Answer:
1
Step-by-step explanation:
Using the definition
n[tex]C_{r}[/tex] = [tex]\frac{n!}{r!(n-r)!}[/tex]
where n! = n(n - 1)(n - 2) × 3 × 2 × 1, note that 0! = 1
Given
9[tex]C_{9}[/tex] = [tex]\frac{9!}{9!(9-9)!}[/tex] = [tex]\frac{9!}{9!(0!)}[/tex] = [tex]\frac{9!}{9!}[/tex] = 1
The value of 9C9 or C(9, 9) using Combination is 1.
In combinatorial notation, "9C9" represents the number of combinations of selecting 9 items from a set of 9 items without regard to their order. This can be calculated using the formula:
nCr = n! / (r!(n-r)!)
Here, n = 9 and r = 9.
So, 9C9 = 9! / (9!(9-9)!)
= 9! / (9! × 0!)
Any number divided by 0 is undefined, so the denominator becomes 0!. However, 0! is defined as 1.
Therefore:
9C9 = 9! / (9! × 1)
= 9! / 9!
= 1
Hence, the value of 9C9 is 1.
Learn more about Combination here:
https://brainly.com/question/29595163
#SPJ6
I need the value of O and N in the picture (the diagonal lengths)
Answer:
N=15 O=17
Step-by-step explanation:
since we know this is a rectangle and the lines are diagonals we can assume they create right triangles. For line N we set up the Pythagorean Theorem which is a^2 + b^2 = c^2 and to find N we plug in 9 for a and 12 for b. 9^2 + 12^2 = c^2 c^2 = 225 so now we find the square root of c^2 so c or in this case N = 15, now we repeat this same exact sequence for O but N is now our base and 8 is our height of the triangle so we will plug in 8 for a and 15 for b: 8^2 + 15^2 = c^2 c^2 = 289 and the square root of 289 is 17.
Check the picture below.
What is the equivalent ratio for 5:6
Answer:
30:36
10 : 12
15 : 18
20 : 24
25 : 30
There are sooo many more but here are a few!
Hope this helped.
Using your math skill add 3/4+1/3
Answer: 9/12 + 4/12 which equals 13/12 or 1 1/12
Explanation: The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator. Keep the denominators the same with the answer then add!
Find the area of the rectangle whose vertices have
coordinates (-2,-2), (3,-2), (3, 4) and (-2, 4).
Answer:
Area = 30 square units
Step-by-step explanation:
First, let's try to visualize the problem:
(-2, 4) • | • (3, 4)
|
|
___________|___________
|
(-2, -2) • | • (3, -2)
|
|
Let's find the side lengths;
(-2) - 3 = |-5|, the Base of the rectangle is 5 units.
4 - (-2) = 6, the Height of the rectangle is 6 units.
The formula for area of a rectangle is B × H.
5 × 6 = 30, so the area of the rectangle is 30 units.
A bag contains 77 orange marbles and 21 green marbles. If a representative sample contains 33 orange marbles, then how many green marbles would you expect it to contain? Explain. 100 points :)
Because the ratio of orange marbles to green marbles is ___ in the population, the expected number of green marbles is ___ times the number of orange marbles in the representative sample. There should be ___ green marbles.
9 green marbles are expected in the representative sample.
The expected number of green marbles is 0.27 times the number of orange marbles in the representative sample.
Step-by-step explanation:
Given that,
A bag contains 77 orange marbles and 21 green marbles.A representative sample contains 33 orange marbles and the green marbles not known.So, the expected number of green marbles can be assumed as 'x'.The ratio of orange marbles to green marbles is in proportion to the ratio of orange marbles to green marbles in the representative sample.
To find the value of x :
The proportions are 77/21 = 33/x
Cross multiplying the denominators and keeping x alone on one side,
x = (33 × 21) ÷ 77
x = 693 ÷ 77
x = 9 green marbles.
Therefore, the number of green marbles expected in the representative sample is 9.
To find the how many times the green marbles is to the number of orange marbles in representative sample = 9/33 = 0.27 times.
The green marbles is 0.27 times to orange marbles in the representative sample.
A mailbox on the street is 600 feet from the top of a building. From the mailbox looking up to the tops of that building and a second, taller building, the angle between the buildings is 67degrees. The tops of the buildings are 800 feet from each other. If the angle of elevation from the mailbox to the first building is 53 degrees and the taller building is 60 degrees, how tall is each building... Step by step explanation..Please..Thanks
Answer:
first building: 479.2 ftsecond building: 704.2 ftStep-by-step explanation:
Label the mailbox viewpoint, the top of the first building, and the top of the second building points M, A, and B, respectively.
Consider the triangle MAB. You are told length MA is 600 ft, and length AB is 800 ft. Side AB is opposite the 67° angle at M, so we can use the Law of Sines to find other measures of that triangle. Specifically, we want to know the distance MB.
sin(B)/MA = sin(M)/AB
sin(B) = (MA/AB)sin(M) = 600/800·sin(67°) ≈ 0.690379
B ≈ 43.66°
Then the angle at A is ...
180° -67° -43.66° = 69.34°
and the side MB can be found from ...
MB/sin(A) = AB/sin(M)
MB = (sin(A)/sin(M))AB = sin(69.34°)/sin(67°)·800 ≈ 813.2 . . . feet
__
Now, label points on the ground below A and B as A' and B'. This problem is asking for the heights AA' and BB'. Each of these is opposite the angle of elevation to points A and B, respectively, so can be found using the sine relation:
sin(elevation to A) = AA'/MA
AA' = MA·sin(elevation to A) = 600·sin(53°) ≈ 479.2 . . . ft
Similarly, ...
BB' = MB·sin(elevation to B) = 813.2·sin(60°) ≈ 704.2 . . . feet
The first building is 479.2 ft tall; the second is 704.2 ft tall.
What is 2.3375 rounded to the nearest dollar
Answer:
2.34
Step-by-step explanation:
Nope, it is 2.34 because you round it off and the 2 stays the same the three does to but the other 3 turns into a 4 because the number next to it which is a 7 is 5 and higher so that makes it 2.34 this would make sense from a mathematician even if my profile doesn't say it.
Answer:
The answer is $2
step-by-step explanation:
3 887 860 round it to the nearest million
4,000,000
because the hundred thousand place value is the digit 5 or higher, the millions rounds up!! in this case, the 3 in the millions rounds up to 4 and the rest of the digits on the right turn to 0, also remember commas!!!!!
3 887 860 rounded to the nearest million is 4 000 000.
From the given number 3 887 860, stating the place value of each digit
We have 0 ones (or unit), 6 tens, 8 hundreds, 7 thousands, 8 ten thousands, 8 hundred thousands and 3 million.
Hence, the number we are rounding is 3 (since we are asked to round to the nearest million)
To round a number, we either round up or round down.
If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down; and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.
Since, the number that follows the digit we are rounding is 8, then we round up. We round up by adding 1 to the digit we are rounding and turn the remaining numbers to zeros.
(3+1 = 4)
Hence, 3 887 860 rounded to the nearest million is 4 000 000.
Learn more here: https://brainly.com/question/22958284
Susan's cat loses 1 1/4 pounds. then then it loses another 1/8 pound. what what is the total change in the cat's weight?
Answer:
decrease of 1 3/8 lbs (= 11/8 lbs)
Step-by-step explanation:
given that the cat loses 1 1/4 lbs and 1/8 lbs
1 1/4 can be expressed as an improper fraction 5/4
hence the total weight loss
= 1 1/4 + 1/8
= 5/4 + 1/8
= 10/8 + 1/8
= 11/8
= 1 3/8
Answer:
1 3/8
Step-by-step explanation:
change 1/4 into /8 which is 2/8 then add together which is 3/8 the add the one so 1 3/8
Mar 12: 3
Mar 13: 8
Mar 14: 11
Mar 15: 16
Mar 16: 25
Mar 17: 50
Whats the pattern? Is the pattern linear, quadratic, or exponential? Can you predict the number of cases for march 18, 19 and 20? What about March 25th?
Answer:
Mar 18: 125Mar 19: 318Mar 20: 743Mar 25: 15,070Step-by-step explanation:
The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.
The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...
(6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60
where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.
____
The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.
The values for Mar 12 through Mar 25 are ...
3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070
Answer: Mar 18: 125
Mar 19: 318
Mar 20: 743
Mar 25: 15,070
Step-by-step explanation:
The six seemingly arbitrary points have no common difference or ratio, so cannot be modeled by a linear or exponential function.
The differences of the differences are not constant at any level, so the only polynomial model is 5th-degree. It is ...
(6n^5 -95n^4 +600n^3 -1825n^2 +2814n -1320)/60
where n = days after Mar 11. (Mar 12 corresponds to n=1.) The domain is n ≥ 1.
____
The 5th-degree polynomial increases very fast, but not as fast as an exponential function would.
The values for Mar 12 through Mar 25 are ...
3, 8, 11, 16, 25, 50, 125, 318, 743, 1572, 3047, 5492, 9325, 15070
Step-by-step explanation:
.
Could you guys please help
Answer:
t = 2.76
PLEASE VOTE BRAINLIEST
Step-by-step explanation:
What is the Pythagorean Thereom
Answer:
Step-by-step explanation:
The Pythagorean theorem states that for a right triangle, the sum of the square for each of the sides is equal to the square of the hypotenuse.
See attached for graphic and formula
A circle has a diameter of 12cm. What is the area of the circle in square centimeters?
A) 75.36 cm2
B)113.04 cm2
C)452.16 cm2
D)37.68 cm2
Answer:
B. 113.04 cm^2
Step-by-step explanation:
The area of a circle is:
a=[tex]\pi[/tex]r^2
Because we have the diameter, we need to find the radius.
d=2r
12=2r
Divide by 2 on both sides
r=6
Plug 6 in for "r" in the area formula.
a=[tex]\pi[/tex]r^2
a=[tex]\pi[/tex]6^2
a=36[tex]\pi[/tex]
a=36*3.14
a=113.04 cm^2
So the answer is choice B
Hope this helps!
Meat costs $8.00 per pound at the store. What is the slope and y-intercept?
What is the point of intersection of these two lines? -4x + y = 8 2x - y = 4 (2, 0)
(-6, -16)
(−2/3, −16/3)
(-2, -8)
Answer:
(- 6, - 16 )
Step-by-step explanation:
Given the 2 equations
- 4x + y = 8 → (1)
2x - y = 4 → (2)
Adding the 2 equations term by term will eliminate the term in y
- 2x = 12 ( divide both sides by - 2 )
x = - 6
Substitute x = - 6 into either of the 2 equations and soilve for y
Substituting x = - 6 into (2)
2(- 6) - y = 4
- 12 - y = 4 ( add 12 to both sides )
- y = 16 ( multiply both sides by - 1 )
y = - 16
Solution is (- 6, - 16 )
Express 0.15 as a fraction in simplest form.
Final answer:
To express 0.15 as a fraction, write it as 15/100 and simplify by dividing both the numerator and denominator by 5 to get 3/20 in simplest form.
Explanation:
To express the decimal 0.15 as a fraction in its simplest form, we start by writing it as a fraction with a denominator that reflects its place value. Since 0.15 has two digits after the decimal point, its denominator should be 100. Hence, we have:
0.15 = 15/100
Now, we need to reduce this fraction to its simplest form by canceling equivalent terms in the numerator and the denominator. We notice that both 15 and 100 are divisible by 5. Dividing the numerator and the denominator by 5, we get:
15 ÷ 5 = 3
100 ÷ 5 = 20
Therefore, the fraction 15/100 simplifies to 3/20, which is in its simplest form.
Final answer:
To simplify 0.15 as a fraction, convert it to 15/100 and then divide both numerator and denominator by 5 to get the simplest form, which is 3/20.
Explanation:
To express 0.15 as a fraction in simplest form, we start by recognizing that 0.15 is the same as 15 hundredths, which can be written as 15/100. To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. Both 15 and 100 can be divided by 5, which would give us 3 in the numerator and 20 in the denominator after dividing both by 5. Therefore, the simplest form of the fraction is 3/20.
Which is the graph of f(x) = √x
Answer:
i just need points
Step-by-step explanation:
Great a word problem for x+2=3x-8
01:5
The US Environmental Protection Agency issues a daily report for pollution levels called the
A. Pollution Advisory Warning
B. Air Rating Level
C. Particulates and Pollution Index
D. Air Quality Index
Please select the best answer from the choices provided.
O
A
OB
Answer:D
Step-by-step explanation:
The United States Environmental protection agency (EPA) issues the Air Quality Index (AQI) daily report to communicate to the public the quality of the surrounding air( clean or bad). It also forecast how the quality of air in the environment will be in the nearest future.
what is unusual about the arrangement of the fossils in the diagram
Answer:
The oldest fossil is closer to the surface.
Step-by-step explanation:
Usually, the closer to the core of the Earth, the older the fossils. However, in this image, the oldest fossil is closer to the surface.
Answer:
The younger fossil is in the bottom layer, while the older fossil is in the top layer. These locations are opposite to the principle of superposition.
Step-by-step explanation:
Plato
each of five friends has X action figures in his or her collection. Each friend buys 11 more action figures. Now the five friends have a total of 120 action figures.write an equation that models this problem then solve
Answer:
Each friend has 13 actions
Step-by-step explanation:
Let x represent the actions of each friends
5friends will have 5x actions
And each friend has 11 more actions which means 5(11)=55
It means 5x+55
The total of their actions is 120
It can be written as 5x+55= 120
To solve
5x+55=120
Substrate 55 from both sides
5x=120-55
5x=65
X=65/5
x=13
Which each friend has 13 actions
Final answer:
To model the problem, the equation 5X + 5(11) = 120 is used. Solving this equation leads to finding that the original number of action figures each friend had is X = 13.
Explanation:
Initially, each of the five friends has X action figures in their collection. After purchasing 11 more action figures each, they collectively have a total of 120 action figures. To represent this problem, we can set up an equation where 5 times the original number of action figures per friend, plus 5 times 11 (because each friend buys 11 more), equals 120. Thus, the equation is:
5X + 5(11) = 120
To find the value of X, we need to solve the equation:
Multiply 5 times 11 to simplify the equation: 5X + 55 = 120
Subtract 55 from both sides of the equation: 5X = 120 - 55
Calculate the result on the right side: 5X = 65
Divide both sides by 5 to find X: X = 65 / 5
Thus, the original number of action figures each friend had is X = 13.
2(11x-6)-18 is equal to 22x-30
Answer: Yes they are equal
Step-by-step explanation: First you have to solve 2(11x-6)-18:
2(11x-6)-18
22x - 12 - 18
22x - 30
They equal!
Answer:
0
THE RIGHT HAND SIDE IS EQUAL TO THE LEFT HAND SIDE.
Step-by-step explanation:
2(11x-6)-18 is equal to 22x-30
the above question can as well be expressed as
2(11x-6) - 18 = 22x -30
the next thing is to apply the BODMAS(BRACKET, OF, DIVISION, MULTIPLICATION, ADDITION , SUBTRACTION.) rule by first opening the bracket
22x - 12 -18 = 22x -30
We will proceed to collect the like terms
22x -22x = -30+12+18
0 = -30 +30
0=0
the answer is = 0
THEREFORE THE RIGHT HAND SIDE IS EQUAL TO THE LEFT HAND SIDE.
A circle with a radius of 5 has a sector with a central angle of 9/10pi radians what is the area of the sector
Answer:
11.25pi units² or 35.3 units² (3 sf)
Step-by-step explanation:
½×r²×theta
½ × 5² × 0.9pi
11.25pi units²
Or, 35.3 units² (3 sf)
Please help me! Pic included! will mark brainliest!
Answer:
B) Point G
Step-by-step explanation:
Because point G is equidistant to all of the angles, and cuts all of the sides in half
In the figure BC || DE . Angles__________
CAF and EFA
GAC and DFE
CAF and EFH
GAB and EFA
are congruent______________________________________
By linear pair theorem
because they are corresponding angles of parallel lines cut by a transversal
by vertical angles theorem
by the transistive property of congruence
∠GAC ≅ ∠AFE because they are corresponding angles of parallel lines cut by a transversal. ∠AFE ≅ ∠HFD by the Vertical Angles Theorem. ∠GAC ≅ ∠HFD by the_______________ Property of Congruence.
addition
subtraction
substitution
transistive
CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal. ∠GAC ≅ ∠HFD by the transitive Property of Congruence.
What are congruent angles?Angles that are of the same measurement are called congruent.
Suppose that two angles ∠A and ∠B are of the same measure,
then
[tex]m\angle A = m\angle B[/tex]
is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.
We write the congruency between them as;
[tex]\angle A \cong \angle B[/tex]
In the figure BC || DE .
Angles
CAF and EFA are congruent because they are corresponding angles of parallel lines cut by a transversal.
GAC and DFE are not congruent
CAF and EFH are not congruent
GAB and EFA are not congruent
∠GAC ≅ ∠AFE because they are corresponding angles of parallel lines cut by a transversal.
∠AFE ≅ ∠HFD by the Vertical Angles Theorem.
Therefore, ∠GAC ≅ ∠HFD by the transitive Property of Congruence.
∠AFD = ∠AFE
Two angles that are equal to the same angle must themselves be equal.
( By Transitive property of equality)
Learn more about congruent angles;
https://brainly.com/question/12038510
#SPJ2
For questions 3 - 5, answer the questions about the equations.
3. How many solutions are there to this equation?
3(x - 4) + 5 - x= 2x-7
Answer:
infinite solutions
Step-by-step explanation:
Eliminate parentheses and collect terms:
3x -12 +5 -x = 2x -7
2x -7 = 2x -7
This is true for any value of x. There are an infinite number of solutions.
A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the third toss is 7.5 feet, which takes the ball back to the starting point. What angles are formed by these tosses. Step by Step explanation.. Please
angles formed by these tosses are [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.
Step-by-step explanation:
Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.
The Law of Cosines (also called the Cosine Rule) says:
[tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]
Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:
⇒ [tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]
⇒ [tex]c^2 -a^2 - b^2 = -2ab (cosx)[/tex]
⇒ [tex](cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}[/tex]
⇒ [tex](cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}[/tex]
⇒ [tex](cosx) =0.18310[/tex]
⇒ [tex]cos^{-1}(cosx) = cos^{-1}(0.18310)[/tex]
⇒ [tex]x = 79.45[/tex]
The Law of Sines (or Sine Rule) is very useful for solving triangles:
[tex]\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}[/tex]
We can now find another angle using the sine rule:
⇒[tex]\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}[/tex]
⇒[tex]sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}[/tex]
⇒[tex]Y = 59.02 degrees[/tex]
So, the third angle =[tex]180 - 79.45 - 59.02 = 41.53 degrees.[/tex]
Therefore, angles formed by these tosses are [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.
ANSWER FAST!! BRAINLIEST AND 20 POINTS!! calculate the return on investment in dollars and as a percentage for an investment that you purchase for $500 and sell for $600
MARK BRAILIEST !!!
Answer:
10 percent
600 - 500 = 100
100 divided by .10 = 10 %
Step-by-step explanation:
⭐ Answered by Kash ʕ •㉨• ʔ⭐
⭐ Brainliest would be appreciated!⭐
⭐ If you have questions, leave a comment, I'm happy to help! ⭐
The ratio of the number of white shapes to the number of black shapes is 5:11
The ratio of the number of white circles to the number of white squares is 3:7
The ratio of the number of black circles to the number of black squares is 3:8
Work out what fraction of all the shapes are circles.
Answer:
the fractions of all the shapes are circles can be obtained would be computed as:
[tex]\frac{450}{1600}=\frac{9}{32}[/tex]
Step-by-step explanation:
The fraction of the number of white shapes to the number of black shapes is 5/11.
Let us consider that there are:
500 white shapes1100 black shapesAs the fraction of the number of white circles to the number of white squares is 3:7
It means out of 10 total parts, 3/10 are white circles and 7/10 are white squares.
Calculating Number of white circles:
[tex]\frac{3}{{10}} \times 500=150[/tex]
Calculating Number of white squares:
[tex]\frac{7}{{10}} \times 500=350[/tex]
As the fraction of the number of black circles to the number of black squares is 3:8.
Calculating Number of black circles:
[tex]\frac{3}{{11}} \times 1100=300[/tex]
Calculating Number of black squares:
[tex]\frac{8}{{11}} \times 1100=800[/tex]
As
the total number of circles is 150 + 300 = 450, and the total number of shapes is 500 + 1100 = 1600Therefore, the fractions of all the shapes are circles can be obtained would be computed as:
[tex]\frac{450}{1600}=\frac{9}{32}[/tex]
What is the distance between (0, 0) and
(8, 15) on the coordinate plane?
A. 7 units
B. 8 units
C. 17 units
D. 23 units
Please help me!!!
Answer:
C. 17
Step-by-step explanation:
Distance formula:
[tex] \sqrt{(x_2 - x_1)^{2} + {(y_2 - y_1)}^{2} } \\ \\ = \sqrt{ {(8 - 0)}^{2} + ( {15 - 0})^{2} } \\ \\ = \sqrt{ {(8)}^{2} + {(15)}^{2} } \\ \\ = \sqrt{64 + 225} \\ \\ = \sqrt{289} \\ \\ = 17[/tex]
The correct answer is C. 17 units.
To find the distance between two points on the coordinate plane, one can use the distance formula derived from the Pythagorean theorem. The distance formula is given by:
[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]
where [tex]\( (x_1, y_1) \) and \( (x_2, y_2) \)[/tex] are the coordinates of the two points.
Given the points [tex]\( (0, 0) \) and \( (8, 15) \)[/tex], we can substitute these values into the formula:
[tex]\[ d = \sqrt{(8 - 0)^2 + (15 - 0)^2} \] \[ d = \sqrt{8^2 + 15^2} \] \[ d = \sqrt{64 + 225} \] \[ d = \sqrt{289} \] \[ d = 17 \][/tex]
Therefore, the distance between the points[tex]\( (0, 0) \) and \( (8, 15) \) is 17[/tex]units.