The distance the lifeguard should run along the shore before jumping into the water, can be determined by minimizing the function of time, that is, the time it takes for the lifeguard to reach the child. This problem can be solved either by using calculus or the graphical method with a graphing tool.
Explanation:This problem can be solved using optimization of functions, which is a part of calculus. We would let 'x' be the distance along the shore that the lifeguard runs before jumping into the water. Then the total time taken to reach the child is given by the formula T = x/4 + sqrt((60-x)² + 40²)/1.1. We are looking for the minimum of T as a function of x. However, it would require knowledge of calculus to solve this problem. As an alternative, one can also use a graphing calculator or similar tool to graph the time function and then determine the minimum on the graph.
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Final answer:
To save the child, you should run along the shore for approximately 15 seconds before jumping into the water.
Explanation:
To determine how far along the shore you should run before jumping into the water to save the child, you need to find the time it takes to run along the shore and then swim directly to the child.
First, calculate the time taken to run along the shore using the formula: time = distance / speed. In this case, the distance is 60 meters and the speed is 4 meters per second. So, the time taken to run along the shore is 60 / 4 = 15 seconds.
Next, calculate the time taken to swim directly to the child using the formula: time = distance / speed. In this case, the distance is 40 meters and the speed is 1.1 meters per second.
So, the time taken to swim directly to the child is 40 / 1.1 ≈ 36.364 seconds.
Therefore, the total time taken to save the child is the sum of the time taken to run along the shore and the time taken to swim directly to the child.
So, in order to save the child, you should run along the shore for approximately 15 seconds before jumping into the water.
The distance travelled in (m) by a ball dropped from a height are 128/9,32/3,8,6,...
How much distance will it travel before coming to rest
Answer: it will trave 56.89 meters before coming to rest.
Step-by-step explanation:
This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as
S = a/(1 - r)
where
S = sum of the distance travelled by the ball
a = initial distance or height of the ball
r = common ratio
From the information given,
a = 128/9
r = (32/3)/(128/9) = 0.75
Therefore,
S = (128/9)/(1 - 0.75) = 56.89 meters
The distance travelled is an illustration of the sum to infinity of a geometric sequence.
The ball will a travel 56.89 meters before coming to rest
The sequence is given as:
[tex]\mathbf{128/9, 32/3, 8, 6....}[/tex]
From the sequence above, we have:
[tex]\mathbf{a = 128/9}[/tex] --- the first term
[tex]\mathbf{r = 6/8 = 3/4}[/tex] -- the common ratio
The sum to infinity of a geometric progression is:
[tex]\mathbf{S_{\infty} = \frac{a}{1-r}}[/tex]
So, we have:
[tex]\mathbf{S_{\infty} = \frac{128/9}{1-3/4}}[/tex]
[tex]\mathbf{S_{\infty} = \frac{128/9}{1/4}}[/tex]
Divide
[tex]\mathbf{S_{\infty} = \frac{128}{9} \times 4}[/tex]
[tex]\mathbf{S_{\infty} = \frac{128\times 4}{9} }[/tex]
[tex]\mathbf{S_{\infty} = \frac{512}{9} }[/tex]
[tex]\mathbf{S_{\infty} = 56.89}[/tex]
Hence, the ball will a travel 56.89 meters before coming to rest
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A survey was conducted at two colleges. 500 students at College A participated in the study. The results indicated that on average, the students spent 15 hours per week doing online assignments and its standard deviation was 5 hours. At College B, 400 students participated in the study. The average hours they worked for online assignments was 20 with a standard deviation of 4 hours. Please test whether there is a true difference in the time students spent for online assignments between the two colleges (using a confidence level of 99%).
Answer:
[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges
Step-by-step explanation:
Data given
[tex]\bar X_{1}=15[/tex] represent the mean for sample A
[tex]\bar X_{2}=20[/tex] represent the mean for sample B
[tex]s_{1}=5[/tex] represent the sample standard deviation for A
[tex]s_{f}=4[/tex] represent the sample standard deviation for B
[tex]n_{1}=500[/tex] sample size for the group A
[tex]n_{2}=400[/tex] sample size for the group B
[tex]\alpha=0.01[/tex] Significance level provided
t would represent the statistic
System of hypothesis
The system of hypothesis is the true difference in the time students spent for online assignments between the two colleges, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}\neq 0[/tex]
Since we don't know the deviations the statistic is given by:
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
The degrees of freedom are given by [tex]df=n_1 +n_2 -2=500+400-2=898[/tex]
Replacing the info given we got:
[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges
A polling organization had taken a survey of a sample of 200 people for one of their clients, in order to estimate a population percentage. Now the client would like them to reduce the margin of error by 50% (that is, the new margin of error should be half the original margin of error), while keeping the same level of confidence. To do this, how many people should they now survey
Answer:
They now should survey 800 people.
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].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
Same level of confidence, so same z
Same proportion, so same [tex]\pi[/tex]
We have to change n
We want to reduce the margin of error by half.
M is inverse proportion to the square root of n. That is, as n increases, M decreases.
We want to decrese M by half. So we need to increase n by a factor of 2^2 = 4
The first survey had a sample of 200 people
Increasing by a factor of 4.
200*4 = 800
They now should survey 800 people.
In 2001 polls indicated that 74% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2001? We test the hypothesis that the percentage supporting mandatory testing is less than 74% this year. The P-value is 0.015. Which of the following interpretation of this P-value is valid? Group of answer choices The probability that Americans have changed their opinion on this issue since 2001 is 0.015. If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion. There is a 1.5% chance that the null hypothesis is true.
Answer:
The correct option is option 2.
Step-by-step explanation:
In this case we need to test whether the previous data for the proportion of Americans who favored mandatory testing of students in public schools as a way to rate the school has decreased this year or not.
The hypothesis can be defined as follows:
H₀: The proportion supporting mandatory testing is not less than 74% this year, i.e. p ≥ 0.74.
Hₐ: The proportion supporting mandatory testing is less than 74% this year, i.e. p < 0.74.
It is provided that the p-value of the test is,
p-value = 0.015
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
The p-value of 0.015 or 1.5% implies that, if it is true that 74% of Americans still favor mandatory testing this year, then the probability that the poll results will show that 71% or less with the same opinion is 1.5%.
Thus, the correct option is option 2.
Let's take the speed of sound to be 340 m/s. What would be the length of the pipe in a pipe organ that produces a note with a pitch of 170
Hz?
Answer:
L = 2 m
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m
Step-by-step explanation:
Given;
Speed of sound v = 340 m/s
Frequency of sound f = 170 hz
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is;
Length L = v/f = speed/frequency
L = 340/170
L = 2 m
The length of the pipe in a pipe organ that produces a note with a pitch of 170Hz is 2m
What is the measure of arc AD?
Angle ABD measures (4x + 10). Angle ACD measures
(5x - 2)
GO
Answer:
116°
Step-by-step explanation:
Given that :
∠ ABD measures (4x + 10)
∠ ACD measures (5x - 2)
Then
∠ABD = ∠ACD ( rule : angle by same chord AD )
∠ABD = (4x + 10)°
∠ACD = (5x - 2)°
so we can as well say that :
(4x + 10)° = (5x - 2)°
4x - x = -10 -2
- x = - 12
x = 12
∠ABD = (4x + 10)°
= ( 4 × 12 + 10)°
= 58°
∠ACD = (5x - 2)°
= ( 5 * 12 - 2)°
= 58°
∠AOD = 2∠ABD = 2∠ACD ( since angle by arc AD at center is twice the angle by same arc AC in other arc segment)
∠AOD = 2 × 58°
∠AOD = 116°
Measure of arc AD = 116°
7/10 + 1/6 as a fraction in lowest terms
Answer:
13/15
Step-by-step explanation:
First, you find a common denominator. 10 x 3 and 6 x 5 both equal 30, so 30 can be used as a common denominator. You also have to multiply the numerator by the same number you multiplied in the denominator. Since we did 10 x 3, do 7 x 3, and with the other fraction we did 6 x 5, so do 1 x 5. You should get 21/30 + 5/30. Since they have the same denominator, you can add them. You'll get 26/30, which can still be simplified. 30 divided by 2 is 15, and 26 divided by 2 is 13. The final answer is 13/15.
What is the measure of c?
45°
56°
60°
66°
Answer:
56
Step-by-step explanation:
Just took the quiz
Hope this helps!
Kai ate an ice cream cone at the park last Thursday. The height of the cone was 7
centimeters. The diameter of the base is 4 centimeters. What would be the Volume
of the cone?
Choose a answer
23.2
29.3
40.4
500000000000
Answer:
29.3
Step-by-step explanation:
For Ice-cream Cone
height (h) = 7 cm
diameter (d) = 4 cm
radius (r) = diameter/2 = 4/2 cm
radius (r) = 2 cm
Volume Of A Cone
= π * r^2 * h/3
= 22/7 * 2 * 2 * 7/3
= 22 * 4 * 1/3 cm
= 88/3 cm
= 29.3 cm^3
Thus, the Volume of the cone would be 29.3 cm^3
The box plot suggests that about 50\%50%50, percent of high schools in Orange County have more than what number of band members? Choose 1 answer 80,90,105,115,130
Answer: 105
Step-by-step explanation:
Answer:
105
Step-by-step explanation:
C
Find the value of 18 ÷ 9 · 3.
Answer:
its 6
just simplify the expression.
-Hops
Answer: 6
Divide
18÷9=2
Multiply
2×3=6
Alvin makes pillows for his room he buys 4.5 feet of fabric for 9.60 what is the cost of the fabric per yard?
The cost of the fabric per yard is approximately $6.39.
To find the cost of the fabric per yard, we need to first calculate the cost per foot and then convert it to yards.
Step 1: Calculate the cost per foot of fabric.
[tex]Cost per foot = Total cost / Total feet[/tex]
[tex]Cost per foot = $9.60 / 4.5 feet[/tex]
[tex]Cost per foot = $2.13[/tex]
Step 2: Convert the cost per foot to cost per yard.
Since there are 3 feet in a yard, we can find the cost per yard by multiplying the cost per foot by 3.
[tex]Cost per yard = Cost per foot * 3[/tex]
[tex]Cost per yard ≈ $2.13 * 3[/tex]
[tex]Cost per yard = $6.39[/tex]
Complete correct question:
Alvin makes pillows for his room he buys 4.5 feet of fabric for 9.60 what is the cost of the fabric per yard?
A game between two equally skilled players is ended before a winner is declared. Player A needs 3 more points to win, and player B needs 2 more points to win. How should the stakes be divided between the two players? Blaise Pascal used the Arithmetical Triangle to solve this problem. In the division of the stakes, what is the ratio of player A's winnings to Player B's winnings?
Answer: player A = 11/16 and player B = 5/16
Step-by-step explanation:
If a coin was to be tossed to determine the winner possible outcomes using arithmetical triangle.
Player A needs 2 points = 11
Player B needs 3 points = 5
Total outcome of tossing a coin = 16
Player A = 11/16 = 0.6875
Player B = 5/16 = 0. 3125
Or
Using the fifth roll of the pascal triangle (2+3) outcome
( 1, 4, 6, 4, 1 )
Addition of the first 3 represent Player A chances of winning = ( 1+ 4 + 6 ) = 11
And the last two = ( 1 + 4 ) = 5 represents the chances of team B winning
Total number of outcome = ( 1 + 4 + 6 + 4 + 1 ) = 16
Determine the measures of the unknown angles in the figure.
m∠APD =
m∠CPE =
m∠BPD =
Answer:
Step-by-step explanation:
Lines A B, C D, and D P intersect at point P. Angle A P C is 65 degrees, Angle C P E is blank, angle E P B is 90 degrees, and angle B P D is blank.
Determine the measures of the unknown angles in the figure.
m∠APD =
✔ 115°
m∠CPE =
✔ 25°
m∠BPD =
✔ 65°
The measure of unknown angles
m∠APD = 115
m∠CPE = 25
m∠BPD = 65
What is Linear Pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. They are also referred to as additional angles. Angles that share a vertex are said to be neighbouring. Hence, the linear angles have a common vertex in this instance as well.
Using Linear Pair
<APC + <CPE + <EPB = 180
65 + <CPE + 90 = 180
<CPE = 180 - 155
<CPE = 25
So, <APD = 90 + 25 = 115 degree
<CPE = 25 degree
<BPD = <APC = 65 degree (Vertically opposite angle)
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Paul wants to write equations in the form y=mx+b for the lines passing through point D that are parallel and perpendicular to line h. First he finds the slopes of these two lines. What could he do next to find the y-intercepts?
Answer:
Substitute the slope and the coordinate of D into the equations and solve for b for each equation
Step-by-step explanation:
The equation for a line is y = mx+b
where m is the slope and b is the y intercept
We know m
We have a point (x,y)
We can substitute into the equation and solve for b
Answer:
First option
Step-by-step explanation:
In y = mx + b, m is the slope and b is the y-intercept
Plug in m, and coordinates of D and solve for b
What is the equation of this line in slope intercept form (-1, 5) and (1, -3)
Answer: y= -4x + 1
Step-by-step explanation:
(-1,5) (1,-3)
5-(-3)=8
-1-1=-2
8/-2=-4 negative 4 is the slope. Now find the y-intercept using the formula y=mx + b where b is the y intercept.
so we will plot the y and x values plus the slope to find the y-intercept.
5=-4(-1) + b solve for b
5=4 + b
b=1
so now will write the equation y = -4x +1
If Karim has eight male cousins and twelve female cousins,what fraction of his cousins are female?
PLEASEE HELP WILL mark BRAINLIEST
Answer:
The volume of the sphere is 972π mm³
Step-by-step explanation:
To calculate the volume of a sphere we have to use the following formula:
V = volume
r = radius = 9mm
π = pi
V = ⁴⁄₃πr³
we replace with the known values
V = ⁴⁄₃ * π * (9mm)³
V = π * ⁴⁄₃ *729mm³
V = π * 972mm³
V = 972π mm³
The volume of the sphere is 972π mm³
Marsha wants to determine the vertex of the quadratics vertex of the quadratics functions f(x)=x^2-x+2
Answer:
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
Step-by-step explanation:
Suppose we have a quadratic equation in the following format:
[tex]y = f(x) = ax^{2} + bx + c[/tex]
The vertex of the function is the point [tex](x_{v}, f(x_{v})[/tex], in which
[tex]x_{v} = -\frac{b}{2a}[/tex]
In this problem:
[tex]f(x) = x^{2} - x + 2[/tex]
This means that [tex]a = 1, b = -1, c = 2[/tex]
So
[tex]x_{v} = -\frac{-1}{2} = \frac{1}{2}[/tex]
[tex]f(x_{v}) = f(\frac{1}{2}) = (\frac{1}{2})^{2} - \frac{1}{2} + 2 = \frac{1}{4} - \frac{1}{2} + 2 = \frac{1 - 2 + 8}{4} = \frac{7}{4}[/tex]
The vertex of the function is [tex](\frac{1}{2}, \frac{7}{4})[/tex]
What’s the distance between point A (32,15) and point B (32,29
Answer:
14 units
Step-by-step explanation:
Both points lie on the vertical line x=32, so the distance between them is the difference of their y-coordinates:
29 -15 = 14 . . . . units
The two points are 14 units apart.
Answer:
[tex] d = \sqrt{(32-32)^2 +(15-29)^2} = \sqrt{196}= 14[/tex]
So then we can conclude that the smallest distance between the point A (32,15) and the point B(32,39) is 14
Step-by-step explanation:
When we have a two points on a dimensional space A and B we can find the distance between the two points with the following formula:
[tex] d= \sqrt{(x_A -x_B)^2 +(y_A -y_B)^2}[/tex]
Where (x_A,y_A) represent the coordinates for the point A and (x_B,y_B) represent the coordinates for the point B. And we know that the coordinates are :
A= (32,15) and B= (32,29)
And replacing in the formula for the distance we got:
[tex] d = \sqrt{(32-32)^2 +(15-29)^2} = \sqrt{196}= 14[/tex]
So then we can conclude that the smallest distance between the point A (32,15) and the point B(32,39) is 14
which value for x makes the sentence true
1/8(x-56)=7/8
Answer:
63.
Step-by-step explanation:
To solve this equation, we will first need to multiply both sides by 8 to get rid of the coefficient:
8×[tex]\frac{1}{8}[/tex](x-56)=[tex]\frac{7}{8}[/tex]×8
Now, this will get rid of the fractions, giving us:
x-56= 7
Next, simply add 56 to both sides:
x-56+56= 7+56
This results in:
x=63.
What is the best example of a negative correlation?
Question 1 options:
Volleyball practices in a week and the amount of free time that week.
The amount of time spent jogging and calories burned.
Students in a classroom and number of chairs in the classroom.
The altitude of a plane and the number of passengers on board.
Answer:
gergverkngvneropgeronhnernih[eh[neirvhier,hn[eriin[hnerohper'her
Step-by-step explanation:
Answer:
Common Examples of Negative Correlation. A student who has many absences has a decrease in grades. As weather gets colder, air conditioning costs decrease. If a train increases speed, the length of time to get to the final point decreases.
How are the lengths of the four sides of the parallelogram related ?
Answer:
Step-by-step explanation: Opposite sides of a parallelogram are equal.
Answer:
The opposite sides of the parallelogram have equal lengths.
Step-by-step explanation:
PLATO SAMPLE
There were 47 ducks swimming in a pond. A dog jumped into the pond and scared 29 of the ducks away. After
the dog got out, 5 groups of 3 ducks returned to the pond.
Answer:
Step-by-step explanation:
Originally, there were 47 ducks. After the dog jumped in, there were 29. This means there were 18 ducks.
47 - 29 = 18
After the dog got out 5 groups of 3 ducks came. This means that 15 ducks came back.
5 × 3 = 15
To find the total amount of ducks, add the ducks together.
18 + 15 = 33
To find the number of ducks remaining in the pond, subtract the 29 ducks scared away from the initial 47, then add the 15 ducks that returned in 5 groups of 3, resulting in 33 ducks now present in the pond.
Explanation:The student has asked a question related to a basic arithmetic problem involving ducks in a pond. Initially, there were 47 ducks in the pond. A dog scares 29 ducks away. After the dog leaves, 5 groups of 3 ducks each return to the pond. To solve this, we perform two main steps:
Subtract the number of ducks that were scared away by the dog: 47 - 29 = 18 ducks remaining.Calculate the total number of ducks returning: 5 groups * 3 ducks/group = 15 ducks returning.Add the ducks that returned to the remaining ducks in the pond: 18 + 15 = 33 ducks are now in the pond after the disturbance and return.
Suppose we know that the birth weight of babies is normally distributed with mean 3500g
and standard deviation 500g.
(1) What is the probability that a baby is born that weighs less than 3100g?
a. What are the parameters?
b. Construct the normal distribution density curve, then shade your seeking area.
c. Find the Z-score, and construct the standard normal distribution density curve,
then shade your seeking area.
d. Find the probability.
Answer:
a) [tex]\mu = 3500 gr, \sigma = 500g[/tex]
[tex]X \sim N(\mu =3500, \sigma =500)[/tex]
b) For this case we want to find this probability:
[tex] P(X< 3110)[/tex]
And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.
c) For this case the z score is defined as:
[tex] z =\frac{X-\mu}{\sigma}[/tex]
And replacing we got:
[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]
And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8
d) We can find this probability using the normal standard distribution or excel and we got:
[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]
Step-by-step explanation:
For this problem we define the random variable of interest X defined as "the birth weigth of babies" and the distribution for this variable is normal
Part a
The parameters are given:
[tex]\mu = 3500 gr, \sigma = 500g[/tex]
[tex]X \sim N(\mu =3500, \sigma =500)[/tex]
Part b
For this case we want to find this probability:
[tex] P(X< 3110)[/tex]
And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.
Part c
For this case the z score is defined as:
[tex] z =\frac{X-\mu}{\sigma}[/tex]
And replacing we got:
[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]
And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8
Part d
We can find this probability using the normal standard distribution or excel and we got:
[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]
Find the circumference of the circle.
Answer:
C=2πr
Step-by-step explanation:
Solve for x. 8/9x=32 Enter your answer in the box. x =
Answer:
x = 36
Step-by-step explanation:
Given;
(8/9)x = 32
Solving for x
Multiply through by 9
(8/9)×9 ×x = 32×9
8x = 32×9
Divide through by 8
8x/8 = 32×9/8
x = 36
Evaluate n/6+2 when n =12
Answer:
4
Step-by-step explanation:
n/6+2
Let n = 12
12/6 +2
Division first
2 +2
4
Answer:
4
Step-by-step explanation:
plug in 12 for n and you get :: 12/6 + 2
PEMDAS says to divide first, 12/6 is 2. you add 2 next and you get 4
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The Internet is affecting us all in many different ways, so there are many reasons for estimating the proportion of adults who use it. Assume that a manager for E-‐Bay wants to determine the current percentage of U.S. adults who now use the Internet. How many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points? a. b. In 2006, 73% of adults used the Internet. No known possible value of the proportion.
Answer:
a) At least 842 adults must be surveyed.
b) At least 1068 adults must be surveyed.
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].
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 pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
a) 73% of adults used the Internet.
At least n adults must be surveyed.
n is found when [tex]M = 0.03, \pi = 0.73[/tex]
So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.73*0.27}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.73*0.27}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.73*0.27}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.73*0.27}}{0.03})^{2}[/tex]
[tex]n = 841.3[/tex]
Rounding up
At least 842 adults must be surveyed.
b. No known possible value of the proportion.
Same as above, the difference as the since we do not know the value of the proportion, we use [tex]\pi = 0.5[/tex], which is when the largest sample size is going to be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.5*0.5}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.5*0.5}}{0.03}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.96\sqrt{0.5*0.5}}{0.03})^{2}[/tex]
[tex]n = 1067.11[/tex]
Rounding up
At least 1068 adults must be surveyed.
To be 95% confident that the sample percentage of U.S. adults who use the Internet is in error by no more than 3 percentage points, a total of 1068 adults must be surveyed.
Explanation:To estimate the current percentage of U.S. adults who use the Internet with a 95 percent confidence level and an error margin of no more than three percentage points, we must determine the sample size we need to survey. We'll follow the formula below for estimating the sample size:
n = (Z² * p(1-p)) / E^2
Where n is the sample size, Z is the z-score associated with our desired confidence level (for a 95% confidence level, Z is about 1.96), p is the estimated proportion of the population (based on the 2006 data, we'll use 0.73), and E is the margin of error (which we want to be 0.03).
Plug in the values:
n = (1.96² * 0.73 * 0.27) / 0.03² = 1067.14
Since we cannot survey a fraction of a person, we round up to the next whole number. Therefore, the manager would need to survey 1068 adults in order to be 95 percent confident that the sample percentage is in error by no more than three percentage points.
Learn more about Sample Size Estimation here:https://brainly.com/question/30885988
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A baker uses a coffee mug with a diameter of 8cm to cut out circular cookies from a big sheet of cookie dough.
What is the area AAA of each cookie?
Give your answer in terms of pi.
Answer:
The forumula for finding area of the circle is \pi r^2.
Step-by-step explanation:
Let's find the radius of the mug:
r=\frac{d}{2}=\frac{8}{2}=4
Now, we can to express the area of each cookie in terms of pi:
Area= \pi *4^2=16\pi