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.
9999+8888+777+?=19700
The amount of money Jamie earns is proportional to the number of hours she works. Jamie earns $62.50 working 5 hours. 1) Write an equation that models the relationship between m, the amount of money Jamie earns in dollars, and h, the number of hours she works. 2) How much money would Jamie earn for 11 hours of work?
The given expression represents the area. Find the side length of the square. 64r^2-144r+81
The dimension of the square is 1.125 by 1.125 units and the area of the square is 1.265625 square units.
What is a factorization?It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.
The given expression represents the area of a square is 64r² – 144r + 81.
The dimension of the square will be
Using the formula method, we have
64r² – 144r + 81
Then
[tex]\rm r = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Then we have
a = 64
b = –144
c = 81
Then
[tex]r = \dfrac{-(-144) \pm \sqrt{(-144)^2-4*64*81}}{2*64}\\\\\\r = \dfrac{144 \pm \sqrt{20736- 20736}}{128}\\\\\\r = \dfrac{144}{128}\\\\\\r = 1.125[/tex]
The dimension of the square is 1.125 by 1.125 units and the area of the square is 1.265625 square units.
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A square window has a perimeter of (8x+12) feet. Write an expression that represents the side length of the window (in feet). Please help!!!
The side length of the square window with a perimeter of (8x+12) feet is found by dividing the perimeter by 4, resulting in an expression for the side length as 2x + 3 feet.
Explanation:To find the side length of a square window with a given perimeter, you can use the fact that the perimeter (P) of a square is equal to four times the side length (s). In this case, the perimeter is expressed as (8x+12) feet. Since there are four sides of equal length in a square, you divide the perimeter by 4 to find the length of one side.
The formula for the perimeter of a square is:
P = 4s
Given the perimeter P = (8x+12), we can solve for the side length s by dividing both sides of the equation by 4:
s = (8x+12) ÷ 4
Simplifying the equation, we get:
s = 2x + 3
Therefore, the expression for the side length of the square window in feet is 2x + 3.
If cheese is $4.40 per kilogramme, what should I pay for 200 grammes?
Answer:
Cost of 200 gram chess = $0.88.
Step-by-step explanation:
Given : If cheese is $4.40 per kilogram.
To find : What should I pay for 200 gram.
Solution : We have given
1 kilogram = 1000 gram.
Cost of 1000 gram chess = $4.40.
Cost of 1 gram chess = [tex]\frac{4.40}{1000}[/tex].
Cost of 200 gram chess = [tex]\frac{4.40}{1000}* 200[/tex].
= $0.88.
Therefore, Cost of 200 gram chess = $0.88.
What are the solutions of 12 – x2 = 0?
A. x = and x =
B. x = and x =
C. x = and x =
D. x = 6 and x = –6
The solution of the expression are,
⇒ x = 3.5 and x = - 3.5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 12 - x² = 0
Now, We can simplify as;
⇒ 12 - x² = 0
⇒ 12 = x²
⇒ x = √12
⇒ x = ± 3.5
⇒ x = 3.5 and x = - 3.5
Thus, The solution of the expression are,
⇒ x = 3.5 and x = - 3.5
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Dakota makes a salad dressing by Combining 7 1/3 fluid ounces of oil and 2 1/8 fluid ounces of vinegar in a jar. she then pours 2 1/4 fluid ounces of the dressing on to her salad. How much dressing remains in the jar?
Angelica colored in 0.60 of the squares on her grid. What is the expression 0.60 as tenth in fraction
Complete the equation of the graphed linear function in point-slope form.
y – 6 =
(x –
)
The graph of the function goes through point negative 6, 6 and point negative 8, 2.
The y-value increases by 4 when the x-value increases by 2, so the slope is
... 4/2 = 2
Your equation for the line with slope m through point (h, k) is
... y - k = m(x - h)
and you have m = 2, (h, k) = (-6, 6)
Filling in those values gives
... y - 6 = 2(x - (-6))
Nancy is running 5.3 miles long after 20 minutes she has run 1.45 miles solve the equation to find the number of miles Nancy has to run to get to the end of the trail
Mr.gardener is making 6 great bags.he has 185 chocolate covered raisins to share among the great bags.How many chocolate covered raisins will be in each treat bag ?
Multiply. Write in simplest form. Identify the two whole numbers between which the product lies 24 * 1/5
William has a 26-liter glass tank. First, he wants to put some marbles in it, all of the same volume. Then, he wants to fill the tank with some water until its comepletly full. If he uses 85 marbles, he will have to add 20.9 liters of water. What is the volume of each marble? and How much water is necessary if William uses 200 Marbles?
Answer:
Volume of each Marble: 0.06 liters
Water required for the marbles and water: 14 Liters
What happens if the correlation coefficient equals 0?
There is a strong negative linear relationship between x and y.
There is not a linear relationship between x and y.
There is a strong positive linear relationship between x and y.
There is a weak negative linear relationship between x and y.
Evaluate m+n2 if we know m= 2 and n =-2
Find a particular solution to the nonhomogeneous differential equation y′′+6y′−7y=e4x
A flying squirrel lives in a nest that is 15 feet high in a tree. To reach a fallen acorn that is 8 feet from the base of the tree, how far will the flying squirrel have to glide?
Final answer:
To find the distance the flying squirrel must glide to reach the acorn, the Pythagorean theorem is used. The tree's height (15 feet) and the horizontal distance to the acorn (8 feet) provide the two sides of a right triangle. The squirrel's glide distance is the hypotenuse, calculated to be 17 feet.
Explanation:
To calculate the distance the flying squirrel needs to glide to reach the acorn, we can apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this scenario, the tree height forms one side of a right triangle, the distance from the base of the tree to the acorn forms the second side, and the squirrel's glide path represents the hypotenuse.
Given:
Tree height (side a): 15 feet
Distance from the tree to the acorn (side b): 8 feet
Using the Pythagorean theorem:
c² = a² + b²
c² = 15² + 8²
c² = 225 + 64
c² = 289
c = √289
c = 17 feet
Therefore, the flying squirrel needs to glide 17 feet to reach the acorn.
A cereal box has a height of 32 cm. The base has 160 square cm what is the volume in cubic cm of the box
is x/5 = y/3 a linear function
How could you model 5 students sharing 4 bags of popcorn equally? How much will each student get?
Consider the ratio written like a fraction:
Count of sandwichescount of people→46
But we need the count of sandwiches for 1 person. So we need to change the 6 people into 1 person. To change 6 into 1 divide it by 6
6÷6=1
For ratios, when multiplying or dividing, what we do to the bottomwe do to the top.
So to change 46 into what we want we apply
4÷66÷6=231← Count of sandwichescount of people
So each person ends up with 23 of a sandwich
Now see where the shortcut comes from 46=23 of a sandwich
in how may ways could mushrooms or olives be included in his toppings?
Anyone have a scientific calculator? Can you put in
Sin (40/42)
make sure the mode is set to degree please.
Sam buys 4 tropical fish. Each fish is 5/8 of an inch long. Write an equation that represents 4 x 5/8 as a multiple of a unit fraction.
If 2n is greater than 30 what can n be
It is 76 miles from waterton to middleton. it is 87 miles from middleton to oak hill. driving directly, it is 134 miles from waterton to oak hill. it is 39 miles rom oak hill to jackson. if juan drives from waterton to middleton then from middleton to oak hill, and finally home to waterton, how many miles does he drive?
Juan drives a total of 297 miles if he travels from Waterton to Middleton, then to Oak Hill, and back to Waterton.
Explanation:The student is asking to calculate the total number of miles driven by Juan starting from Waterton to Middleton, then from Middleton to Oak Hill, and then returning home to Waterton.
To find the total distance traveled by Juan, we simply need to add the individual distances of each leg of his trip.
Waterton to Middleton: 76 milesMiddleton to Oak Hill: 87 milesOak Hill to Waterton (directly): 134 milesBy adding these distances, we get the total miles Juan drives:
Total miles driven = 76 + 87 + 134 = 297 miles
Fran painted 1/2 of the fence around her house. What are two other ways to name 1/2?
The fountain is made up of two semicircles and a quarter circle. Find the perimeter and the area of the fountain. Round the perimeter to the nearest tenth of a foot and the area to the nearest square foot. Both have the diameter 20
The perimeter of the fountain = 94.2 ft
The area of the fountain = 628 ft²
Area of a CircleThe formula of the area of a full circle is: πr².Area of semicircle = ½(πr²)Area of quarter circle = ¼(πr²)Perimeter of a CirclePerimeter of a full circle = 2πrPerimeter of semicircle = ½(2πr)Perimeter of quarter circle = ¼(2πr)Given:
Diameter of the semicircle = 20 ft
Therefore, Radius (r) = half of diameter = 10 ft
Radius of the quarter circle = 20 ft
Perimeter of the fountain = ½(2πr) + ½(2πr) + ¼(2πr)
Plug in the values of rPerimeter of the fountain = ½(2π(10)) + ½(2π(10)) + ¼(2π(20))
Perimeter of the fountain = 94.2 ft
Area of the fountain = 2(½(πr²)) + ¼(πr²)
Plug in the values of rArea of the fountain = 2(½(π10²)) + ¼(π20²)
Area of the fountain = 628 ft²
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Prove the divisibility of the following numbers: 10^9+10^8+10^7 by 555
The proof that 10⁹ + 10⁸ + 10⁷ is divisible by 555; Is true and has been proved below
Divisibility of Numbers
Let the number N be expressed as;
10⁹ + 10⁸ + 10⁷
We can factor out 10⁷ to get;
⇒ 10⁷(100 + 10 + 1)
⇒ 10⁷(111)
⇒ 10 × 10⁶(111)
We can factorize 10 further to get;
5 × 2 × 10⁶(111)
⇒ 555 × 2 × 10⁶
Since the answer contains 555, then we can say that it is divisible by 555.
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Paul has a white and blue shirt he also has two trousers of brown and black how many different outfits
Miguel surveyed all the members of the junior high choir about their favorite class. The results from his survey are: Favorite Class Number of Students choir 19 math 7 history 5 English 9 science 4 Miguel concluded, from his results, that the favorite class among the entire student body would also be choir. Which is the best explanation of why his conclusion might not be true?
Answer:
He has surveyed the students who are already participating in the choir. So naturally the number of students who likes the choir class will be higher than in other classes. You can see it reflected in the data.
Step-by-step explanation:
He has surveyed the students who are already participating in the choir. So naturally the number of students who likes the choir class will be higher than in other classes. You can see it reflected in the data.
If he needs to make an inference on the whole school he needs to randomly pick people from the school and ask the same question. Then he can make a better inference about the favorite class of students.
Answer:
His sample group does not represent the entire school body.
Step-by-step explanation: