The equation y = -|x - 3| + 2 written as a piecewise function is;
f(x) = {y = x - 1, if x < -3
{y = -x + 1, if x ≥ -3
How to define piecewise functions?A function can be written as piecewise function if it changes its behavior ( increasing or decreasing ) about a point.
The function f(x) = y = |x| changes its behavior at |x| = 0 i.e , x = 0 .
y = | x | = x , if x < 0
= - x , if x > 0
| x | = a => x = ± a
• | x | ≥ a ( a ≥ 0 ) => x € ( -∞ , -a ] U [ a , ∞ )
• | x | ≤ a ( a ≥ 0 ) => x € [ -a , a ]
The given function is : y = -|x - 3| + 2
The function will change its behavior when; -| x - 3 | = 0
-x + 3 = 0
x = -3
If x < -3 , then ;
y = -(-(x - 3)) + 2
y = x -3 + 2
y = x - 1
If x ≥ -3, then ;
y = -(x - 3) + 2
y = -x + 3 + 2
y = -x + 1
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Consider the following scenario.
the three-number bet
(a) Find the expected value of each $1 bet in roulette. (Round your answer to three decimal places.)
dollars
(b) Interpret it. (Round your answer to one decimal place.)
Over time, you should expect to lose about
cents for every dollar you bet.
Refer to the picture if needed
Considering a discrete distribution modeling the situation, it is found that:
a) The expected value of each $1 bet in roulette is of: -$0.988.
b) The interpretation is given as follows: Over time, you should expect to lose about 999 cents for every dollar you bet.
What is the expected value of a discrete distribution?The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
The total number of outcomes for the three-number bet is of:
10 x 10 x 10 = 1000.
As three numbers are taken, and for each number, there are 10 possible outcomes.
Hence the probability of winning is of:
p = 1/1000.
As there is only one correct sequence.
The probability of losing is of:
p = 1 - 1/1000 = 999/1000.
Considering a payout of $11 for a $1 bet, the distribution of earnings is presented as follows:
P(X = 11) = 1/1000.P(X = -1) = 999/1000.Hence the expected value of a $1 bet is calculated as follows:
E(X) = 11/1000 - 999/1000 = -$0.988.
Which means that you are expected to lose approximately 99 cents for every dollar that you bet.
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someone help pls tysm
The mean of the number of plants (d) increases by 5.5
How to compare the mean of the number of plants?From the question, we have the table of values that can be used in our computation:
In the table, we have the following rows
Plants and Number of tomatoes
The mean of the number of plants is calculated as
Mean plant = Total number of tomatoes/Total number of plants
For the four plants, we have
Total number of tomatoes = 31 + 25 + 6 + 28 = 90
Total number of plants = 4
Substitute the known values in the above equation So, we have the following equation
Mean plant = 90/4
Mean plant = 22.5
For the three plants, we have
Total number of tomatoes = 31 + 25 + 28 = 84
Total number of plants = 3
Substitute the known values in the above equation So, we have the following equation
Mean plant = 84/3
Mean plant = 28
See that the difference is an increment of
Increment = 28 - 22.5
Evaluate
Increment = 5.5
Hence, the mean increases by 5.5
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I WILL GIVE YOU BRAINLIEST JUST HELP ME PLEASE!!!!!
Answer:
B. The graph of K has a greater y-intercept
D. The graph of J has a greater slope.
Step-by-step explanation:
Given a table for function J and an equation for function K, you want to know which has the greater slope, and which has the greater y-intercept.
Y-interceptThe y-intercept is the value of the function when x=0. We see from the table that y=2 corresponds to x=0 for function J.
We see from the equation for function K that the constant is 8. This is the value of y when x=0.
Function K has the greater y-intercept (8 vs. 2).
SlopeThe slope is the change in y-value when x increases by 1 unit. We see from the table that y=7 when x=1, so the change in y from x=0 to x=1 is 7-2 = 5. The slope of function J is 5.
The equation for function K has an x-coefficient of 3. This means a change in x of 1 unit will result in a change in y of 3 units. The slope of function K is 3.
Function J has the greater slope (5 vs. 3).
Additional comment
Both functions are graphed in the attachment. The y-intercepts have their points labeled. The graph with the steeper slope is the blue line, function J.
I really need help step by step please
Answer:
190 cm²
Step-by-step explanation:
Area of prism:Area of one regular hexagon is given. Multiply 23 *2 and it will give the area of two regular hexagons.
There are 6 rectangles. Find the area of one rectangle and multiply it by 6.
Area of regular hexagon = 23 cm²
Area of rectangle = length * width
= 8 * 3
= 24 cm²
Area of the regular hexagon prism = 2* area of regular hexagon + 6*area of rectangle.
= 2*23 + 6*24
= 46 + 144
= 190 cm²
y is directly proportional to x3 When x = 10, y = 250
(a) Find a formula for y in terms of x.
Answer:
y = 0.25x³
Step-by-step explanation:
Since y is directly proportional to x³, then y = kx³, where k is a constant.
When x = 10, y = 250,
250 = k(10)³
1000k = 250
∴ k = 0.25
∴ y = 0.25x³
IXL Please Help Fast!
Suppose that the equations of line [tex]C[/tex] and [tex]D[/tex] are as follows;
[tex]C=a_{1}x+b{_1}y+c_{1}[/tex][tex]D=a_{2}x+b_{2}y+c_{2}[/tex]If these two lines are parallel to each other, the following equality must be satisfied.
[tex]\frac{a_{1}}{b_{1}} =\frac{a_{2}}{b_{2}}\neq \frac{c_{1}}{c_{2}}[/tex]In summary, the slope of the two lines must be equal to each other.
[tex]m_{C}=m_{D}[/tex]We know the equation of line [tex]C[/tex]. Then let us form the equation of line [tex]D[/tex].
[tex]C=x+7y-14[/tex][tex]D=x+7y+c_{1}[/tex]We must find the variable [tex]c_{1}[/tex] by placing the given point [tex](-3,-1).[/tex]
[tex]-3+7(-1)+c_{1}=0[/tex][tex]c_{1}=10[/tex]If we write it in slope-intercept form, the correct answer will be as follows;
[tex]y=-\frac{x}{7} -\frac{10}{7}[/tex]Look at this graph.
y
x
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
0
What is the equation of the line in slope-intercept form?
The slope-intercept definition of the linear function is given as follows:
y = x + 2.
What is the slope-intercept representation of a linear function?The slope-intercept representation of a linear function is obtained by the rule presented as follows:
y = mx + b.
The coefficients of the function, along with their meaning, are shown as follows:
m is the slope of the function, which is the amount by which the function changes when the input x changes by 1.b is the y-intercept of the function, which is the value of y at which the function changes the function crosses the y-axis, that is, when x = 0.For this problem, the values of these coefficients are given as follows:
b = 2, as the function crosses the y-axis at y = 2.m = 1, as when x increases by 1, y increases by 1.Hence the slope-intercept rule for the function is:
y = x + 2.
Missing InformationThe graph of the linear function is given by the image shown at the end of the answer.
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Hi everybody, I'm having trouble with this problem. What is 2,456.75 plus 4.75 x 32
(Please show work) Thank you!
Answer:
Step-by-step explanation:
4.75 x 32=152
2,456.75+152=2608.75
Answer:
2608.75
Step-by-step explanation:
4.75 x 32 = 152
2456.75 + 152 = 2608.75
Given a2 = 6 and a5 = –384 of a geometric sequence, what is the recursive equation for the nth term?m the text.
The recursive equation for the nth term is aₙ = -4aₙ₋₁
How to determine the recursive equation for the nth term?The definition of the functions is given as
a₂ = 2
a₅ = -384
Sequence type = Geometric sequence
The nth term of a geometric sequence is represented as
aₙ = arⁿ⁻¹
So, we have
a₂ = ar = 6
a₅ = ar⁴ = -384
Divide the equations
r³ = -384/6
Evaluate
r³ = -64
Take the cube roots
r = -4
The recursive equation for the nth term is represented as
aₙ = aₙ₋₁ * r
So, we have
aₙ = -4aₙ₋₁
Hence, the equation is aₙ = -4aₙ₋₁
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18. Vocabulary Use Distributive or Commutative to complete the definition.
According to the __________ Property of Multiplication, factors can be multiplied in any order and the product remains the same.
The correct vocabulary for the definition is Commutative.
Commutative property states that the result remains the same even if the order of the numbers are changed during operation.
For multiplication,
[tex]a*b=b*a[/tex]
Thus, the correct vocabulary for the definition is Commutative.
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A geometric progression has 99 terms, the first term is 12 and the last term is 48. What is the 50-th term?
Answer:
21.5
Step-by-step explanation:
geometric progression formula: [tex]A_{n}[/tex]=A*[tex]r^{n-1}[/tex]
where An is nth term
A is first term
r is common ratio
given [tex]A_{99}[/tex] = 48
A=12
we find r
48=12 *[tex]r^{99-1}[/tex]
48/12=[tex]r^{98}[/tex]
[tex]\sqrt[98]{4}[/tex]=r
r=1.014
so to find 50th term
[tex]A_{50}[/tex]=12*[tex]1.012^{50-1}[/tex]
[tex]A_{50}[/tex]=21.53
Find the quotient. 5 divided by 1/4
Answer:
5 : (1/4) = 201 = 20
Step-by-step explanation:
Need help again filling in the table?
Answer:
1.y=-16
2.y=-10
3.y=-4
4.y=2
hope ut helps!
have a nice night
Please help with this question
Answer:
c.
Step-by-step explanation:
You want a linear combination of the given 3×3 matrices.
StrategyWe observe that the answer choices are different in most corresponding terms, so we only need to find the value of one term in order to choose the correct answer.
Linear combinationThe expression applied to the matrices is applied to corresponding terms of the matrices. That is, for ...
[tex]C = -2A +7B[/tex]
you will have ...
[tex]c_{11}=-2a_{11}+7b_{11}\\\\c_{11}=-2(4)+7(7)=-8+49\\\\c_{11}=41[/tex]
This matches choice c.
__
Additional comment
Many graphing calculators and all spreadsheets can do the necessary calculations to help you find the desired result matrix.
Earn 100 points if you give right answer.
Answer:
Conveyor belt 1 is fasterStep-by-step explanation:
GivenConveyor belt1: m(x) = 157.1xFind the equation of p(x) using table.
We see it is a proportional relationship, therefore:
p(x) = kx125.6 = 2kk = 125.6/2k = 62.8Conveyor belt2: p(x) = 62.8x
As we see 157.1 > 62.8 which means conveyor 1 belt is faster.
Answer:
The conveyor belt 1 is faster.
Step-by-step explanation:
Speed of conveyor belt 1,
→ m(x) = 157.1x
Now the speed of conveyor belt 2,
→ p(x) = x
→ p(125.6) = 2x || p(188.4) = 3x
→ x = 125.6/2 || x = 188.4/3
→ [ p(x) = 62.8 ] || [ p(x) = 62.8 ]
Then the fastest conveyor is,
→ m(x) = 157.1x > p(x) = 62.8
→ 157.1x > 62.8
→ Conveyor 1 > Conveyor 2
Hence, the conveyor belt 1 is faster.
Please help I was sick and missed out on class.Thank you
The slope is -5/3
From the question, we have
slope, m = change in y/change in x
= (-6+1)/(8-5)
=-5/3
The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.
Slope of a Line :
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.
As a result, m = change in y/change in x = y/x is the formula for the change in y-coordinate with respect to the change in x-coordinate.
where "m" represents a line's slope.
The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.
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help 10 ponits thanks ∝
Answer:
First we convert the sentence to an equation so:
[tex] \frac{3}{4} x = 24[/tex]
Now to isolate x divide by the recuprical of 3 over 4 which is 4/3
[tex] \frac{3}{4} \times \frac{4}{3} = 24 \times \frac{4}{3} [/tex]
24x4= 96 and 3 remains.
[tex]x = \frac{96}{3} [/tex]
Now we can simplify by 3 and we will get the final answer which is
[tex]x = 32[/tex]
Round your answer to the nearest whole number. Do not include any decimals of % signs in your answer.
In a video game, to cause damage to the final boss, you must attack him with back to back critical hits. Based on your current gear in the game, you only have a 33% chance of attacking with a critical hit.
What is the probability that your first strike will be a critical hit?
What is the probability that your first strike was not a critical hit?
What is the probability that your first strike was a critical hit but not your second strike?
What is the probability that you are able to cause damage?
What is the probability that your strike was not critical but your next 2 attacks were?
The probabilities in this problem are given as follows:
First strike is a critical hit: 33%.First strike is not a critical hit: 67%.First strike is critical and the second is not: 22%.Cause damage: 11%Not critical followed by two criticals: 7%.What are the probabilities?The probabilities for each strike are given as follows:
Critical hit: 33%.Not a critical hit: 67%, as 100 - 33 = 67.The probabilities are independent, meaning that for each trial they are the same.
Thus the probability that your first strike was a critical hit but not your second strike is obtained as follows:
P = 0.33 x 0.67 = 0.2211 = 22%. (rounded).
Damage is caused with two consecutive critical hits, hence:
p = 0.33 x 0.33 = 0.11 = 11%.
The final probability, that your strike was not critical but your next 2 attacks were, is obtained as follows:
p = 0.67 x 0.33 x 0.33 = 0.07 = 7%.
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Suppose the doubling time of an investment of $10000 is 12 years. What is the annual
percentage growth rate?
A. 9.5%
B. 4.1%
C. 5.9%
The annual percentage growth rate is 5.9%
The doubling time of an investment of $10000 is 12 years
The compound interest caluclated annually can be given by
A=P(1 + r/n)^nt
where A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
20000 = 10000(1 + r)¹²
2⁻¹² = 1 + r
r = 1.059 - 1
r = 0.059
Rate of inetrest = 5.9%
Therefore, the annual percentage growth rate is 5.9%
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Eva needs to lease out a music studio to record her new album. The studio charges an
hourly fee of $50 and an initial studio-use fee of $100. Make a table of values and
then write an equation for P, in terms of t, representing the amount of money Eva
would have to pay to use the studio for t hours?
Answer:
Equation:
50t + 100 = P
Table:
T P
0 100
1 150
2 200
3 250
4 300
Step-by-step explanation:
$100 - starting value because it is the initial studio use fee
50t - since 50 dollars is the hourly fee, you have to multiply it by t (time)
pls help!!will give 18 points!!!PLS HELP
Answer:
a = 108°
b = 72°
c = 48°
d = 48°
Step-by-step explanation:
• ∠a and the 72° angle are on a straight line. Therefore they add up to 180°:
∠a + 72° = 180°
⇒ ∠a = 180 - 72°
⇒ ∠a = 108°
• ∠b and the 72° angle are corresponding angles (the angles make an F-shape). Therefore, they are equal:
∠b = 72°
• ∠d and the 48° angle are alternate angles (the angles make a z-shape). Therefore they are equal:
∠d = 48°
• ∠c and ∠d are vertically opposite angles. Therefore, they are equal:
∠c = ∠d
⇒ ∠c = 48°
Please help… offering a lot of points
Answer:
<ABC is bisected by ray BD, 2m<DBC = m<ABC, BC = 1/2AC
Step-by-step explanation:
A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as 3 c greater-than-or-equal-to 240. Which graph represents this inequality?
The number of chocolate bars, c, the sports club must sell in order to reach their goal is 80
The graph which represent the inequality 3c ≥ 240 is attached in the picture.What is the number of chocolate bars that must be sold to reach their goal?An inequality refers to a statement that has two quantities in which one is specifically less than (or greater than) another. Symbols of inequality includes:
Greater than >Less than <Equal to =Greater than or equal to ≥Less than or equal to ≤Let
The number of chocolate bars = cThe inequality that represent the situation is given by
3c ≥ 240
divide both sides by 3c ≥ 240/3
c ≥ 80
Therefore, all real whole numbers greater than or equal to 80 is the number of chocolate bars, c, the sports club must sell in order to reach their goal.
The shaded area to the right of the solid line c = 80 is the graph which represent the inequality.
Complete question:
A sports club needs to raise at least $240 by selling chocolate bars for $3.00 each. Sebastian wants to know how many chocolate bars, c, the sports club must sell in order to reach their goal. He represented this situation as 3c > 240. Which graph represents this inequality?
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Enzo has fish in two aquariums. In one aquarium, the ratio of the number of guppies to the number of goldfish is 2:3. In the other, this ratio is 3:5. If Enzo has 20 guppies in total, the least number of goldfish that he could have is
A. 29
B. 30
c. 31
d. 32
Evaluate this expression: (7 ⋅ 2) + 4^2 - 12 ÷ 4
I don't know how to figure this out
Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.
slope: 45, ordered pair: (0,94)
Answer:
[tex] \huge{ \bold{y = 45x + 94}}[/tex]
Step-by-step explanation:
Equation of a line in slope-intercept form is represented by
[tex]y = mx + c[/tex]
where
m is the slope
c is the y intercept
From the question
m = 45
In order to find c we substitute the point (0,94) into the equation y = mx + c
That's
[tex]94 = 45(0) + c \\ 94 = 0 + c \\ c = 94[/tex]
We now substitute m and c into the equation
We have the final answer as
[tex] \bold{y = 45x + 94}[/tex]
Hope this helps you
I need assistance with this math assignment
Answer:
t=1.33333 seconds
Step-by-step explanation:
1. We are give the the position function, s(t). We must differentiate s(t) twice in order to find the acceleration function, a(t).
s(t) = t⁶-2t⁵
Taking the power rule to differentiate s(t), we find the velocity function, v(t).
v(t) = d/dt (t⁶-2t⁵)
v(t) = 6t⁵-10t⁴
Differentiate v(t) using the power rule again to find the acceleration function, a(t).
a(t) = d/dt (6t⁵-10t⁴)
a(t) = 30t⁴-40t³
2. To find the other t value where acceleration is equal to zero, we must set a(t) to zero.
a(t) = 30t⁴-40t³ = 0
3. Algebraically solve for t. Factoring out 10t³ from a(t), we have:
10t³(3t-4)=0
Our solutions are t=0 and t=4/3.
The other value of t when acceleration is equal to zero is 4/3, or 1.33333 seconds.
A spinner contains the numbers 1 through 75. What is the probability that the spinner will land on a number that is not between 16 and 25, inclusive?
The probability that the spinner would land on a number that is not between 16 and 25 as required in the task content is; 13 / 15.
What is the probability that the spinner would land on a number that is not between 16 and 25?It follows from the task content that the probability that the spinner would land on a number that is not between 16 and 25, inclusive be determined.
Since the spinner contains 1 through 75, the number of event in the sample space is; 75 events.
Also, the number of events between 16 and 25, inclusive is; 10.
Therefore, the number of events outside 16 through 25 is; 75 - 10 = 65.
Therefore, the required probability that the spinner would land on a number that is not between 16 and 25 is;
= 65 / 75
= 13 / 15.
Therefore, the required probability is; 13 / 15.
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Answer:
Step-by-step explanation:
The quadratic expression x^2+7x+N can be factored as (x+g)(x+h)(x+g), where N, g, and h are integers.
Prod wrote that N can be equal to -18.
Eleanor wrote that N can be equal to 13.
Assuming Pod wrote that N could be equal to -18, Pod is correct.
What are Quadratic Equations?
A quadratic equation is an equation with a variable to the second power as its highest power term.
The Standard Form of a Quadratic Equation:
ax² + bx + c = 0
where:
x represents an unknown (variable)a, b, and c represent known numbers, where a ≠ 0x² + 7x - 18 = (x + 9)(x - 2) . . . . . g = 9, h = -2
There are no integer factors of 13 that add to give 7. 13 is prime, so the sum of its integer factors is 1+13 = 14.
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Assume that adults have IQ scores that are normally distributed with a mean of 99.2 and a standard deviation 19.5. Find the first quartile Q,, which is the IQ score separating the bottom 25% from
the top 75%. (Hint: Draw a graph)
The first quartile is
86.135 is the IQ score separating the bottom 25% from the top 75%.
The number between a data set's lowest and median is known as the first quartile. We would utilize a Z table to locate it.
As we are looking on the left side of distribution, value of z-score will be negative.
z-score equation for x : [tex]z = \frac{x-M}{S}[/tex]
[tex]x = zS+M[/tex]
where x = value we're looking for
M = Mean
= 99.2
S = Standard deviation
= 19.5
z = z-score
= -0.67
Putting the value in equation,
x = -0.67*19.5 + 99.2
= -13.065 + 99.2
= 86.135
Hence, 86.135 is the IQ score separating the bottom 25% from the top 75%.
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