Answer:
Step-by-step explanation:
The interval of interest is per hour. This means 60 minutes. Since the number of emails received per hour follows a Poisson distribution and that the average number of emails received per hour is three, it means that
Mean, μ = 3
x is a random variable representing the number of mails received per hour
a) The probability of receiving no emails during an hour is expressed as
P(x = 0)
From the Poisson distribution calculator,
P(x = 0) = 0.0498
b) the probability of receiving at least three emails during an hour is expressed as P(x ≥ 3).
P(x ≥ 3) = 0.577
c) the expected number of emails received during 15 minutes is
3 × 15/60 = 0.75
d) mean = 0.75
From the poisson distribution calculator, P(x = 0) = 0.47
In this activity, you will use equations to represent this proportional relationship: Olivia is making bead bracelets for her friends. She can make 3 bracelets in 15 minutes.
Part A
Find the constant of proportionality in terms of minutes per bracelet.
Part B
What does the proportionality constant represent in this situation?
Part C
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part A. Be sure to assign a variable for each quantity.
Part D
Now find the constant of proportionality in terms of number of bracelets per minute.
Part E
What does the proportionality constant represent in this situation?
Part F
Write an equation to represent the proportional relationship. Use the constant of proportionality you found in part D. Be sure to assign a variable for each quantity.
Part G
How are the constants of proportionality you found in parts A and D related?
Part H
Are the two equations you developed in parts C and F equivalent? Explain.
Answer:
Step-by-step explanation:
A) The constant of proportionality in terms of minutes per bracelet is
15/3 = 5 minutes per bracelet
B) The constant of proportionality represents man hour rate
C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
t = kb
D) the constant of proportionality in terms of number of bracelets per minute is
3/15 = 1/5
E) The constant of proportionality represents production rate
F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,
b = kt
G) The constants of proportionality are reciprocals
H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.
Answer:the sample answers, change them up so you dont get in trouble
A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:
constant of proportionality=15 MINUTES/3 BRACELETS=5 minutes per bracelet.
B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.
C Here’s one way to set up the equation:
time = constant of proportionality × number of bracelets
Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.
thats all ik srry
Step-by-step explanation:
What is the positive solution of x2 – 36 = 5x?
Answer:
9
Step-by-step explanation:
x² − 36 = 5x
x² − 5x − 36 = 0
(x − 9) (x + 4) = 0
x = 9 or -4
Fathi has \$1.10$1.10dollar sign, 1, point, 10 in his printing account. Each sheet of paper he uses reduces his printing account balance by \$0.25$0.25dollar sign, 0, point, 25. Fathi wants to print out a PDF document that is 474747 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each side of the sheet. After Fathi prints, what will be the balance in his printing account?
Answer:
$-4.90.
Step-by-step explanation:
Fathi has $1.10. Each sheet costs him $0.25. He wants to print 47 pages.
If he prints double sided, then he will use 47 / 2 = 23.5 sheets of paper. But he can't print a half-sheet, so he will use 24 sheets of paper.
Each sheet costs $0.25. 0.25 * 24 = 6. The printing will cost him $6.
Since he only has $1.10, his remaining balance will be 1.1 - 6 = -4.9. The balance on his printing account will be $-4.90.
Hope this helps!
Answer:
-1.90
Step-by-step explanation:
Khan Academy
I got it right for sure
What are the vertex and X intercepts of the graph of the function below Y =(x+4)(x-2)
Answer:
Vertex: ( -1 , − 9 )
X intercepts (0,-4)(0,2)
Step-by-step explanation:
Answer:
( -1, -9)
And
x-intercepts: (-4, 0), (2,0)
Step-by-step explanation:
Sacrificed my grade
X = ??????geometryyyy
Answer:
3.75Step-by-step explanation:
Using Secant-Secant theorem we can find the value of x.
The product of one segment and its external segment is equal to the product of the other segment and its external segment.
5 × 3 = x × 4
15 = 4x
15/4 = x
3.75 = x
A random sample of 13 items is drawn from a population whose standard deviation is unknown. The sample mean is x¯ = 950 and the sample standard deviation is s = 10. Use Appendix D to find the values of Student’s t.
1. Construct an interval estimate of mu with 99% confidence. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
2. Construct an interval estimate of mu with 99% confidence, assuming that s = 20. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
3. Construct an interval estimate of mu with 99% confidence, assuming that s = 40. (Round your answers to 3 decimal places.)
The 99% confidence interval is from_____ to ______ .
Answer:
1. The 99% confidence interval is from 941.527 to 958.473
2. The 99% confidence interval is from 933.054 to 966.946
3. The 99% confidence interval is from 916.108 to 983.892
Step-by-step explanation:
The confidence interval is given by
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]
Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by
[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]
Where n is the sample size,
s is the sample standard deviation,
[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level
The t-score corresponding to 99% confidence level is
Significance level = α = 1 - 0.99 = 0.01/2 = 0.005
Degree of freedom = n - 1 = 13 - 1 = 12
From the t-table at α = 0.005 and DoF = 12
t-score = 3.055
1. 99% Confidence Interval when s = 10
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]
The 99% confidence interval is from 941.527 to 958.473
2. 99% Confidence Interval when s = 20
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]
The 99% confidence interval is from 933.054 to 966.946
3. 99% Confidence Interval when s = 40
The margin of error is
[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]
So the required 99% confidence interval is
[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]
The 99% confidence interval is from 916.108 to 983.892
As the sample standard deviation increases, the range of confidence interval also increases.
Diane's bank is offering 5% interest, compounded monthly. If Diane invests $10,500 and wants $20,000 when she withdrawals, how long should she keep her money in for? Round to the nearest tenth of a year.
Answer:
The time period is 13 years.
Step-by-step explanation:
Interest rate (r )= 5% or 5%/12 = 0.42% per months
The investment amount (Present value) = $10500
Final expected amount (future value) = $20000
Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.
Use the below formula to find the time period.
Future value = present value (1 + r )^n
20000 = 10500(1+0.0042)^n
1.9047619 = (1+0.0042)^n
1.9047619 = 1.0042^n
n = 153.74 months.
Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)
A random sample of n = 8 E-glass fiber test specimens of a certain type yielded a sample mean interfacial shear yield stress of 32.9 and a sample standard deviation of 4.9. Assuming that interfacial shear yield stress is normally distributed, compute a 95% CI for true average stress. (Give answer accurate to 2 decimal places.)
Answer:
[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]
[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=32.9[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=4.9 represent the sample standard deviation
n=8 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
the degrees of freedom are given by:
[tex]df=n-1=8-1=7[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value for this cae would be [tex]t_{\alpha/2}=2.365[/tex]
Now we have everything in order to replace into formula (1):
[tex]32.9-2.365\frac{4.9}{\sqrt{8}}=28.80[/tex]
[tex]32.9+2.365\frac{4.9}{\sqrt{8}}=37.00[/tex]
Julie has three boxes of pens. The diagram shows expressions for the number of pens in each box. Look at these equations.
Equals B +12
B equals C +4
Write an equation to show the relationship between a + c
Answer:
a=c+16here,
a=b+12
b=a-12----> equation (i)
b= c+4
putting the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
hope this helps...
Good luck on your assignment...
The value of a + c is 16.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
a=b+12
So, b=a-12 ---- equation (i)
and, b= c+4
Substitute the value of b from the equation (I)
a-12=c+4
a=c+4+12
a=c+16
Hence, the value of a+ c is 16.
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How do you solve 36 times [tex]\sqrt{3}[/tex]
Answer:
62.3538
Step-by-step explanation:
There is nothing to solve. If you need a decimal value, you can use a calculator or table of square roots.
I need help urgent plz someone help me solved this problem! Can someone plz help I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer: a) 8.779 years
b) 8.664 years
Step-by-step explanation:
a)
[tex]A=P\bigg(1+\dfrac{r}{n}\bigg)^{nt}[/tex]
A: accumulated amount (balance)P: principal amount (original/initial investment)r: interest rate (convert to a decimal)n: number of times compounded per yeart: number of yearsGiven: A = 1800, P = 900, r = 8% = 0.08, n = 3, t = unknown
[tex]1800=900\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\2=\bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=ln \bigg(1+\dfrac{0.08}{3}\bigg)^{3t}\\\\\\ln\ 2=3t\ ln\bigg(1+\dfrac{0.08}{3}\bigg)\\\\\\\dfrac{ln\ 2}{3\ ln\bigg(1+\dfrac{0.08}{3}\bigg)}=t\\\\\\\large\boxed{8.779=t}[/tex]
b)
[tex]A=Pe^{rt}[/tex]
[tex]1800=900e^{0.08t}\\\\\\2=e^{0.08t}\\\\\\ln\ 2=0.08t\\\\\\\dfrac{ln\ 2}{0.08}=t\\\\\\\large\boxed{8.664=t}[/tex]
Q‒1. [5×4 marks] a) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? (150) b) How many three-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? c) How many odd numbers can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once? d) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6? e) How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 if each digit can be used only once?
Answer:
a) 294
b) 180
c) 75
d) 174
e) 105
Step-by-step explanation:
I assume that for each problem, the first digit can't be 0.
a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.
6×7×7 = 294
b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.
6×6×5 = 180
c) Again, each digit can only be used once, but this time, the last digit must be odd.
If only the last digit is odd, there are 3×3×3 = 27 possible numbers.
If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.
If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.
If all three digits are odd, there are 3×2×1 = 6 possible numbers.
The total is 27 + 24 + 18 + 6 = 75.
d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.
If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.
If the first digit is greater than 3, there are 3×7×7 = 147 numbers.
The total is 6 + 21 + 147 = 174.
e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.
If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.
The total is 15 + 90 = 105.
You are graphing Square ABCDABCDA, B, C, D in the coordinate plane. The following are three of the vertices of the square: A(4, -7), B(8, -7),A(4,−7),B(8,−7),A, left parenthesis, 4, comma, minus, 7, right parenthesis, comma, B, left parenthesis, 8, comma, minus, 7, right parenthesis, comma and C(8, -3)C(8,−3)C, left parenthesis, 8, comma, minus, 3, right parenthesis. What are the coordinates of point DDD? \large((left parenthesis , \large))right parenthesis
Answer:
D(4,-3)
Step-by-step explanation:
Given three of the vertices of the square: A(4, -7), B(8, -7),C(8, -3)
Let the coordinate of the fourth vertex be D(x,y).
We know that diagonals of a square are perpendicular bisector. So, the midpoint of both diagonals is the same.
The diagonals are BD and AC
Midpoint of BD = Midpoint of AC
[tex]\left(\dfrac{8+x}{2},\dfrac{-7+y}{2}\right) =\left(\dfrac{4+8}{2},\dfrac{-7+(-3)}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(\dfrac{12}{2},\dfrac{-10}{2}\right)\\ \left(\dfrac{8+x}{2},\dfrac{y-7}{2}\right) =\left(6,-5\right)\\$Therefore$:\\\dfrac{8+x}{2}=6\\8+x=12\\x=12-8\\x=4\\$Similarly$\\\dfrac{y-7}{2}=-5\\y-7=-5*2\\y-7=-10\\y=-10+7=-3[/tex]
The coordinates of the fourth vertex is D(4,-3)
Answer:
(4,-3)
Step-by-step explanation:
What is the volume of the cylinder below? A cylinder with a height of 12 millimeters and diameter of 18 millimeters. 108 pi mm3 216 pi mm3 648 pi mm3 972 pi mm3
Answer:
V =972 pi mm ^3
Step-by-step explanation:
The diameter is 18 so the radius is 1/2 of the diameter
18/2 = 9
r=9
The volume of a cylinder is
V = pi r^2 h
V = pi (9)^2 12
V =972 pi mm ^3
Answer:
972pi mm^3
Step-by-step explanation:
What is the volume of the cylinder below? A cylinder with a height of 12 millimeters and diameter of 18 millimeters. 108 pi mm3 216 pi mm3 648 pi mm3 972 pi mm3
V = (pi)r^2h
r = d/2 = 18 mm/2 = 9 mm
V = (pi)(9 mm)^2(12 mm)
V = 972pi mm^3
I NEED HELP PLEASE, THANKS! :)
Answer:
Option B
Step-by-step explanation:
Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -
[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]
Convert this to slope - intercept form -
[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]
Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -
( 0, 10 ),
( 15, 9 ),
( 17, 0 )
When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -
Option B
Find the rate of change of the height from age 8 to 16 and from age 60 to 80. Express both answers in units of cm per year, to two significant figures. Separate your answers with a comma.
Complete Question
The complete question is shown on the first and second uploaded image
Answer:
a
[tex]z = 6.25 \ cm/yr[/tex]
b
[tex]k = -0.25 \ cm /yr[/tex]
Step-by-step explanation:
From the first image the rate of rate of change of the height from age 8 to 16
is mathematically evaluated from the graph as
[tex]z = \frac{175 - 125}{16-8}[/tex]
[tex]z = 6.25 \ cm/yr[/tex]
From the first image the rate of rate of change of the height from age 60 to 80.
is mathematically evaluated from the graph as
[tex]k = \frac{175 - 170}{60-80}[/tex]
[tex]k = -0.25 \ cm /yr[/tex]
The slope of a line is 1, and the y-intercept is -1. What is the equation of the line written in slope-intercept form?
Answer:
y=x-1
Step-by-step explanation:
since the slope is just one up and one over and it's positive it would just be x
and since the intercept is just -1 it would be y=x-1
The hourly rate of substitute teachers for 12 local school districts is given below. Assuming that the data are normally distributed, use a TI-83, or TI-84 calculator to find the 90% confidence interval for the mean hourly rate of substitute teachers in the region.20 13 21 18 19 2219 15 12 12 18 21
Answer:
[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]
[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]
Step-by-step explanation:
Data given
20 13 21 18 19 22 19 15 12 12 18 21
We can calculate the sample mean and deviation with the following formulas:
[tex]\bar X =\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And we got:
[tex]\bar X = 17.5[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=3.61 represent the sample standard deviation
n=12 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=12-1=11[/tex]
Since the Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], the critical value would be given by [tex]t_{\alpha/2}=[/tex]
Now we have everything in order to replace into formula (1):
[tex]17.5-1.796\frac{3.61}{\sqrt{12}}=15.63[/tex]
[tex]17.5+1.796\frac{3.61}{\sqrt{12}}=19.37[/tex]
Joan is selling handmade bead necklaces
at a local art fair. She paid $180 to
reserve her booth. The cost of supplies
for each necklace averages $2. So, her
cost, y, for x necklaces is represented by
y = $180 + 2x. If she sells her necklaces
for $12, her revenue, y, is represented
by y = 12x.
The solution of this system is the break-
even point, the point beyond which she
starts making a profit.
HELP PLS QUICK
Answer:. x = 18
Step-by-step explanation:
Solve by substitution. Given: y= 12x. Rewrite the original equation y= 180 + 2x to 12x = 180 +2x. Subtract 2x from both sides. 10x = 180. Then divide both sides by 10.
x=18
So once she has sold 18 necklaces, she has covered her costs (180 + 36) and she begins to make a profit.
Which statements about the dilation are true? Check all that apply. Triangle X prime Y prime Z prime. Point X prime is 2 units from the center of dilation C and point Z prime is 3 units from the center of dilation. Triangle X Y Z. Point X is 5 units from point C and point Z is 7.5 units from point C.
Answer:
A,B,E
Step-by-step explanation:
Just took the quiz
Answer:
A,B,E
Step-by-step explanation:
Give me brainliest.
Mahesh has Rs 150 and he buys a pen costing Rs 75 now he has to buy a copies costing Rs 10 each what is the maximum number of copies did he buy?
Answer:
7
Step-by-step explanation:
Rs 150- Rs 75=Rs 75 remaining
Rs 75/10= 7 as whole
Step-by-step explanation:
given,
total amnt =rs.150
cost of pen= rs.75
now,
left money =150_75
=rs.75
now,cost of 1 copy=10
then , no. of copies=75/10
=7.5
so he can buy 7 copies.
Choose the correct number to finish the sentence. For the function f(x)=√x+4, the average rate of change to the nearest hundredth over the interval 2 ≤ x ≤ 6 is? A. 0.2 B. 0.17 C. 0.16 D. 0.18
Answer:
See below under "explanation".
General Formulas and Concepts:
Algebra I
Functions
Function NotationAverage Rate of Change Formula:
[tex]\displaystyle \text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}[/tex]
Step-by-step explanation:
*Note:
The function is unclear, so I will provide 2 possible answers.
Step 1: Define
Identify given.
[tex]\displaystyle \begin{aligned}1. \ f(x) & = \sqrt{x} + 4 \\2. \ f(x) & = \sqrt{x + 4} \\\end{aligned}[/tex]
[tex]\displaystyle \text{Interval: } 2 \leq x \leq 6[/tex]
Step 2: Find Average Rate of Change
For the 1st function:
[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\big( \sqrt{b} + 4 \big) - \big( \sqrt{a} + 4 \big)}{b - a} \\& = \frac{\big( \sqrt{6} + 4 \big) - \big( \sqrt{2} + 4 \big)}{6 - 2} \\& = \frac{\sqrt{6} - \sqrt{2}}{4} \\& = 0.258819 \\& \approx \boxed{0.26} \\\end{aligned}[/tex]
∴ the average rate of change, if using the 1st defined function, will be approximately 0.26.
For the 2nd function:
[tex]\displaystyle\begin{aligned}\text{Average Rate of Change} & = \frac{\sqrt{b + 4} - \sqrt{a + 4} }{b - a} \\& = \frac{\sqrt{6 + 4} - \sqrt{2 + 4}}{6 - 2} \\& = \frac{\sqrt{10} - \sqrt{6}}{4} \\& = 0.178197 \\& \approx \boxed{0.18} \\\end{aligned}[/tex]
∴ the average rate of change, if using the 2nd defined function, will be approximately 0.18.
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Topic: Algebra I
To pass a certain marksmanship test, an individual is required to shoot at a target until he hits it six times. He is judged on the number of trials that are necessary to achieve this. If the probability of his hitting a target on any trial is 0.25, what is the probability that he requires 18 shots?
Answer:
The probability that he requires 18 shots is 0.04785
Step-by-step explanation:
To answer this, we shall be using the negative binomial distribution
From the question;
P = 0.25 , r = 6
q will be 1-p = 1-0.25 = 0.75 Which is the probability of missing a target on any trial
P(X = 18) = (18-1)C(6-1) (0.25)^6 (0.75)^(18-6)
P(X = 28) = 17C5 (0.25)^6 (0.75)^12) = 0.04785
The 2010 General Social Survey asked the question: "After an average work day, about how many hours do you have to relax or pursue activities that you enjoy?" to a random sample of 1,155 Americans.^41 A 95% confidence interval for the mean number of hours spent relaxing or pursuing activities they enjoy was (1.38, 1.92). Interpret this interval in context of the data. Suppose another set of researchers reported a confidence interval with a larger margin of error based on the same sample of 1,155 Americans. How does their confidence level compare to the confidence level of the interval stated above? Suppose next year a new survey asking the same question is conducted, and this time the sample size is 2,500. Assuming that the population characteristics, with respect to how much time people spend relaxing after work, have not changed much within a year. How will the margin of error of the 95% confidence interval constructed based on data from the new survey compare to the margin of error of the interval stated above?
Answer:
- How does their confidence level compare to the confidence level of the interval stated above?
Provided all the other parameters involved in the determination of margin of error remains constant, the confidence level of the interval obtained by the second set of researchers (with a larger margin of error) is definitely greater than the confidence of the first stated interval.
- How will the margin of error of the 95% confidence interval constructed based on data from the new survey compare to the margin of error of the interval stated above?
Provided all the other parameters involved in the determination of margin of error remains constant, the margin of error of the confidence interval of data from the new survey will be less than the margin of error of the initially stated interval because the margin of error is inversely proportional to the sample size and the sample size of the new survey (2500) is more than the sample size of the old survey (1155).
Step-by-step explanation:
Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.
Mathematically,
Confidence Interval = (Sample mean) ± (Margin of error)
Margin of Error is the width of the confidence interval about the mean.
It is given mathematically as,
Margin of Error = (Critical value) × (standard Error of the mean)
Since the sample sizes are so large, the critical value for this would be obtained from the z-distribution tables.
And critical value increases with higher confidence level.
Which directly translates to margin of error increasing with higher confidence level.
A) Hence, if all other parameters stay the same, the margin of error can only be larger if the confidence level of the second researchers is more than than the confidence level at which the initial research was carried out.
B) In the determination of the margin of error
Margin of Error = (Critical value) × (standard Error of the mean)
Standard error of the mean = σₓ = (σ/√n)
where σ = population standard deviation or sample standard deviation for a sample size that's very large
n = sample size
If the critical value stays the same (the tests in the two years being considered are performed at the same level) and the standard deviation too remain almost the same (the question asks us to assume that the population characteristics, with respect to how much time people spend relaxing after work, have not changed much within a year), the margin of error is obviously inversely proportional to the sample size.
Margin of error = (zσ/√n)
zσ = constant = k
Margin of error = (k/√n)
So, if the sample size increases, the new margin of error that will be obtained will be lesser.
Hope this Helps!!!
Solve the system of linear equations.
Answer:
dependent systemx = 2 -ay = 1 +az = aStep-by-step explanation:
Let's solve this by eliminating z, then we'll go from there.
Add 6 times the second equation to the first.
(3x -3y +6z) +6(x +2y -z) = (3) +6(4)
9x +9y = 27 . . . simplify
x + y = 3 . . . . . . divide by 9 [eq4]
Add 13 times the second equation to the third.
(5x -8y +13z) +13(x +2y -z) = (2) +13(4)
18x +18y = 54
x + y = 3 . . . . . . divide by 18 [eq5]
Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:
y = 3 -x . . . . solve eq5 for y
x +2(3 -x) -z = 4 . . . . substitute into the second equation
-x +6 -z = 4
x = 2 - z . . . . . . add x-4
y = 3 -(2 -z)
y = z +1
So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...
x = 2 -a
y = 1 +a
z = a
_____
Check
First equation:
3(2-a) -3(a+1) +6a = 3
6 -3a -3a -3 +6a = 3 . . . true
Second equation:
(2-a) +2(a+1) -a = 4
2 -a +2a +2 -a = 4 . . . true
Third equation:
5(2-a) -8(a+1) +13a = 2
10 -5a -8a -8 +13a = 2 . . . true
Our solution checks algebraically.
How fast was the battery charged? _______ percent per minute. How long did it take the battery to be fully charged? ________ minutes.
Answer:
Q1 is: 2.2 percent per minute
Q2 is: 35 minutes
Step-by-step explanation:
For the first question, take 89 percent, and subtract 23 from it, then divide by 30 minutes for the rate per minute.
For the second question take 23 percent, find out how much is left until 100 percent (77 percent) and use the rate from the last question (2.2 percent per minute), to find out how much time charging 77 percent takes. (You get 35 by using: 77 divided by 2.2)
Calculate
(14x5x4) / (28 x 2)
Answer:
5
Step-by-step explanation:
(14 × 5 × 4) ÷ (28 × 2)
Solve brackets.
280 ÷ 56
Divide.
= 5
Please help I don’t understand And I need an explanation
Hey there! :)
Answer:
56 m².
Step-by-step explanation:
To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:
Solve for the rectangle: (A = l × w)
A = 8 × 5
A = 40 m²
Solve for the triangle: (A = 1/2 (bh))
A = 1/2(4 · 8)
A = 1/2(32)
A = 16 m².
Add up the two areas:
40 + 16 = 56 m².
Answer:
Area of triangle+ the area of rectangle
Step-by-step explanation:
Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²
Area of rectangle is length × breadth= 5×8: 40 m²
Area of the shape is 40m²+16m²= 56m²
Ron is weighs 140 kg, and the doctor said that he must to start losing weight. How long will it take for Ron to get to 105 kg if he loses 500g per week?
Answer:
Step-by-step explanation:
Ron needs to lose 35 kgs in order to be 105 kgs. 35000 grams equals 35 kgs. Divide 35000 by 500 and you get 70 weeks.
To double check it, 500 grams equals 0.5 kgs. 0.5*70=35. This equation represents weight lost per week*time=total weight loss.
The explaination might not be the best but I hope it helped you:)
Two random samples are taken from private and public universities
(out-of-state tuition) around the nation. The yearly tuition is recorded from each sample and the results can be found below. Test to see if the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions. Assume unequal variances. Use a 1% level of significance.
Private Institutions (Group 1 )
43,120
28,190
34,490
20,893
42,984
34,750
44,897
32,198
18,432
33,981
29,498
31,980
22,764
54,190
37,756
30,129
33,980
47,909
32,200
38,120
Public Institutions (Group 2)
25,469
19,450
18,347
28,560
32,592
21,871
24,120
27,450
29,100
21,870
22,650
29,143
25,379
23,450
23,871
28,745
30,120
21,190
21,540
26,346
Hypotheses:
H0: μ1 (?) μ2
H1: μ1 (?) μ2
What are the correct hypotheses for this problem?
-A. H0: μ1 = μ2 ; H1: μ1 ≠ μ2
-B. H0: μ1 = μ2 ; H1: μ1 > μ2
-C. H0: μ1 ≤ μ2 ; H1: μ1 ≥ μ2
-D. H0: μ1 < μ2 ; H1: μ1 = μ2
-E. H0: μ1 ≠ μ2 ; H1: μ1 = μ2
-F. H0: μ1 ≥ μ2 ; H1: μ1 ≤ μ2
Answer:
Step-by-step explanation:
For private Institutions,
n = 20
Mean, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05
Standard deviation = √(summation(x - mean)²/n
Summation(x - mean)² = (43120 - 34623.05)^2+ (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95
Standard deviation = √(1527829234.95/20
s1 = 8740.22
For public Institutions,
n = 20
Mean, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15
Summation(x - mean)² = (25469 - 25063.15)^2+ (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95
Standard deviation = √(283738188.55/20
s2 = 3766.55
This is a test of 2 independent groups. Let μ1 be the mean out-of-state tuition for private institutions and μ2 be the mean out-of-state tuition for public institutions.
The random variable is μ1 - μ2 = difference in the mean out-of-state tuition for private institutions and the mean out-of-state tuition for public institutions.
We would set up the hypothesis. The correct option is
-B. H0: μ1 = μ2 ; H1: μ1 > μ2
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(x1 - x2)/√(s1²/n1 + s2²/n2)
t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)
t = 9559.9/2128.12528473889
t = 4.49
The formula for determining the degree of freedom is
df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²
df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114
df = 26
We would determine the probability value from the t test calculator. It becomes
p value = 0.000065
Since alpha, 0.01 > than the p value, 0.000065, then we would reject the null hypothesis. Therefore, at 1% significance level, the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions.