Answers
a) The probability of selecting two different colors is obtained as 9/10.
b) The probability of not selecting a yellow marble is obtained as 3/20.
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
a) To find the probability of selecting two different colors, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.
So the probability of selecting two different colors can be found by calculating the probability of selecting two marbles of the same color and subtracting that from 1.
The probability of selecting two marbles of the same color from the first bag is (2/5) x (1/4) = 1/10, since there are 2 red marbles out of 5 total marbles in the bag, and the probability of selecting a second red marble is 1/4.
The probability of selecting two marbles of the same color from the second bag is 0, since there is only one marble of each color.
So the probability of selecting two different colors is -
1 - (1/10 + 0) = 9/10
Therefore, the probability value is 9/10.
b) To find the probability of not selecting a yellow marble, we can again use the complement rule.
The probability of not selecting a yellow marble is equal to 1 minus the probability of selecting a yellow marble from either bag.
The probability of selecting a yellow marble from the first bag is 1/5, since there is one yellow marble out of 5 total marbles in the bag.
The probability of selecting a yellow marble from the second bag is also 1/4, since there is one yellow marble out of 4 total marbles in the bag.
So the probability of not selecting a yellow marble is -
1 - (1/5 + 1/4) = 3/20
Therefore, the probability value is 3/20.
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Related Questions
The mean earnings of a university undergraduate student is enrolled in a Business program is $28,000 per year. Assume that the average salaries follow a normal distribution with a standard deviation of $2,500.
Required
a. Find the probabilities that a student makes more than $30,000?
b. What is the probability that a student would make between $27,000 and $32,000?
c. What is the probability that a student would make less than $23,150?
Answers
a. The probability that a student makes more than $30,000 is 0.0668.
b. The probability that a student makes between $27,000 and $32,000 is 0.9545.
c. The probability that a student makes less than $23,150 is 0.0062.
Probability is the likelihood that something will occur. When we don't know how an occurrence will turn out, we can discuss the likelihood or likelihood of various events. Statistics is the study of occurrences that follow a chance distribution.
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Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on
Answers
To find the total amount of milk used, we simply add the amount of milk used for the pancake recipe and the amount used for drinking. So we add 9 cups and 394 cups together, giving us a total of 403 cups of milk.
We can calculate the total amount of milk that Luke used for the pancake recipe and the additional amount he used for drinking.
For the pancake recipe, Luke used 9 cups of milk.
For drinking, Luke used an additional 394 cups of milk.
Total amount of milk used = Milk used for pancake recipe + Milk used for drinking
= 9 cups + 394 cups
= 403 cups of milk.
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The complete question is:
Lube used to 9 cups of milk for a pancake recipe to drink another 394 cups of milk how about about how much milk did Luke is using on the recipe?
Mr stoves is investing $1500 on a bank account that would give him 3. 7% compounded monthly. What would be his final balance after 10 years?
Answers
Mr stove's final balance after 10 years if he invested 1500 on a bank account that would give him 3. 7% compounded monthly is $2,170.37
What would be his final balance after 10 years?A = P(1 + r/n)^nt
Where
P = $1500
r = 3.7% = 0.037
n = monthly = 12
t = 10 years
So,
A = P(1 + r/n)^nt
A = 1,500.00(1 + 0.037/12)^(12×10)
A = 1,500.00(1 + 0.0030833333333333)¹²⁰
A = $2,170.37
Ultimately, Mr stove will have $2,170.37 as his balance after 10 years.
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100 points hurry and mark brainly
Jennifer bought three of the same shirt and paid $63 after the 30% discount. What was the original price of each shirt? Show your work or explain in words how did you get the answer.
Answers
2.1x = 63
x = 30
a line segment is drawn between (4,8) and (8,5). find it’s gradient.
Answers
the slope goes by several names
• average rate of change
• rate of change
• deltaY over deltaX
• Δy over Δx
• rise over run
• gradient
• constant of proportionality
however, is the same cat wearing different costumes.
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{5}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{5}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{4}}} \implies \cfrac{ -3 }{ 4 } \implies - \cfrac{3 }{ 4 }[/tex]
In 2002, the population of a state was 6.7 million people and was growing at a rate of about 0.32% per year. At this growth rate, the function f (x) = 6.7(1.0032)x gives the population, in millions x years after 2002. Using this model, find the year when the population reaches 7 million people. Round your answer to the nearest whole number.
Answers
The population will reach 7 million people approximately 21.67 years after 2002. Rounding to the nearest whole number, this corresponds to the year 2024.
The year when the population reaches 7 million can be determined using the population model given, f(x) = 6.7(1.0032)x, where x is the number of years following 2002.
When we solve for x while setting f(x) equal to 7, we obtain:
[tex]7 = 6.7(1.0032)^x[/tex]
By multiplying both sides by 6.7, we obtain:
[tex]1.04478 = 1.0032^x[/tex]
When we take the natural logarithm of both sides, we obtain:
ln(1.04478) = x * ln (1.0032)
After finding x, we obtain:
x = ln(1.04478) / ln (1.0032)
x ≈ 21.67
Hence, approximately 21.67 years after 2002, the population will reach 7 million. This corresponds to the year 2024 when rounded to the next whole number.
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help plssssssssssssssssssssssssssss
Answers
Answer: First Picture 100:60 = The answer is A. 5:3 | The Second Picture K/12=8/24 the answer is A. k=4 | Third Picture is A. 4 | Fourth Picture answer is B. 4 teachers for every 64 students | And Final Picture answer is D. 9.33 miles per hour, Wendy Was Faster. | Hope this helps out today!!
Step-by-step explanation: Its simple math its just either x2 or what's it divided off
7. Higher Order Thinking Point N has
coordinates (3, 4). On a quiz yesterday, Ari
incorrectly claimed that if you rotate N 180°
about the origin, the coordinates of N' are
(-4, 3). What are the correct coordinates
for N'? What was Ari's likely error?
Answers
The correct coordinates of N' is (-3, -4).
What is Rotation:Rotation of coordinates involves changing the orientation of a point or object in a plane about a fixed point called the center of rotation.
This process can be accomplished by applying a set of transformation rules to the original coordinates of the object.
When a point (x, y) rotated about the origin at 180° then the coordinates resultant point are (-x, -y).
Here we have
Point N has coordinates (3, 4)
Given that the point N is rotated about 180°
As we know when the point (x, y) rotated about the origin at 180° then the resultant point is (-x, -y)
Here (3, 4) is rotated about 180°
The resultant point N' is (-3, -4)
Therefore,
The correct coordinates of N' is (-3, -4).
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If matrix A = [-4,k; -7,2]
for what value of k does the matrix have one eigenvalue of
multiplicity 2?
Answers
To find the value of k for which the matrix A has one eigenvalue of multiplicity 2, we can use the characteristic equation of the matrix. The characteristic equation is det(A-λI)=0. For a given matrix, this equation will yield a polynomial equation of degree equal to the dimension of the matrix.
In this case, the equation is (λ+4)(λ-2) = 0. Solving this equation gives us two distinct eigenvalues of λ= -4 and λ=2. This means that for any value of k, the matrix A will have two distinct eigenvalues, and thus cannot have one eigenvalue of multiplicity 2. Therefore, the matrix A cannot have one eigenvalue of multiplicity 2 no matter what value of k is used.
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12. The amount of money in a savings account earning yearly interest is represented by the
expression 750(1+0.012), where t is in years since the account was opened. What does
(1+0.012) represent?
A
B
C
D
The account earns $0.012 in yearly interest.
The account earns $1.20 in yearly interest.
The account earns 1.2% in yearly interest.
The account earns 12% in yearly interest.
Answers
Answer:
C. The account earns 1.2% in yearly interest.
Step-by-step explanation:
The expression 750(1+0.012) represents the amount of money in a savings account earning yearly interest after t years, where t is the number of years since the account was opened.
The expression (1+0.012) represents the interest rate as a decimal. The value 0.012 represents 1.2% in decimal form, which is the yearly interest rate earned by the account.
Therefore, (1+0.012) represents the account's yearly interest rate as a decimal, which is 1.2%.
The graph below shows the variation in the average temperature of Earths surface from 1950-2000, according to one source
Answers
The years 1960–1965 saw the greatest change in temperature variation per unit of time.
What is Slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
The graph for average temperature variation v/s time is given.
To find during which year maximum temperature variation with time:
We have to find the year with maximum magnitude of slope |m|.
Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}\\[/tex]
Consider m for year 1950-1955:
m = 0 [line parallel to x-axis]
Consider m for year 1955-1960:
[tex]\frac{-0.05-0}{1955-1960}\\\\= 0.01[/tex]
Consider m for year 1960-1965:
[tex]\frac{-0.15-0}{1965-1960}\\\\= -0.03[/tex]
Consider m for year 1965-1970:
m = 0.01 {same as of 1955-1960}
Consider m for year 1970-1975:
m = 0 [line parallel to x-axis]
Consider m for year 1975-2000:
[tex]\frac{0.4-(-0.1)}{2000-1975}\\\\= 0.02\\[/tex]
|m| is maximum for year 1960-1965
Hence, the temperature variation changed the most per unit time in the year 1960-65.
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At a club fundraiser a group of students washed 60 cars in one weekend the rest of the weekend they washed
75 cars what was the percent of increase in the number of cars washed
Answers
Give an example of a linear function that has a minimum value but no maximum value. Specify the domain and whether the function is increasing or decreasing.
Select all linear functions with a minimum value but no maximum value.
The decreasing function f(x)=10−3x over the domain x≤9 has a minimum value but no maximum value .
The decreasing function f(x)=5x−1 over the domain x≥−7 has a minimum value but no maximum value.
The increasing function f(x)=2x+5 over the domain x≥ 5has a minimum value but no maximum value .
The increasing function f(x)=7−2x over the domain x≥10 has a minimum value but no maximum value .
Answers
The two linear functions that have a minimum value but no maximum value are:
f(x) = 10 - 3x over the domain x ≤ 9
f(x) = 5x - 1 over the domain x ≥ -7
Determining linear functions that have minimum value but no maximum valueFrom the question, we are to determine the linear function that have minimum value but no maximum value
The decreasing function f(x) = 10 - 3x over the domain x ≤ 9 has a minimum value but no maximum value.
Domain: x ≤ 9
This function is decreasing since the slope is negative.
The minimum value occurs at x = 9, where f(9) = 10 - 3(9) = -17.
Since the slope is negative, the function continues to decrease without bound as x approaches negative infinity.
The decreasing function f(x) = 5x - 1 over the domain x ≥ -7 has a minimum value but no maximum value.
Domain: x ≥ -7
This function is increasing since the slope is positive.
The minimum value occurs at x = -7, where f(-7) = 5(-7) - 1 = -36.
Since the slope is positive, the function continues to increase without bound as x approaches positive infinity.
Hence, the functions are:
f(x) = 10 - 3x over the domain x ≤ 9
f(x) = 5x - 1 over the domain x ≥ -7
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In a group of 100 students, 60 liked mathematics and 50 liked science.If 10 did not like any of the subjects , by using Venn-diagram, find the numbers of students who like both the subjects
Answers
Answer:
Below
Step-by-step explanation:
See Venn diagram below :
I need help doing the math homework
Answers
By algebra properties, the factor form of polynomials are listed below:
(a + b) · (a - b) (a + b) · (a² - a · b + b²) (a - b) · (a² + a · b + b²) (x² + 6) · (x + √6) · (x - √6) (4 · c + 1) · (16 · c² - 4 · c + 1) (k - 3) · (k² + 3 · k + 9) (∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²] 3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n) a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1) y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²) 9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²] (w - 4) · (w - 9) p · (p + 12) · (p - 7)How to factor polynomials
In this problem we need to factor 13 cases of polynomials, whose results must be derived by algebra properties. The factor form of the polynomial is:
Case 1:
a² - b²
(a + b) · (a - b)
Case 2:
a³ + b³
(a + b) · (a² - a · b + b²)
Case 3:
a³ - b³
(a - b) · (a² + a · b + b²)
Case 4:
x⁴ - 36
(x² + 6) · (x² - 6)
(x² + 6) · (x + √6) · (x - √6)
Case 5:
64 · c³ + 1
(4 · c + 1) · (16 · c² - 4 · c + 1)
Case 6:
k³ - 27
(k - 3) · (k² + 3 · k + 9)
Case 7:
54 · x³ + 250 · y³
(∛54 · x + ∛250 · y) · [(∛54 · x)² - (∛54 · x) · (∛250 · y) + (∛250 · y)²]
Case 8:
3 · m⁴ - 48 · n²
(√3 · m² - 4√3 · n) · (√3 · m² + 4√3 · n)
3 · (m² - 4 · n) · (m² + 4 · n)
3 · (m - 2 · √n) · (m + 2 · √n) · (m² + 4 · n)
Case 9:
a⁷ · b² - a · b²
a · b² · (a⁶ - 1)
a · b² · (a³ + 1) · (a³ - 1)
a · b² · (a + 1) · (a² - a + 1) · (a - 1) · (a² + a + 1)
Case 10:
x³ · y² - 343 · y⁵
y² · (x³ - 343 · y³)
y² · (x - 7 · y) · (x² + 7 · x · y + 49 · y²)
Case 11:
9 · y⁷ - 144 · y
y · (9 · y⁶ - 144)
y · (3 · y³ - 12) · (3 · y³ + 12)
9 · y · (y³ - 4) · (y³ + 4)
9 · y · (y - ∛4) · [y² + ∛4 · y + (∛4)²] · (y + ∛4) · [y² - ∛4 · y + (∛4)²]
Case 12:
w² - 13 · w + 36
(w - 4) · (w - 9)
Case 13:
p³ + 5 · p² - 84 · p
p · (p² + 5 · p - 84)
p · (p + 12) · (p - 7)
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Solve the system of equations using a calculator and a
matrix
1. 3x-6y=12, 2x-4y=8
Answers
The solution to the system of equations using a calculator and a matrix (3x-6y=12, 2x-4y=8) is x = 12 and y = 8.
To solve the system of equations using a calculator and a matrix, you will need to follow these steps:
1. Convert the system of equations into a matrix. In this case, the matrix will be:
```
| 3 -6 | | 12 |
| 2 -4 | | 8 |
```
2. Use your calculator to find the inverse of the coefficient matrix (the matrix on the left). The inverse of the coefficient matrix is:
```
| -2/3 3/2 |
| -1/3 3/4 |
```
3. Multiply the inverse of the coefficient matrix by the constant matrix (the matrix on the right) to find the solution. The solution will be:
```
| -2/3 3/2 | | 12 | = | 12 |
| -1/3 3/4 | | 8 | | 8 |
```
4. Simplify the solution to get the values of x and y. The solution will be:
```
x = 12
y = 8
```
Therefore, the solution to the system of equations is x = 12 and y = 8.
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PLEASE HELP :(
Isabella is collecting pledges for a walk-a-thon. Her mother has pledged a flat donation of $20, and her grandmother has pledged $2 per kilometer. If Isabella walks a certain distance, the two donors will end up owing the same amount. What is that distance?
Write a system of equations, graph them.
Answers
Answer:
Step-by-step explanation:
25 becuase 3 times 52 is that plus 32 is 73 and isabella with be rivher then ever than muh hahaha
Does anyone know the answer?
Answers
Answer:
33.7°
Step-by-step explanation:
the direction angle is calculated as
tanΘ = [tex]\frac{y}{x}[/tex] ( Θ is the direction angle ) , then
tanΘ = [tex]\frac{-4}{-6}[/tex] = [tex]\frac{2}{3}[/tex]
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{2}{3}[/tex] ) ≈ 33.7° ( to the nearest tenth )
5. (3 marks) Determine the area of the parallelogram formed by the following vectors:
u = (1,2,2) , v = (4.4.0)
Answers
The area of the parallelogram formed by the vectors u and v is 12.
The area of a parallelogram formed by two vectors u and v can be determined by finding the cross product of the two vectors and then taking the magnitude of the resulting vector.
First, we need to find the cross product of u and v:
u × v = [(2)(0) - (2)(4), (2)(4) - (1)(0), (1)(4) - (2)(4)] = [-8, 8, -4]
Next, we need to find the magnitude of the resulting vector:
|u × v| = √((-8)² + (8)² + (-4)²) = √(64 + 64 + 16) = √144 = 12
Therefore, the area of the parallelogram formed by the vectors u and v is 12.
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How to find a height of a trapezoid with phythagorean theorem
Answers
Height of a trapezoid with Pythagorean theorem is = √{Hypotenuse ^2 - Base ^2}
Trapezoid has two parallel sides and two non parallel sides. The length of the parallel sides are unequal but the length of the non parallel sides are equal.
Thus the trapezoid can be divided into three parts where one is rectangle ( which has length equal to the shortest length of the parallel sides) and two triangles which are equal ( having equal base, height and hypotenuse).
The Pythagoras theorem on the triangular part of the trapezoid can be stated as ,
Hypotenuse ^2 = Base ^2 + Height ^2
⇒ Height ^2 = Hypotenuse ^2 - Base ^2
⇒ Height = √{ Hypotenuse ^2 - Base ^2}
where, Height of the triangle is equal to that of the trapezoid it belongs to;
Hypotenuse of the triangle is the non parallel but equal side of the trapezoid;
Base of the triangle is = {(length of the longest side of parallel sides of trapezoid) - (length of the shortest side of parallel sides of trapezoid) }/2
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Please help me with this math problem!! Will give brainliest!! :)
According to a recent survey of students about the juice they preferred, 20% of the students preferred cranberry juice, 40% preferred orange juice, 20% preferred grapefruit juice, and the remaining students preferred tomato juice. If each student preferred only 1 juice and 250 students preferred tomato juice, how many students were surveyed?
Answers
Answer: 1250 students
Step-by-step explanation:
20% + 40% + 20% = 80%
100% - 80% = 20%
If 250 is 20%, then it's just 250 x 5 = 1250
given is the area of the region which is bounded by y = x^3, y =
8, and x = 0. find the volume generated when it is revolved about
the y-axis.
A. 9/8 pi
B. 96/5 pi
C. 45/7 pi
D. 34/7 pi
Answers
Given y = x³, y = 8, and x = 0, we need to find the volume generated when it is revolved about the y-axis.To solve this problem, we will use the washer method. We will draw the region to better understand it. Area that is bounded by y = x³, y = 8, and x = 0, volume comes as 45/7 pi. The correct answer is option C
Now, let's draw the region we want to rotate around the y-axis. Below is the graph of the region after shading it. region which is bounded by , y = 8, and x = 0. We can see from the graph above that the region is between y = x³ and y = 8.
Thus the radius of our washer would be : R = 8 - x³ The height of the washer is dx (infinitesimal thickness). The width of the washer is given. We can now write the integral for the volume generated by the region V. Thus the volume generated when it is revolved about the y-axis is 45/7 pi. Therefore, the correct option is C.
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we can descirbe 3x-2 as an expression
Answers
Answer: In each of the terms 3x 2 and 7x, x is a variable, and in both terms, we are multiplying a number by the variable. In the first term, 3x 2, 3 is being multiplied by the variable, so 3 is a coefficient. In the second term, 7x, 7 is being multiplied by the variable, so 7 is a coefficient.
Step-by-step explanation:
Calculate the perimeter of the trapezoid in millimeters
Answers
Answer:
135 mm
Step-by-step explanation:
The perimeter is found by adding all sides together. Since the answer is to be in millimeters, two side lengths must be converted.
1 centimeter = 10 millimeters
1.5 x 10 = 15 mm
6 x 10 = 60 mm
Now, add all sides together:
60 + 15 + 20 + 40 = 75 + 60 = 135 mm
Power of test related to
A type 1 error
B type 2 error
C type 1 and type 2
D non of sbovr
Answers
Answer:
B
Step-by-step explanation:
The correct answer is Option C - Type 1 and Type 2. The power of a test is the probability of rejecting the null hypothesis when it is false; in other words, it is the probability of avoiding a type II error.
The power may also be thought of as the likelihood that a particular study will detect a deviation from the null hypothesis given that one exists. A Type 1 error occurs when a hypothesis test results in rejecting a true null hypothesis, and a Type 2 error occurs when a hypothesis test fails to reject a false null hypothesis.
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Watch help video Use synthetic division to find the result when x^(3)-6x^(2)+13x is divided by x-1. If there is a remainder, express the result in the
Answers
The result is x^(2)-7x+20 with a remainder of -20. So the final answer is x^(2)-7x+20-20/(x-1).
To find the result of the division using synthetic division, we need to follow these steps:
Write the coefficients of the dividend in a horizontal line, leaving spaces for the divisor and the result. In this case, the coefficients are 1, -6, and 13.Write the constant term of the divisor in the first space. In this case, the constant term is -1.Bring down the first coefficient to the result line.Multiply the first term of the result by the divisor and write the product in the next space on the dividend line.Add the two numbers in the next column and write the sum on the result line.Repeat steps 4 and 5 until all the coefficients have been used.The last number on the result line is the remainder. If there is a remainder, express the result in the form of a fraction with the remainder as the numerator and the divisor as the denominator.The result is x^(2)-7x+20 with a remainder of -20. So the final answer is x^(2)-7x+20-20/(x-1).
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The volume of a sphere is 1230pi what is the radius
Answers
r=(3 1230/4pi)^1/3
r=6.65
x^2-8x+5=25 solve by completeing the square
Answers
We have the following response after answering the given question: As a result, the following are the answers to the equation: [tex]x = 4 + 6 = 10[/tex] and [tex]x = 4 - 6 = -2[/tex]
What is equation?In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.
We may use the completing the square method to solve the equation x2 - 8x + 5 = 25 by doing the following steps:
[tex]x^2 - 8x + 5 - 25 = 0\\x^2 - 8x - 20 = 0\\(-8/2)^2 = c\\16 = c\\x^2 - 8x + 16 - 16 - 20 = 0\\(x - 4)^2 - 36 = 0\\(x - 4)^2 = 36\\x - 4 = +6\\x = 4 + 6[/tex]
As a result, the following are the answers to the equation:
[tex]x = 4 + 6 = 10[/tex]
[tex]x = 4 - 6 = -2[/tex]
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DefineT:R2→R2byT(x)=T−([x1x2])=[3x1−−2x22x2]- a) Letu=[u1u2]andv=[v1v2]be two vectors inR2and let c be any scalar. Prove thatTis a linear transformation. - b) Find the standard matrixAofT. - c) Is T one-to-one? Prove your answer using the matrix A.
Answers
a)T(u) + T(v) T is a linear transformation
b)[3 -2 ; 2 0]
c)T is one-to-one.
a) To prove that T is a linear transformation, we need to show that it satisfies two conditions.
1. Additivity: T(u + v) = T(u) + T(v)
Let u = [u1, u2] and v = [v1, v2], then
T(u + v) = T([u1 + v1, u2 + v2]) = [3(u1 + v1) - 2(u2 + v2), 2(u2 + v2)]
= [3u1 - 2u2 + 3v1 - 2v2, 2u2 + 2v2]
= [3u1 - 2u2, 2u2] + [3v1 - 2v2, 2v2]
= T(u) + T(v)
2. Homogeneity: T(cu) = cT(u)
Let u = [u1, u2] and c be any scalar, then
T(cu) = T([cu1, cu2]) = [3cu1 - 2cu2, 2cu2] = c[3u1 - 2u2, 2u2]
= cT(u)
Therefore, T satisfies both conditions, and is a linear transformation.
b) The standard matrix of T is the matrix A = [3 -2 ; 2 0]
c) To determine whether T is one-to-one, we look at the matrix A. Since the matrix A has a non-zero determinant, which is equal to -4, then T is one-to-one.
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New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $54. A. What is the probability that a hotel room costs $227 or more per night (to 4 decimals)?
Answers
The probability that a hotel room costs $227 or more per night in New York City is 0.3406.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Lets standardize the value of $227 per night using the formula:
z = (x - μ) / σ
where x is the value we are interested in, μ is the mean of the distribution, and σ is the standard deviation of the distribution. Substituting the given values, we get:
z = (227 - 205) / 54
z = 0.4074
We need to find the probability that a hotel room costs $227 or more per night, which is equivalent to finding the probability that a standardized value is greater than or equal to 0.4074.
Using a standard normal table, we find:
P(Z ≥ 0.4074) = 1 - P(Z < 0.4074)
P(Z ≥ 0.4074) = 1 - 0.6594
P(Z ≥ 0.4074) = 0.3406
Therefore, the probability that a hotel room costs $227 or more per night in New York City is approximately 0.3406.
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The probability that a hotel room costs $227 or more per night is 0.3446
What is probability distribution?Probability distribution yields the possible outcomes for any random event. It is also defined based on the underlying sample space as a set of possible outcomes of any random experiment. These settings could be a set of real numbers or a set of vectors or a set of any entities. It is a part of probability and statistics.
Random experiments are defined as the result of an experiment, whose outcome cannot be predicted. Suppose, if we toss a coin, we cannot predict, what outcome it will appear either it will come as Head or as Tail. The possible result of a random experiment is called an outcome. And the set of outcomes is called a sample point. With the help of these experiments or events, we can always create a probability pattern table in terms of variables and probabilities.
GIven,
The mean hotel room rate ( [tex]\mu[/tex]) is $205 per night and standard deviation ([tex]\sigma[/tex]) of $54. A.
p( x > 225 )
we can't this to standard normal using [tex]z =\frac{X- \mu}{\sigma}[/tex]
[tex]z=\frac{227-205}{54} \approx0.4074[/tex]
p (z > 0.4074 ) = area to the right at 0.4074
p( x > 225 ) = p (z > 0.4074 ) = 1 - p (z < 0.4074)
= 1 - 0.6554 (from z table)
= 0.3446
Hence, probability that a hotel room costs $227 or more per night (to 4 decimals) 0.3446
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