Answers
The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.
What is the piecewise defined function behind the graph?
In this problem we have a piecewise defined function formed by three functions: (i) Linear equation, (ii) Quadratic equation, (iii) Linear equation. The first function is y = 40, for 0 ≤ x < 15.
The second function can be found based on the knowledge of three points:
y = a · x² + b · x + c
(x₁, y₁) = (15, 40)
40 = 225 · a + 15 · b + c
(x₂, y₂) = (45, 2.5)
2.5 = 2025 · a + 45 · b + c
(x₃, y₃) = (65, 20)
20 = 4225 · a + 65 · b + c
And the quadratic equation is y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65.
And the latter linear equation is:
y = m · x + b
m = (30 - 20)/(90 - 65)
m = 0.4
And the x-intercept is:
b = y - m · x
b = 20 - 0.4 · 65
b = - 6
The linear equation is y = 0.4 · x - 6, for x ≥ 65.
The piecewise defined function is formed by the following three functions: y = 40, for 0 ≤ x < 15, y = 0.0425 · x² - 3.8 · x + 87.438, for 15 ≤ x < 65 and y = 0.4 · x - 6, for x ≥ 65.
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Related Questions
Store A has sold 67 mugs and sells 11
mugs every week. Store B has sold 13
mugs and sells 17 mugs every week.
How many weeks (w) will it be before
Store B sells as many mugs (m) as
Store A?
m = 11w + 67
m = 17w + 13
[?] weeks
Answers
Answer:
9 weeks.
Step-by-step explanation:
m = 11w + 67
m = 17w + 13
So:
11w + 67 = 17w + 13
67 - 13 = 17w - 11w
54 = 6w
w = 9.
If Avogadro's number of pennies is divided equally among the 246 million men, women, and children in the United States, how many dollars would each receive
Answers
USD per person = $[tex]2.31[/tex] × [tex]10^{13}[/tex].
What is the US dollar?The US dollar is the official currency of the United States and a number of other countries. The Coinage Act of 1792 established the United States dollar on equal footing with the Spanish silver dollar, divided it into 100 cents, and authorized the minting of coins denominated in dollars and cents.To find how many dollars would each receive:
Avogadro's number of pennies is divided equally among 261 million people.
Avogadro's number is [tex]6.022[/tex] × [tex]10^{23}[/tex].
To find the number of pennies each person will receive, we divide [tex]6.022[/tex] × [tex]10^{23}[/tex] by 261 million.
Pennies per person = [tex]\frac{6.022 * 10^{23} }{261 million} = \frac{6.022 * 10^{23} }{261 * 10^{6} } = 2.31 * 10^{15}[/tex]
This is equal to the number of cents each person receives.
To convert pennies into dollars, 1 USD = 100 pennies, divide [tex]2.31 * 10^{15}[/tex] by [tex]100[/tex].
USD per person = [tex]\frac{2.31 * 10^{15} }{100} = $2.31 * 10^{13}[/tex]
Therefore, USD per person = $[tex]2.31[/tex] × [tex]10^{13}[/tex].
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The question you are looking for is here:
If Avogadro's number of pennies is divided equally among the 261 million men, women, and children in the United States, how many dollars would each receive?
The formula m =1/2(a+b) gives the mean M of two numbers a and b
a.express a in terms of m and b
b.hence find a when m=19 and
b=23
Answers
Answer:
a = 2m - b , a = 15
Step-by-step explanation:
(a)
m = [tex]\frac{1}{2}[/tex] (a + b) ← multiply both sides by 2 to clear the fraction
2m = a + b ( subtract b from both sides )
2m - b = a
(b)
when m = 19 and b = 23 , then
a = 2(19) - 23 = 38 - 23 = 15
a. 'a' in terms of m and b is given by: a = 2m - b.
b. when m = 19 and b = 23, the value of 'a' is 15.
a. To express a in terms of m and b, we can rearrange the mean formula:
m = (1/2)(a + b)
Now, we'll solve for 'a':
Multiply both sides by 2 to eliminate the fraction:
2m = a + b
Subtract 'b' from both sides:
2m - b = a
So, 'a' in terms of m and b is given by: a = 2m - b.
b. Now that we have the expression for 'a', we can find its value when m = 19 and b = 23:
a = 2m - b
a = 2(19) - 23
a = 38 - 23
a = 15
So, when m = 19 and b = 23, the value of 'a' is 15.
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Experiments done without replacement will result in:
Answers
When sampling is finished without replacement, each member of a population could also be chosen just once. during this case, the chances for the second pick are full of the results of the primary pick. The events are considered to be dependent or not independent.
lets understand with the help of an Example
You have a good, well-shuffled deck of 52 cards. It consists of 4 suits. The suits are clubs, diamonds, hearts and spades. There are 13 cards in each suit consisting of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king) of that suit.
Sampling without replacement:
Suppose you decide three cards without replacement. the primary card you choose out of the 52 cards is that the K of hearts. you place this card aside and pick the second card from the 51 cards remaining within the deck. it's the three of diamonds. you place this card aside and pick the third card from the remaining 50 cards within the deck. The third card is that the J of spades. Your picks are . Because you have got picked the cards without replacement, you can not pick the identical card twice.
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100 POINTS!!! PLEASE HELP ASAP EXPERTS! PLEASE I'M BEGGING!!
The function H(t) = −16t2 + 64t + 12 shows the height H(t), in feet, of a baseball after t seconds. A second baseball moves in the air along a path represented by g(t) = 10 + 10.4t, where g(t) is the height, in feet, of the object from the ground at time t seconds.
Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)
Part B: Explain what the solution from Part A means in the context of the problem. (4 points)
Answers
Answer:
A)
[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]
Between 3 and 4 seconds.
B) The baseballs will collide between 3 and 4 seconds.
Step-by-step explanation:
Given functions:
[tex]H(t)=-16t^2+64t+12[/tex]
[tex]g(t)=10+10.4t[/tex]
Part ASubstitute the values of t = 1, 2, 3 and 4 into the two functions:
[tex]H(1)=-16(1)^2+64(1)+12=60[/tex]
[tex]H(2)=-16(2)^2+64(2)+12=76[/tex]
[tex]H(3)=-16(3)^2+64(3)+12=60[/tex]
[tex]H(4)=-16(4)^2+64(4)+12=12[/tex]
[tex]g(1)=10+10.4(1)=20.4[/tex]
[tex]g(2)=10+10.4(2)=30.8[/tex]
[tex]g(3)=10+10.4(3)=41.2[/tex]
[tex]g(4)=10+10.4(4)=51.6[/tex]
Create a table with the found values:
[tex]\begin{array}{|c|c|c|}\cline{1-3} t & H(t) & g(t)\\\cline{1-3} 1 & 60 & 20.4\\\cline{1-3} 2 & 76 & 30.8\\\cline{1-3} 3 & 60 & 41.2\\\cline{1-3} 4 & 12 & 51.6\\\cline{1-3} \end{array}[/tex]
The solution to H(t) = g(t) is between 3 and 4 seconds as:
When t = 3, H(t) > g(t)
When t = 4, H(t) < g(t)
To prove this, equate the equations and solve for t:
[tex]\implies -16t^2+64t+12=10+10.4t[/tex]
[tex]\implies -16t^2+53.6t+2=0[/tex]
Using the Quadratic Formula to solve for t:
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
[tex]\implies t=\dfrac{-53.6 \pm \sqrt{53.6^2-4(-16)(2)} }{2(-16)}[/tex]
[tex]\implies t=\dfrac{53.6 \pm \sqrt{3000.96}}{32}[/tex]
[tex]\implies t=3.39, -0.04\:\:(\sf 2\:d.p.)[/tex]
As time is positive, t = 3.39 s (which is between 3 and 4 seconds).
Part BWhen the two baseballs are at the same height they will collide.
Therefore, the baseballs will collide between 3 and 4 seconds (when t = 3.39 s).
Jagrit is looking at two computer repair stores.
Store 1: Data-Fix
The total cost charged by Data-Fix is represented by the graph
as shown.
a) Write an equation to model the relation of total cost, C, and
number of hours, n as shown in the graph.
b) One of the points on the graph is (3, 60). Explain the
meaning of this point, in the context of this scenario.
Store 2: Comput-Repair
It charges a fixed cost of $10 plus $15 per hour for repair
services.
c) Write an equation to model the relation of total cost, C, and
number of hours, n, in Comput-Repair.
d) On the grid provided, graph the line that describes the fee structure for Compu-Repair.
e) What are the coordinates of the point of intersection?
f) What does it mean in this scenario?
g) Based on the point of intersection, how would you advise Jagrit when trying to choose between the two
computer repair stores? Fully explain your answer supported by the information from the graph.
PLEASE I DON'T HAVE TIME
Answers
See below for the solution of each question
The equation of the modelThe points are given as:
(3,60) and (5, 80)
The equation is calculated as:
[tex]C(n) = \frac{C_2 -C_1}{n_2 -n_1} * (n - n_1) + C_1[/tex]
This gives
[tex]C(n) = \frac{80- 60}{5-3} * (n - 3) + 60[/tex]
Evaluate the quotient
C(n) = 10 * (n - 3) + 60
Expand
C(n) = 10n - 30 + 60
Evaluate
C(n) = 10n + 30
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10n + 30
Explain the points on (3, 60)The point (3, 60) means he paid $60 for 3 hours
The equation of the model for Comput-RepairHere, we have:
Fixed = $10
Hourly rate = $15
The equation is calculated as:
C(n) = Fixed + Rate * Number of hours
This gives
C(n) = 10 + 15n
Hence, the relation of total cost, C, and number of hours, n is C(n) = 10 + 15n
The graph of the fee structure for Compu-RepairThe equation is represented as:
C(n) = 10 + 15n
See attachment for the graph
The coordinates of the point of intersectionThis is the point where the two lines intersect.
From the graph, we have the point of intersection to be:
(n, C(n)) = (4, 70)
The meaning in this scenarioThis means that the charges for Comput-Repair and Data-Fix are the same after 4 hours
Advice JargitBased on the point of intersection, it is best that Jargit uses Compu-Repair because they have a lesser hourly rate
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Charlotte is solving the following equation for X (x+3)^2-10=2 her first steps are given below (x+3)^2=12 x+3= + square root 12
Answers
The values of the x in the given equation are x = 6.46 and x = -0.46
Solving an equationFrom the question, we are to solve the equation for x
The given equation is
(x+3)² -10 = 2
First, add 10 to both sides of the equation
(x+3)² -10 +10 = 2 +10
(x+3)² = 12
Now, take the square root of both sides to get
x + 3 = ±√12
∴ x = 3 ± √12
x = 3+√12 OR 3-√12
x = 3 + 3.46 OR 3 - 3.46
x = 6.46 OR -0.46
Hence, the values of the x in the given equation are x = 6.46 and x = -0.46
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Can someone help me please
Answers
Answer:
D. (4,0) and (-4,0)
C. there is one discontinuity at x=3
Step-by-step explanation:
Roots can be found by setting f(x)=0:
f(x)=(x^2-16)/(x^2-2x-3)
0=(x^2-16)/(x^2-2x-3), multiply both sides by x^2-2x-3 to get rid of the denominator
0=x^2-16, use difference of squares to factor it
0=(x+4)(x-4)
x=4,-4
Therefore the roots are (4,0) and (-4,0)
Discontinuities are when f(x) is undefined, and f(x) is undefined when something is divided by 0
Set the denominator equal to 0:
0=x^2-6x+9, use the form a^2 - 2ab + b^2 to factor
0=(x-3)^2
x=3
Therefore, there is a discontinuity at x=3
What is the midpoint of the segment shown below?
Answers
Answer:
The correct answer choice is D
which of the following is equivalent to the logarithmic equation below?
Answers
Answer:
A
Step-by-step explanation:
using the rule of logarithms
[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex] , then
[tex]log_{2}[/tex] 8 = 3 ⇒ 2³ = 8
Answer:
A
Step-by-step explanation:
loga(b)=x
a^x=b
since the answer to log2(8)=3
a^3=8
b=8
a=2
so 2^3=8
I hope this helped!
There are 86,400, frames of animation in 1 hour of anime.
How many frames are there per second?
There are 3,600, seconds in 1 hour.
Answers
Answer:
There are 24 frames of animation in 1 second of anime. Step-by-step explanation: There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.
what is the volume of a sphere with a radius of 6 inches
Answers
Answer:
288pi in^3 , which is 904.78 in^3 to nearest hundredth.
Step-by-step explanation:
V = 4/3 pi r^3
= 4/3 pi * 6*3
= 288pi in^3
= 904.7786842 in^3
Question 12 of 20
Subtract.
(2x²+5)-(4x-3)
OA. 2x²-4x+2
OB. -2x² +8
OC. 2x2²-4x+8
OD. -2x²+2
Answers
Answer:
C
Step-by-step explanation:
Distribute the negative, (2x^2 + 5) + (-4x+3)
Add like terms, 2x^2 - 4x +(5+3)
2x^2-4x+8
The lengths of three sides of a triangle are 2x + 1/5 feet , 4x + 1/2 feet , and x+ 1 5 . what is the perimeter of the triangle? the drondown menuto complete the answer
Answers
Answer:
7x + 9/10 ft
Step-by-step explanation:
To find the perimeter of a triangle, add the lengths of the three sides
P = 2x + 1/5 + 4x + 1/2 + x+ 1/ 5
Combine like terms
P = 7x + 2/5 +1/2
Get a common denominator
P = 7x + 2/5(2/2) + 1/2 * (5/5)
= 7x + 4/10 + 5/10
= 7x + 9/10
Solve for this equation:
x(x+3)(x+3)=0
Answers
Answer:
x^3+6x^2+9x
if you are trying to find the original function
if not, and you are trying to find the zeros is
x=-3
x=0
Step-by-step explanation:
multiply x(x+3)
x^2+3x
then multiply that by x+3 and that should give you the answer
Answer:
x = 0 or x = -3 or x = -3
Step-by-step explanation:
set up factors as:
x = 0
x + 3 = 0
x + 3 = 0
the first will remain as x = 0 while the others become x = -3 once subtracted
i hope this helped!
Player A throws the ball 25 yards to Player B. After catching the ball, Player B immediately turns 90 degrees to his left
and runs with the ball for 30 yards. At the end of the play, how far away is the ball from where it started? Round your
answer to the nearest whole number.
Answers
Answer:
39
Step-by-step explanation:
The formula d=1/2n+26 relates the nozzles pressure n (in pounds per square inch) of a free hose and the maximum horizontal distance the water reaches d (in feet). How much pressure is needed to reach a fire 50 feet away?
Answers
The pounds of pressure needed to reach a fire 50 feet away is 48 pounds
Formulad = 1/2n + 26
where
n = nozzle pressure in pounds per square feetd = distance the water reachesIf d = 50 feet
d = 1/2n + 26
50 = 1/2n + 26
50 - 26 = 1/2n
24 = 1/2n
n = 24 ÷ 1/2
n = 48 pounds
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The citizens of a state may only register to vote after proving to have submitted their census survey.
Answers
The citizens of a state may only register to vote after proving to have submitted their census survey is a "false" statement.
What is census survey?In order to create statistics that define populations and their characteristics, such as age, education, housing, and income, the U.S. Census Bureau compiles data from households.
The purpose of census survey are-
We obtain this information by posing questions to members of the household regarding the occupants of the home, apartment, mobile home, or group housing.The census helps our communities decide where to build everything from homes to hospitals, from schools to supermarkets, and it provides information about who we are as a country and where we are headed. It aids in the government's decision-making about the allocation of cash and assistance to cities and states.It aids in predicting the nation's economic needs, such as those for electricity, housing, food, etc. figuring out the country's population size, standard of life, and number of unemployed people.To know more about census, here
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The complete question is-
The citizens of a state may only register to vote after proving to have submitted their census survey.(True/False)
Find the coefficient of t to the 4th power in the expansion of (-9t-9) to the 7th power select one: a. -25,515 b. -100,442,349 c. -167,403, 915 d. -4,782, 969
Answers
The coefficient of t to the 4th power in the given expansion is -167403915.
Option (c) is the correct answer.
What is an expansion?An expansion of a product of sums uses the fact that multiplication distributes across addition to represent it as a sum of products. A polynomial expression can be expanded by repeatedly substituting equivalent sum of products for subexpressions that multiply two other subexpressions, at least one of which is an addition, up until the expression becomes a sum of (repeated) products. Simplifications like grouping similar terms or canceling terms may also be used during the expansion.
Given expansion=[tex](-9t-9)^{7}[/tex]
Coefficient of the 4th power of t in the expansion,
=[tex]_{7} {C} _{7-4} (-9t)^{4}(-9)^{7-4}[/tex]
=[tex]_{7}C_{3}(-9)^{4}t^{4}(-9)^{3}[/tex]
=[tex]_{7}C_{3}(-9)^{7}t^{4}[/tex]
=[tex]35t^{4}(-9)^{7} \\[/tex]
=[tex]35t^{4}(4782969)[/tex]
= -167403915[tex]t^{4}[/tex]
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A study analyzed the average yearly salt intake in the united states from 2012 thru 2017. the data is summarized in the table: the study found that the data after the year 2012 can be modeled by the function f(x) = 52.3x + 3,548, where x is the the number of years since 2012 and f(x) is the total amount of salt ingested in grams. describe the significance of 3,548.
Answers
The significance of 3,548 estimates the average grams of salt used in 2012.
A connection between independent variables and the dependent variable.is defined by the function.
Functions help to represent graphs and equations. A function is represented by two variables, one is dependent, and another one is an independent function.
The study discovered that the function can represent the data after the year 2012 as,
f(x) = 52.3x + 3,548
Where x is the number of years since 2012.
Hence, The significance of 3,548 estimates the average grams of salt used in 2012.
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Someone do this please
Answers
Answer: 102 degrees
Step-by-step explanation:
The remote angle theorem is that two remote angles are equivalent to the exterior angle. Both 51 degrees are remote angles, and angle 4 is the exterior.
51 + 51 = Angle 4
Angle 4 = 102 degrees
Sofa co is selling sofas with a 33% discount off the original price to reduce its stock. Calculate the discounted price of a sofa originally selling for £999.00. Please show your working.
Answers
Find the area of the convex polygon with vertices (0,5), (-1,2), (4,4), (-3,-4) and (2,0).
Answers
The area of the convex polygon is 21.5 square units
How to determine the area of the convex polygon?The vertices are given as:
(0,5), (-1,2), (4,4), (-3,-4) and (2,0)
The area is then calculated as:
A = 0.5 * |x1y2 - x2y1 +x2y3 - x3y2 + ....... |
So, we have:
A = 0.5 * |-1 * 5 - 2 * 0 + 0 * 4 - 5 * 4 + 4 * 0 - 4 * 2 +2 * -4 - 0 * -3 - 3 * 2 + 4 * 1|
Evaluate
A = 0.5 * |-43|
Remove the absolute bracket
A = 0.5 * 43
This gives
A = 21.5
Hence, the area of the convex polygon is 21.5 square units
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Can someone help me please
Answers
Answer:
[tex]y=7x[/tex]
I hope this helps and that you can give a brainliest!
Step-by-step explanation:
If x and y vary directly, that means that y is directly proportional to x. So, the parent function is y = kx.
So, by plugging in the given y=42 when x=6 into this parent function, we get:
42=6k
If we solve for k, we end up with 7.
Now if we plug in the value of k back into the parent function of this scenario, we get:
[tex]y=7x[/tex]
I am stuck on the answer for this question
Answers
Answer:
12/13
Step-by-step explanation:
Trigonometric ratio:[tex]\sf Cos \ x = \dfrac{adjacent \ side \ to \ \angle x}{hypotenuse}\\\\[/tex]
[tex]\sf = \dfrac{XY}{ZX}\\\\=\dfrac{36}{39}\\\\=\dfrac{36 \div3}{39 \div 3}\\\\=\dfrac{12}{13}[/tex]
your anwer would be 12/13 love
Juan bought a sweater for $15.95 and two shirts for $9.00 each. how much did juan spend on clothes?
Answers
Answer:
Step-by-step explanation:
Well first you have:
$15.95 for one sweater
$9.00 each for two shirts
You would double the amount $9.00 which would be:
9 + 9 = 18 or Multiply 9 x 2 = 18
So this would total to 15 + 18 = $33
The sum of a number and its reciprocal is 122/11. Find the
number.
O -11
09
O 11
Answers
Answer:
11
Step-by-step explanation:
if the some of a number is an restrocal is 122 upon 11 find the integers value of x let the number bees two values of x i e 11 and 1 upon 11 are possible hence required in future value of x is 11
By use of technology, we investigated Mary’s investment and created the model, M(x) = 3.03(1.28)2x, in thousands of dollars. What was Mary’s initial investment? $4.96 $3,030 $4,960 $3.03
Answers
Using an exponential function, it is found that Mary's initial investment was of $3,030.
What is an exponential function?An exponential function is modeled by:
[tex]y = ab^x[/tex].
In which:
a is the initial value.b is the rate of change.Her investment model, in thousands of dollars, is:
[tex]M(x) = 3.03(1.28)^{2x}[/tex]
Then a = 3.03, since we measure the amount in thousands of dollars, Mary's initial investment was of $3,030.
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Find the equation of the line through point (−1,4) and parallel to 5x+y=4. Use a forward slash (i.e. "/") for fractions (e.g. 1/2 for 12).
Answers
The equation of the parallel line is y = -5x - 1
How to determine the line equation?The equation is given as:
5x + y = 4
Make y the subject
y = -5x + 4
The slope of the above equation is
m = -5
Parallel lines have equal slope.
This means that the slope of the new line is 5
The equation is then calculated as:
y = m(x - x1) + y1
So, we have:
y = -5(x + 1) + 4
Expand
y = -5x - 5 + 4
Evaluate
y = -5x - 1
Hence, the equation of the parallel line is y = -5x - 1
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HALP URGENT PLS im dum
x =x=x, equals
^\circ
∘
Answers
Answer:
x = 55°
Step-by-step explanation:
That square box indicates a right angle.
A right angle is 90°.
We know that angle x and the 35° angle are making up this 90° angle together.
So, the equation to show what this ship looks like is the following:
[tex]x+35=90[/tex]
This is a simple equation, that if we solve, we get:
[tex]x=55[/tex]
So, x is 55°.
Considering the angle of the ray, it is found that the value of x is of x = 55º.
What is the angle of the ray?The ray has an angle of 180º. It is composed by:
Angle x.An angle of 35º.An angle of 90º.Hence:
x + 35 + 90 = 180
x = 180 - 125
x = 55º.
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