Answer:
10
Step-by-step explanation:
he heights of adults in a certain town have a mean of 65.42 inches with a standard deviation of 2.32 inches. A random sample of 144 adults living in the center of the town was selected and their mean height was found to be 64.82 inches. Find the probability that a sample of this size would have a mean of 64.82 inches or less.
Answer:
0.001 = 0.1% probability that a sample of this size would have a mean of 64.82 inches or less.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The heights of adults in a certain town have a mean of 65.42 inches with a standard deviation of 2.32 inches.
This means that [tex]\mu = 65.42, \sigma = 2.32[/tex]
Sample of 144:
This means that [tex]n = 144, s = \frac{2.32}{\sqrt{144}} = 0.1933[/tex]
Find the probability that a sample of this size would have a mean of 64.82 inches or less.
This is the pvalue of Z when X = 64.82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.82 - 65.42}{0.1933}[/tex]
[tex]Z = -3.1[/tex]
[tex]Z = -3.1[/tex] has a pvalue of 0.001
0.001 = 0.1% probability that a sample of this size would have a mean of 64.82 inches or less.
The graph of r = -3 + 5cos theta is symmetric about the __________.
a.
y-axis only
c.
Origin only
b.
x-axis only
d.
No symmetry
The graph of r = -3 + 5cosθ is symmetric about the option (B) x axis only
What is Symmetry?In mathematics, symmetry has a more precise definition, and is usually used to refer to an object that is invariant under some transformations; including translation, reflection, rotation or scaling.
Given that,
The graph of r = -3 + 5cosθ is symmetric about what?
When we plot the graph we can say that it is symmetric about x axis only.
Hence, the graph of r = -3 + 5cosθ is symmetric about the option (B) x axis only
Learn more about Symmetry click;
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The cost of 7 chairs is equal to the cost of 2 tables. If the cost of 6 chairs and 5 tables is Rs.10,575, find the cost of 12 chairs.
Answer:
5,400
Step-by-step explanation:
7c = 2t; t = 7c/2
6c +5t = 10575
6c + 5(7c/2) = 10575
6c + 35c/2 = 10575
multiply all through by 2
12c + 35c = 21,150
47c = 21,150
c = 21150/47 = 450
12 chairs = 450 × 12 = 5,400
Sam buys 3 different types of fruit in 3-fourths pound baskets. Maria has 1 and 1-fourth pounds fruit.
How many pounds of fruit do they have altogether?
While Vivian was visiting her sister in Springfield, she bought a set of bunk beds that was marked down 25% from an original price of $80. If the sales tax in Springfield is 10%, what was the total cost of the set of bunk beds?
Answer:
66 i think
Step-by-step explanation:
If (X + A) is multiplied times (X + B), the final term of the resulting trinomial will be:
Answer:
AB
Step-by-step explanation:
Using FOIL (first outer inner last) u can determine that the final term will be produced by multiplying the last terms in each bracket. These are A and B, so the final term of the resulting trinomial is AB.
You can check this by fully expanding (x + A)(x + B):
[tex](x + A)(x + B)\\= x^{2} + Bx + Ax + AB[/tex]
the terms B and A are usually numbers, so Bx and Ax tend to get added together to form a middle term. hope this helps!
In a study, Phoenix Marketing International identified Bridgeport, Connecticut; San Jose, California; Washington, DC; and Lexington Park, Maryland, as the four U.S. cities with the highest percentage of millionaires (Kiplinger website). Consider a sample of data that show the following number of millionaires for samples of individuals from each of the four cities. City Bridgeport,San Jose,Washington,Lexington Park, MillionaireCTCAD.C.MD Yes45333634 No455267364366 a. What is the estimate of the percentage of millionaires in each of these cities (to 1 decimal)
Answer:
The estimate of the percentage of millionaires in each of these cities:
Bridgeport San Jose Washington Lexington Park
CT CA D.C. MD
Percentage of
Millionaires 9% 12% 9% 8.3%
Step-by-step explanation:
Data and Calculations: City
Bridgeport, San Jose, Washington, Lexington Park,
Millionaire CT CA D.C. MD
Yes 45 36 36 33
No 455 264 364 367
Sample 500 300 400 400
Percentage of
Millionaires 45/500 36/300 36/400 33/400
= 0.09 0.12 0.09 0.0825
= 9% 12% 9% 8.3%
Using the percentage concept, it is found that the estimate of the percentage of millionaires in these cities is of 9.25%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
Researching the problem on the internet, it is found that:
A total of 45 + 34 + 37 + 32 + 455 + 266 + 363 + 368 = 1600 people were surveyed, hence b = 1600.Of those, 45 + 34 + 37 + 32 = 148 are millionaires, hence a = 148.Then:
[tex]P = \frac{148}{1600} \times 100\% = 9.25\%[/tex]
The estimate of the percentage of millionaires in these cities is of 9.25%.
More can be learned about the percentage concept at https://brainly.com/question/10491646
Which fraction is equivalent to (7-3)*3/10^4-10^2
A. 16/25
B. 1/25
C. 8/1125
D. 16/2475
Answer:
C.8/1125 is the answer......
50 points! Please help fast I need this done ASAP!!! Only answer if you know it. Random answers will be reported!
Help Please! I'll Give Brainliest!
Answer:
A
Step-by-step explanation:
the answer is a
Help please! Thank you!!
Answer:
alternate exterior angle is answer
Answer:
Angle 2 and angle 8 are alternative exterior angles
An FBI agent orders a block of ballistics gel. The gel weighs 54 pounds per cubic foot. What is the weight of the block of gel?
Answer:
22.5 Pounds
Step-by-step explanation:
This is correct because i did it on Big Ideas and got it correct with 22.5.
If x = -3, find
pls answer
Answer:
x² - 1 = 8
Step-by-step explanation:
Given the following algebraic expression;
x² - 1
When x = -3
Substituting the value of x, we have;
x² - 1 = (-3)² - 1
x² - 1 = 9 - 1
x² - 1 = 8
Method II.
x² - 1 = (x - 1)(x + 1)
Substituting the value of x, we have;
x² - 1 = (-3 - 1)(-3+ 1)
x² - 1 = -4(-2)
x² - 1 = 8
HELPPPPPPP MEEEEEEEEEEEE
Answer:
man thats hard
Step-by-step explanation:
Here are the noon temperatures (in degrees Celsius) in a particular Canadian city on Thanksgiving Day for the 10 years from 2002 through 2011: 0, 3, 6, 8, 2, 9, 7, 6, 4, 5. Describe the typical temperature and the amount of variation to a person who has never had a course in statistics. Give three ways of describing the representative temperature and two ways of describing its variation, explaining the differences and how you figured each. (You will learn more if you try to write your own answer first, before reading our answer at the back of the book.)
Answer:
a) Three ways of describing the representative or typical temperatures are the mean, median, and mode.
The mean = 5. This is the average temperature. It is calculated by adding up the varying temperatures each year and dividing by 10.
Median = 5.5. This is the middle value in the temperature table. There are two middle numbers (5 and 6) in the dataset. They are added and divided by two.
Mode = 6. This is the value that occurs more than other values in the dataset. The value 6 occurred twice more than other values.
b) The two ways of describing the variation of temperatures are the variance and the standard deviation.
Variance = 7. This is a measure of how spread out a data set is. It is calculated as the average squared deviation of each number from the mean of a dataset.
Standard Deviation = 2.65. The standard deviation measures the dispersion of a dataset relative to its mean and is calculated as the square root of the variance.
Step-by-step explanation:
a) Data and Calculations:
Noon Temperatures (in degrees Celsius) in a particular Canadian City on Thanksgiving Day:
Year Degree Difference Squared
Celsius Difference
2002 0 -5 25
2003 3 -2 4
2004 6 1 1
2005 8 3 9
2006 2 -3 9
2007 9 4 16
2008 7 2 4
2009 6 1 1
2010 4 -1 1
2011 5 0 0
Sum 50 70
Mean = 5 (50/10)
Variance = 7 (70/10)
Standard Deviation = 2.65 (Square root of variance)
Median = 0, 2, 3, 4, 5, 6, 6, 7, 8, 9 (the values are arranged numerically.)
= (5 + 6)/2 = 5.5
Mode = 6 (occurred twice more than other values)
The symbol used to seperate the tenths and ones is called a?
The answer you are looking for is called a
Decimal
Have a beautiful day!
~!!!! HELP IM IN 7TH GRADE LEARNING 9TH AND 8TH PLEASE HELP !!!!~
QUESTION~
The graph of g(x) = 4|x| − 3 maps a
person’s path from their house to
school, and their path from school
to a friend’s house. At what point
is the school located?
Answer:
It would be (0,-3) ^^you can see on the graph
1. Sprint PCS offers a monthly cellular phone plan for $39.99. It includes 450 anytime minutes and charges $.45 per minute for additional minutes. a. x represents __________________ (2 points) b. f(x) represents ___________________ (2 points) c. Write out your piecewise function, including the domain.
Answer:
[tex]f(x) = \left \{ {{39.99; 0 \le x \le 450} \atop {0.45x - 162.51; \ x>450}} \right.[/tex]
Step-by-step explanation:
Given
Charges: $39.99 for first 450 minutes
Charges: $0.45 for additional minutes
(a): What is x
x represents the total minutes
(b): What is f(x)
f(x) represents the total monthly cellular charges
(c): The piecewise function
For the first 450 minutes, the function is:
[tex]f(x) = 39.99;\ 0 \le x \le 450[/tex]
For additional minutes.
In (a), the total minutes is x.
So, we have:
Total Charges = Charges for first 450 minutes + Charges for additional minutes * (Minutes after 450 minutes)
[tex]Total\ Charges = 39.99 + 0.45 * (x - 450)[/tex]
[tex]f(x) = 39.99 + 0.45 * (x - 450)[/tex]
Open bracket
[tex]f(x) = 39.99 + 0.45x - 0.45 * 450[/tex]
[tex]f(x) = 39.99 + 0.45x - 202.5[/tex]
Collect Like Terms
[tex]f(x) = 0.45x+39.99 - 202.5[/tex]
[tex]f(x) = 0.45x-162.51[/tex]
The range of the above function is: x > 450.
So, the piecewise function is:
[tex]f(x) = \left \{ {{39.99; 0 \le x \le 450} \atop {0.45x - 162.51; \ x>450}} \right.[/tex]
Verizon Wireless charges
$0.09 for every 5 text
messages sent. How much
is your bill if you send 75
texts?
Make this into a equation
Answer:
$1.35
Step-by-step explanation:
$0.09/5 = $0.018
75 x $0.018 = $1.35
can i be brainiest...
I have 15 pounds of flour. How many batches of pizza dough can I make from 1 bag of flour?
Answer:
with one pound of pizza dough you can make one large pizza or two 10-inch pizzas.
so 15 Large pizzas or 30 10 in pizzas
Step-by-step explanation:
A ring-shaped region is shown below.
Its Inner radius is 11 cm, and its outer radius is 17 cm.
Find the area of the shaded region. Use 3.14 for pi. Do not round your answer.
Answer:
527.52 cm²
Step-by-step explanation:
Area of the shaded region = area of the outer circle - area of the inner circle
Area of circle is given as πr²
Radius of inner circle = 11 cm
Area of outer circle = 17 cm
π = 3.14
Thus:
Area of shaded region = 3.14*17² - 3.14*11²
= 907.46 - 379.94
= 527.52 cm²
Suppose that a balanced, six-sided die has been altered so that the faces are 1, 2, 3, 4, 5, and 5. If the die is tossed five times, and the number on the uppermost face is recorded each time, what is the probability that the numbers recorded are 1, 2, 3, 4, and 5 in any order
Answer:
0.0309
Step-by-step explanation:
Faces on dice ( 1, 2, 3, 4, 5, 5)
Number of outcomes = 6
With 5 repeated twice
P(event A) = Required outcome / Total possible outcomes
Required outcome :
Number of 5's = 2 * distinct faces!
Required outcome = 2 * 5! = 2 * 120 = 240
Total possible outcomes = (number of faces)^distinct Numbers = 6^5 = 7776
Required / total possible = 240 / 7776
= 0.0308641
= 0.0309
A research group is interested in gauging perceptions about health club memberships among health club members. Specifically, they wish to determine the percentage of monthly paying members in the United States that believe health club memberships are not too expensive. They listed the members of the health club located nearby in alphabetical order and took every tenth member until they succeeded in contacting 150 members. What kind of sampling method have they used? Choose the correct answer below.
A. Cluster sampling
B. Multistage sampling
C. Stratified random sampling
D. Systematic sampling
Answer:
D. Systematic sampling
Step-by-step explanation:
Systematic sampling is a type of probability sampling method in which sample members of a large population are selected according to a random starting position and a constant, periodic interval. This interval, called the sample interval, is calculated by dividing the population size by the desired sample size.so correct option is D. Systematic sampling .Please help me answer this:)
Will give you brainlst ^
Okay, got it!
Here's the graph (sorry if it's confusing I'm going to try my best)
Print Electronic Total
Youths 33 28 61
Adults 33 37 70
Total 66 65 131
Hope this helps!
what is the length of the hypotenuse
Answer:
65 ft
Step-by-step explanation:
You can find the length of the hypotenuse using the formula a^2+b^2=c^2 where c is the hypotenuse and the other two sides are a and b.
16^2=256
63^2=3969
256+3969=4225
4225=c^2
Get c by itself by taking the square root of both sides.
This leaves you with c=65
equations similar to 4x + 12
Answer:
2(2x+6) is the same problem in a different format.
Step-by-step explanation:
Distribute the 2 to each place which gives you 4x+12
Answere : 4 times (x + 3)
Which equation is represented by the graph below?
Answer:
y = [tex]\frac{2}{3}x[/tex] + 6
Step-by-step explanation:
PLEASE HELP ME WITH BOTH QUESTIONS ASAP!!!!!!!!!
Answer:
I have #1, answer is 400
Step-by-step explanation:
80% of 500 is 400
Answer:
First one is 400
Step-by-step explanation:
Roshanda was curious if students in her class would complete a maze faster if fast-paced music was playing in the background. She randomly assigned each student in her class to one of three groups: fast-paced music, slow-paced music, or no music. She timed each student as they individually completed a maze with their corresponding music (or no music) in the background. Students who worked with the fast-paced music, on average, completed the maze significantly faster than students in the other groups.
Can we conclude that the fast-paced music caused her classmates to finish the maze faster? Why?
(A) Yes, because the study included each student in her class
(B) Yes, because the adults were randomly selected
(C) Yes, because the students were randomly assigned to treatment and control groups
(D) Not necessarily, because the sample size was too small
(E) Not necessarily, because this wasn't an experiment
Answer: (E) Not necessarily, because this wasn't an experiment
Step-by-step explanation:
As much as the results would suggest that the fast-paced music was responsible for the faster finishing time, this conclusion cannot be authoritatively made because this was not technically an experiment but rather a test to satisfy curiosity.
An experiment is planned and is scientific. It has more stringent requirements that ensure causation that Roshanda did not meet before she engaged in this trial so we cannot say for a fact that her findings are objective.
Answer: C. yes, the students were randomly assigned to treatment and control groups.
Step-by-step explanation:
Russell is purchasing a $175,000 home with a 30-year mortgage. He will put
down $15,000 down payment. Use the table below to find his monthly PMI
payment
Base-To-Loan %
Fixed-Rate Loan
30 yrs. 15 yrs.
ARM 2% + 1 Year Cap
30 yrs.
15 yrs.
95.01% to 97%
0.90% 0.79%
n/a
n/a
90.01% to 95%
0.78% 0.26%
0.92%
0.81%
85.01% to 90%
0.52% 0.23%
0.65% 0.54%
85% and Under
0.32% 0.19%
0.37% 0.26%
O A. $97.50
B. $1170
O c. $1248
O D. $104.00
104.00
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