Answer:
The sampling distribution of the sample mean is approximately normal with mean 72 and standard deviation 1.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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.
Normally distributed with mean 72 and standard deviation 6.
This means that [tex]\mu = 72, \sigma = 6[/tex]
A random sample of size 36
This means that [tex]n = 36, s = \frac{6}{\sqrt{36}} = 1[/tex]
The sampling distribution of the sample mean is
By the Central Limit Theorem, it is approximately normal with mean 72 and standard deviation 1.
Using the following image , find the value for x
Step-by-step explanation:
Here, two angles i.e, (x + 13)° and (4x + 2)° are forming a straight line, thus the sum of these two angles will be 180° because they are forming a linear pair.
[tex]\longrightarrow[/tex] (x + 13) + (4x + 2) = 180°
[tex]\longrightarrow[/tex] x + 13 + 4x + 2 = 180°
[tex]\longrightarrow[/tex] 5x + 15 = 180°
[tex]\longrightarrow[/tex] 5x = 180° ― 15
[tex]\longrightarrow[/tex] 5x = 165°
[tex]\longrightarrow[/tex] x = 165° ÷ 5
[tex]\longrightarrow[/tex] x = 33°
Therefore, the value of x is 33°.
Quick Check!
[tex]\longrightarrow[/tex] x + 13
[tex]\longrightarrow[/tex] (33 + 13)°
[tex]\longrightarrow[/tex] 46°
And, another angle :
[tex]\longrightarrow[/tex] (4x + 2)°
[tex]\longrightarrow[/tex] {4(33) + 2}°
[tex]\longrightarrow[/tex] (132 + 2)°
[tex]\longrightarrow[/tex] 134°
★ Sum of the angles should be 180° :
[tex]\longrightarrow[/tex] (x + 13) + (4x + 2) = 180°
[tex]\longrightarrow[/tex] 46° + 134° = 180°
[tex]\longrightarrow[/tex] 180° = 180°
L.H.S = R.H.S, hence verified!
The value of x is 33
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
What is linear pair of angles?"It is formed when two lines intersect each other at a single point. "" The angles are adjacent to each other.""The sum of angles of a linear pair is always 180° "What are supplementary angles?"Two angles are supplementary angles if the sum of the angles is 180° "
For given question,
angle (x + 13) and angle (4x + 2) form linear pair of angles.
So, these angles are supplementary angles.
⇒ (x + 13)° + (4x + 2)° = 180°
We solve above equation to find the value of x
⇒ x + 4x + 13 + 2 = 180
⇒ 5x + 15 = 180
⇒ 5x = 165
⇒ x = 33
Therefore, the value of x is 33
Learn more about the supplementary angles here:
https://brainly.com/question/13045673
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In point estimation a. data from the sample is used to estimate the population parameter. b. the mean of the population equals the mean of the sample.
Answer:
a. data from the sample is used to estimate the population parameter.
Step-by-step explanation:
Given
Point estimation
Required
The true statement
Point estimation literally means taking data from the sample to estimate the corresponding population parameter
For instance:
Sample mean estimates population mean
Sample standard deviation estimates population standard deviation
Sample variance estimates population variance
Hence;
(a) is correct
f(x) = -16x^2 + 22x + 3
Answer:
factor???
Factored Form: y= (-1)(8x+1)(2x-3)
Step-by-step explanation:
What is the prime factorization of 30?
O A. 2.2.3.5
O B. 5.6
O C. 3.10
O D. 2.3.5
D. 2.3.5 is the correct answer
Which equation represents the line that passes through points (1, –5) and (3, –17)?
Answer:
y = -6x + 1
Step-by-step explanation:
y = mx + b
b = slope = (-5 - (-17))/(1 - 3) = 12/(-2) = -6
y = -6x + b
-5 = -6(1) + b
b = 1
y = -6x + 1
Answer:
[tex]y=-6x+1[/tex]
Step-by-step explanation:
The linear equation with slope m and intercept c is given as follows:
[tex]y=mx+c[/tex]
The formula for slope of line with points [tex](x_{1} ,y_{2} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] can be expressed as,
[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
The line passes the points that are [tex](1,-5)[/tex] and [tex](3,-17)[/tex]
The slope of the line can be obtained as follows:
[tex]m=\frac{-17-(-5)}{(3)-1}[/tex]
[tex]m=\frac{-12}{2}[/tex]
[tex]m=-6[/tex]
The slope of the line is [tex]-6[/tex]
The line passes through the point [tex](3,-17)[/tex]
Substitute 3 for x, - 6 for m and -17 for y in equation [tex]y=mx+c[/tex] to obtain the value of c.
[tex]-17=-6(3)+c[/tex]
[tex]-17=-18+c[/tex]
[tex]-17+18=c[/tex]
[tex]1=c[/tex]
The equation is [tex]y=-6x+1[/tex]
Hence, the equation of the line that passes through the points [tex](1,-5)[/tex] and [tex](3,-17)[/tex] is [tex]y=-6x+1[/tex]
Put -3.0-3.45, -15, and -3.15 in order from least to greatest.
Answer:
-15 -3.45 -3.15 -3.0
Step-by-step explanation:
What is the Value of the expression 1/4(c cubed + d squared) when c = -4 and d = 10
Answer: 9
Step-by-step explanation:
[tex]\frac{1}{4} (c^{3}+d^{2})[/tex]
c = -4d = 10Substitute in the values into the expression:
[tex]\frac{1}{4} ((-4)^{3}+10^{2})\\\\=\frac{1}{4}(-64+100)\\\\=\frac{1}{4}(36)\\\\=\frac{36}{4} =9[/tex]
Simplify the radical expression below square root of 5/64
A square root 5/8
B 5/64
C square root 5/64
D 5/8
Answer:
a
Step-by-step explanation:
square root distribute to numerator and denominator so both get square rooted [tex]\sqrt{5}[/tex]/8
Multiply 3x (2x - 1)
Answer:
6x^2 - 3x
[tex]6x^2-3x[/tex]
Step-by-step explanation:
3x (2x-1)
multiply 3x by 2x -> 6x^2
multiply 3x by -1 -> -3x
Answer:
The answer is [tex]6x^{2} -3x[/tex].
Step-by-step explanation:
To solve for the answer, start by using the distributive property. The distributive property is a property of multiplication used in addition and subtraction and states that two or more terms in addition or subtraction with a number are equal to the addition or subtraction of the product of each of the terms with that number.
The distributive property for this problem will look like [tex](3x*2x)+(3x*-1)[/tex], and when the problem is simplified, it will look like [tex]6x^{2} -3x[/tex]. The final answer is [tex]6x^{2} -3x[/tex].
Hello, please help me!!
Answer:
0.14
Step-by-step explanation:
P(A|B) asks for the probability of A, given that B has happened. This is equal to the probability of A and B over the probability of B (see picture)
Here, the question is asking if someone is taking the bus given that they are a senior.
The probability of someone being a senior and taking the bus is 5/100, or 0.05 . The probability of someone being a senior is 35/100, or 0.35
Our answer is then 0.05/0.35 = 1/7 = 0.14
An elected government official is interested in the opinion of teachers in her voting area. She randomly selected five schools at random from the 20 schools in her area and then interviews each of the teachers in those five schools. The government official is using
Answer:
a simple random sample (SRS).
Step-by-step explanation:
In Statistics, sampling can be defined as a process used to collect or select data (objects, observations, or individuals) from a larger statistical population using specific procedures.
There are various types of sampling used by researchers and these are;
1. Systematic sampling.
2. Convenience sampling.
3. Stratified sampling.
4. Cluster sampling.
5. Random sampling.
Random sampling also referred to as simple random sample (SRS) involves randomly selecting a subset of a larger population.
In this scenario, an elected government official randomly selected five schools at random from the 20 schools in her area and then interviews each of the teachers in those five schools, in order to get their opinions about voting. Thus, the government official is using a simple random sample (SRS).
which linear inequality represents the graph below?
A. y < -1/4x-4
B. y < 4x-4
C. y < -1/4x+4
D. y < -4x+4
Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n
inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer,
while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches
greater than the box he originally planned to build?
O 3n2 + 2n
312 + 3n+3
O 6n2 + 3n
O 6n2 + 3n+3
Given:
Edge of a cubic box = n inches.
He decided to make the box 1 inch taller and 2 inches longer, while keeping its depth at n inches.
To find:
How many cubic inches greater than the box he originally planned to build?
Solution:
Edge of a cubic box is n inches, so the volume of the original cube is:
[tex]V_1=(edge)^3[/tex]
[tex]V_1=n^3[/tex]
According to the given information,
New width of the box = n+1
New length of the box = n+2
New height of the box = n
So, the volume of the new box is:
[tex]V_2=Length\times width\times h[/tex]
[tex]V_2=(n+2)(n+1)n[/tex]
[tex]V_2=(n^2+2n+n+2)n[/tex]
[tex]V_2=(n^2+3n+2)n[/tex]
[tex]V_2=n^3+3n^2+2n[/tex]
Now, the difference between new volume and original volume is:
[tex]V_2-V_1=n^3+3n^2+2n-n^3[/tex]
[tex]V_2-V_1=3n^2+2n[/tex]
So, the volume of new box is 3n^2+2n cubic inches more than the original box.
Therefore, the correct option is A.
(3x^3)^2 write without exponent
Answer:
9*x*x*x*x*x*x.
Step-by-step explanation:
(3x^3)^2
= 3^2 * x^(3*2)
= 3^2 * x^6
= 9*x*x*x*x*x*x
For which of these research situations would linear regression be the best statistical test to perform?
A) independent variable = city of residence
dependent variable = miles driven per week
B) independent variable = gender
dependent variable = salary
C) independent variable = age
dependent variable = reaction time in milliseconds
D) independent variable = college major
dependent variable = political affiliation
Answer:
C) independent variable = age
dependent variable = reaction time in milliseconds
Step-by-step explanation:
The linear regression statistical test is best used for research experiment where there is a single dependent and one independent variable whjre both variables are numeric. In the given options above, the city of residence, gender, college major and political affiliation are all possible categorical variables and age, salary, miles driven and reaction time are all numerical variables. Hence, the best situation in which to use linear regression is a test where both the independent and dependent variables are either age, salary, reaction time or miles driven.
currently, the US interest rate is at 2% annually. how long it will take an investor to make 10% of money from an investment if the bank pays simple interest
Answer:
5 years
Step-by-step explanation:
Please help solve and explain this
can you put the whole question here
9.
For a normal distribution with mean 20 and standard deviation 5, approximately what percent of
the observations will be between 5 and 35?
A. 50%
B. 68%
C. 95%
D. 99.7%
Answer: D. 99.7%
Step-by-step explanation:
Scores that lies within the first deviation(1σ) =
(20 - 5) to (20 + 5) → 15 to 25
Scores that lies within the second deviation(2σ) =
(20 - 5 - 5) to (20 + 5 + 5) → 10 to 30
Scores that lies within the third deviation(3σ) =
(20 - 5 - 5 - 5) to (20 + 5 + 5 + 5) → 5 to 35
As shown by the distribution graph below, 99.73% of the scores lies within the third deviation(3σ).
How many orders are possible to view 6 videos from a stack of 8 videos?
Answer:
28
Step-by-step explanation:
We know that ,
n C r = n! / ( n - r)! r! 8! / ( 8 - 6)! 6!8! / 2! × 6! 7 × 8 / 2 × 1 28In parallelogram ABCD, line AC is congruent to line BD. Is ABCD a rectangle?
A. Yes
B. No
C. Cannot be determined
9514 1404 393
Answer:
A. yes
Step-by-step explanation:
The diagonals of a rectangle are congruent and bisect each other.
The diagonals of a parallelogram bisect each other. If they are also congruent, then the parallelogram is a rectangle.
Answer:
Yes.
Step-by-step explanation:
Press option yes
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Answer:
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OKAY
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Use the arithmetic progression formula to find the sum of integers from 75 to 100.75,76,77....99,100.
Answer:
The sum is 2275
Step-by-step explanation:
Given
[tex]75,76,77....99,100[/tex]
Required
The sum
Using arithmetic progression, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where:
[tex]T_1 = 75[/tex] --- first term
[tex]T_n = 100[/tex] --- last term
[tex]n = T_n - T_1 + 1[/tex]
[tex]n = 100 - 75 + 1 = 26[/tex]
So, we have:
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
[tex]S_n = \frac{26}{2}*(75 + 100)[/tex]
[tex]S_n = 13*175[/tex]
[tex]S_n = 2275[/tex]
3z+8=12+3x-z
I need help someone help me
Answer:
z=3x/4+1 x=4z/3-4/3
Step-by-step explanation:
F(x)=-x^2-4 for x= -3
Answer:
5Step-by-step explanation:
Given:
f(x)=-x²-4Substitute x= -3:
f(-3) = (-3)² - 4 = 9 - 4 = 5A city has a population of 350,000 peopleSuppose that each year the population grows by 7.75%What will the population be after 6 years Use the calculator provided and round your answer to the nearest whole number
Answer:
335%
Step-by-step explanation:
the difference when a number doubled is subtracted from 3
Answer: Let the number be x
3-2x is the equation.
Solve using the elimination method. 2x + 7y = 36
6x - 7y = - 60
Answer:
[tex]x=-3[/tex]
[tex]y=6[/tex]
Step-by-step explanation:
Elimination method:
[tex]2x+7y=36[/tex]
[tex]6x-7y=-60[/tex]
Add these equation to eliminate y:
[tex]8x=-24[/tex]
Then solve [tex]8x=-24[/tex] for x:
[tex]8x=-24[/tex]
[tex]\frac{8x}{8} =\frac{-24}{8}[/tex]
[tex]x=-3[/tex]
Add the value of x to solve y:
[tex]2x+7y=36[/tex]
Substitute [tex]-3[/tex] for x in [tex]2x+7y=36[/tex]
[tex](2)(-3)+7y=36[/tex]
[tex]7y-6=36[/tex]
[tex]7y=36+6[/tex]
[tex]7y=42[/tex]
[tex]y=42/7\\[/tex]
[tex]y=6[/tex]
{ [tex]x=-3[/tex] and [tex]y=6[/tex] }
hope this helps....
A farmer sells four of his farm products Maize, Potatoes, carrots and tomatoes in each of 2 towns into classes of 3 customers. Consumers, Retailers, and wholesellers .
Town1 Maize, Potatoes Carrots tomatoes
consum. 4. 6. 7. 4.
Retailer. 3. 2. 1. 6.
wholesa. 4. 3. 5. 3.
Town2. Maize. Potatoes.Carrots.tomatoes
consum. 4. 5. 3. 6.
Retailer. 7. 8. 4. 4.
wholesa. 2. 4. 6. 1.
In order to sell his produce in these towns , the farmer pays commission to salesman, town managers and division managers as shown.
salesman.townmanagers.divisionmanage
6%. 5%. 2%
4%. 3%. 3%
Selling price per bag is:
Maize Sh 200
Potatoes sh 1000
Carrots sh 700
Find total sales in units by potatoes.
Answer:
Step-by-step explanation:
The total mass of 8 identical dictionaries is 9.92 kilograms. What is the mass, in kilograms, of one dictionary? Enter your answer in the space provided
Write an equation that represents the line.
Answer:
Y = 2/3X + 4/3
Step-by-step explanation:
(1,2) (4,4)
M = 2/3
Y = 2/3X + b
4 = 8/3 + b
12 = 8 + 3b
4 = 3b
B = 4/3
Y = 2/3X + 4/3