Sin(θ) is negative for θ ∈ (π, 3π/2) U (3π/2, 2π).
Cos(θ) is negative for θ ∈ (π/2, π) U (π, 3π/2).
To determine the values of θ for which sin(θ) is negative, we need to consider the unit circle and the quadrants in which sin(θ) takes negative values.
On the unit circle, sin(θ) represents the y-coordinate of the point corresponding to the angle θ. Sin(θ) is negative in the third and fourth quadrants of the unit circle.
In the third quadrant, the angle θ lies between π and 3π/2. In this quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) are negative.
In the fourth quadrant, the angle θ lies between 3π/2 and 2π. In this quadrant, the x-coordinate (cosine) is positive, but the y-coordinate (sine) is negative.
Therefore, the values of θ for which sin(θ) is negative are:
θ ∈ (π, 3π/2) U (3π/2, 2π)
Next, to determine the values of θ for which cos(θ) is negative, we again consider the unit circle and the quadrants in which cos(θ) takes negative values.
Cos(θ) represents the x-coordinate on the unit circle. Cos(θ) is negative in the second and third quadrants of the unit circle.
In the second quadrant, the angle θ lies between π/2 and π. In this quadrant, both the x-coordinate (cosine) and the y-coordinate (sine) are negative.
In the third quadrant, the angle θ lies between π and 3π/2. In this quadrant, the x-coordinate (cosine) is negative, but the y-coordinate (sine) is positive.
Therefore, the values of θ for which cos(θ) is negative are:
θ ∈ (π/2, π) U (π, 3π/2)
for such more question on quadrants
https://brainly.com/question/17482667
#SPJ8
What is the standard form of this function?
f(x) = (x − 2)2 + 6
Answer:
f(x) = x² - 4x + 10
Step-by-step explanation:
the standard form of a quadratic function is
f(x) = ax² + bx + c ( a ≠ 0 )
given
f(x) = (x - 2)² + 6 ← expand the factor using FOIL
= x² - 4x + 4 + 6 ← collect like terms
= x² - 4x + 10 ← in standard form
Calculate the are of rectangle A.you must use area=length×breadth
HELPPPP!!!!!!!!Fill in the table using this function rule.
Answer:
This is not the answer but if u have Spanchat you can go to the AI and ask him to fill in the table using this function rule, list x, and then put the equation and he'll give you the table
Step-by-step explanation:
[tex] \huge{ \tt{ \boxed{ \tt{answer}}}}[/tex]
★Refer the attachment mate!! Follow for more★
polynomial standard form of x^2-x^6+x^8-5 ?
The standard form of the polynomial x^2 - x^6 + x^8 - 5 is:
x^8 - x^6 + x^2 - 5
To express the polynomial x^2 - x^6 + x^8 - 5 in standard form, we arrange the terms in descending order of their exponents.
The given polynomial can be rewritten as:
x^8 - x^6 + x^2 - 5
In the standard form of a polynomial, the terms are arranged in descending order of their exponents. So, let's rearrange the terms:
x^8 - x^6 + x^2 - 5
The standard form of the polynomial x^2 - x^6 + x^8 - 5 is:
x^8 - x^6 + x^2 - 5
for such more question on polynomial
https://brainly.com/question/15702527
#SPJ8
Given that the two expression(r+ a)(r – 15) and r² – br-75 are indentical calculate the value of b
Answer:
b = 10
Step-by-step explanation:
expand expression and compare like terms.
(r + a)(r - 15) ← expand using FOIL
= r² - 15r + ar - 15a ← factor out r from second/ third terms
= r² + r(a - 15) - 15a
compare with r² - br - 75
then
- 15a = - 75 ( divide both sides by - 15 )
a = 5
and
a - 15 = - b ← substitute a = 5
5 - 15 = - b
- 10 = - b ( multiply both sides by - 1 )
10 = b
need help with this question trying to figure out this question
3x-15=x+33
or, 3x-2x=33+15
THEREFORE X=48 UNITS
THIS IS THE CORRECT QNSWER
K
The diagram to the
right illustrates a
hypothetical demand
curve representing the
relationship between
price (in dollars
per unit) and
quantity (in 1,000s of
units per unit of time).
The area of the
triangle shown on the
diagram is $.
(Enter your response
as an integer.)
100
90-
80-
70-67
60-
50-
40-
30-
20-17
10-
D
23
20 30 40 50
60
Quantity (1,000s of units per unit of time)
10
73
70 80 90 100
Answer:
OK, HERE IS YOUR ANSWER
Step-by-step explanation:
AI-generated answer
We are given a demand curve in the form of a graph, and we are asked to find the area of the triangle shown on the diagram. The formula for finding the area of a triangle is:
Area = 1/2 x base x height
In this case, the base of the triangle is the quantity in thousands of units per unit of time, and the height of the triangle is the price in dollars per unit.
The base of the triangle can be calculated as the difference between the quantities at the two endpoints of the demand curve. From the graph, we can see that the quantity at the left endpoint is 20, and the quantity at the right endpoint is 50. Therefore, the base of the triangle is:
Base = 50 - 20 = 30
The height of the triangle can be calculated as the difference between the prices at the two endpoints of the demand curve. From the graph, we can see that the price at the left endpoint is $90, and the price at the right endpoint is $70. Therefore, the height of the triangle is:
Height = 90 - 70 = 20
Now, we can use the formula to find the area of the triangle:
Area = 1/2 x base x height
Area = 1/2 x 30 x 20
Area = 300
Therefore, the area of the triangle shown on the diagram is $300. Hence, the correct answer is 300.
Mark me as brainliestThe area of the triangle in the demand curve diagram can be found using the formula for the area of a triangle which is 1/2 * base * height. From the points provided, we are able to calculate an area of 2450 dollars.
To answer this question, we need to understand how to calculate the area of a triangle which is represented by the equation: Area = 1/2 * base * height. From the diagram, we can find these values:
Base: The quantity 1,000s of units per unit of time which is the x-axis,
Height: Price per unit (dollars) which is the y-axis.
Assuming that the triangle's points intersect at 10 (on the y-axis) and 70 (on the x-axis) with a hypotenuse ending at 80 on the y-axis. The base would be 70 - 0 = 70, and the height would be 80 - 10 = 70.
Plugging these values into our formula, we get Area = 1/2 * 70 * 70 = 2450 dollars. So the area of the triangle is 2450 dollars.
Learn more about area of the triangle here:
https://brainly.com/question/34237015
#SPJ2
The probable question may be:
The diagram to the right illustrates a hypothetical demand curve representing the relationship between price (in dollars per unit) and quantity (in 1,000s of units per unit of time).
The area of the triangle shown on the diagram is $. (Enter your response as an integer.) 100 90- 80- 70-67 60 50- 40 30- 20-17 10- D 23 73 20 30 40 50 60 70 80 90 Quantity (1,000s of units per unit of time) 10 100
14 − {7 + 4 · 3 - [(-2)² · 2 - 6]}+ (2² + 6 - 5 · 3) + 3 - (5 - 2³ / 2) =
Answer: -6
Step-by-step explanation:
1. Evaluate the expressions inside the innermost brackets and braces first:
[tex]\((-2)^2 \cdot 2 - 6 = 4 \cdot 2 - 6 = 8 - 6 = 2\)[/tex]
So, the expression becomes:
[tex]\(14 - \{7 + 4 \cdot 3 - 2\}+ (2^2 + 6 - 5 \cdot 3) + 3 - (5 - 2^3 / 2)\)[/tex]
2. Continue evaluating the expressions inside the braces:
[tex]\(7 + 4 \cdot 3 - 2 = 7 + 12 - 2 = 17\)[/tex]
So, the expression becomes:
[tex]\(14 - 17 + (2^2 + 6 - 5 \cdot 3) + 3 - (5 - 2^3 / 2)\)[/tex]
3. Now, evaluate the expressions inside the parentheses:
[tex]\(2^2 + 6 - 5 \cdot 3 = 4 + 6 - 15 = -5\)[/tex]
[tex]\(5 - 2^3 / 2 = 5 - 8 / 2 = 5 - 4 = 1\)[/tex]
So, the expression becomes:
[tex]\(14 - 17 - 5 + 3 - 1\)[/tex]
4. Finally, perform the remaining operations:
[tex]\(14 - 17 - 5 + 3 - 1 = -3 - 5 + 3 - 1 = -6\)[/tex]
So, the result of the expression is -6.
If set is equivalent to the set of natural numbers that are multiples of 4
Answer:
2 4 8 16 and so on and so forth
The perimeter of the pentagon below is 64 units. Find the length of side PQ.
Write your answer without variables.
Answer:
PQ=20
Step-by-step explanation:
1) 11+x+2+3x-1+10+2x=64
2) 6x+22=64
3) 6x=42
4) x=7
5) PQ = 3(7)-1 = 20
Car A is rated at 32 mi/gal (miles per gallon) for city driving and 30 mi/gal for highway driving. Car B is rated at 29 mi/gal city and 36 mi/gal highway. How many gallons of gas would each vehicle consume for the following amounts of driving? (a) 300 mi of city driving plus 100 mi of highway driving (b) 100 mi of city driving plus 300 mi of highway driving
Data that does not take numerical form is referred to as: (2)
(1) Continuous data;
(2) Quantitative data;
(3) Qualitative data;
(4) Discrete data.
Assume the average nightly payroll for a city’s downtown restaurants on the weekend is $2200 with a standard deviation of $300. The distribution has a bell-shaped curve. A manager wants to be 99% sure he has this cost covered for the next four weeks and puts away $10,000. Will he have enough? Use your z-score formula result to justify your answer. Please respond with the dollar amount and round to the nearest dollar.
Hint: Round your z-value to the hundredths place and direction of the graph will matter.
Given statement solution is :- The manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.
To determine if the manager will have enough funds to cover the nightly payroll for the next four weeks, we need to calculate the total cost for four weeks and compare it to the amount set aside.
The nightly payroll has a mean of $2200 and a standard deviation of $300. Since there are seven nights in a week, the weekly payroll can be calculated as:
Weekly Payroll = Nightly Payroll * Number of Nights in a Week
= $2200 * 7
= $15,400
To calculate the total cost for four weeks, we multiply the weekly payroll by four:
Total Cost for Four Weeks = Weekly Payroll * Number of Weeks
= $15,400 * 4
= $61,600
Now, let's calculate the z-score using the formula:
z = (X - μ) / σ
Where:
X = Total Cost for Four Weeks
μ = Mean of the distribution
σ = Standard deviation of the distribution
z = ($61,600 - $2200) / $300
z = $59,400 / $300
z ≈ 198
To determine if the manager will have enough funds to cover the payroll, we need to find the proportion of the distribution that is less than or equal to the z-score. This can be done by consulting a standard normal distribution table or using statistical software.
For a z-score of 198, the proportion in the tail of the distribution is essentially 1 (or 100%). This means that the manager is virtually guaranteed to have enough funds to cover the payroll for the next four weeks.
Since the manager has set aside $10,000, which is less than the calculated total cost of $61,600, he will indeed have enough funds to cover the payroll.
Therefore, the manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.
For such more questions on Funds Cover Payroll: Confirmed
https://brainly.com/question/32039603
#SPJ8
If A is the set of positive integers defined as
A = {x:x²+x-6=0}. Find the value of X satisfying the
solution set.
The value of x that satisfies the equation x² + x - 6 = 0 is x = 2 or x = -3.
To find the value of x that satisfies the equation x² + x - 6 = 0, we can solve the quadratic equation by factoring or using the quadratic formula.
Option 1: Factoring
To factor the quadratic equation, we need to find two numbers whose product is -6 and whose sum is +1 (the coefficient of x).
The numbers that satisfy this condition are +3 and -2.
Therefore, we can rewrite the equation as (x + 3)(x - 2) = 0.
Setting each factor equal to zero, we have x + 3 = 0 or x - 2 = 0.
Solving these equations gives x = -3 or x = 2.
Option 2: Quadratic Formula
The quadratic formula states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b² - 4ac)) / (2a).
In our equation, a = 1, b = 1, and c = -6.
Substituting these values into the formula, we have:
x = (-1 ± √(1² - 4(1)(-6))) / (2(1)).
Simplifying the expression inside the square root, we get:
x = (-1 ± √(1 + 24)) / 2.
x = (-1 ± √25) / 2.
x = (-1 ± 5) / 2.
This gives us two solutions: x = (-1 + 5) / 2 = 4 / 2 = 2, and x = (-1 - 5) / 2 = -6 / 2 = -3.
For similar question on equation.
https://brainly.com/question/30645878
#SPJ8
smerelda simplified a complex fraction. Her work is shown below.
Negative 5 and one-fourth divided by three-halves = negative StartFraction 21 over 4 EndFraction divided by three-halves = (Negative StartFraction 21 over 4 EndFraction) (Three-halves) = Negative StartFraction 24 over 6 EndFraction = negative 4
What errors did Esmerelda make? Select three options.
Esmerelda converted the mixed number to the wrong improper fraction.
Esmerelda added the numerators.
Esmerelda added the denominators.
Esmerelda did not divide –24 by 6 correctly.
Esmerelda did not use the reciprocal of the divisor.
Answer:
Step-by-step explanation:
ACTUAL ANSWER
(-5¼)/(3/2)
= -{(20+1)/4}/(3/2) //CONVERTING INTO IMPROPER FRACTION
= (-21/4)/(3/2)
= (-21/4) x (2/3) // MULTIPLYING BY RECIPROCAL
= (-21x2)/(4x3)
= -42/12
= -(7x6)/(2x6) TAKING 7 AS COMMON FACTOR
= -7/2
STEPS FOLLOWED BY ESMERELDA
(-5¼)/(3/2)
= -{(20+1)/4}/(3/2)
= -(21/4)/(3/2)
= -(21/4) x (3/2)
= -(21+3)/(4+2)
= - (24/6)
= -4
HENCE THE ERRORS COMMITTED BY HER ARE:-
1. ESMERALDA ADDED THE NUMERATORS
2. ESMERALDA ADDED THE DENOMINATORS
3. ESMERALDA DID NOT USE THE RECIPROCAL OF THE DIVISOE
5.3 Suppose the radius of a second solid metal ball, B₂, is half the radius of ball B₁. Suppose ball B₂ was put into the tank of water instead of ball B₁. Would the surface of the water be 4cm below the top of the tank? Explain your answer. (5)
If ball B₂ is placed in the tank instead of B₁, the surface of the water would not be 4cm below the top of the tank. It would be lower than that, indicating that ball B₂ causes a lesser rise in the water level due to its smaller volume.
No, the surface of the water would not be 4cm below the top of the tank if ball B₂ with a radius half of B₁ was placed in the tank instead.
The water level in a tank is determined by the volume of the object submerged in it, not just the radius of the object. The volume of a sphere is directly proportional to the cube of its radius.
Let's assume the radius of ball B₁ is r. Then, the radius of ball B₂ would be (1/2) * r.
The volume of ball B₁ can be calculated as V₁ = (4/3) * π * r³.
Similarly, the volume of ball B₂ can be calculated as V₂ = (4/3) * π * (1/2 * r)³ = (1/6) * (4/3) * π * r³.
The volume of water displaced by ball B₁ would be equal to V₁, which would cause the water level to rise.
However, the volume of water displaced by ball B₂ would be equal to V₂, which is only (1/6) of V₁. This means that ball B₂ would displace less water compared to B₁, resulting in a lower rise in the water level.
Therefore, if ball B₂ is placed in the tank instead of B₁, the surface of the water would not be 4cm below the top of the tank. It would be lower than that, indicating that ball B₂ causes a lesser rise in the water level due to its smaller volume.
for such more question on surface
https://brainly.com/question/20771646
#SPJ8
You have found a store that is unique. All the shirts sell for a set price and all the pants are also priced the same in the entire store! You have purchased 3 shirts and 2 pants for $104.81 and your friend has purchased 2 shirts and one pant for $61.33. Set up and solve a system of linear equations. How much is one shirt?
Answer:
17.85$
Step-by-step explanation:
Let x be 1 shirt price
Let y be 1 pant price
we have the following equation
3x+2y = 104.81$ (1)
2x+y = 61.33$ => multiply two sides by 2 => 4x + 2y = 122.66 (2)
=> (2) - (1) => x = 17.85$
So one shirt is 17.85$
Find the inverse of the matrix, use an algorithm for finding A^-1 by row reducing [A I]
[------------------]
| 1 0 -3 | 1 0 0 |
| 3 1 -4 | 0 1 0 |
| 4 2 -4 | 0 0 1 |
[------------------]
Answer:
A: A^-1 = [[-2,-3,-1.5],[-2,-4,-2.5],[-1,1,-.5]]
Step-by-step explanation:
Answer:
To find the inverse of the matrix A, we will use the row reduction method. We will augment matrix A with the identity matrix I and perform row operations until A is transformed into the identity matrix. The resulting matrix on the right side will be the inverse of A.
Step-by-step explanation:
Augment the matrix A with the identity matrix I:
[ 1 0 -3 | 1 0 0 ]
[ 3 1 -4 | 0 1 0 ]
[ 4 2 -4 | 0 0 1 ]
Perform row operations to transform the left side of the augmented matrix into the identity matrix:
R2 = R2 - 3R1
R3 = R3 - 4R1
[ 1 0 -3 | 1 0 0 ]
[ 0 1 5 | -3 1 0 ]
[ 0 2 8 | -4 0 1 ]
Perform row operations to further transform the left side of the augmented matrix into the identity matrix:
R3 = R3 - 2R2
[ 1 0 -3 | 1 0 0 ]
[ 0 1 5 | -3 1 0 ]
[ 0 0 -2 | 2 -2 1 ]
Multiply the third row by -1/2 to make the pivot element of the third row equal to 1:
R3 = (-1/2) * R3
[ 1 0 -3 | 1 0 0 ]
[ 0 1 5 | -3 1 0 ]
[ 0 0 1 | -1 1 -1/2 ]
Perform row operations to further transform the left side of the augmented matrix into the identity matrix:
R1 = R1 + 3R3
R2 = R2 - 5R3
[ 1 0 0 | 2 0 3/2 ]
[ 0 1 0 | 2 -4 5/2 ]
[ 0 0 1 | -1 1 -1/2 ]
The resulting matrix on the right side of the augmented matrix is the inverse of matrix A:
[ 2 0 3/2 ]
[ 2 -4 5/2 ]
[ -1 1 -1/2 ]
Therefore, the inverse of matrix A is:
[ 2 0 3/2 ]
[ 2 -4 5/2 ]
[ -1 1 -1/2 ]
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 2 14 9 25
Female 6 4 19 29
Total 8 18 28 54
If one student is chosen at random,
Find the probability that the student was female OR got an "A".
Round answer 4 places after the decimal if needed.
The answer to four decimal places, the probability is approximately 0.6481.
To find the probability that a randomly chosen student is either female or received an "A," we need to calculate the sum of the probabilities of these two events occurring individually and subtract the probability of both events occurring simultaneously.
Let's start by calculating the probability of selecting a female student. From the given information, we know that there are 29 female students out of a total of 54 students. Therefore, the probability of selecting a female student is 29/54.
Next, we need to determine the probability of selecting a student who received an "A." Looking at the table, we can see that there are a total of 8 students who received an "A" grade out of 54. Hence, the probability of selecting a student who received an "A" is 8/54.
To find the probability of both events occurring, we need to consider the intersection of the two events, which is the set of female students who also received an "A." According to the table, there are 2 female students who received an "A." Therefore, the probability of selecting a female student who received an "A" is 2/54.
Now, we can calculate the probability of selecting a female student OR a student who received an "A" by summing the individual probabilities and subtracting the probability of both events occurring simultaneously:
Probability (Female OR "A") = Probability (Female) + Probability ("A") - Probability (Female AND "A")
= 29/54 + 8/54 - 2/54
= 35/54
For more such questions on probability
https://brainly.com/question/25839839
#SPJ8
What is the slope of the line that contains these points?
x
39
40
41
42
y
36
29
22
15
Answer:
Slope = -7
Step-by-step explanation:
Take any two points from the table:
(39 , 36) ⇒ x₁ = 39 & y₁ = 36
(41 , 22) ⇒ x₂ = 41 & y₂ = 22
Substitute the points in the below formula:
[tex]\boxed{\bf Slope = \dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf = \dfrac{22-36}{41-39}\\\\\\=\dfrac{-14}{2}\\\\=-7[/tex]
express 30.725 correct to one decimal place
Answer:
30.7
Step-by-step explanation:
30.725 to one decimal place is 30.7. To round/correct to one decimal place, it would be the tenths. So, look at the hundredths place number (2), and if its greater than 5, add 1 to the tenths place (7 changes to 8), and if its less than 5, don't do anything (7 stays as 7).
Hope this helps! :)
Answer:
The value corrected to one decimal place is 30.7
Step-by-step explanation:
The value 30.725 has three decimal places. The number 7 is in the one's place, the number 2 is in the tenth place, and the number 5 is in the hundredth place.
To round off, if the value in a place is equal to or above 5, the previous place number is increased by one; else it remains the same. In this case, the hundredth place is 5, so we add 1 to the tenth place. This gives us 2 + 1 = 3. Therefore, the number is expressed with two decimal places as 30.73.
To express it as one decimal place, we look at the value in the tenth place, which is 3. As 3 is less than 5, the one's place remains the same.
Thus, the value is 30.7 when expressed with one decimal place.
Learn more about decimal places,
https://brainly.com/question/20563248
What fraction subtracted from 5/12 will yield an answer that is equal to the difference between 2/3 and 1/2?
The fraction that, when subtracted from 5/12, yields the same result as the difference between 2/3 and 1/2, is 1/4.
To find the fraction that, when subtracted from 5/12, gives the same result as the difference between 2/3 and 1/2, we need to compute both the difference and the subtraction, and then find the fraction that represents their equality.
The difference between 2/3 and 1/2 can be found by subtracting the two fractions:
2/3 - 1/2 = (4/6) - (3/6) = 1/6
Now, let's represent the fraction we are looking for as "x." We can set up the equation:
5/12 - x = 1/6
To solve for "x," we need to isolate it on one side of the equation. We can do this by subtracting 5/12 from both sides:
-x = 1/6 - 5/12
To simplify the right side, we need a common denominator, which is 12:
-x = 2/12 - 5/12
Now we can combine the numerators:
-x = (2 - 5)/12 = -3/12 = -1/4
To solve for "x," we multiply both sides of the equation by -1:
x = 1/4
For more such questions on fraction
https://brainly.com/question/78672
#SPJ8
. If the cone has a height of 10 cm and a diameter of 18 cm, what is its volume?
Answer:
[tex]\Huge \boxed{\boxed{\bf{Volume = 848.23 cm^3}}}[/tex]
Step-by-step explanation:
To calculate the volume of a cone with a height of 10 cm and a diameter of 18 cm, we can use the formula:
[tex]\LARGE \boxed{\tt{V = \frac{1}{3} \times \pi \times r^2 \times h}}[/tex]
➤V = volume
➤r = radius
➤h = height
Since the diameter is 18 cm, the radius is half of that, which is 9 cm. Now, we can plug in the values:
[tex]\tt{V = \frac{1}{3} \times \pi \times (9)^2 \times 10}[/tex][tex]\tt{V = \frac{1}{3} \times \pi \times 81 \times 10}[/tex][tex]\tt{V = \pi \times 270}[/tex]The volume of the cone is [tex]\tt{270\pi \approx 848.23 \texttt{ cm}^3}[/tex]
__________________________________________________________
Please help me asap
Answer:
A. x+y+z=35,000
4x+6y+12x-194,000
2y-z=0
Step-by-step explanation:
The system of equations is:
x + y + z = 35,000 (total investment is $35,000) 4x + 6y + 12z = 19,400 (the investor wants an annual return of $1940 on the three investments) y = 2z (the client wants to invest twice as much in A bonds as in B bonds)
The answer is A.
The first equation represents the total amount of money invested in the three types of bonds. The second equation represents the total annual return on the investments, which is equal to the sum of the individual returns on each type of bond. The third equation represents the client's preference for investing in A bonds over B bonds.
The system of equations can be used to solve for the values of x, y, and z, which represent the amounts invested in AAA, A, and B bonds, respectively.
Answer:
[tex]\textsf{A.} \quad \begin{cases}x+y+z=35000\\4x+6y+12z=194000\\2z-y=0\end{cases}[/tex]
Step-by-step explanation:
A system of equations is a set of two or more equations with the same variables. It allows us to model and solve problems that involve multiple equations and unknowns.
An investment firm recommends that a client invest in bonds rated AAA, A, and B. The definition of the variables are:
Let x be the number of AAA bonds.Let y be the number of A bonds.Let z be the number of B bonds.The average yield on each of the three bonds is:
AAA bonds = 4%A bonds = 6%B bonds = 12%We have been told that the total investment is $35,000. Therefore, the equation that represents this is the sum of the three investments equal to 35,000:
[tex]x+y+z=35000[/tex]
To find the annual return on each investment, multiply the number of bonds by the average yield (in decimal form). Given the investor wants a total annual return of $1940 on the three investments, the equation that represents this is the sum of the product of the investment amount for each bond type and its corresponding yield, equal to $1940.
[tex]0.04x+0.06y+0.12z=1940[/tex]
Multiply all terms by 100:
[tex]4x+6y+12z=194000[/tex]
Finally, given the client wants to invest twice as much in A bonds as in B bonds, the equation is:
[tex]y=2z[/tex]
Subtract y from both sides of the equation:
[tex]2z-y=0[/tex]
Therefore, the system of equations the models the given scenario is:
[tex]\begin{cases}x+y+z=35000\\4x+6y+12z=194000\\2z-y=0\end{cases}[/tex]
Help me please. You can get 20 points
a. The marginal profit function Py is Py = -30x + 47y - 915 and
b. Change in profit if price increase by 1 cent is 831 cents.
Understanding Profit FunctionTo find the marginal profit functions Px and Py, we need to find the partial derivatives of the profit function P(x, y) with respect to x and y, respectively.
Given:
P(x, y) = (x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)
a. Marginal profit function Px:
To find Px, we differentiate P(x, y) with respect to x while treating y as a constant:
Px = ∂P/∂x = (∂/∂x) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]
Expanding the terms and simplifying:
Px = (55 - 4x + 5y) + (x - 40)(-4) + (70 + 5x - 7y)(5)
Simplifying further:
Px = 55 - 4x + 5y - 4x + 40 + 350 + 5x - 7y
Combining like terms:
Px = 355 - 3x - 2y
b. Marginal profit function Py:
Similarly, to find Py, we differentiate P(x, y) with respect to y while treating x as a constant:
Py = ∂P/∂y = (∂/∂y) [(x - 40)(55 - 4x + 5y) + (y - 45)(70 + 5x - 7y)]
Expanding the terms and simplifying:
Py = (x - 40)(5) + (70 + 5x - 7y)(-7) + (y - 45)(5)
Simplifying further:
Py = 5x - 200 - 7y - 490 - 35x + 49y + 5y - 225
Combining like terms:
Py = -30x + 47y - 915
This is the profit function Py.
b. Estimating the daily change in profit:
To estimate the daily change in profit, we need to evaluate Px and Py at the given prices and calculate the change in profit when the prices are increased as specified.
Given initial prices:
First brand price (x) = 70 cents
Second brand price (y) = 73 cents
To estimate the change in profit, we substitute the initial prices into Px and Py and calculate the results:
Px(70, 73) = 355 - 3(70) - 2(73)
= 355 - 210 - 146
= -1
Py(70, 73) = -30(70) + 47(73) - 915
= -2100 + 3431 - 915
= 416
The daily change in profit can be estimated by multiplying the changes in price (1 cent for the first brand and 2 cents for the second brand) with the respective marginal profit functions:
Change in profit = ΔP ≈ Px(70, 73) * 1 + Py(70, 73) * 2
≈ -1 * 1 + 416 * 2
≈ -1 + 832
≈ 831 cents
Therefore, the estimated daily change in profit when the salesperson increases the price of the first label by 1 cent and the price of the second label by 2 cents is 831 cents.
Learn more about profit function here:
https://brainly.com/question/16866047
#SPJ1
Order the following fractions from least to greatest: 11/4, −2, −1/8
To order the fractions from least to greatest, we need to compare their values. The given fractions are 11/4, -2, and -1/8. The answer of the given question -2, -1/8, 11/4
Let's start by converting the mixed number -2 into a fraction. A mixed number consists of a whole number and a fraction. To convert it to a fraction, we multiply the whole number by the denominator of the fraction part and add the numerator. Then, we place the result over the original denominator. In this case, -2 can be written as -2/1.
Now we have the following fractions: 11/4, -2/1, and -1/8.
To compare these fractions, we can find a common denominator. The least common multiple (LCM) of the denominators 4, 1, and 8 is 8. So, we will rewrite the fractions using 8 as the common denominator:
11/4 = 22/8
-2/1 = -16/8
-1/8 remains the same
Now we have 22/8, -16/8, and -1/8. We can see that -16/8 is the smallest, followed by -1/8, and finally 22/8.
Therefore, in order from least to greatest, the fractions are:
-16/8, -1/8, 22/8
Simplifying further, we have:
-2, -1/8, 11/4
Note that we simplified the fractions, but the order remains the same. The fractions are ordered based on their numerical values, with the least value first and the greatest value last.
For more such questions on fractions
https://brainly.com/question/17220365
#SPJ8
When partitioning a line segment, what is the rational form of the ratio 2:3?
Update the answer is: 2/5.
Answer:
The rational form of the ratio 2:3 is 2/5
Step-by-step explanation:
For those of us who don't know or don't remember what rational means, it just means fraction, and in this case is asking as to convert ratio 2:3 into a fraction.
-First thing is to add the ratio:
2+3=5
-Now, we are going to place 5 as the denominator of the fraction, and we are going to keep the 2 from the ratio (it will always be the first number of our ratio, for example, if the ratio is 6:1 we'd be keeping the 6), and place it on the numerator place:
2:3 = 2/5
-So, that would be pretty much it, by the way, I know that the question was upgraded, but I don't mind to have 5 points more.
Please Solve, Thank you!
The graph which shows the interval notation of the inequality 3 > - x > - 7 is option C.
How to solve inequality using graph?3 > - x > - 7
Break the compound inequality into two and solve each
3 > - x
divide both sides by -1
-3 < x
- x > - 7
divide both sides by -1
x < 7
So the solution to the inequality is
-3 < x < 7
Therefore, it can be interpreted that x is greater than -3 and less than 7
Read more on inequality?
https://brainly.com/question/25275758
#SPJ1
Based on a survey, 33% of likely voters would be willing to vote by internet instead of the in-person traditional method of voting. For each of the following, assume that 12 likely voters are randomly selected. Complete parts (a) through (c) below.
a. What is the probability that exactly 9 of those selected would do internet voting? (round to 5 decimal places)
b. If of the selected voters would do internet voting, is 9 significantly high? Why or why not? (round to 5 decimal places)
(A). No, because the probability of or more is ---, which is low.
(B). Yes, because the probability of or more is ---, which is not low.
(C). No, because the probability of or more is ----, which is not low.
(D). Yes, because the probability of or more is ---, which is low.
c. Find the probability that at least one of the selected likely voters would do internet voting. (round to 3 decimal places)
Answer:
a. 0.00166
b. 0.00200
Overall B is correct because it has the prossibilty of getting more votes. 0.00200
Step-by-step explanation:
What is the length of leg s of the triangle below?
45
1012
A. 10-2
OB. 10
O C. 1
OD. 5√2
E 5
45
F. 5.6
Answer:
B
Step-by-step explanation:
