A survey found that 8 out of 10 parents approved of the new principal’s performance. If 4 parents name are chosen with replacement what is the probability they all approve of the principal’s performance

Answer:

y = -4.9/5.4x - 1.17

Step-by-step explanation:

First let's convert the equation to standard form of y = mx + b.

4.9x + 5.4y = 3

Subtract 4.9x from both sides.

5.4y = -4.9x + 3

Divide each term by 5.4.

y = -4.9/5.4x + 0.56

If two lines are parallel to each other, they have the same slope slopes.

The first line is y = -4.9/5.4x + 0.56. Its slope is -4.9/5.4. A line parallel/perpendicular to this one will also have a slope of -4.9/5.4.

Plug this value (-4.9/5.4) into your standard point-slope equation of y = mx + b.

y = -4.9/5.4x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-3.6, 2.1). Plug in the x and y values into the x and y of the standard equation.

2.1 = -4.9/5.4(-3.6) + b

To find b, multiply the slope and the input of x (-3.6)

2.1 = 3.27 + b

Now, subtract 3.27 from both sides to isolate b.

-1.17 = b

Plug this into your standard equation.

y = -4.9/5.4x - 1.17

This equation is parallel/perpendicular to your given equation (y = -4.9/5.4x + 0.56) and contains point (-3.6, 2.1)

Hope this helps!

Hello!

32 students (girls+boys)

20 (girls)

32-20 = 12 (boys)

The ratio of girls to the boys

= 20:12

= 5:3

D is the answer.

Good studies!

Answer:

desmos .com

Step-by-step explanation:

Answer: See the graph below

Step-by-step explanation:

Concept:

Formula for circle: (x - k )² + (y - h)² = r²

Center = (k, h)

Radius = r

**Disclaimer** variables used can be different

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

Solve:

Given: (x - 2)² + (y + 3)² = 16

Center = (2, -3)

Radius = √16 = 4

Hope this helps!! :)

Please let me know if you have any questions

Answer:

1, 4, 9, 16, 25

Step-by-step explanation:

The pattern increases by an odd number. It can be seen that;

n²

for the first pattern

1²=1

for the second pattern

2²=4

for the third pattern

3²=9

for the forth pattern

4²=16

for the fifth pattern

5²=25

Answer:

B) 9

Step-by-step explanation:

Because there's a square between the 2 angles, that means these angles are complementary (angles that add up to 90°). So:

5x - 9 + 6x = 90

11x - 9 = 90

11x = 90 + 9

11x = 99

x = 9

Answer:

B.9

Step-by-step explanation:

The way to solve this is by noticing that these angles are complementary(they add up to 90 degrees). So you add the equations together and equal them to 90. 5x-9+6x=90.Then you solve to find that x=9.

Answer:

116y = 96.28

----      ---------

116        116

y = 0.83--------

Answer:

0.83-------

Step-by-step explanation:

Answer:

25 girls and 50 boys

Step-by-step explanation:

let x be the number of boys

let x/2 be the number of girls

x + x/2 = 75

3x/2 = 75

3x = 150

x = 50

there are 50 boys and 50/2 = 25 girls.

check:

50 + 25 = 75

Answer:

1/5^5

Step-by-step explanation:

Flip the equation into a fraction.

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Answer:

G = 78°

H = 98°

Step-by-step explanation:

Opposite angles in a cylic quadrilateral are supplementary. Therefore:

G + E = 180°

Substitute

8x + 1 + 11x + 8 = 180°

Add like terms

19x + 9 = 180°

19x + 9 - 9 = 180° - 9

19x = 171

19x/19 = 171/19

x = 9

G = 8x + 1

Plug in the value

G = 8(9) + 1 = 73°

H + F = 180° (opposite angles of a cyclic quadrilateral is equal?

Plug in the values

6y - 4 + 5y - 3 = 180°

Add like terms

11y - 7 = 180

11y = 180 + 7

11y = 187

y = 187/11

y = 17

H = 6y - 4

Plug in the value of y

H = 6(17) - 4

H = 98°

Answer:

see explanation

Step-by-step explanation:

Under a clockwise rotation about the origin of 90°

a point (x, y ) → (- y, x ) , then

(3, 3 ) → (- 3, 3 )

(3, 4 ) → (- 4, 3 )

(5, 3 ) → (- 3, 5 )

Answer:

280

Step-by-step explanation:

Use the formula: (a((r^n)-1))/(r-1)

= (7((3^4)-1))/(3-1)

The sum of the given geometric series is 280.

We have given that,

a1=7, n=4 and r=3

We have to determine the sum of a geometric series

[tex]S_n=(a((r^n)-1))/(r-1)[/tex]

[tex]= (7((3^4)-1))/(3-1)[/tex]

[tex]=280[/tex]

Therefore the sum of the given geometric series is 280.

To learn more about the geometric series visit:

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Answer:

There is a slight problem with this question

Do numbers starting with "0" count as a digit position

I would say no, thus the answer is 4...

if you are allowed to use 0 then the answer is 8

in other words if the question was using only 4's and 1's then the answer would be 8  

Step-by-step explanation:

000

004

040

044

400

404

440

444

Answer:

V = 24.28 in ^3

Step-by-step explanation:

The area of the base is

A =5/2 × s × a  where s is the side length and a is the apothem

A = 5/2 ( 2.13) * .87

A = 4.63275

The volume is

V = Bh  where B is the area of the base and h is the height

V = 4.63275 ( 5.24)

V =24.27561 in^3

Rounding to the  hundredth

V = 24.28 in ^3

Answer:

1/8

Step-by-step explanation:

9/16 * 4/18

Rewriting

9/18 * 4/16

9/18 = 1/2   and 4/16 = 1/4

1/2 * 1/4

1/8

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

[tex]\frac{9}{16}[/tex] x [tex]\frac{4}{18}[/tex] = [tex]\frac{(9)(4)}{(16)(18)}[/tex]

[tex]\frac{(9)}{(18)}[/tex] = [tex]\frac{1}{2}[/tex]

[tex]\frac{4}{16}[/tex] = [tex]\frac{1}{4}[/tex]

[tex]\frac{(1)(1)}{(2)(4)}[/tex] = [tex]\frac{1}{8}[/tex]

Answer:

the first one...

the cost of renting the ally for 14 hours

Step-by-step explanation:

Answer:

the first one

the number of dollars it costs to rent the bowling lane for14 hours

Answer:

The slope is -3/4 and a point on the line is (-5,4)

Step-by-step explanation:

This equation is in point slope form

y -y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

Y-4=-3/4(x+5)

Y-4=-3/4(x -  -5)

The slope is -3/4 and a point on the line is (-5,4)

Answer:

[tex]Given:[/tex]

[tex]8x-6 > 12 + 2x[/tex]

[tex]8x-2x>12+6[/tex]

[tex]6x>18[/tex]

[tex]x>18/6[/tex]

[tex]x>3[/tex]

[tex]5>3[/tex]

[tex]ANSWER: D)\:5[/tex]

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

Hope it helps...

Have a great day!!

1. a= 19

2.2 ( second option)

3.C

4D

Answer:

v =  14 km/h

Step-by-step explanation:

d = 0.0067[tex]v^{2}[/tex] + 0.15v

differentiate the function with respect to v to have;

d = 0.0134v - 0.15

given that the distance without skidding = 37 m (0.037 km) , then;

0.037 = 0.0134v - 0.15

0.0134v = 0.037 + 0.15

             = 0.187

v = [tex]\frac{0.187}{0.0134}[/tex]

  = 13.9552

v =  14 km/h

The speed of the car travelling would be 14 km/h to be able to stop within 37m.

Answer:

the formula

Step-by-step explanation:

substitute the formula with the numbers give n-2 is number of sides -2 fyi

Answer:

B. [tex]T(x) = 2.9\cdot (1.05)^{4\cdot x + 5}[/tex]

Step-by-step explanation:

The approximate population in the region is the product of the number of cities in a region and the approximate number of people per city, that is:

[tex]T(x) = C(x)\cdot P(x)[/tex] (1)

If we know that [tex]C(x) = 2.9\cdot (1.05)^{x}[/tex] and [tex]P(x) = (1.05)^{3\cdot x + 5}[/tex], then the formula for the approximate population in the region is:

[tex]T(x) = [2.9\cdot (1.05)^{x}]\cdot [(1.05)^{3\cdot x + 5}][/tex]

[tex]T(x) = 2.9\cdot (1.05)^{4\cdot x + 5}[/tex]

Hence, correct answer is B.

Answer:

24/60 does not like 36/60 does like

36/60 = .6 which is 60% chance

Step-by-step explanation:

The probability that Ryan will pick a jelly bean that has a flavor he likes is 0.7

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

[tex]P(A)=\frac{n(A)}{n(S)}[/tex]

where, [tex]n(A)[/tex] is the number of favorable outcomes

is [tex]n(S)[/tex] the total number of events in the sample space.

From given data:

Ryan received a box of jelly beans with

Grape - 16

Licorice - 10

Cherry - 12

Lemon - 14

Lime - 8

So, there are total 16 + 10 + 12 + 14 + 8 = 60 jelly beans.

Ryan does not like licorice or lime.

⇒ 10 + 8 = 18 jelly beans he does not like.

This means, he likes 60 - 18 = 42 jelly beans.

Now, we find the probability of jelly beans that has a flavor he likes.

⇒ P = (number of grape, cherry, lemon jelly beans) / (total number of jelly beans)

⇒ [tex]P=\frac{42}{60}[/tex]

⇒ [tex]\bold{0.7}[/tex]

Therefore, the probability that Ryan will pick a jelly bean from the full box that has a flavor he does like is 0.7

Learn more about probability here:

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t=2w-1

OPTION A is the correct answer...

9514 1404 393

Answer:

  B.  3x² +2 = 0

Step-by-step explanation:

The equation of A has a couple of real roots. We're pretty sure there are complex numbers that will satisfy this equation, but we don't know how to find them. (We suspect a typo, and that the equation is supposed to be 2x² +1 = 7x, which has only real roots.)

__

The equation of B can be rewritten as ...

  x² = -2/3

This will have complex roots.

__

The discriminants of both equations C and D are positive, so those have only real roots.

  2x² -5x -1   ⇒   d = (-5)² -4(2)(-1) = 33

  3x² -6x -1   ⇒   d = (-6)² -4(3)(-1) = 48

Answer:

A, B, E

Step-by-step explanation:

Exterior angles are angles that are outside the shape. In this case, angle 4, 3 and 2 are exterior angles.

Answer:

the first one x is 6 and y is 11

the second one y is 5 and x is 3

the third one x is 15 and y is 17

the fourth one y is 15 and x is -12

Step-by-step explanation:

to find the first answer you have to use the actual equation given and substitute the value of x in it

y=-2(-6)/3+7

=12/3+7

=4+7

=11

the second one is quite different because the value of y has been given and not x so you have to substitute the value of y in the equation which is 5

5=-2x/3+7

5-7=-2x/3

-2/1=-2x/3

-2x/-2=-6/-2

x=3

for the third one you have to solve it like the first one

y=-2(15)/3+7

=10+7

=17

the fourth one is similar to the second one

15=-2x/3+7

15-7=2x/3

8=2x/3

-2x/-2=24/-2

x=-12

I hope this helps

Answer:

4x -12

Step-by-step explanation:

8 - 4(-x + 5)

Distribute

8 -4(-x) -4(5)

8 +4x -20

4x -12

answer 4( - 3 + x)

answer

[tex]4( - 3 + x)[/tex]

[tex]8 - 4( - x + 5)[/tex]

answer

[tex] - 12 + 4x[/tex]

Answer:

A

Step-by-step explanation:

Got it right!! <3

Pls mark brainliest ^^

Answer:

a. The required proof is obtained from triangles OAB and ABC formed by joining AB and that we have;

A[tex]\hat O[/tex]B + 2∠C = 180°, 2·A[tex]\hat P[/tex]B + 2∠C = 180°

∴ A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B

b. i) P[tex]\hat S[/tex]S = P[tex]\hat R[/tex]Q, given that angles subtended by the same arc or chord are equal, therefore, in ΔPQS, we have;

[tex]\left | PS \right |[/tex] = [tex]\left |PQ \right |[/tex]

ii) S[tex]\hat Q[/tex]P = 45°, [tex]S\hat R Z[/tex] =90°

Step-by-step explanation:

a. The given parameters are;

The center of the circle is point O

Points on the circumference of the circle = A, B, and P

Required to be proved, A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B

Let ∠O represent A[tex]\hat O[/tex]B and let ∠P' represent A[tex]\hat P[/tex]B

We draw a line from the center O to the point P, and a line joining points A and B on the circumference of the circle

In ΔOAB, we have;

∠O + 2∠C = 180° (The sum of the interior angles of a triangle)

In ΔAPB, we have;

∠P' + ∠(C - a) + ∠(P' + C + a) = 180°

∴ 2·∠P' + 2·∠C = 180°

Therefore, by addition property of equality, we get;

∠O = 2·∠P'

Therefore;

A[tex]\hat O[/tex]B = 2·A[tex]\hat P[/tex]B

b. i) The given parameters are;

Points on the circle = P, Q, R, and S

P[tex]\hat Q[/tex]S = P[tex]\hat R[/tex]Q

According to circle theory, the angles which an arc or chord subtends in a given segment are equal, therefore;

P[tex]\hat S[/tex]S = P[tex]\hat R[/tex]Q

Therefore, P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S by transitive property of equality

P[tex]\hat S[/tex]S and P[tex]\hat Q[/tex]S are base angles of ΔPQS, given that P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, we have;

ΔPQS is an isosceles triangle with base QS and therefore, the sides PS and PQ are the equal sides

Therefore, we have;

[tex]\left | PS \right |[/tex] = [tex]\left |PQ \right |[/tex]

ii) Given that SQ is the diameter of the circle, we have by circle theorem, the angle subtended on the circumference by the diameter = 90°

∴ [tex]S\hat PQ[/tex] = 90°

From (i), we have that P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, therefore, in triangle ΔPQS, we have;

[tex]S\hat PQ[/tex] + P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180°

Therefore;

90° + P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180°

P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 180° - 90° = 90°

P[tex]\hat S[/tex]S = P[tex]\hat Q[/tex]S, therefore, P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 2·S[tex]\hat Q[/tex]P

P[tex]\hat S[/tex]S + S[tex]\hat Q[/tex]P = 2·S[tex]\hat Q[/tex]P = 90°

S[tex]\hat Q[/tex]P = 90°/2 = 45°

S[tex]\hat Q[/tex]P = 45°

Similarly, given that SQ is the diameter, of the circle the angle [tex]S\hat R Q[/tex] formed by jointing S to Q is 90°

[tex]S\hat R Q[/tex] = 90°

[tex]S\hat R Q \ and \ S\hat R Z[/tex] are angles on a straight line and are therefore, supplementary, therefore;

[tex]S\hat R Z[/tex] = 180° - [tex]S\hat R Q[/tex]

[tex]S\hat R Z[/tex] = 180° - 90° = 90°

[tex]S\hat R Z[/tex] =90°.

Answer:

Another example of a number who's square root is greater than the number is  [tex]\sqrt{0.49}[/tex] which is 0.7

Step-by-step explanation:

This square root is larger than the number because it is a decimal. When you multiply a decimal by a decimal, the decimal point becomes greater. For example: 0.7 multiplied by 0.7 equals 0.49 which has 2 decimal places, while 0.7 only has one.