What is the probability that this year's graduation will fall on the birthday of exactly one of the 68
Seniors? What is the probability that there is more than one such Senior?

The required money to be invested in order to save $5000 is $4677.26.

The compound interest is a form of interest where the rate of interest is applied on the amount obtained after every interval of time.

The principal for each interval is the sum of interest And the principal for the previous interval.

Suppose the amount to be invested be P.

The rate of interest for monthly compounding is given as 4.5/12 = 0.375%.

Time is given as 18 months.

This implies number of time period is 18.

Plug n = 18, r = 0.375% and A = 5000 in A = P(1 + r/100)ⁿ as,

⇒ 5000 = P(1 + 0.375/100)¹⁸

⇒ P = 4677.26

Hence, the amount of money that should be invested is obtained as $4677.26.

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Answer:

The intersection of the two intervals = 4, 5, 6,.......∞ = (4, ∞)

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,+∞ = (-3, ∞)

Step-by-step explanation:

The given intervals are;

First interval  = (-3, ∞)

Second interval  = (4, ∞)

Using the number line, we therefore, the first interval includes, -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,∞

The second interval includes 4, 5,.....,∞

Which gives the intersection as 4, 5, 6,.......∞

The union is the interval that combines the two sets of intervals which is given as follows;

The union of the two intervals = -3, -2, -1, 0, 1, 2, 3, 4, 5,.....,∞

There is one way to implement a function in Python that takes in an array of integers and returns the smallest positive integer that does not occur in the array.

def smallest_missing_positive(a):

   #Create a set to store the unique elements in the array

   unique_set = set(a)

   #Iterate through the positive integers starting from 1

   for i in range(1, len(a) + 2):

       #If the current integer is not in the set, return it

       if i not in unique_set:

           return i

This function first converts the input array into a set, which removes any duplicate elements. It then iterates through the positive integers starting from 1 up to the length of the array plus 2. For each integer, it checks whether it is in the set of unique elements from the input array. If it is not, the function returns that integer as it is the smallest positive integer that does not occur in the array.

For example, when the function is called with the input array [1, 3, 6, 4, 1, 2], it will return 5 as it is the first missing positive number.

You can also use a set and difference() method of set to check the missing elements from 1 to maximum element of array+1 and find the missing first one, this method is more efficient than the above one when the array is large.

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The Distance that Ellie ran each evening is 16.5 miles for a entirety week.

We can use the following equation to find how many miles, x, Ellie ran each afternoon:

x + 2.5(3) = 24

Here, x represents the number of miles Ellie ran each afternoon, 2.5 represents the number of miles she ran each morning, and 3 represents the number of days she trained. The total number of miles she ran, 24, is on the right side of the equation.

To solve for x, we can start by simplifying the left side of the equation:

x + 7.5 = 24

Then, we can subtract 7.5 from both sides:

x = 16.5

So, Ellie ran 16.5 miles each afternoon.

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The slope intercept form of the equation is

y = -1/4x -11/4

One of the most popular ways to describe a line's equation is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope intercept formula may be used to get the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on the line fulfills.

The slope intercept form is a technique for figuring out a straight line's equation in the coordinate plane. Any point's coordinates on a straight line must fulfill a certain relation, which is known as the equation of a straight line.

Any location that is not on the line will not fulfill the coordinates.

This equation's solution is simple to find. A straight line's slope, or angle of inclination from the x-axis, and the intercept it makes with the y-axis are both necessary to determine the slope intercept form of the line.

The line passes through (1,-3)

slope = -1/4

The equation of the line

y = mx + c

here m is the slope and c is the intercept.

putting the point and slope in the equation

-3 = -1/4 *1 + c

⇒ c = -11/4

So the slope intercept form of the equation is

y = -1/4x -11/4

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To find the third angle of a triangle if you know the measures of the other two angles, you can use the fact that the sum of the measures of the angles in any triangle is always 180 degrees.

For example, let's say you know that angle A measures x degrees and angle B measures y degrees. To find the measure of angle C (the third angle), you can use the following equation:

x + y + C = 180°

To solve for C, you can subtract x and y from both sides of the equation:

C = 180 - x - y

So, the measure of angle C is equal to 180 degrees minus the measure of angle A and angle B.

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Answer: get yio colors straightv

Step-by-step explanation:

The height of the equilateral triangle when its side length is given as 8 inches is calculated to be 6.93 inches.

The equilateral triangle has all sides and angles equal. The angles are always equal to 60 degrees.

Given that,

Side length of the equilateral triangle = 8 inches

Angles = 60 degrees

Height = ?

Therefore, let us find the height of the triangle using the Pythagoras theorem,

c² = a² + b²

8² - 4² = b²

b² = 64 - 16

b² = 48

b = 6.93 inches

Thus, the height of the equilateral triangle is calculated to be 6.93 inches.

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Gary, Mary, and Rory have 96 candies altogether.

Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".

After Gary gives Mary half of all his candies, he would have x/2 candies.

Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.

And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.

Now, we know that Gary would have 12 more candies than he had originally, which means:

x/2 + x/8 = x/2 + x/4 - 12

We can combine like terms and simplify the equation:

x/2 + x/8 = x/4 + x/4 - 12

x/8 = 12

x = 8 * 12

x = 96

Thus, Gary, Mary, and Rory have 96 candies altogether.

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The equation representing the asked situation is (9 - 2.5) = 6.5

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, The temperature in Knowlton is 2.5 C colder than the terminal Elmwood.

We know, that, if temperature is colder in any area A than another area B then, A will have less temperature than B.

Therefore, temperature in Knowlton is less than that of in Elmwood.

Therefore, if the temperature in Elmwood is 9 the temperature in Knowlton will be 9-2.5 = 6.5

Hence, the required equation is  9-2.5 = 6.5

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Answer:

Step-by-step explanation:

we konw the speed of burn is 1.25 inchs per hour. so, the left candle is

15-1.25t. the answer is L=15-1.25t

Answer:

d

Step-by-step explanation:

[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=1\\ y=27 \end{cases}\implies 27=ab^1\implies 27=ab \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} x=2\\ y=243 \end{cases}\implies 243=ab^2\implies 243=abb\implies \cfrac{243}{ab}=b \\\\\\ \stackrel{\textit{substituting from the 1st equation}}{\cfrac{243}{27}=b\implies \boxed{9=b}} \\\\\\ 27=ab\implies \cfrac{27}{b}=a\implies \cfrac{27}{9}=a\implies \boxed{3=a}~\hfill {\Large \begin{array}{llll} y=3(9)^x \end{array}}[/tex]

4 is the range of the data set in the given set.

The space between the highest and lowest values in a data collection is known as the range. Similar units to the data are used to quantify variability. Variability is increased with larger values. The range has several limitations but is the most straightforward statistical measure of dispersion to compute and comprehend.

This means that the range might alternatively be described as the distance between the highest and lowest observation.

In the given data set,

range = maximum frequency - minimum frequency

range = 5 - 1

range = 4

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Answer: 5.6

Step-by-step explanation:

the opposite of an negative number...

So your answer would be....

        =5.6

Answer:

[tex]5.6[/tex] or [tex]\dfrac{1}{-5.6}[/tex]

Step-by-step explanation:

The additive inverse of [tex]-5.6[/tex] is [tex]-1 \cdot -5.6 = \boxed{5.6}[/tex]

or...

If you mean the multiplicative inverse of  [tex]-5.6[/tex], then the answer would be [tex]\dfrac{1}{-5.6}[/tex]

The percentage statement is 9.5 is 19% of 50

From the question, we have the following parameters that can be used in our computation:

9.5 is what % of 50

Complete the blank with x

So, we have the following representation

9.5 = x% of 50

So, we have

9.5 = x% * 50

Divide both sides by 50

0.19 = x%

Multiply both sides by 100

So, we have

x = 19

Hence, the solution is 19

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For given right triangle, the length of hypotenuse x = 4/√3

Here we have been given a 30° - 60°- 90° right triangle.

A side opposie to angle 60 degrees measures 2 units.

And x is the hypotenuse of right tirnagle.

To find the value of x, consider sine of angle 60 degrees.

sin(60°) = (opposite side of angle 60°) / hypotenuse

From tirgonometric table, sin(60°) = √3 / 2

So, above equation becomes,

√3/ 2 = 2/x

x = 2 × (2/√3)

x = 4/√3

We can see that the value of x is in in simplest radical form with a rational denominator.

Therefore, x = 4/√3

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The rule for g(x) = f(x-1)-3 is g(x) = (x-1)⁶-3(x-1)³ - 1

A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable. Based on the information given, we can see that the variables that are illustrated in the question are f and g.

In order to write the rule for g(x) = f(x-1)-3 when f(x) = x⁶ - 3x³ + 2, replace x with x-1 in f(x) and subtract 3. That is:

g(x) =  f(x - 1) - 3

g(x) = (x-1)⁶ - 3(x - 1)³ + 2 - 3

g(x) = (x-1)⁶ - 3(x - 1)³- 1

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the first 4 term is (1+2x)^6

The option that is not true about cluster sampling is option  A: Cluster sampling has the advantage of reducing sampling variability.

Cluster sampling often leads to larger sampling variability than other types of sampling methods, such as simple random sampling or stratified sampling, because clusters may not be a representative sample of the population and the individuals within a cluster may be more similar to each other than to individuals in other clusters.

Therefore, This increases the chance that the sample will not be representative of the population, which can result in a higher level of sampling error.

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Answer: 7.785,7.476,7.293,8.37.7.9

Step-by-step explanation:

P(even) is  50%

It is simple to calculate the likelihood of one die roll.

Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.

First, keep in mind that a prime number is an integer that has exactly two factors: 1 and the number itself (which is why 1 does not qualify: it has only one factor). The appropriate numbers from 6 onward are 2,3,5. Your response, given that there are six sides, is: P(prime) = 3/6 = 1/2 = 50%

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The Osborne 1 was the first laptop ever released, and it weighed 11 kg in 1981. Since then, the average rate of weight decrease has been 4.7% per year. This means that in 2019, a laptop would have weighed around 2.3 kg.

1981: 11 kg

1982: 10.5 kg (11 kg - 0.55 kg = 10.5 kg)

1983: 10.02 kg (10.5 kg - 0.48 kg = 10.02 kg)

1984: 9.55 kg (10.02 kg - 0.47 kg = 9.55 kg)

2019: 2.3 kg (3.44 kg - 1.14 kg = 2.3 kg)

The Osborne 1 was the first laptop ever released in 1981, and it weighed 11 kg. Since then, the average rate of weight decrease has been 4.7% per year. This means that the mass of a laptop decreases by 0.47 kg every year on average. So, in 1982 it would have weighed 10.5 kg, in 1983 it would have weighed 10.02 kg, and so on. By 2019, the weight of a laptop would have decreased to 2.3 kg as a result of this 4.7% average rate of weight decrease.

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The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.

The median of the data is the middle value of the data which is also known as the central tendency of the data and is known as the median.

The median for odd data will be

Median = [(n + 1) / 2]th

The median for even data will be

Median = {[n / 2 + (n + 2)/ 2] / 2}th

The data is given below.

23, 15, 32, 27, 19, 11, 30, 19, 22

Arrange the data in ascending order. Then we have

11, 15, 19, 19, 22, 23, 27, 30, 32

Then the median of the following 9 numbers is calculated as,

Median = [(9 + 1) / 2]th

Median = (10 / 2)th

Median = 5th

Median = 22

The median of the following 9 numbers 23, 15, 32, 27, 19, 11, 30, 19, 22 will be 22.

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The coefficient of XY in 7xy is 7

Any integer or symbol that multiplies the variable of a single term or the terms of a polynomial to represent a constant value is known as a coefficient in mathematics. In some phrases, a letter might be substituted for the usual number. For example, x is the variable and a and b are the coefficients in the formula: ax2 + bx + c.

What is a coefficient?

A coefficient is a quantity or number that is coupled with a variable. Frequently, an integer is multiplied by the variable and written next to it. The variables that don't have a corresponding number are presumed to have a coefficient of 1.

Seven is the coefficient of XY in 7xy.

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[tex]( x - 4 ) + ( 2x - 7 )[/tex]

Combine Like Terms:

[tex](x+2x)+(-4+-7)[/tex]

[tex](3x)+(-11)[/tex]

[tex]\fbox{3x - 11}[/tex]

Answer:3x-11

Step-by-step explanation:

(x-4)+( 2x-7)

x-4+2x-7

3x-11

The sine , cosine and tangent of an acute angle can be find by using:

Acute Angle:

Acute angles are defined as angles less than 90 degrees, i.e. angles between 0° and 90°. Examples include 60°, 30°, 45°. A triangle with all interior angles less than 90° is called an acute triangle. For example, an equilateral triangle is an acute triangle because its interior angles are 60°.

Sine of an Acute Angle :

The sine of an angle in a right triangle is the ratio of the opposite side of the angle to the hypotenuse. The sine function is the important periodic function in trigonometry, with period 2π. To understand the derivation of sin x, consider the unit circle centered at the origin of the coordinate plane. On the boundary (perimeter) of this circle the variable point P moves. Note that P is in the first quadrant and OP makes an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis.

Cosine:

Cosine or cos x is the trigonometric periodic function. Imagine a unit circle centered at the origin of the coordinate plane. The variable point P moves on the circumference of this circle. From the figure, we can see that P is in the first quadrant and OP forms an acute angle of x radians with the positive x-axis. PQ is the perpendicular from P to the horizontal axis. A triangle is therefore formed by connecting the points O, P, and Q as shown. where OQ is the base and PQ is the height of the triangle.

Tangent:

The tangent function is one of the six most important trigonometric functions, commonly written as tan x. It is the ratio of the opposite side to the adjacent side of the angle considered in a right triangle. There are various trigonometric identities and formulas related to the tangent function that can be derived using various formulas. The period expression for the tangent function f(x) = a tan (bx) is given by Period = π/|b|. The tangent function tan x is periodic, with period π/1 = π (because b = 1 for tan x).

So the formula for tan x is:

tan x = sin x/cos x

tan x = opposite side/adjacent side

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Using combination, 5184 nine-digit numbers can be made using each of the digits 1 through 9 exactly once with the digits alternating between odd and even.

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to arrange the components of set A, as you can see.

If the first letter is even, there are 4 first digit possibilities (not 5 because it can't start with 0), 4 third digit possibilities, 3 fifth digit possibilities, etc., making the total 4!

If an odd number is the first letter, there will be 5!*4! different ones.

Add the two together now.

4*4!*4! + 5!*4!=5184

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Yes, A triangle has sides of lengths 10, 24, and 26 is a right triangle.

A right-angled triangle is a triangle with one of the angles at 90 degrees. A 90-degree angle is called a right angle.

The formula states that in a right triangle:

The square of the hypotenuse is equal to the sum of the square of the base and the square of the altitude.

(Hypotenuse)² = (Base)² + (Altitude)²

c²=a²+b²

The three numbers which satisfy the above formula are the Pythagorean triplets

Properties of right angle:

consider c=26 a=10, b=24 substitute in above formula:

26²=10²+24²

⇒676=100+576

⇒676=676

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Answer:

25x^6y^2

Step-by-step explanation:

Since it is a square all sides are the same. So you multiply 5x^3y and 5x^3y together to get the area. That would get you 25x^6y^2.