Answer:
A
Step-by-step explanation:
The design of the survey leads to bias because a nonresponse error was made in this design. This type of sampling only represents those who answered the survey; it does not represent the entire population.
Only 56% of response were received this means the entire population did not participate in the survey only a chuck of them answered the survey. This can lead to a biased result, an assumption.
A real estate agent has 17 properties that she shows. She feels that there is a 50% chance of selling any one property during a week. The chance of selling any one property is independent of selling another property. Compute the probability of selling less than 3 properties in one week. Round your answer to four decimal places.
Answer:
0.0011 = 0.11% probability of selling less than 3 properties in one week.
Step-by-step explanation:
For each property, there are only two possible outcomes. Either they are sold, or they are not. The chance of selling any one property is independent of selling another property. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
A real estate agent has 17 properties that she shows.
This means that [tex]n = 17[/tex]
She feels that there is a 50% chance of selling any one property during a week.
This means that [tex]p = 0.5[/tex]
Compute the probability of selling less than 3 properties in one week.
This is
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{17,0}.(0.5)^{0}.(0.5)^{17} \approx 0[/tex]
[tex]P(X = 1) = C_{17,1}.(0.5)^{1}.(0.5)^{16} = 0.0001[/tex]
[tex]P(X = 2) = C_{17,2}.(0.5)^{2}.(0.5)^{15} = 0.0010[/tex]
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0.0001 + 0.0010 = 0.0011[/tex]
0.0011 = 0.11% probability of selling less than 3 properties in one week.
A square has a side of 10x. Write and simplify an expression for the perimeter of the square. Then calculate the perimeter of the square if
X=12
Answer:
Step-by-step explanation:
perimeter = 4(10x) = 40x units
if x = 12, perimeter = 480x units
Recall that the Fibonacci Sequence is defined by the recurrence relation, a0 = a1 = 1 and for n ≥ 2, an = an−1 + an−2 . a. Show that f(x) = 1 1−x−x 2 is the generating function of the Fibonacci Sequence. b. Find ???? and β such that 1 − x − x 2 = (1 − ????x)(1 − βx). c. Find A and B in terms of ???? and β, such that 1 1−x−x 2 = A 1−????x + B 1−βx. d. Use the results of the previous parts to obtain a formula for an.
Answer:
Step-by-step explanation:
From the given information:
[tex]a_n = a_{n-1} + a_{n-2}; \ \ \ n \ge 2 \\ \\ a_o = 1 \\ \\ a_1 =1 \ \ \ \ \ since \ \ a_o = a_1 = 1[/tex]
A)
[tex]a_n - a_{n-1} - a_{n-2} = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2}(a_n -a_{n-1}-a_{n-2} ) x^n = 0 \\ \\ \implies \sum \limits ^{\infty}_{n=2} a_nx^n - \sum \limits ^{\infty}_{n=2} a_{n-1}x^n - \sum \limits ^{\infty}_{n=2}a_{n-2} x^n = 0 \\ \\ \implies (a(x) -a_o-a_1x) - (x(a(x) -a_o)) -x^2a(x) = 0 \\ \\ \implies a(x) (1 -x-x^2) -a_o-a_1x+a_ox = 0 \\ \\ \implies a(x)(1-x-x^2)-1-x+x=0 \\ \\ \implies a(x) (1-x-x^2) = 1[/tex]
[tex]\mathbf{Generating \ Function: a(x) = \dfrac{1}{1-x-x^2}=f(x)}[/tex]
B)
[tex]If \ \ 1 -x-x^2 = (1 - \alpha x) ( 1- \beta x) \\ \\ \implies 1 -x - ^2 = 1 + \alpha \beta x^2 - ( \alpha + \beta )x \\ \\ \text{It implies that:} \\ \\ \alpha \beta = -1 \\ \\ \alpha + \beta = 1 \\ \\ \implies \alpha = ( 1-\beta) \\ \\ ( 1- \beta) \beta = -1 \\ \\ \implies \beta - \beta^2 = -1 \implies \beta - \beta^2 -1 = 0\\ \\ \beta = \dfrac{-(-1) \pm \sqrt{(-1)^2 -4(1)(-1)}}{2(1)}[/tex]
[tex]\beta = \dfrac{1\pm \sqrt{5}}{2} \\ \\ \beta = \dfrac{1 + \sqrt{5}}{2} \ \ and \ \ \alpha = \dfrac{1 - \sqrt{5}}{2}[/tex]
C)
[tex]\dfrac{1}{1-x-x^2}= \dfrac{A}{1-\alpha x}+ \dfrac{\beta}{1-\beta x} \\ \\ = \dfrac{A(1-\beta x) + B(1-\alpha x)}{(1-\alpha x) (1 - \beta x)} \\ \\ = \dfrac{(A+B)-(A\beta+B\alpha)x}{(1-\alpha x) (1-\beta x)}[/tex]
[tex]\text{It means:} \\ \\ A+B=1 \\ \\ B = (1-A) \\ \\ A\beta+ B \alpha =0 \\ \\ A\beta ( 1 -A) \alpha = 0 \\ \\ A( \beta - \alpha ) = -\alpha \\ \\ A = \dfrac{\alpha}{\alpha - \beta } \\ \\ \\ \\ B = 1 - \dfrac{\alpha }{\alpha - \beta} \implies \dfrac{\alpha - \beta - \alpha }{\alpha - \beta } \\ \\ =\dfrac{-\beta }{\alpha - \beta} \\ \\ \mathbf{B = \dfrac{\beta }{\beta - \alpha }}[/tex]
D)
[tex]\text{The formula for} a_n: \\ \\ a(x) = \dfrac{\alpha }{\alpha - \beta }\sum \limits ^{\infty}_{n=0} \alpha ^n x^n - \dfrac{\beta}{\beta - \alpha }\sum \limits ^{\infty}_{n=0} \beta x^n \\ \\ \implies \sum \limits ^{\infty}_{n =0} \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta}x^n \\ \\ a_n = \dfrac{\alpha ^{n+1}- \beta ^{n+1}}{\alpha - \beta } \\ \\ \\ a_n = \dfrac{1}{\sqrt{5}} \Big (\Big( \dfrac{\sqrt{5}+1}{2}\Big)^{n+1}- \Big ( \dfrac{1-\sqrt{5}}{2}\Big) ^{n+1}\Big)[/tex]
Question 27
27. If an increase in one quantity brings about a corresponding decrease in the
other and vice versa, then the two quantities vary
a) sometimes directly and sometimes inversely b) directly
c) inversely d) none of these
ОА
Ов
Ос
OD
Answer:
c) inversely
Step-by-step explanation:
In Mathematics an inverse relationship can be defined as a relationship between two variables, in which an increase in the value of one variable leads to a decrease in the value of the other variable i.e as the value of one variable becomes large, the value of the other variable becomes small.
Mathematically, an inverse relationship is given by the formula;
A = K/B
Where;
A and B are the variables.
K is the constant of proportionality.
Hence, if an increase in one quantity brings about a corresponding decrease in the other and vice versa, then the two quantities vary inversely.
Help Please!!!
Thanks
Answer:
d i hope please be d please please
A jury pool has 18 people that are married and 22 people that are not married, from which 12 jurors will be selected. Assuming that each person is equally likely to be chosen and that the jury is selected at random, find the probability that the jury consists of the following. (Give answer as a fraction or a decimal out to at least 4 places. If your answer is very small use scientific notation out to 4 decimal places for example 3.3421E-6.)
Find the volume of the cone th=20 in and r=8 in. Solve in terms of pi and round off the decimal to the
nearest tenths.
Answer:
426.7pi
Step-by-step explanation:
V = 1/3 pi r2h
1/3 × 22/7× 8 × 8 × 20
426.7 pi
By what percent will a fraction increase is decreased by 10% and its denominator is decreased by 50%
Answer:
Let's assume the fraction is 1/1
decreasing 1 by 10% = .9
decreasing 1 by 50% = .5
So the fraction becomes .9/.5 = 1.8
So its value increases by 180%
Step-by-step explanation:
Solve. -x < 20
Graph on a number lin
Answer:
x > -20
Step-by-step explanation:
-x < 20
When dividing by negative numbers, flip the inequality.
x > -20
inclusive -> open circle
greater than -> to the right
open circle at -20 going to the right
You had a bag of fruit snacks that you shared with 4 friends. Each of you got 175 or fewer fruit snacks. The inequality x÷4≤175 models this situation. Solve the inequality to find the number of fruit snacks that were in the bag.
Answer:
Step-by-step explanation:
It’s 20
Which function is shown in the graph below?
On a coordinate plane, an exponential function shows decay. It rapidly decreases into quadrant 1 and approaches y = 1 in quadrant 1.
y = (one-half) Superscript x + 3 Baseline minus 1
y = (one-half) Superscript x minus 3 Baseline + 1
y = (one-half) Superscript x minus 1 Baseline + 3
y = (one-half) Superscript x + 1 Baseline minus 3
Answer:
Option B, y = 2 Superscript x + 2 Baseline + 3
Step-by-step explanation:
I could be wrong tbh. I graphed it on a graphing website and the graph from B matched up with the graph shown in the question.
Hope this helps Bye =)
The exponential function is given by [tex]y=(\frac{1}{2})^{x-3} +1[/tex]
Exponential functionAn exponential function is in the form:
y = abˣ
Where y,x are variables, a is the initial value of y and b is the multiplication factor.
The exponential function is given by [tex]y=(\frac{1}{2})^{x-3} +1[/tex]
From the point (0, 9):
[tex]y=(\frac{1}{2})^{0-3} +1=9[/tex]
Also at point (3, 2):
[tex]y=(\frac{1}{2})^{3-3} +1=2[/tex]
Find out more on Exponential function at: https://brainly.com/question/12940982
In triangle ABC, angle C is a right angle. If cos A = 5 8, what is the value of cos B?
Answer:
65
Step-by-step explanation:
The cost of making a chair is $28 correct to the nearest dollar. Calculate the lower and upper bounds for the cost of making 450 chairs
Answer:
$12,375
$12820.50
Step-by-step explanation:
To obtain a rounded value of $28 (to nearest dollar) the lowest and highest possible value before rounding will be : 27.50 and 28.49
Hence,
Lower bound = $27.50
Upper bound = $28.49
Therefore. Cost of making 450 chairs ;
27.50 * 450 = $12,375 (lower bound)
28.49 * 450 $12820.50 (upper bound)
Number Question ID: 15573
Drag these decimals into order from highest at the top to lowest.
8.3
8.31
8.301
8.03
8.031
Answer:
8.31
8.3
8.301
8.03
8.031
I think that's the answer.. not sure th
PLEASE HELP!!!! ILL GIVE BRAINLIEST!
Explain why the two figures below are not similar. Use complete sentences and provide evidence to support your explanation.
Answer: because the figure on the left is negative and more wide open while the other one is not only smaller but also positive and it’s more shut
Step-by-step explanation:
So the X-axis of the Figure on the left is going form point -3 to 0 while the other figure on the right is going form 3 to 5. And the Y- axis of the figure on the left is 2 while the right is 1 which proves that the figure on the left is bigger then the other
Your Also supposed to add all the point like first look for the Y and the X of I with J Then look for H and K then look for G and L the look for the slope of all those and then add them,then do the same with the left one and see which ones more and how much more
Analyze the results of the correlation using the given residual plot.
Answer:
Last one
Step-by-step explanation:
Answer:Analyze the results of the correlation using the given residual plot.
Residual
Step-by-step explanation:
Triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
What length of segment A'B?
The length of segment A'B' from the triangle A'B'C' is 6 units.
Given that, triangle A'B'C' is the image of ABC under a dilation with a scale factor of 2.
In the given triangle ABC, AB=3 units
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
2=Dimensions of the new shape/3
Dimensions of the new shape=6 units
Therefore, the length of segment A'B' from the triangle A'B'C' is 6 units.
To learn more about the scale factor visit:
https://brainly.com/question/22312172.
#SPJ1
Factorise the following expressions.
Answer:
Q.1 a²+10a+24
splitting the middle.
a²+6a+4a+24
=a(a+6)+4(a+6)
(a+6)(a+4)
Q.2 x²+9x+18
splitting the middle
x²+6x+3x+18
x(x+6)+3(x+6)
(x+6)(x+3)
what is the H.C.F of 2³×3²
If i put a 100$ into the stock market and the stock market increase by 2% per year. how much money would i have after a year
Answer:
$102
Step-by-step explanation:
2% of $100 = 0.02 * $100 = $2
The increase is $2.
$100 + $2 = $102
Answer: $102
Answer:
100 x 0,2 x 1 year(12/12 months)
=$102 after a year
the sum of the three sisters' ages is 51. If ava is 6 years older than
Camila, and Camila is twice as old as Luna, what are the ages of the
three sisters?
Create an equation with only one variable.
9514 1404 393
Answer:
Luna is 9Camila is 18Ava is 24Step-by-step explanation:
We can express all of the ages in terms of Luna's age. Letting L represent Luna's age, we have ...
Luna's age: LCamila's age: 2LAva's age: 2L +6The total of their ages is then ...
L +2L +(2L+6) = 51 . . . . an equation with one variable
5L = 45
L = 9
Luna is 9, Camila is 18, and Ava is 24.
PLEASE HELP!!!
Which expression are equal to 6³×2 6÷2³?
O12 6
O12³
O6³
O2 6×3³
O2³×3³
Answer:
(6³×2^6)÷2³=6³×2^(6-3)=6³×2³=(6×2)³=12³is your answer(1728)
As the student council treasurer, you prepare the budget for your class rafting trip. Each large raft
costs $100 to rent and each small raft costs $40 to rent. You have $1,600 to spend. Write and
solve a linear equation to find the number of small rafts you can rent if you rent 12 large rafts.
Answer:
10 small rafts
Step-by-step explanation:
(1600- 1200) / 40 = 10
1600- 1200 = 400
400 / 40 = 10
12 large rafts costs $1200 so subtract that amount from you budget. If you do that you will have $400 left. So I divided $400 by the amount of money each small raft cost whitch was $40 per small raft so i got the quotient of 10.
Sorry if i worded that weirdly but you get the point.
P.s sorry if it isn't comlety correct but i did my best so... ya
im super confused pls help
The 1st flat-bar, or cross, or other operator means:
-9-(-7)
-9-(-7)
-9--7
-9+7
7-9
-2
---
hope it helps
GEOMETRY
PLEASE HELP
PICTURE INCLUDED
Answer:
x = 25°
Step-by-step explanation:
3x + 30 + 2x + 3x + 30 + 4x = 360° (a full circle contains 360°)
12x + 60° = 360°
12x = 300°
x = 25°
Someone help me
Right now.
Jill wants to solve the following system using the elimination method:
Y = X + 8
y = 3x - 11
What number should the equation = x + 8 be multiplied by to eliminate x?
3
Answer:
3
Step-by-step explanation:
y= x + 8..... (1)
y= 3x - 11..... (2)
y - x = 8..... (3)
y - 3x = -11..... (4)
eliminating x:
(3) × 3: 3y - 3x = 24 ........ (5)
(4) × 1: y - 3x = -11 ......... (6)
(5) - (6): 2y = 35
Divide both sides by 2, therefore, y = 17.5
substitute the value of y into (3)
y - x = 8
17.5 - x = 8
17.5 - 8 = x
9.5 = x
I hope it'll help
Convert the angle −4.5 radians to degrees, rounding to the nearest 10th
Answer:-257.8
Step-by-step explanation:
a. Identify the relationship between the two
angles.
b. Write the equation used to represent the
relationship between the two angles.
c. Solve for the unknown variable.
Answer:
a - Mutual
b - (x+21)+(2x+3)=90
c - 3x +24 =90
3x=90-24
3x=66
X=22