Answer:
85.25
Step-by-step explanation:
155 x (11/20) =85.25 feet
Rationalize the denominator and simplify:
Answer:
∛(2b)
Step-by-step explanation:
[tex]\displaystyle\frac{\sqrt[3]{4b^2}}{\sqrt[3]{2b}}=\sqrt[3]{\frac{4b^2}{2b}}=\sqrt[3]{2b}[/tex]
In the diagram GH bisects ∠FGI
A.Solve for x and find m∠FGH
B.Find m∠HGI
C.Find m∠FGI
A.x=
Answer:
The answer to your question is:
a) ∠FGH = 34°
b) ∠HGI = 34°
c) ∠FGI = 68°
Step-by-step explanation:
We know that GH bisects ∠FGI
a) Find ∠FGH
∠ FGH = 5x - 6
∠ HGI = 6x -14
∠ FGH = ∠ HGI
5x - 6 = 6x - 14
5x - 6x = -14 + 6
-1x = - 8
x = 8
∠ FGH = 5(8) - 6
= 40 - 6
= 34°
b) m∠HGI = 6(8) -14
= 48 - 14
= 34°
c) m∠FHI = ∠ FGH + ∠ HGI
= 34 + 34
= 68°
Lean ground beef is advertised at $1.78/lb. What is the price per kilogram? (There are approx. 2.2 lbs in 1 kg)
Answer:
The answer to your question is: $ 3.92 / kg
Step-by-step explanation:
Data
Lean ground beef cost = $1.78
price of 1 kg = ?
Equivalence 1 kg = 2.2 lbs
Process (rule of three)
$1.78 ------------------- 1 pounds
x ------------------- 2.2 pounds
x = 2.2(1.78) / 1 = $ 3.92 / kg
Two cars pass on a straight highway while traveling in opposite directions. One car is traveling 6 miles per hour faster than the other car. After 2.5 hours the two cars are 275 miles apart. Find the speed of each car.
Answer:
1st car is 6mph 2nd car is 100mph
Step-by-step explanation:
ans to first car is in the question
and just subtract total travelled distance of car 1 after 2.5 hours. then subtrct it from the total distance and with the remaining distance solve for speed of other car which is distance over time.
The speed of the slower car is 52 mph, and the speed of the faster car is 52 mph + 6 mph, which equals 58 mph. This was calculated using the relationship between speed, distance, and time.
Let's denote the speed of the slower car as v miles per hour (mph), which means the faster car will have a speed of (v + 6) mph. Since they are travelling in opposite directions, their speeds add up when determining how far apart they will be over a period of time.
Combined speed = v + (v + 6) = 2v + 6 mph
After 2.5 hours, they are 275 miles apart. Using the formula for distance, which is Distance = Speed ×Time, we have:
Distance = (2v + 6) × 2.5
275 miles = (2v + 6) × 2.5
Solving for v, we divide both sides by 2.5:
110 = 2v + 6
Now, subtract 6 from both sides:
104 = 2v
Finally, divide by 2 to find the speed of the slower car:
v = 52 mph
Therefore, the speed of the slower car is 52 mph, and the faster car is 52 mph + 6 mph, which equals 58 mph.
correlation of a scatter plot question in image
Answer:
For this question there appears to be absolutely no association. The points are all over the place and there is not consistent factors at play here.
Which scenario is most likely the one shown on the graph?
the total amount of money in the cash register, y, containing $50 in change and small bills and x $100 bills
the total number of puzzle pieces, y, in a brand new 50-piece puzzle, and x brand-new 100-piece puzzles
the total weight of the barbell, y, where the bar weighs 50 pounds and x 100-pound weights are added to it
the total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce
Answer:
The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.
Step-by-step explanation:
The scenario that is most likely to be shown in the graph is:
The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.
We can see that the initial calories are 50 as shown in the graph.
When x=0 the value on the y-axis is 50.
And this value is increasing by 100 units.
Answer:
The total number of calories, y, in a salad with vegetables containing 50 calories topped with x ounces of salad dressing at 100 calories per ounce.
Choice D.
Step-by-step explanation:
Rate data often follow a lognormal distribution. Average power usage (dB per hour) for a particular company is studied and is known to have a lognormal distribution with parameters μ = 4 and σ = 2. What is the probability that the company uses more than 270 dB during any particular hour?
The probability that the company uses more than 270 dB during any particular hour is approximately 0.8963 or 89.63%.
To find the probability that the company uses more than 270 dB during any particular hour, we need to use the properties of the lognormal distribution.
The lognormal distribution is characterized by two parameters: μ (mean of the logarithm of the data) and σ (standard deviation of the logarithm of the data).
μ = 4
σ = 2
To find the probability of the company using more than 270 dB, we need to convert this value to the logarithmic scale and then calculate the corresponding probability.
Convert 270 dB to the logarithmic scale:
Let X be the random variable following a lognormal distribution with parameters μ and σ. The logarithm of X is normally distributed with mean μ and standard deviation σ.
Using the lognormal properties, we can convert 270 dB to the logarithmic scale:
ln(270) = 5.5984 (approximately)
Calculate the probability of X being greater than ln(270):
We now need to find the probability of X being greater than ln(270) in the lognormal distribution with parameters μ = 4 and σ = 2.
Using statistical software, a lognormal distribution table, or a calculator, we find the probability P(X > ln(270)) to be approximately 0.8963.
for such more question on probability
https://brainly.com/question/23417919
#SPJ1
To find the probability that the company uses more than 270 dB during any particular hour, we can use the properties of the lognormal distribution. The lognormal distribution is characterized by its parameters μ and σ, where μ is the mean and σ is the standard deviation of the natural logarithm of the variable. In this case, μ = 4 and σ = 2. The probability is approximately 0.227.
Explanation:To find the probability that the company uses more than 270 dB during any particular hour, we can use the properties of the lognormal distribution. The lognormal distribution is characterized by its parameters μ and σ, where μ is the mean and σ is the standard deviation of the natural logarithm of the variable. In this case, μ = 4 and σ = 2.
To find the probability, we can convert the value of 270 dB to its corresponding value on the lognormal distribution. Let's call this value x. Using the formula x = e^μ + σ^2/2, we have x = e^4 + 2^2/2 = 54.598.
Now, we can use the cumulative distribution function (CDF) of the lognormal distribution to find the probability that the company uses more than 270 dB. The CDF gives us the probability that the variable is less than or equal to a given value.
Since we want the probability that the variable is greater than 270 dB, we can subtract the CDF value from 1. Using a calculator or a statistical software, we can find that the CDF of the lognormal distribution at x = 54.598 is approximately 0.773. Therefore, the probability that the company uses more than 270 dB during any particular hour is 1 - 0.773 = 0.227.
What is a transformation
Answer:
Transformation is the altering of shapes using different operations.
Step-by-step explanation:
The different operations of transformation are translation, reflection, and rotation.
Step-by-step explanation: A transformation is when we change the position or size of a given figure.
In part a, notice that we can flip the triangle on the left over the following line to the position of the triangle on the right. When we flip a figure over a line to create a mirror image, the new image is called a reflection. Therefore, the transformation shown in part a is called a reflection.
In part b, notice that we can turn the triangle on the top to the position of the triangle on the bottom. When we turn a figure to a new position, it's called a rotation. Therefore, the transformation in part b is a rotation.
In part c, notice that we can slide the triangle on the left to the position of the triangle on the right. When we slide a figure to a new position, it's called a translation. Therefore, the transformation in part c is a translation.
In part d, notice that the triangle on the left has been reduced in size to form the triangle on the right. When we reduce or increase the dimensions of a figure while maintaining its shape, the new image is called a dilation. Therefore, the transformation in part d is a dilation.
Find P(2) using this probability distribution. Round to 2 decimal places as needed.
Answer:
P (2) = 0.1
Step-by-step explanation:
The table has X and P(X), you have to search the X and see its P(X) and thats the probability
Simplify.
(6x – 5 + 4x2) + (2x - 2)
The solution of the expression (6x – 5 + 4x²) + (2x - 2) will be;
⇒ 4x² + 8x - 7
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ (6x – 5 + 4x²) + (2x - 2)
Now, Solve the expression is solve as,
⇒ (6x – 5 + 4x²) + (2x - 2)
⇒ 6x – 5 + 4x² + 2x - 2
⇒ 4x² + 6x + 2x - 5 - 2
Solve common terms,
⇒ 4x² + 8x - 7
Therefore,
The solution of the expression (6x – 5 + 4x²) + (2x - 2) will be;
⇒ 4x² + 8x - 7
Learn more about the mathematical expression visit:
https://brainly.com/question/4344214
#SPJ5
The mean distance of the Moon from Earth is 2.39x10^5 miles. Assuming that the orbit of the Moon around Earth is circular and the 1 revolution takes 27.3 days, find the linear speed of the Moon.
Express your answer in miles per hour.
If the orbit of the Moon around Earth is circular and the 1 revolution takes 27.3 days, the linear speed of the moon is 2291.94335 miles/hour.
The speed with which an object moves in a linear path is known as its linear speed.
The following are given:
The mean distance of the moon from Earth (r) is [tex]2.39\times10^5[/tex] miles.
The total distance covered by the moon in 1 revolution is 2πr.
The time taken for 1 revolution by the moon (T) is 27.3 days.
It is known that there are 24 hours in a day.
So, 27.3 days = 27.3 × 24 hours
The linear speed(v) of the moon can be calculated by dividing the distance covered by the time taken to complete a revolution as follows:
[tex]v = \dfrac{2\pi r}{T}[/tex]
[tex]=\dfrac{2\times3.14\times2.39\times10^5}{27.3\times24}\\= 2291.94335\ miles/ hour[/tex]
Therefore, the linear speed of the moon is 2291.94335 miles/hour.
Learn more about Linear speed here:
https://brainly.com/question/9276746
#SPJ12
To find the linear speed of the Moon, we calculate its circumference and divide it by the time taken for one revolution. The linear speed of the Moon is approximately (2π(2.39x10^5)) / (27.3 x 24) miles per hour.
Explanation:To find the linear speed of the Moon, we first need to calculate its circumference. The circumference of a circle is given by the formula C = 2πr, where r is the radius. In this case, the radius is the mean distance of the Moon from Earth, which is 2.39x10^5 miles. So, the circumference is 2π(2.39x10^5) miles.
To find the linear speed, we need to divide the circumference by the time it takes for the Moon to complete one revolution around Earth. Since each revolution takes 27.3 days, we need to convert that to hours. There are 24 hours in one day, so 27.3 days is equal to 27.3 x 24 hours. Finally, we divide the circumference by the time to get the linear speed in miles per hour.
Therefore, the linear speed of the Moon is approximately (2π(2.39x10^5)) / (27.3 x 24) miles per hour.
Learn more about Linear speed of the Moon here:https://brainly.com/question/13705319
#SPJ3
The weekly pay for working a job is given by the function P(h) = 15h, where "h" is the number of hours worked. The company restricts workers to a maximum of 40 hours per week. The tax on the pay is given by the function T(P) = 0.18P, where "P" is the weekly pay. What is the BEST description of the domain for the tax function T(P)? A) {0, 1, 2, 3, ..., 40} B) {0, 15, 30, 45, ..., 600} C) {any nonnegative real number ≤ 40} D) {any nonnegative real number ≤ 600}
Answer:
Either B or D.
Step-by-step explanation:
I consider both options valid. It all depends on how the employer is keeping track of time, ie if the pay "ticks" every 60 minutes, or an employee is allowed to clock in half hours.
Will I be able to work 30 and a half hour for example? If I'm allowed to, D.
If I have to work multiple of 60 minutes, B.
Answer:
The answer is D
Step-by-step explanation:
Kam can make 72 cookies in 3 hours at his house, while Madison can make 120 cookies in 4 hours at her house. How long would it take for them to make a total of 200 cookies together
Answer:
The answer to your question is: 3.7 hours
Step-by-step explanation:
Kam can make 72 cookies/ 3 hours
Madison can make 120 cookies/4 hours
Time to make 200 cookies together = ?
First, calculate the number of cookies make per hour
Kam 72 ---------------- 3
x ---------------- 1 hour
x = 72/3 = 24 cookies/h
Madison
120 ------------- 4 hours
x --------------- 1 hour
x = 120 / 4 = 30 cookies
Now we write and equation where "t" will be time
24t + 30t = 200 and solve it
54t = 200
t = 200/54
t = 3.7 hours
The time taken by both of them will be 3.7 hours.
What is the ratio of two numbers?The ratio of two numbers a and b can be written as a : b = a/b.
The ratio of two quantities is the unit rate of one quantity with respect to the other.
The given problem can be solved as follows,
The number of cookies made by Kam in 1 hour = 72/3 = 24.
The number of cookies made by Madison in 1 hour = 120/4 = 30.
The total number of cookies made by them in one hour = 30 + 24 = 54.
The time taken to make 200 cookies is the ratio of 200 and 54 as given below,
Time taken by both to make 200 cookies = 200/54 = 3.7 hours.
Hence, Kam and Madison would take 3.7 hours to make the cookies together.
To know more about ratio click on,
brainly.com/question/13419413
#SPJ5
The school board asked Han to conduct a study on the attitudes of faculty regarding the proposed school uniform policy. Han stops by the teachers' lounge and surveys the faculty present. Which nonrandom sampling approach did Han employ?
Answer:
Han used a convenience nonrandom sampling approach
Step-by-step explanation:
The convenience nonrandom sampling approach consists in collecting a sample just because it is convenient. This means that the subjects are easy to select.
Han did precisely this, he went to the teacher's lounge and surveyed the faculty present there. He did not put any further effort like, for example, wait for more teachers to have a larger sample or make sure the ratio between female and male teachers was the same.
Ticket sales for a spaghetti dinner total $2475. There are four times as many adult tickets sold as children's tickets. The prices of the tickets for adults and children are $10 and $5, respectively. Find the number of children's tickets sold.
Answer:
55 children's tickets
Step-by-step explanation:
Let the number of adult tickets sold = a
Let the number of children tickets sold = c
As per the statement "The adult tickets were sold four times as many as children's tickets".the equation will be
a = 4c ----- (1)
As per second statement "the prices of the tickets for adults and children are $10 and $5 respectively."
The total price of the adult tickets = 10a
the total price of the children tickets = 5c
total tickets were sold for = $2,475
So the equation will be
10a + 5c = 2,475 ------(2)
Now substitute the the value of a from equation (1) to equation (2).
10(4c) + 5c = 2,475
40c + 5 c = 2,475
45c = 2,475
c = [tex]\frac{2475}{45}[/tex]
c = 55
The number of children's tickets 55.
Final answer:
To find the number of children's tickets sold in a spaghetti dinner event with given total sales and ticket prices, set up and solve the relevant equations step by step.
Explanation:
Given:
Total ticket sales for a spaghetti dinner = $2475
Adult ticket price = $10
Children's ticket price = $5
Number of adult tickets sold = 4 times the number of children's tickets sold
To find: Number of children's tickets sold
Step-by-Step Solution:
Let the number of children's tickets sold be x
Number of adult tickets sold = 4x
Write the equation: 5x + 10(4x) = 2475
Solve for x to find the number of children's tickets sold
x = 55
A finite set of points in the plane has the property that the triangle formed by any 3 of them has area less than 1.Prove that there is a triangle of area 4 that contains all the points
Explanation:
All of the points must be contained within a circle that will circumscribe an equilateral triangle of area 1. (We refer to this as the inscribed triangle.) Any points on the circle that do not form an equilateral triangle will form a triangle with an area less than 1. Likewise for any points within the circle.
The circle can be circumscribed by an equilateral triangle whose side length is double that of the inscribed triangle. Since the side length is double, the circumscribing triangle will have an area 2² = 4 times that of the inscribed triangle.
The inscribed triangle has an area of 1, so the circumscribing triangle must have an area of 4.
Jenna believes that she doesn't have an aptitude for statistics, so doesn't put much effort into her statistics class. She performs poorly in the class, supporting her initial belief. This is an example of a(n):
Answer:
Self-fulfilling prophecy
Step-by-step explanation:
According to my research on studies conducted by various psychologists, I can say that based on the information provided within the question this is an example of a Self-fulfilling prophecy. This is defined as a phenomenon of when an individual believes something will happen a certain way, and that event ends up happening only because the individual changed their behaviors and actions causing it to happen. Which is what Jenna did with her statistics class.
I hope this answered your question. If you have any more questions feel free to ask away at Brainly.
Answer:
Self-fulfilling prophecy
Step-by-step explanation:
A self-fulfilling prophecy is the social and psychological phenomenon that, when exposed to a personal belief, a person will change its conduct or behaviour in order to confirm or make real that particular belief in order to avoid cognitive dissonance or the fact of being wrong.
Jenna believes she is bad in statistics. But that belief, which is not really or necessarily true, makes her change her behaviour and not study or abandon her effort to become better at statistics, which at the same time makes her perform badly in statistics in the future. This reinforcing loop maintains the belief and prophecy going in time.
The newly elected president needs to decide the remaining 6 spots available in the cabinet he/she is appointing. If there are 10 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed?
Answer: There are 151,200 ways the members can be appointed.
Step-by-step explanation:
Since we have given that
Number of eligible candidates = 10
Number of remaining spots available = 6
Here, rank matters.
so, we will use "Fundamental theorem of counting or by Permutation":
So, Number of different ways the members can be selected is given by
[tex]^{10}P_6=10\times 9\times 8\times 7\times 6\times 5\\\\=151,200[/tex]
Hence, there are 151,200 ways the members can be appointed.
The number of different ways the president can appoint the members of the cabinet given that order matters and there are 10 eligible candidates for the remaining 6 positions is 151,200.
Explanation:The question is asking for the number of different ways the six remaining cabinet positions can be filled, given that there are ten eligible candidates and rank matters. This scenario is an example of a permutation problem in combinatorics, a subfield of mathematics. A permutation is an arrangement of objects in a specific order. If rank matters, this means that the order in which the candidates are chosen for the cabinet positions is important. In this case, the formula for permutations is applicable. The formula for permutation when there are 'n' items available (10 eligible candidates) and 'r' items are chosen (6 positions) is given by nPr = n! / (n-r)!. Substituting these values, we have 10P6 = 10! / (10-6)!. After performing the calculation, we find there are 151,200 different ways in which the president can appoint the members of the cabinet.
Learn more about Permutations here:https://brainly.com/question/23283166
#SPJ11
Select the correct interpretation of the probability of getting an 11 when a pair of dice is rolled. Interpret an event as significant if its probability is less than or equal to 0.05.
Answer:
1/18
Step-by-step explanation:
We are considering that we have 2 dices with 6 faces each (so, the probability to gettig any face in any dish is 1/6). To get an 11, we only have two ways to obtain it:
Dice 1= 6 and Dice 2 =5
or
Dice 1= 5 and Dice 2 =6
So, the probability of the event is given as:
P(Dice1=5 ∧ Dice2=6) ∪ P(Dice1=6 ∧ Dice2=5) = P(Dice1=5) x P(Dice2=6) + P(Dice1=6) x P(Dice2=5) = 1/6 x 1/6 + 1/6 x 1/6 = 1/36 + 1/36 = 2/36 = 1/18.
As 1/18 = 0,055, and 0,055 > 0,05, we consider the event as not significative (according to the definition of significance in the sentence).
Answer:
When you throw a dice, the total number of options that you can get is the product of the number of options for each dice, this means that the total number of combinations is:
c = 6*6 = 36 combinations.
Now, the combinations where the dice add to 11 are:
5 in one dice and 6 in the other.
6 in one dice and 5 in the other.
so out of 36 combinations, we have 2 options where we have an 11.
then the probability is the combinations that add to 11 divided by the total number of combinations:
p = 2/36 = 1/18 = 0.056
the probability is greater than 0.05, so it is significant.
Choose all of the angles that are coterminal with -150°.
-510°
-210°
150°
210°
570°
Answer:
210, 150
Step-by-step explanation:
Answer:
-510, 210 and 570.
Step-by-step explanation:
I'm on the same assignment right now! If you draw them you will see that those are the answers.
Use differentiation rules to find the values of a and b that make the function f(x) = ( x 2 if x ≤ 2, ax3 + bx if x > 2 differentiable at x = 2.
To make the function differentiable at x = 2, we must ensure continuity by matching function values and differentiability by equating derivatives from both sides at x = 2. Solving the system of equations obtained from these conditions will give the values of a and b.
Explanation:To find the values of a and b that make the function f(x) = { x² if x ≤ 2, ax³ + bx if x > 2 } differentiable at x = 2, we need to ensure both continuity and differentiability of f(x) at this point. First, continuity at x = 2 requires that the limits from the left and the right are the same, meaning f(2) = 2² = 4 should equal a(2)³ + b(2). Second, for differentiability, the derivatives from the left and right at x = 2 must also be equal. The derivative of x² is 2x, so f'(2) = 4. Differentiating ax³ + bx gives 3ax² + b, so f'(2) = 12a + b must also equal 4. Solving these equations:
4 = 8a + 2b4 = 12a + bgives us a system of equations that when solved, will provide the exact values of a and b required.
What is the inverse of the function f(x)=\sqrt[3]{7x-21}-3f(x)= 3 7x−21 −3f, (, x, ), equals, root, start index, 3, end index, square root of, 7, x, minus, 21, end square root, minus, 3 ?
given the equation is written in text so the signs and operators are weird, i don't understand the question but an inverse of any function can be found by switching f(x) or y with x.
For example if f(x) = 3x, then the inverse is x = 3y or y=x/3
Final answer:
The inverse of the function [tex]f(x) = \sqrt[3]{7x - 21} - 3[/tex] is found by first expressing the function as [tex]y = \sqrt[3]{7x - 21} - 3,[/tex] then isolating x, and finally expressing x in terms of y, resulting in the inverse function[tex]f^{-1}(y) = \frac{(y + 3)^3 + 21}{7}.[/tex]
Explanation:
To find the inverse of the function [tex]f(x) = \sqrt[3]{7x-21} - 3,[/tex] we want to solve for x in terms of y. First, we replace f(x) with y to get [tex]y = \sqrt[3]{7x-21} - 3.[/tex] We then solve for x using the following steps:
Add 3 to both sides of the equation to get[tex]y + 3 = \sqrt[3]{7x-21}.[/tex]
Raise both sides to the power of 3 to eliminate :[tex](y + 3)^3 + 21 = 7x.[/tex]
Finally, divide by 7 to isolate x, so[tex]x = \frac{(y + 3)^3 + 21}{7}.[/tex]
Thus, the inverse function is [tex]f^{-1}(y) = \frac{(y + 3)^3 + 21}{7}.[/tex]
In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different lots. This occurs when holding tanks are replenished and the remaining portion of a lot is insufficient to fill the tanks. Only 5% of batches with material from a single lot require reprocessing. However, the viscosity of batches consisting of two or more lots of material is more difficult to control, and 40% of such batches require additional processing to achieve the required viscosity. Let A denote the event that a batch is formed from two different lots, and let B denote the event that a lot requires additional processing. Determine the following probabilities:
a. P(A)
b. P(A')
c. P(B\A)
d. P(B\A')
e. P(A ∩ B)
f. P(A ∩ B')
g. P(B)
Step-by-step explanation:
By the problem we know that our events are:
[tex]A=[/tex]A batch is formed from two different lots.
[tex]B=[/tex]A batch requires additional processing.
So, according to that:
a) [tex]P(A)=3%=0.03[/tex]
Because P(A) and [tex]P(A^{'} )[/tex] are complementary events
b) [tex]P(A^{'} )=1-P(A)=1-0.03=0.97=97%[/tex]
Because of the problem, we know that:
c) [tex]P(B/A)=0.4=40%[/tex]
and,
d) [tex]P(B/A^{'} )=0.05=5%[/tex]
From the formula
e) P(A ∩ B)= P(A)*P(B/A)=[tex](0.03)*(0.4)=0.012[/tex]
f) P(A ∩ B')=P(A)-P(A ∩ B)=[tex]0.03-0.012=0.018[/tex]
And, finally
g) P(B)=P(B/A)*P(A)+P(B/A')*P(A')=[tex](0.4)*(0.03)+(0.05)(0.97)=0.0605[/tex]
(a)Probability of P(A) = 0.03 (b)Probability ofP(A') = 0.97.(c) Probability of P(B|A) = 0.40 (d) Probability of P(B|A') = 0.05 (e) Probability of P(A ∩ B) = 0.012. (f)Probability of P(A ∩ B') = 0.03 - 0.012 = 0.018. (g) Probability ofP(B) = 0.0605.
Let's determine the various probabilities step-by-step for the given scenario.
P(A): Probability that a batch is formed from two different lots.Given: P(A) = 0.03 (3% of all batches).
P(A'): Probability that a batch is formed from a single lot.P(A') = 1 - P(A) = 1 - 0.03 = 0.97.
P(B|A): Probability that a batch requires additional processing given it is formed from two different lots.Given: P(B|A) = 0.40 (40% of such batches).
P(B|A'): Probability that a batch requires additional processing given it is formed from a single lot.Given: P(B|A') = 0.05 (5% of such batches).
P(A ∩ B): Joint probability that a batch is formed from two different lots and requires additional processing.P(A ∩ B) = P(B|A) * P(A) = 0.40 * 0.03 = 0.012.
P(A ∩ B'): Joint probability that a batch is formed from two different lots and does not require additional processing.P(A ∩ B') = P(A) - P(A ∩ B) = 0.03 - 0.012 = 0.018.
P(B): Total probability that a batch requires additional processing. P(B) = P(B|A) * P(A) + P(B|A') * P(A') = (0.40 * 0.03) + (0.05 * 0.97) = 0.012 + 0.0485 = 0.0605.
Write an equation of the line with the given slope, m, and y-intercept (0.b).
m=8, b = 3
The equation is______
(Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation.)
Answer:
y = 8x + 3
Step-by-step explanation:
The slope-intercept form of the equation of a line is ...
y = mx + b
Putting 8 where m is, and 3 where b is, we get ...
y = 8x + 3
_____
Yes, it's really that simple.
The equation of the line with a slope of 8 and a y-intercept of 3 is y = 8x + 3. This is found by substituting the given values into the slope-intercept formula, which is y = mx + b.
Explanation:In Mathematics, the slope-intercept form of a linear equation is given by the formula y = mx + b, where 'm' represents the slope of the line and 'b' represents the y-intercept of the line. So, for the question, since the given slope, m = 8, and the y-intercept, b = 3, you can substitute these values into the formula to get the equation of the line. This results in the equation y = 8x + 3.
Learn more about Line Equation here:https://brainly.com/question/35689521
#SPJ3
Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their check dash in service, American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.
Answer:
This is cluster sampling.
Step-by-step explanation:
American Airlines randomly selects 110 flights during a certain week and surveys all passengers on the flights.
This is a type of cluster sampling.
This type of sampling is done by dividing the population into different groups and a simple random sample of clusters is selected from the population.
The length of a living room rug is 12 1/2 feet, and the width is 10 3/4 feet. There is a loveseat that covers 12 1/2 squrare feet of the rug and an entertantment center that cover 6 squrare feet. What is the area of the rug that can be seen?
Answer:
134.375 - 12.5 - 6 = 115.875
The area of the rug that can be seen after covering love seat and entertainment center is 115.875 square feet.
What is rectangle?A rectangle is a part of a quadrilateral, whose sides are parallel to each other and equal.
Given that,
The length of rug in living room = 12¹/₂ feet = 25 /2 feet.
And the width of rug = 10 ³/₄ feet= 43 /4 feet.
The area of the rug = width x length = 25/2 x 43 / 4 = 1075 / 8 = 134.375 square feet.
Also given that,
A love seat having area = 12¹/₂ square feet.
And area of entertainment center = 6 square feet
Area covered by love seat and entertainment center = 12.5 + 6 = 18.5 square feet
The remaining area that can be seen = 134.375 - 18.5 = 115.875 square feet.
The required area is 115.875 square feet.
To know more about Rectangle on:
https://brainly.com/question/15019502
#SPJ5
A major purpose of preparing closing entries is to a) adjust the asset accounts to their correct current balances. b) update the Retained Earnings account. c) close out the Supplies account. d) zero out the liability accounts.
Answer:
b) update the Retained Earnings account.
Step-by-step explanation:
A major purpose of preparing closing entries is to - update the Retained Earnings account.
Retained earnings are defined as those profits, that a company has earned to date minus any dividends or other money paid to investors.
Whenever we make an entry to the accounting records, that affects a revenue or expense account, this retained earning amount is adjusted.
The major purpose of preparing closing entries is to update the Retained Earnings account by transferring the balances of temporary accounts to it, effectively resetting these accounts for the next period. This ensures that the company's financial statements only reflect the transactions of the current period.
Explanation:The student's question relates to the major purpose of preparing closing entries in accounting. The correct answer to the question is b) update the Retained Earnings account. Closing entries are an essential part of the accounting cycle that serves to transfer the balances of temporary accounts (like revenues, expenses, dividends/distributions, and income summary) to the Retained Earnings account to reflect the changes that occurred over the period. This process resets the balance of the temporary accounts to zero, ready for the next accounting period, while updating the balance of the Retained Earnings to reflect the net income or loss that was earned or incurred during the period.
'T-accounts' help visualize the transactions and balances of accounts including assets, liabilities, and equity. When closing entries are made, we are not adjusting asset or liability accounts (which are permanent accounts) directly. Instead, we close temporary accounts to a permanent equity account, typically Retained Earnings, based on the principle that assets will always equal liabilities plus net worth.
The steps in preparing closing entries generally involve: first, closing all revenue accounts to Income Summary; second, closing all expense accounts to Income Summary; third, closing the Income Summary account to Retained Earnings; and lastly, closing any dividends or distributions to Retained Earnings.
Keira and Javier are grouping equations based on the number of operations needed to solve them in order to solve them in order to solve the equation -5(2+x)=53
To solve the equation -5(2+x)=53, we need to use the order of operations and follow the steps mentioned in the detailed answer. The solution to the equation is x=-12.6.
Explanation:In order to solve the equation -5(2+x)=53, we need to use the order of operations. Let's break it down step by step:
First, we need to distribute the -5 to both 2 and x. This gives us -10-5x=53.Next, we combine like terms by adding 10 to both sides of the equation, which gives us -5x=63.Finally, we divide both sides of the equation by -5 to isolate the variable x. This gives us x=-12.6.So, the solution to the equation -5(2+x)=53 is x=-12.6.
Learn more about Solving Equations here:https://brainly.com/question/18322830
#SPJ2
The man entered an orchard that had 7 guards and picked some apples. When he left, he gave the first guard half his apples and 1 apple more. To the second guard, he gave half his remaining apples and 1 more. He did the same to each of the remaining five guards and left the orchard with 1 apple. How many apples did he gather in all? Explain how you solved the problem.
Answer:
896 apples
Step-by-step explanation:
We need to order this data to solve the problem. "X" will be the total number of apples he collected.
"He gave the first guard half of his apples and 1 apple more". Mathematically:
[tex]Guard 1 = \frac{X}{2}+1\\[/tex]
"To the second guard, he gave half his remaining apples and 1 more". Mathematically:
[tex]Guard2 = \frac{X}{4}+1[/tex]
"He did the same to each of the remaining five guards". Mathematically:
[tex]Guard3to7 = \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]
Now we need to calculate "X" (total number of apples he collected). Let's sum all of the data above, that's our "X":
[tex]X= \frac{X}{2}+1 + \frac{X}{4}+1 + \frac{X}{8}+1+\frac{X}{16}+1+\frac{X}{32}+1+\frac{X}{64}+1+\frac{X}{128}+1[/tex]
Solving this equation results in X = 896 apples.
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!! THIS IS THE LAST DAY TO COMPLETE THIS ASSIGNMENT AND I DESPERATELY NEED TO FINISH THIS ASSIGNMENT WITH AN 100%.
Answer: it is B.) 7,000,000
Step-by-step explanation: