Using the margin of error for the z-distribution, the sample sizes are given as follows:
a) 822.
b) 1068.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.We have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Item a:
The estimate is of [tex]\pi = 0.26[/tex], hence we solve for n when M = 0.03.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.96\sqrt{\frac{0.26(0.74)}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.96\sqrt{0.26(0.74)}[/tex]
[tex]\sqrt{n} = \frac{1.96\sqrt{0.26(0.74)}}{0.03}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.26(0.74)}}{0.03}\right)^2[/tex]
n = 821.2
A sample of 822 is needed.
Item b:
No prior estimate, hence [tex]\pi = 0.5[/tex].
[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 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.03}\right)^2[/tex]
n = 1067.11
A sample of 1068 is needed.
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At a school there are five lessons in a day in total the five lessons last 4 hours assume that each session lasts the same amount of time how many minutes long is the final lesson
Answer:
48 minutes long
Step-by-step explanation:
For a total amount of minutes the lessons are, take 4x60. 4 for the total time in the lessons and 60 for 60 minutes in an hour. 4x60= 240 minutes.
Take 240/5. 240 is the total number of minutes and with the five lessons being the same amount of time, you divide the total number of minutes by the number of lessons. 240/5= 48 minutes
A bag contains 39 colored marbles. There are 6 blue marbles, 14 red marbles, 8 yellow marbles, and 11 clear marbles. What is the ratio of blue marbles to red marbles?
Answer:
[tex]6:14=3:7[/tex]
Step-by-step explanation:
There are 6 blue marbles and 14 red marbles, so the ratio of blue marbles to red marbles [tex]=6:14=3:7[/tex]
A 40 percent discount on a sweater resulted in a saving of $14.40. Find the original price.
Answer:
$36
Step-by-step explanation:
14.40 is 40% of 36.
Answer:
$36
Step-by-step explanation
40/100 = 14.4/?
100 * 14.4 = 1440
1440 / 40 = 36
Benjamin threw a rock straight up from a cliff that was 96 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation
h=-161² +116t+96, how long will it take for the rock to hit the water?
Answer:
8 seconds
Step-by-step explanation:
When it hits the water h = 0
0 = -16t^2 + 116t + 96 ( I corrected the equation in the question)
solve for 't' using quadratic formula t = 8 s ( and - .75 s <===throw out)
The line graph shows the performance of stock over a 5 - day period. Describe what is misleading about the display.
The graph is misleading because it doesn't begin at zero and the graph starts on Mon.
What is a line graph?A line graph is a graph made up of segments of straight lines that connect the depicted data points.
We have a line graph shown in the picture that represents the stock price over a 5 - day period.
As we can see in the graph,
The graph starts on the Mon and price was $11.4(approximated)
Examples of "classic" deceptive graphs include those in which the vertical scale is off, skips digits, or doesn't begin at zero.
Thus, the graph is misleading because it doesn't begin at zero and the graph starts on Mon.
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Tracy made a Venn diagram to compare the numbers of students in her English and history classes. How many students are in Tracy's English class?
The total number of persons that are ion Tracy's English class is given as 21.
How to find the persons in the English Class
We have the Venn diagram showing that there are 14 people in English
15 people in history
While there is a number of 7 students intersecting the two subjects.
Hence the people that attend both history and English are 7.
From here we would know that an English class would be made up of 14 + 7 persons
= 21 persons.
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? Question
Kim sells fruit at the farmers market. Her week starts out slow, but she gets much busier later in the week. The sequence that
represents the total kilograms of a fruit she sold the first 4 days of a week is 5, 15, 45, and 135.
Of(n) = 5(3)-1
Of(n) = 3(5)-1
□ f(n) =
(3)"
Of(n) =
(3)"
f(n) = (5)"
E Save &
Identify the explicit and exponential forms of the function, f (n), representing the number of kilograms of fruit sold on the
nth day.
Select all the correct answers.
Submit
Using a geometric sequence, the formula for the number of kilograms of fruit sold on the nth day is:
[tex]f(n) = 5(3)^{n - 1}[/tex]
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:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
For this problem, the first term and common ratio are given as follows:
[tex]a_1 = 5, q = 3[/tex]
Hence the function can be written as:
[tex]f(n) = 5(3)^{n - 1}[/tex]
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Each leg of a 45°-45°-90° triangle measures 14 cm. what is the length of the hypotenuse? 7 cm 7 startroot 2 endroot cm 14 cm 14 startroot 2 endroot cm
Answer:
[tex]14\sqrt{2}[/tex]
Step-by-step explanation:
In a 45°-45°-90° triangle, the legs = x and the hypotenuse = [tex]x\sqrt2}[/tex]
x = 14
[tex]x\sqrt{2} =14\sqrt{2}[/tex]
Answer:
d
Step-by-step explanation:
14 startroot 2 endroot cm
Which side of the original parallelogram corresponds to the y-centimeter side of the enlarged parallelogram? explain how you know. a small parallelogram has a left side length of 10 centimeters and a top side length of 15 centimeters. a larger parallelogram has a left side length of x centimeters and top side length of y centimeters. not drawn to scale the ____-centimeter side corresponds to the y-centimeter side.
The 15 cm side is equivalent to the y centimeter side.
A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
So from the given question the given figure can be inferred which is attached below
The "y" side of the parallelogram corresponds to the bigger side of the parallelogram, as seen in the figure, and the "x" side corresponds to the shorter side.
Since "y" relates to the longer side and the longer side is 15 cm, the 15 cm side is equivalent to the y centimeter side.
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Solve |1-4x| > 7
(x-1.5
(xlx < -1.5 UX>1.5)
(xx<-1.5 UX > 2)
If [tex]1-4x\ge0[/tex], then by definition of absolute value
[tex]|1-4x| = 1-4x > 7 \implies 4x < -6 \implies x < -\dfrac32[/tex]
On the other hand, if [tex]1-4x<0[/tex], then
[tex]|1-4x| = -(1-4x) = -1 + 4x > 7 \implies 4x > 8 \implies x > 2[/tex]
So, the overall solution to the inequality is interval union
[tex]\left(x < -\dfrac32\right) \cup (x > 2)[/tex]
I need the answers asap
Answer:
The red is the pre-image. The blue is after the 1st transformation. The green is after the 2nd transformation.
Step-by-step explanation:
This is because; you can see the tiny marks. 1 mark next to the letter represents 1 transformation while 2 marks next to letter symbolize the 2nd transformation! I hope this helped you :D
Which of the following is a true statement about functions?
Look below at image attached
The true statement about functions is D. If f and g are functions, then (f + g)(-2) = (g + f)(-2).
How to depict the information?It should be noted that a function is used to define the relationship that's exist between rte variables.
In this case, when f and g are functions, then (f + g)(-2) = (g + f)(-2).
Therefore, the correct option is D.
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George bought socks for "$"300 and planned to sell them for $6 a pair. write an inequality to find the minimum number of socks he has to sell in order to make a profit of more than 210.
The inequality 6s - 300 > 210 represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.
In the question, we are given that George bought socks for $300.
Therefore, George's total cost = $300.
We assume the number of pairs of socks George sells to be s.
The unit price per pair quoted by George = $6
Therefore, George's total sales = $6s.
We know that the profit over a transaction is given as the difference between sales and costs, that is,
The profit = The total sales - the total costs,
or, profit = 6s - 300.
In the question, we are required to make a profit of more than 210.
This can be shown by the inequality,
6s - 300 > 210.
Thus, the inequality 6s - 300 > 210 represents the minimum number of socks (s) when George bought socks for "$"300 and planned to sell them for $6 a pair, and want to make a profit of more than 210.
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What is the sum of the series infinity e n-1 -3(3/8)^n?
the answer for the question above is 9/5
how many solution does the pair of equation Y is equal to -3 and Y is equal to 6 have
Answer:
4
Step-by-step explanation:
it takes four equations
A machine is designed to fill toothpaste tubes, on an average, with 5.8 ounces of toothpaste. The manufacturer does not want any underfilling or overfilling. The correct hypotheses to be tested are
The correct hypothesis that can be set up for this test is given as
H0: mu = 5.8
Ha: mu ≠ 5.8
What is a statistical hypothesis?This is the method of inference that is made in a statistical testing in order to know if the dat available is able to support the claims that have been made.
What the manufacturer wants to know is the average filling of the machine. If it is within 5.8 or not.
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Write the number which is seventeen less than ten
thousand and four:
A number which is 17 less than 10,004:
10,004-17=9987
Hope it helps!
help meee please i need help
Answer:
81pi
Step-by-step explanation:
You are asking yourself the area of pi*r^2 could with r as 9. pi*9^2. solve and you get 81pi :D
Sides that match up between two similar figures are called corresponding sides.
Use the diagram of two similar triangles to complete the proportion below.
Answer 1 box 1 :height of fox
Answer 2 Box 1 :length of trees shadow
Answer 3 box 1 :length of foxes shadow
Answer 1 box 2 :height of fox
Answer 2 Box 2 :height of tree
Answer 3 box 2 :length of foxes shadow
please help my grandmother will beat me if I get this wrong
The diagram of two similar triangles to complete the proportion is; Height of Person/Height of flower = Length of a person's shadow/Length of flowers' shadow.
How to solve similar triangles?From the concept of similar triangles, we know that If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor.
Applying this similar triangles theorem to our question, we can say that;
Height of a person/length of a person's shadow = Height of flower/length of a flower's shadow
We can rewrite this to get;
Height of Person/Height of flower = Length of a person's shadow/Length of flowers' shadow.
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I need help with this problem.
x3+4x
Answer: x=0 x=2i x=-2i
if your factoring: x(x^2+4)
Step-by-step explanation:
(if your solving for x)
[tex]x^{3} +4x\\x(x^{2} +4)\\\\x=0\\\\x=\frac{-b}{2a}\frac{+}{-} \frac{\sqrt{b^2-4ac}}{2a} \\\\x=\frac{0}{2}\frac{+}{-} \frac{\sqrt{0^2-16}}{2} \\x={0}}\frac{+}{-} \frac{\sqrt{-16}}{2} \\[/tex]
[tex]x={0}}\frac{+}{-} \frac{4i}{2} \\\\\\x=\frac{+}{-}2i[/tex]
How would you simplify the fraction
4/28?
O
AIA
1
0 5
1/28
Answer:
1/7
Step-by-step explanation:
Divide the top and bottom by 4 to get
1 / 7
Answer:
1/7
Step-by-step explanation:
4 and 28 are divisible by 4.
4/4 = 1
28/4 = 7
4/28 = 1/7
If the probability is 50% what is the probability of getting 2 goals out of 5?
please help!
Using the binomial distribution, it is found that there is a 0.3125 = 31.25% probability of getting 2 goals out of 5.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
n = 5, x = 2, p = 0.5.
Hence the probability is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]
0.3125 = 31.25% probability of getting 2 goals out of 5.
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A farmer plants the same amount every day, adding up to 413 acres at the end of the year. If the year is 58 over, how many acres has the farmer planted?
Using proportions, it is found that the farmer has planted 258 acres.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
He plants 413 acres during the entire year, hence, considering he plants an equal amount daily, and the year is 5/8 over, the amount he has planted is:
A = (5/8) x 413 = 258 acres.
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Mateo is making lemonade. he needs 1 1/4 cups of suger.If he can only find 1/8 cup measuring cup.What should you suggest he do.
Answer:
Mateo can measure out the sugar 10 times using the 1/8 measuring cup because 10 times 1/8 equals 1 1/4
Step-by-step explanation:
4 (-15 - 3p ) - 4 (-p + 5 )
A. (-8p - 80)
B . ( -13p - 80 )
C. ( -8p + 80 )
D ( 8p - 80)
Answer:
Answer A is correct
Step-by-step explanation:
4 (-15 - 3p ) - 4 (-p + 5 )
First, solve the brackets.
-60 - 12p + 4p - 20
Combine like terms.
- 80 - 8p
∴ - 8p - 80
Solve for n.
11(n – 1) + 35 = 3n
n = –6
n = –3
n = 3
n = 6
In triangle ABC, m∠ABC = (4x – 12)° and
m∠ACB = (2x + 26)°. Yin says that if x = 19, the triangle must be equilateral. Is he correct? Justify your answer.
Triangle A B C is shown. Angles A B C and B C A are congruent.
The value of ∠ABC is 64 degree at x = 19 degree ,therefore Yin is not right about the value of x .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that
m∠ABC = (4x – 12)°
m∠ACB = (2x + 26)°
Let m∠ACB = y degree
It is asked that if x =19 degree , is the triangle equilateral
m∠ABC = (4x – 12)° = 4 *19 -12 = 64 degree
As in an equilateral triangle , the angles are all equal and equal to 60 degree.
If the value of ∠ABC is 64 degree at x = 19 degree ,therefore Yin is not right about the value of x .
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Answer:No, Yin is not correct. If
x = 19, the measure of angle ABC = 4(19) – 12 = 64. Therefore, the two base angles measure 64°. An equilateral triangle is equiangular, so each angle would have to measure 60° because there are 180° in a triangle.
Step-by-step explanation: Because ;0
What is the slope of the line that goes through the points (-4,2) and (8,5)?
The slope of a straight line passing through the points (-4, 2) and (8, 5) is 1/4.
What is Slope of a straight line?
The slope of a straight line measures the rate of change of variable 'y' with respect to independent variable 'x'. Mathematically -
m = (y₂ - y₁)/(x₂ - x₁) = tan Ф
Given is a line that passes through the points (-4, 2) and (8, 5).
The slope of a straight line passing through two points is given by -
m = (y₂ - y₁)/(x₂ - x₁)
The coordinates given are (-4, 2) and (8, 5).
Substituting them in the formula, we get -
m = (y₂ - y₁)/(x₂ - x₁)
m = (5 - 2)/(8 + 4)
m = 3/12
m = 1/4
Therefore, the slope of a straight line passing through the points (-4, 2) and (8, 5) is 1/4.
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Find x in the following 45°-45°-90° right triangle. Geometry!!! pls help
Answer:
6
Step-by-step explanation:
An electronics shop sells only TVs, phones and tablets. Number sold Select all of the statements below that are true. Number of electronic devices sold 80 60- 40 20 0 Monday Tuesday Wednesday Day Key TV Phone Tablet The largest total number of electronic devices sold was on Wednesday The smallest number of TVs sold was on Monday The same number of phones was sold on each of Monday, Tuesday and Wednesday On Tuesday, more tablets were sold than any other type of electronic device An electronics shop sells only TVs , phones and tablets . Number sold Select all of the statements below that are true . Number of electronic devices sold 80 60 40 20 0 Monday Tuesday Wednesday Day Key TV Phone Tablet The largest total number of electronic devices sold was on Wednesday The smallest number of TVs sold was on Monday The same number of phones was sold on each of Monday , Tuesday and Wednesday On Tuesday , more tablets were sold than any other type of electronic device
A graph is a way to represent a lot of data in such a visual format. The correct statements are A, B, and D.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
The statement that is correct about the given table is,
A.) The largest total number of electronic devices sold was on Wednesday.
B.) The smallest number of TVs sold was on Monday.
D.) On Tuesday, more tablets were sold than any other type of electronic device
hence, the correct statements are A, B, and D.
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