The number of ways to split the integers, given the condition and using the Fundamental Counting Theorem, is of:
144.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes considering all trials is calculated by the multiplication of the factorials as presented as follows:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Given the condition that the greater number is at least 2 times the lesser number we have that the pairs are composed by one number between 1 and 7 and another number between 8 and 14.
Hence the pairs of each number are built as follows:
For the pair of the number 7, there are only one possible outcome, which is of 14.For the pair of the number 6, there are two possible outcomes, which are of either 12 or 13.For the pair of the number 5, there are three possible outcomes, which are of either 10, 11, and whichever of 12 or 13 is not paired with 6.For the pair of the number 4, there are four possible outcomes, which are of either 8, 9, and the two remaining numbers that are not paired with 5 or 6.For the pair of the number 3, there are three possible outcomes, which are the remaining numbers that are not paired with 4, 5 or 6.For the pair of the number 2, there are two possible outcomes, which are the remaining numbers that are not paired with 3, 4, 5 or 6.For the pair of the number 1, there is one possible outcome, which is the remaining numbers that is not paired with 2,3, 4, 5 or 6.Hence the number of ways to split the numbers is:
2 x 3 x 4 x 3 x 2 = 144.
(the numbers were multiplied because of the Fundamental Counting Theorem).
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3. Use the graph of f(x) below to answer the following questions. Approximate answers are okay.
Answer:
Step-by-step explanation:
f(0) = 4
f(x)=0 when x = 0.75
f(x) =5 when x =3
A{ x ∈ R ║ 3≤x}
According to a recent survey of 43 million citizens in the United States, 8 million were planning to start a new degree program or continue their education in the next year. According to this data, what is the probability that a random U.S. citizen you meet is not planning to start a new degree program or continue their education in the next year? (Round to four decimal places.)
The probability of people not planning a new degree = [tex]\frac{35}{43}[/tex]
What is probability ?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
And while solving these type of question we calculate the probability of a particular event.
The survey has 43 million people
Given is 8 million were planning to start a new degree program
Thus the probability of people planning a new degree program = 8 million divided by 43 million
Thus the probability of people not planning a new degree = 1 - [tex]\frac{8 million}{43 million}[/tex]
which is equal to [tex]\frac{35,000,000}{43,000,000}[/tex]
which on solving further will give us:
P ( people not planning a new degree ) = [tex]\frac{35}{43}[/tex]
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Seven people work at an office. Every day they draw straws to decide who will have to pick up lunch for the office. Janice has just joined the office (so there are now eight people). She knows that it's unlikely she will have to pick up lunch on her first day, and on the second day as well. How many days must past before it becomes probable that Janice will have had to pick up lunch at least once?
Given the frequency and number of possible outcomes, the number of days that must pass before it becomes probable that Janice will have had to pick up lunch at least once is 8.
Note that the probability of any of the staff at the office picking the food is 1/8.
Even if She does not pick up lunch on her first day or second, the number of days that must pass to make sure that Janice picks up lunch AT LEAST once is 1 in 8 days.
What is probability?The formula to compute the probability of an event is equivalent to the ratio of favorable outputs to the total number of outputs. It is to be noted that probabilities always range between 0 and 1.
The expression is given as:
P (E) = f/O; where
P(E) is the Probability of an event E happening;
f = The number of possible outcomes for an event (frequency)
n = Total number of outputs that are likely
Hence,
P(E) = 1/8
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An x-ray machine for animals costs 125,000. If the loan is for 10 years, and the interest paid is $65,625, what is the interest rate on the loan?
The interest rate on the loan is 5.25%.
How to calculate the rate?It should be noted that the formula for calculating the simple interest is given as:
Interest = (Principal × Rate × Time) / 100
In this case,
Interest = 65625
Principal = 125000
Time = 10
Interest = (Principal × Rate × Time) / 100
65625 = (125000 × R × 10)/100
Cross multiply
6562500 = 1250000R
Divide
R = 6562500 / 1250000
R = 5.25
The rate is 5.25%
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One way that a company can raise money for expansion is to sell stock. When you buy a share of a company's stock, you become a shareholder, or part owner, of that company. The cost of a share is often represented in points, where each points represents one dollar. When a stock gains points, its shares increase in value, and when a stock loses points, its shares decrease in value. For instance, if a stock gains three points one day, each share of its stock is worth three dollars more than it was the day before. Positive decimal numbers are used to represent gains, and negative decimal numbers are used to represent losses.
On Monday, the closing value of a share of stock in Company ABC, was 74.01. On Tuesday, it closed at 73.67, and on Wednesday, it closed at 74.32. On Thursday, the change in stock value was -1.48. And, on Friday, Company ABC's stock gained 0.89 points. Answer the following questions based on Company ABC's stock performance this week.
One shareholder owns 13 shares of Company ABC's stock. What was the total value of their stock in this company at the close of Tuesday? $
equation if he started his day on Wednesday with 75 end he ended with 74.32 he lost -0.68 of his share hope this helped there a lot of extra information in the question
An equation is written as expressions, connected by an equals signal ("=").[2] The expressions on the two facets of the equals signal are referred to as the "left-hand side" and "right-hand side" of the equation. Very regularly the right-hand side of an equation is assumed to be zero. Assuming this doesn't lessen the generality, as this can be realized through subtracting the right-hand side from each facets.
The most common sort of equation is a polynomial equation (commonly known as also an algebraic equation) wherein the 2 facets are polynomials. the edges of a polynomial equation incorporate one or greater terms
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14. Reflection: in the line y=x
Rotation: 180 about the origin
The image of the end points X(-3 , 1) and Y(4 , -5) is
X'' = (-1 , 3) and Y'' = (5 , -4).
Given, a line segment with end points X(-3 , 1) and Y(4 , -5)
We have to find the image of the points after the given composition,
Reflection in the line y = x.
Rotation 180° about the origin.
After the reflection the image of the points X and Y be,
X' = (1 , -3) and Y' = (-5 , 4)
Now, after the rotation of the points of 180° about the origin be,
X'' = (-1 , 3) and Y'' = (5 , -4)
Hence, the image of the end points X(-3 , 1) and Y(4 , -5) is
X'' = (-1 , 3) and Y'' = (5 , -4).
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A restaurant has 33,500 gallon aquarium and a 500 gallon aquarium. How many times greater is the capacity of the larger aquarium than the smaller aquarium?
Answer:
67
Step-by-step explanation:
33,500/500 = 67
To check our work:
67 x 500 = 33,500
Answer:
67 percentStep-by-step explanation:
Please help. Find x and y. NEED ASAP
Answer:
x=10
y=5
Step-by-step explanation:
you have to find the length
Consider the following data: x −7 −6 −5 −4 −3 P(X=x) 0.2 0.1 0.2 0.2 0.3 Step 1 of 5 : Find the expected value E(X). Round your answer to one decimal place.
The expected value of the given discrete distribution is presented as follows:
E(X) = -4.7.
How to obtain the expected value of a discrete distribution?The expected value of a discrete distribution is obtained with the sum of each outcome multiplied by it's respective probability.
The distribution in this problem, which contains the outcomes and their probabilities, is presented as follows:
P(X = -7) = 0.2.P(X = -6) = 0.1.P(X = -5) = 0.2.P(X = -4) = 0.2.P(X = -3) = 0.3.Hence the expected value of the distribution is calculated as follows:
E(X) = -7 x 0.2 - 6 x 0.1 - 5 x 0.2 - 4 x 0.2 - 3 x 0.3 = -4.7.
(each value from the distribution above, that is, -7, -6, -5, -4 and -3 was multiplied by it's respective probability and then these values were added).
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If Pam has 40 dollars in her account, how much money does her brother have in his account? Use a tape diagram to
support your answer.
Answer:
[tex] \binom{?}{?} [/tex]
Step-by-step explanation:
$40 Pam use type diagram
$45. bro
simplify the expresion (5÷5)+5×(5²- 5)
Answer: 101
Step-by-step explanation: 1+5x20 then 100+1= 101
please help me due today
Answer: B
Step-by-step explanation: I believe this is correct. The arrows on both run all trough the x-axis, so it would be negative infinity to positive infinity. Then, you go from open circle ( ( ) -3 to closed circle ( } ) 4.
NO LINKS!! Please help me with this symmetry part 2
Functions that are symmetric with respect to the x-axis are those with even degree of y, i.e y², y⁴ etc.
Correct choices are:
x = 1/8y²x = - y² + 9
Answer:
[tex]x=\dfrac{1}{8}y^2[/tex]
[tex]x=-y^2+9[/tex]
Step-by-step explanation:
Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:
f(x, y) = f(x, −y)To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.
Therefore, any function that includes the term y² will be symmetric with respect to the x-axis since (-y)² = y².
[tex]\begin{aligned}&\textsf{Given}: \quad& x&=\dfrac{1}{8}y^2\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=\dfrac{1}{8}(-y)^2\\&\textsf{Simplify}: \quad &x&=\dfrac{1}{8}y^2\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.
[tex]\begin{aligned}&\textsf{Given}: \quad& x&=-y^2+9\\&\textsf{Replace $y$ for $(-y)$}: \quad& x&=-(-y)^2+9\\&\textsf{Simplify}: \quad &x&=-y^2+9\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the x-axis.
What is the simplified form of |-10-(-20)|-|-6+2|+|12-6|
Answer:
12
Step-by-step explanation:
|-10+20| - |-4| + |6|
10 - 4 + 6
12
The sum of two numbers is 42. The sum of 5 times the 1st number and 9 times the 2nd number is 190. What are the two numbers?
Step-by-step explanation:
x + y = 42
5x + 9y = 190
x = 42 - y
5(42 - y) + 9y = 190
210 - 5y + 9y = 190
210 + 4y = 190
4y = -20
y = -5
x = 42 - y = 42 - -5 = 42 + 5 = 47
A funicular carries passengers up an embankment to an observation point. If the length of the track is 51.1 meters and the angle of inclination is 35 degrees 7, determine the height of the embankment.
The height of the embankment is 8.19 meters
How to determine the height of the embankment.Information from the question
the length of the track is 51.1 meters
the angle of inclination is 35 degrees
The height of the embankment is worked using SOH CAH TOA
The direction of movements describes a right angle triangle of
opposite = x meters
hypotenuse = 10 miles
The height is calculated using cos, CAH let the height be x
cos 35 = adjacent / hypotenuse
cos 35 = x/ 10
x = 10 * cos 35
x = 8.19 meters
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Which Form is the following equation in?
y = −7(x + ²)² + 11 Vertex Form Standard Form Factored Form
Answer:
Factored form is the form of the equation.
hey please solve this
Answer:
∴ x = 70°, y = 70°, z = 40°
Step-by-step explanation:
x = 180° - 110° (adjacent angles on a straight line)
= 70°
Since triangle PQR is an isosceles triangle,
∴ y = x = 70°
∴ z = 180° - 70° - 70° (angle sum of a triangle)
= 40°
4.5÷0.9= what is 4.5 divided by 0.9 equal to .explain
Answer: The answer is 5.
Step-by-step explanation:
4.5 ÷ 0.9 = 450/90.
Convert decimal 4.5 to fraction 45/10
Convert decimal 0.9 to fraction 9/10
Divide 450/90
Simply 450/90 = 5
Answer:
5
Step-by-step explanation:
The function f(x) is graphed below. What is true about the graph on the interval from point e to point f?
Answer: It is positive and increasing
Step-by-step explanation:
From point e to f it is clearly going up, and is part of the positive side of the graph.
Suppose that the volume of water in the rain barrel decreased by 4
58
gallons in 4 minutes. What will be the change in the volume of water after 1 minute.
The change in the volume of water after 1 minute is 1 5/32 gallons.
How to calculate the change in volume?Given that the volume of water in the rain barrel decreased by 4 5/8 gallons in 4 minutes.
The change after 1 minute will be:
= Total volume of water / Number of minutes
= 4 5/8 ÷ 4
= 37/8 ÷ 4
= 37/8 × 1/4
= 37 / 32
= 1 5/32
The change is 1 5/32 gallons.
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See the question above. I don’t understand how I was wrong to do the LCM of 50 and 60, which is 300, so that’s the distance where the friends will meet, and d/s = time, so 300/50 and 300/60 are 6 and 5, and the average of that is 5.5, but the real answer seems to be approx. 18.2? Please solve the question AND explain my mistake.
Answer:
Step-by-step explanation:
so this is a combined work problem, both of the people are moving towards each other. They are both doing some of the work to move towards each other.
one is moving at 50 , the other at 60 , directly towards each other. Now change the problem to one moving at 50+60 =110 at a destination 200 away
now you can solve this pretty easily , i'm guessing
200/110 = 1.818181
or approx. 1.82 hours
got it?
Factor 3x+11y if the expression cannot be factored
The expression 3x+11y cannot be factorized.
What is factorization?
To factorise an algebraic statement, we first identify the terms' highest common factors before organising the words in the appropriate way. An algebraic expression's factorization is, to put it simply, the process of expansion in reverse. The same way, as the product of their factors, are the algebraic expressions written in algebra. The only difference is that in an algebraic expression, variables and integers are combined to perform mathematical operations like addition or subtraction.
Here the given expression 3x+11y didn't have any common factors.
The given expression has two variables 3x and 11y and they didn"t have any common terms.
Hence the expression 3x+11y cannot be factored.
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Simplify the power (3x^2 y)^4
Answer:
(3x^2 y)^4
first apply the index power to all the numbers.
3^4= 81
then you multiply the two indices.
x^2 x 4= x^8
y^4
the answer is:
81 x^8 y^4
Use the table below to find d/dx[5f(x)-4x] x=2
The value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
From the table:
At x=2,
f'(x) = 4
f(x) = 4x
= d/dx(5*4x - 4x)
= d/dx(20x - 4x)
= d/dx(16x)
= 16
Therefore the value of derivative of d/dx[5f(x)-4x] at x=2 = 16.
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2009
Evaluate x y for the following values of x and y.
value of x value of y value of xy
1
5
-205
1
67
1
-1
11
.
-1
-7.93
-1
-11
Answer:meh
Step-by-step explanation:good enough
During a football game the parents of the Devils football players sell nachos and popcorn to raise money for
new uniforms. They charge $8.50 for nachos, and $6.00 for a bag of popcorn. The parents collect $883.50 in
sales during the game. They sell a total of 126 items. Set up a system of equations and solve to determine
how many nachos and bags of popcorn were sold.
Number of nachos sold:
Number of bags of popcorn:
The equation is 8.50x + 6y = 883.50
Number of nachos sold is 51
Number of bags of popcorn sold is 75
Given,
The cost for nachos = $8.50
The cost of a bag of popcorn = $6.00
The total amount collected = $883.50
Total number of items sold = 126
We have to find an equation and solve to determine the number of nachos and bags of popcorn sold;
Here,
x be the number of nachos sold
y be the number of bags of popcorn sold
Then,
x + y = 126
x = 126 - y
Now,
8.50x + 6y = 883.50
Solve the equation using x as 126 -y.
That is,
8.50(126 - y) + 6y = 883.50
1071 - 8.50y + 6y = 883.50
1071 - 2.50y = 883.50
1071 - 883.50 = 2.50y
y = (1071 - 883.50) / 2.50
y = 187.50/2.50
y = 75
Now.
x = 126 - y
x = 126 - 75
x = 51.
Therefore,
The equation is 8.50x + 6y = 883.50
Number of nachos sold is 51
Number of bags of popcorn sold is 75
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Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. The z score corresponding to a woman with a height is 2.56. How tall is the woman?
Answer:
70
Step-by-step explanation:
Had this question too ;)
How many values of x must be excluded in the expression (x+9)(x-5)?
The number of values of x to be excluded is 2.
To find out the values of x that must be excluded in the expression
(x+9)(x-5) as follows:
The value of x is 2.
We are given to find the number of value of x that must be excluded in the expression below:
E = (x+9)(x-5)
We have to exclude those values of x for which the expression E becomes undefined.
Since E is a rational expression, so the becomes undefined only when the denominator becomes 0.
That is,
(x+9)(x-5) = 0
= x+9 = 0 x-5 = 0
= x = -9 x = 5
Therefore, we need to exclude the values x = -9 and x =5.
So, there are two values of x to be excluded from the given expression.
Hence the answer, the number of values of x to be excluded is 2.
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Julie had $20.00 in her pocket. She spent $7.40. About what percent of her money does she still have?
63%
First, we have to take 20.00 - 7.40 which gets us 12.60.
Then, we use the formula where we put the 12.60 on top of a fraction bar, and the 20.00 on bottom.
We do 12.60 x 100 which makes 1260.
Lastly, we divide that by the 20.00 which gets us 63.
So, Julie has 63% of her money left.
I hope this helped!!!