A group of people were asked whether they prefer soup or salad for lunch.
The table shows the probabilities of the results

Let A represent having soup and B represent having salad for lunch.
Which statement is true?

A. Having soup and salad for lunch are independent events because P(A]B) = P(A) and P(BA) = P(B)

B. Having soup and salad for lunch are independent events because P(A]B) + P(A) and P(BA) + P(B)

C. Having soup and salad are not independent events because P(A]B) + P(A) and P(BA) + P(B)

D. Having soup and salad for lunch are not independent events because P(A]B) = P(A) and P(BA) = P(B)

Answer:

904.8 m²

Step-by-step explanation:

needed formulas:

surface of a circle: πr²

circumference of a circle: 2πr

The top and bottom are circles with radius 9, and surface π9² = 81π m²

The side is a rectangle of 2·π·9·7 long, so that is 126π m²

Brings the total to 81π + 81π + 126π = 288π ≈ 904.8 m²

Answer:

Greater than 2+5

Answer:

in half of the baskets

Step-by-step explanation:

half of 40 baskets is 20 baskets

Answer:

-26

Step-by-step explanation:

2 × 3 + 4 − 6^2

PEMDAS

exponents are first in this equation

2 × 3 + 4 − 36

Then multiply

6 +4 -36

Then add and subtract from left to right

10-36

-26

Answer:

A) -26

Step-by-step explanation:

2 * 3 + 4 - 6²

Use PEMDAS to figure out the equation.

Pass parenthesis since there are none in the equation.

Evaluate all of the exponents.

2 * 3 + 4 - 36

Evaluate all of the multiplication in the equation.

6 + 4 - 36

Pass division since there isn't any in the equation.

Evaluate all of the addition in the equation.

10 - 36

Evaluate all of the subtraction in the equation.

-26.

Answer:

A) 13

Step-by-step explanation:

If you recall the formula for finding a diagonal, or a^2 + B^2 = C^2, you will get 12^2 + 5^2 = C^2, if you solve that, you will get 13!

Answer:

4 and 5

Step-by-step explanation:

Let's make an equation to solve. Let's call "one number" x. Another number is 1 more than x, so now we have x + 1. x plus x + 1 is equal to 9... and this gives us our equation:

x + (x + 1) = 9

We can now simplify by adding like terms together:

2x + 1 = 9

Now, let's take away 1 from both sides:

2x = 8

We can finally divide both sides by 2 to isolate x:

x = 4

One of our numbers is 4. Our other number is one more than 4, and 4 + 1 = 5. So our numbers are 4 and 5.

Hopefully this was helpful! If you need more help, let me know.

Answer:

Yes it is linear. Standard Form: 4x - y = -9

Step-by-step explanation:

Answer:

A) 115°

Step-by-step explanation:

if PQ || RS then those two angles are supplementary

Step-by-step explanation:

[tex] = - \frac{5}{3} + 2 \frac{1}{3} [/tex]

[tex] = - \frac{5}{3} + \frac{7}{3} [/tex]

[tex] = \frac{2}{3} [/tex]

Answer:

[tex] \sf \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] \sf = - \frac{5}{3} + 2 \frac{1}{3} [/tex]

[tex] \sf = 2 \frac{1}{3} - \frac{5}{3} [/tex]

[tex] \sf = \frac{7}{3} - \frac{5}{3} [/tex]

[tex] \sf = \frac{7 - 5}{3} [/tex]

[tex] \sf = \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] \frac{4.8}{1 \frac{7}{9} } = (1.2b) \div 6 \frac{2}{3} [/tex]

[tex] \frac{ \frac{48}{10} }{ \frac{16}{9} } = \frac{12b}{10} \div \frac{20}{3} [/tex]

[tex] \frac{48 \times 9}{10 \times 16} = \frac{12b}{10} \times \frac{3}{20} [/tex]

[tex] \frac{432}{160} = \frac{36b}{200} [/tex]

[tex]432 \times 200 = 160 \times 36b[/tex]

[tex]86400 = 5760b[/tex]

[tex]b = \frac{86400}{5760} [/tex]

[tex]b = 15[/tex]

An ellipse has the general equation

(x/a)² + (y/b)² = 1

(actually, this is an ellipse whose semimajor and -minor axes are parallel to the x- and y-axes, but one can rotate any ellipse so that it has the same configuration, and the area remains constant)

Convert to a kind of rescaled polar coordinates, using

x = a r cos(t)

y = b r sin(t)

Then the interior of such an ellipse is the set

E = {(r, t) : 0 ≤ r ≤ 1 and 0 ≤ t ≤ 2π}

The area of E is then given by the integral

[tex]\displaystyle \iint_E dA[/tex]

Compute the Jacobian determinant for this change of coordinates. The Jacobian is

[tex]J = \begin{bmatrix}x_r & x_t \\ y_r & y_t\end{bmatrix} = \begin{bmatrix}a \cos(t) & -a r \sin(t) \\ b \sin(t) & b r \cos(t)\end{bmatrix}[/tex]

Then we have Jacobian determinant

|det(J)| = |a b r cos²(t) + a b r sin²(t)| = |a b r| = |a b| r

since r ≥ 0.

The area of E is then

[tex]\displaystyle \iint_E dA = \iint_E |ab| r \, dr \, dt[/tex]

[tex]\displaystyle \iint_E dA = \int_0^{2\pi} \int_0^1 |ab| r \, dr \, dt[/tex]

[tex]\displaystyle \iint_E dA = 2\pi |ab| \int_0^1 r \, dr[/tex]

[tex]\displaystyle \iint_E dA = \boxed{\pi |ab|}[/tex]

Answer:

A = 103°; B = 77°; C = 46°

Step-by-step explanation:

A + 45° + 32° = 180°

A + 77° = 180°

A = 180° - 77°

A = 103°

A + B = 180°

103° + B = 180°

B = 180° - 103°

B = 77°

B + C + 57° = 180°

77° + 57° + C = 180°

134° + C = 180°

C = 180° - 134°

C = 46°

I hope I've helped you.

Answer:

x= (5,0) y= (0,1)

Step-by-step explanation:

Answer:

-7x + 7y - 14

Step-by-step explanation:

Answer:

It is 23

Step-by-step

23 becaauae if you use x and -2 its bets 23

Answer:

Line 1: Is parallel Line 2: Is Neither Line 3: Is parallel

Answer:

Step-by-step explanation:

`

Answer:Possible Answers: 13.2%. 5.7%. 15.0%.

Step-by-step explanation:

Answer:

Slope = - 3

Step-by-step explanation:

Formula : -

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

( x1, y1 ) = ( - 1, 4 )

Here,

x1 = - 1

y1 = 4

( x2, y2 ) = ( 1, - 2 )

Here,

x2 = 1

y2 = - 2

Slope = ( - 2 - 4 ) / ( 1 - ( - 1 ) )

= - 6 / ( 1 + 1

= - 6 / 2

Slope = - 3

Therefore,

The slope of the line through ( - 1, 4 ) and ( 1, - 2 )

is - 3.

Answer:

$17.60

Step-by-step explanation:

Answer:

the answer is a

Step-by-step explanation:

the reason its a is because it just it

Answer:

90% off

Step-by-step explanation:

Your question is incomplete.

If these are the statement.. The answer is below:

The grocery bill before the coupons were used was 10 times as much as the bill after the coupons were used.

The grocery bill after the coupons were used was 10 times as much as the bill before the coupons were used.

The grocery bill before the coupons were used was 100 times as much as the bill after the coupons were used.

The grocery bill after the coupons were used was 100 times as much as the bill before the coupons were used.

Answer:

The grocery bill before the coupons were used was 10 times as much as the bill after the coupons were used.

Step-by-step explanation:

The price after coupons were used is $20, and the price before was $200. $20 · 10 =$200

Answer:

90

Step-by-step explanation:

Answer:

The constant factor between consecutive terms of a geometric sequence is called the common ratio. Example:  To find the common ratio  find the ratio between a term and the term preceding it. r=42=2. 2 is the common ratio.

Answer:

a. y = 3^x

yep

ype

pey

Answer:

a

Step-by-step explanation:

plug the points into the equations

3¹=3

3²=9

3³=27

3⁴=81

3⁵=243

these are all true equations, so the answer is a

Answer:

On average, he exercises 2.875 hours per week.

Step-by-step explanation:

Just do 11 1/2 (11.5) divided by 4, and you get your answer of 2.875 hours per week.

Answer:

Option D is your answer.

Step-by-step explanation:

Remember that the x-values are the x coordinates and the y-values are the y coordinates in an ordered pair. Ordered pairs are written like this (x,y).

So for line r, you got (-6,4), (-3,0), and (0,-4).

But you only need two of these pairs to determine slope. Let's do that real quick, by using this formula. (Sorry if it's small)⤵⤵⤵

[tex] \frac{y _{2} - y _{1} }{x _{2} - x _{1} } [/tex]

We'll use (-6,4) and ( -3,0).

0 - 4 = -4

-3 - (-6) = -3 + 6 = 3

So slope of line r is -4/3.

Now we'll do the same for line s:

Ordered pairs = (-5,-4), (5,0), and (20,6)

We'll use (-5,-4) and (5,0).

0 - (-4) = 0 + 4 = 4

5 - (-5) = 10

So slope of line s is 4/10 or 2/5.

Now we got to find the option choice that has these as the slopes.

We'll turn each into slope-intercept form.

A)

- Subtract 4x on both sides to get

3y = -4x - 12, then divide 3 on both sides to get y = -4/3 x - 4.

- Subtract 2x on both sides to get

-5y = -2x + 10, then divide -5 on both sides to get y = 2/5 x - 2.

B)

- Add 4x on both sides to get

3y = 4x + 12, the divide 3 on both sides to get y = 4/3 x + 4.

- Subtract 2x on both sides to get

-5y = -2x - 10, divide -5 on both sides to get y = 2/5 x + 2.

C)

- Subtract 4x on both sides to get

-3y = -4x - 12, then divide -3 on both sides to get y = 4/3 x + 4.

- Add 2x on both sides to get

-5y = 2x + 10, then divide -5 on both sides to get y = -2/5 x -2.

D)

- Add 4x on both sides to get

-3y = 4x - 12, then divide -3 on both sides to get y = -4/3 x + 4.

- Add 2x on both sides to get

5y = 2x + 10, then divide 5 on both sides to get y = 2/5 x + 2.

After all that writing we can tell that D is our answer, because both -4/3 and 2/5 appear as slopes.

Sorry this may seem like a lot, but the process really isn't that hard. Hope this helps :)