The experimental probability that the number rolled was odd is
23 over 60.
What is experimental probability?
Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A trial is a repeating of an experiment that is performed a certain number of times.
We are given a table showing he frequency of each number rolled.
We know that the odd number outcomes are 1, 3 and 5.
So,
P (x = 1) = 8/60
P (x = 3) = 6/60
P (x = 5) = 9/60
So, the experimental probability that the number rolled was odd is
⇒P ( x is odd) = P (x = 1) + P (x = 3) + P (x = 5)
⇒P ( x is odd) = 8/60 + 6/60 + 9/60
⇒P ( x is odd) = 23/60
Hence, the experimental probability that the number rolled was odd is 23 over 60.
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Four children are playing a card game. The chart shows the number of cards each child has in his or her stack.
Name Number of Cards
Chris 7
Mike 8
Sally 10
Susan 25
Which is equivalent to Mike’s portion of the total number of cards?
A.) 2/25
B.) 16%
C.) 8/25
D.) 80%
(PLEASE EXPLAIN HOW YOU GOT THIS ANSWER)
The requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
From the given data,
Name Number of Cards
Chris 7
Mike 8
Sally 10
Susan 25
Total cards = 50
Now equivalent to Mike’s portion of the total number of cards is given as ,
= Mike cards/total card
= 8 / 50 × 100%
= 4/25×400%
= 16%
Thus, the requried equivalent to Mike’s portion of the total number of cards is 16%. Option B is correct.
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find the value of x y and z
The values of x, y and z are;
x. x = 60° y = 55°
xi. x = 68° y = 56° z = 56°
xiii. x = 40° y = 50°
xiv. x = 40° y = 50°
What is a Triangle?A triangle is a 3-sided polygon that has three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle that always equals 180 degrees. This property is called angle sum property of triangle.
x. x = 60° (corresponding angles are equal)
y + 65° + 60° = 180° (Sum of angles in a triangle equals 180°)
y + 125° = 180°
y = 180° - 125°
y = 55°
xi. y = 56° (corresponding angles are equal)
y = z = 56° (angles in equal sides of a triangle are equal)
x + 56° + 56° = 180° (Sum of angles in a triangle equals 180°)
x + 112° = 180°
x = 180° - 112°
x = 68°
xiii. x + 140° = 180° (sum of angles on a straight line equals 180°)
x = 180° - 140°
x = 40°
y + 90° + 40° = 180° (sum of angles in a triangle equals 180°)
y + 130° = 180°
y = 180° - 130°
y = 50°
xiv. y + 130° = 180° (sum of angles on a straight line equals 180°)
y = 180° - 130°
y = 50°
x + 90° + 50° = 180° (sum of angles in a triangle equals 180°)
x + 140° = 180°
x = 180° - 140°
x = 40°
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Find the cost per pound of a house blend of coffee that is made from 10 lb of Central American coffee that costs $9 per pound and 40 lb of South American coffee that costs $5.50 per pound.
The cost per pound of a house blend of coffee is $ 5 per pound.
What is the cost price?
The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.
Here, we have
Weight of Central American coffee = 10 lb
Cost of Central American coffee = $7 per pound
Total value of Central American coffee = weight × cost = 10 ×7 = $ 70
Weight of South American coffee = 40 lb
Cost of South American coffee = $ 4.50 per pound
Total value of Central American coffee = weight × cost = 40 ×4.50 = $ 180
Total weight of house blend coffee = Weight of Central American coffee + weight of South American coffee
= 10 +40 = 50 lb
The total value of house blend coffee = value of Central American coffee + value of South American coffee
= $ 70 + $ 180 = $ 250
Cost per pound of house blend coffee = ( total value of house blend coffee) / (total weight of house blend coffee)
= 250 / 50 = $ 5 per pound
Hence, the cost per pound of a house blend of coffee is $ 5 per pound.
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what is the solution to 4+5ex+2=11?
The solution to the equation is (a) x = ln(7/5) - 2
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
4 + 5e^(x + 2) = 11
Evaluate the like terms in the equation
So, we have the following representation
5e^(x + 2) = 7
Divide through the equation by 5
This gives
e^(x + 2) = 7/5
Take the natural logarithm of both sides
x + 2 = ln(7/5)
So, we have
x = ln(7/5) - 2
Hence, the solution is x = ln(7/5) - 2
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do you believe that this conjectures "all numbers coming from the question p=n²-n+41 are prime numbers"?
Answer: No
Step-by-step explanation:
Valid only for numbers less than 40.
P(40) = 412 which is not a prime number
-12,1 and x,7 when m = 1/8
The x has a value of 36. The line's two points are (-12, 1) and (36, 7).
The purpose of slope calculation?The slope of a line frequently represents the steepness and direction of the line. The slope of a straight line between the two locations, (x1,y1) and (x2,y2), can be easily determined by calculating the difference between their coordinates.
We can apply the slope formula to determine the value of x:
m is the slope and (x1, y1) and (x2, y2) are two points on the line, with m = (y2 - y1) / (x2 - x1).
We are given the point (x1, y1) = (-12, 1) and the slope m = 1/8. We are also given the y-coordinate of the other point as y2 = 7.
Plugging in the known values, we get:
1/8 = (7 - 1) / (x - (-12))
Simplifying and solving for x, we get:
1/8 = 6 / (x + 12)
1 = 48 / (x + 12)
x + 12 = 48
x = 36
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The correspondence f: X- Yis defined by the function ((-18, -31), (-9, -23), (4, 2), (11, 5), (14, 12)). Consider the
correspondence g that includes the ordered pairs of f.
Which additional ordered pairs can be included in g, assuming g is a function. SELECT ALL THAT APPLY.
A(-9, 11)
B (-7,-10)
C (5, 12)
D (4, 15)
E (14,20)
Answer:
B. (-7, -1)
C. (5, 12)
Step-by-step explanation:
A function can only have one output for a specific input
In math terminology that means if y = f(x) is a function of x then the mapping from x to y is 1:1
Or,
For a specific value of x, there can be one and only one value for y
This is often referred to as a vertical line test; if a vertical line parallel to the y-axis is drawn for any x value it should intersect the function graph at one and only one point
g(x) includes all the ordered pairs of f(x) therefore the ordered pairs of g(x) are:
{ ( -18, -31), (-9, -23), (4, 2), (11, 5), (14, 12) }
Looking at the answer choices:
A. (-9, 11) will violate the 1:1 correspondence between x and y since (-9, -23) is already a pair
B. (-7, -1) is OK. There is no other entry with x = -7
C. (5, 12) is OK. There is no other entry with x = 5
D. (4, 15) will violate; there is already an entry for x = 4: (4, 2)
E. (14,20). This will also violate the properties of a function since there exists an entry for x = 14, namely (14, 20)
A person on a moving sidewalk travels 28 feet in 7 seconds. The moving sidewalk has a length of 200 feet. How long will it take to move from one end to the other?
It will take 50 seconds for the person to travel from one end to the other at the current speed.
How long will it take to move from one end to the other?
We know that the person travels 28 feet in 7 seconds, remember that speed is defined as the quotient between distance and time, then the person's speed is:
s = 28ft/7s = 4ft/s
Now we want to find the time T that it takes for the person to travel the 200 feet of the sidewalk, then we need to solve:
(4ft/s)*T = 200ft
T= 200ft/(4 ft/s) = 50s
It takes 50 seconds.
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Nakeisha is trying to pick out an outfit for the first day of school. She can choose from 2 pairs of pants, 6 t-shirts, and 3 pairs of shoes. How many different outfits does Nakeisha have to choose from?
Answer:
Step-by-step explanation:
multiply all numbers together
2 x 6 x 3 = 36
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
Answer:
the iqr is the best measure of variability
The IQR is the best measure of variability, and it equals 4.
Option C is the correct answer.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
The appropriate measure of variability for the data is the interquartile range (IQR), which is the range of the middle 50% of the data.
In other words, it is the difference between the third quartile (Q3) and the first quartile (Q1).
From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.
This means that Q1 is 17 and Q3 is 21.
The IQR is:
IQR = Q3 - Q1 = 21 - 17 = 4
Thus,
The IQR is the best measure of variability, and it equals 4.
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7y² - 13y + 2 = 0
2.1.1 Solve for y. Round your answer to two decimal places.
The solution of the quadratic equation for y is given as follows:
y = 0.17 and y = 1.69.
How to solve the quadratic equation?The quadratic equation for this problem is defined as follows:
7y² - 13y + 2 = 0.
The coefficients are given as follows:
a = 7, b = -13 and c = 2.
Hence the discriminant is of:
D = (-13)² - 4 x 7 x 2
D = 113.
The first root is of:
y = (13 + sqrt(113))/14
y = 1.69.
The second root is of:
y = (13 - sqrt(113))/14
y = 0.17.
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3 days is 72 hours in those 72 hours i slept 12. 5% how many hours did i sleep in those three days?
You slept for 9 hours in those three days, calculated by multiplying 12.5% of the total hours (72) by 72, which equals 9.
To calculate the number of hours slept in three days, we first need to determine how many hours there are in three days.
As given, 1 day has 24 hours. So, three days will have 3 x 24 = 72 hours.
Now, we are told that you slept for 12.5% of those 72 hours. To calculate this, we multiply the percentage by the total number of hours:
12.5% x 72 hours = (12.5/100) x 72 = 0.125 x 72 = 9 hours
Therefore, you slept for 9 hours in those three days.
Percentage is a way to express a proportion or ratio as a fraction of 100. The sign "%" is widely used to represent it. For example, if you had 20 apples and you ate 5 of them, you would have consumed 25% of the apples (5 out of 20).
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Solve the word problem below. Enter your answer in simplest terms, using the
slash (/) to represent the fraction bar.
A recipe for a soup calls for 2/4 cup of chopped onion and 1/6 cup of chopped
celery. What is the total amount of celery and onion needed for the soup
Answer:
2/3 cups
Step-by-step explanation:
The recipe calls for 2/4 cup of onion and 1/6 cup of celery. To find the total, we need to add the two fractions together; the amount of onions(2/4 cup or 1/2 a cup if simplified), and the amount of celery(1/6). To do this, we need to find a common denominator. We can do this buy finding a common multiple between 2 and 6.
Multiples of 2: 2, 4, 6, 8, 10, 12...
Multiples of 6: 6, 12, 18, 24, 30...
A common multiple is 6. 1/2x3/3=3/6 <--- an equivalent fraction of 1/2
Now both fractions have the same denominator:
Onions: 3/6
Celery: 1/6
3/6+1/6 = 4/6
4/6 simplifies to 2/3.
The total amount of celery and onion need for the soup is 2/3 cup
Answer:
2/3 cups
Step-by-step explanation:
2. Find the number of ways in which 9 different computer games can be shared out between Wendy, Jim and Hannah so that each person receives an odd number of computer games.
Using combinatorics, there are 1926 ways to distribute 9 different computer games among Wendy, Jim, and Hannah so that each person receives an odd number of games.
What is the number of ways the game is shared between themIf each person receives an odd number of games, then the number of games must be 1, 3, 5, or 7. There are four odd numbers to choose from.
We can use combinatorics to find the odd number in each turn.
Let's consider each odd number in turn.
If each person gets 1 game, then we are looking for the number of ways to choose 3 games out of 9 to distribute. This is simply the number of combinations of 3 things taken from a set of 9 things, which is 9C3, or (9!)/(3!6!) = 84.
If each person gets 3 games, then we are looking for the number of ways to choose 3 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 6 games to distribute to the other two people. The number of ways to choose 3 games out of 9 is again 84, but we must multiply this by the number of ways to choose 3 games out of the remaining 6. This is 6C3, or (6!)/(3!3!) = 20. Therefore, the total number of ways to distribute 9 games with each person getting 3 games is 84*20 = 1680.
If each person gets 5 games, then we are looking for the number of ways to choose 5 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 4 games to distribute to the other two people. The number of ways to choose 5 games out of 9 is 126, and the number of ways to choose 4 games out of the remaining 4 is 1. Therefore, the total number of ways to distribute 9 games with each person getting 5 games is 126*1 = 126.
If each person gets 7 games, then we are looking for the number of ways to choose 7 games out of 9 to distribute to one person. Once those games have been chosen, we are left with 2 games to distribute to the other two people. The number of ways to choose 7 games out of 9 is 36, and the number of ways to choose 2 games out of the remaining 2 is 1. Therefore, the total number of ways to distribute 9 games with each person getting 7 games is 36*1 = 36.
Adding up the number of ways to distribute the games in each case, we get 84 + 1680 + 126 + 36 = 1926.
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96 Vistors in 6 Hours. How many visitors per hour?
Answer:
16 visitors per hour
Step-by-step explanation:
96/6 = 16
Use the Slope Formula to calculate the slope of a line with these two points. Find the slope of the line that passes through (5, 4) and (10, 6). m = rise run 92 – 91 X2 - X1 Simplify your answer and write it as a proper fraction, improper fraction, or integer
Find the prime factorization of
the number 90.
Order the factors from least to greatest.
Remember, 1 is not a prime number.
[?] × [ ] × [ ] × [ ]
X
X
Enter the number that belongs in the green box.
Answer:
2
Step-by-step explanation:
the prime factorization of the number 90 is
2, 3, 3, 5
what is 5.4772 rounded to the nearest whole number
Answer:
5
Step-by-step explanation:
5.4772
To round to the nearest whole number, look at the number to the right of it (4) if 5 or greater round the 5 up to '6' o/w leave it as '5'
What type of angle are these?
Answer:
alternate exterior angles
Step-by-step explanation:
congruent alternete exterior angles
the relationship between the amount of time a basketball player spent practicing the day before a game and the number of points he scored in the game is graphed on the scatter plot shown. scatter plot titled basketball players, with the x axis labeled time practicing in minutes and the y axis labeled points scored with points at 0 comma 10, 10 comma 15, 15 comma 18, 25 comma 25, 30 comma 28, 30 comma 30, 45 comma 35, 70 comma 40, 70 comma 45, 80 comma 45, 90 comma 50, and 120 comma 60 describe the type and degree of association in the scatter plot and what it means in terms of the time the player spent practicing and the number of points he scored in the game.
By examining the shape and degree of association on the scatter plot, we can gain insights into the nature of the relationship between the variables and make predictions about their behavior in the future.
A scatter plot is a graphical representation of a set of data that shows the relationship between two variables.
The type of association between the two variables can be identified by the shape of the scatter plot. If the points on the plot form a linear pattern, then the association is said to be linear. If the points on the plot form a curved pattern, then the association is said to be nonlinear.
The degree of association between the two variables can be determined by the strength of the correlation coefficient, which is a measure of how closely the points on the scatter plot follow a linear pattern. The correlation coefficient ranges from -1 to 1, where a correlation coefficient of 1 indicates a perfect positive linear association, a correlation coefficient of -1 indicates a perfect negative linear association, and a correlation coefficient of 0 indicates no association between the two variables.
In this scenario, if the scatter plot shows a linear pattern and the correlation coefficient is positive, it means that there is a positive association between the amount of time the player spent practicing and the number of points he scored in the game.
On the other hand, if the correlation coefficient is negative, it means that there is a negative association between the two variables, which implies that the more time the player spent practicing, the lower the number of points he scored in the game.
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John wants to have 600 copies. His local print shop charges $10 for the First 200 copies and $15 for every additional 100 copies
Part A: How much will the 600 copies cost, including a sale tax of 6%?
Part B: If the number of sets of 100 is represented by x, write an equation to express the cost, y.
Part C: Use the equation to determine the cost of 900 copies. Include the 6% sales tax in the total final cost.
The cost of 600 copies is $90.10
The cost of 900 copies is $137.80.
The equation that expresses cost is y = 1.06 x ($10 + $15x)
What is the equation that expresses cost?The equation that represents the information in the question is:
Total cost = 1 + sales tax x [cost of the first 100 copies + (x x cost of every additional 100 copies)]
y = 1.06 x ($10 + $15x)
Cost of 600 copies:
x = (600 - 100) / 100 = 500 / 100 = 5
y = (1 + 6/100) x [$10 + (5 x $15)]
y = 1.06 x [$10 + $75)
y = 1.06 x $85
y = $90.10
Cost of 900 copies:
x = (900 - 100) / 100 = 800 / 100 = 8
y = (1 + 6/100) x [$10 + (8 x $15)]
y = 1.06 x [$10 + $120)
y = 1.06 x $130
y = $137.80
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Perform the operation and simplify the resulting fraction: 7/3a - 8/5 + 4/15a
After solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.
What are fractions?A fraction in mathematics is a number that is stated as a percentage, such as 1/2 or 2/3.
The number on top denotes the component of the unit under consideration, while the number at the bottom indicates the total number of parts that make up one unit.
An element of a whole is a fraction.
The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.
A fraction appears in the numerator or denominator of a complex fraction.
So, we have the operations:
7/3a - 8/5 + 4/15a
Now, solve as follows:
7/3a - 8/5 + 4/15a
7/3a + 4/15a - 8/5
7*5 + 4 /15a - 8/5
39/15a - 8/5
Therefore, after solving the given expression 7/3a - 8/5 + 4/15a, the resultant answer is fractions is 39/15a - 8/5.
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There are 28 students in a class.
13 of the students are boys.
Two students from the class are chosen at random.
a) If the first person chosen is a boy, what is the probability that
the second person chosen is also a boy?
Give your answer as a fraction.
b) What is the probability that both students chosen are girls?
Give your answer as a fraction.
a) The probability that the second person chosen is also a boy is; 13/28
b) The probability that both students chosen are girls is; 5/18
How to find the probability of selection?The parameters given in the question are;
Total number of students in the class = 28 students
Number of boys in class = 13 students
Number of girls = 28 - 13 = 15 students
a) Probability of the first student being selected as a boy is;
P(First is boy) = 13/28
b) The probability that both students chosen are girls is;
P(both girls) = (15/28) * (14/27) = 5/18
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How many solutions does this system have?
Answers:
None
1
2
3
Infinite
Simplify.
Rewrite the expression in the form 8n.
(8−8)(8³) =
The above expression in terms of 8n can be written as 8(0).
What is expression?
An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. A number, a variable, or a mix of numbers, variables, and operation symbols make up an expression.
We are given a an expression (8-8)(8³)
Now the first bracket after simplifying we get an answer is 0.
Hence the expression can be given in the form of 8(n) as 8(0)
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on friday, terry completes a self-monitoring scale and receives a score of 49. on the following tuesday, he fills out the scle again and receives a score of 28. terry's scores on this self-monitoring scale do not appear to be
If on the following Tuesday, Terry fills out scale again and receives a score of 28 , then Terry's scores on the Self-Monitoring Scale do not appear to be Reliable .
The Terry's scores on the Self-Monitoring Scale do not appear to be reliable, because there is a significant difference between his score on Friday and his score on the following Tuesday.
The Reliability is defined as the consistency of measurement over time or across different conditions.
In this case, if Terry's scores on the Self-Monitoring Scale were reliable, we would expect them to be consistent or stable over time.
However, his score on Tuesday is significantly lower than his score on Friday suggests that there may be some inconsistency in his responses .
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Anthony makes 6 1/8 gallons of lemonade for a family picnic. His family drinks 2 1/4 gallons of the lemonade. Which of these containers is the SMALLEST Anthony can use to store the remaining lemonade?
Answer:
3 and 7/8 gallons remaining
Step-by-step explanation:
You did not give the container options, but hopefully this will help
A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is 84 square inches. Write an equation you can use to find the width (in inches).
On solving the provided question we cans ay that The side of the square is w/2, then its area is: A = (w/2)² = w²/4
what is a square?A square is an equilateral quadrilateral with four equal sides and four equal angles according to Euclidean geometry. It is also known as a rectangle with two neighboring sides that have the same length. Having all four equal sides and all four equal angles, a square is an equilateral quadrilateral. 90 degree or straight angles are square angles. In addition, the square's diagonals are equally spaced and split at a 90-degree angle. a neighboring rectangle with two equal sides. a quadrilateral with four right angles and four sides of equal length. a parallelogram having two adjacent, equal sides that form a right angle. straight-sided rhombus.
The side of the square is w/2, then its area is:
A = (w/2)² = w²/4
The darkened region represents the difference between the square's and rectangle's areas:
[tex]14w - w^2/4 = 84\\56w - w^2 = 336\\w^2 - 56w + 336 = 0[/tex]
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When I add a number to another number four times as big the results is 30, find the first number
By using a system of equations of two variables we concluded that the first number was 6
Let the numbers be x and y and their sum gives z
The equation for the sum of 2 numbers:
x + y = z -(1)
We know, z = 30 and y = 4 times x = 4x
Putting values of y and z in equation (1), we get
x + 4x = 30
Solving for x, we get
5x = 30
x = 30/5 = 6
To get the value of y, put the value of x in y = 4x and we get
y = 4 x 6 = 24
So the real equation was
6 + 24 = 30
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Triangle JGR is similar to triangle MST. Which
statement is not always true?
A. LJ LM
C. LR LT
B. LG LT
D. LG LS
The angle corresponding to each other of the different triangles are equal. The correct option is D.
What is a similar triangle?"Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion ".
Here given, ΔJGR is similar to a triangle ΔMST
So, from the definition of a similar triangle,
angle J ≅ angle M
angle G ≅ angle S
angle R ≅ angle T
Hence, option D is correct.
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