A. The values of α and β are α = 36 and β = 3.
B. Calculating this value using a statistical software or table, we find P(X ≤ 18) ≈ 0.795.
C. The probability that a student spends at most 18 min using the terminal is approximately 0.795, and the probability that a student spends between 15 and 27 min is approximately 0.592.
(a) In a gamma distribution, the mean (μ) and variance (σ^2) are related to the shape parameter (α) and rate parameter (β) as follows:
μ = α / β
σ^2 = α / β^2
Given that the mean is 12 min and the variance is 36 min, we can set up the following equations:
12 = α / β
36 = α / β^2
To solve these equations, we can divide the second equation by the first equation:
36 / 12 = α / β / (α / β^2)
3 = β
Substituting the value of β back into the first equation:
12 = α / 3
α = 36
So, the values of α and β are α = 36 and β = 3.
(b) To find the probability that a student uses the terminal for at most 18 min, we can use the cumulative distribution function (CDF) of the gamma distribution. The CDF for a gamma distribution is given by:
F(x) = 1 - Γ(α, βx) / Γ(α)
where Γ(α, βx) is the incomplete gamma function.
Using this formula, we can calculate the probability:
P(X ≤ 18) = 1 - Γ(36, 3 * 18) / Γ(36)
Calculating this value using a statistical software or table, we find P(X ≤ 18) ≈ 0.795.
(c) To find the probability that a student spends between 15 and 27 min using the terminal, we can subtract the probabilities of being below 15 min from the probability of being below 27 min:
P(15 ≤ X ≤ 27) = P(X ≤ 27) - P(X ≤ 15)
Using the same formula as in part (b), we can calculate these probabilities:
P(X ≤ 27) = 1 - Γ(36, 3 * 27) / Γ(36)
P(X ≤ 15) = 1 - Γ(36, 3 * 15) / Γ(36)
Subtracting these probabilities, we find P(15 ≤ X ≤ 27) ≈ 0.592.
Therefore, the probability that a student spends at most 18 min using the terminal is approximately 0.795, and the probability that a student spends between 15 and 27 min is approximately 0.592.
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help me pleasee, my brain won't work
The given fractions have equal value, so Liam is correct.
How to find the equivalent fractions?Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.
Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.
Thus, we can say that:
The fraction -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.
The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient
The fractions have equal value, so Liam is correct
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Isosceles Triangle BCD has base angles C and D. If m angleB = (13x – 35)°, m angleC = (5x – 19)°, and m angleD = (2x + 14)°, what is the measure of m angleD? Type just the number.
I'm kinda stuck rn.
Step-by-step explanation:
Answer:-Its Isosceles
So, base angles is equal.
[tex]13x - 35 = 5x - 19[/tex]
[tex]13x - 5x = -19 + 35[/tex]
[tex]8x = 16[/tex]
[tex]x = 2[/tex]
So, 2x+14 will be
[tex]2 \times 2 + 14[/tex]
So, 18° is the answer.
Hope it HELPS ☃️
I'm studying for a quiz but I don't know how to do these two questions! Can someone explain them to me?
Answer:
11. m∠ABD = 28°
Other Q. m∠1 = 61°
Step-by-step explanation:
11) Extend line BE. Because of the Alternate Interior Angles Theorem, ∠ABE is congruent to ∠BEF. m∠BEF = 118°, so m∠ABD + m∠DBE = 118°. Because ∠DBE is a right angle, it equals 90°. So m∠ABD + 90° = 118°. So m∠ABD = 28.
Other Q.) Looking only at line a, line b, and the line next to angle 3 and angle 1. ∠3 is congruent to ∠1 + 74° by the Corresponding Angles Theorem. Now, we have:
m∠3 = m∠1 + 74°
So we have to find the measure of angle 3.
Angle 3 is supplementary to 45°, meaning their sum is 180°, because they're linear pairs.
180 - 45 = m∠3
= 135°
Now, plug in the values to the previous:
m∠3 = m∠1 + 74°
135° = m∠1 + 74°
m∠1 = 135 - 74
= 61°
I NEED HELP NOW YOU WILL GET BRAILIEST
-21 = 0.07z−21=0.07z what does z equal
Answer:
z = -300
Step-by-step explanation:
-21=0.07z
-21/0.07= 0.07z/0.07
-300= z
If this helps please mark brainliest.
10/ an instant lottery game gives you probability 0.08 of winning in any one play. plays are independent of each other. a. if you play 5 times, what is the probability that you win on none of your plays? b. what is the probability that you win 3 or more of your 5 plays of this game?
a. The probability that you win on none of your 5 plays is approximately 0.6634. b. The probability that you win 3 or more of your 5 plays of this game is approximately 0.004497.
To solve these problems, we'll use the binomial probability formula.
a. The probability of winning in any one play is 0.08, so the probability of losing in any one play is 1 - 0.08 = 0.92.
The probability of winning on none of your 5 plays can be calculated as the probability of losing on each play, which is 0.92, raised to the power of the number of plays.
P(losing all 5 plays) = (0.92)^5 = 0.6634 (rounded to four decimal places)
Therefore, the probability that you win on none of your 5 plays is approximately 0.6634.
b. To find the probability of winning 3 or more of your 5 plays, we need to calculate the probability of winning 3, 4, or 5 plays and sum them up.
P(winning 3 or more plays) = P(winning 3 plays) + P(winning 4 plays) + P(winning all 5 plays)
P(winning 3 plays) = C(5, 3) *[tex](0.08)^3 * (0.92)^2[/tex]
= 10 * 0.000512 * 0.8464
≈ 0.00434 (rounded to five decimal places)
P(winning 4 plays) = [tex]C(5, 4) * (0.08)^4 * (0.92)^1[/tex]
= 5 * 0.000032768 * 0.92
≈ 0.000151 (rounded to six decimal places)
P(winning all 5 plays) = [tex](0.08)^5[/tex]
≈ 0.000006 (rounded to six decimal places)
Now we can sum up these probabilities:
P(winning 3 or more plays) ≈ 0.00434 + 0.000151 + 0.000006
≈ 0.004497 (rounded to six decimal places)
Therefore, the probability that you win 3 or more of your 5 plays of this game is approximately 0.004497.
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2- 10+ x = 6 -8 + 12
Please answer ASAP :)
Answer: X=18
Step by Step:
2−10+x=6−8+12
Step 1: Simplify both sides of the equation.
2−10+x=6−8+12
2+−10+x=6+−8+12
(x)+(2+−10)=(6+−8+12)(Combine Like Terms)
x+−8=10
x−8=10
Step 2: Add 8 to both sides.
x−8+8=10+8
x=18
Answer:
[tex]x = 18[/tex]
Step-by-step explanation:
[tex]2 - 10 + x = 6 - 8 + 12 \\ - 8 + x = - 2 + 12 \\ - 8 + x = 10 \\ x = 10 + 8 \\ x = 18[/tex]
What is the answer and can you explain why please
Answer:
f⁻¹(x) = (x + 3) / 2
Step-by-step explanation:
y = 2x − 3
To find the inverse, switch x and y, then solve for y.
x = 2y − 3
x + 3 = 2y
y = (x + 3) / 2
I drove 320 miles in 5 hours, how many miles did I drive in 2 hours?
Answer:
128 miles
Step-by-step explanation:
320/5=x/2 640=5x x=128
Rewrite in simplest terms: f - 3(2f - 2)
a loan payment of $1000 was due 60 days ago and another payment of $1200 is due in 30 days. what's the single payment 90 days from now is required to pay off the two obligations if interest is to be 12% and agreed focal date is on 90 days from now?
The single payment required 90 days from now to pay off the two obligations, including interest, is approximately $2230.41.
To calculate the single payment required to pay off the two obligations, we need to consider the interest accrued over the specified time period.
Let's break down the problem into two parts:
1. Loan payment of $1000 due 60 days ago:
This payment has already accrued interest for 60 days. To calculate the total amount owed, we need to calculate the interest accrued. The formula to calculate simple interest is:
Interest = Principal * Rate * Time
Here, the principal amount is $1000, the interest rate is 12% (0.12 as a decimal), and the time is 60/365 years (since we're assuming a 365-day year). Using these values, we can calculate the interest accrued as:
Interest1 = $1000 * 0.12 * (60/365)
2. Loan payment of $1200 due in 30 days:
This payment will accrue interest for the remaining 30 days until the agreed focal date, which is 90 days from now. Using the same formula, we can calculate the interest accrued as:
Interest2 = $1200 * 0.12 * (30/365)
To find the total amount required to pay off the two obligations, we sum the principal amounts and the accrued interest:
Total payment = $1000 + Interest1 + $1200 + Interest2
Now, let's calculate the values:
Interest1 = $1000 * 0.12 * (60/365) = $19.18 (approx.)
Interest2 = $1200 * 0.12 * (30/365) = $11.23 (approx.)
Total payment = $1000 + $19.18 + $1200 + $11.23 = $2230.41 (approx.)
Therefore, the single payment required 90 days from now to pay off the two obligations, including interest, is approximately $2230.41.
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What is the simplified form of the expression?
-7h + 3h² – 4h - 3
Answer:
3h² - 11h - 3
General Formulas and Concepts:
Combining like termsStep-by-step explanation:
Step 1: Write expression
-7h + 3h² - 4h - 3
Step 2: Simplify
Combine like terms (h): 3h² - 11h - 3[tex]\blue{\bold{\underline{\underline{Answer:}}}}[/tex]
[tex]\tt{\green{Simplified\:\:form = 3h^2 - 11h - 3}}[/tex]
[tex]\orange{\underline{\underline{\bold{Step\:-\:by\:-\:Step\: Explanation:}}}}[/tex]
[tex]\sf -7h + 3h^2 - 4h - 3[/tex]
Combining all like terms,
[tex] \longrightarrow \sf 3h^2 - 7h - 4h - 3[/tex]
[tex]\leadsto \underline{\boxed{\sf{\pink{ 3h^2 - 11h - 3}}}}[/tex]
Find the midpoint of the line segment joining points A and B A(2,-5); B(6,1)
Answer:
The answer is ( 4 , - 2)Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
[tex]M = ( \frac{x1 + x2}{2} , \: \frac{y1 + y2}{2} ) \\[/tex]
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
A(2,-5); B(6,1)
So we have
[tex]M = ( \frac{2 + 6}{2} \: , \: \frac{ - 5 + 1}{2} ) \\ = ( \frac{8}{2} \: , \: - \frac{4}{2} )[/tex]
We have the final answer as
( 4 , - 2)Hope this helps you
Hi please help! I already got the 1st answer and the 3rd one I just need help on B and D thank you!!
Step-by-step explanation:
Try for B - 0.0000000009 or one less zero
Try for D - 0.00000000006 or one less zero.
Hoped this helped.
Customers can rent canoes from Bob’s Boats for $40 per day with a deposit fee of $30. Ned’s Water World charges $55 per day with no deposit fee. When will the cost be the same for both places?
Answer:
ill help
Step-by-step explanation:
If sin?(Łº) + cos²(42) = 1, then what does L equal?
Answer:
Ł=42°
Step-by-step explanation:
We have the equation:
[tex]\sin^2(\L) +\cos^2(42)=1[/tex]
Remember from the Pythagorean Identity that:
[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]
So, the angles within our trig functions must be exactly the same.
Therefore, since the angle within cosine is 42°, this means that our angle within sine, Ł, must also be 42°.
And we're done!
7+(a+b)=(7+a)+b what property is that
Need help on this Advanced algebra problem
Answer:
8 m, 17 m and 22 m
Step-by-step explanation:
The first side is x
The second is 1 more than twice the first = 2x + 1
The third is 2 less than 3 times the first = 3x - 2
Sum the 3 sides and equate to 47
x + 2x + 1 + 3x - 2 = 47, that is
6x - 1 = 47 ( add 1 to both sides )
6x = 48 ( divide both sides by 6 )
x = 8
Thus
side 1 = 8 m
side 2 = 2x + 1 = 2(8) + 1 = 16 + 1 = 17 m
side 3 = 3x - 2 = 3(8) - 2 = 24 - 2 = 22 m
What is three over two x plus three equal to zero
QUESTION → [tex]\frac{3}{2}x + 3 = 0[/tex]
Start by subtracting 3 from both sides to get [tex]\frac{3}{2}x = -3[/tex].
Now multiply both sides by the reciprocal of 3/2, which is 2/3.
On the left, we have x, and on the right, -3(2/3) is -2.
So we have x = -2.
Answer:
x = -2
Step-by-step explanation:
Over means a fraction.
Equal means "="
3/2x + 3 = 0
~Subtract 3 to both sides
3/2x = -3
~Multiply 2/3 to both sides
x = -2
Best of Luck!
16 The equation of a circle in the xy-plane is given as x² + y² + 16x-20y = 60. What are the coordinates of the center of this circle? A. (-16, 20) B. (-8, 10) C. (8,-10) D. (16, -20)
The coordinates of the center of the circle with the equation x² + y² + 16x - 20y = 60 are (-8, 10).
To find the center of the circle, we need to rewrite the equation in the standard form (x - h)² + (y - k)² = r², where (h, k) represents the center coordinates and r represents the radius.
To do this, we complete the square for both the x and y terms. We rearrange the given equation as (x² + 16x) + (y² - 20y) = 60.
To complete the square for the x terms, we add (16/2)² = 64 to both sides of the equation. Similarly, for the y terms, we add (-20/2)² = 100 to both sides. This gives us x² + 16x + 64 + y² - 20y + 100 = 60 + 64 + 100.
Simplifying further, we have (x + 8)² + (y - 10)² = 224. Comparing this with the standard form, we can see that the center coordinates are (-8, 10). Therefore, the correct answer is B. (-8, 10).
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The cost, in dollars, of parking a car in a busy downtown area for h hours is $10 + $3h.
Which statement is correct?
A.
For every hour the car is parked, the cost increases by $10.
B.
For every hour the car is parked, the cost increases by $7.
C.
For every hour the car is parked, the cost increases by $13.
D.
For every hour the car is parked, the cost increases by $3.
Answer:
c
Step-by-step explanation:
the area add that to the number of hours
The cost of a movie ticket is $20, and the cost is predicted to increase by 2% each year over the next 10 years. Find the cost of a ticket after 10 years.
Answer: $24.38
Step-by-step explanation:
So since the cost of a movie ticket is $20 and the cost is predicted to increase by 2% each year over the next 10 years. to find the cost after 10 years you want to solve for x.
so x=20(1.02)^10
20 is the initial cost and 0.02 is the rate of growth. expressed as a decimal number, the base is b=1+0.02=1.02 and the exponent 10 is the number of years
A college student is interested in whether apartments with larger square footage tend to have higher rent prices. She calls several apartment buildings to inquire about the rent price and square footage of the apartments they have available Identify the explanatory and response variables. Which variable should be on which axis of a scatterplot this student creates ?
A) Rent price is the explanatory variable and square feet is the response variable. Rent price should be placed on th horizontal axis of the scatterplot and square feet on the vertical axis.
B) Rent price is the explanatory variable and square feet is the response variable. Rent price should be placed on the vertical axis of the scatterplot and square feet on the horizontal axis. C)Square feet is the explanatory variable and rent price is the response variable. Square feet should be placed on the horizontal axis of the scatterplot and rent price on the vertical axis .
D)Square feet is the explanatory variable and rent price is the response variable . Square feet should be placed on the vertical axis of the scatterplot and rent price on the horizontal axis
D) A scatterplot is not an appropriate graphical display for this data set .
Answer:
Ans. C. Square feet is the explanatory variable and rent price is the response variable. Square feet should be placed on the horizontal axis of the scatterplot and rent price on the vertical axis.
Step-by-step explanation:
did the test
If h(x) is the inverse of f(x), what is the value of h(f(x))?
0
1
x
f(x)
Answer: x
Step-by-step explanation:
The inverse undos any changes to x, reversing those changes will leave x. Ex: f(x)=x+2. The inverse (from replacing x with y and y with x and solving for y) is h(x)=x-2. Plugging x+2 into h(x) (composition of functions) results in x. 2 and -2 cancel out.
Answer:
C
Step-by-step explanation:
on edge
1. 4, 16.64,
Common ratio
Answer:
4
Step-by-step explanation:
1, 4, 16,64,
1*4=4
4*4=16
16*4=64
The common ratio is what we are multiplying by
We are multiplying by 4 so the common ratio is 4
Plz do this it is 6th grade math
Answer:
A. 6 B. 4 C. 6
Step-by-step explanation:
I never learned about the diagram My 6th grade standards must have been different than yours.sorry
101. i-The repair bill on your car is $316.55. The charge for parts was
$148.55. A mechanic worked on your car for 4 h. What was the charge
per hour for labor?
Answer:
$42.00 per hour of labor
Step-by-step explanation:
$316.55-$148.55=$168.00
$168.00÷4 hours of labor=$42 an hour
2. (15 points) You need to study for your math and physics finals. Your grade on both exams is proportional to the number of hours per day (so capped at 24 total hours) you spend studying that subject times your ability to absorb the material. You estimate that your ability to absorb math material falls from 100% by 4% for every hour you spend studying math and Page 2 of 4 by 3% for every hour you spend studying physics. Similarly, you find your ability to absorb physics material falls by 2% for each hour of studying math and by 5% for each hour of studying physics. (a) Find the optimal number of hours that you should study math and physics to maximize your average grade. Set the problem up and define all the variables and find the answer. (b) If you studied the optimal number of hours you found in part (a), which exam would you be better prepared for? (c) Now assume that your exam scores in both subjects improves by an additional 10% for every hour of the day that you do not study math or physics. Now what is the optimal number of hours spent studying for the two exams? (d) Examine the sensitivity of your answer to the additional 10\% benefit he gets from the time not studying. How would increasing the effect of this benefit affect your average grade?
A. These equations will give us the optimal values of x and y.
B. (b) To determine which exam you would be better prepared for, we compare the Math_grade and Physics_grade using the optimal values obtained in part (a).
C. We can follow the same steps as in part (a) to set up the equations and find the optimal number of hours spent studying for the two exams.
D. the specific impact would depend on the magnitude of the increase and how it interacts with the other variables and constraints in the problem.
(a) Let's define the variables:
Let x represent the number of hours spent studying math.
Let y represent the number of hours spent studying physics.
We want to maximize the average grade, which is proportional to the product of the hours spent studying and the ability to absorb the material.
The math grade is proportional to x * (1 - 0.04x) * (1 - 0.02y)
The physics grade is proportional to y * (1 - 0.03y) * (1 - 0.05x)
We want to maximize the average grade:
Average grade = (math grade + physics grade) / 2
Now, let's set up the optimization problem:
Maximize: (x * (1 - 0.04x) * (1 - 0.02y) + y * (1 - 0.03y) * (1 - 0.05x)) / 2
Subject to:
0 ≤ x ≤ 24 (maximum hours per day)
0 ≤ y ≤ 24 (maximum hours per day)
To solve this optimization problem, we can use calculus or numerical optimization methods.
(b) To determine which exam you would be better prepared for, calculate the average grade for the optimal number of hours obtained in part (a). Compare the average grade of math and physics to determine which one is higher.
(c) Now, assuming the exam scores improve by an additional 10% for every hour not studying, we need to modify the objective function in the optimization problem. Let's redefine the variables:
Let x represent the number of hours spent studying math.
Let y represent the number of hours spent studying physics.
Let z represent the number of hours not spent studying (24 - x - y).
The math grade is proportional to x * (1 - 0.04x) * (1 - 0.02y)
The physics grade is proportional to y * (1 - 0.03y) * (1 - 0.05x)
The additional benefit is 10% * z.
The new objective function to maximize the average grade is:
(x * (1 - 0.04x) * (1 - 0.02y) + y * (1 - 0.03y) * (1 - 0.05x) + 0.1 * z) / 2
Subject to:
0 ≤ x ≤ 24 (maximum hours per day)
0 ≤ y ≤ 24 (maximum hours per day)
z = 24 - x - y
(d) To examine the sensitivity of the answer to the additional 10% benefit from not studying, you can perform sensitivity analysis by changing the percentage value and observing the effect on the average grade. Increasing the effect of this benefit would likely result in a higher average grade as more emphasis is placed on the additional benefit gained from not studying. However, the exact impact would depend on the specific values used and the relationships between the variables and grades.
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-3(-x+4)=5+3(x+1) please help
Answer:
No solution.
Step-by-step explanation:
Step 1: Write equation
-3(-x + 4) = 5 + 3(x + 1)
Step 2: Solve for x
Distribute: 3x - 12 = 5 + 3x + 3Combine like terms: 3x - 12 = 3x + 8Subtract 3x on both sides: -12 ≠ 8Here, we see that x has to equal no solution. No value of x would make the equation true.
Answer:
no solutions
Step-by-step explanation:
distribute the parenthesis
3x - 12 = 5 + 3x + 3
move all variables to one side of the equation and the constants to the other
3x - 3x = 5 + 3 + 12
0 = 20
there are no solutions
What’s the solution (8x+27)°
Answer:
Step-by-step explanation:
If that is to the 0, well anything to the 0 is 1.
Answer:
= 8
Step-by-step explanation:
Let p: It is raining
Let q: Robert is laughing.
Assume p is true. Select two statements that must logically be true.
p ∨ q
p ∧ q
q → p
p → q
q ↔ p
HELP IK ITS THE FIRST ONE WHATS THE SECOND ONE!!!
Answer:
1) [tex]p\,\lor\,q[/tex], 2) [tex]q\implies p[/tex].
Step-by-step explanation:
We selected the following two statements based on the fact that [tex]p[/tex] is true: 1) [tex]p\,\lor\,q[/tex], 2) [tex]q\implies p[/tex]. We proceed to explain the reason behind each selection:
1) [tex]p\,\lor \,q[/tex]: Because the entire proposition is logically true when any of the two proposition is true.
2) [tex]q \implies p[/tex]: Because the entire proposition is logically true when the conclusion of the condition is true.
Answer:
1,3
Step-by-step explanation:
