Given the function:
p(r) = 3 - r
Let's graph the function using 6 points.
Input the different values for r and solve for p(r).
• When r = -2:
p(-2) = 3 - (-2)
p(-2) = 3 + 2
p(-2) = 5
Ordered pair: (r, p) ==> (-2, 5)
• When r = -1:
p(-1) = 3 - (-1)
p(-1) = 3 + 1
p(-1) = 4
Orderd pair: (-1, 4)
• When r = 0:
p(0) = 3 - 0
p(0) = 3
Ordered pair: (0, 3)
• When r = 1:
p(1) = 3 - 1
p(1) = 2
Ordered pair: (1, 2)
• When r = 2:
p(2) = 3 - 2
p(2) = 1
Ordered pair: (2, 1)
To graph the function, plot the given ordered pairs on the graph and connect using a straight edge.
Therefore, we have table:
r p(r) Ordered pair
-2 5 (-2, 5)
-1 4 (-1, 4)
0 3 (0, 3)
1 2 (1, 2)
2 1 (2, 1)
The graph is attached below:
Shyla answered 38 out of 40 questions correctly on the quiz. What percent did she answer correctly? She answered 95% correctly. Show the proportion and work that gives that answer.
Answer: I think 90 %
Step-by-step explanation:
Answer:
it is 95%
Step-by-step explanation:
Kai and Finley were studying together for their exams the
following day. They had planned to spend the entire two days
after the exams hiking to a log cabin on the Winslow trail. The trail
was closed on Mondays, Wednesdays, and weekends.
On which day of the week was their exam scheduled?
Their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.
How to determine which day of the week was their exam scheduledTo determine the day of the week on which Kai and Finley's exam was scheduled, we need to consider the information provided about the trail being closed on Mondays, Wednesdays, and weekends.
If they had planned to hike to the log cabin for two days after the exams, and the trail is closed on weekends, it means they cannot start hiking on Saturday or Sunday.
Since they cannot start hiking on Saturday or Sunday, the two possible options for the exam day would be Monday or Wednesday, as they have not specified whether the hike starts immediately after the exams or the day after.
However, we can conclude that their exam was not scheduled on Monday, as the trail is closed on Mondays, and they had planned to hike immediately after the exams.
Therefore, their exam must have been scheduled on Wednesday, allowing them to start hiking on Thursday after the exams.
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read the instructions first
then graph
Polya created his famous four-step process for problem solving, which is used all over to aid people in problem solving:
Step 1: Understand the problem.
Step 2: Devise a plan (translate).
Step 3: Carry out the plan (solve).
Step 4: Look back (check and interpret
Answer:
Step-by-step explanation:
Step 1:
Age of grace = x
Age of her son = y
Step 2:
x > 20
x + y ≥ 60
Step 3:
x +y ≥ 60
y ≥ -x +60
Step 4
(45, 22)
x > 20 ; y ≥ -x + 60
45 > 20 ; 22 ≥ -45 + 60
22 ≥ 15
That was no help what is it
Answer:
I am confused in many ways
Describe the transformations of the parent function to graph ( in picture). List at least 5 points that could be used to graph this function accurately without the use of a calculator
Notice that the parent function of f(x) is:
\(g(x)=\sqrt[3]{x}.\)Now, to determine the transformations, we recall the following:
The graph of a function h(x)
1.- horizontally translated n units to the left is represented by the following function:
\(l(x)=h(x+n),\)2.- vertically translated down m units:
\(l(x)=h(x)-m,\)3.- reflected over the x-axis:
\(l(x)=-h(x).\)Therefore, f(x) is g(x) translated 2 units to the left, reflected over the x-axis, and translated 4 units down.
To determine 5 points on the graph, we evaluate the graph at x=-2, x=6, x=-10, x=-1, x=-3, and get:
\(\begin{gathered} f(-2)=-4, \\ f(6)=-2-4=-6, \\ f(-3)=1-4=-3, \\ f(-10)=2-4=-2, \\ f(-1)=-1-4=-5. \end{gathered}\)Therefore, the points (-2,-4),(6,-6),(-3,-3),(-10,-2),(-1,-5) are on the graph.
Answer:
f(x) is
\(g(x)=\sqrt[3]{x}\)translated 2 units to the left, reflected over the x-axis, and translated 4 units down.
5 points on the graph:
(-2,-4),(6,-6),(-3,-3),(-10,-2),(-1,-5).
Mrs. O'Dell has 8 different
vegetables to plant in her
garden. She wants to divide
her garden into 8 squares. Each
square should be the same size.
Help Mrs. O'Dell divide her
garden into 8 squares. What is
the measurement of each side
of the squares?
The measurement of each of the squares will guarantee Mrs. O'Dell has 8 different squares and they are all the same size are 75 centimeters by 100 centimeters.
How to divide the total area into 8 squares which are the same size?To begin, let's identify the best way to divide the total area. For this, there are 2 options:
Create two rows each with 4 squares = 4 x 2 = 8Create four rows each with 2 squares = 2 x 4 8=Let's use the first pattern:
Length: 3 meters / 4 = 0.75meters or 75 centimetersWidth= 2 meters / 2 = 1 meter or 100 centimetersBased on this, the dimensions for each section should be 75 centimeters by 100 centimeters.
Note: This question is incomplete; here is the missing section:
Dimensions of the garden: 3 meters x 2 meters
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Help!!! Name a line skew to line AE containing point C.
Answer:
PC is the answer my friend.
Where does the normal line to the paraboloid z = x2 + y2 at the point (1, 1, 2) intersect the paraboloid a second time?
Answer:
the intersection point is ( -5/4, -5/4, -9/8)
Step-by-step explanation:
F(x,y,z) = x² +y² -z= 0
Then find differential of each terms then we have
∀f(x)=2x
∀f(y)=2y
∀f(z)=-1
The partial differential which is the director vector is at F(x,y,z)= (1,1,2)
Vf(1,1,2) = (2,2,-1)
But the given point is ( 1.1,2)
Then the parametric equation of normal line will be
x= 1+2t
y= 1+2t
z= 2 -t
The parametric equation can be formed as
(1+2t)² + (1+2t)² - (2-t)= 0
If we expand the expression above we have,
2(1+4t+4t²) - 2+t= 0
0= 8t² + 9t
t= 0 or t= -9/8
Substitute the value of t into the parametric equation above
At t=0
x= 1+2t; x= 1+2(0)=1
y= 1+2t; y= 1+2(0)=1
z=2 -t ; z= 2-(0)= 2
At =0 , we have (1,1,2)
At t= -9/8
x= 1+2t; x= 1+2(-9/8)=-5/4
y= 1+2t; y= 1+2(-9/8)=-5/4
z=2 -t ; z= 2-(-9/8)= -9/8
Therefore, the intersection point is ( -5/4, -5/4, -9/8)
The normal intersects the paraboloid at \((-\frac{5}{4},-\frac{5}{4},\frac{25}{8} )\)
Paraboloid:A surface all of whose intersections by planes are either parabolas and ellipses or parabolas and hyperbolas.
Given function is,
\(z = x^2 + y^2\)
We can write the given function as,
\(F(x,y,z)=x^2+y^2-z\)
Compute the gradient \(F\) by using the formula,
\(\nabla F(x,y,z)=\left\langle 2x,2y,-1\right\rangle\)
At (1,1,2) we get,
\(\nabla F(x,y,z)=\left\langle 2,2,-1\right\rangle\)
The equation of the tangent plane at (1,1,2) is,
\(2(x-1)+2(y-1)-(z-2)=0\\2x+2y-z-2=0\\\frac{x-1}{2}=\frac{y-1}{2}=\frac{z-2}{-1}=t\\ x=2t+1,y=2t+1,z=-t+2\)
Replace the values of \(x,y,z\) in \(z = x^2 + y^2\) and then solve for \(t\) then,
\(-t+2=(2t+1)^2+(2t+1)^2\\8t^2+9t=0\\t=0,-\frac{9}{8}\)
Substituting the value into the parametric equations,
\(x=2(-\frac{9}{8} )+1,y=2(-\frac{9}{8} )+1,\ and \ z=-(-\frac{9}{8} )+2\\x=-\frac{5}{4}, \ y= -\frac{5}{4} ,z=\frac{25}{8}\)
Therefore, the normal intersects the paraboloid at \((-\frac{5}{4},-\frac{5}{4},\frac{25}{8} )\)
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Use the pic for more info plz
Answer:
C.70
Step-by-step explanation:
100 Points! Algebra question. Graph the function. Photo attached. Thank you!
The cost of each pound of grass seed is $6.
A graph of the solution for the cost of each pound of grass seed is shown below.
How to determine the cost of each pound of grass seed?In order to determine the cost of each pound of grass seed, we would assign a variable to the cost of each pound of grass seed and then translate the word problem into an algebraic linear equation.
Let the variable x represent the cost of each pound of grass seed.
Since Lori bought 3.6 pounds of grass seed and she was charged $22.90, including a tax of $1.30, an algebraic linear equation that best represent this situation is given by;
3.6x + 1.30 = 22.90
3.6x = 22.90 - 1.30
3.6x = 21.60
x = 21.60/3.6
x = $6.
In conclusion, we would sue an online graphing calculator to plot the solution for the cost of each pound of grass seed as shown in the image attached below.
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)The mean voltage of a battery is 15 and S.D 0.2.Find the probability that four such batteries connected in series will have combined voltage of 60.8 or more volts
The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.
In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.
The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.
The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.
Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.
First, we need to standardize the value of 60.8 using the formula:
Z = (X - μ) / σ
Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, the standardized value is:
Z = (60.8 - 60) / sqrt(0.16)
Z = 0.8 / 0.4
Z = 2
Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.
Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
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The graphs below show the sales of touchless thermostats, y, for the first 8 months last year. Both graphs show the same information.
Touchless Thermostat
Touchless Thermostat
Sales ($)
80,000
60,000
40,000
20,000
0
Sales
2
4
6
Months since
Start of the Year
Graph A
8
Sales ($)
40,000
30,000
20,000
10,000
0
Sales
To emphasize the slow increase in sales, it would be best for Samantha to use
Samantha should use this graph for her presentation because the sales
2
4 6 8
Months since
Start of the Year
Graph B
Samantha is preparing a presentation and wants to emphasize that the sales increased slowly over the first 8 months last year.
Complete the following sentences.
for her presentation.
Y
on this graph.
To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
How to determine the appropriate graph?
The graphs that complete the question are added as an attachment
From the attached graph, we have the following highlights:
The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....
The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....
The above means that graph B is a misleading graph
Hence, Benjamin should use graph A for his report
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Given the inequality 12.5 < n < 12.6, what is a possible value for n?
Step-by-step explanation:
The given expression states taht any number between 12.5 and 12.6 would fall into the possible value category for n. We can use 12.51, 12.55, 12.575 along with any number between 12.5 and 12.6.
Hope this helps!
Royce kept track of the inches of snowfall in his town over a 15-day period. Royce’s data is given below. 1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3 Which box plot shows this data set?
Answer:
The correct option - Figure A
Step-by-step explanation:
The exact question is as follows :
Given - Royce kept track of the inches of snowfall in his town over a 15-day period. Royce's data is given below.
1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3
To find - Which box plot shows this data set?
Solution -
Given the data is -
1, 0, 0, 3, 5, 0, 0, 0, 2, 2, 1, 7, 2, 2, 3
Firstly,
Arrange the data from smallest to largest
0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, 5, 7
Now,
Find the median
Median is the middle value - i.e. (15 + 1)/2 = 8th value
So, we get Median = 2
Now,
Find the Quartile -
The first quartile is the median of the data points to the left of the median.
i.e. Median of 0, 0, 0, 0, 0, 1, 1
so, we get
Q1 = 0
The third quartile is the median of the data points to the right of the median.
i.e. Median of 2, 2, 2, 3, 3, 5, 7
so, we get
Q3 = 3
Now,
Compute the min and the max
Minimum value = 0
Maximum value - 7
So,
five number summary is -
0, 0, 2, 3, 7
And we draw the box as follows -
So,
The correct option - Figure A
Enter the decimal represented by the shaded square.
The shaded square represents ___?
Answer:
I believe it's 0.3 because its 30/100 which represents 30% and 30% as a decimal is 0.3
help me answer this please
Answer:
3,952 ft
Step-by-step explanation:
Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.
sin8°=\(\frac{550}{c}\)
csin8°=550
c=550/sin8°
c= 3,952
For questions 3-4, use the graph of the polynomial function to find the factorization of the polynomial. Assume there is no constant term. 3
3. The factored polynomial is p(x) = (x - 1)(x - 5)
4. The factored polynomial is p(x) = (x + 3)²
What is a polynomial?A polynomial is a mathematical expression in which the power of the unknown is greater than or equal to 2.
3. To factorize the polynomial using the graph, we see that the polynomial cuts the x - axis at x = 1 and x = 5.
This implies that its factors are (x - 1) and (x - 5)
So, the factored polynomial is p(x) = (x - 1)(x - 5)
4. To factorize the polynomial using the graph, we see that the polynomial touches the x - axis at only one point x = -3. So,it has repeated roots
This implies that its factors are (x - (-3)) = (x + 3) twice
So, the factored polynomial is p(x) = (x + 3)²
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help me please please please
The angle measures for this problem are given as follows:
a = 62º.b = 118º.c = 62º.d = 62º.How to obtain the angle measures?The sum of the measures of the internal angles of a triangle is of 180º.
The triangle in this problem is ABC, hence the measure of a is obtained as follows:
a + 68 + 50 = 180
a = 180 - (68 + 50)
a = 62º.
c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:
c = 62º.d = 62º.Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:
a + b = 180
62 + b = 180
b = 118º.
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Simplify 79.5-2.58 x (3.63-1.63) to the third power
Answer:
a
Step-by-satep explanation:
Write 6.7% and 0.056% as a simplified fraction ( please )
Answer:
67/1000 and the other one is 7/12500
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
The true statements are
The value of f(–10) = 82
The graph of the function is a parabola.
The graph contains the point (20, –8).
What is a Parabola:A parabola is a type of conic section that is formed when a plane intersects a cone in such a way that the angle between the plane and the vertical axis of the cone is equal to the angle between the plane and a generator (a straight line passing through the vertex and the base of the cone).
The resulting shape is a symmetrical, U-shaped curve. The standard form of the parabola is a quadratic function.
Here we have
The quadratic function f(x) = x²/5 – 5x + 12
Now check each option as follows
1. The value of f(–10) = 82
To check this find f(-10) as follows
f(-10) =1/5 (-10)²– 5(-10) + 12 = 20 + 50 + 12 = 82
Hence, The value of f(–10) is equal to 82
2. The graph of the function is a parabola.
As we know the standard equation of a parabola is a quadratic function that is in the form of ax² + bx + c
Hence, the quadratic function represents a parabola
3. The graph of the function opens down.
In the given function f(x) = x²– 5x + 12, the coefficient of the x² term is 1. Since the coefficient of x² is positive, the parabola opens upwards.
Hence, The graph of the function opens down is false
4. The graph contains the point (20, –8).
To check this substitute the point in f(x)
=> –8 = 1/5(20)²– 5(20) + 12
=> –8 = 80 – 100 + 12
=> –8 = –8 [ Which is true ]
Hence, The graph contains the point (20, –8).
5. The graph contains the point (0, 0).
=> 0 = (0)²– 5(0) + 12
=> 0 = 12 [ which is not true ]
Hence, The graph doesn't contain the point (0, 0).
Therefore,
The true statements are
The value of f(–10) = 82
The graph of the function is a parabola.
The graph contains the point (20, –8).
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Juice A cost 0.10 cent more per ounce than juice B. 12 ounce juice A cost $5.64 total. How much per ounce juice B cost
Answer:
5.64/12= .47 but that box cost 10cents more than box B so you then you subtract .10 and get .37 per ounce for box B
Describe the transformations from the parent function y=^3 to (x-3)-4
Answer:
y shifted 3 units right
y shifted 4 units down
Step-by-step explanation:
A boat is 100 miles away from the marina, sailing directly towards it at 10 miles per hour. Write an equation for the distance of the boat from the marina after t hours.
Answer:
Step-by-step explanation:
The formula for determining distance is expressed as
Distance = speed × time
From the information given,
Speed of boat = 10 miles per hour
It means that the distance that the boat covered after t hours is 10 × t = 10t miles
Since the boat is 100 miles away from the marina and it is sailing directly towards it, then the equation for the distance of the boat from the marina after t hours is
Distance = 100 - 10t
if you multiply the slopes of two perpendicular lines the product is -1 (as long as neither line is vertical.) use that fact and the graph to complete the statements below
Based on the given information, we know that the slope of line q is -1, and since line p is perpendicular to line q, the product of their slopes is -1. Therefore, the slope of line p is 1 (the reciprocal of -1).
What is slopes?Slope is a measure of the slope of the line.
It is defined as the change in y divided by the change in x between two points on the line.
Slope determines the direction and steepness of a line and can be positive, negative, zero, or undefined.
To find the equation of line p, we need to use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
We know that the slope of line p is 1, and we can find the y-intercept by looking at the point where the line intersects the y-axis, which appears to be (0,2) on the graph.
The equation for line p is y = x + 2.
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Computer systems analysts
Database administrators
Computer software engineers,
systems software
Gaming and sports book writers
and runners
Environmental science and
protection technicians, including
health
Manicurists and pedicurists
Physical therapists
Physician assistants
504
650
119 154
350 449
18 24
36
78
47
100
220
29.0
28.6
28.2
28.0
28.0
27,6
27.1
146
34
99
5
10
22
47
18
Bachelor's degree
Bachelor's degree
Bachelor's degree
Short-term on-thi
Associate degree
Postsecondary vocational award
Master's degree
Master's degree
173
66
83
27.0
Based on the above table, what is the fastest growing listed occupation for those without a college degree?
a. Gaming and sports book writers and runners
b. Dental assistants
c. Marriage and family therapists
d. Manicurists and pedicurists
Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.
Therefore option A is correct.
What is a college degree?The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.
With reference to the table, the occupations that do not require a college degree are:
Gaming and sports book writers and runnersEnvironmental science and protection technicians, including healthManicurists and pedicuristsWe were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.
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A trucker wanted to track how long it took to reach Bismarck. When she started out, her clock
read 7:00AM. When she refueled, the clock read 8:00AM. After reaching Bismarck, the clock read
10:00AM. How many hours did it take this trucker to reach Bismarck?
Answer:
Below
Step-by-step explanation:
From 7 to 10 AM is THREE hours (if the times are all on the same day)
L 2. (a) Which term of the arithmetic progression 8 - 6i, 7 – 4i, 6 — 2i, ... is purely imaginary [3]
Answer:
10iStep-by-step explanation:
8-7=1
7-6=1
The real part of the complex numbers is following an arithmetic progression with first term 8 and common difference 1.
………………………………………
-6+2=-4
-4+2=-2
THe Imaginary part of the complex numbers is following an arithmetic progression with first term -6 and common difference 2.
………………………………………
Then the term she of the sequence can be written:
(8 - n) + i(-6 + 2n)
………………………………………
We get a purely imaginary term when its real part is nul :
⇒ 8 - n = 0
⇒ 8 = n
………………………………………
If we take n = 8
⇒ -6 + 2n = -6 + 2×8 = -6 + 16 = 10
Therefore,
The term of the arithmetic progression 8 - 6i, 7 – 4i, 6 — 2i, ... which is purely imaginary is :
10i
Felix is constructing a three-dimensional figure. First he draws the views for the figure. A bottom row of 6 cubes, second row of 3 cubes, and top row of 3 cubes. A column of 2 cubes. A bottom row of 6 cubes, and second row of 2 cubes. Column of 3 cubes. Which views can Felix use to construct the same figure? A bottom row of 6 cubes, second row of 3 cubes, and top row of 1 cube. A bottom row of 6 cubes and second row of 2 cubes. A bottom row of 6 cubes, second row of 3 cubes, and top row of 1 cube. A bottom row of 6 cubes and second row of 2 cubes. A bottom row of 6 cubes, second row of 3 cubes, and top row of 1 cube. A column of 2 cubes. A column of 3 cubes. A bottom row of 6 cubes and second row of 2 cubes. A column of 2 cubes. A column of 3 cubes.
A view which Felix can use to construct the same figure include the following: A. a bottom row of 6 cubes, second row of 3 cubes, and top row of 1 cube.
What is an isometric sketch?In Mathematics and Geometry, an isometric sketch is sometimes referred to as an isometric drawing and it can be defined as a graphical (pictorial) representation of a physical object or geometric shape in technical and engineering drawings, especially by drawing all its three dimensions (3D) at full scale;
Front viewEnd viewPlanIn this context, we can reasonably infer and logically deduce that the front view is a view which Felix can use to construct the same three-dimensional figure because its orientation influences the other views.
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HELP PLEASE ASAP!!!
The entire graph of the function g is shown in the figure below. Write the domain and range of g as intervals or unions of intervals.
Answer:
D= [-4,-1) U (2,4)
R = [-3,5)