Answer:
(a) 0.40
(b) 0.049
(c) [tex]\bar p\sim N(0.40,0.049^{2})[/tex]
(d) Explained below
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]E(\bar p)=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]SE(\bar p)=\sqrt{\frac{p(1-p)}{n}}[/tex]
Given:
n = 100
p = 0.40
As n = 100 > 30 the Central limit theorem is applicable.
(a)
Compute the expected value of [tex]\bar p[/tex] as follows:
[tex]E(\bar p)=p=0.40[/tex]
The expected value of [tex]\bar p[/tex] is 0.40.
(b)
Compute the standard error of [tex]\bar p[/tex] as follows:
[tex]SE(\bar p)=\sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{0.40(1-0.40)}{100}}=0.049[/tex]
The standard error of [tex]\bar p[/tex] is 0.049.
(c)
The sampling distribution of [tex]\bar p[/tex] is:
[tex]\bar p\sim N(0.40,0.049^{2})[/tex]
(d)
The sampling distribution of p show that as the sample size is increasing the distribution is approximated by the normal distribution.
7/3 + 4/7 plz help me it’s 14 point
Answer:
2 19/21, 61/21
Step-by-step explanation:
First, lets make the denimonators, "3 and 7" common. 3 and 7 are prime numbers, so the common denonminator is "21".
For 7/3, multiply by "7/7" and for 4/7 multiply by "3/3".
49/21 + 12/21
Add.
61/21
61 is a prime number so this answer will be your final answer.
(unless you have to put it as a mixed number which would be 2 19/21)
Answer:
61/21
Step-by-step explanation:
The 2 fractions must have a common denominator and you do that by finding the LCM and the multiply the numerators by what you multiplied the denominators by in order to get that number. From here you must add the numerators together and keep the denominator the same and then you get that answer. You cannot simplify anymore so your answer is above.
(hope you get it right)
Mark Brainliest Please
Plz Help!!!!!!!!!! 14. Teenagers should sleep between 8 and 10 hours per night. Sarah typically sleeps 2 hours less than this per night. Which inequality describes the amount of time that Sarah sleeps? A. 10 < x < 12 B. 8 < x < 10 C. 6 < x < 12 D. 6 < x < 8 E. 8 + 2 < 8 < 10 F. 8 < x < 10 + 2
Answer:
The amount of time that Sarah sleeps is 6<x<8
Step-by-step explanation:
Mathematical inequality is that proposition that relates two algebraic expressions whose values are different. It is a proposition of relation between two different elements, either by greater, lesser, greater or equal inequality, or less or equal.
A compound inequality (or combined inequality) is two or more inequalities joined with or and and.
When two inequalities are joined with and, they are often written as a double inequality.
You know that teenagers should sleep between 8 and 10 hours per night.. Being x the number of hours slept per night, this can be represented by the following double inequality:
8<x<10
If Sarah normally sleeps 2 hours less per night, this indicates that she sleeps between (8-2) and (10-2) hours per night, that is, between 6 and 8 hours. Represented by a double inequality, Sarah normally sleeps:
6<x<8
The amount of time that Sarah sleeps is 6<x<8
PLEASE HELP! Thanks if you do!
Answer:
x=2 and y=−3
Step-by-step explanation:
Answer this please and thank you
Answer:
The Answer is x^2/2
Step-by-step explanation:
The ^ is the power of _
In this case ^ is the power of 2.
6. Find CA*
Please help it’s so confusing
Answer:
The answer is 19.
Step-by-step explanation:
3x+1+12=9x+1
3x+13=9x+1
13=6x+1
12=6x
x=2
3(2)+1+12=19
Answer:
CA = 19
Step-by-step explanation:
3x + 1 + 12 = 9x + 1
combine like terms
3x + 13 = 9x + 1
Subtraction property of equality
3x - 3x + 13 = 9x - 3x + 1
13 = 6x + 1
Subtraction property of equality
13 - 1 = 6x + 1 - 1
12 = 6x
Division property of equality
12/6 = 6x/6
2 = x
Symmetric property of equality
x = 2
Substitute x for 2
9(2) + 1 = 19
Consider the following.
P = −0.1s3 + 6s2 + 400.
Required:
a. Find the amount s of advertising (in thousands of dollars) that maximizes the profit P (in thousands of dollars).
b. Find the point of diminishing returns.
Answer:
A) s = $40 (in thousands of dollars)
B) point of diminishing returns is at;
(20, 2000) in thousands of dollars
Step-by-step explanation:
We are given the profit function as;
P = −0.1s³ + 6s² + 400
A) To maximize the profit, we need to find the first derivative and equate it to zero.
Thus;
dP/ds = -0.3s² + 12s
At dP/ds = 0, we have;
-0.3s² + 12s = 0
0.3s² = 12s
0.3s = 12
s = 12/0.3
s = $40 (in thousands of dollars)
B) To find the point of diminishing returns, we need to find the 2nd derivative of the given profit function and equate to zero.
Thus;
d²P/ds² = -0.6s + 12
At d²P/ds² = 0, we have;
-0.6s + 12 = 0
0.6s = 12
s = 12/0.6
s = 20
At s = 20,
P = −0.1(20)³ + 6(20)² + 400
P = -800 + 2400 + 400
P = 2000
Thus; point of diminishing returns is at;
(20, 2000) in thousands of dollars
What is the minimum possible value of this decimal? Use words, pictures, or numbers to explain your reasoning.
Answer:
if 2.4 is there it will become -2. 4
To simplify an expression, should we apply the Order of Operations in top-down or bottom-up order?
Answer:
To simplify an expression, we should apply the order of operations top-down
Step-by-step explanation:
The order of operation can be represented as;
BODMAS
If we have an expression to simplify, then the order of operations is from left to right
This means that it is in a top-down fashion i.e from brackets to subtraction and not bottom-up order from subtraction to bracket
The double number line shows that 5 pounds of avocados cost $9.
0
Avocados
5
(pounds)
Cost
H
(dollars)
0
9
Based on the ratio shown in the double number line, what is the cost for 1 pound of avocados?
S
Answer:
$1.8
Step-by-step explanation:
Given :
5 pounds of avocado = $9
This means that 5 pounds of avocado cost $9; The cost of 1 pound of Avocado can be obtained thus ;
Let cost of 1 pound of avocado = a
5 pounds = $9
1 pound = a
Cross multiply
5 * a = $9 * 1
5a = 9
Divide both sides by 5
5a / 5 = 9/5
a = 1.8
Hence, 1 pound of avocado will cost $1.8
Tracy wants to buy some pies for her sisters and she has a budge
apple pies, $4.5 banana pies, and $5.5 chocolate pies. She wants
sisters and must buy as many chocolate pies as apple pies and ba
How many of each item should she buy? Write a system of equati
this problem.
# of applie pies =
# of banana pies =
# of chocolate pilis
Answer:
Tracy must buy 4 apple pies, 4 banana pies, and 8 chocolate pies.
Step-by-step explanation:
The complete question would be:
"Tracy wants to buy some pies for her sisters and she has a budget of $82 to spend on $5 apple pies, $4.5 banana pies, and $5.5 chocolate pies. She wants 16 pies for her sisters and must buy as many chocolate pies as apple pies and banana pies combined. How many of each item should she buy?
Write a system of equations of this problem."
Then, we will write a system of equations according to the information given in the problem:
We must consider each type of pie as an unknown, so:
x: the amount of apple pies
y: the amount of banana pies
z: the amount of chocolate pies
As she has a budget of $82, the amount of each pie must be multiplied by its price and the total sum must be 82:
5x + 4.5y + 5.5z =82 (1)
The total amount of pies must be 16:
x + y + z = 16 (2)
And the amount of chocolate pies must be equal to the quantity of apple pies and banana pies combined:
z= x + y (3)
System of equations:
(1) 5x + 4.5y + 5.5z =82
(2) x + y + z = 16
(3) z= x + y
First, we subtract x and y on 3 on both sides:
z - (x + y )= x + y - (x + y)
-x -y +z = 0
Then, we add 2 and 3:
(2) x + y + z = 16
(3) -x -y +z = 0
2 z=16
z=8
We replace the value of z on 3 and substract x on both sides:
x + y =8
y=8 - x
We use this on equation 1:
5x + 4.5y + 5.5z =82
5x + 4.5×(8-x) + 5.5×8=82
5x + 36 - 4.5x + 44 = 82
0.5x + 80 =82
0.5x=82-80
0.5x=2
x=2/0.5
x=4
We replace the values of x and z on equation 2:
x + y + z = 16
4 + y + 8 = 16
y + 12 = 16
y=16-12
y= 4
Tracy must buy 4 apple pies, 4 banana pies, and 8 chocolate pies.
The contents of seven similar containers of sulfuric acid are 9.8, 10.2, 10.4, 9.8,10.0, 10.2, and 9.6 liters. Find a 95% confidence interval for the mean contents of all such containers, assuming an approximately normal distribution. (Round your answers into two decimal places.)
Answer:
The 95 confidence interval is [tex]9.738 < \mu < 10.262 [/tex]
Step-by-step explanation:
The sample size is n = 7
The sample data is 9.8, 10.2, 10.4, 9.8,10.0, 10.2, and 9.6 liters
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{\sum x_i }{n }[/tex]
=> [tex]\= x = \frac{ 9.8 + 10.2 + 10.4 +\cdots + 9.6}{7 }[/tex]
=> [tex]\= x = 10[/tex]
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{\frac{\sum ( x_i - \= x)^2 }{n-1} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ ( 9.8 - 10)^2 + ( 10.2 - 10)^2+ \cdots + ( 9.6 - 10)^2}{7-1} }[/tex]
=> [tex]\sigma =0.283[/tex]
Note : We are making use of t distribution because n is small i.e n < 30
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
=> [tex]df = 7 - 1[/tex]
=> [tex]df = 6[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the t distribution table the critical value of at a degree of freedom of is
[tex]t_{\frac{\alpha }{2}, 6 } = 2.447 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} , 6} * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.447 * \frac{0.283}{\sqrt{7} }[/tex]
=> [tex]E = 0.262 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]10 -0.262 < \mu <10 + 0.262[/tex]
=> [tex]9.738 < \mu < 10.262 [/tex]
A certain code is a sequence of 7 digits. What is the probability of generating 7 digits and getting the code consisting of 1, 2, . . ., 7 if each digit can be repeated?
Answer:
The code has 7 digits:
Here you are asking:
"What is the probability that the code is consisting only of the digits {1, 2, 3, 4, 5, 6, 7}?"
Ok, first we must calculate the number of all the possible codes.
Suppose that each digit is an independent event.
Each one of those events has 10 possible outcomes {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
And we have 7 of those.
The total number of possible combinations is equal to the product of the number of outcomes for each event, then the total number of possible combinations is:
C = 10^7.
Now let's calculate the number of possible codes if we only use the digits in the restriction.
We can do exactly the same as above, but now in each case, we have 7 possible outcomes for each digit, then in this case the number of possible combinations is:
c = 7^7.
Now the probability of generating at random a code that only uses the digits {1, 2, 3, 4, 5, 6, 7} is equal to the quotient between the number of codes that only use these digits, and the total number of possible codes.
P = c/C = (7^7)/(10^7) = (7/10)^7 = 0.082
The original cost of a TV is $800. It is currently in sale for 25% off. What is the price if TV on sale?
a. $200
b. $775
c. $600
d $1000
Please help me find the missing measurements of this :)
Answer:
4mm
Step-by-step explanation:
The ratio of the two congruent shapes are 2.5:1
15 : 6 = 2.5 : 1
15/6 = 2.5
5 : 2 = 2.5 : 1
5/2 = 2.5
Therefore, 10 : x = 2.5 : 1
10/x = 2.5
x = 4
Answer: 15, 2, 6, and 5
Step-by-step explanation: they are equal to the measurements listed
How many times can 8 go into 0?
Answer:
0 times because 8 is greater than 0
Step-by-step explanation:
Answer:
the answer would be 0 because if you try to put 8 into 0, it wont so your answer would be 0
Let 2x - 1 represents the time Anna and Tamara travel the first two days
and 3x - 4 represents the time they travel the last two days.
Write an algebraic expression that represents the total time
Anna and Tamara travel over the four days.
Answer:
5x-5
Step-by-step explanation:
add the expression and simplify 2x - 1 + 3 x -4 add 2x and 3x
5x-1-4 subtract 4 from -1
equals 5x-5
The perimeter of a rectangular outdoor patio is 66 ft. The length is 3 ft greater than the width. What are the dimensions of the patio?
Answer:
width = 15 ft
length = 18 ft
Step-by-step explanation:
lets assume the width is w, and length is l.
For the first equation, we all know that a rectangle is 2 widths and 2 lengths added up, which in "math" language looks like this:
2w+2l= 66
for the second equation, the problem says that the length is 3 ft greater than the width. From there, we can derive the equation:
w+3 = l
Now you can substitute one of the variables, length or width, but it is easier to do length. The equation ends up being:
2(w+3) + 2w = 66
Distributive property:
2w+6+2w = 66
which is equal to:
4w+6 = 66
which finally is:
w=15 ft.
Now that we know the width, we can just add 3 to the width to get the length, according to the problem. You get:
L = 18 ft.
6. If the sequence below is an arithmetic sequence then what will the next two numbe
the sequence be?
Sequence: 3, 9....
a. 18, 36
c. 15, 45
b. 27,81
d. 15, 21
how do i plot this??
Answer:
its pretty simple actually put a point after the -1 (-0.9) and move left twice from -1 to get the plot point -1.2
Pls help for Algebra 11b = 143
Answer:
b= 13.................................
Step-by-step explanation:
143/11
How do you solve this problem ?
Answer: 7.04
Step-by-step explanation:
Subtract 154.94- 147.88 because its asking how much more you made on the second paycheck then the first. So in order to get the answer subtract
At the supermarket you can fill your own honey bear container. A customer buys 12 oz of honey for $5.40.
How much honey can you buy per dollar?\
Ella and some friends are going to a movie. Each movie ticket costs $5. Create an equation that shows the relationship between how many friends, n, attend the movie and the total cost in dollars, c.
Answer:
lets say ella and 3 other friends went, so since there is 4 people in total, there will be 4 $5 dollar tickets, so you multiply 5 and 4 which is $20.
Step-by-step explanation:
Joe makes $3.50 per hour working at a convenience store. If he gets a bonus of $25 this
week, how many hours must he work to make at least $165?
Answer:
40
Step-by-step explanation:
Working backwards, he has to get 140 from working hours alone. 140/3.5=40. He has to work 40 hours to get at least 165
What is the discriminant of the quadratic equation: (multiple choice)
Answer:
85
Step-by-step explanation:
The equation for the discriminant is
b^2-4(a)(c)
Plug your numbers in from the equation.
1=a, -7=b, -9=c
(-7)^2-4(1)(-9)
49-(-36)
49+36
85
What is the slope of a line that is perpendicular to the line y = x + 4?
The slope of the line is
Answer:
-1
Step-by-step explanation:
Answer:
- 1/6 is correct
perpendicular refers to the opposite of 1/6 therefor being negative 1/6
Step-by-step explanation:
In the figure, <6 and <3 are
Answer:B
Step-by-step explanation
HURRY ILL GIVE 10 BRAINLY POINTS
What is 1 times 300
Answer:
300
Step-by-step explanation:
Answer:
300
Step-by-step explanation:
300 x 1 = 300
1 x 300 = 300
The temperature in a town is 27.6°F during the day and -13.9°F at night. Find the difference in the temperatures.
Answer:
41.25 I believe
Step-by-step explanation:
Answer:
41.5 degree difference
Step-by-step explanation:
Can someone draw this for me? NEED HELP
It's for a test. Will make you brainliest!!!!!
Answer:
Step-by-step explanation:
