The sample space for the random experiment of playing blackjack until a loss or a maximum of three games are played is represented by the set {l, wl, ww}.
Explanation:The sample space for this scenario comprises of all possible outcomes of playing "blackjack" until the person loses or has played three games. We represent win and loss by w and l respectively. By these definitions, we get the following possibilities: l (losing on the first game), wl (winning the first game then losing the second), and ww (winning the first two games and decide not to play a third game or it wasn't possible to play a third game). This assumes that the player stops after either losing a game or after playing the third game, even if he won that.
Note that the scenario where the player wins all three games (www) is not included in the sample space because the problem states that the player will stop playing as soon as they lose a game.
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In Ellen's math class, there are 2 boys for every 3 girls . What is the the following ratio of boys to girls in the class ?
A . 17/21
B . 14/21
C . 7/14
D. 11/17
Sal bought three CDs for 1598 each a computer cable for 3995 and a case for his MP3 player for 2499 sales tax is 7% to the nearest cent what is the total cost of his purchases
Pleaseee helppppppp
Dennis ran a mile in 593.7 seconds. Martina ran a mile in 573.36 seconds. What was the difference in their running times ?
A . 5.14 seconds
B . 6.01 seconds
C . 20.34 seconds
D . 26.01 seconds
The perimeter of a triangle is 133 inches. If one side of the triangle is five more than the shortest side, and the longest side is 14 more than the shortest side, find the lengths of the three sides?
side 1 = x
side 2 = x+5
side 3 = x+14
perimeter = side 1 + side 2 + side 3
133 = x + (x+5) + (x +14)
133=3x + 19
114=3x
x=114/3 = 38
side 1 = 38
side 2 = x+5 = 38+5 = 43
side 3 = x+14 = 38+14 = 52
38+43+52 = 133
side lengths are 38, 43 & 52
Solve for v 14v-8v=24
Given the Vectors s=(-3,2) and t= (-9,-4), find 6s and s+t
At a certain time, the length of a rectangle is 5 feet and its width is 3 feet. At that same moment, the length is decreasing at 0.5 feet per second and the widthis increasing at 0.4 feet per second.
What is the length of the diagonal at that time?
How fast is the length of the diagonal changing? Is this length increasing or decreasing?
estimate the product 731+207
Choose the fraction that goes in the blank? 1/2 < _ < 4/5
I don't understand how they got 2/3
Consider the function f(x) = (x − 3)2(x + 2)2(x − 1). The zero has a multiplicity of 1. The zero −2 has a multiplicity of?
The zero with a multiplicity of 1 is x = 1, and the zero x = -2 has a multiplicity of 2.
How to find the multiplicity of zeros in a polynomial?For a general polynomial like:
[tex]p(x) = (x - x_1)^n*(x - x_2)^m*...[/tex]
The zero x₁ has a multiplicity of n (same as the exponent in the term where the zero appears), while the zero x₂ has a multiplicity m.
Now let's go to our polynomial:
[tex]f(x) = (x - 3)^2(x + 2)^2(x - 1)[/tex]
Here we can see that the only zero with a multiplicity of 1, is x = 1, while the zero x = -2 has a multiplicity of 2.
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Answer:
first one is 1 and second is 2
Step-by-step explanation:
just got it right
Which equation does the graph of the systems of equations solve? two linear functions intersecting at 4, 1 the answers are one fourthx + 2 = 2x − 7 one fourthx + 2 = −2x − 7 −one fourthx + 2 = 2x − 7 −one fourthx + 2 = −2x − 7
Analyzing the graphs of a periodic functions (need help)
Find f(-5), if f(x) = -x^2 - 2x+1
Ivan was given two data sets, one without an outlier and one with an outlier.
Data without an outlier: 108, 113, 105, 118, 124, 121, 109
Data with an outlier: 108, 113, 105, 118, 124, 121, 109, 61
How is the median affected by the outlier?
Answer:
b
Step-by-step explanation:
The outlier affects the median of the data sets collected by Ivan by reducing the median.
What is an outlier?An outlier is a number that is way smaller or way larger than that of other numbers in a data set. The outlier in the data set is 62. Median is the number at the center of a data set.
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You are hiking on a trail that leads to the top of a mountain. At 12 P.M. you reach an elevation of 3700 feet. At 4 P.M. you reach an elevation of 4500 feet. What is your mean hourly change in elevation?
Answer: 200 ft per hour
Step-by-step explanation:
Given : You are hiking on a trail that leads to the top of a mountain.
At 12 P.M. you reach an elevation of 3700 feet. At 4 P.M. you reach an elevation of 4500 feet.
The formula for the mean hourly change in elevation is :-
[tex]\dfrac{\text{Change in elevation}}{\text{Time in hours}}[/tex]
From the given information, the change in elevation=4500 ft-3700 ft= 800 ft
Time taken = 4 hours [From 12 pm to 4 pm]
Now, Mean hourly change in elevation=[tex]\dfrac{800}{4}=200[/tex]
Hence, the mean hourly change in elevation = 200 ft
if I have 3 layers of 14 cases per layer of an item,how many total cases should I have
The total number of cases I should have is 42.
How many cases should I have?
Multiplication is the mathematical operation that is used to determine the product of two or more numbers.
Total number of cases = number of layers x cases per layer
14 x 3 = 42
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Set up a system of equations for the following scenario. Then solve for the system. Three students buy different combinations of tickets for a baseball game. The first student buys 2 senior, 1 adult, and 2 student tickets for $51. The second student buys 1 adult and 5 student tickets for $55. The third student buys 2 senior, 2 adult, and 7 student tickets for $75. Set up a system of equations to find the price of each ticket.
What is the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5)
Answer: 10 square units.
Step-by-step explanation:
The area of triangle with vertices [tex](x_1,y_1),(x_2,y_2)\text{ and }(x_3,y_3)[/tex] is given by :-
[tex]A=\dfrac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)][/tex]
Given : The vertices of triangle : (2,0), (6,0), (8,5)
Then , the area of the triangle will be :_
[tex]A=\dfrac{1}{2}[(2)((0)-(5))+(6)((5)-(0))+(8)((0)-(0))\\\\\Rightarrow A=\dfrac{1}{2}[20]\\\\\Rightarrow A=10\text{ square units}[/tex]
Hence, the number of square units in the area of the triangle whose vertices are points (2,0), (6,0), (8,5) = 10
he IQ scores of 500 college football players are randomly selected. Which graph would be most appropriate for these data: histogram, bar chart, pie chart, multiple bar graph, or slack plot?
subtract, 8 3/8 - 10 1/6
Find the surface of a cylinder with a base diameter of 4yd and a height of 6yd
The sum of differences between the group mean and the grand mean summed over all groups for a given set of observations is called _____ variance.
With 400,000 sq ft or 16% of total office space. How much space did the city have
The Jurassic Zoo charges $14 for each adult admission and $9 for each child. The total bill for the 214 people from a school trip was $2081. How many adults and how many children went to the zoo?
a=adult
c=child
a+c=214
c=214-a
9c+14a=2081
9(214-a)+14a=2081
1926-9a+14a=2081
5a=155
a=155/5=31
31 adults
183 children
check
31*14 = 434
183*9=1647
1647+434=2081
Autumn is thinking about buying a car. The table below shows the projected value of two different cars for three years.
Number of years 1 2 3
Car 1 (value in dollars) 38,000 32,000 26,000
Car 2 (value in dollars) 38,000 32,300 27,455
Part A: What type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? Explain your answer. (2 points)
Part B: Write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)
Part C: Autumn wants to purchase a car that would have the greatest value in 6 years. Will there be any significant difference in the value of either car after 6 years? Explain your answer, and show the value of each car after 6 years. (4 points)
The value of Car 1 decreases linearly and can be described by a linear function. Without an exact exponential function for Car 2, we'll assume it may have a slower depreciation rate compared to Car 1. Autumn should consider Car 2 to likely have greater value after 6 years.
Explanation:Part A: Identifying the Type of Function
To determine which type of function best describes the value of each car after a fixed number of years, we must look at the rate at which the car's value decreases. For Car 1, the value decreases by a constant amount each year ($6,000), which suggests a linear function. Conversely, Car 2 does not decrease by the same amount each year, but rather by amounts that seem to be getting progressively larger, hinting at an exponential function.
Part B: Writing the Functions
The linear function for Car 1 can be represented as f(x) = -6,000x + 44,000, since we start at $44,000 and decrease by $6,000 each year. For Car 2, an exponential decay function may fit the data; however, with only three points provided, determining the exact exponential function would require more complex regression analysis which we do not perform here. Assuming the rate of depreciation remains similar, we might estimate the function for Car 2 using a linear approximation for simplicity.
Part C: Future Car Value Comparison
Extending the linear depreciation model for Car 1, its value after 6 years would be f(x) = -6,000(6) + 44,000 = $8,000. A precise prediction for Car 2 after 6 years cannot be determined without an accurate exponential function, but it's apparent that Car 2 depreciates less rapidly than Car 1. Therefore, Autumn would likely find that Car 2 retains more value over 6 years.
Consider the words typically associated with geometry. Are there any words that would be hard to precisely define? What words can you think of?
The words typically associated with geometry are:
Points, Lines, Plane, and angle.
We have,
In geometry,
There are some words that can be challenging to precisely define or may have different interpretations.
Here are a few examples:
- Point: While a point is commonly understood as a location with no size or dimension, providing an exact definition can be difficult without relying on terms like "location" or "position."
- Line: A line is often described as a straight path extending infinitely in both directions. However, defining it without using similar geometric concepts like "straight" or "infinitely" can be challenging.
- Plane: A plane is typically defined as a flat, two-dimensional surface that extends infinitely in all directions. However, explaining it without referencing terms like "flat" or "two-dimensional" can be complex.
- Angle: An angle is formed by two intersecting lines or line segments. Describing it precisely without using terms like "intersects" or "measures" can be difficult.
Thus,
These words require a level of understanding of basic geometric concepts and often rely on other geometric terms for precise definitions.
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(15+23)+7=15+(___+7)
What are two numbers whose sum is 11 and whose product is -60?
The radius of a circular park is 114 yd. To the nearest yard, what is the circumference of the park?
circumference = 2 x pi x r
using 3.14 for pi
2 x3.14x114=715.92
round to 716 yards
Answer:
The circumference of a circle is 715.92 yd.
Step-by-step explanation:
Formula
[tex]Circumference\ of\ a\ circle = 2\pi r[/tex]
Where r is the radius of a circle.
As given
The radius of a circular park is 114 yd.
[tex]\pi = 3.14[/tex]
Put in the formula
[tex]Circumference\ of\ a\ circle = 2\times 3.14\times 114[/tex]
Circumference of a circle = 715.92 yd
Therefore the circumference of a circle is 715.92 yd.
yesterday's low temperature was -2.5 degrees celsius. today's low temperature is 5 times as low as yesterday's low temperature. what was the low temperature today?
Answer:
The temperature is -12.5 degrees Celsius.
Step-by-step explanation:
The daily maximum temperature, or high, describes how warm you can expect the air to be, usually from 7 a.m. to 7 p.m. The daily minimum temperature, or low, tells how much the air is expected to cool, usually overnight from 7 p.m. to 7 a.m.