velocity = 24 m/s
v, final velocity = 15 m/s
t, time = 12 s
The formula for acceleration is:
a = (v – vi) / t
a = (15 – 24) / 12
a = - 0.75 m/s^2 (deceleration)
Angles A and B are complementary. If m/ A= 3x - 8 and m/ B = 5x + 10, whqt is the measure of each angle ? Show your work and explain the steps
1. The measure of angle A is [tex]\(22^\circ\).[/tex]
2. The measure of angle B is[tex]\(68^\circ\).[/tex]
Explanation:To find the measures of angles A and B, we can use the fact that they are complementary, meaning their measures add up to[tex]\(90^\circ\).[/tex]Let's set up an equation using the given information:
[m_A + m_B = 90]
Given that[tex]\(m_A = 3x - 8\)[/tex]and (m_B = 5x + 10), substitute these expressions into the equation:
3x - 8 + 5x + 10 = 9
Combine like terms:
8x + 2 = 90
Subtract 2 from both sides:
8x = 88
Divide by 8:
x = 11
Now that we know the value of (x), we can find the measures of angles A and B:
[tex]\[m_A = 3x - 8 = 3(11) - 8 = 33 - 8 = 25\][/tex]
[tex]\[m_B = 5x + 10 = 5(11) + 10 = 55 + 10 = 65\][/tex]
Therefore, the measure of angle A is \(25^\circ\) and the measure of angle B is [tex]\(65^\circ\).[/tex] To check, we can verify that these angles are indeed complementary:
25 + 65 = 90
So, angles A and B satisfy the condition of being complementary.
What shape has 6 sides?
Question 10 options:
pentagon
hexagon
decagon
octagon
Save
A B) hexagon is the shape with 6 sides.
A hexagon is a polygon with six straight sides and six angles. In geometry, hexagons are commonly used in various designs and structures due to their symmetry and stability.
Regular polygon refers to a polygon with equal sides and equal angles, such as a hexagon. Hexagons have the property of being equilateral and equiangular, making them regular polygons.
Six Electron Groups form an octahedron, which is a polyhedron made up of identical equilateral triangles and has six identical vertices, showcasing the connection between the number six and geometric shapes.
Therefore, option B is correct.
Please help with 3 questions thank you.
1. an angle congruent to a given angle
2. x = 68, y = 75
3. corresponding angles
Write the following linear equation in standard for: 2y = -8x - 18 ??
A.y = -4x - 9
B.8x + 2y = -18
C.2y + 18 = -8x
D.18 + 8x = -2y
find gh if g(5,-1) and h(1,-3). write your answer in simplest radical form.
Which graph represents the solution set of the system of inequalities?
{3y≥x−9
3x+y>−3
the solid line passes through (0,-3) and (0,9)
dotted line passes through (0,-3) and (0,-1)
see attached sketch
Answer:
The image shows the solution for the given inequalities.
Step-by-step explanation:
We are given the following information in the question:
[tex]3y \geq x-9\\3x+y>-3[/tex]
We have to plot the solution for the given inequality.
The image attached shows the solution to the given inequalities.
The red shaded portion is the solution to the first inequality and the blue shaded region is the solution for the second inequality.
The common shaded portion is the solution common to both the inequalities.
The dotted blue line is not a part of the solution for both the inequality.
The local park has 4 bike racks. Each bike rack can hold 15 bikes. There are 16Bikes in the bike rack’s. What expression shows the total number of empty spaces in the bike racks
"The correct expression to show the total number of empty spaces in the bike racks is [tex]\( 4 \times 15 - 16 \).[/tex]
To arrive at this expression, we start by calculating the total capacity of all the bike racks combined. Since there are 4 bike racks and each can hold 15 bikes, the total capacity is [tex]\( 4 \times 15 \).[/tex] This gives us the maximum number of bikes that can be parked in all the racks.
Next, we subtract the number of bikes that are currently parked in the racks from the total capacity. There are 16 bikes parked. Therefore, the expression to find the number of empty spaces is:
[tex]\[ \text{Total capacity} - \text{Number of bikes parked} \][/tex]
Substituting the given numbers into the expression, we get:
[tex]\[ 4 \times 15 - 16 \][/tex]
This expression represents the total number of empty spaces in the bike racks. When evaluated, it will give us the number of spaces available for additional bikes to be parked."