Answer:a
a
[tex]336.04 < \mu < 443.96[/tex]
b
The margin of error will increase
c
The margin of error will decreases
d
The 99% confidence interval is [tex]0.4107 < p < 0.4293[/tex]
Step-by-step explanation:
From the question we are told that
The sample size [tex]n = 19[/tex]
The sample mean is [tex]\= x = \$\ 390[/tex]
The standard deviation is [tex]\sigma = \$ \ 120[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table
So
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{120}{\sqrt{19} }[/tex]
=> [tex]E = 53.96[/tex]
The 95% confidence interval is
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]390 - 53.96 < \mu < 390 - 53.96[/tex]
=> [tex]336.04 < \mu < 443.96[/tex]
When the confidence level increases the [tex]Z_{\frac{\alpha }{2} }[/tex] also increases which increases the margin of error hence the confidence level becomes wider
Generally the sample size mathematically varies with margin of error as follows
[tex]n \ \ \alpha \ \ \frac{1}{E^2 }[/tex]
So if the sample size increases the margin of error decrease
The sample proportion is mathematically represented as
[tex]\r p = \frac{210}{500}[/tex]
[tex]\r p = 0.42[/tex]
Given that the confidence level is 0.99 the level of significance is [tex]\alpha = 0.01[/tex]
The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }[/tex]
=> [tex]E = 0.0093[/tex]
The 99% confidence interval is
[tex]\r p - E < p < \r p + E[/tex]
[tex]0.42 - 0.0093 < p < 0.42 + 0.0093[/tex]
[tex]0.4107 < p < 0.4293[/tex]
Divide write the quotient in lowest term 1 1/3 divided by 1 3/4
Answer:
7/3 or 2 1/3
Step-by-step explanation:
1 1/3 ÷ 1 3/4
Change to improper fractions
(3*1+1)/3 ÷ (4*1+3)/4
4/3 ÷ 7/4
Copy dot flip
4/3 * 7/4
Rewriting
4/4 * 7/3
7/3
As a mixed number
2 1/3
Answer:
11/3÷13/4
11/3×4/13
44/39=
1.1282
Suppose that 80% of all registered California voters favor banning the release of information from exit polls in presidential elections until after the polls in California close. A random sample of 25 registered California voters is selected.
Required:
a. Calculate the mean and standard deviation of the number of voters who favor the ban.
b. What is the probability that exactly 20 voters favor the ban?
Answer:
a. Mean = 20
Sd = 4
b. Probability of X = 20 = 0.1960
Step-by-step explanation:
we have
n = 25
p = 80% = 0.8
mean = np
= 0.8 * 25
= 20
standard deviation = √np(1-p)
= √25*0.8(1-0.8)
=√4
= 2
probability that exactly 20 favours ban
it follows a binomial distribution
= 25C20 × 0.8²⁰ × 0.2⁵
= 53130 × 0.01153 × 0.00032
= 0.1960
Probability of X = 20 = 0.1960
A highway department executive claims that the number of fatal accidents which occur in her state does not vary from month to month. The results of a study of 140 fatal accidents were recorded. Is there enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month? Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fatal Accidents 8 15 9 8 13 6 17 15 10 9 18 12
Answer:
There is enough evidence to reject the highway department executive's claim about the distribution of fatal accidents between each month, as the Variance is 14 and the Standard Deviation = 4 approximately.
There is a high degree of variability in the mean of the population as explained by the Variance and the Standard Deviation.
Step-by-step explanation:
Month No. of Mean Squared
Fatal Accidents Deviation Difference
Jan 8 -4 16
Feb 15 3 9
Mar 9 -3 9
Apr 8 -4 16
May 13 1 1
Jun 6 -6 36
Jul 17 5 25
Aug 15 3 9
Sep 10 -2 4
Oct 9 -3 9
Nov 18 6 36
Dec 12 0 0
Total 140 170
Mean = 140/12 = 12 Mean of squared deviation (Variance) = 170/12 = 14.16667
Standard deviation = square root of variance = 3.76386 = 4
The fatal accidents' Variance is a measure of how spread out the fatal accident data set is. It is calculated as the average squared deviation of the number of each month's accident from the mean of the fatal accident data set. It also shows how variable the data varies from the mean of approximately 12.
The fatal accidents' Standard Deviation is the square root of the variance, and a useful measure of variability when the distribution is normal or approximately normal.
Find x. A. 3√3 B. 3 C. 2√3/3 D. √63
Answer:
[tex]\huge\boxed{\sf x = 3\sqrt{3}}[/tex]
Step-by-step explanation:
Cos 30 = Adjacent / Hypotenuse
Where Adjacent = x , Hypotenuse = 6
[tex]\frac{\sqrt{3} }{2}[/tex] = x / 6
x = [tex]\frac{\sqrt{3} }{2}[/tex] * 6
[tex]\sf x = 3\sqrt{3}[/tex]
solve for x: -3(x + 1)= -3(x + 1) - 5
Answer:
No solution : 0= -5Step-by-step explanation:
[tex]-3\left(x+1\right)=-3\left(x+1\right)-5\\\\\mathrm{Add\:}3\left(x+1\right)\mathrm{\:to\:both\:sides}\\\\-3\left(x+1\right)+3\left(x+1\right)=-3\left(x+1\right)-5+3\left(x+1\right)\\\\\mathrm{Simplify}\\\\0=-5\\\\\mathrm{The\:sides\:are\:not\:equal}\\\\\mathrm{No\:Solution}[/tex]
Charlie needs a $275,000 mortgage and he'd like to pay it off in 30 years. He is considering two banks. Bank A: 3.5% with monthly payments of $1234.87 Bank B: 4% with monthly payments of $1312.89 Charlie doesn't think a 0.5% difference is that much. What is the difference between these two bank loans with total interest paid over the life of the loan?
Answer:
Difference in interest= $41,250
Step-by-step explanation:
To calculate the interest paid on each bank loan we use the following formula
Interest = Principal * Rate * Time
For Bank A
Interest = 275,000 * 0.035 * 30
Interest = $288,750
For Bank B
Interest = 275,000 * 0.04 * 30
Interest = $330,000
Therefore
Difference in interest= 330,000 - 288,750
Difference in interest= $41,250
Therefore if the mortgage is taken from Bank B he will pay an extra $41,250 on the loan.
The 0.5% difference in rates has a large impact over the 30 year term loan
Find the inverse of the following function.
Answer:
The inverse is 1/64 x^2 = y x ≥ 0
Step-by-step explanation:
f(x) = 8 sqrt(x)
y = 8 sqrt(x)
Exchange x and y
x = 8 sqrt (y)
Solve for y
Divide each side by 8
1/8 x = sqrt(y)
Square each side
(1/8 x)^2 = (sqrt(y))^2
1/64 x^2 = y
The inverse is 1/64 x^2 = y x ≥ 0
since x ≥0 in the original function
Answer:
[tex]\Huge \boxed{\mathrm{D}}[/tex]
Step-by-step explanation:
[tex]f(x)=8\sqrt{x}[/tex]
[tex]\sf Replace \ with \ y.[/tex]
[tex]y=8\sqrt{x}[/tex]
[tex]\sf Switch \ the \ variables.[/tex]
[tex]x= 8\sqrt{y}[/tex]
[tex]\sf Divide \ both \ sides \ of \ the \ equation \ by \ 8.[/tex]
[tex]\displaystyle \frac{x}{8} =\sqrt{y}[/tex]
[tex]\sf Square \ both \ sides \ of \ the \ equation.[/tex]
[tex]\displaystyle (\frac{x}{8} )^2 =y[/tex]
[tex]\displaystyle \frac{x^2 }{64} =y[/tex]
[tex]\displaystyle f^{-1}(x)=\frac{1}{64} x^2[/tex]
Select the function that represents a parabola with zeros at x = –2 and x = 4, and y-intercept (0,–16). A ƒ(x) = x2 + 2x – 8 B ƒ(x) = 2x2 + 4x – 16 C ƒ(x) = x2 – 2x – 8 D ƒ(x) = 2x2 – 4x – 16
Answer:
D. [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]
Step-by-step explanation:
Any parabola is modelled by a second-order polynomial, whose standard form is:
[tex]y = a\cdot x^{2}+b\cdot x + c[/tex]
Where:
[tex]x[/tex] - Independent variable, dimensionless.
[tex]y[/tex] - Dependent variable, dimensionless.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Coefficients, dimensionless.
In addition, a system of three linear equations is constructed by using all known inputs:
(-2, 0)
[tex]4\cdot a -2\cdot b + c = 0[/tex] (Eq. 1)
(4, 0)
[tex]16\cdot a + 4\cdot b +c = 0[/tex] (Eq. 2)
(0,-16)
[tex]c = -16[/tex] (Eq. 3)
Then,
[tex]4\cdot a - 2\cdot b = 16[/tex] (Eq. 4)
[tex]16\cdot a + 4\cdot b = 16[/tex] (Eq. 5)
(Eq. 3 in Eqs. 1 - 2)
[tex]a - 0.5\cdot b = 4[/tex] By Eq. 4 (Eq. 4b)
[tex]a = 4 + 0.5\cdot b[/tex]
Then,
[tex]16\cdot (4+0.5\cdot b) + 4\cdot b = 16[/tex] (Eq. 4b in Eq. 5)
[tex]64 + 12\cdot b = 16[/tex]
[tex]12\cdot b = -48[/tex]
[tex]b = -4[/tex]
The remaining coeffcient is:
[tex]a = 4 + 0.5\cdot b[/tex]
[tex]a = 4 + 0.5\cdot (-4)[/tex]
[tex]a = 2[/tex]
The function that represents a parabola with zeroes at x = -2 and x = 4 and y-intercept (0,16) is [tex]f(x) = 2\cdot x^{2}-4\cdot x -16[/tex]. Thus, the right answer is D.
Answer:
D ƒ(x) = 2x2 – 4x – 16
Step-by-step explanation:
a family spent $93 at a carnival.
*they spent $18 on tickets and $30 on food. they spent the rest of the money on games.
which equation can be used to to find "g", the amount of money used on games.
Answer: 93-(18+30)=g
93-48=g
45=g
Step-by-step explanation: yup
The answer is 93-18-30-g=0 or 18+30+g=93
cindy was asked by her teacher to subtract 3 from a certain number and then divide the result by 6 instead, she subtracted 6 and then divided the result by 3 giving an answer of 25 what would her answer have been if she had worked the problem correctly?
Answer:
13
Step-by-step explanation:
let the number be x
how Cindy worked it out :
(x -6) ÷ 3 = 25
x -6 = 75
x = 81
How she should have worked it out:
(x - 3) ÷ 6
(81 - 3) ÷ 6
78 ÷ 6 = 13
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 53.9 for a sample of size 24 and standard deviation 5.6. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level). Assume the data is from a normally distributed population. Enter your answer as a tri-linear inequality accurate to three decimal places.
_______ < μ < _________ please teach using calculator method
Answer:
The estimate is
[tex]52.02 < \mu < 55.78[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\ = x = 53.9[/tex]
The sample size is n = 24
The standard deviation is [tex]\sigma = 5.6[/tex]
Given that the confidence level is 90% the level of significance is mathematically represented as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10 \%[/tex]
[tex]\alpha = 0.10[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table.The value is
[tex]Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} } = 1.645[/tex]
The reason we are obtaining critical value of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because [tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval ( [tex]1 - \alpha[/tex] ) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex] is just the area of one tail which what we required to calculate the margin of error
NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }[/tex]
substituting values
[tex]E = 1.645 * \frac{5.6 }{ \sqrt{24} }[/tex]
[tex]E = 1.880[/tex]
The estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]53.9 - 1.880 < \mu < 53.9 + 1.880[/tex]
[tex]52.02 < \mu < 55.78[/tex]
HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Option (B)
Step-by-step explanation:
The given expression is,
[tex]\sqrt{22x^6}\div\sqrt{11x^4}[/tex]
We can rewrite this expression as,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }[/tex]
Solving it further,
[tex]\frac{\sqrt{22x^6}}{\sqrt{11x^4} }=\frac{\sqrt{22(x^3)^2} }{\sqrt{11(x^2)^2} }[/tex] [Since [tex]x^3\times x^3=x^6[/tex] and [tex]x^{2}\times x^{2}=x^4[/tex]]
[tex]=\sqrt{\frac{22(x^3)^2}{11(x^2)^2} }[/tex] [Since [tex]\frac{\sqrt{a} }{\sqrt{b} }=\sqrt{\frac{a}{b} }[/tex]]
[tex]=\frac{x^3}{x^2}\sqrt{\frac{22}{11} }[/tex]
[tex]=x\sqrt{2}[/tex]
Therefore, quotient will be x√2.
Option (B) will be the correct option.
PLEASE HELPPPPP!!!!!!!!!!!!!!!Which relationships have the same constant of proportionality between y and x as the following graph?Choose two answers!!
Answer:
B, E
Step-by-step explanation:
You can use these strategies to compare the given graph and the other representations.
A & B) See if the point (x, y) = (8, 6) marked on the first graph works in the given equation.
A -- 6y = 8x ⇒ 6(6) = 8(8) . . . FALSE
B -- y = (3/4)x ⇒ 6 = (3/4)8 . . . True
__
C) Compare this graph to the given graph. They don't match.
__
D & E) Plot a point from the table on the given graph and see where it falls.
D -- The point (x, y) = (3, 4) lies above the line on the given graph.
E -- The point (x, y) = (4, 3) lies on the given graph.
_____
Choices B and E have the same constant of proportionality as shown in the given graph.
Answer:
B and E
Step-by-step explanation:
average age of 15 students of iub 11years if teacher is also included average age becomes 13 years how old is teachers
Answer: the teacher is 43
Step-by-step explanation: if you take 11 and multiply it by 15 you get 165 if you take 208 and divide it by 16 you get 13.
so basically you subtract 208 from 165 to get 43
To which number sets of numbers does the number 3.567...belong?
Answer:
It's irrational numberIf the decimal digits do not repeat in some known pattern, then the number is irrational. We cannot write it as a ratio or fraction of two integers. If it did have a pattern, then we can use algebra to find the fractional representation of that number. Based on what is shown, it looks like there is no pattern so that's why the value is irrational. The number is also a real number as this is the case with any number you'll encounter unless you're dealing with complex numbers (but your teacher may not have introduced that topic yet).
Simplify 3m2 (−6m3 )
Answer:
3m2(-6m3)
since it's a term you have to multiply it by the number in bracket
6m(-6m3)
6m(-18m)
-108m²
PLEASE HELP! You do not have to answer all questions but can someone explain to me on where I am even suppose to begin? I don't even know how to answer a single one of these questions.
Step-by-step explanation:
For problems 1 through 15, evaluate the function at the given x value.
1. f(5) = 2(5) − 1 = 9
2. f(3) = 3² − 3(3) − 1 = -1
3. f(0) = 2(0) + 5 = 5
So on and so forth.
Then, match each answer with the corresponding letter.
The answer to #1 was 9. 9 corresponds to the letter A.
The answer to #2 was -1. -1 corresponds to the letter C.
The answer to #3 was 5. 5 corresponds to the letter P.
Finally, write each letter with its corresponding problem number.
So everywhere you see a 1, write A.
Everywhere you see a 2, write C.
Everywhere you see a 3, write P.
Continue until every blank has a letter and the problem is solved.
Answer:
For problems 1 through 15, evaluate the function at the given x value.
1. f(5) = 2(5) − 1 = 9
2. f(3) = 3² − 3(3) − 1 = -1
3. f(0) = 2(0) + 5 = 5
So on and so forth.
Step-by-step explanation:
Find the product . Write your answer in exponential form 8^-2•8^-9
Answer:
8^-11
Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
Then we have ...
(8^(-2))·(8^(-9)) = 8^(-2-9) = 8^-11
Mrs. Simpson’s calculus class has an exam with an average score of 80 and standard deviation of 15. Assume that exam scores are normally distributed. If Mrs. Simpson decides to give an A grade to students who score in the top 20% of the class, what exam score is needed in order to get the A grade? (3pts)
Answer:
93 is the exam score needed in order to get the A grade in Mrs Simpson’s test
Step-by-step explanation:
Let x be the score that gives an A grade
Mathematically from the z-score formula, we know that;
z-score = x-mean/SD
From the question, x = ? , mean = 80 and SD = 15
Thus;
z-score = x-80/15
But in this question, we have the probability but we do not have the z-score
So we need the z-score that is equivalent to 20%
20% is same as 0.2
Using the standard normal distribution table, a probability of 0.2 corresponds to a z-score of 0.84
Thus, mathematically;
0.84 = x-80/15
x-80 = 15(0.84)
x-80 = 12.6
x = 80 + 12.6
x = 92.6 which is approximately 93
Let f(x) = - 4x + 5. Find and simplify f(x + 2).
Answer:
-4x - 3.
Step-by-step explanation:
f(x) = -4x + 5.
f(x + 2) = -4(x + 2) + 5
= -4x - 8 + 5
= -4x - 3.
Hope this helps!
Answer:
f(x+2)=-4x-3
Step-by-step explanation:
We are given:
[tex]f(x)= -4x+5[/tex]
and asked to find f(x+2). Therefore, we must substitute x+2 for each x in the function.
[tex]f(x+2)=-4(x+2)+5[/tex]
Now, simplify. First, distribute the -4. Multiply each term inside the parentheses by -4.
[tex]f(x+2)=(-4*x)+(-4*2)+5\\f(x+2)=-4x+(-4*2)+5\\f(x+2)=-4x-8+5[/tex]
Next, combine like terms. There are 2 constants (terms without a variable) that can be added. Add -8 and 5.
[tex]f(x+2)=-4x(-8+5)\\f(x+2)=-4x-3[/tex]
f(x+2) is -4x-3.
Suppose that y varies directly with x and y=20 when x=2 Find y when x=8
Answer:
80
Step-by-step explanation:
x y
2 = 20
8 = x
cross multiply( 8*20)/2
= 4 * 20
= 80
The difference between teenage female and male depression rates estimated from two samples is 0.07. The estimated standard error of the sampling distribution is 0.03. What is the 95% confidence interval
Answer:
The 95% confidence interval is [tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean difference is [tex]\= x_m - \= x_f = 0.07[/tex]
The standard error is SE = 0.03
Given that the confidence interval is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha =0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{ \alpha }{2} } * SE[/tex]
substituting values
[tex]E = 1.96 * 0.03[/tex]
[tex]E = 0.0588[/tex]
The 95% confidence interval is mathematically represented as
[tex](\= x_m - \= x_f ) - E < \mu_m - \mu_f <(\= x_m - \= x_f ) + E[/tex]
substituting values
[tex]0.07 - 0.0588 < \mu_m - \mu_f <0.07 + 0.0588[/tex]
[tex]0.0112 < \mu_m - \mu_f < 0.1288[/tex]
The difference between teenage female and male depression rates are given. The 95% percent confidence interval can be obtained using mean and standard error relation.
The confidence interval is (0.0016 , 0.1584).
Given:
The depression rates is [tex]0.07[/tex].
The standard error of sampling distribution is [tex]0.03[/tex].
The critical value [tex]z=1.96[/tex]
Write the relation for mean and standard error.
[tex]\mu\pm z_{\rm critical}+\rm standard\: error[/tex]
Substitute the value.
[tex]0.07\pm 1.96\times 0.03=(0.1288,\:0.0112)[/tex]
Therefore, the upper and lower boundary is [tex](0.1288,\:0.0112)[/tex]. Thus, The confidence interval is (0.0016 , 0.1584).
Learn more mean and standard error here:
https://brainly.com/question/20215215
Find the interquartile range of the following data set.
Number of Points Scored at Ten Basketball Games
57 63 44 29 36 62 48 50 42 34
a .21
B.28
C. 6
D. 34
Answer:
b.28 its ans is no.b
Step-by-step explanation:
no point score in basketball
Will Give Brainliest Please Answer Quick
Answer:
Option (2)
Step-by-step explanation:
If a perpendicular is drawn from the center of a circle to a chord, perpendicular divides the chord in two equal segments.
By using this property,
Segment MN passing through the center Q will be perpendicular to chords HI ans GJ.
By applying Pythagoras theorem in right triangle KNJ,
(KJ)² = (KN)² + (NJ)²
(33)² = (6√10)² + (NJ)²
NJ = [tex]\sqrt{1089-360}[/tex]
NJ = [tex]\sqrt{729}[/tex]
= 27 units
Since, GJ = 2(NJ)
GJ = 2 × 27
GJ = 54 units
Option (2) will be the answer.
Which defines a line segment?
two rays with a common endpoint
O a piece of a line with two endpoints
O a piece of a line with one endpoint
all points equidistant from a given point
Answer:
O a piece of a line with two endpoints
Step-by-step explanation:
O a piece of a line with two endpoints
A piece of a line with two endpoints.
What is a line segment?In geometry, a line segment is a part of a line this is bounded by distinct end points and includes every point on the line this is between its endpoints.
What are the examples of line segments in real life?A ruler, a scale, a stick, a boundary line.Learn more about line segments here https://brainly.com/question/2437195
#SPJ2
two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 109 feet, and ball 2 is dropped from a height of 260 feet. Use the function f(t) -16t^2+h to determine the current height, f(t), of a ball from a height h, over given time t.
When does ball 1 reach the ground? Round to the nearest hundredth
Answer: 5.22 seconds
Step-by-step explanation:
t represents time and y represents the height.
Since we want to know when the ball hits the ground, find t when y = 0
Ball 1 starts at a height of 109 --> h = 109
0 = -16t² + 109
16t² = 109
[tex]t^2=\dfrac{109}{16}\\[/tex]
[tex]t=\sqrt{\dfrac{109}{16}}[/tex]
[tex]t=\dfrac{\sqrt{109}}{2}[/tex]
t = 5.22
=> H = 109
=> 0 = -16t² + 109
=> 16t² = 109
=> t² = 109/16
=> t = 109/2
=> t = 5.22 sec
Therefore, 5.22 second is the answer.
An Uber driver provides service in city A and city B only dropping off passengers and immediately picking up a new one at the same spot. He finds the following Markov dependence. For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25. If he is in city B, the probability that he has to drive passengers to city A is 0.45. Required:a. What is the 1-step transition matrix? b. Suppose he is in city B, what is the probability he will be in city A after two trips? c. After many trips between the two cities, what is the probability he will be in city B?
Answer:
a. 1-step transition matrix is be expressed as:
[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]
b. The probability that he will be in City A after two trips given that he is in City B = 0.585
c. After many trips, the probability that he will be in city B = 0.3571
Step-by-step explanation:
Given that:
For each trip, if the driver is in city A, the probability that he has to drive passengers to city B is 0.25
If he is in city B, the probability that he has to drive passengers to city A is 0.45.
The objectives are to calculate the following :
a. What is the 1-step transition matrix?
To determine the 1 -step transition matrix
Let the State ∝ and State β denotes the Uber Driver providing service in City A and City B respectively.
∴ The transition probability from state ∝ to state β is 0.25.
The transition probability from state ∝ to state ∝ is 1- 0.25 = 0.75
The transition probability from state β to state ∝ is 0.45. The transition probability from state β to state β is 1 - 0.45 = 0.55
Hence; 1-step transition matrix is be expressed as:
[tex]P= \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right][/tex]
b. Suppose he is in city B, what is the probability he will be in city A after two trips?
Consider [tex]Y_n[/tex] = ∝ or β to represent the Uber driver is in City A or City B respectively.
∴ The probability that he will be in City A after two trips given that he is in City B
=[tex]P(Y_0 = 2, Y_2 = 1 , Y_3 = 1) + P(Y_0 = 2, Y_2 = 2 , Y_3 = 1)[/tex]
= 0.45 × 0.75 + 0.55 × 0.45
= 0.3375 + 0.2475
= 0.585
c. After many trips between the two cities, what is the probability he will be in city B?
Assuming that Ф = [ p q ] to represent the long run proportion of time that Uber driver is in City A or City B respectively.
Then, ФP = Ф , also p+q = 1 , q = 1 - p and p = 1 - q
∴
[tex][ p\ \ \ q ] = \left[\begin{array}{cc}0.75&0.25\\0.45&0.55\\\end{array}\right] [ p\ \ \ q ][/tex]
0.75p + 0.45q = q
-0.25p + 0.45q = 0
since p = 1- q
-0.25(1 - q) + 0.45q = 0
-0.25 + 0.25 q + 0.45q = 0
0.7q = 0.25
q = [tex]\dfrac{0.25} {0.7 }[/tex]
q = 0.3571
After many trips, the probability that he will be in city B = 0.3571
Please help look at the question in image
Answer:
In part 1, the value for D is given. Putting D as 1 gives us the answer 17/20
In part 2, the value of E is given as 1, putting E as 1 gives us D = 20/17
A waiter earns $11.00 an hour and approximately 10% of what he serves in a shift. If he works a 6 hour shift and takes $425 in orders, his total earnings for the six hours would be:
Answer:
108.50
Step-by-step explanation:
First find the wages
11* 6 = 66 dollars
Then figure the commission
10% of 425
.10 * 425
42.5
Add the two amounts together
42.5+66
108.50
Let the sample size of leg strengths to be 7 and the sample mean and sample standard deviation be 630 watts and 32 watts, respectively.
(a) Is there evidence that leg strength exceeds 600 watts at significance level 0.05? Find the P-value. There is_________ evidence that the leg strength exceeds 600 watts at ? = 0.05.
A. 0.001 < P-value < 0.005
B. 0.10 < P-value < 0.25
C. 0.010 < P-value < 0.025
D. 0.05 < P-value < 0.10
(b) Compute the power of the test if the true strength is 610 watts.
(c) What sample size would be required to detect a true mean of 610 watts if the power of the test should be at least 0.9? n=
Answer:
a. There is_sufficient evidence that the leg
C. 0.010 < P-value < 0.025
b. Power of test = 1- β=0.2066
c. So the sample size is 88
Step-by-step explanation:
We formulate the null and alternative hypotheses as
H0 : u1= u2 against Ha : u1 > u2 This is a right tailed test
Here n= 7 and significance level ∝= 0.005
Critical value for a right tailed test with 6 df is 1.9432
Sample Standard deviation = s= 32
Sample size= n= 7
Sample Mean =x`= 630
Degrees of freedom = df = n-1= 7-1= 6
The test statistic used here is
Z = x- x`/ s/√n
Z= 630-600 / 32 / √7
Z= 2.4797= 2.48
P- value = 0.0023890 > ∝ reject the null hypothesis.
so it lies between 0.010 < P-value < 0.025
b) Power of test if true strength is 610 watts.
For a right tailed test value of z is = ± 1.645
P (type II error) β= P (Z< Z∝-x- x`/ s/√n)
Z = x- x`/ s/√n
Z= 610-630 / 32 / √7
Z=0.826
P (type II error) β= P (Z< 1.645-0.826)
= P (Z> 0.818)
= 0.7933
Power of test = 1- β=0.2066
(c)
true mean = 610
hypothesis mean = 600
standard deviation= 32
power = β=0.9
Z∝= 1.645
Zβ= 1.282
Sample size needed
n=( (Z∝ +Zβ )*s/ SE)²
n= ((1.645+1.282) 32/ 10)²
Putting the values and solving we get 87.69
So the sample size is 88
