Step-by-step explanation:
[tex]\tt 33-5(x-4)=3[/tex]
[tex]\tt 33-5x+20=3[/tex]
[tex]\tt 53-5x=3[/tex]
[tex]\tt -5x=3-53[/tex]
[tex]\tt 5x=50[/tex]
[tex]\tt x=10[/tex]
I hope it's helpful
What is 1800 * ? * 1 = 198
1800 * ? * 1 = 198
let x be the ?
By shifting 1800*1 into right hand side
x= 198/1800
x= 11/100= 0.11
Final answer = 0.11
Chris is buying a yard of material for a art project. two stores have the material she needs. compare prices to find which material is the better. explain how you know
artistic supplies- $1.25ft
craft center- $3 yards
As a pot of tea cools, the temperature of the tea is modeled by a differentiable function H for Osts 10, where time t is measured in minutes and temperature H(t) is measured in degrees Celsius. Values of H(t) at selected values of time t are shown in the table. Use a trapezoidal sum with the four subintervals indicated by the table to estimate 1 10 Soº H
By using the Trapezoidal sum with the four subintervals indicated by the table the sum is 52.95.
What is Trapezoidal sum?
The trapezoidal rule is a method for roughly approximating the definite integral in calculus. The area of the region that roughly fits the shape of a trapezoid under the graph of the function f(x) is how the trapezoidal rule operates.
A Riemann sum is a technique for calculating the area under a curve by adding the areas of rectangles or trapezoids drawn along the curve. Triangular Riemann Sum: A trapezoidal Riemann sum determines the area under a curve by adding the areas of trapezoids.
Let, [tex]\frac{1}{10}\int\limits^1_00 {H(t)} \, dt[/tex] is the average temperature of the tea, in degree Celsius, over the 10 minutes.
[tex]\frac{1}{10}\int\limits^1_0_0 {H(t)} \, dt = \frac{1}{10}(2*\frac{66+60}{2}+ 3*\frac{60 + 52}{2}+4*\frac{52+44}{2}+1*\frac{44+43}{2} \\ \frac{1}{10}\int\limits^1_0_0 {H(t)} \, dt = 52.95[/tex]
Hence, by using the Trapezoidal sum with the four subintervals indicated by the table the sum is 52.95.
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What is the equation of the line in slope-intercept form that passes through point (4, 5) and is parallel to the line y = −2x − 2?
Answer:
y = -2x + 13
Step-by-step explanation:
In order to write an equation of the line in slope-intercept form, we first have to look at the equation:
y = mx + b
We know that m represents slope, and b represents the y-intecept, in other words, what y is equal to when x is equal to zero.
We already have y and x, (4,5), and the slope of the line, since the two lines are parellel, they share the same slope. So now, we have to pulg those values into the equation and solve for b:
(4,5)
y = 5
x = 4
m = -2
y = mx + b
(5) = (-2)(4) + b
5 = -8 + b
13 = b
So, equation of the line in slope-intercept form that passes through point (4, 5), is y = -2x + 13
Remeber that you can always graph to check your work!
I hope this helps! :)
this is a late assignment and I am really close to failing please help
Answer: 14.825
Step-by-step explanation:
First , do 2 * 5.3 because it's 2a, you'll have to do 2 * a. This equals 10.6.
Second, you'll need to do 5.3 * 1.25. Why? Because in the problem you need to do a * b, which is that. It equals 6.62500.
Lastly, put it all together! 10.6 + 6.62500 - 2.4 equals 14.825.
What is the volume, in cubic inches, of the cone below?
Answer:
27π
Step-by-step explanation:
Volume = 1/3πr²h
=1/3*(3)²9π
=27π
◄) A large square is composed of 16 smaller squares that are all the same size. Each of the small squares has an area of 4 square units. What is the side length of the large square?
Answer:
8
Step-by-step explanation:
Each of the small squares has an area of 4 square units
so its length is 2 because 2*2 =4
so 4 small squares = 8 each side
The coefficient of x^7 in the expression (x^3+4/x^2)^4 is
The coefficient of x⁷ in the given expression is 16.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
Given is the expression [x³ + (4 / x²)]⁴.
[x³ + (4 / x²)]⁴ = (x³ + 4x⁻²)⁴
= (x³ + 4x⁻²)² (x³ + 4x⁻²)²
= (x⁶ + 8x + 16x⁻⁴) (x⁶ + 8x + 16x⁻⁴)
= x¹² + 8x⁷ + 16x² + 8x⁷ + 64x² + 128x⁻³ + 16x² + 128x⁻³ +
256x⁻⁸
Rearranging with like terms, we get,
= x¹² + 16x⁷ + 96x² + 256x⁻³ + 256x⁻⁸
Hence the coefficient of x⁷ is 16.
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a disabled sailboat is drifting in a straight line at 4 miles per hour. a coast guard rescue craft is trailing it by 11 miles, moving along the same path at a rate of 29 miles per hour. how long will it be before the rescue craft reaches the sailboat?
It will take the rescue craft 0.44 hours or 26.4 minutes to reach the sailboat.
The time required for the rescue craft to reach the sailboat can be calculated by using the formula for relative velocity:
Relative Velocity = Velocity of the Rescue Craft - Velocity of the Sailboat
= 29 mph - 4 mph = 25 mph
Therefore, the time required for the rescue craft to reach the sailboat is given by:
time= Distance/Relative Velocity
= 11 miles/25 mph
= 0.44 hours
Therefore, it will take the rescue craft 0.44 hours or 26.4 minutes to reach the sailboat.
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Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
y=88(0.977)^x
3% is the percentage rate of increase or decrease.
What does exponential decay mean?
A process known as exponential decay describes how a quantity depletes over time, with the rate of depletion become proportionately slower as the quantity shrinks. Finding the exponential drop—a rapid reduction over time—is made easier by the exponential decay formula.
The exponential decay formula is used to calculate various types of decay, including radioactivity decay, half-life, and population decay. The formula for f(x) is f(x) = a (1 - r)x.
The formula for exponential decay is y=a(1-r)x.
r is the decay rate, expressed as a decimal.
In this case, r = .03 which represents 3%
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one person drives 70,000 miles in a car that averages 30 miles per gallon (mpg). how much gasoline are they using?
The person is using approximately 2,333.333 gallons of gasoline.
The average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.
To calculate the amount of gasoline used, you can use the formula:
gasoline used = total miles driven / mpg
Where total miles driven is 70,000 miles and mpg is 30.
Plugging these values into the formula, we get:
Gasoline used = 70,000 miles / 30 mpg = 2,333.333 gallons
So the person is using approximately 2,333.333 gallons of gasoline.
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How do you prove theorem 8.9 Class 9?
In the triangle the line segment joining the midpoints 'S' and 'T' of the sides PQ and PR implies that ST || QR.
As given in the question,
Diagram is attached.
As per the attached diagram we have,
Given : In triangle PQR with midpoints S and T of sides PQ and PR respectively.
To prove : ST is parallel to QR.
Proof : First construct a line through R parallel to PQ such that it meet the extended line of ST at point 'U'
In triangle PST and triangle RTU,
PQ|| RU and SU is the transversal
∠PST ≅ ∠RUT ( alternate angles )
∠PTS ≅ ∠RTU ( vertically opposite angles)
PT ≅TR ( 'T' is the midpoint of PR )
By AAS we have
ΔPST ≅ΔRTU
By congruent part of congruent triangle we have,
PS ≅ RU
⇒ SQ ≅ RU
In quadrilateral QSUR,
SQ ≅ RU
SQ || RU ( as PQ || RU by construction )
Quadrilateral with one pair of opposite side congruent and parallel implies it is a parallelogram.
Quadrilateral QSUR is a parallelogram.
⇒ SU || QR
S - T - U
⇒ ST is parallel to QR
Therefore, in the given triangle line segment formed by joining the midpoints of the other two sides is parallel to third side.
The above question is incomplete , the complete question is :
Prove theorem 8.9 : The line segment joining the midpoints of the two sides of the given triangle is parallel to the third side .
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evaluate the double integral_d (x^2 + 2y) dA, D is bounded by y = x, y = x^3, x ≥ 0
After evaluating the double integral, the result, 0.27, is determined by the stated statement.
What is the definition of an integral?In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or maybe a new function, the inverse of which comprises the original result (indefinite integral). The value produced after integrates or adding the words of a function that is split into an unending number of terms is referred to as an integral value in general.
The double integral is an example.
[tex]\iint_D\left(x^2+2 y\right) d A[/tex] where d is enclosed by the lines y = x & y = x³.
In the region D, x varies from 0 to 1, and y varies from y = x³ to y = x
[tex]\therefore \iint_D\left(x^2+2 y\right) d A=\int_{x=0}^1 \int_{y=x^3}^x\left(x^2+2 y\right) d y d x[/tex]
[tex]=\int_{x=0}^1\left[x^2 y+y^2\right]_{x^3}^x d x[/tex]
[tex]=\int_{x=0}^1\left[x^2\left(x-x^3\right)+\left[x^2-\left(x^3\right)^2\right]\right] d x=\int_{x=0}^1\left[x^3-x^5+x^2-x^6\right] d x[/tex]
[tex]\left.=\frac{x^4}{4}-\frac{x^6}{6}+\frac{x^3}{3}-\frac{x^7}{7}\right]_0^1[/tex]
= [tex]\frac{1}{4}-\frac{1}{6}+\frac{1}{3}-\frac{1}{7}[/tex]
= 23/84
= 0.27
[tex]\therefore \iint_D\left(x^2+2 y\right) d A=0.27[/tex]
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The area and perimeter of arectangular field are 60m² and 32 m respectively. Find the length and breadth of the fueld
This square-based oblique pyramid has a volume of 125\text{ m}^3125 m 3 125, start text, space, m, end text, cubed. 5\text{ m}5 m5\text{ m}5 m What is the height of the pyramid
If the volume of the square based Pyramid is 125 m³ and the base is of 5m then the height of the pyramid is 15 m .
The Volume of the Square based pyramid is = 125 m³ ;
the measure of the side of base of pyramid is = 5m ;
So , the Area of the base of pyramid is = [tex]5 \times 5[/tex] = 25 m² ;
We know that the formula for the Volume of the pyramid is = [tex]\frac{1}{3} \times Area\; Of \;Square \times Height[/tex] ;
Substituting the values ;
we get ;
⇒ [tex]125= \frac{1}{3} \times 25 \times Height[/tex] ;
On solving further ,
we get ;
⇒ [tex]\frac{125\times 3}{25}[/tex]
⇒ 15 m .
Therefore , The Height of the Pyramid is 15 m.
The given question is incomplete , the complete question is
This square-based oblique pyramid has a volume of 125 m³ and the length of the side of the base is 5m . What is the height of the pyramid ?
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you are driving on a highway and are about 140 miles from a state border. you set your cruise control at 60 miles per hour and plan to turn it off within 30 miles of the border on either side. find the minimum and maximum numbers of hours you will have cruise control on.you will travel at least hour(s) and at most hour(s) with cruise control on.
The minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).
To find the minimum and maximum numbers of hours you will have cruise control on, you need to calculate the distance you will travel with cruise control on and divide it by your speed.
The minimum distance you will travel with cruise control on is
140 miles - 30 miles = 110 miles.
The maximum distance you will travel with cruise control on is
140 miles + 30 miles = 170 miles.
To convert these distances into hours, you will divide them by your speed of 60 miles per hour.
Minimum hours: 110 miles / 60 mph = 1.83 hours
Maximum hours: 170 miles / 60 mph = 2.83 hours
Therefore, the minimum number of hours you will have cruise control on is 1.83 hour(s) and the maximum is 2.83 hour(s).
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Find the area of the following figure. Pictures are not drawn to scale. Round answers to the nearest tenth.
The area of the trapezium is 36.3 unit squared.
How to find area of a figure?The figure above is a trapezium. Therefore, the area of a trapezium can be represented as follows:
Hence,
area of a trapezium = 1 / 2 (a + b)h
where
h = heighta and b are the top and base of the trapeziumTherefore,
area of a trapezium = 1 / 2 (a + b)h
where
a = 4b = 7 + 1.5 = 8.5Using Pythagoras's theorem,
c² = a² + b²
where
a and b are the legsc is the hypotenuseh² = 6² - 1.5²
h²= 36 - 2.25
h = √33.75
h = 5.80947501931
h = 5.81
Therefore,
area of the trapezium = 1 / 2 (4 + 8.5)5.8
area of the trapezium = 1 / 2 (12.5)5.8
area of the trapezium = 72.5 / 2
area of the trapezium = 36.3 units²
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Need help 30 points....
in triangle abc, the measure of the largest angle is 32 less than 3 times the smallest angle. the measure of the middle angle is 8 more than half the measure of the largest angle. what is the measure of the middle angle? _______ degrees
The measure of the middle angle of triangle abc is 52°
Let the largest angle of triangle be x, the smallest angle be z, and the third angle be y.
Given that the measure of the largest angle is 32 less than 3 times the smallest angle.
So, we get an equation,
x = 3z - 32 ............(1)
Also, the measure of the middle angle is 8 more than half the measure of the largest angle.
So, we get an equation,
y = 8 + (x/2) .......(2)
From equation (1),
z = (x + 32)/3 ..........(3)
We know that the sum of all angles of triangle is 180 degrees.
x + y + z = 180
Substitute the values of y and z in above equation.
x + 8 + (x/2) + (x + 32)/3 = 180
6x + 48 + 3x + 2(x + 32) = 1080
9x + 48 + 2x + 64 = 1080
11x + 112 = 1080
11x = 1080 - 112
11x = 968
x = 88
Substituting above value of x in equation (2)
y = 8 + (88/2)
y = 8 + 44
y = 52 degrees
Therefore, the middle angle of triangle measures 52 degrees.
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ace pharmaceutical has developed a drug that it believes will help lower cholesterol and blood pressure at a significantly greater rate than fish oil. researchers wish to test the new drug and compare the results to those of fish oil and of a placebo. a total of 300 volunteers suffering from hypertension and high cholesterol will participate in the study. part a explain how you would carry out this test in a completely randomized experiment.
The subjects would be randomized at random to receive the new medication, fish oil, or a placebo. The effectiveness of the new variance medicine would next be evaluated by comparing the outcomes of the various therapies.
The test would be conducted using a completely randomized experiment. This means that the 300 volunteers would be randomly assigned to the three different treatments: the new drug, fish oil, or the placebo. This ensures that any differences between the groups can be attributed to the treatments, and not any other factor. The volunteers would be monitored for a period of time, and the results of the treatments would be compared to determine the effectiveness of the new drug. This could be done through measuring changes in cholesterol and blood pressure levels, as well as any side effects of the treatments. In addition, the volunteers’ health and dietary habits should be monitored to ensure that any differences between the treatments are not caused by any other factors.
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Find an equation for a line passing through (10,10) that is perpendicular to the line with equation 5x+8y=-9. Write your equation in
The equation of a line passing through (10,10) that is perpendicular to the line with equation 5x + 8y = -9 is y - 10 = (8/5)(x - 10) or y = (8/5)x - 6.
Get the slope of the line 5x + 8y = -9 by rewriting it in slope-intercept form. Subtract 5x from both sides and divide by 8.
y = (-5/8)x - (9/8)
The slope of this line is -5/8. The negative reciprocal of -5/8 is 8/5. Therefore, the slope of the line that is perpendicular to 5x + 8y = -9 is 8/5.
Using point-slope form, determine the equation of the line.
y - y₁ = m(x - x₁)
y - 10 = (8/5)(x - 10)
or using the slope-intercept form,
y = mx + b
y = (8/5)x + b
10 = (8/5)10 + b
b = -6
y = (8/5)x - 6
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(02.05 HC)
The functions f(x) = -(x + 4)2+2 and g(x) = (x - 2)2-2 have been rewritten using the completing-the-square method. Apply your knowledge of
functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning
X544
ΩΣ
For a quadratic function [tex]y=ax^2+bx+c[/tex], we know the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].
It is easy to see that for a function of the form [tex]y=a(x-h)^2+k[/tex], the vertex of the graph is a maximum if and only if [tex]a < 0[/tex], and a minimum if and only if [tex]a > 0[/tex].
Therefore, the vertex of the graph of [tex]f(x)[/tex] is a maximum, and the vertex of the graph of [tex]g(x)[/tex] is a minimum.
X, Y and Z form the vertices of a triangle, where
∠
YXZ = 57°,
∠
YZX = 47°, and XZ = 7.2cm.
Calculate the length of YZ rounded to 1 DP
Answer:
Step-by-step explanation:
In the diagram, four squares of side length 2 are placed in the corners of a square of side length 6. Each of the points $W$, $X$, $Y$, and $Z$ is a vertex of one of the small squares. Square $ABCD$ can be constructed with sides passing through $W$, $X$, $Y$, and $Z$. What is the maximum possible distance from $A$ to $P$
In this problem, you have a square with side length 6 and four smaller squares with side length 2 placed in the corners. The points W, X, Y, and Z are the vertices of the smaller squares. The goal is to find the maximum possible distance between points A and P.
[asy] size(200); pair A,B,C,D,P,W,X,Y,Z; A=(0,4); B=(4,4); C=(4,0); D=(0,0); P=(2,2); W=(0,6); X=(6,6); Y=(6,0); Z=(0,0); draw(A--B--C--D--cycle); draw(W--X--Y--Z--cycle); draw(A--P--C); label("A",A,NW); label("B",B,NE); label("C",C,SE); label("D",D,SW); label("P",P,S); label("W",W,N); label("X",X,NE); label("Y",Y,S); label("Z",Z,SW); [/asy]
The point A is located on the bottom-left corner of the square with side length 6, and the point P is the center of the square $ABCD$. To find the maximum distance from A to P, we need to find the longest diagonal of the square $ABCD$.
The longest diagonal of a square is the one that goes from one corner of the square to the opposite corner. In this case, the longest diagonal goes from point A to point C, which is a distance of 6 units. Therefore, the maximum possible distance from A to P is 6 units.
1kg of apples costs £1.12 more than 1 kg of pears.
1kg of apples costs £2.35 less than 1 kg of bananas.
Jackson buys 3 kg of apples, 3 kg of pears and 2 kg of bananas. The total cost is £25.02
How much does 1 kg of apples cost?
Answer:
1 kg of apples cost £2.96-----------------------------------------------
Let the cost of a 1 kg of apples be x.
Then pear costs x - 1.12 and banana costs x + 2.35.
The total cost is 25.02:
3x + 3(x - 1.12) + 2(x + 2.35) = 25.023x + 3x - 3.36 + 2x + 4.7 = 25.028x + 1.34 = 25.028x = 25.02 - 1.348x = 23.68x = 23.68/8x = 2.96In the figure, point $A$ is the center of the circle, the measure of angle $RAS$ is 74 degrees, and the measure of angle $RTB$ is 28 degrees. What is the measure of minor arc $BR$, in degrees
In circle A, angle RAS is 74 degrees and angle RTB is 28 degrees. The measure of minor arc BR is 81 degrees.
The figure is in the attached picture.
Notice that:
AS = AR = radii of the circle.
Hence, triangle SAR is an isosceles triangle, and ∠ASR = ∠ARS.
The sum of angles in a triangle is 180°.
Therefore,
∠ARS + ∠ASR+ 74° = 180°
Since ∠ASR = ∠ARS,
2∠ARS + 74° = 180°
2∠ARS = 106°
∠ARS = 53°
and
∠ASR = ∠ARS = 53°
Angle in a straight line:
∠AST + ∠ASR = 180°
∠AST = 180° - ∠ASR = 180° - 53° = 127°
Refer to triangle SAT:
∠SAT = 180° - 28° - 127° = 25°
The measure of minor arc BR = ∠RAB
∠RAB = 180° - 74° - 25°
∠RAB = 81°
The picture in your question is missing, but most likely it was in the attached picture.
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What is formula data type?
Formula data type is used to determine different values based on a variety of fields in the existing table.
It also helps to create a pattern that takes input from all the fields and gives you the final value. Other fields include constants or functions and by using formula data type, you can remove the need to repeatedly enter the same information again and again. It also eliminated the margin of error that could occur during manual entry in the entirety of your work. Formula data type is used to help solve a combination of different equations that have different fields and/or equations.
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How do I do this help me please
Answer: A. Yes
B. Yes
C. No
Step-by-step explanation:
A. 2z = 40 and z = 20, 20 is a solution of the equation because when you substitute z = 20 into the equation 2z = 40, the equation becomes true.
B. n + 5 = 20 and n = 15, 15 is a solution of the equation because when you substitute n = 15 into the equation n + 5 = 20, the equation becomes true.
C. v = 12 and v = 16, 12 is not a solution of the equation because v is assigned to 12 and 16 both, but the equation only has one solution, a variable can't be assigned to two different values.
In general, when solving equations, we check if the value of the variable makes the equation true. if it does it's a solution, if not it's not a solution.
two ice cream machines make a total of 320 gallons in a certain amount of time. working together for the same length of time, how many gallons of ice cream can each number of machines make? 3 ice cream machines
3 ice cream machines will make a total of 480 gallons for the same length of time and 4 ice cream machines will make a total of 640 gallons for the same length of time.
For the quantity 3 ice cream machines will make.
2 ice cream machines produce a total of 320 gallons in a certain amount of time.
If 2 ice cream machines can make a total of 320 gallons. Then,
3 ice cream machines will produce a total of x gallons in the same amount of time
x = (320 × 3)/2
x = 480 gallons
Hence, 3 ice cream machines will produce a total of 480 gallons.
For the quantity 4 ice cream machines will make.
If 2 ice cream machines can make a total of 320 gallons. Then,
4 ice cream machines will produce a total of y gallons in the same amount of time
y = (320 × 4)/2
y = 640 gallons
Hence, 4 ice cream machines will produce a total of 640 gallons.
--The given question is incomplete, the complete question is
"Two ice cream machines make a total of 320 gallons in a certain amount of time. Working together for the same length of time, how many gallons of ice cream can each number of machines make?
3 ice cream machines
4 ice cream machines"--
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A student used the sieve of eratosthenes to find all prime numbers less than 100. create a step-by-step set of directions to show how to complete it. use the word bank to help guide your thinking as you write the directions. some words may be used just once more than once or not at all.please help i am lost
Utilizing the Sieve of Eratosthenes method is simple. In order to encircle the remaining numbers, we must cancel all multiples of each prime number starting with 2 (including the number 1, which is neither a prime nor a composite).
What the sieve of Eratosthenes to find all prime numbers?The Sieve of Eratosthenes can be used to locate all prime numbers that are less than 100, as seen in the example below. In ten rows, start by writing the numbers 1 through 100.
Therefore, based on the preceding table, we can conclude that the prime numbers 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 are. There are ten prime numbers between 50 and 100 in all. The required prime numbers are those that are surrounded.
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what is the probability that the average electric service paid by the sample of electric service customers will exceed $170? show your work.
a) According to the central limit theorem, the mean is $142 and the standard deviation is $0.7488.
b) Nearly normal according to the central limit theorem.
c) 0.0901 = 9.01% probability that the average cable service paid by a sample of cable service customers exceeds $170 in the central limit theorem.
Normal probability distribution:
The normal probability distribution, discovered by Abraham De Moivre in 1733, approximates the binomial probability distribution when a particular experiment has a very large number of trials. In 1774 Laplace studied the mathematical properties of the normal probability distribution. By historical error, the discovery of the normal distribution was attributed to Gauss, first mentioned in his 1809 paper. In the 19th century, many scientists discovered that measurement errors in a particular experiment followed a pattern (usual error curve). ), which was very well approximated by this probability distribution.
Central Limit Theorem:
The central limit theorem is a statistical theory that for large sample sizes with finite variance, samples are normally distributed and the mean of the sample is approximately equal to the mean of the entire population.
According to the Question:
The average monthly charge is $142 with a standard deviation of $29.
This is μ = 142 and σ = 29
Part a:
The mean and standard deviation of the sampling distribution of x to show your research and support your argument:
1500 samples (over 30).
According to the Central Limit Theorem
The mean is 142 $
The standard deviation is s = [tex]\frac{29}{\sqrt{1500} }[/tex] = 0.7488
Part b:
Shape of sampling distribution of X.
Due to the large sample size, the shape of the sample distribution is almost normal. According to the central limit theorem, which states that the sampling distribution converges to the normal distribution as the sample size increases. Mean ~ N(142, 0.749²)
Part C:
The probability that the average cable service paid by a sample of cable service customers exceeds $170.
Therefore, by the central limit theorem, the p-value of Z when X= 170
Z = x - μ/ σ
By the Central Limit Theorem:
Z = 170 - 142 / 0.7488
= 28/ 0.7488
= 37.34 exceeds 0.9099
Using the Z probability calculator :
P(Z > 1.335) = 0.09093
Complete Question:
The amount people pay for cable service varies quite a bit but the mean monthly fee is $142 and the standard deviation is $29. the distribution is not normal many people pay about $76 for basic cable and about $160 for premium service but some pay much more. a sample survey is designed to ask a simple random sample of 1,500 cable service customers how much they pay. let x hat be the mean amount paid.
Part a: what are the mean an standard deviation of the sample distribution of x hat show your work and justify your reasoning.
Part b: what is the shape of the sampling distribution of x hat justify your answer.
Part C: what is the probability that the average cable service paid by the sample of cable service customers will exceed $170? show your work.
Learn more about Central Limit Theorem:
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