A survey of athletes at a high school is conducted, and the following facts are discovered: 28% of the athletes are football players, 25% are basketball players, and 24% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that they are either a football player or a basketball player

distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$

so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$

Answer:

Distance=17 units

Step-by-step explanation:

Coordinates of the origin: (0, 0)

Coordinates of the point in question: (-15, 8)

Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:

[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]

Answer:

y = -2x/3 + 531

Step-by-step explanation:

Answer: Angle Addition Postulate

Step-by-step explanation:

In the given picture, we have ∠MRO and ∠MRS on line SRO.

So, ∠SRO = ∠MRO +∠MRS  [By angle addition postulate]

So the postulate that justify the statement " ∠SRO = ∠MRO +∠MRS" is Angle Addition Postulate.

Answer:

Yes, we can.

Step-by-step explanation:

Hello, I found this one.

[tex]\displaystyle \sum_{n=0}^{\infty} \dfrac{1}{n!}[/tex]

We can prove that it exists and it is equal to e.

But this is nor arithmetic nor geometric.

Thank you

Answer:

H

Step-by-step explanation:

Answer:

5 ml of 50% syrup solution will be used to create the final solution

Step by step Explanation:

Let the amount of 50% solution that was used = b

Which means ( 30 - b ) is the amount of 1/200 solution used then we can derive an equation as follows,

set up will then be,

0.5b +0.05(30 -b) = 1/8 (30)

We can simplifiy this as

0.5b+ 1.5 -0.05b = 3.75

Then make b the subject of the formula we have

0.45b = 2.25

b= 2.25/0.45

b = 5 ml

Therefore, 5ml of 50% syrup solution will be used to create the final solution

Answer:

they can pick 27 berry's

Step-by-step explanation:

I think-

They can pick 1.29 liters of berries in 1 minute working together.

--------------------------------------------

The together rate is the sum of each separate rate. In this question:

--------------------------------------------

Together, they can pick x liters, and the rate is: [tex]\frac{1}{x}[/tex]

Then

[tex]\frac{1}{x} = \frac{3}{8} + \frac{4}{10}[/tex]

[tex]\frac{1}{x} = \frac{15 + 16}{40}[/tex]

[tex]\frac{1}{x} = \frac{31}{40}[/tex]

Applying cross multiplication:

[tex]31x = 40[/tex]

[tex]x = \frac{40}{31}[/tex]

[tex]x = 1.29[/tex]

They can pick 1.29 liters of berries in 1 minute working together.

A similar question is given at https://brainly.com/question/23323624

Answer:

11

Step-by-step explanation:

she divides the number of pencils equally

so the number of pencils per student is 152/13

which is 11.692...

but she can't give 0.69 of a pencil so she gives only the whole part 11

and she keeps 9 pencils

Answer:

71.2 km²

Step-by-step explanation:

Triangles: 1/2(8)(3.9)=15.6 (2 of them - front and back)

Base: 8x2=16

Side: 4x2=8

Slant:8x2=16

15.6+15.6+16+8+16=71.2

Answer:

x = 28

Step-by-step explanation:

12/x = 3/7

Using cross products

3x = 12*7

3x = 84

Divide by 3

x = 28

Answer:

b

Step-by-step explanation:

If a negative number times another number is positive, that means that the other number is also negative because multiplying two negative numbers gives you a positive number. Therefore, a - b must be negative. In order for the difference of two numbers to be negative, the number being subtracted must be bigger than the number it's being subtracted from. For example, in 2 - 7, 7 > 2 but 2 - 7 is negative, the same goes for 3 - 8, 4 - 10, etc. Therefore, b must be greater.

By reading the graph, we can say that the solution is nonviable because A. the percent filled cannot be negative B. the time cannot be negative.

Reading a graph means interpreting what information is being conveyed by the graph and getting meaningful insights from it.

Learn more about reading the graph here

https://brainly.com/question/24934767

#SPJ2

Answer:

less than or equal to it hope this helps you!

Answer:

x=6

Step-by-step explanation:

We know that point C is in the middle of point A and point B.

That means that when these two equations are added they should be equal to the length of AB which is 41.

5x+3x-7=41

add 7 to both sides

8x=48

divide both sides by 8.

x=6

ANSWER:

               It is C

NO EXPLANATION

Answer:

-0.65

Step-by-step explanation:

Step 1: Write out fraction

-13/20

Step 2: Evaluate fraction

-13/20 = -0.65

Answer: 6/7

Step-by-step explanation: Since the Greatest common factor of 84 and 98 is 14, you divide both sides of 84/98 by 14 to get 6/7

Answer:6/7

Step-by-step explanation:The greatest common factor of both numerator and denominator is 14.So if you divide 84 by 14 you will get 6 and if you divide 98 by 14 you get 7.

Answer:

Translation

Step-by-step explanation:

Translations move shapes without changing their side lengths or angles.

Answer:

translation(s)

Step-by-step explanation:

translation(s) mean that you move a shape but not change the lenghts and some,... stuff

Answer:

Step-by-step explanation:

The graph of function f(x)+2 is moved 2 units up compared to the graph of f(x).

It means the x-coordinate is the same and the y-coordinate of f(x)+2 is increased by adding 2 to y-coordinate of f(x).

-8 + 2 = -6

x = 21

y = 8

=========================================================

Explanation:

Since the y is giving you trouble, I recommend ignoring it for now. Luckily we don't need the y value at first.

Let's solve for x.

The two angles (10x-61) and (x+10) form a straight angle which is 180 degrees.

So,

(10x-61) + (x+10) = 180

10x-61 + x+10 = 180

11x - 51 = 180

11x-51+51 = 180+51 .... adding 51 to both sides

11x = 231

11x/11 = 231/11 .... dividing both sides by 11

x = 21

Since x = 21, the upper right angle (10x-61) is equal to

10x-61 = 10*21-61 = 210-61 = 149

-------------

We can now focus on the (18y+5) angle. This is set equal to 149 since vertical angles are congruent

18y+5 = 149

18y+5-5 = 149-5 ... subtracting 5 from both sides

18y = 144

18y/18 = 144/18 .... dividing both sides by 18

y = 8

--------------

Or we could add the angles (18y+5) and (x+10), set them equal to 180, and solve for y like that

(18y+5)+(x+10) = 180

18y+5 + x+10 = 180

18y+5+21+10 = 180 .... plug in x = 21

18y+36 = 180

18y+36-36 = 180-36 ... subtract 36 from both sides

18y = 144

18y/18 = 144/18 .... dividing both sides by 18

y = 8

We get the same result.

--------------

As a check, plugging y = 8 into 18y+5 should lead to 149

18y+5 = 18*8+5 = 144+5 = 149

This confirms the y value answer

Answer:

both angles are the same, so you can use it interchangeably in proving.

But i suggest you to mantain only one, because it's easier to understand and it looks better.

Answer:

a or b

Step-by-step explanation:

it just looks like b or a

H(t) = -4.9t^2 + 25t + 2

Height is a function of time

plug in 0, 1,2,3,4, and 5 to find the height at 0, 1,2,3,4, and 5 seconds.

at t = 0

H(0) = -4.9(0)^2+25(0) + 2 = 2 meters

Repeat for T=1,2,3,4 and 5

Notice the ball peaks around t = 3 seconds and starts to descend.  

H(1) = (-4.9)(1^2) + 25(1) + 2 = 22.1 meters

H(2) = (-4.9)(2^2)+25(2)+2=32.4 meters

H(3) = 32.9 meters

H(4) = 23.6 meters

H(5) = 4.5 meters

Answer: A.14x + 6; the answer is a polynomial

Step-by-step explanation:

Since all of the variables have integer exponents that are positive this is a polynomial.

Answer:

Answer:

The distance between the two train stations is 1728 km

Step-by-step explanation:

The speed of the bus = 54 km/h

The speed of the truck = 48 km/h

When the bus and truck meet again, the distance covered by the bus = 216 km more than he distance traveled by the truck

Let the distance between the two train stations = x

Let the location where they first meet be y from station A we have;

The location where they meet again = y - 216 km

Therefore, we have;

Location where they

The time for the truck and the bus to meet again = t

Therefore, 54 × t - 48 × t = 216 km

6·t = 216 km

t = 36 hours

Therefore, the time for the bus to travel x + 216 km = 36 hours

54 × 36 = 1944 = x + 216

x = 1944 - 216 = 1728 km

The distance between the two train stations = 1728 km.

Answer:

y= -2x^2 + 12x -14

Step-by-step explanation:

when I put the points into a graphing calculator this is what I got so I think the answer is -2

Answer:

Step-by-step explanation:

It is -2

Answer:    The x intercept for Line A is 2  and the x-intercept for line B is -6.

Step-by-step explanation:

Line A uses the equation   y = -1/2x + 1   and to find the x intercept y has to be zero so set the equation equal  0 and solve for x.

0 = -1/2x + 1       Subtract one from both sides

- 1               -1  

-1 = -1/2x              divide both sides by -1/2

x = 2    

So the x intercept for A is   2  

For Line B it already indicates the  x intercept because that is when y is 0. So when  y  is  0  then x is -6.

Answer:

Vertex =(5,7)

Latus rectum = 2

Step-by-step explanation:

The general equation of a parabola can be expressed as x = a(y-h)²+k where 'a' is a constant and (h,k) is the vertex of the parabola.

Comparing the general equation with the given equation x= 1/2(y - 5)² + 7, it can be seen that a = 1/2, h = 5 and k = 7. Hence the vertex of the equation is (5,7) on comparison.

The length of the latus rectum of a parabola is 4a

On comparing the equation with the general equation, a = 1/2

Length of the latus rectum = 4(1/2)

Length of the latus rectum = 4/2 = 2

Hence the vertex is (5,7) and the length of latus rectum is 2

Answer:

360°

Step-by-step explanation:

The figure is irregular which means it must be completely rotated to have matching sides and vertices. A full rotation is equal to 360°.

Answer:

10

Step-by-step explanation:

-3 = 7 - x

Add x to both sides

x -3 = 7 - x +x

x - 3 = 7

Now, add 3 to both sides

x - 3 + 3 = 7 + 3

x = 10

Answer:

[tex]\boxed{10}[/tex]

Step-by-step explanation:

[tex]-3=7- \sf BLANK[/tex]

[tex]\sf Subtract \ 7 \ from \ sides.[/tex]

[tex]-3-7=-7+7- \sf BLANK[/tex]

[tex]-10=- \sf BLANK[/tex]

[tex]\sf Multiply \ both \ sides \ by \ -1.[/tex]

[tex]-10(-1)=(-1)- \sf BLANK[/tex]

[tex]10= \sf BLANK[/tex]