There are 365 ways of forming an executive Committee of four in a social club consisting of 15 members
Understanding Permutation and CombinationIf a particular man must be in the committee, we can choose the remaining 3 members from the remaining 14 members. The number of ways to choose 3 members from 14 is given by the combination:
14Cr3 = [tex]\frac{14!}{3! 11!}[/tex] = [tex]\frac{14x13x12}{3x2x1}[/tex] = 364
Therefore, there are 364 ways of forming an executive committee of four in a social club consisting of 15 members, if a particular man must be in the committee.
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A bicyclist is riding on a path modeled by the function f(x) = 0.03(10x − x2), where x and f(x) are measured in miles. Find the rate of change of elevation at x = 1.
Answer: [tex]0.024\ \text{miles per sec}[/tex]
Step-by-step explanation:
Given
Path is changing according to the function [tex]f(x)=0.03(10x-x^2)[/tex]
Rate of change of the elevation is given by the derivative of the function
[tex]\Rightarrow f'(x)=0.03(10-2x)[/tex]
At [tex]x=1\ f'(x) \ \text{is}[/tex]
[tex]\Rightarrow f'(x=1)=0.03(10-2\times 1)\\\Rightarrow f'(x=1)=0.03(8)\\\Rightarrow f'(x=1)=0.24\ \text{miles per sec}[/tex]
Using derivatives, it is found that the rate of change of elevation at x = 1 is of 0.24.
What is the rate of change of a function f(x)?The rate of change of a function f(x) at x = a is given by:[tex]f^{\prime}(a)[/tex]
In this problem, the function is:
[tex]f(x) = 0.03(10x - x^2)[/tex]
Hence:
[tex]f^{\prime}(x) = 0.3 - 0.06x[/tex]
At x = 1:
[tex]f^{\prime}(1) = 0.3 - 0.06(1) = 0.24[/tex]
The rate of change of elevation at x = 1 is of 0.24.
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35. Graph the following system of equations and find the x-coordinate of the solution.
3x+ 3y=3
Y=-1/2x+2
x=2
x= -2
X = 3
x=0
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Answer:
(b) x = -2
Step-by-step explanation:
The graph shows the lines intersect at (x, y) = (-2, 3).
The x-coordinate of the solution is x = -2.
Help ASAP PLEASE (STATISTICS) !!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
i cant see it good
Step-by-step explanation:
prob its me
In this problem, y = 1/(1 + c1e−x) is a one-parameter family of solutions of the first-order DE y' = y − y2. Find a solution of the first-order IVP consisting of this differential equation and the given initial condition. y(0)=-1/3
If y (0) = -1/3, then
-1/3 = 1 / (1 + C e ⁻⁰)
Solve for C :
-1/3 = 1 / (1 + C )
-3 = 1 + C
C = -4
So the particular solution to the DE that satisfies the given initial condition is
[tex]\boxed{y=\dfrac1{1-4e^{-x}}}[/tex]
A mountain path is 12.1 miles long. If a hiker walks along the path at a rate of 1.96 miles per hour, in approximate how many hours will the hiker walks the entire trail ?
Answer:
6.2 hours
Step-by-step explanation:
d=rt where d is distance, r = rate and t - time
12.1 = 1.96t
Divide each side by 1.96
12.1/1.96 = 1.96t/1.96
6.17346 = t
Answer: 6.2 hours
Step-by-step explanation: I divided 12.1 by 1.96
Factorise 2a – 4a3 + 6abc
Evaluate -b*2--2bx*2-x when x=2
Step-by-step explanation:
-2b+4b(2-x)=
-2b+8b-8b=-2b
Find the measure of c
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Answer:
140°
Step-by-step explanation:
The long arc intercepted by angle c is 360° -80° = 280°. The measure of inscribed angle c is half the measure of the arc it intercepts.
c = 280°/2 = 140°
9. Which is a true statement about the denominator in a fraction?
(Select one answer)
It is always a negative number
It cannot be 0
It has to be an even number
It is always smaller than the numerator
Answer:
It cannot be 0
Step-by-step explanation:
it can also be positive number :2/4
it can be odd number too:3/9
it is bigger than numerator bcoz we have to divide it for numerator
So, 0 number cannot be put as denominator in fraction is true statement
Find the slope, if it exists, of the line containing the points (10,-3) and (10,-8).
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
m=
Answer:
The slope is undefined.
Step-by-step explanation:
The line must pass through the points (10,-3) and (10,-8), meaning that it must be vertical. The slope of a line is undefined if the line is vertical.
The perimeter of rhombus EFGH is 48 cm and the measure of ZFE) = 60
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Answer:
a. 12 cm
b. 90°
c. 60°
Step-by-step explanation:
The relevant relationships are ...
all sides of a rhombus have the same lengththe diagonals of a rhombus are perpendicular bisectors of each otherthe diagonals of a rhombus divide the figure into 4 congruent triangles__
a) The perimeter, 48 cm, is the sum of four equal side lengths, so any given side is (48 cm)/4 = 12 cm.
GH = 12 cm
__
b) Angle EJF is where the diagonals meet. It is a right angle.
∠EJF = 90°
__
c) Angle EFJ is the complement of the one marked, so is 30°. Angles EHJ and GHJ are congruent to that, so both are 30°. Angle EHG is the sum of those two congruent 30° angles, so is ...
∠EHG = 60°
A pair of fair dice are rolled. Find the probability of rolling a sum that is a multiple of 3 or a multiple of 4.
Answer:
0.5555 = 55.55% probability of rolling a sum that is a multiple of 3 or a multiple of 4.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Possible outcomes:
For the pair of dice:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
So 36 total outcomes.
Desired outcomes:
Sum being multiplies of 3 or multiples of 4, so:
(1,2), (1,3), (1,5)
(2,1), (2,2), (2,4), (2,6)
(3,1), (3,3), (3,5), (3,6)
(4,2), (4,4), (4,5)
(5,1), (5,3), (5,4)
(6,2), (6,3), (6,6)
3 + 4 + 4 + 3 + 3 + 3 = 20
Probability:
[tex]p = \frac{20}{36} = 0.5555[/tex]
0.5555 = 55.55% probability of rolling a sum that is a multiple of 3 or a multiple of 4.
Find the domain of fg. f(x) = x2 +1 g(x) = 1/x a. all real numbers c. all real numbers, except -1 b. all real numbers, except 0 d. all real numbers, except 1
Write the following as an inequality.
x is greater than – 3 and less than or equal to 4
Use x only once in your inequality.
Answer:
-3<x≤4
Step-by-step explanation:
Answer:
4 [tex]\geq[/tex] x > -3
Step-by-step explanation:
I just put the written form into inequality form.
Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked out.
t (h) 0 2 4 6 8 10
r(t) (L/h) 8.8 7.6 6.8 6.2 5.7 5.3
V=_____ upper estimate
V= ______lower estimate
The exact amount of oil that leaks out for 0 ≤ t ≤ 10 is given by the integral,
[tex]\displaystyle\int_0^{10}r(t)\,\mathrm dt[/tex]
Then the upper and lower estimates of this integral correspond to the upper and lower Riemann/Darboux sums. Since r(t) is said to be decreasing, this means that the upper estimate corresponds to the left-endpoint Riemann sum, while the lower estimate would correspond to the right-endpoint sum.
So you have
• upper estimate:
(8.8 L/h) (2 h - 0 h) + (7.6 L/h) (4 h - 2h) + (6.8 L/h) (6 h - 4h) + (6.2 L/h) (8 h - 6h) + (5.7 L/h) (10 h - 8 h)
= (2 h) (8.8 + 7.6 + 6.8 + 6.2 + 5.7) L/h)
= 70.2 L
• lower estimate:
(7.6 L/h) (2 h - 0 h) + (6.8 L/h) (4 h - 2h) + (6.2 L/h) (6 h - 4h) + (5.7 L/h) (8 h - 6h) + (5.3 L/h) (10 h - 8 h)
= (2 h) (7.6 + 6.8 + 6.2 + 5.7 + 5.3) L/h)
= 63.2 L
what sum of money must be invested the interest of 4% to given on interest Rs900 in 5 yearr
Answer:
5
Step-by-step explanation:
trust
A satellite orbits earth at a speed of 22100 feet per second (ft/s). Use the following facts to convert this speed to miles per hour (mph). 1 mile = 5280 ft 1 min = 60 sec 1 hour = 60 min
15,068 mi/hr
Step-by-step explanation:
[tex]22100\:\frac{\text{ft}}{\text{s}}×\frac{1\:\text{mi}}{5280\:\text{ft}}×\frac{60\:\text{s}}{1\:\text{min}}×\frac{60\:\text{min}}{1\:\text{hr}}[/tex]
[tex]=15,068\:\text{mi/hr}[/tex]
The speed of 22100 feet per second will be 15068.18 miles per hour.
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Unit conversion is the expression of the same property in a different unit of measurement. Time, for example, can be expressed in minutes rather than hours, and distance can be converted from miles to kilometres, feet, or any other length measurement.
Given that the speed of the satellite is 22100 feet per second. The speed in miles per hour will be calculated as,
22100 ft /s = ( 22100 x 3600 ) / 5280
22100 ft/s = 79560000 / 5280
22100 ft/s = 15068.18 miles per hour
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Please help me with this question and don't report
Answer:
50 ft
Step-by-step explanation:
For this problem we will use the Pythagorean theorem which is: a^2+b^2= c^2
I found the length for both of the legs on this triangle which are: 30 ft (for the side on the far left) and 40ft (for the other leg of the triangle whose hypotenuse is the walkway).
Now that we know the two legs we can use the Pythagorean theorem:
40^2 + 30^2 = 2500
then take the square root of 2500 in order to find the hypotenuse length:
Square root of 2500= 50ft
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Answer:
50ft
Step-by-step explanation:
trust me on this answer
8b²+7b factorize it i want the explantion also pll help
b(8b+7)
Answer:
Solution given;
8b²+7b
let look what is common there;
8*b*b+7*b
over here b is common
take common and keep other remaining on bracket
b(8b+7)
In a simple way b(8b+7) is a factorise form of
8b²+7b
Need Help this is due in 30 minutes!
Answer:
E
Step-by-step explanation:
Since all the numbers are hundredths decimals, let multiply by the power of 2 of the base 10. So let multiply the equation by
[tex]10 {}^{2} [/tex]
So our new equation is
[tex]3 3{x}^{2} + 71x - 14 = 0[/tex]
Solve by AC method
[tex]ac = - 462[/tex]
[tex]b = 71[/tex]
We must think of two numbers that
Multiply to -462 and Add to 71. Set up equation
The numbers are 77 and -6.
So our new equation is
[tex] {33x}^{2} + 77x - 6x - 14 = 0[/tex]
Solve by factoring by grouping
[tex](33 {x}^{2} + 77x) - (6x - 14)[/tex]
Factor out 11 for the first equation
[tex]11x(3x + 7) - 2(3x + 7)[/tex]
So our factors are
[tex](11x - 2)(3x + 7)[/tex]
Set each equal to zero
[tex]11x - 2 = 0[/tex]
[tex]11x = 2[/tex]
[tex]x = \frac{2}{11} [/tex]
[tex]3x + 7 = [/tex]
[tex]3x = - 7[/tex]
[tex]x = \frac{ - 7}{3} [/tex]
A student is chosen at random from a large statistics class and asked how much time (in whole hours) she spent studying during the past 24 hours. Describe the sample space S of possible outcomes:
Answer:
24
Step-by-step explanation:
The sample space is the total possible values of an experiment or research. Since the total number of hours is 24, then the total possible number (or the limit she can use have) is 24. This she cannot exceed this 24 hour limit. Then we call this the total possible outcome and thus the sample space.
Does the point (0, 0) satisfy the equation y = x2?
Answer:
The point is a solution
Step-by-step explanation:
y = x^2
Substitute the point into the equation and see if it is true
0 = 0^2
0=0
True
Question 1
The perfect square among the following options is
8
Say
27
216
256
Answer:
217 is the perfect swuare i think
What is the solution to the equation x^2 + 10x + 75 = 0?
What is the surface area of the composite figure?
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Answer:
382 cm²
Step-by-step explanation:
The side facing is a trapezoid with bases 8 and 14 cm, and height 7 cm. Its area is ...
A = 1/2(b1 +b2)h
A = (1/2)(8 +14)(7) = 77 . . . . cm²
The perimeter of the face is ...
7 cm + 8 cm + 9 cm + 14 cm = 38 cm
The total surface area is the sum of the lateral area and the base area.
SA = LA + BA
SA = (38 cm)(6 cm) + 2×(77 cm²) = 228 cm² + 154 cm²
SA = 382 cm²
The surface area of the composite figure is 382 square centimeters.
_____
Additional comment
The lateral area is the width of a rectangular face (6 cm) times the total of all of the lengths of those faces. That total is the perimeter of the trapezoidal base (38 cm).
There are two trapezoidal bases that contribute area. The first calculation figured the area of one of them.
help
The points (63, 121), (71, 180), (67, 140), (65, 108), and (72, 165) give the weight in pounds as a function of height in inches for 5 students in
a class. Give the points for these students that represent height as a function of weight
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
{(121, 140), (180, 71), (140, 67), (108, 65), (165, 72);
{(121, 71), (180, 63), (140, 67), (108, 65), (165, 72)}
{(63, 121), (71, 180), (67, 140), 65, 108), (72, 165))
Answer:
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
Step-by-step explanation:
We have:
Weight as a function of height.
Give the points for these students that represent height as a function of weight:
Inverse of the input, that is, in the (x,y) format, (x,y) -> (y,x), the coordinates are exchanged, and thus, the correct option is:
{(121, 63), (180, 71), (140, 67), (108, 65), (165, 72)}
A ladder leans against the side of the a house. The ladder is 19 feet long and forms an angle of elevation of 75 degree when leaned against the house. How far away from the house is the ladder? Round your answer to the nearest tenth.
=============================================================
Explanation:
Focus entirely on the triangle on the right side. The other parts of the drawing are not necessary. In my opinion, they are distracting filler.
Refer to the diagram below.
We have an unknown adjacent side, let's call it x, that's along the horizontal part of the triangle.
The hypotenuse however is known and it is 19 ft
We use the cosine ratio to tie the two sides together
cos(angle) = adjacent/hypotenuse
cos(75) = x/19
19*cos(75) = x
x = 19*cos(75)
x = 4.9175618569479 which is approximate
x = 4.9
The base of the ladder is roughly 4.9 feet away from the base of the house.
Side note: make sure your calculator is in degree mode.
Let $f(x) = x^2 - 2x$. Find all real numbers $x$ such that $f(x) = f(f(x))$. List your solutions separated by commas in any order
==========================================================
Explanation:
The given function is f(x) = x^2 - 2x
Let's apply function composition like so
[tex]f(x) = x^2 - 2x\\\\f(f(x)) = (f(x))^2 - 2(f(x))\\\\f(f(x)) = (x^2-2x)^2 - 2(x^2-2x)\\\\[/tex]
In the second step, I replaced every x with f(x). Then in the third step, I replaced f(x) with x^2-2x on the right side.
Setting this equal to f(x) gets us
[tex]f(f(x)) = f(x)\\\\(x^2-2x)^2 - 2(x^2-2x) = x^2-2x\\\\[/tex]
which is a bit cluttered. However, we have "x^2-2x" show up three times. Let's say w = x^2-2x
If we replaced all those "x^2-2x" expressions with w, then we get,
[tex](x^2-2x)^2 - 2(x^2-2x) = x^2-2x\\\\w^2 - 2w = w\\\\[/tex]
Which looks more manageable
-----------------------------------------------
Let's solve for w
w^2 - 2w = w
w^2 - 2w-w = 0
w^2 - 3w = 0
w(w - 3) = 0
w = 0 or w-3 = 0
w = 0 or w = 3
----------------------------------------------
If w = 0, then,
w = x^2 - 2x
x^2 - 2x = w
x^2 - 2x = 0
x(x - 2) = 0
x = 0 or x-2 = 0
x = 0 or x = 2 are two solutions (out of four total)
-------------------------------------------------
Or, if w = 3, then,
w = x^2 - 2x
x^2 - 2x = w
x^2 - 2x = 3
x^2 - 2x - 3 = 0
(x - 3)(x + 1) = 0
x-3 = 0 or x+1 = 0
x = 3 or x = -1 are the other two solutions
-----------------------------------------------
To summarize, the four solutions are: x = -1, x = 0, x = 2, x = 3
The angles in a triangle are 100, 40, and 40 degrees. Classify the triangle by its angles and sides.
A. Right isosceles
B. Right Scalene
C. Obtuse scalene
D. Acute isosceles
E. Acute scalene
F. Obtuse isosceles
Answer:
F. Obtuse isosceles
Step-by-step explanation:
Since we have an angle that is 100 degrees, we have an obtuse angle
We have two angles that are 40, which means we have two sides that are equal length, because two angles have the same measure. That means it is isosceles
The triangle is an obtuse isosceles
(12 1/3 * 2) + (10 3/4 * 2)
Answer:
[tex](12\frac{1}{3} *2)+(10\frac{3}{4} *2)\\\\=(\frac{12(3)+1}{3} *2)+(\frac{10(4)+3}{4} *2)\\\\=\frac{37*2}{3} +\frac{43*2}{4} \\\\=\frac{74}{3} +\frac{86}{4} \\\\=\frac{74(4)+86(3)}{3*4} \\\\=\frac{296+258}{12} \\\\=\frac{554}{12}[/tex]
