Use the given zero to write P(x) as a product of linear and irreducible
quadratic factors. P(x) = x^4 + 6x^3 + 4x^2 + 24x, zero: 2i
Answers
The polynomial P(x) = \(x^{4} + 6x^{3} +4x^{2} +24x\) can be factored as (x - 2i)(x + 2i)(x)(x + 3).
We are given that 2i is a zero of the polynomial P(x). Since complex zeros occur in conjugate pairs, -2i is also a zero of P(x). Therefore, we can express P(x) as a product of linear and irreducible quadratic factors using these zeros.
To begin, we can write P(x) as (x - 2i)(x + 2i)Q(x), where Q(x) represents the remaining factors. Since P(x) is a quartic polynomial, Q(x) must be a quadratic polynomial. We can expand the product (x - 2i)(x + 2i) using the difference of squares:
(x - 2i)(x + 2i) =\(x^{2} -(2i)^{2} =x^{2} -(4i^{2} )=x^{2} -4(-1) = x^{2} +4\).
Thus, we have P(x) = (x - 2i)(x + 2i)(\(x^{2} +4\)).
Finally, we can factor the remaining quadratic factor, \(x^{2}\) + 4, as (x - 0i)(x + 0i + 2i) = (x)(x + 2i).
Combining all the factors, we get the complete factorization of P(x) as (x - 2i)(x + 2i)(x)(x + 2i).
Therefore, P(x) can be written as a product of linear and irreducible quadratic factors as (x - 2i)(x + 2i)(x)(x + 2i).
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Related Questions
g (x) = x 3 - 3
what is the value of x when g (x) = 24? enter in the box
Answers
Answer:
69.
im not kidding, haha, good luck!
There are four security stations placed around a
stadium, labeled A through D in the figure. Each
station will be occupied by a guard chosen
randomly from a group of 6 volunteers: Aaron,
Blake, Chelsea, Daria, Eddie, and Francis. What is
the probability that Daria and Blake will be chosen
to be the security guards?
A) 1/15
B) 2/15
C) 4/15
D) 2/5
Answers
The probability of Daria and Blake being chosen together is 1/15. So correct option is A.
Describe Probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. Probabilities can be expressed as fractions, decimals, or percentages.
The concept of probability is used in a wide range of fields, including mathematics, statistics, science, engineering, finance, and economics. It is used to make predictions and decisions based on uncertain outcomes.
The probability of an event can be calculated by dividing the number of ways the event can occur by the total number of possible outcomes. This is known as the classical definition of probability. Other methods of calculating probability include empirical probability, which is based on observations or experiments, and subjective probability, which is based on personal judgment or opinion.
The total number of ways to choose 2 guards from 6 volunteers is given by the combination formula:
C(6,2) = 6! / (2! * 4!) = 15
Out of these 15 possible combinations, there is only one way to choose Daria and Blake together. Therefore, the probability of Daria and Blake being chosen together is:
1/15
So, the answer is (A) 1/15.
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suppose we have a continuous random variable over -2 < x < 5. what is p(x = 1)?
Answers
We have a continuous random variable over -2 < x < 5 so p(x = 1) = 0 because the probability at any given point for any continuous random variable is always 0.
Probability is a measure of the likelihood of a particular event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to happen.
Probability at any given position is always zero for any continuous random variable. This is because the probability of a single value occurring for a continuous random variable is always 0 because the range of values for the random variable is infinite and therefore the probability of a single value occurring is 0.
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Write one trigonometric expression that can be used to find the value of x by replacing the variable a with the correct value.
A triangle with base side labeled 4, vertical leg labeled 3, and hypotenuse labeled 5. Angle at right vertex is marked right angle. Angle at left vertex is labeled x degrees.
Answers
Evaluating x = sin^(-1)(3/5) expression using a calculator or trigonometric table will give the value of x in degrees.
To find the value of x in the given triangle with base side labeled 4, vertical leg labeled 3, and hypotenuse labeled 5, we can use the trigonometric expression involving the sine function.
The sine function relates the ratio of the length of the vertical leg to the length of the hypotenuse in a right triangle. In this case, we have:
sin(x) = opposite/hypotenuse = 3/5
Therefore, the trigonometric expression that can be used to find the value of x is: sin(x) = 3/5
By taking the inverse sine (also known as arcsine or sin^(-1)) of both sides of the equation, we can solve for x:
x = sin^(-1)(3/5)
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Write an equation to represent each graph shown on the coordinate system.
Answers
The equations represents each graph shown on the coordinate system are:
a) y = 3x + 2
b) y = 2
c) y = 2x - 2
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
We have,
The points where a line passes through them in each given graph:
a) (-1, -1) and (0, 2)
b) (-1, 0) and (2, 0)
c) (0, -2) and (1, 0)
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).
To find the slope of the line, we can use the slope formula:
m = (y₂ - y₁) ÷ (x₂ - x₁)
a)
(-1, -1) and (0, 2)
m = (y₂ - y₁) ÷ (x₂ - x₁)
m = (2 - (-1)) ÷ (0 - (-1))
m = 3 ÷ 1
m = 3
The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.
Since the given line passes through points (0, 2),
y = 3x + b
2 = 3(0) + b
b = 2.
The equation:
y = 3x + 2
b)
(-1, 0) and (2, 0)
m = (y₂ - y₁) ÷ (x₂ - x₁)
m = (0 - 0) ÷ (2 - (-1))
m = 0
the y-intercept of the line passes through points (0, 2),
y = (0)x + b
2 = b
b = 2.
The equation:
y = 2
c)
(0, -2) and (1, 0)
m = (0 - (-2)) ÷ (1 - (0))
m = 2 ÷ 1
m = 2
the y-intercept of the line passes through points (0, -2),
y = 2x + b
2 = 2(-2) + b
b = -2.
The equation:
y = 2x - 2
Hence, the equations represents each graph shown on the coordinate system are:
a) y = 3x + 2
b) y = 2
c) y = 2x - 2
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Can i have some help please
Answers
Answer:
bababooey
Step-by-step explanation:
Use the information provided to solve the word problem below. The cost of a school banquet is $65 + $11n, where n is the number of people attending. Which is the cost for 70 people? a. $147 b. $834 c. $835 d. $146 Please select the best answer from the choices provided A B C D
Answers
Answer:
$835 (Answer c)
Step-by-step explanation:
Write out the Cost function: C(n) = $65 + ($11/person)n
Then the total cost for 70 people would be C(70) = $65 + ($11/person)(70 people)
C(70) = $65 + $770 = $835 (Answer c)
Use implicit differentiation to find the points where the parabola defined by x^2-2xy+y^2+4x-8y+16=0.
has horizontal and vertical tangent lines.
The parabola has horizontal tangent lines at the point(s).....
The parabola has vertical tangent lines at the point(s)
Answers
The parabola has horizontal tangent lines at the point (-2, 0), and it has vertical tangent lines at all points where y = 0.
To find the points where the given parabola has horizontal and vertical tangent lines, we can use implicit differentiation. Let's differentiate the equation of the parabola with respect to x.
Differentiating both sides of the equation:
\(d/dx (x^2 - 2xy + y^2 + 4x - 8y + 16) = d/dx (0)\)
Using the chain rule and product rule, we obtain:
2x - 2y(dy/dx) - 2xy' + 2yy' + 4 - 8(dy/dx) = 0
Simplifying the equation gives:
2x - 2xy' + 4 - 8(dy/dx) + 2yy' = 2y(dy/dx)
Now, let's find the points where the parabola has horizontal tangent lines by setting dy/dx = 0. This will occur when the slope of the tangent line is zero.
Setting dy/dx = 0, we have:
2x - 2xy' + 4 = 0
Next, let's find the points where the parabola has vertical tangent lines. This occurs when the derivative dy/dx is undefined, which happens when the denominator of the derivative is zero.
Setting 2y(dy/dx) = 0, we have:
2y = 0
Solving for y, we find y = 0.
Substituting y = 0 into the equation 2x - 2xy' + 4 = 0, we can solve for x.
2x - 2(0)y' + 4 = 0
2x + 4 = 0
2x = -4
x = -2
Therefore, the parabola has horizontal tangent lines at the point (-2, 0), and it has vertical tangent lines at all points where y = 0.
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At the football game they sold $4 pizzas and $2 sodas which made the school$260 the number of Sodas sold was five more than three times a number of pizzas sold determine the amount of pizza and sodad sold
Answers
\(\Huge \textsf{Answer:\fbox{25 pizzas and 80 sodas sold.}}}\)
\(\Huge \textsf{Step-by-step explanation}\)
\(\LARGE \bold{\textsf{Step 1: Assign Variables}}\)
\(\textsf{Let's assign a variable for the number of pizzas sold, we will call it \textit{"p."}}\\\textsf{And we will assign the variable\textit{"s"} for the number of sodas sold.}\)
\(\LARGE \bold{\textsf{Step 2: Write equations based on the given information}}\)
\(\large \bold{ \textsf{From the problem, we know that:}}\)
\(\bullet \textsf{The school made \$260 from seeling 4 pizzas and 2 sodas.}\\\\\bullet \textsf{The number of sodas sold was five more than three times the number of pizzas sold.}\)
\(\large \bold{ \textsf{We can use this information to write two equations:}}\)
\(\text{Equation 1} : 4p + 2s = 260 \text{(since each pizza costs \$4 and each soda costs \$2)}\)
\(\text{Equation 2} : s = 3p + 5 \text{(The number of sodas sold was 3 times the number of}\\\text{pizzas sold plus 5)}\)
\(\LARGE \bold{\textsf{Step 3: Solve the system of equations}}\)
\(\large \textsf{To solve the system of equations, we can substitute Equation 2 into Equation}\\\textsf{1 for \textit{"p"}:}\)
\(\bullet \textsf{4\textit{p} + 2\textit{s} = 260}\\\\\bullet \textsf{4\textit{p} + 2(3\textit{p} + 5) = 260}\)
\(\large \textsf{Simplifying this expression gives us:}\)
\(\textsf{10\textit{p} + 10 = 260}\)
\(\large \textsf{Subtracting 10 from both sides:}\)
\(\textsf{10\textit{p} = 250}\)
\(\large \textsf{Dividing both sides by 10}\)
\(\textsf{\textit{p} = 25}\)
\(\large \textsf{Now that we know the number of pizzas sold, we can use Equation 2 to find}\\\textsf{the number of sodas sold:}\)
\(\bullet \textsf{\textit{s} = 3\textit{p} + 5}\\\\\bullet \textsf{\textit{s} = 3(25) + 5}\\\\\bullet \textsf{\textit{s} = 75 + 5}\\\\\bullet \textsf{\textit{s} = 80}\)
\(\large \textsf{So, 25 pizzas and 80 sodas were sold.}\)
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please help me with this
Answers
Answer:
B
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
HOPE THIS HELPSSSS
in linear regression, what are we trying to forecast? a) Beta parameter
b) Dependent variable
c) Independent variable
d) Y-intercept of the linee
Answers
In linear regression, we are trying to forecast the dependent variable based on the independent variable.
Option C is the correct answer.
We have,
In linear regression, the dependent variable is the outcome variable or the response variable that we want to predict or explain, while the independent variable is the predictor variable or explanatory variable that helps us in predicting the dependent variable.
The beta parameter and y-intercept are coefficients of the linear regression equation that help in determining the relationship between the dependent and independent variables.
Thus,
In linear regression, we are trying to forecast the dependent variable based on the independent variable.
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Consider the game below. Select all the strategy profiles that are Pareto-efficient. (B,D) (B,C) (A,D) \( (A, C) \)
Answers
The Pareto-efficient strategy profiles in the given game are (B,C) and (A,D).
Pareto efficiency is a concept in game theory that refers to a state where no player can be made better off without making at least one other player worse off. In other words, it represents an allocation of resources or strategies where it is impossible to improve the situation for one player without harming another.
In the given game, the strategy profiles (B,C) and (A,D) are Pareto-efficient. Let's examine each of them individually:
1. Strategy profile (B,C): In this profile, Player A chooses strategy B while Player B chooses strategy C. This profile is Pareto-efficient because if we were to change the strategy of one player, it would result in a worse outcome for the other player. Player A cannot be made better off without making Player B worse off, and vice versa.
2. Strategy profile (A,D): In this profile, Player A chooses strategy A while Player B chooses strategy D. Similar to the previous case, this profile is also Pareto-efficient. Any alteration in the strategies of the players would lead to a less favorable outcome for at least one of the players.
The remaining strategy profiles, (B,D) and (A,C), are not Pareto-efficient. For instance, in the profile (B,D), if Player A were to switch to strategy A, both players would benefit without harming the other. Hence, (B,D) is not Pareto-efficient.
In summary, the strategy profiles (B,C) and (A,D) are Pareto-efficient because any change in the strategies of the players would result in a worse outcome for at least one player. This demonstrates the concept of Pareto efficiency in the given game.
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Find the diameter of a sphere with a surface area of 196π square centimeters
Answers
\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ SA=196\pi \end{cases}\implies \begin{array}{llll} 196\pi =4\pi r^2\implies \cfrac{196\pi }{4\pi }=r^2 \implies 49=r^2 \\\\\\ \sqrt{49}=r\implies 7=r~\hfill \underset{diameter}{\stackrel{2(7)}{14}} \end{array}\)
Chelsea left the WHite House and traveled toward the capital at an average speed of 34km/h. Jasmine left at the same time and traveled in the opposite direction with an average speed of 65km/h. Find Jasmine's and Chelsea's time, rate, and distance.
Answers
The distance traveled by Jasmine and Chelsea is given by the equations of speed and J = 20.4 km and C = 39 km , where T is the time taken and T = 0.6 hours
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the speed of Jasmine be represented as S₁ = 34 km/h
Let the speed of Chelsea be represented as S₂ = 65 km/h
Now , the distance traveled by Jasmine = J
And , the distance traveled by Chelsea = C
The measure of J = measure of C
So , the distances are the same
Let the time taken by both Jasmine and Chelsea be T
Now , Speed = Distance / Time
Substituting the values in the equation , we get
Distance D = 34T
And , distance D = 65T
Now , the total distance D = 59.4 km
So , 34T + 65T = 59.4
On simplifying the equation , we get
99T = 59.4
T = 0.6 hours
Hence ,
The distance traveled by Jasmine and Chelsea are 20.4 km and 39 km respectively
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rectangular prism 4 units and 2 1/8 units2
Answers
Answer:
17/2 units^3
Explanation:
The volume of the rectangular prism is given by
Volume = width * height* length
Now we are already given that
width * height = 2 1/8 units
Therefore, our equation for volume becomes
Volume = 2 1/ 8* length
since length = 4 units, we have
Volume = 2 1/8 * 4
Volume = 17 /2 units
which is our answer!
9(x+3)=4x-3 can you guys help look for x
Answers
Answer: x=-6
Step-by-step explanation:
9(x+3)=4x-3
9x+27=4x-3 ⇔ distributive property (take off parentheses)
5x+27=-3 ⇔ subtraction property of equality (subtract 4x on both sides)
5x=-30 ⇔ subtraction property of equality (subtract 27 on both sides)
x=-6
Hope this helps!! :)
Please let me know if you have any question
Answer:
simplify both sides and get 9x+27=4x+−3 then subtract 4x and get 5x+27=−3 and subtract -27 and divide answer by 5 to get x=-6
Please help this is due soon
Answers
Answer:
c=42
Step-by-step explanation:
One mechanic services 4 drilling machines for a steel plate manufacturer. Machines break down on an average of once every 4 working days, and broakdowns tend to Poisson distribution. The mechanic can handie an average of one repair job per day. Repairs follow a negative exponential distribution: a) On the average, how many machines are waiting for service? The average number of machines waiting for service is (Round your response to three decimal places.)
Answers
Therefore, the average number of machines waiting for service is 0.083 (rounded to three decimal places).
To calculate the average number of machines waiting for service, we can use the concept of the M/M/1 queue, where arrivals follow a Poisson distribution and service times follow a negative exponential distribution.
In this case, the arrival rate (λ) is 1 breakdown every 4 working days, and the service rate (μ) is 1 repair job per day.
The utilization factor (ρ), which represents the system's utilization, can be calculated as ρ = λ/μ = (1/4)/(1) = 1/4.
The average number of machines waiting for service (Lq) can be calculated using the formula Lq = ρ² / (1 - ρ).
Plugging in the values, we have Lq = (1/4)²/ (1 - 1/4) = 1/12.
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Can you please help me I need help asap thanks
Answers
Answer:
36
Step-by-step explanation:
True/False. the amount of rainfall in your state last month is an example of discrete data.
Answers
Answer: False
Step-by-step explanation:
Discrete means secret and that data is not discrete as it can be acess by anyone.
True. The amount of rainfall in your state last month is an example of discrete data.
Explanation:The answer to the question is True. The amount of rainfall in a state last month is an example of discrete data.
Discrete data is a type of data that can only take on specific values. In this case, the amount of rainfall can be measured in specific units, such as inches or millimeters, and cannot have values between those units.
Other examples of discrete data include the number of students in a classroom, the number of cars passing through a toll booth, or the number of coins in a piggy bank.
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Set of the following functions. Find (f•g)(-9) Simplify your answer.
Answers
First, solve for (f • g)(x)
\(\begin{gathered} \text{Given:} \\ f(x)=x^2+7 \\ g(x)=-x+4 \\ \\ (f\cdot g)(x)=f(x)\cdot g(x) \\ (f\cdot g)(x)=(x^2+7)(-x+4) \\ (f\cdot g)(x)=(x^2)(-x)+(x^2)(4)+(7)(-x)+(7)(4) \\ (f\cdot g)(x)=-x^3+4x^2-7x+28 \end{gathered}\)Not that we have (f • g)(x), we solve for (f • g)(-9)
\(\begin{gathered} (f\cdot g)(x)=-x^3+4x^2-7x+28 \\ (f\cdot g)(-9)=-(-9)^3+4(-9)^2-7(-9)+28 \\ (f\cdot g)(-9)=-(-729)^{}+4(81)+63+28 \\ (f\cdot g)(-9)=729^{}+324+63+28 \\ (f\cdot g)(-9)=1144 \end{gathered}\)8y- 10 =
What is y ?
Answers
+10 +10
8y = 10
/8 /8
Y= 1.25
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 17 14 19 50
Female 6 20 18 44
Total 23 34 37 94
If one student is chosen at random,
Find the probability that the student got a B:
Find the probability that the student was female AND got a "C":
Find the probability that the student was female OR got an "B":
If one student is chosen at random, find the probability that the student got a 'B' GIVEN they are male:
Answers
The student got a B: 0.36, the probability that the student was female AND got a "C": 0.19, the probability that the student was female OR got an "B": 0.45, the student got a 'B' GIVEN they are male: 0.28.
Given the grades and gender of a group of students are summarized below: A B C Total Male 17 14 19 50Female 6 20 18 44 Total 23 34 37 94
Therefore, Total number of students = 94
The probability that the student got a B: We have to find the probability that the student got a B.
The number of students who got B = 34P (getting B) = Number of students who got B / Total number of students= 34 / 94P (getting B) = 0.36
The probability that the student was female AND got a "C": We have to find the probability that the student was female AND got a "C".
The number of female students who got C = 18P (Female AND getting C) = Number of female students who got C / Total number of students= 18 / 94P (Female AND getting C) = 0.19
The probability that the student was female OR got a B:We have to find the probability that the student was female OR got a B.
The number of female students who got B = 20
The number of male students who got B = 14
The number of students who got B (including male and female students) = 34
The number of female students who didn't get B = 44 - 20 = 24P (Female OR getting B) = (Number of female students who got B + Number of students who didn't get B) / Total number of students= (20 + 24) / 94P (Female OR getting B) = 0.45
If one student is chosen at random, find the probability that the student got a 'B' GIVEN they are male: We have to find the probability that the student got a B given they are male.
P (getting B / Male) = Number of male students who got B / Total number of male students= 14 / 50P (getting B / Male) = 0.28
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{...,-3 -2 -1 0 1 2 3,...}
A.irrational numbers
B.Natural numbers
C.Rational Numbers
D.Integers
E.Real numbers
F.Whole numbers
Help-
Answers
Answer:
F,D
Step-by-step explanation:
i had that test
If an object is projected upward with an initial velocity of 125 ft per sec, its height h after t seconds is h = - 161? + 125t. Find the height of the object after 5 seconds
Answers
Answer:
464 ft
Step-by-step explanation:
h = 125t - 161
h = 125(5) - 161
h = 625 - 161
h = 464
Determine whether the situation is linear or nonlinear, and proportional or nonproportional. Joanna is paid $10 per hour. The situation is (select) and (select) .
Answers
Answer:
The situation is linear and proportinal
Step-by-step explanation:
Hopes this help!!
The situation is linear and proportional for Joanna is paid $10 per hour.
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant.
Given,
Joanna is paid $10 per hour.
Let earnings of Joanna is y and number of hours be x
then,
Joanna earning in x hours
y = 10x
Which is linear equation
and
y/x = 10 = k
Earning and number of hours are proportional.
Hence, Joanna is paid $10 per hour is linear and proportional situation.
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Ann spends $14 each time she travels the toll roads. She started the month with $224 in her toll road account. The amount, A (in dollars), that
she has left in the account after t trips on the toll roads is given by the following function.
A(t)=224-14t
Answer the following questions.
(a) How much money does Ann have left in the account after 8 trips on the toll roads?
$
(b) How many trips on the toll roads can she take until her account is empty?
trips
Answers
a) After 8 trips she has $112 left in her account.
b) The total number of trips that she can do is 16.
How much money does Ann have left in the account after 8 trips on the toll roads?
We know that the amount A that she has left in the account after t trips on the toll roads is given by the following linear function.
A(t)=224-14t
The amount that she has left after 8 trips is what we will get if we evaluate the function in t = 8.
A(8) = 224 - 14*8 = 112.
She has $112 left.
B) Here we need to find the value of t such that A(t) = 0, then we need to solve:
224 - 14t = 0
224 = 14t
224/14 = t
16 = t
She can do a total of 16 trips.
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which point is not on the graph of y =2x + 3?
Answers
Answer:
i'm pretty sure its D
Step-by-step explanation:
if you make a graph yourself you'll see all the rel;relationship match except for d
the time spent waiting in the line is approximately normally distributed. the mean waiting time is 6 minutes and the standard deviation of the waiting time is 2 minutes. find the probability that a person will wait for more than 4 minutes. round your answer to four decimal places.
Answers
The probability that a person will wait for more than 4 minutes is 0.9332
\(\mu=7\text{ min}\)
\(\sigma=2\text{ min}\)
\(x=4\text{ min}\)
Using the z-score formula,
\(z=\frac{x-\mu}{\sigma}\)
Hence,
\(z=\frac{4-7}{2}\)
\(z=\frac{-3}{2}\)
\(z=-1.5\)
From the z-scores table, the probability that a person will wait for more than 4 minutes is
\(z=-1.5\)
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help with this slope
Answers
Answer:
20,100 I think
Step-by-step explanation:
Answer:
20/10
Step-by-step explanation:
goes up 20
goes to the right 10