Using the Central Limit Theorem, it is found that the standard deviation for the sampling distribution of sample means is given by:
[tex]s = \frac{\sigma}{\sqrt{51}}[/tex].
In which [tex]\sigma[/tex] is the population standard deviation.The Central Limit Theorem states that, the sampling distribution of sample means of size n, from a population with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], has mean [tex]\mu[/tex] and standard deviation, which is also called standard error, [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this question, 51 samples, hence, [tex]n = 51[/tex]
Hence, applying the Central Limit Theorem, the standard deviation for the sampling distribution of sample means is given by:
[tex]s = \frac{\sigma}{\sqrt{51}}[/tex].
In which [tex]\sigma[/tex] is the population standard deviation.A similar problem, which also involves the Central Limit Theorem, is given at https://brainly.com/question/24663213
find x if 2^x=8^3x-8
Step-by-step explanation:
First we have to same the bases.
As we know 8=2^3.
Replace 8 with 2^3.
Like this .
2^3x=2^3(2x+1).
Now 3x=3(2x+1) distribute 3 by the Barker.
3x=6x+3.
6x+3=3x.
6x-3x=-3.
3x=-3.
X=-1.
You deposit $5000 into a savings
account. If you cam a simple
interest rate of 3%, how much
interest will you earn after 5 years
FIND THE ERROR Fern is finding the slope of the line that passes through (-2, 8) and (4. 6). Determine in which step she made an error. Ex
Answer:
Step 1, she reversed the values of x. It should have been 4 - (-2) not -2 - 4.
Step-by-step explanation:
Fern made a mistake in writing equation [1] where she wrote {-2 - 4} in the denominator in place of {4 -(-2)}.
What is the general equation of a straight line?
The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept
Given is Fern who is finding the slope of the line that passes through (-2, 8) and (4, 6).
In order to find the slope of the line, the following formula is used -
m = (y₂ - y₁)/(x₂ - x₁)
So, the slope of the line passing through the given points can be calculated using the following steps -
m = (6 - 8)/{4 -(-2)} ..[1]
m = -2/6
m = -1/3
Fern made mistake in writing equation [1]. She should have written
{4 -(-2)} in the denominator in place of {-2 - 4}
Therefore, fern made a mistake in writing equation [1] where she wrote {-2 - 4} in the denominator in place of {4 -(-2)}.
To solve more questions on straight lines, visit the link below-
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HELPPPPP ASAP!!!! I’m on a limit
Answer:
look at the photo.........find the sum of the first 8 terms of the geometric sequence 2,4,8,16,..
(with solution)
PA HELP PO THANKYOUU
Answer:
I think the common difference is 2. The formula to create the sequence is n (number) is multiplied by 2.
1 x 2 = 2
2 x 2 = 4
4 x 2 = 8
8 x 2 = 16
16 x 2 = 32
32 x 2 = 64
64 x 2 = 128
128 x 2 = 256
256 is the 8th term of the sequence. Since your question says that we should look for the sum, add the number of the sequence I guess.
2 + 4 +8 + 16 + 32 + 64 + 128 + 256 = 510
HELP PLS! Suppose the year of car accidents per day in Wilmington NC has been recorded for the past year. The table below is a probability distribution table representing the data collected.
1) what is the probability that on a randomly selected day there were no accidents?
2) find the probability there will be at least 2 accidents
3) on any given day how many accidents should the Wilmington police expect to have.
According to the discrete distribution given:
1) There is a 0.18 = 18% probability that on a randomly selected day there were no accidents.
2) There is a 0.7 = 70% probability that there will be at least 2 accidents.
3) On any given day, the Wilmington police should expect to have 2.03 accidents.
The distribution is:
[tex]P(X = 0) = x[/tex]
[tex]P(X = 1) = 0.12[/tex]
[tex]P(X = 2) = 0.32[/tex]
[tex]P(X = 3) = 0.25[/tex]
[tex]P(X = 4) = 0.13[/tex]
Item 1:
The sum of the probabilities has to be 100% = 1, hence:
[tex]x + 0.12 + 0.32 + 0.25 + 0.13 = 1[/tex]
[tex]x + 0.82 = 1[/tex]
[tex]x = 0.18[/tex]
0.18 = 18% probability that on a randomly selected day there were no accidents.
Item 2:
This probability is:
[tex]P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.32 + 0.25 + 0.13 = 0.7[/tex]
0.7 = 70% probability that there will be at least 2 accidents.
Item 3:
The expected value is the sum of each outcome multiplied by it's respective probability, hence:
[tex]E(X) = 0.18(0) + 0.12(1) + 0.32(2) + 0.25(3) + 0.13(4) = 2.03[/tex]
On any given day, the Wilmington police should expect to have 2.03 accidents.
A similar problem is given at https://brainly.com/question/25653146
If you make an initial deposit of $1000 in an account that yields 5% interest
annually. Find your balance at the end of a year.
Show your work !
SI
$1 000 × 4 % × 10 = $400
CI
($1 000 × 1.04 ^10) - $1 000 = $1 480.24 - $1 000 = $480.24
Interest on interest only applies to Compound Interest.
Excluding year 1, which yields $40 [the same as SI] the interest on interest yields $480.24 - $40 = $440.24
- BRAINLIEST answerer
The solution is $ 1050
The interest on a deposit of $ 1000 at 5% for an year will be $50 and the amount after one year is $ 1050.00
What is Simple Interest?
Simple interest is a method of calculating interest that ignores the impact of compounding. While interest frequently compounds throughout the course of a loan's set periods, simple interest does not. Simple interest is calculated by multiplying the principal amount by the interest rate, times the number of periods.
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Given data ,
Let the simple interest be represented as S
Now , the initial amount or principal be P = $ 1000
The rate of interest R = 5 %
The time period T = 1 year
So , the simple interest is given by the equation
Simple Interest = ( Principal Amount x Rate x Time Period ) / 100
Substituting the values in the equation , we get
Simple Interest S = ( 1000 x 5 x 1 ) / 100
On simplifying the equation , we get
Simple Interest S = 5000/100
Simple Interest S = $ 50
And , the amount after one year = Principal + Simple Interest
The amount after one year A = $ 1000 + $ 50
The amount after one year A = $ 1050.00
Hence , the amount is $ 1050.00
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Solve. −6.6x=−4 What is the solution to the equation? Enter your answer as a simplified fraction in the box. x =
Answer:
20/33
Step-by-step explanation:
i took the test
Answer:
x = 20/33
Step-by-step explanation:
−6.6x = −4
Divide both sides by -6.6
x = -4/(-6.6)
x = 40/66
x = 20/33
Answer: x = 20/33
PLEASE ANSWER 20 POINTS
Answer:
the pic wont load for me
Step-by-step explanation:
you're so cool! I hope you have an awesome day!
Answer:
The functions each have a positive Slope
a.)True, False
Step-by-step explanation:
Function A Slope: (y2-y1)/(x2-x1) = (7-3)/(2-1) = 4
Function B Slope: Count Four Boxes up from the 2 intercepts and then 2 over --> 4/2 = 2
These are both positive but 4 does not equal 2
a.) We have just proved that they have different slopes now we must determine if they have the same b. Because we know the slope of Function A we can simply move backward to get to x=0
When X=0 y= 3-4 = -1 And because in Function B we can clearly see the b at y=4 this is false.
Hope this helps and makes you have an Awesome Day!
What is the equation, in slope-intercept form, that relates the cost compared to the miles traveled for a Green Cab?
Step-by-step explanation:
Red taxi : y = 2x + 2
Green taxi : y = x + 5
Y are the costs of a ride, X are the miles of a ride.
The y-intercepts are the cost of just getting into a cab.
So, that is $2 for a red cab and $5 for a green cab.
Every mile with a red cab costs $2, while every mile with a green cab costs $1.
Hope this helps :)
Find the values of x and y.
Answer:
x= 38
y= 71
Step-by-step explanation:
The triangle shown in the figure is an isosceles triangle, a triangle having two sides equal.
The two sides marked with a "dash" are said to be equal.
STEP I:If we label off the triangle as ABC with AD being the extended length (containing 108°).
We'll get,
AB = AC
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
STEP II:*Property*
"If two sides of a triangle are equal their corresponding base angles are equal too."
=> ∠BAC = ∠BCA . . . . (¡)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
STEP III:From the figure, ∠BCA is equal to y.
*Property*
"Two angles on a straight line sum up to 180°"
∠BAC can be found out by subtracting 109° from the straight angle (180°).
=> ∠BAC = 180 - 109
=> ∠BAC = 71°
Substituting these values in eqn. (¡):
71 = y
Hence, the value of y is 71°
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
STEP IV:*Property*
"The exterior angle(angle on the extended side) of a triangle is equal to the sum of it's interior opposite angles."
Here,
Interior angles = x and y (= 71)Exterior Angle = 109°=> 109 = x + 71
=> 109 - 71 = x
=> x = 38°
Hence, the value of x is 38°.
YAll plssssss help me with 5 plsssssssss
Answer:
8 and 2
Step-by-step explanation:
If you add them together you get 10. (8 + 2 = 10)
If you multiply them you get 16. (8 x 2 = 16)
Have a great day! (I'd love brainiest if you could give it to me!)
Four equations are graphed on the coordinate grid: which set of equations has (-2,5) as its solution?
How to do multiplication large numbers.
Answer:
The main reason to know the multiplication table is so you can more easily multiply larger numbers. For example, suppose you want to multiply 53 x 7. Start by stacking these numbers on top of another, aligning the ones place. Draw a line underneath, and then multiply 3 by 7. Because 3 x 7 = 21, write down the ones digit (1) and carry the tens digit (2) to the tens column:
Next, multiply 5 by 7. This time, 5 x 7 = 35. But you also need to add the 2 that you carried over, which makes the result 37. Because 5 and 7 are the last numbers to multiply, you don’t have to carry, so write down the 37 — you find that 53 x 7 = 371:
When multiplying larger numbers, the idea is similar. For example, suppose you want to multiply 53 by 47. Be sure to align the stacked numbers by the ones place. (The first few steps — multiplying by the 7 in 47 — are the same, so pick up the next step.) Now you’re ready to multiply by the 4 in 47. But remember that this 4 is in the tens column, so it really means 40. So to begin, put a 0 directly under the 1 in 371:
This 0 acts as a placeholder so that this row is aligned properly.
When multiplying by larger numbers with two digits or more, use one placeholding zero when multiplying by the tens digit, two placeholding zeros when multiplying by the hundreds digit
Chloe was given a box of assorted chocolates for her birthday. Each night, Chloe treated herself to some chocolates. There were originally 30 chocolates in the box and after 2 nights, there were 24 chocolates remaining in the box. Write an equation for C,C, in terms of t,t, representing the number of chocolates remaining in the box tt days after Chloe's birthday.
Answer:
3 chocolates each night
Step-by-step explanation:
C-3
t-1
simplify |-4/5-1/10| + |-3/4+5/2|
Answer:
2 13/20
Step-by-step explanation:
53/20
Simplify
2 13/20
1\4-2\5
plese help and thank
you
Answer:
3/20
Step-by-step explanation:
3/20 I sure, Just trying this one
What is the ratio of apples to bananas?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
3 :4
Answer:
a
Step-by-step explanation:
it has the same a prime bundle
i need help again...
Answer:
2 again and the next one is 3
Step-by-step explanation:
A wooden beam is (3y2 + 7y+1) meters long. If a piece of length (y2 - 10) meters is cut off, express the length of the
remaining piece of beam as a polynomial in y.
Answer:
2y^2 +7y +11
Step-by-step explanation:
The remaining length is the difference between the original and the length cut off:
remaining = whole length - piece length
remaining = (3y^2 +7y +1) -(y^2 -10)
= 3y^2 +7y +1 -y^2 +10 = (3 -1)y^2 +7y +(1 +10)
remaining = 2y^2 +7y +11
(7+7b)+(-2+8c)+(1+5d)
Answer: 7b + 8c + 5d + 6
Step-by-step explanation:
1) (7+7b)+(-2+8c)+(1+5d)
combine like terms (starts with the ones with variables)
2) 7b + 8c + 5d
now all you need to do is add the numbers without variables
3) 7b + 8c + 5d + (7 + -2 + 1)
4) 7b + 8c + 5d + 6
the first term of an arithmetic sequence is a b and the second term is a c. What is the explicit formula to find the nth term of the sequence?
Step-by-step explanation:
every new term is created by adding a constant (I call here x) to the previous term.
a1 = b
a2 = c = a1 + x = b + x
a3 = a2 + x = a1 + 2x = b + 2x
so, we see
an = a1 + (n-1)x = b + (n-1)x
from a1 and a2 we know
c = b + x
x = c - b
so, ultimately we have
an = b + (n-1)(c-b)
The explicit formula to find the nth term of the sequence will be aₙ = cn - nb + 2b - c.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The first term of an arithmetic sequence is b and the second term is c.
a₁ = b
a₂ = c
Then the common difference is given as,
d = a₂ - a₁
d = c - b
Then the explicit formula to find the nth term of the sequence will be given as,
aₙ = b + (n - 1) × (c - b)
aₙ = b + cn - c - nb + b
aₙ = cn - nb + 2b - c
The explicit formula to find the nth term of the sequence will be aₙ = cn - nb + 2b - c.
More about the arithmetic sequence link is given below.
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100 POINTS! Select the correct answer.
Which system of equations is represented by this graph?
Answer:
A
Step-by-step explanation:
Remember, the equation of slope-intercept is y=mx+b
We see that for A, that the first equation's slope is -2/3. That means we are going to move down two and left five. The reason why we are going down is that the slope is negative. We also know that our y-intercept is -4. So we first plot the point (0,-4). Then we move down two and left five. We apply the same knowledge with the second equation. When we plot both equations, we get the same exact graph as the picture.
how much time is required to change 22Ns momentum by a force of 20N.
Answer: time is 1.1 sec
Step-by-step explanation:
Answer:
1.1s
Step-by-step explanation:
t=m/F
t=time, m=momentum, F=Force
t=22/20= 1.1s
Explain how you know when you can factor to solve quadratics as opposed to using the square root method
Answer:
If there's a common factor, divide both sides of the equation by that number to simplify the situation. If b = 0 (no bx term), go to the square root method. (if c is positive, there are no solutions). If c = 0, then one of your solutions is x = 0
Step-by-step explanation:
hope this helps!!!!
need helpi dont really get it to need help
Answer:
C
Step-by-step explanation:
There are 12 months in 1 year , then
3 lots of 4 months in 1 year and
3 × 3 = 9 lots of 4 months in 3 years
cost of lessons = $174 × 9 = $1566 → C
A family of four drove to Disney World: It took 12 hours to get there. Parking was $15. The total cost of parking and admission was $195. How much was each ticket?
Carey and Patrick both borrowed money from Melinda. Carey owes Melinda $25.00. Patrick owes Melinda 3/4 the amount that Carey owes. How much does Patrick owe Melinda?
Answer:
$18.75
Step-by-step explanation:
multiply 25 * 3/4 ( 0.75) and you get 18.75
14. At a local fruit stand, Luisa spends $5.25 for 2 pounds of strawberries. At this rate, how much can she expect to pay for 3.5 pounds of strawberries? (round to the nearest hundredt
h) Proportion Answer