Answer:
9:20
Step-by-step explanation:
The ratio of the surface area of similar solid is equal to the square of the ratio of their corresponding linear measures.
If the ratio of their corresponding linear measures is a:b, the surface area ratio will be (a/b)².
Therefore, (A/B )² = 9/16
square root both sides A/B = √9/√16 A/B = 3/4 A:B = 3:4
The ratio of volume of two similar solid is the ratio cube of their corresponding linear measures.
Therefore, (B/C)³ = 27/125 cube root both sides B/C = 3/5 B:C = 3:5
To make the ratio equivalent A:B:C = 9:12:20
A:C = 9:20
What is the distance between (8, -3) and (4, - 7)?
Answer:
[tex]distance=\sqrt{32}[/tex] , which agrees with answer "c" in your list of possible options
Step-by-step explanation:
Use the formula for distance between two points [tex](x_1,y_1)[/tex], and [tex](x_2,y_2)[/tex] on the plane:
[tex]distance = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance= \sqrt{(4-8)^2+(-7-(-3))^2} \\distance= \sqrt{(-4)^2+(-4)^2} \\distance=\sqrt{16+16}\\distance=\sqrt{32}[/tex]
According to the National Association of Theater Owners, the average price for a movie in the United States in 2012 was $7.96. Assume the population standard deviation is $0.50 and that a sample of 30 theaters was randomly selected.
Required:
a. Calculate the standard error of the mean.
b. What is the probability that the sample mean will be less than $7.75?
c. What is the probability that the sample mean will be less than $8.10?
d. What is the probability that the sample mean will be more than $8.20?
Answer:
(a) The standard error of the mean is 0.091.
(b) The probability that the sample mean will be less than $7.75 is 0.0107.
(c) The probability that the sample mean will be less than $8.10 is 0.9369.
(d) The probability that the sample mean will be more than $8.20 is 0.0043.
Step-by-step explanation:
We are given that the average price for a movie in the United States in 2012 was $7.96.
Assume the population standard deviation is $0.50 and that a sample of 30 theaters was randomly selected.
Let [tex]\bar X[/tex] = sample mean price for a movie in the United States
The z-score probability distribution for the sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean price for a movie = $7.96
[tex]\sigma[/tex] = population standard deviation = $0.50
n = sample of theaters = 30
(a) The standard error of the mean is given by;
Standard error = [tex]\frac{\sigma}{\sqrt{n} }[/tex] = [tex]\frac{0.50}{\sqrt{30} }[/tex]
= 0.091
(b) The probability that the sample mean will be less than $7.75 is given by = P([tex]\bar X[/tex] < $7.75)
P([tex]\bar X[/tex] < $7.75) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{7.75-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z < -2.30) = 1 - P(Z [tex]\leq[/tex] 2.30)
= 1 - 0.9893 = 0.0107
The above probability is calculated by looking at the value of x = 2.30 in the z table which has an area of 0.9893.
(c) The probability that the sample mean will be less than $8.10 is given by = P([tex]\bar X[/tex] < $8.10)
P([tex]\bar X[/tex] < $8.10) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{8.10-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z < 1.53) = 0.9369
The above probability is calculated by looking at the value of x = 1.53 in the z table which has an area of 0.9369.
(d) The probability that the sample mean will be more than $8.20 is given by = P([tex]\bar X[/tex] > $8.20)
P([tex]\bar X[/tex] > $8.20) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{8.20-7.96}{\frac{0.50}\sqrt{30} } }[/tex] ) = P(Z > 2.63) = 1 - P(Z [tex]\leq[/tex] 2.63)
= 1 - 0.9957 = 0.0043
The above probability is calculated by looking at the value of x = 2.63 in the z table which has an area of 0.9957.
Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. Suppose that we select 3 random samples of 500 adults from this population. Which of the following is most likely to occur with the three samples?
A. The number that had never been married will equal 20% in each of the three samples.B. The number that had never been married will vary in each sample due to the random selection of adults.C. The average for the three samples of the number of adults that had never been married will equal 20%.D. The number of adults that had never been married will increase for each sample because the number is generally increasing over time.
Answer:
Option B
Step-by-step explanation:
The number that had never been married will vary in each sample due to the random selection of adults.
This number will vary in each sample to the random selection process but they might or might not be as close as possible to one another after sampling.
The answer to – 7x + y = -10
Step-by-step explanation:
y=7x-10
Answer:
[tex]\huge \boxed{y=7x-10}[/tex]
Step-by-step explanation:
[tex]-7x+y=-10[/tex]
[tex]\sf Add \ 7x \ on \ both \ sides.[/tex]
[tex]-7x+y+7x=-10+7x[/tex]
[tex]y=7x-10[/tex]
Justin spent $23 on fruit at grocery store. He spent a total of $25 at the store. What percentage of the total did he spend on fruit?
Step-by-step explanation:
In my opinion maybe he has spent 98%
Imagine you have a rectangular wooden block with dimensions of 10 cm x 3 cm x 8 cm (L x W x H). Required:a. What is the volume of your wooden block?b. What is the density of this wooden block if it has a mass of 168 g?
Answer:
a) The volume of the wooden block is 240 cm^3.
b) The density of the wooden block is 0.7 g/cm^3.
Step-by-step explanation:
The volume of the rectangular wooden block can be calculated as the multiplication of the length in each dimension: length, wide and height.
With dimensions 10 cm x 3 cm x 8 cm, the volume is:
[tex]V=L\cdot W\cdot H = 10\cdot 3\cdot 8=240[/tex]
The volume of the wooden block is 240 cm^3.
If we know that the mass of the wooden block is 168 g, we can calculate the density as:
[tex]\rho = \dfrac{M}{V}=\dfrac{168}{240}=0.7[/tex]
The density of the wooden block is 0.7 g/cm^3.
Pls help marking Brainliest! (x-1)(x-1)=?
Answer:
Brainleist!Step-by-step explanation:
x^2-2x+1thats the answer...
just: Expand the polynomial using the FOIL method.
Answer:
(x-1)(x-1)=(x-1)² because it's the same thing multiplied by itself
Using FOIL method:
(x-1)(x-1)=
x²-x-x+1=
x²-2x+1
At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound- shaped and symmetric. What percentage of the player's serves were between 115 mph and 145 mph
Answer:
15.74% of the player's serves were between 115 mph and 145 mph
Step-by-step explanation:
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.
In this question, we have that:
[tex]\mu = 100, \sigma = 15[/tex]
What percentage of the player's serves were between 115 mph and 145 mph
This is the pvalue of Z when X = 145 subtracted by the pvalue of Z when X = 115.
X = 145
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{145 - 100}{15}[/tex]
[tex]Z = 3[/tex]
[tex]Z = 3[/tex] has a pvalue of 0.9987
X = 115
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{15}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.9987 - 0.8413 = 0.1574
15.74% of the player's serves were between 115 mph and 145 mph
y= -3/2x-6 x=15 plssssssssssssssssssssssss help
Answer:
-45/2 - 12/2 = -57/2
Step-by-step explanation:
Substitute 15 for x in the given equation: y = (-3/2)x - 6 becomes
y = (-3/2)(15) - 6 = -45/2 - 6 when x = 15. This is equivalent to -57/2
100 pts You have a bag of 15 marbles: 5 blue, 3 red, 4 green, and 3 yellow. You draw 3 marbles without replacement. Which action, performed before the draws, increases the probability of drawing 3 green marbles in a row?
Answer:
see below
Step-by-step explanation:
You can remove one or more of the other color marbles to increase the probability of drawing a green marble
or
You can add one or more green marbles to have more green marbles in the bag
Solve for x: −3x + 3 < 6
Answer:x>-1
Step-by-step explanation:
Step 1: Subtract 3 from both sides.
-3x+3-3<6-3
-3x<3
Step 2: Divide both sides by -3.
-3x/-3<3/3
X>-1
Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience, she knows that 60% of her students do homework regularly. Moreover, 95% of the students who do their homework regularly generally pass the course. She also knows that 85% of her students pass the course.
a. What is the probability that a student will do homework regularly and also pass the course?
b. What is the probability that a student will neither do homework regularly nor will pass the course?
c. Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.
d. Are the events "pass the course" and "do homework regularly" independent? Explain.
Answer:
a) The probability that a student will do homework regularly and also pass the course = P(H n P) = 0.57
b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P') = 0.12
c) The two events, pass the course and do homework regularly, aren't mutually exclusive. Check Explanation for reasons why.
d) The two events, pass the course and do homework regularly, aren't independent. Check Explanation for reasons why.
Step-by-step explanation:
Let the event that a student does homework regularly be H.
The event that a student passes the course be P.
- 60% of her students do homework regularly
P(H) = 60% = 0.60
- 95% of the students who do their homework regularly generally pass the course
P(P|H) = 95% = 0.95
- She also knows that 85% of her students pass the course.
P(P) = 85% = 0.85
a) The probability that a student will do homework regularly and also pass the course = P(H n P)
The conditional probability of A occurring given that B has occurred, P(A|B), is given as
P(A|B) = P(A n B) ÷ P(B)
And we can write that
P(A n B) = P(A|B) × P(B)
Hence,
P(H n P) = P(P n H) = P(P|H) × P(H) = 0.95 × 0.60 = 0.57
b) The probability that a student will neither do homework regularly nor will pass the course = P(H' n P')
From Sets Theory,
P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1
P(H n P) = 0.57 (from (a))
Note also that
P(H) = P(H n P') + P(H n P) (since the events P and P' are mutually exclusive)
0.60 = P(H n P') + 0.57
P(H n P') = 0.60 - 0.57
Also
P(P) = P(H' n P) + P(H n P) (since the events H and H' are mutually exclusive)
0.85 = P(H' n P) + 0.57
P(H' n P) = 0.85 - 0.57 = 0.28
So,
P(H n P') + P(H' n P) + P(H n P) + P(H' n P') = 1
Becomes
0.03 + 0.28 + 0.57 + P(H' n P') = 1
P(H' n P') = 1 - 0.03 - 0.57 - 0.28 = 0.12
c) Are the events "pass the course" and "do homework regularly" mutually exclusive? Explain.
Two events are said to be mutually exclusive if the two events cannot take place at the same time. The mathematical statement used to confirm the mutual exclusivity of two events A and B is that if A and B are mutually exclusive,
P(A n B) = 0.
But, P(H n P) has been calculated to be 0.57, P(H n P) = 0.57 ≠ 0.
Hence, the two events aren't mutually exclusive.
d. Are the events "pass the course" and "do homework regularly" independent? Explain
Two events are said to be independent of the probabilty of one occurring dowant depend on the probability of the other one occurring. It sis proven mathematically that two events A and B are independent when
P(A|B) = P(A)
P(B|A) = P(B)
P(A n B) = P(A) × P(B)
To check if the events pass the course and do homework regularly are mutually exclusive now.
P(P|H) = 0.95
P(P) = 0.85
P(H|P) = P(P n H) ÷ P(P) = 0.57 ÷ 0.85 = 0.671
P(H) = 0.60
P(H n P) = P(P n H)
P(P|H) = 0.95 ≠ 0.85 = P(P)
P(H|P) = 0.671 ≠ 0.60 = P(H)
P(P)×P(H) = 0.85 × 0.60 = 0.51 ≠ 0.57 = P(P n H)
None of the conditions is satisfied, hence, we can conclude that the two events are not independent.
Hope this Helps!!!
Please help !! Correct and first answer I’ll give you brainesttttt ! What is the equation of the line?
Step-by-step explanation:
can u give image PlZzzzz ....
Answer:
Hey!
Your answer should be Y=2x+4
Step-by-step explanation:
Hope this helps!
Please help with this problem
Answer:
The length of the short side is 14.5 units, the length of the other short side is 18.5 units, and the length of the longest side is 23.5 units.
Step-by-step explanation:
The Pythagorean Theorem
If a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
This relationship is represented by the formula:
[tex]a^2+b^2=c^2[/tex]
Applying the Pythagorean Theorem to find the lengths of the three sides we get:
[tex](x)^2+(x+4)^2=(x+9)^2\\\\2x^2+8x+16=x^2+18x+81\\\\2x^2+8x-65=x^2+18x\\\\2x^2-10x-65=x^2\\\\x^2-10x-65=0[/tex]
Solve with the quadratic formula
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-10,\:c=-65:\quad x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}\\\\x_{1}=\frac{-\left(-10\right)+ \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5+3\sqrt{10}\\\\x_{2}=\frac{-\left(-10\right)- \sqrt{\left(-10\right)^2-4\cdot \:1\left(-65\right)}}{2\cdot \:1}=5-3\sqrt{10}[/tex]
Because a length can only be positive, the only solution is
[tex]x=5+3\sqrt{10}\approx 14.5[/tex]
The length of the short side is 14.5, the length of the other short side is [tex]14.5+4=18.5[/tex], and the length of the longest side is [tex]14.5+9=23.5[/tex].
Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. Then, from the gas station, she travels 5 miles to return home. The entire trip forms a triangle. What was the smallest angle made at her trip? A. At the gas station B. At Lucy's home C. At the post office D. It depends on the direction she is traveling
Answer:
the correct choice is A. At the gas station
Step-by-step explanation:
Lucy starts at home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. As it is known south and east directions form right angle. Since the entire trip forms a triangle, this triangle is right with right angle at the post office.
Call the vertices of this triangle P - post office, G - gas station, H - home. Then HP and PG are legs of this triangle and GH is hypotenuse.
From the given data:
HP=3;
PG=4;
GH=5;
∠P=90°.
The smallest angle is opposite to the smallest side. The smallest side is leg HP, so the smallest angle is G that is the angle at gas station.
Answer:
a
Step-by-step explanation:
Margo borrows $1700, agreeing to pay it back with 4% annual interest after 6 months. How much interest
will she pay?
Round your answer to the nearest cent, if necessary.
Answer:
$1733.67
Step-by-step explanation:
Simple interest rate formula: A = P(1 + r)^t
Simply plug in your known variables
A = 1700(1 + 0.04)^0.5
A = 1733.67
Remember that t is time in years.
State the size of angle 'n' in the triangle illustrated below.
Answer:
Option B
Step-by-step explanation:
<r = 32 degrees (alternate angles )
<r = <n = 32 degrees (vertical angles)
PROBLEM 6. 10 A histogram has mean 70 and standard deviation 5 If the histogram is not bell shaped but it is symmetric. Find the least proportion of data falls between 70 and 80 If the histogram is bell shaped. Find the proportion of data between 65 and 77
Answer:
a. 0.4772 = 47.72 %
b. 0.7605 = 76.05 %
Step-by-step explanation:
What we must do is calculate the z value for each value and thus find what percentage each represents and the subtraction would be the percentage between those two values.
We have that z is equal to:
z = (x - m) / (sd)
x is the value to evaluate, m the mean, sd the standard deviation
a. ind the least proportion of data falls between 70 and 80 If the histogram is bell shaped:
So for 70 copies we have:
z = (70 - 70) / (5)
z = 0
and this value represents 0.5
So for 80 copies we have:
z = (80 - 70) / (5)
z = 2
and this value represents 0.9772
p (70 > x > 80) = 0.9772 - 0.5
p (70 > x > 80) = 0.4772 = 47.72 %
b. Find the proportion of data between 65 and 77
So for 65 copies we have:
z = (65 - 70) / (5)
z = -1
and this value represents 0.1587
So for 77 copies we have:
z = (77 - 70) / (5)
z = 1.4
and this value represents 0.9192
p (65 > x > 77) = 0.9192 - 0.1587
p (65 > x > 77) = 0.7605 = 76.05 %
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. In a talent competition, half of the contestants are eliminated in each round. At the end of the nth round, 32 contestants remain. If there were 1,024 contestants at the start of the competition, what is the value of n? The value of n is .
Answer:
n =32
Step-by-step explanation:
If 1 contestant is eliminated each round
then of 1024contestants
32 left
1024/32=32
Answer:
n=32
Step-by-step explanation:
Simplify the expression by combining like terms
15 + 12x – 5.2 + 4y - 7
9.8 +12x+y-7
2.8+12x+4y
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. The classes are open to any of the 100 students in the school. There are 28 students in the Spanish class, 26 in the French class, and 16 in the German class. There are 12 students who are in both Spanish and French, 4 who are in both Spanish and German, and 6 who are in both French and German. In addition, there are 2 students taking all 3 classes. If two students are randomly chosen, what is the probability that at exactly one of them does exactly two language classes.
Answer:
The probability that at exactly one of them does exactly two language classes is 0.32.
Step-by-step explanation:
We can model this variable as a binomial random variable with sample size n=2.
The probability of success, meaning the probability that a student is in exactly two language classes can be calculated as the division between the number of students that are taking exactly two classes and the total number of students.
The number of students that are taking exactly two classes is equal to the sum of the number of students that are taking two classes, minus the number of students that are taking the three classes:
[tex]N_2=F\&S+S\&G+F\&G-F\&S\&G=12+4+6-2=20[/tex]
Then, the probabilty of success p is:
[tex]p=20/100=0.2[/tex]
The probability that k students are in exactly two classes can be calcualted as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{2}{k} 0.2^{k} 0.8^{2-k}\\\\\\[/tex]
Then, the probability that at exactly one of them does exactly two language classes is:
[tex]P(x=1) = \dbinom{2}{1} p^{1}(1-p)^{1}=2*0.2*0.8=0.32\\\\\\[/tex]
N
Write the rate as a unit rate
729 riders in 9 subway cars
А
The unit rate is
This
(Simplify your answ
riders/car
Answer:
Unit rate = 81 riders/ car.
Step-by-step explanation:
Given
729 riders in 9 cars
we have to find unit rate in terms of riders per car
let the the riders per car (i.e rate) be x.
If there are 9 cars then
total no. of riders in 9 cars = no. of cars * riders per car = 9*x = 9x
given that 729 riders in 9 cars
then
9x = 729
=> x = 729/9 = 81
Thus, riders per car = x = 81.
Unit rate is 81 riders per car.
Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!
Answer:
See the answers below.
Step-by-step explanation:
[tex]a.\:\frac{f\left(x\right)-f\left(a\right)}{x-a}=\frac{2x^2-x-5-\left(2a^2-a-5\right)}{x-a}\\\\=\frac{2x^2-x+a-2a^2}{x-a}\\\\=\frac{2\left(x+a\right)\left(x-a\right)-1\left(x-a\right)}{x-a}\\\\=\frac{\left(x-a\right)\left[2\left(x+a\right)-1\right]}{x-a}\\\\=2x+2a-1\\\\\\b.\:\frac{f\left(x+h\right)-f\left(x\right)}{h}=\frac{2\left(x+h\right)^2-\left(x+h\right)-5-\left(2x^2-x-5\right)}{h}\\\\=\frac{2\left(x^2+2xh+h^2\right)-\left(x+h\right)-5-\left(2x^2-x-5\right)}{h}\\[/tex]
Expand and simplify to get:
[tex]=\frac{2h^2+4xh-h}{h}\\\\=\frac{h\left(2h+4x-1\right)}{h}\\\\=2h+4x-1[/tex]
Best Regards!
Please answer this correctly
Answer:
The number of employees classified into groups as shown below:
1 - 10: 3 6 (2companies)
11-20: 16 (1 company)
21-30: 25, 26, 27 (3 companies)
31-40: 34, 35, 35, 35, 36 (5 companies)
41-50: 41, 43, 48, 48 (4 companies)
Hope this helps!
Answer:
11-20 is 1
31-40 is 5
Step-by-step explanation:
Just count the amount
Hope that helps :D
. A foreman for an injection-molding firm admits that on 23% of his shifts, he forgets to shut off the injection machine on his line. Failure to shut down at night causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 5% to 15%. The plant manager randomly selects a molding from the early morning run and discovers it is defective. What is the probability that the foreman forgot to shut off the machine the previous night?
Answer:
P(F | D) = 47.26%
There is a 47.26% probability that the foreman forgot to shut off the machine the previous night.
Step-by-step explanation:
A foreman for an injection-molding firm admits that on 23% of his shifts, he forgets to shut off the injection machine on his line.
Let F denote the event that foreman forgets to shut off the machine.
Failure to shut down at night causes the machine to overheat, increasing the probability that a defective molding will be produced during the early morning run from 5% to 15%.
Let D denote the event that the mold is defective.
If the foreman forgets to shut off the machine then 15% molds get defective.
P(F and D) = 0.23×0.15
P(F and D) = 0.0345
If the foreman doesn't forget to shut off the machine then 5% molds get defective.
P(F' and D) = (1 - 0.23)×0.05
P(F' and D) = 0.77×0.05
P(F' and D) = 0.0385
The probability that the mold is defective is
P(D) = P(F and D) + P(F' and D)
P(D) = 0.0345 + 0.0385
P(D) = 0.073
The probability that the foreman forgot to shut off the machine the previous night is given by
∵ P(B | A) = P(A and B)/P(A)
For the given case,
P(F | D) = P(F and D)/P(D)
Where
P(F and D) = 0.0345
P(D) = 0.073
So,
P(F | D) = 0.0345/0.073
P(F | D) = 0.4726
P(F | D) = 47.26%
B
Round your answer to the nearest hundredth.
A
9
B
5
Answer:
56.25°
Step-by-step explanation:
The definition of the cosine function tells you that
cos(B) = BC/BA
B = arccos(BC/BA) = arccos(5/9)
B ≈ 56.25°
Among coffee drinkers, men drink a mean of 3.2 cups per day with a standard deviation of 0.8 cups. Assume the number of cups per day follows a normal distribution.
a. What proportion drink 2 cups per day or more?
b. What proportion drink no more than 4 cups per day?
c. If the top 5% of coffee drinkers are considered "heavy" coffee drinkers, what is the minimum number of cups consumed by a heavy coffee drinker?
d. If a sample of 20 men is selected, what is the probability that the mean number of cups per day is greater than 3?
Answer:
a) 0.9332 = 93.32% drink 2 cups per day or more.
b) 0.8413 = 84.13% drink no more than 4 cups per day
c) The minimum number of cups consumed by a heavy coffee drinker is 4.52.
d) 86.86% probability that the mean number of cups per day is greater than 3
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.
In this question, we have that:
[tex]\mu = 3.2, \sigma = 0.8[/tex]
a. What proportion drink 2 cups per day or more?
This is 1 subtracted by the pvalue of Z when X = 2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2 - 3.2}{0.8}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
1 - 0.0668 = 0.9332
0.9332 = 93.32% drink 2 cups per day or more.
b. What proportion drink no more than 4 cups per day?
This is the pvalue of Z when X = 4.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4 - 3.2}{0.8}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
0.8413 = 84.13% drink no more than 4 cups per day
c. If the top 5% of coffee drinkers are considered "heavy" coffee drinkers, what is the minimum number of cups consumed by a heavy coffee drinker?
This is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 3.2}{0.8}[/tex]
[tex]X - 3.2 = 1.645*0.8[/tex]
[tex]X = 4.52[/tex]
The minimum number of cups consumed by a heavy coffee drinker is 4.52.
d. If a sample of 20 men is selected, what is the probability that the mean number of cups per day is greater than 3?
Sample of 20, so applying the central limit theore with n = 20, [tex]s = \frac{0.8}{\sqrt{20}} = 0.1789[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 3.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3 - 3.2}{0.1789}[/tex]
[tex]Z = -1.12[/tex]
[tex]Z = -1.12[/tex] has a pvalue of 0.1314
1 - 0.1314 = 0.8686
86.86% probability that the mean number of cups per day is greater than 3
Please answer this correctly
Answer:
30
Step-by-step explanation:
Answer:
It would decrease by 9.
Step-by-step explanation:
52 is the original mean or the initial mean.
43 is the final mean.
52-43 = 9
So 9 is the difference.
Hope this helped!
Where is my phone? I seem to have lost my phone. I know where I last saw it but it has been moved since then and I need help to locate it. It started at the following coordinates A (14, -12); B (14, -19); C (10, -19); D (10, -14); E (13, -14); F (13, -12). My Mom told me she translated it 6 units to the left Then my little brother said he had reflected it over the Y-axis My friend many found it and translated it 9 units up Dad said he tripped over it and reflected it over the X-axis My sister then rotated it 900 clockwise Uncle Jose translated it 5 units left and 4 units down Cousin Michelle then said she rotated it 900 clockwise Finally my dog picked it up and translated it 5 units down and 10 units to the right Where is my phone? Using the scenario on this page do the following. Graph the preimage using the given points. Label points (A, B, C, ...) Transform the objects using the information provided. Show each transformation and label. (A', B', C', ...) Determine the final location. Write a 2 to 3 sentence explain on how you found the phone location.
Answer:
see attached
Step-by-step explanation:
The attachments show the initial (brown) and final (blue) positions of the phone. The spreadsheet shows all the intermediate locations and the formulas used to determine them.
The two reflections cancel the total of 180° of CW rotation, so the net result is simply a translation. That translation is up by 9 units.
__
Translation up adds to the y-coefficient; translation right adds to the x-coefficient. Down or left use negative values.
90° CW does this: (x, y) ⇒ (y, -x)
Reflection across y does this: (x, y) ⇒ (-x, y)
Reflection across x does this: (x, y) ⇒ (x, -y)
The temperature is −18.2 Celsius in South Dakota and -9.7 Celsius Minnesota. Which one of the following inequalities correctly compares the temperatures? Choose 1 answer: Which one of the following descriptions is correct?
Answer:
The answer is A) -9.7 > -18.2
Step-by-step explanation:
This is because, when you are thinking about negative numbers, the closer they are to 0, the greater they are. So, it is warmer in Minnesota.
Answer:
A and A
Step-by-step explanation: