A hockey game between two teams is 'relatively close' if the number of goals scored by the two teams never differ by more than two. In how many ways can the first 12 goals of a game be scored if the game is 'relatively close'?
This question falls under the combinatorial mathematics branch. Due to the complex nature of the problem which involves permutations and combinations, it's necessary to use a systematic approach or a computer algorithm to find the total number of scoring sequences that keeps the game 'relatively close'. Hence, the actual numerical answer would require a stronger background in combinatorics.
Explanation:This question belongs to the subject of combinatorial mathematics, particularly involving permutations and combinations. In this scenario, 'relatively close' is defined as the number of goals scored by the two teams never differing by more than two. The total number of goals scored in the game is twelve.
Let's denote the two teams as Team A and Team B. The game can start in three ways: either Team A scores twice, Team B scores twice, or each team scores once. After that, at any point, the next goal can either maintain the score within the 'relatively close' range of two goals or equalize the score.
Determining the total number of scoring sequences under these conditions requires generating a tree diagram and counting all the possible paths, subject to the condition that the absolute difference between the number of goals for the two teams does not exceed two at any stage. Due to the combinatorial complexity, this task could be difficult without using a systematic approach or computer algorithm.
Therefore, to actually answer this question, one would require a stronger background in combinatorics, and most likely the assistance of programming or mathematics software to execute a brute force count or implement a more advanced mathematical solution.
Learn more about Combinatorial Mathematics here:https://brainly.com/question/32415345
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a dinosaur fossil is 92,170,000 years old. How can you express this age in scientific notation with the highest level of precision?
Answer: Its age is expressed as [tex]9.217\times 10^7[/tex]
Step-by-step explanation:
Since we have given that
Age of dinosaur fossil = 92170000 years old
We need to write in scientific notation with the highest level of precision.
Since we know that Scientific notation means put the decimal just after unit digit and for all remaining digit there is to the power of 10.
So, it becomes,
[tex]92170000=9.217\times 10^7[/tex]
Hence, its age is expressed as [tex]9.217\times 10^7[/tex]
How many 53/4 pieces of yarn can be cut from a roll that is 60 inches long? please i really need help
The quantity demanded x for a product is inversely proportional to the cube of the price p for p > 1. When the price is $10 per unit, the quantity demanded is 64 units. The initial cost is $150 and the cost per unit is $2. What price will yield a maximum profit?
Explain what each variable in the formula represents.
Will give brainlist
Suppose a ball is completely submerged inside a cylinder filled with water displacing some of the water in the cylinder. Assume the ball and the cylinder both have a diameter of 10 centimeters, and the diameter of the ball is the same as the height of the cylinder. Determine the volume of water that can remain in the cylinder after the ball is inserted so that the water rises to the top edge of the cylinder without spilling
Answer:the volume of cylinder is 785
volume of the sphere is 523.33
the volume of the water that can remain is 261.8
Step-by-step explanation: algebra nation answer
-2x+y=1.3 2(0.5x-y)=4.6
Plz help me with this
4/5 of the books in a library of fiction books. What percentage of the books or fiction books?
What is the answer for 20x21
what is the area of this trapezoid
Right the slope intercept of the equation of the line through the given point with the given slope through (2, 1) slope = 5/2 m= b= equation:_____________
The table below represents a linear function f(x), and the equation represents a function g(x): X) -1, 0, 1 F(x) -5, -1, 3 G(x)=2x+8
Part A. Wrote a sentence to compare the slope of the two functions and shows the steps you used to determine the slope of f(x) and g(x)
Part B which functions has greater y-intercept. Justify
Paige works at a department store and has a commission rate of 3 percent. Her sales for the quarter were $4,596. If she earns $50 per day and she worked 30 days in the quarter, what is the total amount she earned?
Here's what the equation would look like:
30(50) + 0.03(4596)
1500 + 137.88
Paige earned $1637.88.
Answer:
Paige earned $1637.88.
Step-by-step explanation:
i did it enginuity
Anyone? please i need help
Answer:
[tex]y= 5x-7[/tex]
Step-by-step explanation:
Using slope-intercept form:
The equation of line is given by:
[tex]y=mx+b[/tex] .....[1]
where,
m is the slope of the line
b is the y-intercept.
As per the statement:
The points (3, 8) and (2, 3) fall on a particular line.
Using slope(m) formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points we have;
[tex]m = \frac{3-8}{2-3}=\frac{-5}{-1}=5[/tex]
⇒m = 5
Put m = 5 in [1] we have;
[tex]y=5x+b[/tex]
Substitute the point (3, 8) we have;
8 = 5(3)+b
8 = 15+b
Subtract 15 from both sides we have;
[tex]-7 = b[/tex]
or
b = -7
Then we have;
[tex]y= 5x-7[/tex]
Therefore, the equation of line in slope intercept form is, [tex]y= 5x-7[/tex]
a bird is in a tree 30 feet off the ground and drops at Twigs at lands on a rose bush 25 ft below. the function h(t)=-16t^2+30, where T represents the time in seconds gifts the height H and feet of The Twig above the ground as it falls when will The Twig land on the bush
Answer:
After 1.25 seconds the twig land on the bush.
Step-by-step explanation:
Given function that shows the height of twig from the ground after t seconds,
[tex]h(t)=-16t^2+30[/tex]
When twig is on the bush,
h(t) = 5 feet ( ∵ the distance from bush to ground = 30 - 25 = 5 feet )
[tex]\implies -16t^2+30=5[/tex]
[tex]-16t^2=-25[/tex]
[tex]t^2=\frac{25}{16}[/tex]
[tex]\implies t=\pm \frac{5}{4}[/tex]
Since, time can not be negative,
Hence, t = [tex]\frac{5}{4}[/tex] ≈ 1.25
Therefore, after 1.25 seconds the twig land on the bush.
if an arc has a measure of 97° and the circle has radius = 10, what is the arc length
Final answer:
The arc length of a circle with a radius of 10 units and a central angle of 97° is calculated using the formula for arc length, yielding an arc length of approximately 16.975 units.
Explanation:
The question asks us to find the arc length of a circle with a certain radius when a central angle is given. To find the arc length, we use the formula:
Arc length (s) = (θ/360) × 2πr
Where θ is the central angle in degrees, r is the radius of the circle, and π is approximately 3.14159. Since we know the central angle is 97° and the radius is 10, we can plug these values into the formula:
s = (97/360) × 2×π×10
s ≈ (97/360) × 2× 3.14159 × 10
s ≈ 16.975
Therefore, the arc length is approximately 16.975 units.
Two angles are complementary. If the measure of one angle is twice the measure of the other angle, what is the measure of the larger angle?
Answer:
70 is the answer choise I picked it and got it correct
Step-by-step explanation:
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James cut 1 1/4 dozen flower for a bouquet. Gwen added 1 2/4 dozen flowers to the bouquet. How many dozen flowers are there altogether?
Flower cut for a bouquet by James =[tex] 1\frac{1}{4} [/tex]
Flower cut for a bouquet by Gwen=[tex] 1\frac{2}{4} [/tex]
Flower cut for a bouquet by James and Gwen is the sum of flowers cut by both.
Flower cut for a bouquet by James and Gwen=[tex] 1\frac{1}{4} +1\frac{2}{4} =(1+1)+(\frac{1}{4} +\frac{2}{4} =(2)+\frac{3}{4} =2\frac{3}{4} [/tex]
Flower cut for a bouquet by James and Gwen =[tex] 2\frac{3}{4} [/tex]
Uniforms are sold in packages of 8 - the stores 127 employees will be given 3 uniforms
Share £747 in the ratio 2:7 between Tom and Ben
radical functions. please help me!
A rectangular prism has a length of 12 in., a width of 5 in., and a height of 4 1/4 in.
The prism is filled with cubes that have edge lengths of 1/4 in.
How many cubes are needed to fill the rectangular prism?
Enter your answer in the box.
To fill the rectangular prism, how many cubes are needed.
Answer:
64
Step-by-step explanation:
took the test
You sell 3 hamburgers at $2.10 each plus 0.38 tax. A customer gives you a $10.00 bill. How much change does he get?
Given is the Rate of each hamburger = 2.10 dollars each.
The number of hamburgers that we sell = 3 hamburgers.
Charges for all 3 hamburgers = 3 x 2.10 = 6.30 dollars.
Tax charged on these 3 hamburgers = 0.38 dollars.
Total Bill = Charges for 3 hamburgers + Tax
Total Bill = 6.30 + 0.38 = 6.68 dollars.
Customer paid = 10 dollars.
The amount to be returned to customer = Bill paid by customer - Total Bill charged = 10 - 6.68 = 3.32 dollars.
Hence, the customer would get a change of 3.32 dollars.
I have to translate these into algebraic expressions. three-fifths x subtracted from 4 times one-eighth w. the other one is 60% of the product of one-twelfth y and two-thirds z.
The final algebraic expressions are: [tex]\frac{1}{2} w - \frac{3}{5} x[/tex] and [tex]\frac{1}{30} yz[/tex]
Sure, let's break down each part of your question step-by-step to translate them into algebraic expressions.
Three-fifths x subtracted from 4 times one-eighth w
Let's identify the components first:
"Three-fifths x" is written as [tex]\frac{3}{5} x[/tex]."4 times one-eighth w" is written as [tex]4 \times \frac{1}{8} w[/tex] or simply [tex]\frac{4}{8} w[/tex].Now, write the expression for "three-fifths x subtracted from 4 times one-eighth w":
[tex]\frac{4}{8} w - \frac{3}{5} x[/tex]
Simplifying [tex]\frac{4}{8} w[/tex] to [tex]\frac{1}{2} w[/tex], the algebraic expression becomes:
[tex]\frac{1}{2} w - \frac{3}{5} x[/tex]
60% of the product of one-twelfth y and two-thirds z
Let's identify the components first:
"One-twelfth y" is written as [tex]\frac{1}{12} y[/tex]."Two-thirds z" is written as [tex]\frac{2}{3} z[/tex]."Product of one-twelfth y and two-thirds z" is written as [tex]\frac{1}{12} y \times \frac{2}{3} z[/tex].First, calculate the product:
[tex]\frac{1}{12} y \times \frac{2}{3} z = \frac{2}{36} yz = \frac{1}{18} yz[/tex]
Now, we need "60% of that product":
60% can be written as [tex]0.60[/tex], so the expression becomes:
[tex]0.60 \times \frac{1}{18} yz = \frac{3}{90} yz = \frac{1}{30} yz[/tex]
So, the algebraic expression for "60% of the product of one-twelfth y and two-thirds z" is:
[tex]\frac{1}{30} yz[/tex]
Select all that apply. Which of the following decimal numbers are examples of terminating decimals? Here is all the choices... 0.6868 14.1 832.15902... 23.7 9.125 1,087.59014
Are similar this triangles
if x <0, which integer does not satisfy the inequality x+2 <1
Answer:x+2<1x<1-2x<-1-1 does not satisfy the inequality because though-1 is lesser than 0 but not lesser than
Maria spent 4/7 of her money on a book and saved the rest. What fraction of her money did Maria save?