Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is ( 89.772 , 64.228 )
Define z-distribution confidence interval?The confidence interval is:
= μ ± z ( σ / [tex]\sqrt{n}[/tex] )
Where,
μ X is the sample mean.
z is the critical value.
n is the sample size.
σ is the standard deviation for the population.
In this problem, we have a 99% confidence level, hence [tex]\alpha =0.99[/tex] , z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2}[/tex] = 0.995,
So the critical value z- distribution is z = 2.575.
The other parameters are given as follows:
Mean μ = 77
Standard deviationσ = 7
Sample size two side n = 2
Hence the lower and upper bound of the interval are given, respectively, by:
= μ ± z ( σ / [tex]\sqrt{n}[/tex] )
= μ + z ( σ / [tex]\sqrt{n}[/tex] ) , μ - z ( σ / [tex]\sqrt{n}[/tex] )
= 77 + 2.575 ( [tex]\frac{7}{\sqrt{2} }[/tex] ) , 77 - 2.575 ( [tex]\frac{7}{\sqrt{2} }[/tex] )
= 77 + 2.575 ( [tex]\frac{7}{1.41}[/tex] ) , 77 - 2.575 ( [tex]\frac{7}{1.41}[/tex] )
= 77 + 2.575 ( 4.96 ) , 77 - 2.575 ( 4.96 )
= 77 + 12.772 , 77 - 12.772
= ( 89.772 , 64.228 )
Therefore,
Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is ( 89.772 , 64.228 )
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Which of the following best describes the second law passed under the Morrill Act?
Eastern schools had to research which crops were suitable for farms in Midwestern America.
Answer:
Step-by-step explanation:
class council is selling prom tickets for $55 per person.the senior class consists of 342 students,who are each allowed to bring one date from another school.complete the table(if needed) and answer the questions below
Answer: Here is a completed table for the scenario described:
Class Number of Students Number of Dates Total Tickets Sold
Senior 342 342 684
Total Revenue
$37,620
Based on this information, the following information can be determined:
The senior class is selling a total of 684 prom tickets.
The total revenue from prom ticket sales for the senior class is $37,620.
I hope this helps! Let me know if you have any other questions.
Someone please help me finde out what’s (2y+3)(x+3)
Answer:
2xy + 3x + 6y + 9
Step-by-step explanation:
2y times x = 2xy
3 times x = 3x
2y times 3 = 6y
3 times 3 = 9
I am playing a walking game with myself. On move 1, I do nothing, but on move n where 2 \le n \le 25, I take one step forward if n is prime and two steps backwards if the number is composite. After all 25 moves, I stop and walk back to my original starting point. How many steps long is my walk back?
Answer:
21 steps
Step-by-step explanation:
There are 9 prime numbers and 15 composite numbers between 2 and 25. So, a prime number would be 1 step forward, and a composite number would be 2 steps back.
[tex]1*9+(-2)*15=9-30=-21[/tex]
We then take the absolute value of -21 to get 21 as our answer.
Hope this helped! :)
please help, this is my finals & i don’t know it
The equation that relates the graph is a) y= - 1/2(x-3)²+2
How to find Slope intercept?Here Let put x=7
y= -1/2(x-3)²+2
= -1/2(7-3)²+2
= -1/2(4)²+2
= -1/2(16)+2
= - 8+2
= - 4
Hence (7,-4) is marked.
Slope-intercept equations are a particular kind of linear equation. It follows the overall structure. The two real numbers in this example are and. For instance, they are slope-intercept form linear equations. SlopeIn mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. There is no definitive solution to the question of why the letter m is used for slope, but O'Brien (1844), who developed the equation of a straight line, uses it for the first time in English. A line is defined by the equation y = mx + b, which is also known as the slope-intercept form.To learn more about Slope intercept refer to:
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Age is an example what kind of data categorical or quantitative?
Age, BMI, creatinine, and the amount of time between conception and death are a few examples of quantitative characteristics.
How do you know if data is categorical or quantitative?Any variable where the data indicate amounts is referred to be a quantitative variable (e.g. height, weight, or age). Any variable where the data reflect groupings is referred to be a categorical variable.A categorical variable's data will always be qualitative, while a numeric variable's data will always be quantitative. As a result, based on whether the variable is numeric or categorical, you may determine the kind of data before it is collected.Data types that may be kept and recognized based on the names or labels assigned to them are referred to as categorical data. Data that is expressed as numbers rather than in any linguistic or descriptive form is referred to as numerical data.Learn more about quantitative data refer to :
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A function p(x) is shown on the graph below.
O True
O False
Answer:
True
Step-by-step explanation:
The point [tex](0,3)[/tex] lies on the graph.
help me pls help help
Answer:
6. Scalene, No congruent sides
7. Isosceles, 2 congruent sides
8. Equilateral, All congruent sides
The teacher grades 16 of the 48 quizzes before school.
If the teacher grades 15 of the remaining quizzes after school, how many quizzes still need to be graded?
Responses
8 quizzes
8 quizzes
23 quizzes
23 quizzes
25 quizzes
25 quizzes
40 quizzes
The number of quizzes still need to be graded is 17quizzes.
What is an algebraic equation?There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.
For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.
Algebraic equations in mathematics frequently have one or more variables.
It is given that,
grades of the teacher out of 48 quizzes before school = 16
grades of the teacher of the remaining quizzes after school = 15
Let us assume 'X' as the number of quizzes still need to be graded.
then X= 48-16+15
=48-31
=17
Hence, The number of quizzes still need to be graded is 17quizzes.
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The number of quizzes still need to be graded is 17 quizzes.
What is an algebraic equation?There are many different ways to define an equation. In terms of algebra, an equation is a claim that demonstrates the equality of two mathematical expressions.For instance, the two equations 5x + 4 and 16, which are separated by the 'equal' sign, make up the equation 5x + 4 = 16.Algebraic equations in mathematics frequently have one or more variables.It is given that,grades of the teacher out of 48 quizzes before school = 16, grades of the teacher of the remaining quizzes after school = 15.Let us assume 'X' as the number of quizzes still need to be graded.then X= 48-=48-31
=17
Hence, The number of quizzes still need to be graded is 17 quizzes.
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Madelyn and Kaia are competing to see who can sell the most tickets for the Winter Dance. On Monday, Madelyn sold 22 and then sold 30 per day after that.
Kaia sold 53 on Monday and then sold 20 per day after that.
Write an equation to represent the number of tickets that Madelyn sold.
Write an equation to represent the number of tickets that Kaia sold.
Write a system of equations. What is the appropriate method for solving the system?
Solve the system of equations. Explain the meaning of your solution.
The equations found for the number of tickets sold when 22 tickets are sold on Monday and 30 per day after are sold by Madelyn, and 53 tickets are sold on Monday and 20 per day after that are;
Tickets sold by Madelyn is; y = 22 + 30·x
Tickets sold by Kaia is; y = 53 + 20·x
A system of equation obtained from the details in the question can be presented as follows
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The appropriate method for solving the system is to equate equivalent values of one of the variable obtained from each equation in the system.
The solution of the system of equation is; x = 3.1, which indicates that it takes about 3.1 days for the number of tickets sold by Madelyn and Kaia to be equivalent.
What is an equation?An equation consists of two expressions that are joined by the 'equals to' (=) sign.
The number of tickets for the Winter Dance Madelyn sold = 22
Number of tickets per day Madelyn sold after that = 30 per day
Number of tickets Kaia sold on Monday = 53
Number of tickets per day Kaia sold after that = 20 per day
Let x represent the number of days since Monday, and let y represent the number of tickets sold
Therefore;
The number of tickets Madelyn sold, y = 22 + 30·x
The number of tickets Kaia sold, y = 53 + 20·x
The system of equations from the specified information is the equation for the number of tickets Madelyn sold and the number of tickets Kaia sold combined, which can be presented as follows;
y = 22 + 30·x...(1)
y = 53 + 20·x...(2)
The method of solving the equations is by plugging in the value of y from equation (1) in equation (2), as follows;
22 + 30·x = 53 + 20·x
30·x - 20·x = 53 - 22 = 31
10·x = 31
x = 31 ÷ 10 = 3.1
The meaning of the solution of the system of equation, x = 3.1, is that the number of days for the number of tickets sold by Madelyn and Kaia to be the same is about 3 days
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State all integer values of x in the interval [-4, 2] that satisfy the following Inequality:
4x + 5<-6
Integer values of x in the interval [-4, 2] that satisfy the following Inequality: 4x + 5 < -6 are -4 and -3.
What is inequality?In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.
A sign of inequality can be used to show that one of the two variables is larger than, more than or equal to, less than, or equal to another value.
Income gap, gender inequality, access to health care, and social class are some of the most prominent instances of social inequality.
Given the inequality:
4x + 5 < -6
Therefore the all values of x which satisfy the given inequality on the interval [-4,2].
So, x= -4 and x= -3
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please help, this is my finals & i don’t know it
Answer:
i think that answer is correct
Step-by-step explanation:
LWhat's the slope of the line connecting (1, 3) to (4, -2)? (You may enter your answer as a fraction. Otherwise, round
your answer to 2 decimal places.)
Answer:
-5/3
Step-by-step explanation:
Let's use the formula [tex]S = \frac{rise}{run}[/tex]
We can rewrite this as [tex]S = \frac{y_{1}-y_{2}}{x_1-x_2}[/tex]
The points we have are (1, 3) and (4, -2)
Now we just insert them into the equation and solve:
[tex]\frac{3-(-2)}{1-4}=\\\frac{5}{-3}=\\-\frac{5}{3}[/tex]
one number is 4 less than 3 times a second number. Two times the first number decreased by two times the second is 8. what is the value of the larger number?
A.4
B.12
C.8
D.2
E.14
Answer:
Step-by-step explanation: To solve the problem, we can use the given information to set up a system of equations and solve for the values of $x$ and $y$. Specifically, we are given that one number is 4 less than 3 times a second number, and that two times the first number decreased by two times the second is 8.
Let $x$ represent the larger number, and $y$ represent the second number. We can write the given information as a system of equations as follows:
x &= 3y - 4
2x - 2y &= 8
Solving this system of equations, we find that $x = 12$ and $y = 2$. Therefore, the value of the larger number is 12
imagine that we are interested in 1 bed and 1 bath condos in the pacific heights neighborhood of san francisco. let's say that the empirical distribution of the mean square footage generated via bootstrapping is roughly normal with a mean of 883 sqft and a standard deviation of 270 sqft. what range of square footage values would contain 95% of the data?
The range of the square footage values for the given mean , standard deviation and 95% confidence interval is equal to (1257.26 , 508.74).
As given in the question,
Sample size 'n' = 2
Sample mean '[tex]\bar{x}[/tex]' = 883 sq ft
Standard deviation 'σ' = 270 sq ft
95% confidence interval.
95% confidence interval = 1 - 0.95
= 0.05
Critical value for 95% is [tex]Z_{0.05}[/tex] = 1.96
Population mean for the given confidence interval is given by :
= [tex]\bar{x}[/tex] ± [tex]Z_{0.05}[/tex] (σ / √n)
= 883 ± 1.96 ( 270 / √2)
= 883 ± 374.26
= ( 1257.26 , 508.74 )
Therefore , the range of the square footage values for the 95% confidence interval is equal to ( 1257.26 , 508.74 ).
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Below are the fees of a parking lot.
First 2 hours = $5
Every 1/2 hour (or part of a half hour) afterward = $3.50
Mr. Garcia parked his car from 5:00pm to 11:15pm on the same day. How much did he pay for par
Answer:
145.54$
Step-by-step explanation:
Hope this help! <3
5(x+6) - 2x = 3(x+10)
Answer:
All Real Numbers
Step-by-step explanation:
I assume you are solving for x.
The Interval Notation would be: (-∞,∞)
The length of a side of a cube is 4x units. In cubic units, what is the volume of the cube?
Answer:
volume of cube= l^ 3
=(4x)^3
=64x^3 cubic units
14. Harold borrowed $9,000 for 5 years at an APR of 3.6%.
a. What is Harold's monthly payment? Round to the nearest cent. (Round your answer to the nearest cent and use the rounded answer for further calculations)
b. What is the total amount that Harold paid in monthly payments for the loan?
c. What is the amount Harold will pay in finance charges?
a. Harold's monthly payment is given as follows: $164.13.
b. The total amount paid is given as follows: $9,847.8.
c. The finance charge is of: $847.8.
What is the monthly payment formula?The monthly payment formula is defined as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which the parameters are listed as follows:
P is the initial amount.r is the interest rate.n is the number of payments.The values of these parameters for this problem are given as follows:
P = 9000, r = 0.036, n = 5 \times 12 = 60.
Then:
r/12 = 0.036/12 = 0.003.
Then the monthly payment is calculated as follows:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 9000\frac{(0.003)(1.003)^{60}}{(1.003)^{60} - 1}[/tex]
A = $164.13.
Then the total amount paid is of:
Total = 60 x 164.13 = $9,847.8.
Meaning that the finance charge is given as follows:
9847.8 - 9000 = $847.8.
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A line passes through the points (−4, 7) and (5, −8). What is the slope of the line?
Answer:
-5/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1) ==> (x1, y1), (x2, y2) are the coordinates and
m is the slope
(x1, y1), (x2, y2) ==> (x1=-4, y1=7), (x2=5, y2=-8)
m=(-8-7)/(5-(-4)) ==> plug in known values
m=(-15)/(5+4) ==> simplify
m=-15/9
m=-5/3
given a cubic function, what would be the maximum number changes of direction (turning points)? given a cubic function, what would be the maximum number changes of direction (turning points)? 0 1 3 2
The maximum number changes of direction (turning points) = 3
What is Direction?
The direction of an object's motion or tendency is indicated by its direction.
The main directions are East, South, West, and North.
Concept:
Not every cubic function has a definite turning point. but their are 3 turning point and depends upon the type of the cube
The first derivative of the function becomes zero and the second derivative might either be positive or negative at a turning point of the function.
The function would not have a turning point if the set of real numbers containing the roots of the first derivative of the function included none.
The point would not be a turning point but an inflexion point of the curve if the function has a root in the set of real numbers but its second derivative is zero at that location. Additionally, such a process would not have a turning point.
Think about the equation f(x)=x3. There isn't a turning point in this function. Rather, it has an inflection point at x=3.
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PLEASE HELP ASAP!!!
Sharon wants to switch from cable to satellite TV. She calls Great Vista Satellite to get a quote. After looking at her cable bill, the salesperson explains that they can provide the same 300 channels Sharon has for $0.20 less per channel. If she switches, her monthly satellite bill will come to $180.
Which equation can Sharon use to find c, the average amount the cable company charges per channel?
0.20(c - 300)
0.20c - 300
300(c - 0.20)
300c - 0.20
How much on average does the cable company charge per channel?
The equation Sharon can use to find c, the average amount the cable company charges per channel is 300(c - 0.20) = 180.
The cable company charges an average of $0.80 per channel.
What is an Equation?An equation involves two expressions or statement on two sides connected with an equal sign.
Total number of channels = 300
Let c be the cable company charges per channel.
Then the charge satellite company charges per channel = c - 0.20
Monthly charge of satellite company = 300(c - 0.20)
Monthly satellite bill = $180
So, 300(c - 0.20) = $180
⇒ c - 0.20 = 180/300
⇒ c - 0.20 = 0.60
⇒ c = 0.60 + 0.20
⇒ c = 0.80
Hence the equation used to find the cable company charge per channel is 300(c - 0.20) = 180 and the cable company charge per channel is $0.80.
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Zhi bought 18 tickets for games at a fair. Each game requires 3 tickets. Zhi wrote the
expression 18
3g to
find the number of tickets she has left after playing g games.
Diego correctly wrote another expression, 3(6 -
g), that will also find the number of
tickets Zhi has left after playing g games.
Use the drop-down menus to explain what each part of Zhi's and Diego's expressions
mean.
Answer:
Zhi's Expression:
18: The total number of tickets
3: The number of tickets required for each game
g: The number of games played
Diego's Expression:
3: The number of tickets required for each game
(6 - g): The total number of tickets minus the number of games played
Step-by-step explanation:
Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5). They plan to meet up at the hill located halfway between there two houses what is the coordinate location of the Hill
The coordinate location of the hill halfway between them is (1, -1).
How to find the distance between two points?Jack's house is located at the point (-2, 3) and Jill's house is located at the point (4, -5). They plan to meet up at the hill located halfway between there two houses.
The coordinate location of the hill can be calculated as follows:
using mid point formula,
(x, y) = (x₁ + x₂ / 2, y₁ + y₂ / 2)
using the end points (-2, 3) and (4, -5)
(x, y) = (-2 + 4 / 2, 3 - 5 / 2)
(x, y) = (2 / 2. -2 / 2)
(x, y) = (1, -1)
Therefore, the coordinate location of the hill is (1, -1).
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The
graph below shows the solution to which system of inequalities?
The graph in the problem shows the system of inequalities written below
y ≥ 2
y < x
How to know the equations that suits the inequality graphsThere are some points that help in interpreting inequality graphs.
Firstly, arranging the equation such that y is the subject of the formula
Secondly look out for line type: dashed lines or solid lines
dashed lines means there is no equality sign in the inequality > OR <solid line means there is equality in the inequality ≤ OR ≥
Thirdly is the shaded portion
shading above the line defines greater than shading below the line defines less than
Equipped with this information, on of the line is dashed line and the other is solid line,
the solid line is a horizontal line and shaded above the line which is
y ≥ 2
the dashed line is shaded below the line will hence be a less than
y < x
This makes the first option the best choice
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The graph shows the parent function f(x)=0.75^x
the answer; the graph on the top right
+ 1 -- translates the graph upward changing the y intercept from (0,1) to (0,2)
to find the point at 1, just plug in 1 for x
What is the slope of the equation 3x+20=-4?
The slope of the equation 3x+20=-4 is 8.
How may mathematical expressions be made simpler?
Mathematical operations may be made more simpler by using the right order of operations. Exponents, words in parentheses, multiplication, division, addition, and ultimately subtraction are the right order of operations. PEMDAS is a helpful acronym that you may use to remember this.
1. Subtract 20 from both sides
[tex]\begin{aligned}& 3 x+20=-4 \\& 3 x+20-20=-4-20\end{aligned}[/tex]
2. Simplify
Subtract the numbers
3 x=-24
3. Divide both sides by the same factor
[tex]\begin{aligned}& 3 x=-24 \\& \frac{3 x}{3}=\frac{-24}{3}\end{aligned}[/tex]
4 Simplify
Cancel terms that are in both the numerator and denominator
Divide the numbers
x=-8
Y = mx + b, where m is the slope and b is the y-intercept, is the slope equation utilising the equation of a line.
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It costs $270 for 3 people to go on a fishing trip. How many people can go for $1,080?
Answer:12
Step-by-step explanation:
270/3=90, this is the amount it costs for 1 person to go
1080/90=12
12 people can go for $1080
Solve for x in the circle
An angle is outside a circle if its vertex is outside the circle and its sides are tangents or secants. Here the angle is formed by two tangents,
The value of x is 80°.
What is a Tangent?The tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency.
Calculation:As we know that the complete angle of the circle is 360°
The answer for x° is 360° - 260° = 100°
⇒ 260°- 100° = 160° now,
⇒ 160°/2 = 80°
∴ x = 80°
Hence, for the given two tangents formed the answer for x° = 80°
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Which is the equation for line b
Answer: C
Step-by-step explanation:
Slope is rise over run. Let's start at (0,0) and we want to see when the line hits another point, which can be (2,1.5). We count that starting from 0, the point goes up by 3 and then runs by 4. Therefore, the answer is 3/4, which is C.
