What's the fewest number of people in a room where it's probable (>50%) that a pair of them share a birthday

Step-by-step explanation:

a linear function is following

y = ax + b

that means the ratio of the y and x differences between the data points is constant (a).

an exponential function is in the form y = a^x. or some constant variations of it.

the base is constant (a), and the exponent of the constant is the variable (x).

1.

clearly exponential.

this is the typical graph of an exponential function.

it looks like y = 2^x, as e.g. f(4) = 2⁴ = 16, and the graph seems to be at least very close to this.

2.

exponential.

y = 3^(x - 0.5)

3¹ = 3

3² = 9

3³ = 27

3⁵ = 243

this is just y = 3^x shifted to the right by 0.5 units.

3.

linear.

the difference ratio between the data points is constant :

x is the row number (1, 2, 3, 4, 5, ...).

y is the number of seats per row (14, 16, 18, 20, 22, ...).

so,

(16-14)/(2-1) = 2/1 = 2

(18-16)/(3-2) = 2/1 = 2

...

(22-14)/(5-1) = 8/4 = 2

always constant (2).

4.

neither.

it is y = x²

when you compare 4. and 1. you see the clear difference between the 2 graphs.

5.

exponential.

remember, y = a^x.

well, here, a = 1/2. but that is still constant and doesnot change the principle.

the factor 10 stretches the graph a bit up (in fact, this 10 is the starting number of an exponential growth). but the function in its core is still exponential.

6.

linear.

when written that way, it just means that x = n, and for every increase of n by 1, y (f(n)) increases by +4.

so, the difference ratio stays constant (4/1 = 4).

A triangle has sides of 7, 24, and 25 cm. The length of the hypotenuse is equal to 25 cm if the triangle is a right triangle.

The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious.

49, 576, and 625 are the results of squaring the lengths of the side of the.

49 + 576 = 625\s(7)2 + (24)2 = (25)2

As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.

the hypotenuse is 25 cm long.

Angles of 16.26 degrees and 73.74 degrees are suitable.

Yes, since 72+242=252 (sum of squares on smaller two sides equals square on largest side).

The triangle's sides are 7 cm, 24 cm, and 25 cm, as is obvious. 49, 576, and 625 are the results of squaring the lengths of the side of the. As a result, the aforementioned equation satisfies Pythagoras's theorem. As a result, it is a right-angled triangle.

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Answer:

Step-by-step explanation:

x ÷ 48 = 4

Multiplying both sides by 48 we get:

x ÷ 48 x 48 = 4 x 48

x =  192

Answer:

when pi = 3.14, A = 63.535

when pi = pi, A = 63.61725

Step-by-step explanation:

Area of a circle = pi × radius (4.5) squared (^2)

solving for "xx"

[tex]\sqrt{xx - 2}=7\implies \sqrt{xx - 2}=7\implies (\sqrt{xx - 2})^2=(7)^2 \\\\\\ xx-2=49 \implies xx=51[/tex]

Since the tallest man is a lone individual, he can only take a seat in the center. The four other men can sit in 4! = 24 different positions.

We'll take pictures of five people standing in a row, all of varying heights. The tallest individual must be in the middle, so. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

The likelihood that an event will take place. the proportion between the total number of conceivable outcomes and the number of outcomes in a comprehensive collection of equally likely alternatives that result in a given occurrence. Probability is a measure of the likelihood that an event will occur or the likelihood that something will happen. If we throw a coin into the air,

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Answer:

12.

V. E=(1-a)(1+a)(1+a^2)(1+a^4)(1+a^8)

Step-by-step explanation:

1-a^16=(1-a^8)(1+a^8)

1-a^8=(1-a^4)(1+a^4)

1-a^4=(1-a^2)(1+a^2)

1-a^2=(1-a)(1+a)

1-a^16=(1-a)(1+a)(1+a^2)(1+a^4)(1+a^8)

The given expression is equivalent to 22 for x = 17 and y = 12.

Given is the expression as follows -

2x - y

For x = 17 and y = 12, we can evaluate the expression as -

2 x 17 - 12

34 - 12

22

Therefore, the given expression is equivalent to 22 for x = 17 and y = 12.

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Answer: 80% rent or 72 students

Step-by-step explanation:

20 percent of 90 is 18

So 18 kids own instruments

100-20=80%

So 80% of kids do rent instruments

Or

18x4= 72 kids rent

per year unit rate becomes 6 inches. This can be solved using the concept of unit rate.

A unit rate is a price for one of anything. This is expressed as a proportion with such a base of one. For instance, you would cover 7 yards on average every second if you covered 70 yards in 10 seconds. The ratios of 70 yards in 10 seconds and 7 yards in 1 second are both rates, however, the latter is a unit rate.

A rate is the ratio of two different measurement units, whereas a unit rate seems to be the ratio of two different units of measurement for just a single object.

unit rate for 30 inches per 5 years:

= 30 inches / 5 years

= 6 inches / 1 year

Thus, per year unit rate becomes 6 inches.

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The median of the distinct positive values of all of the fractions less then or equal to 1 with positive integer denominators less than or equal to 5 is 11/20.

In the statistics, the median is the value in the middle of a data set. It means that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. The middle number is found by ordering all data points and picking out the one in the middle or if there are two middle numbers, taking the mean of those two numbers. We have to arrange data values from lowest to highest value. The median is the data value in the middle of the set. If there are 2 data values in the middle the median is the mean of those 2 values.

The set of numbers are,

1 /5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1

we have to take the average of middle two .

The middle of the set are 1/2 and 3/5. and the average of these two is 11/20.

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The sine of an acute angle in a right triangle is the ratio of the angle of the triangle to the opposite side of the hypotenuse.

Trigonometric ratios:

Trigonometric ratios are the ratios of the lengths of the sides of a triangle. These ratios in trigonometry relate the aspect ratio of a right triangle to each angle. A basic trigonometric ratio is the ratio of sin, cos, and tan, or the ratio of sin, cos, and tangent. Other important trigonometric ratios cosec, sec, and cot can be derived from sin, cos, and tan, respectively.

Acute Sine Ratio:

The tangent function examines the ratio of his two legs of a right triangle. You can also use the ratio of leg length divided by hypotenuse length.

In a right triangle, each angle has an opposite side and an adjacent side. And there is always a hypotenuse. On the opposite side and the hypotenuse we are dealing with the sine ratio. The sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse. In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

Let's examine some properties of the sine ratio using the Pythagorean theorem. For a right triangle, let the lengths of the triangle be a, b, and c. where a is the length of the other side of A and b is the length of the other side of B.

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Answer:

The answer to the proportion is 45:25.

Step-by-step explanation:

To solve this proportion, we can use cross multiplication. That is, we can multiply the numerator of the first ratio (45) by the denominator of the second ratio (10) and the numerator of the second ratio (50) by the denominator of the first ratio (?). This will give us

45 x 10 = 500 and 50 x ? = 500.

If we divide both sides of the equation by 50, we get

? = 25.

Therefore, the answer to the proportion is 45:25.

1. You have $25 to spend on snacks for movie night with 4 of your friends. If individual boxes of raisins are $1.50, find the amount of money that remains per person for popcorn and a drink.

To find the amount of money that remains per person after buying raisins, we first need to find the total cost of the raisins. If 4 boxes of raisins cost $1.50 each, then 4*1.50 = $6 is spent on raisins.

To find the amount of money that remains for popcorn and drinks, we subtract the cost of the raisins from the total amount of money: 25-6 = $19.

Since there are 5 people in total (you and 4 friends), we divide the remaining money by 5 to find the amount per person: 19/5 = $3.80 per person.

2. The cost for a town’s soccer league banquet is $960. There are 60 players in the soccer league. Determine the cost per player for the town if each player pays $5 to attend the banquet.

To find the cost per player, we divide the total cost of the banquet by the number of players: 960/60 = $16 per player

3. To solve the equation 2/3(x−4)=−10, Izzy wants to multiply both sides of the equation by the reciprocal of the fraction. Name the reciprocal.

The reciprocal of the fraction 2/3 is 3/2

4. There are 2 types of tickets to attend an awards dinner—silver and gold. The gold tickets are $8 more than the silver. If Patrick bought 10 tickets at each level and spent a total of $140, find the price of each ticket.

Let's call the cost of a silver ticket x.

The cost of a gold ticket is x + 8.

We know that Patrick spent 10x + 10(x+8) = $140

We can simplify that: 10x + 10x + 80 = 140

Then we have 20x + 80 = 140

Then we have 20x = 60

And x = 3

Then the price of a silver ticket is $3 and the price of a gold ticket is $3+8 = $11

5. Kendra is making bread, but the recipe she’s using makes 4 loaves. She only wants to make one loaf. The changed recipe calls for 2 1/2 cups of flour and sugar combined. If the original recipe calls for 2 cups of sugar, find the amount of flour (in cups) in the original recipe.

If the original recipe calls for 2 cups of sugar and the changed recipe calls for 2 1/2 cups of flour and sugar combined, then the original recipe calls for 2 1/2 - 2 = 1/2 cup of flour.

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Answer:

53

Step-by-step explanation:

The value of the measure of ∠O in the given triangle will be 65°

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In ΔNOP;

PN ≅ OP

So, ∠O = ∠N

And, Measure of ∠P = 50°

Now,

In the ΔNOP;

The sum of all the three angles are 180°.

The value of the measure of ∠O = x

We get;

∠O + ∠N + ∠P = 180°

Substitute ∠P = 50° and ∠O = ∠N = x we get;

x + x + 50 = 180

2x + 50 = 180

2x = 180 - 50

2x = 130

x = 65

Thus, The value of the measure of ∠O will be 65°.

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The average rate of driving from Newyork to Boston is d. 54 mph.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, The distance you drive is proportional to the time.

We know, The arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Therefore,

The average rate of driving is,

= (216/4) mph.

= 54 mph.

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Answer:

33 degrees

Step-by-step explanation:
Angle 1 and 2 add up to a right angle which is 90 degrees. To find 2, subtract 57 from 90

90-57=33

Therefore 33 degrees is the answer

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The variable for the equation 2n - 3 =7 is 5.

What is variable ?

A variable is a symbol used to denote a mathematical object in mathematics. Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable.

A variable is a quantity that could change depending on the circumstances of an experiment or mathematical problem. Typically, a variable is denoted by a single letter. The general symbols for variables most frequently used are the letters x, y, and z.

An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown.

Then variable is n

Variable is an alphabet that depend on number.

Then the variable there is n

And the coefficient of the variable is 2

The coefficient is the number behind a variable

And the value of the variable is

2n-3=7

Add 3 to both sides

2n-3+3=7+3

2n=10

Divide both side by 2

2n/2=10/2

n=5

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The line x= -4 is a vertical line passing through x-axis.

It is a distance of 4 units from the x-axis and is parallel to the y-axis.

Vertical Line in a coordinate plane refers to a line that is perpendicular to the Y-axis. From top to bottom and from bottom to top, it is a straight line. The x-coordinate of every point along this line will be the same. The points of vertical lines include, for instance, (2,0), (3,0), (-4,0), etc. Similar to this, a horizontal line is a line that runs parallel to the x-axis from left to right.

There is no slope to the vertical lines. It follows the y-axis parallel, hence the slope is not known. As a result, the equation for the vertical line that at any point, let's say 'a', crosses the x-axis is:

x = a

where x is a point on the line's coordinate.

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Answer:

h = 24

Step-by-step explanation:

h ÷ 7.5 = 3.2

Multiply both sides by 7.5

h = 3.2 × 7.5

h = 24

The inverse of the given function is y = -1/5(x + 1).

The graph the function and its inverse is shown in the image attached below.

In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of this function f(x) = -1 - 1/5x, we would interchange both the input value (x) and output value (y) as follows:

y = -1 - 1/5x

x = -1 - 1/5y

Adding 1 to both sides of the function, we have:

x + 1 = -1/5y

Multiplying both sides of the function by -1/5, we have:

y = -1/5(x + 1)

The workers in shift B earns the bonus.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Mean is found by adding all the data values and then dividing with number of values in the set.

Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}

Number of data in shift A = 12

Mean = (77 + 91 + 82 + 68 + 75 + 72 + 85 + 65 + 70 + 79 + 94 + 86) / 12

         = 944 / 12

         = 78.67

Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}

Number of data in shift B = 12

Mean = (68 + 93 + 53 + 100 + 77 + 86 + 91 + 88 + 72 + 74 + 66 + 82) / 12

         = 950 / 12

         = 79.17

The workers in the shift with the highest mean will earn a bonus. It is shift B.

Hence the workers in shift B earn the bonus.

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The full question is as follows :

The following are daily outputs from shift A and shift B at a factory.

Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}

Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}

Q. Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?

The midpoint of the x-intercepts of f(x) = (x - 4)(x + 4) is (0, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

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Elizabeth has a box that can hold exactly 24 unit cubes. It could also be said that her box has 24 cubic units. So, option D. is correct.

A cubic unit is a unit of measurement for volume. It represents the amount of space an object occupies in three dimensions: Length, Width and Height. It is often used to measure the volume of three-dimensional shapes such as cubes, square prisms, cylinders, and spheres. Cubic units are most commonly measured in cubic meters or cubic feet, but they can also be expressed in smaller units such as cubic centimeters or cubic inches.

The total volume of the box is 24 cubic units. A side of the box may measure 2 units x 3 units x 4 units = 24 cubic units.

Choice A is incorrect. This is because the area of ​​a shape is a measure of the two-dimensional space it occupies, and the volume of a shape is a measure of the three-dimensional space it occupies.

Choice B is incorrect. This is because the area of ​​a shape is a measurement of the two-dimensional space it occupies, not its volume.

Option C is incorrect because it states that the box has a volume of 12 cubic units, but it is not because the volume he has is 24 cubic units.

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Corresponding angle pairs - (1,5) , (2,6) , (3,7) and (4,8)

Constant or Zero polynomial, Linear polynomial, Quadratic polynomial, Cubic polynomial, and Quartic polynomial are the five kinds of polynomials.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials may be located. Expressions with additional operations are considered non-polynomial expressions.

Constant Polynomial Function: P(x) = a = ax.

Zero Polynomial Function: P(x) = 0; where all ai's are zero, i = 0, 1, 2, 3, …, n.

Linear Polynomial Function: P(x) = ax + b.

Quadratic Polynomial Function: P(x) = ax2+bx+c.

Cubic Polynomial Function: ax3+bx2+cx+d.

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7x and 7x2 are NOT like terms.

Terms with identical variables (like x or y) and any exponents (like the 2 in x2). Similar phrases can be combined. Similar or like terms are those that only differ in numerical coefficient but have the same literal coefficients raised to the same powers. Related terms are those that have the same exponent applied to similar variables. Dissimilar or unlike terms are those that do not have the same literal coefficients raised to the same powers. Only the numerical coefficients can change in terms similar to those of algebra.

However, because to the various exponents, 7x and 7x2 are NOT similar expressions.

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The function increases on [0,∞] and decreases on [-∞,0]. The absolute minimum value of f is 0, and its relative minimum value is the same (0,0).

When x<  0, you can see on the graph that there is a "open circle" at (0, 0).

Thus, due to the graph's indefinitely high y values, there is likewise no absolute maximum value for f.

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