Answer:
1 tube of paint is $2.25.
Step-by-step explanation:
We can set this as an equation first. Since we know that the canvas is $6.95 and the total is $24.95, those are the values that we will work with to determine the tube price. We can set the tube price as 8x, x being the tube price, and 8 being the number of tubes Ishi plans to buy. Now, we can set an equation:
6.95 + 8x = 24.95
8x = 18
x = 18/8 (simplified is 9/4, or 2.25)
Answer:
$ 2.25
Step-by-step explanation:
A= $6.95
B= (Cost of each tube) x 8
C= $24.95
A+B = C
The length of a piece of string is x cm long. Another piece measures x+5cm long. If the second piece is 20% longer than the first,calculate the value of x.
Answer:
x = 25 cm
Step-by-step explanation:
20% =
20/100 = 0.20
20% longer =
20% + 100% =
120% =
120/100 = 1.20
Hence, x+5 is 1.20 times that of x:
x * 1.20 = x + 5
1.2x = x + 5
1.2x - x = 5 ==> subtract x on both sides to move x to one side of the
equation
1.2x - 1x = 5 ==> 1x = x
(1.2 - 1)x = 5 ==> distribution property
0.2x = 5
x = 25 ==> multiply both sides by 5 ( 0.2 * 5 = 1 )
a segment is created from points a and b. to copy segment ab, which of the following needs to be identified for the construction? the distance between point a and a point not on the segment the midpoint of points a and b the midpoint between point b and a point not on the segment the distance between points a and b
The correct answer among the following option is , the distance between point a and b of segment ab.
What are Points?
A point is denoted by a dot(.). A point represents position only. It has no size.
Points given in the question are a and b.
What is Line Segment?
A line segment is a part of line with a definite start point and a definite end point.
Their are infinite number of point between the end and start point of the segment.
For the construction,
To copy the segment ab, The distance between the two points a nd b is required.
To calculate the distance, Use the distance formula if the co-ordinates of point a and b are given.
The distance can also be measured using a measuring instrument like
a ruler, A measuring tape if the co-ordinates are not given.
As the distance between both the points a and b is known, A new segment can be drawn of the same distance as ab using two new points and can be named cd or a'b'.
To copy the segment ab, The distance between the point a and b is required.
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Answer:the distance between points a and b
Step-by-step explanation: took the test and got it right
grandma famous punch uses a ratio of 5 cups of cranberry juice and 2 cups of sprite. if she needs a total of 56 cups of famous punch how amy cups of cranberry and how many cups of sprite to make 56 cups of punch
You will need 280 cups of cranberry juice and 56 cups of Sprite to make 56 cups of the famous punch.
What is the ratio definition?
A ratio is a mathematical comparison of two or more values or quantities. It is usually written as a fraction, with the first value or quantity being the numerator and the second value or quantity being the denominator.
To make 56 cups of famous punch using the ratio of 5 cups of cranberry juice to 2 cups of Sprite, you can use the following method:
Write the ratio of cranberry juice to Sprite as a fraction: 5 cups cranberry juice / 2 cups sprite
Multiply the fraction by the desired number of cups of punch: (5 cups cranberry juice / 2 cups sprite) x 56 cups punch
Simplify the equation by cross-multiplying: 5 cups cranberry juice x 56 cups punch = 2 cups sprite x 56 cups punch
Solve for the number of cups of cranberry juice: 5 cups cranberry juice x 56 cups punch = 280 cups of cranberry juice
To find the amount of Sprite use the ratio 5:2, meaning you have to use 2 cups of sprite for every 5 cups of cranberry juice. So use 280/5*2 = 56 cups of sprite
Hence, you will need 280 cups of cranberry juice and 56 cups of Sprite to make 56 cups of the famous punch.
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Simplify the following expression. 7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}
The term, [tex]\frac{1}{49}[/tex] is simplified form of the expression [tex]7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}[/tex].
What is simplest form?The top and bottom of a fraction are said to be in its simplest form if they only share the number one. For the top & bottom to remain whole numbers, you cannot divide them further.
Additionally, lowest terms, or simple form, may be used.
The simplest form of a fraction, for instance, is 4/5. Apart from 1, there isn't a number that divides both 4 and 5. Not in its simplest form is the fraction 3/6. Numerator & denominator can both be divided by 3.
Given to simplify the expression
[tex]7^{-\dfrac{5}{6}} \ \cdot\ 7^{-\dfrac{7}{6}}[/tex]
[tex]7^{(-\dfrac{5}{6}-\dfrac{7}{6})}[/tex]
[tex]7^{(\dfrac{-5-7}{6})}[/tex]
[tex]7^{(\dfrac{-12}{6})}[/tex]
[tex]7^{(-2)}[/tex]
[tex]\dfrac{1}{7} \times \dfrac{1}{7}[/tex]
[tex]\dfrac{1}{49}[/tex]
Thus, [tex]\frac{1}{49}[/tex] is simplified form of the expression [tex]7^{-\frac{5}{6}} \ \cdot\ 7^{-\frac{7}{6}}[/tex].
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A 400 g sample is composed of 100 g of cesium (Cs) and 300 g of iodine (1).
What is the percent by mass of Cs in the sample?
A. 50.0%
B. 70.0%
C. 25.0%
D. 75.0%
Answer: C. 25%
Step-by-step explanation: This is a basic probability problem. First, you must find the total which is in question. 400 grams is the total in this case. The Cs make up 100 grams of this. Next, you put the part over the whole, and divide. 100/400= 0.25. When you want to find the probability with the probability sign, you move the decimal place two points to the right and then add the sign. Hence, 25%.
The bearing from the Pine Knob fire tower to the Colt Station fire tower is N 65° E, and the two towers are 29 kilometers apart. A fire spotted by rangers in each tower has a bearing of N 80° E from the Pine Knob and S 70° E from Colt Station (see figure). Find the distance of the fire from each tower. (Round your answers to two decimal places.)
From Pine Knob:
The distance of the fire from each tower is:
i. From Pine Knob: 41 kilometers
ii. From Colt Station: 15 kilometers
What is Bearing?Bearing as a topic in mathematics can be used to determine the exact position or location of an object considering its angle of position and distance to a reference point.
Considering the given question; let the distance of the fire (F) from Pine knob (PK) be represented by x, and that from Colt Station (CS) be represented by y.
Angle at PK = 80 - 65
= 15^o
Angle at CS = 65 + 70
= 135^o
Angle at F can be determined as;
15 + 135 + F = 180 (sum of angle in a triangle)
150 + F = 180
F = 30^o
So that applying the Sine rule to determine the distances of the fire from PK and CS, we have;
a/Sin A = b/Sin B = c/Sin C
29/Sin 30 = y/Sin 15 = x/ Sin 135
29/Sin 30 = y/Sin 15
y = (29*Sin 15)/ Sin 30
= 7.5052/ 0.5
= 15.0104
y = 15 kilometers
29/Sin 30 = x/Sin 135
x = (29*Sin 135)/ Sin 30
= 20.5059/ 0.5
= 41.0118
x = 41 kilometers
Therefore, the distance from Pine Knob to the fire is 41 kilometers. While the distance from Colt Station to the fire is 15 kilometers.
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regina takes yoga classes 2days a week at the community center
The option that will cost less money from Regina is $8 a class.
How to calculate the word problem?A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real life scenario given.
Since the cost for the classes at the community center is $72, plus an additional one-time fee of $12 to rent
the yoga equipment used in class. The amount will be:
= $72 + $12
= $84
The other cost at $8 a class for 2 weeks will be:
= $8 × 10 days
= $80
The second option is cheaper.
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Yoga classes are offered 2 days a week for 6 weeks
at both the community center and the local gym.
The cost for the classes at the community center is
$72, plus an additional one-time fee of $12 to rent
the yoga equipment used in class. The cost at the
local gym is $8 a class. Regina wants to know which
class she can take for less money.
write the given system as a matrix equation and solve by using the inverse coefficient matrix. use a graphing utility to perform the necessary calculations.
The given system of equations can be written as a matrix equation and solved by using the inverse coefficient matrix. The inverse coefficient matrix is 1/10 [4 -2], [3 5], and when multiplied by the vector of variables [x, y] the vector of constants [4, 10] is obtained. This gives the solution x = 6 and y = 2.
Given system:
x + 2y = 4
3x + 4y = 10
Matrix equation:
[x y] [1 2] [4]
[ ] = [ ] x [ ]
[3 4] [3 4] [10]
Inverse coefficient matrix:
1/10 [4 -2]
[3 5]
Solution:
1/10 [4 -2] [x] [4]
[3 5] [y] = [10]
x = 6
y = 2
The given system of equations can be written as a matrix equation which can be solved by using the inverse coefficient matrix. This inverse coefficient matrix is found by calculating the inverse of the matrix of coefficients of the variables. In this case, the matrix of coefficients is [1, 2], [3, 4], and the inverse of this matrix is 1/10 [4 -2], [3 5]. Multiplying this inverse coefficient matrix by the vector of variables [x, y] will give the vector of constants [4, 10]. This allows us to solve for the variables, giving x = 6 and y = 2. Therefore, the solution of the given system of equations is x = 6 and y = 2.
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if latex: f\left(x\right) represents the total output of a farm, in tons, in the week of 2015 ( ), and you know that , which of the following questions can you answer?\
Both questions can be answered by using the function f(x).The function f(x) represents the total output of a farm in tons in the week of 2015, and the value of x is known. This means that by using the value of x, the total output of the farm in 2015 and the output of the farm in the week of 2015 can both be calculated.
The function f(x) is a mathematical representation of the total output of a farm in tons for the week of 2015. The value of x is known, which means that by using this value, the total output of the farm in 2015 as well as the output of the farm in the week of 2015 can both be calculated. Therefore, both of the questions can be answered by using the function f(x). Knowing the total output of the farm in 2015 can help to better understand the production of the farm over the course of the year, while the output of the farm in the week of 2015 can be used to gain insights into the weekly production of the farm. With this information, decisions can be made to improve the production and efficiency of the farm.
The function f(x) can be used to answer both questions regarding the total output of a farm in 2015 and the output of the farm in the week of 2015.
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The lengths of the sides of a triangle are 3 cm, 10 cm, and 11 cm. Find the lengths of the segments into which the bisector of each angle divides the opposite side.
The lengths of the segments into which the bisector of each angle divides the opposite side: 12.7, 20.4 and 9.8 respectively
How to find the lengths?The median of a triangle is defined as the length of a line segment that extends from a vertex of the triangle to the midpoint of the opposing side. A triangle can have three medians, all of which will intersect at the centroid (the arithmetic mean position of all the points in the triangle) of the triangle
The medians of the triangle are represented by the line segments ma, mb, and mc. The length of each median can be calculated as follows:
Ma = √(2b²) + (2c²) - a²
. Mb = √(2a²) + (2c²) - b²
Mc = √(2a²) + (2b²) - c²
Applying the formulas
⇒Ma = √(2*3²) + (2*11²) - 10²
Ma = √(18) + (242) - 100
Ma = √160
Ma = 12.7 units
Mb = √(2a²) + (2c²) - b²
Mb = √(2*10²) + (2*11²) - 3²
Mb = √(200) + (242) - 9
Mb = √415
Mb = 20.4 units
Mc = √(2*10²) + (2*3²) - 11²
Mc = √(200) + (18) - 121
Mc = √97
Mc = 9.8
The bisector of each angle divides the opposite side into: 12.7, 20.4 and 9.8 units respectively
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solve for X
will give brainliest
Assume that 13% of people are left-handed. If we select 5 people at random, find the probability of each outcome described below.
a) The first lefty is the fifth person chosen.
b) There are some lefties among the 5 people.
c) The first lefty is the second or third person.
d) There are exactly 3 lefties in the group.
e) There are at least 3 lefties in the group.
f) There are no more than 3 lefties in the group.
The first lefty is the fifth person chosen is7.45%
There are some lefties among the 5 people is, 50.16%
What is probability?Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability. A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being expressed as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.The first lefty is the fifth person chosen is
[tex](.87)^4(.13)=.07447=7.45 \%[/tex]
There are some lefties among the 5 people is,
[tex]$$1-(.87)^5=.50157=50.16 \%$$[/tex]
The first lefty is the second or third person.
[tex]$(.87)(.13)+(.87)^2(.13)=.211497=21.15 \%_0$[/tex]
There are exactly 3 lefties in the group.
[tex]$(5, .13,3)=.0166=1.66 \%$[/tex]
There are at least 3 lefties in the group,
[tex]1 \text { - binomadf }(5, .13,2)=.0179=1.79 \%[/tex]
There are no more than 3 lefties in the group
[tex]\text { binomcdf }(5, .13,3)=.9987=99.87 \%[/tex]
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Select the law that shows that the two propositions are logically equivalent. -((w V p) ^(-91q1w)) -(w V p) v-(-91qAw) a. DeMorgan's law b. Distributive lawc. Associative law d. Complement law
The rule demonstrating the logical equality of the two claims. -((w V p) ^(-91q1w)) DeMorgan's law has the form -(w V p) v-(-91qAw).
What is meant by DeMorgan's law?By using their opposites, De Morgan's Laws explain how mathematical assertions and concepts are connected. The intersection and union of sets are connected by complements according to De Morgan's Laws in set theory. The De Morgan's Laws are rules of propositional logic that use negation to connect conjunctions and disjunctions of propositions.The complement of the intersection of the complements of two sets A and B is equal to the complement of the union of two sets A and B, according to De Morgan's first law. According to De Morgan's Law, "(P and Q)" and "not (not P or not Q)" are logically equal. If they are logically similar, then it should follow that "(P and Q)" implies "not (not P or not Q)," and "not (not P or not Q)" implies "(P and Q)".To learn more about DeMorgan's law, refer to:
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What is 2×21 using the distributive property
Answer:
42 is the answer
Step-by-step explanation:
for distributive property of multiplication you could use...
2 x 3 x 7
as 3 x 7 is 21
19. Zaire gets a bonus with his club for every frisbee golf hole on which he makes a score of 4.
He played last week and scored a 4 on 7 holes. Zaire will get an extra bonus if he has a
total of 60 points from scores of 4 after he finishes today. On how many holes does he
need to score a 4 today?
Please help!!!
Zaire has a total of 7 holes * 4 points/hole = 28 points from scores of 4 from last week.To reach 60 points, he needs to score 4 on 60 - 28 = 32 more holes today. So, Zaire needs to score a 4 on 32 holes today.
How many holes does Zaire need to score a 4 on today in order to reach a total of 60 points?To calculate the number of holes on which Zaire needs to score a 4 today, we can use the following equation:X = (60 - (4 x 7)) / 4Where X is the number of holes on which Zaire needs to score a 4 today, 60 is the total number of points he needs to reach to get the bonus, 4 is the number of points he gets for each hole on which he scores a 4, and 7 is the number of holes on which he scored a 4 last week.Here's the step-by-step explanation:Subtract the total number of points he earned last week (4 x 7) from the total number of points he needs to reach the bonus (60).Divide the result by the number of points he earns for each hole on which he scores a 4 (4).So X = (60 - (4 x 7)) / 4 = (60 - 28) / 4 = 32 / 4 = 8Therefore, Zaire needs to score a 4 on 8 holes today to get the bonus.To learn more about Frisbee problems refer:
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A poll is given, showing 80% are in favor of a new building project.If 9 people are chosen at random, what is the probability that exactly 3 of them favor the new building project?
help quick!!!!!!
Answer: 30%
Step-by-step explanation:
because e9 people are chosen and 9 divided by 3 is 3 and 3 x 10 =30
15. Katie is making salsa, which consists just of tomatoes and onions. She makes 8 identical jars of salsa, each of which
has some cups of tomatoes and 2.1 cups of onions. The 8-jars have a total of 41.6 cups of both tomatoes and onions.
How many cups of tomatoes are in each jar?
According to the given statement, 37.9 cups of tomatoes in each jar.
What is linear equations?A system of linear equations is a set of equations with two or more variables. A linear equation is one that can be expressed as ax + b = c, where x is a variable and a, b, and c are constants.
A group of two or more linear equations that share the same variables is known as a system of linear equations. As an illustration, consider the set of linear equations below:
2x + 3y = 10
4x + 6y = 20
x and y are the same variables, and the equations are linear equations. The solution to this system of linear equations is x = 2, y = 2.
This question can be solved using the system of linear equations.
Solving the system of equations gives:
T = 7.4 cups of tomatoes in each jar
Step 1: Calculate the total amount of tomatoes used.
Total tomatoes = 8 jars x cups of tomatoes per jar
Total tomatoes = 8 x (41.6 - 2.1)
Total tomatoes = 303.2 cups
Step 2: Divide the total amount of tomatoes by the total number of jars.
Cups of tomatoes per jar = Total tomatoes ÷ 8
Cups of tomatoes per jar = 303.2 ÷ 8
Cups of tomatoes per jar = 37.9 cups
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A cook at a restaurant is calculating the amounts of ingredients needed to make
soup for the next 5 days. For each of these days, she will use 2 1/8 pounds of
carrots and y pounds of celery. She will use a total of 19 3/8 pounds of carrots and celery to make all the soup.
Which equation shows how to find the number of pounds of celery, y, she will use to make the soup each day.
The equation that shows the number of pounds of celery(y) the cook will use each day is 8y+17= 31 and y = 1 ¼
What is linear equation?A linear equation is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.
For each day , the cook will use 2 1/8 pounds of carrot and y pounds of celery
therefore total = 17/8 +y
for 5 days the total carrot and celery used =( 17/8 + y) ×5
for 5 days 19 3/8 pounds of carrot and celery is used . Therefore;
155/8 = 5(17/8+y)
for each day, divide both sides by 5
155/8×1/5 = 17/8+y
31/8 = 17/8+y
collect like terms
y = 31/8-17/8
multiply through by 8
8y = 31-17
8y+17 = 31
therefore the equation that can be used to find the pound of celery used per day is 8y+17= 31
and y = 14/8 = 7/4 = 1 ¼
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Recall the equation for a circle with centre (h,k) and radius r. At what point in the first quadrant does the line with equation y=1.5x+5 intersect the circle with radius 5 and centre (0,5)?
The equation for the circle is (x-h)^2 + (y-k)^2 = r^2. Substituting the values, we get (x-0)^2 + (y-5)^2 = 25.
Substituting y=1.5x+5 into the equation, we get (x-0)^2 + (1.5x+5-5)^2 = 25
Simplifying, we get 1.5x^2 +15x+25=25
Solving, we get x=1.
Therefore, the point of intersection is (1,1.5).
The line y=1.5x+5 intersects the circle with radius 5 and centre (0,5) at the point (1,1.5) in the first quadrant.
The equation for a circle with centre (0,5) and radius 5 is (x-0)^2 + (y-5)^2 = 25. When this equation is combined with the line equation y=1.5x+5, it can be solved to find that the line intersects the circle at the point (1,1.5), which is located in the first quadrant.
The equation for the circle is (x-h)^2 + (y-k)^2 = r^2. Substituting the values, we get (x-0)^2 + (y-5)^2 = 25.
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Answer all of these I forgot them
A function built from pieces of different functions over different intervals.
How does one locate the piecewise specified formula?Finding a Piecewise Function’s Equation: Find the equation for both y=mx+b lines. If there is an O, the equation is > or; if there is a •, the equation is or. In the equation, the line represents X.
A piecewise function is one that is constructed from parts of distinct functions at different intervals. For example, we may write a piecewise function f(x) that returns -9 when -9 x -5, 6 when -5 x -1, and -7 when -1.
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ten points are placed on a circle. what is the greatest number of different lines that can be drawn so that each line passes through two of these points(A) 12 (B) 15 (C) 25 (D) 30(E) 36
The greatest number of different line segment that can be drawn so that each line passes through two of these points is 36. This is because every pair of points can be connected by a line, and with ten points, there are 45 pairs.
The greatest number of different lines that can be drawn so that each line passes through two of these points is 36. This is because every pair of points can be connected by a line, and with ten points, there are 45 pairs. Since each line can only be drawn once, the total number of different lines that can be drawn is 45 divided by two, which is equal to 36. In addition, the number of lines that can be drawn from each point to the rest of the points is 9, and since there are 10 points, the total number of lines that can be drawn is 90. However, this number is redundant since each line can only be drawn once, so the greatest number of lines that can be drawn is 36.
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(07.04 mc) which of the following is the solution to the differential equation dy over dx equals 2 times x times y all over quantity x squared plus 1 end quantity comma with the initial condition y(3)
The solution to the differential equation with the initial condition given is y(x)= (x² + 1)⁴.
Step 1: The given differential equation is dy/dx = 2xy/(x² + 1). Rearranging the equation, we get dy = 2xy dx/(x² + 1).
Step 2: Integrating both sides, we get ∫dy = ∫2xy dx/(x² + 1). On the left side, we have ∫dy = y + C, where C is the constant of integration. On the right side, we have ∫2xy dx/(x² + 1) = x² y + C.
Step 3: Substituting the initial condition y(3) = 6 in the solution, we get 6 = 3² y + C. Solving for C, we get C = 6 - 9y.
Step 4: Substituting C = 6 - 9y in the solution, we get y(x) = (x² + 1)⁴
The solution to the differential equation with the initial condition given is y(x)= (x² + 1)⁴.
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A downtown parking lot charges $5 per hour for the first 2 hours, then $2.50 per hour after that. What equation describes the total cost y as a function of the hours x?
The equation y = 5x for x ≤ 2 and y = 10 + 2.5(x-2) for x ≥ 2.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given that,
First, the two-hour rate of charge is $5 per hour
y = 5x for x ≤ 2
Over the 2 hours, the rate of charge is $2.5 per hour
y = 10 + 2.5(x-2) for x ≥ 2.
Hence "The equation y = 5x for x ≤ 2 and y = 10 + 2.5(x-2) for x ≥ 2".
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We choose a number from the set 10, 11,12,...,99) uniformly at random. (a) Let X be the first digit and Y the second digit of the chosen number. Show that X and Y are independent random variables. (b) Let X be the first digit of the chosen number and Z be the sum of the two digits. Show that X and Z are not independent
X and Z are not independent random variable as P(X = x and Z = z) and P(X = x) * P(Z = z) are not equal for most values of x and z by using their joint probability
To prove that two random variables are independent, to show that their joint probability distribution is equal to the product of their individual probability distributions. Start with part (a) and then move on to part (b).
(a) Let X be the first digit and Y be the second digit of the chosen number from the set {10, 11, 12, ..., 99}.
Step 1: Calculate the probabilities of X and Y individually.
To find the probability of X taking any particular value,
there are 9 numbers (10 to 99) that start with each digit from 1 to 9. Since we choose a number uniformly at random, each first digit has an equal chance of being selected.The probability of X taking any value x (where x is a digit from 1 to 9) is given by:
P(X = x) = (number of numbers starting with digit x) / (total numbers)
= 9 / 90
= 1 / 10
Similarly, for Y, since there are 10 digits (0 to 9) and choose the second digit uniformly at random, the probability of Y taking any value y is:
P(Y = y) = (number of numbers with digit y as the second digit) / (total numbers)
= 10 / 90
= 1 / 9
Step 2: Calculate the joint probability P(X, Y).
The joint probability is the probability that X takes a particular value x and Y takes a particular value y simultaneously.
P(X = x and Y = y) = (number of numbers with digit x as the first digit and digit y as the second digit) / (total numbers)
= 1 / 90
Step 3: Check if X and Y are independent.
Two random variables X and Y are independent if and only if their joint probability equals the product of their individual probabilities.
P(X = x and Y = y) = P(X = x) * P(Y = y)
1 / 90 = (1 / 10) * (1 / 9)
Since the equation holds for all values of x and y, conclude that X and Y are independent random variables.
(b) Let X be the first digit of the chosen number and Z be the sum of the two digits.
Step 1: Calculate the probabilities of X and Z individually.
Calculated the probability distribution for X in part (a), which is P(X = x) = 1 / 10 for x = 1 to 9.
To calculate the probability distribution for Z, the sum of the two digits:
For Z = 0: There is only one number, 10, with a sum of digits equal to 0.
P(Z = 0) = 1 / 90
For Z = 1: There are two numbers, 10 and 01, with a sum of digits equal to 1.
P(Z = 1) = 2 / 90
= 1 / 45
For Z = 2: There are three numbers, 11, 20, and 02, with a sum of digits equal to 2.
P(Z = 2) = 3 / 90
= 1 / 30
For Z = 3: There are four numbers, 12, 21, 03, and 30, with a sum of digits equal to 3.
P(Z = 3) = 4 / 90
= 2 / 45
For Z = 4: There are five numbers, 13, 31, 04, 40, and 22, with a sum of digits equal to 4.
P(Z = 4) = 5 / 90
= 1 / 18
For Z = 5: There are four numbers, 14, 41, 23, and 32, with a sum of digits equal to 5.
P(Z = 5) = 4 / 90
= 2 / 45
For Z = 6: There are three numbers, 15, 51, and 24, with a sum of digits equal to 6.
P(Z = 6) = 3 / 90
= 1 / 30
For Z = 7: There are two numbers, 25 and 52, with a sum of digits equal to 7.
P(Z = 7) = 2 / 90
= 1 / 45
For Z = 8: There are two numbers, 26 and 62, with a sum of digits equal to 8.
P(Z = 8) = 2 / 90
= 1 / 45
For Z = 9: There is only one number, 36, with a sum of digits equal to 9.
P(Z = 9) = 1 / 90
Step 2: Calculate the joint probability P(X, Z).
The joint probability is the probability that X takes a particular value x and Z takes a particular value z simultaneously.
Formula:
P(X = x and Z = z) = (number of numbers with digit x as the first digit and the sum of digits equal to z) / (total numbers)
Check the case where X = 1 and Z = 2 as an example:
Numbers with digit 1 as the first digit and a sum of digits equal to 2: 12 and 21 (two numbers)
P(X = 1 and Z = 2) = 2 / 90
= 1 / 45
Step 3: Check if X and Z are independent.
To determine if X and Z are independent, we need to compare their joint probability to the product of their individual probabilities for all values of x and z.
However, if compare the joint probabilities P(X = x and Z = z) to P(X = x) * P(Z = z), find that they are not equal for most values of x and z.
Therefore, conclude that X and Z are not independent random variables.
as P(X = x and Z = z) and P(X = x) * P(Z = z) are not equal for most values of x and z.
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The distribution of IQ (Intelligence Quotient) is approximately normal in shape with a mean of 100 and a standard deviation of 20.
According to the standard deviation rule, ____% of people have an IQ between 80 and 120. Do not round.
Using the Empirical Rule, it is discovered that the proportion of people in a population with IQs ranging from 80 to 120 is 0.95 = 95%.
What is Empirical Rule?It specifies the following for a normally distributed random variable:
68% of the measurements are within one standard deviation of the mean.
95% of the measurements are within 2 standard deviations of the mean.
99.7% of the measurements are within 3 standard deviations of the mean.
Given a mean of 100 and a standard deviation of 20, we can calculate:
80 = 100 - 2 x 20.
120 = 100 + 2 x 20.
Because these are both the most extreme values within two standard deviations of the mean, then the proportion of people in a population with IQ scores between 80 and 120 is 0.95 = 95%.
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75% of the Pottery Club members paid their $5.00 dues. If there are 48 members, how many members paid?
Answer:
36 members paid the total money that would be made would be $180
Step-by-step explanation:
48*75%=36
36*5=180
Given right triangle ABCABC with altitude \overline{BD}BDdrawn to hypotenuse ACAC. If AC=12AC=12 and DC=4,DC=4, what is the length of \overline{BC}BCin simplest radical form?
The length of the side BC of right triangle ABC can be found by applying the Pythagorean theorem with AC = 12 and DC = 4. The length of BC can be expressed in simplest radical form.
Using the Pythagorean Theorem, BC^2 = AC^2 - DC^2
= 12^2 - 4^2
= 144 - 16
= 128
Therefore, BC = [tex]\sqrt{128}[/tex]= 2[tex]\sqrt{32}[/tex] = 8[tex]\sqrt{2}[/tex]
The length of the side BC of a right triangle ABC can be found by applying the Pythagorean theorem. The Pythagorean theorem states that the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, AC = 12 and DC = 4, so BC^2 = AC^2 - DC^2 = 144 - 16 = 128. Therefore, which is the length of \overline{BC}BC in its simplest radical form. This result can be verified by calculating the length of the hypotenuse AC and confirming that it is equal to the square root of the sum of the squares of BC and DC.
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If f(x) = 5x²-3x + 3, find f'(1).
[tex]f(x)=5x^2-3x+3\implies \left. \cfrac{df}{dx}=10x-3 \right|_{x=1}\implies 10(1)-3\implies 7[/tex]
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. The volume of each small box is 9 cubic feet and the volume of each large box is 12 cubic feet. A total of 20 boxes of paper were shipped with a combined volume of 216 cubic feet. Graphically solve a system of equations in order to determine the number of small boxes shipped, x,x, and the number of large boxes shipped, yy.
The number of large box is 12 and small box is 8.
What is cube?
The term "cube" refers to a solid three-dimensional shape in mathematics or geometry that has six square faces, eight vertices, and twelve edges. It is also asserted to be a conventional hexahedron. You must be familiar with the three-by-three Rubik's cube, which is the most prevalent example in daily life and can help to increase brain capacity. Similar to this, you'll run into a lot of real-world examples, like 6 sided dice, etc. Solid geometry is the study of three-dimensional objects with surface areas and volumes. Cube, cylinder, cone, and sphere are some of the other solid shapes. Here, we'll talk about its definition, attributes, and relevance to mathematics.
Given :
The volume of small box is 9 cubic feet
The volume of the large box is 12 cubic feet
The volume of all box is 216 cubic feet
There are 20 boxes of paper shipped.
Total Volume covered by small box will be 9x
Total Volume covered by large box will be 24x
Total volume shipped = 216
9x + 24x = 216
33x = 216
x = 6
So The number of large box is 12 and small box is 8.
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1/4(x - 12) use your understanding of writing expressions to translate the expression
The expansion of 1/4(x - 12) is x/4 - 3
What is expansion of expression?In order to expand and simplify an expression, we need to multiply out the parentheses and then simplify the resulting expression by collecting the like terms. Expanding brackets (or multiplying out) is the process by which we remove parentheses. It is the reverse process of factorisation.
For example 4(3-y) can be expanded by multiplying the factor 4 by 3 and y = 12- 4y
Similarly the expression 1/4(x - 12) can be expanded by firstly multiply the factor ¼ by x and 12
therefore 1/4(x - 12) = 1/4×x -12×1/4
= x/4 - 3
Therefore the expansion of 1/4(x - 12) is x/4 -3
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