The coefficients of the terms on the right side of a binomial equation are the numbers in the triangle.
As the power increases, the expansion becomes more difficult to compute and takes longer. A binomial statement that has been raised to a very high power can be swiftly calculated using the binomial theorem. Find out everything there is to know about the binomial theorem, including its definition, characteristics, and uses.
The binomial theorem can be used to expand an expression that has been raised to any finite power. The binomial theorem is a helpful expansion method having applications in probability, probability theory, and algebra.
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events A and B in some sample sapce each have a probability 0.5 of occuring, while the probability that both occur (simultaneously) is 0.25. what is the probability that neither of A or B occurs? this is the work i did, can i please get some guidance
=============================================
Explanation:
I appreciate you showing your work so far, and your thought process.
Your steps are correct because the events [tex]A \cup B[/tex] and [tex](A \cup B)'[/tex] are complementary, aka opposite. One or the other must happen. It's like a coin flip heads vs tails.
The last thing you need to do really is simplify 1-0.5-0.5+0.25 to get the final answer 0.25
-------------------
This is what I would do as an approach.
P(A u B) = P(A) + P(B) - P(A n B)
P(A u B) = 0.5 + 0.5 - 0.25
P(A u B) = 0.75
So,
P( (A u B)' ) = 1 - P(A u B)
P( (A u B)' ) = 1 - 0.75
P( (A u B)' ) = 0.25
-------------------
Another approach:
Imagine we had 100 people.
50 are in set A to give P(A) = 50/100 = 0.50
50 are in set B to give P(B) = 0.50
25 are in both A and B to get P(A n B) = 25/100 = 0.25
50+50-25 = 75 people are in either A, or B, or both
That leaves 100-75 = 25 in neither set
25/100 = 0.25
I recommend to draw out the Venn Diagram.
What equation should i us
Answer: C
Step-by-step explanation:
The length of the PR would be 82.
Option (A) is correct.
What is an expression?
An expression is a combination of numbers, variables, and mathematical operations that represents a value or a computation. Expressions can be simple or complex and can include constants, variables, and various mathematical operations such as addition, subtraction, multiplication, and division. Expressions are often used to represent mathematical operations in algebraic, trigonometric, and calculus problems. They can be evaluated to find a numerical value or simplified to reveal underlying mathematical relationships.
In the given figure, the length of both line segments is equal, hence
PR = 10x + 842
PQ + QR = 10x + 842
8x + 678 + 12 = 10x + 842
First we can subtract 12 from both sides of the equation:
8x + 678 = 10x + 830
Then we can subtract 8x from both sides of the equation:
678 = 2x + 830
Then we can subtract 830 from both sides of the equation:
-152 = 2x
Then we can divide both sides of the equation by 2:
x = -76
So PR = 8x + 678 + 12
PR = 8(-76) + 678 + 12
PR = -608 + 678 + 12
PR = -608 + 690
PR = 82
Hence, the length of the PR would be 82.
Option (A) is correct.
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A survey found that 12 out of every 15 people in the United States
prefer eating at a restaurant over cooking at home. If 400 people
selected eating at a restaurant on the survey, how many people
took the survey?
If 12 out of every 15 people prefer eating at a restaurant, then 12/15 of the people who took the survey chose that option. We know that 12/15 of the total number of people who took the survey is equal to 400 people, so we can set up the equation:
(12/15)x = 400
To find the total number of people who took the survey, we can solve for x by multiplying both sides of the equation by 15/12:
x = (400)(15/12)
x = 500
So, 500 people took the survey.
21•15 equals
(20+1)•15
The value of 21•15 equals (20+1)•15. This is true.
How to calculate the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value of 21•15 will be:
= 21 × 15
= 315
Also (20+1)•15 will be:
= 21 × 15
= 315
Therefore, they're equal.
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Complete question
The value of 21•15 equals (20+1)•15. True or false?
Use a model to solve t+4=5.
The model to solve t + 4 = 5 is that John hast number of oranges and got 4 more making 5 oranges.
How to explain the model?A mathematical model is an abstract, mathematically based description of a physical system. Mathematical modeling is the process of creating a mathematical model.
To make a prediction or offer insight, mathematical modeling is the process of creating a mathematical representation of a real-world scenario.
The equation t + 4 = 5 can be solved by subtracting 4 from both sides of the equation:
t + 4 = 5
t = 5 - 4
t = 1
So t = 1 is the solution to the equation
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there i 2 worker, one can make a houe in 2 day the other one can make houe in 3 day, if they work together how much day it take them to make a houe
The time taken by both the workers working together, which is 2 days.
The time taken to build a house by two workers working together can be calculated using the formula T = (1/W1 + 1/W2)^-1, where W1 and W2 are the working speeds of each worker. In this case, W1 = 2 days and W2 = 3 days. So, the time taken to build a house by both workers together is calculated as follows:
T = (1/2 + 1/3)^-1 = (3/6)^-1 = 6/3 = 2 days
Therefore, both the workers working together will take 2 days to build a house. This is because when two workers work together, the total work done in a given time is equal to the sum of the work done by each worker separately in that given time. In this case, both the workers will take 2 days and 3 days respectively to build the house when working separately, so when they work together the total work done in a given time will be 5 days. This is equal to the time taken by both the workers working together, which is 2 days.
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A cruise line ship left port A and traveled 80 miles due west and then 150 miles due north at this point what is the shortest distance from the cruise to port A in miles
Answer:
170 miles
Step-by-step explanation:
Use 80 miles and 150 miles as the legs of a right triangle, and find the length of the hypotenuse using the Pythagorean theorem.
a² + b² = c²
80² + 150² = c²
6400 + 22500 = c²
c = √28900
x = 170
Answer: 170 miles
Which expression represents the correct form for the quotient and remainder, written as partial fractions, of
8x²³-21²-67x-24?
2x²-x-21
The quotient and remainder, when written as partial fractions, of 8x²³-21²-67x-24 is represented by 2x²-x-21.
Which expression represents the correct form for the quotient and remainder?(8x³-21²-67x-24) = (2x²-x-21) + (6x¹-42)
This is done by dividing 8x²³-21²-67x-24 by 2x² and using long division to find the remainder.
The result of the division is a quotient of 4x²-33x+12 and a remainder of 2x²-x-21.
The remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.To illustrate this further, we can break down the long division process into steps. First, divide 2x² into 8x²³.The result is 4x².
Then, subtract 4x² from 8x²³ to get the remainder of 4x³.
Next, divide 4x² into 21².
The result is 33x.
Then, subtract 33x from 4x³ to get the remainder of 4x²-33x.
Finally, divide 4x²-33x into 67x.
The result is 12. Subtract 12 from 4x²-33x to get the remainder of 2x²-x-21.This remainder is the expression which represents the quotient and remainder, written as partial fractions, of 8x²³-21²-67x-24.To learn more about partial fractions refer to:
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How do you solve the equations that is listed to the right? (8x-9)-(3x-1)
Answer: The answer is 5x-8.
Step-by-step explanation: The equation we have is (8x-9)-(3x-1). The first step is to write the equation as shown:
8x-9-(3x-1)
After that step, next is to apply the distributive law:
8x-9-3x+1
Then, group/combine like terms:
8x-3x-9+1
Then adding similar elements:
5x-9+1
And finally, solving:
5x-8
The graphs shows the speed of a car for 30 seconds. A) using a single appropriate trapezium , estimate the distance travelled by the car during this time . B) is your answer an overestimate or underestimate ?
Answer:
Step-by-step explanation:
a)
0.5 x (a + b) x h
0.5 x (5 + 30) x 30
Area = 525
b) Overestimate
a data analyst for a phone company is analyzing the data of 150 of their customers, which accounts for 1% of their total customers. the analyst wants to determine the average number of hours each day a customer uses their phone, for calls and for texts, during a 30-day period. based on the data, the customers averaged 0.25 hours per day per call and 1.75 hours each day for texts. construct an equation in the correct form of y
Total number of a customer uses his phone each day in hour 0.25t + 1.75
Total number of a customer uses his phone each day in hour (e) = the customer spend time in hour on calls + the customer spend time in hour on texts.
total number of a customer uses his phone each day in hour (e) = the customer spend time in hour on calls + the customer spend time in hour on texts.
the customer spend time in hour on calls = the number of calls the customer made per day (t) times the average time spent by customers per day per hour (0.25 hours)
The number of hours the customer spend on texts is given as 1.75 hours each day.
Therefore required equation is:
e = 0.25t + 1.75
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The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
Range, because it measures the distinction between the highest and lowest values in a dataset, providing a clear estimate of variability for both sets of data. It is unaffected by skewness or symmetry, making it a useful measure of variability for comparing the temperature consistency of Desert Landing and Flower Town.
What is meant by histogram?A histogram is a rough illustration of how numerical values are distributed. Karl Pearson coined the phrase at the beginning.
A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.
A common tool for graphing is the histogram. It is employed to summarise continuous or discrete data that is measured on an interval scale. It is frequently used to provide a convenient manner of illustration for the main characteristics of the data distribution.
Therefore, the correct answer is both option c) and d) Range, because Flower Town is skewed and symmetric.
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Answer:
The correct answer is:
Range, because Flower Town is symmetric
Select the correct answer.
What is the y-intercept of function f?
(-3x - 2,
-∞ <
-x + 1,
-2 ≤ x ≤ 3
2x + 5,
3 ≤ x < 00
f(x)
=
OA. -1
OB. 5
O C. 1
OD. -2
< -2
Answer:
The correct answer is C. 1
Where do these two lines intercept on a graph y= -2x+9 and y=3x-6
These two lines intercept on a graph on the coordinate X(0, 1) Y(9, 7).
How to find this?The term "intercept" refers to the location where a line or curve intersects an axis on a graph. An object's x-intercept is defined as where a point crosses the x-axis. The term "y-intercept" refers to a point that crosses the y-axis. The intersection of the x-axis and the y-axis is what is meant by a line's intercept.
step1
y=-2x+9
graph the line using the slope and y intercept or two points
y=-2x+9
X(0,1) Y(9,7)
step2
y=3x-6
slope 3 y intercept (0,-6)
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Carlos solved the equation below incorrectly.
13(12x−9)=12(x+18) 16x−3=12x+9 14x−3=9 14x=12 x=48
Identify Carlos' error and then solve the equation correctly. (3 points)
Enter your answer and your work or explanation in the space provided.
Answer: Please see explanation column for answer.
x= -36
Step-by-step explanation:
Step 1
from the attachment, Carlo solving is given as
1/3 (1/2x- 9) = 1/2 (x+18)
1/6x-3= 1/2x+9
1/4x-3=9
1/4x=12
x=48
Carlos error started when he subtracted wrongly 1/2 x from 1/6x which gave him 1/4 x instead of - 1/3 x.
Solving correctly, we have that
1/3(1/2x-9) = 1/2(x+18)
1/6x -3= 1/2x+ 9
taking like terms to like terms
1/6x-1/2x= 9+3
(1-3)/6x= 12
-2/6x= 12
-1/3x= 12
multiplying both sides by -3
-1/3x X -3 = 12 X -3
x= -36
For a scale drawing bathroom, 1/6 inch represents an actual length of 1 foot. If the bathroom measures 1 1/2 inches by 2 inches in the drawing, what are it's actual dimensions (length and width)?
Answer:
12ft x 9ft
Step-by-step explanation:
1/6" equals 1' actual ==> 1"=6'actual.
1.5" = 9'
2" = 12'
By utilizing the given scale of 1/6 inch equals 1 foot, the actual length of the bathroom is calculated to be 9 feet and width is 12 feet, from the given measurements of the drawing.
Explanation:The mentioned math problem is based on scale conversion, specifically in the realm of measurement. Given that every 1/6 inch on the scale drawing equals 1 foot in reality, the first step to solving this problem is to convert the measurements of the drawing into scale inches. To convert the length of 1 1/2 inches to the actual length, multiply 1.5 by 6 (as 1 inch is 6 times of 1/6 inch). This equals to 9 feet. Similarly, for the width of 2 inches, multiply 2 by 6 to get 12 feet.
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what is right! its either a or c
Answer: I believe it is A
The scatterplot shows the number of home runs mario hits during his first four seasons on the company softball team. If his output continues to follow the linear model, approximately how many hime runs will Mario hit during his ninth season
y = 32 home runs will Mario hit during his ninth season.
Now, According to the question:
Linear models describe a continuous response variable as a function of one or more predictor variables. They can help you understand and predict the behavior of complex systems or analyze experimental, financial, and biological data. Linear regression is a statistical method used to create a linear model.
According to the graph, we have
The equation is:
y = 3x + 5
Put the value of x = 9
We get:
y = 3 × 9 + 5
y = 32
(Figure out the function of the image, and then bring the value of 'x' into it.)
Hence, y = 32 home runs will Mario hit during his ninth season.
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Make x the subject of m=n+x/p
Answer:
x = p(m-n)
Step-by-step explanation:
we can eliminate the 'p' in the denominator by multiplying each side of the equation by 'p' to get:
mp = np + x
now we can subtract 'np' from each side to get:
mp - np = x
we can further simplify it as:
p(m-n) = x
Answer:
X=n-p×m
Step-by-step explanation:
m=n-x/p
p×m=n-x
n-p×m=n+x-n
X=n-p×m
HURRY PLEASE!!! What are the marginal
column totals?
The marginal column total for the given data is option D: 39; 16.
What is marginal total?
A set of marginal totals is produced when the cell frequencies of a (multidimensional) contingency table are added over one or more of the classifying variables. The row and column totals are the marginal totals for a two-dimensional table.
The sum of the row entries or the sum of the column entries are called the marginal totals. Marginal distributions are computed by dividing the row or column totals by the overall total.
The number of men who prefer to eat fish = 11
The number of women who prefer to eat fish = 6
The number of men who prefer to eat red meat = 28
The number of women who prefer to eat red meat = 10
So, the marginal column total for the number of men who prefer to eat fish and red meat collectively is -
11 + 28 = 39
The marginal column total for the number of women who prefer to eat fish and red meat collectively is -
6 + 10 = 16
Therefore, the marginal total is 39, 16.
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Jayden needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 3. 75 hours and charged him $60 for parts. The total was $528. 75. Write and solve an equation which can be used to determine xx, the cost of the labor per hour
The required equation is x × 3 = 528.75 - 60.
The cost of the labor per hour is $156.25
How do equations work?
The definition of an equation is a mathematical statement with at least two terms that contain variables or equal numbers.
Let x be the cost of the labor per hour.
We know that
x × 3 = labor cost
60 + x × 3 = total cost
We also know that the total cost is $528.75
So we can write the equation:
60 + x × 3 = 528.75
Solving for x:
x × 3 = 528.75 - 60
x × 3 = 468.75
x = 468.75/3
x = 156.25
Therefore, the cost of the labor per hour is $156.25
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have been generated by a linear function?
Answer:
no.................,.............
Let N(t) represent the number of people in line at a BBQ truck, t hours after the food truck opens. Interpret each of the following statements in context.
Each of the given statements are interpreted in context below.
What is the quadratic equation?
A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where x is the variable and a, b, and c are constants. The solutions of the equation are the values of x that make the equation true.
a. N(1) = 11: This statement represents that 1 hour after the food truck opens, there are 11 people in line.
b. N(0) = N(3): This statement represents that at the time the food truck opens, the number of people in line is the same as 3 hours after the food truck opens.
c. N(4) > N(6): This statement represents that at 4 hours after the food truck opens, the number of people in line is greater than at 6 hours after the food truck opens.
d. N(R) = 34: This statement represents that the number of people in line at an unspecified time R is 34. The letter "R" can be any value for time, it is only a placeholder for any arbitrary value.
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Which list orders the decimal numbers 1.47, 4.01, 1.4, and 4.1 from least to greatest?
Answer:
Always start with the first number. The one in 1.47 is less than the 4 in 4.01, so 1.47 is less than 4.01.
Least to greatest is 1.4, 1.47, 4.01, and 4.1
Mia and her children went into a bakery that sells cupcakes for $2.50 each and donuts for $1.25 each. Mia has $30 to spend and must buy no less than 14 cupcakes and donuts altogether. If � x represents the number of cupcakes purchased and � y represents the number of donuts purchased, write and solve a system of inequalities graphically
Answer:
2.50x + 1.25y ≤ 30
x + y ≥ 14
x ≤ 10 and y ≤ 24
Step-by-step explanation:
we can by elimination if we multiply the second inequality by -2.5, we get:
-2.50x - 2.5y ≥ -35
if we add the first inequality to the above we get:
2.50x + 1.25y ≤ 30
+ -2.50x - 2.5y ≥ -35
-1.25y = -5
divide each side by -1.25 to get:
y = 4
therefore, x = 10
if you graph each system you must look for the area where the shading of each inequality overlaps
upon graphing, the solution is x ≥ 10 and y ≤ 24
How to do this question? I don't really know what the lines next to 2t are, or are they just brackets?
Answer:
- 14
Step-by-step explanation:
the bars around 2t , indicate the absolute value of 2t
the absolute value function always gives a positive value , that is
| - a | = | a | = a
so for example
| - 4 | = | 4 | = 4
given
[tex]\frac{2}{3}[/tex] p - | 2t | - s² ( substitute values for p, t and s into the expression )
= [tex]\frac{2}{3}[/tex] × 12 - | 2(- 3) | - (- 4)²
= 2 × 4 - | - 6 | - 16
= 8 - 6 - 16
= 2 - 16
= - 14
A bullet shot straight up is s feet above the
ground after seconds, where f(1) = -16t² + 256t. Find the height of the bullet 3 seconds after it is shot.
The height of the bullet after 3 second is 640m
What is motion under gravity?Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is gravity. In fact, gravity works towards the centre of the Earth.
When an object is thrown up, the height of the object is calculated as h = v²/2g
where v is the velocity and g is the acceleration due to gravity.
v = -16t²+ 256(t)
when t = 3s
v = -16( 3)²+ 256
v = -144+256
v = 112m/s
therefore the height attained by the bullet =
h = 112²/2×9.8
h = 640m
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A net of a rectangular pyramid is shown. The rectangular base has length 25 ft and width 22 ft. The net of the pyramid has length 74.8 ft and width 70.4 ft. Find the surface area of the pyramid.
The surface area of the pyramid is 1702.8 ft².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Rectangular pyramid has a rectangular base and four triangular faces.
Net of the pyramid is shown below.
Area of the rectangular base = 25 × 22 = 550 ft²
Now we have to find the area of four triangular faces.
Area of a triangle = [tex]\frac{1}{2}[/tex] × base × height
Heights of the triangle BCX and ADZ can be found as below :
Combined height of both triangles = 74.8 - 25 = 49.8
Height of each triangle = 49.8 / 2 = 24.9 ft
Area of triangles BCX and ADZ = 2 × ( [tex]\frac{1}{2}[/tex] × base × height)
= Base × height
= 22 × 24.9
= 547.8 ft²
Similarly,
Combined height of triangles ABW and CDY = 70.4 - 22 = 48.4
Height of each triangle = 48.4 / 2 = 24.2 ft
Area of triangles ABW and CDY = Base × height
= 25 × 24.2
= 605 ft²
Total surface area of the pyramid = 550 ft² + 547.8 ft² + 605 ft²
= 1702.8 ft²
Hence 1702.8 ft² is the total surface area of the pyramid.
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Marshall has b buttons. He gives away 13 buttons. Write an expression that shows the number of buttons Marshall
has left.
Answer:
Since Marshall gives away 13 buttons out of b buttons, it means that b is an expression of a number which is greater than 13. Therefore,the answer is b - 13.
can someone help me with this question?
The final balace in Tracy's bank account is $ 361.80.
How to follow transactions in a bank account
In this question we must pay attention to every movement in a bank account and determine final balance within. The hint is having an active reading in the meaning of translating every Tracy's movement in additions and subtractions, First, we translate very sentence into numbers and signs:
Tracy's checking account: + $ 300.00
Tracy bought new sneakers: - $ 63.00
Tracy deposited a paycheck: + $ 43.25
Tracy wrote a check: - $ 17.75
Tracy wrote a check: - $ 9.45
Tracy made a withdrawal at her bank: - $ 20.00
Tracy deposited a paycheck: + $ 43.25
Tracy wrote a check: - $ 18.00
Tracy made a withdrawal at another bank: - $ 20.00 - $ 1.50
Tracy deposited her birthday money: + $ 125.00
Second, calculate the final balance in Tracy's account:
x = 300.00 - 63.00 + 43.25 - 17.75 - 9.45 - 20.00 + 43.25 - 18.00 - 20.00 - 1.50 + 125.00
x = 361.80
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