Usando el teorema fundamental de conteo, se encuentra que 132 maneras diferentes de otorgar las medallas.
¿Qué es el teorema fundamental de conteo?Es un teorema que establece que si hay n cosas, cada una con [tex]n_1, n_2, \cdots, n_n[/tex] formas de hacer, cada cosa independiente de la otra, el número de formas en que se pueden hacer es:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
En este problema:
12 participantes pueden ganar la medalla de oro, o sea, [tex]n_1 = 12[/tex].11 participantes pueden ganar la medalla de plata, todos con excesion de lo que gano la medalla de plata, o sea, [tex]n_2 = 11[/tex].Así, el número de maneras diferentes en que se pueden otorgar las medallas es dado por:
[tex]N = n_1 \times n_2 = 12 \times 11 = 132[/tex]
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Solve the following equations for 0 ≤ theta ≤ 360º cosec(2 — 45°) = 2
Step-by-step explanation:
here ,
[tex]cosec \alpha = \frac{1}{ \sin( \alpha ) } [/tex]
now,
cosec(2-45°)=2
or,
1/sin(2-45°) =2
or,
1/sin2cos45°-cos2sin45=2
or,
[tex] \frac{1}{ \sin(2) \frac{1}{2} - \cos(2) \frac{1}{2} } = 2[/tex]
or,
sorry I have that much qualifications to work on this question and hoping this much will make bit easy for you to solve it further
A group of 5 friends each have x action figures in their collections. Each friend buys 6 more action figures. Now the 5 friends have a total of 150 action figures. How many action figures did each friend start with?
Answer:
29
Step-by-step explanation:
The problem is 5x + 6 = 150
I subtract 6 from each sides except the one with the variable.
6 - 6 = 0 and 150 - 6 = 144.
Then I bring 5x down.
Then I divided 5x with 5 and 144 with 5.
I got 28.8 for x, which means the friends had 28.8 action figures each.
And I don't think it would be possible for them to have 28.8 action figures, so you round to a whole number which would give you the answer 29.
I think I that makes sense.
Harper surveyed 800 of the students in her school about their favorite color. 424
students said their favorite color was blue. What percentage of the surveyed students
said their favorite color was blue?
Using it's concept, it is found that the percentage of students surveyed that said their favorite color was blue was of 53%.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
In this problem, 424 out of the 800 students surveyed said their favorite color was blue, hence the percentage is given by:
[tex]P = \frac{424}{800} \times 100\% = 53\%[/tex]
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What is the answer to 9!= and 12!=
Answer:
permutation is multiplying numbers from the number given to its last end. so that 9*8*7*6*5*4*3*2*1=is answer. thesame for 12!
Answer:
9! = 362,880
12!=479,001,600
Step-by-step explanation:
the symbol ! simply means factorial
9! = 9×8×7×6×5×4×3×2×1= 362,880
12! = 12×11×10×9×8×7×6×5×4×3×2×1=479,001,600
The shaded shape is a square. What are the coordinates of A and B?
the length of the bottom side is 17-3 = 10
to be a square all sides need to be 10 units.
A(7,13)
B (17,13)
A circle has a radius of 18 ft. Find the length s of the arc intercepted by a central angle of 1.1 radians.
Do not round any intermediate computations, and round your answer to the nearest tenth.
The length of the arc of the circle will be 19.8 ft.
What is an arc of the circle?The arc of the circle is the distance of the circumference of the circle formed sector of the circle at a particular angle.
The formula for the length of the arc of the circle will be given as:-
Arc = Angle x radius
We have Angle = 1.1 radians Radius = 18ft
Arc = 1.1 x 18
Arc = 19.8 ft.
Therefore the length of the arc of the circle will be 19.8 ft.
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(03.04 MC) Two pieces of bread, banana and whole wheat, were left out on a kitchen counter and mold began to grow on them. The area of mold growth B(t), in mm2, on the piece of banana bread present after time t weeks, can be represented by the equation B(t) = 20(1.06)t. The area of mold growth W(t), in mm2, present on the piece of whole wheat bread after t weeks is represented in the table. t (in weeks) 1 2 3 4 W(t) (in mm2) 40.8 41.62 42.45 43.30 Which statement best compares the mold growth rates of the banana bread and the whole wheat bread? Question 16 options: The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was twice the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was half the mold growth rate of the whole wheat bread. The mold growth rate of the banana bread was a third the mold growth rate of the whole wheat bread.
Answer:
(a) The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
Step-by-step explanation:
The equation for exponential growth can be written in the form ...
f(t) = a·b^t
where a is the initial value, and b is the growth factor for time period t. The growth factor is related to the growth rate by ...
b = 1 +r . . . . . where r is the growth rate in time period t
__
banana breadThe equation for the area of mold on the banana bread is given as ...
B(t) = 20·1.06^t
Comparing to our generic equation, we see ...
a = 20b = 1.06 = 1 + 0.06The growth rate of the mold on the banana bread is given as 0.06 = 6% per week.
__
whole wheat breadWe are given some values of t and area that we can use to find the growth rate of mold on the whole wheat bread.
W(1) = 40.8 = a·b^1
W(4) = 43.30 = a·b^4
The ratio is ...
W(4)/W(1) = (a·b^4)/(a·b^1) = b^3 = 43.30/40.8
Then the value of b can be found to be ...
b = ∛(43.30/40.8) ≈ 1.02002 ≈ 1 + 0.02
The growth rate of mold on the whole wheat bread is about 0.02 = 2% per week.
__
comparison of growth ratesThe mold growth rate on the banana bread compared to that on the whole wheat bread is ...
(banana bread growth rate)/(whole wheat bread growth rate) = 6%/2% = 3
We can conclude ...
The mold growth rate of the banana bread was three times the mold growth rate of the whole wheat bread
You purchase a new car today.the value of that car depreciates based on the function f(t)=12,000(0.96)^t, where t is measured in years after purchase. How much is the car worth after 3/2 years, rounded to the nearest dollar
Considering the definition of exponential function, the value of the car is 11,287.25 dollars.
What is exponential functionAn exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:
f(x)= aˣ
Being a a positive real, a > 0, and different from 1, a ≠ 1.
When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.
What is the price of the carIn this case, the value of that car depreciates based on the function f(t)=12,000×[tex]0.96^{t}[/tex] where t is measured in years after purchase.
After 3/2 years, the value of the car is calculated as:
f(3/2)=12,000×[tex]0.96^{3/2}[/tex]
Solving:
f(3/2)= 11,287.25
Finally, the value of the car is 11,287.25 dollars.
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5. Use an inequality symbol (<, >,=, S) to compare -3 +7-10-2
A. >
B.<
C. ≤
D. =
If the question should read as the following, then I hope my answer will help; -3 +7 _ -10 - 2
Answer: A. >
Step-by-step explanation:
Given:
-3 + 7 _ -10 - 2
Simplify both sides by combining like terms:
4 _ -12
Compare, knowing that 4 is greater than -12:
4 _ -12
4 > -12
A. >
EASY POINTS Which of the following is best defined as segments that intersect at a right
angle?
A. Intersecting segments
B. Perpendicular segments
C. Parallel segments
D. Coplanar segments
Answer:
I would say B.
Step-by-step explanation:
Perpendicular lines meet at a right angle.
Answer: B
Step-by-step explanation:
what is the median data set 25, 17, 38, 11,
Answer:
21
Step-by-step explanation:
Answer:
Median = 21
Step-by-step explanation:
Arrange in ascending order,
→ 11, 17, 25, 38
Now take the middle two,
→ 17 & 25
Then the median data will be,
→ (17 + 25)/2
→ 42/2 = 21
Hence, the median is 21.
PLSSS HELPP Match the value to the correct image. Not all values will be used.
Find the approximate surface area of each right regular prism.
arrowRight
arrowRight
arrowRight
Answer:
open your book and start reading, you should study before the open your book and find it yourself
Which is the best estimate of the distance between the point (-25, 10) and the origin?
O 8 units
O 15 units
O23 units
O 27 units
(Please answer!)
Answer:
27 Units
Step-by-step explanation:
To find the distance using x and y components, use the Pythagorean theory [tex]a^2 + b^2 = c^2[/tex]. Set a as your x-coordinate and b as your y-coordinate (although you can flip them if you so desire). The result will you the square of your distance, so take the square root.
Alternatively, we can solve for C and find that [tex]c = \sqrt{a^2 + b^2}[/tex] or in this case [tex]distance = \sqrt{-25^2 + 10^2}[/tex].
This shows us that distance = 26.93 which is close enough to 27.
For more information: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-pythagorean-theorem/v/the-pythagorean-theorem
which expression represents the following calculation? subtract 1.9 from the product of 7.4 and 3.
A (7.4 + 3) - 1.9
B 7.4 x (3 - 1.9)
C (7.4 x 3) - 1.9
D (7.4 x 1.9) - 3
Answer:
The answer to the question is C
Step-by-step explanation:
as the question state that 1.9 is subtracted from the 7.4×3 so tge 1.9 will be removed ffrom it .
y= x^2-4x+3 in vertex form
Answer:
[tex]y=(x-2)^2-1[/tex]
Step-by-step explanation:
Complete the square
[tex]y=x^2-4x+3\\\\y+1=x^2-4x+3+1\\\\y+1=x^2-4x+4\\\\y+1=(x-2)^2\\\\y=(x-2)^2-1[/tex]
The ratio of the one leg of the right triangle to the other leg of the right triangle must be 8:7. Determine the greatest length of one leg of the right triangle given the other leg of the right triangle is 10.5 feet.
Answer:
534
Step-by-step explanation:
Find the area of the circle. A circle has a diameters of 17 centimeters. Pi value is 3.142
Answer:
Area of the circle = 227.0095 cm^2
Step-by-step explanation:
Given:
Diameter (D) = 17 cmπ = 3.142To Find:
Area of the circle
Soln:
We know that,
Area of the circle: πr²
where:
π = 3.142r = radiusBut we don't know the radius,as the diameter is given.We could use the formula of diameter & plug the value of it do find the radius.
We know that,[tex] \rm \: Diameter = 2(r)[/tex]
Where
r = radiusSubstitute the value of Diameter:
Diameter = 2r
17 = 2r
17/2 = r
8.5 = r
r = 8.5
Now we got the radius, so substitute radius onto the formulae:
Area of the circle = πr²Ar(circle) = π(8.5)²Ar(circle) = 72.25π(Answer in terms of π)Ar(circle) = 72.25 * 3.142Ar(circle) = 227.0095 cm^2[tex]\text{Area of circle} = \pi\cdot \text{Radius}^2\\\\\\~~~~~~~~~~~~~~~~~~=\pi~ \left( \dfrac{\text{Diameter}}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=3.142 \left(\dfrac{ 17}2 \right)^2\\\\\\~~~~~~~~~~~~~~~~~~=227.0095~ \text{cm}^2[/tex]
Point T is on line segment S U ‾ SU . Given S T = 6 ST=6 and T U = 10 , TU=10, determine the length S U ‾ . SU
If Point T is on the line segment S U, then ST + TU = SU, Hence the length of SU is 16.
What is addition?The addition is one of the mathematical operations. The addition of two numbers results in the total amount of the combined value.
If Point T is on the line segment S U, then ST + TU = SU
Given;
S T = 6 and T U = 10
Substitute
SU = ST + TU
SU = 6 + 10
SU = 16
Hence the length of SU is 16.
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evaluate 10 + 8÷4 - 12
Answer:
0
Step-by-step explanation:
evaluate 10 + (8÷4) - 12
Answer:
0
Step-by-step explanation:
First of all we need to divide then add then only subtract
12. Find the value of x.
HELP PLS HELP
Answer:
x = 16
Step-by-step explanation:
SR = ST ⇒ Two sides are equal. So, ΔSRT is an isosceles triangle.
The angles opposite to equal sides are equal.
⇒ ∠STR = ∠R
∠STR = 4x - 28
Linear pair: If a ray stands on a line, then the adjacent angles are supplementary and they are called linear pair
∠STR + ∠STU = 180° {linear pair}
4x - 28 + 9x = 180
4x + 9x - 28 = 180 {Combine like terms}
13x- 28 = 180
Add 28 to both the sides
13x = 180 + 28
13x = 208
Divide both sides by 13
x = 208/13
[tex]\sf \boxed{x = 16}[/tex]
Answer:
x = 16
Step-by-step explanation:
since SR = ST , then Δ RST is isosceles with the 2 base angles congruent.
∠ STR = ∠ SRT = 4x - 28
∠ STR and ∠ STU are a linear pair and sum to 180° , that is
9x + 4x - 28 = 180
13x - 28 = 180 ( add 28 to both sides )
13x = 208 ( divide both sides by 13 )
x = 16
Which statements can be used to accurately compare the functions? Select two options. [ g(x) has the lowest minimum. f(x) has the greatest maximum. All three functions have a y-intercept. All three functions have an x-intercept. 2 The domain of all three functions is the same.
The statement all three functions have a y-intercept and the statement f(x) has the greatest maximum can be used to accurately compare the functions.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
From the graph, we can see all the functions have y-intercept:
At x = 0
f(0) = 1
g(0) = -1/2
h(0) = -5
The f(x) has the greatest maximum, which is 10
Thus, the statement all three functions have a y-intercept and the statement f(x) has the greatest maximum can be used to accurately compare the functions.
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if y=4 when x= -4, find y when x=7
Answer:
Answer:y=-7
Step-by-step explanation:
When x=-4 then y=4 and if x=7 then y=-7
Because y=-x
write 2(3x+5)+4(2x-1) in the form of a(bx+c)
The equivalent expression of 2(3x+5)+4(2x-1) is 2(7x + 3)
How to rewrite the expression?The expression is given as:
2(3x+5)+4(2x-1)
Open the brackets
6x + 10 + 8x - 4
Evaluate the like terms
14x + 6
Factor out 2
2(7x + 3)
Hence, the equivalent expression of 2(3x+5)+4(2x-1) is 2(7x + 3)
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What is the volume of the solid
Answer:
A.264
Step-by-step explanation:
((Area Of triangle*height)=Volume
Area of triangle is the base of the triangle multiplied by height of triangle divided by 2
((8*6)/2)*11=264
What is the volume of a gift box with a length of
12 inches, a width of 5 inches, and a height of
3 inches?
Answer:
180 inches
Step-by-step explanation:
The volume of a rectangular prism is length x width x height. So you would do (12)x(5)x(3) which would get you 180 inches.
Help :') ................................
Answer:
1. 90
2. 120
3. 30
4. 60
Step-by-step explanation:
Hope it helps
what is the surface area of this? giving out 30 pts
Multiply:
(5x−1)(5x+4)
Answer: 25x^2+15x-4
Step-by-step explanation:
Multply 5x by the other 5x
25x^2
Multiply 5x by 4
20x
Multiply -1 by 5x
-5x
Multiply -1 by 4
-4
Add them together
25x^2+20x-5x-4
Combine like terms
20x-5x=15x
25x^2+15x-4
If sine of the quantity x plus y end quantity equals one half times sine of x plus radical 3 over 2 times cosine of x. What is the value of y?
A. pi over 2
B. pi over 3
C. pi over 4
D. pi over 6
The value of y from the given trig expression is pi/3 rad
Trigonometry identityThese identities are expressed in terms of sine, cosine and tangent
Given the expression
[tex]sin(x+y)=\frac{1}{2}sinx+\frac{\sqrt{3}}{2} cosx[/tex]
Expand sin(x+y)
sin(x+y) = sinxcosy + cosxsiny
Compare both equations
cosy = 1/2
y = arccos(1/2)
y = 60 degrees
y = pi/3 rad
Hence the value of y from the given trig expression is pi/3 rad
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Answer:
The answer is pi/4
When you input all the other values into the equation, they aren't true. When you input pi/4 the equation is true.
Joe is a carpenter and needs a ladder long enough to reach to a second story window that is 17 ft. from the ground. If he sets the ladder three feet from the base of the building, to the nearest tenth of a foot, how tall must the ladder be in order to reach the frame of the window? Explain your answer.
triangle - left side 17 feel, bottom 3 feet, right side - ladder
A- 17.3 ft
B- 16.7 ft
C- 20 ft
D- 25 ft