The sample size should be 1843 at 99% confidence level with margin of error of 3%.
What is Inferential statistics?
By studying the samples that were drawn from the population data, inferential statistics aids in the development of a solid knowledge of the data. By utilising numerous analytical techniques, it aids in the creation of population-level generalisations.
Given, Margin of error (m) = 0.03
z (at 99% confidence level)=2.576
We know that, Sample size(n) = (z/m)^2 p (1-p)
In order to find the sample size, we must know the value of proportion.
here, the value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.
Now, we've p = 0.5
∴ Sample size = (z/m)^2 p (1-p)
= (2.576/0.03)^2 × 0.5 × (1-0.5)
= 1843 (approx).
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a survey that found that 351 of 547 business travelers use a laptop computer on overnight business trips. based on this survey, what is the sample proportion of business travelers who use a laptop computer on overnight business trips? (round your answer to four decimal places.)
The sample proportion of the business travelers who use a laptop computer on overnight trips is 0.6417.
Given:
a survey that found that 351 of 547 business travelers use a laptop computer on overnight business trips.
we are asked to find the sample proportion based on this survey, who use a laptop computer on overnight business trips = ?
sample proportion:
The sample proportion (p) indicates the percentage of people in a sample who exhibit a particular quality or attribute. Divide the number of individuals (or items) who have the desired attribute by the overall sample size to obtain the sample proportion.
P = X/N
P = 351/547
P = 0.641681
round off to four decimal places.
P = 0.6417
Hence we get the sample proportion as 0.6417
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Exhibit 6-3 The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds. Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players? a. 196 b. 151 c. 249 d. None of the answers is correct.
Option B, The center 95% of players had an average weight of 151 pounds.
Football players' weights have a mean of 200 pounds as well as a standard deviation of 25 pounds, which corresponds to a normal distribution.
So, let x represent a football player's weight.
X ≅ N(200, (25)²)
The minimal weight of the center 95% of the members is
P(X > 95) = P((95 - 200) ÷ 25) < (X - µ) ÷ σ)
P(X > 95) = P(-4.2 < z)
P(X > 95) = - P(z < -4.2)
P(X > 95) = 0.1512
The needed percentage is 0.1512 × 100 = 151.2 percent.
A probability distribution that is equal around the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
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The soup pot is 8. 5 inches tall with a radius of 4 inches. What is the volume of the soup pot? answer choices are rounded to the nearest tenth cubic inch.
The volume of the soup pot is 427.04 inches³
The soup pot is 8. 5 inches tall with a radius of 4 inches
We need to find the volume of the soup pot
What is volume?
Volume, is defined as the space that a body occupies. it is the ratio of the mass of object to its density.
Volume of cylinder = 3.14r²h
Where r represents the radius of the cylinder and h represents the height of the cylinder.
Volume of cylinder = 3.14 x 4 x 4 x 8.5
Volume = 427.04 inches³
Thus, the required volume of the soup pot when it is s 8. 5 inches tall with a radius of 4 inches is 427.04 inches³
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You pend 2/3 hour reading a book daily. How many hour did you pend reading after a week?
The total number of hours spent on reading in a week is 14/3 hours.
Define the term fraction of a number?A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated.The components of a whole or group of items are described by fractions. The numerator is the figure only at top of the line. It details the number of equal portions which have been taken from the total or collection. The denominator is the figure that appears below the line.For the given question-
Number of hours spent of reading = 2/3 hours.
Total number of days in a week = 7.
Total number of hours spent on reading = 2/3 x 7
Total number of hours spent on reading = 14/3
Thus, the total number of hours spent on reading in a week is 14/3 hours.
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question content area top part 1 deborah has two pairs of slacks, six shirts, and five sweaters. from how many combinations can she choose if she chooses a pair of slacks, a shirt, and a sweater each day?
Deborah can choose from a total of 60 combinations.
Here, we are given that Deborah has two pairs of slacks, six shirts, and five sweaters.
She has to choose a pair of slacks, a shirt, and a sweater each day.
She can choose a pair of slacks in 2 ways
Similarly, she can choose a shirt to wear in 6 ways and a sweater in 5 ways.
Since, she wears each one of these items each day, the total number of combinations can be found by multiplying the possibilities for each item as follows-
2 × 6 × 5
= 60
Thus, Deborah can choose from a total of 60 combinations.
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Stella wants to build up her emergency fund to $10,000. She has $2,000 now and plans on saving $320 every month. To model the situation, she creates this equation, where x represents the number of months and y represents the total amount in her emergency fund:.
The linear equation that represents the total amount in her emergency fund after x number of months be
y = 320x + 2000
Given, Stella wants to build up her emergency fund to $10,000. She has $2,000 now and plans on saving $320 every month.
we have to model the situation in a linear equation,
Let the number of months be, x
and the total amount in her emergency fund be, y
As, she starts with $2000 so the y-intercept will be 2000
also she save $320 every month so the slope be 320
So, the equation be,
y = 320x + 2000
Hence, the linear equation that represents the total amount in her emergency fund after x number of months be
y = 320x + 2000
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The number of
Logan has $0.87 worth of pennies and nickels. He has a total of 31 coins altogether.
Determine the number of pennies and nickels Logan has.
Answer:
17 pennies, 14 nickels
Step-by-step explanation:
let p = pennies and n = nickels
p + n = 31 coins
p = 31 - n
0.01p + 0.05n = $0.87
0.01(31 - n) + 0.05n = 0.87
0.31 - 0.04n = 0.87
0.04n = 0.56
n = 14
p = 31 - 14
p = 17
hope this made sense :)
You have $8.80 in Pennie’s and nickels you have twice as many nickels as pennies write a system of linear equations that model the situation how many coins do you have
Answer:
Step-by-step explanation:
Let p be the number of pennies and n be the number of nickels. As you have $8.80 in total (given that pennies are worth $0.01 and nickels are worth $0.05)
0.01p + 0.05n = 8.80
You also know that there are twice as many nickels than pennies (or alternatively, there are 2 nickels for every penny).
n = 2p
You can substitute this value of n into the first equation
0.01p + 0.05n = 8.80
0.01p + 0.05(2p) = 8.80
0.01p + 0.10p = 8.80 (multiplying out the brackets)
0.11p = 8.80 (collecting the p's)
p = 80
Putting this back into the second equation
n = 2p
n = 2(80) = 160
So there are 160 nickels and 80 pennies.
You can put this back into the first equation to check it.
0.01p + 0.05n = 8.80
0.01(80) + 0.05(160) = 0.80 + 8 =8.80
How do you solve 11=2B+17, what is B
Answer:
b=-3
Step-by-step explanation:
11=2b+17
subtract 11 from both sides
then you get 2b+6=0
so b=-3
Answer: -3
Step-by-step explanation:
Hey! Here's a simple solution -
Step 1 - Subtract 17 from both sides -
11 - 17 = 2B + 17-17
-6 = 2B
Step 2 - Divide both sides by 2
-3 = B
B= -3
Hope this helped you! Peace out!
you roll two fair dice. find the probability that the first die is a 6 given that the minimum of the two numbers is a 4.
Step-by-step explanation:
answers is 1 and 2 by 3
all the best
The probability of getting the 6 on the first die given that the minimum of two numbers is 0.11.
What is the probability?Probability is a branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely a proposition is to be true. The probability of an event is a number between 0 and 1, where 0 indicates the event's impossibility and 1 indicates certainty.
Given that Two dice are rolled.
Then the sample space (n) = 36
Possible outcomes = {(6,1), (6, 2), (6, 3), (6, 4)}
Probability = 4/36
= 0.11
Hence, the probability of getting the 6 on the first die given that the minimum of two numbers is 0.11.
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from a group of 3 freshmen, 4 sophomores, 4 juniors, and 3 seniors, a committee of size four is randomly selected. find the probability that the committee will consists of only sophomores or juniors? round your answer to 2 decimal places.
Probability of randomly selecting four committee members with only sophomores or juniors is equal to 0.77.
As given in the question,
Total number of group members including 3 freshmen, 4 sophomores, 4 juniors, and 3 seniors = 14
Number of members required to form a committee = 4
Condition apply:
Committee consists of only sophomores or juniors
Let 'A' represents the sophomores
'B' represents the juniors
Total number of possible outcomes = ¹⁴C₄
Event A and B are independent of each other.
Favourable outcomes are :
2(⁴C₀⁴C₄ + ⁴C₁⁴C₃) +⁴C₂⁴C₂
Required probability
= 2(⁴C₀⁴C₄ + ⁴C₁⁴C₃) +⁴C₂⁴C₂ / ( ¹⁴C₄)
= [2( 1 + 16) + 36 ] / ( 7 × 13 )
= 70 / 91
=0.77
Therefore, the probability of the committee consists of only sophomores or juniors is equal to 0.77.
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A goalie makes 15 saves in 5 games. What is the unit rate of saves per game?
Answer:
Step-by-step explanation:
15/5= how many saves per game
1 game = 3 saves
Answer:
The unit rate is 3 saves per game.
Step-by-step explanation:
15 / 5 = 3
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a family begins a car trip at 2:00pm. at 5:00pm, the car has traveled a total of 80 miles. use the mean value theorem to explain why
In one hour, the car covered a distance of 26.66 miles
Given,
The time when the trip begins = 2.00 pm
Distance travelled till 5.00 pm = 80 miles
Here,
Mean value Theorem;-
The Mean Value Theorem says that there exists a point c in the interval (a, b) such that f'(c) equals the function's average rate of change throughout [a, b] if a function f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).
The Mean Value Theorem is as follows. F is constant over I if f′(x)=0 over a period I. If f′(x)=g′(x) over I for two differentiable functions f and g, then f(x)=g(x)+C for some constant C.
Here,
2 pm to 5 pm = 3 hours
80 miles in 3 hours
That is,
80/3 = 26.66 miles per hour
That is,
The car travelled a distance of 26.66 miles in an hour.
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Assume the birth of a boy or a girl is equally likely. The probability that a single child is born a girl is one-half. What is the probability that the next child born to the same familiy will also be a girl?.
There is a 1/4 probability that the family's next child will be a girl.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
So, the probability that the next child born will also be a girl:
We know that:
There is a 50% chance that a female will be the only kid born.
That is: 1/2
The likelihood that the family's subsequent kid will be a girl is:
1/2 * 1/2 = 1/4
Therefore, there is a 1/4 probability that the family's next child will be a girl.
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Ernesto guesses there are 69 marbles in a jar, but there are actually 60.
What is the percent error in Ernesto's guess?
Answer:
15%
Step-by-step explanation:
Since the problem is to find how much 69 is as a percent if 60 is 100%, we can use a rule of three, simple, direct proportion to do it:
60 = 100%
68 = x
x = 69x100/60
x = 115
That means 69 is 115% of 60, which means that the error is of:
115 - 100 = 15%
Hope this helps, have a great day! :D
let n be a three digit positive integer with all different signs. what can we say about the difference between n and its reverse
By using the expanded form of a number, it can be concluded that
Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99
What is expanded form of a number?
Every number can be written as a sum of the place value of its digit. This is known as expanded form of a number
Let the three digit positive integer be n = abc where a, b and c are distinct positive integers
n can be written as 100a + 10b + c
Its reverse is n' = cba
n' can be written as 100c + 10b + a
Difference between the number and its reverse
= 100a + 10b + c - 100c - 10b -a
= 99a - 99c
= 99(a - c)
= Since a and c are distinct, a - c [tex]\neq[/tex] 0
Difference between a three digit positive integer with all digits distinct and its reverse is surely divisible by 1, 3, 9, 11, 33, 99
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Jordan and his children went into a grocery store and he bought $13.50 worth of apples and mangos. Each apple costs $1.50 and each mango costs $0.75. He bought 6 more mangos than apples. Determine the number of apples and the number of mangos that Jordan bought.
The number of apples and the number of mangos that Jordan bought is
8 apples and 2 mangoesHow to find the amount Jordan boughtThe worth of apple and mango is $13.50
Each apple costs $1.50 and each mango costs $0.75
let the amount of apple by x then amount of mangoes be y. such that
1.50x + 0.75y = 13.50
6 more mangoes than apples this means that
x = y + 6
x - y = 6
the two equations formed are
1.50x + 0.75y = 13.50
x - y = 6
solving the simultaneous equation gives
x = 8
y = 2
The number of apples bought is 8 and the number of mangoes bought is 2
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Plsss help!
Geometry A
Brainliest
According to the perpendicular bisector theorem, the statement that is true is: B. BI = BK.
What is the Perpendicular Bisector Theorem?The perpendicular bisector theorem states that if a line segment bisects another line segment perpendicularly, therefore, any point on the perpendicular would be the same distance from the endpoints of each of the line segment that was bisected.
In the diagram above, we are told that line segment AB is a perpendicular bisector of line segment IK. This means that, according to the perpendicular bisector theorem, any point on line segment AB, would be equidistant to the endpoints of line segment IK.
This implies that:
The length of BI is the same as the length of BK. Thus, the correct answer is: B. BI = BK.
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a textbook store sold a combined total of 340 history and sociology textbooks in a week. the number of history textbooks sold was three times the number of sociology textbooks sold. how many textbooks of each type were sold?
Answer:
85 sociology books
255 history books
Step-by-step explanation:
h = history textbooks
s = sociology textbooks
h + s = 340
h = 3s
3s + s = 340
4s = 340
s = 85
h = 3s = 3(85) = 255
Answer:
255 history textbooks
85 sociology textbooks
Step-by-step explanation:
Define the variables:
Let x be the number of history textbooks sold.Let y be the number of sociology textbooks sold.Given information:
Total number of textbooks sold in a week was 340.The number of history textbooks sold was three times the number of sociology textbooks sold.Create a system of equations with the given information and defined variables:
[tex]\begin{cases}x+y=340\\\;\;\;\:\:\:\:x=3y\end{aligned}[/tex]
Substitute the second equation into the first equation and solve for y:
[tex]\implies 3y+y=340[/tex]
[tex]\implies 4y=340[/tex]
[tex]\implies y=340 \div 4[/tex]
[tex]\implies y=85[/tex]
Substitute the found value of y into the second equation and solve x:
[tex]\implies x=3 \times 85[/tex]
[tex]\implies x=255[/tex]
Therefore, the number of each type of textbooks sold were:
255 history textbooks.85 sociology textbooks.in base 10, the number 2013 ends in the digit 3. in base 9, on the other hand, the same number is written as (2676)9 and ends in the digit 6. for how many positive integers b does the base-b-representation of 2013 end in the digit 3?
As described in number system the of positive integers is 13
what is number system ?
A numeral system, also known as a mathematical notation, is a way of writing numbers that uses digits or other symbols to represent the numbers in a given set in a standardised way. In different numeral systems, the same set of symbols may represent various numbers.
Solution:
we want the integers b such that
2013 = 3 ( modb)
=> b is a factor of 2010
since 2010 has 2 * 3 * 5* 67 it has
(1+1)(1+1)(1+1)(1+1) = 16 factors
since b cannot equal to 1, 2, or 3, as these cannot have 3 in there base representation, our answer is 16 - 3 =13.
therefore the number of positive integers is 13
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6. If mLABE = 2n +7 and mZEBF = 4n-13, find mZABE.
Answer: 18°
Step-by-step explanation:
The question doesn’t state where F is in relation to A, B or E, so we have to guess. Here are two guesses.
If ABF is a straight line then ∠ABE+∠EBF=180, so 2n+7+4n-13=180, 6n-6=180.
Divide each side by 6: n-1=30 so n=31 and m∠ABE=2n+7=2×31+7=62+7=69°.
If BF bisects ∠ABE, then ∠ABE=2×∠EBF, so 2n+7=2(4n-13)=8n-26. So 6n=33 and, dividing both sides by 3: 2n=11. Therefore m∠ABE=2n+7=11+7=18°.
Question
A local movie theater sells tickets at different prices for an adult and for a child. The price of an adult’s ticket is $10.50 and the price of a child’s ticket is $6.50 . If the theater sells a total of 65 tickets for a total price of $594.50 in an afternoon, how many child tickets did the theater sell?
Answer:22
Step-by-step explanation:
a child is 40 inches tall, which places her at the 90th percentile of all children of similar age. the heights for children of this age form an approximately normal distribution with a mean of 38 inches. based on this information, what is the standard deviation of the heights of all children of this age?
Since the mean height of all children this age is 38 inches, the z-score is 1.282, and the child's height is 40 inches, the standard deviation of all children's heights will be 1561.
What is standard deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a larger range, a low standard deviation suggests that the values tend to be near to the established mean. The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed.
Here,
The z-score which separates the top 10% of a normally distributed
population is 1.282.
Since z = (x-u)/sigma
1.282 = (40-38)/sigma
sigma = 2/1.282
sigma = 1/0.641 = 1561
The standard deviation of the heights of all children of this age will be 1561 as mean is 38 inch and z-score is 1.282 as well as the height of child is 40 inch.
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Suppose you want to reduce the amount of sugar in your cookie recipe. You decide to subtract ⅛ of cup of sugar from the original amount of ¾ of a cup. How much sugar is now in your recipe? Show your work using two different methods.
The amount of sugar in final recipe will be 5/8
What are fraction?Fractions are used to represent smaller pieces (or parts) of a whole.
Given that, You decide to subtract ⅛ of a cup of sugar from the original amount of ¾ of a cup.
3/4-1/8 = 5/8
Hence, The amount of sugar in final recipe will be 5/8
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Sue wants to leave her grandson a nice inheritance. She has decided to deposit
$350.00 each month into an ordinary annuity that earns 4% compounded monthly.
How much will be in the account after 30 years rounded
The amount that would be in the account in 30 years will be $245,371.
How much will be in the account?An ordinary annuity is when a series of payment is made at the end of the period over a number of years.
The formula that can be used to determine the future value of an ordinary annuity is: monthly deposit x annuity factor
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r= monthly interest rate = 4/12 = 1/3%n = number of periods = number of years x number of compounding : 30 x 12 = 360$350 x (1.0033)^360 - 1} / 0.0033 = $245,371
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Hey y’all can y’all help me again
Answer:
Answer
Step-by-step explanation:
10. is (-1,0)
12. is (3,0)
14. is (1,0)
ABC is congruent to what by what
Answer:
Step-by-step explanation:
Since two angles of △ABC are congruent to two angles of △PQR, the third pair of angles must also be congruent, so ∠C≅∠R, and △ABC≅△PQR by ASA. The corresponding congruent angles are: ∠A≅∠P, ∠B≅∠Q, ∠C≅∠R. The corresponding congruent sides are: AB ≅ PQ, BC ≅ QR, AC ≅ PR.
How is a constant term different than a variable for an expression that represents a real word situation
A constant does not change its value over time. A variable, on the other hand, changes its value dependent on the equation.
What is a tern!?A term is either a number, a variable, or the product of a number and a variable. A coefficient is your term's numerical factor. A constant term is one that only contains a number. In other words, a constant term contains no variables.
Constants are algebraic expression terms that only contain numbers. That is, they are the terms that do not have variables. We call them constants because their value never changes because the term contains no variables that can change its value.
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I need help with this please asap
Answer:
estimate - 455
actual sum 376
What is the equation of the line that passes through the point (8,6) and has a slope of 0?.
The equation of line that passes through the point (8,6) and has a slope of 0 is y = 6.
Define the equation of the line?The set of points that make up a line in a coordinates system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line with in coordinate axis as a set of variables, x, and y.As the sated question-
The passing point; (x1, y1) = (8,6)
slope m = 0
Thus, equation lo line by slope intercept form is-
y - y1 = m(x - x1)
y - 6 = 0(x - 8)
y = 6
Thus, the equation of the line that passes through the point (8,6) and has a slope of 0 is y = 6.
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