Answer:
Step-by-step explanation:
Hello!
Full Text:
As part of its "It Can Wait" campaign to discourage texting while driving, AT&T recently released the results of separate surveys concerning the extent of texting while driving among adults twd_commutor_survey and among teens att_teen_survey_executive . In the survey of the adults, 496 of n1 = 1,011 adult drivers (49.06%) said they text while driving. In the survey of the teens, 516 of n2 = 1,200 (43%) said they text while driving.
Question 1. Calculate a 98% confidence interval for the difference padult - pteen in the proportions of adults that text while driving and the proportion of teens that text while driving. (use 4 decimal places in your answers) lower bound upper bound
Be:
X₁: Number of adult drivers that text while driving, out of 1011.
n₁= 1011
x₁= 496
p₁'= 496/1011= 0.4906
X₂: Number of teen drivers that text while driving, out of 1200.
n₂= 1200
x₂= 516
p₂'= 516/1200= 0.43
For the 98% CI for p₁-p₂
[tex]Z_{1-\alpha /2}= Z_{0.99}= 2.326[/tex]
(p₁'-p₂')±[tex]Z_{1-\alpha /2}[/tex] * [tex]\sqrt{\frac{p'_1(1-p'_1)}{n_1} +\frac{p'_2(1-p'_2)}{n_2} }[/tex]
(0.4906-0.43)±2.326*[tex]\sqrt{\frac{0.4906(1-0.4906)}{1011} +\frac{0.43(1-0.43)}{1200} }[/tex]
0.0606±2.326*0.0212
[0.011; 0.11]
Using a 98% confidence level, you'd expect that the interval [0.011; 0.11] contains the difference between the population proportion of adults that text while driving and the population proportion of teens that ext while driving.
Question 2. Choose the correct interpretation of the above confidence interval. Note: 2 submissions allowed.
To decide over a hypothesis test using a confidence interval there are several conditions that should be met:
1) The hypotheses should be two-tailed:
H₀: p₁ - p₂= 0
H₁: p₁ - p₂≠ 0
2) The confidence level of the interval and the significance level of the test should be complementary, this means that if the interval was constructed with a level 1 - α: 0.98 then the test should be made using α: 0.02.
Naturally, the hypotheses and the CI should be made for the same parameters.
If all conditions are met, the decision criteria is as follows:
If the CI contains the value stated in the null hypothesis, the decision is to not reject the null hypothesis.
If the CI doesn't contain the value stated in the null hypothesis, the decision is to reject the null hypothesis.
In this case, the value stated in the null hypothesis is "zero" and is not included in the interval, so the decision is to reject the null hypothesis. You can conclude that the population proportions of adults and teens that text while driving are different.
Considering that the CI is positive, we can think that the proportion of adults that text while driving is grater than the proportion of teens that text while driving.
Options:
1) Since 0 is not in the confidence interval, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
2) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of teens that text while driving is greater than the proportion of adults that text while driving.
3) Since the confidence interval is entirely positive, the surveys provide evidence that the proportion of adults that text while driving is greater than the proportion of teens that text while driving.
4) Since 0 is not in the confidence interval, the surveys provide evidence that there is no significant difference between the proportions of adults and teens that text while driving.
The correct option is: "3"
I hope this helps!
How many solutions does the equation –2(3x – 1) = –6x – 1 have?
What about 2(3x – 1) = 6x – 2?
What about 2(3x – 1) = –6x – 2?
Answer: See below
Step-by-step explanation:
–2(3x – 1) = –6x – 1
-6x + 2 = -6x - 1 (IMPOSSIBLE, ZERO)
2(3x – 1) = 6x – 2
6x - 2 = 6x - 2 (INFINITE)
2(3x – 1) = –6x – 2
6x - 2 = -6x - 2 (ONE, x can be the number 0)
Solve the system using substitution.
5x+ 4y = 10
4x - y = 8
Answer:
Step-by-step explanation:
hello
from 4x-y=8 we can say that y = 4x-8
we substitute in the first equation to get
5x + 4 (4x-8) = 10
then
5x + 16 x -32 = 10
<=> 21x = 32+10=42
<=> x = 42/21 = 2
and then y = 8-8=0
don t hesitate if you need any further explanation
thanks
Answer: x = 2, y = 0 or (2 , 0)
Step-by-step explanation:
Solving using substitution is where you solve for a variable in one of the two equations in the system then plug it into the other.
For an easier plug in we can take the second equation. 4x-y = 8.
From here we need to isolate the y variable which is easier to isolate than x, in my opinion.
Subtract the 4x over.
-y = 8-4x
Now divide by a -1 so y is positive.
y= -8 + 4x
Now plug this in for y in the other equation.
5x + 4(-8 + 4x) = 10
Distribute the 4.
5x - 32 + 16x = 10
Combine like terms
21x - 32 = 10
Add the 32.
21x = 42
Divide by 21.
x = 2
Now that we have solved for one variable we can plug this into either equation and solve for the other.
I will plug it into the second equation.
4(2) - y = 8
Simplify.
8 - y = 8
Subtract 8.
-y = 0
Divide by -1.
y = 0
So the x and y values are.
x = 2
y = 0
H is directly proportional to the square root of p h= 5.4 when p = 1.44 find h when p =2.89
Answer:
h=7.65
Step-by-step explanation:
H is directly proportional to the square root of p;
Let k be the constant of proportionality;
Means h=k√p
This means for corresponding points of h and p such that (h1,p1) and (h2,p2) we have;
h1/√p1=h2/√p2
Let h= 5.4 when p = 1.44 and h when p =2.89 be respectively (h1,p1) and (h2,p2)
So that
5.4/√1.44=h/√2.89
5.4/√1.44 ×√2.89 = h
7.65= h
h=7.65
45% of 40 is 18% of what number?
Answer:
100
Step-by-step explanation:
40 / 100= .4
.4 x 45 = 18
18/18= 1
1x 100= 100
Answer:
100
Step-by-step explanation:
:D
The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in eight high-crime areas of Miami, Florida, yielded the following results.
Number of Crimes by Area
A B C D E F G H
before 14 7 4 5 17 12 8 9
after 2 7 3 6 8 13 3 5
Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the p-value
Answer:
Step-by-step explanation:
Hello!
There was a special program funded, designed to reduce crime in 8 areas of Miami.
The number of crimes per area was recorded before and after the program was established in each area. This is an example of a paired data situation. For each are in Miami you have recorded a pair of values:
X₁: Number of crimes recorded in one of the eight areas of Miami before applying the special program.
X₂: Number of crimes recorded in one of the eight areas of Miami after applying the special program.
Area: (Before; After)
A: (14; 2)
B: (7; 7)
C; (4; 3)
D: (5; 6)
E: (17; 8)
F: (12; 13)
G: (8; 3)
H; (9; 5)
To apply a paired sample test you have to define the variable "difference":
Xd= X₁ - X₂
I'll define it as the difference between the crime rate before the program and after the program.
If the original populations have a normal distribution, we can assume that the variable defined from them will also have a normal distribution.
Xd~N(μd; σd²)
If the crime rate decreased after the special program started, you'd expect the population mean of the difference between the crime rates before and after the program started to be less than zero, symbolically μd<0
The hypotheses are:
H₀: μd≥0
H₁: μd<0
α: 0.01
[tex]t= \frac{X[bar]_d-Mu_d}{\frac{S_d}{\sqrt{n} } } ~~t_{n-1}[/tex]
To calculate the sample mean and standard deviation of the variable difference, you have to calculate the difference between each value of each pair:
A= 14 - 2= 12
B= 7 - 7= 0
C= 4 - 3= 1
D= 5 - 6= -1
E= 17 - 8= 9
F= 12 - 13= -1
G= 8 - 3= 5
H= 9 - 5= 4
∑Xdi= 12 + 0 + 1 + (-1) + 9 + (-1) + 5 + 4= 29
∑Xdi²= 12²+0²+1²+1²+9²+1²+5²4²= 269
X[bar]d= 29/8= 3.625= 3.63
[tex]S_d=\sqrt{\frac{1}{n-1}[sumX_d^2-\frac{(sumX_d)^2}{n} ] } = \sqrt{\frac{1}{7}[269-\frac{29^2}{8} ] } = 4.84[/tex]
[tex]t_{H_0}= \frac{3.63-0}{\frac{4.86}{\sqrt{8} } } = 2.11[/tex]
This test is one-tailed to the left and so is the p-value, under a t with n-1= 8-1=7 degrees of freedom, the probability of obtaining a value as extreme as the calculated value is:
P(t₇≤-2.11)= 0.0364
The p-value is greater than the significance level, so the decision is to not reject the null hypothesis. Then at a 1% significance level, you can conclude that the special program didn't reduce the crime rate in the 8 designated areas of Miami.
I hope it helps!
Using the t-distribution, it is found that since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.
At the null hypothesis, it is tested if there has been no reduction, that is, the subtraction of the mean after by the mean before is at least 0, hence:
[tex]H_0: \mu_A - \mu_B \geq 0[/tex]
At the alternative hypothesis, it is tested if there has been a reduction, that is, the subtraction of the mean after by the mean before is negative, hence:
[tex]H_1: \mu_A - \mu_B < 0[/tex]
For both before and after, the mean, standard deviation of the sample(this is why the t-distribution is used) and sample sizes are given by:
[tex]\mu_B = 9.5, s_B = 4.504, n_B = 8[/tex]
[tex]\mu_A = 5.875, s_A = 3.5632, n_A = 8[/tex]
The standard errors are given by:
[tex]s_A = \frac{3.5632}{\sqrt{8}} = 1.2596[/tex]
[tex]s_B = \frac{4.504}{\sqrt{8}} = 1.5924[/tex]
For the distribution of differences, the mean and standard error are given by:
[tex]\overline{x} = \mu_A - \mu_B = 5.875 - 9.5 = -3.625[/tex]
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{1.2596^2 + 1.5924^2} = 2.0304[/tex]
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.Hence:
[tex]t = \frac{\overline{x} - \mu}{s}[/tex]
[tex]t = \frac{-3.625 - 0}{2.0304}[/tex]
[tex]t = -1.7854[/tex]
The p-value is found using a t-distribution calculator, with t = -1.7854, 8 + 8 - 2 = 14 df and a left-tailed test with a significance level of 0.01, as we are tested if the mean is less than a value.
Using the calculator, the p-value is given by 0.048.Since the p-value of the test is 0.048 > 0.01, there is not enough evidence to conclude that there has been a decrease in the number of crimes since the inauguration of the program.
You can learn more about the use of the t-distribution to test an hypothesis at https://brainly.com/question/13873630
In a bag of skittles 12 are yellow, 10 purple, 8 red, 9green and 22 orange. If 5 were selected from the bag. Calculate using counting technique what is the probability that:
A). exactly 2 are red
B). At most 2 are red
Answer:
a) 11.03% probability that exactly two are red.
b) 98.64% probability that at most 2 are red.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, the order in which the skittles are chosen is not important. So we use the combinations formula to solve this question.
Combinations formula:
[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]
In this question:
12 + 10 + 8 + 9 + 22 = 61 skittles.
A). exactly 2 are red
Desired outcomes:
2 red, from a set of 8.
3 non-red, from a set of 61 - 8 = 53.
So
[tex]D = C_{8,2}*C_{53,3} = \frac{8!}{2!(8-2)!}*\frac{53!}{3!(53-3)!} = 655928[/tex]
Total outcomes:
Five skittles from a set of 61. So
[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{655928}{5949147} = 0.1103[/tex]
11.03% probability that exactly two are red.
B). At most 2 are red
Desired outcomes:
None red(5 from a set of 53)...
One red(from a set of 8), and four non-read(4 from a set of 53).
Two red(655928), as found in a.
So
[tex]D = C_{53,5} + C_{8,1}*C_{53,4} + 655928 = \frac{53!}{5!48!} + \frac{8!}{1!7!}*\frac{53!}{4!49!} + 655928 = 5868213[/tex]
Total outcomes:
Five skittles from a set of 61. So
[tex]T = C_{61,5} = \frac{61!}{5!(61-5)!} = 5949147[/tex]
Probability:
[tex]p = \frac{D}{T} = \frac{5868213}{5949147} = 0.9864[/tex]
98.64% probability that at most 2 are red.
Find the area of the trapezoid with the numbers 4, 3, 3 ,1
Answer:
The answer depends on the shape of the trapezoid...
Step-by-step explanation:
A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel. (trapezium)
Area = (a+b/2) * h
IF the sides are a = 3 ,b = 3 and height = 4
THEREFORE:
(3+3/2) * 4
6/2 * 4
3 * 4
12
Hope it helped.... Please mark as brainliest..thanks!!!
What is a factor of 10 but not a multiple of 2
5
Step-by-step explanation:
5 goes into 10 but 2 does not go into 5
Line segment Q R , Line segment R S are Line segment S Q midsegments of ΔWXY. Triangle R Q S is inside triangle X Y W. Point R is the midpoint of side X Y, point S is the midpoint of side Y W, and point Q is the midpoint of side X W. The length of Q R is 2.93 centimeters, the length of R S is 2.04 centimeters, and the length of Q S is 2.28 centimeters. What is the perimeter of ΔWXY? 11.57 cm 12.22 cm 12.46 cm 14.50 cm
Answer:
14.50 cm
Step-by-step explanation:
The Midsegment Theorem states that the midsegment connecting the two sides of a triangle is parallel to the third side, and its length is half that of the third side.
Thus, ∆XYZ is similar to ∆QRS with a scale factor of 2.
Also, the perimeter of ∆XYZ is twice that of ∆QRS.
For ∆QRS, P = 2.93 cm + 2.04 cm + 2.28 cm = 7.25 cm
∴ The perimeter of ∆XYZ = 2 × 7.25 cm =14.50 cm
The Perimeter of triangle WXY is 14.5cm
The formula for calculating the perimeter of the triangle WXY is given as:
Perimeter of triangle WXY = XY + YZ + XY
From the given triangle;
QR = 2.93cmQS = 2.28cmRS = 2.04cmAlso,
XR = RY = QR = 2.93cmZS = SY = QS = 2.28cmZQ = QX = RS = 2.04cmPerimeter of triangle WXY = 2QR + 2QS + 2RS
Perimeter of triangle WXY = 2(2.93) + 2(2.28) + 2(2.04)
Perimeter of triangle WXY = 5.86 + 4.56 + 4.08
Perimeter of triangle WXY = 14.5cm
Hence the Perimeter of triangle WXY is 14.5cm
Learn more on perimeter of triangles here: https://brainly.com/question/24382052
find the complete factored form of the polynomial -44a^3 + 20a^6
Answer:
[tex]4a^3(5a^3-11)[/tex]
Step-by-step explanation:
→Take out the GCF (Greatest Common Factor). The GCF is [tex]4a^3[/tex] because both [tex]-44a^3[/tex] and [tex]20a^6[/tex] can be divided by it, like so:
[tex]-44a^3+20a^6[/tex]
[tex]4a^3(5a^3-11)[/tex]
PLEASEE HELP ME!!!!!!
Answer:
I). X= 1,0. II) 1.72
Step-by-step explanation:
Using quadratic formula
What is the range of a function?
Answer:
The set of all output values of a function. Example: when the function f(x) = x2 is given the values x = {1,2,3,...} then the range is {1,4,9,...}
To the nearest degree, what is the measure of the central angle for faucets?
Answer:
43°
Step-by-step explanation:
A 14 gram sample of a substance that's used to preserve fruit and vegetables has a k-value of 0.1092. Find the substance's half-life, in days. Round your answer to the nearest tenth. N=Noe^-kt
Answer:
t = 6.3
Step-by-step explanation:
N=Noe^(-kt)
No = 14 grams
k = .1092
We want to find t when N = 7 or 1/2 of 14
N=Noe^(-kt)
7 = 14 e ^ (-.1092t)
Divide each side by 14
1/2 = e ^ (-.1092t)
take the natural log of each side
ln (1/2) = ln e ^ (-.1092t)
ln (1/2) = -.1092t
Divide each side by -.1092
ln (1/2)/ -.1092 = t
t≈6.3475
Rounding to the nearest tenth
t = 6.3
Answer: 6.3
Step-by-step explanation:
3 1/3 + (-2 1/4) + 1 5/6=
Answer:
[tex]2\dfrac{11}{12}[/tex]
Step-by-step explanation:
The first step is to ensure that all of the fractions have a common denominator.
[tex]3\dfrac{1}{3}+\left( -2\dfrac{1}{4} \right) + 1\dfrac{5}{6}= \\\\3\dfrac{4}{12} - 2\dfrac{3}{12} +1 \dfrac{10}{12}= \\\\1\dfrac{1}{12}+1\dfrac{10}{12}= \\\\\boxed{2\dfrac{11}{12}}[/tex]
Hope this helps!
The city of Eden completed a new light rail system to bring commuters and shoppers into the downtown area and relieve highway congestion. City planners estimate that each year, 15% of those who drive or ride in an automobile will change to the light rail system; 80% will continue to use automobiles; and the rest will no longer go to the downtown area. Of those who use light rail; 5% will go back to using an automobile, 80% will continue to use light rail, and the rest will stay out of the downtown area. Assume those who do not go downtown will continue to stay out of the downtown area. The transition matrix associated with this Markov chain is a.an absorbing stochastic matrix. b.a regular stochastic matrix.
Answer:
Step-by-step explanation:
To check which option is correct we will first make transition matrix.
Let the state 1 and state 2 represent the automobile and light rail
So, the transition is given by
[tex]P=\left[\begin{array}{ccc}0.80+0.05&0.15\\0.5+0.15&0.80\end{array}\right][/tex]
[tex]P=\left[\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right][/tex]
Since P as no any entry zero so, P as not absorbing stochastic matrix
Also,
[tex]|P| = \left|\begin{array}{ccc}0.85&0.15\\0.20&0.80\end{array}\right| \\\\=0.85\times0.8-0.15\times0.2\\\\=0.65\neq0[/tex]
since |P| ≠ 0
Hence, Markov chain is a regular stochastic matrix.Write 7.3 as a mixed number.
Answer:
7 3/10
Step-by-step explanation:
7.3=7+0.3= 7+ 3/10= 7 3/10
A community center sells a total of 305 tickets for a basketball game. An adult ticket costs $5. A student ticket costs $1. The sponsors collect $693 in ticket sales. Find the number of each type of ticket sold.
Answer: student tickets = 208
Adult tickets = 97
Step-by-step explanation:
x + y = 305
x = 305 - y
5x + y = 693
Substituting
5 (305 - y) + y = 693
1525 - 5y + y = 693
-4y = -832
y = 832 / 4 = 208
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.8 inches and a standard deviation of 2.54 inches. What percentage of men are SHORTER than 67 inches
Answer:
14.69% of men are SHORTER than 67 inches
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
The heights of adult men in America are normally distributed, with a mean of 69.8 inches and a standard deviation of 2.67 inches.
This means that [tex]\mu = 69.8, \sigma = 2.67[/tex]
What percentage of men are SHORTER than 67 inches
This is the pvalue of Z when X = 67. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{67 - 69.8}{2.67}[/tex]
[tex]Z = -1.05[/tex]
[tex]Z = -1.05[/tex] has a pvalue of 0.1469
14.69% of men are SHORTER than 67 inches
(3xy)*x*у
х
Зуз
Зхуз
9xуз
9x5уз
Answer:
3 x^2 y^2
Step-by-step explanation:
Simplify the following:
3 x y x y
3 x y x y = 3 x^2 y^2:
Answer: 3 x^2 y^2
How much of other chemicals must be evaporated from 400 grams of a hand sanitizer
that is 24% alcohol to strengthen it to a hand sanitizer that is 30% alcohol? Correct your
answer to the nearest whole number.
Answer:
24 g
Step-by-step explanation:
We first find the mass of 24 % alcohol in 400 g of hand sanitizer. Let x be the mass of alcohol. So, x/400 × 100 % = 24 %
x/400 = 0.24
x = 0.24 × 400
= 96 g
The mass of the other chemicals is thus 400 g - 96 g = 304 g
We now find the mass of 30 % alcohol in 400 g of hand sanitizer. Let y be the mass of alcohol. So, y/400 × 100 % = 30 %
y/400 = 0.30
y = 0.30 × 400
= 120 g
The mass of the other chemicals is thus 400 g - 120 g = 280 g
The mass of other chemicals that needs to be evaporated is thus 304 g - 280 g = 24 g
Which graph represents the following system of inequalities? Y>5x-1 and then y less than or equal to x+3 please it's for Plato
Answer:
y=3
Step-by-step explanation:
If we use LCM and take 3 plus y it equals x so if x equals x it is then y
Answer:
D
Step-by-step explanation:
I took the Plato Course
Please answer this correctly without making mistakes
Answer:
It would be 131.95 if they want the answer in pi it would be 42 pi
Step-by-step explanation:
The average amount of rain per year in Greenville is 49 inches. The standard deviation is 8 inches. Find the probability that next year Greenville will receive the following amount of rainfall. Assume the variable is normally distributed.
A) At most 55 inches of rainB) at least 62 inches of rainC) Between 46 and 55 inches of rainD) How many inches of rain would you consider to be an extremely wet year?
Answer:
The probability that next year Greenville will receive the following amount of rainfall A) At most 55 inches of rain is 0.7734, B) at least 62 inches of rain is 0.0516, C) Between 46 and 55 inches of rain is 0.0387
D Having rainfall of above 65 inches would be considered as an extremely wet year
Step-by-step explanation:
A. To find the probability that next year Greenville will receive at most 55 inches of rain we would have to make the following calculation:
P(X<55)
=P((X-mean)/s<(55-49)/8)
=P(Z<0.75)
=0.7734
The probability that next year Greenville will receive at most 55 inches of rain is 0.7734
B. To find the probability that next year Greenville will receive at most 62 inches of rain we would have to make the following calculation:
P(X>62)
=P(Z>(62-49)/8)
=P(Z>1.63)
=0.0516
The probability that next year Greenville will receive at most 62 inches of rain is 0.0516
C. To find the probability that next year Greenville will receive at Between 46 and 55 inches of rain we would have to make the following calculation:
P(46<X<54)
=P((46-49)/8 <Z<(54-49)/8)
=P(-0.38 <Z< 0.63)
=0.3837
The probability that next year Greenville will receive Between 46 and 55 inches of rain is 0.3837
D. Here consider a value that is more two standard deviations above the mean as an unusual vale. That is:
X=2σ+μ
=2(8)+49
=65
Therefore, having rainfall of above 65 inches would be considered as an extremely wet year.
The sum of the two digits of a certain two-digit number equals the square root of the number? What is the number?
Answer:
81
Step-by-step explanation:
2-digit squares are 16, 25, 36, 49, 64, 81.
Their sums of digits, are ...
7, 7, 9, 13, 10, 9
The square 81 has a sum of digits equal to its square root.
Solve (x + 1)2 - 4(x + 1) + 2 = 0 using substitution.
U=
х
4(x +1)
O x +1
(x + 1)2
Answer:
Step-by-step explanation:
We are given the equation [tex](x+1)^2-4(x+1)+2=0[/tex]. Consider the substitution u = (x+1). Then the equation turns out to be [tex]u^2-4u+2=0[/tex]
Recall that given a second degree polynomial of the form [tex]ax^2+bx+c =0[/tex] then its solutions are given by the expression
[tex] x = \frac{-b \pm \sqrt[]{b^2-4ac}}{2a}[/tex]
In our case, a = 1, b = -4 and c =2. Then the solutions are
[tex]u_1 = \frac{4+\sqrt[]{(-4)^2-4(2)}}{2} = 2 +\sqrt[]{2}[/tex]
[tex]u_2 = \frac{4-\sqrt[]{(-4)^2-4(2)}}{2} = 2 -\sqrt[]{2}[/tex]
We have that x = u-1. So the original solutions are
[tex]x_1 = 2 +\sqrt[]{2}-1 = 1 + \sqrt[]{2}[/tex]
[tex]x_2 =2 -\sqrt[]{2} -1 = 1 - \sqrt[]{2}[/tex]
Answer: x+4
Step-by-step explanation: part one- x+4
Part two- 3+sqrt21 over 2 +4 & 3- sqrt21 over 2 +4
what is the percentage 33% of $145.00
Answer:
47.85
Step-by-step explanation:
33% of 145
of means multiply
Changing to decimal form
.33* 145
47.85
Step-by-step explanation:
cross multiply, set up ur equation like so
33. x
100 = 145
100x=4785
100
x=47.85
Solve the following equation using the quadratic formula: 3(x+4)2 - 81 = 0
Answer:
[tex]-4\pm 3\sqrt{3}[/tex]
Step-by-step explanation:
[tex]3(x+4)^2-81=0 \\\\3(x^2+8x+16)-81=0 \\\\3x^2+24x+48-81=0 \\\\3x^2+24x-33=0 \\\\x=\dfrac{-24\pm\sqrt{24^2+4(3)(33)}}{2(3)}= \\\\\dfrac{-24\pm\sqrt{972}}{6}= \\\\\dfrac{-24\pm 18\sqrt{3}}{6}= \\\\-4\pm 3\sqrt{3}[/tex]
Hope this helps!
Suppose that twelve bats was used in the experiment. For each trail, the zoo keeper pointed to one of two "feeders". Suppose that the bats went to the correct feeder one that the zoo keeper pointed at) 9 times. Find the 95% confidence interval for the population proportion of times that the bat would follow the point.
a) 0.505,0.995
b) 0.32, 0.81
c) 046, 091
Answer:
a) 0.505,0.995
Step-by-step explanation:
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 12, \pi = \frac{9}{12} = 0.75[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue 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}} = 0.75 - 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.505[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.995[/tex]
So the correct answer is:
a) 0.505,0.995
Which inequality represents the sentence below? Four and nine tenths less than the product of a number and six is no more than eighteen and one-eighth. 4 and StartFraction 9 over 10 EndFraction minus 6 x less-than-or-equal-to 18 and StartFraction 1 over 8 EndFraction 6 x minus 4 and StartFraction 9 over 10 EndFraction less-than-or-equal-to 18 and StartFraction 1 over 8 EndFraction 4 and StartFraction 9 over 10 EndFraction less-than 6 x + 18 and StartFraction 1 over 8 EndFraction 6 x minus 4 and StartFraction 9 over 10 EndFraction less-than 18 and StartFraction 1 over 8 EndFraction
Answer:
D. 6x-4 9/10<= 18 1/8
Step-by-step explanation:
Sorry I'm a little late :(