Answer:
A) A sphere has no bases.
E) The lateral face of a cylinder is in the shape of a rectangle.
The correct statements which are true about three-dimensional figures are,
A) A sphere has no bases.
E) The lateral face of a cylinder is in the shape of a rectangle.
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
To find correct statements which are true about three-dimensional figures.
Now, We know that;
In a sphere, it has no base.
And, In a cylinder, The lateral face is in the shape of a rectangle.
Thus, The correct statements which are true about three-dimensional figures are,
A) A sphere has no bases.
E) The lateral face of a cylinder is in the shape of a rectangle.
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A convenience sample of forty people is taken from a population. Which of the following is a reason why you can not make a statistical inference on the population?
The sample size is not large enough.
The population isn’t given to be approximately normal.
The sample is not given to be normally distributed.
The wrong sampling method was used.
Answer:
The wrong sampling method was used.
Step-by-step explanation:
In convenience sampling, first few responses are considered and not all parameters are considered. This is the easiest method of sampling but least effective
(D) The wrong sample method was used.
Sample:The term 'sample' can mean -
A sample is a statistical term for a portion of a population.A digital discrete sample of a continuous analog signal is called a sample (signal).A sample, a specimen, or a little amount of anything.An illustration showing the meeting point of a color channel and a pixel.Sample history is an abbreviation for the questions that emergency medical personnel should ask.A product sample is a small amount of a consumer good that is provided to a customer so that they can test it out before making a purchase.Statistics:The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. Populations can refer to a variety of groupings of individuals or things, such as "every individual living in a nation" or "each atom making up a crystal." Every facet of data, including the planning of data collecting in terms of the layout of surveys and experiments, is covered by statistics.Therefore, the correct answer if the problem is (D) the wrong sample method was used.
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compare 9 X 10^4 to 3 X 10^2
Step-by-step explanation:
[tex]9 \times {10}^{4} = 900 \times {10}^{2} \\ \\ 3 \times {10}^{2} \\ \\ \because \: 900 > 3 \\ \purple{ \boxed{ \bold{\therefore \: 9 \times {10}^{4} > 3 \times {10}^{2}}}}[/tex]
the loudness, L, measured i in decibels (Db), of a sound intencity, I, measured in watts per square meter, is defined as L=10logI/I0, where I0=10^-12 and is the least intense sound a human ear can hear. what is the approximate loudness of a rock concert with a sound intensity of 10^-1
The approximate loudness of a rock concert with a sound intensity of 10⁻¹
is 110 Db.
Loudness
Since the loudness L measured in decibel (Db) of a sound intensity I is given by
L = 10㏒(I/I₀) where
I = intensity of sound and I₀ = least intense sound human ear can hear = 10⁻¹².Since we want to determine the approximate loudness of a rock concert with a sound intensity of 10⁻¹. So, I = 10⁻¹
Loudness of the rock concertSo, substituting the values of the variables into L, we have
L = 10㏒(I/I₀)
L = 10㏒(10⁻¹/10⁻¹²)
L = 10㏒10¹¹
L = 11 × 10㏒10
L = 110㏒10
L = 110 (since ㏒10 = 1)
So, approximate loudness of a rock concert with a sound intensity of 10⁻¹
is 110 Db.
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Answer:110
Step-by-step explanation:
took the test
To gain access to his account, a customer using an automatic teller machine (ATM) must enter a four-digit code. If repetition of the same four digits is not allowed (for example 5555), how many possible combinations are there?
Final answer:
The number of possible four-digit PIN combinations for an ATM, where no repetition of the same four digits is allowed, is 5040. This is calculated by multiplying the number of choices for each digit position, which are 10, 9, 8, and 7 respectively.
Explanation:
Calculating ATM PIN Code Combinations
To determine the number of possible four-digit PIN combinations for an ATM that does not allow the repetition of the same four digits (such as 5555), we have to consider how many choices we have for each digit. Since there are 10 possible digits (0-9) for each placement and repetition of the same four digits is not allowed, the first digit can be any of the 10 digits, the next digit can also be any of the 10 digits (except for the first digit), and so on.
The number of combinations can be calculated using factorial notation. For the first digit, there are 10 possibilities. For the second digit, there are 9 remaining possibilities (since the digit cannot be the same as the first), for the third digit, there are 8 possibilities, and for the fourth digit, there are 7 possibilities.
The calculation then becomes 10 x 9 x 8 x 7, which equals 5040 possible combinations. This shows that there are numerous ways to create a unique four-digit code without repeating the same digit four times.
Which value of x satisfies the equation?
1.6+x=4.8
Answer:
x=3.2
Step-by-step explanation:
This question is asking us to solve for x, and to do that, we need to get the variable by itself.
1.6+x=4.8
Subtract 1.6 from both sides
1.6-1.6+x=4.8-1.6
x=3.2
So, 3.2 is the value of x that satisfies the equation.
Jared made 4 bird houses in 3 days. How many days will work to make 20 bird houses?
Answer:
15 days
Step-by-step explanation:
We can use a ratio to solve
4 bird houses 20 bird houses
--------------------- = -------------------------
3 days x days
Using cross products
4x = 3*20
4x = 60
Divide each side by 4
4x/4 = 60/4
x = 15
15 days
Answer:
15 days
Step-by-step explanation:
i hope this help you
An employee joined a company in 2009 with a starting salary of $50,000. Every year this employee receives a raise of $1000 plus 5% of the salary of the previous year.
a) Set up a recurrence relation for the salary of this employee n years after 2009.
b) What will the salary of this employee be in 2017?
c) Find an explicit formula for the salary of this employee n years after 2009.
Answer:
(a) The required recurrence relation for the salary of the employee of n years after 2009 is [tex]a_n=1.05a_{n-1}+1000[/tex].
(b)The salary of the employee will be $83421.88 in 2017.
(c) [tex]\therefore a_n=70,000 . \ 1.05^n-20,000[/tex]
Step-by-step explanation:
Summation of a G.P series
[tex]\sum_{i=0}^n r^i= \frac{r^{n+1}-1}{r-1}[/tex]
(a)
Every year the salary is increasing 5% of the salary of the previous year plus $1000.
Let [tex]a_n[/tex] represents the salary of the employee of n years after 2009.
Then [tex]a_{n-1}[/tex] represents the salary of the employee of (n-1) years after 2009.
Then [tex]a_n= a_{n-1}+5\%.a_{n-1}+1000[/tex]
[tex]=a_{n-1}+0.05a_{n-1}+1000[/tex]
[tex]=(1+0.05)a_{n-1}+1000[/tex]
[tex]=1.05a_{n-1}+1000[/tex]
The required recurrence relation for the salary of the employee of n years after 2009 is [tex]a_n=1.05a_{n-1}+1000[/tex].
(b)
Given, [tex]a_0=\$50,000[/tex]
[tex]a_n=1.05a_{n-1}+1000[/tex]
Since 2017 is 8 years after 2009.
So, n=8.
∴ [tex]a_8[/tex]
[tex]=1.05 a_7+1000[/tex]
[tex]=1.05(1.05a_6+1000)+1000[/tex]
[tex]=1.05^2a_6+1.05\times 1000+1000[/tex]
[tex]=1.05^2(1.05a_5+1000)+1.05\times 1000+1000[/tex]
[tex]=1.05^3a_5+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^3(1.05a_4+1000)+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^4a_4+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^4(1.05a_3+1000)+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^5a_3+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^5(1.05a_2+1000)+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^6a_2+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^6(1.05a_1+1000)+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^7a_1+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^7(1.05a_0+1000)+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^8a_0+1.05^7\times1000+1.05^6\times1000+1.05^51000+1.05^4\times1000+1.05^3\times 1000+1.05^2\times 1000+1.05\times 1000+1000[/tex]
[tex]=1.05^8a_0+(1.05^7+1.05^6+1.05^5+1.05^4+1.05^3+1.05^2+1.05+1)1000[/tex]
[tex]=1.05^8 \times 50,000+\frac{1.05^8-1}{1.05-1}\times 1000[/tex]
[tex]=1.05^8\times 50,000+20,000(1.58^8-1)[/tex]
[tex]=70,000\times 1.05^8-20,000[/tex]
≈$83421.88
The salary of the employee will be $83421.88 in 2017.
(c)
Given, [tex]a_0=\$50,000[/tex]
[tex]a_n=1.05a_{n-1}+1000[/tex]
We successively apply the recurrence relation
[tex]a_n=1.05a_{n-1}+1000[/tex]
[tex]=1.05^1a_{n-1}+1.05^0.1000[/tex]
[tex]=1.05^1(1.05a_{n-2}+1000)+1.05^0.1000[/tex]
[tex]=1.05^2a_{n-2}+1.05^1.1000+1.05^0.1000[/tex]
[tex]=1.05^2(1.05a_{n-3}+1000)+(1.05^1.1000+1.05^0.1000)[/tex]
[tex]=1.05^3a_{n-3}+(1.05^2.1000+1.05^1.1000+1.05^0.1000)[/tex]
...............................
.................................
[tex]=1.05^na_{n-n}+\sum_{i=0}^{n-1}1.05^i.1000[/tex]
[tex]=1.05^na_0+1000\sum_{i=0}^{n-1}1.05^i[/tex]
[tex]=1.05^n.50,000+1000.\frac{1.05^n-1}{1.05-1}[/tex]
[tex]=1.05^n.50,000+20,000.(1.05^n-1)[/tex]
[tex]=(50,000+20,000)1.05^n-20,000[/tex]
[tex]=70,000 . \ 1.05^n-20,000[/tex]
[tex]\therefore a_n=70,000 . \ 1.05^n-20,000[/tex]
The employee’s salary is dictated by the recurrence relation where S_n = S_(n-1) + 1000 + 0.05*S_(n-1). This formula is used to iteratively calculate the salary increase each year, providing an accurate salary for any given year after 2009. However, an explicit formula for this scenario may not be straightforward due to the increment's dependency on the previous year's salary.
Explanation:The subject of this problem is recurrence relation, a mathematical concept that uses a formula to establish the relationship between successive terms in a numerical sequence. The employee's salary problem can be expressed by the following recurrence:
Part a)
S_n = S_(n-1) + 1000 + 0.05*S_(n-1), where S_n represents the salary in year n and S_(n-1) refers to the prior year's salary.
Part b)
To calculate the salary in 2017, you start with the initial salary in 2009 and apply the formula for each subsequent year. After doing this for 8 years (2017 being 8 years past 2009), the salary is found to be $60,796.32.
Part c)
Unfortunately, a simple explicit formula may not exist for this scenario because of percentage increment based on the previous year's salary. However, the salary can be accurately calculated for any given year using the recurrence relation established in Part (a).
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Solve the following expressions:
1. 3² + 4²
2. 2² + 5²
3. 10² - 8²
4. √81
5. √144
6. √225
Step-by-step explanation:
3² + 4² = 9 + 16 = 252² + 5² = 4 + 25 = 2910² - 8² = 100 - 64= 36√81 = √9² = 9√144= √12² = 12√225 = √15² = 15Hope it will help you :)
HELP FAST PLZ I HAVE LITTLE TIME I DONT WANT TO FAIL.
Given:
Given that the diameter of the circle is [tex]\frac{7}{2} \ cm[/tex]
We need to determine the radius, circumference in terms of π and circumference using π = 3.14.
Radius:
The radius of the circle can be determined using the formula,
[tex]r=\frac{d}{2}[/tex]
Substituting [tex]d=\frac{7}{2}[/tex], we get;
[tex]r=\frac{(\frac{7}{2})}{2}}[/tex]
Simplifying, we get;
[tex]r=\frac{7}{4} \ cm[/tex]
Thus, the radius of the circle is [tex]\frac{7}{4} \ cm[/tex]
Circumference in terms of π:
The circumference of the circle can be determined using the formula,
[tex]C=2 \pi r[/tex]
Substituting [tex]r=\frac{7}{4} \ cm[/tex], we get;
[tex]C=2 \pi (\frac{7}{4})[/tex]
[tex]C=\frac{7}{2} \pi \ cm[/tex]
Thus, the circumference in terms of π is [tex]\frac{7}{2} \pi \ cm[/tex]
Circumference using π = 3.14:
Substituting π = 3.14 in the circumference of the circle [tex]C=\frac{7}{2} \pi \ cm[/tex], we get;
[tex]C=\frac{7}{2}(3.14)[/tex]
[tex]C=10.99 \ cm[/tex]
Thus, the circumference of the circle is 10.99 cm
The distribution of the scores on a standardized math exam in a school district is skewed to the right. Which of the following statements is true about this distribution? Please hurry it is a timed test
Answer:
If the distribution is skewed right, then the mode is greater than the mean.
Step-by-step explanation:
There's a graph below that I hope will help!
The true statement is that the mode of the scores is greater than the mean score
How to determine the true statement?From the question, we understand that:
The distribution is skewed to the right
For a right skewed distribution, the mean value is lesser than the mode value
i.e. mean < mode or mode > mean
Hence, the true statement is that the mode of the scores is greater than the mean score
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what is 62 kilograms decreased by 32%
Answer:
0.68 * 62 = 42.16 kilos
Step-by-step explanation:
0.32 * 62 = 19.84
62 - 19.84 = 42.16 kilos
0.68 * 62 = 42.16 kilos
Answer:
42.16kg
Step-by-step explanation:
32% of 62= 19.84
62-19.84=42.16
While playing a trivia game Adam answer eight questions correct in the first half and two questions correct in the second half if each question was worth eight points what's his final score
Answer:
80 points
Step-by-step explanation:
First Half: Second Half: Total Right Answers
8 questions right + 2 questions right = 10 questions right
10*8 points a piece = 80 points
Thus, his total score is 80 points.
To find Adam's final score, we need to calculate the total points from both the first and second halves of the trivia game. Each question is worth 8 points.
First HalfAdam answered 8 questions correctly:
8 questions × 8 points per question = 64 points
Second HalfAdam answered 2 questions correctly:
2 questions × 8 points per question = 16 points
Total ScoreNow, we add the points from both halves:
First half: 64 pointsSecond half: 16 pointsTotal Score = 64 points + 16 points = 80 points
Therefore, Adam's final score in the trivia game is 80 points.
This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane.
xxx yyy
-79−79minus, 79 -68−68minus, 68
-68−68minus, 68 -51−51minus, 51
-57−57minus, 57 -34−34minus, 34
What is the xxx-intercept of the line?
Answer:
(-35, 0)
step-by-step explanation:
The x-intercept of the line does not exist.
Explanation:The x-intercept of a line represents the point where the line intersects the x-axis. To find the x-intercept, we need to look for a point on the graph where y is equal to zero. Based on the given table, there is no pair of coordinates where the y value is equal to zero. Therefore, the line does not intersect the x-axis and the x-intercept does not exist.
Getaway Travel Agency surveyed a random sample of 454545 of their clients about their vacation plans. Of the clients surveyed, 212121 expected that they would go on 333 vacations in the next year. There are 516516516 Getaway Travel Agency clients. Based on the data, what is the most reasonable estimate for the number of Getaway Travel Agency clients who expect to go on 333 vacations in the next year? Choose 1 answer: Choose 1 answer:
Answer:
241 clients
Step-by-step explanation:
His problem can be solved using the principle of proportionality or rule three.
We can take advantage of the proportion between respondents who tell us the number of respondents and how many expect to go on vacation and the total number of workers, therefore:
Respondents /// Whole company
Vacations 21 x
Total 45 516
then x equals:
x = (516 * 21) / (45)
x = 240.8
x = 241 clients
This means that approximately 241 clients expect to go on vacation throughout the company.
Answer:
241
Step-by-step explanation:
its the answer for khan academy
hope this helps
You buy a ticket to the Warriors game for $409.20. You get the ticket and it says the
cost was originally sold for $62. What was the markup?
A pizza chain records how long it takes customers to receive their delivery orders. Suppose the distribution of these delivery times is strongly skewed to the right with a mean of 30 minutes and a standard deviation of 10 minutes. Management plans on calculating the mean delivery time from a random sample of 25 orders. We can assume independence between orders in the sample.
What is the probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean?
Answer:
The probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean cannot be calculated.
Step-by-step explanation:
As given in the question statement, the distribution of delivery times is strongly skewed to the right. The population distribution is skewed to right. Too much skewed distribution can cause the statistical model to work ineffectively and affects its performance. The probability can also not be calculated because the sample size is too small. Small sample size affects the results and makes them less reliable because it results in a higher variability and likelihood of skewing the results.
Answer:
We cannot calculate this probability because the sampling distribution is not normal.
Step-by-step explanation:
Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.
Which is a quadratic function?
f(x) = 2x + x + 3
f(x) = 0x2 – 4x + 7
f(x) = 5x2 – 4x + 5
Answer:
C. f(x)=5x^2-4x+5 is the correct answer on edge 2021
A rectangle has a lenght that is 9 inches less than twice its width. The area of the rectangle is 180 square inches. What is the width of the rectangle?
Answer:
12 inches
Step-by-step explanation:
In this question, we are asked to calculate the width of a rectangle having a length 9 inches less than twice it’s width and given the area of the rectangle.
First, we identify that the length is 9 inches less than twice the width
meaning if length is l and width is w; then l = (2w-9) inches
Mathematically the area of the rectangle is l * w ; meaning w * (2w-9)
This has a value equal to 180
w * (2w-9) = 180
opening the bracket;
2w^2 -9w = 180
2w^2 -9w - 180 = 0
solving this quadratic equation;
w = 12 or -7.5
since width cannot be negative, w = 12 inches
Answer:
The width of the triangle is 18.65 inches
Step-by-step explanation:
From the question, we have;
Length, L = Width, W - 9
Also the area is given by
L × W = 180
Therefore, we have
(W - 9) × W= 180
W² - 9·W = 180
W² - 9·W - 180 = 0
Factorizing or solving with quadratic formula
[tex]\frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
a = 1
b = -9 and
c = -180
we get
(W + 9.65)(W-18.65) =0
Therefore W = - 9.65 or 18.65
Therefore, the Width, W = 18.65 and the length = W - 9 = 18.65 - 9 =9.65
The width of the triangle = 18.65 inches.
For what values of x is x2-36=5x true?
Answer:Its B. -4 and 9
Step-by-step explanation:
Answer:
x = - 4, x = 9
Step-by-step explanation:
Given
x² - 36 = 5x ( subtract 5x from both sides )
x² - 5x - 36 = 0 ← in standard form
Consider the factors of the constant term (- 36) which sum to give the coefficient of the x- term (- 5)
The factors are - 9 and + 4, since
- 9 × 4 = - 36 and - 9 + 4 = - 5, thus
(x - 9)(x + 4) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 9 = 0 ⇒ x = 9
Question Help
A bag contains 7 green marbles and 35 white marbles. If a representative sample contains 2 green
marbles, then how many white marbles would you expect it to contain? Explain.
Answer:
10
Step-by-step explanation:
35/7 = 5, so the white marbles appears 5 times often.
If we have 2 green marbles and we want to maintain the same ratio of green to white marbles (so the same assumption that white appears 5 times often) we need to multiply that by 5.
Find the domain of the following function:
y = x^3 − 8
________
x^2 + 5x + 6
Select the appropriate response:
A) domain: x cannot equal −3, −2
B) domain: x equals −3, −2
C) None of the above
Help please! 40 points!
Answer:
The answer is C.
Step-by-step explanation:
You can do it by solving both equations :
y = x³ - 8
Let y=0,
x³ - 8 = 0
x³ = 8
x = ³√8
= 2
x² + 5x + 6 = 0
(x+3)(x+2) = 0
x = -3
x = -2
So the domain for 1st equation is 2 and 2nd equation is -2 & -3.
In 1st equation, the answer cannot be option A & B and in 2nd equation, the answer is B.
Answer:
A) domain: x cannot equal −3, −2
Step-by-step explanation:
y = x^3 − 8
________
x^2 + 5x + 6
The function is undefined when the denominator goes to zero
x² + 5x + 6 = 0
x² + 3x + 2x + 6 = 0
x(x + 3) + 2(x + 3) = 0
(x + 2)(x + 3) = 0
x = -3, -2
Domain can take any value except -2 and -3
A class of 25 students shares a class set of 100 markers. On a day with 5 students absent, which statement is true?
A
For every 5 students, there is 1 marker.
B
For every 4 students, there is 1 marker.
C
For each student, there are 4 markers.
D
For each student, there are 5 markers.
Answer:
D
Step-by-step explanation:
Answer:
D. For each student, there are 5 markers.
Step-by-step explanation:
A class of 25 students shares a set of 100 markers.
5 students are absent.
Therefore,
No. of students present = 25 - 5 = 20
No. of markers = 100
No. of markers each student gets = 100/20 = 10/2 = 5
Hence, each student gets 5 markers.
Like charges repel and unlike charges attract. Coulomb’s law states that the force F of attraction or repulsion between two charges, q1 and q2 is given by F= kq1q2/f^2, where k is constant and r is the distance between the positive charges. Suppose you were to graph F as a function of r for two positive charges
Coulomb's law explains the force between two charges. The force between two identical charges decreases as the distance between them increases. If graphed, this relationship will form a hyperbola.
Explanation:In physics, particularly electromagnetism, Coulomb's law explains the force between two charges. As per the law, the force (F) between two charges (q1 and q2) separated by a distance (r) is given by the equation, F = kq1q2/r^2. Here, k is Coulomb's constant.
From this formula, we can conclude that force is inversely proportional to the square of the distance between two charges. In other words, as the distance (r) between two identical positive charges increases, the force (F) of repulsion between them decreases.
If we were to graph F as a function of r for two positive charges, the graph would be a hyperbola. This is because the equation represents an inverse square relationship. The force will decrease rapidly as the distance increases and is indicated by a curve that starts high when r is small and approaches zero as r gets larger.
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A 1,127-foot tree has grown at a constant rate each year. In the equation below, t is the age of the tree in years.
23t = 1,127
What is the unit rate in the equation above?
Answer:
Your answer will be 17
Step-by-step explanation:
Simply multiply and take away the t and add into the 9+ after your equation
What’s 20 times 1000
to answer this it's simple
the answer is 20,000
A hypothesis test was used to see if less than 5% of all Americans would still drive to work if gas prices went above $10.00 a gallon. The P-value for this test was 0.03. We can conclude that only 3% of all Americans would still drive to work if gas prices went above $5.00.True / False.
Answer:
The correct option is;
False
Step-by-step explanation:
Here, we note that the proportion of the test statistic which is used in the test is 5% and the P-value for the test is 0.03
The hypothesis test is meant to check if people will still drive to work when the gas prices are above $10.00 and the suggestion was that we can conclude that when the fuel price is above $5.00 everyone would still drive to work without a P-value for the test, hence we can not come to the stated conclusion.
A researcher wishes to estimate, with 95% confidence, the proportion who own a laptop. A previous study shows that 70% of those interviewed had a laptop computer. How large a sample should the researcher select so that the estimate will be within 3% of the true proportion?
Answer:
The sample needs to be at least n = 897 in size.
Step-by-step explanation:
Given
Confidence Level = 95%
Let p = those who had laptop
p = 70% = 0.7
Margin of Error = 3% = 0.03
Let n = required sample.
To estimate the proportion of laptop owners with 95% confidence, first the z-value is calculated. [tex]z_{(a/2)}[/tex]
Given that confidence level = 95%
α = 1 − 95 %
α = 1 − 0.95
α = 0.05
So;
[tex]z_{(a/2)}[/tex] = [tex]z_{(0.05/2)}[/tex]
[tex]z_{(a/2)}[/tex] = [tex]z_{(0.025)}[/tex]
From the z table
[tex]z_{(0.025)} = 1.96[/tex]
Using formula for margin of error
[tex]M.E = z_{(0.025)} * \sqrt{\frac{pq}{n} }[/tex]
where p + q =1
q = 1 - p
q = 1 - 0.7
q = 0.3
So,
[tex]M.E = z_{(0.025)} * \sqrt{\frac{pq}{n} }[/tex]
[tex]0.03 = 1.96 * \sqrt{\frac{0.7 * 0.3}{n} }[/tex] --- Make n the subject of formula
First, square both sides
[tex]0.03^{2} = 1.96^{2} * {\frac{0.7 * 0.3}{n} }[/tex] ------ Multiply both sides by [tex]{\frac{n}{0.03^{2}}}[/tex]
[tex]0.03^{2} * {\frac{n}{0.03^{2}}} = 1.96^{2} * {\frac{0.7 * 0.3}{n} } * {\frac{n}{0.03^{2}}}[/tex]
[tex]n = 1.96^{2} * {\frac{0.7 * 0.3}{0.03^{2}} }[/tex]
[tex]n = {\frac{0.806736}{0.0009} }[/tex]
[tex]n = 896.473[/tex]
Hence, the sample needs to be at least n = 897 in size.
AB and DE are chords that intersect at point F inside circle C as shown. If the measure of arc EA = 40° and the measure of arc DB = 70°.
What is the measure of ∠AFE?
Select one or more:
a. 700
b. 400
c. 1250
d. 550
Answer:
[tex]d) \ 55\textdegree[/tex]
Step-by-step explanation:
-we apply the relationship of chords intersecting within a circle:
-when two chords intersect to form a vertex of an angle within a circle, the measure of the angle is equal to one-half the sum of the measures of the two arcs intercepted by the angle and its vertical angle:
[tex]\angle AFE=0.5(arc\ EA +arc \ BD)\\\\=0.5(40+70)\\\\=55\textdegree[/tex]
Hence, the measure of ∠AFE is 55°
20 = r + 11
Solve the equation.
Answer: r = 9
Step-by-step explanation:
Simplifying
20 = r + 11
Reorder the terms:
20 = 11 + r
Solving
20 = 11 + r
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '-1r' to each side of the equation.
20 + -1r = 11 + r + -1r
Combine like terms: r + -1r = 0
20 + -1r = 11 + 0
20 + -1r = 11
Add '-20' to each side of the equation.
20 + -20 + -1r = 11 + -20
Combine like terms: 20 + -20 = 0
0 + -1r = 11 + -20
-1r = 11 + -20
Combine like terms: 11 + -20 = -9
-1r = -9
Divide each side by '-1'.
r = 9
Simplifying
r = 9
Answer:
r=9
Step-by-step explanation:
Step 1: Flip the equation
r + 11 = 20
Step 2: Subtract 11 from both sides
r + 11 - 11 = 20 - 11
In circle O, the radius is 4, and the
measure of minor arc AB is 120
degrees. Find the length of minor
arc AB to the nearest integer.
Answer:
The length of minor arc AB is 8
Step-by-step explanation:
In this question, we are asked to calculate the length of the minor arc.
Mathematically, the length of an arc can be calculated using the formula below;
Length of an arc = θ/360° × 2πr
Where θ is the angle subtended by the arc which is 120° according to the question, r is the radius of the circle which is 4 according to the question.
Plugging these values, we have
Length of minor arc AB = 120/360 × 2 × 22/7 × 4 = 8.34 = 8 to the nearest integer
The length of the minor arc AB in circle O with a radius of 4 and a central angle of 120 degrees, rounded to the nearest integer, is 8 units.
Explanation:In the context of circle geometry, the length of a minor arc can be calculated by using the formula: arc length = (central angle/360) x (2π x radius). Given in the problem, we have a radius of 4 units and a minor arc with a measure of 120 degrees. Substituting the given values into the formula, the arc length becomes (120/360) x (2π x 4) which simplifies to (1/3) x (8π) = 8π/3 units.
However, the question asks for the minor arc length to the nearest integer. In this case, you would calculate 8π/3 which approximately equals 8.37758, but when rounded to the nearest integer, it would be 8.
Learn more about Arc length here:
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