assuming that no one is born on feb. 29 (leap day), how many people should be selected to guarantee that at least 7 were born on the same day, not considering the year?

Answer:

-1/-3 s the slope

Step-by-step explanation:

(7,-1) and (6,-4)

-4-(-1)=-3

6-7=-1

so -1/-3 is the slope

The area of the figure made up of a semicircle and a triangle is 63.25 ft²

An equation is a mathematical expression that contains two or more numbers and variables linked together by mathematical operations such as exponents, multiplication, division, addition, subtraction and so on.

The figure is made up of a semicircle and a triangle.

The semicircle has a diameter of 10 feet. Hence:

Area of semicircle = (1/2) * π * diameter²/4

Substituting:

Area of semicircle = (1/2) * π * 10²/4 = 39.25 ft²

The triangle has a base of 8 ft and height of 6 ft. hence:

Area of triangle = (1/2) * base * height

Substituting:

Area of triangle = (1/2) * 8 ft * 6 ft = 24 ft²

The area of the figure = Area of triangle + Area of semicircle

Area of figure = 24 ft² + 39.25 ft² = 63.25 ft²

The area of the figure is 63.25 ft²

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The commission earned on the sale of $1253.70 is $233.20

A fee paid to an agent or employee for transacting a piece of business or performing a service is called commission.

Given that, there is a commission of 18.6% on the sale of $1253.70

Therefore,

The commission earned = 1253.70 × 18.6%

= 1253.70 × 18.6 / 100

= 233.20

Hence, the commission earned on the sale of $1253.70 is $233.20

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Porosity calculated as ratio of pore to total vol. Plot of porosity vs averaging length scale (edge of square used for averaging). Rep. elemental vol = vol of square used for averaging.

The porosity as a function of the averaging length scale can be calculated as follows:

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True , Every matrix transformation is a linear transformation.

Is there a linear transformation for every matrix operation?

Despite the fact that every linear transformation is a matrix transformation, not all linear transformations are matrix transformations.      

                                    Because of this, it's possible that we'll encounter a linear transformation in which we're unable to locate a matrix to carry out the mapping.

What alteration does matrix entail?

In a two-dimensional or three-dimensional space, the transformation matrix converts one vector into another vector, which may be comprehended geometrically.

                                    Stretching, squeezing, rotation, reflection, and orthogonal projection are some of the often utilized transformations.

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The values are evaluated to give;

1. 11p + 4q

2. -12a + 8

An algebraic expression is an expression that is composed of terms, coefficients, variables, factors and constants.

From the information given, we have that;

3p +5(2q+p)+3p-6q

expand the bracket, we get;

3p + 10q + 5p + 3p - 6q

collect and add the like terms

11p + 4q

Then,

Z+8-6(z-2a)+5z

expand the bracket

z + 8 - 6z - 12a + 5z

collect and add the like terms

-12a + 8

Hence, the expression are 11p + 4q and -12a + 8

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The solution of the system of equation is , x= -4 & y= -8.

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

here, we have,

from the given graph we get,

one line is passing through the points (0,10) , ( 4,28)

so, the equation of the line can be,

4y= 18x + 40

and, second line is passing through the points (0,8) , (1,12)

so, the equation of the line can be,

y= 4x+8

solving the equations we get,

x= -4

y= -8

Hence, The solution of the system of equation is , x= -4 & y= -8.

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Simplified expression for the amount is 5(36+23m) .

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Step 1: Form an equation for the amount of money Troy has received after m months.

If the total months that Troy's grandfather has given him money is m, then the number of months that Troy's mother has given him money is m - 3.

⇒ Total amount in account = 300 + 75m + 40(m - 3)

                                             = 300 + 75m + 40m-120

                                             =180 + 115m

                                            =5(36+23m)

Hence, Simplified expression for the amount is 5(36+23m) .

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The total volume of the ice cream is -4.76 cubic inches.

The volume of the frustum of a cone can be calculated as follows:

V = (1/3) × π × h × (r1² + r2² + r1 × r2), where r1 and r2 are the radii of the top and bottom base of the cone.

And the volume of a sphere can be calculated as follows:

V = (4/3) × π × r³, where r is the radius of the sphere.

To calculate the total volume of the ice cream, we need to subtract the volume of the cone from the volume of the sphere.

Let's first calculate the radii of the top and bottom base of the cone.

r1 = (di/2) = (1.25/2) = 0.625 in.

r2 = (d0/2) = (2.25/2) = 1.125 in.

Now, we can estimate the volume of the cone.

V_cone = (1/3) × π × h × (r1² + r2² + r1 × r2)

= (1/3) × π × 2 × (0.625² + 1.125² + 0.625 × 1.125)

= 6.45 cubic inches.

Next, let's calculate the radius of the sphere.

r_sphere = (di/2) = (1.25/2) = 0.625 in.

And finally, we can calculate the volume of the sphere.

V_sphere = (4/3) × π × 0.625³

= 1.69 cubic inches.

So, the total volume of the ice cream is given by:

V_ice_cream = V_sphere - V_cone

= 1.69 - 6.45

= -4.76 cubic inches.

Note: Since the volume of the cone is larger than the volume of the sphere, the total volume of the ice cream will be negative, indicating that it is not possible to fill a frustum of a cone with ice cream in the manner described.

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--The given question is incomplete; the complete question is

"A frustum of a cone is filled with ice cream such that the portion above the cone is a hemisphere. Define the variables di=1.25 in., d0=2.25 in., h=2 in., and determine the volume of the ice cream."--

The value of the variable, x is 45 degrees

We have that the polygon is one with eight sides, that is, it is a regular octagon.

To determine the interior angle, we have

(n - 2) 180

n is the number of sides

(8-2)180

1080 degrees

Now, divide it by the number of sides

1080/8 = 135 degrees

Note that angles on a straight line is equal to 180

Then,

x + 135 = 180

Collect like terms

x = 180 -135

subtract the values

x = 45 degrees

Hence, the value is 45 degrees

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Answer:

y = 10

Step-by-step explanation:

[tex]\displaystyle \frac{6+9+18}{3}=\frac{12+y}{2}\\ \\\frac{33}{3}=\frac{12+y}{2}\\ \\11=\frac{12+y}{2}\\ \\22=12+y\\\\10=y[/tex]

3

6+9+18

=

2

12+y

3

33

=

2

12+y

11=

2

12+y

22=12+y

10=y

answer: 10=y

x>-4 is the solution of the inequality -8x < 32

A relationship between two expressions or values that are not equal to each other is called 'inequality.

The given inequality is -8x < 32

Minus eight times of x less than thirty two.

We need to solve for x which is a variable.

Divide both sides by 8

-x<4

x>-4

Hence, x>-4 is the solution of the inequality -8x < 32

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The sector area for the figure below is 268.19.

The quantity of space included within the sector's perimeter is referred to as the sector's area in a circle. A sector always starts at the circle's center. The area of a circle encompassed between its two radii and the arc next to them is known as the sector of a circle. The sector of a circle that most often symbolizes half of a circle is a semicircle.

The area of sector is given by the formula:

A = (pi)r² × α/360

where, r is the radius and α is the angle of the sector.

Substituting the value of r and α in the formula we have:

A = pi (16)² × 120/ 360

A = 268.19

Hence, the sector area for the figure below is 268.19.

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The required sum of the given partial sequence is 33525.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
The sum of the partial sequence.
[tex]= \sum_{n=1}^{75}12n - 9[/tex]

[tex]= \sum_{n=1}^{75}12n - \sum_{n=1}^{75} 9\\= 34200-675\\=33525[/tex]

Thus, The required sum of the given partial sequence is 33525.

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5 triangles could be formed from the polygon pictured.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The given figure is an irregular heptagon (7 unequal sides).

Now,

Taking a common vertex A we can draw the triangles as given below.

We see that,

There are 5 triangles that can be drawn.

Thus,

5 triangles can be formed.

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

The graph

On the graph, we have

x = dozen

y = cookies

This means that

(3, 36) means 3 dozens required 36 cookies

What ordered pair describes the unit rate?

Using the ordered pair in (a):

The unit rate of the pair (3, 36) is 36/3 = 12.

This means that for every 1 dozen change, there is a corresponding 12 cookies change

Step-by-step explanation:

The set of points for which y is a function of x is given as follows:

B.

A relation represents a function when each input value is mapped to a single output value.

For set B in the context of this problem, we have that:

As there are no repeated inputs, this is the set that represents y as a function of x.

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The correct option regarding the addition of vectors t and v is given as follows:

A. <-1, -11>.

The standard notation of a vector is given as follows:

<x,y>.

In which:

To add two vectors, we add the elements at the same component.

Then the addition of vectors t and v is given as follows:

t + v = <2, -10> + <-3, - 1> = <2 - 3, -10 -1> = <-1, -11>.

From the result obtained above, the correct option in the context of this problem is given by option A.

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When there are an even number of observations, and the observations are in order from smallest to largest, the median is:The average of the two middle observations.

The median is a measure of central tendency that is commonly used for data sets with an odd number of observations. When there are an even number of observations, the median is defined as the average of the two middle observations. This provides a representative value that splits the data set in half, with half of the observations having values lower than the median, and half having values higher.

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The probability that the car selected was a domestic car and older than 2 years is 0.63 or 63%.

Probability is a mathematical concept that quantifies the likelihood or chance of an event occurring. It is a value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In between, probabilities reflect the degree of certainty that an event will occur, with values closer to 1 indicating a higher likelihood of occurrence and values closer to 0 indicating a lower likelihood.

The probability of an event is calculated by taking the ratio of the number of favorable outcomes to the total number of possible outcomes.

domestic car older than 2 years/total domestic cars = (28 + 12 + 23)/100 = 63/100 = 0.63 = 63%

Therefore, the probability of selecting a car that is less than 2 year given that it is a domestic car is 0.63 or 63%.

*The problem seems incomplete, attached might be the complete version of it.

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Answer:

Step-by-step explanation:

OK YOU ARE GOOD OH AND IT

5/8

The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

y = a (1 ± r)ˣ

The rate is 6% for 20 years semiannually. Then the rate is given as,

r = 0.06 / 2

r = 0.03

Then the time is given as,

x = 20 (2)

x = 40

Then the exponential function is given as,

A = $2000 × (1 + 0.03)⁴⁰

A = $2000 × (1.03)⁴⁰

A = $2000 × 3.262

A = $6524.1

The exponential function is A = $2000 × (1 + .03)⁴⁰ and the amount is $6524.1.

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Answer:

see below

Step-by-step explanation:

Susan

4lbs of coffee

2lbs of nuts

Tom

2lbs of coffee

4lbs of nuts

6 hrs per day.

if only coffee x = (4+2)*6=36lbs

if only nuts y = (4+2)*6=36lbs

The number of atoms in the compound will be 54 atoms.

Chemistry's fundamental building block is an atom. It is the smallest fraction of matter into which electrically charged particles cannot be released. It is also the smallest piece of substance with chemical element-like characteristics.

The number of atoms in 2 Sr3(PO4)2 can be determined by counting the number of each type of atom present in the compound. In 2 Sr3(PO4)2, there are:

2 x 3 = 6 Sr atoms

2 x 2 x 4 = 16 P atoms

2 x 2 x 8 = 32 O atoms

So, there are a total of 6 + 16 + 32 = 54 atoms in 2 Sr3(PO4)2.

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The number  300 can be written as 300/1 as a quotient of integers to show that it is rational.

A rational number is a number of the form p/q, where q not equal to 0 and p  and q must be co-primes.

To write a number in the form of quotient of integer, we write it as , where p/q.

Here,  300 can be written as  300/1 or 600/2 .

But we should also take care that p and q must be co-primes.

Co-primes are the pairs of numbers that have only one common factor which is 1.

So, 300 can be written as 300/1

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Answer:

Here you have

Step-by-step explanation:

8 x 7 x 6 = 336 cm²

The rationalized surds are;

1) 20 + 5√3/13

2) 12√7 - 24/7

3) 6√2  + 6√3/5

The surd has to do with an irrational number. In this case we are asked to find the value of the following surds.

1) The conjugate of the denominator is; 4 + √3 and the rationalize we have;

5/4 - √3 * 4 + √3/4 + √3

20 + 5√3/16 + 4√3 - 4√3 - 3

20 + 5√3/13

2) The conjugate of the denominator is; √7 - 2

To rationalize we have;

12/√7 + 2 * √7 - 2/√7 - 2

12√7 - 24/7 -2√7 + 2√7

12√7 - 24/7

3) The conjugate of the denominator is √2 + √3

To rationalize we have;

6/√2 - √3 * √2 + √3/√2 + √3

6√2  + 6√3/2 + √6 - √6 + 3

6√2  + 6√3/5

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The model used by Victor in the linear equation is incorrect,

The parameters are that;

Victor saved: $89.25

Cost of the bicycle = $129.85

Thus, to find the amount extra that he will need to purchase the bicycle, the equation model should be;

$89.25 + x = $129.85

This can be expressed in words as;

The amount of money he already has saved + the amount of money he still requires = the total price of the bike.

An equation that correctly represents this problem can show the sum of the amount of money he already has and the amount of money he needs equals the total cost of the bicycle

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Complete question is;

Victor has saved $89.25 for the bicycle that he wants. The bicycle costs $129.85. Victor writes the equation below to help him determine the additional amount that he needs to solve to have enough to buy the bicycle.

89.25 + 129.85 = x

Does Victor's equation correctly model the problem?

The distance between the third base and the player is 150 feet.

Pythagoras' theorem states that “In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base, and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle of 90°. The sides of a right triangle (say a, b, and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.

In the diagram attached, we can see the locations of the 1st base, 2nd base, 3rd base, and Home plate.

Since these four points form a square of which diagonals are equal in size.

So if we find the distance between the 1st and 3rd base that will be equal to the distance between the Home plate to the second base.

To find the nearest distance,

By applying "Pythagoras' Theorem"

[tex]nearest \ distance =\sqrt{120^2+90^2}\\\\=\sqrt{22500}\\\\=150\ feet.[/tex]

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The line representing the equation part of the constraint 7x1 + 4x2 28 goes through the following two points e. none of the above.

The equation of a line can be represented as y = mx + b, where m is the slope of the line and b is the y-intercept. The line representing the equation of a constraint, such as 7x1 + 4x2 = 28, would be a straight line in a two-dimensional graph.

The points given in the options a, b, c, and d are pairs of x and y coordinates. To determine if any of these points lie on the line representing the constraint equation, we would need to substitute the x and y values into the equation and see if the equality holds.

For example, for option a, if we substitute x = 4 and y = 0 into the equation, we get 7 * 4 + 4 * 0 = 28, which is not true. Hence, none of the given points in the options lie on the line representing the constraint equation.

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