Answer:
The minimum number of subjects needed is 385.
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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/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].
95% confidence, within 5 percentage points, and a previous estimate is not known.
The sample size is n for which M = 0.05. We don't know the true proportion, so we use [tex]\pi = 0.5[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.05})^2[/tex]
[tex]n = 384.16[/tex]
Rounding up:
The minimum number of subjects needed is 385.
The graph of the piecewise function f(x) is shown.
What is the range of f(x)?
6
5
O {x1-2 sx<4)
O {x1-2
Oy1-5
O {1-5 sys-1)
3+
2+
1
-7 -6 -5 -4 -3
-
1
3
4
5
8
The range is virtually the answer to the question,
"In which interval can find all y-values of the function".
So you look at the y-axis and see that your function begins with [tex]y=-5[/tex] (including -5 because of the dot on the graph) and ends at including [tex]y=-1[/tex].
So the interval notation is,
[tex]y\in[-5,-1][/tex]
But you are asked to specify the set notation of the interval, to do so first rewrite the interval using inequality operators, say we find some y in between (and including) -5 and -1,
[tex]-5\leq y\leq-1[/tex]
To specify that this is a set use curly bracelets and a bar,
[tex]\{y\mid-5\leq y\leq-1\}[/tex].
The y before bar is a step function and everything followed after the vertical bar is the range of the step function.
Hope this helps.
Using it's concept, it is found that the range of f(x) is given by:
{y|-5 <= -y <= -1}
What is the range of a function?The range of a function is the set that contains all possible output values. In a graph, it is given by the values of y, that is, the values of the vertical axis.
In the function described by this graph, the vertical axis assumes values between -1 and -5, inclusive, hence the range is given by:
{y|-5 <= -y <= -1}
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sample of 45 bottles of soft drink showed a variance of 1.1 in their contents. The process engineer wants to determine whether or not the standard deviation of the population is significantly different from 0.9 ounces. Using a significance level of 0.01, what are the critical values of the test
Answer:
The correct solution is "23.58 and 71.89".
Step-by-step explanation:
Given:
Sample,
n = 45
df = 45 - 1
= 44
then,
⇒ [tex]X_R^2 = X_{\frac{\alpha}{2},df }^2[/tex]
[tex]=71.89[/tex]
or,
⇒ [tex]X_L^2 = X_{1-\frac{\alpha}{2}, df }^2[/tex]
[tex]=23.58[/tex]
What is the product of (2x - 5)(2x + 5)2 ?
did from six times a certain number the result is 96 what is the number
Answer:
The number is 16
Step-by-step explanation:
Number : x
Procedure and resolution:
6x = 96
x = 96/6
x = 16
Good Luck!Evaluate the expression for x = 3 and y= 4.
[tex]\\ \large\sf\longmapsto -\dfrac{4x^3}{3y^2}[/tex]
[tex]\\ \large\sf\longmapsto -\dfrac{4(3)^3}{3(4)^2}[/tex]
[tex]\\ \large\sf\longmapsto -\dfrac{4(27)}{3(16)}[/tex]
[tex]\\ \large\sf\longmapsto -\dfrac{108}{48}[/tex]
[tex]\\ \large\sf\longmapsto -\dfrac{9}{4}[/tex]
find the range of values of a for which 11- 2a>1 is ____
Answer:
a<5
Step-by-step explanation:
11-2a>1
-2a>1-11
-2a>-10
a<5
Complete the problems. (From Example 2)
1. How much compound interest will $50,000 have earned in 10 years at 6.4% annual interest compounded
quarterly?
Answer:
Compound interest is $7,037,339.2
Step-by-step explanation:
[tex]{ \boxed{ \bf{A=P(1+ \frac{r}{100} ) {}^{n} }}}[/tex]
substitute:
[tex]{ \sf{ = 50000(1 + \frac{6.4}{100}) {}^{10} }} \\ \\ = { \sf{50000(1.64) {}^{10} }} \\ \\ { = \sf{7037339.2}}[/tex]
There are 16 more people in front of Kollam on a line than behind him. There are five times as many people in front of him as behind him. How many people are on the line?
Answer:
There are 21 people in the line (including Kollam himself).
The volume of a gas with a pressure of 1.2 atm increases from 1.0 L to 4.0 L. What is the final pressure of the gas, assuming constant temperature?
(a) 1.2 atm
(b) 0.30 atm
(c) 3.3 atm
(d) 4.8 atm
(e) 1.0 atm
Answer:
(b) 0.30 atm
Step-by-step explanation:
Given data
Initial pressure= 1.2atm
Initial volume= 1.0L
Final volume= 4.0L
Final pressure= ???
Let us apply the gas formula to find the Final pressure
P1V1= P2V2
Substitute
1.2*1= x*4
Divide both sides by 4
1.2/4= x
x= 0.3atm
Hence the final pressure is 0.3 atm
Write a 6-digit number that fits the description.
1. The value of its thousands digit is 5,000.
2. The value of its hundreds digit is 700.
3. Its tens digit is 2 less than the thousands digit.
4. Its hundred thousands digit is the same as the hundreds digit.
The number is?
Answer:
175731 is one of the answers of the 6 digit number
some others are:
275732
375733
475734
575735
675735
775734
875732
The 6-digit number is 175731.
What is the place value strategy?The place value strategies are defined as math strategies that use to assist you in resolving your elementary math problems, use your places values, such as tens and hundreds. It is possible to employ enlarged notation or compensation. Using regrouping techniques, you can make the problem easier by compensating for addition.
Let the number would be ABCDEF
Given the condition that the value of its thousands of digits is 5,000.
So C = 5
Given the condition that the value of its hundreds of digits is 700.
So D = 7
Given the condition that Its tens digit is 2 less than the thousand digits.
So E = 5-2 = 3
Given the condition that Its hundred thousand digits is the same as the hundred digits.
So B = 7
Therefore, all possible answers:
275732
375733
475734
575735
675735
775734
875732
Hence, the 6-digit number is 175731
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Which equation represents an exponential function that passes through the point (2, 36)?
O f(x) = 4(3)
O fx) = 4(x)
O f(x) = 6(3)
O f(x) = 6(x)
Answer: It would be the first equation because:
Step-by-step explanation:
In order to be an exponential function, the X
variable has to be in the exponent, that eliminates
the second and fourth answers
f(X) = 4(3)X
using the point (2,36)
f(2) = 4 (3)2
= 4 (9 )
= 36
The equation which represents an exponential function is f ( x ) = 4 ( 3 )ˣ
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
Let the point on the graph be P ( 2 , 36 )
So , when x = 2 , the value of y = 36
f ( x ) = 4 ( 3 )ˣ be equation (1)
when x = 2
f ( 2 ) = 4 ( 3 )²
f ( 2 ) = 4 x 9
f ( 2 ) = 36
Hence , the exponential equation is f ( x ) = 4 ( 3 )ˣ
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In my town, it's rainy one third of the days. Given that it is rainy, there will be heavy traffic with probability 1/2, and given that it is not rainy, there will be heavy traffic with probability 1/4. If it's rainy and there is heavy traffic, I arrive late for work with probability 1/2. On the other hand, the probability of being late is reduced to 1/8 if it is not rainy and there is no heavy traffic. In other situations (rainy and no traffic, not rainy and traffic) the probability of being late is 0.25. You pick a random day.
a. What is the probability that it’s not raining and there is heavy traffic and I am not late?
b. What is the probability that I am late?
c. Given that I arrived late at work, what is the probability that it rained that day?
Answer:
a) 0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.
b) 0.2292 = 22.92% probability that I am late.
c) 0.5454 = 54.54% probability that it rained that day.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
2/3 probability of not raining.
If not raining, 1/4 probability of heavy traffic.
1 - 0.25 = 0.75 = 3/4 probability of not late.
So
[tex]p = \frac{2}{3} \times \frac{1}{4} \times \frac{3}{4} = \frac{2}{16} = 0.125[/tex]
0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.
b. What is the probability that I am late?
0.5 of (1/3)*(1/2) = 1/6(rainy and heavy traffic).
0.25 of (1/3)*(1/2) = 1/6(rainy and no traffic).
1/8 = 0.125 of (2/3)*(3/4) = 1/2(not rainy and no traffic).
0.25 of (2/3)*(1/4) = 1/6(not rainy and traffic). So
[tex]P(A) = 0.5\frac{1}{6} + 0.25\frac{1}{6} + 0.125\frac{3}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25 + 3*0.125 + 0.25}{6} = 0.2292[/tex]
0.2292 = 22.92% probability that I am late.
c. Given that I arrived late at work, what is the probability that it rained that day?
Event A: Late
Event B: Rained
0.2292 = 22.92% probability that I am late.
This means that [tex]P(A) = 0.2292[/tex]
Probability of late and rain:
0.5 of 1/6(rain and heavy traffic).
0.25 of 1/6(rain and no traffic). So
[tex]P(A \cap B) = 0.5\frac{1}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25}{6} = \frac{0.75}{6} = 0.125[/tex]
Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.125}{0.2292} = 0.5454[/tex]
0.5454 = 54.54% probability that it rained that day.
1.) Three numbers form a geometric sequence whose common ratio is 0.5. If the first is reduced to 10 more than one quarter its value, the second decreased by 10, and the third increased by 10 more than twice its value, the resulting three numbers form an arithmetic sequence. Determine the original three numbers.
Let x be the first number in the sequence, so the first three numbers are
{x, 0.5x, 0.5²x}
Then
{x/4 + 10, 0.5x - 10, 2(0.5²x) + 10}
is arithmetic, so there is some constant c such that
0.5x - 10 = x/4 + 10 + c ==> x/2 - 10 = x/4 + 10 + c
2(0.5²x) + 10 = 0.5x - 10 + c ==> x/2 + 10 = x/2 - 10 + c
Solve the second equation for c :
x/2 + 10 = x/2 - 10 + c
c = 20
Substitute this into the first equation and solve for x :
x/2 - 10 = x/4 + 10 + 20
x/4 = 40
x = 160
Then the terms are
{160, 80, 40}
Find the value of k if y-' is a factor of y³ + 4y² + ky - 6
Answer:
1
step by step explanation
hope this helps :)
WILL GIVE 25 POINTS FOR ANSWERING AND BRAINIER!!!
Which answer choice correctly complete the sentence?
Asking the “Did you Check” questions is an important step in the Problem Solving Plan because you can
A. determine if your answers are reasonable.
B. organize your thoughts.
C. understand the problem better.
D. define your strategy easier.
Answer:
A
Step-by-step explanation:
It just makes the most sense
f(x)=3(x+5)+4/xwhat is f (a+2) solve this problem with showing the work
7 people can pave a driveway in 9 hours. how long will it take for 11 people to pave a driveway?
Answer:
Step-by-step explanation:
If 7 people can pave the drive in 9 hours, we can use that information in equation form to find out how long it would take 1 person to pave the drive alone.
[tex]\frac{7}{x}=\frac{1}{9}[/tex] and cross multiply
x = 63. That means that it would take 1 person, working alone, 63 hours to get the job done. If that be the case, and assuming that the 2 added people work at the same rate as do the first 9, we simply divide that time alone into 11 parts.
It would take 11 people [tex]5.\bar{27}[/tex] hours to pave that driveway.
Please help guys need help
Answer:
A) slope = 20.
B) The slope of 20 dollars per hour means that for every hour, the price of the service call increases by 20 dollars (or you could say the price of the service call is 20 dollars every hour, both work.)
Step-by-step explanation:
Recall that slope is y2 - y1 / x2 - x1.
Excellent. We are provided with two points: (1, 60) and (3, 100). Let’s enter this into our formula.
Slope = (100 - 60) / (3 - 1) = 40 / 2 = 20.
Now, to determine what the slope means, we can look at the axis titles on the graph. The x axis title is hours, or time in hours. The y axis title is price of the service call in dollars. Therefore, the slope is price (in dollars) per time (in hours).
This can be restated as: The slope of 20 dollars per hour means that for every hour, the price of the service call increases by 20 dollars (or you could say the price of the service call is 20 dollars every hour, both work.)
Hope this helps!
there were 578 tickets sold for a basket all game. the activity cardholder's tickets cost $1.25 and the non-cardholders' tickets cost $2.00. the total amount of money collected was $880.00. how many of each kind of ticket were sold?
9514 1404 393
Answer:
non-cardholder: 210cardholder: 368Step-by-step explanation:
Let n represent the number of non-cardholder tickets sold. Then total revenue is ...
2.00n +1.25(578 -n) = 880.00
0.75n + 722.50 = 880.00
0.75n = 157.50 . . . . . . . . . . . subtract 722.50
n = 210 . . . . . . . . . . . . . . . divide by 0.75. Number of non-cardholder tickets
578 -n = 368 . . . . . number of cardholder tickets
368 cardholder and 210 non-cardholder tickets were sold.
Country Financial, a financial services company, uses surveys of adults age 18 and older to determine whether personal financial fitness is changing over time. A recent sample of 1000 adults showed 410 indicating that their financial security was more than fair. Just a year prior, a sample of 900 adults showed 315 indicating that their financial security was more than fair. Conduct the hypothesis test and compute the p-value. Round your answer to four decimal places. What is the 95% confidence interval estimate of the difference between the two population proportions? Round your answers to four decimal places.
Answer:
hey, how you're day going
Step-by-step explanation:
.................
8 A test rocket is fired and follows a path described by y = 0.1x(200 – x). The height is y metres above
ground and x is the horizontal distance in metres.
How far does the rocket travel horizontally?
b How high does the rocket reach mid-flight?
Answer:
a) The rocket travels 200 meters horizontally.
b) The height of the rocket mid-flight is of 1000 meters.
Step-by-step explanation:
Height of the rocket:
The height of the rocket, in meters, after an horizontal distance of x, is given by:
[tex]y = 0.1x(200 - x)[/tex]
a) How far does the rocket travel horizontally?
This is x when [tex]y = 0[/tex]. So
[tex]0.1x(200 - x) = 0[/tex]
Then
[tex]0.1x = 0[/tex]
[tex]x = 0[/tex]
And
[tex]200 - x = 0[/tex]
[tex]x = 200[/tex]
So
The rocket travels 200 meters horizontally.
b How high does the rocket reach mid-flight?
This it the height y when x = 0, so:
[tex]y = 20*100 - 0.1*100^2 = 1000[/tex]
The height of the rocket mid-flight is of 1000 meters.
Suppose that appearances of a foe to battle (that is, a random encounter) in a role-playing game occur according to a Poisson process, and the average rate equals one appearance per two minutes. Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?
Answer:
Rate parameter of [tex]\mu = 0.5[/tex]
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
One appearance per two minutes.
This means that [tex]m = 2[/tex]
Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?
[tex]\mu = \frac{1}{m} = \frac{1}{2} = 0.5[/tex]
So
Rate parameter of [tex]\mu = 0.5[/tex]
What are the zeros of f(x) = x^2 - x - 12?
A. x= -4 and x= 3
B. x=-3 and x = 4
C. x=-2 and x = 6
D. x=-6 and x = 2
Answer:
B. x = -3 and x = 4
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringSolving quadraticsStep-by-step explanation:
Step 1: Define
Identify
f(x) = x² - x - 12
Step 2: Solve for x
Factor: (x - 4)(x + 3) = 0Solve: x = 4, -3can yall answer it in the box like the numbers
Answer:
Hi!
Step-by-step explanation:
1234567890987654211234567890......
Step-by-step explanation:
12345678890098764321
What is the order of rotational symmetry for the figure?
A. 2
B. 3
C. 1
D. 4 or more
The order of rotational symmetry for the figure will be 2. The correct option is A.
What is rotational symmetry?A shape exhibits rotational symmetry when it retains its appearance following a little amount of rotation by a partial turn. The number of different orientations in which an object appears exactly the same for each rotation is known as the degree of rotational symmetry.
The number of full rotations a shape may undergo while maintaining its appearance is its order of rotational symmetry. The triangle never seems the same after being rotated a complete 360 degrees, with the exception of when it is returned to its original starting position.
Therefore, the order of rotational symmetry for the figure will be 2. The correct option is A.
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Làm ơm giúp tôi giải bài tập kinh tế vi mô này với
Step-by-step explanation:
i don't know this language
Please I need the answer ASAP!!!!
Step-by-step explanation:
D
*not sure about this answer pls tell me i ak right or wrong
If you get a raise from $12 per hour to $15 per hour, what is the percent change?
Answer:
25%
Step-by-step explanation:
Formula to calculate the percent change :-
Change in distance from $12 per hour to $15 per hours = 15-12=3 per hour
Previous value = $12 per hour
Now, the percent change will be :_
Hence, the percent change for from $12 per hour to $15 per hour= 25%
(I copied this answer from JeanaShupp from question-11653373 [no links])
Hey good morning I need help ASAP thank you guys
Answer:
A 59
Step-by-step explanation:
Higher sample size is generally always more accurate
cubed root of 8 to the power of x
Answer:
your answer is 2
Step-by-step explanation:
I hope this help
