Answer:0.76
0.58
Conclusion you are More likely to win by playing regular defense
Step-by-step explanation:
Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Taking the strategy of "regular" defense,
P(winning) = 42
P(losing) = 8
Total regular defense games = 50
Taking the strategy of "prevent" defense,
P(winning) = 35
P(losing) = 15
Total regular prevent games = 50
Total games = 100
Probability of winning when playing regular defense = 42 / 50 = 0.84
Probability of winning when playing prevent defense = 35 / 50 = 0.7
Hence, Probability of winning when playing regular defense is greater than probability of winning when playing prevent defense.
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Divide the following polynomial and then place the answer in the proper location on the grid. Write your answer in order of descending powers of y. (y^3 - y^2 + y + 3) ÷ (y + 1)
PLEASE HELPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
PRETTY PLEASE WITH ICING AND CHERRIES ON TOP
given,
[tex] \frac{ {y}^{3} - {y}^{2} + y + 3}{y + 1} \\ = \frac{ {y}^{3} + {y}^{2} - 2 {y}^{2} - 2y + 3y + 3}{x + 1} \\ = \frac{{y}^{2} (y + 1) - 2y(y + 1) + 3(y + 1)}{(y + 1)} \\ = \frac{(y + 1)( {y}^{2} - 2y + 3) }{(y + 1)} \\ = {y}^{2} - 2y + 3[/tex]
Final answer:
The polynomial y^3 - y^2 + y + 3 divided by y + 1 results in a quotient of y^2 - y + 2, with a remainder of 1. The complete division statement is (y^3 - y^2 + y + 3) / (y + 1) = y^2 - y + 2 + 1/(y + 1).
Explanation:
To divide the polynomial y^3 - y^2 + y + 3 by y + 1, we use polynomial long division. First, divide y^3 by y to get y^2, subtract the result from the polynomial, and bring down the next term. Repeating this process gives us the following steps:
Divide y^3 by y to get y^2. Multiply y + 1 by y^2 and subtract from the original polynomial.
Bring down the next term, which is y, and divide -1 by y to get -1. Multiply y + 1 by -1 and subtract from the result of the first step.
Bring down the last term, which is 3, and divide 2 by y to get 2. Multiply y + 1 by 2 and subtract to get the remainder.
The final quotient of this division is y^2 - y + 2, and the remainder is 1.
The result of the division is y^2 - y + 2 with a remainder of 1. To express this as a complete division statement, we write:
(y^3 - y^2 + y + 3) ÷ (y + 1) = y^2 - y + 2 + 1/(y + 1)
In the map below, the path from the zebras to the monkeys is parallel to the path from the tigers to the elephants.
What is the distance between the lions and the monkeys?
a.40 feet
b.88 feet
c.92 feet
d.198 feet
Answer:
Step-by-step explanation:
88
The distance between the lions and the monkeys is 88 feet
To determine the distance between the lions and the monkeys, we make use of the following equivalent ratio
x : 132 = 80 : 120
Express as fraction
[tex]\frac{x}{132} = \frac{80}{120}[/tex]
Solve for x
[tex]x = \frac{80}{120} * 132[/tex]
Multiply
[tex]x = 88[/tex]
Hence, the distance between the lions and the monkeys is 88 feet
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Solve the equation 2x^2+8x-1=0 by completing the square. Give you answers correct to 2 decimal places.
The given quadratic equation 2x² + 8x - 1 = 0 can be rearranged as (x + 2)² = 4.5 through the method of completing the square. Taking the square root of both sides gives two solutions for x: x = -2 + √4.5 and x = -2 - √4.5, when rounded to two decimal places.
Explanation:To solve the equation 2x² + 8x - 1 = 0 by "completing the square", we first divide everything by the coefficient of x², in this case 2, to make the equation look like x² + 4x - 0.5 = 0. The coefficient of x now becomes 4.
We then take half of this coefficient, square it and add it to both sides of the equation. Half of 4 is 2, and squaring it gives us 4. So the equation now reads as x² + 4x + 4 = 4 + 0.5 which simplifies to x² + 4x + 4 = 4.5.
This equation can be further simplified by realizing that (x + 2)² = x² + 4x + 4, thus we have (x + 2)² = 4.5. Taking the square root of both sides finally gives us x = -2 ± √4.5, giving us two solutions for x to two decimal places, that are x = -2 + √4.5, and x = -2 - √4.5.
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To solve the equation by completing the square, divide by the leading coefficient, move the constant term to the other side, complete the square, take the square root of both sides, and then solve for x, yielding two solutions: approximately -0.12 and -3.88.
Explanation:To solve the equation 2x²+8x-1=0 by completing the square, follow these steps:
Divide the entire equation by 2 to simplify the coefficient in front of x^2, resulting in x²+4x-0.5=0.Move the constant term to the other side: x²+4x=0.5.To complete the square, add the square of half the coefficient of x to both sides. This number is (4/2)² = 4, so add 4 to both sides giving x²+4x+4=4.5.The left-hand side is now a perfect square: (x+2)²=4.5.Take the square root of both sides: x+2=±√4.5.Subtract 2 from both sides to solve for x: x= -2 ± √4.5.Computing the square root of 4.5 and subtracting 2 gives two solutions, accurate to two decimal places: x≈-0.12 and x≈-3.88.Learn more about Completing the Square here:
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Jorge wants to collect data about the amount of time 8th graders spend weekly on the internet. Which method would be the best way to collect data
Answer: Random samples
Step-by-step explanation: Jorge could ask how many hours people spend on the internet each day and then multiply that number by 7 for each person.
The best method for Jorge to collect data about 8th graders' internet usage is to conduct a survey.
Design the Survey: Create a set of questions focused on the amount of time spent on the internet. For example, 'How many hours per day do you spend on the internet?'etc
Distribution: Distribute the survey to the target group, either through paper forms during school hours or digitally through email or school platforms.
Data Collection: Collect the responses. Ensure that anonymity is maintained to get honest answers.
Analysis: Compile the data and calculate the average time spent online by 8th graders. Use graphical representations like bar charts or pie charts to visualize the data.
Presentation: Present the findings in a written report or a digital presentation, detailing the average time spent and highlighting any noticeable trends or patterns.
By conducting a survey, Jorge can efficiently gather accurate and representative data about the internet usage habits of 8th graders.
A sphere has diameter 28 cm. If the diameter is divided by 2, what is the effect on the surface area?
The surface area is divided by 8.
The surface area is multiplied by 8.
The surface area is multiplied by 4.
The surface area is divided by 4.
Answer:
The surface area is divided by 4.
Step-by-step explanation:
Surface area of a sphere is 4πr².
When the diameter is 28 the radius is 14. So: 4π(14)² = 784π
If you cut the diameter in half you get 14. The radius is now 7.
4π(7)² = 196π.
784/4 = 196 so divided by 4.
A Web music store offers two versions of a popular song. The size of the standard version is 2.5 megabytes (MB). The size of the high-quality version is 4.4 MB. Yesterday, the high-quality version was downloaded four times as often as the standard version. The total size downloaded for the two versions was 5427 MB. How many downloads of the standard version were there?
Answer:
270 downloads
Step-by-step explanation:
Call x the number of times the standard quality version was downloaded and call y the number of times the high quality version was downloaded.
So, we know that
[tex]2.5x + 4.4y = 5427[/tex] MB (1)
We also know that the high-quality version was downloaded four times as often as the standard version.
So
[tex]y = 4x[/tex] (2)
We substitute equation (2) in equation (1) and solve for x.
[tex]2.5x + 4.4 (4x) = 5427\\\\2.5x +17.6x = 5427\\\\20.1x=5427\\[/tex]
[tex]x = 270\ downloads[/tex]
The histogram below shows the number of properties in a town that sold within certain time periods.
Why might the graph be considered misleading?
The scales on the x- and y-axes are unequal.
The interval on the x-axis is too large for the data set.
The scale on the y-axis misrepresents the difference in the heights of the bars.
The interval on the y-axis is too large for the data set.
Answer:
Option c) The scale on the y-axis misrepresents the difference in the heights of the bars.
Step-by-step explanation:
Given is a histogram that shows the number of properties in a town that are sold within certain periods.
On x axis is given number of days to sell and on y axis the number of properties
X axis is given in interval form with interval width 30 and on y axis scales are marked as 0,1,2....12,13 etc
The mistake is on y axis after 0, 10 is marked with unit distance from 0 but from 10 to 11 also distance is shown as 1 unit.
Hence correct option is
Option c) The scale on the y-axis misrepresents the difference in the heights of the bars.
Answer:
C
Step-by-step explanation:
E2020
Gustave measured his pace and determined that for him, sss steps make up one mile. One day Gustave walked 630063006300 steps, which was 333 miles. Write an equation to describe this situation. How many steps are in one mile for Gustave?
Answer: Equation to describe this situation.
[tex]3s=6300[/tex]
Number of steps in one mile for Gustave =2100
Step-by-step explanation:
Given : Gustave measured his pace and determined that for him, s steps make up one mile.
1 mile = s steps (1)
One day Gustave walked 6300 steps, which was 3 miles.
i.e. 3 miles = 6300 steps (2)
Using (2), the number f steps in 3 steps will be :_
3 miles = 3s steps (3)
From (2) and (3), we have
[tex]3s=6300[/tex]
Dividing both sides by 3 , we get
[tex]s=\dfrac{6300}{3}=2100[/tex]
Hence, the number of steps in one mile for Gustave =2100
Gustave takes 189 steps to walk one mile. We derived this by dividing the total steps, 63,000, by the distance in miles, 333. The equation used was 63000 = s * 333.
To determine how many steps are in one mile for Gustave, we start with the information provided:
Gustave took 63,000 steps, which equals 333 miles.Step 1: Write the Equation
We can write the equation as:
63000 = s * 333
Step 2: Solve for s
To find out how many steps make up one mile, we solve for s by dividing both sides of the equation by 333:
s = 63000 / 333
Step 3: Calculate the Value
When we divide 63,000 by 333, we get:
s = 189
This means that Gustave takes 189 steps to walk one mile.
Example Calculation
Since 63,000 steps equal 333 miles, and dividing both 63,000 steps by 333 miles gives us the number of steps per mile:
189 steps per mile.
In conclusion, Gustave takes 189 steps to walk one mile. This equation and process help us determine the number of steps per mile based on the given total steps and distance covered.
Which function rule matches the graph below?
The endpoints of a line segment are located at (–3, –4) and (–15, –20). What are the coordinates of the midpoint of the line segment? A. (–10.5, –14) B. (–9, –12) C. (–7.5, –10) D. (–6, –8)
Answer:
Answer B: (-9, -12)
Step-by-step explanation:
I like to approach this problem by finding the halfway points in the x-direction and the y-direction, separately.
x-direction: find the average of -3 and -15, which is -18/2, or -9. The x-coordinate of the midpoint is therefore -9.
y- direction: find the average of -4 and -20, which is -12.
Thus, the midpoint is located at (-9, -12) (Answer B)
There are 60 sixth graders taking an
online math class. Only 25% are
planning to attend the virtual field
trip to learn about math careers.
How many sixth graders will be
attending the virtual field trip?
The answer is:
There will be 15 graders attending the virtual field trip.
Why?We know that there are 60 sixth graders taking an online math classes but only 25% are planning to attend the virtual field trip, so, if we want to calculate how many sixth graders will be attending the virtual field trip, we need to calculate the 25% of the total sixth graders
Before solving, we need to convert the given percent number (25%) to a real number by dividing it by 100, so, solving we have:
[tex]\frac{25(percent)}{100}=0.25[/tex]
Now, calculating how many graders are 25% of the total graders, we have:
[tex]GradersAttending=TotalGraders*PercentOfGradersAttendingTheVirtualTrip[/tex]
[tex]GradersAttending=60graders*0.25=15graders[/tex]
So, we have that there will be 15 graders attending the virtual field trip.
Have a nice day!
Answer:
15
Step-by-step explanation:
To get 25% of 60, you need to divide 25 by 10, your answer should be 0.25, next, you multiply 0.25 by 60, the answer if 15, another way, is by multiplying 15 by 4, that would make 60. (Have a great day, hope this helps, please mark me brainliest if it does help, sorry for answering really late)
Suppose that a restaurant chain claims that its bottles of ketchup contain 24 ounces of ketchup on average, with a standard deviation of 0.4 ounces. If you took a sample of 49 bottles of ketchup, what would be the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample?
A. 24+-0.029
B. 24+-0.057
C. 24+-0.229
D. 24+-0.114
Answer:
D. 24+-0.114
Step-by-step explanation:
The question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle given the following statistics;
Sample mean = 24
standard deviation, σ = 0.4
Sample size , n = 49
The confidence interval for a population mean is calculated using the formula;
Sample mean ± z-score*(σ/sqrt(n))
The z-score associated with a 95% confidence interval, from the standard normal tables, is;
1.96
Substituting these values into the formula;
24 ± 1.96*[tex]\frac{0.4}{\sqrt{49} }[/tex]
= 24 ± 0.112
From the choices given, choice D is closest to the above expression;
Please please help me out
Area = base * height
Area = 15 * 8 = 120 square centimeters
Instead of the three dots, write a digit to make the fraction reducible. (Find all possible cases.) 12.../23...
Answer:
{0, 1, 2, 4, 5, 6, 8}
Step-by-step explanation:
120/230 = 12/23
121/231 = 11/21
122/232 = 61/116
123/233 -- not reducible
124/234 = 62/117
125/235 = 25/47
126/236 = 63/118
127/237 -- not reducible
128/238 = 64/119
129/239 -- not reducible
___
All even digits will make the fraction reducible, as will the digit 5. Then the digits we're not sure of are 1, 3, 7, 9. Appending 1 to the given numbers makes them divisible by 11, so that digit is included in our list.
Ending digits 3, 7, 9 result in fractions that are not reducible. (Numbers 127, 233, and 239 are prime numbers.)
Answer:
0,1,2,4,5,6,8
Step-by-step explanation:
PLEASE HELP ASAP 40 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
x^2+2x+5
Step-by-step explanation:
Can't really explain on a computer, but if you want to know how to do it look at www.emathhelp.net
Which of the following is true because of the Commutative Law of Addition?
2 + 11 + 16 = 11 + 16 + 2
2 + 11 + 16 = 20 + 9
2 + 11 + 16 = 29
2 + 11 + 16 = 2 + 11 + 16
Answer:
2+11+16=11+16+2
Step-by-step explanation:
According to the commutative law of addition,
(A+B)+C=(C+B)+A
i.e.A+B+C=C+B+A
Answer:
A
Step-by-step explanation:
Which graph represents the function f(x) = |x| – 4? Mark this and return
Answer:
look at graph attached
Step-by-step explanation:
it is moved 4 down from the parent function
What is the cosine ratio for angle F?
Answer:
option D
Step-by-step explanation:
Given in the question, a right angle triangle FGH.
Base of triangle = 12
Height of triangle = 5
Hypotenuse of triangle = 13
To solve the question we will use trigonometry identity.
cos(F) = adj / hypocos(F) = height / hypo
cos(F) = 5 / 13
So the cosine ration for angle F is 5 / 13
Please help me out please
x = [5]
y = [2]
I really hope this answer helps you out! It makes my day helping people like you and giving back to the community that has helped me through school! If you could do me a favor, if this helped you and this is the very best answer and you understand that all of my answers are legit and top notch. Please mark as brainliest! Thanks and have a awesome day!
Answer x = ?
y = 0
Have good day
Please help me out please
Answer:
31
Step-by-step explanation:
For rectangle ABCD, AC and BD are the lengths of the diagonals. The diagonals of a rectangle are congruent.
AC = BD
3x + 7 = 131 - x
Add x to both sides.
4x + 7 = 131
Subtract 7 from both sides.
4x = 124
Divide both sides by 4.
x = 31
4−(−5∗9−1)÷2+(5)2−7
Answer:
Your answer will be 30
Step-by-step explanation:
Describe the relationship between the two acute angels in a right triangle
Answer:
they are complementary
Step-by-step explanation:
The sum of angles in a triangle is 180°. When one of those angles is a right angle (90°), the sum of the other two must be 90°. When the sum of two angles is 90°, they are said to be complementary angles.
Please please help!!!!!!!!
Answer:
C
Step-by-step explanation:
To find the inverse, let y = f(x) then rearrange making x the subject, that is
y = 5(x + 3)³ - 2 ( add 2 to both sides )
y + 2 = 5(x + 3)³ ( divide both sides by 5 )
(x + 3)³ = [tex]\frac{y+2}{5}[/tex]
Take the cube root of both sides
x + 3 = [tex]\sqrt[3]{\frac{y+2}{5} }[/tex]
Subtract 3 from both sides
x = [tex]\sqrt[3]{\frac{y+2}{5} }[/tex] - 3
Change y back into terms of x, so
[tex]f^{-1}[/tex] (x ) = [tex]\sqrt[3]{\frac{x+2}{5} }[/tex] - 3 → C
Please help me find the slope of the line graphed below!
Answer:
slope = - 3
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 = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, - 3) ← 2 points on the line
m = [tex]\frac{-3-0}{0+1}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3
Here it is described. Its really easy.
Which three-dimensional figure is formed by the rotation given?
PLeaseee help 12p!!
Shown below
Step-by-step explanation:What if you rotate a plane figure around a straight line called the axis? Well, in doing so, you will get what in mathematics is called a solid of revolution, which is a solid figure. In this case, we have a triangle with a side matching the axis and this side. The solid that result when rotating that triangle is a cone. The side that matches the axis is the height of the cone while the side perpendicular to the axis is the radius of the base of the cone. The rotation is performed by the hypotenuse of the triangle (a straight line) through the origin and by an angle of 360 degrees.
A bag has 3 red marbles, 2 blue and 4 yellow. What is the theoretical probability of pulling a red?
Answer:1/3
Step-by-step explanation:
3 (amount of reds)
------------------------
3+2+4 (sum of all marbles red+Blue+Yellow)
simplfy
3 /3
---- =1/3
9 /3
To find out the theoretical probability of drawing a red marble, divide the total number of red marbles (3) by the total number of marbles (9). Therefore, the theoretical probability is 1/3.
Explanation:
The subject of your question falls under the branch of Mathematics and it's about a concept known as theoretical probability. In this case, the total number of marbles in the bag is 3 red + 2 blue + 4 yellow = 9 marbles. The probability of drawing a red marble from the bag is calculated by dividing the number of red marbles by the total number of marbles. Therefore, the theoretical probability of pulling a red marble is 3/9 which simplifies to 1/3, meaning there is a one in three chance of drawing a red marble.
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What is the exact value of sin 30 degrees?
Answer:
1/2
Step-by-step explanation:
Final answer:
The exact value of sin 30 degrees is 0.5, and this is derived from the special 30-60-90 triangle.
Explanation:
The value of sin 30 degrees is 0.5.
This can be determined using the unit circle or by using the trigonometric function of 30 degrees.
When we evaluate sin 30 degrees, we can look at the special right triangle with angles 30-60-90 where the ratio of the opposite to the hypotenuse in a 30-degree angle is 1/2. In this triangle, the side opposite to the 30-degree angle is half the length of the hypotenuse. Therefore, sin 30 degrees is equal to 1/2 or 0.5.
Can someone please answer this
Answer: y = sqrt x
Explanation:
In order to draw the graph of this function you will need to identify some of the values.
If x=0, then y = sqrt 0.
If x=1, then y = sqrt 1.
If x=2, then y = sqrt 2.
(This repeats.. you get the idea)
Plot these points and draw a curve through them. Your answer should look just like the graph in your question.
Please answer this multiple choice question CORRECTLY for 30 points and brainliest!
Answer:
D
Step-by-step explanation:
because you need to times the indice 2 by the 3
find the radius of a cylinder with a volume of 108ft and height of 12 ft
Answer:
1.69 ft (approx.)
Step-by-step explanation:
Formula for Volume of cylinder: pi x radius squared x height
Plug in 108 for volume, 3.14 for pi and 12 for height:
108 = 3.14 x r squared x 12
Multiply 3.14 and 12
108 = 37.68 x r squared
Divide both sides by 37.68
2.87 = r squared
"Unsquare" both sides (square root)
1.69 ft. = radius (approximate answer, rounded to nearest hundredth)
Answer:
1.69 ft
Step-by-step explanation:
V = πr²h formula of a cylinder.
Volume = 108 ft
Height = 12 ft
Radius = r
V = πr²h
108 ft = 22/7 × r² × 12 ft
π = 22/7 or 3.14
108 ft = 264/7r²
108 ft = 37.71r²
divide both sides by 37.71
108 ft/37.71 =r²
2.86 ft = r²
square root both side
√2.86 ft = √r²
the square cancels the square root
1.69 ft.
To check
V = πr²h
108 = 22/7 × (1.69)² 12
108 = 22/7 × 2.8561 × 12
108 = 107.61≈108
108 ft = 108 ft.