The product of 3 and a number is 33. What is the number?
Answers
Answer:
11
Step-by-step explanation:
3x = 33
x = 33/3
x = 11
Answer:
The number is 11
Step-by-step explanation:
Product means multiply, is means equals
3 * n = 33
Divide each side by 3
3n/3 = 33/3
n = 11
Related Questions
In Spring 2017, data was collected from a random selection of STA 2023 students. One of the questions asked how many hours they had exercised in the past 24 hours.For the 39 randomly selected upperclassmen, the sample mean was 0.76 and sample standard deviation was 0.75.For the 35 randomly selected underclassmen, the sample mean was 0.60 and the sample standard deviation was 0.73.What is the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen?
Answers
The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16.
To find the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen, you need to subtract the sample mean of underclassmen from the sample mean of upperclassmen.
Sample mean of upperclassmen = 0.76
Sample mean of underclassmen = 0.60
Point estimate = Sample mean of upperclassmen - Sample mean of underclassmen
Point estimate = 0.76 - 0.60
Point estimate = 0.16
The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16, which indicates that on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours.
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Question 2 of 10
Question 2
"If two lines intersect, then the lines are coplanar."
Identify the following statements as the contrapositive, converse, or inverse of the
statement above.
• If two lines do not intersect, then the lines are not coplanar. inverse
+
• If two lines are coplanar, then the lines intersect. converse
• If two lines are not coplanar, then the lines do not intersect.
contrapositive
C
Answers
The inverse of the conditional statement is : if two lines do not intersect, then the lines are not coplanar.
Conditionals are commands used in programming languages to handle decisions.
Conditional statements are those that have both a hypothesis and a conclusion. It is also known as a "If-then" statement. If the conclusion and the hypothesis are both true, the conditional statement is untrue.They include conditional statements, conditional expressions, and conditional constructions. Particularly, conditionals carry out various calculations or actions according on whether a boolean condition set by the programmer evaluates to true or false. The decision is always made in terms of control flow by selecting changing the control flow based on some situation.The contrapositive statement is : If two lines are not coplanar, then the lines do not intersect.
The converse statement is : If two lines are coplanar, then the lines intersect.
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Avion buys a pair of shoes for $250 plus an 9% tax. Brandon buys a pair of shoes for $220 plus an 9% tax. Write the difference in the amount Avion and Brandon paid, including tax. Round your answer to the nearest cent.
Answers
The total amount that Avion paid (including taxes) is:
\(250(1+0.09)=250(1.09)=272.50\)dollars, and the total amount that Brandon paid (including taxes) is:
\(220\cdot(1+0.09)=220(1.09)=239.80\)dollars.
Then, the difference in the amount Avion and Brandon paid is:
\(272.50-239.80=32.70\)Answer: $32.70.
Fuzzy Temperature Control A fuzzy controller adjusts the cold air flow according to the size (V: volume) of the controlled room and its ambient temperature (T). The air flow is adjusted by controlling the angle (F) of a shutter inside the intake pipe that supplies cold air. Partial flow is proportional to the shutter angle. An angle of 90° allows maximum air flow, while an angle of 0° completely closes the shutter and stops the air flow. This is depicted in the following diagram. Intake Pipe Cold Air Flow Input Variables The table to the right shows the input and output variables of the fuzzy controller. The fuzzy knowledge base is shown below. Room Size: V Ambient Temperature: T Angle of Cold Air Flow: F Output Variable Fuzzy Knowledge Base 1 IF (V is low AND T is low) THEN F is low 2 IF (V is low AND T is medium) THEN F is medium 3 IF (V is low AND T is high) THEN F is high 4 IF (V is medium AND T is low) THEN F is medium 5 IF (Vis medium AND T is medium) THEN F is medium 6 IF (V is medium AND T is high) THEN F is high 7 IF (V is high AND T is low) THEN F is medium 8 IF (V is high AND T is medium) THEN F is high 9 IF (V is high AND T is high) THEN F is high The fuzzy sets "low", "medium", and "high" are defined next for each one of the input and output variables. 1) Room Size: V Fuzzy Membership Functions for Controlling Room Temprature 02- 0 80 100 120 60 Room Bize In Cubio Meters 2) Ambient Temperature: T Degree of Membership 0.8- 0.6 40 -low(x) -medium) high 140 160 Fuzzy Membership Functions for The Ambient Temperature 1 08- 06- 04- 02- XXX 10 30 40 50 20 Temperature in Degrees Celdout 3) Angle of Cold Air Flow: F Fuzzy Membership Functions for The Angle of Cold Air Flow 1.2 LEXEXET 0.2 0 20 60 80 100 40 Angle in Degrees low(x) -medium(x) -high(x) medium(K) -high(x) Fuzzy membership functions for the temperature (T) T Low T Medium(T) High (T) 0 1 0 0 2 1 0 0 4 1 0 0 6 1 0 0 8 1 0 0 10 0.75 0.25 0 12 0.5 0.5 0 14 0.25 0.75 0 16 0 1 0 18 0 1 0 20 0 1 0 22 0 1 0 24 0 1 0 26 0 0.75 0.25 28 0 0.5 0.5 30 0 0.25 0.75 32 0 0 1 34 0 0 1 36 0 0 1 38 0 0 1 40 0 0 1 In the above-mentioned fuzzy controller, the room size is 35 cubic meters and the ambient temperature is 28°. 1. Use the MIN/MAX method to find the fuzzy membership function for the shutter angle (F). 2. Use the center of gravity method to find the crisp value of F.
Answers
1. Using MIN/MAX method, the value of all membership functions = 0
2. Since all the values are 0, the center of gravity cannot be determined, and the crisp value of the fuzzy control system F cannot be calculated
To find the fuzzy membership function for the shutter angle (F) using the MIN/MAX method, we need to evaluate the fuzzy rules based on the given inputs for room size and ambient temperature.
Given:
Room Size (V) = 35 cubic meters
Ambient Temperature (T) = 28°
1. Evaluate the fuzzy rules:
Based on the fuzzy knowledge base, we need to determine the degree of membership for each fuzzy set for the inputs V and T. Then, using the MIN operator, we find the minimum degree of membership for each fuzzy set in F.
Using the given inputs, we can find the degree of membership as follows:
Degree of membership for Fuzzy Rule 1:
V is low (0) AND T is low (0) = MIN(0, 0) = 0
Degree of membership for Fuzzy Rule 2:
V is low (0) AND T is medium (0.5) = MIN(0, 0.5) = 0
Degree of membership for Fuzzy Rule 3:
V is low (0) AND T is high (0) = MIN(0, 0) = 0
Degree of membership for Fuzzy Rule 4:
V is medium (0) AND T is low (0) = MIN(0, 0) = 0
Degree of membership for Fuzzy Rule 5:
V is medium (0) AND T is medium (0) = MIN(0, 0) = 0
Degree of membership for Fuzzy Rule 6:
V is medium (0) AND T is high (0) = MIN(0, 0) = 0
Degree of membership for Fuzzy Rule 7:
V is high (1) AND T is low (0) = MIN(1, 0) = 0
Degree of membership for Fuzzy Rule 8:
V is high (1) AND T is medium (0) = MIN(1, 0) = 0
Degree of membership for Fuzzy Rule 9:
V is high (1) AND T is high (0) = MIN(1, 0) = 0
2. Determine the fuzzy membership function for F:
Based on the fuzzy rules and the MIN operator, the fuzzy membership function for F can be determined. Since all the degrees of membership are 0, the fuzzy membership function for F will be 0 for all values of F.
Now, to find the crisp value of F using the center of gravity method, we'll calculate the centroid of the fuzzy membership function for F. However, since all the values are 0, the center of gravity cannot be determined, and the crisp value of F cannot be calculated.
Therefore, the crisp value of F cannot be determined based on the given inputs.
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Ricardo works 44 hours at $10.00
per hour with time and a half for
all time over 40 hours. Find
Ricardo's gross pay.
Answers
Ricardo's gross pay.: $460
What is Multiplication?
A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied. For instance, the result of multiplying 6 and 5 is 30, and the result of multiplying x and (2+x) is (2+x) (indicating that the two factors should be multiplied together).
Separating the straight time with over time
44 - 40 = 4hours
Convert 4 hours to time and a half .
To do so multiply 4 hours with 1.5
4 x 1.5 = 6 hours
Adding straight time to time and a half
40 + 6 = 46
46 hours of time to compute gross pay
Multiply the total time by the rate per hour
46 x 10 = $460
Hence, Ricardo's gross pay is $460
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A particle moving along a curve in the xy-plane has position.
Answers
The position of a particle moving along a curve in the xy-plane can be described using parametric equations, where x and y are both functions of a third variable, usually time (t).
1. Parametric equations are equations that express the coordinates of a point (x, y) in the xy-plane in terms of a single variable, often time (t). In this case, x = f(t) and y = g(t), where f(t) and g(t) are functions of time.
2. To find the position of the particle at any given time, plug the value of time (t) into both functions, f(t) and g(t), to find the corresponding x and y coordinates. The position of the particle at time t is given by (x(t), y(t)).
3. To visualize the path of the particle, you can plot the curve described by the parametric equations x = f(t) and y = g(t) on the xy-plane. The particle moves along this curve as time progresses.
4. If you need to find the particle's velocity or acceleration, you can calculate the first and second derivatives of the position functions with respect to time.
In summary, the position of a particle moving along a curve in the xy-plane can be described by parametric equations, which relate the x and y coordinates to a third variable, usually time (t). The position of the particle at any given time can be found by plugging in the value of time into the parametric equations.
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Mark the statements that are true.
Answers
Answer:
Hi there!
The correct choices are: A, B, C
Step-by-step explanation:
π in radians equals to 180°
A is correct because 180/3 = 60
C is correct because 180/4 = 45
The measure angles π and π/4 is true
What is Radian and degree?Radian, When we rotate the radius completely around the circle, it completes one rotation. The angle subtended at the center of the circle by the radius after one complete rotation is 2π radians. The angle in radians subtended by the radius at the center of the circle is the ratio of the length of the arc to the length of the radius. When the length of the arc becomes equal to the length of the radius, the angle subtended at the center becomes 1 radian. We denote the unit radian as rad. Radians is the SI unit of measuring angles.
Degree Angles are measured in degrees. One revolution is divided into 360 equal parts and each part is called a degree. The angle subtended at the center of the circle after one complete rotation of the radius is 360°. The symbol for degrees is denoted by '°'. Degrees is not an SI unit to measure angles but it is an accepted unit to measure. Hence, while solving problems, it is preferred to convert the unit of angle from radians to degrees to understand it better. The instrument used to measure an angle in degrees is a protractor. Comparing the measures of the angle for a complete rotation, we observe,360 Degrees = 2π Radians180 Degrees = π Radians
According to the question
To convert radians to degrees, multiply by 180/p,
like this: degrees = radians x (180 / π )
To convert degrees to radians,
multiply by p/180, like this
radians = degrees x ( π/180)
(A)
This will use the formula for radians to degrees. π/3 x (180/π) The pi's cancel, leaving you with: 180/3 = 60 degrees False
(B)
An angle that measures π/6 radians also measures 30°π/6 x (180/π) = 30 degrees. True
(C)
An angle that measures π/3 radians also measures 60°π/3 x (180/π) = 60 degrees. True
(D) An angle that measures 180 degrees also measures π/2π/2 x (180/π) = 90 degrees. False
hence, measure angles π and π/4 is true, therefore option B and C are true
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Choose a coefficient b that makes this system singular. Then choose a right side g that makes it solvable. Find two solutions in that singular case.
2x + by =16
4x + 8y = g.
Answers
To make the system singular, we need the coefficient of one of the variables to be a multiple of the coefficient of the same variable in the other equation. Let's choose b = 4, which makes the first equation a multiple of the second:
2x + 4y = 16
4x + 8y = g
To make the system solvable, we need the two equations to not be parallel, which means the slopes must be different. Let's choose g = 32, which gives the second equation a slope of 1/2:
2x + 4y = 16
4x + 8y = 32
We can solve this system using substitution or elimination. Let's use elimination:
-2(2x + 4y = 16) -> -4x - 8y = -32
4x + 8y = 32
0 = 0
We see that the last equation is always true, which means the system has infinitely many solutions. We can find two solutions by setting x = 0 and solving for y:
2(0) + 4y = 16
y = 4
So one solution is (0,4). Now let's set y = 0 and solve for x:
2x + 4(0) = 16
x = 8
So another solution is (8,0).
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Find the Surface area of the trapezoid
please help
show work
Answers
Answer:
259.5
Step-by-step explanation:
8.1*12=97.2
Area of trapiezium = 1/2(b+a)h
(2.8+8.1)=10.9
10.9*3/2=16.35
16.35*2=32.7
2.8*12=33.6
33.6+32.7+97.2=163.5
4*12*2=96
163.5+96=259.5
Let f(x)=√3x-9 and g(x)=3x^2-9
Is f an inverse of g? Show your work algebraically and explain your answer
Answers
The function pairs f(x) =√3x - 9 and g(x) = 3x² - 9 are not inverse functions
How to determine the inverse of the functions?From the question, we have the following parameters that can be used in our computation:
The functions are given as
f(x) =√3x - 9 and g(x) = 3x² - 9
Solving f(x), we have
The function needs to be represented as an equation
y =√3x - 9
Swap the positions of x and y
x =√3y - 9
So, we have
x² = 3y - 9
Make y the subject
y = (x² + 9)/3
So, the inverse function is
g(x) = (x² + 9)/3
This is different from g(x) = 3x² - 9
Hence, they are not inverse functions
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A company that makes hair products had 9000 people try new shampoo of the 9000 people 72 had a mild allergic reaction what percent of the people had a mild allergic reaction
Answers
Answer:
0.8%
Step-by-step explanation:
Number of people had mild allergic attack = 72
% of people who had mild allergic attack = 72/9000 × 100%
= 0.8%(Answer)
Carson and Romeo are floating in a lake. They each
start swimming away from the shore.
The graph shows that the two lines in the system of
equations that represent Carson's and
Romeo's distances from shore over time are the
same lines.
Distance from Shore
Answers
The completed statement that described the situation indicated by the graph of the linear system of equations representing Carson and Romeo distance from the shore is presented as follows;
The graph of the system of equations show that Romeo was floating close to Carson and then swam alongside Carson
The system of equations represented on the graph has an infinite number of solutions because the two lines in the system of equations are the same line
What is a linear system of equations?A system of linear equations are a set of linear equations that are formed by the same variables, and which work together.
The points on the graph of the equation, obtained from a diagram of a similar question online are; (0, 5), (1, 6), (2, 7), (3, 8), (4, 9) (5, 10)
Therefore, the slope of the equation representing the distance from the shore is, m = (6 - 5)/(1 - 0) = 1
The y-intercept, the point where x = 0, is (0, 5), which indicates that the y-intercept is c = 5
The equation of the line in slope-intercept form, y = m·x + c, therefore is; y = x + 5
Please find attached the graph in the question of the equation created with MS Excel
The details of the question obtained from a similar question on the internet indicate that the graph of the equation of Carson's distances and the graph of the equation of Romeo's distances are the same straight lines.
The y-intercept of the graph represent the location where the Carson and Romeo where initially floating, therefore;
Romeo was floating close to Carson
The coinciding graphs indicates that Carson and Romeo swam side by side
The equations of the distances which are equivalent, indicates that the system of equations has an infinite number of solutions
The reason the system of equations have an infinite number of solutions is because the two lined overlap
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please help I really need this
No links!!
No spams!!
Answers
Answer:
725
Step-by-step explanation:
On another planet, the isotopes of titanium have the given natural abundances. What is the average atomic mass of titanium on that planet? average atomic. mass \( = \)
Answers
Using the given natural abundances of titanium-46, titanium-47, and titanium-48, we find that the average atomic mass of titanium on this planet is approximately 46.4 amu.
To calculate the average atomic mass of titanium on another planet, we need to consider the natural abundances of its isotopes. The average atomic mass is calculated by multiplying the mass of each isotope by its relative abundance and summing up these values.
Let's assume that the three isotopes of titanium on this planet are denoted as titanium-46, titanium-47, and titanium-48. The natural abundances of these isotopes are given as follows:
Isotope Natural Abundance
Titanium-46 70%
Titanium-47 20%
Titanium-48 10%
To calculate the average atomic mass, we multiply the mass of each isotope by its relative abundance and sum up these values. The atomic masses of titanium-46, titanium-47, and titanium-48 are approximately 46.0 amu, 47.0 amu, and 48.0 amu, respectively.
Average Atomic Mass of Titanium:
(46.0amu×70%)+(47.0amu×20%)+(48.0amu×10%)
=(32.2amu)+(9.4amu)+(4.8amu)
=46.4amu
Therefore, the average atomic mass of titanium on this planet is approximately 46.4 atomic mass units (amu).
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find c, and show your work
Answers
Answer: C = 1 square unit
Step-by-step explanation:
Since C is equal to the area (I think, by the looks of it) You can use the square units that it covers (1) and find the area.
Formula for area of a square is side length * side length. This means the area is 1 * 1.
sarah had 28 stickers and put x number of stickers on her binded. haylee had 40 stickers and put three times as many stickers on her locker as sarah put on her binder. how many stickers did sarah put on her binder if they had the same number of stickers left?
Answers
Answer:
Number of stickers Sarah had = 28
Number of stickers she put on her binder = x.
Number of stickers left with her = 28 - x
Number of stickers Haylee had = 40
Number of stickers she put on her locker = 3x
Number of stickers left with her = 40 - 3x
Both Sarah and Haylee had the same number of stickers left.
28 - x = 40 - 3x
=> 3x - x = 40 - 28
=> 2x = 12
=> x = = 6
Step-by-step explanation:
Pick the correct inequality.
A .
B.
C.
D .
Answers
Answer:
B
Step-by-step explanation:
-6 -------------------->
---------------> = x
x ------>
-6 NOT 6
Therefore is B
Assignment
about the solutions.
Martin decided to buy 3 bags of grapes weighing 4 į pounds each. How much did all 3 bags of grapes weigh?
Answers
1 bag of grapes = 4 pounds
Martin bought 3 bags so:
4 pounds x 3 = 12 pounds
Hope this helps
a home improvement builder can build decks on house. if a deck is attached to a house, then he must obtain a building permit whereas if it is not physically attached to the house then he does not. if you were to create a data model to represent this it would be a(n) data model.
Answers
If you were to create a data model to represent the scenario of a home improvement builder building decks on a house, it would be a logical data model. This model would include entities such as "home improvement builder," "house," "deck," and "building permit," and their relationships and attributes.
The data model could help in tracking building permits for attached decks, monitoring improvements and ensuring that all necessary steps are taken to ensure that the deck is built safely and in compliance with building regulations. Or to represent this situation, you can create a conditional data model. In this model, you would store information about the home improvement project, including whether the deck is attached to the house or not. Based on this data, the model will determine if a building permit is required for the deck construction. This approach allows you to efficiently manage and process the data related to building permits and deck construction in the context of home improvement projects.
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What is the sum of the 3rd
prime number and the 2nd
square number?
Answers
Step-by-step explanation:
First 3 Prime Numbers are
2 , 3 , 5
Therefore, Sum of the square of these numbers will be
2^2 + 3^2 + 5^2
= 4 + 9 + 25
= 38
Hence the answer is 38
Hello there!
The third prime number is
\(5.\)
The second square number is 4. Add them together and get 9 as your answer.
Now, what is a prime number? It's a number that has only 2 factors (1 and itself)
If you multiply a number times itself, you get a square number.
Hope this helps you!
~Just an emotional teen who listens to her favourite songs
\(Silent Nature\)
How can you write the expression 7(b – 2) in words?
Answers
Answer:
seven times the difference of a number b, and two
Step-by-step explanation:
hope this helps
Students rented buses and vans to go attend the southwood staff/ student hockey game. There were 8 vans and 12 buses for 360 students
a) write an equation to describe this relationship
b) if there were 12 students per van, how many students fit in each bus?
Answers
Therefore, each bus can hold 22 students if there were 12 students per van.
What is equation?In mathematics, an equation is a statement that asserts the equality of two expressions. Equations typically contain one or more variables, which are symbols that can represent different values. Solving an equation means finding the value or values of the variable(s) that make the equation true.
Here,
a) Let V be the number of vans and B be the number of buses. We know that there were 8 vans and 12 buses, so we can write:
V + B = 20 (the total number of vehicles)
We also know that there were 360 students in total. If we assume that each van can hold 12 students, and each bus can hold some number of students, we can write:
12V + bB = 360 (the total number of students)
where b is the number of students that each bus can hold.
b) We can use the equation we derived in part a) and substitute V = 8 to solve for B:
V + B = 20
8 + B = 20
B = 12
So there were 12 buses in total. We can then use the equation 12V + bB = 360 and substitute V = 8 and B = 12 to solve for b:
12V + bB = 360
12(8) + b(12) = 360
96 + 12b = 360
12b = 264
b = 22
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Is the vertical component of velocity ever zero? If so, where?
Answers
The vertical component of velocity can be zero at specific points in the motion of an object.
What is Velocity?
Velocity is a vector quantity that describes the rate of change of an object's position in space over time. It is defined as the displacement of an object divided by the time interval during which the displacement occurred.
The vertical component of velocity can be zero at specific points in the motion of an object. This occurs when the object reaches the highest point in its vertical motion and begins to fall back down. At this point, the vertical component of velocity changes direction from upward to downward, and its magnitude becomes zero. This moment is known as the "instant of maximum height" or "instant of maximum altitude." Beyond this point, the vertical component of velocity becomes negative, indicating that the object is moving downward.
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Solve the following equation, and check your solution. Be sure to show all work in order to receive full credit.
Solve -17 + = 33.
Answers
Answer:
250
Step-by-step explanation:
-17+n/5=33
add 17 to both sides
n/5=50
now multiply both sides by 5
n/5x5=n 50x5=250
n=250
Line RS bisects segment PQ at R. If RQ = x + 9 and RP = 2x, find PQ.
Answers
Answer:
PQ measures 36 units.
Step-by-step explanation:
Line RS bisects segment PQ at R. By the definition of a bisector:
\(\displaystyle PR = RQ\)
Hence:
We are given that RQ = x + 9 and RP = 2x, and we want to determine PQ.
Solve for x. Substitute:
\(\displaystyle (2x) = (x+9)\)
Hence:
\(\displaystyle x = 9\)
PQ is given by:
\(\displaystyle PQ = PR + RQ\)
Since PR = RQ:
\(\displaystyle PQ =2PR\)
Substitute and evaluate:
\(\displaystyle \begin{aligned} PQ &= 2PR \\ &= 2(2x) \\ &= 4x \\ &= 4(9) \\ &= 36 \end{aligned}\)
Hence, PQ measures 36 units.
Enter the equation of each line y=mx+/-b.
Answers
Answer:
1. y = 5/2x - 4
2. y = -5x - 3
3. y = 2x - 4
4. y = -4/3x - 1
5. y = -5/2x - 1
6. y = 1/4x - 2
Step-by-step explanation:
Find the present value of payments at the end of each quarter of
$245 for ten years with an interest rate of 4.35% compounded
monthly.
Answers
The present value of payments at the end of each quarter of $245 for ten years with an interest rate of 4.35% compounded monthly is approximately $25,833.42.
To find the present value of the payments, we can use the present value formula for an ordinary annuity. The formula for the present value of an ordinary annuity is:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
Where:
PV = Present Value
PMT = Payment amount
r = Interest rate per period
n = Number of periods
In this case, the payment amount is $245, the interest rate is 4.35% compounded monthly, and the number of periods is 10 years or 40 quarters (since there are 4 quarters in a year).
Let's plug in the values into the formula:
PV = $245 * ((1 - (1 + 0.0435/12)^(-40)) / (0.0435/12))
First, let's simplify the exponent part:
(1 + 0.0435/12)^(-40) ≈ 0.617349
Now, let's plug in the values and calculate:
PV = $245 * ((1 - 0.617349) / (0.0435/12))
PV = $245 * (0.382651 / 0.003625)
PV = $245 * 105.4486339
PV ≈ $25,833.42
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what is the lowest value of the rangee of the function shown on the graph? -♾️, -2, 0, 3
Answers
The correct option is -2. The range of function is found to be minimum is -2.
Explain the term minima of the function?The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, respectively. Let's first examine the function's local maximum and minimal values before delving further into maxima and minima.A function's global minimum is its lowest value across the entire function's range, whereas a localized minimum is its lowest value within a specific local area.
From the given graph of the function:
To get the lowest point of the range of the function, check the value where graph is turning.
This, shows the minima of the function which is -2 at x = 3.
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Negative air pressure created by an air pump makes a vacuum cleaner able to collect air and dirt into a bag or other container. Below are several readings from a pressure gauge. Write rational numbers to represent each of the readings, and then order the rational numbers from least to greatest.
Gauge Readings ( pounds per square inch )
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Pressure readings ( pounds per inch) answers:
Answers
The ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
To represent the gauge readings as rational numbers, we can express them as fractions with a common denominator.
Given readings:
25 psi pressure
13 psi vacuum
6.3 psi vacuum
7.8 psi vacuum
1.9 psi vacuum
2 psi pressure
7.8 psi pressure
Expressed as rational numbers with a common denominator:
25 psi = 25/1
13 psi = 13/1
6.3 psi = 63/10
7.8 psi = 78/10
1.9 psi = 19/10
2 psi = 2/1
7.8 psi = 78/10
Now, let's order these rational numbers from least to greatest:
1.9 psi = 19/10
6.3 psi = 63/10
7.8 psi = 78/10
7.8 psi = 78/10
13 psi = 13/1
25 psi = 25/1
2 psi = 2/1
Ordered from least to greatest:
19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1
Therefore, the ordered rational numbers representing the gauge readings from least to greatest are 19/10, 63/10, 78/10, 78/10, 13/1, 25/1, 2/1.
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Using a minimum of three points, create two linear functions. Prove the line created works exclusively with the three points by justifying how the x-value and y-value fit into the equation for the line.
Answers
The equation of the line passing through the point (-1, 1) and (0, 10) is y = 9x + 10
What is a linear function?A linear function is in the form:
y = mx + b
Where y, x are variables, m is the rate of change and b is the y intercept.
From the table, using the point (-1, 1) and (0, 10) ,hence:
\(y-1=\frac{10-1}{0-(-1)} (x-(-1))\\\\y=9x+10\)
The equation of the line passing through the point (-1, 1) and (0, 10) is y = 9x + 10
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