In a normal distribution, the mean is ____ it's mean and mode
Final answer:
In a normal distribution, the mean, median, and mode are all the same, since it is symmetric around the mean. The standard deviation affects the shape of the distribution, and the empirical rule states that most values lie within two standard deviations of the mean. Differences in symmetry may cause the mean, median, and mode to diverge, with the mean being most affected by skewness.
Explanation:
In a normal distribution, the mean is equal to the median and mode, by definition. This is because the normal distribution, which is also known as the Gaussian distribution, is symmetrically shaped like a bell curve around the mean (μ). The mean indicates the center of the distribution and the point of symmetry, while the median divides the data such that half of the values are above it and half are below. The mode is the most frequently occurring value in the data set, and in a perfect normal distribution, it coincides with the mean and median.
The standard deviation (σ) is a measure of the spread of the distribution. If the standard deviation is increased, the curve becomes wider and flatter, while a decrease in σ makes the distribution steeper and narrower. Additionally, the location of μ on the X-axis can shift the entire graph to the left or right, but the shape of the graph remains the same. The empirical rule helps us understand that approximately 95% of values lie within two standard deviations from the mean.
Drawing from the collaborative exercise provided, by recording the heights and creating histograms with smooth bell-shaped curves, one can calculate the mean and identify how characteristics such as skewness affect the mean, median, and mode, especially in non-symmetric distributions. In these cases, the mean can be influenced by the direction of the skew more than the median, pulling it towards the tail of the distribution.
Complete the expansion of (a + b)6 with a = 1 and b = 0.3.
(dont add everything together)
(1 + 0.3)^6 = (____)^6 + 6(____)^5(____) + 15(____)^4(____)^2 + 20(____)^3(____)3 + 15(____)^2(____)^4 + 6(___)(___)^5 + (____)^6
Answer:
[tex](1+0.3)^{6}=(1)^6+6(1)^{5}(0.3)+15(1)^{4}(0.3)^{2}+20(1)^{3}(0.3)^{3}+15(1)^{2}(0.3)^{4}+6(1)^{1}(0.3)^{5}+(0.3)^{6}[/tex]
Step-by-step explanation:
This is an expansion of the expression [tex](a+b)^{6}[/tex]. In general you can expand expressions of this form by a formula known as the binomial theorem. This formula establishes that
[tex](a+b)^{n}=\sum_{k=0}^{n} {n\choose k} a^{n-k}b^{k}[/tex]
Where the coeficients [tex]n\choose k[/tex] are called binomial coeficients, and can be computed by the formula
[tex]{n\choose k} =\frac{n!}{(n-k)! k!}[/tex]
where [tex]n!=1\times 2\times 3\times \cdots\times n[/tex].
A school has 18 left-handed students. If 8% of the total number of students in the school are left-handed, what is the total number of students in the school?
Is 200 milliliter equivalent to 2 liters
In the diagram, m∠3 = 120° and m∠12 = 80°. Which angle measures are correct?Check all that apply.m∠1 = 60°m∠13 = 80°m∠6 = 80°m∠5 = 60°m∠10 = 120°m∠ 14 = 100°
we are given
m∠3 = 120° and m∠12 = 80°
we will check all
Calculation of m∠1:
we can see that angles 1 and 3 are linear
so, their sum must be 180
m∠1+m∠3 = 180°
now, we can plug values
m∠1+ 120°= 180°
m∠1=60°
Calculation of m∠13:
we know that
angles 12 and 13 are alternate angles
so, they must be equal
m∠13=m∠12 = 80°
m∠13= 80°
Calculation of m∠6:
we know that
angles 3 and 6 are alternate angles
so, they must be equal
m∠3=m∠6 = 120°
m∠6= 120°
Calculation of m∠5:
we know that
angles 1 and 5 are corresponding angles
so, they must be equal
m∠1=m∠5 = 60°
m∠5= 60°
Calculation of m∠10:
we can see that angles 10 and 12 are linear
so, their sum must be 180
m∠10+m∠12 = 180°
now, we can plug values
m∠10+ 80°= 180°
m∠10=100°
Calculation of m∠14:
we know that
angles 10 and 14 are corresponding angles
so, they must be equal
m∠10=m∠14 = 100°
m∠14= 100°
Answer:
A, B, D, F
Step-by-step explanation:
Well to summarize what the previous person mentioned:
1 = 60
13 = 80
6 = 120
5 = 60
10 = 100
14 = 100
So given that information the correct answers are:
A, B, D, F
For a track meet, Tara ran the 1,600 m event at constant speed in 5 minutes and 20 seconds. What was her speed?
What are the roots of the equation?
x^2+24=−11x
Enter your answers in the boxes.
Answer:
[tex]x_1 = -8[/tex]
[tex]x_2 = -3[/tex]
Step-by-step explanation:
Given the equation:
[tex]x^2+24 = -11x[/tex]
Add 11x to both sides we have;
[tex]x^2+11x+24 = 0[/tex]
Split the middle terms we have;
⇒[tex]x^2+8x+3x+24 = 0[/tex]
⇒[tex]x(x+8)+3(x+8)= 0[/tex]
⇒[tex](x+8)(x+3)= 0[/tex]
By zero product property we have;
x+8 = 0 and x+3= 0
⇒x = -8 and x = -3
Therefore, the roots of the given equations are:
[tex]x_1 = -8[/tex]
[tex]x_2 = -3[/tex]
Two fair dice are rolled. what is the (conditional) probability that the first dice lands on an even number given that at least one of the dice lands on a 6?
Cecil Green sells golf hats. He knows that most people will not pay more than $20 for a golf hat. Cecil needs a 40% markup on cost. What should Cecil pay for his golf hats? (Round your answer to the nearest cent.) Cecil pays $
Final answer:
Cecil should pay $14.29 for his golf hats.
Explanation:
To determine what Cecil should pay for his golf hats, we need to calculate the cost price and apply the 40% markup. Let's assume the cost price is 'x'. Since Cecil needs a 40% markup on cost, the selling price will be 140% of the cost.
To find the selling price, we can use the equation: 140% of 'x' = $20. Solving this equation, we get: x = $20 / 1.4 = $14.29.
Therefore, Cecil should pay $14.29 for his golf hats.
Find the x-intercepts (if any) for the graph of the quadratic function.
6x^2 +12x+5=0
Give your answers in exact form. Show your work
annual college tuition and fees are 8000$. Books and other charges cost 1000$ per year. If Tony receives a $4500 scholarship each year, how much more will he need to pay for 1 year of college?
Find the fifth term of an=3n-5
Is the sequence arithmetic? If so, identify the common difference. 15,22,35,46,...
A student rolls a number cube whose six faces are numbered 1 through 6. What is the sample space for this experiment? S = {2, 4, 6} S = {1, 2, 3, 4, 5, 6} S = {6} S = {1, 2, 3, 4}
HURRY PLEASE HELP
Answer: {1, 2, 3, 4, 5, 6}
Step-by-step explanation:
Sample space is the set of all possible outcomes for a certain experiment.Given : A student rolls a number cube whose six faces are numbered 1 through 6.
Then, the possible outcomes of rolling it = 1, 2, 3, 4, 5, 6
Then , the sample space for this experiment = set of all possible outcomes
= {1, 2, 3, 4, 5, 6}
what is 5 1/2 × 2 1/3
You borrow $350 from your aunt and agree to repay her $400 in 18 months. What interest rate (to the nearest tenth) are you paying?
What is the length of one leg of the triangle
Answer:
Step-by-step explanation:
The length measure of the second leg of the right-angle triangle is 12 units.
What is the measure of the missing leg length of the triangle?Given the parameter:
Hypotenuse = 15 units
Length of leg1 = 9 units
Length of leg2 = x
To determine the measure of the missing side length of the right triangle, we use the Pythagoras theorem.
It is expressed as:
( hypotenuse )² = ( leg 1 )² + ( leg 2 )²
Plug in the given values:
( 15 )² = ( 9 )² + ( leg 2 )²
Simplifying, we get:
225 = 81 + ( leg 2 )²
( leg 2 )² = 225 - 81
( leg 2 )² = 144
Take the square roots:
leg 2 = √144
leg 2 = 12 units
Therefore, the second leg measures 12 units.
The question is not complete, the complete question is:
A right triangle's leg is 9 and the hypotenuse is 15, What is the length of of the other leg of the triangle?
Learn more about trigonometric ratio here: https://brainly.com/question/28038732
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Find the radius of the circle whose equation is 3x² + 3y² = 75.
Answer: 5 units
Step-by-step explanation:
We know that the general equation of a circle having center at (h,k) and radius r is given by :-
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Given : The equation of a circle : [tex]3x^2 + 3y^2 = 75[/tex]
Taking 3 as common from the left side of the given equation , we get
[tex]3(x^2 + y^2) = 75[/tex]
Divide 3 on both the sides , we get
[tex]x^2 + y^2 = 25[/tex]
Comparing to the general equation of circle , we get
[tex]r^2 = 25\\\\\Rightarrow\ r=5[/tex]
Hence, the radius of the circle = 5 units
The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was bought at a wholesale price of $ 1 1 3 . 0 0 $113.00dollar sign, 113, point, 00, and Jessica's Furniture Store marks up all furniture by 4 5 % 45%45, percent. At what price should the manager sell the couch?
Which is a cubic function? a. f(x) = 3x + 1 b. f(x) = 3x2 + x + 2 c. f(x) = 5x3 + 2x + 1 d. f(x) = x3 + x4 + 5
Answer:
Option C is a cubic function
Step-by-step explanation:
Given the options we have to choose the cubic function
Cubic function is the function with degree 3 i.e the highest power of variable is 3.
Option a: [tex]f(x)=3x+1[/tex]
The above polynomial has highest power 1 i.e of degree 1
∴ not a cubic function
Option b: [tex]f(x)=3x^2+x+2[/tex]
The above polynomial has highest power 2 i.e of degree 2
∴ not a cubic function
Option c: [tex]f(x)=5x^3+2x+1[/tex]
The above polynomial has highest power 3 i.e of degree 3
∴ above is a cubic function
Option d: [tex]f(x)=x^3+x^4+5[/tex]
The above polynomial has highest power 4 i.e of degree 4
∴ not a cubic function
Which is the most reasonable conjecture about the data shown in the scatter plot?
I think B? I'm not sure..
Sela's piano lesson starts at 4:45pm the lesson is 30 minutes long
the piano lesson ends at 5:15
which pair of angles are corresponding angles
a. 1 and 2
b. 1 and 5
c. 2 and 7
d. 2 and 5
The function given by Upper A left parenthesis t right parenthesis equals 0.0265 t cubed minus 0.444 t squared plus 1.774 t plus 8.76A(t)=0.0265t3−0.444t2+1.774t+8.76, 0 less than or equals t less than or equals 100≤t≤10, can be used to estimate the amount, in billions of dollars, invested by large oil companies in exploration for new reserves t years after 19951995. Find the relative extreme points, and sketch a graph of the function.
whats the equation of the line?
Tom and Sonya were comparing their answers on a math problem. It was an order of operations problem, and they each had a different answer. Tom had an answer of 11, and Sonya had an answer of 104. Which student correctly solved the order of operations problem given by the teacher?
(5^2 +6)–(7•4)+8
onsider the following pseudocode function. function Crunch(x R) if x ≥ 100 then return x/100 else return x + Crunch(10 · x) (a) Compute Crunch(4). Crunch(4) = (b) What happens if you try to compute Crunch(−23)? What does this suggest about an appropriate precondition for this function?
What is the area of the hexagon? Numerical answer only!
The manager of a video game store found that 35 of the 140 people who preordered the latest baseball game canceled their orders the day before the game was released. He used that data to create a simulation to predict the probability that future customers will cancel their preorders.
Using the data presented in the problem, you are asked to predict the probability that future customers will cancel their preorders. To find the probability, you have to divide the number of people who cancelled their preorders by the total number of people who preordered.
35 people / 140 people = .25 or 25% probability that the future customers will cancel their preorders.
Answer:
A
Step-by-step explanation:
Dr. Clarence invested $5000 in an account that draws 3.2% interest, compounded annually. What is the total value of the account after 5 years?