The graph of f(x) is shown below of g(x) and f(x) are inverse functions, which graph represents g(x)
Answer:
It's B
Step-by-step explanation:
Given that we have the graph of f(x), we want to see which one is the graph of its inverse. i just had that question and i got a 100 on it
find the exact value of the expression. cos π/16 cos 3π/16 - sin π/16 sin 3π/16
The exact value of the expression \(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16\ is\ (2 + \sqrt2)/4\).
How to simplify and evaluate expressions involving trigonometric functions?We can use the following trigonometric identity:
cos(a-b) = cos(a)cos(b) + sin(a)sin(b)
We have:
\(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16 \\= cos(3\pi /16 - \pi /16) \\= cos \pi /8\)
Now, using the half-angle identity \(cos(\theta/2) = ^+_-\sqrt{[(1 + cos \theta)/2]\), we can simplify cos π/8:
\(cos \pi /8 \\= cos(\pi /4 - \pi /8) \\= cos \pi /4\ cos \pi /8 + sin \pi /4\ sin \pi /8 \\= 1/\sqrt{2} \times \sqrt{[(1 + cos \pi /4)/2]} + 1/\sqrt{2} \times \sqrt{[(1 - cos \pi /4)/2]} \\= 1/\sqrt{2} \times \sqrt{[(1 + 1/\sqrt{2})/2]} + 1/\sqrt{2} \times \sqrt{[(1 - 1/\sqrt{2})/2] }\)
\(= 1/\sqrt{2} \times \sqrt{[(2 + \sqrt{2})/4] }+ 1/\sqrt{2} \times \sqrt{[(2 - \sqrt{2})/4]} \\= 1/2 \times \sqrt{(2 + \sqrt{2})} + 1/2 \times \sqrt{(2 - \sqrt{2})} \\= \sqrt{2}/2 + \sqrt{2}/2\sqrt{2} + \sqrt{2}/2 - \sqrt{2}/2\sqrt{2} \\= \sqrt{2}/2 + \sqrt{2}/4 \\= (2 + \sqrt{2})/4\)
Therefore, the exact value of the expression \(cos \pi /16\ cos 3\pi /16 - sin \pi /16\ sin 3\pi /16\ is\ (2 + \sqrt2)/4\).
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Given h(x) = -5x + 3, solve for x when h(x) = 3.
Answer:
x=0
Step-by-step explanation:
if
h(x)= -5x+3
h(x)= 3
then
-5x+3 = 3
solve for x
-5x=0
x=0
Find the maximum and minimum values of the function y = 2 cos(0) + 7 sin(0) on the interval [0, 27] by comparing values at the critical points and endpoints.
The maximum value of the function y = 2 cos(0) + 7 sin(0) on the interval [0, 27] is 7 and the minimum value is -2.
Here, the given function is y = 2 cos(0) + 7 sin(0). Now, we have to find the maximum and minimum values of the given function on the interval [0, 27] by comparing values at the critical points and endpoints. The given function is the sum of two functions: f(x) = 2cos(0) and g(x) = 7sin(0).Let's first consider the function f(x) = 2cos(0): The range of the function f(x) is [-2, 2].Let's now consider the function g(x) = 7sin(0): The range of the function g(x) is [-7, 7].Hence, the maximum value of y = f(x) + g(x) on the given interval is 7 and the minimum value is -2.
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A pet store owner, Brooklyn, needs to determine how much food she needs to feed the animals. Brooklyn knows that she needs to order the same amount of bird food as hamster food. She needs four times as much dog food as bird food and needs half the amount of cat food as dog food. If Brooklyn orders 600 packages of animal food, how much dog food does she buy? Let b represent the number of packages of bird food Brooklyn purchased for the pet store.
Answer:
She ordered 85.7 packages as dog food
Step-by-step explanation:
Let b represent bird food, d represent dog food and c represent cat food.
The bird food is 4 times as much dog food. This can be represented as b = 4d
Also, the dog food is half the amount of cat food, it can be represented as d = 1/2c. Therefore, c = 2d
The total feed is 600.
Therefore dog feed + cat feed + bird feed = 600
d + 2d + 4d = 600
7d = 600
d = 600/7 = 85,7
She ordered 85.7 packages as dog food.
Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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The given table shows the estimated number of internet users from 2001 to 2010. The number of users for each year is shown in millions.
Find the slope of the line segment that represents the change in internet users from the year 2004 to 2007
The slope of the line segment representing the change in internet users from 2004 to 2007 is approximately 133.33 million users per year.
To find the slope of the line segment representing the change in internet users from 2004 to 2007, we need to determine the change in the number of internet users and divide it by the change in years.
Given the table, let's look at the data for the years 2004 and 2007:
Year 2004: 800 million internet users
Year 2007: 1,200 million internet users
To find the change in the number of internet users, we subtract the number of users in 2004 from the number of users in 2007:
1,200 million - 800 million = 400 million.
Next, we need to determine the change in years. Since we are calculating the slope for a three-year period, the change in years is 2007 - 2004 = 3 years.
Finally, we can calculate the slope by dividing the change in the number of internet users by the change in years:
Slope = Change in number of internet users / Change in years
= 400 million / 3 years
≈ 133.33 million users per year.
Therefore, the slope of the line segment representing the change in internet users from 2004 to 2007 is approximately 133.33 million users per year.
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2) What does the rate of change represent in context of the data? A) The price of airfare increases by $0.30 for each mile traveled. The price of airfare decreases $0.30 for each mile traveled. ( The price of airfare increases by $0.70 for each mile traveled. D) The price of airfare decreases $0.70 for each mile traveled.
The graph relationship is betsween distance travelled and price of the airfare. The rate of change gives information on how one quantity changes in relation to another. The equation is given as
y = 0.7x + 200
The price of airfare increases by $0.70 for each miles travelled.
We can see that as the distance increases the price of airfare also increases.
What is the slope intercept ?
PLEASE HELP ME
Jessica used Fraction 2 over 3 yard of fabric to make a scarf. Can she make 2 of these scarves with Fraction 1 and 3 over 4 yards of fabric, and why?
Yes, because the quotient of Fraction 1 and 3 over 4division signfraction 2 over 3 is 2 and 5 over 8
No, because the quotient of Fraction 2 over 3division signFraction 1 and 3 over 4 is 1 and 2 over 12
No, because the quotient of Fraction 1 and 3 over 4division signfraction 2 over 3 is 1 and 2 over 12
Yes, because the quotient of Fraction 2 over 3division signFraction 1 and 3 over 4 is 2 and 5 over 8
Hey there mate ☺️!,
\( \frac{2}{3} \)yard of fabric = 2 feet of this fabric = which is used to make 1 scarf
\(1 \times \frac{3}{4} \) yards = ?
1 yard = 3 feet = 36 inches
\( \frac{3}{4} \) of 36
\( \frac{36}{4} \) = 9
→ 9 x 3 = 27
→ 36 + 27 = 63
Therefore, 63 inches of fabric means that she can make 2 scarves as 2 scarves would use 48 inches or 4 feet, since 1 scarf uses only 2 feet. She will also have 15 inches of extra fabric.
By Benjemin ☺️
What is the mode of 2 6 5 3 0 3 4 3 2 4 5 2 4?
The given values are 2,6,5,3,0,3,4,3,2,4,5,2,4
There are the following values as shown in the given data.
To find the mode first we have to assign each value that how many times it appears.
1. 2-3 the number 2 appears only Three times.
2. 6-1 the number 6 appears one time.
3. 5-2 the number 5 appears only two times.
4. 3-3 the number 3 appears only three times.
5. 0-1 the number 1 appears only one time.
6. 4-3 the number 4 appears only Three times.
So, the mode of the given data is 4,3,2 as it appears the most number of times.
If a given set of values with two modes is bimodal, a given set of numbers with three modes is trimodal, and any set of numbers with more than one mode is multimodal.
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Identify the slope and y-intercept. If the equation is in standard form, you may need to switch it to slope-intercept form. Sketch the graph of each line.
y = -4/ 5 x
Answer:
the slope is -4/5 and the y-intercept is 0
Step-by-step explanation:
All of the options are correct. Most economic data can be modeled as a higher-order ARMA(p, q) model. Spikes in the autocorrelation function indicate autoregressive terms. Spikes in the partial-autocorrelation function indicate moving-average terms. For an ARMA(p, q) model, both the autocorrelation and partial-autocorrelation functions show abrupt stops.
Actually, not all of the options are correct. The statement "Most economic data can be modeled as a higher-order ARMA(p, q) model" is not entirely accurate. While it is true that many economic time series exhibit some degree of autocorrelation and can be modeled using ARMA models, not all economic data can be accurately represented by these models.
In fact, some time series may require more complex models such as state-space models, VAR models, or GARCH models to capture the underlying dynamics.
Regarding the other statements:
Spikes in the autocorrelation function do indicate autoregressive terms, as autocorrelation measures the correlation between a time series and its past values.
Spikes in the partial-autocorrelation function do indicate moving-average terms, as partial-autocorrelation measures the correlation between a time series and its past values, controlling for the effects of intermediate lags.
For an ARMA(p, q) model, the autocorrelation function should show an abrupt stop at lag p, indicating the presence of p autoregressive terms. The partial-autocorrelation function should show an abrupt stop at lag q, indicating the presence of q moving-average terms.
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How to change variables to expressions?
Answer:
USE SOCRACTIC IT WOULD REALLY HELP
True or False:
8. V 40 has an infinite non-repeating decimal expansion.
9. The number 0.56 is a rational number
10. 200 and 500 are integers.
11. All numbers with infinite decimal expansions are irrational.
12.
the numbers -8, -3, 5, 17 are all whole numbers.
Answer:
Below.
Step-by-step explanation:
8. True ( all numbers of the form √n where n is not a perfect square have this property)
9. True ( we can write it as 56/100 or 14/25).
10. True.
11. False. ( 1/3 is rational and its decimal form is 0.333............. )
12. False. ( negative numbers are not whole numbers).
3 Find mLABC.
A
(50-x)
✓
B
80°
(2x + 40)°
D
Answer:
∠ ABC = 40°
Step-by-step explanation:
the 3 angles lie on a straight line ABE and sum to 180° , that is
50 - x + 80 + 2x + 40 = 180
x + 170 = 180 ( subtract 170 from both sides )
x = 10
Then
∠ ABC = 50 - x = 50 - 10 = 40°
PLAYGROUND There are 87 children at a playground. There are 23 more boys than girls. How many of each are at the playground?
Answer:
G=32 B=55
Step-by-step explanation:
55+32=87
I know this answer is right bc I got it right on my ws.
How do you tell if a pair of equations are parallel perpendicular or neither?
Two non-vertical lines in the same plane are said to be parallel if they have the same slope. No two parallel lines will ever cross. A set of non-vertical lines within the same plane are considered to be perpendicular if they meet at a right angle.
Perpendicular lines and parallel lines both meet at 90 degrees, although parallel lines never do. Lines are perpendicular if the slope of one line is equal to the reciprocal of the second line's negative slope.
Lines that have the same slope are therefore said to be parallel, and if the slope of one line is equal to the negative reciprocal of the slope of the other, the two lines are said to be perpendicular; otherwise, they are just intersecting lines.
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Students at a school went on a trip. The given equation models the total cost of the trip, where x is the number of students who went on the trip.
Answer:
50 students
Step-by-step explanation:
Students at a school went on a trip. The given equation models the total cost of the trip, where x is the number of students who went on the trip.
18x = 900
How many students went on the trip?
Given equation:
18x = 900
Where,
x = number of students who went on the trip
Number of students who went for the trip
18x = 900
x = 900/18
x = 50 students
Therefore, 50 students went for the trip
if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other. a) true b) false
The statement "if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other" is true. The dot product of two vectors is zero if and only if the vectors are perpendicular.
The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. When the dot product is zero, it means that the cosine of the angle between the vectors is zero, which occurs when the vectors are perpendicular.
In other words, the dot product being zero indicates that the vectors are at a 90-degree angle to each other, supporting the statement that they are perpendicular.
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10/ 6 2/3 please asap
Answer:
what is the symbol between the 2 fractions?
What is the probability of hitting
a blue square on this dartboard?
Answer:
Total area of Dartboard = 8×12 = 96
Area of blue squares = 3 × 2² = 12
Probability( hitting blue squares )= 12/96 = 1/8
write in standard form x2 + y = 2x -4
Answer:
y = - x² + 2x - 4
Step-by-step explanation:
The equation of a parabola in standard form is
y = ax² + bx + c ( a ≠ 0 )
Given
x² + y = 2x - 4 ( subtract x² from both sides )
y = - x² + 2x - 4 ← in standard form
list all the zeros whose multiplicity is odd
Answer:
degree 4odd multiplicity: -1, 4even multiplicity: -4f(x) = -(x +4)²(x +1)(x -4)Step-by-step explanation:
You want the zeros, their multiplicity, the degree, and the equation of the polynomial shown in the graph.
Axis crossingConsider a zero at x = 1, for example. This corresponds to a factor of (x-1).
For values of x > 1, this factor will be positive. For values of x < 1, this factor will be negative. The sign of the factor changes at x=1. The same will be true for any odd power of this factor. (The graph crosses the x-axis.)
Consider the same zero with even multiplicity. The factors corresponding to that zero will have even degree: (x-1)² or (x-1)⁴, for example. For values of x > 1, the sign of this term will be positive. For values of x < 1, the sign of this term will also be positive. The sign of the term does not change at x=1 for even multiplicity. (The graph does not cross the x-axis.)
DegreeThe degree of the polynomial will be the sum of the multiplicities of its zeros. From left to right, the zeros and their multiplicities are ...
-4, multiplicity 2-1, multiplicity 1+4, multiplicity 1The sum of the multiplicities is 2+1+1 = 4, so the least possible degree is 4.
Odd multiplicityFrom the above list, the zeros with odd multiplicity are ...
-1, 4
Even multiplicityThe zero with even multiplicity is ...
-4
EquationA polynomial of even degree has a U-shape, opening upward or downward. This graph opens downward, indicating the leading coefficient is negative. The least product of the found factors will be ...
f(x) = -(x +4)²(x +1)(x -4)
__
Additional comment
The attached graph shows the function with a scale factor that makes the graph approximate the one shown. With a leading coefficient of -1, the local minimum is considerably less than the value shown in the problem statement. Your function is constrained to have a leading coefficient of ±1, so the answer here has it as -1.
Please help!!
I have to find the slope of the blue line on the graph
Answer:
2
Step-by-step explanation:
Using points (0,0) and (2,4)
slope= (y2 - y1)/(x2 - x1)
= (4-0)/(2-0)
= 4/2
= 2
what is speaker? what is printer
Answer:
A speaker is a term used to describe the user who is giving vocal commands to a software program. ... A computer speaker is an output hardware device that connects to a computer to generate sound. The signal used to produce the sound that comes from a computer speaker is created by the computer's sound card
Step-by-step explanation:
rate nyoooo plssss
2. A supermarket display consists of boxes of cereal. The bottom row has 51 boxes. Each row has six fewer boxes than the row below it. The display has seven rows.
(a) Write and use a function to determine how many boxes are in the top row. Show your work.
(b) Use the appropriate formula to determine the number of boxes in the entire display. Show your work.
PLEASE ANSWER ASAP
Answer:
A
Step-by-step explanation
You need to multiply 6 times 7 and rest that to 51 the answer is 9
ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°, what is the value of m?
6
17
90
102
Answer:
The correct answer is option B. 17
Step-by-step explanation:
It is given that, ZX bisects ∠WZY. If the measure of ∠YXZ is (6m – 12)°
To find the value of m
From the figure we can see that, triangle WYZ is an isosceles triangle.
ZW = ZY
Then <YXZ = <WXZ = 90°
It is given ∠YXZ = (6m – 12)°
(6m – 12)° = 90°
6m = 90 + 12 = 102
m = 102/6 = 17
Therefore the value of m = 17
The correct answer is option B. 17
Answer:
its 17. so B
Step-by-step explanation:
just did it
When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 47 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 2 batteries do not meet specifications. A shipment contains 7000 batteries, and 2% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
The probability that this whole shipment will be accepted is (Round to four decimal places as needed.)
To calculate the probability that the entire shipment will be accepted, we need to determine the probability that at most 2 batteries do not meet specifications out of the 47 tested.
Let's define a binomial random variable X as the number of batteries that do not meet specifications out of the 47 tested. The probability of a single battery not meeting specifications is 2% or 0.02, and since each battery is tested independently, we have a binomial distribution.
Using the binomial probability formula, the probability mass function is given by:
P(X = k) = C(47, k) * (0.02)^k * (0.98)^(47-k)
To find the probability that at most 2 batteries do not meet specifications, we sum the probabilities for k = 0, 1, and 2:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Calculating these probabilities:
P(X = 0) = C(47, 0) * (0.02)^0 * (0.98)^47
P(X = 1) = C(47, 1) * (0.02)^1 * (0.98)^46
P(X = 2) = C(47, 2) * (0.02)^2 * (0.98)^45
We can now sum these probabilities to get the probability of accepting the whole shipment:
P(acceptance) = P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Calculating these probabilities and summing them will give us the answer.
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What is a formula for the nth term of the given sequence?
180, -240, 320...
im lost