A function of the form y= A sin (Bx-C)+D that has period 8, phase shift -2, and the range -12 ≤y≤-4 is y = 4 sin (π/4 x + π/2) - 8
To write a function of the form y = A sin (Bx - C) + D that has a period of 8 and phase shift of -2, we can use the general formula:
y = A sin [(2π/P)(x - C)] + D
where P is the period, C is the phase shift, and D is the vertical shift. In this case, P = 8 and C = -2, so we have:
y = A sin [(2π/8)(x + 2)] + D
Simplifying the equation, we get:
y = A sin (π/4 x + π/2) + D
To find the amplitude A and vertical shift D that satisfy the range -12 ≤ y ≤ -4, we can use the fact that the sine function oscillates between -1 and 1. If we set A = 4, then the maximum value of y is 4 + D, and the minimum value of y is -4 + D. To ensure that the range is -12 ≤ y ≤ -4, we need to choose D such that:
4 + D ≤ -4 and -4 + D ≥ -12
Solving these inequalities, we get:
-8 ≤ D ≤ 0
Therefore, a function that satisfies the given conditions is:
y = 4 sin (π/4 x + π/2) - 8
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What function is represented in the graph?
Select one:
У = 3(4^x)
y = 4(3^x)
y = 4(.25)^x
y = 2(.25^x)
Answer:
The correct function is y = 4(.25^x).
Select the correct answer.
Which graph represents the solution to this system of inequalities?
x+y<4
2x-3y²12
O A.
-10
y 10
-5
10
The two inequalities that the graph represents are:
y < -x + 4
y ≤ ²/₃x - 4
How to interpret the Inequality Graph?An inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
The formula for the equation of a line in slope intercept form is:
y = mx + c
where:
m is slope
c is y-intercept
The first inequality is the one with the dashed line and a y-intercept of 4 and so since shaded below line, we will use the symbol <.
The slope from two coordinates on the line (0, 4) and (4, 0) is:
(0 - 4)/(4 - 0) = -1
Thus, inequality is:
y < -x + 4
The first inequality is the one with the solid line and a y-intercept of -4 and so since shaded below line, we will use the symbol ≤.
The slope from two coordinates on the line (0, -4) and (6, 0) is:
(0 + 4)/(6 - 0) = 2/3
Thus, inequality is:
y ≤ ²/₃x - 4
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Four cars are for sale. The red car costs $15,000, the blue car costs $18,000, the green car costs $22,000, and the white car costs $20,000. Use the table to identify all possible samples of size n = 2 from this population and their sample minimums. The first sample is done for you.
Sample
n = 2 R, B R, G R, W B, G B, W G, W
Costs
($1000s) 15, 18 15, 22 15, 20 18, 22 18, 20 22, 20
Sample
Mean 15 15 15 18 18 20
What is the mean of all six sample minimums?
What is the value of the population minimum?
Is the sample minimum an unbiased estimator of the population minimum?
Answer:
Step-by-step explanation:The six sample minimums are 15, 15, 15, 18, 18, and 20.
To find the mean of all six sample minimums, we add them up and divide by 6:
(15 + 15 + 15 + 18 + 18 + 20) / 6 = 16.1667
So the mean of all six sample minimums is $16,166.67.
The population minimum is the smallest cost among the four cars, which is $15,000.
The sample minimum is a biased estimator of the population minimum. Since the samples are of size 2, the probability of obtaining the population minimum as the sample minimum is only 1/3 (when the minimum of the two cars selected is the population minimum). Therefore, the sample minimum tends to underestimate the population minimum.
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
The required statements that are true for the given function are mentioned below.
There are many possible statements that could be true for the function h, given the information provided. Here are a few examples:
is a linear function that passes through the points (-2, 2) and (8, 19).
h is a quadratic function that has a maximum value of 25 at x = 11.
h is a piecewise function that equals 1 for -3 ≤ x ≤ 0, 2x + 3 for 0 < x ≤ 4, and 19 - x for 4 < x ≤ 11.
h is a logarithmic function that equals 1 at x = -3 and approaches 25 as x approaches 11.
Each of these statements is consistent with the given domain, range, and function values at x = -2 and x = 8. There are many other possible statements that could be true for h as well.
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A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings Sauce (cups) Oregano (tsp)
5 15 two and a half
7
At this rate, how much sauce and oregano will be needed to make 7 servings?
The recipe will need 17 cups of sauce and three and a half teaspoons of oregano for 7 servings.
The recipe will need 21 cups of sauce and 5 teaspoons of oregano for 7 servings.
The recipe will need 21 cups of sauce and three and a half teaspoons of oregano for 7 servings.
The recipe will need 17 cups of sauce and 5 teaspoons of oregano for 7 servings.
The recipe will need 21 cups of sauce and three and a half teaspoons of oregano for 7 servings. The correct option is C.
How to calculate the valueThe sauce to oregano ratio for five servings is equal to 15 cups and 2.5 teaspoons, respectively. For a single portion of the recipe, this computes to 3 cups and 0.5 teaspoons.
It should be noted that to attain the correct amount needed for seven servings, simply multiply each part of the ratio by seven. Consequently, you should use 21 cups of sauce and three and one-half teaspoons of oregano. All together, this recipe requires 21 cups of sauce and three and a half teaspoons of oregano for 7 servings.
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Determine if the two expressions are equivalent and explain your reasoning. 9a+ 12 and 3(3a+4)
Yes because in the second expression, you use the distributive property, multiplying the 3 by the 3a and the 4 in parentheses. This equals 9a+12, which is the other expression
a museum closes in 4 1/2 hours. You walk to the museum and spend 3/4 hour at each of the first 3 exhibits. The museum closes after you spend another 1 1/2 hours at the museum. How long did it take you to walk to the museum
The total time taken to walk the museum is t = 3/4 of an hour
Given data ,
Let the time spent at the first 3 exhibits = 3/4 + 3/4 + 3/4 = 9/4 hours
Let the time spent at the museum after the first 3 exhibits = 1 1/2 = 3/2 hours
Total time spent at the museum = 9/4 + 3/2 = (9/4 + 6/4) = 15/4 hours
Since the museum closes after you spend a total of 4 1/2 hours at the museum, we can subtract the total time spent at the museum from the closing time to find the time it took you to walk to the museum:
Closing time - Total time spent at the museum = 4 1/2 - 15/4
On simplifying the equation , we get
A = 9/2 - 15/4
On subtracting the fractions , we get
9/2 - 15/4 = (18/4) - (15/4) = 3/4
Hence , it took you 3/4 hour, or 45 minutes, to walk to the museum
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Solve please! A pyramid with the sides of 2.24 cm and a height of 4 and the base of 3.
1. The diagram below shows the net of a pyramid with all its labeled sides.
2. The surface area; S = L + B
3. The total surface area = 22.44 cm².
How do we solve for the total surface area?To calculate the total surface area, we use the formula to find Area = (1/2) x b x h.
After we've found the area, we say
Total surface area = 1/2 x 2.24 x (3 x 4) + (3)²
= 22.44 cm²
The above answers are based on the full questions below;
A pyramid with the sides of 2.24 cm and a height of 4 and the base of 3.
1. Draw a net for the pyramid. Label all sides with measurement?
2. Write an expression for the surface area of the pyramid and then find the total surface area
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What is the equation for the line of reflection?
On a coordinate plane, triangle A B C has points (6, 3.7), (5.4, 2), (1, 3). Triangle A prime B prime C prime has points (3.7, 6), (2, 5.4), (3, 1).
The equation of line of reflection of the coordinates is
y = x
What is line of reflection?Mathematics gives the concept of a line of reflection, otherwise known as a line of symmetry. This line acts as a mirror for any figure, where when shown through its reflection, the image becomes congruent to the initial shape.
In simpler words, the line of reflection is like an invisible partition that accurately segments a figure into two identical halves, each resembling the other in more ways than one.
The image is attached and upon investigation shows that the equation of y = x matches the equation of line of reflection
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A bushel of apples costs $15.00 in the U.S. The same apples cost 1,600 yen in Japan. If the exchange rate is 80 yen per dollar, what is the real exchange rate? Is there a possibility for arbitrage? Explain and defend your answer.
The real exchange rate is 0.75.
It is not possible to make a profit by buying apples in one country and selling them in another.
We have,
To find the real exchange rate, we need to compare the price of apples in the two countries in terms of their respective currencies.
In the U.S., a bushel of apples costs $15.00.
In Japan, the same apples cost 1,600 yen.
Using the exchange rate of 80 yen per dollar, we can convert the cost in yen to dollars:
1,600 yen / 80 yen per dollar
= $20.00
So, the price of a bushel of apples in Japan is equivalent to $20.00 in the U.S.
The real exchange rate is the ratio of the prices of the same goods in two different countries, taking into account the exchange rate.
In this case, the real exchange rate is:
Real exchange rate = Price in U.S. / Price in Japan
= $15.00 / $20.00
= 0.75
This means that it takes 0.75 U.S. dollars to buy the same goods in Japan which would cost 1 Japanese yen.
To determine if there is an arbitrage opportunity, we need to compare the real exchange rate with the actual exchange rate.
If the real exchange rate is greater than the actual exchange rate, there is an arbitrage opportunity for someone to buy the good in one country and sell it in another country for a profit.
However, if the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.
In this case,
The real exchange rate is 0.75, while the actual exchange rate is 80 yen per dollar, or 0.0125.
Since the real exchange rate is less than the actual exchange rate, there is no arbitrage opportunity.
Therefore,
The real exchange rate is 0.75.
It is not possible to make a profit by buying apples in one country and selling them in another.
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if I made a profit of $3,250 after selling stocks for $10,500 after 4 years what was my average annual percentage game.
Answer:
To calculate the average annual percentage gain, we need to use the formula:
Average annual percentage gain = ((Ending value / Beginning value)^(1/n) - 1) x 100%
where:
- Ending value = the value of the investment at the end of the period
- Beginning value = the value of the investment at the beginning of the period
- n = the number of years
In this case, the beginning value of the stocks is not given, so we cannot calculate the exact average annual percentage gain. We only know the profit and the ending value. However, we can make an estimate assuming that the profit is equal to the gain, i.e., there were no transaction costs or other fees.
If the profit was $3,250 and the ending value was $10,500, then the beginning value was:
Beginning value = Ending value - Profit
Beginning value = $10,500 - $3,250
Beginning value = $7,250
The number of years is given as 4.
Using the formula above, we can estimate the average annual percentage gain as:
((10,500 / 7,250)^(1/4) - 1) x 100%
= (1.1267^(0.25) - 1) x 100%
= (1.0266 - 1) x 100%
= 0.0266 x 100%
= 2.66%
Therefore, the estimated average annual percentage gain is 2.66%.
Step-by-step explanation:
Find the measure of the exterior angle 1
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Answer: C: 144
Step-by-step explanation:
First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.
Next subtract this from 180 to find the exterior angle.
180- 36 = 144 degrees
thats the meaure of the exterior angle!
Answer:144
First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.
Next subtract this from 180 to find the exterior angle.
180- 36 = 144 degrees
Your goal is to create a college fund for your child. Suppose you find a fund that offers an APR 6% of . How much should you deposit monthly to accumulate $ 85,000 in 18 years?
Monthly you should deposit approximately $241 to accumulate $ 85,000 in 18 years.
Given that,
f = 85000
r = 6% = 0.06/12 = 0.005
n = 17×12 = 204
We know that, a = (f×r)/((1+r)ⁿ⁻¹)
a is the annuity.
f is the future amount.
r is the interest rate per time period.
n is the number of time periods.
Here,
a = (85000×0.005)/((1.005)²⁰⁴⁻¹)
a = 240.6356536
a ≈ $241
Therefore, monthly you should deposit approximately $241 to accumulate $ 85,000 in 18 years.
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631 in 2013 and 877 in 2014 what is the increase
The percent increase from 2013 to 2014 is given as follows:
39%.
How to obtain the percent increase?The percent increase from 2013 to 2014 is obtained applying the proportions in the context of the problem.
The amounts were of 631 in 2013 and 877 in 2014, hence the percentage of 2014's amount relative to 2013's amount is given as follows:
877/631 x 100% = 139%.
The initial amount has a percentage of 100%, hence the percent increase from 2013 to 2014 is given as follows:
139% - 100% = 39%.
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What is the meaning of "there is some [tex]k \in I[/tex] such that [tex]D_{i}\subseteq D_{k}[/tex] and [tex]D_{j}\subseteq D_{k}[/tex]?
The given statement "there is some k∈I such that [tex]D_{i}[/tex]⊆[tex]D_{k}[/tex] and [tex]D_{j}[/tex]⊆[tex]D_{k}[/tex]means that there is a set [tex]D_{k}[/tex] in a collection of sets I that contains all the elements of both sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex].
For example, let's say we have a collection of sets I that includes sets A, B, C, D, E, and F. If we have two sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex], where [tex]D_{i}[/tex] is the set of all even numbers, and [tex]D_{j}[/tex] is the set of all positive integers less than or equal to 10, then we can say that there exists a set [tex]D_{k}[/tex] in I that contains both [tex]D_{i}[/tex]and [tex]D_{j}[/tex] as subsets.
In this case, the set [tex]D_{k}[/tex] could be the set of all even positive integers less than or equal to 10. This set contains all the elements of [tex]D_{i}[/tex] and [tex]D_{j}[/tex], making them both subsets of [tex]D_{k}[/tex]. The statement "there is some k belongs I such that [tex]D_{i}[/tex] is a subset of [tex]D_{k}[/tex] and [tex]D_{j}[/tex] is a subset of [tex]D_{k}[/tex]" is a way to express this relationship between the sets.
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Drag the tiles to the boxes to form correct pairs.
Find the sum of each pair of vectors and match it with the magnitude of the resultant vector.
The dragging of the tiles to the appropriate places is given below.
How to explain the information1. 5.83 m/s > magnitude 4.5 m/s, direction angle 55˚ magnitude 3m/s, direction angle 135°
2. 4.05 m/s > magnitude 3.5 m/s, direction angle 35˚ magnitude 4 m/s, direction angle 150˚
3. 5.29 m/s > magnitude 6 m/s, direction angle 120˚ magnitude 2 m/s, direction angle 240˚
4. 3.32 m/s > magnitude 3 m/s, direction angle 70° magnitude 5 m/s, direction angle 210˚
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i need help asap!!!
Part C
Determine the meanmedianstandard deviation, and interquartile range for each data setThen, use the graphing tool to determine the value of the standard deviation
Using the statistical tool, the following were arrived at:
Standard Deviation = 4.68737.Mean = 9.6Median = 9IQR = IQR = Q3-Q1 = 12 - 7 = 5.What is the definition of Interquartile Range (IQR)?It should be noted that when arranged from lowest to highest, the IQR represents the central 50% of values.
Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).
These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.
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help help help help help help
for a new customer top golf charges $10 for a player card and $2 per hour. write and solve a linear equation to find the cost for a new customer to rent a bay for 6 hours.
A linear equation to find the cost for a new customer to rent a bay is y = 2x + 10.
The cost for a new customer to rent a bay for 6 hours is equal to $22.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about the amount of money top golf charges a new customer, the cost can be modeled by this linear equation:
y = mx + c
y = 2x + 10
When x = 6 hours, the cost can be calculated as follows;
y = 2x + 10
y = 2(6) + 10
y = $22.
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1. Find the area. 15 cm summ · 12 cm 20 cm
It seems there are two numbers missing between "15 cm summ" and "12 cm". Please provide the complete values so I can help you solve the problem.
Find the 7th term of the geometric sequence whose common ratio is 2/3 and whose first term is 8
we know that general term for gp is [tex]a_{n}[/tex] = a [tex]r^{n-1}[/tex]
where r = common ratio
a = first term
putting values we get
8th term = 8x 64/729
= 0.702
hence the 8th term is 0.702
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You have 979,584 grams of a radioactive kind of argon. If its half-life is 2 hours, how much
will be left after 10 hours?
Answer:
Step-by-step explanation:
John needs to paint one wall in his school. He knows that 1 can of paint covers 24 square feet.
Since John cannot buy a fraction of a can, he needs to round up to the nearest whole number. So, John needs at least 5 cans of paint to cover the entire wall as per the height and length.
To calculate the area of the wall, we need to multiply the height and the length of the wall.
From the diagram, we can see that the height of the wall is 2 meters and the length is 5 meters.
So the total area of the wall is:
Area = height x length
Area = 2 meters x 5 meters
Area = 10 square meters
To convert this to square feet, we can use the conversion factor:
1 square meter = 10.764 square feet
So:
Area = 10 square meters x 10.764 square feet/square meter
Area = 107.64 square feet
Since 1 can of paint covers 24 square feet, John needs:
Number of cans = Area ÷ Coverage per can
Number of cans = 107.64 square feet ÷ 24 square feet/can
Number of cans = 4.485 cans
Thus, John needs at least 5 cans of paint to cover the entire wall.
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Your question seems incomplete, the probable complete question is:
John needs to paint one wall in his school. He knows that 1 can of paint covers an area of 24 square feet.
John uses a meter stick to measure the dimensions of the wall as shown.
[1 meter = approximately 39 inches]
What is the fewest number of cans of paint John can use to paint the wall?
Find the missing angle
Answer:
none
Step-by-step explanation:
None, 106 is from the numbers being added and it is a right angle
Solve the following for θ, in radians, where 0≤θ<2π.
−6sin2(θ)−5sin(θ)+3=0
Answer:correct answers 0.42
2.73
Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):
-6u^2 - 5u + 3 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = -6, b = -5, and c = 3. Substituting these values, we get:
u = (5 ± sqrt(5^2 - 4(-6)(3))) / 2(-6)
u = (5 ± sqrt(109)) / (-12)
Therefore, either:
sin(θ) = (5 + sqrt(109)) / (-12)
or:
sin(θ) = (5 - sqrt(109)) / (-12)
you collect $20.92 for selling 4 video games and 2 cellphones on a website. Your friend collects $23.44 for selling 4 video games and 3 cell phones on a website. How much do you collect for each videogame
Let's call the cost of each video game "x". We can set up two equations based on the information given:
4x + 2(0.01) = 20.92 (the 0.01 represents the commission fee for each phone)
4x = 20.92 - 0.02
4x = 20.90
x = 5.225
So each video game costs $5.225.
We can double-check our answer using the information about the friend's sales:
4(5.225) + 3(0.01) = 23.44
20.90 + 0.03 = 23.44
23.44 = 23.44
So our answer is correct.
Office Services An auto mechanic has total receipts of $1861.16 for a certain day. He determines that $1240 of this is labor. The remaining amount is for parts plus 6% sales tax on the parts only. Find the amount of the sales tax he collected.
The amount of sales tax he collected from the office services would be =$658.43
How to calculate the amount of sales tax?To calculate the amount of sales tax,the percentage tax amount should be determined as follows.
The total receipts from the office services = $1861.16
The amount that is for labor = $1240
The amount for parts = 1861.16-1240
= $621.16
The tax amount = 6/100 × 621.16
= 3726.96/100
= $37.27
Therefore the amount sale tax = 621.16+37.27 = $658.43
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Tan(x) times cos(x) simplify it to single trig
Using trigonometric identities, the given expression, tan(x) × cos(x), simplified to a single trigonometry is sin(x)
Simplifying trigonometric identitiesFrom the question, we are to simplify the given trigonometric expression
From the given information
The given expression is
tan(x) × cos(x)
From trigonometric identities, we know that
tan(x) = sin(x) / cos(x)
Now,
Substituting this value in the given expression
tan(x) × cos(x)
We get
sin(x) / cos(x) × cos(x)
Simplifying further
sin(x) / cos(x) × cos(x) = sin(x)
Hence,
The simplified expression is sin(x)
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The phone case you want to buy is marked down 30%, and you have a 25% off coupon. You pay $42.00. Can this equation be used to find the original price of the phone case? If so, what is the original price of the item? Explain
Answer:
meaning that you're answer would be $7.34 please make brainliest
Step-by-step explanation: