(1 point) Dylan wants to determine a 99 percent confidence interval for the true proportion p of high school students in the area who attend their home basketball games. Out of n randomly selected students he finds that that exactly half attend their home basketball games. About how large would n have to be to get a margin of error less than 0.01 for p
Answers
Answer:
n would have to be at least 16577
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which
z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).
The margin of error is:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
Out of n randomly selected students he finds that that exactly half attend their home basketball games.
This means that \(\pi = 0.5\)
99% confidence level
So \(\alpha = 0.01\), z is the value of Z that has a pvalue of \(1 - \frac{0.01}{2} = 0.995\), so \(Z = 2.575\).
About how large would n have to be to get a margin of error less than 0.01 for p
A sample size of n is needed. n is found when M = 0.01. So
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.01 = 2.575\sqrt{\frac{0.5*0.5}{n}}\)
\(0.01\sqrt{n} = 2.575*0.5\)
\(\sqrt{n} = \frac{2.575*0.5}{0.01}\)
\((\sqrt{n})^2 = (\frac{2.575*0.5}{0.01})^2\)
\(n = 16576.6\)
Rounding up
n would have to be at least 16577
When the error margin is smaller than 0.01, the value of n will be 16576.6.
What is a confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.
Given that;
Confidence interval = 99 %
Randomly selected students,n
margin of error,M0.01
The margin of error for the given information is;
\(\rm M = z \frac{\sigma(1-\sigma)}{n} \\\\\ 0.01 = 2.575 \frac{0.5(0.5)}{n} \\\\ 0.01 \sqrt n = 2.575 \times 0.5 \\\\ \sqrt n = \frac{2.575 \times 0.5}{0.01} \\\\ n = 16576.6\)
Hence, the value of n for which the margin of error is less than 0.01 will be 16576.6.
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Related Questions
Felicia is planning a bridal shower for her best friend. At the party, she wants to serve 3 beverages, 3 appetizers, and 3 desserts, but she does not have time to cook. She can choose from 15 bottled drinks, 11 frozen appetizers, and 14 prepared desserts at the supermarket. How many different ways can Felicia pick the food and drinks to serve at the bridal shower?
Answers
Answer:
27,327,300
Step-by-step explanation:
The number of ways she can choose 3 beverages from 15 is ₁₅C₃ = 455.
The number of ways she can choose 3 appetizers from 11 is ₁₁C₃ = 165.
The number of ways she can choose 3 desserts from 14 is ₁₄C₃ = 364.
So the total number of combinations is 455 × 165 × 364 = 27,327,300.
A group of friends wants to go to the amusement park. They have no more than $390 to spend on parking and admission. Parking is $16.75, and tickets cost $34 per person, including tax. What is the maximum number of people who can go to the amusement park?
Answers
Answer:
10 people
Step-by-step explanation:
First, I subtracted $16.75 from $390. I got an answer of $373.25. Next, I divided $373.25 by 34 people. The answer then rounded out to 10 People. So in conclusion 10 people can go to the amusment park.
2. The mean temperature in an area is 74 degrees Fahrenheit. The sum of the temperatures is
2,516. How many temperatures are in the set?
Answers
To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.
Number of temperatures = Sum of temperatures / Mean temperature
In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.
Number of temperatures = 2,516 / 74
Calculating the division:
Number of temperatures ≈ 34.05
Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.
which property is illustrated by the following ?
if a = b + 7 and b + 7 = 9, then a = 9
Answers
Step-by-step explanation:
Associative property
We know
a + (b + c) = (a + b) + c
a = b + 7
b + 7 = 9
Rearrange Eq. 2
9 = b + 7
a = b + 7
Hence,
Value of a is 9
1. You are given the 3rd and 5th terms of a geometric sequence. Describe how to determine the 10th term without finding the general term.
Answers
The 10th term of the geometric sequence is given as follows:
\(a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}\)
What is a geometric sequence?A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
\(a_n = a_1q^{n-1}\)
In which \(a_1\) is the first term.
Using the mth term as the reference, we have that:
\(a_n = a_mq^{n-m}\)
Hence:
\(a_5 = a_3q^2\)
\(q = \sqrt{\frac{a_5}{a_3}}\)
And then the 10th term is given as follows:
\(a_{10} = a_5\left(\sqrt{\frac{a_5}{a_3}}\right)^{n-5}\)
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Select the correct answer.
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?
A.
ABCD is a parallelogram with non-perpendicular adjacent sides.
B.
ABCD is a trapezoid with only one pair of parallel sides.
C.
ABCD is a rectangle with non-congruent adjacent sides.
D.
ABCD is a rhombus with non-perpendicular adjacent sides.
Answers
Answer:
Trapezoid
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
At a restaurant, hot chocolate can be purchased in two different cup sizes. A 12-ounce cup costs $3.60 and a 16-ounce cup costs $4.80.
Is the linear relationship between cup size and cost also proportional? Why or why not?
Yes, the constant of proportionality is 0.3.
Yes, there is no constant of proportionality.
No, the constant of proportionality is 0.3.
No, there is no constant of proportionality.
Answers
Answer:
Step-by-step explanation:
Yes, the constant of proportionality is 0.3.
Answer:
Yes, the constant of proportionality is 0.3.
Step-by-step explanation:
12-ounce cup costs $3.60 => 1 ounce = $3.60 / 12 = $0.3
16-ounce cup costs $4.80 => 1 ounce = $4.80 / 16 = $0.3
$0.3 = $0.3
Yes, the constant of proportionality is 0.3.
10 points if you solve this!!!
Answers
Answer:
x = 128
Step-by-step explanation:
Right angles are 90 degrees. 90 + 90 + 52 = 232. 360 (angles in a quadrilateral) - 232 = 128.
Answer:
ans is 128
Step-by-step explanation:
90+90+52+x=360(all sides of triangle is 360)
180+52+x=360
232+x=360
x=360_232
x=128
If 13 metres of a uniform iron rod weights 23.4 kg then what will be the weight of 6 metres of the same rod?
Answers
Answer:
Solution:
Here,
\(\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}\)
Weight of 13 m of rod=23.4 kg
Weight of 1 m of rod=23.4/13 kg
[less length,less weight]
Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg
[more length,more weight]
Thus,the weight of 6 m of rod is 10.8 kg.
Alternative method:
Let,the required weight be x kg.
Then,
\(\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}\)
We know that,
More length of iron rod(\(\red{\uparrow}\)) will have the more weight(\(\red{\uparrow}\)).
So,using the rule of direct proportion;
i.e. Ratio of length=Ratio of weight
\( \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }\)
\( \rm{13x = 6 \times 23.4}\)
\( \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}\)
\( \therefore{x = 10.8}\)
Thus,the weight of 6 m long iron rod is 10.8 kg.
Does anyone know the answers to this whole assessment??? AQR
Answers
Answer:
No sorry I dont have the assessment. But I hope you have a wonderful day!
Step-by-step explanation:
how do u solve 3(1 - 3g) = -8g + 14 ?
Answers
Answer:
3 - 9g = -8g + 4
-9g + 8g = 4 -3
g = -1
It takes 6 slices of bread, 9 oz of cheese, and 2 oz of butter tomake three grilled-cheese sandwiches. What is the cost per sandwichif bread (18 slices) costs $1.90, 1 lb of cheese costs $2.49, and1/2 lb of butter costs $1.29?a. $.78b. $4.87c. $2.12d. $1.62
Answers
Step 1: Write the equivalence of each unit
\(\begin{gathered} 1lb\Rightarrow16\text{ oz} \\ 1\text{ lb of cheese }\Rightarrow\text{ 16 oz of che}ese \\ \frac{1}{2}\text{ lb of butter }\Rightarrow\text{ 8 oz of butter} \end{gathered}\)Step 2: Calculate the cost of producing 3 grilled-cheese sandwiches
\(\begin{gathered} 18\text{ slices of bread cost \$1.90} \\ 1\text{ slice will cost x} \\ \Rightarrow x=\frac{1.90}{18} \\ 6\text{ slices of bread will cost=}\frac{1.90}{18}\times6=\text{ \$0.63} \end{gathered}\)\(\begin{gathered} 1\text{ lb of cheese cost \$2.49 } \\ \text{ Since 1 lb is equal to 16 oz} \\ 16\text{ oz of cheese cost \$2.49} \\ 1\text{ oz of cheese will cost \$x} \\ \Rightarrow\text{ \$x=}\frac{2.49}{16}\text{ } \\ 9\text{ oz will cost }\Rightarrow\text{ }\frac{2.49}{16}\times9=\text{ \$1.40} \end{gathered}\)\(\begin{gathered} \frac{1}{2}\text{ lb of butter cost \$1.29} \\ \text{ This implies } \\ 8\text{ oz of butter will cost \$1.29} \\ 1\text{ oz of butter will cost \$x} \\ \Rightarrow\text{ \$x =}\frac{1.29}{8} \\ 2\text{ oz will then cost =}\frac{1.29}{8}\times2=\text{ \$0.32} \\ \end{gathered}\)From the above calculations we can calculate the cost of producing three grilled-cheese sandwiches as
\(0.63+1.40+0.32=\text{ \$2.35}\)Thus, the cost per sandwich is given as
\(\frac{2.35}{3}=\text{ \$0.78}\)Hence, the cost per sandwich is $0.78
Option A is the right answer
9 1/4 - 3/4 =
6 4/9 - 3 11/12 =
3 11/15 - 1 5/6 =
4 5/14 - 3 17/21
Answers
Answer:
8 1/2
2 19/36
1 9/10
23/42
A printer can print 12 pages in 9 seconds. What is the closet estimate of the number of pages it can print in one minute
Answers
Solve : 1 − | 0.2(m−3)+ 1/4| =0
Answers
Answer:
1-{0.2(m-3)+¼}=0
1{0.2m-0.6+¼}=0
1-{(0.8m-2.4+1)/4}=0
1-(0.8m-1.4)/4=0
lcm
(4-0.8m-1.4)/4=0
(2.6-0.8m)/4=0
cross multiply
2.6-0.8m=0
m=2.6/0.8
m=3.25
The solution of the expression are,
⇒ m = 3.25
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Expression is,
⇒ 1 - | 0.2 (m - 3) + 1/4 | = 0
Now, We can simplify as;
⇒ 1 - | 0.2m - 0.6 + 1/4| = 0
⇒ 1 - |0.2m - 0.6 + 0.25| = 0
⇒ 1 - |0.2m - 0.35| = 0
⇒ 1 = 0.2m + 0.35
⇒ 1 - 0.35 = 0.2m
⇒ 0.2m = 0.65
⇒ m = 3.25
Thus, The solution of the expression are,
⇒ m = 3.25
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NEED HELP ASAP
MATH !
Answers
Answer:
C
Step-by-step explanation:
the scale from QRP to FGH is 2x, since we go vice versa, divide the same side on the other triangle by 2
To find the scale, I saw that the 5cm went to 10. (please give brainliest if this helps!)
Answer:
C.7cm
Step-by-step explanation:
...............
A tank is full of water. The tank is a right circular cylinder lying on its side (length is parallel to horizon), with radius 2 m, and length 5 m. Find the work required to pump the water out of a spout that rises 2 m above the tank. Set up the integral, but do NOT evaluate. The base of a solid is a circular disk with radius
Answers
W =∫ lower power (-r) to higher power (r + h) (h + r - x) 2pgl \(\sqrt{r^2+x^2}\) dx is the integral for the effort needed to pump water out of a spout that is 2 m above the tank.
What is meant by Integral?Integral: In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or a new function, the derivative of which is the original function (indefinite integral).
r = 2m
l= 5m
sinθ=x/r
\(dv=2l\sqrt{r^2+x^2} dx\)
Let g be the acceleration brought on by gravity, and let p be the density of water.
dm = p dv
dw = dmg (h + r - x)
dw = pg (h + r - x) dx
dw = 2lpg (h + r - x) \(\sqrt{r^2+x^2}\) dx
w = ∫dw
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) \(\sqrt{r^2+x^2}\) dx
Therefore, the integral for the work required to pump the water out of a
spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) \(\sqrt{r^2+x^2}\) dx
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Which number line represents the solution to the inequality 125x + 200 ≥ 1,200?
Answers
Find the x- and y-intercepts of the graph of x - y = 37. State each answer as an
integer or an improper fraction in simplest form.
Answers
The solution is, the x-intercept is (19,0) and the y-intercept is (0,-19).
What are y-intercept & x-intercepts of quadratic function?The y-intercept of the function is where the graph crosses y-axis.
The x-intercept is where the graph crosses the x-axis.
here, we have,
Given:
The equation of the graph is, x - y = 37.
The objective is to find the x-intercept and y-intercept of the graph.
Explanation:
At x-intercept the value of y will be zero.
In the given equation, at y = 0,
so, x - 0 = 37
or, x = 37
Thus, the coordinate is (37,0).
Similarly, at y-intercept the value of x will be zero.
In the given equation, at x = 0,
0-y = 37
or, y = -37
Thus, the coordinate is (0,-37).
Hence, the x-intercept is (19,0) and the y-intercept is (0,-19).
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What is the area of a circle with a circumference
of 25.12 meters?
Answers
Area of a circle=πr^2
circumference of a circle= 2πr
circumference of a circle=25.12
2πr=25.12
r=25.12÷2π=4
radius=4
Are of circle= πr^2=π4^2=50.28cm^2
there are 35 rides at a large theme park. a team of journalists wants to interview some customers to get their opinion on the best rides in the park. the journalists randomly choose 5 of the rides and interview all of the people exiting those rides.
Answers
The correct option Cluster random sample.
In cluster random sampling, at first the population is divided into several small non-overlapping sub-populations and these sub-populations are called clusters.
The size of the cluster may or may not be equal.
Units within the cluster should be as heterogeneous as possible, i.e. one cluster could represent the population, and units between the clusters should be homogeneous.
Then simple random sampling is used to select some sample cluster and all the units of the selected cluster are taken as sample units.
Cluster sampling can be more cost-effective than simple random sampling, especially if the population is dispersed across a large geographical area.
However, cluster sampling methods tend to be less efficient than either simple random sampling methods or stratified sampling methods and often require a larger sample size.
The entire population: here all customers are divided into several clusters: here 35 rides. Sample of clusters: here 5 rides are selected and all items in the selected 5 clusters are included in the sample.
Therefore, the correct option is Cluster random sample.
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y=-0.024x^2+0.0791x+4.873
Answers
The equation y = \(-0.024x^2\) + 0.0791x + 4.873 represents a quadratic function with a downward-opening parabol
The given expression is a quadratic equation in the form y = -0.024x^2 + 0.0791x + 4.873. Let's analyze its components and characteristics.
The equation represents a quadratic function, where x is the independent variable and y is the dependent variable. The coefficients in front of each term determine the shape, position, and direction of the graph.
The term with the highest power of x is -0.024x^2, which indicates a downward-opening parabola. The coefficient -0.024 determines the steepness of the curve. A negative coefficient means the parabola is concave down.
The term 0.0791x is the linear term and determines the slope of the line. A positive coefficient indicates an upward or positive slope. It affects the overall direction and position of the graph.
The constant term 4.873 is the y-intercept. It indicates the point at which the graph intersects the y-axis when x = 0.
To analyze the graph of the quadratic equation further, we can calculate the vertex. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a and b are the coefficients of x^2 and x, respectively. In this case, a = -0.024 and b = 0.0791. Substituting these values into the formula, we have x = -0.0791 / (2 * -0.024) ≈ 1.643. By substituting this x-coordinate into the equation, we can find the y-coordinate of the vertex.
Overall, the equation y =\(-0.024x^2 + 0.0791x\) + 4.873 represents a quadratic function with a downward-opening parabola. The specific properties, such as the vertex and other key points, can be determined by further calculations and analysis of the equation.
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Numerical Problems: a. From From the given figure, identify which path represents distance and displacement. Also, calculate the length of paths (distance travelled and displacement). h Hantra initial point A 9m 3m B 5m G 6m C C E
Answers
Path A-B-C-E represents the distance traveled, which is 18 meters.
Path A-G-C-E represents the displacement, which is 17 meters.
From the given figure, we can identify the paths and calculate the distance and displacement.
Path A-B-C-E represents the distance traveled, and path A-G-C-E represents the displacement.
Let's calculate the lengths of both paths:
Distance traveled (Path A-B-C-E):
Length of AB = 9m
Length of BC = 3m
Length of CE = 6m
Total distance traveled = Length of AB + Length of BC + Length of CE
= 9m + 3m + 6m
= 18m
Therefore, the distance traveled along path A-B-C-E is 18 meters.
Displacement (Path A-G-C-E):
Length of AG = 5m
Length of GC = 6m
Length of CE = 6m
Total displacement = Length of AG + Length of GC + Length of CE
= 5m + 6m + 6m
= 17m
Therefore, the displacement along path A-G-C-E is 17 meters.
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An angle measures 59 degrees what is the measure of its supplement
Answers
Answer:
add up to 90 degree
Step-by-step explanation:
I need help for questions 1,2 and 3 thanks
Answers
Answer:
1. 5km/hr
2. 165km/hr
3 2.5m/s
Answer:
1 6.32km/h
2 The average speed of the helicopter will be 96km/ hr or 1.6km/min.
3 2.5 m per second
4 0.002 km/h
Step-by-step explanation:
hope this helps
Which fraction and decimal forms match the long division problem?
Answers
Answer:
0.44444444
Step-by-step explanation:
Answer: 4/9 and 0.4 repeating
Step-by-step explanation:
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
Answers
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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What is the median for the data shown below?
S= [110, 105, 126, 65, 134, 102, 78, 80, 119, 67, 88]
Answers
Answer:
102
Step-by-step explanation:
The median of a data set is found by putting the data set in ascending numerical order and identifying the middle number. If there are an odd number of data values in the data set, the median is a single number. If there are an even number of data values in the data set, the median is the average of the two middle numbers. Sorting the data set for the values entered above we have:
65 , 67 , 78 , 80 , 88 , 102 , 105 , 110 ,119 , 126 , 134
Since there is an odd number of data values in this data set, there is only one middle number. With 11 data values, the middle number is the data value at position 6. Therefore, the median is 102.
Answer:
102
Step-by-step explanation:
1. The median is the quantity that's in the middle of a data set.
2. First, we have to arrange the given data set from least to greatest:
65, 67, 78, 80, 88, 102, 105, 110, 119, 126, 1343. Now, when we try and locate the middle number, we can see that the number is 102.
Therefore, the median is 102.
The ratio of the number of cars to vans in a parking lot is 8:3 and the ratio of the number of motorbikes to vans is 2:5. If there are 15 motorbikes find the number of cars.
Answers
Answer: Number of cars = 100
Step-by-step explanation:
Ratio given:
\(\frac{Cars}{Vans} =\frac{8}{3}\)
\(\frac{Motorbikes}{Vans} =\frac{2}{5}\)
Find cars if motorbikes = 15
\(\frac{15}{Vans} = \frac{2}{5}\)
\(Vans = \frac{75}{2}\)
Vans = 37.5
using the ration of cars to vans:
\(\frac{Cars}{37.5} =\frac{8}{3}\)
Cars = 100
In the figure below, tan B = 4/3. If BC = 15 and DA = 3, what is the length of DE ?
A. 8
B. 12
C. 6
D. 9
Answers
Answer:12
Step-by-step explanation:
The length of the segment in the right triangle is 6 unit.
What is an angle ?An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.
Interior angles:- The inner angle made by the intersection of two polygonal sides.
Exterior angles:- The outer angle made by the intersection of two polygonal sides.
Given that,
A right angle triangle,
In which, tan B = 4/3, BC = 15 and DA = 3,
the length of DE = ?
suppose, the length of BD is x
and the length of DE is h.
we can use trigonometric formula her;
sin B = AC/BC
sin B = AC/15
if the value of tan B is 4/3 then the value of sin B will be 4/5.
AC/15 = 4/5
AC = 12
Now, tan B = 4/3 = 12/AB
AB = 16
Now we can use similarity of triangles;
DE/BD = AC/AB
DE = BD x (AC/AB)
BD = AB/2
DE = 8 x 12/16
= 6
Therefore, the length of DE is 6 unit.
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