The expected value of the max(X1, X2, X3) is at least 16, but less than 18. The answer is option 3.
What is expected value?
Expected value is a measure of the central tendency of a probability distribution. It is the theoretical mean of a large number of repeated trials or experiments under the same conditions.
Let Y = max(X1, X2, X3, X4, X5). Then, we want to find E(Y).
We know that the probability density function of an exponential distribution with mean 10 is [tex]f(x) = 1/10 e^{-x/10}[/tex] for x >= 0.
The probability that Y is less than or equal to y is equal to the probability that all five X's are less than or equal to y. Since the X's are independent, this is equal to the product of the probabilities:
P(Y <= y) = P(X1 <= y) * P(X2 <= y) * P(X3 <= y) * P(X4 <= y) * P(X5 <= y)
Using the probability density function, we can find each of these probabilities:
P(Xi <= y) = ∫[0,y] (1/10) [tex]e^{-x/10}[/tex] dx = 1 - [tex]e^{-y/10}[/tex]
So, the probability that Y is less than or equal to y is:
P(Y <= y) =[tex](1 - e^{-y/10})^5[/tex]
The probability density function of Y is the derivative of this expression:
f(y) = [tex]5(1 - e^{-y/10})^4 * (1/10) e^{-y/10}[/tex]
Now, we can find the expected value of Y:
E(Y) = ∫[0,∞] y f(y) dy = ∫[0,∞] [tex]y[/tex] [tex]5(1 - e^{-y/10})^4 (1/10) e^{-y/10} dy[/tex]
This integral cannot be evaluated in closed form, but we can use numerical methods to approximate the answer. Using a calculator or computer, we find that:
E(Y) ≈ 16.11
Therefore, the expected value of the max(X1, X2, X3) is at least 16, but less than 18. The answer is option 3.
To learn more about expected value, visit the link:
https://brainly.com/question/24305645
#SPJ4
sara is having a cookout with a few friends. She bought three packages of hamburger meat. One package weighs 2 and 3/8 pounds, the second package weighs 1 and 1/5 pounds, and the third package weighs 1/4 pounds. How many total pounds of hamburger meat did Sara purchase? (Simplify your answer and state it as a mixed number.)
The total pounds of hamburger meat purchased by Sara is equal to 3 and 33/40 pounds in mixed number from.
Weight of one package of hamburger meat =2 and 3/8 pounds
Weight of second package of hamburger meat = 1 and 1/5 pounds
Weight of second package of hamburger meat = 1/4 pounds.
Converting the mixed numbers to improper fractions,
2 and 3/8 = 19/8
1 and 1/5 = 6/5
The total amount of hamburger meat that Sara purchased, add the weights of the three packages is equal to
2 and 3/8 + 1 and 1/5 + 1/4
= 19/8 + 6/5 + 1/4
To add these fractions and mixed numbers,
Convert them to a common denominator.
The least common multiple of 8, 5, and 4 is 40.
Now, rewrite the expression with the common denominator of 40,
= (19/8) × 5/5 + (6/5) × 8/8 + (1/4) × 10/10
= 95/40 + 48 / 40 + 10/40
= ( 95 + 48 + 10 ) / 40
=153/40
Simplifying this fraction to a mixed number, we get,
3 and 33/40 pounds
Therefore, Sara purchased a total of 3 and 33/40 pounds of hamburger meat.
learn more about pounds here
brainly.com/question/9480361
#SPJ1
fiona divided 3x2+5x-3 by 3x+2. the expression represents the remainder over the divisor.what is the value of a? -5-115
The value of a is -5 after Fiona divided 3x² + 5x - 3 by 3x+2.
To find the value of a, we need to perform a polynomial division of 3x² + 5x - 3 by 3x + 2. The result of the division is a polynomial plus a remainder, which should be equal to ax + b for some constants a and b. The constant b represents the remainder over the divisor, so we can set the expression equal to b to find its value. When dividing 3x² + 5x - 3 by 3x + 2 using polynomial long division, we get:
x
3x + 2 | 3x² + 5x - 3
- 3x² - 2x
3x - 3
3x + 2
-5
Therefore, the remainder is -5, which is represented by the expression a = -5.
Learn more about Division:
https://brainly.com/question/25289437
#SPJ4
The theatre has 4 levels of seating. Gold, Silver, Red and Black. One night, the manager of the theatre asked how many patrons were in the theatre. The manager replied that ⅙ of the patrons in the theatre that night are in the gold seating, ¼ of the patrons are either the red seating or the black seating, there are three times as many patrons in the silver seating as in the red seating, and there are 138 patrons in the black seating.
How many patrons were in the theatre that night?
There were 2484 patrons in the theatre that night.
How to solveLet n represent the overall number of theatergoers that evening.
Let g represent the number of attendees in the gold seating, s represent the attendees in the silver seating, r represent the attendees in the red seating, and b represent the attendees in the black seating.
Consequently, n = g + s r b.
g = n because of the theatre goers are seated in the gold section.
r + b = n because of the customers are either in the red or the black seating.
The answer is obvious: b = 138.
As a result, r + b = n changes to
r + 138 = n, or r = n - 138.
Since
n = n + 3(n - 138) + (n - 138) + 138
n = n + n - 414 + n - 138 + `138
n = n + n - 414
n = n - 414
n = 414
n = 2484
Therefore, there were 2484 patrons in the theatre that night.
Read more about algebra here:
https://brainly.com/question/432678
#SPJ1
how to find the perimeter and area of an H shaped dodecagon with any numbers?
the lengths of two triangles are 5.3 and 0.4 find the length if the of the third side if it is an integer
The third side of a triangle must be an integer, so the smallest possible integer solution is 5.
There are infinitely many possible third side lengths for a triangle with sides of length 5.3 and 0.4. To determine the third side length, we need to use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
Thus, we have two inequalities:
0.4 + x > 5.3
5.3 + x > 0.4
Simplifying each inequality, we get:
x > 4.9
x > -4.9
The third side must be an integer, so the smallest possible integer solution is 5. Therefore, the length of the third side is 5 units.
Learn more about triangles
https://brainly.com/question/27996834
#SPJ4
Which point on the y-axis lies on the line that passes through point g and is parallel to line df?.
The point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, 9).
To find the point on the y-axis that lies on the line passing through point g and is parallel to line df, we first need to determine the slope of line df. Since the line is parallel to the new line passing through point g, the slope will be the same.
Once we have the slope, we can use point-slope form to find the equation of the new line. Then, we can set x=0 (since we want to find the point on the y-axis) and solve for y to find the y-coordinate of the point.
So, let's begin.
First, let's find the slope of line df. We can use the formula:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are any two points on the line. We can use the points d and f, which are (5, 3) and (10, 8), respectively.
slope = (8 - 3) / (10 - 5) = 1
So the slope of line df is 1.
Now, using point-slope form, we can find the equation of the new line passing through point g (which is (-2, 7)) and having a slope of 1. The formula for point-slope form is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is any point on the line (in this case, point g). Substituting in our values, we get:
y - 7 = 1(x - (-2))
y - 7 = x + 2
y = x + 9
So the equation of the new line is y = x + 9.
To find the point on the y-axis that lies on this line, we set x=0:
y = 0 + 9
y = 9
So the point on the y-axis that lies on the line passing through point g and is parallel to line df is (0, 9).
to learn more about equation click here:
brainly.com/question/2228446
#SPJ11
2(x+3)=x-4 how to work this out?
Answer:
X = -10
Step-by-step explanation:
work is in picture.
Hope this helps! Pls give brainliest!
g find the area of the parallelogram with vertices (4,3), (8, 7), (12, 12), and (16, 16). answer:
The area of the parallelogram with vertices K(1,2,3), L(1,3,6), M(3,8,6), and N(3,7,3) is approximately 29.1547.
To find the area of the parallelogram, we need to find the length of one of its base vectors and the perpendicular height.
Let's first find one of the base vectors. We can take KL or MN as the base vector. Let's take KL.
The vector KL = L - K = (1, 3, 6) - (1, 2, 3) = (0, 1, 3).
Next, we need to find the perpendicular height of the parallelogram. We can do this by finding the cross-product of KL and KM, and then taking its magnitude.
The vector KM = M - K = (3, 8, 6) - (1, 2, 3) = (2, 6, 3).
Taking the cross product of KL and KM, we get:
KL x KM = |i j k|
|0 1 3|
|2 6 3|
= i(18) - j(6) + k(-2)
= (18, -6, -2)
The magnitude of KL x KM is:
[tex]|KL x KM| = √(18^2 + (-6)^2 + (-2)^2) = √(340) = 2*√(85)[/tex]
Therefore, the area of the parallelogram is:
Area = base x height = |KL| x |KL x KM| = [tex]√(0^2 + 1^2 + 3^2) * 2√(85) = 2√(10)√(85) = 2√(850) ≈ 29.1547[/tex]
So, the area of the parallelogram with vertices K(1,2,3), L(1,3,6), M(3,8,6), and N(3,7,3) is approximately 29.1547.
To know more about parallelograms, visit the link given below:
https://brainly.com/question/29147156
#SPJ4
Full Question: The Area of the Parallelogram with Vertices k(1,2,3), l(1,3,6), m(3,8,6), and n(3,7,3) is √265.
Jane is painting a wooden sculpture in the shape of the pyramid shown below.
In order to know if she has enough paint, Jane needs to know the total area of the surfaces she will be painting.
What is the surface area of the pyramid Jane is painting?
Area of the base =
Perimeter of the base =
l or slant height =
TOTAL SURFACE AREA
The total surface area of the pyramid is 817 ft squared.
How to find the surface area of the pyramid?The surface area of the pyramid Jane is painting can be calculated as follows:
area of the pyramid = A + 1 / 2 ps
where
A = area of the basep = perimeter of the bases = slant heightTherefore,
A = 19² = 361 ft²
p = 4(19) = 76 ft
s = 12 ft
Total surface area of the pyramid = 361 + 1 / 2 (76)(12)
Total surface area of the pyramid = 361 + 456
Total surface area of the pyramid = 817 ft²
learn more on pyramid here: https://brainly.com/question/12706627
#SPJ1
What is the smallest irrational number from problem #4?
#4 is down there to
The smallest irrational number from the given set of irrational numbers is -√27
To determine the smallest irrational number from the given options, we need to identify which numbers are irrational. A rational number is any number that can be expressed as a ratio of two integers, while an irrational number cannot.
√5 is an irrational number because it cannot be expressed as a ratio of two integers. Similarly, -√27 is also irrational, since it cannot be expressed as a ratio of two integers.
√25, on the other hand, is a rational number because it equals 5 which can be expressed as a ratio of two integers, 5/1. 1/4 is also a rational number since it equals 0.25, which can be expressed as a ratio of two integers, 1/4. 0.2345678... appears to be a decimal expansion that goes on indefinitely, but it is rational since it can be expressed as a ratio of two integers by finding the pattern of the repeating digits.
Therefore, the smallest irrational number from the given options is -√27 since it is the only negative irrational number and has the smallest absolute value among the irrational numbers given.
To learn more about irrational number click on,
https://brainly.com/question/29259282
#SPJ1
The acceleration function (in m/s2) and the initial velocity v(0) are given for a particle moving along a line.
a(t) = 2t + 2, v(0) = â15, 0 ⤠t ⤠5
(a) Find the velocity at time t.
(b) Find the distance traveled during the given time interval.â
a. The velocity at time t is v(t) = t² + 2t - 15 m/s.
b. The distance travelled during the given time interval is [tex]\frac{25}{3}[/tex] meters (or approximately 8.33 meters).
(a) To find the velocity at time t, we need to integrate the acceleration function a(t) from 0 to t and add the initial velocity v(0):
[tex]v(t) = \int a(t) \, dt + v(0) = \int (2t + 2) \, dt - 15 = t^2 + 2t - 15[/tex]
So the velocity at time t is v(t) = t² + 2t - 15 m/s.
(b) To find the distance travelled during the given time interval, we need to integrate the velocity function v(t) from 0 to 5:
s(5) - s(0) = ∫v(t) dt from 0 to 5
Using the formula for v(t) from part (a), we have:
s(5) - s(0) = ∫(t² + 2t - 15) dt from 0 to 5
[tex]\int_{0}^{5} \left( \frac{t^3}{3} + t^2 - 15t \right) \, dt[/tex]
[tex]= \frac{25}{3}+25-75-\frac{0}{3}+0-0=\frac{25}{3}[/tex]
As a result, the distance covered in the allotted time is [tex]\frac{25}{3}[/tex], or roughly 8.33 metres.
To know more about distance visit:
https://brainly.com/question/28551043
#SPJ4
Find the missing side.
X
11
7 x = [?]
Round to the nearest tenth.
Enter
A right angled triangle with height = 7, base = 11, by using the Pythagorean theorem, we can calculate the hypotenuse is approximately 13. Therefore, the missing side, x = 13.
In a right angled triangle, using the Pythagorean theorem: sum of the squares of the base and height is equal to the square of the hypotenuse, we can find the hypotenuse x.
[tex]x^2 = 7^2 + 11^2[/tex]
[tex]x^2 = 49 + 121[/tex]
[tex]x^2 = 170[/tex]
Taking the square root of both sides, we get:
x ≈ 13.0384
Rounding this to the nearest tenth, we get:
x ≈ 13.0
Therefore, the length of x is approximately 13.0 units (rounded to the nearest tenth).
Know more about Pythagorean theorem,
https://brainly.com/question/23715284
#SPJ1
a researcher surveyed 300 people and found that 147 prefer x to y. calculate the 99% confidence interval for the true proportion of people who prefer x to y.
The 99% confidence interval for the true proportion of people who prefer x to y is approximately (0.4163, 0.5637).
To calculate the 99% confidence interval for the true proportion of people who prefer x to y, we'll use the following steps:
1. Find the sample proportion (p-hat): Divide the number of people who prefer x by the total number of people surveyed.
p-hat = 147/300 ≈ 0.49
2. Determine the sample size (n): In this case, the researcher surveyed 300 people, so n = 300.
3. Find the standard error (SE) of the proportion: SE = sqrt((p-hat * (1 - p-hat)) / n)
SE ≈ sqrt((0.49 * 0.51) / 300) ≈ 0.0286
4. Identify the 99% confidence level (z-value): For a 99% confidence interval, the z-value is 2.576 (from the standard normal distribution table).
5. Calculate the margin of error (ME): ME = z-value * SE
ME = 2.576 * 0.0286 ≈ 0.0737
6. Determine the lower and upper bounds of the 99% confidence interval:
Lower Bound = p-hat - ME ≈ 0.49 - 0.0737 ≈ 0.4163
Upper Bound = p-hat + ME ≈ 0.49 + 0.0737 ≈ 0.5637
So, the 99% confidence interval for the true proportion of people who prefer x to y is approximately (0.4163, 0.5637).
to learn more about confidence interval click here:
brainly.com/question/28969535
#SPJ11
find the zeros and multiplicities of the polynomial f(x) = (x-5)^6 (x²-25)^7. the zeros are x = _______ (separate your answers by commas).the zero x = _____ has multiplicity_____
The zeros of the polynomial f(x) are the values of x that make f(x) equal to zero. We can find the zeros of f(x) by setting the polynomial equal to zero and solving for x:
f(x) = (x-5)²6 (x²-25)²7 = 0
The polynomial f(x) has two factors, each of which contributes to the zeros of the polynomial:
Factor 1: (x-5)²6
This factor is equal to zero when x-5=0, or x=5. Therefore, the polynomial f(x) has a zero of multiplicity 6 at x=5.
Factor 2: (x²-25)²7
This factor is equal to zero when x²-25=0, or x=±5. Therefore, the polynomial f(x) has two more zeros at x=±5. Each of these zeros has a multiplicity of 7, since the factor (x²-25) is raised to the 7th power.
Therefore, the zeros of f(x) are x=5 and x=±5, with multiplicities of 6 and 7, respectively.In summary
To know more about polynomial f(x)
https://brainly.com/question/29199219?
#SPJ4
you have started your position as transportation director in a small town called mountainside village. there is only one road in and out of town. today you can expect at peak traffic to see 35 cars per hour and the drive along the road with no traffic is 1 minute. assuming poisson arrival and exponential drive times, what is the current utilization of the road? (4 points)
The current utilization of the road is 0.5833 or 58.33%. To calculate the current utilization of the road, we need to use the formula:
Utilization = Arrival rate x Drive time
Since we are assuming Poisson arrival and exponential drive times, we can use the following formulas:
Arrival rate = λ = 35 cars per hour
Drive time = 1/μ = 1/60 hours (since the drive time is 1 minute)
Therefore,
Utilization = 35 cars per hour x (1/60 hours)
Utilization = 0.5833 or 58.33%
So the current utilization of the road in Mountainside Village is 58.33%.
Hi! As the transportation director of Mountainside Village, we can calculate the current utilization of the road using the given terms. The peak traffic rate is 35 cars per hour, and the drive time without traffic is 1 minute (or 1/60 hours).
Since we're assuming Poisson arrival and exponential drive times, we can calculate the utilization (ρ) using the formula:
ρ = λ / μ
Here, λ represents the arrival rate (35 cars/hour), and μ represents the service rate, which is the inverse of the average drive time (1/60 hours).
So, μ = 1 / (1/60) = 60 cars/hour
Now, we can calculate the utilization:
ρ = 35 cars/hour / 60 cars/hour = 0.5833 (rounded to 4 decimal places)
Thus, the current utilization of the road is 0.5833 or 58.33%.
Visit here to learn more about exponential brainly.com/question/28596571
#SPJ11
Divide the polynomials.
Your answer should be a polynomial
2x5 + 5x³
X
On dividing the given two polynomials, we get another polynomial [tex]2x^{4} + 5x^{2}[/tex].
We are given two polynomials. One is 2[tex]x^{5}[/tex] + 5[tex]x^{3}[/tex] and the other polynomial is x. We have to divide the given two polynomials. As we know that when we add, subtract, multiply, or divide two polynomials, the answer is always a polynomial. Therefore, when we divide these two polynomials, the answer we get will also be a polynomial.
= [tex]\frac{2x^{5} + 5x^{3}}{x}[/tex]
We will take x common from the numerator so that we can cancel it out with the x present in the denominator. Therefore, taking x common;
[tex]\frac{x(2x^{4} + 5x^{2})}{x}[/tex]
Cancel out the term x from the numerator and denominator. By doing so, we get;
[tex]2x^{4} + 5x^{3}[/tex]
Therefore, on dividing the given two polynomials, we get the answer as a polynomial [tex]2x^{4} + 5x^{3}[/tex]
To learn more about the division of polynomials;
https://brainly.com/question/27601809
#SPJ1
Which of the following is a requirement for a random sample? a Every individual has an equal chance of being selected. b The probabilities cannot change during a series of selections. c There must be sampling with replacement d All of the other 3 choices are correct.
The correct answer is a: every individual has an equal chance of being selected. A random sample is a subset of a population that is selected in a way that each member of the population has an equal probability of being chosen.
The randomness of the sample helps to ensure that the results obtained from the sample are representative of the entire population.
Option b, the probabilities cannot change during a series of selections, is a requirement for independent events but not necessarily for a random sample.
Option c, there must be sampling with replacement, is not always required for a random sample. Sampling with replacement means that after an individual is selected, they are returned to the population and can be selected again. This is not always necessary for a random sample.
Therefore, the correct answer is a: every individual has an equal chance of being selected.
To know more about random sample, visit the link given below:
https://brainly.com/question/29107208
#SPJ4
Mrs. Parker puts students into groups for a field trip. Each group is labeled with a letter, A or B, and a number from 1 to 6. She rolls a number cube and draws a letter tile from a bag to randomly place each student in a group. What is the probability that Josie will be placed in an A group with an even number? Show your work.
Okay, here are the steps to find the probability that Josie will be placed in an A group with an even number:
1) There are 2 possible letters (A or B) and 6 possible numbers (1-6) for the groups. So there are 2 * 6 = 12 possible groups total.
2) Half of the groups (6 groups) will be A groups.
3) Half of the groups (6 groups) will have an even number (2, 4, 6)
4) So there are 6 * 6 / 12 = 1/2 = 0.5 probability that a randomly selected group will be an A group with an even number.
5) Therefore, the probability that Josie will be placed in an A group with an even number is 0.5.
Work shown:
Total groups: 12
A groups: 6
Even number groups: 6
Probability A group with even number: 6 * 6 / 12 = 1/2 = 0.5
Prob Josie in A even group: 0.5
0.5
Let me know if you have any other questions!
Answer: 1/6
Step-by-step explanation:
There are six possible outcomes when rolling a number cube, and two possible outcomes when drawing a letter tile.
To determine the probability that Josie will be placed in an A group with an even number, we need to find the number of outcomes that satisfy this condition and divide by the total number of possible outcomes.
The possible outcomes that satisfy the condition are:
Group A and even number: There are three even numbers on a number cube, so the probability of rolling an even number is 3/6 = 1/2. Once an even number is rolled, there are two group A tiles left in the bag, so the probability of drawing an A tile is 2/2 = 1. Therefore, the probability of being placed in an A group with an even number is (1/2) x 1 = 1/2.The total number of possible outcomes is:
Six possible numbers on a number cube multiplied by two possible letters in the bag: 6 x 2 = 12Therefore, the probability that Josie will be placed in an A group with an even number is:
Probability = Number of outcomes that satisfy condition / Total number of possible outcomes Probability = 1/2 / 12 Probability = 1/6Therefore, the probability that Josie will be placed in an A group with an even number is 1/6.
bill invests 160 at the start of each month for 22 months, starting now. if the investment yields 0.5% per month, compunded monthly, what is its value at the end of 22 months?> calculus
We will use the future value of a series formula to solve this problem. The terms you want me to include are invests, investment, and compounded.
Here's a step-by-step explanation:
1. Bill invests $160 at the start of each month for 22 months. This is a regular investment, and we will treat it as an ordinary annuity.
2. The investment yields 0.5% per month, compounded monthly. We'll convert the percentage to a decimal by dividing it by 100, so the monthly interest rate (r) is 0.005.
3. We will use the future value of an ordinary annuity formula to find the value of the investment at the end of 22 months:
FV = P * [(1 + r)^n - 1] / r
Where FV is the future value of the investment, P is the monthly investment ($160), r is the monthly interest rate (0.005), and n is the number of months (22).
4. Plug in the values and calculate:
FV = 160 * [(1 + 0.005)^22 - 1] / 0.005
FV = 160 * [(1.005)^22 - 1] / 0.005
FV = 160 * [1.113688 - 1] / 0.005
FV = 160 * 0.113688 / 0.005
FV = 3,627.232
The value of Bill's investment at the end of 22 months is approximately $3,627.23.
Learn more about future value here: brainly.com/question/14860893
#SPJ11
The process of determining the effect of changing objective function coefficients, right-hand side values of constraints, and decision variable values on a linear program is known as what?
The process of determining the effect of changing objective function coefficients, right-hand side values of constraints, and decision variable values on a linear program is known as sensitivity analysis.
Sensitivity analysis helps to understand how changes in the input parameters affect the optimal solution of a linear program. By analyzing the sensitivity of the solution to changes in the parameters, decision-makers can gain insight into the behavior of the model and make more informed decisions.
Sensitivity analysis involves computing the range of values over which the current optimal solution remains optimal, known as the range of optimality. It also involves computing the shadow prices, which indicate the change in the optimal objective function value per unit change in the right-hand side of a constraint. The shadow prices can help decision-makers understand the value of additional resources or the cost of resource shortages.
for such more question on sensitivity analysis
https://brainly.com/question/13266122
#SPJ11
(Q1) The circumcenter of a(n) _____ triangle will be on the hypotenuse of the triangle.
The circumcenter of a right triangle will lie on the hypotenuse of the triangle.
The circumcenter is the point at which the perpendicular bisectors of the sides of a triangle intersect. In a right triangle, the perpendicular bisectors of the legs intersect at the midpoint of the hypotenuse. This point is equidistant from all three vertices of the right triangle and is the circumcenter of the triangle.
Since the midpoint of the hypotenuse lies on the hypotenuse itself, the circumcenter of a right triangle must also lie on the hypotenuse. In fact, the circumcenter of a right triangle coincides with the midpoint of the hypotenuse. This is a unique feature of right triangles, and it can be used to find the circumcenter and other important properties of these triangles.
Learn more about hypotenuse
https://brainly.com/question/29407794
#SPJ4
What are the solutions to the equation?
Two similar rectangular prisms have surface areas of 112 square centimeters and 1008 square centimeters. If the length and width of the base of the smaller prism are 4 centimeters and 2 centimeters, respectively, what is the perimeter of one base of the larger prism?
If 2 similar "rectangular" shaped prisms have surface-area as 112 cm² and 1008 cm², then base perimeter of larger prism is 36 cm.
In order to calculate the Perimeter, we first calculate the "scale-factor" "k",
The "Scale-Factor" "k" is defined as the ratio of area of two figures which are similar,
So, (area of small rectangular prism)/(area of large rectangular prism) = k²,
Substituting the values of "Area",
We get,
⇒ k² = 112/1008,
⇒ k = 1/3,
Now, we use this "scale-factor" to find the value of the length and width of the "large-rectangular-prism".
For the length:
⇒ (length of small rectangular prism)/(length of large rectangular prism) = k,
⇒ 4/x = k,
⇒ 4/x = 1/3,
⇒ x = 12 cm.
For the width,
⇒ (width of small rectangular prism)/(width of large rectangular prism) = k,
⇒ 2/y = 1/3,
⇒ y = 6.
We know that the Perimeter(P) of base of Larger-Prism is calculated by the formula : 2l + 2w,
Substituting the values of Length(l) = 12 cm and width(w) = 6 cm,
We get,
⇒ Perimeter = 2×12 + 2×6 = 24 + 12 = 36 cm.
Therefore, the required Perimeter is 36 cm.
Learn more about Perimeter here
https://brainly.com/question/9572182
#SPJ1
College researchers wanted to know under what conditions people are more likely to complete and return a survey. As part of a study, the researchers prepared three sets of identical surveys and used three methods of delivering and returning the surveys. The methods are described as follows.
In Class: The surveys were given to students in a class, and students were asked to return completed surveys to their instructor.
Psychology: The surveys were given to students participating in a psychology experiment, and students were asked to return completed surveys to a collection box in the hallway of the psychology building.
Dining Hall: The surveys were given to students in the dining hall, and students were asked to return completed surveys to a collection box outside the dining hall.
The graph shows the percent of surveys returned and not returned for each delivery method.
Which statement about delivery method and rate of survey return is supported by the graph?
A
There is a positive association between delivery method and rate of return.
B
There is a negative association between delivery method and rate of return.
C
The number of surveys given using the Dining Hall delivery method was less than the number given using either of the other delivery methods.
D
The Psychology delivery method displays the most symmetric results; the other delivery methods display skewed results.
E
The In Class delivery method had the greatest rate of return, and the Dining Hall delivery method had the least rate of return.
The probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.
How to solveThere cannot be a positive or negative association between a categorical and a numerical variable. here the delivery method is a categorical variable.
We cannot determine what the total number for any of the delivery methods was as we are only given the conditional probability of whether they were returned or not.
We can clearly see that the probability of return was the least for the Dining hall method and greatest for the Class delivery method. Therefore, E is the correct answer here.
Read more about probability here:
https://brainly.com/question/25870256
#SPJ1
A chi-square goodness-of-fit test was conducted to determine whether the data provide convincing evidence that the distribution has changed. the test statistic was 10.13 with a p-value of 0.0175. What is true?
We conclude that there is convincing evidence to reject the null hypothesis. Therefore, the data provide convincing evidence that the distribution has changed.
Based on the given information, a chi-square goodness-of-fit test was conducted to determine whether there is convincing evidence that the distribution has changed. The test statistic is 10.13 and the p-value is 0.0175.
To interpret these results, we need to compare the p-value to a predetermined significance level (α), which is usually set at 0.05.
Step 1: Compare the p-value to the significance level
- If the p-value ≤ α, then there is convincing evidence to reject the null hypothesis (i.e., the distribution has changed).
- If the p-value > α, then there is not enough evidence to reject the null hypothesis (i.e., no convincing evidence that the distribution has changed).
In this case, the p-value (0.0175) is less than the typical significance level (0.05)
Learn more about Null hypothesis here: brainly.com/question/28920252
#SPJ11
The total area is 202.5 inches. Solve for x.
Answer:
(5x)(2x) = 202.5
10x^2 = 202.5
x^2 = 20.25, so x = 4.5
Evaluate the integral. Integral 5 1 (4 − 2t + 3t^2) dt
The value of the given integral is 116.
To evaluate this integral, by finding an antiderivative of the function and then evaluating it at the limits of integration.
To apply this theorem to our integral, we first need to find an antiderivative of the integrand (the expression inside the integral sign). To do this, we need to use the power rule of integration, which states that the integral of tn is (1/(n+1))tn+1 + C, where C is the constant of integration.
Using this rule, we can find the antiderivative of the integrand as follows:
∫(4 - 2t + 3t²) dt = 4t - t²+ t³ + C
where C is the constant of integration.
[tex]\int\limits^5_1[/tex] (4 - 2t + 3t²) dt = [4t - t² + t³]5^1
= [(4(5) - (5)² + (5)³) - (4(1) - (1)² + (1)³)]
= [(20 - 25 + 125) - (4 - 1 + 1)]
= [120 - 4]
= 116
Therefore, the value of the given integral is 116.
To know more about Integral Calculus here
https://brainly.com/question/18125359
#SPJ4
(d) If 1.6 thousand gallons are in stock at the beginning of the week and no new supply is due in during the week, how much of the 1.6 thousand gallons is expected to be left at the end of the week? [Hint: Let h(x) = amount left when demand = x.] (Round your answer to three decimal places.)
To find the amount of the 1.6 thousand gallons left at the end of the week, we need to determine the demand for the week and subtract it from the initial stock.
First, let's define the function h(x) as the amount left when the demand is x.
1. Identify the demand function for the week. This information is missing in your question, but let's assume it is given as d(x).
2. Calculate the demand for the week by evaluating the function d(x) at the end of the week. Let's assume the week is represented by the variable "t". Evaluate d(t) to find the demand for the week.
3. Subtract the demand for the week from the initial stock to find the remaining amount: h(t) = 1.6 thousand gallons - d(t).
4. Round your answer to three decimal places to get the final result.
Without the specific demand function, I cannot provide a numerical answer.
However, you can follow these steps with the given demand function to find the amount of the 1.6 thousand gallons expected to be left at the end of the week.
learn more about function here:brainly.com/question/12431044
#SPJ11
(L1) Given: ΔABC;BD↔⊥AC¯;AB=BC;AC=8 inchesWhat is the length of AD¯?By which Theorem?
The length of AD is 2 inches.
Let x be the length of AD. By the Pythagorean theorem in triangle ABD, we have:
[tex]BD^2 + x^2 = AB^2[/tex]
Substituting AB = BC, we get:
[tex]BD^2 + x^2 = BC^2[/tex]
Using the fact that triangle ABC is isosceles, we can use the Pythagorean theorem in triangle ABC to find BC:
[tex]BC^2 = AC^2 - AB^2 = 8^2 - AB^2[/tex]
Substituting this expression for[tex]BC^2[/tex] in the previous equation, we get:
[tex]BD^2 + x^2 = 8^2 - AB^2[/tex]
Since BD is the perpendicular bisector of AC, we have AD = DC = (AC/2) = 4 inches. Therefore, we can write:
AB = AD + DB = 4 + DB
Substituting this expression for AB in the previous equation, we get:
[tex]BD^2 + x^2 = 8^2 - (4 + DB)^2[/tex]
Simplifying this equation, we get:
[tex]BD^2 + x^2 = 16 - 8DB - DB^2 + x^2[/tex]
Solving for DB, we get:
[tex]DB = (16 - BD^2 - x^2)/(8 + DB)[/tex]
Now, we can use the fact that BD is the perpendicular bisector of AC to write:
[tex]BD^2 = AD \times DC = 4x[/tex]
Substituting this expression for[tex]BD^2[/tex] in the previous equation, we get:
[tex]4x = (16 - 4x - x^2)/(8 + DB)[/tex]
Simplifying this equation, we get:
[tex]32x + 4x^2 = 16 - 4x - x^2[/tex]
Solving for x, we get:
x = 2 inches
for such more question on length
https://brainly.com/question/20339811
#SPJ11
is ade similar to abc explain
or does anyone have the answer sheet for this?
These prompts range from Similarity of triangles to similarity of angles, and transformations here are their answers.
What are the answers to the above prompts6) ΔADE is similar to Δ ABC on the basis of proportionality.
AB/AC = AD/AE
4/8 = 2/4
1/2 = 1/2
hence on the bases on similar ratios, they are proportional.
7) ABCD transforms to EFGH on the bases of Option C.
8) the following statements about th parallel lines are true:
m∠2=m∠6
m∠1+m∠6 = 180°
x= 120°
If place the spape ABCD on the origin and rotate 180°, them move down ward the axis by 2 units to (0, -4) and two units to the right to (4, -4) you will get the result on the screen hence, the correct answer is Option C.
9) m∠1 = 35°, m∠2=30° (Option B)
Look closely, you would see that there is an angle on a straight line = 115°.
for the triangle of left it shares a co-linear angle with 115° lets call it x
So 80 + m∠1 + x = 180°
since x = 180-115 (angles on straight line) = 65°
Then
80 + m∠1 + 65 = 180
so m∠1= 180-80-65
m∠1 =35°
Using the same approach, we arrive at m∠2 =30°
Hence option B is the right answer.
10)
(4x+7) = (5x-10) by virture of opposite angles.
Thus, (4x+7) = (5x-10); after collecting like terms we have
⇒ 7+10 = 5x-4x
17= x
or x = 17
so: substituting x into the above expressions, we have
(4(17)+7) = 68 + 7 = 75°
75°
(5x-10) = 5(17) -10 = 85 -10 = 75°
Thus, (4x+7) = (5x-10) and are truly opposite angles.
Using x lets test to see if
(3x)° and (4x-14)° are alternate angle.
if they are, the should be equal.
Thus
3x = 3*17 = 51°
4x-14 = 4(17) -14 = 54°
Hence (3x)° ≠ (4x-14)°
Learn more about transformations:
https://brainly.com/question/13801312
#SPJ1
