The caloric content for ice cream C is 250 calories while the caloric content for ice cream B is 270 calories.
How to determine the caloric contentTo determine the caloric content, we will assign algebraic notations to each of the dessert types.
1 Icecream + 2 Blueberry pie = 790 calories
3 icecream + 2 Blueberry pie = 1290 calories
Now the first equation will be subtracted from the second equation as follows:
2 icecream = 500 calories
So, 1 ice cream is 250 calories.
Also, since, 1 icecream serving equals 250 calories, 2 Blueberry pies = 790 - 250 = 540 calories, and 1 Blueberry pie equals 270 calories.
Complete question:
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories. Find the caloric content of each item.
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(-6,-4), (0, -4), and (2,-4)
What is the equation of this line?
Answer: y = -4
Step-by-step explanation:
Based on these three given points, we can tell that this line is a horizontal line because there is no slope. All of the points have the same y-value, -4.
This means the equation of the line is:
y = -4
See attached for a visual representation. I have graphed the given points over the top of the equation we wrote for the line.
The parent function f ( x ) = 3 √ x is transformed to g ( x ) = 2 f ( x − 3 ) Which is the graph of g ( x ) ?
The graph of the function g(x) has an equation of g(x) = 6√(x - 3)
Identifying the graph of the function g(x)?From the question, we have the following parameters that can be used in our computation:
f(x) = 3√x
The transformed function g(x) is given as
g(x) = 2f (x − 3)
In f(x) = 3√x , we have
f(x - 3) = 3√(x - 3)
Multiply both sides by 2
So, we have
2f(x - 3) = 2 * 3√(x - 3)
Evaluate the products
2f(x - 3) = 6√(x - 3)
Recall that
g(x) = 2f (x − 3)
So, we have
g(x) = 6√(x - 3)
This means that the graph of the function g(x) has an equation of g(x) = 6√(x - 3)
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Find the areas of the trapezoids.
The areas of the trapezoids is,
A = 48 sq units.
Since, The formula to find the area of a trapezoid of a trapezoid is,
⇒ A = 1/2(b₁ + b₂ )h.
Hence, it is stated that the height of each unit is 2.
Now let's substitute the variables in the formula with the actual bases and heights as;
A = 1/2(8 + 4)8,
A = 6 × 8,
A = 48 sq units.
Thus, the areas of the trapezoids is,
A = 48 sq units.
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m ∠ � = ( � + 21 ) ∘ ∠A=(x+21) ∘ and m ∠ � = ( 4 � − 30 ) ∘ ∠B=(4x−30) ∘ , then find the measure of ∠ � ∠B.
The measure of angle B is given as follows:
m < B = 49.2º.
What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
The measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.As the angles are complementary, the value of x is obtained as follows:
x + 21 + 4x - 30 = 90
5x - 9 = 90
5x = 99
x = 19.8.
Hence the measure of angle B is obtained as follows:
m < B = 4 x 19.8 - 30
m < B = 49.2º.
Missing InformationThe measures are given as follows:
m < A = (x + 21)ºm < B = (4x - 30)º.The angles are complementary, and it asks for the measure of angle B.
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A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 4.5 ft by 11.5 ft by 10.5 ft. The container is entirely full. If, on average, its contents weigh 0.4 pounds per cubic foot, and, on average, the contents are worth $4.60 per pound, find the value of the container’s contents. Round your answer to the nearest cent.
The value of the container's contents is approximately $983.25
What is the value of the container's contents?To find value of the contents, we must calculate its volume first.
Volume = length x width x height
Volume = 4.5 ft x 11.5 ft x 10.5 ft
Volume = 534.375 cubic feet
The container is full and its contents have a volume of 534.375 cubic feet. If its contents weigh 0.4 pounds per cubic, then, total weight of the contents is:
= Volume x Weight per cubic foot
= 534.375 cubic feet x 0.4 pounds per cubic foot
= 213.75 pounds
If the contents are worth $4.60 per pound on average, then the total value of the contents is:
= Weight x Value per pound
= 213.75 pounds x $4.60 per pound
= $983.25.
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a grocery store sells a 7 oz bag of raisins for $1.10 and a 9oz bag of raisins for $1.46. Which size bag has the lower price per ounce?
To determine which size bag has the lower price per ounce, we need to calculate the price per ounce for each bag.
For the 7 oz bag, the price per ounce is:
1.10 / 7 = 0.1571
For the 9 oz bag, the price per ounce is:
1.46 / 9 = 0.1622
Therefore, the 7 oz bag has the lower price per ounce, at approximately $0.16 per ounce, compared to the 9 oz bag at approximately $0.16 per ounce. So, if the goal is to get the most value for your money, it would be better to purchase the 7 oz bag of raisins.
y=7x-3 what slope and y intercept
Answer:
Slope = 14.000/2.000 = 7.000 x-intercept = 3/7 = 0.42857 y-intercept = -3/1 = -3.00000
y intercept = -3
slope = 7/1
The parent function is reflected across the x-axis and compressed by a factor 0.5
The rule used to obtain the transformed function is given as follows:
g(x) = -0.5f(x).
What are transformations on the graph of a function?Examples of transformations are given as follows:
Translation: Translation left/right or down/up.Reflections: Over one of the axes or over a line.Rotations: Over a degree measure.Dilation: Coordinates of the vertices of the original figure are multiplied by the scale factor.The parent function in this problem is given as follows:
f(x).
The parent function is reflected across the x-axis, hence:
g(x) = -f(x).
The parent function is also compressed by a factor 0.5, hence:
g(x) = -0.5f(x).
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PLSSS.the function : ℝ → ℝ, () = 2^, : (0; +∞) → ℝ, () = √4 + 1 + 1.show
that the graphs of the functions and intersect at the abscissa point x=2
[tex]f(2) = g(2) = 4[/tex], which means that the graphs of the two functions intersect at x = 2.
What is the abscissa point?To show that the graphs of the functions [tex]f(x) = 2^x[/tex] and [tex]g(x) = \sqrt(4x + 1) + 1[/tex] intersect at the abscissa point x = 2, we need to show that both functions have the same value at [tex]x = 2.[/tex]
First, we evaluate f(2):
[tex]f(2) = 2^2 = 4[/tex]
Next, we evaluate g(2):
[tex]g(2) = \sqrt(4(2) + 1) + 1 = \sqrt9 + 1 = 4[/tex]
Therefore, [tex]f(2) = g(2) = 4[/tex] , which means that the graphs of the two functions intersect at [tex]x = 2[/tex] .
To visualize this, we can plot the two functions on the same set of axes:
As we can see from the graph, the two curves intersect at the point (2, 4).
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The complete question is: How can you show that the graphs of the functions f(x) = [tex]2^x[/tex] and g(x) = √(4x + 1) + 1 intersect?
The company performed another experiment in which they tested three website designs to see which one would lead to the highest probability of a purchase. The first (design A) used enhanced product information, the second (design B) used extensive iconography, and the third (design C) allowed the customer to submit their own product ratings. After 6 weeks of testing, the designs delivered probabilities of purchase of 4.5%, 5.2%, and 3.8% respectively. Equal numbers of customers were sent randomly to each website design. what is the probability that a customer who visited made a purchase?
The probability that a customer who visited any of the three website designs made a purchase is 4.5%.
To find the probability that a customer who visited any of the three website designs made a purchase, we need to find the average probability of purchase across all three designs.
We can do this by taking the mean of the three probabilities:
Mean probability = (4.5% + 5.2% + 3.8%) / 3
= 13.5% / 3
= 4.5%
This assumes that the customers were randomly assigned to each design and that there were no other factors that may have influenced their purchasing behavior. Additionally, the sample size and duration of the experiment may also affect the accuracy of the results.
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Marcus looked up the path that he had taken on his run this morning on the map shown below.
To the nearest mile, the distance that Marcus ran is 6 miles.
How to calculate the distanceTo calculate the total distance that Marcus ran in the morning, we will sum up the distance for all the routes that he ran.
From the map, the distances that Marcus ran are as follows:
1 inches + 3 inches + 2 inches + 3 inches
= 8.3 inches
The scale then shows that 4 inches equal 3 miles. Now, we convert 8.3 inches to miles and this gives us:
8.3 inches × 3 miles/4 inches
= 6.225
To the nearest miles, this is 6 miles.
Complete Question:
Marcus looked up the path that he had taken on his run this morning on the map shown below.
To the nearest mile, what is the total distance that he ran?
6 miles
8 miles
11 miles
25 miles
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AP calc please help me
a) over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.
b) the average temperature of the water in the system is 1527.
c) over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.
a) g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt
g'(-3) = -2
b) The absolute maximum value of g on the closed interval [-5, 5]=
10 + 2√7.
c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.
What is right Riemann sum formula?
The right Riemann sum formula uses the right-most value of each interval as the value of the function over that interval.
a) g(5) = 2(5) + [tex]\int\limits^5_0[/tex] ƒ(t) dt
= 10 + 2√7
g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt
g'(-3) = 2 + [tex]\int\limits^3_0[/tex]ƒ'(t) dt
= 2 - (4 + 0)
= -2
b) The absolute maximum value of g on the closed interval [-5, 5]=
10 + 2√7.
This is because the highest value of ƒ(t) dt on the interval= 4√7, which occurs at x = 2.
The highest value of g is thus given by 10 + 2√7.
c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.
This is because ƒ'(t) dt is undefined at these points, so the second derivative of g is also undefined.
a) To evaluate the S'(t) dt, we need to calculate the area under the curve of the temperature data given in the table. To do this, we use the trapezoidal rule. This gives us the following:
[tex]\int\limits^10_0[/tex] S'(t) dt = [(142 + 210 + 254 + 280 + 274 + 268)/2] × 8
= 17,088
This means that over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.
This can be interpreted in the context of the problem as the average rate at which the temperature of the water in the solar steam power system is changing over the given time interval.
b) To approximate the average temperature of the water in the system using a right Riemann approximation, we need to calculate the area under the curve of the temperature data given in the table. We can do this using the right Riemann sum formula, which gives us the following:
Right Riemann Approximation = [(210 + 254 + 280 + 274)/4] × 6 = 1527
In this case, the right-most value of each interval is lower than the true average over that interval, so the approximation will be lower than the true average.
c) To determine the total change in the temperature of the system for the interval 10≤t≤20, we need to calculate the area under the curve of the equation S'(t)=-√2xe (√x²-100)/x.
This can be done using the definite integral of the equation, which gives us the following:
Total Change = ∫1020-√2xe (√x²-100)/x dx
= -14,351
This means that over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.
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7) If a professor can grade 5 essays in 40 minutes, the professor can grade 32 essays in 256 minutes. (10pts)
O True
O False
Answer:
O True
Step-by-step explanation:
Unit rate of essays/minute:
40 minutes / 5 essays = 8 essays/minute
256 essays / 32 minutes = 8 essays/minute
The unit rates are equal.
Answer: O True
Correct answer gets brainliest!!!!
Answer: I believe the only option would be Length.
The length determines the distance between the two endpoints.
I can't think of a reason why you'd need to use height or width when measuring a line on a graph. Besides if it were height, it'll just be the length of the line when vertical. And all generated graphed lines have the same width. You wouldn't need to measure it.
Hopefully it's correct.
need help asap
How many square feet of outdoor carpet will
we need for this hole?
3 ft
2 ft
12 ft
,1 ft
2 ft
ft²
The area needed for the green region is 40 square feet.
How to find the area?To do so, we can take the area of the whole green area, and then remove the areas of the two holes.
Remember that the area of any rectangle is the product of the two dimensions.
For the green one:
A = 4ft*12ft = 48 ft²
Removing the two areas for the holes we have:
a1 = 3ft*2ft = 6ft²
a2 = 1ft*2ft = 2ft²
Remove that:
green area= 48 ft² - 6ft² - 2t² = 40ft²
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Riley runs a stable that boards a range of horses.
white 3
bay 2
palomino 9
black 1
Considering this data, how many of the next 20 horses that come to board should you expect to be white horses?
_____ white horses
Since there are 3 white horses in a total of 15 horses, the ratio of white horses, to the total number of horses are 1 : 5 So for 20 total number of horses, the number of white horses should be 4. The ratio of white horses to the total number of horses is 4 : 20 which is 1: 5
Therefore, 4 of the next 20 horses that come to board should you expect to be white horses
2x+15-8=14
find the value of x
Answer:
x = 3.5
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, simplify. Combine like terms. Like terms are terms that share the same amount of the same variables:
[tex]2x + 15 - 8 = 14\\2x + (15 - 8) = 14\\2x + (7) = 14[/tex]
Next, isolate the variable, x. First, subtract 7 from both sides of the equation:
[tex]2x + 7 = 14\\2x + 7 (-7) = 14 (-7)\\2x = 14 - 7\\2x = 7[/tex]
Finally, divide 2 from both sides of the equation:
[tex]2x = 7\\\frac{(2x)}{2} = \frac{(7)}{2}\\ x = \frac{7}{2}\\ x = 3.5[/tex]
x = 3.5 is your answer.
~
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Answer:
[tex]\bold{\Large \boxed{x=\frac{7}{2}}}[/tex]
Step-by-step explanation:
To solve the equation [tex] 2x+15-8=14 [/tex] for x, we need to isolate x on one side of the equation.
We can do this by first combining the constants on the right-hand side of the equation:
[tex]2x+15-8=14[/tex]
[tex]2x+7=14[/tex]
Next, we can isolate x by subtracting 7 from both sides of the equation:
[tex]2x=7[/tex]
Finally, we can solve for x by dividing both sides of the equation by 2:
[tex]x=\frac{7}{2}[/tex]
Therefore, the solution to the equation [tex]2x+15-8=14[/tex] is [tex]\bold{x=\frac{7}{2}}[/tex].
help with this question
Charges for advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is a percentage of the population of 110 million TV households. The CBS television show 60 Minutes recently had a rating of 7.8, indicating that 7.8% of the households were tuned to that show. An advertiser conducts an independent survey of 100 households and finds that at least b+1 were tuned to 60 Minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting at least 5+1 tuned to
60 Minutes.
The probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes is only 0.02%.
How to calculate the probabilityP(X <= 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
P(X = k) = (100 choose k) * 0.078^k * (1 - 0.078)^(100-k)
P(X <= 4) = (100 choose 0) * 0.078^0 * (1 - 0.078)^(100-0) + (100 choose 1) * 0.078^1 * (1 - 0.078)^(100-1) + (100 choose 2) * 0.078^2 * (1 - 0.078)^(100-2) + (100 choose 3) * 0.078^3 * (1 - 0.078)^(100-3) + (100 choose 4) * 0.078^4 * (1 - 0.078)^(100-4)
Using a calculator or software, we can find that:
P(X <= 4) = 0.000203
This means that the probability is 0.02%.
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Charges for TV advertising on a TV show are based on the number of viewers, which is measured by the rating. The rating is the percentage of population of 110 million TV households.The CBS television show 60 minutes recently had a rating of 7.8, indicating that 7.8% of the household were tuned to that show.An advertiser conducts an independent survey of 100 households and finds that only 4 were tuned to 60 minutes. Assuming that the 7.8 rating is correct, find the probability of surveying 100 randomly selected households and getting 4 or fewer tuned to 60 minutes.Does the result suggest that the rating of 7.8 is too high?
Suppose in an orchard the number of apples in a tress is normally distributed with a mean of 300 and a standard deviation of 30 apples. Find the probability that a given tree has between 300 and 390 apples.
Using a normal distribution calculator and entering the mean as 300, the standard deviation as 30 and the range (300 to 390), the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.
How the probability is determined:Probability refers to the chance or likelihood that an expected event occurs out of many possible events.
Probability lies between 0 and 1, depending on the degree of certainty.
Mean = 300
Standard deviation = 30
Range = 300 to 390
Thus, the probability that a given tree has between 300 and 390 apples is 0.4987 or 49.87%.
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A soccer ball is kicked in the air off a 27.0-meter high hill. The equation h(t) = -2t^2 + 4t + 27 gives the approximate height h, in meters, of the ball t in seconds after it is kicked. Does the ball reach a height of 40 m?
The ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.
To determine if the ball reaches a height of 40 meters, we can substitute h(t) = 40 into the equation and solve for t.
40 = -2t² + 4t + 27
Rearranging the terms, we get:
2t² - 4t - 13 = 0
We can solve for t using the quadratic formula:
t = [4 ± √(4² - 4(2)(-13))]/(2(2))
t = [4 ± √(176)]/4
t ≈ 3.38 or t ≈ -0.88
Since time cannot be negative, we can discard the negative solution. Therefore, the ball reaches a height of 40 meters at approximately 3.38 seconds after it is kicked.
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Which is a recursive formula for this geometric sequence?
-18
, -14
, -12
, -1, . . .
The recursive formula for the geometric sequence is given as follows:
[tex]a_1 = -\frac{1}{8}[/tex][tex]a_n = 2a_{n - 1}[/tex]What is a geometric sequence?A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.
The first term of the sequence is given as follows:
[tex]a_1 = -\frac{1}{8}[/tex]
Each term is the previous term multiplied by two, hence the common ratio is given as follows:
q = 2.
Then each term is the previous term multiplied by two, and the recursive rule is given as follows:
[tex]a_n = 2a_{n - 1}[/tex]
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find the value of x in the cube
Answer:
3√3 ft or 5.20 ft
Step-by-step explanation:
The main diagonal of any cube can be found by multiplying the length of one side by the square root of 3. Where “x” is the cube side.
x = L × √3
x = 3 × √3
x = 3 × 1.7
x = 5.20 ft
There are 15 tables at a wedding reception,
5 of which have purple centerpieces.
1) What is the probability that a randomly
selected table will have a purple centerpiece?
◄) Write your answer as a fraction or whole
number.
Answer:
1/3
Step-by-step explanation:
There are 15 tables and 5 have a purple centerpiece. Divide 15 by 5 to get the probability of a randomly selected table being purple.
5/15 is 5 out of 15. 5/15 simplifies to 1/3.
NEED HELP FOR MATH HW! I need some help number 3 WITHOUT the use of a t1-83
Step-by-step explanation:
Here is a graph from Desmos....you should be able to see where the function is > 0
Mariana is making a large pot of pasta. She mixes together 518 pounds of pasta, 6 pounds of sauce, and 478
pounds of onions.
To find out how many 12
pound servings can she make, which two equations would you need?
A.
518+478+6=16
B.
518+478−6=4
C.
4÷12=8
D.
16÷12=32
E.
16×12=8
We need to use equations C and D:
C. 4 ÷ 12 = 1/3
D. 16 ÷ 12 = 4/3
To find out how many 12-pound servings Mariana can makeWe need to divide the total amount of pasta by 12. Therefore, we need to use equations C and D:
C. 4 ÷ 12 = 1/3
D. 16 ÷ 12 = 4/3
Equation C shows that each serving is 1/3 of a pound
Equation D shows that Mariana can make 4/3 servings
Therefore, Mariana can make 4/3, or approximately 1.33, servings of 12 pounds each.
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What is the answer to this ?
Answer:
Triangle P has been rotated clockwise by 90° about the point (0,0).
PLEASE MARK IT THE BRAINLIEST!!!!
Kadeesha borrowed some money from her friend in order to help buy a new video
game system. Kadeesha originally borrowed $120 and agreed to pay back her friend
$8 per week. Make a table of values and then write an equation for L, in terms of t,
representing the amount Kadeesha owes her friend after t weeks.
Number of Weeks Amount of Money Owed
0
1
2
3
You must answer all questions above in order to submit.
attempt 1 out of 2
An equation for L, in terms of t, representing the amount Kadeesha owes her friend after t weeks is L = 8t + 120.
The table of values is as follows;
Number of Weeks Amount of Money Owed
0 $120
1 $128
2 $136
3 $144
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would assign variables to the amount of money that Kadeesha borrowed originally and the number of weeks respectively, and then translate the word problem into a linear equation as follows:
Let the variable L represent amount of money that Kadeesha owed.Let the variable t represent number of weeks.Since Kadeesha originally borrowed $120 and agreed to pay back her friend $8 per week, a linear equation which can be used to model the total amount of money that Kadeesha owed is given by;
L = 8t + 120
When t = 0, the value of L is given by;
L = 8(0) + 120
L = $120.
When t = 1, the value of L is given by;
L = 8(1) + 120
L = $128.
When t = 2, the value of L is given by;
L = 8(2) + 120
L = $136.
When t = 3, the value of L is given by;
L = 8(3) + 120
L = $144.
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The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
Group of answer choices
x = 0°, 30°, 150°, 180°
x = 0°, 180°, 210°, 330°
x = 30°, 90°, 150°, 270°
x = 90°, 210°, 270°, 330°
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
How to solveFor the frequencies to be the same, we need to find values of n and m such that:
n = m
Solving for n and m, we get:
n = m = 2
So both functions complete two cycles in the interval [0, 2π).
We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:
2sin2x = sin x
2sin2x - sin x = 0
sin x (2sin x - 1) = 0
sin x = 0 or 2sin x - 1 = 0
sin x = 0 when x is an integer multiple of π.
2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.
Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
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Jeff is buying tickets for a group of concerts. He wants tickets for at least 8 concerts. Each ticket for an afternoon concert costs $15 and each ticket for an evening concert costs $30. Jeff wants to spend no more than $300.
Which system of inequalities can Jeff use to find the number of tickets he can buy?
A. x + y ≥ 8 and 300 ≥ 15x + 30y
B. x + y ≤ 8 and 300 ≥ 15x + 30y
C. x + y ≥ 300 and 8 ≥ 15x + 30y
D. x + y ≤ 300 and 8 ≤ 15x + 30y
Answer:
(A.)
Step-by-step explanation:
you just have to follow the order that there going in so when they say less than you use the less than sign