Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average rate of change.
Answers
The average rate of change is 4.
What is function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The rate of change in interval [0, 2]
r=[h(2)-h(0)]/2
h(2)=(2)²+2(2)-6
h(2)=4+4-6
h(2)=2
h(0)=(0)²+2(0)-6
h(0)=0+0-6
h(0)=-6
So, r=[h(2)-h(0)]/2
r=[2-(-6)]/2
r=(8)/2
r=4
Learn more about this concept here:
https://brainly.com/question/9645290
#SPJ1
![Find The Average Rate Of Change Of Each Function Over The Interval [0, 2]. Match Each Representation](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/Mk2pIgBmUxKvUt972vzMARCGHawWetHq.png)
Related Questions
Convert 203 yards into meters.
Hint: 1 yard=0.91 meters
203 yards=[blank]−−−−−− meters
Enter your answer as a number that correctly fills in the blank.
Round the answer to two decimal places, like this: 45.53
Answers
Answer:
184.73
Step-by-step explanation:
1 yard = 0.91m
203 yard=?
(203x0.91)/1=184.73.
+1(415) 450-6164
A financial planner has three portfolios: A, B, and C. Because investors have different tolerances for risks, 35% of people are likely to invest in portfolio A, 25% are likely to invest in B, and 40% are likely to invest in C. Each portfolio has both stocks and bonds, and investors are equally likely to choose either.
This is a tree diagram that represents the probability of investors choosing the different financial products.
What is the probability of an investor choosing both stocks AND bonds from portfolio B?
Answers
The probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
A financial planner has three portfolios: A, B, and C.
Each portfolio has stocks and Bond
P(stock) = 0.5
P(bond) = 0.5
Customers are equally likely to choose stocks.
P(stock and bond from B) = P(stock, B) + P(bond, B)
= 0.25×0.5 + 0.25×0.5
= 0.25 or
= 25%
Thus, the probability of an investor choosing both stocks AND bonds from portfolio B is 0.25 or 25%.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ1
What are the solution(s) to the quadratic equation 9x² = 4?
0 x =
and x =
0 x =
I
69
4
and x = -
2
0 x = ² and x = -²
2
Ono real solution
Answers
Answer:
x= 2/3, -2/3
Step-by-step explanation:
9x² = 4
To solve this quadratic, divide each side by 9
x^2 = 4/9
Take the square root of each side
sqrt(x^2) = sqrt(4/9)
x = ±2/3
Answer:
x = ± [tex]\frac{2}{3}[/tex]
Step-by-step explanation:
9x² = 4 ( divide both sides by 9 )
x² = [tex]\frac{4}{9}[/tex] ( take square root of both sides )
x = ± [tex]\sqrt{\frac{4}{9} }[/tex] = ± [tex]\frac{\sqrt{4} }{\sqrt{9} }[/tex] = ± [tex]\frac{2}{3}[/tex]
x = - [tex]\frac{2}{3}[/tex] , x = [tex]\frac{2}{3}[/tex]
Which equation would have real zero(s) corresponding to the x-intercept(s) of the graph below?
Answers
Answer:
the first one listed (y = -[tex]2^{x}[/tex] + 4)
Step-by-step explanation:
a 0 at an x-intercept means that when plugging in that number, you get a 0 as a y-value.
So, the easiest method to use is to plug x=2 into each equation listed, because we can see that (2,0) is a point on this graph
if y= -[tex]2^x\\[/tex] + 4
y = -2² + 4
y = -4 + 4
y = 0
This means that this graph has corresponding real zero(s) to the function y= [tex]-2^x[/tex] + 4
(I chose which graph to test by looking to see which option seemed right)
Sam pays #512 .75k less than the amount rob pays for his meal .ridwan pays three times the amount rob pays for his meal. if the total amount paid by them is #47,645.25k. How much does same paid for his meal
Answers
The amount paid by sam will be 11526.75k for the meal.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
Sam pays 512 .75k less than the amount rob pays for his meal .ridwan pays three times the amount rob pays for his meal. if the total amount paid by them is 47,645.25k.
We will form an expression from the data given above in the question.
Amount paid by Sam = ( r - 512.75 )
Amount paid by rob = r
( r - 512.75 ) + 3r = 47645.25
( r + 3r ) = 47645.25 + 512.75
4r = 48158
r = 12039.5
The amount paid by sam will be calculated as:-
S = r - 512.75
S = 12039.5 - 512.75
S = 11526.75
Therefore the amount paid by sam will be 11526.75k for the meal.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ1
What are the features of the quadratic function f(x)=(x-3)(x+7)?
Answers
Answer:
It's vertex (-2,-25)x-intercept x₁=-7,x₂=3y-intercept f(0)=-21domain,xER or x is an element of real numberit's neither even nor odd functionIn a stadium, 1,000 tickets were sold. Children’s tickets cost $2.50 each and adults’ tickets cost $5.00 each. The revenue collected for the game was $4,000. How many children’s tickets were sold? How many adults’ tickets were sold?
Answers
Answer:
400 children tickets and 600 adult tickets.
Step-by-step explanation:
children tickets in total cost=400x2.50
=1000
adult tickets in total cost=600x5.00
=3000
total cost is 4000
A container is an open cylinder whose height and radius are of equal length. The total surface area of the container is 300 cm³. Find the radius of the container.
Answers
Answer:
The radius of the container is approximately 4.89 cm
Step-by-step explanation:
GivenA container with:
r = hS = 300 cm²To findThe radius of the containerSolutionUse the equation for total surface area of cylinder:
S = 2πr² + 2πrh or S = 2πr(r + h)Since we have r = h and the value of S is known, let's solve this equation:
2πr(r + h) = 3002πr(r + r) = 3002πr(2r) = 3004πr² = 300πr² = 753.14r² = 75r² = 75/3.14r² = 23.89 (rounded)r = √23.89r = 4.89 cm (rounded)53 points!!! find x. do not round your answer. 5cm 6cm 12cm x
Answers
Answer:
16.6
Step-by-step explanation:
By the property of intersecting secants.5(5+x) = 6(6+12)-> 25 + 5x = 6*18-> 5x = 108 - 25-> 5x = 83-> x = 83/5-> x = 16.6find the value of x
Answers
Answer:
1 = 120
2 = 120
Step-by-step explanation:
75 POINTS PLEASE RESPOND ASAP
Have you ever been swimming in a pool, and your eyes were red when you get out? This means the chemicals in the pool were not adjusted correctly! More specifically, the measurement of the pool's pH was not quite right.
pH is a measurement of hydronium ions and can be modeled by the function f(x) = −log10x. The variable x represents the amount of hydronium ions, and f(x) gives the pH level.
Different liquids have ideal pH values that are different. Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, and a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
Use your graph to find the ideal pH level if the amount of hydronium ions is raised to 0.50.
The pool company developed new chemicals that transform the pH scale. Using the pH function f(x) = −log10x as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Be sure to label each transformation on the graph.
f(x) + 1
f(x + 1)
Answers
ANSWER :
The pH level of a swimming pool indicates the level of acidity or alkalinity
of the swimming pool.
Correct Responses;
First Part: Please find attached the required graph of the pH function created with MS Excel.
The pH value is 0 when x = 1
The pH value is 1 when x = 0.1
The pH level if the hydronium ions is raised to 0.50 is approximately 0.301029996.
Second Part: The transformation that results in a y-intercept is f(x + 1), because f(0 + 1) exists and is equal to 0.
STEPS
Method by which the above responses are obtained
First part
The given pH function is f(x) = -㏒₁₀x
Where;
x = The amount of hydronium ions
A substance with a pH < 7 is acidic
A substance with a pH > 7 is alkaline
A neutral solution has pH = 7
Water is a neutral solution
The graph of the pH function created with MS Excel is attached
The table of values of the graph is as follows;
From the graph, we have;
When the pH value is 0, the hydronium ion concentration is 1
The pH value is 1 when x = 1 × 10⁻¹ = 0.1
The pH level if the hydronium ions, x = 0.5 is given from the graph as follows;
pH = f(0.5) = -㏒₁₀(0.5) ≈ 0.301029996
The pH value when the hydronium ions is 0.5 is pH ≈ 0.301029996
Second Part
Using f(x) = -㏒₁₀x as the parent function, the graph of f(x) + 1, and f(x + 1) are plotted
From the graph, we have;
The graph of f(x) + 1 = -㏒₁₀x + 1
The graph of f(x + 1) = The graph of -㏒₁₀(x + 1)
At the y-intercept, x = 0, therefore;
f(x) + 1 = f(0) + 1 = -㏒₁₀0 + 1 = Undefined
f(x + 1) = f(0 + 1) = -㏒₁₀(0 + 1) = 0
Therefore;
The transformation that results in a y-intercept is f(x + 1) because f(0 + 1) is 0, which is defined.
Learn more about the pH here:
https://brainly.com/question/26145256
there were 3 parts to Ritas race she ran the first part which was 4/9 of the total distance, in 20 minutes she ran the second part which was 2/5 of the remaining distance, in 12 minutes. She finally ran the third part in 15 minutes at the speed of 300 meters per minute.
How long was the first part of the race? What was Ritas speed in that section of the race?
Answers
Answer:
3/5 .................................. 6/9
Step-by-s4tep explanation:
Answer:
300 meters per minute
Step-by-step explanation:
Step 1
Determine the fraction of the total distance for each part of the race.
Given:
1st part of race = 4/9 of total distance2nd part of race = 2/5 of remaining distance[tex]\begin{aligned} \implies \sf 2nd\:part & = \sf \dfrac{2}{5}\:of\:remaining\:distance\\ & = \sf \dfrac{2}{5} \times\left(1-\dfrac{4}{9}\right)\\& = \sf \dfrac{2}{9}\:of\:total\:distance\end{aligned}[/tex]
[tex]\begin{aligned}\implies \sf 3rd\:part & = \sf 1-1st\:part-2nd\:part\\& = \sf 1-\dfrac{4}{9}-\dfrac{2}{9}\\& = \sf \dfrac{1}{3}\:of\:total\:distance\end{aligned}[/tex]
Step 2
Determine the distance of the third part of the race.
Given:
time = 15 minutesspeed = 300 meters per minute[tex]\begin{aligned}\sf Distance & = \sf speed \times time\\& = \sf 300 \times 15\\& = \sf 4500 \:\:meters\end{aligned}[/tex]
Step 3
If the third part of the race (which is 1/3 of the total distance) is 4500m, then the distance of the whole race is:
[tex]\begin{aligned} \sf Total\:distance & = \sf 4500 \times 3\\& = \sf 13500\:meters \end{aligned}[/tex]
Step 4
Determine the distance of the 1st part of the race:
[tex]\begin{aligned}\sf Distance\:of\:1st\:part\:of\:race & = \sf \dfrac{4}{9} \:of\:total\:distance\\& = \sf \dfrac{4}{9} \times 13500\\& = \sf 6000\:meters \end{aligned}[/tex]
Step 5
Determine the speed of the 1st part of the race:
Given:
time = 20 minutesdistance = 6000 m[tex]\begin{aligned}\sf Speed\:of\:1st\:part\:of\:race & = \sf \dfrac{distance}{time}\\& = \sf \dfrac{6000}{20}\\ & = \sf 300\:meters\:per\:minute\end{aligned}[/tex]
What is the domain of f(x) = 5x – 7?
{x | x > –7}
{x | x < –7}
{x | x > 0}
{x | x is a real number}
Answers
Answer: Choice D) x is a real number
Reason:
We can replace x with any number we want without any restriction. There's no issues dealing with division by zero errors for instance, and we also don't have negatives under square roots to worry about. The domain of any linear function is always "the set of all real numbers".
Extra info: The domain in interval notation is [tex](-\infty, \infty)[/tex] which could be thought of as [tex]-\infty < x < \infty[/tex], i.e. x is between negative infinity and positive infinity.
Answer:
d
Step-by-step explanation:
Work out the angle of elevation from the
rabbit to the top of the tree.
18 m
9√3m
Not drawn accurately
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:Angle \:\: of \:\: elevation= 30° [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Let the angle of elevation be " x "
[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{9 \sqrt{3} }{18} [/tex]
[tex]\qquad \tt \rightarrow \: \cos(x) = \dfrac{ \sqrt{3} }{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = \cos {}^{ - 1} \bigg( \cfrac{ \sqrt{3} }{2} \bigg ) [/tex]
[tex]\qquad \tt \rightarrow \: x = 30 \degree \: \: or \: \: \cfrac{ \pi}{6} \: \: rad[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
The angle is 60 degree.
Step-by-step explanation:
First of all, we will find the height if the tree by using Pythagorean theorm.
Let, height of tree be x.
18^2=(9(3^1/2))^2+x^2
324=243+x^2
x^2=324-243
x^2=81
x=9
Now, let the angle be y.
tan y= x/base
tan y=9/9×(3^1/2)
tan y=1.73
y=cot 1.73
y= 60
Determine the measure of angle BFE 1 ) 69 degrees 2 ) 112 degrees 3 ) 11 degrees 4 ) 224 degrees
Answers
Answer:
option 2
Step-by-step explanation:
the chord- chord angle BFE is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, that is
∠ BFE = [tex]\frac{1}{2}[/tex] ( BE + DC) = [tex]\frac{1}{2}[/tex] (72 + 152)° = [tex]\frac{1}{2}[/tex] × 224° = 112°
which equation matches this graph?
Answers
The first function represents the graph of a function provided in the picture option first is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a graph of a function shown in the picture.
[tex]\rm f\left(x\right)\ =\ -\sqrt{\left(x-3\right)}\ +\ 2[/tex]
x - 3 ≥ 0
x ≥ 3
Plug x = 3
f(x) = 2
Thus, the first function represents the graph of a function provided in the picture option first is correct.
Learn more about the function here:
brainly.com/question/5245372
#SPJ1
which expression is equivalent to 354x + 332, If x=0?
Answers
Answer:
10x + 332
when, x=0
Step-by-step explanation:
Please give me brainlist.
The average daily high temperature in [tex] ^{\circ}C[/tex] in Karachi, Pakistan, on the [tex]t^{\text{th}}[/tex] day of the year is approximately
[tex]\qquad T(t) = 29 - 5\cos\left(\dfrac{2\pi (t- 12)}{365}\right)[/tex]
What are the highest and lowest average daily highs in Karachi? Give exact answers.
[tex]\rule{250pt}{2pt}[/tex]
Please explain it "thoroughly" in 'sentences' and with mathematical expression how exactly you'd figure out the answer. I know the answer. I need an elaborate explanation of the method. It's an imperative part of the question to explain your answer otherwise your answer would be considered incomplete
Giving 25 points, thanks (both in your answer and profile)!5 stars and of course brainliest!!!
Answers
Given expression
[tex]\\ \rm\Rrightarrow T(t)=29-5cos\left(\cfrac{2\pi (t-12)}{365}\right)[/tex]
Now
We know according to property of cosine function
It has range of [-1,1] for all intervals .This property is enough for our calculations
Let's check
As t represents no of days hence it can't be negative
t must be a whole number set memberSo
for positive interval
We shall use the cosine interval [0,π]We know that
cosπ is -1cos0=1Hence it's enough for our range [-1,1]
Now
In the expression
29 is the vertical shiftLet
[tex]\sf cos\left(\cfrac{2\pi(t-12)}{365}\right)=n[/tex]
Substitute n for lowest and highest value of range
When n=-1
[tex]\\ \rm\Rrightarrow T(\pi)=29-5(-1)=29+5=34°C[/tex]
When n=1
[tex]\\ \rm\Rrightarrow T(0)=29-5(1)=29-5=24°C[/tex]
Highest average daily high=34°Clowest average daily high=24°CAnswer:
Highest temperature: 34°C
Lowest temperature: 24°C
Explanation:
In a Normal Trigonometry Function: y = A + B sin(x) or y = A + B cos(x)
Maximum value: A + |B|
Minimum value: A - |B|
In this trigonometric function, A = 29, B = -5
Hence find minimum/maximum:
Maximum value: A + |B| = 29 + |-5| = 34
Minimum value: A - |B| = 29 - |-5| = 24
Hence, the maximum/highest temperature is 34°C and minimum/lowest temperature is 24°C in Karachi, Pakistan.
Find more at :
https://brainly.com/question/27117441
WILL MARK BRAINLIEST!!! According to the synthetic division below, which of the following statements are true? Check all that apply.
Answers
According to the given synthetic division, the statements that are true are; Options A, C and E
How to carry out Synthetic Division?
In the synthetic calculation we use the coefficient of the dividend
with the factors of the function.
Therefore;
3 , -13 , 4 are the coefficient of the dividend 3x² - 13x + 4
Therefore, the divisor is 4 and as such x = 4 is a root of f(x) = 3x² - 13x + 4
Also, it means that (x - 4) is a factor of the dividend F(x) = 2x² - 2x - 12
- The quotient is the last line of the synthetic division. Thus, the coefficients of quotient are 3, -1.
- The quotient is 1 degree less than the dividend and so the degree of the dividend is 2.
- The degree of the quotient is 1 and so the he quotient is 3x - 1.
Thus, options A, C and E are correct
Read more about Synthetic Division at; https://brainly.com/question/13133440
#SPJ1
There is a bag filled with 6 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
Answers
Answer:
1/11
Step-by-step explanation:
probability =total number of items ÷ 1
=11÷1
=1/11
Lyanna opens a bank account with a deposit of $200. She earns 3%
interest per year. How much money will Lyanna have in her account after
the first year?
Answers
Answer:
$206
Step-by-step explanation:
Lyanna will earn 3% on her capital within 1 year.
In total, she will have 103%.
$200 x 103% = $206
In the diagram below, triangle lmn is congruent to cba. What is the length of segment ln?
Answers
Answer:
this is step by step explenation
see more...
Which values of a and b make the following equation true?
(5x7y²)(-4x²y5)--20xy
a=11, b = 7
a = 11, b = 10
a=28, b = 7
a=28, b= 10
Answers
Answer:
A. is correct answer
Step-by-step explanation:
full explanation
√4x-3-1=√x+1
What is the value of x
Answers
Kit and Kat are building a kite for the big kite festival. Kit has already
cut his sticks for the diagonals. He wants to position P so that he will
have maximum kite area. He asks Kat for advice. What should Kat
tell him?
Answers
Kat should tell Kim that It's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
How to calculate the area of a kite?In Mathematics, the area of a kite is equal to one-half the product of the length of its diagonals. Mathematically, the area of a kite can be calculated by using this formula:
A = ½ × d₁ × d₂
Where:
A is the area of a kite.d₁ and d₂ are the length of the diagonals of a kite.Since Kit has already cut his sticks for the diagonals, Kat should tell him that it's too late to change the area of this kite because the length of the diagonals of a kite determines its area.
Read more on area of a kite here: https://brainly.com/question/9593985
#SPJ1
how much is 20 Pepsi if one Pepsi is sold at the rate of 20 naira
Answers
Answer:
Let x= cost of 20 pepsi
so 1 Pepsi = 20 naira
20 = x
x= 20*20
x= 400 naira
Therefore the cost of 20 pepsi is 400 naira
In your research study measuring the relationship between time spent playing video games and course grades, you find that grades increase at about the same rate as time spent playing video games decreases. What do you conclude
Answers
Research study measuring relationship suggests that video games may have a detrimental effect on an individual's grades.
This study analyzes the correlation between video game usage and academic performance. Scholastic Aptitude Test (SAT) and grade-point average (GPA) scores were used to gauge academic performance. The amount of time a student spends playing video games has a negative correlation with students' GPA and SAT scores. As video game usage increases, GPA and SAT scores decrease.
A chi-squared analysis found a p value for video game usage and GPA was greater than a 95% confidence level (0.005 < p < 0.01). This finding suggests that dependence exists. SAT score and video game usage also returned a p value that was significant (0.01 < p < 0.05). Chi-squared results were not significant when comparing time spent studying and an individual's SAT score. This research suggests that video games may have a detrimental effect on an individual's GPA and possibly on SAT scores. Although these results show statistical dependence, proving cause and effect remains difficult, since SAT scores represent a single test on a given day. The effects of video games maybe be cumulative; however, drawing a conclusion is difficult because SAT scores represent a measure of general knowledge. GPA versus video games is more reliable because both involve a continuous measurement of engaged activity and performance. The connection remains difficult because of the complex nature of student life and academic performance. Also, video game usage may simply be a function of specific personality types and characteristics.
Learn more about research study measuring here:
https://brainly.com/question/15326922
#SPJ10
Find the surface area for the rectangular prism below.
Please answer with steps! :)
Answers
1. Identify your variables using let statements.
2. Determine the equations for the linear system.
3. Determine the solution to the linear system (point of intersection)
4. Explain the meaning of the solution using a therefore statement.
Chris is mixing 2 different types of fruit juice together for a summer drink. The two types of juices he is using is one that is 30% strawberry concentrate and the other is 55% lemon concentrate. If he wants 2 L that is 40% concentrate of the fruit juices, how much of each should be used to create the drink?
Answers
The meaning of the solution is; Therefore, 1.2 liters of the strawberry concentrate and 0.8 liters of the lemon concentrate.
What is the solution to the system of equations?It follows from the task content that the variables are;
let x be the amount of 30% strawberry concentrate.
let y be the amount of 55% lemon concentrate.
The equations of the linear system according to the task content are as follows;
x + y = 20.30x + 0.55y = (2 ×0.4)From the first equation; x = 2-y;
Hence, upon substitution; we have;
0.30(2-y) + 0.55y = 0.8
0.25y = 0.2.
y = 0.2/0.25 = 0.8L.
Hence, x = 2- 0.8 = 1.2L.
Read more on simultaneous equation;
https://brainly.com/question/148035
#SPJ1
question 10 please
need help
Answers
Answer:
Denes Dynamos =
2012 attendance = 34500
2013 attendance = 30705
change = 30705 - 34500= -3795
change percentage = -3795 * 100 / 34500 = -11%
Edgefield Eagles =
2012 = 24100
2013 = 21208
change = -2892
change Percentage = -2892 * 100 / 24100 = -12%
