By adding up all the possible ways to distribute the coupon and subtracting it from the possible ways to distribute the 10 coupons to the 15 men, we can determine the total number of ways at least a woman can receive a coupon.
- The entire number of options for dividing the coupons among the 20 customers is the same as the total number of ways to choose a subset of 10 items from a set of 20.
In other terms, 20/10 = 20!/ 10!10 is the combinatorial number of 20 and 10.
- We must use the same calculation as above, but with a set of 15 items rather than 20, to get the total number of alternatives for distributing the coupons among the 15 males.
We now have 15/10, which is 15!/10!5! possibilities.
To ensure that at least one woman receives a coupon, we have 20/10 - 15/10 distribution options.
What does "combination" mean?A combination is made up of r items chosen without replacement from a set of n items, where the order is irrelevant.
How many different ways that n other items can be combined in a circle exist?The amount of circular permutations of n other objects, taken r at a time, is nPr 2r if clockwise and anti-clockwise configurations are not considered to be distinct. Combinations are various groups or choices made from a variety of items, either all or some of them.
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How do you simplify i^100?
The solution of i^100 = 1 is [tex]i^{100} = 1[/tex] .
Simplify
Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Power
In mathematical relationships, power is referred to the number of times a number is multiplied by itself meaning the number you get raising a number to an exponent whereas an exponent can be defined as the number of times the number is used in a multiplication. Exponents are often known as powers or indices.
Exponents
Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner. For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 34, where 4 is the exponent and 3 is the base. The whole expression 34 is said to be power.
Rewrite [tex]i^{100}[/tex] as [tex](i^{4} )^{25}[/tex]
One to any power is one.
1
From the fact that [tex]i^{2}[/tex] = −1,
Then
([tex]-1^{50}[/tex]) = 1 as −1 raised to any even power is 1.
[tex]i^{100} = 1[/tex]
i^100 = 1
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10. A statue casts a shadow 30 feet long. At the same time, a person who is 5 feet tall casts a
shadow that is 6 ft long. How tall is the statue?
A. 30 ft
B. 25 ft
C. 18 ft
D.12.5 ft
Two angles which each measure less than 90° are complementary.
If the statement is false give a counterexample.
Responses
A False; 40° and 50°.False; 40° and 50°.
B False; 110° and 20°.False; 110° and 20°.
C False; 30° and 80°.False; 30° and 80°.
D The statement is true.
The given statement is true. The example is 40° and 50°.
What is counterexample?
An example that satisfies the condition(s) of a mathematical statement but does not result in the conclusion of the statement is referred to as a counterexample.
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
If the sum of two angles is 90°, then the angles are complementary angles each other.
40° and 50° both angles are less than 90°.
The sum 40° and 50° is 90°.
Thus, 40° and 50° are complementary to each other.
Therefore the given statement is true.
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Given the following exponential function, identify whether the
change represents growth or decay, and determine the
percentage rate of increase or decrease.
y = 3300(0.949)^x
The function simulates exponential decay, and it degrades by 5.1% for every increment in x.
What is exponential growth & exponential decay?Explosive increase and decay are common in situations where quantities change rapidly. It has been suggested that exponential development and decay follow a geometric progression. Quantities that change exponentially rather than continually are referred to be exponentially growing or decaying.
As per the given data in the question,
An exponential function with the formula y = a[tex]r^x[/tex] is the function that is given.
a = 330
r = 0.949
The function indicates exponential growth if the base r is larger than 1. The function shows exponential decline if indeed the base r is far less than 1. In this instance, the function depicts exponential decline because the base r is smaller than 1, or 0.949.
If we want to describe the rate of reduction as a percentage, we can remove the base r by 1 and multiply it by 100.
The rate of reduction as a percentage in this instance is:
1 - 0.949 = 0.051 ×100
= 5.1%.
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What theorem would this one be?
Answer:
C. Yes, SAS
Step-by-step explanation:
You want to know the congruence theorem that lets you say ∆ACD≅∆CAB, given that AB=CD and AB║CD.
Congruent trianglesThe triangles are congruent if an angle or side can be shown congruent, in addition to at least one angle and at least one side.
Here, the sides AB and CD are shown congruent. The side AC is congruent to itself, so we only need the angle(s) between them to show the triangles are congruent.
The Alternate Interior Angles theorem tells you that transversal AC creates congruent angles CAB and ACD with respect to the parallel lines AB and CD.
Hence we can show triangle ACD and CAB are congruent by the SAS congruence theorem.
Yes, The triangle is congruent by Angle - Side - Angle congruence theorem.
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
⇒ AB || CD
Now,
In figure,
⇒ AB || CD
So, In triangle ACD and triangle CAB;
⇒ AB || CD
So, By definition of alternate angles,
⇒ ∠ BAC = ∠ DCA
And, ∠ DAC = ∠ ACB
Here, Line AC is common in both tringle.
Hence, By Angle - Side - Angle congruence theorem,
⇒ Δ ACD ≅ Δ CAB
Thus, The triangle is congruent by Angle - Side - Angle congruence theorem.
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Find the simple interest on $1975 for 4.5 years at rate of 9.1% per year
Answer:
$808.76
Step-by-step explanation:
You want the simple interest earned on $1975 at the rate of 9.1% per year for 4.5 years.
InterestThe amount of simple interest is given by the formula ...
I = Prt
where principal P is invested at rate r for t years.
ApplicationUsing the given values, the amount of interest earned is ...
I = $1975·0.091·4.5 = 808.7625 ≈ $808.76
The amount of simple interest is $808.76.
<95141404393>
What is the first step made in copying the length of a line segment AB onto another line from the lesson? O Without changing the setting of the compass, place the compass point on one endpoint of the new line segment and swing it so that it intersects the second segment. O Using your straightedge, construct a segment that is longer than the given segment. O Use the compass to measure the length of the segment. O Find a line segment or create a line segment by using your straightedge.
The first step is to draw a line longer than the given AB line.
What is line segment?An area or portion of a line with two endpoints is referred to as a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.
What is the difference between line and line segment?A line can be extended on both ends forever while a line segment has endpoints.
Step 1: You are instructed to copy line segment AB.
Step 2: A line segment that is longer than line segment AB is drawn in step two. Identify C as one of its endpoints.
Step 3: Position the anchor on one endpoint of line segment AB and the pencil point on the other endpoint of the segment by opening your compass.
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a simple random sample of 64 concert tickets was drawn from a normal population. the mean and standard deviation of the sample were $120 and $25, respectively. we want to determine whether the mean of tickets is not equal to $125. find the p-value for this hypothesis testing.
By using the hypothesis test, to determine whether the mean of tickets is not equal to $125 is calculated as 58%.
We must compute the sample's z-score using the sample mean and standard deviation in order to determine the p-value for this hypothesis test. The z-score calculates how far the sample mean deviates from the population mean by standard deviations.
The difference between the two means is $5 if the population mean is $125 and the sample mean is $120. Given that the sample's standard deviation is $25,
z-score = [tex]\frac{5}{25}[/tex] = 0.2.
We must utilize the z-score to hunt for the equivalent value in a typical normal table in order to determine the p-value. The chance of selecting a sample with a mean of $120 from a population with a mean of $125 is known as the p-value.
The probability that a sample with a z-score of 0.2 would be taken from a population with a mean of $125 is the p-value in this instance. When we look for 0.2 in a typical normal table, we discover that the p-value is roughly 0.58. As a result, 0.58 is the p-value for this hypothesis test. The probability that a sample with a mean of $120 would be taken from a population with a mean of $125 is therefore 58%.
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as more independent variables are added to a regression model, the coefficient of determination tends to increase. how is this bad?
This bad is because It can lead to adding variables with little or no predicative power.
Given,
In the question:
As more independent variables are added to a regression model, the coefficient of determination tends to increase.
How is this bad?
Now, According to the question:
Let's know:
What is meant by a regression model?
A regression model is a statistical model that estimates the relationship between one dependent variable and one or more independent variables using a line (or a plane in the case of two or more independent variables).
Hence, This bad is because It can lead to adding variables with little or no predicative power.
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The graph of a linear function passes through (-8,4) and (4,5).What is the equation of the function?
The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear equation or function is given as ;
y = mx + b
The slope (m) associated with two points (x₁, y₁) and (x₂, y₂) is given by
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope associated with (-8,4) and (4,5) will be as,
m = (5 - 4)/(4 + 8) = 1/12
Thus, y = (1/12)x + b
Put (4,5)
5 = (1/12)4 + b
b = 5 - 1/3
b = 14/3
Thus, y = (1/12)x + 14/3
Hence "The linear function that passes through (-8,4) and (4,5) will be y = (1/12)x + 14/3".
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suppose you have a 3-year lease on a truck that allows 10,000 miles per year, with a 32 cents per mile penalty for overages. in the first year you drive 9,295 miles, in the second year 11,040 miles, and in the third year 12,093 miles. how much of a mileage penalty, if any, do you owe?
Therefore , the total mileage penalty you owe is $1,002.56
What is equation ?In algebra, an equation is a well-formed formula that connects two expressions with the equals sign to express the equality of the two terms. For example, in French, an équation is described as comprising one or more variables, whereas in English, an equation is any well-formed formula that consists of two expressions connected with the equals sign.
Here,
Given:
a truck with a three-year lease and a 10,000-mile annual mileage cap
32 cents per mile penalty for overages
a) first year you drive 9,295 miles
therefore,
Projected Total Miles= Actual Average Miles per day * Length of Lease
9,125 miles = 25 * 365 days
Allowed Total Miles =Annual Miles Allowed / 12 months * Length of Lease
10,000 miles = 10,000 / 12 months * 12 months
Projected Excess Miles = 0
Projected Lease-end Mileage Charge =Projected Excess Miles * Excess Miles Charge
$0.00 = 0 * $0.32
Therefore first year no excess milage penalty
b)second year you drive 11,040 miles
Projected Total Miles Actual Average Miles per day * Length of Lease
10,950 miles = 30 * 365 days
Allowed Total Miles =Annual Miles Allowed / 12 months * Length of Lease
10,000 miles = 10,000 / 12 months * 12 months
Projected Excess Miles =Projected Total Miles - Allowed Total Miles
1040 miles = 11,040 - 10,000
Projected Lease-end Mileage Charge = Projected Excess Miles * Excess Miles Charge
$332.8 = 1040 * $0.32
Therefore second year $332.8 excess milage penalty
C)third year you drive 12,093 miles
Projected Total Miles Actual Average Miles per day * Length of Lease
10,950 miles = 30 * 365 days
Allowed Total Miles =Annual Miles Allowed / 12 months * Length of Lease
10,000 miles = 10,000 / 12 months * 12 months
Projected Excess Miles =Projected Total Miles - Allowed Total Miles
2093 miles =12,093 - 10,000
Projected Lease-end Mileage Charge = Projected Excess Miles * Excess Miles Charge
$669.76= 2093 * $0.32
Therefore second year $669.76 excess milage penalty
Therefore , the total mileage penalty you owe is $669.76 + $332.8=$1,002.56
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Jayden and his children went into a grocery store and he bought $8 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought twice as many bananas as apples. By following the steps below, determine the number of apples, x,x, and the number of bananas, y,y, that Jayden bought.
Determine three ways to have twice as many bananas as apples:
The number of apples that Jayden bought is 4 and the number of bananas he wants to buy is 8.
The number of ways we can have twice as many bananas as apples is:
8 bananas 4 apples
10 bananas 5 apples
12 bananas 6 apples
How many apples and bananas did Jayden buy?The first step is to form of system of equations that represent the question:
x + 0.50y = 8 equation 1
y = 2x equation 2
The substitution method would be used to determine the required values.
x + (0.50 x 2x) = 8
x + x = 8
2x = 8
x = 8 / 2
x = 4
Substitute for x in equation 2:
y = (2 x 4)
y = 8
The total number of fruits bought is 12 (4 + 8):
The number of ways we can have twice as many bananas as apples :
8 bananas 4 apples
10 bananas 5 apples
12 bananas 6 apples
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Graph the functions to find the x values that satisfy the inequality.
f(x)=-2(x+3)^2+5
g(x)=x+7
For what values of x is f(x)≤g(x)?
Options:
(-∞,∞)
No values of x
[-5, -2]
(-∞, -5]∪[-2, ∞)
no value of x for f(x) ≤ g(x)
What do you mean by function?
Function, in mathematics, a formula, rule, or law that defines the relationship between one variable (the independent variable) and another (the dependent variable).
The types of functions can be roughly classified into four types. Based on item:
One-to-one functions, many-to-one functions, on functions, one-to-one, and within functions.
Given functions:
f(x)=-2(x+3)^2+5
g(x)=x+7
According to the graph given for the functions there is no value of x for which f(x) ≤ g(x) .
Therefore, no value of x for f(x) ≤ g(x)
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the edge of a cube is growing at a rate of 6 inches per second at the instant when the edge of the cube has a length of 11 inches. what is the rate of change of the volume of the cube at that instant?
The edge of a cube is growing at a rate of 6 inches per second at the instant when the edge of the cube has a length of 11 inches. Hence, the rate of change of the volume of the cube at that instant will be 2178 [tex]inches^3[/tex] /s.
The volume of the cube V = [tex]a ^ 3[/tex]
where 'a' is the edge.
Rate of increase of volume = dV / dt = 3a^2 da/dt.
da/dt = 6 inches /s
dV / dt = 3 [tex]a^2[/tex] da/dt.
When a = 11 inches.
dV /dt = 3 x [tex]11 ^2[/tex] x 6
= 3 x 121 x 6
= 2178 [tex]inches^3[/tex] /s
Hence, the rate of change of the volume of the cube at that instant will be 2178 [tex]inches^3[/tex] /s.
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8x - 3 /AX 4x + 3 When angles form a linear pair, their sum is 180°. 8x - 3+ 4x + 3 = 180 [?]x + [] = 180
Answer:
12x + 0 = 180x = 15Step-by-step explanation:
You are given the equation 8x -3 +4x +3 = 180 and asked to simplify it and solve for x.
SimplifiedCollecting terms, we have ...
(8 +4)x +(-3 +3) = 180
12x + 0 = 180
Dividing by the coefficient of x gives ...
x = 180/12 = 15
The value of x is 15.
A circular pond has a diameter of 30 feet. The City of Puebla wants to build a fence enclosing the pond. How many feet of fencing does the city need to enclose the pond?
The amount of fencing feet the city needs to enclose the pond is 94.29 feet.
What is perimeter?Perimeter can be defined the total distance around an object.
To calculate the amount of fencing the city needs to enclose the pond, we use the formula for the perimeter of a circle.
Formula:
P = πd............ Equation 1Where:
P = Perimeter of the pondd = Diameter of the pondπ = PieFrom the question,
Given:
d = 30 feetπ = 22/7Substitute these values into equation 1
P = 30×22/7P = 94.29 feet.Hence, the feet of fencing needed is 94.29 feet.
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Which of the following are quadratic equations?
(v) 2x^2 −3x +9=0
2x^2 −3x +9=0 is the given equation that is quadratic.
What is quadratic?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.
Is a quadratic 2 or 4?Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."
As highest power of variable is 2 so the expression 2x^2 −3x +9=0 is quadratic.
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Karen has a bag containing 423 rubber ducks.
If Karen gives 30 rubber ducks to every person she meets, then she will have enough for _____ people and she will have _____ extra ducks left over.
Answer:
karen will have enough for 14 people, and she will have 3 extra ducks left over
Step-by-step explanation:
divide 423 by 30
423/30 = 14
14 times 30 is 420, so subtract 420 from the total number of rubber ducks
423 - 420 = 3
so, karen will have enough for 14 people and 3 ducks will be left over !!
Answer:
Karen we'll have enough for 14 people and have 3 ducks left over.
question content area top part 1 compare the slopes of the lines for y=f(x) and y=g(x) to determine if they are parallel.
A line's steepness can be determined by looking at its slope.Slope of the line is 15.
How do you find slope of a line?Determine the coordinates of two points along the line that you choose.Find the difference between these two points' y-coordinates (rise). Find the difference between these two points' x-coordinates (run).
Slope of a line passing through two points (x1 ,y1)and will be given by,
Slope 'm' =y2 - y2/ x2- x1
Function 'f' passes through two points (0, 20) and (1, 35).
Slope of the line = 35 -20/1-0= 15
In a similar manner, function 'g' passes through (0, 22) and (1, 37).
Slope of the line = 37 - 22/ 1-0 = 15
Therefore, m1 = m2
Since, slopes of both the lines are equal, lines will be parallel.
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Phillip has 18 video games. Emily has r video games. Together, Phillip and Emily have a combined total of less than 30 video games. What is an inequality that could be used to represent this situation
The inequality that represents relationship the number of video games of Phillip and Emily is 18 + r < 30.
What are types of symbols to connect two expressions?
There are two types symbols that connect two expressions. One is known as equal sign and another one is inequality. There are various symbol under inequality and they are less than, greater than, less than or equal, greater than or equal.
Given that Phillip has 18 video games. Emily has r video games.
The number of video games that Phillip and Emily have is 18 + r.
Also given that together, Phillip and Emily have a combined total of less than 30 video games.
Thus 18 + r < 30
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10. What was the snow level at 8 a.m., when x = 8?
The snow level at 8 a.m., when x = 8, was 30cm.
What is linear equation?The simplest equation for expressing and resolving an unknown number is a linear equation in one variable. It is usually a straight line and is easily pictorial portrayed. A simple way to convey a mathematical assertion is with a linear equation. Unknown numbers can be represented by any variable or symbol. There are several easy ways to solve a linear equation.
solutiony = 2x + 14.
Here, y is the amount of snow in inches, and x is the number of hours after midnight
To find the snow level at 8 a.m. we take the value of x = 8.
⇒ y = 2*8 + 14
⇒ y = 16 + 14
⇒ y = 30cm
So, The snow level at 8 a.m., when x = 8, was 30cm.
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this question is incomplete. The complete question is
the snow level is modeled by the function y = 2x + 14. Here, y is the amount of snow in inches, and x is the number of hours after midnight (x = 0). 10. What was the snow level at 8 a.m., when x = 8?
Solve the following equation for x. 10 = 2 - 4 (ax - 3) a. -5/a b. 5/a c. 1/a d. -1/a
Answer: c. [tex]\frac{1}{a}[/tex].
Step-by-step explanation:
10 = 2 - 4(ax - 3)
10 = 2 - 4ax + 12
10 = 14 - 4ax
Minus 14 on both sides.
-4 = -4ax
Divided -4 on both sides.
1 = ax
Divided a by both sides to solve x.
[tex]\frac{1}{a}[/tex] = x
Therefore, the answer is c.
what is 2 divided by 238
Answer:
0.0084033613
Step-by-step explanation:
The lid of a rectangular box of side
[tex]40cm \: by \: 10m[/tex]
is to be sealed all round with tape.
[tex]what \: is \: the \: length \: of \: the \: tape \: required[/tex]
Question 11
Erica recorded the number of sales she made during each of the first 4 months when she began her new career. Erica plotted the data on a coordinate grid, and she noted that the data correlate to an exponential equation, as shown What is the domain of the function shown in the graph?
The domain of the graph is {1, 2, 3, 4}
What is Domain?"All the values" that are input into a function are referred to as the domain of a function. The set of all potential inputs for a function is its domain.
Given:
As, we know domain of a function is the set of all possible inputs for the function.
from the Graph, we can find the coordinates ( 1, 10), (2, 20), (3, 40) and ( 4, 80)
So, the domain of the graph is {1, 2, 3, 4}
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The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs.
Which ratio represents the number of votes for hot dogs to chicken?
Responses
1/5
2/5
3/5
5/2
The ratio represents the number of votes for hot dogs to chicken is 2/5 ,
What is ratio?
Comparing two numbers by dividing them is how ratios work. Your formula would be A/B if you were contrasting one data point (A) with another data point (B). By doing so, you are multiplying information A by information B.Given,
Number of members voted for pizza = 6
Number of members voted for chicken = 10
Number of members voted for hot dogs = 20 - (10 +6) = 4
Now we have to determine the ratio represents the number of votes for hot dogs to chicken.
Number of members voted for hot dogs / Number of members voted for chicken = 4/10
= 2/5
Thus, the ratio represents the number of votes for hot dogs to chicken is 2/5.
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Which inequality represents all the values of x for y<(or equal to)-6(x-18)-2 when y=46
The value of x is x ≤ 9 for which y ≤ -5(x - 18) - 2 when y = 43.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The given inequality is y ≤ -5(x - 18) - 2.
Now the values of x when y = 43 is,
43 ≤ - 5(x - 18) - 2.
43 ≤ - 5x + 90 - 2.
43 - 88 ≤ - 5x.
- 45 ≤ - 5x.
5x ≤ 45.
x ≤ 9.
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Tristan has $1.40 worth of nickels and dimes. He has twice as many nickels as dimes. Write a system of equations that could be used to determine the number of nickels and the number of dimes that Tristan has. Define the variables that you use to write the system.
The equation will be d(x+2y) = $1.40,where x = cost of dimes , y = cost of nickels, t = number of dimes.
What is an equation?
In mathematics, equation represent two expressions are equal.
e.g. x + 2y = 3,
Here , x + 2y is one expression and 3 is another, which are equated using equal to symbol.
Let's us consider ,
Number of dimes = t
Then number of nickels = 2t
Cost of one dime = x
Cost of one nickel = y
Then the total cost = xt +2yt
And total cost given = $1.40
So, the final equation = t(x+2y) = 1.40
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compare the y-intercept and the rate of change of the following items
Answer:
A) They have the same y intercept and the same rate of change
Step-by-step explanation:
Write the equation for the line passing through the points (2,4) and (12,7)
Slope [tex]\frac{7-4}{12-2}[/tex] = [tex]\frac{3}{10}[/tex] = .3
y intercept (b)
y = mx + b
Use 2 fox x, 4 for y and .3 for m
y=mx + b
4 = .3(2) + b
4 = .6 + b Subtract .6 from both sides
3.4 = b
The equation is
y = .3x + 3.4
The two equation are identical so the slope and y intercepts are the same.
compare the y-intercept and the rate of change of the following items. Option (d) The rates of change are the same, but the y-intercepts are different. is correct.
for rates,
we will find the slope of I and II
slope = dy/dx = change in y/change in x
for both of them when we compare the slope, it is 0.3.
for y-intercepts.
equation for II should be formed in order to compare with the y-intercept of I which is 3.4.
y-7=0.3(x-12) .................(i)
so, the y-intercept is 7 for II
thus, the y-intercepts of given eq are not equal.
Draw a line with the given slope through the given point. What other point
lies on that line?
Answer:
a. Point B
b. Point D
c. Point E
d. Point B
Step-by-step explanation:
See the attached image for a graphed solution with color-coded lines drawn.
