2. There are 367 students in a class. If two students are chosen at random, what is the probability in percentage that the two students will shared the same birthday​

The answer is Option B :)

The function that represents the graph is  [tex]f(x)=\frac{1}{x-2}[/tex].

Option B

Given :

The graph of the function

Step-by-step explanation:

From the given graph , the vertical asymptote is at x=2

Lets find out the vertical asymptote of each function

To find out vertical asymptote we set the denominator =0

[tex]f(x)=\frac{1}{2x} \\2x=0\\x=0 \\\\\\f(x)=\frac{1}{x-2} \\x-2=0\\x=2[/tex]

The second function has vertical asymptote at x=2

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Answer:

If they are opposite.

Answer:

x = 9

Step-by-step explanation:

-2x = 18 - 4x

-2x + 4x = 18

2x = 18

x = 18/2

x = 9

Answer:

x=9

Step-by-step explanation:

-2x = 18 -4x

+4x        +4x

2x  = 18

÷2    ÷2

x=9

Hey there! :)

Answer:

Choice 3: David's equation is correct because their spending will be multiplied by the number of months and then subtracted from their savings.

Step-by-step explanation:

In the question, $12,350 is given as the initial value and '240x' is the monthly spending in terms of x.. When writing the equation, we must subtract 240x because the money is being spent.

The correct equation for this situation would be:

y = 12,350 - (240x).

Thus, David's Equation is correct.

answer: the denominator of the improper fraction is the sum of the numerator and the product of denominator and the whole number of the mixed fraction.

Answer:

It is the same denominator of the fraction.

Step-by-step explanation:

[tex]1\frac{1}{5} = \frac{x}{y}[/tex]

[tex]1\frac{1}{5} = \\1=\frac{5}{5}\\\frac{1}{5} = \frac{1}{5}\\\frac{5}{5} +\frac{1}{5} =\frac{6}{5}[/tex]

Answer:

Here You Go! I'm not really sure about this one but i tried.

Step-by-step explanation:

Answer:

Step-by-step explanation:

To prove this we should first make a little representation to get an idea of how will proceed to work .

To solve it we should use vectors so the first step is to identify this vectors :

NOW LET'S IDENTIFY THEIR COORDINATES :

We get :

We notice that the opposite ones have the same coordinates so the edges are parallel .

If we want to check more we can calculate the lenghts :

So AB=DC

So AD=BC

SO ABCD IS A PARALLELOGRAM

Answer:

50 %

Step-by-step explanation:

Answer:

57°

Step-by-step explanation:

Δ AOB has 2 equal sides as radius of the circle, this is isosceles triangle

So the angles ∠OAB= ∠OBA

∠AOB= 66° and sum of 3 angles = 180°

So  ∠OAB= (180° - 66°)/2= 57°

Answer:

solution,

Area of trapezoid:

[tex] \frac{a + b}{2} \times h \\ = \frac{2 + 4}{2} \times 2 \\ = \frac{6}{2} \times 2 \\ = 6 \: {units}^{2} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

2.5 gallons

Step-by-step explanation:

Quarts of juice Mary bought = 10 quarts

1 quart = 0.25 gallons

10 quarts = 0.25×10 = 2.5 gallons

Therefore she bought 2.5 gallons

Hope this helps : ) . Have a nice day !

Answer:

12 3/5

Step-by-step explanation:

Distributive property is when you take a number for example 3 and multiple all of the numbers inside the () in this case 4 1/5

1. multiple 3 by 4 =12

2 multiple3 by 1/5= 3/5

3 write your awnser 4 3/5

Hoped this helped

Answer:

The average speed on this trip was 46.15 mph. The correct option is A.

Step-by-step explanation:

In order to calculate the average speed, we need to apply the following formula:

[tex]v_{avg} = \frac{\text{distance}}{\text{time}}[/tex]

We were given the distance between the two cities in miles, therefore we can directly apply it to the expression. Although the time was given in the hh:mm 12 h format and we need a diference in hours, so we will convert that as shown below:

[tex]\text{time departure} = 9 + \frac{50}{60} = 9.83 \text{ h}[/tex]

[tex]\text{time arrival} = 12 + 5 + \frac{30}{60} = 17.5[/tex]

The elapsed time of the trip is the difference between these:

[tex]\text{time} = 17.5 - 9.83 = 7.67 \text{ h}[/tex]

We can now apply it to the formula:

[tex]v_{avg} = \frac{354}{7.67} = 46.15 \text{ mph}[/tex]

The average speed on this trip was 46.15 mph. The correct option is A.

Answer:

The statement is true

Step-by-step explanation:

We have been given an equation of hyperbola

In the given equation of hyperbola center is located at h at -1 and k at 2. so:

C:(h,k) = (-1,2)

Coordinated of the foci of the hyperbola are given as:

Foci: (h, k ± c)

Substitute the values of h and k into the coordinated of foci of hyperbola.

Foci: (-1, 2 ± c)

Where c can be found by using the given formula

c = √(a²+b²)

c = √(16+144)

c = 4√10

So the the coordinates of the foci are:

Foci: (-1, 2 - 4√10) and (-1, 2 + 4√10)

Thus, the statement given is true

Answer:

1/2

Step-by-step explanation:

cuz it must be between 0 to 1 and 1/2 was in the middle so yet

The fraction number represents the position of the point on the number line will be 4/8.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The number line is shown. There are eight sections in the number between the numbers 0 and 1.

And the point is on the fourth section of the number line. Then the position of the point on a number line is given in the numerical form and will be calculated as,

⇒ 4 / 8

The fraction number represents the position of the point on the number line will be 4/8.

More about the number line link is given below.

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Answer:

B. -0.2 And 0.5

step-by-step explanation:

I used the graphing calculator on google :)

The solution to the equation using the graphing calculator is –0.2 and 0.5.

The equation is given as

0 = 5x2 – 1.5x – 0.5

Using the graphing calculator we are to find the values of X1 and X2 using these values

A1 = 5

B1 = -1.5

C1 = -0.5

The resulting output would be X1 = -0.2. X2 = 0.5

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Step-by-step explanation:

2x+3y=-14------equation i ×1

3x+y=-14--------equation ii ×3

2x+3y=-14

9x+3y=-42

-7x =- 28

x=4

Substitute for x in equation ii

3x+y= -14

3(4)+y=-14

12+y=-14

y=-14-12

y=- 26

Answer:

12

Step-by-step explanation:

because the more the root the faster the plant grows

Answer:

70.257924 m^2

Step-by-step explanation:

Answer:

13<x<39 (range of hours)

Step-by-step explanation:

2<x<6 (x is the range of days)

Since each workday is 6.5 hours, multiply everything by 6.5:

13<x<39 (the new x is the range of hours)

Answer:

Step-by-step explanation:

a.  

L

=

329.9

c

m

2

;

S

=

373.9

c

m

2

.

b.  

L

=

659.7

c

m

2

;

S

=

483.8

c

m

2

.

c.  

L

=

659.7

c

m

2

;

S

=

813.6

c

m

2

.

d.  

L

=

329.9

c

m

2

;

S

=

483.8

c

m

2

.

Surface Area of a Cone:

In the three dimensional geometry, a cone is a shape that has a circular base and a lateral surface is associated with a vertex and the base.

The height of the cone is the length of a line segment that joins the base to the vertex of the cone.

The radius of the cone is the same as the radius of the base.

Surface area of a cone

(a) Lateral Surface Area

If  

l

and  

r

are the slant height and radius of a cone then its lateral surface area is given by the formula-

L

=

π

r

l

where  

L

is the lateral surface area of the cone

(b) Total surface area

It is the sum of the area of the circular base and the lateral surface area of the cone.

S

=

L

+

π

r

2

S

=

π

r

l

+

π

r

2

Where  

S

is the total surface area of the cone

Answer and Explanation:

Given that the radius and slant height of a right cone is  

7

c

m

and  

15

c

m

respectively

r

=

7

c

m

l

=

15

c

m

So the lateral surface area of the cone-

L

=

π

r

l

L

=

π

(

7

)

(

15

)

L

=

105

π

L

=

105

(

3.14159

)

L

=

329.866

L

≈

329.9

c

m

2

And the total surface area of the cone-

S

=

L

+

π

r

2

S

=

329.9

+

π

(

7

)

2

S

=

329.9

+

49

(

3.14159

)

S

=

329.9

+

153.937

S

=

483.83

c

m

2

So the lateral area and total area of a right cone are  

329.9

c

m

2

and  

483.8

c

m

2

respectively.

Answer:

Step-by-step explanation:

Step-by-step explanation:

a.  

L

=

329.9

c

m

2

;

S

=

373.9

c

m

2

.

b.  

L

=

659.7

c

m

2

;

S

=

483.8

c

m

2

.

c.  

L

=

659.7

c

m

2

;

S

=

813.6

c

m

2

.

d.  

L

=

329.9

c

m

2

;

S

=

483.8

c

m

2

.

Surface Area of a Cone:

In the three dimensional geometry, a cone is a shape that has a circular base and a lateral surface is associated with a vertex and the base.

The height of the cone is the length of a line segment that joins the base to the vertex of the cone.

The radius of the cone is the same as the radius of the base.

Surface area of a cone

(a) Lateral Surface Area

If  

l

and  

r

are the slant height and radius of a cone then its lateral surface area is given by the formula-

L

=

π

r

l

where  

L

is the lateral surface area of the cone

(b) Total surface area

It is the sum of the area of the circular base and the lateral surface area of the cone.

S

=

L

+

π

r

2

S

=

π

r

l

+

π

r

2

Where  

S

is the total surface area of the cone

Answer and Explanation:

Given that the radius and slant height of a right cone is  

7

c

m

and  

15

c

m

respectively

r

=

7

c

m

l

=

15

c

m

So the lateral surface area of the cone-

L

=

π

r

l

L

=

π

(

7

)

(

15

)

L

=

105

π

L

=

105

(

3.14159

)

L

=

329.866

L

≈

329.9

c

m

2

And the total surface area of the cone-

S

=

L

+

π

r

2

S

=

329.9

+

π

(

7

)

2

S

=

329.9

+

49

(

3.14159

)

S

=

329.9

+

153.937

S

=

483.83

c

m

2

So the lateral area and total area of a right cone are  

329.9

c

m

2

and  

483.8

c

m

2

respectively.

Answer:

d

Step-by-step explanation:

d

a) a as a column vector is [tex]\left(\begin{array}{c}1\\-2\end{array}\right)[/tex]

b) 2a -b as a column vector is [tex]\left(\begin{array}{c}1\\-7\end{array}\right)[/tex]

To write a vector as a column vector, the number at the top is the magnitude of the x component (horizontal component) of the vector and the number at the bottom is the magnitude of the y component (vertical component) of the vector

Magnitude of the vertical component = 1

Magnitude of the vertical component = -2

NOTE: Negative sign indicates that the direction of the vector is downwards

Thus, vector a as a column vector is

[tex]a = \left(\begin{array}{c}1\\-2\end{array}\right)[/tex]

Hence, a as a column vector is [tex]\left(\begin{array}{c}1\\-2\end{array}\right)[/tex]

Magnitude of the vertical component = 1

Magnitude of the vertical component = 3

[tex]b = \left(\begin{array}{c}1\\3\end{array}\right)[/tex]

Now, we are to work out 2a - b

That is,

[tex]2a -b = 2 \left(\begin{array}{c}1\\-2\end{array}\right)-\left(\begin{array}{c}1\\3\end{array}\right)[/tex]

[tex]2a -b = \left(\begin{array}{c}2\\-4\end{array}\right)-\left(\begin{array}{c}1\\3\end{array}\right)[/tex]

[tex]2a -b = \left(\begin{array}{c}2-1\\-4-3\end{array}\right)[/tex]

[tex]2a -b = \left(\begin{array}{c}1\\-7\end{array}\right)[/tex]

Hence, 2a -b as a column vector is [tex]\left(\begin{array}{c}1\\-7\end{array}\right)[/tex]

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Answer:

a) 90°

b) 56°

Step-by-step explanation:

If we connect O with B to get two isosceles triangles: ΔAOB and ΔBOC

∠BOC= is central angle ans is twice as ∠BAC, so equals to 2*34°= 68°

Then ∠BCA= (180°- 68°)/2= 56°

∠ABC= ∠ABO+∠CBO= 34°+56°= 90°

Answer:

True, this is a function

Step-by-step explanation:

There is a 1 to one correspondence between x and y

Each x goes to one y, so this is a function

Answer:

1 & 2

Step-by-step explanation:

Remote interior angles are the angles inside of a triangle but not on the same straight line as the exterior angle (4)

Answer:

<1 and <2 are the remote interior angles for angle 4

Step-by-step explanation:

The remote interior angles that correspond to angle 4 are the angles that are in the triangle that are not adjacent to angle 4

<1 and <2 are the remote interior angles

Answer:

( a ) 463 " human resource professionals " believe that the appearance of a job applicant is most important for a good first impression

( b )  Percent wise the confidence interval should be from about 86.6% to 93.4%

Step-by-step explanation:

I believe these first two parts here is sufficient enough to get you started!

" In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression. Part A: Among the 514 human resource professionals who were surveyed, how many of them said that the appearance of a job applicant is most important for a good first impression?

Part B: Construct a 99% confidence interval estimate of the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression. "

_____

( a ) We are given that n = 514, and p = 90%. The number of human resource professionals that said that the appearance of a job applicant is most important for a good first impression, should be the following -

514 x [tex]\frac{90}{100}[/tex]

= [tex]\frac{46260}{100}[/tex]

= 462.6

As the count of people can't be expressed as a fraction, the solution should be about 463 " human resource professionals. "

_____

( b ) Here the confidence level is 0.99 percent. Knowing that -

1 - ∝ = 0.99,

∝ = 1 - 0.99... = 0.01

Therefore, a 99% confidence interval estimate of the proportion of all human resource professionals believing that the appearance of a job applicant is most important for a good first impression should be calculated as directed in the attachment. By that the interval ranges as such -

0.8659 < p < 0.9341

And percent wise the confidence interval should be from about 86.6% to 93.4%

Answer: h(x) = 3*(1/6)^(x + 4)

Step-by-step explanation:

if we have a function g(x), and we want to create another function h(x) such that:

h(x) is a vertical contraction/dilation of factor a.

Then h(x) = a*g(x).

h(x) is a right shift of N units (N positive):

h(x) = g(x - N)

Then:

A vertical shink of factor 1/3 means that:

h(x) = (1/3)*g(x)

And a left shift of 4 units (or a right shift of -4 units) means that

h(x) = (1/3)g(x - (-4)) = (1/3)*g(x + 4)

and we know that:

g(x) = 9*(1/6)^x

Then:

h(x) = (1/3)*9*(1/6)^(x + 4) = 3*(1/6)^(x + 4)

Answer:

(2,1)

Step-by-step explanation:

The point (2,1) is the only point that is not included in the shaded region so I would assume that it's not a solution to the system.

Answer:

1. A = 2184 yd. P = 212 yd.

Step-by-step explanation:

1. To find the perimeter of an object you need to do this formula: 2L * 2W which is 2 times the length times 2 times the width.

To find the Area you have to do this formula: H * W which means height times width.

2. They would need the area to fill the rectangle since you need to fill it and the area is the inside of the rectangle

3. She will need the perimeter since she is walking around the field and the perimeter is the outside (around) the shape.