Linear Piecewise Defined Functions
Assignment Active
Graphing a Piecewise-Defined Function
Which graph represents the piecewise-defined function f(x) = -x +4, 0≤x <3 ?
6,
x 23
Answers
The graph of the function f(x) = -x +4, 0≤x <3 is shown in the first option, which is labeled as 6. This graph shows the line y = -x + 4 for x-values between 0 and 3, and the rest of the graph is undefined. Therefore, the correct answer is 6.
In this case, the function f(x) has two different formulas: one for x-values between 0 and 3 (inclusive of 0, but not inclusive of 3), and another for x-values greater than or equal to 3. The first formula is -x + 4, and the second formula is undefined.
To graph this function, we need to plot the line y = -x + 4 for x-values between 0 and 3 (inclusive of 0, but not inclusive of 3), and leave the rest of the graph undefined.
We can see that the line y = -x + 4 passes through the point (0, 4) and has a slope of -1. Therefore, we can plot the point (0, 4) and use the slope to find other points on the line. For example, when x = 1, y = -1 + 4 = 3, so we can plot the point (1, 3). Similarly, when x = 2, y = -2 + 4 = 2, so we can plot the point (2, 2).
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Related Questions
30-60-90 triangle..find the value of x?
Answers
Answer:
A. y = 9√3
Step-by-step explanation:
The relationship of the sides of the triangles are as follows:
First leg = x
Second leg = x√3
Hypotenuse = 2x
Since we know the first leg is 9, multiply that by √3.
Therefore, y = 9√3.
Find the sum of the series. 4+16/2!+64/3!+⋯ 1−ln2+(ln2)2/2!−(ln2)3/3!+⋯
Answers
The sum of the series 4 + 16/2! + 64/3! + ... is 8e^4 - 4.
The given series is a geometric series with the common ratio of 4. The general term of the series can be written as (4^n)/(n!), where n starts from 0.
To find the sum of the series, we can use the formula for the sum of an infinite geometric series:
S = a / (1 - r),
where S is the sum of the series, a is the first term, and r is the common ratio.
In this case, a = 4 and r = 4. Substituting these values into the formula, we have:
S = 4 / (1 - 4) = -4/3.
Therefore, the sum of the series 4 + 16/2! + 64/3! + ... is -4/3.
Similarly, for the series 1 - ln(2) + (ln(2))^2/2! - (ln(2))^3/3! + ..., it is an alternating series with the terms alternating in sign. This series can be recognized as the Maclaurin series expansion of the function e^x, where x = ln(2). The sum of this series is e^x = e^(ln(2)) = 2.
Therefore, the sum of the series 1 - ln(2) + (ln(2))^2/2! - (ln(2))^3/3! + ... is 2.
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Given AB= 20, BV=12, VA=14 and SR is a mid segment, find the given lengths
Answers
Given:
AB= 20, BV=12, VA=14 and SR is a mid segment.
To find:
The lengths of SR and AR.
Solution:
SR is a mid segment. So, SR is parallel to the non-included side BV and the length of SR is half of BV.
\(SR=\dfrac{1}{2}BV\)
\(SR=\dfrac{1}{2}(12)\)
\(SR=6\)
SR is a mid segment. So, it divides the included sides in two equal parts. It means R is the midpoint of VA.
\(AR=\dfrac{1}{2}VA\)
\(AR=\dfrac{1}{2}(14)\)
\(AR=7\)
Therefore, the measure of SR is 6 units and the measure of AR is 7 units.
Andres drew a circle with the center at (3,5) and a diameter of 6 units. The circle is translated 5 units to the left and 4 units down. which of the coordinates is NOT on the circumference of the translated circle?
F.(-5,1)
G.(-2,-2)
H.(-4,-3)
J.(-2,-4)
Answers
Answer:
J.) (-2,-4)
Step-by-step explanation:
(Computer Exercise) In this exercise, we study the effect of educational attainment on the time spent sleeping per week using the data in PS2 Q4.dta, which contains observations for 676 individuals. Consider the simple regression model: sleep =β
0
+β
1
educ+u, where sleep is minutes spent sleeping at night per week and educ is years of schooling. (a) Find the sample mean and standard deviation of sleep and educ: (b) Draw a scatter plot of sleep versus educ. Do you observe a positive/negative/no correlation between these two variables? (c) Run the regression of sleep on educ (with an intercept). Write down the estimated equation together with the sample size and R
2
. (d) Interpret the estimated coefficient on educ: (e) Draw a scatter plot of sleep against educ with the fitted regression line (based on the regression in (c)) displayed in the same figure.
Answers
The effect of educational attainment on the time spent sleeping per week is examined using the simple regression model sleep = β0 + β1educ + u. The sample mean and standard deviation of sleep and educ can be calculated using the data in PS2 Q4.dta.
What is the sample mean and standard deviation of sleep and educ?To find the sample mean of sleep and educ, sum up all the values of sleep and educ respectively and divide by the total number of observations.
The standard deviation can be calculated by taking the square root of the variance, where the variance is the average of the squared deviations from the mean.
These calculations provide measures of central tendency and dispersion for the variables sleep and educ.
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The sum of the interior angles of a polygon is 540. what polygon is this
Answers
Answer:
pentagon has the sum of interior angles as 540
Step-by-step explanation:
i hope this will help you :)
Answer:
pentagon
Step-by-step explanation:
The sum of the interior angles of a triangle (in a plane) is 180°, the sum of the interior angles of a quadrilateral is 360°, the sum of the interior angles of a pentagon is 540°, the sum of the interior angles of a hexagon is 720°, and in general, the sum of the interior angles of an n-gon (a polygon with n sides) is 180°× (n-2).
JUST SOME EXTRA POINT YK
the sum of three and five to the third power times five plus one
Answers
Answer:
2561
Step-by-step explanation:
sum of three and five: 3 + 5 = 8
To the third power: 8^3 = 512
Times five: 512 * 5 = 2560
Plus one: 2560 + 1 = 2561
So:
2561
on a 7 question multiple-choice test, where each question has 2 answers, what would be the probability of getting at least one question wrong?
Answers
The probability of getting at least one question wrong on a 7 question multiple-choice test with two answers for each question is 1 - (1/4)^7, which is approximately 99.2%.
The probability of getting one question wrong on a 7 question multiple-choice test with two answers for each question is 1/4. This is because there are two options for each question, and if you choose the wrong one, you get the question wrong. Therefore, the probability of getting all 7 questions wrong is (1/4)^7, or one in 16,384. The probability of getting at least one question wrong on the test is 1 - (1/4)^7, which is equal to 1 - 1/16,384, or approximately 99.2%. To calculate the probability of getting at least one question wrong, you subtract the probability of getting all 7 questions correct from 1. This is because if you do not get all 7 questions correct, then you must have gotten at least one question wrong.
The complete question: On a 7 question multiple-choice test, where each question has 4 answers, what would be the probability of getting at least one question wrong? Give your answer as a fraction
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A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are
the same as the proportion of the general population of young adults in the U.S. A recent study stated that the proportion
of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected
data from a random sample of 75 adults in the city of interest, report 6 of them smoke at least twice a week or more in the
last month.
What is p-value for the claim?
Answers
The p-value for the claim is 0.0576.
We must run a hypothesis test to find the p-value for the assertion. Here are descriptions of the null and competing hypotheses:
Null Hypothesis (H₀): Young adults in the city share the same smoking patterns as young adults in general in the United States.
Alternative Hypothesis (H₁): The percentage of young adults in the city who smoke differs from the percentage of young adults in the U.S.
To analyse the data, we can perform a hypothesis test for a single proportion, more precisely a one-sample proportion test. Let's use this method to determine the p-value.
We must first calculate the sample proportion's standard error:
SE = \(\sqrt{\frac{p_{0} \times (1 - p_{0})}{n}}\)
where:
p₀ = proportion of young adults who reported smoking at least twice a week or more in the last month (given as 0.16)
n = sample size (given as 75)
SE = sqrt((0.16 * (1 - 0.16)) / 75) ≈ 0.0421
Next, we calculate the test statistic (z-score) using the observed sample proportion:
z = (\(\hat{p}\) - p₀) / SE
where:
\(\hat{p}\) = observed sample proportion (6 out of 75)
p₀ = proportion of young adults who reported smoking at least twice a week or more in the last month (given as 0.16)
SE = standard error of the sample proportion (0.0421)
\(\hat{p}\) = 6/75
\(\hat{p}\) = 0.08
z = (0.08 - 0.16)/0.0421
z ≈ -1.897
Now that we have the probability of seeing a test statistic with either tail as severe as -1.897, we can calculate the p-value.
p-value ≈ P(Z ≤ -1.897) + P(Z ≥ 1.897)
The p-value is about 0.0576, according to a standard normal distribution table or statistical software.
As a result, the claim's p-value is roughly 0.0576.
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Find the distance between the points (-8, -3) and (-8, -9).
Answers
Step-by-step explanation:
PQ=√(x2-x1)²+(y2+y1)²
x1 = -8,x2 = -8,y1= -3,y2= -9
=√(-8 -8)²+(-9-3)²
=√-12²
=√144
=12
PLEASE ANSWER ASAP !!!!! WILL GIVE BRAINLIEST
Answers
Answer:
\(\sqrt{\frac{3V}{\pi*h}} = r\)
Step-by-step explanation:
\(V = \frac{1}{3}\pi r^2h\\3V = \pi r^2h\\\frac{3V}{\pi*h} = r^2\\\sqrt{\frac{3V}{\pi*h}} = r\)
Answer:
r = +/- \(\sqrt{\frac{3v}{\pi h}\}\)
Step-by-step explanation:
v = 1/3 pi r^2 h
multiply both sides by 3
3v = pi r^2 h
dived both sides by pi h
3v/pi h = r^2
take sqrt of both sides
+/- sqrt( 3v/pi h) = r
1. Turn this standard notation 25,000,000 into scientific notation.
Answers
Answer:
25,000,000 = 2.5 × 10^7
The ^ is raised to the power.
Hope this helps :)
Step-by-step explanation:
2.5 × 10^7 = 25,000,000
Please help me! I'll give brainliest!
Answers
Answer:
16. Angle 2 is 30° and angles 1 & 3 are 150°
17. Equilateral (all sides are equal)
18. A, B, D
19. A, B. (8 angles and all sides are congruent)
20. False.
Step-by-step explanation:
angle 2 is a corresponding (ish) angle to the one marked 30°, so they are the same. and then the other angle is supplementary to the 30° one, therefore they must add up to 180 degrees. 180-30= 150 so that is angle 1 and 3.
Answer:
question 1 - angle 1 and 2 the answer is 150 and angle 3 is 30
question 2 - the triangle is an equilateral
Question 3 - A,B,D
question 4 - A,B
Step-by-step explanation:
HELPP FAST
Siobhan deposits $1200 into a savings account that pays 5.2% annual interest compounded monthly. What will be the balance after
4 years? Round to the nearest cent
Answers
Answer:
Step-by-step explanation:
A = P(1 + r/n)nt for compound interest
A = final amount
p = principal invested
r = interest rate as a decimal
t = # years invested
In this case A = 1200(1 + .03/1)1(3)
A = 1200(1.03)3
A = 1311.27
To find how much of the final total was interest you must subtract out the principal amount invested
I = 1311.27 - 1200 = $111.27
Siobhan deposits $1200 into a savings account that pays 5.2% annual interest compounded monthly. The amount will be $269.75.
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
\(CI = P\left(1 +\dfrac{R}{100}\right)^T - P\)
The final amount becomes:
\(A = CI + P\\\\A = P\left(1 +\dfrac{R}{100}\right)^T\)
A = P(1 + r/n)nt for compound interest
A = final amount
p = principal invested
r = interest rate as a decimal
t = # years invested
In this case
\(A = 1200\left(1 +\dfrac{5.2}{100}\right)^4\)
A = 1200 ( 1.22)
A = 1469.75
The total was interest you must subtract out the principal amount invested.
I = 1469.75 - 1200
I = $269.75
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A florist is making bouquets for a wedding. She starts with 85 flowers. She makes 7 bouquets. She has 15 flowers left over. What equation can be used to solve the number of flowers, x the florist uses in each bouquet?
Answers
Answer:
x = (85 - 15)/7
Step-by-step explanation:
x = (85 - 15)/7
x = 10
Which of the following is the Inverse of y = 3x?
a) f-1(x) = 1/3x b) f-1(x) = 3x c) f-1(x) = 3/x d) f-1(x) = x/3
Answers
The correct answer is d) f^(-1)(x) = x/3, as it represents the Inverse relationship of y = 3x.
To find the inverse of a function, we need to switch the roles of x and y and solve for the new y.
The given function is y = 3x.
To find its inverse, let's swap x and y:
x = 3y
Now, solve this equation for y:
Dividing both sides of the equation by 3, we get:
x/3 = y
Therefore, the inverse function of y = 3x is f^(-1)(x) = x/3.
Among the given options:
a) f^(-1)(x) = 1/3x
b) f^(-1)(x) = 3x
c) f^(-1)(x) = 3/x
d) f^(-1)(x) = x/3
The correct answer is d) f^(-1)(x) = x/3, as it represents the inverse relationship of y = 3x.
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If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.5, then P(A ∩ B) =
a. 0.10
b. 0.90
c. 0.00
d. 0.20
Answers
The probability of A and B occurring simultaneously (P(A ∩ B)) is c. 0.00.
In this scenario, A and B are stated to be mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa.
Given that P(A) = 0.4 and P(B) = 0.5, we can deduce that the probability of A occurring is 0.4 and the probability of B occurring is 0.5. Since A and B are mutually exclusive, their intersection (A ∩ B) would be an empty set, meaning no outcomes can be shared between the two events. Therefore, the probability of A and B occurring simultaneously, P(A ∩ B), would be 0.
To further clarify, let's consider an example: Suppose event A represents flipping a coin and getting heads, and event B represents flipping the same coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, the intersection of events A and B would be empty. Therefore, the probability of getting both heads and tails in the same coin flip is 0.
In this case, since events A and B are mutually exclusive, the probability of their intersection, P(A ∩ B), is 0.
Therefore, the correct answer is: c. 0.00
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What is the vertex of the parabola: y=2(x-3)2^+4
Answers
Answer:
Vertex: (3,4)
Step-by-step explanation:
Vertex form of the quadratic equation
The vertex form of the quadratic function has the following equation:
\(y=a(x-h)^2+k\)
Where (h, k) is the vertex of the parabola that results when plotting the function, and a is a coefficient different from zero.
The parabola is given as:
\(y=2(x-3)^2+4\)
Comparing with the equation:
a=2, Vertex: (3,4)
The graph of the parabola is shown in the image below
the radius of the base of a cylinder is 7cm and height is 8cm find the volume and surface area of the solid cylinder
Answers
Answer:
Volume=1232cm Surface area=660cm
Step-by-step explanation:
Volume=π x r² x t
=22/7 x 7 x 7 x 8
=1232cm
Surface area=2 x π x r x (r+t)
=2 x 22/7 x 7 x (7+8)
=44 x 15
=660cm
SORRY IF I AM WRONG, I'M TRYING MY BEST
evaluate each expression (-1) • 2 • 3
Answers
Answer:
-6
Step-by-step explanation:
-1 * 2 * 3
= -2 * 3
= -6
Answer:
-1 x 2 = -2
-2 x 3 = -6
Answer:
-6
What is the area, in square meters, of the rhombus above?
Answers
Answer:
C
Step-by-step explanation:
Answer:
Answer is D
Step-by-step explanation:
In order to find the answer you would need to multiply 7 square meters by 7.9 square meters which would get 55.3 square meters.
You buy 3.17 pounds of pears, 1.35 pounds of apples, and 1.78 pounds of grapes. what is your total bill?
pears: $1.19 per pound
apples: 1.29 per pound
grapes: 0.99
Answers
Answer:
3.17 + 1.35 + 1.78= 6.3 dollars i think
Step-by-step explanation:
Answer:
The answer is $7.40. You multiply the cost by the unit price then add them. So 3.17*1.09, 2.35*1.19, and 2.35*.99
Step-by-step explanation:
— 8х + 3y = 17
8x — 9y = — 19
Answers
Answer:
x= 83y−17 and y= 83x+17
hope it helps
which of the following is not a characteristics of a plane?
a. flat surface
b. length and width
c. two endpoints
d. undefined term
Answers
Answer:
its not b, its c
Step-by-step explanation:
two endpoints is the correct answer, im in geometry right now
Answer:
The answer to your question would be C
Step-by-step explanation:
C. two endpoints.
A plane is a flat surface that extends indefinitely in two dimensions.
so if its indefinitely extending why would there be endpoints.
THANK U PLEASE RATE THIS ANSWER <33
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Answers
Answer:
Least to greatest:
Figure C
Figure A
Figure B
-5a2 +9 – 2a + 3a+1 – 3a
А
B
-
-2a2 + 6a – 9
-15a2 6a +9
-8a² 5a - 10
-2a2 - 5a - 10
с
D
Answers
Answer:
D. -2a∧2-5a+10
Step-by-step explanation:
Christopher is choosing between two cell phone plans that offer the
same number of free minutes. T-Mobile's plan is $39.99 with additional
minutes costing $0.45 each. Verizon's plan is $44.99 with additional
minutes costing $0.40 each. Which equation will let you know how many
additional minutes, a, it will take for the two plans to cost the same? *
39.99a +0.45 = 44.99a + 0.40
39.99 a + 0.45 = 44.99a -0.40
39.99 +0.45a = 44.99 + 0.40a
39.99 + 0.45a = 44.99a +0.40
Answers
Answer:
39.99 + 0.45a = 44.99 + 0.40a you're welcome (:
tell whether each point is on the graph of f(x)=|x|.If it is, give the coordinates of another point with the same y value. (11,11)
Answers
The point (11,11) will lie on the graph of the function f(x) = IxI
What is coordinate?
The x-coordinate informs us of a point's separation from the y-axis, which is the vertical axis. The abscissa is another term for the x-coordinate. The y-coordinate shows how far a point is from the horizontal axis, or x-axis. The term "ordinate" also applies to the y-coordinate.
the function: f(x) = IxI
The function will have every positive and negative integer contained within itself.
So coordinates of another point with the same y value (11,11) will lies on the graph so as (-11,11).
Hence point (11,11) will lie on the graph of the function f(x) = IxI
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Assume X And Y Are Functions Of T. Evaluate dy/dt for 3xy-2x+5y^3= - 190, with the conditions dx/dt = 20
Answers
The expression for dy/dt is:
\(dy/dt = (40 - 60y)/(3x + 15y^2)\)
How to evaluate dy/dt for \(3xy-2x+5y^3= - 190\), with the conditions dx/dt = 20?We are given the equation:
\(3xy - 2x + 5y^3 = -190\)
To find dy/dt, we will take the derivative of both sides of the equation with respect to t:
\(d/dt (3xy - 2x + 5y^3) = d/dt (-190)\)
Using the product rule and chain rule, we get:
\(3x(dy/dt) + 3y(dx/dt) - 2(dx/dt) + 15y^2(dy/dt) = 0\)
Substituting the given value of dx/dt = 20, we have:
\(3x(dy/dt) + 3y(20) - 2(20) + 15y^2(dy/dt) = 0\)
Simplifying the above equation, we get:
\((3x + 15y^2)(dy/dt) = 40 - 60y\)
Dividing both sides by \((3x + 15y^2),\) we get:
\(dy/dt = (40 - 60y)/(3x + 15y^2)\)
Therefore, the expression for dy/dt is:
\(dy/dt = (40 - 60y)/(3x + 15y^2)\)
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In solving the beam equation, you determined that the general solution is X. y = = 1/2x^4 - 1/6q₁ x^3 + 1/2 x. Given that y'' (1) = 3 determine q1 ₁
Answers
We have the general solution of the beam equation: y = 1/2 x⁴ - (1/6)q₁ x³ + (1/2) x
Given that y'' (1) = 3
So we can find the second derivative of y: y' = 2x³ - (1/2)q₁x² + (1/2)and y'' = 6x² - q₁x
Therefore, y''(1) = 6 - q₁
From the given information: y''(1) = 3
Putting this value into the above equation:3 = 6 - q₁=> q₁ = 6 - 3=> q₁ = 3
The value of q₁ is 3.
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