The number of ways the 6 books can be arranged on the 4 shelves by Amanda is 360 ways
How to determine the ways of the books can be arranged?From the question, we have the following parameters that can be used in our computation:
Total number of books, n = 6
Total number of shelves, r = 4
The number of ways the books could be arranged on the shelves is calculated using the following permutation formula
Total = ⁿPᵣ
Where
n = 6 and r = 4
Substitute the known values in the above equation, so, we have the following representation
Total = ⁶P₄
Apply the permutation formula
ⁿPᵣ = n!/(n - r)!
So, we have the following representation
Total = 6!/2!
Evaluate the quotient
Total = 360
Hence, the number of ways is 360
Read more about permutation at
https://brainly.com/question/11732255
#SPJ1
Help me pls in math to solve these thank u
Step-by-step explanation:
y = mx + b
m = 3
b = 2
y = 3x + 2
______________________
y = mx + b
m = 1/2
b = -1
y = 1/2x + (-1)
y = 1/2x -1
Mike has $90,000 to invest and can invest in two different funds. He invests some of the money at 5% per year and the rest at 8% per year. How much should mike invest in each fund in order to earn $5220 from both funds per year?
Using a system of equations, Mike should invest $66,000 in investment A and $24,000 in investment B to earn $5,220 from both funds per year.
How are the amounts determined?We can solve a system of equations to determine the amounts that should be invested in each fund to earn the stated amount yearly.
A system of equations is also called simultaneous equations because they can be solved together.
The total investible funds = $90,000
The expected annual earnings = $5,220
The earnings from investment A = 5% or 0.05
The earnings from investment B = 8% or 0.08
Equations:A + B = 90,000 ... Equation 1
0.05A + 0.08B = 5,220 ... Equation 2
Multiply equation 1 by 0.05:
0.05A + 0.05B = 4,500 ... Equation 3
Subtract Equation 3 from Equation 2:
0.05A + 0.08B = 5,220
-0.05A + 0.05B = 4,500
=0.03B = 720
= 24,000 (720/0.03)
B = $24,000
From Equation 1, substitute B = 24,000 to get A:
A + B = 90,000
A + 24,000 = 90,000
= 66,000
A = $66,000
Thus, we can conclude that Mike with $90,000 should invest $66,000 in Investment A earning 5% per year, and $24,000 in Investment B earning 8% annually to earn a total of $5,220 from both funds.
Learn more about a system of equations at https://brainly.com/question/12526075
#SPJ1
Write the equation of each parabola in vertex form Vertex=(1,3) Point =(2,5)
[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\begin{cases} h=1\\ k=3 \end{cases}\implies y=a(x-1)^2 + 3\hspace{5em}\textit{we also know that} \begin{cases} x=2\\ y=5 \end{cases} \\\\\\ 5=a(2-1)^2 + 3\implies 2=a(1)^2\implies \cfrac{2}{(1)^2}\implies 2=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=2(x-1)^2 +3 \end{array}} ~\hfill[/tex]
1. To call London, a long distance phone company charges a fixed rate for the first minute different rate for each additional minute. If a 12 minute phone call costs $2.35 and a 25 inute call costs $3.65, how much are their rates?
With the Application of Algebraic expression first minute call charge is $1.126 and next every minute will be charge at $0.14
what is Algebraic expression?
Using the operations +, -,, or, a group of numbers or variables can be combined to form an expression. Expressions in algebra that include variables, numbers, and mathematical operators differ from expressions in arithmetic that simply contain numbers and mathematical operators.
solution:
Let first min charge =x
And charge for each additional minute = y
Now we have two equations
x+11y=2.35……(1)
x+17y=3.65……..(2)
Sub. (1) from (2)
6y = 1.3
y= 0.316
Put value in equation (1)
x+11×0.316=2.35
x=2.35- 3.476
X= 1.126
Therefore, first minute call charge is $1.126 and next every minute will be charge at $0.14
To learn more about Algebraic expression from the given link
https://brainly.com/question/4344214
#SPJ1
essment
15. Tolen has 18 dog treats. He gives the
same number of treats to 6 dogs at the
animal shelter. Which two equations
could be used to find the number of
treats each dog gets?
A
(B)
18+6=24 and 24 - 6 = 18
18 6 3 and 6 X 3 = 18
18
D6÷3=2 and 6 ÷ 2 = 3
18 1 and 1 X 18 = 18
The two equations that could be used to find the number of
treats each dog gets is B) 18 / 6 = 3 and 6 X 3 = 18 So, the option B is the correct answer
What is an equation?
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the right-side expression from both sides' expressions, this won't limit the generality.
A condition on a variable is what an equation in algebra is. It can only be satisfied if the variable has a specific value. That indicates that only the value of x = 9 may satisfy the equation 2x - 5 = 13.
There are several sorts of equations as well, including:
Linear equations
Quadratic equations
cube-based equations
Differential equations
Parametric equations
As Tolen has 18 dog treats and he has 6 dogs to feed so each dog will get 3 treats i.e. (18 / 6 = 3) or we can there are 6 dogs and Tolen has 18 dog treats to finish so he will give 3 dog treats to each dog i.e.
(6 X 3 = 18)
Learn more about Equation from the link below
https://brainly.com/question/28971008
#SPJ1
Discuss the coordinates of a point P(x, y) on a coordinate plane, and how these can be
described by its distance, r, from the origin and the angle made with the positive x-axis.
The distance between any coordinate (x,y) and the origin is given by the equation presented as follows:
D = square root of (x² + y²).
The angle between these coordinates and the positive x-axis is given as follows:
Angle = arctan(y/x).
How to obtain the distance and the angle?The distance between two points on a coordinate line is equivalent to the hypotenuse of a right triangle.
The sides of the triangle are represented by the differences of the x-coordinates and the y-coordinates of each point.
For the origin, the coordinates are (0,0), hence the distance of any point from the origin is given by the equation presented as follows:
D = square root of (x² + y²).
For the angle, we have that:
The opposite side to the angle is the difference between the y-coordinates.The adjacent side to the angle is the difference between the x-coordinates.Hence the tangent is applied, as follows:
tan(Angle) = y/x
Angle = arctan(y/x).
More can be learned about the distance between two points at https://brainly.com/question/7243416
#SPJ1
The height of a model rocket, H(t), is a function of the time since it was
launched, t.
Height (feet)
450-
400-
350-
300-
250-
200-
150-
100
50-
0
0
H(t)
10
30
20
Time (seconds)
What is the domain of H(t)?
40
Step-by-step explanation:
the domain is the interval or set of all valid x- (or input-)values. in our case here t-values.
the graph shows us
0 <= t <= 35
For the given condition on the graph, the domain of the function is
0 ≤ t ≤ 36.
What is function?A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical connections in the sciences. A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output.
Here,
The correct answer is option B. 0 ≤ t ≤ 36
To do this question, the main thing is to look at picture.
We know from the graph that this is a quadratic function, So t has to be less than some positive number.
{ if t → -∞, H(t) → -∞, not in the line with the actual situation}
and look at the graph, the point where H(t) equals zero, one is 0 and one is 36.
The domain for the function is 0 ≤ t ≤ 36 for given condition in the graph.
For more information on function,
brainly.com/question/28193995
#SPJ5
If a sum of $500 were shared among a group of people in the following ratios, how much would each person receive?
a. 6:4
b. 1:4:5
c. 1:8:1
d. 8:9:8
e. 10:5:4:1
the temperature Monday evening was 16.4 c the temperature dropped an average of 1 1/4 degrees each hour for the next 14 hours until it reached its lowest temperature for the day on Tuesday. The high temperature was 21.3 C. What is the difference between the low temperature and the high temperature on Tuesday?
The difference between the low temperature and the high temperature on Tuesday is -1.1°C.
What is the difference between the low temperature and the high temperature on Tuesday?From the information given, the temperature Monday evening was 16.4 c the temperature dropped an average of 1 1/4 degrees each hour for the next 14 hours until it reached its lowest temperature for the day on Tuesday.
Therefore, the temperature on Tuesday will be:
= 1 1/4(14)
= 17.5
The difference in the temperature will then be:
= 16.4°C - 17.5°C
= -1.1°C.
Learn more about temperature on:
brainly.com/question/24746268
#SPJ1
don't deposited $7,000 in an account earning 10% interest compounded annually to the nearest cent how much interest will he earn in 4 years
Interest in $2800 when deposited $7,000 in an account earning 10% interest compounded annually.
Define simple interest.Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows $5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Given
Principal = $7000
Rate = 10%
Time = 4 years
Using simple interest formula,
PRT
7000 × 0.1× 4
2800
Interest in $2800 when deposited $7,000 in an account earning 10% interest compounded annually.
To learn more about simple interest, visit:
https://brainly.com/question/28739900
#SPJ1
Answer: 3,248.70
Step-by-step explanation: You can use this formula when working with compound interest:
B=p(1+r)t
In this formula, B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
The interest is the balance minus the principal.
solve
Write the rate as a decimal.
10%=0.10
Calculate the balance.
B
= p(1+r)t
= $7,000(1+0.10)4
= $7,000(1.10)4
= $7,000(1.4641)
= $10,248.70
Now use this to find the interest, which is the balance minus the principal.
$10,248.70–$7,000=$3,248.70
The interest will be $3,248.70.
Supposed that on January 1 you have a balance of $5600 on a credit cars whose APR is 17%, which you want to pay off in 1 year. Assume that you make no additional charges to the card after January 1.
Parts:
A. Calculate your monthly payments.
B. When the card is paid off, how much will you have paid since January 1?
C. What percentage of your total payment from part (b) is interest?
Answer:
A. $510.75
B. $6,129.00
C. 8.63%
Step-by-step explanation:
You want the monthly payments, total amount paid, and fraction going to interest for the payoff of a $5600 credit card balance at an annual rate of 17% interest.
A. PaymentsThe monthly payments can be found using the amortization formula:
A = P(r/12)/(1 -(1 +r/12)^(-12)) . . . . . P is the principal amount, r is the rate
This formula gives the monthly payment for payoff in 1 year.
A = 5600(0.17/12)/(1 -(1 +0.17/12)^-12) ≈ 510.75
The monthly payment is $510.75.
B. Total paidYou will have made 12 monthly payments of $510.75, for a total of ...
12 × $510.75 = $6,129.00
You will have paid $6,129.00.
C. Fraction to interestThe fraction of your total payoff that goes to interest is ...
(6129 -5600)/6129 = 1 -(5600/6129) ≈ 0.0863 = 8.63%
About 8.63% of your total payment is interest.
__
Additional comment
Spreadsheets and calculator apps can be used to find these values. You need to be careful to specify that payments are made at the end of the month.
The amount to interest is slightly more than half the interest that would be due if the interest rate were used to calculate simple interest. Our answer of 8.63% is slightly higher than 17%/2 = 8.5%, so passes the reasonableness check.
When m of the original line is -3,m of the perpendicular line is ……..
slope(m) of the perpendicular line is 1/3.
What is meant by slope?Slope of a line in mathematics is defined as its steepness. It is calculated as rise(difference of y- coordinates) over run(differences of x- coordinates) .
What is meant by perpendicular lines?Two lines which intercept each other at an angle of 90 degree are known as perpendicular lines.
According to the given data and using the formula of perpendicular slope(m1*m2=-1);
Slope(m1) of original line =-3
Let the slope of perpendicular line be m2
m1*m2=-1
-3*m2=-1
m2=1/3
hence slope (m2) =1/3
To learn more about slope visit to the given link:
https://brainly.com/question/28771374
#SPJ1
[tex]\int\limits x^3 \sqrt{x^2 +1} dx[/tex]
The solution to the given integration problem is;
[tex]\frac{[(x^{2} + 1)x^{\frac{3}{2} } *(3x^2 - 2)]}{15} + C[/tex]
How to evaluate an Integral?We want to integrate the function x³[√(x² + 1)dx]
This is expressed as;
∫x³[√(x² + 1)dx]
Preparing for substitution we have;
∫2x[x²√(x² + 1)/2dx]
Make u = x²
du/dx = 2x
dx = (1/2x) du
Thus, we now have;
¹/₂∫u√(u + 1)du
¹/₂∫(u^(3/2) - √u) du
Applying power rule and solving this gives us;
[tex]\frac{(x^2 + 1)x^{\frac{5}{2} } }{5} - \frac{(x^2 + 1)x^{\frac{3}{2} } }{3}[/tex]
= [(x² + 1)^(3/2) (3x² - 2)]/15 + C
Thus, that is the solution of solving the integration problem.
Read more about Integrals at; https://brainly.com/question/22008756
#SPJ1
Andrea skip counted using this number line to find the product of 4 and 7
Which division problem in the same fact family could Andrea use to check her work?
A. 0÷4=7
B. 7÷4 = 28
OC. 14÷4 = 7
D. 21+7=4
E. 28+7=4
Andrea could use 28÷7 = 4 this division problem to check her work.
Check one-by-one:
A. 0÷4=7
The answer to 7 divided by 0 is 0. This is due to the fact that dividing a non-zero number by zero is mathematically impossible. See complete response below.
B. 7÷4 = 28
The acronym PEMDAS, which stands for parenthesis, exponents, multiplication and division from left to right, as well as addition and subtraction from left to right, can be used to recall the order of operations.7 * 4 = 28 is the correct value where this value is 1.7
C. 14÷4 = 7
The value of the above is not equated because 3.5 ≠ 7
D. 21÷7 = 4
Where 21÷7 is 3. Hence this is also not a correct answer.
E. 28÷7=4
7 * 4 = 28, which is correct equation.
Hence, Andrea could use 28÷7 = 4 this division problem to check her work.
To know more about division check the below link:
https://brainly.com/question/25289437
#SPJ1
Use the figure shown for Exercises 22 and 23.
What is m∠DEG if m∠DFE=70°
The value of ∠ DEG = 20° in the given triangle. The value of b in the given triangle is 22.6.
a) ∠ DEG = ? if ∠DFE = 70°
Here, ∠F = ∠D = 70°
∠G = 90°
Sum of triangle = 180°
∠D + ∠E + ∠G = 180°
70° + 90° + x = 180°
160° + x = 180°
x = 180° - 160°
x = 20°
b) if a = 8 , c =24 then b = ?
∠DGE is right angle. It follows Pythagoras theorem:
What is pythagoras theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.DG² + GE² = DF²
8² + X² = 24²
X² = 576 - 64
X² = 512
X = 22.6
Hence, the value of b in the given triangle is 22.6.
To know more about triangle check the below link:
https://brainly.com/question/17335144
#SPJ4
Please i need help right now Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station.
The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task.
(1, 2), (2, 4), (3, 8), (4, 16)
Part A: Is this data modeling an arithmetic sequence or a geometric sequence? Explain your answer. (2 points)
Part B: Use a recursive formula to determine the time she will complete station 5. Show your work. (4 points)
Part C: Use an explicit formula to find the time she will complete the 9th station. Show your work.
Part A:
This data appears to be modeling a geometric sequence because the time to complete each station is increasing by a constant factor. For example, the time to complete station 2 is 4 minutes, which is double the time it took to complete station 1. Similarly, the time to complete station 3 is 8 minutes, which is double the time it took to complete station 2, and so on.
Part B:
To find the time Aurora will take to complete station 5 using a recursive formula, we can use the formula:
a_n = a_1 * r^(n-1)
where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).
We are given that a_1 = 2 and a_2 = 4, so we can solve for r:
r = a_2 / a_1
= 4 / 2
= 2
Then we can use this value of r to find the time it takes to complete station 5:
a_5 = a_1 * r^(5-1)
= 2 * 2^4
= 2 * 16
= 32
Therefore, Aurora will take 32 minutes to complete station 5.
Part C:
To find the time Aurora will take to complete station 9 using an explicit formula, we can use the formula:
a_n = a_1 * r^(n-1)
where a_n is the time it takes to complete station n, a_1 is the time it takes to complete station 1, and r is the common ratio (the factor by which the time increases from one station to the next).
We are given that a_1 = 2 and a_2 = 4, so we can solve for r:
r = a_2 / a_1
= 4 / 2
= 2
Then we can use this value of r to find the time it takes to complete station 9:
a_9 = a_1 * r^(9-1)
= 2 * 2^8
= 2 * 256
= 512
Therefore, Aurora will take 512 minutes to complete station 9.
say no more
which of the following identifies and describes the student model that is most consistent with the data in the table?
The correct answer to the task above about the statements which identifies and describes the student model that is most consistent with the data in the table is:
What is describes?
To describe something is to put into words its appearance, nature, attributes, etc. The word is frequently used to describe a scene or an event with vividness of personal perception. To narrate is to describe what happened in detail, usually by describing an event or series of events in the chronological sequence in which they occurred.
Student Model 1 shows that sharks and ray-finned fishes share some structural similarities and are the most closely related among the four groups.
The correct answer choice is option b.
What is meant by the classification of living organisms?
The classification of living organisms simply refers to the grouping of living things together on the basis of their similarities and differences.
However, based on the information given on the table in the image above, the sharks and ray-finned fishes share some structural similarities and are the most closely related among the four groups which is most consistent therein.
In conclusion, it can therefore be deduced from the explanation given above that the students model 1 gave a very good description of features which are consistent in the organisms.
To learn more about describes visit
https://brainly.com/question/18916761
#SPJ4
Conduct a test at the a=0.05 level of significance by determining (a) the null and alternative hypotheses, (b) the test statistic, and (c) the P-value. Assume the samples were obtained independently from a large population using simple random sampling.
Test whether p1>p2. The sample data are x1=119, n1=253, x2=134, and n2=311.
a) The hypothesis are given as follows:
Null: [tex]H_0: p_d = 0[/tex].Alternative: [tex]H_1: p_d > 0[/tex].b) The test statistic is of: z = 0.94.
c) The p-value is of: 0.1736.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that p1 is greater than p2, that is, if the subtraction is of zero, hence:
[tex]H_0: p_d = 0[/tex].
At the alternative hypothesis, it is tested if there is enough evidence that p1 is greater than p2, that is, if the subtraction is greather than zero, hence:
[tex]H_1: p_d > 0[/tex].
What are the mean and the standard error for the distribution of differences?For each sample, the mean and the standard error are given as follows:
[tex]p_1 = \frac{119}{253} = 0.4704, s_1 = \sqrt{\frac{0.4704(0.5296)}{253}} = 0.0314[/tex].[tex]p_2 = \frac{134}{311} = 0.4309, s_1 = \sqrt{\frac{0.4309(0.5691)}{311}} = 0.0281[/tex].Hence, for the distribution of differences, the mean and the standard error are given as follows:
[tex]p_d = p_1 - p_2 = 0.4704 - 0.4309 = 0.0395[/tex][tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0314^2 + 0.0281^2} = 0.0421[/tex]What are the test statistic and the p-value?The test statistic is given by the division of the estimate of the proportion of differences by the standard error, hence:
z = 0.0395/0.0421 = 0.94.
We have a right-tailed test, as we are testing if the mean is greater than a value, with z = 0.94. Hence, looking at the z-table, the p-value is of:
0.1736.
More can be learned about the test of an hypothesis at https://brainly.com/question/13873630
#SPJ1
The maximum temperature is: ______________________
Answer:
56.7C
Step-by-step explanation:
The highest temperature on the was 56.7C and it is recorded in United States on 10 July 1913
Simplify and state the restrictions on the domain:
Answer:
its the first option explanation is up top
b. An investment worth i costs $10 to withdraw, then the remaining amount is shared
between four people. Suppose each person gets $40. How much was the
investment worth?
Equation:
Solve it:
Answer:
the equation 10 = x - y
Step-by-step explanation:
Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.
We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.
We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.
Therefore, the initial value of the investment was $50.
Evaluate 11 − 2(12 + 4) ÷ 2^2 need step by step process, thanks.
Find the slope (-2,-9) and (-1,-3)
-3+9. -6
------= ---
-2+3. -1
the answer is 6
A garden table and a bench cost $1007 combined. The garden table costs $57 more than the bench. What is the cost of the bench?
Answer:
Below
Step-by-step explanation:
bench + ( bench + 57) = 1007
2 bench = 950
bench = $ 475
QR is a midsegment of triangle BCD. Solve for the value of x.
The value of x is 3 units.
What is the mid-point segment of the triangle?
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
We have,
In ΔBCD
QR = x - 2 units
BD = x + 7 units
A line segment that connects two midpoints of the sides of a triangle is called a midsegment.
Mid-point segment of the triangle:
QR = 1/2(BD) .............(1)
x - 2 = 1/2(x + 7)
2(x - 2) = x + 7
2x - 4 = x + 7
2x - x = 7 - 4
x = 3
Hence, the value of x is 3 units.
To learn more about the mid-point segment of the triangle visit,
brainly.com/question/14317178
#SPJ1
Match each linear system with one of the phase plane direction fields.
(The blue lines are the arrow shafts, and the black dots are the arrow tips.)
I need help. I don't know how to use the eigenvalues and take that information and put it on a graph. Please explain thoroughly! Thanks.
The correct match for each linear system with one of the phase plane direction fields will be:
1:B
2:C
3:D
4:A
What is plane?
In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.
To know more about plane,
brainly.com/question/2834992
#SPJ4
The time between arrivals of small aircraft at a county airport is exponentially distributed with a mean of one hour. Round the answers to 3 decimal places. (a) What is the probability that more than three aircraft arrive within an hour? (b) If 30 separate one-hour intervals are chosen, what is the probability that no interval contains more than three arrivals? (c) Determine the length of an interval of time (in hours) such that the probability that no arrivals occur during the interval is 0.41.
(a) The probability that more than three aircraft arrive within an hour is 0.2970.
(b) The probability that no interval contains more than three arrivals is 2.56.
(c) The length of an interval of time is 0.891 hours.
The time between arrivals of small aircraft at a country airport is exponentially distributed with a mean of one hour.
(a) We will find the probability that more than three aircraft arrive within an hour,
P(X > 3) = 1 - P(X ≤ 3)
= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))
= 1 - [ ( [tex]e^{-4/3}[/tex] 1° / 0!) + ( [tex]e^{-4/3}[/tex] 1¹ / 1!) + ( [tex]e^{-4/3}[/tex] 1² / 2!) + [tex]e^{-4/3}[/tex] 1³/ 3!]
= 1 - (0.7029)
P(X > 3) = 0.2970
(b) Now we calculate probability that no interval contains more than three arrivals if 30 separate one-hour intervals are chosen,
(1 - P(X > 3)³°) = (1 - 0.2970)³°
= 2.56
(c) Let the length of an interval of time is t, the calculation for t is given as;
P(X = 0) = 0.41
[tex]e^{-t}[/tex](t)° / 0! = 0.41
[tex]e^{-t}[/tex] = 0.41
- t = ln(0.41)
- t = -0.891
t = 0.891 hours
Therefore the length of an interval of time such that the probability that no arrivals occur during the interval is 0.41 is 0.891 hours.
To know more about probability here
https://brainly.com/question/22883765
#SPJ4
The size of a wolf population in a national park increases according to the formula y=y₀ e^{0.027 t}, where t is time in years and y₀ is the initial population at time 0 . If the size of the current population is 58 wolves, find how many wolves there will be in 5 years.
In 5 years, there will be ? wolves.
(Round to the nearest whole number as needed.)
Answer:
66
Step-by-step explanation:
y = 58 e^(0.027 * 5)
y = 58 e^(0.135)
y = 58 * 1.144537
y = 66.383133
y = 66
What is the equation of the line that passes
through the point (-3, 4) and has a slope of
2/3?
Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below.
Negative 5 x minus 3.5 greater-than 6.5. Negative 5 x greater-than 10. x greater-than negative 50.
She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol
How to calculate errors did Parul make?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has different meanings to different people, it is prone to misunderstanding in public discourse. However, some distinctions are shared.
We are given
-5x - 3.5>6.5
Since, we have to solve for x
so, we will isolate x on anyone side
step-1:
Add both sides by 3.5
-5x - 3.5+3.5>6.5+3.5
-5x>10
step-2:
Divide both sides by -5
we know that whenever we divide both sides by negative sign , it's inequality gets revered
so, we get
-5x/5<-50/-5
we get
x<10
so,
She should divide both sides by -5 while she multiplied by -5 on other side and she also did not change the > symbol to a < symbol
The complete question is : Parul attempted to solve an inequality but made one or more errors. Her work and the graph she drew are shown below. What errors did Parul make? Check all that apply. She added 3.5 to both sides when she should have subtracted. She should have divided both sides by as her first step. She divided one side by -5 while multiplying the other side by -5. She did not change the > symbol to a < symbol. She used a closed circle instead of an open circle on the number line.
To learn more about inequality refer to :
https://brainly.com/question/24372553
#SPJ1