Using it's concept, the average rates of change are given as follows:
a. 1264.03 soda per person per year.
b. 5851.89 soda per person per year.
c. 128010.89 soda per person per year.
What is the average rate of change of a function?The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
For this problem, the function is given as follows:
f(x) = 5.852x^4 - 0.002x³ + 0.006x² + 0.029x + 47.855.
From 1990 to 1996, we have t = 0 to t = 6, hence:
f(0) = 47.855.f(6) = 5.852(6)^4 - 0.002(6)³ + 0.006(6)² + 0.029(6) + 47.855 = 7632.01.Hence the rate is:
(7632.01- 47.855)/6 = 1264.03.
1264.03 soda per person per year.
From 1990 to 2000, we have t = 0 to t = 10, hence:
f(0) = 47.855.f(10) = 5.852(10)^4 - 0.002(10)³ + 0.006(10)² + 0.029(10) + 47.855 = 58566.75.Hence the rate is:
(58566.75 - 47.855)/10 = 5851.89.
5851.89 soda per person per year.
From 2005 to 2010, we have t = 15 to t = 20, hence:
f(15) = 5.852(15)^4 - 0.002(15)³ + 0.006(15)² + 0.029(15) + 47.855 = 296300.39.f(20) = 5.852(20)^4 - 0.002(20)³ + 0.006(20)² + 0.029(20) + 47.855 = 936354.84.Hence the rate is:
(936354.84 - 296300.39)/5 = 128010.89.
128010.89 soda per person per year.
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4-5 what are the answers!! please give correct answers ill give brainlist!!!!
Answer:
4a.) 0.0005 = 5 x 10 to the exponent -4
4b.) 0.0025 = 2.5 x 10 to the exponent -3
5a.) 2 x 10 to the exponent -2 = 0.02
5b.) 16 x 10 to the exponent -4 = 0.0016
Tip:
The number being multiplied has to be less than or equal to 10. Count the places the decimal point moves from the end of the number to the number in the original equation.
Example: 0.05 = 5 x 10 to the exponent -2
0.05 has 2 spaces for the decimal point to move up to 5 going right. We use a negative decimal because 0.05 is less than 5. Here is an example where the exponent is positive:
5000 = 5 x 10 to the exponent 3
5000 has 3 spaces for the decimal point to move down to 5 going left.
The total weight of 15 boxes is 45 pounds. How muchwould 40 boxes weigh
Answer:
40 boxes would weigh 120 pounds. nice
15/45 = 40 x 3 = 120 pounds
Step-by-step explanation:
:)
Solve, 3|x−4|−6≤9.
Graph the solution on the number line.
Answer:
Step-by-step explanation:
Wayne recorded the eye colors of the people who have already signed up for a lecture on genetics.
green 2
blue 30
brown 38
What is the experimental probability that the next person to sign up will have blue eyes?
Write your answer as a fraction or whole number.
P(blue)=
The experimental probability of next person to have Blue eyes is 3/7.
Probability :Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
It is based on the possible chances of something to happen.
Probability (P) = Number of a Favourable outcome {n (E)} / Total number of outcomes {n (S)}
Simply, P = n (E) / n (S)
Given, Eye colors of the people
Green = 2
Blue = 30
Brown = 38
To find the probability of next person to have blue eyes, first we will add the given eye colors
Total number of Eye Colors = 2 + 30 + 38 = 70
Number of Blue Eyes = 30
Then, Probability to have blue eyes P(blue) = Number of Blue Eyes / Total number of Eye Colors
= 30/70
= 3/7
So, there is 3/7 chances to next person to have blue eyes.
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Answer:
3/7
Step-by-step explanation:
A girl owns 1 pairs of pants, 3 shirts, 4 ties, and 3 jackets. How many different outfits can the girl wear to school if each outfit must consist of one of each item?
Answer: She can wear 3 outfits to school because
Step-by-step explanation: She is able to wear the pants multiple times so she can have 1 pants 1 shirt 1 tie and 1 jacket for three days
PLEASE HELPPPP
In a particular year, a total of 60,831 students studied in two of the most popular host countries when traveling abroad. If 5981 more students studied in the most popular host country than in the
second most popular host country, find how many students studied abroad in each country.
There were …..
students who studied abroad in the most popular host country.
Answer:
66812
Step-by-step explanation:
60831+5981=66812
Hey, could somebody help me out with this?
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Tracey paid $145 for an item that was originally priced at $360. What percent of the original price did Tracey pay?
Round your percentage answer to two decimal places.
Do NOT include a
%
symbol with your answer.
Answer:
Tracy paid 40.28 percent of the total price.
how do you solve this problem
chan is filling a box with 1 inch cubes. he filled the bottom layer with 5x1 inch cubes long, and 4x1 inch cubes wide. The box is 6 inches tall.
Answer:
120 cubes will fill the box
Step-by-step explanation:
You want to know the number of 1-inch cubes it takes to fill a box that is 5 cubes long, 4 cubes wide, and 6 inches tall.
LayerTo cover the bottom of the box, Chan needs to make an array of cubes that has 4 rows with 5 cubes in each row. That layer will have ...
4 × 5 = 20 . . . . cubes per layer
VolumeEach layer occupies 1 inch of height, and the box is 6 inches high. The volume of the box will be filled with six of these layers. That will take this many cubes:
(6 layers) × (20 cubes/layer) = 6 × 20 cubes = 120 cubes
Chan will need 120 cubes to fill the box.
Use the segment addition postulate to solve for the length of BC, if AC = 16, BC = x + 11, and AB = 3x-7.
The zookeeper mentioned that the scale used to weigh some of the larger animals can be off by 12 pounds. The scale read 438.2 lbs. for one of the larger animals. If the animal’s actual weight is x pounds, write an expression to represent the number of pounds the weight on the scale is from the actual weight of the animal. Then explain the range of values in which the actual weight might be.
The actual weight of the animal is between 450.2 and 426.2 pounds
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Inequality can be used to show that two variables or numbers are not equal to each other.
The weight of the larger animals can be off by 12 pounds. Let x represent the actual weight of the animal. If the scale reads 438.2 lbs, hence:
|x - 438.2| = 12
x - 438.2 = 12; or -(x - 438.2) = 12
x = 450.2; or x = 426.2
The actual weight of the animal is between 450.2 and 426.2 pounds
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WILL GIVE BRAINIST.
1. The soccer team is making pizzas for a fundraiser. They put1/4 of a pound of cheese on each pizza. If they have 12 one-pound packages of cheese, how many pizzas can they make? pizzas ?
2. Dan purchased 3 ½ yards of mulch for his garden. Mulch costs $25 a yard. How much did Dan pay for his mulch? $
3. Mr. Hamilton owns 2 ¾ acres of land. He plans to buy 1 and 1/3 more acres. How many acres will he own? Write your answer as an improper fraction. acres
PLEASE HELP ANSWERING THIS QUESTION QUICKLY! THIS QUESTION IS SO CONFUSED!
Based on the graph above, estimate to one decimal place the average rate of change from x=1 to x=3 (Blank).
Explain!
Thanks!
The average rate of change from x=1 to x=3 is -1
How to find the average rate of change from x=1 to x=3?On the given graph, we have the following function values
f(1) = 6
f(3) = 4
The average rate of change from x=1 to x=3 is then calculated as
Rate = [f(3) - f(1)]/[3 - 1]
This gives
Rate = [4 - 6]/[3 - 1]
Evaluate
Rate = -1
Hence, the average rate of change from x=1 to x=3 is -1
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Question
Shonda jogs 5 miles per hour.
Graph the relationship between the number of hours Shonda jogs and the total number of miles jogged.
here hope this helps u
Positive multiples of 4
Answer:
4, 8, 12, 16, 20, 24, 28, 32, 36, and 40 are some multiples of 4 that are positive.
Find the average rate of change of f (x)=x-2√x on the interval [1, 9].
The average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
What is average rate of change?It is a measure of how much the function changed per unit, on average, over that interval.
We have,
f(x) = x - 2√x
On the interval [1,9].
[1, 9] = [a, b]
The average rate of change:
= f(b) - f(a) / b - a
= f(9) - f(1) / 9 - 1
= [(9 - 2√9) - (1 - 2√1)] / 8
= [ (9 - 6) - (1 - 2) ] / 8
= (3 + 1) / 8
= 4 / 8
= 1/2
Thus the average rate of change of f(x) = x - 2√x on the interval [1, 9] is 1/2.
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the difference between nine times a number and one more than five times the number
The required expression for the given statement is 4x + 1.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
The given statement is,
the difference between nine times a number and one more than five times the number
Let x be the number.
Thus, we have
nine times a number = 9x
one more than five times the number = 1 - 5x
Thus, the numerical expression we get is
9x + (1 - 5x)
Expanding we get
9x + 1 - 5x
Solving we get
4x + 1
this is the required expression
Thus, the required expression for the given statement is 4x + 1.
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help me if you can please
Answer:
f(0) = 5, f(7) = 1328, f(-5) = -460
Step-by-step explanation:
[tex]f(x) = 4x^3 - 7x + 5[/tex]
We should substitute the values in the brackets into the equation to find the function's value at that x point.
[tex]f(0) = 4(0)^3 - 7(0) + 5\\\to f(0) = 5[/tex]
[tex]f(7) = 4(7)^3 - 7 \times 7 + 5\\\to f(7) = 4 \times 343 - 49 + 5\\\to f(7) = 1328[/tex]
[tex]f(-5) = 4(-5)^3 - 7(-5) + 5\\\to f(-5) = 4 \times -125 + 35 + 5\\\to f(-5) = -460[/tex]
wats the answer help mee
Answer:
6
Step-by-step explanation:
The diameter is half of the given radius, therefore, split the radius in half.
[tex]\frac{12\:in^2}{2} = 6\:in^2[/tex]
. If C lies between A and B on AB, then AC + CB = AB. What can you logically conclude about AB?
Answer: AB is twice the size of AC and twice the size of CB
Step-by-step explanation: "Lies between" means that it's in the middle. C is in the middle of A and B. A to C would be the same distance of C to B because C seperates the segments into 2 equal halves. AB is the whole segment including C, you could do AC + AC if you substituted it for the lengths and you would still get AB
Solve the linear equation 7x+4^2=12x-8
Answer:
x = 24/5
Step-by-step explanation:
A group of 15 students were assigned a novel to read during class. The data below represents the number of pages each student read.8, 8, 10, 11, 12, 12, 13, 14, 16, 16, 18, 18, 18, 20, 24Which of the following box plots correctly summarizes the data?
The box plots that correctly summarize the data is the option B from the image
This is further explained below.
What are box plots?Generally, a straightforward method of depicting statistical information on a plot, in which a rectangle is used to represent the second and third quartiles of the data, and in which the median value is typically shown by a vertical line drawn within the rectangle.
On each side of the rectangle, there are two horizontal lines that represent the lower quartile and the higher quartile.
A boxplot is a graphical representation of the distribution of data that is based on a summary of five numbers and follows a defined format.
In conclusion, The box plot in the illustration with choice B accurately summarizes the data.
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CQ
Image attached
A group of 15 students were assigned a novel to read during class. The data below represents the number of pages each student read.
8, 8, 10, 11, 12, 12, 13, 14, 16, 16, 18, 18, 18, 20, 24
Which of the following box plots correctly summarizes the data?
A
B.
C.
D
In the lab, Miguel has two solutions that contain alcohol and is mixing them with each other. He uses twice as much Solution A as Solution B. Solution A is 12% alcohol and Solution B is 16% alcohol. How many milliliters of Solution B does he use, if the resulting mixture has 120 milliliters of pure alcohol? Number of milliliters of Solution B: X Ś
Miguel uses 300 mL Solution B and 600 mL Solution A.
What is termed as the percentages?A percentage is a relative value that symbolizes the hundredth part of any quantity.One percent (symbolized 1%) is one hundredth part; thereby, 100 percent symbolizes the entire amount as well as 200 percent clarifies twice the given amount.Let x represent the amount of Solution B used.
2x = the quantity of Solution A used.
Solution A is alcohol = 12%.
Solution B is alcohol = 16%.
Given that 12% = 0.12 and 16% = 0.16, we can calculate the following equation:
2x(0.12) + x(0.16) = 120 (Recall that pure alcohol has a concentration of 100% = 1.00.)
0.24x + 0.16x = 120
0.40x = 120
x = 300 mL
Thus, Miguel makes use of 300 mL of Solution B and 2(300) = 600 mL of Solution A.
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Solve the equation 5k^2−20k=15 . Present exact values of the solutions. If there are more than one solutions, separate them by a comma.
The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.
What are the roots of the equation?Let the equation be ax² + bx + c = 0.
Then the roots of the equation will be
[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}\\[/tex]
The quadratic equation is given below.
5k² - 20k = 15
Simplify the equation, then we have
k² - 4k = 3
k² - 4k - 3 = 0
Then the roots of the equation will be
[tex]\rm k = \dfrac{ -(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times (-3) }}{2 \times 1}\\\\k = \dfrac{4 \pm \sqrt {28}}{2}[/tex]
Simplify the equation, then we have
k = (4 ± 5.30) / 2
k = (4 + 5.30) / 2, (4 - 5.30) / 2
k = 4.65, -0.65
The solutions of the quadratic equation 5k² - 20k = 15 will be 4.65 and negative 0.65.
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6.2 HELPPPPPPPP!!!!!!!!!!!!!!!!!!!!
Graph the image of the figure using the transformation given.
Captionless Image
LAST 3 PICS ARE THE OPTIONS
Answer: It's the third answer choice.
Step-by-step explanation:
It is the only one that LOOKS like it's reflected over the y-axis (i check the math as well)
help help help.........
Answer:
The answer is A
Is 7 a solution of 5x - 3 = 12 ? Justify your answer
Answer:
Step-by-step explanation:
NO x=3
[tex]f(x)=x^{2} +2x-24[/tex]
What is the slope of the line represented by the equation y = x - 3?
O-3
--3--
45
O3
Answer:
Slope is 1
Step-by-step explanation:
From the general linear equation:
[tex]{ \rm{y = mx + c}}[/tex]
m is the slope
Comparing with the equation given:
[tex]{ \rm{y = { \green{1}}x - 3}}[/tex]
2x + 5 < -3 or 6x - 5 > 7
Answer: 2x-5/3=7
Tiger shows you, step by step, how to Isolate x (Or y or z) in a formula