104 consumers bought at least one of the three labels, 12 consumers bought labels A and B but not C 44 consumers bought label A and 91 consumers bought none of these labels because of the equations.
To find the number of consumers who buy the product sold under at least one of the three labels, we need to add up the number of consumers who buy the product under each label individually and those who buy the product under multiple labels.
However, we need to be careful not to double count those who buy the product under all three labels. Therefore, the formula for this calculation is:
At least one of the three labels = (A only) + (B only) + (C only) + (A and B only) + (A and C only) + (B and C only) + (A, B, and C)
Plugging in the given values, we get:
At least one of the three labels = 15 + 20 + 28 + 12 + 9 + 12 + 8 = 104 consumers
To find the number of consumers who buy the product sold under labels A and B but not C, we simply use the value given for those who buy only those sold under labels A and B:
Labels A and B but not C = 12 consumers
To find the number of consumers who buy the product sold under label A, we need to add up the number of consumers who buy the product under label A individually and those who buy the product under label A and one or both of the other labels. Therefore, the formula for this calculation is:
Label A = (A only) + (A and B only) + (A and C only) + (A, B, and C)
Plugging in the given values, we get:
Label A = 15 + 12 + 9 + 8 = 44 consumers
Finally, to find the number of consumers who buy the product sold under none of these labels, we subtract the number of consumers who buy the product under at least one of the three labels from the total number of consumers surveyed:
None of these labels = Total consumers - At least one of the three labels = 195 - 104 = 91 consumers
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VI. Solve for roots using the Quadratic Formula: A.
4x 2
−9x+2=0
B.
2x 2
−7x−1=0
The roots of equation A are 2 and 0.25.
The roots of equation B are 3.14 and -0.64.
To solve for the roots of a quadratic equation using the Quadratic Formula, we can use the formula:
x = (-b ± √(b² - 4ac)) / (2a)
Where a, b, and c are the coefficients of the equation.
For equation A, a = 4, b = -9, and c = 2. Plugging these values into the Quadratic Formula, we get:
x = (-(-9) ± √((-9)² - 4(4)(2))) / (2(4))
x = (9 ± √(81 - 32)) / 8
x = (9 ± √49) / 8
x = (9 ± 7) / 8
This gives us two possible values for x:
x = (9 + 7) / 8 = 2
x = (9 - 7) / 8 = 0.25
Therefore, the roots of equation A are 2 and 0.25.
For equation B, a = 2, b = -7, and c = -1. Plugging these values into the Quadratic Formula, we get:
x = (-(-7) ± √((-7)² - 4(2)(-1))) / (2(2))
x = (7 ± √(49 + 8)) / 4
x = (7 ± √57) / 4
This gives us two possible values for x:
x = (7 + √57) / 4 ≈ 3.14
x = (7 - √57) / 4 ≈ -0.64
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Write each expression in terms of sines and/or cosines, and then simplify: 37. sec x / tan x. 38. cot x / csc x 39. sin x / csc x + cos x / sec x 40. 1/sin²x – 1/tan^2 x 41. (1 - sin a)(1 + sin a) 42. (sec a – 1) ( sec a + 1)
43. cos B tan B +1 ) (sin B -1)
44. (1 + cos B) (1 – cot B sin B)
45. 1 + cos a tan a csc a / csc a
46. (cos a tan a + 1 ) ( sin a – 1) / cos^2 a
37. sec x / tan x = (1/cos x) / (sin x/cos x) = cos x / sin x = cot x
38. cot x / csc x = (cos x/sin x) / (1/sin x) = cos x / sin^2 x = cos x * (1/sin^2 x) = cos x * (csc^2 x)
39. sin x / csc x + cos x / sec x = (sin x / 1/sin x) + (cos x / 1/cos x) = sin^2 x + cos^2 x = 1
40. 1/sin²x - 1/tan^2 x = (1/sin^2 x) - (1/(sin^2 x/cos^2 x)) = (1/sin^2 x) - (cos^2 x/sin^2 x) = (1 - cos^2 x)/sin^2 x = sin^2 x/sin^2 x = 1
41. (1 - sin a)(1 + sin a) = 1 - sin^2 a = cos^2 a
42. (sec a - 1)(sec a + 1) = sec^2 a - 1 = tan^2 a
43. (cos B tan B + 1)(sin B - 1) = (cos B * sin B/cos B + 1)(sin B - 1) = (sin B + 1)(sin B - 1) = sin^2 B - 1 = -cos^2 B
44. (1 + cos B)(1 - cot B sin B) = (1 + cos B)(1 - cos B/sin B * sin B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B - cos^2 B/sin^2 B) = (1 + cos B)(1 - cos^2 B/sin^2 B) = (1 + cos B)(sin^2 B/sin^2 B) = (1 + cos B) * 1 = 1 + cos B
45. 1 + cos a tan a csc a / csc a = 1 + (cos a * sin a/cos a * 1/sin a) / (1/sin a) = 1 + (sin a / sin a) / (1/sin a) = 1 + 1/(1/sin a) = 1 + sin a = sin a + 1
46. (cos a tan a + 1)(sin a - 1) / cos^2 a = (cos a * sin a/cos a + 1)(sin a - 1) / cos^2 a = (sin a + 1)(sin a - 1) / cos^2 a = (sin^2 a - 1) / cos^2 a = -cos^2 a / cos^2 a = -1
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17. Name the polyhedron that can be constructed using the given net. Assume squares and equilateral triangles were used to form each net. a. b.
The polyhedron that can be constructed using this net is a triangular pyramid.
A triangular pyramid is a polyhedron that has four faces, with one of the faces being a square and the other three faces being equilateral triangles. The given net shows a square in the center, with three equilateral triangles attached to each of its sides. When the net is folded along the edges, the square becomes the base of the pyramid and the three equilateral triangles become the sides of the pyramid. Therefore, the polyhedron that can be constructed using this net is a triangular pyramid.
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Mattie Evans drove 140 miles in the same amount of time that it took a turbopropeller plane to travel 440 miles. The speed of the plane was 150 mph faster than the speed
of the car. Find the speed of the plane.
By forming and solving the equations we know that the speed of the plane was 220 mph.
What are equations?In mathematical formulas, the equals sign is used to indicate that two expressions are equal.
A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation.
like 3x + 5 = 15, for instance.
Equations come in a wide variety of forms, including linear, quadratic, cubic, and others.
So, d = rt.
t = d/r
The distances are equal.
140/r = 440/(r + 150)
Cross multiply:
140(r + 150) = 440r
140r + 21,000 = 440r
300r = 21,000
r = 70
70 + 150 = 220 mph
Therefore, by forming and solving the equations we know that the speed of the plane was 220 mph.
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How do you graph y=1/2x and y=x+2
Answer:
To graph y = 1/2x and y = x + 2, follow these steps:
Make a table of values for each equation. Choose several values of x, plug them into the equation, and solve for y. For y = 1/2x, you might choose x = -2, -1, 0, 1, and 2. For y = x + 2, you might choose the same values of x.
For y = 1/2x:
x | y
-2 | -1
-1 | -1/2
0 | 0
1 | 1/2
2 | 1
For y = x + 2:
x | y
-2 | 0
-1 | 1
0 | 2
1 | 3
2 | 4
Plot the points from each table on a graph. For y = 1/2x, plot the points (-2, -1), (-1, -1/2), (0, 0), (1, 1/2), and (2, 1). For y = x + 2, plot the points (-2, 0), (-1, 1), (0, 2), (1, 3), and (2, 4).
Draw a line through each set of points. The line for y = 1/2x should have a slope of 1/2 and pass through the point (0, 0). The line for y = x + 2 should have a slope of 1 and pass through the point (0, 2).
Label the axes and the lines. You can label the x-axis "x" and the y-axis "y". Label the line for y = 1/2x "y = 1/2x" and the line for y = x + 2 "y = x + 2".
Check your graph. Make sure each point is plotted correctly and the lines are drawn accurately. You can also check your graph by plugging in other values of x and making sure the corresponding points are on the lines.
Use simultaneously equation to eliminate one value and find the other then you find the value of the other one by substituting the value that u find from the other one eg: eliminate X find the value of y and then substitute y in one of your equation to find the value of X.
tollowing operation and express in sil (x^(2)-11x+30)/(x-6)-:(x^(2)-12x+35)/(9x^(3))
The given operation (x²-11x+30)/(x-6)-(x²-12x+35)/(9x³) expressed in simplest form is x - 11 + 29.89x⁻¹- 2x⁻²+ 8x⁻³ - (3.89)x⁻⁴.
To express this operation in simplest form, we need to find the common denominator and combine the numerators.
Find the common denominator. The common denominator of (x-6) and (9x^(3)) is (9x^(3))(x-6).
Multiply each fraction by the common denominator to get the same denominator for both fractions.
(x²-11x+30)/(x-6) * (9x³)/(9x³) = (9x³)(x²-11x+30)/(9x³)(x-6)
(x²-12x+35)/(9x³) * (x-6)/(x-6) = (x-6)(x²-12x+35)/(9x³)(x-6)
Combine the numerators and keep the same denominator.
(9x³)(x²-11x+30) - (x-6)(x²-12x+35) / (9x³)(x-6)
Simplify the numerator by distributing and combining like terms.
(9x⁵-99x⁴+270x³) - (x³-18x₂+72x-35) / (9x³)(x-6)
9x⁵-99x⁴+269x³-18x²+72x-35 / (9x³)(x-6)
Simplify the denominator by multiplying.
9x⁵-99x⁴+269x³-18x²+72x-35 / 9x⁴-54x³
Simplify the fraction by dividing each term in the numerator by the term in the denominator with the highest power.
(9x⁵/9x⁴)-(99x⁴/9x⁴)+(269x³/9x⁴)-(18x²/9x⁴)+(72x/9x⁴)-(35/9x⁴)
Simplify each term.
x - 11 + (269/9)x⁻¹- (18/9)x⁻²+ (72/9)x⁻³ - (35/9)x⁻⁴
Combine like terms.
x - 11 + (29.89)x⁻¹ - (2)x⁻² + (8)x⁻³- (3.89)x⁻⁴
Therefore, the operation (x²-11x+30)/(x-6)-(x²-12x+35)/(9x³) expressed in simplest form is x - 11 + 29.89x⁻¹- 2x⁻²+ 8x⁻³ - (3.89)x⁻⁴.
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How to solve probability?
The runner should choose the second cooler, because the probability of selecting a sports drink and a water from the first cooler is about 24.98% and the second cooler is about 25.86%.
To calculate the probability of selecting a sports drink and a water bottle from each cooler, we need to use the following formula:
Probability of selecting a sports drink and a water bottle = (number of sports drinks / total number of bottles) x (number of water bottles / (total number of bottles - 1))
For the first cooler, the probability of selecting a sports drink and a water bottle is:
(19/39) x (20/38) = 0.2498, or about 24.98%
For the second cooler, the probability of selecting a sports drink and a water bottle is:
(14/29) x (15/28) = 0.2586, or about 25.86%
Therefore, the runner should choose the second cooler, because it has a slightly higher probability of selecting a sports drink and a water bottle.
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The__________of an angle is the point where the sides of the angle intersect
Help please<3
A fruit bowl contains a mixture of oranges kiwis and limes the ratio of oranges to kiwis is 3:5 steve picks a fruit at random from the fruit bowl the probability of it being a orange is 1/4 what is the probability that it is a lime
The probability of Steve picking a lime at random from the fruit bowl is 1/3.
How to evaluate for the probability of picking a lime.Using the ratio given to find the proportion of oranges and kiwis in the fruit bowl. Let the number of oranges be 3x and the number of kiwis be 5x. Then the total number of fruits in the bowl is 3x + 5x + L, where L is the number of limes.
Given probability of picking an orange is 1/4, probability of picking a particular fruit from the bowl is calculated as:
number of that fruit / total number of fruits
1/4 = 3x / (3x + 5x + L)
Simplifying this equation, we get:
3x + 5x + L = 12x
L = 4x.
Substituting L = 4x and simplifying, we get:
probability of picking a lime = 4x / (3x + 5x + 4x) = 4/12 = 1/3
Therefore, the probability of picking a lime from the fruit bowl is 1/3.
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what is 1+1-5/34x + 14y+7
Answer:
[tex] - \frac{5x}{34} + 14y + 9[/tex]
Step-by-step explanation:
Just making sure. If the way the equation is written is
[tex]1 + 1 - \frac{5}{34} x + 14y + 7[/tex]
then yeah, that's the answer. If it's formatted differently, send a comment so that I could give you the proper answer.
i’m the diagram , triangle NPQ is similar to triangle NLM and PL = 5, find the lengths of NP AND NL
Therefore , the solution of the given problem of triangle comes out to be NL = √(100 + 20LM2) * 10 * 4 .
What is a triangle exactly?A triangular is a polygon because it has 2 different or more additional parts. It has a straightforward rectangle form. Only the sides A, B, and C can differentiate a triangle from a parallelogram. When the sides are not exactly collinear, Euclidean geometry results in a singular surface rather than a cube. If a shape has three edges and three angles, it is said to be triangular. The intersection of a quadrilateral's three edges is known as an angle. The sum of a triangle's edges is 180 degrees.
Here,
By removing NP:, we can resolve this system of equations.
NL Equals NP(LM + NL + 5). (5 - LM)
NL = NP(LM - PQ + 5) (LM)
NL(5 - LM) = NP(LM + NL + 5)(LM - PQ + 5) (LM)
By enlarging and condensing, we obtain:
NP = 2NL Plus LM / 5LM
Now that we know this, we can put it into one of the equations to find NL:
(2NL Plus LM / 5LM)
NL = (LM Plus NL + 5) (5 - LM)
By condensing and rearrangeing, we obtain:
(2NL Plus LM) = 0 when (NL2 - 10NL - 5LM2)
The quadratic algorithm yields:
NL = √(100 + 20LM2) * 10 * 4 alternatively,
=> NL = (10 - √(100 + 20LM2)) / 4
NL can never be negative, so we pick the positive root:
NL = √(100 + 20LM2) * 10 * 4
Now that we have this, we can put it into one of the equations to find NP:
NP = 2NL Plus LM / 5LM
NP = 5LM / (2(10 + √100 + 20LM^2)) / 4 + LM)
NP is equal to 5LM / (5 + √(25 + 5LM2)).
The widths of NP and NL are as follows:
NP is equal to 5LM / (5 + sqrt(25 + 5LM2)).
NL = (10 - √(100 + 20LM2)) / 4
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Please help
Solve the equation for x.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. X = (Type an integer or a fraction. Simplify your answer.)
B. The solution is all real numbers.
C. There is no solution.
Answer:
X=5
Step-by-step explanation:
instructions refer to the image
A container built for transatlantic shipping is constructed in the shape of a right
rectangular prism. Its dimensions are 2.5 ft by 13.5 ft by 9 ft. If the container is
entirely full and, on average, its contents weigh 0.28 pounds per cubic foot, find the
total weight of the contents. Round your answer to the nearest pound if necessary.
The volume of a right rectangular prism is given by the formula below
[tex]V=whl[/tex]
Thus, in our case,
[tex]V=2.5\times13.5\times9=303.75[/tex]
The volume of the container is 1116.5ft^3.
Finally, multiply the total volume by the density given in the problem, as follows
[tex]weight=303.75\times0.28=85.05[/tex]
⇒ [tex]weight[/tex] ≈ [tex]85[/tex]
Rounded to the nearest pound, the answer is 85 pounds.
Decide
whether perimeter or area would be used to solve the following
problem concerning the measure of the quantity.
Determining
the cost of replacing a linoleum floor with a wood
floor.
Perimeter would not be used to solve the problem of determining the cost of replacing a linoleum floor with a wood floor. Perimeter is a measure of the boundary of a two dimensional shape, such as a square, rectangle, or triangle. This measure would not be useful in calculating the cost of replacing a floor, as the cost of the flooring materials will depend on the total area of the floor, rather than its perimeter.
Area is the measure of the two dimensional space of a shape, and would be the correct measure to use when calculating the cost of replacing a floor. Area is calculated by measuring the length and width of the floor, then multiplying them together. The cost of the flooring materials can then be calculated by multiplying the area of the floor by the cost of the materials per square foot. This would give an accurate figure for the total cost of the flooring materials.
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Tell whether each scale reduces enlarges or preserves the size of an actual object
1 cm:12 m
6 ft: 10 in
1km : 1000 m
Answer and Step-by-step explanation:
1 cm: 12 m
This scale reduces the size of an actual object. For example, if a car is 4 meters long in real life, it would be represented as 0.33 cm on a map that uses this scale (4 meters divided by 12).
6 ft: 10 in
This scale enlarges the size of an actual object. For example, if a room is 10 feet wide in real life, it would be represented as 60 inches on a blueprint that uses this scale (10 feet multiplied by 6).
1 km: 1000 m
This scale preserves the size of an actual object. For example, if a park is 2 kilometers wide in real life, it would be represented as 2000 meters on a map that uses this scale.
2. (a) If the moments of variate 'X' are defined by E(X") 0.6, r = 1, 2, 3, that P(X 0) - 0.4, P(x P (x2) - 0. 2 show 1) = 0.6, 6 (b) What do you mean by convergence in probability ? State two laws of
The moments of a variate 'X' are defined by the expected value of the variate raised to the power of r, where r is an integer. In this case, the moments of 'X' are defined by E(X^r) = 0.6, for r = 1, 2, 3. This means that the expected value of X, X^2, and X^3 are all equal to 0.6. The probability of an event occurring is represented by P(X). In this case, P(X > 0) = 0.4, P(X = 1) = 0.6, and P(X^2 = 1) = 0.2. Convergence in probability refers to the concept that a sequence of random variables converges to a specific value with a probability of 1 as the number of trials approaches infinity.
These probabilities represent the likelihood of X being greater than 0, equal to 1, and squared equal to 1, respectively. This means that the probability of the sequence being within a certain distance of the specific value approaches 1 as the number of trials increases.
Two laws of convergence in probability are the Law of Large Numbers and the Central Limit Theorem. The Law of Large Numbers states that the average of a sequence of random variables converges to the expected value as the number of trials approaches infinity. The Central Limit Theorem states that the distribution of the sum of a sequence of random variables approaches a normal distribution as the number of trials approaches infinity.
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Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
A geometric sequence is shown below.
5, 11, 29, 83, ...
Which function describes this sequence?
The given sequence is not a geometric sequence, the quotients between consecutive numbers are different.
Which function describes this sequence?Remember that the recursive formula for a geometric sequence is:
f(n) = r*f(n - 1)
Where r is the common ratio.
Here we have the terms:
5, 11, 29, 83
To get the value of r, take the quotient between consecutive terms:
r = 11/5 = 2.2
r = 29/11 = 2.63
r = 83/29 = 2.86
We should get the same value of r for every ofthese quotients, then we can conclude that the given sequence of numbers is not a geometric sequence, is other type of sequence.
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need someone to help me understand how to do an Exponential Equation
Answer: p = (3.6 x 10^4)(0.03)^2
Step-by-step explanation:
The parametric equations of a curve are:
2x=
cotθ
-
cscθ and
4y=2cscθ-
2cotθ
Find the Cartesian equation ( y = f(x)) for
the curve
The Cartesian equation ( y = f(x)) for the curve is y = -x.
To find the Cartesian equation of the curve, we need to eliminate the parameter θ from the given parametric equations. We can do this by rearranging the equations and solving for θ in terms of x or y, and then substituting that value into the other equation.
First, let's rearrange the first equation to solve for cotθ:
2x = cotθ - cscθ
2x + cscθ = cotθ
cscθ - cotθ = -2x
Next, let's rearrange the second equation to solve for cscθ:
4y = 2cscθ - 2cotθ
2cscθ = 4y + 2cotθ
cscθ = 2y + cotθ
Now, let's substitute the value of cscθ from the second equation into the first equation:
2y + cotθ - cotθ = -2x
2y = -2x
y = -x
Therefore, the Cartesian equation of the curve is y = -x.
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Colleen has a wooden board that is 12 3/4 feet long. She cuts the board into three pieces. Two of the pieces are both 4 7/12 feet long.
How long is the other piece of Colleen's board?
Answer:
Step-by-step explanation: I don’t know
Cleo added 3a + 4b and got 7ab. Three of these statements explain why her answer is wrong. Which does NOT?
3a and 4b are not like terms, hence they cannot be added, and the result of the expression is 3a + 4b and not 7ab.
What are like terms?Like terms are terms that share these two features:
Same letters. (algebraic variables).Same exponents.If two terms are like terms, then they can be either added or subtracted.
3a and 4b on this problem are not like terms, as the letters, in this case a and b, are different.
Thus, the expression cannot be simplified, as only like terms, which are terms whose definition we gave in this explanation, can be simplified.
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We use the factor theorem, which states that if k is a root of the polynomial equation In our problem, we hawe P(2)=0 and P(-3)-0, Thus, x-2 and x+3 are both fact,
We can write P(x) as P(x) = (x - 2)(x + 3)Q(x), where Q(x) is another polynomial.
This is the factored form of P(x), and it can be used to find other roots or to simplify the polynomial equation.
The factor theorem is a useful tool in finding the factors of a polynomial equation. The theorem states that if k is a root of the polynomial equation P(x) = 0, then x - k is a factor of P(x).
In our problem, we have P(2) = 0 and P(-3) = 0. This means that 2 and -3 are both roots of the polynomial equation P(x) = 0. According to the factor theorem, this means that x - 2 and x + 3 are both factors of P(x).
Therefore, we can write P(x) as P(x) = (x - 2)(x + 3)Q(x), where Q(x) is another polynomial. This is the factored form of P(x), and it can be used to find other roots or to simplify the polynomial equation.
In conclusion, the factor theorem is a useful tool in finding the factors of a polynomial equation. In our problem, we used the factor theorem to find the factors x - 2 and x + 3 of the polynomial equation P(x) = 0.
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Find all exact solutions on the interval [0, 2π). Look for opportunities to use trigonometric identities. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
I know the right answers, but am not sure how to get there. Answers are 11pi/6,7pi/6 and pi/2
Please help.
sin2(x) − cos2(x) − sin(x) = 0
The exact solutions to the equation sin^2(x) - cos^2(x) - sin(x) = 0 in the interval [0, 2π) are π/2, 7π/6, and 11π/6.
How to determine the exact solution to the equationGiven that
sin^2(x) - cos^2(x) - sin(x) = 0
Let's use the identity cos^2(x) + sin^2(x) = 1 to rewrite the equation:
sin^2(x) - (1 - sin^2(x)) - sin(x) = 0
Open the bracket and evaluate the like terms
2sin^2(x) - sin(x) - 1 = 0
Now we can solve for sin(x) using the quadratic formula:
sin(x) = [-b ± √(b² - 4ac)]/2a
Where
a = 2, b = -1 and c = -1
So, we have
sin(x) = [1 ± √((-1)² - 4 * 2 * -1)]/2*2
sin(x) = [1 ± √9]/4
sin(x) = (1 ± 3) / 4
Evaluate and split
sin(x) = 1 or sin(x) = -1/2.
If sin(x) = 1, then x = π/2.
If sin(x) = -1/2, then we can use the unit circle to find the solutions in the interval [0, 2π):
sin(x) = -1/2 when x = 7π/6 or 11π/6.
Therefore, the solutions in the interval [0, 2π) are π/2, 7π/6, and 11π/6.
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What is the center of this ellipse?
(x-3)^2/4 + (y - 1)^2/9 = 1
The center of the ellipse is,
⇒ (3, 1)
What is an expression?An expression which is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division is called an mathematical expression.
We have to given that;
The equation of ellipse is,
⇒ (x - 3)²/4 + (y - 1)²/9 = 1
Now, We know that;
General form of the ellipse is,
⇒ (x - h)²/a + (y - k)²/b = 1
Where, (h, k) = the center of the ellipse.
Hence, We get;
The equation of ellipse is,
⇒ (x - 3)²/4 + (y - 1)²/9 = 1
By comparing;
The center of the ellipse is,
⇒ (h, k) = (3, 1)
Thus, The center of the ellipse is,
⇒ (3, 1)
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At the beginning of spring, Shaniece planted a small sunflower in her backyard. When it was first planted, the sunflower was 25 inches tall. The sunflower then began to grow at a rate of 0.5 inches per week. How tall would the sunflower be after 10 weeks? How tall would the sunflower be after ww weeks?
The sunflower would be 30 inches tall after 30 weeks. The sunflower be after w weeks would be 25 + 0.5 * w inches tall.
What do you mean by expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
To calculate the height of the sunflower after 10 weeks, we can use the formula:
=>height = starting height + growth rate * time elapsed
where the starting height is 25 inches, the growth rate is 0.5 inches per week, and the time elapsed is 10 weeks.
So the height after 10 weeks would be:
=>height = 25 + 0.5 * 10 = 25 + 5 = 30 inches
Therefore, the sunflower would be 30 inches tall after 10 weeks.
To calculate the height after w weeks, we can use the same formula:
=>height = 25 + 0.5 * w
So the height after w weeks would be:
=>height = 25 + 0.5 * w inches
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The number of days, D, to complete resarch is inversely proportional to the number of resaerchers, R, who are working. The research takes 125 days to complete with 16 people working on it. How many people are needed for 40 days?
Answer:
50 people
Step-by-step explanation:
Given a research project that take 16 people 125 days to complete, you want to know the number of people needed to complete the project in 40 days.
People-daysIn math, project effort is measured in people×days. That value is considered to be a constant for a given project. This makes the number of people inversely proportional to the number of days, and vice versa.
(16 people)×(125 days) = 2000 people·days = (p people)×(40 days)
Dividing by 40 days, we have ...
p people = (2000 people·days)/(40 days) = 50 people
50 people are needed to complete the research in 40 days.
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Additional comment
In real life, more people may get in each other's way. Or too few people may cause motivation, cooperation, and synergy to be lost. The maxim, "adding people to a late project makes it later" has a certain basis in reality.
write an exponentia function with a parent base of 2 that has a domain of {x|xeR }and a range of {y|y>-5}
The exponential function that satisfies the given conditions is y = 2ˣ- 6.
An exponential function with a parent base of 2 can be written as y = 2ˣ. To ensure that the range is {y|y>-5}, we need to add a constant term to the function.
We can write the exponential function as y = 2ˣ + k, where k is a constant term.
To find the value of k, we can plug in the smallest value in the range, which is -5, and solve for k:
-5 = 2ˣ + k
k = -5 - 2ˣ
Since the domain is {x|x∈R}, we can plug in any value for x. Let's plug in 0 for x:
k = -5 - 2⁰
k = -5 - 1
k = -6
So, the exponential function with a parent base of 2 that has a domain of {x|x∈R} and a range of {y|y>-5} is y = 2ˣ - 6.
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Its an unexact root
and I know its 3∛6 but i need procedures you can also do the rest :)
D) [tex]\sqrt[3]{162}[/tex]
E)[tex]\sqrt[3]{375}[/tex]
F)[tex]\sqrt[4]{405}[/tex]
The product of 3∛6 and 2∛6 is equals to 18.
What is underroot ?
In mathematics, the symbol "√" is called the radical symbol, and the expression written under it is called a radicand.
To simplify 3∛6, we can use the fact that the cube root of a number can be written as a power of that number with an exponent of 1/3. Therefore, 3∛6 can be rewritten as 6^(1/3) raised to the power of 3.
D) To add 3∛6 and 2∛6, we can first factor out the common term of ∛6:
3∛6 + 2∛6 = (3 + 2)∛6 = 5∛6
So the sum of 3∛6 and 2∛6 is 5∛6.
E) To subtract 2∛6 from 4∛6, we can again factor out the common term of ∛6:
4∛6 - 2∛6 = (4 - 2)∛6 = 2∛6
So the difference between 4∛6 and 2∛6 is 2∛6.
F) To multiply 3∛6 by 2∛6, we can use the fact that the product of two roots with the same index can be found by multiplying the radicands together:
3∛6 x 2∛6 = (3 x 2)∛(6 x 6) = 6∛36
Since the cube root of 36 is 3 (3 x 3 x 3 = 27 and 4 x 4 x 4 = 64), we can simplify this further:
6∛36 = 6 x 3 = 18
Therefore, the product of 3∛6 and 2∛6 is equals to 18.
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Can someone explain how to graph quadratic functions please i'm so confused
To graph a quadratic function, follow the steps explained to obtain the smooth curve of the quadratic function.
What is the graph of a quadratic function?
Graphing quadratic functions involves plotting the points on a coordinate plane that satisfy the equation of the function. Quadratic functions are typically written in the form:
f(x) = ax^2 + bx + c
where;
a, b, and c are constants.To graph a quadratic function, you can follow these steps:
Determine the vertex of the parabola. The vertex is the highest or lowest point on the parabola and is given by the formula:x = -b / 2a
y = f(x)
You can find the x-coordinate of the vertex by using the formula above, and then substitute it into the function to find the corresponding y-coordinate.
Determine the y-intercept of the parabola. The y-intercept is the point where the parabola intersects the y-axis, and it can be found by setting x = 0 in the function and solving for y.Find the x-intercepts of the parabola, if they exist. The x-intercepts are the points where the parabola intersects the x-axis, and they can be found by setting y = 0 in the function and solving for x. If the discriminant (b^2 - 4ac) is negative, then the parabola does not intersect the x-axis.Plot the vertex, y-intercept, and any x-intercepts on a coordinate plane. The vertex is the highest or lowest point on the parabola and is located on the axis of symmetry, which is the vertical line passing through the x-coordinate of the vertex.Draw the parabola by sketching a smooth curve through the points you've plotted. If the coefficient a is positive, the parabola opens upwards and if a is negative, the parabola opens downwards.Learn more about quadratic function here: https://brainly.com/question/1214333
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