The interpretation of the 1001 measurements in the third set of data vary due to reasons are as follow,
Measurement error, Random variation and Sampling error.
Measurement error: The measurand being measured may have inherent variability, but measurement error can also contribute to variation in the data set.
Random variation: Even if the same measurand is being measured under the same conditions, there may be random fluctuations in the system or the environment that can cause variation in the data.
Sampling error: If the 11 measurements were not taken at random from the population of interest, then the variation could be due to sampling error.
For the 1001 measurements in the second and third data sets, some possible explanations for the variation could be measurement error, systematic variation, changes in the measurand and Sampling error.
Thus, variation in data can have many different causes, and it is important to carefully consider the context and specific factors that may be contributing to the variation when interpreting the results.
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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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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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PLUMBING A plumber charges $50 to visit a house plus $40 for every hour of work. Define a variable and write an
expression to represent the total cost of hiring a plumber.
The expression to represent the total cost of hiring a plumber is y = 50 + 40x
How to determine the expression to represent the total costFrom the question, we have the following parameters that can be used in our computation:
Charges = $50 for visiting
Rate = $40 every hours
Represent the number of hour with x and the total charge with y
Using the above as a guide, we have the following:
y = Charges + Rate * x
Substitute the known values in the above equation, so, we have the following representation
y = 50 + 40x
Hence, the equation is y = 50 + 40x
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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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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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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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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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Find the sum of the polynomials (ax^2+2x-5) and (-2ax^2+a) and evaluate that sum when a=7 and x=-5
Answer:
29+3374=32483 that is the solution for the question
hope this helps <3
These charts show state sales tax as of 2015. Alabarna Florida Georgia Hawaii Idaho Indiana lowa Kentucky Idaho State Mississippi Hawaii Wisconsin 4% 6% 4% 4% 6% 7% 6% 6% Louisiana Maryland Michigan Mississippi 4% 6% 6% 7% New York North Dakota Oregon Pennsylvania 6% 5% 8 Students from various states are attending a marching band conference. Each uniform costs $135 before state sales tax is added. Complete the table to show the total cost of uniforms with tax, for each group of students. Number of Students 10
5
15 Rhode Island South Carolina South Dakota Vermont West Virginia Wisconsin Wyoming 7% 6% 4% Total Cost of Uniforms
Completing the table to show the total cost of uniforms with tax, for groups of students from the four states is as follows:
State Number Total Cost
of Students (After-tax)
Idaho 10 $1,431.00
Mississippi 5 $722.25
Hawaii 15 $2,106.00
Wisconsin 8 $1,134.00.
How is the total cost for each group determined?The total cost for each group of students from the four states can be determined by multiplication.
The multiplication operation for each group or state first computes the total cost before tax and the total cost after tax.
The total cost after tax uses the sales tax factor or rate to multiply the total cost before tax.
Generally, sales taxes are levied by state and local governments to check the consumption and production of certain items and to increase the revenue of the government.
The price before state sales tax of each uniform = $135
Relevant Taxes and Number of Students:
State Number of Students Sales Tax Rate
Idaho 10 6%
Mississippi 5 7%
Hawaii 15 4%
Wisconsin 8 5%
State Number Total Cost Total Cost
of Students (Before tax) (After-tax)
Idaho 10 $1,350 $1,431.00 ($135 x 10 x 1.06)
Mississippi 5 $675 $722.25 ($135 x 5 x 1.07)
Hawaii 15 $2,025 $2,106.00 ($135 x 15 x 1.04)
Wisconsin 8 $1,080 $1,134.00 ($135 x 8 x 1.05)
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15 POINTSSS!!!!!!! HELP A GIRL OUTTTTTTTT
The function that represents an exponential growth would be = f(X) = 0.3 ( 1.05) ^x. That is option C.
What is an exponential growth?An exponential growth of a function is defined as the growth that shows increase rates with respect to a given time.
There are two types of exponential functions: exponential growth and exponential decay.
The function that shows an exponential growth has the formula = f (x) = b^x, when b > 1.
From the examples given in the options above, the correct option that represents the exponential growth is f(X) = 0.3 ( 1.05) ^x. Thai so because 1.05 is greater than 1.
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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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Determine if the triangles are similar.
A. Yes, SSS
B. Yes, SAS
C. Yes, AA
D. No, not similar
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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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
You are distributing (multiplying) the three to all the terms in the parentheses.
Start:
3(x-2) = 4x + 2
Next:
3x - 6 = 4x +2
After that simplify:
-8 = x
Hope this helps!
Answer:
3x - 6 = 4x + 2 x = -8Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The property we use,
→ Distributive property.
The equation is,
→ 3(x - 2) = 4x + 2
Then the value of x will be,
→ 3(x - 2) = 4x + 2
→ 3(x) - 3(2) = 4x + 2
→ 3x - 6 = 4x + 2
→ 3x - 4x = 2 + 6
→ -x = 8
→ [ x = -8 ]
Hence, the value of x is -8.
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
What are the Big Ideas or Focal Points in the mathematics
curriculum in grades 6?
The Big Ideas or Focal Points in the mathematics curriculum for grade 6 are: 1. Ratios and Proportional Relationships
2. The Number System. 3. Expressions and Equations. 4. Geometry. 5. Statistics and Probability.
1. Ratios and Proportional Relationships: Students should be able to understand and use ratios to describe relationships between quantities, and use proportional reasoning to solve problems.
2. The Number System: Students should be able to understand and use negative numbers, and perform operations with multi-digit numbers and decimals.
3. Expressions and Equations: Students should be able to write and evaluate expressions, and use equations to solve problems.
4. Geometry: Students should be able to understand and use the properties of shapes and the relationships between them.
5. Statistics and Probability: Students should be able to use data to make predictions and understand the concept of probability.
These Big Ideas or Focal Points are the key concepts that students should master in grade 6 mathematics in order to be prepared for higher-level math courses.
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The__________of an angle is the point where the sides of the angle intersect
Help please<3
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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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
You bought water bottles to sell and spent a total of $50. You sell each bottle for $2. Which graph shows how many bottles you have to sell to earn back the money spent on water?
The graph that shows the number of bottles that need to be sold to earn back the money spent on water is Graph C.
How to find the graph ?The number of bottles that need to be sold to earn back the amount spent on water is :
= Total spent / profit per bottle
= 50 / 2
= 25 bottles
Graph C starts from - $ 50 to show that the amount you have is - $ 50 to show the amount spent on the bottles.
Graph C then ends at 25 bottles to show that this is where you would need to stop to have made back what you spent.
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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.
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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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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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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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.
Two families attended a baseball game the first family bought three bags of popcorn in for souvenir cups which totaled $40 that second family but eight bags of popcorn in for souvenir cups which totaled $60 how much did one bag of popcorn cost
Two families attended a baseball game bought popcorns and souvenir, the cost of each pack of popcorn is $4 and cost of each pack of souvenir is $7.
An expression that depicts the relationship between two or more variables and numbers is called an equation. The provided information can be represented as, using equations:
let x be the price of popcorn and y be the price of souvenir.
First family:
[tex]3x+4y=40[/tex](equation 1)
Second family:
[tex]8x+4y=60[/tex] (equation 2)
We have a system of 2 equations with 2 variables.
3x + 4y = 40
8x + 4y = 60
We are asked for the price of 1 bag of popcorn, x, so we will eliminate y and solve for x.
from equation 2,
[tex]8x+4y=60\\4y=60-8x[/tex]
divide both sides by 4
[tex]\frac{4y}{4} =\frac{60-8x}{4} \\y=15-2x[/tex]
now putting the value of y in equation 1
[tex]3x+4(15-2x)=40\\3x+60-8x=40\\-5x=-20\\x=4\\[/tex]and [tex]y=7[/tex]
Hence, the cost of popcorn is $4 and cost of souvenir is $7.
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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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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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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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