Answer:
Information is given about a polynomial f(x), whose coefficients are real numbers. Find the remaining zeros of f. Use the rational zeros theorem .
What is the rise of y = 4/1 x -1
Answer:
4
Step-by-step explanation:
HELP ASAP!!! BRAINLIEST!!! Write a cubic function whose graph passes through the given points.
(-1,0) (0,2) (2,0) (1,0)
f(x) = (3/16)(x+4)(x-4)(x-2)
Does this help?
Select the correct answer.
Which statement is a converse of p?
p: If every fourth card drawn is a spade, then 25% of the cards in a deck would be spades.
A. If 25% of the cards in a deck are spades, then every fourth card drawn would be a spade.
B. If every fourth card drawn isn't a spade, then 25% of the cards in a deck aren't spades.
C. If 25% of the cards in a deck aren't spades, then every fourth card drawn wouldn't be a spade.
D. If every fourth card drawn isn't a spade, then 75% of the cards in a deck are spades.
C is the correct answer.
can someone help me with this but please with details on how u got the answer:
The function’s average rate of change over the interval from x: 1 to x:2 is:
The function’s average rate of change over the interval from x = 1 to x = 2 is: -2. The correct option b.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
We have the interval from x = 1 to x = 2.
To find the function’s average rate of change over the interval from x = 1 to x = 2 is:
We interpreted the interval in the coordinate form.
The curve from (1, 2) to (2, 0) is a straight line.
And the slope of the line is the average rate of change of the function.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
m = (0-2) / (2-1)
m = -2/1
m = -2
Therefore, the average rate of change is -2.
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Consider the following classical recursive algorithm for computing the factorial n! of a non-negative integer n: FACTORIAL(n): if n=0 return 1 else return n · FACTORIAL(n-1) (a) How many multiplications does this algorithm perform? (b) How many bits are required to write n! in binary? Express your answer in the form θ(f(n)), for some familiar function f(n). [Hint: (n/2)^n/2 < n! < n^n.]
(c) your answer (b) should convince you that the number of multiplications is not a good estimate of the actual running time of FACTORIAL. we can multiply any k-digit number and any l-digit number in O(k-l) time using either the lattice algorithm or duplation and mediation. what is the running time factorial if we use this multiplication algorithm as a subroutine?
The recursive factorial algorithm performs n multiplications, but the number of bits required to write n! in binary is θ(n^n). This means that the number of multiplications is not a good estimate of the actual running time of the algorithm. The running time of the algorithm is actually O(n!), which is exponential in n.
The number of multiplications performed by the recursive factorial algorithm can be calculated as follows:
T(n) = 1 + T(n-1)
where T(n) is the number of multiplications performed when n! is calculated.
This can be solved using the following formula:
T(n) = n
The number of bits required to write n! in binary can be calculated as follows:
b(n!) = n log2(n) + n - 1
This can be solved using the following formula:
b(n!) = θ(n^n)
As can be seen, the number of bits required to write n! in binary is much larger than the number of multiplications performed by the recursive factorial algorithm. This is because the number of multiplications is only a measure of the number of operations performed, while the number of bits required to write n! in binary is a measure of the amount of data that must be processed.
The running time of the recursive factorial algorithm is O(n!), which is exponential in n. This is because the algorithm must recursively calculate the factorial of all numbers from 1 to n. The number of multiplications performed by the algorithm is only a small factor of the overall running time.
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At the Muttart Conservatory, the arid pyramid
has 4 congruent triangular faces. The base of
each face has length 19.5 m and the slant height:
of the pyramid is 20.5 m. What is the measure
of each of the three angles in the face? Give the
measures to the nearest degree.
The measure of each of the three angles in the face of the arid pyramid, to the nearest degree, is 31 degrees.
To find the measure of each of the three angles in the face of the arid pyramid, we can use trigonometric ratios based on the given information.
The slant height of the pyramid (20.5 m) can be thought of as the hypotenuse of a right triangle, with the base of each face (19.5 m) as one of the legs.
The other leg can be calculated as the height of the triangle.
Using the Pythagorean theorem, we can find the height (h) of the triangle:
\(h^2\) = (slant height)^2 - (base)^2
\(h^2 = 20.5^2 - 19.5^2\)
\(h^2 = 420.25 - 380.25\)
\(h^2 = 40\)
h = √40
h = 2√10
Now, we can calculate the sine of one of the angles (θ) in the face:
sin(θ) = opposite/hypotenuse
sin(θ) = h/slant height
sin(θ) = (2√10)/20.5.
Taking the inverse sine of both sides, we can find the measure of the angle θ:
θ = \(sin^{(-1)\)((2√10)/20.5)
θ ≈ 30.5 degrees
Since there are three congruent angles in the face of the pyramid, each angle measures approximately 30.5 degrees.
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A gymnast scores a total of 125 points in the first 4 meets of the season. At this rate, how many points will she score by the end of 14 meets
Answer:
i dont know but will u date me
Step-by-step explanation:
A linear model of this situation contains the values (15, 300.2) and (26, 177.88) where x represents the number of square inches knitted on the scarf and y represents the number of yards remaining on the ball of yarn. How many yards of yarn did Paula start with?
Answer: Paula starts with 301.5 yarns.
Step-by-step explanation:
Equation of a line passing through two points (a,b) and (c,d) is given by:-
\((y-b)=\dfrac{b-d}{a-c}(x-a)\)
Given: x= number of square inches knitted on the scarf
y= number of yarns remaining on the ball of yarn
The equation of a line passing through (15, 300.2) and (26, 177.88):
\((y-300.2)=\dfrac{26-15}{177.88-300.2}(x-15)\\\\\Rightarrow (y-300.2)=\dfrac{11}{-122.32}(x-15)\\\\\Rightarrow (y-300.2)=\dfrac{11}{-122.32}(x-15)\)
To find initial point, put x=0
\(y-300.2=-\dfrac{11}{122.32}(0-15)\\\\\Rightarrow\ y-300.2=\dfrac{375}{278}\\\\\Rightarrow\ y=\dfrac{375}{278}+300.2\\\\\Rightatrrow\ y=301.5 \ \ (approx)\)
Hence, Paula starts with 301.5 yarns.
If a random sample of five households is selected, is it valid to use the Central Limit Theorem to describe the sampling distribution of the sample mean? Explain.
Yes, it is valid to use the Central Limit Theorem (CLT) to describe the sampling distribution of the sample mean, even for a random sample of five households. Although a sample size of five is relatively small, the CLT still applies as long as the sample is random and independent.
The Central Limit Theorem is a fundamental concept in statistics that states that, under certain conditions, the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the shape of the population distribution.
While a sample size of five may be considered small, the CLT still holds for this case. The key consideration is that the sample is selected randomly and each observation is independent of the others. As long as these conditions are met, the CLT can be applied, even for small sample sizes.
In practice, larger sample sizes are generally preferred to ensure better approximation to the normal distribution. However, the CLT provides a theoretical foundation for the validity of using the normal distribution as an approximation for the sampling distribution of the sample mean, even with relatively small sample sizes like five households.
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find the equation of the line below. I need it before wednesday so can you help if you know the answer to the question, thanks.
Will give first person to answer brainliest!! At a local baseball game, tickets cost $4 for adults and $2 for students. If there were a total of 94
people at the game and the ticket revenues were $294, how many students and how many adults
attended?
Answer:
let x adult and y student attended
x+y= 94
x=94-y
again
4x+2y = 294 53 adults and 41 student attended
376-4y+2y =294 the event
2y =82
y=41
substituting the value of y in
x+y =94
x= 94-41 = 53
Step-by-step explanation:
Let T be a linear operator on a finite dimensional inner product space V. (1) Prove that ker(T*T) = ker T. Then deduce that rank(T*T) = rank(T) (2) Prove that rank(T*) = rank(T). Then deduce that rank(TT*) = rank(T).
We have shown that rank(T*) = rank(T) and rank(TT*) = rank(T).
To prove the given statements, we'll make use of the following properties:
For any linear operator T on a finite-dimensional inner product space V, we have ker(T*) = (Im T)⊥ and Im(T*) = (ker T)⊥, where ⊥ denotes the orthogonal complement.
For any linear operator T on a finite-dimensional inner product space V, we have rank(T) = dim(Im T) and nullity(T) = dim(ker T).
Now let's prove the statements:
(1) We want to show that ker(T*T) = ker(T).
First, note that TT is a self-adjoint operator since (TT)* = T*T.
Let v be an element in ker(TT), then (TT)(v) = 0. Taking the inner product of both sides with v, we get ⟨(T*T)(v), v⟩ = ⟨0, v⟩ = 0.
Since TT is self-adjoint, we have ⟨TT(v), v⟩ = ⟨v, TT(v)⟩. Thus, 0 = ⟨v, TT(v)⟩.
Since the inner product is positive-definite, it follows that T*T(v) = 0, which implies v is in ker(T).
Conversely, let v be an element in ker(T). Then Tv = 0, and hence (TT)(v) = T(Tv) = T*(0) = 0.
Therefore, we have shown that ker(T*T) = ker(T).
Now, using the fact that rank(T) = dim(Im T) and nullity(T) = dim(ker T), we can deduce that rank(TT) = rank(T) using the rank-nullity theorem: rank(TT) = dim(Im TT) = dim(V) - nullity(TT) = dim(V) - nullity(T) = rank(T).
(2) We want to prove that rank(T*) = rank(T) and then deduce that rank(TT*) = rank(T).
Using the properties mentioned above, we have rank(T*) = dim(Im T*) = dim((ker T)⊥) = dim(V) - dim(ker T) = dim(Im T) = rank(T).
Now, we can conclude that rank(TT*) = rank(T) using the result from part (1): rank(TT*) = rank((T*)) = rank(T).
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square root of 50 multiplied by square root of 7d squared
we were told the results are based on a random sample of ann arbor teens. is the following statement about the remaining assumption correct or not correct?we need to have a simple size n that is large enough, namely that the sample size n is at least 25.O CorrectO Incorrect
Correct. The assumption that the sample size should be at least 25 is correct. This is because, for a sample to be representative of the population, it should have enough observations to provide a reasonable estimate of the population parameters.
A sample size of at least 25 is generally considered the minimum requirement for statistical analysis. The statement about the remaining assumption is correct. In order to make valid inferences from a random sample, it is important to have a large enough sample size (n). A common rule of thumb is that the sample size should be at least 25. This helps to ensure that the sample is representative of the population and increases the accuracy of the results.
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how many solution does 8m=-48 have
Answer:
1 solution
Step-by-step explanation:
8m = - 48 ( divide both sides by 8 )
m = - 6 ← is the only solution
Multiply (2.86 × 10−9)(9.2 × 1015). Write the final answer in scientific notation.
26.312 × 10−135
2.6312 × 10−134
26.312 × 106
2.6312 × 107
The final answer in scientific notation is 26.312 × 10^6.
A way of representing numbers in terms of a decimal number between 1 and 10—but not 10 itself multiplied by a power of 10—is known as scientific notation.
Generally speaking, scientific notation is
All numbers in scientific notation are expressed in their standard form as
N × 10^m
the product of N times 10 is raised to the power of m, where m is an integer and N is any real number. The significand is the real number N, while the order of magnitude is the integer m.
The number of significant figures in the number is indicated by the digit word in the scientific notation. Only the decimal point is used in the exponential term.
(2.86 × 10^−9)(9.2 × 10^15)
= 26.312 × 10^6.
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is the following graph a function?
A. yes
B. no
Answer:
Yes
Step-by-step explanation:
You can use the Vertical line test to figure this out, and sure enough none of the points touch the vertical line.
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A fashion photographer needs to hire a stylist to prepare his models. Jayla charges $156 for showing up, plus $63 per hour. Sally charges $158 plus $62 per hour. The photographer realizes that, given the expected duration of his photo shoot, either stylist would cost him the same amount. What would the cost be? What would the duration be?
Either stylist would cost $ if the shoot lasted. hours
The duration of shoot would be 2 hours and Either stylist would cost $282 if the shoot lasted 2 hours.
A fashion photographer needs to hire a stylist to prepare his models.
Let the number of hours stylist take = x
Jayla charges $156 for showing up, plus $63 per hour. So, this can be mathematically written as ,
156 + 63x equation 1
Sally charges $158 plus $62 per hour. So, this can be mathematically written as ,
158 + 62x equation 2
As per the question, the expected duration of his photo shoot, either stylist would cost him the same amount. So we can equate equation 1 and equation 2. On equating equation 1 and equation 2 , we will get
156 + 63x = 158 + 62x
⇒ x = 2
So, the duration would be 2 hours.
Jayla cost = Sally cost = 156 + 63x = 156 + (63 × 2) = 282
Either stylist would cost $282 if the shoot lasted 2 hours.
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What is the domain of the function
Answer:
third answer is correct
Step-by-step explanation:
3. Veronica is making two scarves. The scarves will be square. She graphs the first scarf with
vertices at P(-2, 4), Q(4, 4), R(-2,-2), and S(4, -2). She will graph the second reflected in
the line x = -3. Find the coordinates of the image of the second scarf.
X
According to the graph reflection we find out that the coordinates of the image of the second scarf are (-3,4), (3,4), (-3,-2), and (3,-2) respectively.
It is given to us that -
Veronica is making two scarves which will be square shaped
The first scarf has vertices at P(-2, 4), Q(4, 4), R(-2,-2), and S(4, -2)
The graph for second scarf is reflected in the line x = -3.
We have to find the coordinates of the image of the second scarf.
According to the given information, the image of the second scarf is reflected in the line x = -3. This implies there is no change in the y coordinates of the vertices of the second scarf.
Therefore, according to the graph reflection we find out that the coordinates of the image of the second scarf are (-3,4), (3,4), (-3,-2), and (3,-2) respectively.
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Use the cubic regression capability of your calculator to find a cubic model for this data. Round your coefficients to the nearest tenth.
x: 1,2,3,4,5,6,7,8,
y: 39,43,43,46,56,61,57,52
y = __x^3 + __x^2 + __x + __.
x: 1, 2, 3, 4, 5, 6, 7, 8
y: 39, 43, 43, 46, 56, 61, 57, 52
Using the cubic regression analysis, we obtain the following cubic model equation:
y = -0.3x^3 + 4.2x^2 - 4.4x + 43.1
Rounding the coefficients to the nearest tenth, the cubic model equation becomes:
y = -0.3x^3 + 4.2x^2 - 4.4x + 43.1Please note that the coefficients are rounded to the nearest tenth for simplicity.
A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that apply.
The correct statements are:
The triangle and trapezoid area formulas have 1/2.
The parallelogram and rectangle formulas are both the same.
In the trapezoid formula, the bases are added.
What is a triangle?A triangle is a polygon with three sides and three vertices. A triangle's angles add up to 180 degrees.
Area of a triangle = 1/2 x base x height
A trapezium is a quadrilateral that is convex. A trapezium is made up of at least two parallel sides. Area of a trapezium = 1/2 x (sum of the lengths of the parallel sides) x height
A rectangle is a quadrilateral in two dimensions with four right angles. Area of a rectangle = length x width
A parallelogram is a quadrilateral with two parallel sides. The opposite sides equal in length
Area of a parallelogram = base x height
Hence, the correct statements are options (A), (B), and (D).
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The question seems to be incomplete the correct question would be:
A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The neighborhood is
considering how to split up the area. Which statements about the formulas for finding areas are true? Check all that
apply.
A. The triangle and trapezoid area formulas have 1/2.
B. The parallelogram and rectangle formulas are both the same.
C. In the parallelogram formula, the bases are added.
D. In the trapezoid formula, the bases are added.
E. In the triangle formula, the sides are added, then multiplied by 1/2
In a free-throw contest, three players take the same number of shots. Player A makes 47 of 55 shots. Player B makes 0.84 of his shots. Player
makes 87% of her shots. Who wins?
O Player A
O Player B
O Player
O A and C tie.
Answer:
Player C
Step-by-step explanation:
Player A:
He made 47 of his 55 shots.
In percentage, this translates to;
47/55 × 100% = 85.45%
Player B: conversion ratio = 0.84
In percentage, this translates to 84%
Player C:
She made 87% of her shots
Player C had the highest conversion percentage and is thus the winner
Help me Plzzzzz!! ASAP!
The function f(x) is shown in the graph.
Which type of function describes f(x)?
a) Exponential
b) Logarithmic
c) Rational
d) Polynomial
The function that describes the graph is an exponential function
How to determine the function type?From the graph, we have the following highlights:
Initially, when x increases; y seem not to increaseThen, x and y increase at the same timeFinally, y increase and x seem not to increaseThe above is the description of an exponential function
Hence, the function that describes the graph is an exponential function
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angle <1 and angle <2 are complementary angles. The measure of angle <1 is 42 degrees. The measure of angle <2 is 4x degrees. Find the value of x. The figure is not drawn to scale.
The value of x is 12.
we have, <1 = 42 degree
<2 = 4x degree
As, <1 and <2 are Complementary Angle.
So, the sum of <1 and <2 will be 90 degree
<1 + <2 = 90
42 + 4x = 90
4x = 90-42
4x = 48
x= 48/4
x= 12
Thus, the value of x is 12.
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A building in the shape of a cube has a width of 45 ft., a length of 45 ft., and a height of 45 ft. An architect wants to build a scale model of the building that is 30% smaller in volume. What is the height of the new building? Round to the nearest hundredth.
Answer:
39.96 ft
Step-by-step explanation:
\(45^3 = 9112591125 - 0.3 * 91125 = 91125 * (1 - 0.3) = 91125 * 0.7 = 63787.5 63787.5 ^(^\frac{1}{3} ^) = 39.95568008\)
the niagara falls incline railway has an angle of elevation of 30° and a total length of 196 feet. how many feet does the niagara falls incline railway rise vertically? ..... feet
The Niagara Falls incline railway rises vertically by approximately 98 feet.
The angle of elevation of 30° indicates the angle between the incline railway and the horizontal ground. The total length of the incline railway is given as 196 feet.
To find the vertical rise, we can use trigonometry. The vertical rise can be determined by calculating the sine of the angle of elevation and multiplying it by the total length of the incline railway:
Vertical rise = Total length × sine(angle of elevation)
Vertical rise = 196 ft × sin(30°)
Vertical rise ≈ 196 ft × 0.5
Vertical rise ≈ 98 ft
Therefore, the Niagara Falls incline railway rises vertically by approximately 98 feet.
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The width of a rectangle is 2 units less than the length. The area of the
rectangle is 48 square units. What is the width, in units, of the rectangle?
Answer:
6 units
Step-by-step explanation:
Let's call the length of the rectangle "L" and the width "W".
From the problem, we know that the width is 2 units less than the length, so we can write:
W = L - 2
We also know that the area of the rectangle is 48 square units, so we can write:
A = L * W
Substituting the first equation into the second equation, we get:
48 = L * (L - 2)
Expanding the brackets, we get:
48 = L^2 - 2L
Rearranging, we get:
L^2 - 2L - 48 = 0
Now we can use the quadratic formula to solve for L:
L = (-b ± sqrt(b^2 - 4ac)) / 2a
In this case, a = 1, b = -2, and c = -48. Substituting these values into the formula, we get:
L = (2 ± sqrt(4 + 192)) / 2
L = (2 ± sqrt(196)) / 2
L = (2 ± 14) / 2
So, L = 8 or L = -6. We can ignore the negative solution, so the length of the rectangle is 8 units.
Now we can use the first equation to find the width:
W = L - 2
W = 8 - 2
W = 6
Therefore, the width of the rectangle is 6 units.
the height of a house is 52 ft. a tree beside the house is 7 ft more than twice as tall. what is the height of the tree? enter your answer in the box. ft
Answer: 111 ft tall. Thats a big tree!
Step-by-step explanation: if its seven more than two times the height of the house, do 52 X 52 + 7 which equals 111 ft.