The ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.
To solve this problem
The idea of combinations can be used.
The number of ways to select k items from a set of n items is given by the formula for combinations:
C(n, k) = n! / (k! * (n - k)!)
In this case, n = 8 (the total number of routines they have learned) and k = 6 (the number of routines they will perform).
Using the formula, we can calculate:
C(8, 6) = 8! / (6! * (8 - 6)!)
= 8! / (6! * 2!)
The factorial function is represented in this case by the exclamation symbol (!).
The sum of all positive integers from 1 to n is the factorial of the number n.
Calculating the factorials involved:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40,320
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
2! = 2 * 1 = 2
Plugging in these values:
C(8, 6) = 40,320 / (720 * 2)
= 40,320 / 1,440
= 28
Therefore, the ballroom dance couple can arrange their performance in 28 different ways by selecting 6 routines out of the 8 they have learned.
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What is the solution to this system?
3x+2y=6
-4x+ 5y = 15
4-3-2-1
1 2 3 4 5
-
S
Answer:
solution: (0,3)
Step-by-step explanation:
You can find the solution when the two lines intersect.
A. How many combinations of the 5 white balls and 1 red ball are possible?
The number of combinations of the 5 white balls and 1 red ball are possible is 1.
We are given that;
White balls=5
Red ball=1
Now,
To find the number of combinations of 5 white balls and 1 red ball, we can use the combinations formula12:
[tex]nCr = n! / (r! (n-r)!)[/tex]
where n is the total number of objects, r is the number of objects to be selected, and ! is the factorial operator.
we can plug in these values into the formula:
[tex]6C6 = 6! / (6! (6-6)!) 6C6 = 6! / (6! 0!) 6C6 = 1 / (1 1) 6C6 = 1[/tex]
So, there is only one combination of 5 white balls and 1 red ball. This makes sense because the order of selection does not matter in a combination. No matter how we arrange the balls, we will always have the same group of 5 white balls and 1 red ball.
Therefore, by combinations and permutations the answer will be 1.
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Write in exponential form. ln54.60=4
Step-by-step explanation:
ln 54.60 = 4 e^x both sides
e ^ (ln 54.60) = e^4
54.60 = e^4 Done.
El valor de la asintota vertical
The vertical asymptote of the function are x = ±1/2
Given that we need to determine what is value of the vertical asymptote of the function =
(2x + 1) / (4x²-1)
To find the vertical asymptote of the function f(x) = (2x + 1) / (4x² - 1), we need to determine the values of x for which the denominator becomes zero.
This is because division by zero is undefined, and the function may have vertical asymptotes at those points.
The denominator of the function is 4x² - 1.
To find the values of x that make the denominator zero, we can set it equal to zero and solve for x:
4x² - 1 = 0
Adding 1 to both sides:
4x² = 1
Dividing both sides by 4:
x² = 1/4
Taking the square root of both sides:
x = ±√(1/4)
Simplifying further, we get:
x = ±1/2
Therefore, the values of x that make the denominator zero are x = -1/2 and x = 1/2. These are the vertical asymptotes of the function.
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Translation =
What is value of the vertical asymptote of the function =
(2x + 1) / (4x²-1)
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:
I need help with this.
Answer:
Step-by-step explanation:
Area of parallelograph = bh
b=20 h =42
A=(20)(42) = 840 mm²
A right triangle has a hypotenuse of 9 and a leg of 2 to the square root of 6 what is the missing side
The missing side of the right triangle is √57
To find the missing side of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.
Let's assume the missing side is represented by the variable x.
According to the Pythagorean theorem:
(2√6[tex])^2 + x^2 = 9^2[/tex]
Simplifying, we have:
[tex]4 \times 6 + x^2 = 81\\24 + x^2 = 81\\x^2 = 81 - 24\\x^2 = 57[/tex]
Taking the square root of both sides, we get:
x = √57
Thus, the missing side of the right triangle is √57
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1. Find the volume of the rectangular prism. Use the
volume formula V = L*W*H to justify your answer.
10 cm
L= 10cm
W= 8cm
H=12cm
Volume = 80cm
12 cm
8 cm
V=
Step-by-step explanation:
prism
v=1/2 X 12cm X 8cm
V= 48
rectangular prism
v=80cm+48cm
v=128cm
(09.01 LC)
What is the relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc
length s of the arc?
A)C=360°(s)(A)
B)C=360 degrees s over A
C)C=360 degrees(s+A)
D)C = 360°A over s
The relationship between the circumference C of the circle in which the degree measure A of a central angle of a circle intercepts an arc length s of the arc is
B) C=360 degrees s over A
How to find the relationshipThe relationship between the circumference C of a circle and the degree measure A of a central angle that intercepts an arc length s of the arc can be described by the formula:
s = A / 360 * C
Make C the subject of the formula
s = AC / 360
360s = AC
rearranging
AC = 360s
C = 360 degrees s / A
C = (s / A) * 360°
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Answer:
[tex]\textsf{B)} \quad C=\dfrac{360^{\circ}\:s}{A}[/tex]
Step-by-step explanation:
In a circle, the ratio of an arc length (s) to the circumference (C) is equal to the ratio of the measure of the arc's central angle (A) to 360°.
This is because:
The circumference (C) represents the distance around the entire circle, and so an arc (s) is a fraction of the whole circumference. In a circle, there are 360° in total, and so a central angle (A) is a fraction of 360°.Therefore, this can be expressed as:
[tex]\dfrac{s}{C}=\dfrac{A}{360^{\circ}}[/tex]
Cross multiply:
[tex]360^{\circ} \cdot s=C \cdot A[/tex]
Now, divide both sides by A to isolate C:
[tex]\dfrac{360^{\circ} \cdot s}{A}=C[/tex]
Therefore, the relationship between the circumference (C) of the circle in which the degree measure (A) of a central angle of a circle intercepts an arc length (s) of the arc is:
[tex]\large\boxed{\boxed{C=\dfrac{360^{\circ}\:s}{A}}}[/tex]
∆ACB is bisected by segment CP. m
What is the approximate area of ∆ACB?
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Where the above is given, Area of Δ ACB ≈ 282.62
Why is this so?
The area of a triangle is given as
Area = 1/2 Base x Height
In this case,
Base = AB
Height = CP
Thus, it is correct to state that Area of Δ ACB = 1/2AB * CP.
How is this so?
First we need to find the height and hypotenuse of the triangle.
that is CP and CB.
CB = a/Cos (63)
CB = 26.43227
CP = √(CB²-PB²)
CP = √(26.4322711750232² - 12²)
CP = 23.55133
Area of ΔPCB = (CP x PB)/2
(12 × 23.551326066062)/ 2
= 141.30796
Since ΔPCB = ΔPCA
and ΔACB = ΔPCB + ΔPCA
Thus,
Area of ΔACB = 141.30796 + 141.30796 = 282.61592
≈ 282.62
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
Write the quadratic equation in standard form that corresponds to the graph shown below.. Please help.
The quadratic equation in standard form that corresponds to the graph shown above is f(x) = x² + 2x - 8
What is the general form of a quadratic function?In Mathematics and Geometry, the standard form of a quadratic function can be modeled and represented by using the following mathematical expression;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.In this scenario and exercise, we would write a quadratic function that represent f(x) in standard form and with a leading coefficient of 1 by using the roots (-4, 0) and (2, 0) as follows;
f(x) = (x + 4)(x - 2)
f(x) = x² - 2x + 4x - 8
f(x) = x² + 2x - 8
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simplify 9/14divided7/10
Answer:
45/49
Step-by-step explanation:
The first step to dividing fractions is to find the reciprocal (reverse the numerator and denominator) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. Finally, simplify the fractions if needed.
9/14 * 10/7 = 90/98
divide the numerator and the denominator by 2.
90 * 2 = 45
98 * 2 = 49
45/49
give the rule in words of this pattern 10,13,17,238
Answer:
a set of numbers in order of least to greatest
the headlights on a car are set so the light beam drops 2 in. for 26 ft measured horizontally. If the headlights are mounted 24 in. above the ground, how far ahead of the car will they hit the ground?>
Answer:
0.168 ft aprox
Step-by-step explanation:
To solve this problem, we can use similar triangles and proportions. Let's denote the distance ahead of the car where the light beam hits the ground as "x" (in feet).
According to the given information, the light beam drops 2 inches for every 26 feet horizontally. We can set up the following proportion:
2 inches / 26 feet = x inches / x + 26 feet
To solve for x, we can cross-multiply and solve the resulting equation. Let's convert inches to feet to maintain consistent units:
2 inches = 2/12 feet = 1/6 feet
1/6 feet / 26 feet = x feet / x + 26 feet
1/6 * (x + 26) = 26 * x
x/6 + 26/6 = 26x
x + 26 = 156x
156x - x = 26
155x = 26
x = 26 / 155 ≈ 0.168 ft
Therefore, the headlights will hit the ground approximately 0.168 feet (or 2.016 inches) ahead of the car.
xA radioactive isotope is decaying at a rate of 20% every hour. Currently there are 15 grams of the substance.
Questions:
A. Write an equation that will represent the number of grams present after n hours
B. How much will be left after 24 hours (one day)? (Round to the nearest hundredth)
C. After how many hours will there be approximately one gram left?
B. After 24 hours, approximately 2.49 grams will be left.
C. After approximately 18.13 hours, there will be approximately one gram left.
A. To represent the number of grams present after n hours, we can use the equation:
N(n) = 15 × (1 - 0.2)^n
Where:
N(n) is the number of grams present after n hours,
15 is the initial amount of the substance in grams,
0.2 represents the decay rate of 20% per hour, and
^n represents the exponentiation operation.
B. To find out how much will be left after 24 hours, we can substitute n = 24 into the equation from part A:
N(24) = 15 × (1 - 0.2)^24
Calculating this expression, we find that approximately 2.49 grams will be left after 24 hours.
C. We need to determine the number of hours it takes until there is approximately one gram left. We can set up the equation:
1 = 15 × (1 - 0.2)^n
To solve for n, we can divide both sides of the equation by 15 and then take the logarithm (base 0.8) of both sides:
log(0.8)(1/15) = n
Using a calculator or logarithmic properties, we find that approximately 18.13 hours are required until there is approximately one gram left.
Therefore, the answers are:
B. After 24 hours, approximately 2.49 grams will be left.
C. After approximately 18.13 hours, there will be approximately one gram left.
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You are asked to use the grouping method to factor x^2 - 12x + 13
How should the term -12x be rewritten?
A) 1x +35x
B)-5x -7x
C) 5x+7x
D) -1x-35x
The zeros of this expression are irrational, so it cannot be factored using integers.
When factoring a quadratic expression, we are trying to express it as the product of two binomial factors.
In some cases, such as when the quadratic has irrational zeros, it may not be possible to factor it using integers.
In the case of the quadratic expression x² - 12x + 13, the discriminant (b^2 - 4ac) is equal to (-12)² - 4(1)(13)
= 144 - 52
= 92.
Since the discriminant is positive and not a perfect square, the zeros of the quadratic are irrational.
This means that the expression cannot be factored into two binomial factors with integer coefficients.
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Which of the following is the result of expanding ____
A.8.5
b.15.5
C.32
D.60
The sum between n = 1 and n = 5 is 15.5, so the correct option is the second one.
Which is the value of the summatory?Here we have the summatory:
[tex]\sum^{5}_{n = 1} 2^{n - 2}[/tex]
So we just need to add the 5 terms (between n = 1 and n = 5)
So we will get the sum:
S = [ 2¹⁻² + 2²⁻² + 2³⁻² + 2⁴⁻² + 2⁵⁻²]
S = [2⁻¹ + 2⁰ + 2¹ + 2² + 2³]
S = [0.5 + 1 + 2 + 4 +8]
S = 15.5
So the correct option is the second one.
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Simplify. Write your answers without exponents. 4^ -5/2= (1/16)^-3/2=
Please look at photo for accuracy
The value of the given expression is,
[tex]4^{- 5/2[/tex] = 1/32
[tex](1/16) ^ {- 3/2[/tex] = 64
We have to given that,
Expressions to solve are,
⇒ [tex]4^{- 5/2[/tex]
And, [tex](1/16) ^ {- 3/2[/tex]
We know that,
Exponentiation is the process of expressing huge numbers in terms of powers. That is, exponent refers to the number of times a number has been multiplied by itself
Now, We can simplify the given expression,
By using law of exponents
We get,
⇒ [tex]4^{- 5/2}[/tex]
⇒ [tex]2^{2(- 5/2)}[/tex]
⇒ 2⁻⁵
⇒ 1/2⁵
⇒ 1/32
Thus,
The value of [tex]4^{- 5/2[/tex] = 1/32
The given expression is,
⇒[tex](1/16) ^ {- 3/2[/tex]
By using law of exponents
We get,
⇒ [tex]16 ^{3/2}[/tex]
⇒ [tex](4^2)^{3/2}[/tex]
⇒ 4³
⇒ 64
The value of [tex](1/16) ^ {- 3/2[/tex] = 64
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What is the solution to the proportion 2/3 m/9
Does 10, 15, 18 equal a right triangle
Answer:
Not a right triangle
Step-by-step explanation:
[tex]10^2+15^2\stackrel{?}{=}18^2\\100+225\stackrel{?}{=}324\\325\neq324[/tex]
As the sides of the triangle do not follow the Pythagorean Theorem, then the triangle is not a right triangle.
Which choice is a solution to this system of equations? -x=y-4 y=4x+9
The solution to the system of equations is x = 5.4 and y = -1.4
How to determine the solution to the system of equations?From the question, we have the following parameters that can be used in our computation:
-x=y-4 y=4x+9
So, we have
-x = y - 4
y = 4x + 9
Rewrite the equation as
x = -y + 4
y = 4x + 9
So, we have
y = 4(-y + 4) + 9
Open the bracket and evaluate
5y = 9 - 16
So, we have
y = -1.4
Recall that
x = -y + 4
So, we have
x = 1.4 + 4
Evaluate
x = 5.4
Hence, the solution is x = 5.4 and y = -1.4
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What is the surface area of this composite solid? show your work
The surface area of this composite solid is 265.36 units².
How to calculate the surface area of a rectangular prism?In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:
Surface area of a rectangular prism = 2(LH + LW + WH)
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;
Surface area of rectangular prism = 2[3 × 5 + (3× 10) + (5 × 10)]
Surface area of rectangular prism = 2[15 + 30 + 50]
Surface area of rectangular prism = 190 units².
Surface area (SA) of a cylinder = 2πrh + 2πr²
Surface area (SA) of a cylinder = 2 × 3.14 × 2 × 4 + 2 × 3.14 × 2²
Surface area (SA) of a cylinder = 50.24 + 25.12
Surface area (SA) of a cylinder = 75.36 units².
Therefore, we have:
Surface area of composite solid = 190 units² + 75.36 units².
Surface area of composite solid = 265.36 units²
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determine the volume of the following spheres with the given dimensions. to break the code find the mean of all your answers. round your answers to the hundreth place. use 3.14 for an approximation for pi.
The calculated volume of the sphere is 44602.24 ft³
How to determine the volume of the sphereFrom the question, we have the following parameters that can be used in our computation:
Radius = 22 ft
The volume of a sphere can be expressed as;
V = 4/3πr³
Where
r = 22
substitute the known values in the above equation, so, we have the following representation
V = 4/3π * 22³
Evaluate
V = 44602.24
Therefore the volume of the sphere is 44602.24 ft³
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Question
Determine the volume of the following spheres with the given dimensions. to break the code find the mean of all your answers. round your answers to the hundreth place. use 3.14 for an approximation for pi.
Radius = 22 ft
The circumference of the cylinder below is 4 cm and the height is 6 cm. What is the curved surface area of the cylinder? If your answer is a decimal, give it to 1 d.p. circumference 4 cm Height 6 cm
The curved surface area of the cylinder is 24 cm².
We have,
To find the curved surface area of a cylinder, we need to know its height (h) and the circumference of its base (C).
Given:
Circumference (C) = 4 cm
Height (h) = 6 cm
The formula to calculate the curved surface area of a cylinder is A = Ch, where A is the curved surface area, C is the circumference, and h is the height.
Substituting the given values:
A = 4 cm x 6 cm
A = 24 cm²
Therefore,
The curved surface area of the cylinder is 24 cm².
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There are 840 learners and 17 teachers at Orefile Primary school.what is the learner to teacher ratio?
Answer: 49.4 thats the answer i devided it
predict what will happen to the coordinates of a point (x,y) as the point reflects across a line to produce point (x1,y1)
The reflections are described below.
We know that,
There are two types of reflection:
Reflection with respect to X-axis:
The x-coordinates of a point stay constant when it is mirrored across the X-axis. However, the Y-coordinates are changed into their inverse signs.
As a result, the X-axis reflection of the point (x, y) is (x, -y).
Reflection with respect to Y- axis:
The Y-coordinates of a point stay constant when it is mirrored across the Y-axis. However, the X-coordinates are changed into their inverse signs.
As a result, the Y-axis reflection of the point (x, y) is (-x, y).
Now the reflection is as following:
The point (x, y) when reflected across the x-axis becomes (x', y') = (x, -y)
The point (x, y) when reflected across the y-axis becomes (x', y') = (-x, y)
The point (x, y) when reflected across the line y = x becomes (x', y') = (y, x)
The point (x, y) when reflected across the line y = -x becomes (x', y') = (-y, x)
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Fred is buying A New
refrigerator for his
Apartment. His friend has A
4-year-old refrigerator that
he will sell to Fred for only
$200, but the refrigerator
Needs About $350 iN
repairs. The local Appliance
shop hAs A New model for
$615, plus 7% sales tax.
How much sales tax will Fred pay if he buys the new refrigerator?
Fred will pay $43.05 in sales tax if he buys the new refrigerator.
To calculate the sales tax Fred will pay for the new refrigerator, we first need to find the amount of the sales tax.
The cost of the new refrigerator is $615.
To calculate the sales tax, we multiply the cost by the tax rate of 7%:
So, Sales tax = 7% of $615
Sales tax = (7/100) x $615
Sales tax = $43.05
Therefore, Fred will pay $43.05 in sales tax if he buys the new refrigerator.
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identify the initial amount a and growth/decay factor b.
y= -2(.5)^x
In the equation [tex]y = -2(0.5)^x[/tex], the initial amount (a) is -2, and the growth/decay factor (b) is 0.5.
In the given equation, [tex]y = -2(0.5)^x[/tex], we can identify the initial amount and the growth/decay factor.
The equation is in the form of exponential decay, as the base (0.5) is between 0 and 1, resulting in the function decreasing as x increases.
The initial amount, denoted as "a," is the coefficient in front of the exponential term. In this case, the initial amount is -2. This means that when x = 0, y = -2.
The growth/decay factor, denoted as "b," is the base of the exponential term. In this equation, the base is 0.5. The value of the base determines how quickly the function decreases or decays.
To summarize:
Initial amount (a) = -2
Growth/decay factor (b) = 0.5
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What does the x-intercept of the graph represent in terms of the football?
a. The x-intercept represents the maximum vertical height that the football reaches.
b . The x-intercept represents the time it took for the football to reach its maximum height.
c. The x-intercept represents the height where the football was when the ball was kicked.
d. The x-intercept represents how far away the football landed from where it started horizontally.
The x-intercept in the graph represent the height where the football was when the ball was kicked.
How to find the x-intercept?The x-intercept is the point where the graph of the line crosses the x-axis.
Therefore, the x-intercept the value of x when y equals to zero.
Therefore, let's find what the x-intercept of the graph represent in terms of the football.
The graph shows the height of the ball in metres after t second.
The y axis represent the height while the x-axis represent the time.
Hence, he x-intercept represents the height where the football was when the ball was kicked.
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What is the value of x?
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Using a trigonometric relation, we can see that the value of x is 10.39
How to find the value of x?Here we have a right triangle. We can see that we know the measures of the hypotenuse, and the angle opposite to the side x.
Then to get the value of x, we can use the trigonometric relation:
sin(a) = (opposite cathetus)/hypotenuse.
Replacing the values that we know, we will get.
sin(60°) = x/12
solve that for x:
12*sin(60°) = x
10.39 = x
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