Eight people skiing downhill in a race can finish in 40,320 different orders.
Calculating probabilities for a set of possibilities keeping in account the order they are in is called permutation ([tex]{n}_P_{r}[/tex]).
If we overlook the order, it becomes a problem of combination ([tex]{n}_C_{r}[/tex]).
Permutation plays an important role in probability problems where the order of the possible outcomes is concerned. It does not allow repetition of outcomes.
Mathematically, permutation can be represented as:
[tex]{n}_P_{r}=\frac{n!}{(n-r)!}[/tex]
where 'n' represents the total objects/values/instances and 'r' represents our selected number of objects/values/instances.
In this case, we have total 8 drivers (n=8) and 8 positions we are selecting i.e. the order skiing people finish in (r=8);
[tex]{n}_P_{r}=\frac{8!}{(8-8)!}=\frac{8!}{0!}=\frac{40320}{1}[/tex]
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work out the area of a circle with diameter of 14 give your answer in pi
Answer:
Area is probably around 153.94
Step-by-step explanation:
Answer:
49π or 153.93804
Step-by-step explanation:
The formula for area of a circle is Pi * radius^2. The radius is half of the diameter, so the radius is 7. We then square 7, getting 49, and multiply that by pi, getting us 49π or 153.93804
Last year janet purchased a $1,000 face value corporate bond with an 8% annual coupon rate and a 15-year maturity. At the time of the purchase, it had an expected yield to maturity of 10. 45%. If janet sold the bond today for $820. 17, what rate of return would she have earned for the past year?.
57.15% is i interest rate of return would she have earned for the past year.
What exactly does "interest rate" mean?
An interest rate informs you of how much borrowing will cost you and how much saving will pay off. Therefore, the interest rate is the amount you pay for borrowing money and is expressed as a percentage of the total loan amount if you are a borrower.Par value = 1000
coupon rate = 8%
no of compounding period per year = 1
interest per period = $80
number of year to maturity = 15
no of compounding period till maturity = 15
market rate of return = 12.09%
Bond purchase price = PV(RATE,NPER,PMT,FV) * -1
Bond purchase price = $722.77
Rate of return of past year = 57.15%
= (1055.86+80-722.77)/722.77
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there are 15 servings in a 10.5-ounce bottle of barbecue sauce. how many ounces are in a serving
There are 1.42 ounces are in a serving of barbecue sauce.
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We have been given that there are 15 servings in a 10.5-ounce bottle of barbecue sauce.
Thus, 15 servings = 10.5-ounce bottle of barbecue sauce.
One ounce bottle of barbecue sauce = 15/10.5 x 1
= 1.42
Therefore, there are 1.42 ounces are in a serving of barbecue sauce.
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simplify (3x²y5)3 please help
The simplified answer for the given value (3x²y⁵)³ is 27x⁶y¹⁵.
The first step is to find the cube of the values inside the bracket
⇒ (3x²y⁵)³= (3³ × (x²)³ × (y⁵)³)
⇒ 3³ × x⁶ × y¹⁵
⇒ 27x⁶y¹⁵
Hence, the simplified answer for the given value (3x²y⁵)³ is 27x⁶y¹⁵.
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14. What is the
solution to 34x + 95 = 3(14x + 9)?
Answer:
Solution
x=17/2
Step-by-step explanation:
Answer: x = 17/2
Step-by-step explanation: distribute 34x+95=3(14x+9)
subtract from both sides 34x+95−95=42x+27−95
34
Directions: Determine if the given equations are parallel, perpendicular, or neither. 3x + 2y = 8 and 2x + 3y = -12
find the exponential equation using points (-1,6) and (2,3/4)
Answer: 3
Step-by-step explanation:
You are solving a system of equations y1 = abx1 and y2 = abx2, so plug the x and y coordinates into the equations to solve for a and b:6 = ab1 & 3/4 = ab-2Since a = 6/b, we can use this in the second equation to solve for b:3/4 = (6/b)b-23/4 = 6/b36/(3/4) = b38 = b32 = b,which means that a = 3.Now we just input our a and b values into y = abx, so our equation is y = 3*2x. I hope this helps
If I am 165 centimeter tall. And Roberto is 1.7 meters tall who is taller?
Answer:
"Centi" means hundred so, a centimeter is a meter times 100. Divide 165 centimeters by 100 to convert it to meters. 165/100=1.65. If you are 1.65 meters, and Roberto is 1.7 meters tall, Roberto is taller.
Hope this helped!
Help me solve the word problem below. Will mark brainliest.
Answer:
Step-by-step explanation:
a man is in a boat that is floating 175 feet from the base of a 200 foot cliff. what is the angle of depression between the cliff and the boat?
A boat is moving 175 feet from the base and a man is in the boat. The height of cliff is 200 feet. We need to find the angle between the cliff and the boat.
We have a right angled triangle where base is 175 ft and height is 200 ft.
We know that tan θ = opposite / adjacent
= 200 / 175
So θ = tan ^-1 (200 / 175)
So θ = 48.8 degree
Here is a function, double numbers (int x), what data type will this function take in?.
The data type this function take is int.
What is data type?Data type is an attribute of a piece of data that instructs a computer how to interpret its value. Example data type is,
integer (int)boolean (bool)double (double)float (float)string (str)In the question, the function is double numbers (int x). The parameter used in this function is int. Even if it try to pass the double value into the function it will take an integer value corresponds to double value and the function always return the data to integer.
Thus, the function only take integer (int) data type.
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please I need help in this question
Answer:
Step-by-step explanation:
A is an integer by 10 as even and by 3 as odd as timed would be in power also by 3 then, B, in scientific writing is.... 140 OBVI
Write an equation of the line that passes through (7, 10) and is perpendicular to the line y = -x - 9.
Equation of the line that passes through (7, 10) and is perpendicular to the line y = x - 9 is y = -x + 17.
Given,
The equation, y = x - 9
Slope = m = 1
Slope of line perpendicular to given line = -1/m = -1/1 = -1
Let the equation of line be y = mx + c
Passes through A(7,10)
10 = -1(7) + c
10 = -7 + c
c = 10 + 7
= 17
Therefore, the equation of line is y = -x + 17
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3. Find the measure of the angle indicated.
Answer:
∠ D = 94°
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ CBY is an exterior angle of the triangle, then
∠ C + ∠ D = ∠ CBY , that is
49° + ∠ D = 143° ( subtract 49° from both sides )
∠ D = 94°
of the cars sold during the month of july, 85 had air conditioning, 102 had automatic transmission, and 71 had power steering. 6 cars had all three of these extras. 22 cars had none of these extras. 22 cars had only air conditioning, 65 cars had only automatic transmissions, and 31 cars had only power steering. 10 cars had both automatic transmission and power steering. how many cars had air conditioning and automatic transmission but not power steering? a) 30 b) 27 c) 6 d) 4 e) 33 f) none of the above.
27 cars had air conditioning and automatic transmission but not power steering.
What is venn diagram ?A Venn diagram is a diagram that uses circles to show the relationships between things or finite groups of things. Intersecting circles have one thing in common, but non-intersecting circles do not have these features.
Venn diagrams help visualize the similarities and differences between two concepts. They have long been recognized for their usefulness as educational tools. Venn diagrams have been used as part of introductory logic curricula and in elementary school planning around the world since the mid-20th century.
Venn diagrams help show how different concepts and elements intersect. At a glance, you can see how things are similar, how they differ, and where and how they overlap. The center of a Venn diagram (the intersection of two or more circles) often represents a connection or main idea that can be decomposed into various other circles, and labels on the outer part are more common than labels in the center. is clear. .
Calculationcalculation has been attached below .
27 cars had air conditioning and automatic transmission but not power steering
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Which of the following expressions
or equations reflects "x squared
multiplied by ten equals one hundred"?
A) 10x²-100
B) 10x²+100
C) 10x²=100
D) 100 -10x²
The expression that reflects x squared multiplied by ten equals one hundred is option C) 10x²=100.
The following components make up an expression in mathematics:
Constant: It has a predetermined numerical value.A variable does not accept any fixed values. According to the requirement, values are assigned.The terms "constants," "variables," or "constants multiplied by variable" are all acceptable (s). An expression's terms are separated by a "+" or "" sign.Operators: The four operations of addition (+), subtraction (-), multiplication (-), and division (-), also known as operators, are used to combine the terms of an expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows:
Expression: (Math Operator, Number/Variable, Math Operator)
Hence, the expression that reflects x squared multiplied by ten equals one hundred is option C) 10x²=100.
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HI PLS HELP ME ON MY MATH HOMEWORK I WILL ALSO GIVE BRAINLIEST
The correct alternative, based on the parallel, triangle sum, and isosceles triangle criteria, is 2.
How to spot the correct optionAlternative 1
Since the base angle of an isosceles triangle is 52 degrees, let's say the third angle is x, and according to the triangle sum property,
x + 2 * 52 = 180,
x = 76.
triangle at the base
32 + 2x = 180 (triangle sum property for isosceles triangle)
x = 74
In accordance with the triangle sum property for isosceles triangles, the figure demonstrates that the base angle of the triangle at its base is also equal to 76.
False choice: Angles 74 and 76 are not equal.
Alternative 2:
x + 2 * 76 = 180 (triangle sum property for isosceles triangle)
x = 28
The diagram demonstrates that the triangle at the base angle has angle = 28.
124 + 2x = 180 (triangle sum property for isosceles triangle)
x = 28
Since the two angles 28 and 28 are equivalent, the choice is correct.
Alternative 3
wood you believe it, I past plain geometry - wrong
would you believe it, I passed plain geometry - correct
Alternative 4
The parallelogram's isosceles triangle, with a base angle of 27,
Using the alternate internal angle theorem, 29's base angle is displayed.
at same point as 27 and both angles are not being equal.
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You are designing a candle-making kit. Each kit will contain 25 cubic inches of candle wax and a mold for making a model of the pyramid-shaped building at the Louvre Museum in Paris, France. You want the height of the candle to be 2 inches less than the length of each side of the candles square base. What should the dimensions of your candle mold be?
Yolanda paid $12.24 for a 6.35-kg bag of dog food. A few weeks later, she paid $13.99 for a 7.48-kg bag at a different store.
Find the unit price for each bag. Then state which bag is the better buy based on the unit price.
Round your answers to the nearest cent.
Answer:
Step-by-step explanation:
First bag's unit price=$1.92 per kg Second bag's unit price=$1.87 per kg
The second bag is the better deal
Step-by-step explanation:
Divide the price by the weight to get the unit price per kg
The lowest number is the better buy
13#A toy manufacturer wants to see how long, on average, a new toy captures children's attention. He tests 11 children selected at random and finds that their mean attention span is 22 minutes with a standard deviation of 5 minutes. If we assume that attention spans are normally distributed, find a 90% confidence interval for the mean attention span of children playing with this new toy. Give the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas. )Lower limit:Upper limit:
The lower limit of the confidence interval is 18.80 and the upper limit of the confidence interval is 25.19
Confidence interval = sample mean ± margin of error
Margin of error = z*population standard deviation/[tex]\sqrt{n}[/tex]
The level of confidence is represented by z==2.12
the size of the sample n=11
sample mean= 22
confidence interval = sample mean ± z*population standard deviation/[tex]\sqrt{n}[/tex]
upper limit of confidence interval = sample mean + z*population standard deviation/[tex]\sqrt{n}[/tex]
=22+2.12*5/[tex]\sqrt{11}[/tex]=25.19
lower limit of confidence interval = sample mean - z*population standard deviation/[tex]\sqrt{n}[/tex]
=22-2.12*5/[tex]\sqrt{11}[/tex]=18.80
Therefore, the lower limit of the confidence interval is 18.80 and the upper limit of the confidence interval is 25.19
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A baeball team ell for two game. The ratio of old ticket to unold ticket for the firt game wa 7 : 3. For the econd game, the ratio wa 13 : 2. There were 24 unold ticket for the econd game. How many ticket were old for the firt game?
The number of tickets that were sold for the first game was 84 tickets .
In the question ,
it is given that
the ratio of sold tickets to unsold tickets in the first game = 7:3 ,
so , number of tickets sold in first game = 7x
number of tickets unsold in the first game = 3x
the ratio of sold tickets to unsold tickets in the second game = 13:2 ,
so , number of tickets sold in second game = 13x
number of tickets unsold in the second game = 2x
given the number of unsold tickets in the second game = 24
that is 2x = 24
x = 12
number of tickets sold in first game = 7x = 7(12) = 84
Therefore , The number of tickets that were sold for the first game was 84 tickets .
The given question is incomplete , the complete question is
A baseball team sell tickets for two game. The ratio of sold ticket to unsold ticket for the first game was 7 : 3. For the second game, the ratio was 13 : 2. There were 24 unsold ticket for the second game. How many ticket were sold for the first game?
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If the coefficient a in the general quadratic equation is equal to 12, what is the focal length for the
parabola, c', equal to?
The focal length of the parabola is 1/48
What is focal length of a parabola?The term focal length as used in parabolic equation refers to the distance between the vertex of the parabola and the focus.
This distance is measured in the direction of the symmetry
The formula for the focal length in terms of a is
a = 1 / 4p
where p is the focal length
make p the subject of the formula by cross multiplying
a * 4 * p = 1
4a * p = 1
p = 1 / 4a
p = 1 / 4 * 12
p = 1 / 48
p = 1/48
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Why is triangle area divided by 2?.
To find the area of a triangle, multiply the base area by the height and then divide by 2. Dividing by 2 comes from being able to divide a parallelogram into two triangles. For example, in the illustration on the left, the area of each triangle is equal to half the area of the parallelogram.
What is area of triangle?The area of a triangle is defined as the total space occupied by the three sides of the triangle in a two-dimensional plane.The basic formula for the area of a triangle is half the product of the base and the height, or A = 1/2 × w × h.This formula applies to all types of triangles, including scalene, isosceles, and equilateral triangles. Recall that the base and height of a triangle are perpendicular to each other.The area of a triangle is the area enclosed by the sides of the triangle.The area of a triangle varies from triangle to triangle depending on the length of the sides and the interior angles. The area of a triangle is expressed in square units. B. m2, cm2, in2, etc.Hence, To find the area of a triangle, multiply the base area by the height and then divide by 2. Dividing by 2 comes from being able to divide a parallelogram into two triangles. For example, in the illustration on the left, the area of each triangle is equal to half the area of the parallelogram.
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Help please!
What is the rate of change of the function?
The slope of the line m is -2 if the line passes through (4, -3) and (0, 5) the answer is -2.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the graph:
(4, -3) and (0, 5)
The slope of the line m = (5+3)/(-4)
The slope of the line m = -2
Thus, the slope of the line m is -2 if the line passes through (4, -3) and (0, 5) the answer is -2.
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This image would be used for part c.
Question B: During what interval(s) of the domain is the baseball’s height decreasing the fastest?
Options: A= 6 < x < 8; the slop is the steepest for this interval
B= 8 < x < 10; the slop is the steepest for this interval
C= 6 < x < 10; the slop is decreasing for this interval
D= 6 < x < 12; is where the slope is decreasing
Step-by-step explanation:
it decreases the fastest, where it drops the most feet in the same period of time.
the dots are made in 2 seconds intervals.
between the seconds 6 and 8 the ball drops from 65 ft to 25 ft (a drop of 65 - 25 = 40 ft).
bergen the seconds 8 and 10 the ball drops from 25 ft to 5 ft (a drop of 25 - 5 = 20 ft).
and then between the seconds 10 and 12 the ball drops from 5 ft to 0 ft (a drop of 5 ft).
so, A is the right answer. with 40 ft in 2 seconds the ball is dropping the most (= the fastest) between the seconds 6 and 8. which means the slope is negatively the steepest there = the height is decreasing the fastest.
Simplify
3√b^2
and no it is not 3b
The simplified form of the given expression is 9b
Simplifying an ExpressionFrom the question, we are to simplify the given expression
The given expression is 3√b^2
This expression can be properly written as
(3√b)²
To simplify the expression,
First, we will expand the expression by applying one of the rules of exponents
(3√b)²
Applying the rule of exponent
3² × (√b)²
9 × b
= 9b
Hence,
The simplified expression is 9b
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which is the solution set for ?
- 4 (-x+a)+5<8
The solution of the given function is x < 3 + 4a.
What is a function?
A function is uniquely represented by the set of all pairings (x, f (x)), known as the function graph, which is a popular way of visualizing the function. When the domain and codomain are real number sets, each pair may be thought of as the Cartesian coordinates of a point in the plane. Functions are frequently employed in science, engineering, and the majority of mathematical areas. Most disciplines of mathematics say that functions are "the major subjects of investigation." If the domain and codomain set of two functions f and g are the same and their output values agree over the whole domain, they are equivalent.
The solution of the given function is
-4(-x+a)+5<8
or, 4x - 4a + 5 < 8
or, x < 8 - 5 + 4a
or, x < 3 + 4a
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solve for x.
3/4 (-4.2 - x) = 5
Answer: x = -10.8666667
Step-by-step explanation:
What is the slope of the line that passes through the points ( − 6 , 5 ) and ( − 3 , 20 ) ? Write your answer in simplest form.
Answer:
slope = 5
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 5 ) and (x₂, y₂ ) = (- 3, 20 )
m = [tex]\frac{20-5}{-3-(-6)}[/tex] = [tex]\frac{15}{-3+6}[/tex] = [tex]\frac{15}{3}[/tex] = 5
4 7. It takes of a roll of ribbon to wrap six packages. What fraction of a roll does it take to wrap three packages?
The fraction of a roll it takes to wrap three packages is 1/2.
Fraction is a comparison between two mathematical quantities or numbers.
Given that, wrapping six packages takes a roll of ribbon.
wrapping 1 package takes = 1/6 of roll of ribbon.
Wrapping 3 packages takes = 3*(1/6) = 1/2 of roll of ribbon.
Hence fraction of a roll it takes to wrap three packages is 1/2.
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Factor the polynomial: -2x³ - 4x² - 6x
Answer:
−2x (x² + 2x + 3)
