Trapezoidal Rule: [tex](b-a)^3 / 96n^2,[/tex] Simpson's Rule: [tex](b-a)^5 / 2880n^4\\[/tex]. Both approximations have error of 0.0208.
For the Trapezoidal Rule, the formula for estimating the error is |E| ≤ (b − a)3/12n2[max |f ''(x)|], a ≤ x ≤ b. In this case, the integral is from x=1 to x=3, so b-a = 2. Plugging in all the values, we get [tex]|E| ≤ 2^3/12(4)^2(2)[/tex] or |E| ≤ 0.0208. For the Simpson's Rule, the formula for estimating the error is |E| ≤ (b − a)5/180n4[max |f (4)(x)|], a ≤ x ≤ b. Again, b-a = 2. Plugging in all the values, we get[tex]|E| ≤ 2^5/180(4)^4(2)[/tex] or |E| ≤ 0.0208. Therefore, the error in approximating the integral with n = 4, using the Trapezoidal Rule and Simpson's Rule, is 0.0208.
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how many different rational numbers between $\dfrac{1}{1000}$ and $1000$ can be written either as a power of $2$ or as a power of $3$, where the exponent is a (possibly negative) integer?
The number of different rational numbers between [tex]$\dfrac{1}{1000}$[/tex] and 1000 that can be written either as a power of 2 or as a power of 3, where the exponent is a (possibly negative) integer, is 33.
To find all of the possible rational numbers, we need to find all the integer exponents for 2 and 3 that satisfy the conditions. [tex]2^0 = 1, 2^{-3} = 1/8, 2^{-2} = 1/4, 2^{-1} = 1/2, 2^1 = 2, 2^2 = 4, 2^3 = 8[/tex], and so on.
Similarly, for 3, we have [tex]3^0 = 1, 3^{-3} = 1/27, 3^{-2} = 1/9, 3^{-1} = 1/3, 3^1 = 3, 3^2 = 9, 3^3 = 27[/tex], and so on.
By combining the positive and negative exponents of 2 and 3, we get 33 different rational numbers that satisfy the conditions.
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Please help!
Effect options: Bounce/Cross
Answer:
14. cross, bounce, cross
15. cross, bounce
16. [tex]x^{4}-12x^{3}+48x^2-64x[/tex]
Step-by-step explanation:
16.
x(x-4)(x-4)(x-4)
x(x-4)(x^2-8x+16)
x^3-8x^2+16x-4x^2+32x-64
x^4-12x^3+48x^2-64x
Tony made cookies of circumference 45 cm. Find the area of each cookie made by tony.
Answer:
the area of each cookie made by Tony is approximately 63.62 square cm.
Step-by-step explanation:
The area of a cookie can be found if we know its radius. To find the radius, we can divide the circumference by 2 times pi (π).
Let's call the radius of the cookie "r".
45 cm / (2 * π) = r
Now that we have the radius, we can find the area using the formula:
π * r^2 = area
So,
π * r^2 = π * (45 / (2 * π))^2 = (45^2) / (4 * π)
Therefore, the area of each cookie made by Tony is approximately 63.62 square cm.
Use substitution to determine whether the given value of the variable is a solution of the equation 4n+4=14; n=2.5
Answer: To determine whether 2.5 is a solution to the equation 4n + 4 = 14, we can substitute 2.5 for n in the equation and see if it makes the equation true.
So, if we substitute 2.5 for n in the equation:
4(2.5) + 4 = 14
Expanding the left-side expression:
10 + 4 = 14
Simplifying further:
14 = 14
Since the equation is true, we can conclude that 2.5 is a solution to the equation 4n + 4 = 14.
Step-by-step explanation:
Solve for x. Please show all work. ∛(4x-1)-7=-4.
The value of x from the given equation is 7.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is ∛(4x-1)-7=-4.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, ∛(4x-1)-7=-4
∛(4x-1)=3
Cubing on both side of an equation, we get
(∛(4x-1))³=3³
4x-1=27
4x=28
x=7
Therefore, the value of x is 7.
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Problem #5
A silo is shaped like a cone and contains wheat. The radius is 10 feet and the height is 15
feet. If the silo can release wheat from its bottom at the rate of 25 cubic feet per minute, how
long would it take for the silo to empty fully? Round your answer to the nearest minute. Use
the approximate value of л, that is 3.14.
The volume of wheat in the silo is about 1,570 feet and it would take about 63 minutes at the given rate for the silo to empty fully.
What is volume?The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
Various forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to find the volume for each of these shapes.
The silo is in the shape of cone, so use the formula of volume of a cone to find volume of wheat the tank can hold.
The formula to find volume of a cone is:
V = 1/3 · πr2h -----(1)
Substitute π ≈ 3.14, r = 10 and h = 15 in (1).
V ≈ 1/3 · 3.14 · 102 · 15
V ≈ 1/3 · 3.14 · 100 · 15
V ≈ 1,570
So, the volume of wheat in the silo is about 1,570 feet.
Silo can release wheat from its bottom at the rate of 25 cubic feet per minute.
= 1,570 / 25
= 62.8
≈ 63
Hence, it would take about 63 minutes for the silo to empty fully.
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There are 48 new houses being built in a neighborhood last month 2/3 of them were sold this month 1/4 of the remaining houses were sold how many houses are left to be sold 
Answer:
12
Step-by-step explanation:
2/3 of 48 is 32, 16 leftover.
1/4 of 16 is 4, 12 leftover
answer=12
Is AABC a right triangle?
20
A
9
C
15
a. Yes
b. No
Answer:
No it's not!
Pythagorean theorem
15² + 9² = it's not 20
15² + 9² = 17 so
NO
Could you please help me with 1, 2, 3, 4, 6, and 8 please it will mean a lot
After rewriting the expression [tex]4 ^ {( 2x -4)}[/tex] using distributive property, [tex]4^{2x} . 4^{-4}[/tex] is the equivalent expression.
Describe expression.In mathematics, it is acceptable to multiply, divide, add, or negate. The construction of an expression looks like this: Amount, a mathematical operator, and an expression A mathematical expression's variables can be numbers, amounts, or functions (such as addition, subtraction, multiplication or division etc.)
Contrasting concepts and language is typical practice. Any mathematical statement that rates systems, numbers, and then an arithmetic operation between them is referred to as an expression, sometimes known as a formula. For instance, the arithmetic operator + separates the word m from the terms 4m and 5 in the balanced formula, just as it does for the variable m in the phrase 4m + 5.
given
Expressions that are equivalent do the same thing even when they have distinct appearances.
Two quadratic expressions that are analogous have the same value when we use the same value for the variable.
[tex]4 ^ {( 2x -4)}[/tex]
[tex]4^{2x} . 4^{-4}[/tex]
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Lucy and Daniela sat on a see-saw . Lucy weighs 50kg,sat 3.5metres away from the pivot on the other side . find the mass of Daniela if the see-saw was balanced .
To balance a see-saw, the product of the distance of the person's weight from the pivot and their weight must be equal on both sides.
Let's call Daniela's mass "m".
The force on Lucy's side is:
distance * weight = 3.5 meters * 50 kg = 175 kg * meters
The force on Daniela's side is:
distance * weight = d * m
Since the see-saw is balanced, the two forces must be equal:
3.5 * 50 = d * m
Solving for m, we get:
m = 175 / d
Without knowing the distance "d" that Daniela is sitting from the pivot, it is impossible to calculate her weight.
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Help with this question please?
Henry will be tossing a coin twice. Which list represents all possible outcomes?
Responses
A Head, tailHead, tail
B Head, head
Tail, tail
Head, tail
Tail, headHead, head Tail, tail Head, tail Tail, head
C Head, headHead, head
D Head, head
Tail, tail
Head, tail
Answer:
The correct answer is D: Head, head Tail, tail Head, tail Tail, head.
Step-by-step explanation:
When Henry tosses a coin twice, there are four possible outcomes, each with equal probability:
Head, head
Tail, tail
Head, tail
Tail, head
-1/3d + 4/5 = 1/2 what is d?
The required value of d in the given arithmetic operation is 9/10.
What are subtraction and addition?
The two main arithmetic operations that we learn to add and subtract two or more integers or other mathematical values are addition and subtraction. To add, one must add two or more numbers or values to produce a new number. The inverse of addition is subtraction and vice versa.
For instance, 10 - 1 = 9 if 9 + 1 = 10. That demonstrates that adding 1 produces the number 10 when added to 9, but subtracting 1 from 10 produces the number 9.
Given, -1/3d + 4/5 = 1/2
[tex]\frac{-1}{3} d+\frac{4}{5} =\frac{1}{2} \\\\\frac{-1}{3} d =\frac{1}{2}-\frac{4}{5}\\\\\frac{-1}{3} d = \frac{5-8}{10}\\\\\frac{-1}{3} d = \frac{-3}{10}\\\\\frac{d}{3}=\frac{3}{10}\\\\d = \frac{9}{10}[/tex]
So, the required value of d = 9/10.
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Let g(x) be the indicated transformation of f(x). Write the rule for g(x).
7. f(x)=2x, shift the graph vertically 2 units
8. f(x)= x-3; horizontal stretch by a factor of 3
9. f(x)=X: vertical compression by a factor of
Let g(x) be the indicated combined transformation of f(x) = x. Write
the rule for g(x).
10. horizontal stretch by a factor of 5 followed by a horizontal
shift right 2 units
11. vertical shift down 3 units followed by a vertical compression
by a factor of
12. reflection across the y-axis followed by
a vertical shift up 4 units
Solve.
13. Tia's earnings can be represented by the function f(x) = 5x + 120,
where x is the number of hours she works. If she works 3 additional
hours, her earnings function is g(x) = 5(x + 3) + 120. What type of
transformation can be applied to the graph of fto get the graph of g?
Answer:
g(x) = 2x + 2
g(x) = 3(x-3)
g(x) = 1/3x
g(x) = 5(x + 2)
g(x) = 1/3(x - 3) + 3
g(x) = -x + 4
Vertical shift of 3 units to the right.
Step-by-step explanation:
y varies as t. If y = 6 when t =4, calculate:
a) the value of y, when t = 6
b) the value of t, when y = 4
Answer:
see explanation
Step-by-step explanation:
given y varies as t , then the equation relating them is
y = kt ← k is the constant of variation
to find k use the condition y = 6 when t = 4
6 = 4k ( divide both sides by 4 )
[tex]\frac{6}{4}[/tex] = k , that is
k = [tex]\frac{3}{2}[/tex]
y = [tex]\frac{3}{2}[/tex] t ← equation of variation
(a)
when t = 6 , then
y = [tex]\frac{3}{2}[/tex] × 6 = 3 × 3 = 9
(b)
when y = 4 , then
4 = [tex]\frac{3}{2}[/tex] t ( multiply both sides by 2 to clear the fraction )
8 = 3t ( divide both sides by 3 )
[tex]\frac{8}{3}[/tex] = t
A 10 kg object is attached to a spring and is pulled 0.5 m from its rest position at an angle of 30 degrees to the horizontal. The spring has a spring constant of k and is compressed 0.3 m. Calculate the potential energy stored in the spring and the rope, taking into account the horizontal and vertical components of the displacement.
Step-by-step explanation:
The potential energy stored in the spring can be calculated using the equation:
PE_spring = 1/2 * k * x^2
where k is the spring constant and x is the displacement of the spring from its rest position. In this case, x = 0.5 m.
The potential energy stored in the rope can be calculated as the gravitational potential energy of the object, which is given by:
PE_rope = m * g * h
where m is the mass of the object (10 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical displacement of the object.
The horizontal and vertical components of the displacement can be calculated using trigonometry:
x = 0.5 * cos(30) = 0.5 * sqrt(3)/2 m
y = 0.5 * sin(30) = 0.5/2 m
The total potential energy stored in the spring and rope is given by the sum of their individual potential energies:
PE = PE_spring + PE_rope = 1/2 * k * x^2 + m * g * h
Substituting in the given values, we find:
PE = 1/2 * k * (0.5 * sqrt(3)/2)^2 + 10 * 9.8 * (0.5/2 + 0.3)
Note: The spring constant (k) is not given, so the answer is given in terms of k.
Answer:
Step-by-step explanation:
The potentpotentialial energy stored in a spring is calculated by 1/2 * k * x^2, where k is the spring constant and x is the displacement from its rest position. The potential energy stored in the rope is calculated as m * g * h, where m is the object's mass, g is acceleration due to gravity and h is the object's vertical displacement. The total potential energy is the sum of these two energies. In this case, the horizontal and vertical components of the displacement can be calculated using trigonometry and then used to find the total potential energy stored in the spring and rope.
Hurry 4 1/2 -(2 1/3-1 1/4)
13/4 is the value of [tex]4\frac{1}{2} -(2\frac{1}{2}-1 \frac{1}{4})[/tex]
What is Fraction?A fraction represents a part of a whole.
The given expression is [tex]4\frac{1}{2} -(2\frac{1}{2}-1 \frac{1}{4})[/tex]
Convert each mixed fraction to improper fraction
9/2-(5/2-5/4)
9/2-(10-5/4)
9/2-5/4
LCM of 4 and 2 is 4
18-5/4
13/4
Hence, 13/4 is the value of [tex]4\frac{1}{2} -(2\frac{1}{2}-1 \frac{1}{4})[/tex]
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4. Warm turkey Tom is cooking a large turkey a holiday meal. He wants to be sure that the turkey is safe to eat, which requires a minimum internal temperature of 165°F. Tom uses a thermometer to measure the temperature of the turkey meat at four randomly chosen points. The minimum reading is 170°F.
The sample consists of 4 selected sites, and the corresponding parameter is the population's minimum temperature. The lowest temperature for the sample is 170 °F .
what is sample ?The sampling size is the number of records which used derive estimates for a certain population. A sample size from the population was selected. The amount of subjects the observations that compose up a study is referred to as the "sample size." This number is sometimes referred to as the symbol n. Two statistical traits are influenced by the sample size: 1) The accuracy of our estimations; 2) The power of investigations to draw conclusions. The samples represent the outcomes of random tests. A specific value is selected from a set of possible values when sample a random variable. This particular value is a sample. The potential values and their possibilities are determined by the random variable's posterior distribution.
given
A parameter is a descriptive measure for a population, as opposed to a statistic, which is a descriptive measure for a sample.
170 F is a statistic because it represents the sample minimum temperature and is based on a sample of four randomly selected sites.
The corresponding parameter is changed to the minimum population temperature.
The lowest temperature for the sample is 170F. (F).
Minimum population temperature as a parameter
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the variable of interest in the outcome of a study.
The concept is a Dependent Variable. It's the outgrowth variable of interest that's observed to see whether it's told by a manipulated variable.
The dependent variable is the variable that's being measured or tested in a trial. One way to help identify the dependent variable is to the flashback that it depends on the independent variable.
When experimenters make changes to the independent variable, they also measure any performing changes to the dependent variable. An experimenter might also choose dependent variables grounded on the complexity of their study.
Stability is frequently a good sign of an advanced quality-dependent variable. The dependent variable belongs on the y-axis ( perpendicular line).
Question
What type of variable is the outgrowth of a study?
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this is urgent i need help asap
Answer:
32.) Yes
33.) 7
34.) No because 40 is less than 50
Step-by-step explanation:
32.)
Were trying to see is 35 is 3/4ths of 50, so we set up a ratio and solve
[tex] \frac{3}{4} = \frac{x}{50} [/tex]
Next we cross multiply
[tex]4x = 150[/tex]
Lastly divide by 4
[tex]x = 37.5[/tex]
33.) We have to convert 2/5 and 5/6 into a value over 30.
For 2/5, 5 times 6 is 30. 2 times 6 is 12, so we get 12/30 playing Chess.
6 times 5 is 30. 5 times 5 is 25. Making it 25/50 playing Sudoku
[tex] \frac{12}{30} = chess \: \frac{25}{30} = sudoku[/tex]
Since 5 don't play sudoku and 18 don't play chess.
18+5 = 23...
30-23 = 7
34.) The picture to the right shows 20 stamps.
Two sheets of stamps means 20x2 = 40, which is less than 50
8) The graph shows the total cost C of making x photocopies at a copy shop.
Making Photocopies
Total cost (dollars)
40
35
30
25
00
0
100 200 300 400 500
Number of copies
X
a) Does it cost more money to make 100 photocopies or
101 photocopies? Explain.
b) You have $40 to make photocopies. Can you buy more
than 500 photocopies? Explain.
a) it costs more money to make 100 photocopies
b) you can buy more than 500 photocopies for $40
What are coordinates?
A pair of numbers that use the separations between the two reference axes to define the location of a point on a coordinate plane. usually represented by the x- and y-values, respectively, (x, y).
a) In the graph , 100 photocopies cost $10,
For 101 photocopies, the point on the line comes below of 10 on y axis
So, it costs more money to make 100 photocopies
b) graph arrow shows line moves on...
so, you can buy more than 500 photocopies for $40
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Solomon has read 1/3 of his book. He finishes the book by reading the same amount each night for 5 nights. a. What fraction of the book does he read each of the 5 nights?
an unfair coin has probability 0.4 of landing heads. the coin is tossed three times. what is the probability that it lands heads at least once? round the answer to four decimal places.
The probability that it lands heads at least once is 1.0720.
Probability is the measure of the likelihood of an event occurring. In this case, we are looking at the probability of a coin landing heads at least once after three tosses.
Let's denote the event of the coin landing heads on the first toss as event A, the event of the coin landing heads on the second toss as event B, and the event of the coin landing heads on the third toss as event C.
The probability of landing heads at least once is equal to the sum of the probabilities of each individual event occurring (A, B, or C) minus the probability of all three events occurring (A and B and C).
P(A or B or C) = P(A) + P(B) + P(C) - P(A and B and C)
Since the coin is unfair and has a probability of 0.4 of landing heads, P(A) = P(B) = P(C) = 0.4.
Using the formula for the probability of multiple events happening simultaneously, we find that P(A and B and C) = P(A) * P(B) * P(C) = 0.4 * 0.4 * 0.4 = 0.064.
Plugging in all the values, we get:
P(A or B or C) = 0.4 + 0.4 + 0.4 - 0.064 = 1.136 - 0.064 = 1.072
Rounding to four decimal places, the answer is 1.0720, which means that the probability of the coin landing heads at least once after three tosses is 1.0720.
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Does anyone know the answer to this question?
Answer:
x = 41
Step-by-step explanation:
Supplementary Angles rule (straight lines in total have the angle of 180):
180 - 147 = 33
Total angles in a triangle equal 180:
180 - 33 - 106 = x
x = 41
One of the legs of a right triangle measures 2 cm and the other leg measures 7 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
The measure of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
For the given triangle, let's call the length of the hypotenuse "h". Then, using the Pythagorean theorem:
h^2 = 2^2 + 7^2
h^2 = 4 + 49
h^2 = 53
h = √53
Rounding to the nearest tenth, h = 7.3 cm.
So, the measure of the hypotenuse of the right triangle with legs of length 2 cm and 7 cm is 7.3 cm.
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Can someone help me find the area of this please
Edit: Nevermind i just realised what i did wrong lol
The area of the given shape is 90.4 cm².
What is the area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.
On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.
Given the shape of the boat, which contain, a rectangle and two right triangles,
total area = area of rectangle + area of triangle,
dimensions of the rectangle are,
length = 12 cm width = 5.2 cm
area of rectangle = l*b
area of rectangle = 12*5.2
area of rectangle = 62.4 cm²
area of triangle = 1/2*b*h
height = 8 cm
total base of both triangles = 3 + 4
base = 7 cm
area of triangle = 1/2*8*7
area of triangle = 28 cm²
total area = 62.4 cm² + 28 cm²
total area = 90.4 cm²
Hence the area is 90.4 cm².
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Choose all that correctly interprets the relationship between x and y. Each system of equations represents the cost of flowers at a florist
Red roses cost x dollars and daisies cost y dollars.
4x + 4y - 36
x + 2y - 12
Thus, red roses cost twice as much as daisies.
Red roses cost x dollars and tulips cost y dollars.
2x + 3y - 24
2x + y - 16
Thus, red roses cost 50 percent more than tulips.
White roses cost x dollars and red roses cost y dollars.
2x + y - 22
x + 3y - 26
Thus, white roses cost twice as much as red roses
Tulips cost x dollars and daisies cost y dollars.
2x + 3y = 17
x + y = 7
Thus, tulips cost 50 percent more than daises.
White roses cost x dollars and tulips cost y dollars.
3y - 20
2x + y = 20
Thus, white roses cost twice as much a tulips.
White roses cost x dollars and daisies cost y dollars.
3x + 2y = 30
x + y - 11
The equations can be solved using algebraic methods to find the value of x and y and understand the cost difference between different flowers.
Each system of equations represents the cost of flowers at a florist. By using two equations, we can determine the relationship between the cost of different flowers.
For the first system of equations where red roses cost x dollars and daisies cost y dollars, we can see that 4x + 4y - 36 represents the cost of red roses and x + 2y - 12 represents the cost of daisies. By solving for x and y, we can determine that red roses cost twice as much as daisies.
In the second system of equations where red roses cost x dollars and tulips cost y dollars, we can see that 2x + 3y - 24 represents the cost of red roses and 2x + y - 16 represents the cost of tulips. Solving for x and y, we can determine that red roses cost 50 percent more than tulips.
In the third system of equations where white roses cost x dollars and red roses cost y dollars, we can see that 2x + y - 22 represents the cost of white roses and x + 3y - 26 represents the cost of red roses. Solving for x and y, we can determine that white roses cost twice as much as red roses.
The fourth system of equations where tulips cost x dollars and daisies cost y dollars can be represented by 2x + 3y = 17 and x + y = 7. By solving for x and y, we can determine that tulips cost 50 percent more than daisies.
The fifth system of equations where white roses cost x dollars and tulips cost y dollars can be represented by 3y - 20 and 2x + y = 20. By solving for x and y, we can determine that white roses cost twice as much as tulips.
In the last system of equations where white roses cost x dollars and daisies cost y dollars, we can see that 3x + 2y = 30 represents the cost of white roses and x + y - 11 represents the cost of daisies. By solving for x and y, we can determine the relationship between white roses and daisies.
In conclusion, by using two equations for each system of flowers, we can determine the relationship between their costs.
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Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−15, −15), B′(15, 15), C′(0, 15). Determine the scale factor used.
5
1/5
12
1/12
The solution is Option A.
The dilation scale factor is given by the equation D = 5
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
Given data ,
Let the dilation scale factor be represented as D
Now , the equation will be
The coordinates of the triangle ΔABC is given as
A ( -3 , -3 ) , B ( 3 , 3 ), C ( 0 , 3 )
And , coordinates of the triangle ΔA'B'C' is given as
A′ ( -15 , -15) , B′ ( 15 , 15 ) , C′ ( 0 , 15 )
The dilation factor is given by D = x₂ / x₁ or D = y₂ / y₁
Substituting the values in the equation , we get
D = -15 / -3 = 5
And , D = 15 / 3 = 5
Hence , the dilation factor is 5
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A cubic polynomial function f has a leading coefficient of 2 and a constant term of 5. When f(-1) = 2 and F(1) = 14, what is f(0.5)?
f(0.5) = ?
Explain your reasoning.
The value of the cubic polynomial evaluated at x = 0.5 is equal to 8.
How to derive a cubic polynomial
In this problem we find the case of a cubic polynomial in standard form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are real coefficients.
The values of the coefficients must be determined on the knowledge of the leading coefficient (a = 2), the constant term (d = 5) and two values (y(- 1) = 2, f(1) = 14). First, substitute the leading coefficient and the constant term in the definition:
y = 2 · x³ + b · x² + c · x + 5
y - 2 · x³ - 5 = b · x² + c · x
Second, form the system of linear equations by using the given values:
b - c = - 1
b + c = 7
Third, solve the resulting system by numerical methods:
(b, c) = (3, 4)
Fourth, write the resulting polynomial:
y = 2 · x³ + 3 · x² + 4 · x + 5
Fifth, evaluate the polynomial at x = 0.5:
y = 2 · 0.5³ + 3 · 0.5² + 4 · 0.5 + 5
y = 8
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A pool has a depth of 12 feet and a width of 14 feet. If it holds 1680 cubic feet of water, what is the length of the pool
Answer:
Step-by-step explanation:
Volume is whl.
= 1680 = (14)(12)(x)
= 1680 = 168x
= x = 10
The length is 10ft
Answer: 10 Feet
Step-by-step explanation:
Volume of pool = Length x Width x Depth = LxWxD
We know D = 12 feet W = 14 feet
So Lx 14 x 12 = 1680 Solving for L = 10 feet
you created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. does the graph show any trend? if
A scatterplot of miles per gallon (MPG) against weight can reveal the relationship between the two variables. If there is a trend in the graph, it can help us understand the relationship between the two variables.
For example, if the graph shows a negative correlation, meaning that as the weight of the vehicle increases, the MPG decreases, this trend may be what is expected, as heavier vehicles typically have lower fuel efficiency. On the other hand, if the graph shows no trend or a positive trend, it would indicate that weight and MPG are not significantly related, which might not be what was expected.
It is important to keep in mind that a scatterplot can only show the relationship between two variables and cannot provide a definitive explanation of the cause-and-effect relationship between them
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Complete Question: you created a scatterplot of miles per gallon against weight; check to make sure it was included in your attachment. does the graph show any trend? if yes, is the trend what you expected? why or why not?