When n is large the distribution of the sample means will approach a normal distribution.
The central limit theorem (CLT) is a statistical theory that predicts that given a large enough sample size from a population with a certain level of variation, the mean of all the samples from that population will be close to the population mean.
To put it another way, the central limit theorem predicts with absolute certainty the form of the distribution of means when we take repeated samples from a certain population. In particular, the distribution of means derived from repeated sampling will tend toward normality as sample sizes increase.
In other words, when n is large, the distribution of the sample means will resemble a normal distribution if we continually pick independent, random samples of size n from any population.
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Will mark brainlist! Pls help
Solve for x on the diagram below
Answer:
n/a
Step-by-step explanation:
Where's the diagram?
What is the equation of the following line?
Answer:
A
Step-by-step explanation:
(1.6x10-^7)/(9.11x10^-3)
Answer:
0.0000175631 or \(\frac{175631}{10000000000}\)
Step-by-step explanation:
\(\frac{(1.6)(10^{-7})}{(9.11)(10^{-3})}\)
Solve Numerator
\((1.6)(10^{-7})=(1.6)(\frac{1}{10000000})=\frac{16}{100000000} =0.00000016\)
Solve Denominator
\((9.11)(10^{-3})=(9.11)(\frac{1}{1000} )=\frac{911}{100000} =0.00911\)
Divide
\(0.00000016/0.00911\)
0.0000175631 or \(\frac{175631}{10000000000}\)
Is line BC parallel to line DE?
Which of the binomials below is a factor of this trinomial?
5x2 + 14x-3
Answer:
The answer is D. x + 3
Step-by-step explanation:
The factors of 5x2 + 14x - 3 are:
(5x-1) and (x+3)
On Thursday, rrr centimeters of rain fell on Deborah's garden. On Saturday, 15\%15%15, percent more rain fell on the garden.
The expression r+0.15rr+0.15rr, plus, 0, point, 15, r describes the number of centimeters of rain Deborah's garden got on Saturday. We can also use the expression 1.15r1.15r1, point, 15, r to represent the same quantity.
Answer:
The centimeters of rain on Thursday r
How many more centimeters of rain fell on Saturday than on Thursday 0.15r
The centimeters of rain on Saturday 1.15r
Step-by-step explanation:
Answer:
The centimeters of rain on Thursday r
How many more centimeters of rain fell on Saturday than on Thursday 0.15r
The centimeters of rain on Saturday 1.15r
Step-by-step explanation:
When slave starting a disabled vehicle, which of the following is an important safety consideration?
a. Ensure the battery caps are removed from bothvehicles batteries during the save start
b. Connecting the slave cable to the disables vehicle fisrt may cause damage to the batteries
c. The slaving vehicle engine must be running while connecting the slave cable
When slave starting a disabled vehicle, the term that serves an important safety consideration is c. The slaving vehicle engine must be running while connecting the slave cable
What is slave starting a vehicle?The dead car is started while the live vehicle's engine is running by inserting a slave cable into the receptacle on each vehicle.
Vehicles with manual transmissions rely heavily on the clutch slave cylinder. When the pedal is depressed, the clutch is disengaged and the transmission is shifted thanks to the slave and clutch master cylinders.
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help me please please
Answer:
(x - 2)² + (y +8)² = 4Step-by-step explanation:
Equation of circle:\(\sf\boxed{(x-h)^2+(x-k)^2=r^2}\)
Here, h , k are the co ordinates of the center and r is the radius
\(\sf (x - 2)^2 + (y-[-8])^2 = 2^2\\\\(x - 2)^2 + (y + 8)^2= 4\)
A line has a y-intercept of 8 and a slope of 4. What is its equation in slope-intercept form?
Answer:
y = 4x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 4 and c = 8 , thus
y = 4x + 8 ← equation of line
The equation in slope-intercept form is y = 4x+8
What is the equation of a line?The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.
Given that, a line has a y-intercept of 8 and a slope of 4.
We know that, the general equation of a line is given by, y = mx+c
where m is slope and c is the y intercept,
Here, m = 4 and c = 8
Therefore, the equation can be, y = 4x+8
Hence, The equation in slope-intercept form is y = 4x+8
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Solve for x. Round to the nearest tenth, if necessary.
Evaluate the expression (4p - m) where m=-4 and p=2
Show the work plz.
Answer:
12
Step-by-step explanation:
(4p - m)
Let m = -4 and p=2
( 4* 2 - (-4))
Multiply
8 - -4
Add
8+4
12
Answer:
Step-by-step explanation:
m = - 4 & p =2
4p - m = 4*2 - (-4)
= 8 + 4
= 12
Re-write the following system of equations in matrix format and solve them by using Cramer's rule. z+5x= 24 3x+2z+3y=7 -x+2y=-9
The solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.
The given system of equations is given as,z + 5x = 243x + 2z + 3y = 7-x + 2y = -9
To solve the given system of equations by using the Cramer's rule, we have to first represent the given system in matrix format.
Matrix format: ⎡1 0 5⎤ ⎡x⎤ ⎡24⎤ ⎢0 3 2⎥ ⎢y⎥=⎢7⎥ ⎣-1 2 0⎦ ⎣z⎦ ⎣-9⎦
Using the formula for Cramer's rule, we know that,
x = Dx / D, y = Dy / D, z = Dz / D, whereD is the determinant of the coefficient matrix, Dx is the determinant of the matrix obtained by replacing the x column with the constant matrix, Dy is the determinant of the matrix obtained by replacing the y column with the constant matrix, and Dz is the determinant of the matrix obtained by replacing the z column with the constant matrix.
Calculation of D: D = | A | = ⎡1 0 5⎤ ⎡0 3 2⎥ ⎣-1 2 0⎦
Applying the Laplace expansion along the first column, D = 1 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦| D = 6 Calculation of Dx: Dx = ⎡24 0 5⎤ ⎡3 2⎤ ⎢7 3 2⎥ ⎢-1 2⎥ ⎣-9 2 0⎦ ⎣2 0⎦
Applying the Laplace expansion along the first column, Dx = 24 |⎡3 2⎤| - 0 |⎡-1 2⎤| + 5 |⎡-9 2⎤| |⎣3 2⎦| |⎣3 2⎦| |⎣3 2⎦|
Dx = -18
Calculation of Dy: Dy = ⎡1 24 5⎤ ⎡0 2 2⎤ ⎢0 7 2⎥ ⎢-1 -1 0⎥ ⎣-1 -9 0⎦ ⎣2 0 0⎦
Applying the Laplace expansion along the second column, Dy = 0 |⎡1 5⎤| - 24 |⎡0 2⎤| + 5 |⎡0 2⎤| |⎣-1 0⎦| |⎣-1 0⎦| |⎣-1 0⎦|
Dy = 10
Calculation of Dz: Dz = ⎡1 0 24⎤ ⎡0 3 2⎥ ⎢0 3 7⎥ ⎢-1 2 -1⎥ ⎣-1 2 -9⎦ ⎣3 2 0⎦
Applying the Laplace expansion along the third column,
Dz = 24 |⎡3 2⎤| - 10 |⎡-1 2⎤| + 0 |⎡-1 3⎤| |⎣2 0⎦| |⎣2 0⎦| |⎣2 0⎦|
Dz = -24
Now we have the values of D, Dx, Dy and Dz.
Therefore, x = Dx / D, y = Dy / D, z = Dz / D,x = -18/6 = -3 y = 10/6 = 5/3 z = -24/6 = -4
Hence, the value of x, y, and z is (-3, 5/3, -4) respectively.
Therefore, the solution of the given system of equations is (-3, 5/3, -4) by using Cramer's rule.
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Each side of a square is (7 + 3x) units. Which is the perimeter of the square?
CLE
2x units
28 + 3x units
12x units
49 + 9x units
Answer:
49 + 9x units
Step-by-step explanation:
perimeter is sum of all the sides
Is it true that since sin^2x + cos^2x = 1, then sin(x) + cos(x) = 1? Explain your answer.
It is not true that sin(x) + Cos(x) = 1 based solely on the identity sin^2x + cos^2x = 1.
No, it is not true that sin(x) + cos(x) = 1 based solely on the identity sin^2x + cos^2x = 1. The reason is that there is no direct relationship between sin(x) and cos(x) that can be derived from this identity alone. In fact, sin(x) and cos(x) are related by the Pythagorean trigonometric identity sin^2x + cos^2x = 1, but this does not imply that sin(x) + cos(x) equals 1.
To see why, consider the following example: let x = π/4. Then sin(x) = cos(x) = √2/2, so sin(x) + cos(x) = √2. On the other hand, sin^2x + cos^2x = 1, which is true, but it does not imply that sin(x) + cos(x) = 1. Therefore, it is important to be careful when manipulating trigonometric identities and to avoid making assumptions that are not justified by the identity itself.
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Great make greatest 5 digit number 4 2 and 0
To create the greatest 5-digit number using the digits 4, 2, and 0, we need to place the highest value digit in the leftmost position. Therefore, the greatest 5-digit number that can be created using the digits 4, 2, and 0 is 42,000.
By arranging the digits in this order, you ensure that you have the largest possible value while still using only the given digits 4, 2, and 0. In this case, the digit 4 is the highest value digit. So we place it in the ten-thousands place. This gives us 40,000. Now we need to fill in the remaining four digits. Since we want to create the greatest possible number, we need to use the next highest digit, which is 2, in the thousands place. This gives us 42,000. We can then use the remaining digit, which is 0, in the hundreds, tens, and ones places. to create the greatest 5-digit number, we need to start with the highest value digit and place it in the leftmost position. Then, we fill in the remaining digits with the next highest value digits in descending order. This ensures that we create the greatest possible number.
The greatest 5-digit number using the digits 4, 2, and 0, you can repeat the digits as needed. Place the largest digit (4) in the leftmost position to maximize the value, and then fill in the remaining positions with the next largest digit (2), followed by the smallest digit (0).
Therefore, the greatest 5-digit number that can be created using the digits 4, 2, and 0 is 42,000.
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AKJL-AWJX. Identify the coordinates of X and the scale factor.
y
W(0, 16)
urc
K(0,6)
Jx
L(-8,0)
Rachel covered a single lap of 1,210 m in 55 s. Calculate her speed in m/s
Answer:
22 m/s
Step-by-step explanation:
Take the distance and divide by the time
1210 m/55s
22 m/s
Answer:
22m/sStep-by-step explanation:
\(speed = \frac{distantce}{time} \\ = \frac{1210m}{55s} \\ = 22m {s}^{ - 1} \)
What is the probability that a randomly selected person from the survey prefers bacon.
The probability that a randomly selected person from the survey prefers bacon would be 60% in this example. However, without knowing the specific numbers, we cannot calculate the probability accurately.
To determine the probability that a randomly selected person from the survey prefers bacon, we need additional information such as the total number of respondents in the survey and the number of people who prefer bacon. Without this information, it is not possible to calculate the exact probability.
The probability can be calculated by dividing the number of people who prefer bacon by the total number of respondents in the survey. If the survey provides these specific numbers, we can use the formula:
Probability = Number of people who prefer bacon / Total number of respondents
For example, if the survey includes 100 respondents and 60 of them prefer bacon, the probability would be:
Probability = 60 / 100 = 0.6 or 60%
Therefore, the probability that a randomly selected person from the survey prefers bacon would be 60% in this example. However, without knowing the specific numbers, we cannot calculate the probability accurately.
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does the equation y = x represent a function
Yes it's a linear function
Answer:
Yes since x only equals y, which is one solution.
Step-by-step explanation:
Helppp me out this is my last question
Answer:
option 3
Step-by-step explanation:
how to determine if a function crosses the horizontal asymptote
To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.
1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.
2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.
3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.
4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.
If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.
It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.
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Kevin rented a truck for one day. There was a base fee of $14. 99 , and there was an additional charge of 73 cents for each mile driven. Kevin had to pay $182. 16 when he returned the truck. For how many miles did he drive the truck?
Kevin must have driven 229 miles in the rented truck.
To solve this problem, we can use the following formula:
Total cost = base fee + (mileage rate x number of miles)
We know that Kevin had to pay a total of $182.16 when he returned the truck. We also know that there was a base fee of $14.99, so the remaining amount must be due to the mileage charge. Let's subtract the base fee from the total cost:
$182.16 - $14.99 = $167.17
Now we can set up an equation to solve for the number of miles driven:
$167.17 = $0.73/mile x number of miles
To solve for the number of miles, we can divide both sides of the equation by $0.73:
number of miles = $167.17 / $0.73
number of miles = 229
Therefore, Kevin must have driven 229 miles in the rented truck.
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The scale factor of the dimensions of two similar wood floors is 4:3. It costs $153 to refinish the smaller wood floor. At this rate, how much would it cost to refinish the larger wood floor?
With the given scale factor, The cost to refinish the larger wood floor is $204
How to determine the amount for the larger wood?The scale factor is given as:
Scale factor = 4 : 3
This means that:
x : 153 = 4 : 3
Where x represents the cost to refinish the larger wood floor
Express as fraction
x/153 = 4/3
Multiply both sides by 153
x = 204
Hence, the cost to refinish the larger wood floor is $204
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what is the highest common factor of 21 and 6 thanks :)))))
Answer:
The highest common factor of 21 and 6 is 3
Step-by-step explanation:
What is the sum of (x ^ 2 - 3x + 2) and (5x ^ 2 - 3x - 8)
Answer:
6x^2-6x-6
Step-by-step explanation:
(x^2-3x+2)+(5x^2-3x-8)
x^2+5x^2-3x+(-3x)+2+(-8)
6x^2-3x-3x+2-8
6x^2-6x+2-8
6x^2-6x-6
Form a linear equation for the given statement and draw its graph:
Taxi fare for the first km is charged at Rs 20 and Rs 10 is charged for another extra
1 km.
Step-by-step explanation:
See the image for solution
Hope it helps
Have a great day
HELP!!!
Only question 16
Answer:
Cost is $255
Step-by-step explanation:
Cost = 150 + 15d ( d = day(s) )
Cost = 150 + 15(7) ( d becomes 7 because the boat is rented for 7 days )
Cost = 150 + 105
Cost = 255
Hopefully this helped!
Brainiest please?
Answer:
The cost of Juan's rent of the boat in 7 days is 255
Step-by-step explanation:
Cost = 150 + 15d
--
==>> D = days
--
Cost = 150 + 15(7)
--
150 + 105 = Cost
--
255 = Cost
FINAL
Paul wants to buy a bicycle that costs $86.50. He has saved $60. He earns $5.30 an hour working after school and can save half of his total earnings. How many hours will he have to work to buy the bicycle?
Answer:
10 hours
Step-by-step explanation:
86.50-60=26.50
5.30/2=2.65
2.65*10=25.50
so 10 hours of work to buy the bicycle
Answer as quickly as you possibly can
Answer:
m = 3/2
Step-by-step explanation:
You want to find the slope, or the change in y coordinates over change in x-coordinates.
The first given point is E(-2, -4)
The second point is F(2, 2)
Coordinates are given in (x, y), so following the equation and computing the x and y coordinates of E - F for both the numerator and denominator:
\(\frac{y_2 - y_1}{x_2-x_1} = \frac{-4 -2}{-2 -2} = \frac{-6}{-4} = \frac{3}{2}\)
You could also have went the other way and calculated F - E for the numerator and denominator and get the same answer.
Finally, to check you can also look at the graph through the rise over run (rise/run) method and see that from E, you go up 3 (rise) and to the right 2 (run) to get to the next point on the line.
Yes or no on each one
Answer:
NO
YES
NO
YES
Step-by-step explanation:
for example :
(4³)³ = 4^9
4³.4³ = 4^6