The average rate of change will be given by 16a + b
What is average rate?Average Rate: A single rate that applies to real estate at many locations and is calculated as the weighted average of the various rates that are appropriate at each site.
It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.
Given:
A general quadratic function of x is given by f(x) = ax² +bx +c
Now, the rate of change of the function f(x) is given by df(x)/ dx.
Therefore, df(x)/ dx = 2ax+ b
Now, the value of x ranges between 4 ≤ x ≤ 12.
So, at x= 4
df(x)/ dx = 2a(4) + b= 8a+ b
and, x= 12
df(x)/ dx = 2a(12) + b= 24a+ b
Thus, the average rate of change will be given by
(8a+ b) + (24a+ b) / 2
= 32a+ 2b/ 2
= 16a + b
Learn more about Average rate here:
https://brainly.com/question/13596336
#SPJ6
In his living room rashad has a window shaped liked a rectangle . It is 7.2 feet high and 8.7 feet wide. What is the area of the window
Answer:62.64
Step-by-step explanation:
You have to multiply them
Which ordered pair must be removed to make the relation a function. {(1, −5), (2, −4), (3, 4), (4, 3), ( 3, -4)}
Answer:
I actually have no idea
Step-by-step explanation:
Answer:
either the ordered pair (3 , 4) or (3 , -4)
Step-by-step explanation:
a function is where there is only one x to each y value
each x value must not be the same
An Ice Hockey rink is a rectangle with a perimeter of 174 meters. The length is 9 meters more than twice the width. What equation describes this problem? (Remember that the perimeter is twice the length plus twice the width)
Answer:
Let width be x metres
so, length is "9 metres more than twice the width" --> 9+2x
So, perimeter is x + x + (9+2x) + (9+2x) = 174
6x + 18 = 174
6x = 156
x = 156/6
x = 26m
width = 26m
length is therefore 9+2(26) --> 9+52 --> 61m
Step-by-step explanation:
Ileana buys a large circular pizza that is divided
into eight equal slices. She measures along the
outer edge of the crust from one piece and finds it
to be 5 1/2 inches. What is the diameter of the pizza
to the nearest inch?
- 4 inches
- 7 inches
- 8 inches
- 14 inches
Answer:
14
Step-by-step explanation:
the edge of one slice of pizza is 5.5 and there are eight slices so i multiplied 5.5 by eight to get the circumference
the circumference is 44 so i divided that by pi to get the diameter which was 14 after you round
if your more of a numbers/formula person this might be more helpful:
circumference: 5.5 x 8 = 44
formula for diameter is [tex]d=\frac{C}{\pi }[/tex]
so, [tex]d=\frac{44}{\pi }[/tex]
[tex]d=14[/tex]
The diameter of the pizza is 14 inches.
Given that the pizza is divided into 8 equal slices and one of the outer edges measures 5 1/2 inches.
When need to find the diameter of the pizza.
What is the formula to find the circumference of the circle?The formula to find the circumference of the circle is 2πr.
Since a pizza is divided into 8 equal parts.
So, the circumference of 1 part=2πr/8=πr/4
πr/4=5.5 inches.
⇒πr=22
⇒r=7 inches.
Then, diameter=14 inches.
Therefore, the diameter of the pizza is 14 inches.
To learn more about the circumference of a circle visit:
https://brainly.com/question/27177006.
#SPJ5
A leading dental journal has claimed that 64% of young adults do not brush their teeth
regularly. A dental hygienist wants to conduct a survey to verify this with her young adult patients and wants to do so with a margin of error of +/-5%. What minimum sample size,
rounded to the nearest whole person, would the hygienist need to use?
Answer:
About 30%
Step-by-step explanation:
Well, um...
If 64% did not, then 36% of them do.
So, about 30% Do.
HURRY PLEASEEEEE!!!!
Use r = 2 and r = 5 to determine if the two expressions are equivalent.
r + 4(2 + r) – 12 8 + 2r – 6
Complete the statements.
1.When r = 2, the first expression is ?.
2.When r = 2, the second expression is 6.
3.When r = 5, the first expression is 21.
4.When r = 5, the second expression is .?
5.The expressions are not equivalent.
The two expressions are not equivalent to each other at r =2 and r = 5.
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.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Use r = 2 and r = 5 to determine if the two expressions are equivalent.
r + 4(2 + r) – 12 8 + 2r – 6
First put r = 2 in both the expressions:-
E1 = 2 + 4 ( 2 + 2 ) -12
E1 =6
E2 = 8 + ( 2 x 2 ) - 6
E2 = 6
Secondly, put r = 5 in both the expressions.
E1 = 2 + 4 ( 2 + 5 ) - 12
E1 = 30
E2 = 8 + ( 2 x 5 ) -6
E2 = 12
The two expressions are not equivalent at r = 2 and r =5.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ5
Answer: 6, 12
Step-by-step explanation:
proof :)
PLEASE HELP!
put the following fractions in order from smallest to biggest
1/2, 3/4, 3/8, 5/8, 5/16, 7/16, 9/16 and 11/16 inches
How much concentrated 12 M sulfuric acid should be added to prepare a 250 mL of 1.5 m solution?
Choose the correct answer
Answer:
Option D
Step-by-step explanation:
Assuming you're referring to slope, the rule is rise/run or "rise over run" so as i look at this line i see it rises 1 unit and then runs back or negatively 4 units, therefor the answer is D 1/-4
Please mark as brainliest :)
3 - 2n = 7
Show work please
Answer:
-2
Step-by-step explanation:
3-2n=7
-3 -3
-2n=4
divide both sides by -2
n=-2
Find the parallelogram below. Use the formula: A = b x h.
Answer:A = b x h
Step-by-step explanation:
I can't see the problem but i can give help u have to follow the formuls
DNA TAC ACC TTG GCG ACG ACT Write the mRNA strand then the Amino Acid sequence.
The two dot plots below compare the forearm lengths of two groups of schoolchildren:
Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length in inches. There are markings from 10 to 13 on each line at intervals of one. For the top line there are 4 dots above the first mark, 4 dots above the second mark, and 2 dots above the third mark. For the bottom line there are 2 dots above the second mark, 3 dots above the third mark, and 5 dots above the fourth mark.
Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?
A. Group B, because five children have a forearm length longer than 12 inches.
B. Group B, because a child in the group has the least forearm length of 10 inches.
C. Group A, because no child in the group has a forearm length longer than 12 inches.
D. Group A, because four children in the group have the least forearm length of 10 inches.
Answer:
The corect answer is : Group A because 4 children have a forarm length longer than 12 inches.
Step-by-step explanation:
I did the test and got it right! :D
Answer:
D. Group A, because four children in the group have the least forearm length of 10 inches.
Step-by-step explanation:
It can be seen that more children in group B have forearm length more than 12 inches and there are no children who have forearm length greater than 12 inches in group A. So, based on the visual inspection of the dot plots, group A, appears to have longer average forearm length.In order to verify the claim let us find the meanMean of Group A
[tex]\dfrac{10\times 4+11\times 4+12\times 2}{10}=10.8\ \text{inches}[/tex]
Mean of Group B
[tex]\dfrac{11\times 2+12\times 3+13\times 5}{10}=12.3\ \text{inches}[/tex]
So, group A has shorter average forearm length.
Learn more about mean:
https://brainly.com/question/12019147
https://brainly.com/question/16217700
Is this right? if it isn't, what IS right?
Answer:
You are wrong and the correct answer is vaunted.
Step-by-step explanation:
Why? Because it would be the only applicable word for this sentence.
Omnipotent: Having unlimited power; able to do anything.
Overt: One or shown openly; plainly or readily apparent, not secret or hidden.
Annihilated: Destroy utterly; obliterate.
Vaunted: Praised or boasted about, especially in an excessive way.
There are 8 baseball players in the dugout for practice. Each player shakes hands with each of the other player ONLY ONCE.
How many handshakes are there?
Explanation:
There are 8 players. For each player, there are 7 people to shake hands with. So we have 8*7 = 56 handshakes so far; however, we double count since the sequence AB is the same as BA (where A and B are player names). Order does not matter when it comes to shaking hands. So we have to divide by 2 to fix the double count. We go from 56 to 56/2 = 28. There are 28 different combinations.
You can use the formula [tex]_nC_r = \frac{n!}{r!(n-r)!}[/tex] with n = 8 and r = 2, but the formula is a bit confusing to be honest if you aren't familiar with it. The exclamation marks indicate factorials.
Extra info: The value 28 can be found in Pascals triangle. Look at the row that starts with 1, 8, ... then note how 28 is in the third slot. Keep in mind that you start at r = 0 and count up by 1. So r = 2 corresponds to the third slot.
Answer:
8 players in total
Step-by-step explanation:
explain how the formula for the volume of a cone is derived
Answer:
The volume of a cone is 1 3 π r 2 h \frac { 1 } { 3 } \pi r ^{ 2 } h 31πr2h, where r denotes the radius of the base of the cone, and h denotes the height of the cone.
Step-by-step explanation:
(happy to help)
Final answer:
The volume of a cone is derived using the principle of integrating infinitesimally thin discs along the height of the cone, given by the formula V = ⅓πr²h.
Explanation:
The formula for the volume of a cone is derived using calculus and geometric principles. Consider a cone generated by rotating a line around one of the coordinate axes. If we know the formula for the area A of a circle, it can be extended to find the volume of a cone. The area A of a circle is πr², where r is its radius. The formula for the volume V of a cone is ⅓ × base area × height, which can be expressed as V = ⅓πr²h, with h being the cone's height.
Using integral calculus, the cone's volume is found by stacking infinitesimally thin discs (each with volume πr²dx, where dx is the disc's thickness) along the cone's height. The radius r changes linearly from the base to the apex, following the relationship r = (h - x)tan(a), where a is the semivertical angle of the cone. Thus, you integrate from the apex (0) to the base (h) to find the entire volume of the cone.
A certain shampoo is available in two sizes. A 23.7-ounce bottle costs $4.97 . A 33.8 -ounce bottle costs $7.48 . Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent.
Unit price for the 23.7 Price per ounce
33.8 Price per ounce
Answer:
23.7 ounce = 20 cents per ounce
33.8 ounce = 22 cents per ounce
The 23.7 ounce bottle is a better deal because it is only 20 cents per ounce, rather than 22 cents per ounce.
Determine the area of a triangle with m
Answer:
I'm guessing they're asking about trig functions, topic test. Answer: B) 10 units^2
Step-by-step explanation:
just took the topic test on edge2021
Jan conducts an experiment and tosses a coin 40 times. She gets heads 30 times instead of the expected 20. What could be a reason for this difference?
A) She miscounted.
B) She needs more trials.
C) She needs a different coin.
D) She got 30 and that is close enough.
the answer is B. hope i helped
The baker made 27 pies. Nine of the pies were cherry pies and the rest were pumpkin pies. The baker placed the pumpkin pies in rows of 3 pies each. How many rows of pumpkin pies did the baker make?
27-9=18. The baker made 18 pumpkin pies.
To prove our answer,,
18 divided by 3 is 6, so it is possible to place them in rows by three.
Your confirmed answer is 18.
I hope this helps!
Brainliest?
Use simple interest to find the ending balance.
$53,300 at 4.7% for
3 3/4 years URGENT I will give you brainliest
Answer:
The ending balance would be:
EB = Money x (1 + rate)^year
= 53300 x (1 + 4.7/100)^(3.75) = 63318.01
Hope this helps!
:)
Answer:
$62,694.125
Step-by-step explanation:
Interest = 53300 × (4.7/100) × 3.75
Interest = 9394.135
Balance = 53300 + 9394.135
= $62,694.125
what is the surface area of a storage box that measures 21 centimeters by 18 centimeters by 16 centimeters
Answer:
2004 cm²
Step-by-step explanation:
To solve this problem, you just need to plug your values into the rectangular prism formula: A=2(wl+hl+hw)
Assuming that the length is 21 cm, the width is 18 cm, and the height is 16 cm, your problem would look like this:
A=2((18x21)+(16x21)+(16x18))=2(378+336+288)=2x1002=2004 cm²
Lin says that the inequalities h>150 and h<160 describe her height in centimeters. what do the inequalities tell us about her height?
Answer:
Her height is in between 150 and 160
Step-by-step explanation:
Given
h > 150
h < 160
Required
What do these represent?
First, the inequalities need to be combined.
If h < 160, then this means that 160 > h.
So, h > 150 and 160 > h can be combined to form an inequality in the following form;
160 > h > 150
This.meeans 160 is greater than h and h is greater than 150.
If this is related to her height, it means 160 is greater than her height and her height is greater than 150;
In other words, her height is in between 150 and 160
Which best describes the data for June, July, and August?
A.a cluster
B. a gap
C. low frequency
D. Symmetric
Pls I need this really quick
Answer: A cluster.
Step-by-step explanation:
A cluster has ups and downs and one peak.
Answer:
A: a cluster
Step-by-step explanation:
Which statement is true about this question -4(2p+5)+8p=-11
A. The equation has one solution, p=2
B. The equation has one solution, p=-2
C. The equation has no solution
D. The equation has infinetly many solutions
Option C. The equation has no solution is correct.
Which statement is true about this question -4(2p+5)+8p=-11
What is equation?
Equation is the relationship between variable and represented as is example of polynomial equation.
Since,
The equation terminated while simplifying
-8p-20+8p=-11
-20≠-11
Thus the given equation has no solution at any point.
Learn more about equation here:
brainly.com/question/10413253
#SPJ2
If the spinner is spun 40 times, predict the number of times the spinner would land on Section B
Answer:
11
Step-by-step explanation:
bkbkbk
Find the circumference of a circle with a diameter of 5inches
Answer:
15.7
Step-by-step explanation:
5 times 3.14 will give you circumference of a circle
Answer:
15.7 in
Step-by-step explanation:
Circumference = pi × d
3.14 × 5
15.7 inches
The Cole family owns an above-ground circular swimming pool that has walls made of aluminum. Find the length (l) of aluminum surrounding the pool as shown if the radius is 15 feet. (use π=3.14 )
Answer:
The length of aluminium surrounding the pool is 94.20 ft.
Step-by-step explanation:
The picture represents the circular swimming pool that has walls of aluminium surround it.
The circumference of a circle is the distance around a circle. It is the curved line that goes round the circle. The question wants us to find the circumference of the aluminium surrounding the circular pool.
circumference of a circle = 2πr
circumference of a circle = 2 × 3.14 × 15
circumference of a circle = 30 × 3.14
circumference of a circle = 94.2 ft
The length of aluminium surrounding the pool is 94.20 ft.
Use either the square of a binomial or the
difference of two squares to find the area of
each rectangle.
Answer:
9. 2916 sq. cm
10. 864 sq. in
Step-by-step explanation:
9.) 54 cm * 54 cm = area of square
(50 + 4)*(50 + 4) = 50*50 + 8*50 + 16
= 2500 + 400 + 16 = 2916 sq cm.
10. 24 in * 36 in. = area of rectangle
get: (30 - 6)*(30 + 6) = 30^2- 6^2
= 900 - 36 = 864 sq. in.
Find the slope of a line passing though the given points (1,4) (3,2)