Suppose that among the 6,000 students at a high school, 1,500 are taking honors courses and 1,800 prefer watching basketball to watching football. If 450 students are both taking honors courses and prefer basketball to football, are the events "taking honors courses" and "preferring basketball" independent? No, because StartFraction 1500 Over 6000 EndFraction not-equals StartFraction 1800 Over 6000 EndFraction Yes, because StartFraction 450 Over 1500 EndFraction not-equals StartFraction 450 Over 1800 EndFraction No, because (1,500)(1,800) ≠ 450. Yes, because (StartFraction 1500 Over 6000 EndFraction) (StartFraction 1800 Over 6000 EndFraction) = StartFraction 450 Over 6000 EndFraction.

Answer:

Step-by-step explanation:

Given the amount to keep one adult in a day to be x

Since 7 days = 1 week

Amount it will take to keep one adult for a week will be 7x

one adult = 7x pounds

To get the expression that show how much it costs per week to keep the 8 adults, we will say;

8 adults = y pounds

where y is the required amount

Solving both expressions

one adult = 7x pounds

8 adults = y pounds

Cross multiply

1 * y = 7x * 8

y = 56x

Hence the required expression is y = 56x

Answer:

Step-by-step explanation:

Think of the equation y = mx + b

So the m is the slope and the b is the y-intercept

m/slope= 3 b/y-intercept= -1

Answer:

7 thousandths as a decimal is 0.007

Step-by-step explanation:

The part where "ths" means a decimal. So we put 3 zeros, because a thousand also has 3 zeroes. 7 thousandths as a decimal is 0.007

Hope this helps

Mark me brainliest please :D

Answer:

DFBG

Step-by-step explanation:

At any point in time;

slope m = (y2-y1)/(x2-x1)

1. (3,19) and ((-1,-13)

m = (-13-19)/-1-3 = -32/-4 = 8

Letter here is D

2. we pick out two points to use here from the line

These are ((0,1) and (2,5)

Slope is ;

(5-1)/2-0 = 4/2 = 2

Letter here is F

3. We pick any two points

(1,-8) and (4,-32)

slope =

(-32 + 8)/4-1 = -24/3 = -8

Letter here is B

4. Slope = 8 + 10/0-9 = 18/-9 = -2

letter here is G

Answer:

x = 0

Step-by-step explanation:

In order to solve for x, first combine both fractions on the left

To add 4x-2/8 + 3+x/4 first find the least common denominator of 8 and 4

It's 8 so multiply the numerator and denominator of 3+x/4 by 8, you would get:

8x+24/32

Multiply 4x-2/8 by 4, you will get:

16x-8/32

Now you can add 16x-8/32 + 8x+24/32, you would get:

24x+16/32

Now you can start to solve for x

Your new equation is 24x+16/32 = 1/2

To solve for x, first multiply diagonally, then solve like a regular equation.

Multiply 24x+16 by 2 to get 48x+32

Then multiply 32 by 1 to get 32

Your new equation is 48x+32=32

Now subtract 32 by 32 to get 48x=0

Now divide 48 by 0 to get x=0

Answer:

you can buy 9 poundssss

Answer:

25,000,000

Step-by-step explanation:

5*5=25 and add the 6 zeros

please give thanks :)

Answer:

well for me

Step-by-step explanation:

I think

=25000000

Answer:

$37.50

Step-by-step explanation:

Sale = $50.00 x 25% = $12.50

=> The coat after the discount = $50.00 - $12.50 = $37.50

$37.50

Step-by-step explanation:

Sale = $50.00 x 25% = $12.50

=> The coat after the discount = $50.00 - $12.50 = $37.50

Answer:

any number greater than 5 (so 6 and 8)

Step-by-step explanation:

since the expression on the left is supposed to be greater than 7, 5 cant be an answer because that will equal to 7. Therefore any number greater than 5 will work.

Answer:

B 4.8 inches

Step-by-step explanation:

The scale factors are used to convert a figure into another one with similar characteristics but different lengths, in this example is a triangle, and in order to calculate the measure of the height you just have to multiply the original height by the scale factor:

Answer:

x = 13

Step-by-step explanation:

Find the diagram attached

From the diagram, the sum of angle of the straight line BCD is 180°. Hence;

<BCE+<ECF<90 = 180

<BCE+64+90=180

<BCE+154 = 180

<BCE = 180-154

<BCE = 26°

Next is to get x.

The sum of interior angles <BCE and <BEC is equal to exterior angle <ABE

<BCE + <BEC = <ABE

26+x = 3x

Collect like terms

26 =3x-x

26=2x

x = 26/2

x = 13

Hence the value of x is 13

Answer:

-3/2x +2

Step-by-step explanation:

To find slope: y value - y value over x value - x value

5-(-4) = 9

-2 -4 = -6

9/-6 = -3/2 after you divide each by gcf of 3

y intercept : plug in your y and x values (and your slope ) into the equation: y = mx+b (slope intercept form)

point 1 (-2,5): 5 = (-3/2)(-2)+b

                     5 = 3+b (subtract 3 from both sides)

                      2 = b (your y intercept)

Answer: y=[tex]\frac{-3}{2}[/tex]x+2

Step-by-step explanation:

1. Find the slope of the two coordinates by using the slope-intercept form:

    Slope intercept form=(y₂-y₁)/(x₂-x₁)

    (-4-5)/(4-(-2))

    (-9)/(4+2)

    -9/6 or -3/2

2. Now that we have the slope for these two coordinates, plug them into the point-slope formula.

    Equation for point-slope: y-y₁=m(x-x₁), where m=slope

    y-5=[tex]\frac{-3}{2}[/tex](x-(-2)

    y-5=[tex]\frac{-3}{2}[/tex](x+2)

    y-5=[tex]\frac{-3}{2}[/tex]x-[tex]\frac{6}{2}[/tex]

    y-5=[tex]\frac{-3}{2}[/tex]x-3

(Add 5 to both sides)

    y=[tex]\frac{-3}{2}[/tex]x+2

Answer: -7 (30h - 11) / 4h

Step-by-step explanation:

Answer:

Step-by-step explanation:

All you can do is remove the brackets.

7/2 h * -15h = -52.5 h^2

7/2 h * 1 1/2= 7/2h * 3/2 = 21/4 h =5.25 h

7/2h(-15h + 21/4) = - 52.5 h^2 + 5.25 h = -52 1/2 h^2 + 5 1/4 h

Answer:

f(-6) = 32

f(0) = 2

f(9) = -43

Step-by-step explanation:

Since in this question we are given a function all we have to do is to plug in the values that were indicated in the question and find out what value are we going to get as an output of this function. So we just do the following.....

a)

f(-6) = 2 - 5(-6)

f(-6) = 2 - (-30)

f(-6) = 2 + 30

f(-6) = 32

b)

f(0) = 2 - 5(0)

f(0) = 2 - 0

f(0) = 2

c)

f(9) = 2 - 5(9)

f(9) = 2 - 45

f(9) = -43

Answer:

a = 21.82 if and only if b=10 and c=24

if you meant b=24 c=10

there can't be such a triangle because the hypotenuse is the longest side

Step-by-step explanation:

[tex]a^2+b^2=c^2\\\\a=?\\\\b=24\\\\c=10\\\\\\a^2+(24)^2=(10)^2\\\\a^2=(10)^2-(24)^2\\\\a^2=(10-24)(10+24)\\\\a^2=-14(34)[/tex]

which doesn't work because something squared can't be a negative

if you meant

c=24 and b=10

[tex]a^2+(10)^2=(24)^2\\\\a^2=(24)^2-(10)^2\\\\a^2=(24-10)(24+10)\\\\a^2=(14)(34)\\\\a\approx 21.82[/tex]

9514 1404 393

Answer:

  a = 26  or  21.82

Step-by-step explanation:

If 'a' is the hypotenuse, then ...

  a² = b² +c²

  a² = 24² +10² = 576 +100 = 676

  a = √676 = 26 . . . if 'a' is the hypotenuse

__

If 'a' is the long side, then ...

  b² = c² + a²

  b² -c² = a² = 24² -10² = 576 -100 = 476

  a = √476 ≈ 21.82 . . . if 'a' is the long leg

__

Comment on the question

The problem statement doesn't tell us what side of the triangle is labeled 'a'. There are two possibilities. An answer has been provided for each. Use the one that applies to the figure you are given.

Answer:

A yes

Step-by-step explanation:

Answer:

YES, because the points fall in a straight line when plotted on a graph.

Step-by-step explanation:

To graph these numbers we can take two of the points and put them into two point form and then convert that to slope intercept form.

(2,6) and (4,12)

(y-y1) = [(y2-y1)/(x2-x1)]*(x-x1)

y-6 = [(12-6)/(4-2)]*(x-2)

y = 3x+4

Answer:

See below

Step-by-step explanation:

Statement                                      | Reason                                            

1. m∠A + m∠B + m∠C = 180°         | 1.  Angles in a triangle sum to 180°

2. 28° + x - 4° + 2x = 180°              | 2. Substitution

3. x=(180° - 24°)/3= 156°/3°= 52°   | 3. Algebra

Responder:

125 pesos

Explicación paso a paso:

Dado el ingreso total l (v) obtenido de la venta de lápices por la función

Yo (v) = - 2v ^ 2 + 500v

v es el precio de venta de cada lápiz

Para que el ingreso total sea máximo, entonces dI / dv debe ser cero, es decir, dI / dv = 0

dI / dv = -4v + 500

Dado que dI / dv = 0

0 = -4v + 500

4v = 500

Dividir entre 4

4v / 4 = 500/4

v = 125

De ahí que el precio de venta de cada lápiz sea para que el ingreso total sea máximo es de 125 pesos

Answer:

Step-by-step explanation:

OK so i think triangle c

Answer:

F And C

Step-by-step explanation:

congruent means identical in form

Answer:

21

Step-by-step explanation: You have to first put all the numbers in order and divided it by the amount of numbers that are in ur set and boom ur done.

Answer:

x=-14-y/2

Step-by-step explanation:

divide both sides by -2

-2(2x+y)/-2=28/2

simplify

2x+y=-14

subtract y from both sides

2x+y-y=-14-y

simplify

2x=-14-y

divide both sides by 2

2x/2=-14/2-y/2

simplfy

x=-14-y/2

Answer: SSS and CMW=FPY

Step-by-step explanation:

The lines on each side of the triangle show which sides match. So it is just a case of matching sides with sides.

Answer:

3yx+3yx^2-3y^2

Step-by-step explanation: