The solution is, the expression is => 4*(5-x)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
let, the number is x.
now, when,
4 is multiplied by the difference of 5 and a number.
so, we get,
the expression is => 4*(5-x)
Hence, The solution is, the expression is => 4*(5-x)
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TEACH THIS
WORKSHEETS, ACTIVITIES & GAMES
Complete the sentences with a, an, the, or no article (-).
1. We went to Vietnam on ..... holiday and spent a week in ........ north of ........ country.
2. I've got ........ rabbit and ........ dog......... rabbit's called Snowy and ........ dog's called Eric.
school photo, Kim is standing on ........ right and Harry is standing in ........
middle next to ........ Headmaster.
3. In ........
4. I live in ........ flat in ........ centre of London, very close to ........ Big Ben and
Houses of Parliament.
5. Loch Ness is
Monster.
most famous lake in ........ Scotland because of ........ Loch Ness
ARTICLES
Articles Practice
6. David has ........ job working for ........ United Nations in ........
far away from his office. It takes him ........ hour to get to work.
7. They found ........ Titanic at ........ bottom of ........ Atlantic Ocean.
8. In
...... USA, most people go to work by
clinic because he had
9. My uncle went to ........
10. Phuket is in
11. We went to ........
..... car.
Philippines.
18. There are two bedrooms, one with ........
Netherlands, but he lives
ear infection.
south of ........ Thailand on ........ west coast.
wedding, but we couldn't park near ........ church, so we had to walk
for ten minutes to get there.
12. She decided to go to ........ top of ........ Eiffel Tower to take photos of ........ city.
border of ........ Mexico and ........ United States.
13. El Paso is on ........
....... igloo near ........ Arctic Circle.
14. I know ........ Eskimo. He lives in ........
15. I met ........ Queen of ........ England when I was in ........ UK.
16. My sister stayed at ....
Ritz Hotel for her honeymoon.
17. The man was sent to ........
prison for robbing ........ convenience store in
double bed and one with ........ single bed.
windows of ........ large bedroom look onto ........ small garden.
19. ........ River Nile in Egypt flows into ........ Mediterranean Sea.
20. The population of ........ United Kingdom is approximately 65 million.
ssion granted to reproduce for classroom use.
We went to Vietnam on a holiday and spent a week in the north of the country. 2. I've got a rabbit and a dog. The rabbit's called Snowy and the dog's called Eric.
What are articles?A brief, monosyllabic word called an article is used to indicate whether a noun is specific or not. Normally, articles come before nouns, and because they are employed to describe the noun, they can be thought of as adjectives.
1. We went to Vietnam on a holiday and spent a week in the north of the country.
2. I've got a rabbit and a dog. The rabbit's called Snowy and the dog's called Eric.
school photo, Kim is standing on the right and Harry is standing in the
middle next to the Headmaster.
4. I live in a flat in the centre of London, very close to the Big Ben and
Houses of Parliament.
5. Loch Ness is a Monster.
most famous lake in the Scotland because of the Loch Ness
6. David has a job working for the United Nations in a far away from his office. It takes him an hour to get to work.
7. They found the Titanic at the bottom of the Atlantic Ocean.
8. In the USA, most people go to work by clinic because he had
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Factor 48-6 using GCF
Answer:
I think the answer is six i just searched it or it could be 12
Step-by-step explanation:
The greatest common factor (GCF) of 48 and 6 is 6, so:
48 - 6 = 42.
this isn't college level *laugh*
4. Computing costs to rent an LCD projector. Cesar is renting an LCD projector. The rental company charges a $10 flat fee for administrative costs plus $18 per day for the projector. If Cesar
had a bill of $82, how many days did he keep the projector?
If Cesar had a bill of $82 for renting an LCD projector, he kept the projector for 4 days, based on the linear equation.
How the number of days are determined?To determine the number of days the projector, we deploy linear equation, which is in the form of y = mx + b, where m is the slope, x and y are variables, and b is the y-intercept.
The flat fee for administrative costs = $10
The variable cost per day = $18
The total bill for renting the projector = $82
The number of days = x
Linear Equation:10 + 18x = 82
18x = 72
x = 4
Check:
10 + 18x = 82
10 + 18(4) = 82
10 + 72 = 82
82 = 82
Thus, setting a linear equation, we can determine the number of days the projector was rented as 4 days.
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In the given figure, mHK = 50° and m/GKL = 50°.
Which statement is true?
The measure of ZJ is 25°, and triangle JKG is isosceles.
The measure of ZJ is 50°, and triangle JKG is isosceles.
The measure of ZJ is 25°, and triangle JKG is not isosceles.
The measure of ZJ is 50°, and triangle JKG is not isosceles.
Answer:
Step-by-step explanation:
The answer is A have a nice day :)
diameter of a circle is 13 ft. Find its circumference in terms of pi
Answer:
Step-by-step explanation:
C= 2pi
15= diameter. Radius= 13/2. R= 7.5
C= 2 times pi times 7.2
C=13 pi
C= 47.1
Ver en español
Carmen went rock climbing at the climbing gym for 1
1
2
hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for 1
1
2
times as long. How much time did she spend rock climbing in all?
The total time taken by Carmen in climbing the rocks will be 2¹/₄ hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Carmen went rock climbing at the climbing gym for 1¹/₂ hours on Thursday. On Saturday, she went to Castle Rock State Park and climbed for 1¹/₂ times as long.
The total time of climbing will be calculated as:-
Time = 1¹/₂ x 1¹/₂
Time = ( 3 / 2 ) x ( 3 / 2 )
Time = 9 / 4
Time = 2¹/₄ hours.
Hence, the climbing time would be 2¹/₄ hours.
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A square membrane, size 1X1 is placed on the xy-plane. The edges of the membrane are held fixed and the membrane is stretched into a shape modeled by the function f(x,y)=x(x-1)y(y-1). Supposed that the membrane starts to vibrate from rest. Determine the position of each point on the membrane for t>0. For this problem take c= t so that the equation to solve is up 3 (14+Uv) ; 0
The position of each point on the membrane for t>0 is given by u(x,y,t) = x(x-1)y(y-1) + (14+u) c2t.
The position of each point on the membrane can be determined by solving the equation u xx + u yy = c2u, where u is the displacement of the membrane from its equilibrium position and c is the speed of the wave propagation. Since we are given f(x,y) = x(x-1)y(y-1), we can solve this equation to find u. Differentiating f(x,y) twice with respect to x and y gives us the corresponding derivatives of u. Plugging these derivatives into the equation gives us u xx + u yy = (14+u) c2. Solving this equation yields the displacement of each point on the membrane for t>0. Thus, the position of each point on the membrane for t>0 is given by u(x,y,t) = x(x-1)y(y-1) + (14+u) c2t.
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Grandma Gertrude gave 131313 pieces of jewelry and Grandma Fien gave yyy pieces of jewelry to the Carlson sisters to divide evenly among themselves. There are 555 Carlson sisters.
In a case whereby Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves the number of pieces of jewelry that each sister receive can be expreesed as (13 + y)/5.
How can the the number of pieces of jewelry be calculated?The concept that will be used here is simplification. The pieces of jewelry by Grandma Gertrude is 13 pieces
Then the pieces of jewelry by Grandma Fien can be seen as " y ".
Since 5 Carlson sisters available . The number of pieces of jewelry each sister receive. can be calculated as:
Total jewlry= (13 + y) which is needed by 5 sisters, the each of the sisters will have = [(13 + y)/5]
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complete quesion:
Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves. There are 5 Carlson sisters.
How many pieces of jewelry did each sister receive?
I need help solving this
41x-2
99⁰
140⁰
The value of x based on the information about the triangle is 3.
How to calculate the value of xIt should be noted that the total sum of angles in a triangle is 180°. Based on the information given, this will be illustrated as:
180 - (180 - 140) - (180 - 99)
= 180 - 40 - 81
= 59
Therefore, 41x - 2 + 59 = 180
41x = 180 + 2 - 59
41x = 123
Divide
x = 123 / 41.
x = 3.
The value of x is 3.
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I understand how to make stemplots, but am unsure how to write the data down with the truncated leaf unit of 10. Would 359 be under 3|5, like the example given in the question gives?
The stem-leaf representation of the data is,
0|7 9 9
1|0 1 3 4 4 4 4 5 5 7 7
2|0 5 7
3|5.
What is the stem-leaf plot?The values of the data are divided into a stem and a leaf in a stem-leaf plot.
The initial digit or digits will be put in the stem position, and the final digit will be written in the leaf position.
Let us first rearrange the data in ascending order,
78, 95, 96, 103, 112, 134, 141, 145, 147, 148, 153, 158, 172, 172, 200, 255, 271, 359.
The data is down with the truncated leaf unit of 10, 1|4 represents a number in the 140s.
0|7 9 9
1|0 1 3 4 4 4 4 5 5 7 7
2|0 5 7
3|5.
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Algebra question please helppp
Answer:
min -1 max 3
Step-by-step explanation:
min: when x= -10 so f(x) = ∛-1 = -1
max: when x= 18 so f(x) = ∛27= 3
You know," Ernesto said, "I could help you remember iready pls helps
Answer:
Which tools you need to usethe management of your team wants you to run descriptive statistics on the points scored by your team in the games played at your team's venue in 2013-2015. calculate descriptive statistics including the mean, median, variance, and standard deviation for points scored by your team played at home. make the following edits to the code block below:
in order to calculate the descriptive statistics for the points scored by the team at home in 2013-2015, the mean, median, variance and standard deviation must be calculated using the appropriate formulas.
Descriptive Statistics
Mean: This is a measure of the center of the distribution, calculated as the sum of all values divided by the number of values. In this case, it is the average number of points scored by the team at home in 2013-2015. Formula: Mean = (Sum of all values)/(Number of values).
Median: This is the middle value of the data set after it is sorted in numerical order. It is the value that separates the upper half of the data set from the lower half. In this case, it is the middle value of the points scored by the team at home in 2013-2015. Formula: Median = (Sum of the lower and upper halves of the data set)/2.
Variance: This is a measure of how spread out the data set is, calculated as the sum of the squared differences between each value and the mean, divided by the number of values. In this case, it is the variance of the points scored by the team at home in 2013-2015. Formula: Variance = (Sum of the squared differences between each value and the mean)/(Number of values).
Standard Deviation: This is a measure of how spread out the data set is, calculated as the square root of the variance. In this case, it is the standard deviation of the points scored by the team at home in 2013-2015. Formula: Standard Deviation = Square Root of Variance.
Therefore, in order to calculate the descriptive statistics for the points scored by the team at home in 2013-2015, the mean, median, variance and standard deviation must be calculated using the appropriate formulas.
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simplify the following monomial: 16x^2y-4xy^2-5x^2y+10xy^2
The required simplified form of the given monomial is 11x²y + 6xy².
What is the expression?Expressions are defined as mathematical statements that have a minimum of two terms containing variables or numbers.
The monomial is given in the question, as follows
16x²y - 4xy²- 5x²y + 10xy²
Rearrange the like terms in the above expression,
16x²y - 5x²y - 4xy² + 10xy²
Add similar elements,
11x²y - 4xy² + 10xy²
Subtract similar elements, and we get
11x²y + 6xy²
Thus, the required simplified form is 11x²y + 6xy².
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line a passes through the points (0,4). line b passes through the points (0,7) and (7,0). are the lines parallel
Both lines A and line B have the same slope, hence they are parallel
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The slope of the line passing through points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Two lines are parallel to each other if they have the same slope.
Line A passes through the points (0,4) and (4, 0)
Slope = (0 - 4) / (4 - 0) = -1
Line B passes through the points (0,7) and (7, 0)
Slope = (0 - 7) / (7 - 0) = -1
Since both lines have the same slope, they are parallel
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I need Help on this question.
The equation that represents "triple the input, then subtract 5" will be written as y = 3x - 5.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The output is less than 5 to 3 times the input.
Let 'x' be the input and 'y' be the output. Then the equation is given as,
y = 3x - 5
The equation that represents "triple the input, then subtract 5" will be written as y = 3x - 5.
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Given f(x) = 2x² - x - 12, find f (8)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{f(x) = 2x^2 - x - 12}[/tex]
[tex]\mathsf{f(x) = 2(8)^2 - 8 - 12}[/tex]
[tex]\mathsf{f(x) = 2(8^2) - 8 - 12}[/tex]
[tex]\mathsf{f(x) = 2(8 \times 8) - 8 - 12}[/tex]
[tex]\mathsf{f(x) = 2(64) - 8 - 12}[/tex]
[tex]\mathsf{f(x) = 128 - 8 - 12}[/tex]
[tex]\mathsf{f(x) = 120 - 12}[/tex]
[tex]\mathsf{f(x) = 108}[/tex]
[tex]\huge\text{Therefore your answer should be: }[/tex]
[tex]\huge\boxed{\mathsf{f(x) = 108}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which best describes the solution set for the inequality below?
3x + 7 ≤4x-8 or-2x + 3≥1
Ox≤1or x ≥ 15
Ox≥1 orx≤ 15
Ox≥1
Ox≤ 15
The solution for the given inequalities is x≥15 or x≤1. Therefore, option A is the correct answer.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
The given inequalities are 3x + 7 ≤ 4x-8 or-2x + 3≥1.
Here, 3x + 7 ≤ 4x-8
Subtract 3x on both the sides of an inequality, we get
7 ≤ x-8
Add 8 on both the sides of an inequality, we get
15≤ x
x≥15
Here, -2x + 3≥1
Subtract 3 on both the sides of an inequality, we get
-2x≥-2
Divide -2 on both the sides of an inequality, we get
x≤1
So, x≥15 or x≤1
Therefore, option A is the correct answer.
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The midpoints of the three sides of a triangle are P(-7; -2), Q(-1; 9) and R(5; -3).
Calculate the area of the circumscribed circle of the triangle.
Therefore , the solution of the given problem of area comes out to be Area of circle 85π cm2.
Describe surface areaIts surface area provides a good estimate of its overall size. When computing a right triangle's squared, the surroundings are taken into consideration. The surface area of everything determines its overall size. The sum of the volumes on each of the six horizontal sides makes up the volume of water inside a cuboid. Utilize the following formula to get the box's dimensions: In 2lh, 2lw, and 2hw, the region is the same (SA). The flexible shape's total area serves as a representation of the area.
Here,
Given:
Points :P(-7; -2), Q(-1; 9) and R(5; -3).
The area of the circumscribed circle of the triangle.
is:
=> PQ = √(-7 - (-1))² + (-2 - (-9))²
=> PQ = √85
The radius is √85
=> Area of circle = π(√85)²
=> Area of circle = 85π cm2
Therefore , the solution of the given problem of area comes out to be Area of circle : 85π cm2.
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Choose all of the statements about the quadrilateral and/or the transformed quadrilateral that are correct.
A. The quadrilaterals will be congruent.
B. The quadrilateral will map onto itself.
c. The quadrilateral will now appear in Quadrant IV.
D. The quadrilaterals will have the same orientat
E. The quadrilaterals will be similar but not cong
The statements about the quadrilateral and/or the transformed quadrilateral that are correct are:
The quadrilaterals will be congruent.
Option A is the correct answer.
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
From the graph,
Quadrilateral WXYZ.
We see that,
Quadrilateral WXYZ is in the III Quadrant.
Step 1:
Rotated 180° about the origin.
This means,
Quadrilateral WXYZ is in the I Quadrant.
Step 2:
Reflection across the y-axis.
This means,
Quadrilateral WXYZ is in the II Quadrant.
Now,
Since there is no dilation the transformed quadrilateral will be congruent.
Thus,
The quadrilaterals will be congruent.
Quadrilateral WXYZ is in the II Quadrant.
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The complete question is:
Quadrilateral WXY will be rotated about the origin and then reflected across the y-axis. Choose all of the statements about the quadrilateral and/or the transformed quadrilateral that are correct.
A is four more than three times of B
Answer:
A = 3 * B + 4
Step-by-step explanation:
A - 4=3 * B (given)
A = 3 * B + 4
At least one of the slopes in a system is positive. One of the y Intercepts is above the x-axis and he other is below the x axis and the stopes are opposite reciprocals are each other. The lines meet at where the x value is 6 and the y value is -2 and both of the equations are given in slope-Intercept form. What is the solution to this system?
The solution to the system of equations shown in the graph is (6, -2)
What is an equation?An equation is an expression that uses mathematical operations to show the relationship between numbers and variables. Types of equations are linear, quadratic, cubic and so on.
The standard form of a linear equation is:
Ax + By = C
Where A, B and C are constants
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope and b is the y intercept
The solution to a system of linear equations is the point where the two lines meet.
The lines meet at where the x value is 6 and the y value is -2, hence the solution is (6, -2)
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6th grade math please help (only answer if you know the answer don't guess PELASEE) Marking brainlist!! QUESTION WORTH 60 POINT!!
Which ordered pair represents the point labeled as G?
negative one-half, one and one-fourth
three-fourths, three-fourths
0, negative one and one-fourth
negative one and one-fourth, negative one-half
Answer:
negative one and one-fourth, negative one-half
Step-by-step explanation:
it seems to be the only possible answer because the y value is negative one half
Answer: negative one and one-fourth, negative one-half
If the force acting on an object stays the same, then the acceleration of the object varies inversely as its mass. If an object with a mass of 27 kilograms accelerates at a rate of 2 meters per second per second by a force, find the rate of acceleration of an object with a mass of 3 kilograms that is pulled by the same force.
The rate of acceleration of an object with a mass of 3 kilograms that is pulled by the same force is given as follows:
18 m/s².
What is the relation between force, mass and acceleration?According to Newton's Second Law, the force is given by the multiplication of the mass and of the acceleration, as follows:
F = ma.
The force is obtained as follows, considering a mass of 27 kg and an acceleration of 2 m/s².
F = 27 x 2
F = 54N.
Then the acceleration of an object of 3 kilograms with the same force is given as follows:
3a = 54
a = 54/3
a = 18 m/s².
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The measure of one of the small angles of a right triangle is 45 less than twice the measure of the other small angle. Find the measure of both angles
The measure of both angles is 45.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Right triangle:
One angle = 90
Other angles:
One = 2x - 45
Another = x
Now,
The sum of the three angles = 180
90 + x + 2x - 45 = 180
Add like terms.
90 + 3x - 45 = 180
Add 45 on both sides.
90 + 3x = 180 + 45
Subtract 90 on both sides.
3x = 225 - 90
3x = 135
Divide 3 into both sides.
x = 45
Now,
Other angles:
One = 2 x 45 - 45 = 45
Another = 45
Thus,
Both angles are 45.
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a series is given by 131+232+333+434+535+.... francine correctly applies the ratio test to determine whether the series converges or diverges. which statement reflects francine's conclusion?
A series is given by 131+232+333+434+535+.... francine correctly applies the ratio test, the statement that reflects francine's conclusion is From the ratio test, r=1/3. The series converges.
We must calculate the ratio between two successive phrases in order to perform the ratio test:
The nth term is n / 3n.
The (n + 1)th term is (n + 1) / 3n + 1.
The ratio test: lim | [ (n + 1) / 3n + 1 ] / [ n / 3n ] |
= lim | [ (n + 1) / n ] · [ 3n / 3n + 1 ] |
= lim | [ (n + 1) / n ] · [ 1/3 ] |
= (1/3) · lim | (n + 1) / n |
= (1/3) · lim | ( n/n ) + (1/n) |
= (1/3) · lim | 1 + (1/n) |
= (1/3) · [ lim | 1 | + lim | 1/n |
= (1/3) · [ 1 + 0 |
According to the ratio test, the series converges if this ratio is between -1 and 1 (excluded). This sequence thus comes together.
= (1/3) <--- converges
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Answer:
From the ratio test, r=13. The series converges.
Step-by-step explanation:
I took the Test
Explain how you would draw the triangle given three side lengths: 6 cm, 7 cm, and 9 cm.
Answer:
see attached
Step-by-step explanation:
You want instructions for drawing a triangle with side lengths 6 cm, 7 cm, and 9 cm.
Side lengthsIt works reasonably well to ...
Mark the longest side (9 cm) on a straight line using a ruler. Set a compass to 6 cm and draw an arc using one of the end points as the center.Repeat from the other end point using a setting of 7 cm.The point where the arcs cross is the third vertex of the triangle.
Draw the triangle by connecting the vertices using a straightedge.Below are two inequalities and the graphs of their lines without the shading. By
imagining where the shading should be, identify which point would satisfy BOTH
inequalities.
y<-5/6x+2
y>1/3x+3
Shaded region is between the lines corresponding to both inequalities.
Point that satisfy both inequalities is (-6/7 , 19/7)
What is inequality?Inequalities are the mathematical expressions in which both sides are not-equal. In inequality, unlike in equations, we compare two values.
Given inequalities
y<(-5/6)x+2
equation of the line becomes
y = (-5/6)x + 2 ------(1)
y>(1/3)x+3
equation of the line becomes
y = (1/3)x + 3 --------(2)
By the inequalities
(1/3)x + 3 < y < (-5/6)x + 2
shaded region should be between the lines.
Solving equation 1 and 2
(-5/6)x + 2 = (1/3)x + 3
(-5/6)x - (1/3)x = 3 - 2
(-5 - 2)x/6 = 1
-7x = 6
x = -6/7
Putting value of x in equation 2
y = (1/3)(-6/7) + 3
y = -2/7 + 3
y = (-2 + 21)/7
y = 19/7
Point is (-6/7 , 19/7)
Hence, point that satisfy both inequalities is (-6/7 , 19/7),
shaded region is between both lines corresponding to the inequalities.
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A man is disabled in an accident and wants to receive an insurance payment that will provide him with $2400 at the
end of each month for 20 years. If the payment can be placed in an account that pays 6% compounded monthly, what
size payment should he seek?
He should seek a payment of $
(Simplify your answer. Round to the nearest cent as needed.)
The man should seek a payment of $725.08
How to determine the size paymentThe amount of money he wants to receive can be calculated using the formula for compound interest:
A = P * (1 + r/n)^(nt)
where A = $2400 ---- final amount
P = principal
r = 6%, -- interest rate
n = 12 --- number of times the interest is compounded
t = 20, number of years (20).
So, we have
2400 = P * (1 + 6%/12)^(12 * 20)
This gives
P = 2400/3.310
Evaluate
P = 725.08
So, the man should seek a payment of $725.08
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If a population has mean 100 and standard deviation 20, what is the mean of the sampling distribution of sample size n = 252 b. If a population has mean 100 and standard deviation 20, what is the standard deviation of the sampling distribution of sample size n = 25? 4 c. A given exam has a normal distribution with a mean of 70 and a standard deviation of 10. A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to fall between 66 and 74? d. A given exam has a normal distribution with a mean of 70 and a standard deviation of 10. A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to be less than 70? % e. A given exam has a normal distribution with a mean of 70 and a standard deviation of 10. A sample of size 25 is selected. What percentage of the time would you expect the mean of this sample size to be greater than 68? %
The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.
a. If a population has a mean of 100 and a standard deviation of 20, then the mean of the sampling distribution of a sample size of n=252 will be 100. This is because the sample means of a sampling distribution will always be equal to the population mean.
b. The standard deviation of the sampling distribution of a sample size of n=25 is 4. This is calculated using the formula: σx = σ/√n, where σ is the population standard deviation (20) and n is the sample size (25).
c. The percentage of the time you would expect the mean of the sample size to fall between 66 and 74 is 68.27%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the upper limit (74), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the upper limit is (74-70)/10=0.4. We then use the standard normal table to find the area between -∞ and 0.4, which is 0.6827.
d. The percentage of the time you would expect the mean of the sample size to be less than 70 is 50%. This is because the Z-score for a mean of 70 is 0, and the area below 0 is 0.5 or 50%.
e. The percentage of the time you would expect the mean of the sample size to be greater than 68 is 84.13%. This is calculated using the Z-score formula, which is (x-μ)/σ, where x is the lower limit (68), μ is the population mean (70), and σ is the population standard deviation (10). The Z-score for the lower limit is (68-70)/10=-0.2. We then use the standard normal table to find the area between -∞ and -0.2, which is 0.8413.
The percent of the time you would expect the mean of the sample size of 25 to fall between 66 and 74 is 68.27%, to be less than 70 is 50%, and to be greater than 68 is 84.13%.
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