The function [tex]k(x) = 2x^2[/tex] is which the average rate of change over the interval 1 < x < 5 greater than the average rate of change of g(x).
Given data:
The function is represented as [tex]g(x)=1.8x^2[/tex].
Now, the average rate of change of the function is S.
The value of [tex]S=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}[/tex].
The interval of the function is from 1 < x < 5.
So, for g(x), [tex]S=\frac{f(5)-f(1)}{5-1}[/tex].
The value of S = 10.8
For the function [tex]k(x) = 2x^2[/tex], the rate of change is:
[tex]S=\frac{k(5)-k(1)}{4}[/tex]
[tex]S=\frac{50-2}{4}[/tex]
So, the value of S = 12 and is greater than 10.8
Hence, the function is [tex]k(x) = 2x^2[/tex].
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The complete question is attached below:
For which function is the average rate of change over the interval 1 < x < 5 greater than the average rate of change over the same interval for the function g(x) = 1.8x^2?
A.=f(x) = x^2
B.=g(x) = 1.2x^2
C.=h(x) = 1.5x^2
D.=k(x) = 2x^2
Mary was told that a line goes through the points (1, 3) and (6, -2) and has a slope of 3.
a. Explain why the information Mary was given cannot be correct.
b. If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the
coordinates of another point on the line
c. If the given points are correct for the line, what is the slope? Write an equation for the line
Answer:
a. The slope is incorrect
b. y = 3x, ( 0 , 0 )
c) y = 4 - x
Step-by-step explanation:
Given:-
The slope between two points (1, 3) and (6, -2) is 3.
a. Explain why the information Mary was given cannot be correct.
- The slope between two arbitrary points, ( x1 , y1 ) and (x2 , y2) is given by the following relationship:
slope = ( y2 - y1 ) / ( x2 - x1)
- Use the given points (1, 3) and (6, -2) and determine the slope:
slope = ( -2 - 3 ) / ( 6 - 1 )
slope = ( -5 ) / ( 5 )
slope = -1
- Yes, the given slope is incorrect it should be = -1
b.If the given point (1, 3) and the given slope are correct, what is the equation for the line? Give the coordinates of another point on the line
- We will assume the point (1,3) lies on line with a slope = 3.
- We will use the slope-intercept equation of line:
y = slope*x + c
Where, m : Slope
c : y-intercept
y = 3x + c
Using the given correct point to evaluate the y-intercept (c):
3 = 3*1 + c
c = 0
- The equation of line is,
y = 3x
- The origin (0,0) lies on the line y = 3x.
c. If the given points are correct for the line, what is the slope? Write an equation for the line
- We will assume the points (1, 3) and (6, -2) lies on line with a slope calculated in part (a) to be = -1.
- We will use the slope-intercept equation of line:
y = slope*x + c
Where, m : Slope
c : y-intercept
y = -x + c
Using the given points to evaluate the y-intercept (c):
3 = -1 + c
c = 4
- The equation of line is,
y = -x + 4
Mary's information is incorrect because the slope of the line passing through the points (1, 3) and (6, -2) is -1, not 3. If the slope is actually 3, the line equation is y = 3x and an additional point on the line is (2, 6). If the given points are correct, the line equation is y = -x + 4.
Explanation:To understand these questions, it's important to know how the slope of a line is defined and how to write the equation of a line.
Given two points (x1, y1) and (x2, y2), the slope of the line is calculated as (y2 - y1) / (x2 - x1). For the points given, (1, 3) and (6, -2), the slope would be (-2 - 3) / (6 - 1) = -5/5 = -1. So, the slope of the line passing through these two points is not 3, which contradicts the information given. Therefore, the information Mary was given cannot be correct.
If the point (1, 3) and the slope 3 are correct, the equation of the line is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. Substituting these values we get y - 3 = 3(x - 1). This simplifies to y = 3x. A point on this line can be (2, 6).
If the points (1, 3) and (6, -2) are correct, we've already calculated the slope as -1. To find the equation of the line we use the same formula, y - y1 = m(x - x1). Substituting these values we get y - 3 = -1(x - 1), simplifying to y = -x + 4.
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Selena and Tracey play on a softball team.Selena has 8 hits out of 20 times at bat, andTracey has 6 hits out of 16 times at bat.Based on their past performance, what is theprobability that both girls will get a hit nexttime at bat?[A] 31 40[B] 48 320[C] 1 [D] 14 36
Answer:
The correct option is option [B].
The probability that both girls Selena and Tracey will a next at bat is [tex]\frac{48}{320}[/tex].
Step-by-step explanation:
Independent events:
If A and B are event. The occurrence of one of them does not affect the outcomes of other event. Then A and B are independent events.
P(A and B) =P(A)× P(B)
Dependent events:
If A and B are event. The outcomes of one of them affects the outcomes of other event. Then A and B are called dependent events.
P(A and B) =P(A)× P(B|A)= P(B)×P(A|B)
Given that,
Selena has 8 hits out of 20 times at bat.
The number of hits by Tracey out of 16 is 6 at bat.
A= Selena hits a softball.
B= Tracey hits a softball.
The probability that the Selena his a softball is
=P(A)
[tex]=\frac{8}{20}[/tex]
The probability that the Tracey his a softball is
=P(B)
[tex]=\frac{6}{16}[/tex]
Both event are independent. Sine the events do not affect the outcomes of other event.
The probability that both girls will a next at bat is
=P(A and B)
=P(A)×P(B)
[tex]=\frac{8}{20}\times \frac{6}{16}[/tex]
[tex]=\frac{48}{320}[/tex]
-5-n/9=-8
-3/7=-2/3+x
3x-13=7(x+2)-4(x-7)
1/2x-9=15-5/6x
8(4x-3)=6(-7x-4)
2(a-24)=16-1/3(9a+27)
^^ solve the equations above and explain how you got the answer.
Answer:
ok
1) n=27
2) x=5/21
3) no solution
4) x=18
5) x=0
6) a=11
Step-by-step explanation:
hope this helps you..(:
Sam subtracted 5 from the quotient of a number and 3. Write an algebraic expression to represent the operations that Sam preformed
Answer:
(x/3) - 5.
Step-by-step explanation:
Let the number be x.
The quotient of the number and 3 is x/3.
So the expression is:
(x/3) - 5.
I think of a number multiply by 3,add 4,i get 22
Answer:
6
Step-by-step explanation:
22 - 4 = 18
18 / 3 = 6
Answer:
6
Step-by-step explanation:
22-4=18/3=6
start from what you get that use the inverse to get the the original answer
Consider this data set 1, 2, 5, 7, 9, 11, 12. Match the type of the statistic to the correct value.
upper quartile
lower quartile
TOO 000
minimum
maximum
median
HURRY!!
Answer:
median-7
minimum-1
lower quartile-2
maximum-12
upper quartile-11
Step-by-step explanation:hope this helps
Answer:
The upper quartile is 11.
the lower quartile is 2.
the maximum is 12.
the minimum is 1.
the median is 7.
Step-by-step explanation:
The function y = 8.5(1.1)x models the population in thousands of a town where x is the number of years after 2000. What will be the town's population in 2007? Give the answer to two decimal places.
The population of the town in 2007, according to the exponential growth function y = 8.5(1.1)x, would be approximately 16,630 people.
Explanation:The function given is an exponential growth function, where y = 8.5(1.1)x. Here, the variable y represents the population in thousands and x represents the number of years after 2000. To find the town's population in 2007, we replace x with 7 (since 2007 is 7 years after 2000) and calculate y.
Using the formula, y = 8.5 * (1.1)7. When calculated, we find y to be approximately 16.63. This means that, according to the model, the town's population in 2007 would be approximately 16630 (because the model represents the population in thousands).
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By law, a wheelchair service ramp may be inclined no more than . If the base of a ramp begins 15 feet from the base of a public building, which equation could be used to determine the maximum height, h, of the ramp where it reaches the building's entrance
Answer:
The equation that can be used to determine the maximum height is given as h = 15tan4.76°
Step-by-step explanation:
The question given is lacking an information. Here is the correct question.
"By law, a wheelchair service ramp may be inclined no more than 4.76 degrees. If the base of the ramp begins 15 feet from the base of a public building, which equation could be used to determine the maximum height, h, of the ramp where it reaches the building's entrance"
The whole set up will give us a right angled triangle with the base of the building serving as the adjacent side of the triangle and the height h serving as the opposite side since it is facing the angle 4.76°
The side of the wheelchair service ramp is the hypotenuse.
Given theta = 4.76°
And the base of the building = adjacent = 15feet
We can get the height of the building using the trigonometry identity SOH CAH TOA.
Using TOA
Tan(theta) = opposite/Adjacent
Tan 4.76° = h/15
h = 15tan4.76°
The equation that can be used to determine the maximum height is given as h = 15tan4.76°
If g(x)=x2-2x+11; find g(-2)
Given a sector of a circle has an area of 40.8 square inches and a radius of 8 inches. What is the measure central angle of the circle round to the nearest degree?
Answer: The measure of the central angle of the circle is 73°
Step-by-step explanation: Please see the attachments below
Answer: 287 degree
Step-by-step explanation:
Area of a sector = θ/360 x pi r^2
Where pi = 22/7
Given that the
area = 40.8 square inches
radius = 8 inches
40.8 = θ/360 × 3.143 × 8 × 8
θ = (360 × 40.8)/201.06
θ = 73 degree
The measure of the central angle of the circle = 360 - θ
= 360 - 73
= 287 degree
What problem led to playgrounds becoming more common in America cities
Answer: there were not a lot of safe places kids could play
Step-by-step explanation:
i got it right.
The problem led to playgrounds becoming more common in America cities is: Due to unsafe places.
What is playgrounds?Playgrounds is a safe place that is specifically set aside for children to play.
Playgrounds can tend to contribute to a child social growth when the child plays among is age group or peer group.
Playgrounds is common in America in order to prevent danger and injury because there were not safe places for children to play.
Therefore the problem led to playgrounds becoming more common in America cities is: Due to unsafe places.
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y= 4x - 9 when x = 3
Answer:
3
Step-by-step explanation:
4x3 is 12
12-9 is 3
y = 3
Step-by-step explanation:Plug 3 in for x
y = 4(3) - 9
y = 12-9
y = 3
The scatter plot below represents the distance Robin has traveled in the first 6 hours of a trip. The linear equation representing the line is y=30x + 20.
about how many hours will it take for Robin to travel 320 miles?
Final answer:
To find the number of hours it takes for Robin to travel 320 miles using the equation y = 30x + 20, solve for x, yielding 10 hours.
Explanation:
The question asks about how many hours it will take for Robin to travel 320 miles, given the linear equation representing the distance traveled over time: y = 30x + 20. Here, 'y' represents the distance traveled in miles and 'x' represents the time in hours.
To find the number of hours required to travel 320 miles, we need to solve the equation for x when y is 320.
Let's set up the equation with y as 320:
320 = 30x + 20
To solve for x, subtract 20 from both sides:
300 = 30x
Now, dividing both sides by 30, we get:
x = 300 / 30
x = 10
So it will take Robin 10 hours to travel 320 miles.
Evaluate 6c + e2 when c = 6 and e = 2
[tex]c=6, e=2; so\\6\times6+2\times2=40[/tex]
# 15. Tycho wants to prepare a schedule for his exercise over the next few months. Every
week, he wants to exercise on the same days of the week. He does not want to exercise on
two consecutive days. He wants to exercise three days per week. How many schedules can he
choose from?
(A) 6
(B) 7
(C) 9
(D) 10
(E) 35
There are a total of 9 possible schedules that Tycho can choose from.
Thus, option (C) is correct.
Let consider the days of the week as Monday (M), Tuesday (T), Wednesday (W), Thursday (Th), Friday (F), Saturday (Sa), and Sunday (Su).
To create a schedule for exercise, Tycho needs to choose three days of the week to exercise such that no two exercise days are consecutive.
So, the possibilities are:
1. Tycho chooses Monday, Wednesday, and Friday.
The schedule is MW FSu.
2. Tycho chooses Monday, Wednesday, and Saturday.
The schedule is MW SaSu.
3. Tycho chooses Monday, Thursday, and Saturday.
The schedule is MT F SaSu.
4. Tycho chooses Monday, Thursday, and Sunday.
The schedule is MT SaSu.
5. Tycho chooses Tuesday, Thursday, and Saturday.
The schedule is TThSaSu.
6. Tycho chooses Tuesday, Thursday, and Sunday.
The schedule is TTSaSu.
7. Tycho chooses Tuesday, Friday, and Sunday.
The schedule is TFSaSu.
8. Tycho chooses Wednesday, Friday, and Sunday.
The schedule is W F SaSu.
9. Tycho chooses Wednesday, Thursday, and Saturday.
The schedule is W T FSaSu.
Thus, total of 9 possible schedules that Tycho can choose from.
Thus, option (C) is correct.
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What is the length of PR?
Answer:
[tex]8\sqrt{3}[/tex]
Step-by-step explanation:
2/3 pi radians = 2/3 * 180 = 2 * 60 = 120 degrees
split triangle in half:
30, 60, 90 triangle
1/2 PR= 4 root 3
During a typical shower, 17 gallons of water are used If Jana takes two showers a day what is the ratio of gallons used for one shower to total gallons used
Answer:
[tex]x = \frac{1}{2}[/tex]
Step-by-step explanation:
The ratio of gallons used for one shower is obtained by dividing the total of gallons by the number of showers per day:
[tex]n = \frac{17\,galllons}{2\,\frac{showers}{day} }[/tex]
[tex]n = 8.5\,\frac{gallons}{shower}[/tex]
The ratio of gallons used for one shower to total gallons used is:
[tex]x =\frac{8.5\,gallons}{17\,gallons}[/tex]
[tex]x = \frac{1}{2}[/tex]
Answer:
1:2
Step-by-step explanation:
For the each shower 17gallons is used
Daily shower is twice = 17*2
= 34 gallons
The ratio of the shower to the daily shower will be:
Each shower / daily shower
17/34 = 1/2
1:2
when 5√20 is written in simplest radical form , the result is k√5 what is the value of K
A : 20
B : 10
C : 7
D : 4
Answer:
Step-by-step explanation:
√20 can be rewritten as the product of two radicals: √4√5,
and √4 = 2.
Thus, 5√20 = 5(2)√5 = 10√5. Thus, B: 10 is correct; k = 10.
A 25-foot long board is cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?
Answer:
Longer: 17 ft and Shorter: 8 ft
Step-by-step explanation:
Here is what we know:
a = longer part
b = shorter part
a + b = 25
2b + 1 = a
Let's rearrange the equation
b = 25 - a
Now we can plug this into the other equation.
2(25 - a) + 1 = a
50 - 2a + 1 = a
51 - 2a = a
51 = 3a
a = 17 ft
To find b, plug a into one of the equations.
17 + b = 25
b = 8 ft
I hope this helped! :)
If an item is 4.75 before tax and after is 5.13 how much is the sales tax rate?
Answer:
8%
Step-by-step explanation:
Let's say the tax percent was x%. Then, we can write the equation:
4.75 + x% * 4.75 = 5.13
Notice that both terms on the left have 4.75 so factor that out:
4.75 * (1 + x%) = 5.13
Divide both sides by 4.75:
1 + x% = 5.13/4.75 = 1.08
Subtract 1 from both sides:
x% = 0.08
Remember that % simply means "out of 100", so x% = x/100:
x/100 = 0.08
Multiply both sides by 100:
x = 8
Thus, the tax rate is 8%.
Hope this helps!
It is generally believed that nearsightedness affects about 1212% of children in a certain region. A school district tests the vision of 160160 incoming kindergarten children. How many would be expected to be nearsighted? What is the standard deviation for the number of nearsighted children in this group?
Answer:
Step-by-step explanation:
Total number of kindergarten children in that region that were tested is 160
It is generally believed that nearsightedness affects about 12% of children in a certain region. Therefore,
The expected number of kindergarten children expected to be nearsighted is
12/100 × 160 = 19
Probability of success, p = 0.12
Probability of failure, q = 1 - p = 1 - 0.12 = 0.88
Standard deviation = √npq = √(160 × 0.12 × 0.88) = 4.11
An oil storage tank is a cylinder with a height of 50 feet and a diameter of 20 feet.What is the volume of the tank?Use 3.14 for pi
Answer:
the anser is c
Step-by-step explanation:
just did the quiz and got 100 percent :)
Correct answer is C)
Step-by-step explanation:sorry this may not be helpful but the other answer is (A)
What is 75k industry into a percent?
Answer:
100%
Step-by-step explanation:
One person can complete a task 8 hours sooner than another person. Working together, both people can perform the task in 3 hours. How many hours does it take each person to complete the tasking working alone?
Answer:
it takes 1st person 4 hour and second person is 8 hours
Step-by-step explanation:
Let t is the time (t >0)
We have:
1st person working rate per one task: 1/t-8 2nd person working rate per one task: 1/t Working rate per one task from 2 person: 1/3<=> 1/3 = 1/t + 1/t-8
<=> [tex]t^{2} -14t = -24[/tex]
<=> [tex](t-7)^{2} =25[/tex]
<=> t - 7 = 5
<=> t = 12
So it takes 1st person 4 hour and second person is 8 hours
Answer:
Person A complete the task in 1.125 hours
Person B complete the task in 9 hours
Step-by-step explanation:
Person A complete a task 8 hours sooner than person B
Working together they perform the task in 3 hours
Let call "x" hours person A need to do the task alone
Then person B will take 8*x hours to do the job
In 1 hour person A do 1/x part of the task
In 1 hour person B do 1/8*x part of the task
Then A + B in one hour of work will do
1/x + 1/8x = [ 8 + 1 ]/8*x ⇒ 9/8*x
And according to problem statement that time is 1/3 (one third of the time)
Then 3* (9/8*x) = 3
9 = 8*x
x = 9/8
x = 1.125 hours
And person B will take 8*1,125 = 9 hours
An object is thrown off a 256-foot-tall building, and the distance of the object from the ground is measured every second. The function that models the height, h, of the object after t seconds is h(t) = –16t2 + 96t + 256. Determine the time when the object hits the ground.
After how many seconds does the object hit the ground?
2
4
8
16
Answer:
C. 8
At 8 seconds the object will hit the ground.
Answer: C. 8
Step-by-step explanation:
just did this
The distribution of room and board expenses per year at a four-year college is normally distribute with a mean of $5850 and standard deviation of $1125. Random samples of size 20 are drawn from this population and the mean of each sample is determined. Which of the following mean expenses would be considered unusual?a) 5180b)6180c)6350
Answer:
a) 5180
Step-by-step explanation:
We must calculate with respect to each of the options:
a) 5180
We have that the mean (m) is equal to 5850, the standard deviation (sd) 1125 and the sample size (n) = 20
They ask us for P (x <5180)
For this, the first thing is to calculate z, which is given by the following equation:
z = (x - m) / (sd / (n ^ 1/2))
We have all these values, replacing we have:
z = (5180 - 5850) / (1125 / (20 ^ 1/2))
z = -2.66
With the normal distribution table (attached), we have that at that value, the probability is:
P (z <-2.66) = 0.0039
Which means that the probability is 0.39%, which is a very low probability, which is not necessary to calculate the other options, we already know that this data is very unusual.
The mean expense of (a) 5180 is considered unusual because its z-score is approximately -2.67, which is beyond the usual ±2 range for a normal distribution.
To determine which of the given mean expenses would be considered unusual, we will use the concept of the Standard Error of the Mean (SEM) and the properties of a normal distribution.
The SEM can be calculated as:
[tex]SEM = \frac{\sigma}{\sqrt{n}}[/tex]
Where:
[tex]\sigma[/tex] is the population standard deviation, $1125n is the sample size, 20.So,
[tex]SEM = \frac{1125}{\sqrt{20}} = 251.21[/tex]
We then determine the z-scores for the given mean expenses to see how many standard errors away from the population mean they are. The population mean is $5850.
For 5180: [tex]z = \frac{5180 - 5850}{251.21} \approx -2.67[/tex]For 6180: [tex]z = \frac{6180 - 5850}{251.21} \approx 1.31[/tex]For 6350: [tex]z = \frac{6350 - 5850}{251.21} \approx 1.99[/tex]A z-score beyond ±2 is generally considered unusual. Therefore, the mean expense of 5180 would be considered unusual as its z-score is approximately -2.67.
Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds. This function is shown in the graph below.
What do the x-intercepts represent in this real life situation in regards to the height of the soccer ball at that time?
Gina bought a pound of cheese and used 1/4 of it. She split the rest into 5 equal portions for lunch during the week. Which expression represents the fraction of the remaining cheese Gina eats for lunch each day?
a. 3/4 divided by 5
b. 5 divided by 3/4
c. 1/4 minus 5
d. 1/4 divided by 5
Answer:
The right expression is Option A - 3/4 divided by 5
Step-by-step explanation:
The whole cheese is 1.
Since she ate 1/4 of it, thus, she has,
1 - 1/4 = 3/4 left.
Now she split this remaining cheese into 5 places. Thus, it is expressed as;
(3/4) ÷ 5
This corresponds with option A
Rico wants to find the distance between the points (-2,-3) and (2,-5) his work is shown.|-3| + |-5| = 3+5 = 8the distance is 8 unitsis Riko correct explain why or why not?
Answer:
Riko is wrong
Step-by-step explanation:
To find the distance of two point, we use the following formula:
A (x1, y1)
B (x1, y2)
AB = [tex]\sqrt{(x2-x1)^{2} + (y2-y1)^{2} }[/tex]
In this situation, we have:
A (-2,-3)
B (2,-5)
So the distance is: [tex]\sqrt{(2 - (-2))^{2} + (-5 - (-3))^{2} }[/tex] = [tex]\sqrt{4^{2} + 8^{2} }[/tex] = [tex]\sqrt{80} = 4\sqrt{5}[/tex]
Hope it will find you well.
Sample Response: No, Riko is not correct. The points do not have the same x-coordinates. If you connect the points, they do not form a horizontal or vertical line, so you cannot count spaces or use absolute value to find the distance.
\text{Min}Minstart text, M, i, n, end text Q_1Q 1 Q, start subscript, 1, end subscript \text{Median}Medianstart text, M, e, d, i, a, n, end text Q_3Q 3 Q, start subscript, 3, end subscript \text{Max}Maxstart text, M, a, x, end text 121212 181818 232323 262626 292929 The five-number summary suggests that about 75\%75%75, percent of lakes in Minnesota have more than what number of house boats? Choose 1 answer:
Answer:
18 Houseboats
Step-by-step explanation:
Given the set of numbers
12 18 23 26 29
Minimum = 12
First Quartile, Q₁ = 18
Median, Q₂ = 23
Third Quartile, Q₃ = 26
Maximum = 29
The first 25% of lakes have less than or equal to 18 houseboats.
Therefore, the 5-Number Summary suggests that about 75% of lakes in Minessotta have more than 18 Houseboats.
Answer:
18
YEET
Step-by-step explanation: