The value of p is 2 and 4.
What is a quadratic equation?
Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation. Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.
Here, we have
Given: p² - 6p + 8
we have to solve the quadratic formula or complete the square.
= p² - 6p + 8
= p² -4p - 2p + 8
= p(p-4) -2(p-4)
= (p-4)(p-2)
(p-4)(p-2) = 0
p-4 = 0,
p-2 = 0
p = 4, 2
Hence, the value of p is 2 and 4,
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Your organization is selling tickets to the school dance.
On the first day, the school sold 10 student tickets and
5 guests tickets for a total of $200. On the second day,
you sold 6 student tickets and 2 guest tickets for a total
of $105. What is the price of each ticket?
The price of each student ticket is $12.50 and the price of each guest ticket is $15.
What is substitution method?The substitution method is a technique in algebra for solving systems of equations, which involves solving one equation for one variable, and then substituting that expression into the other equation.
According to question:Let's start by assigning variables to represent the unknown prices of the student and guest tickets.
Let:
x be the price of a student ticket
y be the price of a guest ticket
Using this information, we can set up two equations based on the given information:
Equation 1: 10x + 5y = 200 (from the first day's sales)
Equation 2: 6x + 2y = 105 (from the second day's sales)
Now we have two equations with two unknowns, which we can solve using algebra. To do this, we can use a method called substitution, which involves solving one equation for one variable, and then substituting that expression into the other equation. Here's how to do it:
Solve Equation 1 for y:
10x + 5y = 200
5y = 200 - 10x
y = (200 - 10x)/5
y = 40 - 2x
Substitute y into Equation 2:
6x + 2y = 105
6x + 2(40 - 2x) = 105
6x + 80 - 4x = 105
2x = 25
x = 12.50
So the price of a student ticket is $12.50.
To find the price of a guest ticket, we can substitute x = 12.50 into Equation 1:
10x + 5y = 200
10(12.50) + 5y = 200
125 + 5y = 200
5y = 75
y = 15
So the price of a guest ticket is $15.
Therefore, the price of each student ticket is $12.50 and the price of each guest ticket is $15.
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please help me I need to turn this in now
The volume of a right circular cone that has a height of 3.5 ft and a radius of 18.9 ft is given as follows:
1308.6 ft³.
How to obtain the volume a cone?The volume of a cone of radius r and height h is given by the equation presented as follows, which the square of the radius is multiplied by π and the height, and then divided by 3.
V = πr²h/3.
The parameters for the cone in this problem are given as follows:
Radius of r = 18.9 ft.Height of h = 3.5 ft.Hence the volume of the cone is given as follows:
V = 3.14 x 18.9² x 3.5/3
V = 1308.6 ft³.
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Find the median of first 15 odd numbers 
Answer:
15
Step-by-step explanation:
The first 15 odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29
The formula to find the median of a set of numbers is:
Median = [(n + 1) / 2]th term
where n is the total number of terms in the set.
In this case, we have 15 terms in the set of the first 15 odd numbers. So, substituting n = 15 in the formula, we get:
Median = [(15 + 1) / 2]th term
Median = 8th term
To find the 8th term, we can simply list the first 15 odd numbers in ascending order and count 8 numbers from the beginning of the list. The 8th term is 15.
Therefore, using the formula, we get:
Median = 8th term = 15.
So, the median of the first 15 odd numbers is 15.
what is the acceleration of a bus whose speed changes from 126 m/s to 306 m/s over a period of 3seconds
Answer: The acceleration of the bus can be calculated using the formula:
a = (v2 - v1) / t
where:
a = acceleration
v2 = final velocity = 306 m/s
v1 = initial velocity = 126 m/s
t = time = 3 seconds
Substituting the given values into the formula, we get:
a = (306 m/s - 126 m/s) / 3 s
a = 180 m/s / 3 s
a = 60 m/s^2
Therefore, the acceleration of the bus is 60 m/s^2.
Step-by-step explanation:
Factor equation
4x^6-20x^5+25x^4
Answer:
(14x + y)(14x - y)
Step-by-step explanation:
A=(a, e, i, o, u),B=(a, b, c) and C=(a, c, e, g)
B intersaction C= C intersaction B
The given statement "B ∩ C = C ∩ B" is true, since the intersection of two sets is a commutative operation, which means the order in which we list the sets does not matter.
To find the intersection of two sets, we need to identify the elements that are common to both sets. In this case, we can list the elements of each set and identify their common elements:
B = {a, b, c}
C = {a, c, e, g}
B ∩ C = {a, c}
C ∩ B = {a, c}
As we can see, the intersection of B and C is {a, c}, and the intersection of C and B is also {a, c}. The order in which we list the sets does not affect the result of the intersection operation, since the elements of both sets are the same.
Therefore, we can conclude that B ∩ C = C ∩ B is true, and that the intersection of B and C contains the same elements regardless of the order in which we list the sets.
In summary, the intersection of two sets is a commutative operation, which means that the order in which we list the sets does not affect the result. Therefore, B ∩ C = C ∩ B is true, and the intersection of B and C contains the same elements regardless of the order in which we list the sets.
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Complete question is:
If A=(a, e, i, o, u),B=(a, b, c) and C=(a, c, e, g)
Is B ∩ C= C ∩ B true?
what is the multiplier for 0.85% and 300% growth?
"The multiplier for 0.85% growth is calculated by adding 1 to the percentage as a decimal:
Multiplier for 0.85% growth = 1 + 0.0085 = 1.0085
The multiplier for 300% growth is calculated in the same way:
Multiplier for 300% growth = 1 + 3.00 = 4.00
Therefore, the multipliers for 0.85% and 300% growth are 1.0085 and 4.00, respectively." (ChatGPT, 2023)
g(x)
121x
10
8
6
fo
-6-5-4-3-2-1₂
Of(0) = g(0)
Of(-2) = g(-2)
Of(0) = g(-2)
Of(-2) = g(0)
2
799
-6
-10-
-12+
23
3 4 5 6 x
10)
The statement that is true regarding the graphed functions is that: B. f(-2) = g(-2).
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.At point (2, 0), an equation of the line f(x) can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 0 = (-4 - 0)/(-2 - 2)(x - 2)
y = -x + 2
For line g(x), we have:
y - 4 = (-2 - 4)/(0 + 2)(x + 2)
y = -3(x + 2) + 4
y = -3x - 2
When x = 0, we have:
g(0) = 0 + 2 = 2
f(0) = 0 - 2 = -2.
When x = -2, we have:
g(-2) = -(-2) + 2 = 4
f(-2) = -3(-2) - 2 = 4.
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You have 125% of the tickets required for a prize. What fraction of the required tickets do you have? Do you need more tickets for the prize? Explain.
Yοu dο nοt need mοre tickets fοr the prize, as yοu already have mοre than enοugh.
If yοu have 125% οf the tickets required fοr a prize, it means yοu have mοre than the number οf tickets required.
Tο find the fractiοn οf the required tickets that yοu have, yοu can cοnvert 125% tο a fractiοn and simplify 125% = 125/100 = 5/4
Sο, yοu have 5/4 οf the required tickets. Tο find the fractiοn οf the required tickets that yοu have, yοu need tο divide the number οf tickets yοu have by the number οf tickets required:
fractiοn οf required tickets = (number οf tickets yοu have) / (number οf tickets required)
Let's say the number οf tickets required is x. Then, the number οf tickets yοu have is 1.25 times x, οr 5/4 times x:
(number οf tickets yοu have) = 5/4 * x
Sο, the fractiοn οf required tickets that yοu have is:
fractiοn οf required tickets = (5/4 * x) / x = 5/4
This means yοu have 5/4, οr 1.25 times, the required number οf tickets. Therefοre, yοu dο nοt need mοre tickets fοr the prize, as yοu already have mοre than enοugh.
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A(1)=20 a(n)=a(n−1)⋅ 2 3 What is the 3 rd 3 rd 3, start superscript, start text, r, d, end text, end superscript term in the sequence?
The third term of the given sequence is =60.
The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence. For instance, the natural number sequence 1, 2, 3, 4, 5, 6,... is an example of an arithmetic progression. It has a common difference of 1 between two succeeding terms (let's say 1 and 2). (2 -1). We can see that the common difference between two subsequent words will be equal to 2 in both the case of odd and even numbers
a(1)=20
and
[tex]a_n=a(n-1)*\frac{3}{2}\\\\n=3\\\\a_3=20(2)*\frac{3}{2}\\\\a_3=60[/tex]
The complete question is-
a(1)=20 a(n)=a(n-1)*3/2 What is the 3rd term in the sequence?
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Drop down 1:
Select a Value
(4d + 1) (3d - 1)
(4d - 1) (3d + 1)
(6d + 1) (2d - 1)
(6d - 1) (2d + 1)
Drop down 2:
Select a Value
(3x+4)^2
(3x- 4)^2
(3x + 4) (3x - 4)
(9x + 4) (x- 4)
Drop down3:
Select a Value
(6b - 11w)^2
(6b^2 - 11w^2)
(6b+ 11w) (6b - 11w)
(6b^2 + 11w^2) (6b^2- 11w^2)
Drop down 4
Select a Value
(3y-4)^2
(3y +4) (7y - 4)
(3y - 8) (7y + 2)
(3y + 2) (7y - 8)
Answer:
1): (4d + 1) (3d - 1)
2: (3x- 4)^2
3: (6b+ 11w) (6b - 11w)
4. (3y - 8) (7y + 2)
Step-by-step explanation:
See attached worksheet.
Luke’s parents started a savings account to help him pay for college or a technology school when he turned 11 years old. Each month they put $125 into the savings account, and they continued this until he was 18 years old. The savings account did not accumulate any interest. Luke figured out that the first year of a technology school that he wanted to attend would cost him $12,480. If he had one year to save the rest of the money, how much would he need to save each month?
A. 165
B.40
C.1980
D.1040
B has a savings account, into which he must deposit $40 each month.
What's the point of the example?Interest is frequently calculated as an annual percentage of the amount borrowed. This percentage represents the loan's interest rate. For instance, a bank will pay interest if you deposit money in a high-yield savings account.
From the time he was 11 to the time he was 18, Luke's parents saved for him for 8 years, or 8 years x 12 months every year, or 96 months.
Since they were saving $125 per month throughout this time, Luke had amassed the following sum:
$125/month x 96 months = $12,000
Luke must still pay the following expenses because he needs $12,480 for his first year of technological school:
$12,480 - $12,000 = $480
If he has one year left to save this amount, he will need to save:
$480÷12months = $40per month
Therefore, the answer is B. $40.
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What is the area of a sector with a central angle of 30° and a radius of 12.5 cm?
Use 3.14 for π and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
The area of the sector with a central angle of 30 degrees and a radius of 12.5 cm is 40.89 cm².
What is the area of a sector?The area of a sector is expressed as;
A = ( θ/360 ) × π × r²
where θ is the central angle in degrees, r is the radius, and π is approximately 3.14.
Given the data in the question;
Central angle θ = 30 degreesRadius r = 12.5cmConstant pi π = 3.14Area A = ?Substituting the given values, we get:
Area = ( θ/360 ) × π × r²
Area = (30/360) × 3.14 × 12.5²
Area = 40.885 cm²
Area = 40.89 cm²
Therefore, the measure of the area is 40.89 cm².
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it is believed that 4% of children have a gene that may be linked to juvenile diabetes. researchers at a firm would like to test new monitoring equipment for diabetes. hoping to have 19 children with the gene for their study, the researchers test 729 newborns for the presence of the gene linked to diabetes. what is the probability that they find enough subjects for their study?
The probability of obtaining sufficient participants for their study is 0.0029.
The probability of researchers at a firm finding enough subjects for their study can be calculated using binomial probability.
What is binomial probability?Binomial probability is a probability distribution that calculates the probability of one event's occurrence in a specified number of experiments or trials that produce either positive or negative outcomes.
The probability that an event will occur in n number of trials or experiments is determined using the following formula:
P(X=a) = ⁿCₐ * p^a * (1-p)^(n-a)
Where ⁿCₐ is the number of combinations of "n" items taken "a" at a time.
"p" is the probability of an event occurring.
"(1-p)" is the probability of an event not occurring.
"n" is the number of experiments, and "a" is the number of successful events.
Let us solve the problem now. We have n = 729 and p = 0.04
We need to find out the probability of finding 19 children with the gene for their study. This means that we need to find out P(X=19)Now, we can calculate it as:
P(X=19) = ⁿCₐ * p^a * (1-p)^(n-a)
Putting the given values, we get:
P(X=19) = ⁷²⁹C₁₉ * (0.04)^19 * (1 - 0.04)^(729 - 19)
≈ 0.0029
Hence, the probability of finding enough subjects for their study is 0.0029.
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giving brainly Which equation would you use to find the distance between the two points? A. |2 - 4| B. |2 - (-4)| C. |-5 - 5| D. |2 + (-4)|
The equation we would use to find the distance between the two points is d = √((x2 - x1)² + (y2 - y1)²) = √((2 - (-4))² + (y2 - y1)²) = √(6² + (y2 - y1)²) = √36 + (y2 - y1)²)
To find the distance between two points on a number line or in a coordinate plane, we use the distance formula. The distance formula is given by:
d = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
None of the options provided represents the distance formula in its entirety. However, we can use option B as the first part of the distance formula, since it represents the absolute value of the difference between the x-coordinates of the two points:
|2 - (-4)|
Simplifying this expression gives:
|2 + 4|
|6|
Therefore, the equation we would use to find the distance between the two points is:
d = √((x2 - x1)² + (y2 - y1)²) = √((2 - (-4))² + (y2 - y1)²) = √(6² + (y2 - y1)²) = √36 + (y2 - y1)²)
We still need to determine the y-coordinates of the two points in order to complete the distance formula.
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Write the equation of the line parallel to line p that passes through (2, 5).
Thus, the equation of the line parallel to line p that passes through (2, 5) is y = mx - 2m + 5, where m is the slope of line p.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables, and the goal is to solve for the value(s) of the variable(s) that make the equation true.
For example, the equation 2x + 5 = 11.
Given by the question.
To find the equation of a line parallel to line p that passes through the point (2, 5), we need to know the equation of line p.
Assuming that we have the equation of line p in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, we can use the fact that parallel lines have the same slope to find the equation of the desired line.
Therefore, the equation of the line parallel to line p that passes through (2, 5) is:
y = mx + b (equation of line p)
y - 5 = m (x - 2) (point-slope form with (2, 5))
y = m (x - 2) + 5 (slope-intercept form)
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The polygons are similar: Find the value of x.
The missing lengths of x of the given similar figures are:
9) x = 18
10) x = 5
How to find the length of similar figures?Similar polygons are polygons that have the same shape, but their sizes may vary. Thus, if two polygons are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
9) From the concept of similar triangles, their ratios of similar sides are equal and as such we have:
x/6 = 6/2
x = 6 * 3
x = 18
10) From the concept of similar triangles, their ratios of similar sides are equal and as such we have:
21/7 = 15/x
3x = 15
x = 5
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help me please I need help
Answer:
6cm
Step-by-step explanation:
The volume of the cylinder = π · r² · h
r = 4
h = ?
Let's solve
96π = π · 16 · h
96 = 16 · h
h = 6cm
So, the height is 6cm
Mr. Bowen rents a lane at a bowling alley for 3.5 hours. The cost to rent the lane is $20 per hour. Which expression represents the change in the amount of money he has after paying for the lane?
Answer:
c= 3.5 x 20
Step-by-step explanation:
rent $20 hr
Time 3.5 hr
Cost $70
Based on past experience, a bank believes that 8% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans.(1) (7 points) What's the probability that over 10% of these clients will not make timely payments?(2) (11 pouts) 45% of the timely payments will not be made by under how many percentages of clients?
Thus, 45% of timely payments will not be made by under 100 - (165/200)*100% = 17.5% of clients.
what is binomial distribution?
The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial can result in either a success or a failure.
The distribution is characterized by two parameters: the number of trials n and the probability of success in each trial p. The probability of exactly k successes in n trials can be calculated using the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
(1) To find the probability that over 10% of the clients will not make timely payments, we need to use the binomial distribution. Let X be the number of clients out of 200 who do not make timely payments. Then X has a binomial distribution with parameters n = 200 and p = 0.08. We want to find P(X > 0.1*200) = P(X > 20).
Using the normal approximation to the binomial distribution, we can approximate X with a normal distribution with mean μ = np = 2000.08 = 16 and standard deviation σ = sqrt(np(1-p)) = sqrt(2000.08*0.92) = 3.36.
P(X > 20) can be approximated as P(Z > (20 - 16)/3.36) = P(Z > 1.19), where Z is a standard normal variable. Using a standard normal table or a calculator, we can find that P(Z > 1.19) = 0.1179.
Therefore, the probability that over 10% of the clients will not make timely payments is approximately 0.1179.
(2) Let Y be the number of clients out of 200 who make timely payments. Then Y has a binomial distribution with parameters n = 200 and p = 0.92 (since 8% of clients do not make timely payments, 92% do). We want to find the smallest k such that P(Y < k) > 0.45.
We can use a table of the cumulative binomial distribution or a calculator to find that P(Y < 164) = 0.4443 and P(Y < 165) = 0.4658. Therefore, the smallest k such that P(Y < k) > 0.45 is 165.
Thus, 45% of timely payments will not be made by under 100 - (165/200)*100% = 17.5% of clients.
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The probability that over 10% of these clients will not make timely payments is approximately 0.03.
What exactly is probability?
Probability is a branch of mathematics that deals with the measurement and analysis of uncertainty. It is used to quantify the likelihood or chance of an event occurring, and is expressed as a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event.
Now,
(1) Let X be the number of clients who will not make timely payments out of 200 loans approved. We are given that the probability of not making timely payments is 8%, or 0.08. Since X follows a binomial distribution with n = 200 and p = 0.08, we can use the normal approximation to the binomial distribution to find the probability that over 10% of these clients will not make timely payments:
First, we need to calculate the mean and standard deviation of X:
mean = n * p = 200 * 0.08 = 16
standard deviation = sqrt(n * p * (1 - p)) = sqrt(200 * 0.08 * 0.92) = 3.19
Now we can use the normal distribution with a continuity correction to find the probability:
P(X > 0.1 * 200) = P(X > 20) = P((X - mean) / standard deviation > (20 - mean) / standard deviation)
= P(Z > 1.88) ≈ 0.03
Therefore, the probability that over 10% of these clients will not make timely payments is approximately 0.03.
(2) Let Y be the number of clients who make timely payments out of 200 loans approved. We are given that 45% of the timely payments will not be made, so the probability of making a timely payment is 1 - 0.45 = 0.55. Since Y also follows a binomial distribution with n = 200 and p = 0.55, we need to find the largest value of k such that the probability of at least k clients making timely payments is at least 0.45.
We can use a cumulative binomial distribution to find the probability:
P(Y ≥ k) = 1 - P(Y < k) = 1 - binom.dist(k - 1, n, p, TRUE)
We can then use trial and error to find the largest value of k such that P(Y ≥ k) ≥ 0.45:
P(Y ≥ 127) ≈ 0.455 > 0.45
P(Y ≥ 128) ≈ 0.426 < 0.45
Therefore, the largest value of k such that the probability of at least k clients making timely payments is at least 0.45 is 127. This means that under 63.5% of clients (127/200) will make timely payments.
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2. Kadesh bought 20 shirts at a total cost of R 980. If the large shirts cost
R 50 and the small shirts cost R 40. How many of each size did he buy?
Answer:
18 large shirts
2 small shirts
Step-by-step explanation:
trial and error my boi
Drop down 1:
Select a Value
(2 + 4)(x- 6
(X+ 8)(x- 3)
(x - 8)(x + 3)
(x - 4) (x+ 6)
Drop down2:
Select a Value
(X+ 5)(x - 6)
(x-5)(x+ 6)
(X+ 10)(x - 3)
(X- 15)(x + 2)
Drop down 3:
(X-8)(x-9)
(X+8)(x+9)
(X-12)(x-6)
(X+12)(x+6)
The expressions after factorizing are;
1. (x+4)(x - 6). Option A
2. (x+ 5)(x - 6). Option A
3. (x - 8)(x - 9). Option A
How to determine the expressionsFrom the information given, we have the following quadratic equations;
x² - 2x - 24x² - x -30x² - 17x + 72To factorize the expressions, we need to first, multiply the coefficient of x² by the constant value.
Then, find the pair factors of the product whose sum would give the coefficient of x variable and substitute the values.
For the first expression;
x² - 2x - 24
x² - 6x + 4x - 24
group in pairs
(x² - 6x) + (4x -24)
factorize
x(x - 6) + 4(x - 6): (x+4)(x - 6)
x² - x - 30
x² - 6x + 5x - 30
group in pairs and factorize
x(x - 6) + 5(x - 6): (x+ 5)(x - 6)
x² - 17x + 72
x² - 9x - 8x + 72
Group in pairs and factorize
x(x - 9) - 8(x - 9): (x - 8)(x - 9)
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Sylvie bakes 4 trays of muffins. Each tray contains 8 muffins. She gives away 12 muffins to friends. Let m represent the number of muffins Sylvie has left. Which equation could be used to find the value of m?
The equation that could be used to find the value of "m" is: m = 20
To find the equation to determine the number of muffins Sylvie has left after baking and giving away some, we need to follow these steps:
Calculate the total number of muffins baked by Sylvie: 4 trays x 8 muffins/tray = 32 muffins
Subtract the number of muffins given away from the total baked: 32 muffins - 12 muffins = 20 muffins
Assign the number of muffins left to the variable "m"
Therefore, the equation that could be used to find the value of "m" is:
m = 20
This means that Sylvie has 20 muffins left after giving away 12 to her friends. It's important to note that we used basic arithmetic operations to solve this problem, including multiplication and subtraction, and then assigned the remaining value to a variable to create the equation.
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Ben went on holiday to Australia. He changed £350 into Australian dollars ($).
The exchange rate was £1 = $2.1
(a) Work out how many Australian dollars Ben should have received.
$.......
Ben should have received $735 in Australian dollars at the given exchange rate.
What is an exchange rate?The value of one currency represented in terms of another is called an exchange rate. It is the cost associated with exchanging one currency for another. The dynamics of supply and demand in the market dictate exchange rates, which are continually changing in response to a variety of political and economic variables including inflation, interest rates, trade balances, and geopolitical events. Currency rates have an impact on the price and profitability of transactions between nations, making them crucial for international commerce and investment. As they govern how much foreign currency can be received for a certain quantity of local currency, they are especially crucial for those who travel or transfer money overseas.
Given that, the exchange rate was £1 = $2.1.
Thus,
£350 * $2.1/£1 = $735
Therefore, Ben should have received $735 in Australian dollars.
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What is in the third quadrant of the unit circle
The third quadrant of the unit circle is the region of the circle that lies between 180 degrees and 270 degrees
The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane.
In the coordinate plane, the third quadrant is the quadrant that lies below the x-axis and to the left of the y-axis.
To find what is in the third quadrant of the unit circle, we need to look for the points on the circle that have negative x-coordinates and negative y-coordinates.
Since the radius of the unit circle is 1, we know that any point on the circle can be represented in terms of sine and cosine. Specifically, for any point (x, y) on the circle, we have:
x = cos(θ)
y = sin(θ)
where θ is the angle between the positive x-axis and the line connecting the origin and the point (x, y).
In the third quadrant, both the x-coordinate and the y-coordinate are negative. Therefore, we need to find the angle θ such that cos(θ) is negative and sin(θ) is negative.
We know that cos(θ) is negative in the second and third quadrants, and sin(θ) is negative in the third and fourth quadrants. Therefore, the third quadrant of the unit circle contains the points where:
cos(θ) is negative (i.e., θ is between 90 and 270 degrees or π/2 and 3π/2 radians), and
sin(θ) is negative (i.e., θ is between 180 and 360 degrees or π and 2π radians).
So the third quadrant of the unit circle contains all the points where:
-1 ≤ x ≤ 0 (cosine is negative in this quadrant), and
-1 ≤ y ≤ 0 (sine is also negative in this quadrant).
In other words, the third quadrant of the unit circle is the region of the circle that lies between 180 degrees and 270 degrees (or π and 3π/2 radians) and has both x and y values that are negative.
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if p 62-5x and r =133 find qrs
The answer to this question is that we cannot find qrs without additional information about what q and s represent. We can only make educated guesses based on the context of the problem.
Sure, I'd be happy to help! To find qrs, we need to know what these variables represent. Based on the given information, we know that p=62-5x and r=133, but we don't know what q represents. Therefore, we cannot directly solve for qrs.
However, we can make an educated guess based on the context of the problem. It's possible that q is related to p and r in some way. For example, q could be the sum of p and r, or it could be the product of p and r. Without more information, we can't be sure.
Another possibility is that qrs is actually three separate variables, q, r, and s. In this case, we would need to know what s represents in order to solve for qrs.
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three linear funtions are represented below
help me please
Answer: B
Rate of change is the slope which is the [tex]\frac{rise}{run}[/tex]= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
In the first equation, we will substitute x with any two random numbers to get the y value, which gives us two points. The number you take doesn't matter.
y=2, taking x as 2 so the point is (2,2)
y=1, taking x as 1 so the point is (1,1)
m=[tex]\frac{2-1}{2-1}=1[/tex] SO THE SLOPE FOR A IS 1
In the second equation, we can just pick 2 points on the graph that the line runs through. I picked (2,-1) and (0,-4) to make calculations easy
[tex]m=\frac{-4-(-1)}{0-2}\\ =\frac{-3}{2}\\[/tex]OR THE SLOPE IS -1.5
In the thrid equation, we can again just pick points to find the ROC.
[tex]m=\frac{9-6}{5-4} \\ =3[/tex]THE SLOPE IS 3
Now that we have found this out, we can now find out which one has a bigger ROC.
-1.5<1<3=B<A<C
MARK BRAINLIST IF THIS HELPED PLEASE! LOVE YA <3
Draw bar (AB) of length 7.3cm and find its axis of symmetry. Draw a line segment of length 9.5cm and construct its perpendicular bise
According to the information, the symmetry axis of the 7.3cm bar would be located at 3.65cm. Additionally, the perpendicular bise of the 9.5cm line would be located in 4.75cm
What is the axis of symmetry?An axis of symmetry is a term that refers to an imaginary reference line that allows any figure to divide in two parts, its opposite points are equidistant to each other, that is, they are symmetrical.
What is the perpendicular Bise?The perpendicular Bise is a term to refer to a straight line perpendicular to a given segment. A characteristic of the perpendicular Bise is that it is located at the midpoint of the segment.
According to the above to find the axis of symmetry and the perpendicular bise we must divide the values into 2 to find its half.
7.3cm / 2 = 3.65cm9.5cm / 2 = 4.75 cmNote: This question is incomplete. Here is the complete information:
Attached image
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If I simplify the expression completely for 15 + 8(2y - 9) what do I get?
Answer:
Step-by-step explanation:
16y-57
According to an article, 44% of adults have experienced a breakup at least once during the last 10 years. Of 9 randomly selected adults, find the probability that the number, X, who have experienced a breakup at least once during the last 10 years is:
a. exactly five; at most five; at least five.
b. at least one; at most one.
c. between five and seven, inclusive.
d. Determine the probability distribution of the random variable X.
The prοbabilities are,
a) P(X = 5)=0.204 , P(X ≤ 5) =0.849 and P(X ≥ 5)= 0.355
b) P(X ≥ 1) = 0.995 , P(X ≤ 1)=0.044
c) P(5 ≤ X ≤ 7)= 0.571
What is prοbability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
a) Prοbability οf exactly 5, P(X = 5) then
Using excel binοmial functiοn:
=> BINOM.DIST(5, 9, 0.44, 0)
=> 0.204
Prοbability οf at mοst 5, P(X ≤ 5) then
Using excel binοmial functiοn:
=> BINOM.DIST(5, 9, 0.44, 1
=> 0.849
Prοbability οf at least 5, P(X ≥ 5) = 1 - P(X ≤ 4)
Using excel binοmial functiοn:
=> 1 - BINOM.DIST(4, 9, 0.44, 1)
=> 0.355
b)Prοbability οf at least 1, P(X ≥ 1) = 1 - P(X ≤ 0)
Using excel binοmial functiοn:
=> 1 - BINOM.DIST(0, 9, 0.44, 1)
=> 0.995
Prοbability οf at mοst 1, P(X ≤ 1) =
Using excel binοmial functiοn:
=> BINOM.DIST(1, 9, 0.44, 1)
=> 0.044
c) Prοbability between 5 and 7, P(4 ≤ X ≤ 6) = P(X ≤ 7) - P(X < 5)
=> P(X ≤ 6) - P(X ≤ 3)
=> BINOM.DIST(6, 9, 0.44, 1) - BINOM.DIST(3, 9, 0.44, 1)
=> 0.571
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