who is the fastest man alive?
Usain Bolt set world records for the 100-m and 200-m dashes with impressive maximum speeds and accelerations.
Usain Bolt of Jamaica set the world record for the men's 100-m dash in the 2008 Olympic Games in Beijing. He accelerated for 3.00 s to reach his maximum speed and maintained it for the race. Calculating his maximum speed and acceleration involves understanding his performance data.
For the 100-m dash, Bolt's maximum speed was approximately 12.19 m/s and his acceleration was 2.63 m/s². In the 200-m dash, his maximum speed using the same assumptions was 10.36 m/s. This insight into Bolt's remarkable athleticism showcases his exceptional speed and acceleration capabilities on the track.
4z - 7 in terms of z
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
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:
this math problem is hard
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.
-3x = 4y = 8
X and y intercepts of this equations . Then graph line
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 is the mode of the data set?
103, 77, 90, 102, 103, 81, 78, 84, 84, 87, 99, 103, 118
Question 3 options:
84
90
93
103
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?
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.
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?
How many times is function f called in the code segment below? 25 points?
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
Is the sequence arithmetic? If so, identify the common difference. 15,22,35,46,...
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].
which pair of angles are corresponding angles
a. 1 and 2
b. 1 and 5
c. 2 and 7
d. 2 and 5
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
#SPJ3
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
solve equation (n-1)(n+6)(n+5)=0
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}
Evaluate 0.3 y+\dfrac yz0.3y+zy0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5z, equals, 5.
When [tex]\( y = 10 \) and \( z = 5 \)[/tex], [tex]\( 0.3y + \frac{y}{z} \) equals \( 5 \)[/tex].
Step 1 :To evaluate the expression [tex]\(0.3y + \frac{y}{z}\) when \(y = 10\) and \(z = 5\)[/tex], follow these steps:
1. Substitute the given values of [tex]\(y\) and \(z\)[/tex] into the expression:
[tex]\[0.3 \times 10 + \frac{10}{5}\][/tex]
2. Calculate each term separately:
- [tex]\(0.3 \times 10 = 3\)[/tex]
- [tex]\(\frac{10}{5} = 2\)[/tex]
3. Add the results:
[tex]\[3 + 2 = 5\][/tex]
So, when [tex]\(y = 10\) and \(z = 5\)[/tex], the expression [tex]\(0.3y + \frac{y}{z}\) equals \(5\).[/tex]
Step 2 :1. Multiply 0.3 by 10:
[tex]\[0.3 \times 10 = 3\][/tex]
2. Divide 10 by 5:
[tex]\[\frac{10}{5} = 2\][/tex]
3. Add the results:
[tex]\[3 + 2 = 5\][/tex]
Thus, when [tex]\(y = 10\) and \(z = 5\)[/tex], the expression [tex]\(0.3y + \frac{y}{z}\) equals \(5\).[/tex]
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]
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!
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.
write the rate as a fraction? 17 meters per second
What are the 3 steps for factoring completely?
2. How did the technique of “Factoring by Grouping” get it’s name?
3. How can you tell if Factoring by Grouping works for a problem?
4. What is a perfect square trinomial?
5. a.) How can you tell if a binomial is the difference of two squares.
b.) What is the factored form of the difference of two squares.
6. How do you find the zero’s of a polynomial function?
Factoring completely involves three steps: identifying the GCF, applying the appropriate factoring method, and checking for additional factors. Factoring by grouping is used when there are four terms in an expression and common factors can be factored out separately. An example is given to illustrate the factoring by grouping process.
Explanation:Factoring Completely:Identify the greatest common factor (GCF) of the terms in the expression and factor it out.Apply the difference of squares, trinomial, or grouping method to factor the remaining expression.Check if there are any additional factors that can be factored further.Factoring By Grouping:This technique is used when there are four terms in an expression and there is a common factor between the first two terms and the last two terms. The common factor is factored out separately from the two pairs, and then the resulting binomials are factored further.
Factoring by Grouping Example:Consider the expression 2x + 3y + 4x + 6y. In this case, we can group the terms as (2x + 3y) + (4x + 6y). Common factors can be factored out separately, resulting in (2x + 3y)(1 + 2).
Learn more about Factoring Completely here:https://brainly.com/question/29012163
#SPJ12
Which equation represents the general form a circle with a center at (–2, –3) and a diameter of 8 units?
A.) x^2+y^2+4x+6y-51=0
B.) x^2+y^2-4x-6y-51=0
C.) x^2+y^2+4x+6y-3=0
D.) x^2+y^2-4x-6y-3=0
To find the equation, we will form the general equation of a circle and then will find the equation that matches the equation we formed.
General equation of a circleThe general equation of a circle is given as
[tex](x-h)^2+(y-k)^2 = R^2[/tex]
where, the (h, k) are the coordinates of the center of the circle, and R is the radius of the circle.
The correct option is c.
Given to uscircle with a center at (–2, –3) diameter of 8 unitsTo findthe equation of the circle that represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Radius of the CircleGiven that the diameter of the circle is 8 units. therefore,
[tex]\rm{ Radius\ of\ the\ circle =\dfrac{Diameter}{2} = \dfrac{8}{2}[/tex]
Equation of a circleThe equation of the circle that represents the general form of a circle with a center at (–2, –3) and a radius of 4 units can be found by substituting the values in the equation of a circle:
[tex](x-h)^2+(y-k)^2 = R^2[/tex]
Substituting the values,
[tex][x-(-2)]^2+[y-(-3)]^2 = 4^2\\\\ (x+2)^2+(y+3)^2 = 16[/tex]
[tex](x+2)^2+(y+3)^2 = 16\\\\ (x^2 + 4 + 4x)+(y^2+9+6y) = 16\\\\ x^2 + 4 + 4x+y^2+9+6y = 16\\\\ x^2 + 4x+y^2+6y = 16-4-9\\\\ x^2 + 4x+y^2+6y = 3\\\\ x^2 + 4x+y^2+6y -3 = 0[/tex]
Therefore, the equation which will be in the above form will be the equation we want. As we can see the above equation is similar to option c.
VerificationTo verify that we will plot the graph. The image given below represents the general form of a circle with a center at (–2, –3) and a diameter of 8 units.
Hence, the correct option is c.
Learn more about Circle:
https://brainly.com/question/11833983