The number of ways that Brad can pick groups of four is 715 ways.
How many ways could Brad pick groups of four?Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula is given as:
= n! / ((n – r)! r!)
n = the number of items.
r = how many items are taken at a time.
Based on the information, Brad has a list of thirteen such people and would like to propose some documentaries about four of them. This will be:
n! / ((n – r)! r!)
= 13! / (13 - 4)!4!
= 13! / 9!4!
= 13 × 12 × 11 × 10 / 4 × 3 × 2
= 715
There'll be 715 ways.
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2. A train leaves Alphaville at 13 27. It travels at an average speed of 56 Km/h.
If it arrives in Eastwich at 16 12, What is the distance between the two
towns?
Answer: 13 27 to 15 27 = 2 hours
15 27 to 16 00 = 33 mins
1600 to 16 12 = 12 mins
Total = 2hours + 33 mins + 12 mins = 2 hours 45 mins = 2.75 hours
Distance = Speed x time = 56 x 2.75 = 154 km
Answer: 154 km
Step-by-step explanation:
Which of these is an exponential parent function?A. f(x)=2^x+ 2/3 B.f(x)=2^x C.f(x)=2^x+2 D.f(x)=2^x-3
[tex]2^{x}[/tex] + [tex]\frac{2}{3}[/tex], [tex]2^{x}[/tex], [tex]2^{x}+2[/tex], [tex]2^{x}-3[/tex] are examples of exponential parent function.So all of the given options are true.
What are exponential parent function?Parent function: The most basic function in a family of functions is the parent function. A family of functions is a collection of functions that have similar graph shapes because they all have the same greatest degree.
Four graphs that illustrate the U-shaped graph, or parabola, are displayed in the graph above. We can classify them as belonging to the same family of functions since they all have the same highest degree of two and the same form.
Exponential parent function: Algebraic expressions appear in the exponent of exponential functions. The formula for its parent function is y = [tex]b^{x}[/tex], where b can be any non-zero constant.
For above definitions we can conclude that all options given to us are exponential parent function.
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you are using the plus sign more than once in the example of 2+3=4+5
Answer:
2-3=4-5
Step-by-step explanation:
Need answers quick!
P/8 is larger or equal to -5
P>=40
P>=40
P>=-13
P>=-40
Answer:
(d) P ≥ -40
Step-by-step explanation:
You want the solution to P/8 ≥ -5.
SolutionMultiply both sides of the inequality by 8.
8(P/8) ≥ 8(-5)
P ≥ -40
Check all properties that the following relations on the set of positive integers have: The relations are defined by (x, Y) € R if and only if the indicated condition is satisfied x and Y have a common prime factor A. reflexive B. symmetric C. irreflexive D. transitive E: antisymmetric (b) x _ y is a multiple of 3 A. symmetric B. antisymmetric C: irreflexive D. reflexive E. transitive (c) x and y are both prime A. transitive B. irreflexive C. symmetric D. reflexive E: antisymmetric (d) x and y are twin primes (they are primes and their distance is 2) A. symmetric B. irreflexive C.antisymmetric D. reflexive E: transitive
If x and y have a common prime factor then y and x also have a common prime factor,so x and y are symmetric.
If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.
If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.
x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Step-by-step explanation:
Part a: x and y have a common prime factor
If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.
Reflexive: x and y are not reflexive since {1,1}∉ R(1 has no prime factor)
Symmetric: If x and y have a common prime factor then y and x also have a common prime factor , so x and y are symmetric.
Irreflexive: refer point A(above)
Transitive: x and y are not transitive since {2,9}∉ R(has no common prime factor)
Anti symmetric: x and y are not anti symmetric [Refer point B(above)]
If x and y have a common prime factor then y and x also have a common prime factor, so x and y are symmetric.
b) x - y is a multiple of 3
If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric and x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.so it is reflexive.
Symmetric: If x-y is divisible by 3 then y-x is also divisible by 3.so it is symmetric.
Antisymmetric x-y is not anti symmetric (refer above)
Irreflexive refer point D
Reflexive : x-y is reflexive as x ∈Z+ ,x-y is a multiple of 3.
Transitive: if x-y,y-z is multiples of 3 then x-z is also multiples of 3.so it is also transitive.
(c) x and y are both prime
If x,y and y,z are primes then x,z are also primes.So it is transitive and it is also symmetric If x,y are primes then y,x are also primes.
Transitive: If x,y and y,z are primes then x,z are also primes.So it is transitive.
irreflexive Refer It is not reflexive since {4,4}∉ R(4 is not a prime)
Symmetric: If x,y are primes then y,x are also primes.So it is symmetric..
Reflexive:It is not reflexive since {4,4}∉ R(4 is not a prime)
Antisymmetric: Refer point C
(d) x and y are twin primes (they are primes and their distance is 2)
x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Symmetric: x and y are symmetric since (a,b)∈ R⇒ a,b are prime and their difference is 2⇒(b,a)∈ R
Irreflexive Refer point D
Antisymmetric Refer point A
Reflexive: It is not reflexive since {4,4}∉ R
Transitive: It is not transitive because (3,5)∈R and (5,3)∈R but (3,7)∉ R
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When attempting to do his homework Mark incorrectly uses the addition property of equality below which statement would correct Mark's error?
The addition property of equality states that if two values are equal to a third value, then they are also equal to each other. In this case, 4 is equal to 5+2, so 4 must also be equal to 2+5. However, Mark wrote the equation incorrectly, so the correct statement would be 4 = 5 + 2.
Mark incorrectly uses the addition property of equality, below which statement would correct Mark's error?Mark's statement: 4 = 2 + 5Correct statement: 4 = 5 + 2The addition property of equality is a key concept in mathematics, and it is important to understand and use it correctly. In this case, 4 is equal to 5+2, so the correct statement would be 4 = 5 + 2. This is because the addition property of equality states that if two values are equal to a third value, then they are also equal to each other. Therefore, Mark's statement of 4 = 2 + 5 was incorrect, and the correct statement was 4 = 5 + 2. Understanding and applying the addition property of equality is essential for success in math.
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What are whole numbers integers and rational numbers are the set of whole numbers and their opposites?; What are whole numbers integers and rational numbers?; What are whole numbers and their opposites?; What is a whole number ?
Whole numbers range in size from 0 to infinity.
The collection of rational numbers is p/q, q ≠0.
Integers have no decimal portion and range from -infinity to infinity.
Given that,
We have to finding whole numbers, integers, and rational numbers is necessary.
the collection of whole numbers and their opposites,
The group of numbers that can be expressed as fractions is called ______.
The group of counting numbers and zero is known as ______.
We know that,
What is number system?All of the numbers that are there can be defined or represented using a number system.
Complex numbers (a + ib)
Imaginary numbers
(0 + ib)
Real numbers
(a + i0)
Rational numbers
(perfect squares)
Irrational numbers
(non-perfects squares)
Fractions.
(p/q, q ≠ 0)
Integers
Negative integers is - ∞ to - 1
Positive integers is 1 to ∞
whole numbers is 0 to ∞
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Simplify completely.
(h12/h4)3
Enter your answer in the box.
After solving the given expression using exponents properties, the resultant answer is h²⁴.
What are exponents?Exponentiation is a mathematical process that involves the base b and the exponent or power n.
It is represented as bⁿ and is pronounced as "b to the n."
Positive, negative, zero, and rational exponents are the four different categories. Positive exponents indicate the number of times a base should be multiplied by itself.
So, we have:
(h¹²/h⁴)³
Now, solve as follows using properties:
(h¹²/h⁴)³
(h¹²)³/(h⁴)³
h³⁶/h¹²
h³⁶⁻¹²
h²⁴
Therefore, after solving the given expression using exponents properties, the resultant answer is h²⁴.
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Determine whether AB and XY are parallel, perpendicular, or neither. Graph each line to verify your answer. A(8, 1), B(-2, 7), X(-6, 2), Y(-1, 1)
The slope of the line AB and XY is different. Then the line AB and XY is neither parallel nor perpendicular. The lines are intersecting line.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
The points are given as,
A(8, 1), B(-2, 7), X(-6, 2), Y(-1, 1)
The slope of line AB is given as
m₁ = (7 - 1) / (-2 - 8)
m₁ = 6 / (-10)
m₁ = - 0.6
The slope of line XY is given as
m₂ = (1 - 2) / (-1 + 6)
m₂ = - 1 / (5)
m₂ = - 0.2
The slope of the line AB and XY is different. Then the line AB and XY is neither parallel nor perpendicular. The lines are intersecting line.
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John invests $200 into an account with a 2.7% interest rate that is compounded semiannually how much money will he have in his account if he keeps it for 10 years?
If John invests $200 into an account with a 2.7% interest rate that is compounded semiannually, after 10 years he will have a future value of $261.52.
What is the future value?The future value is the compounded present value at an interest rate into the future.
The future value can be worked out using the FV table or formula. We can also use an online finance calculator to find the future value of present-day investment.
N (# of periods) = 20 semiannual periods (10 years x 2)
I/Y (Interest per year) = 2.7%
PV (Present Value) = $200
PMT (Periodic Payment) = $0
Results:
Future Value (FV) = $261.52
Total Interest = $61.52
Thus, if John invests the present value of $200 into the account, after 10 years, his investment would become $261.52.
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I need help on this question it’s really difficult please
Answer:
See attached
Step-by-step explanation:
You want the graphed figure dilated by different scale factors around different center points.
DilationTo find the image of a dilated point, figure how far it is from the center of dilation, then multiply that distance by the scale factor. Plot the image point at that distance from the center of dilation in the same direction as the original point.
Dilation by a factor of 1/2 cuts all the distances in half. 2 grid squares become 1; 4 grid squares become 2.
Dilation by a factor of 2 multiplies all the distances by 2. 2 grid squares become 4; 4 grid squares become 8.
GraphIn the attached graph, the points are labeled with subscripts a, b, c according to the dilation they correspond to. Note that the center of dilation doesn't move, so Q and Q_a are the same point, and S and S_c are the same point.
find the measure of angle B
Find the missing variable in the following question.
If there is direct variation and y=75 when x=25, find x when y=48
x=16
x=14
x=10
x=12
Hence, [tex]x=16[/tex] when [tex]y=48[/tex].
What is the direct variation?
A direct variation, also called direct proportion is a relationship between two variables [tex]x[/tex] and [tex]y[/tex] that can be written as [tex]y = kx[/tex], [tex]k\neq 0[/tex].
Here given that,
The direct variation and [tex]y=75[/tex] when [tex]x=25[/tex],
As we know that,
[tex]y[/tex]α[tex]x[/tex]
[tex]y=kx[/tex]
[tex]75=k(25)\\\\k=\frac{75}{25}\\\\k=3[/tex]
So, when [tex]y=48[/tex]
[tex]y=kx\\\\48=3x\\\\x=\frac{48}{3}\\\\x=16[/tex]
Hence, [tex]x=16[/tex] when [tex]y=48[/tex].
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Find The Volume V Of The Solid Obtained By Rotating The Region Bounded By The Given Curves About The Specified Line. 3x = Y2, X = 0, Y = 5; About The Y-Axis V =
The Method of Cylindrical Shells will be used to assist.
What is Cylindrical Shells?As previously, we construct a region R that is enclosed on the top by the graph of the function y = f (x), on the bottom by the x axis, and on the left and right by the lines x = a and x = b, respectively (a).
As seen in Figure 1, we then rotate this region around the y-axis (b). Be aware that this is distinct from what we have previously done..
Previously, areas that were described in terms of x-functions were centered on the x-axis or a line that ran parallel to it.
Since the shell is a cylinder, its volume equals the cross-sectional area times the cylinder's height. The cross-sections are annuli, which are essentially circles with holes in the middle and are formed like rings.
According to our question-
V= 2π ∫025/2 x [ 5 - √(2x) ] d x = 625π/ 4 cubic units
USING THE WASHER METHOD
V = ∫05 π (1/4) y4 d y = 625π/ 4 cubic units
Hence, The Method of Cylindrical Shells will be used to assist.
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Which function is represented in the graph? A.) y = sinx
B.) y = cosx
C.) y = sin-1x
D.) y = cos-1x
From the given information, we can that y = [tex]sin^{-1}x[/tex] function is represented in the graph.
What is inverse sine function?The opposite of the sine function is the inverse sine function, commonly referred to as the arcsine function. Since the sine (or sine function) of an angle is equal to the ratio of the opposite side to the hypotenuse, the sine inverse of that ratio will provide the angle's measurement.
According to graph
Domain is [-1, 1]
Range = [tex][-\frac{\pi }{2} ,\frac{\pi }{2} ][/tex]
Set an interval to limit [tex][-\frac{\pi }{2} ,\frac{\pi }{2} ][/tex] the sine-scope function's so that it is one to one and not unlimited.
The limited function is one to one since it satisfies the horizontal line test.
[tex]Each range value (-1 to 1) is within the limited domain (-\frac{\pi }{2} \frac{\pi }{2})[/tex]
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what is the solution to the system of equations x-y=-1 and x-3=- -13?
Answer:
Write in Standard Form
1. The standard form of a linear equation is
Ax + By = Cx-y=-1
2. x = 16
Ig?
I'm not sure.
c define a function calculatenum() that takes one integer parameter and returns 5 times the parameter. ex: if the input is 3, then the output is: 15
The function of calculatenum() is int calculatenum(int n){ return n*6; }.
How to make math operation?Function for math operation in many of programming language is same. It is some of math operation symbol,
+ = function for math addition operation
- = function for math subtraction operation
* = function for math multiplication operation
/ = function for math division operation
Keep in mind, that all math operations can only be performed for int data.
Since the question already give code for input integer parameter, we only write function for multiplication operation. So the function is,
int CalculateNum(int n) {
return n * 6;
}
Thus, the code int calculatenum(int n){ return n*6 } is a function for calculatenum().
Your question is incomplete, but most probably your full question was
define a function calculatenum() that takes one integer parameter and returns 5 times the parameter. ex: if the input is 3, then the output is: 15 (code image attached)
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A bullet train travels in 3 and half hours for 320 km. And ordinary train travels 212 km in 8 and half hours. Work out their average speed. I need it now pls be quick
The average speed of the trains are Bullet train = 91.4 km/hr and Ordinary train = 24.9 km/hr
How to determine the average speed of the trains?From the question, we have the following parameters that can be used in our computation:
Bullet train
Distance = 320 km
Time = 3 and half hours = 3.5
Ordinary train
Distance = 212 km
Time = 8 and half hours = 8.5
By definition, the speed of an object is the ratio of the distance moved by the object and the time travelled by the object
Mathematically, this can be represented as
Speed = Distance : Time
Express as fraction
Speed = Distance/Time
So, we have
Bullet train = 320/3.5 = 91.4
Ordinary train = 212/8.5 = 24.9
Hence, the speed of the ordinary train is 24.9 km per hour
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If f(x) = x ^ 2 - 3x + 11 and g(x)=11x+7, what is (fg)(x) in standard form?
In linear equation, 11x * f(x) + 7 * f(X) is (fg)(x) in standard form .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
f(x) . g(x) = f(x) . ( 11x + 7 )
Multiplicative Distribution Law = f(x) * 11x + f(x) * 7
= 11 * f(x) * x+ 7 * f(x)
= 11x * f(X) + 7 * f(x)
= 11x * f(x) + 7 * f(X)
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What is the result of isolating x2 in the equation below?x2 + (y- 5)2 = 30
Solving the equation x^2 + (y- 5)^2 = 30 for isolating x^2 is x^2 = - y^2 + 10y + 5. (Option D)
Equation is a mathematical statement that expresses values of two mathematical expressions as equal and is indicated by the sign =.
In order to isolate x^2 in the equation x^2 + (y- 5)^2 = 30, the remaining terms must be solved and simplified and collected on the other side.
Given equation is:
x^2 + (y- 5)^2 = 30
Expanding the (y- 5)^2 using formula for square of the difference between the two terms.
In general form: (a – b)^2 = a^2 – 2ab + b^2
Hence,
(y- 5)^2 = y^2 – 2(y)(5) + 5^2 = y^2 – 10y + 25
The original equation becomes,
x^2 + y^2 – 10y + 25 = 30
Subtract y^2 – 10y + 25 from both sides and simplifying:
x^2 + y^2 – 10y + 25 – (y^2 – 10y + 25) = 30 – (y^2 – 10y + 25)
x^2 = 30 – y^2 + 10y - 25
x^2 = - y^2 + 10y + 5
Note: The question is incomplete as it is missing options which are A. x^2 = y^2 + 10y+5 B. x^2 =-y^2 + 10y+25 C. x^2 = 30 - y^2 D. x^2 = - y^2 + 10y+5
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1. Let A and B be two
arbitrary
events.
please prove that
P(A+B)=P(A) + P(B) - P(AB).
The expression P(A + B) = P(A) + P(B) - P(AB) is proved.
Proved is shown below.
What is a set?A set is a collection of items where there are operations such as:
Union of sets, the intersection of sets, complements of sets.
We have,
Consider A = {1, 2, 3, 4, 5}
B = {2, 3, 4, 6, 7}
P (A + B) = P (A U B)
P (AB) = P (A ∩ B) (Common values}
P (AB) = {2, 3, 4}
P (A + B ) = {1, 2, 3, 4, 5, 6, 7}
Now,
P(A + B) = P(A) + P(B) - P(AB)
{1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5} + {2, 3, 4, 6, 7} - {2, 3, 4}
{1, 2, 3, 4, 5, 6, 7} = {1, 2, 2, 3, 3, 4, 4,5, 6, 7} - {2, 3, 4}
{1, 2, 3, 4, 5, 6, 7} = {1, 2, 3, 4, 5, 6, 7}
Thus,
P{A + B) = P(A) + P(B) - P(AB) proved.
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st.asp?test=3&course_week=
27.6 yd
Find the circumference of the circle. Round the answer to the nearest tenth
The circumference of the given circle with the diameter 27.6 yards is 86.7 yards.
What is the circumference?The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center. A meridian is any great circle passing through a point designated a pole.
Given that, the diameter of circle is 27.6 yards
Radius of a circle is the distance from the center of the circle to any point on it's circumference and radius of a circle is half of Diameter.
That is, radius =Diameter/2
So, radius of circle =27.6/2 =13.8 yards
We know that, the circumference of the circle is 2πr
Now, circumference = 2×3.14×13.8
= 86.664
≈ 86.7 yards
Therefore, 86.7 yards is the circumference of the circle.
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Ed Sloan invests $1,600 at the beginning of each year for eight years into an account that pays 10% compounded semiannually. The value of the annuity due is:
rev: 11_18_2019_QC_CS-190807
Multiple Choice
$41,344.48
$20,127.16
$39,744.59
$37,744.48
The value of the annuity due is $39,744.59.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = [tex]P\frac{(1 + r)^n -1(1+ r)}{r}[/tex].
Where, A = amount, P = principle, r = rate, and n = time in years.
Given, r = 10% semiannually so it is (10/2) = 5% or 0.05 and n = 8×2 = 16.
∴ A = [tex]1600\frac{(1 + 0.05)^{16} -1(1+ 0.05)}{0.05}[/tex].
A = [tex]1600\frac{(1.05)^{16} -1(1.05)}{0.05}[/tex]
A = [tex]\frac{1600(2.18 -1.05)}{0.05}[/tex].
A = (1600×1.13)/0.05.
A = $39,744.59
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3 more than the sum of x and y
Step-by-step explanation:
???
(x + y) + 3
this is 3 more than the sum of x and y.
what is the result of the following division 2x3 3x 5 x 3
63:
2x3=6
3x5=15
6+15=21
x 3 =…
63
Step-by-step explanation:
Showwwwwwwwww workkkkkkkkkkkkk
In image.
In the Image is the anser and explanation.
The height (in feet) attained by a rocket 1 seconds into flight is given by
h(t)
13+2112+ 431+ 20. When is the rocket ascending and when is it descending?
--313
Hint: you will first need to determine the time the rocket hits the ground.
==
We can determine whether the rocket is ascending or descending by evaluating the derivative at that time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.
What is a derivative of a function?
The derivative of a function can be interpreted as the slope of the graph of the function or, more precisely, as the slope of the tangent line at a point. Its calculation, in fact, derives from the slope formula for a straight line, except that a limiting process must be used for curves.
To determine whether the rocket is ascending or descending at a given time, we need to find the derivative of the function h(t) and determine whether it is positive or negative.
The derivative of h(t) is given by h'(t) = -t²+42t+43. This is the rate of change of the height of the rocket at any given time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.
At t = 1 second, h'(t) = -1 + 42 + 43 = 44. Since the derivative is positive at t = 1, we know that the rocket is ascending at this time.
Hence, we can determine whether the rocket is ascending or descending by evaluating the derivative at that time. If the derivative is positive, the rocket is ascending. If the derivative is negative, the rocket is descending.
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a bulldozer exerts 1000 pounds of force to prevent a 5000 lb lboulder from rolling down a hil determine the angle of inclination of the hill
The angle of inclination of the hill is 1.369 degrees .
Given :
a bulldozer exerts 1000 pounds of force to prevent a 5000 lb lboulder from rolling down a hil determine the angle of inclination of the hill .
Angle of inclination :
Inclination of a line is the angle between the line and the positive direction of x − axis. Value of this angle is between 0 and 180 degrees . It is measured in anti - clockwise direction from the positive direction of x − axis .
Angle of inclination cos x = 1000 / 5000
cos x = 100 / 500
= 10 / 50
= 1 / 5
x = cos^-1 ( 1/5 )
x = 1.369 degrees .
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Find all solution for the angle “theta” and use “K” to be any integer cos(theta+pi/4)-cos(theta-pi/4)
The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ.
What is a trigonometric function?The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.
The trigonometric function is very good and useful in real-life problems related to the right-angle triangle.
It is known that,
Cos(A + B) = cosAcosB - sinAsinB
Cost(A - B) = cosAcosB + sinAsinB
As per the given,
cos(θ + π/4) - cos(θ - π/4)
(cosθ cos π/4 - sinθ sin π/4) - (cosθ cos π/4 + sinθ sin π/4)
-2 sinθ sin π/4
-2 sinθ (1/√2)
-√2 sinθ
Hence "The value of the given trigonometric function equation cos(θ + π/4) - cos(θ - π/4) will be -√2 sinθ".
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change .350 to hundredths
Answer:
.35
Step-by-step explanation:
Just drop the zero .350 is 350 thousandths = 35 hundredths
