In a large crowd, there are three times as
many men as women. Three people are
chosen at random. Assuming that there are
so many people that choosing three has a
negligible effect on the proportion of men to
women, find the probability that they are
a.all men
b.2 women and 1 man.​

Answer:

The answer is 49 .

Step-by-step explanation:

Do i need to explain ?

Given:

The function is:

[tex]f(x)=-2x^2+7x+4[/tex]

To find:

Express the quadratic equation in the form of [tex]f(x)=a(x-h)^2+k[/tex], then state the minimum or maximum value,axis of symmetry and minimum or maximum point.

Solution:

The vertex form of a quadratic function is:

[tex]f(x)=a(x-h)^2+k[/tex]              ...(i)

Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.

We have,

[tex]f(x)=-2x^2+7x+4[/tex]

It can be written as:

[tex]f(x)=-2\left(x^2-3.5x\right)+4[/tex]

Adding and subtracting square of half of coefficient of x inside the parenthesis, we get

[tex]f(x)=-2\left(x^2-3.5x+(\dfrac{3.5}{2})^2-(\dfrac{3.5}{2})^2\right)+4[/tex]

[tex]f(x)=-2\left(x^2-3.5x+(1.75)^2\right)-2\left(-(1.75)^2\right)+4[/tex]

[tex]f(x)=-2\left(x-1.75\right)^2+2(3.0625)+4[/tex]

[tex]f(x)=-2\left(x-1.75\right)^2+6.125+4[/tex]

[tex]f(x)=-2\left(x-1.75\right)^2+10.125[/tex]                ...(ii)

On comparing (i) and (ii), we get

[tex]a=-2,h=1.75,k=10.125[/tex]

Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.

Maximum value = 10.125

Axis of symmetry : [tex]x=1.75[/tex]

Maximum point = (1.75,10.125)

Therefore, the vertex form of the given function is [tex]f(x)=-2\left(x-1.75\right)^2+10.125[/tex], the maximum value is 10.125, the axis of symmetry is [tex]x=1.75[/tex] and the maximum point is (1.75,10.125).

Answer:

yes , k = 9

Step-by-step explanation:

The equation of a proportional relationship is

y = kx ← k is the constant of proportion

To find k divide both sides by x

[tex]\frac{y}{x}[/tex] = k

Check each ordered pair in the table

k = [tex]\frac{18}{2}[/tex] = 9

k = [tex]\frac{45}{5}[/tex] = 9

k = [tex]\frac{63}{7}[/tex] = 9

Thus the relationship is proportional with k = 9

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {20}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]

[tex] = ( {2}^{2} + {4}^{2} )[/tex]

[tex] = [(2 \times 2) + (4 \times 4)][/tex]

[tex] = (4 + 16)[/tex]

[tex] = 20[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Thank\:you! }}{\orange{❦}}}}}[/tex]

Answer:

[tex]\$6[/tex]

Step-by-step explanation:

Given

See comment for complete question

Required

The difference in the cost of 600 text messages plan

Representing the given data as; Cost to Number of text messages, we have:

[tex]Dial\ Up = \$5 : 100[/tex]

and

[tex]Ring\ Ring= \$8 : 200[/tex]

Multiply the dial-up by 6 to get the cost of 600

[tex]Dial\ Up = \$5 *6 : 100 * 6[/tex]

[tex]Dial\ Up = \$30 : 600[/tex]

So, the cost of 600 text messages is $30 --- for dial-up

Multiply the Ring Ring by 3 to get the cost of 600

[tex]Ring\ Ring= \$8 *3: 200*3[/tex]

[tex]Ring\ Ring= \$24: 600[/tex]

So, the cost of 600 text messages is $24 --- for Ring Ring

The difference (d) is:

[tex]d = \$30 - \$24[/tex]

[tex]d = \$6[/tex]

Answer: 69, -69

Step-by-step explanation:

it is easy buddy not lies

Answer:

"D"

tart at $10 then 4 each day

Step-by-step explanation:

Answer: X or 30

Step-by-step explanation:

through my working i got to 41² is the hypotenuse.

21²+20²=c²

factor out the square

(21+20)²=c²

41²=c²

and 41² is 1681

Answer:

29 units

Step-by-step explanation:

i just took the quiz

Answer:

the answer is given in this picture hope this helps and good luck :)!

Step-by-step explanation:

Step-by-step explanation:

x² -12x+36 =90

(x-6)² =90

x-6. =+-√90

x. =6+-√90

x. =6+-√9×10

x. =6+-3√10

so the answer is first option

Answer:

L=65-15d; continuous

Step-by-step explanation: L stands for the length of the leaf, 65 stands for the original length of the leaf(which will decrease), d stands for the days. the answer is L=65-15d continuous because the original size of the leaf when he bought it was 65(which can decrease over time), every afternoon he cuts the leaf by 15 (which means the size of the leaf is decreasing and by 15 every day) which gives me -15d, if he cuts the leaf by 15 every day and never changes the length of the cut then the function is continuous

Answer:

Step-by-step explanation:

The total distance = 1/6 + 3/8 miles Change the denominators to 24

D = 1/6 + 3/8 = 4*1/6*4 + 3*3 / 8 * 3

D = 4/24 + 9/24

D = 13/24 of mile.

Answer:

10 km/hr

Step-by-step explanation:

Average speed = Total distance travelled / Total time taken

Ardi:

Total distance travelled = 70 km

Total time taken = 35 minutes = 35/60 hour

Average speed = Total distance travelled / Total time taken

= 70 km ÷ 35/60 hr

= 70 × 60/35

= 4,200/35

= 120 km/hr

Lei:

Total distance travelled = 585 km Total time taken = 9:05 - 13:35 = 4 hours 30 minutes

= 4.5 hours

Average speed = Total distance travelled / Total time taken

= 585 km / 4.5 hours

= 130 km/hr

Difference, in km/h, between the average speed of their trains = Lei's train - Ardi's train

= 130 km/hr - 120 km/hr

= 10 km/hr

Answer:

x = 60 cm

Step-by-step explanation:

using Pythagoras theorem which states that:-

Hypotenuse (h)² = perpendicular (p)² + base (b)²

100² = 80² + x²

100² - 80² = x²

10000 - 6400 = x²

3600 = x²

x = 60 cm

Answer:

Um

Step-by-step explanation:

Its half of diameter

Are you thinking of circumference and area?

Answer:

f(2) = - 5

Step-by-step explanation:

Using the recursive rule and f(1) = - 3 , then

f(2) = 2f(1) + 1 = 2 × - 3 + 1 = - 6 + 1 = - 5

Answer:

( -4, -3 )

Step-by-step explanation:

Let's solve by elimination. Reason being there are no variables without coefficients.

−5y+3x=3     Multiply equation by 3. Each term.  

−8y+9x=−12

-15y + 9x = 9       Subtract the to equations

-8y  + 9x = -12

___________

-7y = 21

y = -3

Substitute y into original equation

-5(-3) + 3x = 3

15 + 3x = 3            Subtract 15 both sides

3x = -12                 Divide by 3, both sides

x = -4

Answer:

y=-3

x=-4

Check:

-5(-3)+3(-4) =3

15-12=3

3=3 ✅

-8(-3)+9(-4)=-12

24-36=-12

-12=-12✅

Answer:

a = 2.5, b = 1

Step-by-step explanation:

Given the 2 equations

4a = 5b + 5 → (1)

2a = 3b + 2 → (2)

Multiplying (2) by - 2 and adding the result to (1) will eliminate a

- 4a = - 6b - 4 → (3)

Add (1) and (3) term by term to eliminate a

0 = - b + 1 ( add b to both sides )

b = 1

Substitute b = 1 into either of the 2 equations and solve for a

Substituting into (2)

2a = 3(1) + 2 = 3 + 2 = 5 ( divide both sides by 2 )

a = 2.5

Answer:

a = 2.5

b = 1

Step-by-step explanation:

4a = 5b + 5 and 2a = 3b + 2

→ Multiply the second equation by 2

4a = 6b + 4

→ Subtract this new equation from the first one

0 = b - 1

→ Find b by adding 1 on both sides

b = 1

→ Substitute b into one of the equation

4a = ( 5 × 1 ) + 5

→ Simplify

4a = 10

→ Divide both sides by 4

a = 2.5

Answer:

A is the Answer

Step-by-step explanation:

Since the population is being split up into 2 divisions out of 5,000.

This means District X and Y must add up 5000.

[tex]x + y = 5000[/tex]

District X and Y must differ no more than 500 people.

So this means that X and Y total people difference cannot be over 500 people. So the equation for this is

[tex]x - y \leqslant 500[/tex]

A shows this so A is the answer.

Answer:

Refer to the attachment!~

Answer:

372 shares

Step-by-step explanation:

Let

x = shares owned before the split

Share after split : share before split = 5 : 1

Share after split : share before split = 1,860 : x

Equate both ratios

5 : 1 = 1,860 : x

5/1 = 1,860/x

Cross product

5 * x = 1 * 1,860

5x = 1,860

x = 1,860/5

x = 372

x = shares owned before the split = 372 shares

Sin (angle) = opposite leg / hypotenuse

Sin(x) = 2.1/4

x = arcsin(21./4)

x = 31.7 degrees

Answer:

[tex]x^2 + ( y + 4)^2 = 52[/tex]

Step-by-step explanation:

Equation of circle with center (a , b) and radius, r is :

[tex](x -a)^2 + ( y -b)^2 = r^2[/tex]

Given :  a = 0 , b = - 4

Step 1 : Find the radius.

       Given ( 6 , 0 ) lies on the circle. Therefore the distance between the center (0 , - 4) of the circle and ( 6 , 0 ) gives the radius of the circle.

   [tex]r = \sqrt{( 0 - 6)^2 + ( -4 - 0)^2} \\\\[/tex]

     [tex]= \sqrt{ 36 + 16 } \\\\= \sqrt{52}[/tex]

Step 2 : Equation of circle.

  [tex](x - 0)^2 + (y -( - 4))^2 = (\sqrt{52})^2\\\\x^2 + ( y+ 4)^2 = 52[/tex]

Answer:

4a^2

Step-by-step explanation:

GCF of 12 and 32 is 4.

GCF of a^3 and a^2 is a^2.

Therefore, the answer is 4a^2.

Answer:

JHJHJHJHUJ3480945768

658768

Step-by-step explanation:

684867765543545

Ans x = 0.5

Step-by-step explanation:

[tex]= -4x^{3} + 2x^{2} +\frac{2}{3}x^{2} -\frac{1}{3}x-4x+2\\= -4x^{3}+\frac{8}{3}x^{2} -\frac{13}{3}x+2\\[/tex]

If the equation requires to find x, you can use Casio calculator to solve this by some basic formula:

Step 1: Type [tex]-4x^{3}+\frac{8}{3}x^{2} -\frac{13}{3}x+2[/tex]

Step 2: Press Shift SOLVE (CALC)

Step 3: Press "0" for Solve for X

-> You will find the x is 0.5

x + y= 9 and x - y= 3

rearrange the second equation:

x - y= 3

x = 3 + y

x -3 = y

substitute y with "x-3" in the first equation and solve

x + y= 9

x + (x-3)= 9

2x -3 = 9

2x = 12

x = 6

you could also start with the first equation and substitute y in the second.

graphically speaking, it's the intersection point of to lines, at least the six-part of the point.

Answer:

I hope this helps

Step-by-step explanation: