The probability of drawing two aces from a well-shuffled deck of 52 cards without replacement is 0.45%.
The probability of drawing two aces from a well-shuffled deck of 52 cards without replacement can be calculated as follows:
First, we calculate the probability of drawing an ace on the first draw. Since there are four aces in the deck and 52 cards in total, the probability of drawing an ace on the first draw is:
P(Ace on first draw) = 4/52 = 1/13
Next, we need to calculate the probability of drawing an ace on the second draw, given that an ace was already drawn on the first draw. Since there are now only three aces remaining in the deck and 51 cards in total, the probability of drawing an ace on the second draw is:
P(Ace on second draw given an ace on first draw) = 3/51
To calculate the probability of drawing two aces, we multiply the probability of drawing an ace on the first draw by the probability of drawing an ace on the second draw, given that an ace was already drawn on the first draw:
P(Drawing two aces) = P(Ace on first draw) x P(Ace on second draw given an ace on first draw)
P(Drawing two aces) = (1/13) x (3/51)
P(Drawing two aces) = 0.0045 or approximately 0.45%.
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The creator of two apps records the number of downloads over time a. From Week 6 to Week 8, which app has a greater average rate of change b. WHich app will eventually have a greater number of downloads? Explain.
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 14
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
13) The best prediction is that the college will need about 480 cookies.
14) The correct answer is Bus 47, with a median of 16.
Solution to the aforementioned questionFor Question 13:
The total number of students surveyed is 225. Out of these, 27 students prefer cookies. So, we can estimate that approximately (27/225) * 4000 = 480 students will prefer cookies.
Therefore, the best prediction is that the college will need about 480 cookies.
For Question 14:
The correct graph for displaying the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.
For Question 15:
We can see that the median for Bus 18 is (10+12)/2 = 11 and the median for Bus 47 is (16+16)/2 = 16. Therefore, Bus 47 typically has the faster travel time.
The correct answer is Bus 47, with a median of 16.
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PLEASE PLEASE PLEASE HELP MEEEEEE!!!!!!!!!!!!!!!!!!!!
The femur length for someone with a height of 187 cm is; 55 cm
How to find interpret the scatter plot?The formula for the equation of a line formed by 2 coordinates is;
(y2 - y1)/(x2 - x1) = (y - y1)/(x - x1)
Using the coordinates (30, 127) and (35, 139), we have;
(139 - 127)/(35 - 30) = (y - 127)/(x - 30)
12/5 = (y - 127)/(x - 30)
12(x - 30) = 5(y - 127)
12x - 360 = 5y - 635
5y = 12x + 275
Thus, when the height is y = 187 cm, we have;
5(187) = 12x + 275
935 = 12x + 275
12x = 935 - 275
12x = 660
x = 660/12
x = 55 cm
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You paint four walls. Each wall is a rectangle with a length of 20 feet and a height of 12 feet. One gallon of paint covers about 320 square feet. How many gallons of paint do you need in order to cover the walls?Give explanation
Answer:
To find out how many gallons of paint are needed to cover the walls, we need to first find the total area of the walls.
The four walls are rectangles with a length of 20 feet and a height of 12 feet. So, the area of one wall is:
20 feet x 12 feet = 240 square feet
Since there are four walls, the total area of the walls is:
4 x 240 square feet = 960 square feet
We know that one gallon of paint can cover approximately 320 square feet. To find how many gallons of paint are needed, we can divide the total area of the walls by the area covered by one gallon of paint:
960 square feet ÷ 320 square feet per gallon = 3 gallons of paint
Therefore, you need approximately 3 gallons of paint to cover the walls.
what are the domain and range of the function represented by the set of ordered pairs? {(-10,-6),(-4,-10),(3,8),(9,-2)}. APEX
The domain of the data set {(-10,-6),(-4,-10),(3,8),(9,-2)} are {-10, -4, 3, 9} and the range are {-6, -10, 8, -2}.
How to find the domain and range?The domain of a function is the set of all possible inputs for the function. In other words, the domain of a function is the independent value of a function. The domain are usually the x values.
The range of a function refers to all the possible values y could be. Therefore, the range is the dependent values. The range are usually the y values.
Hence,
The domain of the data set are {-10, -4, 3, 9}
The range of the data sets are {-6, -10, 8, -2}
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A two-digit number is less than 6 times the sum of its digits by 1. The difference between the digit is 1. Find the number.
Answer:
the two-digit number is 65.
Step-by-step explanation:
Let's assume that the tens and units digits of the two-digit number are x and y, respectively.
According to the given condition,
10x + y < 6(x + y) - 1 (less than 6 times the sum of its digits by 1)
Simplifying the above equation, we get:
4x - 5y < -1 (dividing both sides by 2)
Also, it is given that the difference between the digits is 1, so we can write:
x - y = 1 (difference between the digits is 1)
Now, we need to solve these two equations to find the values of x and y.
Multiplying the second equation by 4, we get:
4x - 4y = 4
Adding this equation to the first equation, we get:
4x - 5y + 4x - 4y = 3
Simplifying the above equation, we get:
8x - 9y = 3
Now, we can solve these two equations simultaneously to find the values of x and y.
Multiplying the second equation by 8, we get:
8x - 8y = 8
Subtracting this equation from the previous equation, we get:
y = 5
Substituting this value of y in the equation x - y = 1, we get:
x - 5 = 1
x = 6
Therefore, the two-digit number is 65.
Help, please, is for today.
Help it’s math it a picture
Answer:the first one
Step-by-step explanation:
9PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ALL FAKE ANSWERS WILL BE REPORTED
Answer: sin x= 20/24 x = 34
Step-by-step explanation:
A 40-year-old person who wants to retire at age 60 starts a yearly retirement contribution in the amount of $6,000. The retirement account is forecasted to average a 5% annual rate of return, yielding a total balance of $198,395.72 at retirement age. If this person had started with the same yearly contribution at age 30, what would the difference be in the account balances? A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used. a. $200,732.63 b. $200,237.36
c. $398,633.09 d. $389,633.90
Answer: B.
200,237.36
Step-by-step explanation: just got it right on the quiz
can some one help me please :(
Answer:
100ft²
Step-by-step explanation:
to find the area of the figure you must do the area of the small rectangle plus the area of the large rectangle
area = length* width
so the area of the small rectangle equals
7ft * 4ft = 28ft²
then the large rectangle
9ft*8ft=72ft²
28ft²+72ft²=100ft²
pls hlp thx ur awesome
The value of k is 20.
Describe Equation?An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables and may involve arithmetic operations such as addition, subtraction, multiplication, division, or exponents. The goal of solving an equation is to determine the value of the variable that makes the equation true. Equations are commonly used in algebra and other mathematical fields to model real-world situations and solve problems. They can be written in various forms, including standard form, slope-intercept form, point-slope form, and general form, among others.
Since the sum of two angles on a straight line is always 180 degrees, we can set up an equation:
First angle + Second angle = 180
112 + 3k + 8 = 180
Simplifying the equation, we get:
3k + 120 = 180
Subtracting 120 from both sides, we get:
3k = 60
Dividing both sides by 3, we get:
k = 20
Therefore, the value of k is 20.
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will give brainliest to quickest answer
Answer:
The vertex is option C: (-6, -2)
Step-by-step explanation:
The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)
Pls mark brainliest.
HELP IS VERY MUCH APPRECIATED PLS just tell me what box and number belongs where pls
The area of figures are calculated a follows:
1. 78.5 m² 2. 66.5 m² 3. 35 m² 4. 153.86 m² 5. 70 m²
How to Find the Area of the Figures?1. The area of the circle = πr²
= 3.14 * 5²
= 78.5 m²
2. The figure is a trapezoid, therefore:
Area of the trapezoid = 1/2 * (a + b) * h
= 7(5 + 14)/2
= 66.5 m²
3. Area of triangle = 1/2 * base * height = 1/2 * 14 * 5 = 35 m²
4. The area of the circle = πr²
= 3.14 * 7²
= 153.86 m²
5. Area of parallelogram = base * height = 14 * 5 = 70 m²
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identify a syntax that sets the data type of the registerdate field to ""date"".
To set the data type of the registerdate field to "date", the syntax would depend on the programming language or database management system being used. However, here are some examples:
In SQL, the syntax would be:
ALTER TABLE tablename MODIFY COLUMN registerdate DATE;
This statement modifies the registerdate column in the tablename table to have a data type of DATE.
In PHP, the syntax for creating a table with a register date column of data type DATE would be:
CREATE TABLE tablename (
...,
registerdate DATE,
...
);
This creates a table called tablename with a column called registerdate of data type DATE.
In Python using SQLAlchemy, the syntax for defining a registerdate column of data type Date in a declarative base would be:
from sqlalchemy import Column, Date
class MyTable(Base):
__tablename__ = 'mytable'
registerdate = Column(Date)
This creates a MyTable class with a column called registerdate of data type Date.
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To set the data type of the registerdate field to "date", the syntax would depend on the specific programming language or database system being used. However, a common syntax to set the data type to "date" is:
registerdate DATE;
This syntax would typically be used in the creation of a table or the declaration of a variable in a programming language that supports date data types.
To identify a syntax that sets the data type of the 'registerdate' field to "date", you can use the following SQL statement:
```sql
CREATE TABLE your_table_name (
registerdate DATE
);
```
Here's a step-by-step explanation of the syntax:
1. "CREATE TABLE" is the command to create a new table in the database.
2. "your_table_name" should be replaced with the desired name for your table.
3. Within the parentheses, you define the columns and their data types.
4. "registerdate" is the name of the field that you want to set the data type for.
5. "DATE" is the data type you are setting for the 'registerdate' field.
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Please answer part b
Taking the quotient between the total volume and the flow rate, we can see that the correct option is D.
For how long has Jeremy been watching the falls?We know that water flows at a rate of 1.5*10^4 gallons per second. We know that 6.525*10^6 gallons flowed while Jeremy was watching, then the time that he has been watching is the quotient between these values, we will get:
time = ( 6.525*10^6)/(1.510^4) seconds = (652.5/1.5) second = 435 seconds
We know that 60 secons = 1 minute, then:
435/60 = 7 + 15/60
So he has been watching for 7 minutes and 15 seconds, the correct option is D.
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From a standard deck of cards, your first draw is a black card. You replace the card, and the second draw is a diamond. Which THREE statements are correct for the outcome of the event?
The correct statements for the given probability are-
A) There is a 1/2 chance of drawing the black card.B) 1/4, you'll draw the diamond.D) The compound event's probability is 1/8.Explain about the deck of cards:The following are the key concepts for probability problems to understand:
A deck of cards contains 52 cards in total.There are 13 different card ranks. These ranks include of jack, queen, king, and aces as well as the digits 2 through 10. The ranking is described as being "ace high."Hearts, diamonds, spades, and clubs are the four suits. There are therefore 13 clubs, 13 spades, 13 diamonds, and 13 hearts.Red text is used to print the diamonds and hearts. Black ink is used to print the spades and clubs. Hence, there are 26 red and 26 black cards.Given condition:
Your initial draw is a black card from a regular deck of cards.You switch out the card, and a diamond is drawn on the second draw.Total number of card in deck = 52
Total black cards = 26
Total diamonds = 13
So,
probability ( black card ) = total black card / total cards
probability ( black card ) = 26 /52
probability ( black card ) = 1/2
probability (diamond ) = total number of diamond cards / total cards
probability (diamond ) = 13/ 52
probability (diamond ) = 1/4
probability (compound event) = probability (black and diamond)
probability (compound event) = 1/2 * 1/4
probability (compound event) = 1/8
Thus, The correct statements for the given probability are-
A) There is a 1/2 chance of drawing the black card.B) 1/4, you'll draw the diamond.D) The compound event's probability is 1/8.Know more about the deck of cards:
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Complete question:
From a standard deck of cards, your first draw is a black card. You replace the card, and the second draw is a diamond. Which THREE statements are correct for the outcome of the event?
A) The probability of drawing the black card is 1/2
B) The probability of drawing the diamond is 1/4
C)The probability of the compound event is 1/6
D) The probability of the compound event is 1/8
E) The probability of the compound event is 3/4
the city's pr manager, who never took statistics, claimed the mean score of all ninth graders in the city was the average of 77, 91, and 71, which is 79.7. of course, that is incorrect. what is the mean score for all ninth graders in the city? round to one decimal place.
The mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.
To find the mean score for all ninth graders in the city, we need more information than just three scores. Without additional data, we cannot accurately determine the mean score for all ninth graders in the city.
However, we can calculate the mean of the given scores to verify that it is not 79.7 as claimed by the PR manager:
Mean = (77 + 91 + 71) / 3 = 79.7/3 = 79.7 ÷ 3 ≈ 79.7/3 ≈ 26.6
So the mean score of the given three scores is approximately 26.6, which is not the mean score for all ninth graders in the city.
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Which operation can we use to solve for x in the equation 12+x=15?
A) Add 12 to both sides of the equation
B) Divide both sides of the equation by 12
C) Multiply both sides of the equation by 12
D) Subtract 12 from both sides of the equation
Answer:
Subtract 12 from both sides of the equation
Step-by-step explanation:
Solve for x:
12+x=15
-12 -12
x = 3
Brainlist please.
Answer:
D) Subtract 12 from both sides of the equation.
To solve for x in the equation 12 + x = 15, we need to isolate the variable x on one side of the equation. We can do this by subtracting 12 from both sides of the equation, which gives:
12 + x - 12 = 15 - 12
x = 3
Therefore, the solution for x is 3.
Eat your cereal: Boxes of cereal are labeled as containing 14 ounces. Following are the weights, in ounces, of a sample of 14 boxes. It is reasonable to assume that the population is approximately normal. 14.07 13.99 14.16 14.17 14.15 14.11 14.24 13.99 14.14 14.13 14.20 14.21 14.06 14.05 Send data to Excel Part: 0 / 20 of 2 Parts Complete Part 1 of 2 (a) Construct a 99.9% confidence interval for the mean weight. Round the answers to at least three decimal places. A 99.9% confidence interval for the mean weight is <<μ.
The 99.9% confidence interval for the mean weight is (14.042, 14.202).
What is statistics?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data.
To construct a 99.9% confidence interval for the mean weight, we can use the formula:
CI = X ± Zα/2 * (σ/√n)
where X is the sample mean, Zα/2 is the critical value from the standard normal distribution corresponding to a 99.9% confidence level (which is 3.291), σ is the population standard deviation (which we don't know, so we will use the sample standard deviation as an estimate), and n is the sample size.
First, we need to calculate the sample mean and sample standard deviation:
X = (14.07 + 13.99 + 14.16 + 14.17 + 14.15 + 14.11 + 14.24 + 13.99 + 14.14 + 14.13 + 14.20 + 14.21 + 14.06 + 14.05) / 14 = 14.122
s = sqrt((1/(n-1)) * ∑(xᵢ - X)²) = 0.072
where n is the sample size and ∑(xᵢ - X)² is the sum of squared deviations from the sample mean.
Plugging in the values, we get:
CI = 14.122 ± 3.291 * (0.072/√14) = (14.042, 14.202)
Therefore, the 99.9% confidence interval for the mean weight is (14.042, 14.202).
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A line passes through the points (−4, 50) and (5, −31). What is the equation of the line in slope-intercept form?
Answer:
y = - 9x + 14
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 50 ) and (x₂, y₂ ) = (5, - 31 )
m = [tex]\frac{-31-50}{5-(-4)}[/tex] = [tex]\frac{-81}{5+4}[/tex] = [tex]\frac{-81}{9}[/tex] = - 9 , then
y = - 9x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (5, - 31 )
- 31 = - 9(5) + c = - 45 + c ( add 45 to both sides )
14 = c
y = - 9x + 14 ← equation of line
5. 5 boys and 5 girls sit in a row in a random order (each order is equally likely). what is the probability that no two people of the same sex sit next to each other?
the probability that no two people of the same sex sit next to each other is 2/7.
One way to solve this problem is to use the principle of inclusion-exclusion. Let A be the event that the boys sit next to each other, and let B be the event that the girls sit next to each other. Then, we want to find the probability of the complement of (A or B), which is the probability that neither A nor B occurs.
The probability of A occurring is the same as the probability of the 5 boys sitting in a row, which is 5! (since each order is equally likely). Similarly, the probability of B occurring is 5!. However, we need to subtract the probability of A and B occurring simultaneously. This can be seen as follows: once the boys are seated in a row, there are 6 spaces (between or on the ends) where the girls can be seated. Thus, the probability of A and B occurring is 2*5!*6.
Therefore, the probability of neither A nor B occurring (i.e., the probability that no two people of the same sex sit next to each other) is:
P(neither A nor B) = 1 - P(A or B) = 1 - [P(A) + P(B) - P(A and B)]
= 1 - [(25!) / 10! - (25!6) / 10!]
= 1 - [25!*(1 - 6/9!)]
= 2/7
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what is the probability that a random integer from 91 to 775 is divisible by 14? (all integers in the given range are equally likely to be chosen).
Answer:
There are 775 - 91 + 1 = 685 integers.
In the given range, the smallest multiple of 14 is 98, and the largest multiple of 14 is 770. ((770-98)/14) + 1 = 49 multiples of 14.
So the probability of choosing a multiple of 14 from this range is 49/685.
Basketballs cost 24$. a physical education teacher spent 312$ on basketballs for the school.
Which equation can be used to determine the number (n) of basketballs the physical education teacher purchased?
A. 24+n=312
B. 24/n =312
C. 24n= 312
D. 24 =312-n
URGENT!!!
A cube-shaped box has a volume of 27 in.3. A similar cube-shaped box that holds x in .3 more has its volume modeled by the expression x + 27. If the difference in volumes of the two boxes is 30 in.3, what is the side length of
the second box? Round your answer to the nearest hundredth of an inch.
The side length of the second cube is 3.8 in.
What is a cube?Cube is a solid shape that has all its sides equal.
To calculate the side length of the second cube, we use the formula below
L' = ∛V'............................ Equation 1Where:
L' = Side of the length of the second cubeV' = Volume of the second cubeFrom the question,
Given:
V' = (27+30) = 57 in³Substitute these values into equation 1
L' = ∛(57)L' = 3.8 inHence, the length is 3.8 in
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Need help on the last two as well this math is hard for me to understand
he life expectancy of a typical lightbulb is normally distributed with a mean of 1,975 hours and a standard deviation of 25 hours. What is the probability that a lightbulb will last between 1,950 and 2,050 hours
The probability that a lightbulb will last between 1,950 and 2,050 hours is 0.84, or 84%.
To solve this problem, we need to find the probability that the lifespan of a lightbulb will fall between 1,950 and 2,050 hours.
First, we need to standardize the distribution using the z-score formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean, and σ is the standard deviation.
For x = 1,950 hours:
z = (1,950 - 1,975) / 25 = -1
For x = 2,050 hours:
z = (2,050 - 1,975) / 25 = 3
Now, we need to find the area under the standard normal distribution curve between z = -1 and z = 3. We can use a standard normal distribution table or a calculator to find this area.
Using a standard normal distribution table, we find that the area to the left of z = -1 is 0.1587 and the area to the left of z = 3 is 0.9987. Therefore, the area between z = -1 and z = 3 is:
0.9987 - 0.1587 = 0.84
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If the star Aldebaran rises tonight at 2:00 a.m., when do you expect it to rise next month?
a) 11:00 pm.
b) midnight.
c) 1:00 am. d) 2:00 am. e) 3:00 am
Your answer is option b)
The time at which a star rises shifts approximately 4 minutes earlier each day, due to Earth's orbit around the Sun. Since there are roughly 30 days in a month, we can calculate the change in the rise time of Aldebaran over the course of a month.
Step 1: Calculate the time change over one month
30 days * 4 minutes per day = 120 minutes
Step 2: Convert minutes to hours
120 minutes ÷ 60 minutes per hour = 2 hours
Step 3: Subtract the time change from the current rise time
2:00 am - 2 hours = 12:00 am (midnight)
Therefore, you can expect Aldebaran to rise next month at midnight. The correct answer is b) midnight.
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ANSWER FAST PLEASE!!
Answer:
P(heads) = 1/2
There are 4 prime numbers less than 10: 2, 3, 5, 7.
P(prime number) = 4/10 = 2/5
1/2 × 2/5 = 1/5
Which of the following is the best example of a defined benefits plan?
O a set amount an employee will receive at retirement
O the wages and benefits an employee receives at a job
O the amount of pay an employee receives each hour
O the money the an employer puts into a retirement fund for each employee
Answer:
The best example of a defined benefits plan is: "a set amount an employee will receive at retirement".
In a defined benefits plan, the employer promises to pay employees a specific, predetermined amount of money upon retirement. This amount is typically based on factors such as the employee's salary and years of service. The employer is responsible for contributing to and managing the retirement fund, and the employee receives a guaranteed amount of money upon retirement, regardless of how the fund performs.
The other options listed are not examples of defined benefits plans. The wages and benefits an employee receives at a job are part of their compensation package and may include retirement benefits, but they do not guarantee a specific amount of money at retirement. The amount of pay an employee receives each hour is their hourly wage and is not related to retirement benefits. The money an employer puts into a retirement fund for each employee may be part of a defined benefits plan, but it is not a complete plan in and of itself.