The probability that the randomly selected time interval is longer than 95 minutes while solving for the mean time of the eruptions is 0.3192.
How to solve for the probability of a ramdom sample?mean of x = 85 minutes
σ = 21.25 minutes
x ~ N(σ², μ)
p(x < 95)
1-p(x≤95)
1 - p(z≤0.47)
Using the z table here
1-0.6808 = 0.3192
Probability of x > 95 = 0.3192
b. n = 20
from central limit theorem
1 - p (z < 2.1045)
1-0.99826 = 0.0174
1 - p (z < 2.58)
1-0.9951
= 0.0049
. What we can observe from these results is that as the sample increase is increasing from 1, 20 to 30, the probability keeps decreasing.e. The probability is very small so one has to be doubtful if they are a really the population mean or if it has to be more than that.
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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.
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What is the equation of the line that passes
through the point (-3, 4) and has a slope of
2/3?
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
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)
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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.
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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.
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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.
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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).
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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.
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wright a function that relates the distance traveled,d , to the time,t,
The function that relates the distance traveled to the time is given as follows:
d = vt.
In which v is the average velocity during the time traveled.
What is the relation between velocity, distance and time?The average velocity is calculated as the division of the total distance by the total time, hence the following equation is built to model the proportional relationship between these variables:
v = d/t.
In this problem, we want to relate the distance traveled to the time, hence we have to solve the expression for d, as follows:
d = v x t
d = vt.
(applying cross multiplication to isolate the variable d).
Then it is a proportional relationship in which the average velocity acts as the constant of proportionality.
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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]
Consider the following inequality:
−2(2z−3)≥2z+24
Step 1 of 2 : Write the solution using interval notation.
Answer:
z ∈ (-∞, -3]
Step-by-step explanation:
You want the solution to −2(2z−3)≥2z+24.
SolutionSimplify the inequality:
-4z +6 ≥ 2z +24
-18 ≥ 6z . . . . . . . . . add 4z -24
-3 ≥ z . . . . . . . . divide by 6
The solution is z ∈ (-∞, -3].
A hypothesis test was used to test the hypothesis that men drive faster on average than women. The p-value was 0.16 and the level of significance used was 0.1. Then there is sufficient evidence to conclude that, on average, men drive faster then women O false O true
On average, men drive faster then women
The statement is true.
What is p-value?
The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.
We are given a statement that,
A hypothesis test was used to test the hypothesis that men drive faster on average than women.
The p-value in that case was 0.16 and the level of significance used was 0.1
As the p value is greater than level of significance we can say that the null hypothesis is correct
Hence we can say that on average men drive faster than women
The statement is correct
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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.
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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.
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.
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
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help im in k12 thanks
The graph of the inequality is attached.
What is closed circle in inequality?
Open circles are used for numbers that are less than or greater than (< or >). Closed circles are used for numbers that are less than or equal to and greater than or equal to (≤ or ≥).
Given inequality is x > 3.2.
The inequality sign of the given inequality is grater than.
The graph of the inequality will starts with open circle.
Since x is greater than 3.2. Therefore the given inequality will represent all real numbers that are greater than 3.2.
Thus the inequality will represent all number that lie on right of 3.2 on the number line.
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40% of the treats in a bag of Bark Bites are peanut butter. If there are 12 peanut butter treats, how many treats are in a bag of Bark Bites? Pick the model that represents the problem.
Answer:
30
Step-by-step explanation:
40% of what number is 12?
.4n = 12 Divide both sides by .4
n = 30
Answer:
30
Based on the given conditions, formulate: 12/40%
Multiply both the numerator and denominator with the same integer: 120/40
Cross out the common factor:30
Answer: 30
Find the slope (-2,-9) and (-1,-3)
-3+9. -6
------= ---
-2+3. -1
the answer is 6
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
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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.
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[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.
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find the volume of the composite figure 2 3 2 3 1 1 1 5 8
The total volume is given as 195.36 m³.
What is volume?Volume can be defined as the capacity of any object. It can be calculated by multiplying the base area to the height.
The composite figure consists of three cuboids and two right circular cylinders.
The volume of a cuboid is the product of its length, breadth and height.
And, the volume of cylinder is given as πr²h
As per the figure given in the question the total volume is given as,
3(1 × 5 × 8) + 2 (π × 2² × 3)
= 40 × 3 + 12π × 2
= 120 + 24 × 3.14
= 195.36
Hence, the volume of composite figure is given as 195.36 m³.
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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
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.
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According to a study done by a university student, the probability a randomiy selected individual will not cover his or her mouth when sneezing is 0.267. Suppose you sit on a bench in a mall and
obsorve people's habits as they sneeze.
What is the probability that among 10 randomly observed individuals fewer than 5 do not cover their mouth when sneezing?
Answer:
the total number of random sample n 10
probability of is 0.267
Select the correct answer.
Which equation has only one unique solution?
A. -4|x|+ 1 = -3
B. 9-|12x-1|=9
C. |x-2|-7= 7
D. |13-x|= 3
Answer:
9-|12x-1|=9
Step-by-step explanation:
Solve for x over the real numbers:
9 - abs(12 x - 1) = 9
Subtract 9 from both sides:
-abs(12 x - 1) = 0
Multiply both sides by -1:
abs(12 x - 1) = 0
Eliminate the absolute value:
12 x - 1 = 0
Add 1 to both sides:
12 x = 1
Divide both sides by 12:
Answer: x = 1/12
Answer:
Answer is B
Step-by-step explanation:
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
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