Answer:
a) 2002 different groups of 5 problems can be chosen from the 14 problems.
b) P=0.04995%
c) 21 different groups of 5.
P=1.04895%
Step-by-step explanation:
a)
In order to solve this problem we must ask ourselves: Does the order matter? We can see that in this case the order in which the problems are chosen doesn't really matter, so we are talking about a combination:
[tex]_{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]
in this case, n=14 while r=5, so our combination will be:
[tex]_{14}C_{5}=\frac{14!}{5!(14-5)!}[/tex]
which yields:
[tex]_{14}C_{5}=2002[/tex] which will be the answer for part a.
b)
In order to find the probability we can use the probability formula:
[tex]Probability=\frac{desired \hspace{5}outcome}{number\hspace{5} of \hspace{5} possible \hspace{5} outcomes}[/tex]
so in this case there is only 1 desired outcome out of the 2002 possible outcomes so our probability is:
[tex]P=\frac{1}{2002}[/tex]
which is the same as:
P=0.04995%
c) The same applies to part c. In order to find the number of groups Silvia did, we can make us of the combination formula:
[tex]_{7}C_{5}=\frac{7!}{5!(7-5)!}[/tex]
which yields:
[tex]_{14}C_{5}=21[/tex]
so there are 21 different groups of 5 she did by solving 7 problems.
So we can use the same formula to find the probability that one of the groups she completed comprised the group selected to be graded so we get:
[tex]P=\frac{21}{2002}=\frac{3}{286}[/tex]
which is the same as:
P=1.04895%
(remember that in order to turn a decimal number into a percentage you need to multiply the decimal number by 100)
Given that P(x)=x^5-8x^3-x^2+2, what is the remainder when it is divided by x-5?
Answer:
2102
Step-by-step explanation:
The polynomial function P(x)=x^5-8x^3-x^2+2, if it is divided by x-5, first we need to get x from the divisor as shown
since d(x) = x-5
x-5 = 0
x = 5
Substitute x = 5 into the expression to get the remainder
P(x)=x^5-8x^3-x^2+2
P(5)=(5)^5-8(5)^3-(5)^2+2
P(5) = 3125-1000-25+2
p(5) = 2100+2
P(5) = 2102
Hence the remainder is 2102
Which of the following statements best describes the relationship between the point (5,-20) and the system of
inequalities below?
Answer: The point (5,-20) only satisfies the second inequality statement in the system of inequalities shown.
Step-by-step explanation:
It isn't super clear exactly what you're asking, but the first thing we can do is see if the point (5, -20) satisfies the system of equations.
So, we start by plugging in -20 for y and 5 for x.
y > -2x-3
-20 > (-2)(5) - 3
-20 > -10-3
-20 > -13. - we can see that the coordinates DO NOT satisfy the first inequality, now we can try the second equation.
y ≤ 3x + 2
-20 ≤ 3(5) + 2
-20 ≤ 15 +2
-20 ≤ 17 - this inequality is true because -20 is indeed less than 17.
Hey can anyone help me out please
Suppose y varies directly with x. When
X is 2, y is 10. What is y when x is 4?
the last of my points i really enjoyed being here just the stress of it goodbye fellow brainlest
Answer:
Bye
Step-by-step explanation:
Answer:
thx
Step-by-step explanation:
pls mark brainliest :D
1,If 1 − x, x + 3 and 2x + 1 are consecutive terms of an A.P, then find the common
difference.
Step-by-step explanation:
Since they are consecutive terms in an AP,
(1 - x) + (2x + 1) = 2(x + 3).
=> x + 2 = 2x + 6
=> x = -4.
Therefore the terms are 5, -1 and -7.
=> Common difference = -6.
If x=-1, what is n (x)?
n(x)=-3x+7
Answer:
Step-by-step explanation:
x = -1
n(x = -1) = -3(x) + 7
n(x = -1) = -3(-1) + 7
-3 x -1 = 3
n(x = -1) = 3 + 7
n(x = -1) = 10
I hope this is correct! And I hope this helps :)
Please help how to solve
Which of the following is the best definition of a statistical population?
a. The distribution of all possible values that can be assumed by some statistic, computed from samples of different sizes randomly drawn from different populations.
b. Distribution of some characteristic based on individual observations – for each individual unit we measure the characteristic and then look at the distribution of all of these values.
c. The distribution of all possible values that can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population.
d. The distribution of all possible values that can be assumed by some parameter, computed from a single sample randomly drawn from some population.
c. The distribution of all possible values that can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population.
c. The distribution of all possible values that can be assumed by some statistic, computed from samples of the same size randomly drawn from the same population.
What is the statistical population?A population is the group of people from which a statistical sample is taken in statistics. Therefore, a population is any collection of people who have something in common. A statistically significant portion of a population, rather than the full population, may also be referred to as a sample.
When surveying a big number of people, it is just impracticable to examine everyone who fits the description you are looking at using a population parameter. It is often easier to study a smaller sample of participants, but by applying inferential statistics, it is possible to get a good approximation of the population parameter.
thus, statistical population is the distribution of all of the statistics calculated from all possible samples of the same size.
Therefore, The statistical population, which is calculated from samples of the same size randomly selected from the same population, is the distribution of all potential values that can be assumed by a statistic.
Learn more about statistical population here:
https://brainly.com/question/8222250
#SPJ5
Multiply the following binomials. Write in descending order of degree.
What is the coefficient of the third term?
(3x + 2)(7x - 8)
Answer:
Step-by-step explanation:
if you multiply the polynomials
(3x+2)(7x-8)=21x^2-24x+14x-16=21x^2-10x-16
coefficient of the third term -16
(3x + 2)(7x - 8)
21x^2 - 24x + 14x -16
21x^2 -10x - 16
The power descending order is 2, 1 and 0.
You see, -16 = -16x^0. As you know, x^0 = 1.
So, the coefficient of the third terms is -16.
One of the Starbucks managers strongly believes that the primary functions are to make valued or desired rewards available in the
workplace and clarify for the subordinate the kinds of behavior that will lead to goal accomplishment and valued
rewards Accordingli he is referring to - motivational theory, which is part of the --- motivational perspective/theories
A Substitute, Content
(B) Substitute, Process
Expectancy. Content
D) Expectancy, Process
Answer:
eyeyywhwywhwhehehhehehehehhehe the answer is a
A = {1, 3, 5, 7, 9}
B = {2, 3, 5, 7}
What is A UB?
Answer:
1234579
Step-by-step explanation:
first apply formula.then solved
Use the distributive property to evaluate the following expression: 9 x (4 + 9) . Show your work in your answer.
Answer:
9x + 81
Step-by-step explanation:
If the sides of a square measure 9 3units, then find the length of the diagonal.
4. 3b - 27
HELP ASAP
Answer:
3(b-9)
Step-by-step explanation:
The GCF (greatest common factor) is 3. All you have to do is divide both the numbers by 3. You should get 3(b-9). I hope this helps! ;)
If u steal point i report
Answer:
C = y=4x
Step-by-step explanation:
That answer because if you were to multiply on the way it will have the same graph
Answer:
The third option
Step-by-step explanation:
An object is launched on the moon at 16 feet per second (f/s) from a 1152-foot tall tower. The equation for the object's height s at time t seconds after launch is
s(t) = -16t^2 + 16t + 1152, where s is in feet. When does the object strike the moon’s surface and why?
Answer:
0.5seconds later
Step-by-step explanation:
Given the height modeled by the equation:
s(t) = -16t^2 + 16t + 1152
The velocity of the object at the moon surface is zero
ds(t)/dt = 0
ds(t)/dt = -32t + 16
0 = -32t + 16
32 t = 16
t = 16/32
t = 1/2
t = 0.5seconds
Hence the object strikes the moon surface 0.5seconds later
What is the probability you will roll a number less than 5 on a 6-sided die?
show your work
Answer:
2/3 chance
Step-by-step explanation:
You want to find numbers less than 5, so there are 4 numbers you can use. 4 out of 6 numbers possible is 4/6, or 2/3.
Kiran's family has completed 40% of a trip. They have traveled 80 miles. How far will the total trip be?
Answer:200
Step-by-step explanation:
what should i eat for lunch and also what is 25 to the power of 6 ? ill give brainly if u awnser both
Answer:a samichhh and 244,140,625
Step-by-step explanation:
The graphs of 4 linear functions are shown. Which option COULD correctly give the values for a, b, and c?
A)
a = 3, b = 1, c=4
B)
a = -4, b= -1,C = 3
C)
a = 4, b = -2,c=-4
D
a = -3, b = 2,c = -2
Answer:
It’s c
Step-by-step explanation:
The graph of the linear functions are solved and a = 4, b = -2 , c = -4
What are Linear Equations?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution
On a graph, a linear equation forms a straight line. On a graph, a nonlinear equation produces an S-curve, a bell curve, or another nonlinear shape.
Given data ,
Let the linear function be represented as A
Now , the value of A is
y = f ( x )
Now , the functions on the graph are above and below the y = f ( x )
So , the value of a = positive
And , a = 4
Now , the value of b = negative
And , y = f ( x + b ) is below f ( x )
So , b = -2
And , similarly c = -4
Hence , the linear functions are solved
To learn more about linear equations click :
https://brainly.com/question/10185505
#SPJ2
Natalia solved the problem 74.4/12=6.2. complete the model with partial products check Natalia's work using multiplication
Answer:
Natalia's work is wrong.
Step-by-step explanation:
Natalia divided a decimal number by an entire number. Since division is a operation derived from multiplication, the best approach to check if work was good is multiplying the given result by denomination, that is:
1) [tex]x = 6.2\times 12[/tex] Given.
2) [tex]x = \left(6+0.2\right)\times 12[/tex] Definition of addition.
3) [tex]x = 6\times 12 + 0.2\times 12[/tex] Distributive property.
4) [tex]x = 72 + \frac{2}{10}\times 12[/tex] Definitions of multiplication and decimal number.
5) [tex]x = 72 +[2\cdot (10)^{-1}]\cdot 12[/tex] Definition of division/Associative property.
6) [tex]x = 72 + [2\cdot 12]\cdot (10)^{-1}[/tex] Associative property.
7) [tex]x = 72 + 24\cdot 10^{-1}[/tex] Definition of multiplication.
8) [tex]x = 72 + \frac{24}{10}[/tex] Definition of divsion.
9) [tex]x = 72 + 2.4[/tex] Defintion of decimal number.
10) [tex]x = 74.4[/tex] Definition of addition/Result
Natalia's work is wrong.
The two numbers that multiply together to equal -15 and add together to equal -2 are
Answer:
-5, 3
Step-by-step explanation:
Which is equivalent to the expression below?
Answer:
A
Step-by-step explanation:
Opening the brackets, you get: 3x^2 - 2x + 5 - 2x^2 + 5x - 1
Simplifying, you get : x^2 + 3x + 4
Answer:
a
Step-by-step explanation:
3x^2 - 2x^2= x^2
-2x + 5x = 3x
5- 1 =5
graph the image of this figure after a dilation with a scale factor of 2 centered at the origin use the polygon tool to graph the dilated figure ! Please help 100 pts and brainliest
Answer:
For this answer, I will label the points. Starting at the top left, then top right, then bottom left and bottom right let the points be A, B, C, D.
The new coordinates will be
A(-4,10)
B(4,10)
C(-4,4)
D(4,4)
Step-by-step explanation:
The question is asking for a dilation which is a transformation that makes an image proportionately smaller or larger by a scale factor. The scale factor is how much smaller or larger the shape will be, if the scale factor is between 0 and 1 then it will shrink, if it is greater than one then the image will stretch (be larger). In this case, the scale factor is 2, therefore the image will stretch. Since the center of dilation is the origin, to find the new coordinates simply multiply each x and y value by the scale factor. So A's original coordinates (-2,5) become (-4,10) and so forth. Therefore the equation for this dilation is (x, y) → (2x,2y).
Answer:
See below
Step-by-step explanation:
Points given on the graph:
(-2, 2), (-2, 5), (2, 5), (2, 2)Dilation by a scale factor of 2 will result in coordinates doubled for each point:
(x, y) → (2x, 2y)And the new points will be:
(-2, 2) → (-4, 4)(-2, 5) → (-4, 10)(2, 2) → (4, 4)(2, 5) → (4, 10)See attached for the graph
In the triangle Tan A =
Answer:
Tan=(Opposite/Adjacent)
Step-by-step explanation:
Sin=(Opposite/Hypotnous)
Cos=(Adjacent/Hypotnouss)
Tan=(Opposite/Adjacent)
If u steal point i report
Answer:
The first option
Step-by-step explanation:
The profits of mr cash’s company is represented by the equation p(t)=-3t^2+18t-4, where p(t) is the amount of profit in hundreds of thousands of dollars and t is the number of years of operation. he realizes his company is on the down turn and wishes to sell before he ends up in debt. In what year of operation does Mr. Cash’s business show maximum profit? What is the maximum profit? What time will it be too late to sell business? show work
Answer:
$2300000- max profit5.77 years into operation - zero profit timeStep-by-step explanation:
Given function:
p(t)= -3t^2 + 18t - 4It is a quadratic function with general form of y = ax^2 + bx + c
It opens down if a < 0 and gets maximum value at vertex which is determined at x = -b/2a
For the given function vertex is:
t = -18/-3*2 = 3Maximum value of p is:
p(3) = -3*3^2 + 18*3 - 4 = -27 + 54 - 4 = 23 ($2300000)The time when profit is zero:
-3t^2 + 18t - 4 = 03t^2 - 18t + 4 = 0t = (18 ± √18² - 4*3*4)/2*3 = (18 ± √276)/6 = (18 ± 16.61)/6t = (18 - 16.61)/6 = 0.23 this is the time when company has just started to make profit, it is not applicable as is the past timet = (18 + 16.61)/6 = 5.77 years into operation, after this time there will be no profit2 + 5 please help I am really struggling
Answer:
the answer is 7 the problem is an easy one
Step-by-step explanation:
1/3 + 4 × 2/3 + (-12) ÷ 4