==============================================
Explanation:
The formula to use is n*(n-1)/2
Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = 66
That formula is from the nCr combination formula when r = 2.
---------------------
Here's a visual way to see why that rule works.
Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}[/tex]
In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}[/tex]
Let's also cross out any cell below the main diagonal.
[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}[/tex]
We do this because a mirrored copy is found above the diagonal.
We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.
Those 6 matchups are:
A vs BA vs CA vs DB vs CB vs DC vs DThe order doesn't matter. A matchup like "A vs B" is the same as "B vs A".
We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.
Then we split that in half to get the formula n(n-1)/2.
100 Points! Geometry question. Photo attached. Find the area of the figure. Round to the nearest tenth if necessary. Please show as much work as possible. Thank you!
Answer:
38.9 in²
Step-by-step explanation:
You want the area of the composite figure that is an 8-inch square with a semicircle removed.
Semicircle areaThe missing semicircle has a diameter of 8 in, so a radius of 4 in. The area of that half-circle is ...
A = 1/2πr² = (π/2)(4 in)² = 8π in² ≈ 25.1 in²
Square areaThe area of the square without the semicircle removed is ...
A = s² = (8 in)² = 64 in²
Composite areaAfter removing the semicircle from the square, the remaining area is ...
A = square area - semicircle area
A = 64 in² -25.1 in² = 38.9 in²
The area of the figure is about 38.9 square inches.
<95141404393>
An 80-ounce bottle of apple juice contains 32 ounces of water.
Using the proportion principle , Orange Juice has a greater percentage of water than Apple juice
Calculating ProportionsTo determine which juice has a greater percent of water, we need to calculate the percentage of water in each juice.
Apple juicePercentage of water = (Water content / Total content) * 100
Water content = 32 ounces
Total content = 80 ounces
Percentage of water in apple juice = (32 / 80) * 100 = 40%
Orange juiceWater content = 48 ounces
Total content = 64 ounces
Percentage of water in orange juice = (48 / 64) * 100 = 75%
Comparing the percentages, we can conclude that orange juice has a greater percentage of water (75%) than the apple juice (40%).
Therefore, the orange juice contains a higher percentage of water.
Learn more on proportion : https://brainly.com/question/19994681
#SPJ1
Complete question :
an 80 ounce bottle of apple juice contains 32 ounces of water a 64 ounce bottle of orange juice has 48 ounces of water which juice has a greater percent of water
The radius of a circular play ground is 77m. Calculate the distance covered by a runner is 5 complete rounds around the ground. ( ans2420) how ?
Step-by-step explanation:
To solve this problem, we need to find the circumference of the circular playground and then multiply it by the number of rounds the runner completes.
The circumference of a circle can be calculated using the formula:
Circumference = 2 * π * radius
Given that the radius of the playground is 77m, we can substitute this value into the formula to find the circumference:
Circumference = 2 * π * 77
Now, we need to calculate the distance covered by the runner in 5 complete rounds. Since one round is equal to the circumference, the distance covered in 5 rounds would be:
Distance = 5 * Circumference
Substituting the value of the circumference, we have:
Distance = 5 * (2 * π * 77)
To simplify, we can use an approximation of π as 3.14:
Distance ≈ 5 * (2 * 3.14 * 77)
Calculating further:
Distance ≈ 5 * (6.28 * 77)
Distance ≈ 5 * 483.56
Distance ≈ 2417.8
Therefore, the distance covered by the runner in 5 complete rounds around the circular playground is approximately 2417.8 meters, which can be rounded to 2420 meters (as given in the answer).
Hope this helps!
Answer:
2420
Step-by-step explanation:
Circumference = 2πr
One complete round will be equal to the circumference = 2πr
Five rounds will be five times the circumference
= 5*2πr
= 10πr
[tex]= 10 *\frac{22}{7}*77 \\\\= 10* 22* 11\\\\= 2420[/tex]
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The consistency of the diameters of wheel bearings is vital to the operation of the wheel. The specifications require that the variance of these diameters be no more than 0.0015 centimeter squared. The diameter is continually monitored by the quality-control team. Twenty subsamples of size 10 are obtained every day. One of these subsamples produced bearings that had a variance of 0.00317 centimeter squared. Conduct a hypothesis test to determine if the quality control team should advise management to stop production and search for causes of the inconsistency of the bearing diameters. Use a significance level of 0.05.
Using digits 1to 9 fill in the boxes once write largest and smallest absolute value. Then find the decimal equivalent.
The decimal equivalent of the largest Absolute value, 987654321, is 987,654,321. the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.
The largest and smallest absolute values using the digits 1 to 9, we need to arrange them in a way that maximizes or minimizes the resulting number. Let's consider the boxes as placeholders for the digits.
To determine the largest absolute value:
We place the digit 9 in the leftmost box, as it is the largest digit among 1 to 9. Then we arrange the remaining digits, 8, 7, 6, 5, 4, 3, 2, and 1, from largest to smallest in the remaining boxes. This gives us the number 987654321, which is the largest possible number using the given digits. Therefore, the largest absolute value is 987654321.
To determine the smallest absolute value:
We place the digit 1 in the leftmost box, as it is the smallest digit among 1 to 9. Then we arrange the remaining digits, 2, 3, 4, 5, 6, 7, 8, and 9, from smallest to largest in the remaining boxes. This gives us the number 123456789, which is the smallest possible number using the given digits. Therefore, the smallest absolute value is 123456789.
To find the decimal equivalent of these numbers, we simply read the digits from left to right. The decimal equivalent of the largest absolute value, 987654321, is 987,654,321. The decimal equivalent of the smallest absolute value, 123456789, is 123,456,789.
Thus, the largest absolute value is 987,654,321 and the smallest absolute value is 123,456,789.
To know more about Absolute value.
https://brainly.com/question/24368848
#SPJ8
what 2 reports could be used to verify that retirement contributions were accurately remitted for the most recent payroll period
Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are the Payroll Summary Report and the Retirement Contribution Report.
Two reports that could be used to verify the accuracy of retirement contributions for the most recent payroll period are:
Payroll Summary Report: This report provides a summary of the payroll transactions for the period, including details of employee wages, deductions, and employer contributions.
It should include a specific section or breakdown for retirement contributions, showing the individual employee contributions and the corresponding employer contributions.
By reviewing this report, one can ensure that the retirement contributions have been accurately calculated and remitted.
Retirement Contribution Report: This report specifically focuses on the retirement contributions made by both employees and the employer.
It should provide a detailed breakdown of the contributions for each employee, including the employee's contribution amount, the employer's matching or non-elective contribution amount, and any additional details related to the retirement plan.
This report allows for a comprehensive review of the retirement contributions to verify if they match the expected amounts based on employee records and plan guidelines.
By comparing the information in these reports with the employees' individual contribution records and the retirement plan requirements, it is possible to verify that the retirement contributions were accurately remitted for the most recent payroll period.
For similar question on Retirement Contribution Report.
https://brainly.com/question/28128413
#SPJ8
Two cars leave towns 850 kilometers apart at the same time and travel toward each other. One car's rate is 16 kilometers per hour less than the other's. If they meet in 5 hours, what is the rate of the slower car? Do not do any rounding.
Answer:9.5
Step-by-step explanation:
What is the difference 5 2/6 -2 4/6
Answer:
Therefore, the expression becomes:
7/1 - 2/6
Now, we need to find a common denominator for the fractions, which is 6:
7/1 - 2/6 = (76)/(16) - 2/6
= 42/6 - 2/6
= (42 - 2)/6
= 40/6
Finally, we can simplify the fraction:
40/6 = 20/3
So, the difference between 5 2/6 and -2 4/6 is 20/3.
Step-by-step explanation:
First, let's subtract the whole numbers: 5 - (-2) = 5 + 2 = 7.
Next, let's subtract the fractions: 2/6 - 4/6 = (2 - 4)/6 = -2/6.
Combining the whole number and fraction results, we have:
7 - 2/6
Now, to simplify this result further, we can express 7 as a fraction with a common denominator of 6:
7 = 7/1
Which graph represents the solution set to the system of inequalities?
{ Y ≤ 1/4X-2
Y ≥ −54X+2
ANSWER Down Below
The graph of the system of inequalities:
y ≤ (1/4)*x - 2
y ≥ −(5/4)x +2
Is in the image at the end.
Which is the graph of the system of inequalities?Here we have the system of inequalities:
y ≤ (1/4)*x - 2
y ≥ −(5/4)x +2
To graph this, we just need to graph both of the linear equations, and we need to shade the region below the first line (the one with positive slope) and the region above the second line, the one with negative slope.
Then the graph of the system of inequalities is the graph you can see in the image at the end of the answer.
Learn more about system of inequalities at.
https://brainly.com/question/9774970
#SPJ1
Find the area of the following rectangle. a = 12 ft b = 14 ft A = ft 2
Answer:
The area of the rectangle is 168 ft².
Step-by-step explanation:
Formula: A = lw
where l and w are the length and width of the rectangle respectively.
We're given with the length and the width as
a = 12 ft
b = 14 ft
Let's solve for the area using the formula above.
A = lw
A = 12ft(14ft)
A = 168 ft²
find the missing side. round to the nearest tenth
The required angle is 24.5°.
Given is a right triangle with perpendicular side 16 and the base = 35 we need to find an acute angle in it,
To find the acute angle in a right triangle given the lengths of the perpendicular side and the base, you can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the perpendicular side to the length of the base side.
In this case, the perpendicular side is 16 and the base is 35.
Let's denote the acute angle as θ.
Using the tangent function, we can set up the equation:
tan(θ) = perpendicular side / base
tan(θ) = 16 / 35
To find the value of θ, we can take the inverse tangent of both sides:
θ = tan⁻¹(16 / 35)
θ = 24.5°
Hence the required angle is 24.5°.
Learn more about tangent function, click;
https://brainly.com/question/28994024
#SPJ1
What is the range of g(x) = |x + 3| + 2? A. [-3, ∞) B. (-∞, 2] C. [2, ∞) D. (-∞, ∞)
Answer:
C. [2, + ∞)-----------------
Given function:
g(x) = | x + 3| + 2We know that absolute value is non-negative, hence |x + 3| has a minimum value of 0 when x = - 3. Then the function has a minimum value of 2.
The range is the set of output values. As we see given function has a minimum value of 2 and no maximum value.
It can be shown as:
g ∈ [2, + ∞)The matching choice is C.
Change these fractions into decimals. Do not round your answers:
a. 3 8
b. 1 9
Step-by-step explanation:
3/8 = 0.375
1/9 = 0.1111111111
Answer:
Step-by-step explanation:
Need some help on this question!!!!!
The greater number of packages that can fit in the truck is 24000.
The volume of the part of the truck that is being filled is 375 cubic feet.
We have,
To determine the greater number of packages that can fit in the truck, we need to calculate the volume of both the packages and the part of the truck that is being filled.
The volume of a cube-shaped package:
The side length of the cube-shaped package is 1/4 feet.
The volume of a cube is given by V = s³, where s is the side length.
Therefore, the volume of each package is (1/4)³ = 1/64 cubic feet.
The volume of the part of the truck being filled:
The dimensions of the rectangular prism-shaped part of the truck are:
Length = 8 feet
Width = 6(1/4) feet = 6.25 feet
Height = 7(1/2) feet = 7.5 feet
The volume of a rectangular prism is given by V = length × width × height.
Therefore, the volume of the part of the truck being filled is:
8 × 6.25 × 7.5
= 375 cubic feet.
To calculate the greater number of packages that can fit in the truck, we divide the volume of the part of the truck by the volume of each package:
= 375 cubic feet / (1/64 cubic feet)
= 375 × 64
= 24000 packages.
Therefore,
The greater number of packages that can fit in the truck is 24000.
The volume of the part of the truck that is being filled is 375 cubic feet.
Learn more about prism here:
https://brainly.com/question/12649592
#SPJ1
Compare the functions shown below:
f(x)
polynomial graph with x intercepts at negative 3, negative 2, 1, 2, y intercept at negative 12
g(x)
trig graph with points at 0, 3 and pi over 2, 0 and pi, negative 3 and 3 pi over 2, 0 and 2 pi, 3
Over the interval x = 0 to x = 2π
h(x) = 2x3 − 2x2 − 3x + 2
Which function has the most x-intercepts? (2 points)
f(x)
g(x)
h(x)
All three functions have the same number of x-intercepts.
Answer:
f(x) has the most x intercepts
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer:
The Law of Sines can be used to solve triangles when you have two angles and a side (AAS or ASA) or two sides and a non-included angle (SSA). In this case, triangle A can be solved using the Law of Sines because it has two angles and a side (AAS).
Pls help me!!!
Robin's teacher asked her to find a box that would hold some small
1 inch cubes that the kindergartners used for counting. Robin
found three boxes with the following dimensions: Box A: 4" x 6" x
8" Box B: 6" x 3" x 12" Box C: 6" x 6" x 4" Which box would be
able to hold all the cubes if Robin's teacher had 200 cubes?
To determine which box can hold all the cubes, we need to calculate the volume of each box and compare it to the volume occupied by the cubes.
The volume of a rectangular box is calculated by multiplying its length, width, and height.
Box A:
Volume = 4" x 6" x 8" = 192 cubic inches
Box B:
Volume = 6" x 3" x 12" = 216 cubic inches
Box C:
Volume = 6" x 6" x 4" = 144 cubic inches
Since the cubes have a side length of 1 inch, the volume occupied by 200 cubes would be:
Volume of cubes = 200 cubic inches
Comparing the volumes, we find that:
- Box A has a volume of 192 cubic inches, which is less than the volume of the cubes.
- Box B has a volume of 216 cubic inches, which is greater than the volume of the cubes.
- Box C has a volume of 144 cubic inches, which is less than the volume of the cubes.
Therefore, the box that would be able to hold all 200 cubes is Box B: 6" x 3" x 12".
Find the area of the following regular hexagon.
10
Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
What is the meaning of "formulas with free variables"?
Formulas with free variables are said to be expressions in formal logic that is known to have variables that are not bound by quantifiers.
What is the meaning of "formulas with free variables"?Variables are placeholders with changeable values in logic. A free variable in a formula has no quantifier and can take any value.
Formula meaning varies with variable values. Formulas containing variables that are not assigned specific values are frequently employed to convey open statements or propositions that require further specification.
Learn more about free variables from
https://brainly.com/question/30426662
#SPJ1
In practice, we shall use in formulas other symbols, namely defined pred- icates, operations, and constants, and even use formulas informally; but it will be tacitly understood that each such formula can be written in a form that only involves and as nonlogical symbols.
Concerning formulas with free variables, we adopt the notational conven- tion that all free variables of a formula
(u1,..., Un)
are among u1, ..., un (possibly some u are not free, or even do not occur, in ). A formula without free variables is called a sentence.What is the meaning of "formulas with free variables"?
Write the function f(x) after the following transformation was performed:
Dilation by a factor of 16
tan^2 x-1=0
Solve with steps (in radians)
Answer:
[tex]x=\frac{\pi}{4}+\frac{\pi n}{2}[/tex]
Step-by-step explanation:
[tex]\displaystyle \tan^2x-1=0\\\tan^2x=1\\\tan x=\pm 1\\\\x=\frac{\pi}{4}+\frac{\pi n}{2}[/tex]
3. Solve for x.
X
37°
11
Answer:
13.77 units-----------------------
In the given right triangle we have an angle of 37° and adjacent leg of 11 units given.
Missing is the length of hypotenuse, x.
Use cosine function:
cosine = adjacent leg / hypotenusePlug in known values and solve for x:
cos 37° = 11/xx = 11/cos 37°x = 13.77 (rounded)A recipe calls for 3.5 cups of rice. If a cup of rice weighs 158 grams, and a bag of rice weighs 2 pounds, how many bags would be needed to make 80 recipes? (2.2 lbs. = 1 kg, 1kg = 1000 g) (Convert 80 recipes to bags)
The number of bags of rice that would be needed to make 80 recipes is 48.664 bags.
How many bags would be needed to make 80 recipes?1 recipe = 3.5 Cups of rice
If
1 cup of rice = 158 grams
1 bag of rice = 2 pounds
2.2 lbs. = 1 kg,
1kg = 1000 g
80 recipes = 3.5 cups 80
= 280 cups
1 cup of rice = 158 grams
280 cups = 158 × 280
= 44,240 grams
1kg = 1000 g
44,240 grams = 44.24 kg
2.2 lbs. = 1 kg; x lbs = 44.24
2.2/1 = x/44.24
x = 2.2 × 44.24
x = 97.328 pounds
1 bag of rice = 2 pounds ; x bags = 97.328 pounds
1/2 = x/97.328
97.328 = 2x
x = 48.664 bags
Hence, 48.664 bags of rice is needed for 80 recipes.
Read more on recipe:
https://brainly.com/question/2985210
#SPJ1
What is the y-intercept?
Answer:
-4
Step-by-step explanation:
i jus did this question
Do the ratios 1/3 and 28/36 form a proportion?
No, the given two fractions/ratios do not form a proportion.
Two ratios are said to be forming proportions if and only if the reduced forms of fractions of the two ratios are the same or are equal to each other. For example - [tex]\frac{3}{6}[/tex] and [tex]\frac{1}{2}[/tex] are in proportion because [tex]\frac{3}{6}[/tex] when reduced to the simplest form gives [tex]\frac{1}{2}[/tex] which is the same as the other given ratio.
In the given question, one ratio given is [tex]\frac{1}{3}[/tex] and the other one is [tex]\frac{28}{36}[/tex]. Reducing the second ratio to the simplest form we get [tex]\frac{7}{9}[/tex]. Clearly, the two fractions are not equal. Hence, the given two ratios are not in proportion.
Learn more about ratios and proportions -
https://brainly.com/question/29774220
pleaseseee help
Two one-step equations
Two equations that contains fractions
One equation with distributive property
One equation with decimals
One real-world problem that is solved by an equation
Remember that each equation must include at least one variable
pls help 100 points
Answer:
Step-by-step explanation:
7. These triangles are similar. Find the area of the smaller
triangle to the nearest whole number.
105 ft²
16 ft
12 ft
Answer
79 ft²
59 ft²
49 ft²
89 ft²
The area of smaller triangle is 59 square feet.
The area of the larger triangle is 105 square feet.
And the one side of the larger triangle and the smaller traingle is 16 and 12 feet respectively.
Suppose the height of thesmaller triangle be x feet and the height of the larger triangle be y feet.
Since, the corresponding edges of similar triangles are proportional.
Therefore, y/x=16/12
y=4/3x
Also, the area of larger triangle is 105 square feet.
1/2×4/3x×16=105
The above equation can be written as
1/2×4/3x×4/3×12=105
1/2×x×12=59
Area of smaller triangle = 59 square feet
Hence, the area of smaller triangle is 59 square feet.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ1
find the volume of cylinder 8in r 2in h
Answer:
402.12 or just 402
I am so lost please help
Answer:
(a) - [tex]y=-2x+18[/tex]
(b) - [tex]y=\frac{1}{2} x-\frac{9}{2}[/tex]
Step-by-step explanation:
Given the equation of a line, which we'll call line 1, find the following.
(a) - The equation of a line, which we'll call line 2, that is parallel to line 1 and travels through the point (9,0)
(b) - The equation of a line, which we'll call line 3, that is perpendicular to line 1 and travels through the point (9,0)
Given:
[tex]3y+6x=-6[/tex]
(1) - Write the equation of line 1 in slope-intercept form
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Slope-Intercept Form:}}\\y=mx+b\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ b \ \text{is the y-intercept of the line}\end{array}\right}[/tex]
[tex]3y+6x=-6\\\\\Longrightarrow 3y=-6-6x\\\\\Longrightarrow y=-\frac{6}{3} -\frac{6}{3}x \\\\\therefore \boxed{y=-2x-2}[/tex]
Thus, we can conclude the slope of line 1 is -2.
(2) - Answering part (a)
To find a line that is parallel to line 1, the slopes must be the same, -2. Use the point-slope form for a line to find the equation for line 2.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Point-Slope Form:}}\\y-y_1=m(x-x_1)\\\bullet \ m \ \text{is the slope of the line}\\\bullet \ (x_1,y_1) \ \text{is a point the line passes through}\end{array}\right}[/tex]
[tex]y-y_1=m(x-x_1); \ \text{Recall that} \ m=-2 \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=-2(x-9)\\\\\therefore \boxed{\boxed{ y=-2x+18}}[/tex]
Thus, the equation for line 2 is found.
(2) - Answering part (b)
To find a line that is perpendicular to line 1, the slope of line 3 must be the opposite-reciprocal of line 1's. Once again, use the point-slope form of a line to find the equation of line 3.
[tex]y-y_1=m(x-x_1); \ \text{Recall that} \ m=\frac{1}{2} \ \text{and} \ (x_1,y_1)=(9,0)\\\\\Longrightarrow y-0=\frac{1}{2}(x-9)\\\\\therefore \boxed{\boxed{ y=\frac{1}{2} x-\frac{9}{2} }}[/tex]
Thus, the equation of line 3 is found.