The probability that the duration is at least 4 is 0.0053 (rounded to four decimal places).
What is probability?Probability is represented by a number between 0 and 1, with 0 denoting an impossibility and 1 denoting a certainty.
According to question:(a) Let X be the duration of the contest. Then X can take values from 1 to 6, where 1 indicates that A or B wins the first game, and 6 indicates that the contest ends in a draw after 5 successive draws.
We can find the PMF of X by considering the possible outcomes for each value of X.
P(X = 1) = P(A wins) + P(B wins) = 0.2 + 0.5 = 0.7
P(X = 2) = P(A loses, B loses, A wins or B wins) = 0.3 * 0.3 * (0.2 + 0.5) = 0.054
P(X = 3) = P(A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^4[/tex] * (0.2 + 0.5) = 0.01323
P(X = 4) = P(A loses, B loses, A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^6[/tex] * (0.2 + 0.5) = 0.00243
P(X = 5) = P(A loses, B loses, A loses, B loses, A loses, B loses, A loses, B loses, A wins or B wins) = [tex]0.3^8[/tex] * (0.2 + 0.5) = 0.0004374
P(X = 6) = P(5 successive draws) = [tex]0.3^5[/tex] = 0.00243
Therefore, the PMF of X is:
X 1 2 3 4 5 6
P(X) 0.7 0.054 0.01323 0.00243 0.0004374 0.00243
(b) To find the probability that the duration is at least 4, we need to add the probabilities of X = 4, X = 5, and X = 6.
P(X >= 4) = P(X = 4) + P(X = 5) + P(X = 6) = 0.00243 + 0.0004374 + 0.00243 = 0.0052974
Therefore, the probability that the duration is at least 4 is 0.0053 (rounded to four decimal places).
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Havermill Co. establishes a $400 petty cash fund on September 1. On September 30, the fund is replenished. The accumulated receipts on that date represent $88 for Office Supplies, $167 for merchandise inventory, and $37 for miscellaneous expenses. The fund has a balance of $108. On October 1, the accountant determines that the fund should be increased by $80. The journal entry to record the reimbursement of the fund on September 30 includes a:
Answer:
2,000
Step-by-step explanation:
PLS HELP ME ASAP I NEED IT
Answer:
Step-by-step explanation:
Applying absolute value rule the solutions are:
x + 1/2 = 3/2/3 or x + 1/2 = -3 2/3
Changing to fractions:
x + 1/2 = 11/3 or x + 1/2 = -11/3
and then changing to a common denominator
x + 3/6 = 22/6 or x + 3/6 = -22/6
Solve left equation first:
x + 3/6 - 3/6 = 22/6 - 3/6
x = 19/6 or 3 1/6
Solve the right equation:
x + 3/6 - 3/6 = -22/6 - 3/6
x = -25/6 or -4 1/6
So the two solutions are:
19/6 and -25/6 as improper fractions
And
as mixed numbers: 3 1/6 and -4 1/6
Last year, an investor purchased 120 shares of stock A at $90 per share and 35 shares of stock B at $145 per share. What is the difference in overall loss or gain between selling at the current day's high price or low price?
Therefore, the overall difference in loss or gain between selling at the current day's high price or low price would be $3460.
What is expression?An expression is a mathematical or logical statement that represents a value or a result. It can consist of numbers, variables, operators, and/or functions that are combined in a specific way to form a valid statement. Expressions can be simple, such as a single number or variable, or complex, involving multiple operations and functions. In mathematics, expressions can be used to represent mathematical operations such as addition, subtraction, multiplication, division, exponentiation, and more.
Here,
To calculate the difference in overall loss or gain between selling at the current day's high price or low price for the stocks purchased, we need to know the current day's high and low prices for stock A and stock B. Once we have that information, we can use the following formula:
Difference = (Current day's high price - Purchase price) * Number of shares
Let's assume the current day's high price for stock A is $100 per share and the low price is $80 per share, while the high price for stock B is $150 per share and the low price is $130 per share.
For stock A:
Purchase price = $90 per share
Number of shares = 120 shares
Difference in overall loss or gain for stock A when selling at the high price:
Difference = ($100 - $90) * 120
= $1200
Difference in overall loss or gain for stock A when selling at the low price:
Difference = ($80 - $90) * 120
= -$1080
For stock B:
Purchase price = $145 per share
Number of shares = 35 shares
Difference in overall loss or gain for stock B when selling at the high price:
Difference = ($150 - $145) * 35
= $175
Difference in overall loss or gain for stock B when selling at the low price:
Difference = ($130 - $145) * 35
= -$525
So, the overall difference in loss or gain between selling at the current day's high price or low price would be the sum of the differences for stock A and stock B:
Overall difference in loss or gain = (Difference for stock A when selling at the high price + Difference for stock B when selling at the high price) - (Difference for stock A when selling at the low price + Difference for stock B when selling at the low price)
Overall difference in loss or gain = ($1200 + $175) - (-$1080 + -$525)
= $1855 + $1605
= $3460
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Fill in the table to show the fifth multiple of each fraction.
Write your answers as fractions greater than 1.
Fraction. Fifth Multiple
2/6
7/10
3/8
5/12
7/6
The fifth multiple of each fraction is shown as follows:
1. 2/6 = 5/3
2. 7/10 = 7/2
3. 3/8 = 15/8
4. 5/12 =25/12
5. 7/6 = 35/6
What is the fifth multiple of the numbers?To get the multiple of a fraction, the best thing to do will be to multiply the fraction by the whole number in question. In this case, the whole number is five.
So, to get the right answers, you can begin by multiplying the functions with the whole number five. The values obtained are the fifth multiples. for the fraction, 2/6, the fifth multiple is 5/3.
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Thanks to the help of insurance, non-
profits, family and friends, and
government, the Perez family was able
to make it through their time of need.
How did the family benefit (financially
and emotionally) from each of these
sources?
Insurance? Non-Profits? Family & Friends?
Government?
Overall, the Perez family likely benefited both financially and emotionally from each of these sources during their time of need.
The Perez family likely benefited in different ways from each of these sources during their time of need:
Insurance: If the Perez family had insurance, it is likely that they were able to receive financial assistance to cover some of their expenses. Depending on the type of insurance they had, they may have been able to receive money to pay for medical bills, property damage, or other expenses related to their time of need.
Non-profits: Non-profits may have provided the Perez family with resources such as food, clothing, and shelter during their time of need. These organizations may have also provided emotional support to the family, helping them feel less alone during a difficult time.
Family and friends: Family and friends likely provided the Perez family with emotional support during their time of need, as well as practical assistance such as meals, childcare, and help with household tasks. Financially, family and friends may have also helped the Perez family by providing loans or gifts of money.
Government: The government may have provided the Perez family with financial assistance through programs such as unemployment benefits, food stamps, or housing assistance. Additionally, the government may have provided emotional support to the family through counseling services or other resources.
Overall, the Perez family likely benefited both financially and emotionally from each of these sources during their time of need.
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What is the meaning of "[tex]x=a^{-1}b[/tex] is a solution since [tex]aa^{-1}b=1b=b[/tex]?
Here, a a⁻¹ b = 1b = b shows that a⁻¹ is indeed inverse of a, and x = a⁻¹b is a valid solution to the equation ax = b.
Define the solution of equation?An equation is a statement that two expressions are equal. A solution of an equation is a value (or a set of values) that makes the equation true.
In the equation ax = b, the solution x = a⁻¹b means that if we multiply a by its inverse a⁻¹, we get 1, the multiplicative identity. So, when we multiply both sides of the equation by a⁻¹, we get:
a⁻¹(ax) = a⁻¹b
Multiplying a⁻¹ and a on the left side of the equation gives:
1x = a⁻¹b
which simplifies to x = a⁻¹b. This shows that x = a⁻¹b is a solution to the equation ax = b.
The statement "a a⁻¹ b = 1b = b" means that when we multiply a by its inverse a⁻¹, we get the multiplicative identity 1, and when we multiply 1 by b, we get b. So, a a⁻¹ b = 1b = b shows that a⁻¹ is indeed the inverse of a, and x = a⁻¹b is a valid solution to the equation ax = b.
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A quiz consists of 5 multiple-choice questions with 4 possible responses to each one. In how many different ways can the quiz be answered?
Answer: 1,024 different ways
Step-by-step explanation:
We will use the Fundamental Counting Principle. There are 5 questions, each with 4 possible answers. To use the principle and answer the question, we will multiply 4 by itself 5 times.
4 * 4 * 4 * 4 * 4 = 1,024 different ways
Think of it like this:
you have 4 objects (the 4 answer options, a, b, c, and d)
You are going to chose a group of 5, and the order matters (your answer to question #1 is independent of your choice on #3)
Repetition is allowed (you can answer "c" on all of the questions if you want to)
This is a simple permutation. Use the formula:
[tex]\bold{n^r}[/tex]
where n is the number of objects (the number of answer choices)
and r is the number of objects you will choose (5, one answer for each question)
To solve:
[tex]4^5[/tex]
[tex]1,024 \longleftarrow[/tex] your answer!
Hope this helps! Feel free to ask any follow up questions, and please "vote up" :)
For Sequence A, describe (in words) a way to produce each new term from the previous term. Write a definition for the nth term of Sequence B. If these sequences continue, which will be greater, A(9) or B(9)? Explain or show how you know.
Answer:
Sequence A is defined by subtracting 6 from the previous term and taking the absolute value, while Sequence B is the sum of the first n odd integers. B(9) > A(9).
For Sequence A, The first term is 19.To produce each new term from the previous term, subtract 6 from the previous term, then take the absolute value of the result. That is, if the previous term is x, then the next term is |x - 6|.
The nth term of Sequence B is defined as the sum of the first n positive odd integers. That is, B(n) = 1 + 3 + 5 + ... + (2n - 1) = n².To find A(9) and B(9), we can apply the rules we have for each sequence:
A(0) = 19
A(1) = |19 - 6| = 13
A(2) = |13 - 6| = 7
A(3) = |7 - 6| = 1
A(4) = |1 - 6| = 5
A(5) = |5 - 6| = 1
A(6) = |1 - 6| = 5
A(7) = |5 - 6| = 1
A(8) = |1 - 6| = 5
A(9) = |5 - 6| = 1
B(0) = 0 (the sum of the first 0 odd integers)
B(1) = 1
B(2) = 1 + 3 = 4
B(3) = 1 + 3 + 5 = 9
B(4) = 1 + 3 + 5 + 7 = 16
B(5) = 1 + 3 + 5 + 7 + 9 = 25
B(6) = 1 + 3 + 5 + 7 + 9 + 11 = 36
B(7) = 1 + 3 + 5 + 7 + 9 + 11 + 13 = 49
B(8) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64
B(9) = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81
Therefore, we have A(9) = 1 and B(9) = 81. Since 81 is greater than 1, we know that B(9) is greater than A(9).In a survey about a change in public policy, 100 people were asked if they favor the change, oppose the change, or have no opinion about the change. Of the 100 people surveyed, 50 are male and 37 oppose the change in policy. Of the 37 who oppose the change, 25 are female. What is the probability that a randomly selected respondent to the survey is a man or opposes the change in policy? Express your answer as a percent
Answer: 75%
Step-by-step explanation:
Do the set of points in the figure represent a function?
A. Yes
B. No
Answer:
yes
Step-by-step explanation:
X = 1/4 - 1/6
Determine the value of the x
The value of X in the given fraction is 1/12
What are improper fractions?A fraction is a mathematical expression that represents a part of a whole or a quotient of two numbers. It is expressed as one integer or number (called the numerator) divided by another integer or number (called the denominator), separated by a line or a slash.
Here, we are going to find the LCM of both 4 and 6 to determine the value of X.
LCM = 12
X = 1/4 - 1/6
X = (3 - 2)/12
X = 1/12
Therefore, we can conclude that the value of X in the given fraction is 1/12.
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Consider the following polynomial.
q(x)=6x3+31x2+23x−20
Step 1 of 2 : Use the Rational Zero Theorem to list all of the potential rational zeros.
The potential rational zeros of the given polynomial are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15, ±20, ±30, ±60, ±1/2, ±1/3, ±2/3, ±5/2, ±4/3, ±5/3, ±10/3, ±1/6, ±5/6, ±1/10, ±2/5, ±4/15, ±1/15, ±2/15.
How to calculate potential rational zeroes?
The Rational Zero Theorem states that if a polynomial with integer coefficients has any rational zeros, then they must have the form of a fraction p/q, where p is a constant term factor and q is a leading coefficient factor.
For the given polynomial q(x)=6x^3+31x^2+23x−20, the constant term is -20, and the leading coefficient is 6. Therefore, the potential rational zeros can be expressed as follows:
p/q = ± {factors of the constant term (-20)}/{factors of the leading coefficient (6)}
Possible factors of -20: ±1, ±2, ±4, ±5, ±10, ±20
Possible factors of 6: ±1, ±2, ±3, ±6
Therefore, the potential rational zeros are:
±1/1, ±2/1, ±4/1, ±5/1, ±10/1, ±20/1,
±1/2, ±2/2, ±4/2, ±5/2, ±10/2, ±20/2,
±1/3, ±2/3, ±4/3, ±5/3, ±10/3, ±20/3,
±1/6, ±2/6, ±4/6, ±5/6, ±10/6, ±20/6.
Simplifying and eliminating duplicates, we get:
±1, ±2, ±4, ±5, ±10, ±20,
±1/2, ±2/2, ±4/2, ±5/2, ±10/2, ±20/2 (which simplifies to ±1, ±2, ±3, ±5, ±10, ±20),
±1/3, ±2/3, ±4/3, ±5/3, ±10/3, ±20/3 (which simplifies to ±1/3, ±2/3, ±4/3, ±5/3, ±10/3),
±1/6, ±2/6, ±4/6, ±5/6, ±10/6, ±20/6 (which simplifies to ±1/6, ±1/3, ±2/3, ±5/6, ±5/3, ±10/3).
Therefore, the potential rational zeros of the given polynomial are ±1, ±2, ±3, ±4, ±5, ±6, ±10, ±15, ±20, ±30, ±60, ±1/2, ±1/3, ±2/3, ±5/2, ±4/3, ±5/3, ±10/3, ±1/6, ±5/6, ±1/10, ±2/5, ±4/15, ±1/15, ±2/15.
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in a recent year 23% of all college students were enrolled part-time. if 8.9 million college students were enrolled part-time that year, what was the total number of college students? round answer to the nearest million
The total number of college students is 204,700,000.
What is Percentage?Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.
Here, Percentage of enrolled student for part time = 23%
Total enrolled students = 8.9 millions
Number of part time student = 23% x 8.9 million
[tex]= 0.23 \times 8900000[/tex]
[tex]=204,700,000[/tex]
Thus, the total number of college students is 204,700,000.
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each tank has a diameter of 6 ft and a height of 2 ft the cost is $5 per cubic use 3.14
It would cost $282.60 to fill a cylindrical tank with a diameter of 6 feet and a height of 2 feet.
What is cylinder?A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases of equal size and shape, connected by a curved side.
According to given information:To calculate the cost of filling a tank with a diameter of 6 feet and a height of 2 feet, assuming a cost of $5 per cubic foot and using the value of pi as 3.14, we first need to calculate the volume of the tank.
The volume of a cylinder (which is the shape of the tank) is given by the formula:
V = π[tex]r^2h[/tex]
where V is the volume, r is the radius (half the diameter), and h is the height.
Since the diameter of the tank is 6 feet, the radius is 3 feet. Therefore:
V = 3.14 x [tex]3^2[/tex] x 2
= 56.52 cubic feet
Multiplying the volume of the tank by the cost per cubic foot gives us the total cost of filling the tank:
Total cost = 56.52 x $5
= $282.60
Therefore, it would cost $282.60 to fill a tank with a diameter of 6 feet and a height of 2 feet, assuming a cost of $5 per cubic foot and using the value of pi as 3.14.
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HELP PLSLSSSSSSSSSSSSS
Answer:
Step-by-step explanation:
(Need Help please and thank you!)
The equation of the graph is
d. y = sqrt(x) + 2How to complete the tableThe table is completed by substituting the x to the function y = sqrt(x) + 2
When x = 0:
y = sqrt(0) + 2
y = 0 + 2
y = 2
When x = 1:
y = sqrt(1) + 2
y = 1 + 2
y = 3
When x = 4:
y = sqrt(4) + 2
y = 2 + 2
y = 4
When x = 9:
y = sqrt(9) + 2
y = 3 + 2
y = 5
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Please help me if you can calculate it
I can only calculate Q1 a b c
Question 1
A taxi company reveals that the daily earnings of taxi drivers in the company follows a normal distribution
with a mean of $1062.5 and standard deviation of $350.
(a) Find the probability that a taxi driver earns less than $1500 in a day.
(b) 93.7% drivers earn more than $k a day. Find the value of k.
John is a taxi driver in this company. Besides driving taxi, he has another part time online job. The daily
earnings from the part time online job follow a normal distribution with a mean of $235.5 and standard
deviation of $84.5. The daily earnings from driving taxi and part time online job are assumed to be
independent.
(c) Use T to denote the total daily earning for a day he drives taxi and works on the part time online job.
Find the mean and standard deviation of T. (Round off the mean and standard deviation to the nearest
integer.)
(d) Hence, by using $(L1, L2) to denote the middle 96.6% of the total daily earning T, find the values of L1
and L2. (Round off L1 and L2 to the nearest integer.)
Question 2
Tom is a supermarket manager. He reviewed transaction time when a customer paid by credit card. The
transaction time is normally distribution with mean of 20 seconds and standard deviation of 5 seconds.
(a) For a group of 6 customers, find the probability that 5 customers can finish the transaction within 20
seconds. (Assume that the transaction times of customers are independent.)
After discussion with the network provider, he will upgrade the network so that it is promised that each
transaction time can be reduced by 15%.
(b) Use Y to denote the transaction time after network upgrade. Find the mean and standard deviation of Y.
(c) Calculate the 97th percentile of Y. (i.e. find the value of t such that P(Y
(d) Compare with the transaction time before upgrade, is it (I) a higher proportion, (II) a lower proportion,
or (III) the same proportion of all customers can finish the transaction within 20 seconds? (Just state
your answer, no calculation is needed.)
Question 1:
(a) To find the probability that a taxi driver earns less than $1500 in a day, we need to standardize the value using the given mean and standard deviation, and then find the corresponding probability from the standard normal distribution table:
z = (1500 - 1062.5) / 350 = 1.20
Using the standard normal distribution table, the probability of a standard normal random variable being less than 1.20 is approximately 0.8849. Therefore, the probability that a taxi driver earns less than $1500 in a day is approximately:
P(X < 1500) = P(Z < 1.20) = 0.8849
(b) We need to find the value of k such that 93.7% of the drivers earn more than $k a day. This means that the probability of a driver earning less than or equal to $k a day is 1 - 0.937 = 0.063. We can standardize k using the given mean and standard deviation, and then find the corresponding z-score from the standard normal distribution table:
z = (k - 1062.5) / 350
Using the standard normal distribution table, we find that the z-score corresponding to a probability of 0.063 is approximately -1.51. Therefore:
-1.51 = (k - 1062.5) / 350
k = -1.51 * 350 + 1062.5 = $499.25 (rounded to the nearest cent)
(c) The mean of the total daily earning is:
μT = μ1 + μ2 = 1062.5 + 235.5 = 1298
The variance of the total daily earning is the sum of the variances of the two earnings, since they are assumed to be independent:
σT² = σ1² + σ2² = 350² + 84.5² ≈ 128681
Therefore, the standard deviation of the total daily earning is:
σT ≈ √128681 ≈ 358.5
(rounded to the nearest integer)
(d) To find L1 and L2, we need to find the z-scores corresponding to the lower and upper 2.2% tails of the standard normal distribution:
z1 = -1.81
z2 = 1.81
Then we can use the formula for standardizing a normal random variable to find the corresponding values of T:
z1 = (L1 - μT) / σT
z2 = (L2 - μT) / σT
Solving for L1 and L2, we get:
L1 = μT + z1σT ≈ 1298 + (-1.81) * 358.5 ≈ $645
L2 = μT + z2σT ≈ 1298 + 1.81 * 358.5 ≈ $1951
(rounded to the nearest integer)
Question 2:
(a) We can model the transaction time of a single customer as a normal random variable with mean 20 and standard deviation 5. Then the total transaction time for 6 customers can be modeled as a normal random variable with mean 6 * 20 = 120 and standard deviation √(6 * 5²) = 15. To find the probability that 5 customers can finish the transaction within 20 seconds, we need to standardize the value using this mean and standard deviation, and then find the corresponding probability from the standard normal distribution table:
z = (5 * 20 - 120) / 15 = -0.53
Factor the following polynomials by finding a GCF.
2.) x^2 + x
Answer: Factors of a polynomial is x(x+1)
Step-by-step explanation: To find the GCF, we first seek the greatest common divisor of these two terms.
Taking common x from (x^2+x).
x(x+1)
The equation y = 1.5x can be used to determine y, The number of cups of water needed to cook x cups of rice. Which table shows the relationship between x and y?
Table A is showing the correct relation of equation y=1.5x
Define equationAn equation is a mathematical statement that asserts that two expressions are equal. It typically consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). They are used to model real-world phenomena, to solve problems, and to make predictions. Examples of equations include linear equations, quadratic equations, systems of equations, and differential equations.
Using the relation;
y=1.5x
Putting the value x=9
y=1.5×9
y=13.5
Putting the value x=11
y=1.5×11
y=16.5
On observing the tables, option A is satisfying the relation
Hence, Table A is showing the correct relation of equation y=1.5x.
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The complete question is:
Image is attached below.
Please help ASAP!! thanks!
The exact value of the trigonometric expression, given the conditions of sin and sec is -85/36.
The exact value of the trigonometric expression with u and v in Quadrant III is 304/425.
How to find the exact value ?We are given sin(u) = -3/5 with 3π/2 < u < 2π and cos(v) = 15/17 with 0 < v < π/2.
cos(v - u) = cos(v)cos(u) + sin(v)sin(u)
We are given cos(v) = 15/17 and sin(u) = -3/5. To find sin(v) and cos(u), we can use the Pythagorean identities:
sin^2(v) + cos^2(v) = 1
sin(v) = sqrt(1 - (15/17)^2) = 8/17
Similarly, for cos(u):
sin^2(u) + cos^2(u) = 1
cos(u) = -sqrt(1 - (-3/5)^2) = -4/5
Now we can find cos(v - u):
cos(v - u) = cos(v)cos(u) + sin(v)sin(u)
cos(v - u) = -36/85
Since sec(v - u) = 1/cos(v - u), we have:
sec(v - u) = 1/(-36/85) = -85/36
Since both u and v are in Quadrant III, sin(u) and cos(u) are both negative, and sin(v) and cos(v) are both negative. We are given sin(u) = -7/25 and cos(v) = -15/17.
To find sin(v) and cos(u), we can use the Pythagorean identities:
sin^2(u) + cos^2(u) = 1
cos(u) = -sqrt(1 - (-7/25)^2) = -24/25 (since u is in Quadrant III)
Similarly, for sin(v):
sin^2(v) + cos^2(v) = 1
sin(v) = -sqrt(1 - (-15/17)^2) = -8/17 (since v is in Quadrant III)
Now we can find cos(u + v):
cos(u + v) = (-24/25)(-15/17) - (-7/25)(-8/17)
cos(u + v) = 304/425
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Can some help me? I have to find all possible solutions to that equation. I already found one thank you
The possible solutions to the equation are:
3π/4
π/4
How to solve trigonometric equations?Trigonometric equations involve trigonometric functions such as sine, cosine, tangent, etc. The goal is to solve for the unknown variable in the equation.
csc²x - 2 = 0
csc²x = 2
csc x = √2
sin x = 1/√2 (Remember: csc x = 1/sinx)
x = sin⁻¹(1/√2 )
x = 90° or 135° (sine is positive in 1st and 2nd quadrants)
x = π/4 or 3π/4
Thus, the possible solutions to the equation are x = π/4 or 3π/4.
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Find the interest. All rates are annual interest rates.
3. Principal $200
Rate 9%
Time 1/2
O$9
OSIS
$36
$45
year
(1 point)
The interest is $9.To find the interest, we can use the simple interest formula:
I = P * r * t
what is interest ?
Interest is the amount of money charged by a lender to a borrower for the use of money, usually expressed as a percentage of the amount borrowed. In other words, it is the cost of borrowing money.
In the given question,
To find the interest, we can use the simple interest formula:
I = P * r * t
where I is the interest, P is the principal, r is the annual interest rate as a decimal, and t is the time in years.
Here, the principal is $200, the annual interest rate is 9%, and the time is 1/2 year.
Converting the annual interest rate to a decimal, we get:
r = 9% = 0.09
And, converting the time to years, we get:
t = 1/2 year
Substituting the values into the formula, we get:
I = $200 * 0.09 * (1/2) = $9
Therefore, the interest is $9.
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You spin the spinner and flip a coin. Find the probability of the compound event.
The probability of spinning an even number and flipping heads is what?
1/6
Step-by-step explanation:
the reason is because of the tail and the spinner
Justin is younger than Hassan. Their ages are consecutive integers. Find Justin's age if the product of their ages is 210.
Justin is 14 years old, and Hassan is 15 years old.
What are integers?
The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.
Let's assume that Justin's age is x. Then, Hassan's age is x + 1, since their ages are consecutive integers and Hassan is older than Justin.
We are given that the product of their ages is 210:
x(x + 1) = 210
Expanding the left-hand side and simplifying, we get:
x² + x - 210 = 0
This is a quadratic equation in standard form. We can solve for x by using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 1, and c = -210.
Plugging these values into the formula, we get:
x = (-1 ± √(1² - 4(1)(-210))) / 2(1)
x = (-1 ± √(1 + 840)) / 2
x = (-1 ± √(841)) / 2
We take the positive root because x represents Justin's age, which is a positive integer. Therefore:
x = (-1 + 29) / 2 = 14
So, Justin is 14 years old, and Hassan is 15 years old.
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Need help with HW question 4
The eigen values of the first matrix is λ=4, λ=0 and λ=-3. The eigenvalues of the second matrix is 0 and 6.
What is an eigenvalue and eigenvector?If there is a scalar such that Ax = x, then a non-zero vector x is an eigenvector of A given a square matrix A. The scalar eigenvalue of the eigenvector x is known as the scalar.
To put it another way, when an eigenvector x is added to a matrix A, the outcome is a scalar multiple of x, where the scalar is the eigenvalue.
Many applications of linear algebra depend on eigenvectors and eigenvalues, such as the solution of differential equation systems, identifying the major variables in a dataset, and assessing the stability of dynamic systems.
The eigenvalues of the matrix can be found using the equation:
det(A - λI) = 0
Substituting the values we have:
[tex]\left[\begin{array}{ccc}4&2&0\\0&0&0\\1&0&-3\end{array}\right] - \lambda \left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc} 4 - \lambda &0&0\\0&- \lambda & 0\\1 &0 & -3 - \lambda\end{array}\right][/tex]
Now determine the det of the matrix:
(4 - λ) (-3λ + λ² ) - 0 + 0 = (4 - λ)(λ)(-3 + λ)
Thus the eigen values are:
λ= 4, λ = 0, and λ = 3.
For the second matrix we have:
Given that B has identical rows throughout, B has a rank of 1, and B's null space has a dimension of 2. With two eigenvalues equal to zero and one eigenvalue equal to the trace of B, which is 6, B has two eigenvalues equal to zero.
Hence, the eigenvalues of B are 0 and 6.
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What is the mean of the following set? 2/3, 1/6, 1/3, 2/3, 7/9, 1/3
The mean of the set is 1/2.
What is mean?The mean is a statistical measure that represents the average value of a set of numbers. To calculate the mean, you add up all the values in the set and then divide by the total number of values in the set.
To find the mean of a set of numbers, you add up all the numbers in the set and then divide the result by the total number of numbers in the set.
In this case, the set has six numbers:
2/3, 1/6, 1/3, 2/3, 7/9, 1/3
Adding them up, we get:
(2/3) + (1/6) + (1/3) + (2/3) + (7/9) + (1/3) = 3
So the sum of the numbers in the set is 3.
To find the mean, we divide this sum by the total number of numbers in the set, which is 6:
3/6 = 1/2
Therefore, the mean of the set is 1/2.
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Solve the problem in the picture please!
Answer:
Step-by-step explanation:
d.
carlo is 175 cm tall while his friend reggie is 1680mm tall. after three years carlo grew by 40mm and reggie grew by 7cm. which of the two is taller after a year? how tall in centimeters
After three years, Carlo is taller than Reggie. Carlo is 179 cm tall and Reggie is 175 cm tall.
What is metric system?A method for measuring temperature, length, volume, weight, and distance is known as the metric system. It is founded on three fundamental units that allow us to measure almost anything in the universe.
M- meter, used to measure the lengthKg- kilogram, used to measure the massS- second, used to measure timeTo compare the heights of Carlo and Reggie, we need to convert their heights to the same unit. We can convert Reggie's height from millimeters to centimeters by dividing by 10:
Reggie's height = 1680 mm ÷ 10 = 168 cm
Now we can compare their heights before and after three years:
Carlo before: 175 cmReggie before: 168 cmAfter three years:
Carlo after: 175 cm + 4 cm = 179 cm (since 40 mm = 4 cm)Reggie after: 168 cm + 7 cm = 175 cmTherefore, after three years, Carlo is taller than Reggie. Carlo is 179 cm tall and Reggie is 175 cm tall.
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Question The perimeter of the base of a right square pyramid is 24 cm. The height of the pyramid is 6 cm. What is the volume of the pyramid?
Answer:1152
Step-by-step explanation:monkey
36 Grâce à sa carte "Collège Jeunes", Maël bénéfice d'une réduction de 35% sur une place à 28€ pour assister à un spectacle de patinage. Combien va-t-il payer pour assister au spectacle de patinage ?