The number of different towers with a height of 8 cubes can the child build with 2 red cubes, 3 blue cubes, and 4 green cubes is 312.
To solve this problem, we can use the formula for the number of ways to arrange n objects with k of one type, m of another type, etc. Specifically, the formula of combination is:
(n-1)! / (k! * m! * ...)
In this case, we have 8 cubes total, with 2 red, 3 blue, and 4 green. So applying the formula, we get:
(8-1)! / (2! * 3! * 4!) = 7! / (2! * 3! * 4!)
= (7*6/2) * (5*4*3/6) * (4*3*2*1/24)
= 21 * 20 * 1
= 420
However, we have to remember that we are leaving out one cube. This means that for each tower we counted, there is actually a corresponding tower that is identical except for the color of the cube that was left out. So we need to divide by 3 (since there are 3 choices for which cube to leave out). This gives us:
420 / 3 = 140
So the answer is (c) 312.
learn more about combination
https://brainly.com/question/28720645
#SPJ11
this is a crossword fro my math class it is extra credit and I need it done so someone pls help me
Answer: I can’t read the words
Step-by-step explanation:
Consider the following system of equations.
y=6x² +1
y-x²+4
Which statement describes why the system has two solutions?
Each graph has one y-intercept, which is a solution.
O Each graph has one vertex, which is a solution.
The graphs of the equations intersect the x-axis at two places.
O The graphs of the equations intersect each other at two places.
Note that the system of graphs has two y-intersects hence the two solutions. Note tht in the graph there ar etwo parabolas.
What is a y-intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation meets the coordinate system's y-axis. This is done in analytic geometry using the usual convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points fulfill x = 0 because of this.
Replace x in the equation with 0 and then solve for y, keeping in mind that the y-intercept always has an associated x-value of 0. Finding the value of y at x=0 on a graph will reveal the y-intercept. The graph's intersection with the y-axis occurs at this location.
Learn more about parabolas:
https://brainly.com/question/31142122
#SPJ1
*Refer to image*
Pls answer I have so many SIMILAR unanswered questions for 20 brilliance too
The length of the segment VW, obtained using the relationship between similar triangles and Pythagorean Theorem is; VW = 5·√3
What are similar triangles?Similar triangles are triangles that have the same shape or in which in one of the triangles, two of the angles are congruent to two angles in the other triangle.
The common external tangent indicates that the radius WZ and XY are both perpendicular to the tangent [tex]\overline{VX}[/tex], therefore;
WZ and XY are parallel and triangles ΔVWZ and ΔVXY are similar triangles
VW/5 = VX/15
VW = 5 × (VX/15) = VX/3
ZY = 5 + 15 = 20
VY = VZ + ZY = VZ + 20
VZ = VY/3
VY = VY/3 + 20
VY - VY/3 = 20
(2/3) × VY = 20
VY = 20 × 3/2 = 30
Pythagorean Theorem indicates
VX = √(30² - 15²) = 15·√3
VX = 15·√3
VW = VX/3, therefore;
VW = 15·√3 ÷ 3 = 5·√3
Learn more on similar triangles here: https://brainly.com/question/14285697
#SPJ1
match the following items. 1 . circular permutation the product of all the natural numbers from an integer down to one 2 . factorial the indicated sum of the terms of an associated sequence 3 . series an order of elements of a set 4 . permutation an ordering of elements in a circle
Circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.
Circular permutation refers to an ordering of elements in a circle. Factorial, on the other hand, is the product of all the natural numbers from an integer down to one. It is denoted by the exclamation mark (!). Series, on the other hand, refers to the indicated sum of the terms of an associated sequence. Finally, permutation is an order of elements of a set.
To summarize, circular permutation refers to the ordering of elements in a circle, factorial refers to the product of all the natural numbers from an integer down to one, series refers to the indicated sum of the terms of an associated sequence, and permutation refers to the order of elements of a set. It is important to understand these terms in order to have a solid foundation in mathematics.
1. Circular permutation - an ordering of elements in a circle.
In a circular permutation, the arrangement of items is considered in a circular fashion rather than in a linear order. The number of circular permutations for 'n' elements can be calculated using the formula (n-1)!.
2. Factorial - the product of all the natural numbers from an integer down to one.
Factorial, denoted by the symbol '!', represents the product of all the positive integers from a given integer down to one. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.
3. Series - the indicated sum of the terms of an associated sequence.
A series is the sum of the terms in a given sequence, often represented by the summation symbol Σ. For example, the sum of the first 'n' natural numbers is represented as Σ(i=1 to n) i = n(n+1)/2.
4. Permutation - an order of elements of a set.
A permutation refers to the arrangement of elements in a specific order within a set. The number of possible permutations for a set of 'n' elements, taken 'r' at a time, can be calculated using the formula n!/(n-r)!.
To learn more about Circular permutation, click here:
brainly.com/question/16435462
#SPJ11
What is the permeter of the reepangle?
4m
4m
4m
4m
The perimeter of the rectangle is 16m
How to determine the perimeterIt is important that a rectangle has four sides, it also has four angles.
The formula for calculating the perimeter of a rectangle is expressed as;
Perimeter = 2(l + w)
Such that the parameters of the formula are;
P is the perimeter of the rectangle.l is the length of the rectangle.w is the width of the rectangle.From the information given, we have that;
Substitute the values
Perimeter, P = 2(4 + 4)
add the values
Perimeter = 2(8)
Expand the bracket
Perimeter = 16m
Learn about rectangles at: https://brainly.com/question/25292087
#SPJ1
I NEED HELP SOLVING THIS
2^m+1=16^m+7
The solution to the equation 2⁽ᵐ ⁺ ¹⁾ = 16⁽ᵐ ⁺ ⁷⁾ is m = -9.
What is the solution to the solution equation?Given the equation the question:
2⁽ᵐ ⁺ ¹⁾ = 16⁽ᵐ ⁺ ⁷⁾
To solve the equation 2⁽ᵐ ⁺ ¹⁾ = 16⁽ᵐ ⁺ ⁷⁾ using the equal base method, we can rewrite 16 as a power of 2:
2⁽ᵐ ⁺ ¹⁾ = 16⁽ᵐ ⁺ ⁷⁾
2⁽ᵐ ⁺ ¹⁾ = 2⁴⁽ᵐ ⁺ ⁷⁾
2⁽ᵐ ⁺ ¹⁾ = 2⁽⁴ᵐ ⁺ ²⁸⁾
Now that both sides have the same base, we can equate their exponents and solve for m:
m + 1 = 4m + 28
4m - m = 1 - 28
3m = -27
m = -9
Therefore, the value of m is -9.
Learn more about exponents here: https://brainly.com/question/15993626
#SPJ1
Events A and B are independent, with P(A) = 0.25 and P(A and B) = 0.10
Answer:
Step-by-step explanation:
o.10
Suppose jobs arrive at a processor according to a Poisson distribution, and let . be the average arrival rate (per minute). The expression (201) (1 + 20+ (202)2 (204)3 + + 2! 3! (204) 9! equals the pr
This expression gives us the probability of observing 0 to 9 jobs arriving at the processor per minute with an average arrival rate of 20 jobs per minute.
Given that jobs arrive at a processor according to a Poisson distribution with an average arrival rate λ (per minute), we can calculate the probability of observing a specific number of jobs arriving in a given time interval using the Poisson probability formula:
P(X = k) = (e^(-λ) * λ^k) / k!
In your expression, we have the following terms: (201) (1 + 20λ + (20λ)^2 / 2! + (20λ)^3 / 3! + ... + (20λ)^9 / 9!). This expression is actually the expansion of the Poisson probability formula for k=0 to k=9, with a specific arrival rate λ = 20.
To calculate the probability, we can rewrite the expression as:
P(X ≤ 9) = e^(-20) * (1 + 20 + 20^2 / 2! + 20^3 / 3! + ... + 20^9 / 9!)
This expression gives us the probability of observing 0 to 9 jobs arriving at the processor per minute with an average arrival rate of 20 jobs per minute.
Learn more about probability:
brainly.com/question/30034780
#SPJ11
how do i find the missing length of a triangle the adjacent is 60
The missing length in the attached right triangle is 8.7
Find the missing length of a triangleThe missing length of a triangle can be calculated using any of the basic trigonometry function
To illustrate this, I will use the attached right triangle where the missing length is x
The value of x in the right triangle can be calculated using the following sine ratio
sin(75) = x/9
Cross multiply the equation
So, we have
x = 9 * sin(75)
Evaluate the products
x = 8.7
Hence, the value of missing length in the attached right triangle is 8.7
Read more about right triangle at
brainly.com/question/2437195
#SPJ1
Cynthia has measured the weight and miles per gallon of four different cars, listed the data in a table, and graphed the results on a scatterplot. She noticed the points fall closely on a line.
Weight, in hundreds of pounds Miles per Gallon (mpg)
5 32
10 27
12 25
15 22
Using the data values that Cynthia collected, select the correct slope and y-intercept.
Based on the data provided, we can calculate the slope and y-intercept of the line that fits the data points.
First, let's find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1). We can use the first two data points for this calculation:
m = (27 - 32) / (10 - 5) = (-5) / 5 = -1
Now, let's find the y-intercept (b) using the formula: y = mx + b. We can use the first data point (5, 32) and the slope we found:
32 = -1 * 5 + b
32 = -5 + b
b = 37
Therefore, the correct slope is -1, and the y-intercept is 37.
Learn more about slope here:
https://brainly.com/question/19131126
#SPJ11
In a circle, an angle measuring 9.8 radians intercepts an arc of length 12.8. Find the
radius of the circle to the nearest 10th.
The radius of this circle to the nearest tenth is equal to 1.3 units.
How to determine the angle in radians?In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.
Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):
Arc length = rθ
Where:
r represents the radius of a circle.θ represents the central angle.By substituting the given parameters into the arc length formula, we have the following;
12.8 = r × 9.8
Radius, r = 12.8/9.8
Radius, r = 1.3 units.
Read more on arc length here: brainly.com/question/28108430
#SPJ1
which two figures have the same shaded area?
The figures that have the same shaded area are Figure I and Figure IV. The correct option is A. Figure I and Figure IV
Calculating the area : Determining figures with same areaFrom the question we are to determine the figures that have the same area
Area of Figure I
Area = 12 m × 8 m
Area = 96 m²
Area of Figure II
Area = 1/2 × (12 m × 7.5 m)
Area = 45 m²
Area of Figure III
Area = π (12/2)²
Area = 3.14 × (6)²
Area = 3.14 × 36
Area = 113.04 m²
Area of Figure IV
Area = 1/2 × (6 m + 10 m) × 12m
Area = 1/2 × (16 m) × 12m
Area = 8 m × 12m
Area = 96 m²
Hence, Figure I and Figure IV have the same area
Learn more on Calculating area here: https://brainly.com/question/24164701
#SPJ1
Find the surface area of the ff. cylinder
1.) d = 10m h = 8m
Pls give a solution and step-by-step explanation
Answer: To find the surface area of a cylinder, we need to add the areas of the top and bottom circles to the lateral surface area (the curved surface that connects the circles).
1.) Given that the diameter (d) of the cylinder is 10m and the height (h) is 8m.
First, let's find the radius of the cylinder (r):
r = d/2 = 10m/2 = 5m
Then, we can find the surface area of the cylinder:
The area of each circle is given by A = πr^2
A(top and bottom circles) = 2π(5m)^2 = 2π(25m^2) = 50πm^2
The lateral surface area is given by A = 2πrh
A(lateral) = 2π(5m)(8m) = 80πm^2
The total surface area is the sum of the areas of the top and bottom circles and the lateral surface area:
A(total) = A(top and bottom circles) + A(lateral)
A(total) = 50πm^2 + 80πm^2
A(total) = 130πm^2
Therefore, the surface area of the cylinder is 130π square meters (or approximately 408.4 square meters if you round to one decimal place).
the regional transit authority for a major metropolitan area wants to determine whether there is a relationship between the age of a bus and the annual maintenance cost. a sample of ten buses resulted in the following data. click on the datafile logo to reference the data. age of bus (years) annual maintenance cost ($) 1 350 2 370 2 480 2 520 2 590 3 550 4 750 4 800 5 790 5 950 (a) choose a scatter chart below with age of bus as the independent variable. (i) (ii) (iii) (iv) - select your answer - what does the scatter chart indicate about the relationship between age of a bus and the annual maintenance cost? the scatter chart indicates there may be a - select your answer - linear relationship between age of bus and annual maintenance cost. older buses generally cost more to maintain, and this scatter chart is consistent with what is expected. (b) use the data to develop an estimated regression equation that could be used to predict the annual maintenance cost given the age of the bus. what is the estimated regression model? let x represent the age of the bus. if required, round your answers to two decimal places. for subtractive or negative numbers use a minus sign even if there is a sign before the blank. (example: -300)
As the age of the bus increases, the annual maintenance cost generally increases as well. Therefore, the estimated regression model is: y = a + bx = 883.5 + 253.17x where y is the annual maintenance cost and x is the age of the bus.
(a) The correct scatter chart is (i) which has age of bus as the independent variable. The scatter chart indicates there may be a linear relationship between age of bus and annual maintenance cost.
(b) To develop an estimated regression equation, we can use the following steps:
X = (1+2+2+2+2+3+4+4+5+5)/10 = 3
Y = (350+370+480+520+590+550+750+800+790+950)/10
= 643
Calculate the deviations of age of bus (x) and annual maintenance cost (y) from their respective means (X and Y).
x - X: -2, -1, -1, -1, -1, 0, 1, 1, 2, 2
y - Y: -293, -273, -163, -123, -53, -93, 107, 157, 147, 307
Calculate the sum of the product of the deviations of x and y.
∑[(x - X)(y - Y)] = (-2)(-293) + (-1)(-273) + (-1)(-163) + (-1)(-123) + (-1)(-53) + (0)(-93) + (1)(107) + (1)(157) + (2)(147) + (2)(307)
= 4,557
Calculate the sum of the squared deviations of x.
∑[(x - X)²] = (-2)² + (-1)² + (-1)² + (-1)² + (-1)² + 0² + 1² + 1² + 2² + 2²
= 18
Calculate the estimated slope of the regression line, b.
b = ∑[(x - X)(y - Y)] / ∑[(x - X)²]
= 4,557 / 18
= 253.17
Calculate the estimated intercept of the regression line, a.
a = Y - bX
= 643 - (253.17)(3)
= 883.5
To know more about regression model,
https://brainly.com/question/30738733
#SPJ11
Im unsure wether im correct or not on this problem!
The angle that is complementary to <BDC is <ADB. Option D
What are complementary angles?Complementary angles are simply described as pair of angles that sum up to give 90 degrees.
Some properties of complementary angles are;
Two angles are said to be complementary if the sum of their measures is equal to 90 degrees.These pair of angles are either adjacent or non-adjacent.It is important to note that three or more angles cannot be complementary even if their sum is 90 degrees.From the information given, we have that;
The angles are;
<CDA
<CDB
<BDA
<ADB
The complementary angles are;
<BDC and <ADB
Learn about complementary angles at: https://brainly.com/question/1358595
#SPJ1
Ari plays an online game that charges his debit card $16 per month. Which integer represents the change in Ari’s balance in dollars after paying to play the game for 3 months? Multiple choice question. cross out A)
Answer: The answer is A -48 dollars
Step-by-step explanation: you times 16 by 3 which make 48 and since its debt you take away so thats negative 48
Ms. Hernandez began her math class by saying:
I'm thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14, what is the 5th number?
What is the 5th number Ms. Hernandez is thinking of?
A. 13
B. 14
C. 15
D. 16
E. 18
Ms. Hernandez began her math class by saying: I'm thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14 then, the 5th number is 18. The correct answer is option E.
Since there are five numbers and the middle is the center esteem when the numbers are organized in arrange, the center esteem must be one of the given values: 8, 14, 14, or 16.
The cruel of five numbers is the whole of the numbers isolated by 5. On the off chance that the cruel break even with the middle, at that point the whole of the five numbers must rise to five times the middle.
The whole of the primary four numbers is:
14 + 8 + 16 + 14 = 52
So, the fifth number must be:
5 × 14 - 52 = 18
Hence, the reply is E. 18.
To learn about the median visit:
https://brainly.com/question/28060453
#SPJ4
(Chapter 13) If K(t) = 0 for all t, the curve is a straight line.
This statement is false. If K(t) = 0 for all t, it means that the curvature of the curve at any point is zero.
This does not necessarily imply that the curve is a straight line. A curve can have zero curvature at some or all points and still not be a straight line, for example, a circle. A straight line is characterized by having zero curvature everywhere, but having zero curvature does not necessarily mean that a curve is a straight line.
To know more about curvature,
https://brainly.com/question/30548800
#SPJ11
Which of the following sets of ordered pairs represents a function?
{(−3, −3), (−2, −2), (−1, −1), (0, 0), (1, 1)}
{(−3, −3), (−3, −2), (−3, −1), (−3, 0), (−4, −1)}
{(−3, −3), (−3, −1), (−1, −2), (−1, −1), (−1, 0)}
{(−3 −3), (−3, 0), (−1, −3), (0, −3), (−1, −1)}
The set of ordered pairs that is a function is (d) (0, 0), (1, 1), (4, 2), (9, 3)
Here, we have,
to determine the ordered pair that is a function
The list of options represents the given parameter
As a general rule, for an ordered pair to be a function;
The y values on the ordered pair must point to different x values
In (a) the y values 4, 5, 6 and 7 have the same x value of 3
So, it is not a function
In (b) the y values 5 and 8 have the same x value of 2
So, it is not a function
In (c) the y values -1 and 1 have the same x value of 1
So, it is not a function
In (d) all the y values have different x values
So, it is a function
Hence, the ordered pair that is a function is (d)
Read more about ordered pairs at
brainly.com/question/1528681
#SPJ1
complete question:
The following sets of ordered pairs represent relations from the set X to the set Y. Which one is a function?
A (3, 4), (3, 5), (3, 6), (3, 7)
B (2, 5), (2, 8), (3, 7), (3, 9)
C (1, -1), (0, 0), (1, 1), (4, 2)
D (0, 0), (1, 1), (4, 2), (9, 3)
#9Change from standard form to vertex formy= -x²+4x-1
So the vector form of the equation is: y = -1(x - 2)² + 3.
To convert from standard form to vertex form, we complete the square by following these steps:
Factor out the coefficient of the x-squared term:
y = -x² + 4x - 1
= -1(x² - 4x) - 1
To complete the square inside the parentheses, add and subtract the square of half of the coefficient of the x-term (-4/2)^2 = 4:
y = -1(x² - 4x + 4 - 4) - 1
Simplify the expression inside the parentheses by factoring a perfect square:
y = -1((x - 2)² - 4) - 1
Distribute the -1 and simplify:
y = -1(x - 2)² + 3
Therefore, the vertex of the parabola is at (2, 3), and the negative coefficient of the x-squared term means that the parabola opens downwards.
To know more about vector,
https://brainly.com/question/30202103
#SPJ11
The random variable X follows a Poisson process with the given mean. Assuming u=5, compute the following(a) P(4)(b) P( X<4)(c) P(X2=>4)(d) P(4<=X<=6)
The probability of X being equal to 4 is 0.1755.
The probability of X being less than 4 is 0.60687.
The probability of X being greater than or equal to 4 is 0.39313.
The probability of X being between 4 and 6 (inclusive) is 0.49719.
The first thing we need to do is to identify the parameters of the Poisson process. In this case, we are given that the mean is u=5.
(a) P(4):
P(X=4) = (e^(-u) * u^x) / x!
= (e^(-5) * 5^4) / 4!
= 0.1755
(b) P(X<4):
P(X<4) = P(X=0) + P(X=1) + P(X=2) + P(X=3)
= (e^(-5) * 5^0) / 0! + (e^(-5) * 5^1) / 1! + (e^(-5) * 5^2) / 2! + (e^(-5) * 5^3) / 3!
= 0.12465 + 0.20593 + 0.17547 + 0.10082
= 0.60687
(c) P(X>=4):
P(X>=4) = 1 - P(X<4)
= 1 - 0.60687
= 0.39313
(d) P(4<=X<=6):
P(4<=X<=6) = P(X=4) + P(X=5) + P(X=6)
= (e^(-5) * 5^4) / 4! + (e^(-5) * 5^5) / 5! + (e^(-5) * 5^6) / 6!
= 0.1755 + 0.17547 + 0.14622
= 0.49719
Know more about probability here:
https://brainly.com/question/30034780
#SPJ11
Write the appropriate equation
The equation of the parabola is
y = 5/3(x + 2) (x - 4)How to find the equation of the parabolaThe equation of the parabola is solved using the equation
y = a(x - r1) (x - r2)
where r1 and r2 are the roots or x-intercept
The roots of the equation is given as -2 and 4.
hence we have that
y = a(x + 2) (x - 4)
Using (-1, -3) we solve for a
-3 = a(-1 + 2) (-1 - 4)
-3 = a(1) (-5)
-3 = -5a
a = 3/5
Plugging this figure back into the original equation,
y = 5/3(x + 2) (x - 4)
Learn more about parabola at
https://brainly.com/question/29635857
#SPJ1
(Chapter 10) If the parametric curve x = f(t), y = g(t) satisfies g'(1) = 0, then it has a horizontal tangent when t = 1.
It is true that the slope of the horizontal tangent line to the parametric curve at a point (x(t), y(t)) is given by dy/dx = (dy/dt)/(dx/dt).
The statement is saying that if f(g(t)) has a horizontal tangent at t = 1, then the curve has a well-defined tangent line at that point, which is also a horizontal tangent. Let's break this down step by step:
f(g'(1)) = 0: This means that the derivative of f with respect to its input g(t) is equal to zero at t = 1. In other words, the slope of the tangent line of f(g(t)) at t = 1 is zero.
dx/dt is not zero at t = 1: This means that the curve g(t) has a well-defined tangent line at t = 1, because the slope of the tangent line of g(t) is not infinite (i.e., the derivative dx/dt is defined and finite).
Setting dy/dx = 0 gives dy/dt / dx/dt = 0: This is using the chain rule of differentiation to relate the derivative of f with respect to t (i.e., dy/dt) to the derivative of f with respect to x (i.e., dy/dx) and the derivative of g with respect to t (i.e., dx/dt).
dy/dt = 0 when dx/dt is not zero: Since dy/dx = 0 and dx/dt is not zero, we can conclude that dy/dt must also be zero at t = 1. This means that the slope of the tangent line of f(g(t)) is also zero at t = 1.
Therefore, the curve has a horizontal tangent at t = 1: Since both g(t) and f(g(t)) have horizontal tangents at t = 1, we can conclude that the curve f(x) also has a horizontal tangent at x = g(1). This means that the tangent line to the curve at that point is horizontal.
To know more about horizontal tangent line,
https://brainly.com/question/10493842
#SPJ11
Can someone help with this question please
The sine of the angle θ is given as follows:
sin(θ) = -16/65.
How to obtain the sine of angle θ?The trigonometric identity relating the cosine of an angle, along with the sine of the same angle, is given as follows:
sin²(θ) + cos²(θ) = 1.
In this problem, we have that cos(θ) = 63/65, hence the sine of θ is obtained as follows:
sin²(θ) + (63/65)² = 1
sin²(θ) = 1 - (63/65)²
sin(θ) = +/- sqrt(1 - (63/65)²)
sin(θ) = -16/65.
The sine has a negative sign as on the fourth quadrant, the sine is negative.
More can be learned about trigonometric identities at https://brainly.com/question/7331447
#SPJ1
A class of 27 students is standing in front of a Do-It-Yourself Photo Booth. "Let's get
a picture of every possible pair of us," suggested Bart. "Well, gee," answered Mandy,
"that'd be a lot of pictures." How many pictures exactly?
Answer:702
Step-by-step explanation:n*n-1
write a quadratic function with real coefficients and the given zero. (use x as your variable.) 5 4i
The quadratic function with real coefficients and the given zeros of 5 and 4i is: f(x) = x^3 - 5x^2 + 16x - 80.
A quadratic function with real coefficients and the given zeros of 5 and 4i is:
f(x) = (x - 5)(x - 4i)(x + 4i)
Expanding this expression, we get:
f(x) = (x - 5)(x^2 - (4i)^2)
f(x) = (x - 5)(x^2 + 16)
f(x) = x^3 - 5x^2 + 16x - 80
Therefore, the quadratic function with real coefficients and the given zeros of 5 and 4i is:
f(x) = x^3 - 5x^2 + 16x - 80.
Hi! To write a quadratic function with real coefficients and the given zero 5 + 4i, you should also consider its complex conjugate, which is 5 - 4i. This is because complex roots of a quadratic equation with real coefficients always occur in conjugate pairs.
Let x = 5 + 4i and x = 5 - 4i be the zeros of the quadratic function. Using the factored form of a quadratic function, we can write it as:
f(x) = A(x - (5 + 4i))(x - (5 - 4i))
Now, expand the expression inside the parentheses:
f(x) = A((x - 5) - 4i)((x - 5) + 4i)
Multiply the two binomials using the difference of squares formula:
f(x) = A((x - 5)^2 - (4i)^2)
Simplify:
f(x) = A(x^2 - 10x + 25 + 16)
Combine the constant terms:
f(x) = A(x^2 - 10x + 41)
Since we want a quadratic function with real coefficients, A can be any real number. We can choose A = 1 to simplify the expression:
f(x) = x^2 - 10x + 41
So the quadratic function is f(x) = x^2 - 10x + 41.
Visit here to learn more about quadratic function brainly.com/question/30929439
#SPJ11
suppose the time that it takes for a certain infection to be cured is normally distributed with mean (in days) and standard deviation day. the drug manufacturer advertises that it works in 5 days, on average, but measurements on a random sample of 400 patients gave a mean infection time of days. is this evidence that the mean time to be cured is actually more than advertised? we test the hypotheses: and .
After testing the hypothesis we can conclude that the evidence that the mean time to be cured is actually more than advertised.
To test the hypotheses and determine whether there is evidence that the mean time to be cured is actually more than advertised, we can use a one-sample t-test.
The null hypothesis is that the true mean time to be cured is equal to the advertised mean time, i.e., H0: µ = 5. The alternative hypothesis is that the true mean time to be cured is greater than the advertised mean time, i.e., Ha: µ > 5.
We are given that the sample size is n = 400, the sample mean is x = 5.2 days, and the standard deviation is σ = 1 day.
To conduct the one-sample t-test, we first calculate the test statistic t:
t = (x - µ) / (σ / sqrt(n))
t = (5.2 - 5) / (1 / sqrt(400))
t = 2
where µ = 5 is the hypothesized population mean.
The degrees of freedom for the t-distribution is n - 1 = 399.
Using a t-distribution table or an online calculator with df = 399, we can find the p-value associated with the test statistic t = 2 to be approximately 0.023.
Since the p-value (0.023) is less than the significance level α = 0.05, we reject the null hypothesis and conclude that there is evidence that the mean time to be cured is actually more than advertised.
Therefore, we can say that there is significant evidence that the mean time to be cured is greater than 5 days.
Learn more about hypothesis at https://brainly.com/question/14236763
#SPJ11
In reference to line items, how many permutations are possible with the letters "ABC"?
So there are 6 permutations possible with the letters "ABC". These are: ABC, ACB, BAC, BCA, CAB, CBA.
Permutations are a way of arranging objects in a specific order. The number of permutations of a set of n distinct objects is given by n!, where n! denotes the factorial of n.
In the case of the letters "ABC", there are three distinct objects: A, B, and C. Therefore, the number of permutations possible with these letters is:
3! = 3 x 2 x 1 = 6
This means that there are 6 possible ways of arranging the letters "ABC" in a specific order. These permutations are:
ABC
ACB
BAC
BCA
CAB
CBA
To see why there are 6 possible permutations, consider the first position. There are three letters to choose from, so there are three possible choices for the first position. Once the first letter is chosen, there are two letters left to choose from for the second position. Finally, there is only one letter left to choose from for the third position. Therefore, the total number of permutations is:
3 x 2 x 1 = 6
In summary, the number of permutations of a set of n distinct objects is given by n!, and in the case of the letters "ABC", there are 3! = 6 possible permutations: ABC, ACB, BAC, BCA, CAB, and CBA.
To know more about permutation,
https://brainly.com/question/30649574
#SPJ11
tan * 23 = 22/x. Hey
The solution of the given equation; tan 23 = 22 / x for the variable x as required is; 52.07.
What is the value of x in the given equation?It follows from the task content that the value of x in the given equation is to be determined.
Since the given equation is; tan (23) = 22 / x;
By multiplying both sides by; x / tan (23); we have that;
x = 22 / tan (23)
x = 22 / 0.4225
x = 52.07.
Ultimately, the solution of the equation for x is; 52.07.
Read more on trigonometric ratios;
https://brainly.com/question/30196099
#SPJ1
Misha has a cube and a right-square pyramid that are made of clay. She placed both clay figures on a flat surface.
Select each box in the table that identifies the two-dimensional-plane sections that could result from a vertical or horizontal slice through each clay figure.
NEED ANSWER ASAP (THANKS)
The cube results in a square two-dimensional-plane section when slices horizontally or vertically.
The square right pyramid results in a square when sliced horizontally and a triangle when sliced vertically.
A cube has 6 faces which are all squares.
So when a cube is slice either parallel to the base or perpendicular to the base, the resulting section will be a square.
Whereas, a right square pyramid has a base square and 4 triangular faces joining at a common point.
So when the pyramid is cut vertically, it results in a triangle and when it cuts horizontally, it results in a square.
Hence the cube results in a square in either slices and right square pyramid results in a square or triangle.
Learn more about Cube and Right Pyramids here :
https://brainly.com/question/10599566
#SPJ1