Answer:
Conversion a mixed number 2 5/
6
to a improper fraction: 2 5/6 = 2 5/
6
= 2 · 6 + 5/
6
= 12 + 5/
6
= 17/
6
To find new numerator:
a) Multiply the whole number 2 by the denominator 6. Whole number 2 equally 2 * 6/
6
= 12/
6
b) Add the answer from previous step 12 to the numerator 5. New numerator is 12 + 5 = 17
c) Write a previous answer (new numerator 17) over the denominator 6.
Two and five sixths is seventeen sixths
Unary minus: -17/
6
= -17/
6
Conversion a mixed number 5 1/
4
to a improper fraction: 5 1/4 = 5 1/
4
= 5 · 4 + 1/
4
= 20 + 1/
4
= 21/
4
To find new numerator:
a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/
4
= 20/
4
b) Add the answer from previous step 20 to the numerator 1. New numerator is 20 + 1 = 21
c) Write a previous answer (new numerator 21) over the denominator 4.
Five and one quarter is twenty-one quarters
Divide: -7/
8
: 21/
4
= -7/
8
· 4/
21
= -7 · 4/
8 · 21
= -28/
168
= 28 · (-1)/
28 · 6
= -1/
6
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 21/
4
is 4/
21
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - minus seven eighths divided by twenty-one quarters = minus one sixth.
Add: the result of step No. 2 + the result of step No. 4 = -17/
6
+ (-1/
6
) = -17 + (-1)/
6
= -18/
6
= 6 · -3/
6 · 1
= -3
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 6) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 6 = 36.
In words - minus seventeen sixths plus minus one sixth = minus three.
simplify 27-{ 9+(12-5)÷4} with solution
Answer:
16.25
Step-by-step explanation:
first do 12 -5 = 7. then 7/4 = 1.75 then 9+1.75 = 10.75 and finally 27-10.75= 16.25
In how many years will the population of a town be 26901 from 24400 at the growth rate of 5% per annum ?
Answer:
2 years
Step-by-step explanation:
population in 1 year= 24400*105%=25620
population in 2 year= 25620*105%=26901
what are the exponent and coefficient of the expression 4b-^3
9514 1404 393
Answer:
exponent: -3coefficient: 4Step-by-step explanation:
The coefficient of a term is its constant multiplier. The exponent is the power to which the base is raised.
The term 4·b^(-3) has an exponent of -3, a base of b and a coefficient of 4.
The exponent is -3; the coefficient is 4.
Answer:
exponent = -3 coefficent = 4
Step-by-step explanation:
WHAT IS X³-27 SIMPLIFIED
Answer:
It is (x - 3)³ - 9x(3 - x)
Step-by-step explanation:
Express 27 in terms of cubes, 27 = 3³:
[tex] = {x}^{3} - {3}^{3} [/tex]
From trinomial expansion:
[tex] {(x - y)}^{3} = (x - y)(x - y)(x - y) \\ [/tex]
open first two brackets to get a quadratic equation:
[tex] {(x - y)}^{3} = ( {x}^{2} - 2xy + {y}^{2} )(x - y)[/tex]
expand further:
[tex] {(x - y)}^{3} = {x}^{3} - y {x}^{2} - 2y {x}^{2} + 2x {y}^{2} + x {y}^{2} - {y}^{3} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3x {y}^{2} - 3y {x}^{2} \\ {(x - y)}^{3} = {x}^{3} - {y}^{3} + 3xy(y - x) \\ \\ { \boxed{( {x}^{3} - {y}^{3} ) = {(x - y)}^{3} - 3xy(y - x)}}[/tex]
take y to be 3, then substitute:
[tex]( {x}^{3} - 3^3) = {(x - 3)}^{3} - 9x(3 - x)[/tex]
write the first 10 multiples of 2 and 3 and find LCM.
Answer:
multiples of 2 2,4,6,8,10,12,14,16,18,20
multiples of 3 3,6,9,12,15,,18,21,24,27,30
Step-by-step explanation:
Lcm is 6
1. Determine whether the function f(x)= x³ from i to i is one to one. Explain.
2. Is the function f (x)= 3x+ 4 from the set of integers to integers one to one? Why? 48
Answer:
The function [tex]f:\mathbb Z\to\mathbb Z,~f(x)=3x+4[/tex] is injective (one-to-one).
Step-by-step explanation:
The definition of an injective function follows.
Let [tex]X,Y[/tex] be sets. Let [tex]f:X\to Y[/tex] be a function. We say [tex]f[/tex] is injective if, for all [tex]x,y\in X[/tex], [tex]f(x)=f(y)[/tex] implies [tex]x=y[/tex].
This is the proof that [tex]f:\mathbb Z\to\mathbb Z,~f(x)=3x+4[/tex] is injective.
Let [tex]x,y\in\mathbb Z[/tex] and assume [tex]f(x)=f(y)[/tex]. This means [tex]3x+4=3y+4[/tex]. Subtracting [tex]4[/tex] gives [tex]3x=3y[/tex], then dividing by [tex]3[/tex] gives [tex]x=y[/tex]. Thus [tex]f[/tex] is injective.
Find a formula for the given polynomial.
In this question, we have to identify the zeros of the polynomial, along with a point, and then we get that the formula for the polynomial is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
------------------------
Equation of a polynomial, according to it's zeros:
Given a polynomial f(x), this polynomial has roots such that it can be written as: , in which a is the leading coefficient.
------------------------
Identifying the zeros:
Given the graph, the zeros are the points where the graph crosses the x-axis. In this question, they are:
[tex]x_1 = -2, x_2 = 0, x_3 = 3[/tex]
Thus
[tex]p(x) = a(x - x_{1})(x - x_{2})(x-x_3)[/tex]
[tex]p(x) = a(x - (-2))(x - 0)(x-3)[/tex]
[tex]p(x) = ax(x+2)(x-3)[/tex]
[tex]p(x) = ax(x^2 - x + 6)[/tex]
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
------------------------
Leading coefficient:
Passes through point (2,-8), that is, when [tex]x = 2, y = -8[/tex], which is used to find a. So
[tex]p(x) = a(x^3 - x^2 + 6x)[/tex]
[tex]-8 = a(2^3 - 2^2 + 6*2)[/tex]
[tex]16a = -8[/tex]
[tex]a = -\frac{8}{16} = -0.5[/tex]
------------------------
Considering the zeros and the leading coefficient, the formula is:
[tex]p(x) = -0.5(x^3 - x^2 + 6x)[/tex]
A similar problem is found at https://brainly.com/question/16078990
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Based on the Fundamental Theorem of Algebra, we understand that Polynomials with real Coefficient have at least one real Root and at most a number of Roots equal to its Grade. The Grade is the maximum exponent that Polynomial has and root is a point such that [tex]p(x) = 0[/tex]. By Algebra we understand that polynomial can be represented in this manner known as Factorized form:
[tex]p(x) = \Pi\limits_{i=0}^{n} (x-r_i)[/tex] (1)
Where:
[tex]n[/tex] - Grade of the polynomial.
[tex]i[/tex] - Index of the root binomial.
[tex]x[/tex] - Independent variable.
We notice that polynomials has three roots in [tex]x = -2[/tex], [tex]x = 0[/tex] and [tex]x = 3[/tex], having the following construction:
[tex]p(x) =(x+2)\cdot x \cdot (x-3)[/tex]
[tex]p(x) = (x^{2}+2\cdot x)\cdot (x-3)[/tex]
[tex]p(x) = x^{3}+2\cdot x^{2}-3\cdot x^{2}-6\cdot x[/tex]
[tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex]
The formula that represents the polynomial in the figure is [tex]p(x) = x^{3}-x^{2}-6\cdot x[/tex].
Here is a question related to the determination polynomials: https://brainly.com/question/10241002
prove that is here
[tex]1 - cos {2}a \div 1 - sin a{2} = tan {2} a[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}[/tex]
LHS[tex]\boxed{\sf \dfrac{cosA}{sinA}=cotA}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}[/tex]
[tex]\\ \sf\longmapsto 1-cot2A[/tex]
[tex]\\ \sf\longmapsto 1-\dfrac{1}{tan2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{tan2A-1}{tan2A}[/tex]
[tex]\\ \sf\longmapsto tan2A[/tex]
Coefficient and degree of the polynomial
Answer:
The leading coefficient is -8 as it is a mix of x and cardinal, if it was x alone then it wouldn't be the coefficient, we would use the next number shown.
If it was just a number and no x then it would still be the coefficient.
The degree is 9 as it is the highest power shown.
Step-by-step explanation:
See attachment for examples
The differential equation of a certain system is 20y′′+cy′+80y=0
, where c is called damping constant for what value of c critical damping hapens
Options:
110
64
50
60
Answer:
c=80
Step-by-step explanation:
Based on my reading the critical damping occurs when the discriminant of the quadratic characteristic equation is 0.
So let's see that characteristic equation:
20r^2+cr+80=0
The discriminant can be found by calculating b^2-4aC of ar^2+br+C=0.
a=20
b=c
C=80
c^2-4(20)(80)
We want this to be 0.
c^2-4(20)(80)=0
Simplify:
c^2-6400=0
Add 6400 on both sides:
c^2=6400
Take square root of both sides:
c=80 or c=-80
Based on further reading damping equations in form
ay′′+by′+Cy=0
should have positive coefficients with b also having the possibility of being zero.
find the LCM of 220,440,660 by common division method
Answer: LCM = 1320
Step-by-step explanation:
2 | 220, 440, 660
2 | 110, 220, 330
2 | 55, 110, 165
3 | 55, 55,165
5 | 55, 55 , 55
11 | 11, 11, 11
| 1, 1, 1
= 2 × 2 × 2 × 3 × 5 × 11
= 1320
Therefore the LCM is 1320
Must click thanks and mark brainliest
Determine whether the statement below makes sense or does not make sense. Explain clearly. Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 1.9 to 3.5 hours per day. Therefore, there is 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not.
A. The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100%−95% =5%.
B. The statement makes sense. There is 5% probability that the confidence interval limits do not contain the true value of the sample mean, so the probability it does not contain the true value of the population mean is also 5%.
C.The statement does not make sense. The probability the population mean is greater than the upper limit is 5% and the probability it is less than the lower limit is 5%, so the probability it does not is 5%+5%=10%.
D. The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this.
The correct option is A because
The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100%−95% =5%.
From the question we are told that:
Confidence interval [tex]CI=95\%[/tex]
Mean [tex]\=x =1.9-3.5hours[/tex]
Level of significance (of the alternative hypothesis)
[tex]\alpha=100-95[/tex]
[tex]\alpha=5\%[/tex]
[tex]\alpha=0.05[/tex]
Generally
There is 95% probability that the confidence interval limits actually contain the true value of the population mean.
In conclusion
The it does not fall in this range is Level of significance (of the alternative hypothesis)
100%−95% =5%.
For more information on this visit
https://brainly.com/question/24131141?referrer=searchResults
boat costs $54,000. you pay 10% down and amortize the rest with equal monthly payments over a 15 year period. If you must pay 4.5 % comounded monthly, what is your monthly payment?
3385.8
Step-by-step explanation:
Question
Find the sample variance of the following set of data:
12, 7, 6, 4, 11.
Select the correct answer below:
Answer:
Variance is 256
Step-by-step explanation:
Variance:
[tex]var = \frac{ ({ \sum x})^{2} }{n} - {( \frac{ \sum x}{n} })^{2} [/tex]
x is the number or item in the data
n is the number of terms
[tex]{ \tt{ \sum x = (12 + 7 + 6 + 4 + 11)}} \\ { \tt{ \sum x = 40}}[/tex]
Therefore:
[tex]variance = \frac{ {40}^{2} }{5} - { (\frac{40}{5}) }^{2} \\ \\ = 320 - 64 \\ variance = 256[/tex]
plz with steps plzzzzzz
Answer: [tex]-\frac{\sqrt{2a}}{8a}[/tex]
=======================================================
Explanation:
The (x-a) in the denominator causes a problem if we tried to simply directly substitute in x = a. This is because we get a division by zero error.
The trick often used for problems like this is to rationalize the numerator as shown in the steps below.
[tex]\displaystyle \lim_{x\to a} \frac{\sqrt{3a-x}-\sqrt{x+a}}{4(x-a)}\\\\\\\lim_{x\to a} \frac{(\sqrt{3a-x}-\sqrt{x+a})(\sqrt{3a-x}+\sqrt{x+a})}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{(\sqrt{3a-x})^2-(\sqrt{x+a})^2}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{3a-x-(x+a)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{3a-x-x-a}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\[/tex]
[tex]\displaystyle \lim_{x\to a} \frac{2a-2x}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2(-a+x)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2(x-a)}{4(x-a)(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\\lim_{x\to a} \frac{-2}{4(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\[/tex]
At this point, the (x-a) in the denominator has been canceled out. We can now plug in x = a to see what happens
[tex]\displaystyle L = \lim_{x\to a} \frac{-2}{4(\sqrt{3a-x}+\sqrt{x+a})}\\\\\\L = \frac{-2}{4(\sqrt{3a-a}+\sqrt{a+a})}\\\\\\L = \frac{-2}{4(\sqrt{2a}+\sqrt{2a})}\\\\\\L = \frac{-2}{4(2\sqrt{2a})}\\\\\\L = \frac{-2}{8\sqrt{2a}}\\\\\\L = \frac{-1}{4\sqrt{2a}}\\\\\\L = \frac{-1*\sqrt{2a}}{4\sqrt{2a}*\sqrt{2a}}\\\\\\L = \frac{-\sqrt{2a}}{4\sqrt{2a*2a}}\\\\\\L = \frac{-\sqrt{2a}}{4\sqrt{(2a)^2}}\\\\\\L = \frac{-\sqrt{2a}}{4*2a}\\\\\\L = -\frac{\sqrt{2a}}{8a}\\\\\\[/tex]
There's not much else to say from here since we don't know the value of 'a'. So we can stop here.
Therefore,
[tex]\displaystyle \lim_{x\to a} \frac{\sqrt{3a-x}-\sqrt{x+a}}{4(x-a)} = -\frac{\sqrt{2a}}{8a}\\\\\\[/tex]
Solve for x using the
distributive property.
6(2 - 6x) = -24
X ?
⇛6(2 - 6x) = -24
⇛12 - 36x = -24
⇛-36x = -24 - 12
⇛-36x = -36
⇛x = -36/-36
⇛x = 1
Vehicles that get more than 40 miles per gallon can cross one county’s new bridge for free. Which graph shows the fuel-use rate of vehicles that have to pay to cross the bridge?
Answer:
D
Step-by-step explanation:
More than 40 miles per gallon
Open circle at 40 and line goes to the left
Answer: the answer is C
Step-by-step explanation:
because it is a open circle going to the left
Find the point of intersection for the pair of linear equations.
x +y = 0.3
y=3x + 16.7
Answer:
B
Step-by-step explanation:
You should find the solution for this system of equations (The value of x is the first coordinate for the point of intersection, the value of y is the second coordinate for the point of intersection)
X+y=0.3
y=3x+16.7
use 3x+16.7 instead of y in the first equation(do it to get only x in the first equation)
x+3x+16.7=0.3
4x+16.4=0
4x=-16.4
x=-4.1
y=0.3+4.1=4.4
B
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 2525 hours and the mean lifetime of a bulb is 590590 hours. Find the probability of a bulb lasting for at most 622622 hours. Round your answer to four decimal places.
Answer:
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 590 hours, standard deviation of 25 hours.
This means that [tex]\mu = 590, \sigma = 25[/tex]
Find the probability of a bulb lasting for at most 622 hours.
This is the p-value of Z when X = 622.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{622 - 590}{25}[/tex]
[tex]Z = 1.28[/tex]
[tex]Z = 1.28[/tex] has a p-value of 0.8997.
0.8997 = 89.97% probability of a bulb lasting for at most 622 hours.
Find the area of the triangle with vertices (0,0,0),(−4,1,−2), and (−4,2,−3).
Answer:
0.5*sqrt33
Step-by-step explanation:
A(0,0,0) B(-4,1,-2), c(-4,2,-3)
Vector AB is (-4-0,-1-0, -2-0)= (-4,-1,-2) The modul of AB is sqrt (4squared+
+(-1) squared+ (-2) squared)= sqrt (16+1+4)=sqrt21
Vector AC is (-4,2,-3) The modul of vector AC is equal to sqrt ((-4)squared+ 2squared+(-3)squared)= sqrt(16+4+9)= sqrt29
Vector BC is equal to (-4-(-4), 2-1, -3-(-2))= (0,1,-1)
The modul of BC is sqrt (1^2+(-1)^2)=sqrt2
Find the angle B
Ac^2= BC^2+AB^2-2*BC*AB*cosB
29= 2+21-2*sqrt2*sqrt21*cosB
29= 2+21-2*sqrt42*cosB
cosB= -3/ sqrt42
sinB= sqrt( 1-(-3/sqrt42)^2)=sqrt33/42= sqrt11/14
s=1/2* (sqrt2*sqrt21*sqrt11/14)=1/2*sqrt(42*11/14)= 0.5*sqrt33
hi plz help ASAP tyyy ^^
Answer:
26.75 units²
Step-by-step explanation:
This shape can be split into 3 triangles and a square. Find the area of each shape then add them all up.
[tex]A(Square)=2(2)=4\\\\A(Triangle)=\frac{1}{2}(2)(2)=2\\\\A(Triangle)=\frac{1}{2}(5)(2)=5\\\\A(Triangle)=\frac{1}{2}(9)(3.5)=15.75\\\\A(Shape)=4+2+5+15.75=26.75[/tex]
Therefore, the area of the shape is 26.75 units².
A rectangular window is 48 in long and 36 in wide. Lisa
would like to buy a screen for the window. The cost of
the screen is based on the number of square feet the
screen is. Use the facts to find the area of the window in
square feet.
Conversion facts for length
1 foot (ft) 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)
2
Х
$
?
[tex]\\ \sf\longmapsto Area=Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto Area=48(36)[/tex]
[tex]\\ \sf\longmapsto Area=1728in^2[/tex]
[tex]\\ \sf\longmapsto Area=144ft^2[/tex]
[tex]\\ \sf\longmapsto Area=48yard^2[/tex]
How many terms of the series 2 + 5 + 8 + … must be taken if their sum is 155
9514 1404 393
Answer:
10
Step-by-step explanation:
The sum of terms of an arithmetic series is ...
Sn = (2a +d(n -1))·n/2 = (2an +dn^2 -dn)/2
For the series with first term 2 and common difference 3, the sum is 155 for n terms, where ...
155 = (3n^2 +n(2·2 -3))/2
Multiplying by 2, we have ...
3n^2 +n -310 = 0 . . . . . arranged in standard form
Using the quadratic formula, the positive solution is ...
n = (-1 +√(1 -4(3)(-310)))/(2(3)) = (-1 +√3721)/6 = (61 -1)/6 = 10
10 terms of the series will have a sum of 155.
Step-by-step explanation:
[tex]\displaystyle \ \Large \boldsymbol{} S_n=\frac{2a_1+d(n-1)}{2} \cdot n =155 \\\\ \frac{4+3(n-1)}{2} \cdot n =155 \\\\\\ 4n+3n^2-3n=310 \\\\ 3n^2+n-310=0 \\\\D=1+3720=3721=61^2\\\\n_1=\frac{61-1}{6} =\boxed{10} \\\\\\n_2=\frac{-61-1}{3} \ \ \o[/tex]
A painter can paint 36 feet of molding per hour. How many inches of molding can he paint per hour?
Answer:
432 inches
Step-by-step explanation:
We need to convert feet to inches
1 ft = 12 inches
36 ft * 12 inches/ 1 ft = 432 inches
Determine the domain and range of the relation. *
Speeding up velocity for 5 seconds, same speed for another 10 seconds, slows down for 10 seconds.
Help!!
A.) show work as you evaluate the composition: (g o g) (2)
B.) show work as you find: f^-1 (x)
C.) show a composition of the two functions f and g. Are they inverse functions, explain using a complete sentence
Answer:
Hello,
Step-by-step explanation:
[tex]A)\\g(x)=\dfrac{x-5}{-3} =\dfrac{-x}{3} +\dfrac{5}{3} \\\\(gog)(x)=g(g(x))=g(\dfrac{-x}{3} +\dfrac{5}{3})\\\\=\dfrac{\dfrac{-x}{3} +\dfrac{5}{3} }{3}+\dfrac{5}{3} \\\\\\=\dfrac{-x}{9} +\dfrac{5}{9} +\dfrac{5}{3}\\\\=-\dfrac{x}{9}+\dfrac{20}{9} \\\\\\(gog)(2)=-\dfrac{2}{9}+\dfrac{20}{9} =\dfrac{18}{9}=2 \\\\[/tex]
[tex]B)\\f(x)=y=-3x-5\\exchanging\ y\ and\ x\\x=-3y-5\\3y=-x-5\\\\y=\dfrac{-x}{3} -\dfrac{5}{3} \\\\f^{-1}(x)=\dfrac{-x}{3} -\dfrac{5}{3} \\\\[/tex]
[tex]C)\\\\(fog)(x)\ must\ be\ equal\ to\ x\\\\\\(fog)(x)=g(f(x))=g(-3x-5)\\\\=\dfrac{-(-3x-5)}{3} +\dfrac{5}{3} \\\\=x+\dfrac{5}{3} +\dfrac{5}{3} \\\\\\=x+\dfrac{10}{3}\ and\ not\ x\ !!!\\[/tex]
f(x) and g(x) are not inverse functions.
What is the product of the polynomials below?
(8x2 - 4x-8)(2x +3x+2)
A. 16x4 +16x° - 12x2 - 16x-6
B. 16x4 +16x? - 12x2 - 16x-16
C. 16x4 +16x° - 12x2 – 32x-16
D. 16x4 +16 x° - 12x2 - 32x-6
Answer:
16x⁴+16x³-12x²-32x-16
Step-by-step explanation:
(8x²-4x-8)(2x²+3x+2)
= 16x⁴+24x³+16x²-8x³-12x²-8x-16x²-24x-16
= 16x⁴+16x³-12x²-32x-16
A random sample of 1005 adults in a certain large country was asked "Do you pretty much think televisions are a necessity or a luxury you could do without?" of the
1005 adults surveyed, 522 indicated that televisions are a luxury they could do without Complete parts (a) through (d) below.
Click Here for StatCrunch
(a) Obtain a point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without
pe
(Round to three decimal places as needed)
(b) Construct and interpret a 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do
without Select the correct choice below and fill in any answer boxes within your choice
(Type Integers or decimals rounded to three decimal places as needed. Use ascending order)
O A. We are
% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between and
B. There is a
% chance the proportion of adults in the country who believe that televishans are a luxury they could do without is between
(c) Is it possible that a supermajority (more than 60%) of adults in the country believe that television is a luxury they could do without? Is it likely?
It is
that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence
interval
and
Click to select your answer(s) and then click Check Answer
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From the information given in the exercise, we build the confidence interval and solve this question. First, we have to find the point estimate for the population proportion, then using this point estimate, and sample size, we build the confidence interval. According to the built confidence interval, question c is answered.
Item a:
522 out of 1005 indicated that television is a luxury that they could do without, so:
[tex]\pi = \frac{522}{1005} = 0.5194[/tex]
Thus, the point estimate for the population proportion of adults in the country who believe that televisions are a luxury they could do without is 0.5194.
Item b:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of .
For this problem, we have that:
[tex]n = 1005,\pi = 0.5194[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5194 - 1.96\sqrt{\frac{0.5194*0.4806}{1005}} = 0.4885[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.5194 + 1.96\sqrt{\frac{0.5194*0.4806}{1005}} = 0.5503[/tex]
Thus, the 95% confidence interval for the population proportion of adults in the country who believe that televisions are a luxury they could do without is (0.4885,0.5503). The interpretation is that:
We are 95% confident the proportion of adults in the country who believe that televisions are a luxury they could do without is between 0.4885 and 0.5503.
Item c:
It is possible, but unlikely that a supermajority of adults in the country believe that television is a luxury they could do without because the 95% confidence interval does not contain 60%.
For another example of a confidence interval for a proportion, you can check https://brainly.com/question/16807970
Solve 5x + 3 = -7x + 21
Question 13 plz show ALL STEPS
Step-by-step explanation:
Here are some of the graphs:
Blue is g(x) and Green is f(x). The 2nd graph is for the 13b. It shows our graph after 1 transformation. The 3rd graph is after both transformations.
13a. Let use the following values in
[tex]f(x) = \frac{2}{x} [/tex]
We know by definition of rational function x cannot be zero.
Let find some values across interval 2 through 4.
[tex]f(2) = \frac{2}{2} = 1[/tex]
[tex]f(3) = \frac{2}{3} [/tex]
[tex]f(4) = \frac{2}{4} = \frac{1}{2} [/tex]
Let use the following values in
[tex]g(x) = \frac{3x - 1}{x - 1} [/tex]
By definition of rational function, x cannot be 1 because it will make the denominator zero. Let use some values across the interval 0 through 4.
[tex]g(0) = \frac{0 - 1}{0 - 1} = 1[/tex]
[tex]g(2) = \frac{3(2) - 1}{2 - 1} = {5} [/tex]
[tex]g(3) = \frac{8}{2} = 4[/tex]
[tex]g(4) = \frac{11}{3} [/tex]
So graph this in a table of values. I'll post a picture of the table of values on the top.
13b. We need to write g(x) as a transformation of f(x). If we look at the graphs, g(x) has a asymptote at x=1 while f(x) has a asymptote of 0. This means that we need to move f(x) to the right one unit or move (x-1) units.
We will upgrade the graph.
Now we can just add 3 to f(x) to get to g(x).
In the 3rd graph, notice how both graphs coincide. Our transformations is complete.
The answer is
[tex]g(x) = f(x - 1) + 3[/tex]
13c. We can say this as we move f(x) to the right 1 unit and shift f(x) up 3 units.
