The distribution of the amount of money undergraduate students spends on books for a term is slightly right-skewed, with a mean of $400 and a standard deviation of S80. If a simple random sample of 100 undergraduate students is selected, what is the probability that these students spend, on average, more than $425 on books?
Answers
The probability that on average these students spend more than $425 on books is given as follows:
0.0009 = 0.09%.
How to obtain the probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 400, \sigma = 80, n = 100, s = \frac{80}{\sqrt{100}} = 8[/tex]
The desired probability is one subtracted by the p-value of Z when X = 425, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{425 - 400}{8}[/tex]
Z = 3.125.
Z = 3.125 has a p-value of 0.9991.
1 - 0.9991 = 0.0009 = 0.09%.
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Related Questions
Find the limits given based on the graph.
Answers
Limits of the functions shown in the graph are limx +f(x) = 0 and limx -f(x) = 0. The link between a group of inputs, each of which has a related output, is known as a function.
what are functions ?The study of mathematics covers a variety of topics, including numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist. An easy way to think of a function is as a relationship between inputs and outputs, where each input leads to a single, distinct result. Each function has a respective domain and a codomain, or scope. Functions are typically represented by the letter f. (x). input is x. The accessible functionalities fall into four categories. based on the following elements: on functions, one-to-one functions, many-to-one functions, and within functions.
given
We first take into account how f(x) behaves as x increases unboundedly for the function in the graph below. As x can always increase because the function has no limit, it can never be zero. However, the function's behavior when x rises.
Similar to how x decreases without bound or how we move leftward on the graph, f(x) also seems to be approaching zero.
So in this case we can write:
limx → +∞f(x) = 0
limx → - ∞f(x) = 0
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DIRECTIONS: Use this information to answer Parts A and B. The width of a rectangle is shown. The length is twice the width. Part A 5-1x Write an expression for the perimeter listing each side separately.
Answers
Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.
Define perimeter.In geometry, a shape's perimeter, or overall length, is referred to as its perimeter. The lengths of all a shape's sides and edges are added up to determine its perimeter.
Here,
Given : length = 5 - 1(x) or
=> length = 5-x
Width is twice the length
thus,
=>Width = 2(5-x)
=>Width = 10-2x
So ,To find the perimeter
We use,
=> Perimeter = 2(length + width)
=> Perimeter = 2( 5-x + 10-2x )
=> Perimeter = 2( 15 -3x)
=> Perimeter = 30 -6x
Therefore , the solution of the given problem of perimeter comes out to be the perimeter is represented by the expression of Perimeter = 30 -6x.
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Show 24÷1/4 step by step
Answers
Answer:
96
Step-by-step explanation:
24 divided by 1/4 is 96
you turn 24 into a fraction by putting a one under is and then you keep it change it flip it
24/1 Divided by 1/4
24/1 times 4/1
24 times 4= 96
1 times 1= 1
96/1=96
Please help I was sick and missed out on class thank you.
Answers
Answer: slope=-5 and y-intercept=1
Step-by-step explanation:
The equation given is in slope-intercept form. Slope-intercept for is y=mx+b, where m is slope and b is y-intercept.
This gives m=-5 and b=1.
If f(x)=2(x)^2+5square root (5+2) complete the following statement f(2)= blank
Answers
The complete statement is f(2) = 8+5√7
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here f(x)=2x²+5√7
Thus f(1) = 2×4+5√7
= 8+5√7
Hence, The complete statement is f(2) = 8+5√7
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evaluate 6²-2(5+1+3)
Answers
Answer:
18
Step-by-step explanation:
36-10-2-6
26-8
18
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{6^2 - 2(5 + 1 + 3)}\\\mathsf{= 6^2 - 2(5) - 2(1) - 2(3)}\\\mathsf{= 6^2 - 10 -2(1) - -2(3)}}\\\mathsf{= 6\times 6 - 10 - 2(1) - 2(3)}\\\mathsf{= 36 - 10 - 2(1) - 2(3)}\\\mathsf{= 26 - 2(1) - 2(3)}\\\mathsf{= 26 - 2 - 2(3)}\\\mathsf{= 24 - 2(3)}\\\mathsf{= 18}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{18}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Write an equation of the line passing through (- 5,5) and having slope - 4. Give the answer in slope-intercept form.
The equation of the line in slope-intercept form is:
Answers
Answer:
y = - 4x - 15---------------------------
Slope-intercept form:
y = mx + b, where m is the slope, b is the y-interceptPoint-slope form:
y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point on the lineUse the point-slope form to find the equation and then convert it to slope-intercept form:
y - 5 = - 4(x - (-5))y - 5 = -4(x + 5)y - 5 = - 4x - 20y = - 4x - 20 + 5y = - 4x - 15Sara is saving her money in a piggy bank
and counts it each month. The graph
shows her monthly savings. Choose any
two points and draw a slope triangle.
Dilate the slope triangle along the graph
to determine whether the amount Sara
saves each month is constant.
Answers
Answer: It is not possible for me to draw a slope triangle or dilate it along the graph without more information about Sara's monthly savings.
To determine whether the amount Sara saves each month is constant, you can choose any two points on the graph and use them to calculate the slope of the line connecting them. If the slope is constant for all pairs of points, then the amount Sara saves each month is constant. If the slope is not constant, then the amount Sara saves each month is not constant.
To calculate the slope of the line connecting two points, you can use the following formula:
slope = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points.
You can then use the slope triangle to visualize the slope of the line connecting the two points. If you dilate the slope triangle along the graph and the slope remains constant, then the amount Sara saves each month is also constant.
Step-by-step explanation:
Checkpoint 4 is -117 and checkpoint 3 is -212 how much higher is checkpoint 4 than 3
Answers
Answer:4 = -117,3=-212,4+3
Step-by-step explanation:
Akira is setting tables at the restaurant where she works. She starts with a pile of 85 napkins, and she places 6 napkins on every table she sets
Write an equation that shows how the number of napkins remaining, y, depends on the number of tables akira sets, x
Answers
Answer: y = 85 - 6x
Step-by-step explanation:
Number of napkins remaining: y
Number of tables set: x
Akira starts out with 85 napkins. So, every time she sets a table, she is losing 6 napkins. The steady rate of napkins lost can be written with the following expression, as she is losing 6 napkins per table.
[tex]-6x[/tex]
These napkins are being removed from the total of 85 napkins:
[tex]85 - 6x[/tex]
The above equation also expresses the number of napkins remaining. Writing it as a proper equation:
[tex]y = 85 - 6x[/tex]
The final answer is: y = 85 - 6x
Five people each working eight hours a day can assemble 400 toys in a five day work week. What is the average number of toys assembled per hour per person?
Answers
Answer:
There are 5 people working and each person works 8 hours per day, so there are a total of 58 = <<58=40>>40 hours of work per day.
Over the course of the week, the total number of hours worked is 405 = <<405=200>>200 hours.
The total number of toys assembled is 400 and the total number of hours worked is 200, so the average number of toys assembled per hour per person is 400/200 = <<400/200=2>>2 toys per hour per person. Answer:{2}.
Step-by-step explanation:
a movie theater has 24 screens. ration of action to other films is 1:2. How many action films are currently showing
Answers
Answer: 12
Step-by-step explanation: Because of the ratio we know that half of the screens will be showing action films. Half of 24 is 12, so 12 screens will be playing action.
Greatest common factor
Answers
Step-by-step explanation:
To find the GCD or GCF of two numbers , you should:
List the prime factors of each one of them(the 2 numbers)choose the common number+least exponent multiply themIn a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Triangle with vertices labeled golfer and spectator and hole, with the distance from the golfer to the spectator measuring 140 yards and the distance from the golfer to the hole measuring 200 yards and the vertex of the spectator measuring 120 degrees
If the spectator has an angle of 120° between the golfer and the hole, what is the angle that the golfer has between the spectator and the hole?
60.0°
59.6°
37.3°
22.7°
Answers
The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.
What is sine rule?Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.
The formula for sine rule is sinA/a=sinB/b=sinC/c
Given that, in a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.
Let the angle that the golfer has between the spectator and the hole be x
Here, sin 120°/200 =sin x/140
0.8660/200 =sin x/140
0.00433 = sin x/140
sin x=0.866
x=60°
Therefore, option A is the correct answer.
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Hi hi! The answer would be 22.7°, I took the test a while ago.
Jocelyn has a collection of 100 coins. How many coins represent 25% of her collection?
Answers
25 coins represent 25 percent of Jocelyn's collection.
What is the percentage?A percentage is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.
given, Jocelyn has a collection of 100 coins.
100% of her collection represents = 100 coins
1 % of her collection represents = 100/100 coins
1% of her collection represents = 1 coin
thus,
25% of her collection represents = 1*25 coins
25% of her collection represents = 25 coins
therefore, 25 percent of the collection of Jocelyn represents 25 coins.
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Convert the degree measure to radians or the radian measure to degrees. Then find one positive angle and one negative angle that is coterminal with the given angle.
1. -560°
2. 170°
Answers
-560° in radian is -28π/9 radian and the positive and negative coterminals are 8π/9 and -10π/9 respectively.
170° in radian is 17π/18 radian and the positive and negative coterminals are 53π/18 and -19π/18 respectively
How to convert the degree measure of angle to radians?An angle can be converted from degree to radian by multiplying it by π/180.
1. -560°
-560° × π/180 = -28π/9 radian
2. 170°
170° × π/180 = 17π/18 radian
In general, if θ is any angle in radian, then θ + n(2π) is coterminal angle with θ, for all nonzero integer n.
coterminal of -28π/9:
positive: -28π/9 = -28π/9 + 2(2π) = 8π/9
negative: -28π/9 = -28π/9 + 2π = -10π/9
coterminal of 17π/18:
positive: 17π/18 = 17π/18 + 2π = 53π/18
negative: 17π/18 = 17π/18 - 2π = -19π/18
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Company A charges 125$ annual fee plus 7$ per hour car share fee. Company B charges 110$ plus 10$ per hour. What is the minimum number of hours that a car share needs to be used per year to make company a better deal?
Answers
Answer:
6
Step-by-step explanation:
Let the number of hours be [tex]x[/tex].
[tex]125+7x<110+10x \\ \\ 15+7x<10x \\ \\ 15<3x \\ \\ x>5[/tex]
So, the minimum is 6 hours.
3. Function G is defined by the equation G(x) = [x].
Function R is defined by the equation R(x) = x/+2.
Describe how the graph of function R relates to the graph of G, or sketch the graphs
of the two functions to show their relationship.
Answers
Answer: The function G(x) = [x] returns the greatest integer less than or equal to x. This means that for any value of x, G(x) will be the largest integer that is less than or equal to x. For example, G(3.5) = 3 and G(5) = 5.
The function R(x) = x/+2, x is any real number, this function returns the value of x incremented by 2. In other words, it is the result of adding 2 to x.
On the other hand, the graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1, this means that for every change of 1 unit in the x-axis, the y-axis will change by 1 unit as well.
When we compare the two graphs, we can see that the graph of R(x) is shifted up 2 units from the graph of G(x) . If the graph of G(x) is thought of as the "ground", the graph of R(x) is "floating" two units above it. Also, the graph of R(x) is continuous while the graph of G(x) is not.
To sum up:
-The graph of G(x) is a step function, which start at the negative infinity and jumps up to the next integer at every point.
The graph of R(x) is a line that goes through the point (0, 2) and has a slope of 1
-R(x) is always two units above G(x) , and is a continuous function, while G(x) is not.
Step-by-step explanation:
THIS ONE TOO PLEASE
Answers
A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.
what is equation ?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
given
The line going through the origin equation is also y=2x.
A line that crosses the origin is symbolized by the equation y=mx.
Also, y=2x satisfies the point (0,0)
A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.
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Mrs. Sarto told her son that if he babysat his baby sister, she would pay him $5.80 per hour. If Mrs. Sarto’s son babysits his sister for 5.2 hours, how much money will he be paid?
Answers
Solution
$5,80*5.2 hours =$30.16
Using the paths shown, how long is the shortest route from Lexington to Somerville?
Answers
Answer:
1 [tex]\frac{1}{4}[/tex] miles
Step-by-step explanation:
the routes from Lexington to Somerville are
Lexington → Brookfield → Somerville with distance
[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles
the other route is
Lexington → Brookfield → Yardley → Somerville with distance
[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles
the shortest distance is
Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles
A cake recipe calls for 2 1/3 cups of flour. If Gloria is planning on making 6 cakes for a bake sale, how many cups of flour will she need?
Answers
Answer: Gloria will need 14 cups of flour
Step-by-step explanation: 2 1/3 x 6 = 14
Is the vertex of -x^2q-2x+10=0 parabola a maximum value or minimum value?
Answers
The vertex of the parabola -x² - 2x + 10 = 0 occurs at (-1,11), It is a maximum value.
Determine whether the parabola is maximum value or minimum value?Given the equation of the parabola;
-x² - 2x + 10 = 0
First, the maximum of a quadratic function occurs at;
x = -b/a, if a is negative, the maximum value of the function is f( -b/2a)
f_max(x) = ax² + bx + c occurs at;
x = -b/2a
Now, find the value of x = -b/2a
Plug in a = -1 and b = -2
x = -( -2/2(-1) )
x = -( -2/-2) )
x = -( 1 )
x = -1
Hence;
f(x) = -x² - 2x + 10
f( -1 ) = -( -1 )² - 2( -1 ) + 10
f( -1 ) = -1 + 2 + 10
f( -1 ) = -1 + 12
f( -1 ) = 11
Therefore, maximum occurs at (-1,11).
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There is a raffle for the class of 30
students. There are 3 prizes that are gift
cards for the value of $5, $10 and $25.
How many ways can there be 3 winners of
this raffle?
Answers
Answer:
Having 3 students pick a raffle
Step-by-step explanation:
what is 3 1/3 minus -1
Answers
Answer:
2 1/3
Step-by-step explanation:
Seperate equation
(3 1/2) - 1
( 3 - 1 ) + 1/2
2 and 1/3
2 points How Did I Do? The cost of renting a car is $42 /week plus $0.25 /mile traveled during that week. An equation to represent the cost would be y=42+0.25x , where x is the number of miles traveled.
Answers
The equation to represent the cost of renting the car, given the cost per week and the cost per mile, is y = 42 + 0.25x.
How to formulate the equation ?The total cost of renting the car at any given point, would be:
= Cost to rent per week + ( Cost per mile x Number of miles driven)
If we assume the number of miles driven is denoted by x, then the equation becomes :
= 42 + 0. 25 x
If we further take y to be the total cost, the equation then becomes :
y = 42 + 0. 25 x
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6 divided 109 can you help?
Answers
Answer: 18.1666666667
Step-by-step explanation:
Rashaad has
x
x dimes and
y
y nickels, having no less than 18 coins worth at most $1.50 combined. At least 4 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.
Answers
Answer:
see attached for a graph4 dimes, 22 nickelsStep-by-step explanation:
You want to solve graphically the system of inequalities expressing that Rashaad has no less than a total of 18 dimes (x) and nickels (y) with a combined value of at most $1.50, of which at least 4 are dimes.
InequalitiesAn inequality can be written for each of the constraints:
x + y ≥ 18 . . . . . . . no less than 18 coins
0.10x +0.05y ≤ 1.50 . . . . . . at most $1.50 in value
x ≥ 4 . . . . . . . . . . at least 4 dimes
GraphA graph of these inequalities is attached. The marked points are the vertices of the triangular solution space. Each is a possible solution, along with all of the grid points inside the triangle.
One possible solution is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.
Using graph to solve the system of linear inequality the most likely solutions will be 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50
What is System of Linear InequalitySystems of linear inequalities are equations with two or more linear inequalities that contain two or more variables. These equations can be used to represent real-world problems and to find the solutions of such problems. The solutions of a system of linear inequalities are all the points that are common to all of the linear inequalities in the system.
In this problem, we have to define our variables and then solve this using graphical method. The point of intersection between the two lines lies the solution to the linear inequality.
Let;
x = dimesy = nickelx + y ≥ 18
0.1x + 0.05y ≤ 1.50
x ≥4
Using a graphing calculator to solve this,
The possible solutions is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.
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Four gallons of paint are used to paint 25 chairs. If each chair used the same amount of paint, how many gallons are used to paint each?
Answers
Answer:
0.16 or 0.2 if rounded
Step-by-step explanation:
4 gallons divided by 25 chairs equals 0.16 gallons for each chair
hope this helps <3
I need help with these 4 problems
Answers
As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.
Describe equation.A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 2x - 5 = 15 is an equation. We can find that the variable x has a value of 5 by resolving this equation.
Here,
In New York City, a one-bedroom apartment will cost $1600 in 2020.
Y = mx + c is frequently used as the formula for a straight line graph, where;
gradient = m
The vertical intercept is given by c.
With this knowledge, it is evident from the graph that y = 40x + 800 is the best line of fit for the data presented.
This indicates how much a one-bedroom apartment in New York City will cost in 2020, or 20 years after the year 2000.
y = 40(20) + 800 = $1600
As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.
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