an environmental scientists is conducting research on a particular type of air pollutant. She collects air samples over time and determines the average number of micrograms (ug) of the pollutant in a cubic meter (m^3). Her data are shown in the table below.Which Function models the scientists data?A. F(×)=1.12t +50B. F(×)=50 · 1.12tC. F(×)=50 - 6tD. F(×)=50 · 0.88^t
Answers
If we graph the points of the table in a coordinate system we'll see that they line up like a line function, so option D is not possible.
If we also add the graphs for the other 3 options, we get:
The points don't line up perfectly but they are much closer to the line in blue than the red or black lines.
Therefore answer is option C f(t) = 50 - 6t
Related Questions
A remodeling project calls for sanding a chair with a disksander. The sanding disk used on the sander has a radiusof 4.5 Inches. Find the area of the disk. Use 3.14 for
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5|x +1| + 7 = -38
Solve for x
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Answer: No solutions
Step-by-step explanation:
[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]
However, as absolute value is non-negative, there are no solutions.
Two towns are 1050 miles apart, a group of hikers start from each town and walk the trail toward each other. They meet after a total hiking time of 200 hours. If one group travels 1 1/2 miles Per hour faster than the other group, find the rate of each group
Answers
Answer:
Rate of the faster group = 3.38 miles per hour
Rate of the slower group = 1.88 miles per hour
Explanation:
Let x = rate of the slower group
Therefore the rate of the faster group will be x + 1 1/2 = x + 3/2 = x + 1.5
From the question, we're told that the two groups traveled for a total hiking time of 200 hours.
We know that distance = rate x time
So the distance of the slower group will be = 200x
And the distance of the faster group will be = 200(x + 1.5)
So if the distance between each town is 1050, we can then solve of x as shown below;
[tex]\begin{gathered} 200x+200(x+1.5)=1050 \\ 200x+200x+300=1050 \\ 400x=750 \\ x=\frac{750}{400} \\ x=1.88\text{ mph} \end{gathered}[/tex]Therefore the rate of the faster group = 1.88 + 1.5 = 3.38 mph.
The period T(In seconds) of a pendulum is given by T=2PI(Square root of L/32) Where L stands for length (in feet) of the pendulum If pi =3.14 and the period is 6.28 what is the length
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Let me check your question
[tex]T\text{ = 2}\cdot\text{ 3.14}\cdot\text{ }\sqrt[]{L/\text{ 32}}[/tex][tex]\frac{T}{2\cdot\text{ 3.14}}\text{ = }\sqrt[]{L/\text{ 32}}[/tex]T= the period = 6.28
[tex]\frac{6.28}{6.28}\text{ = }\sqrt[]{L/\text{ 32}}[/tex][tex]L/32=1^2[/tex][tex]L=32[/tex]_________________
Answer
L= 32
Can you please help me out with a question
Answers
The formula for the area of a sector of a circle is:
[tex]A=\frac{\theta}{360}\cdot\pi r^2[/tex]Where
θ is the angle
r is the radius
Given,
θ = 100
r = 7
We substitute into the formula and figure the answer out [remembering to use 3.14159 as π]:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi r^2 \\ A=\frac{100}{360}\cdot(3.14159)(7)^2 \\ A=\frac{5}{18}\cdot(3.14159)(49) \\ A\approx42.76053 \end{gathered}[/tex]Rounding to the nearest thousandth [3 decimal places], we have:
Area = 42.761 square centimetersHELP PLEASEEEEE!!!!!!
Answers
The two rational number D and point R are found as 2/7 and 4/7 respectively.
What is meant by the term rational number?Rational numbers are those that can be specified in the type p/q, for which p and q are integers and q≠0 is a negative number. The distinction among rational numbers as well as fractions is that fractions cannot include a negative denominator or numerator. As a result, the denominator and numerator of a fraction were all numbers (denominator q≠0), whereas the denominator and the numerator of rational numbers are integers.For the given question.
The number line is given with the rational number D and R to be plotted.
There are 7 units between the points 4 and 5.
D point is 2 units right of 4.
Thus, D = 2/7
R point is 4 units right of point 4.
Thus, R = 4/7
Thus, the two rational number D and R are found as 2/7 and 4/7 respectively.
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can you please help me solve this practice problem I really need help
Answers
Question:
Solution:
Step 1: Find the equation of a line:
Notice that the line passes through the point (x2,y2)= (4,-2) and (x1,y1)=(0,3). Then, the slope of this line would be:
[tex]m\text{ = }\frac{Y2-Y1}{X2-X1}=\text{ }\frac{-2-3}{4-0}\text{ = }\frac{-5}{4}\text{ =-}\frac{5}{4}[/tex]now, notice that the y-intercept of this line is b=3. Then, the equation for this line is:
[tex]y\text{ = -}\frac{5}{4}x+3[/tex]Step 2:
note that the shaded region is all points on the line and those above it. So, the shaded region can be represented by the following inequality:
[tex]y\text{ }\ge\text{ -}\frac{5}{4}x+3[/tex]and it is shown graphically like this:
So that, we can conclude that the correct answer is:
[tex]y\text{ }\ge\text{ -}\frac{5}{4}x+3[/tex]Which of the following equations represents a line that passes through thepoints (6,-5) and (-6, -7)?
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Problem
Which of the following equations represents a line that passes through the
points (6,-5) and (-6, -7)?
Solution
For this case the equation for a line is given by:
y= mx +b
And we can find the slope m with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And replacing we got:
[tex]m=\frac{-7+5}{-6-6}=\frac{-2}{-12}=\frac{1}{6}[/tex]Then we can find the intercept with this formula:
-5 = 1/6 (6)+b
And solving for b we got:
b= -5-1 =-6
And our equation would be:
y= 1/6 x -6
And the best option would be:
I.
MEASUREMENT Choosing metric measurement units Fill in the blanks below with the correct units. (a) Amanda bought a candy bar. Its mass was about 50 ? (b) A dollar bill is about 15 ? long (c) The can of soda held about 350 .
Answers
Explanation
We are asked to fill in the missing blanks
Part 1
The weight of a Candy bar is in grams
So the answer will be
Amanda bought a candy bar. Its mass was about 50 grams
Part 2
A dollar bill should be about 15 centimeters
Therefore, the answer is
A dollar bill is about 15 centimeters long
Part 3
A can of soda should a capacity in mililiters
Therefore, the answer will be
The can of soda held about 350 mililiters
What’s the correct answer answer asap for brainlist please
Answers
Answer:
c. you can't be feeling alive with wearing,weakness of body and mind.
Set up the equation for the following word problem and solve the equation. Let x be the unknown number. -26 times a number minus 5 is equal to 56 less than the number. Step 2 of 2: Solve the equation for x. Express your answer as an integer, a reduced fraction, or a decimal number rounded to two pl Answer
Answers
Answer:
Step 1 of 2:
-26x - 5 = x - 56
Step 2 of 2:
17/9 or 1.89
Step-by-step explanation:
1. Putting word statement in algebraic form
Step 1:
Let x be the unknown number ==> x is the unknown variable to be used in the equation and to be solved for
Step 2:
-26 times a number minus 5 ==> -26x - 5
Step 3:
is equal to 56 less than the number ==> = x - 56
Putting it all together:
-26x - 5 = x - 56
2. Solving the equation
-26x - 5 = x - 56
1. Subtract x from both sides:
-26x - 5 - x = x - x -56
-26x -x - 5 = -56
-27x - 5 = -56
2. Add 5 to both sides
-27x - 5 + 5 = -56+ 5
-27x = -51
x = -51/-27 (dividing both sides by -27)
x = 51/27 (negative divide by negative results in positive)
Reduce 51/27 by dividing numerator and denominator by 3
x = (51 ÷ 3)/(27 ÷ 3) = 17/9
= 1.88888.... = 1.89 rounded to two decimal places
Write a sine function that has a midline of 4 , an amplitude of 3 and a period of 2/3
Answers
Given a midline of 4, an amplitude of 3 and a period of 2/3 we are asked to write a sine function.
Explanation
The equation of a sine function is given as
[tex]y=Asin(\frac{2\pi x}{T})+B[/tex]Where A is the amplitude, T is the period and B is the midline of the sine function.
Therefore, we will have;
[tex]\begin{gathered} y=3sin(2\pi x\div\frac{2}{3})+4 \\ y=3sin(2\pi x\times\frac{3}{2}_)+4 \\ y=3s\imaginaryI n(3\pi x)+4 \end{gathered}[/tex]Answer:
[tex]y=3s\imaginaryI n(3\pi x)+4[/tex]metres> -21,23Sup10f3: Wandere first rareAnswerTeir wiced data prosto w will be whermerson is us. There will stand er is danfromGoethe type of boundary lineDashedEnter two points on the boundary lineSelect the repon you wish to be shaded:
Answers
Given
[tex]\begin{gathered} x>-2 \\ y\ge3 \end{gathered}[/tex]The graph
[tex]\begin{gathered} x>-3\text{ the pink colour} \\ y\ge3\text{ the blue colour} \end{gathered}[/tex]Two boundary points
[tex]\begin{gathered} \lparen-2,3) \\ \lparen-2,0) \end{gathered}[/tex]Today, October 20, 2022, seven friends ate lunch together at Chipotle.
Friend #1 eats there every day - including weekends.
Friend #2 eats there every other day - including weekends
Friend #3 eats there every third day - including weekends
Friend #4 eats there every fourth day - including weekends
Friend #5 eats there every fifth day - including weekends
Friend #6 eats there every sixth day - including weekends
Friend #7 eats there every seventh day - including weekends
Assuming that none of them catch Covid or miss any days, what will be the date when the friends again all eat lunch together at Chipotle?
Answers
The most appropriate choice for LCM of two numbers will be given by -
All the friends together can eat lunch on 14th December 2023.
What is LCM?
LCM means Lowest Common Multiple. LCM of two numbers a and b is the least number that is divisible by both a and b.
Friend 1 eats lunch together at Chipotle everyday including weekends
Friend 2 eats lunch together at Chipotle every other day including weekends
Friend 3 eats lunch together at Chipotle every third day including weekends
Friend 4 eats lunch together at Chipotle every fourth day including weekends
Friend 5 eats lunch together at Chipotle every fifth day including weekends
Friend 6 eats lunch together at Chipotle every sixth day including weekends
Friend 7 eats lunch together at Chipotle every seventh day including weekends
Number of days after which all the friends together can eat lunch
= LCM of 1, 2, 3, 4, 5, 6, 7 = 420 days
All the friends together can eat lunch after 420 days
All the friends together can eat lunch on =
(31 - 20) + 30 + 31 + 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 +14 = 14th December 2023
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Helppppppppppppppppppp
Answers
Perpendicular line are reciprocals
slope of the original line = -1/9
slope of the perpendicular line = 9
I need help with thisIt asks to graph the functionIf you can, use Desmos to graph
Answers
Given the function
[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]The graph of the function is dhoe below
Graph the line by plotting any two ordered pairs with integer value coordinates that satisfy the equation.- 21 = 0AnswerKeypadKeyboard ShortcutsPoints can be moved by dragging or using the arrow keys. Any lines or curves will be drawn once allrequired points are plotted and will update whenever a point is moved.10SI10310101
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We are given the following equation of a line.
[tex]-2x=0[/tex]Let us first solve the above equation for x.
Divide both sides of the equation by -2
[tex]\begin{gathered} -2x=0 \\ \frac{-2x}{-2}=\frac{0}{-2} \\ x=0 \end{gathered}[/tex]So, the solution is x = 0
This means that the two ordered pairs must contain the x-coordinate 0 and the y-coordinate can be any value you like.
For example:
(0, -5) and (0, 5)
Here the x-coordinate is 0 and the y-coordinate is -5 and 5.
Let us plot these ordered pairs and the line on the given graph.
3/3=_/21Fill the blank space with the answer
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In the expression 3/3=_/21, it can be observed that 7 is multipled by denominator 3 in order to obtain 21 in in denominator. So same number, 7 is also multiplied with the numerator also.
[tex]\frac{3}{3}\times\frac{7}{7}=\frac{21}{21}[/tex]So, 21 is to be filled at blank space.
Solve for x8x-11=6x-5Simplify your answer as much as possible
Answers
Solve the given equation for x as shown below
[tex]\begin{gathered} 8x-11=6x-5 \\ \Rightarrow8x-11-6x=6x-5-6x \\ \Rightarrow2x-11=-5 \\ \Rightarrow2x-11+11=-5+11 \\ \Rightarrow2x=6 \\ \Rightarrow\frac{2x}{2}=\frac{6}{2} \\ \Rightarrow x=3 \end{gathered}[/tex]Therefore, the solution to 8x-11=6x-5 is x=3.A line has the given slope m and passes through the first point listed in the table. Complete the table so that each point on the table lies on the line.
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A line can be written as an equation in the slope-intercept form:
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
We know the slope:
[tex]m=3[/tex]The y-intercept is the y value of the graph where it intercepts the y-axis, which happens when x = 0.
We know that the point x = 0 and y = 3 is on the line and, since the value of x is 0. the y value is the y-interceot, so:
[tex]b=3[/tex]Thus, we have the equation:
[tex]y=3x+3[/tex]To calculate the other points, we just need to substitute their x values and get their y values:
x = 1:
[tex]y=3\cdot1+3=3+3=6[/tex]So, when x = 1, y = 6
x = 2:
[tex]y=3\cdot2+3=6+3=9[/tex]So, when x = 2, y = 9.
x = 3:
[tex]y=3\cdot3+3=9+3=12[/tex]So, when x = 3, y = 12;
So, the complete table is:
x | 0 | 1 | 2 | 3
y | 3 | 6 | 9 | 12
Hi I need help with this thank you! Previous question that may help answer this one : Line of best fit: ^y1=−0.02 x+4.68 ● Curve of best fit: ^y2=−0.09 x2+1.09 x+2.83 Section 2 Question 1 Using a curve to make a prediction of the y value for an x value between two existing x values in your data set is called interpolation. Suppose the year is 2005, where x = 5 years: (a) Use the equation for the line of best fit to predict the number of cell phones sold during that year. Round answers to one decimal place and be sure to include the appropriate units. Your Answer: we have the linear equation: y1=-0.02x+4.68Where x is the number of years since the year 2000, y1 ----> is the number of cell phones sold. So for the year 2005, x=2005-2000=5 years.substitute:y1=-0.02(5)+4.68y1=4.58Therefore, the answer is 4.6 cell phones sold.(b) Use the equation for the non-linear curve of best fit to predict the number of cell phones sold during that year. Round answers to one decimal place and be sure to include the appropriate units. Your Answer: We have the equation y2=-0.09x^2+1.09x+2.83For x=5 yearssubstitute:y2=-0.09(5)^2+1.09(5)+2.83y2=6.03Therefore, the answer is 6.0 cell phones sold.
Answers
From the information provided we will have that the predictions will be:
*Line of best fit:
[tex]y_1=0.02(13)+4.68\Rightarrow y_1=4.94\Rightarrow y_1\approx4.9[/tex]So, the extrapolation from the line of best fit is 4.9 sold.
*Curve of best fit:
[tex]y_2=0.09(13)^2+1.09(13)+2.83\Rightarrow y_2=32.21\Rightarrow y_2\approx32.2[/tex]So, the extrapolation for the curve of best fit is 32.2 sold.
Question 4 of 10 In the function y + 3 = (2x)2+1, what effect does the number 2 have on the graph, as compared to the graph of y=x"? 2 A. It shrinks the graph vertically to 1/2 the original height. B. It stretches the graph vertically by a factor of 2. C. It stretches the graph horizontally by a factor of 2. O OD. It shrinks the graph horizontally to 1/2 the original width
Answers
The parental function of the graph is,
[tex]y+3=(x)^2+1[/tex]The transformed function of the graph is,
[tex]y+3=(2x)^2+1[/tex]The transformation between the parent function and the transformed function will be resolved graphically.
From the graph above, the parent function is represented with red while the transformed image is represented with green colour.
We can conclude that the parent function was shrinked horizontally by 1/2.
Hence, it shrinks the graph horizontally to 1/2 the original width.
The correct option is Option
suppose there are two types of tickets to a show . advance and same day. advance tickets cost $15 and same day tickets cost 30. for one more performance there are 55 tickets sold in all and the total amount paid for them was 1275. how many tickets of each typer were sold?
Answers
Advanced tickets(x): $15
Same day tickets(y) : $30
For one more performance there are 55 tickets sold
x+ y= 55 (a)
The total amount paid for them was 1275
15x+30y= 1275 (b)
System of equations:
x+y= 55 (a)
15x+30y = 1275 (b)
Solve for x in (a)
x=55-y
Replace x on (b)
15(55-y)+30y = 1275
82
Solve the system by elimination. 2x+3y=06x+9y=0
Answers
We have the next system of equations
2x+3y=0 ...(1)
6x+9y=0 ...(2)
I order to solve this system by elimination we will multiply the first equation by -3
So we will have
-6x-9x=0
then we add the equation above with the second equation
-6x-9x=0
+6x+9y=0
As we can see we obtain 0=0 which means that we have infinity solutions
ANSWER
Infinity solutions
Which value of n makes the following equation true?√n=4020408O 16
Answers
Solution
- The solution steps are given below:
[tex]\begin{gathered} \sqrt{n}=4 \\ \text{ Square both sides} \\ n=4^2 \\ n=16 \end{gathered}[/tex]Final Answer
The answer is 16
which system of equations can be used to determine how many quarters, x, and how many nickels, y, he has?
Answers
Given: Alfred has 12 coins in his piggy bank. Some of the coins are quarters, some are nickels, and have a total of $3.15.
Required: To determine the system of linear equations for the given situation.:
Classify the following triangle. Check all that apply.A. ScaleneB. IsoscelesC. AcuteO D. RightE. EquilateralF. Obtuse
Answers
Answer
Options A and C are correct.
The triangle is a Scalen triangle and it is also an Acute triangle.
Explanation
To answer this question, we first explain what these type of triangles are
According to side lengths,
- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.
- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.
- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.
According to the angles,
- Acute triangle has all of the angles in the triangle being less than 90 degrees.
- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.
- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.
For this triangle,
We can see that all of its sides have different lengths. Hence, the triangle is a Scalene triangle.
Also, each of the angles of the triangle is less than 90 degrees. Hence, the triangle is an Acute triangle.
Hope this Helps!!!
Text-to-Speech6.For the expression, combine like terms and write an equivalentexpression with fewer terms.4- 2x + 5xВ ІΣSave answer and go to next question
Answers
hello
the question given request we write an equivalent expression as the one given which is
[tex]4-2x+5x[/tex]an equivalent expression to the one above would be
[tex]4+3x[/tex]so, we can say
[tex]4-2x+5x=4+3x[/tex]The functions and are defined as follows.
r(x)= -x+1
s(x)= x^2+2
Find the value of r(s(5))
Answers
Answer: [tex]r(s(5))=-26[/tex]
Step-by-step explanation:
[tex]s(5)=5^2 +2=27\\\\r(s(5))=r(27)=-27+1=-26[/tex]
You are dealt one card from a 52-card deck. Find the probability that you are not dealt a card with number from 2 to 9.
Answers
The probability that we do not dealt a card with number 2 to 9 is 5/13
What is Probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
A pack of card = 52 cards
The Cards having Hearts = 13
The Cards having Spade = 13
The Cards having Diamond = 13
The Cards having Clubs = 13
According to question
The cards numbered from 2 to 9 are 8 cards, specifically 2, 3, 4, 5, 6, 7, 8, and 9.
But there are four suits: diamonds, hearts, spades, and clubs.
Therefore you multiply 8 by 4 to get 32
The probability of getting dealt one of those cards would be:
32/52, or
8/13
But we have to find the probability of not getting such cards
Thus,
1 - 8/13 = 5/13
Hence, the probability that you are not dealt a card with number from 2 to 9 will be 5/13
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