Answer:
a) Yes
b) Yes
c) Yes
d) 0.6
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.
A large population has skewed data with a mean of 70 and a standard deviation of 6.
This means that [tex]\mu = 70, \sigma = 6[/tex]
Samples of size 100
This means that [tex]n = 100[/tex]
a) Will the distribution of the means be closer to a normal distribution than the distribution of the population?
According to the Central Limit Theorem, yes.
b) Will the mean of the means of the samples remain close to 70?
According to the Central Limit Theorem, yes.
c) Will the distribution of the means have a smaller standard deviation?
According to the Central Limit Theorem, the standard deviation of the population is divided by the sample size, so yes.
d) What is that standard deviation?
[tex]s = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{100}} = \frac{6}{10} = 0.6[/tex]
So 0.6.
Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat
Answer:
Whe we have two functions, f(x) and g(x), the composite function:
(f°g)(x)
is just the first function evaluated in the second one, or:
f( g(x))
And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:
f(x) = 1/(x + 1)
where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.
Now, we have:
f(x) = x^2
g(x) = x + 9
then:
(f ∘ g)(x) = (x + 9)^2
And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:
x ∈ (-∞, ∞)
(g ∘ f)(x)
this is g(f(x)) = (x^2) + 9 = x^2 + 9
And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:
x ∈ (-∞, ∞)
(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4
And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:
x ∈ (-∞, ∞)
(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18
And again, there are no values of x that cause a problem here, so the domain is:
x ∈ (-∞, ∞)
PLEASE HELP!!!please >_
Answer:
x =56 (corresponding angles are equal)
Answer:
56°
Step-by-step explanation:
Since these two lines are parallel, and these two angles are at the corresponding position, the required angle measure is 56
: Find the perimeter of the polygon.
Can someone please help
Answer:
36
Step-by-step explanation:
The tangents from the same point are equal. Each point of the triangle extend 2 tangents to the circle.
Tangents from the uppest point: 8+8=16
Tangents from the lowest point: 4+4=8
Tangents from the third point:
10-4=6
6+6=12
Perimeter: 16+8+12=36units
Brainliest please~~
At a school, there are two different math classes for children of the same age. The two classes have different teachers. The school principal is interested in gauging the effectiveness of two different teaching methods and asks each teacher to try one of the methods. At the end of the semester both classes are given the same test and the results are compared.
In this experiment, what is the treatment variable?
Give an example of a variable that could confound the results.
Answer:
Treatment variable = Teaching methods
Confounding variable = Teacher's teaching prowess
Step-by-step explanation:
The treatment variable here is that variable which is applied on the student in other to ovtujba measure of the dependent or response variable, the response variable here is the test score, while the treatment variable is the independent variable, which are the teaching methods.
The confounding variable is that variable which is capable of causing a spurious association in our measurement and also has an effect on the test score. However, this variable isn't taken into account during our experiment. One possible confounding variable could be the Teacher's individual teaching prowess regardless of the teaching method. This could cause the student to get a better grasp of what is being taught by one teacher than the other.
Answer:Treatment variable = Teaching methods
Confounding variable = Teacher's teaching prowess
Step-by-step explanation:
1. There are 2 schools. Each school has 3 buildings. Each building has 4 floors. Each floor has 5 classrooms. Each classroom has 6 rows of desks. Each row has 7 desks. How many desks are there in the two schools?
I need help thanksss
Explanation:
We replace x with x-1 to shift 1 unit to the right. This is because we're making each new input 1 smaller than the old input, which means we're moving the xy axis 1 unit to the left while keeping the f(x) curve fixed in place. That gives the illusion f(x) is moving 1 unit to the right.
The -1 at the end will subtract 1 from the y coordinate and shift everything down by 1 unit.
Answer:
D
Step-by-step explanation:
1 unit Right ³√x-1
unit down (³√x-1)-1
What is the slope of the line?
I will mark the brainliest!
Answer:
1
Step-by-step explanation:
Slope = change in y over change in x
If you look at the graph as y goes up 1 x goes up 1
So slope = 1/1 or just 1
Answer:
m=1
Step-by-step explanation:
Hi there!
We're given the graph of a line and we need to find the slope of the line
There are many ways to do this, but the easiest is to calculate it from two points
The formula for the slope (m) calculated from 2 points is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex], where ([tex]x_{1}[/tex],[tex]y_{1}[/tex]) and ([tex]x_{2}[/tex],[tex]y_{2}[/tex]) are points
So we can take 2 points from the graph of the line to find the slope
For example, let's take (-1,0) and (0,1)
Let's label their values to avoid any confusion before we substitute their values into the formula
[tex]x_{1}[/tex]=-1
[tex]y_{1}[/tex]=0
[tex]x_{2}[/tex]=0
[tex]y_{2}[/tex]=1
now substitute into the formula *remember: we have SUBTRACTION in the slope formula
m=[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
substitute
m=[tex]\frac{1-0}{0--1}[/tex]
simplify
m[tex]\frac{1}{0+1}[/tex]
simplify again
m=[tex]\frac{1}{1}[/tex]
divide
m=1
Therefore the slope of the line is 1
Hope this helps! :)
What is the value of f(−2)=2x^3 +3x 2 −39x−20?
Answer:
-65
Step-by-step explanation:
The graph below shows a proportional relationship between x and y. What is the constant of proportionality,
y/x?
Answer:
0.5
Step-by-step explanation:
you just need see at one point. i see at point (1, 0.5)
Tasha needs 75 liters of a 40% solution of alcohol. She has a 20% and a 50% solution available. How many liters of the 20% and how many liters of the 50% solutions should she mix to make the 40% solution?
Answer:
25 liters of 20%
50 liters of 50%
Step-by-step explanation:
x = liters of 50%
75 - x = liters of 20%
50x + 20(75 - x) = 40(75)
50x + 1500 - 20x = 3000
30x = 1500
x = 50
75 - x = 25
Adirondack Savings Bank (ASB) has $5 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 7% for home loans, 12% for personal loans, and 9% for automobile loans. The bank's planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.(a) Formulate a linear programming model that can be used to determine the amount of funds ASB should allocate to each type of loan to maximize the total annual return for the new funds.(b) How much (in dollars) should be allocated to each type of loan? 1) What is the total annual return (in dollars)?2) What is the annual percentage return?
I NEED HELP WITH THIS, THANKS
9514 1404 393
Answer:
g(x) = 3|x|
Step-by-step explanation:
Each value of g is 3 times the corresponding value of f:
g(x) = 3·f(x)
g(x) = 3|x|
express as a single decimal:4+9/100+6/10
Answer:
4.69
Step-by-step explanation:
4+9/100+6/10
4 is a whole number
9/100 = .09
6/10 = .6
Adding together
4+.09+.6
4.69
Answer:
4.69
Step-by-step explanation:
[tex] \small \: 4 + \frac{9}{100} + \frac{6}{10} \\ [/tex]
[tex] \small4 + \frac{9}{100} + \frac{3}{5} \\ [/tex]
[tex] \small \frac{100 \times 4}{100 \times 1} + \frac{9}{100} + \frac{ 3 \times 20}{5 \times 20} \\ [/tex]
common denominator is 100[tex] \small \frac{400}{100 \times 1} + \frac{9}{100} + \frac{ 60}{100} \\ [/tex]
Add the numerator[tex] \small \frac{400 + 9 + 60}{100 \times1} \\ [/tex]
[tex] \small \frac{469}{100 \times 1} \\ [/tex]
Divide we get
4.69
If someone can pls give the answer with steps that would be greatly appreciated :)
Answer:
D
C
Step-by-step explanation:
One equation must have a slope that is the negative reciprocal of the other equation's slope.
The the sentence I've given you is correct, it is probably a little difficult to understand. Let's use an example
y = 1/2 x + 4
The slope of this line = 1/2
Therefore if you want a negative reciprocal, it would - 2 so y=-2x would be perpendicular to y = 1/2x + 4.
Just to be sure you understand, I'll put the graph of these two equations below.
===================================
So to answer your question
8)
is D. All the others have signs that are the same. They are reciprocals but with signs the same.
9) This is a little harder. You have reciprocals in all of them. But the slope must be positive. So that means that only a and c can be true. A does not go through (4,-1). C does.
y = 1/4 * 4 - 2
y = 1 - 2
y = - 1
So the answer is C
Susan was posting gifts to her family. She weighed three envelopes before posting them. Geace Envelope A Envelope B Envelope C • Envelope A weighed x grams. Envelope B was 50 grams lighter than Envelope A. • Envelope C was three times as heavy as Envelope A. If the total weight of the three envelopes was 840 grams, write an equation in x and solve it to find the weight of Envelope A. (
Answer:
5x+50
Step-by-step explanation:
you have one x. An x plus fifty. And 3 mire x's. So 5 x's and a 50.
2. Tricky Flips sells a coin that promises to land on heads 3 out of every 4 times. If the coin is
flipped 20 times, which of the following is the number of times you should expect it to land
on head
Answer:
15
Step-by-step explanation:
Because 3/4 of 20 or 75% of 20 is 15
Help me pleaseee i don’t know this
Answer:
the answer is B because y depends on x
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
Calculate the value of this investment at the end of the 5 years.
Answer:
The value of this investment at the end of the 5 years is of $662.5.
Step-by-step explanation:
Compound interest:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
Dina invests $600 for 5 years at a rate of 2% per year compound interest.
This means that [tex]P = 600, t = 5, r = 0.02, n = 1[/tex]. Thus
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(t) = 600(1 + \frac{0.02}{1})^{t}[/tex]
[tex]A(t) = 600(1.02)^t[/tex]
Calculate the value of this investment at the end of the 5 years.
This is A(5). So
[tex]A(5) = 600(1.02)^5 = 662.5[/tex]
The value of this investment at the end of the 5 years is of $662.5.
For which pair of functions is the vertex of g(x) 2 units to the right of the
vertex of f(x)?
A. f(x) = x2 and g(x) = x2 + 2
B. f(x) = x2 and g(x) = x2 - 2
c. f(x) = x2 and g(x) = (x + 2)2
D. f(x) = x2 and g(x) = (x - 2)2
Answer:
D
Step-by-step explanation:
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then shift left by a units
• If a < 0 then shift right by a units
Here the shift is 2 units to the right
Then
f(x) = x² and g(x) = (x - 2)² → D
Mr. Arju wishs to purchase a house . to buy the house he needs to make a down payment of nu.300000 and also pay nu.15000 every quarter for the next 8 years. the interest charge is 9% per year compounded quarterly. what is the price of the house?
Answer:
The price of the house is $ 853,735.05.
Step-by-step explanation:
Since Mr. Arju wishes to purchase a house, and to buy the house he needs to make a down payment of $ 300,000 and also pay $ 15,000 every quarter for the next 8 years, if the interest charge is 9% per year compounded quarterly, to determine what is the price of the house, the following calculation must be performed:
300,000 + (15,000 x 12 x 8) = X
300,000 + (180,000 x 8) = X
300,000 + 1,440,000 = X
1,740,000 = X
X x (1 + 0.09 / 4) ^ 8x4 = 1,740,000
X x (1 + 0.0225) ^ 32 = 1,740,000
X x 1.0225 ^ 32 = 1,740,000
X x 2.0381030257737 = 1,740,000
X = 1,740,000 / 2.03810
X = 853,735.05
Therefore, the price of the house is $ 853,735.05.
If AJKL * AMNP, which statement must be true?
A video store charges $8 per movie, and the fifth movie is free. How much do you actually pay per movie?
Answer:
$6.40 per movie
Step-by-step explanation:
Since the fifth movie is free, find the total cost by multiplying 8 by 4:
8(4)
= 32
Find how much you actually pay per movie by dividing this by 5:
32/5
= 6.4
So, you are actually paying $6.40 per movie
Answer:
$6.40
Step-by-step explanation:
If you buy five movies, but only pay for the first four, then that is the first amount we need to find. Paying $8 for four movies means you are paying $32. If you are paying $32 for five movies, then you are paying $6.40 per movie.
Math:
8 + 8 + 8 + 8 + 0 = 32
32/5 = 6.4
YA is the angle bisector of ZXYZ. If mZXYZ = 52°, what is mZZYA?
Given:
[tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex].
[tex]m\angle XYZ=52^\circ[/tex]
To find:
The measure of [tex]m\angle ZYA[/tex].
Solution:
It is given that [tex]YA[/tex] is the angle bisector of [tex]\angle XYZ[/tex]. It means
[tex]m\angle XYA=m\angle ZYA[/tex] ...(i)
Now,
[tex]m\angle XYA+m\angle ZYA=m\angle XYZ[/tex]
[tex]m\angle ZYA+m\angle ZYA=52^\circ[/tex] [Using (i)]
[tex]2m\angle ZYA=52^\circ[/tex]
Divide both sides by 2.
[tex]m\angle ZYA=\dfrac{52^\circ}{2}[/tex]
[tex]m\angle ZYA=26^\circ[/tex]
Therefore, the required value is [tex]m\angle ZYA=26^\circ[/tex].
Which one is it I need to know quick and I’ll mark you Brainly
Answer: i think
the corrcect answer is 0.5*10^-1
Step-by-step explanation:
hope this helps
tan^2theta - Sin^2theta = tan^2theta. sin^2theta
explain this step
tan²(θ) - sin²(θ) = sin²(θ)/cos²(θ) - sin²(θ)
-- because tan(θ) = sin(θ)/cos(θ) by definition of tangent --
… = sin²(θ) (1/cos²(θ) - 1)
-- we pull out the common factor of sin²(θ) from both terms --
… = sin²(θ) (1/cos²(θ) - cos²(θ)/cos²(θ))
-- because x/x = 1 (so long as x ≠ 0) --
… = sin²(θ) ((1 - cos²(θ))/cos²(θ))
-- we simply combine the fractions, which we can do because of the common denominator of cos²(θ) --
… = sin²(θ) (sin²(θ)/cos²(θ))
-- due to the Pythagorean identity, sin²(θ) + cos²(θ) = 1 --
… = sin²(θ) tan²(θ)
-- again, by definition of tan(θ) --
If a1 = 6 and an=-5an-1 + 4 then find the value of a4. dont have much time please
Answer:
-666
Step-by-step explanation:
a1 = 6
an = -5 an-1 +4
a2 = -5 a1 +4 = -5*6 +4 = -30 +4 = -26
a3 = -5 a2 +4 = -5 (-26) +4 = 130+4 = 134
a4 = -5 a3 +4 = -5 (134) +4 = -670+4 =-666
How tall is the average human baby ?
Consider a circle whose equation is x^2+y^2-2x-8=0. Which statements are true? Select three options.
Answer:
The radius of the circle is 3 units
The center of the circle lies on the x-axis.
The radius of this circle is the same as the radius of the circle whose equation is x^2 + y^2 = 9
Step-by-step explanation:
if three-fourth of a number is added to 14 gives result less than or equal to 20 .find the number,hense illustrate your answer on a number line
Answer:
x≤8
Step-by-step explanation:
let the number be x
¾x+14≤20
LCM=4
3x+56≤80
3x≤80-56
3x≤24
x≤8
I am unable to add number line here
Pls help I don’t understand this one pls
Answer:
15=225
20= 400
Step-by-step explanation:
the small 2 means multiply that number two times :)
Answer:
[tex]15^2\\[/tex] = 225
[tex]20^{2}[/tex] = 400
Step-by-step explanation:
[tex]x^{2}[/tex] = [tex]x[/tex] × [tex]x[/tex]
basically it's the number times itself
15 × 15 = 225
20 × 20 = 400