Answer:
a) the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204
b) the probability that the sample proportion will be within 0.04 of the population proportion is 0.95
c) sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061
d) the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088
e) gain in precision is 0.1402.
Step-by-step explanation:
a) Let p represent the
Given that
population proportion of complaints settled for new car dealers p = 0.75.
and n = 450
mean of the sampling distribution of the sample proportion is the population proportion p
i.e up° = p
mean of the sampling distribution of the sample proportion p° = 0.75
so standard error of the proportion is;
αp° = √(p( 1-p ) / n)
we substitute
αp° = √(0.75 ( 1-0.75 ) / 450)
=√(0.1875 / 450
= √0.0004166
= 0.0204
therefore the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204
b)
(p° - p) is within 0.04
so lets consider
p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 450)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 450))
= p( -0.04/0.0204 ≤ z ≤ 0.04/0.0204)
= p ( -1/96 ≤ z ≤ 1.96 )
= p( z < 1.96 ) - p( z < -1.96 )
now from the S-normal table,
area of the right of z = 1.96 = 0.9750
area of the left of z = - 1.96 = 0.0250
p( -0.04 ≤ p°- p ≤ 0.04) = p( z < 1.96 ) - p( z < -1.96 ) = 0.9750 - 0.0250
= 0.95
therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.95
c)
population proportion of complaints settled for new car dealers p = 0.75.
n = 200
mean of the sampling distribution of the sample proportion p°.
i.e up° = p
mean of the sampling distribution of the sample proportion p° = 0.75
Sampling distribution of the sample proportion p is determined as follows
αp° = √(p( 1-p ) / n)
we substitute
αp° = √(0.75 ( 1-0.75 ) / 200)
=√(0.1875 / 200
= √0.0009375
= 0.03061
therefore sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061
d)
(p° - p) is within 0.04
so lets consider
p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 200)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 200))
= p( -0.04/0.03061≤ z ≤ 0.04/0.03061)
= p ( -1.31 ≤ z ≤ 1.31 )
= p( z < 1.31 ) - p( z < -1.31 )
now from the S-normal table,
area of the right of z = 1.31 = 0.9049
area of the left of z = - 1.31 = 0.0951
p( -0.04 ≤ p°- p ≤ 0.04) = p( z < 1.31 ) - p( z < -1.31 ) = 0.9049 - 0.0951
= 0.8098
therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088
e)
From b), the sample proportion is within 0.04 of the population proportion; with the sample of 450 complaints involving new car dealers is 0.95.
sample proportion is within 0.04 of the population proportion; with the sample of 200 complaints involving new car dealers is 0.8098.
measured by the increase in probability, gain in precision occurs by taking the larger sample in part (b)
i.e
Gain in precision will be;
0.9500 − 0.8098
= 0.1402
therefore gain in precision is 0.1402.
Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.
Who is correct and why? Use the drop-down menus to explain your answer.
Choose
is correct because 2 11 is a Choose... ya
decimal that can be expressed as a
Choose...
Answer:
Hannah: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.Step-by-step explanation:
The answer choices are:
Gus: 2.11 repeats because there are two 1s.Gus: 2.11 is a repeating decimal because it stops.Hannah: 2.11 is a rational number because it's a decimal.Hannah: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.The correct one is:
Hannah: 2.11 is a terminating decimal that can be written as 2 11/100. Rational numbers can be expressed as fractions.A right triangle has hypotenuse with length 8 inches. If one leg is 5 inches long, how long is the other leg?
Using Pythagoras theorem,
[tex]\sf a^2 + b^2 = c^2[/tex]
Where [tex]\sf a[/tex] and [tex]\sf b[/tex] are the two legs of the triangle, and [tex]\sf c[/tex] is the Hypotenuse.
Putting the given values:
[tex]\sf 5^2 + b^2 = 8^2 \\ \longrightarrow \sf b^2 = 64 - 25 \\ \longrightarrow \sf b^2 = 39 \\ \longrightarrow \sf b = \sqrt{39}\:\:inches[/tex]
Hence, the length of the other leg is,
[tex]\leadsto \underline{\boxed{\mathfrak{\pink{\sqrt{39}\:\:inches}}}}[/tex]
PLZ HELP 100PTS!!! An explanation is welcome
Find the value of t, when d(t)=-24
d(t)=t/2
Answer:
[tex]t=-48[/tex]
Step-by-step explanation:
We have the function:
[tex]d(t)=\frac{t}{2}[/tex]
And we want to find t when:
[tex]d(t)=-24[/tex]
So, let's substitute -24 for our first equation and solve for t:
[tex]-24=\frac{t}{2}[/tex]
Multiply both sides by 2:
[tex]t=-48[/tex]
So, the value of t when d(t)=-24 is -48.
Answer:
Step-by-step explanation:
using the definition of multiplication to explain why a box that is 5 inches high 4 inches wide and 3 inches long has a volume of 5• (3•4) cubic inches explain the parentheses in the expression 5•(3•4)
Given:
Height of box = 5 inches
Breadth (width) of box = 4 inches
Length of box = 3 inches
Volume of box = 5 • (3 • 4) cubic inches
To find:
The explanation for the parentheses in the expression 5•(3•4)
Solution:
We know that,
Volume of a box is
[tex]Volume = length \times breadth \times height[/tex]
Area of a rectangle is
[tex]Area = length \times width[/tex]
Now,
Volume of box = 5 • (3 • 4) cubic inches
In this expression, (3 • 4) represents the product of length and with of the box. So, it means represents area of the base of box and after multiplying the base area with height we get the volume of the box.
Therefore, the parentheses in the expression 5•(3•4) represents the base area of the box.
In Earnest's Yard, the grass grew 2 inches. The next week, Earnest cut 2 inches off of the grass. The total change was 0 inches. Which of the following situations also has a total change of 0?
Answer:
7-7 = 0
Step-by-step explanation:
Sandy brought different toys from the market, she divided the seven toys into seven children , now she has a total of zero toys left
Total toys left = 7 - 7
Total toys left = 0
Ten years ago, Lisa bought a hair salon for 182000 dollars. She built up the business and it is now
worth nine times what she paid for it. She decides to sell half of the business to a friend, and they
become partners. Express the amount Lisa's friend must pay Lisa to buy half the business.
Answer: 819,000
Step-by-step explanation:
182000×9=1638000÷2=819000
Lisa's friend must pay Lisa $819,000 to become her partner in the business, half the worth of Lisa's business today.
What do we mean by the worth of an object?The worth of an object is the price of that object currently. The worth of almost every object in this world is variable (not fixed) with time and use.
How do we solve the given question?In the question, we are said that ten years ago, Lisa bought a hair salon for $182,000. Her business is now worth nine times what she paid.
∴ Worth of the business 10 years ago = $182,000.
Worth of the business now = 9*$182,000 = $1,638,000
We have been informed that Lisa has decided to sell half of her business to a friend. We are asked to find the amount her friend needs to pay, to become her partner.
As we have been told, she is selling half of her business, her friend will need to pay half of her business' worth at the present date.
∴ Her friend pays the amount = 1/2 * worth of the business now
or, Her friend pays the amount = 1/2 * $1,638,000
or, Her friend pays the amount = $819,000.
∴ Lisa's friend must pay Lisa $819,000 to become her partner in the business, half the worth of Lisa's business today.
Learn more about the worth of an object at
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pls help rn if possible
Answer:
I would type these in Math-Way, then select Solve the system of equations (or inequalities, I forget which one). (4, -1, 0) would be the answer.
−18x+21>−15 OR 20x−13≥27
Answer:
I dont know what is your question, but I solved this.
Step-by-step explanation:
-18x>-15-21
-18x>-36
x<2
20x>=27+13
20x>=40
x>2
PLS HELP ME 25 POINTS
The roots of the equation x^2+bx+c=0 are −4 and 2. Find b.
what is the length of AC
Answer:
13
Step-by-step explanation:
count A up to C
While working out, Susie does 25 sit-ups for every 12 push-ups. If she does 60 push-ups, how many sit-ups will she do?
Answer:
125 situps
Step-by-step explanation:
We can use a ratio to solve
25 situp x situps
--------------- = --------------
12 pushup 60 pushups
Using cross products
25 * 60 = 12x
Divide each side by 12
25*60/12 = 12x/12
125 = x
solve each inequality and graph the solutions , ILL MARK BRAINLIST !!!!
Answer:
m>6
Step-by-step explanation:
It is possible to approximate the outside temperature based on how fast crickets are chirping. Suppose on a 50 degree day, you measure 52 chirps in a minute, and on a 74 degree day, you measure 148 chirps in a minute.
evalute a/b for a= -6 and b=-2
Answer:
3
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Define
a/b
a = -6
b = -2
Step 2: Substitute and Evaluate
-6/-2
3
Brad has groups of 10 pennies. Brad counts 40, but he has 6 more stacks to count. How many pennies does he have? Explain your answer to a family member or friend
Answer:
100 pennies
Step-by-step explanation:
each stack is 10 pennies. brad has 4 stacks which equal 40 and has 6 more stack which qual 60. 40+60=100
The number of pennies he has is 100 pennies.
Given,
Brad has groups of 10 pennies.
Brad counts 40, but he has 6 more stacks to count.
We need to find how many pennies he has.
How do we find the total number of given groups?If each group has 20 items the total number of items for M groups is:
= M x 20
We multiply the total number of groups with the number of items in each group.
We have,
1 group = 10 pennies
Brad counts 40 and 6 more stacks to go.
This means 4 groups have been counted.
= 4 x 10
= 40 pennies
Now 6 more stacks:
= 6 x 10
= 60 pennies
Now,
Total number of pennies:
= 40 + 60
= 100 pennies
Thus the number of pennies he has is 100 pennies.
Learn more about percentage errors in counting pennies here:
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What is 73+84=. On Saxon math
Answer:
157
Step-by-step explanation:
You just have to take 73+84, and here is the equation.
73+84=157
OR
First, add the numbers in the ones place.
3+4=7
Now you know that the ones place is 7, we find the tens place.
7+8=15
Since only a 1-digit number can fill up a place, we bring the one over to the hundreds place.
Hence, the answer 157.
HELP ME QUICK PLEASEE!!
4. (03.03 HC)
The table shows the outputs, y, for different inputs, x:
Input (x) 3 4 5 6
Output (y) 3 4 5 6
Part A: Do the data in this table represent a function? Justify your answer. (3 points)
Part B: Compare the data in the table with the relation f(x) - 2x + 16. Which relation has a greater value when x = 6? (2 points)
Part C: Using the relation in Part B, what is the value of x if f(x) - 40? (5 points)
(10 points)
Answer:
A) is a function
B) f(x) is greater
C) x = 12
Step-by-step explanation:
A) Yes, the relation is a function.
A function has a unique input value for each output value. There are no repeated x-values, so this relation is a function.
__
B) The table says y=6 for x=6.
f(6) = 2(6)+16 = 28
f(x) has a greater value for x=6.
__
C) Substituting the given information, we have ...
40 = 2x +16
24 = 2x
12 = x
The value of x is 12 when f(x) is 40.
Find the equation of the line
passing through the points. (5, 2) and (10, 6).??
Henry sends his hawk with a message to his uncle. The hawk flies out against the wind and returns with the wind, spending 3 hours on the whole trip. How far is Henry's uncle from Henry if the speed of the wind is 5 mph, and the hawk flies 50 mph in quiet weather?
Answer:
Distance between Henry and his uncle is 74.25km.
Step-by-step explanation:
Speed of Hawk with wind = 50+5
=55km/hr
Speed of Hawk against wind = 50-5
=45km/hr
we know that ,
[tex]Distance = speed \times time[/tex]
Let the distance between Henry and uncle is d,
According to the question ,
[tex]\frac{d}{55} + \frac{d}{45} = 3[/tex]
[tex]\frac{9d + 11d}{495} =3[/tex]
[tex]20d = 3\times 495[/tex]
[tex]d =\frac{3\times495}{20}[/tex]
d= 74.25km
Hence , the answer is 74.25km
The relation between speed, time, and distance is used. Then the distance between Henry's uncle from Henry is 74.25 miles.
What is speed?The distance covered in an hour is called speed. it is a scalar quantity.
What is relative speed?The concept of relative speed is used when two or more bodies moving with some speed are considered.
Henry sends his hawk with a message to his uncle.
The hawk flies out against the wind and returns with the wind, spending 3 hours on the whole trip.
We know the relation
[tex]\rm speed = \dfrac{distance }{time}[/tex]
Let the distance between Henry's uncle from Henry be x.
The time of the trip is during the traveling remains constant. That is
[tex]\rm T = T_1 + T_2\\\\T = \dfrac{x}{v_1} + \dfrac{x}{v_2}[/tex]
The speed of the wind is 5 mph, and the hawk flies 50 mph in quiet weather. Then we have
[tex]\rm v_1 = 50 - 5 = 45\\\\v_2 = 50 + 5 = 55[/tex]
Then
[tex]\begin{aligned} \rm \dfrac{x}{45} + \dfrac{x}{55} &= 3\\\\\rm \dfrac{9x + 11x }{495} &= 3\\\\\rm 9x + 11x &= 1485\\\\\rm 20x &= 1485\\\\\rm x &= 74.25 \end{aligned}[/tex]
Thus, the distance between Henry's uncle from Henry is 74.25 miles.
More about the speed link is given below.
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Rita charges $50 for 5 tutoring sessions. What is the cost per session?
Answer:
10
Step-by-step explanation:
Answer:
10$
Step-by-step explanation:
If she charges 50$ per 5 session then you need to do is
50 ÷ 5 = 10
Why?
Because you can to break it down to one session.
please i need this now
6. Melanie ran the 400-meter dash six times during track practice. Her times
are shown in the table to the left. If she drops her slowest time, which
measure of center is affected the most, mean or median? Explain.
the table to the left
400-Meter Dash
Attempt Time (s)
1 63.5
2 67.9
3 64.3
4 63.6
5 65.4
6 64.7
2nd question
Directions: Determine which measure of center best represents the data.
Justify your selection, then find the measure of center.
7. The number of wins by a hockey team in the last 8 years: {56, 45, 26, 48, 54,
52, 49, 38} Mean or Medan or Mode
Answer:
(a) Mean
(b) Mean
Step-by-step explanation:
(a) Mean is influenced by two things, occurrence and difference in values. Mode is influenced by one thing only, occurrence. Median is positional in rank order so only indirectly influenced by value.
(b) The mean is the most accurate way of deriving the central tendencies of a group of values, not only because it gives a more precise value as an answer, but also because it takes into account every value in the list.
when three or more numbers are multipiled the product is the same regardless of the order of the multiplicands
Answer:
Associative property of multiplication.
Step-by-step explanation:
Retailers will buy 45 Wi-Fi routers from a wholesaler if the price is $10 each but only 20 if the price is $85. The wholesaler will supply 56 routers at $46 each and 70 at $50 each. Assuming that the supply and demand functions are linear, find the market equilibrium point.
The distance between 4 and 17 is
Step by step of how to find f(g(x)) and g(f(x))
Answers:
[tex]f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}[/tex]
===============================================
Work Shown:
[tex]f(x) = \sqrt[3]{x}\\\\\\f(g(x)) = \sqrt[3]{g(x)}\\\\\\f(g(x)) = \sqrt[3]{\frac{x+1}{x^3}}\\\\\\[/tex]
The idea is to replace every x with g(x). Then you'll plug in the definition of g(x).
---------------------------------
Similarly,
[tex]g(x) = \frac{x+1}{x^3}\\\\\\g(f(x)) = \frac{f(x)+1}{(f(x))^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{(\sqrt[3]{x})^3}\\\\\\g(f(x)) = \frac{\sqrt[3]{x}+1}{x}\\\\\\[/tex]
What is the y-intercept of the graph of the linear function?
Answer:
-6
Step-by-step explanation:
look at the y-axis (the vertical center line) where it passes through it is the intercept
You place a billiard cue against a billiard table. The foot of the billiard cue is 15 cm away from the table and the top of the billiard cue touches the table at a point 60 cm off the ground. What is the slope of the billiard cue?
Answer:
-4Step-by-step explanation:
The billiard cue is 15 cm away from the table
This refers to coordinates of (15, 0)The billiard cue touches the table at a point 60 cm off the ground
This refers to coordinates of (0, 60)The slope is as per slope formula;
m = (60 - 0)/(0-15) = 60/ -15 = -4Thea answer is -4
Answer:
-4
Step-by-step explanation:
The foot of the billiard cue is 15 cm away from the table can be represented by the point (15, 0).
The top of the billiard cue touches the table at a point 60 cm off the ground can be represented by the point (0, 60)
The slope formula can be solve with the formula [ y2-y1/x2-x1 ]
60-0/0-15
60/-15
-4
Best of Luck!
Can someone explain how to solve these? I have 10 questions I need to answer for problems like this & I can't go on until I solve it, so I just need the answer for this one and how to solve it. I need it finished fast because I need to bring up a low grade. Any help would be appreciated.
Solve the equation using a graphical method.
t/3-1/2=t+3/9
Answer:
-1.25
Step-by-step explanation:
t÷3-1÷2 = t÷1+3÷9
2t-3÷6 = 9t+3=9
18t - 27 = 54 + 18
18t -54t = 18 + 27
-36t = 45
Divide through by -36
t = -1.25
Maggie's brother is 4 years younger than four times her age. The sum of their ages is 31.
How old is Maggie?