Write out the sample space for the given experiment. Use the following letters to indicate each choice: M for mushrooms, A for asparagus,S for Shrimp, B for Bacon, F for French, and V for Vinegrette. When deciding what you want to put into a salad for dinner at a restaurant, you will choose one of the following extra toppings: mushrooms, asparagus. Also you will addone of the following meats: Shrimp, bacon. Lastly, you will decide on one of the following dressings: French, vinegrette.​

[tex]{\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

Let [tex]\alpha[/tex] and [tex]\beta[/tex] be the two zeroes of P(x) = [tex]\sf {a}^{2} + bx + c[/tex]

• A polynomial is always equal to it's factors, also the constant "k" is not equal to zero

[tex] \tt \sf {a}^{2} + bx + c = k(x - \alpha )(x - \beta )[/tex]

• Using distributive property

[tex]\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} - \beta x - \alpha x + \alpha \beta \bigg)[/tex]

[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -k (\beta x )- k(\alpha x )+k( \alpha \beta )[/tex]

• Taking common

[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)[/tex]

• Equating coefficients of like terms

[tex] \sf \: a = k - - (2)[/tex]

[tex] \sf b = - k( \alpha + \beta ) - - (3)[/tex]

[tex] \sf c = k \alpha \beta - - (4)[/tex]

★ From 3

[tex] \sf b = - k( \alpha + \beta ) - - (3)[/tex]

★ From 2 we have a = k so we have -

[tex] \sf b = - a( \alpha + \beta ) [/tex]

[tex]\sf - \dfrac{b}{a} = ( \alpha + \beta ) [/tex]

[tex]\sf \therefore \boxed {{ \red{( \alpha + \beta ) = - \dfrac{b}{a} } }}[/tex]

• Sum of zeros = [tex]- \dfrac{b}{a}[/tex]

★ From 4

[tex] \sf c = k \alpha \beta - - (4)[/tex]

★ From 2 we have a = k so we have -

[tex] \sf c = a \: \alpha \: \beta[/tex]

[tex]\sf \dfrac{c}{a} = \alpha \beta[/tex]

[tex]\sf \therefore \boxed {{ \red{( \alpha \beta ) = \dfrac{c}{a} } }}[/tex]

• Product of zeros = [tex] \dfrac{c}{a}[/tex]

Also,

★ From 1

[tex]\tt \sf {a}^{2} + bx + c = k {x}^{2} -kx (\beta + \alpha)+k( \alpha \beta ) - - (1)[/tex]

[tex]\tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( \alpha + \beta ) + ( \alpha \beta \bigg) [/tex]

• Now just put S instead of sum of zeroes and P instead of product of zeroes

[tex] \tt \sf {a}^{2} + bx + c = k \bigg( {x}^{2} -x ( S ) + ( P \bigg) [/tex]

[tex]\tt \sf{a}^{2} + bx + c = \boxed{ \red{ \sf \tt k \bigg( {x}^{2} - Sx + ( P \bigg ) }}[/tex]

[tex]\rule{280pt}{2pt}[/tex]

Answer:

18:12 = A. 3:2

Step-by-step explanation:

Because they are equivalent ratios, they are the same, it also said ratio of strawberries to cherries so I put it in that order.

Can I please have branliest

okay thank you have a good day

Answer

x > 2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that dont contain the variable

Answer:

8%

Step-by-step explanation:

Add 2 and 23 together to get 25.

Divide 2 by 25 to get 0.08.

Covert 0.08 into percentage: 8%

Answer:

25% of 824

25/100 × 824

206

New prices of the TV is

824+206= 1030

Given

[tex] \text{Base = 4} \\ \text{Perpendicular= 8}[/tex]

To Find

Hypotenuse of the triangle.

Assuming,

[tex] \text{Perpendicular = ‘a’}[/tex]

[tex] \text{Base = ‘b’}[/tex]

[tex] \text{Hypotenuse= ‘c’}[/tex]

[tex] \text{(c)² = (a)² + (b)²} \\ \\ \implies \text{ (c)² = (8)² + (4)²} \\ \\ \implies \text{(c)}^{2} = 64 + 16 \\ \\ \implies \text{(c)}^{2} = 80 \\ \\ \implies \text{(c)} = \sqrt{80} \\ \\ \implies\text{(c)} = 8.94[/tex]

[tex]\text{Rounding it to the nearest tenth = 8.9}[/tex]

[tex]\therefore \text{Hypotenuse of the triangle = 8.9}[/tex]

Option D= 8.9 units is the correct answer

Answer:

40% increase

Step-by-step explanation:

7-5=2

plug in:

2/5=x/100

x=40

40% increse

The sandwhich increased by 2 dollars. The amount of change must be divided by the original. 7-5 is 2, which means we must divide 2 by 5. 2/5 is .40. Which translates to 40% or 40/100. This means that the price of the sandwhich increased 40%.

Hope this helped you <3!

Answer:

5.27 × 10⁷ is the scientific notation for 52,700,000.

Answer:

the trip is 10 miles long

Step-by-step explanation:

im sorry i dont know the steps

Applying the volume of a rectangular prism, the following are determined:

A & G has a solution of 120.

B & F: 714

C & E: 56

D & H: 9.5

Volume = base area × height of prism = 1/2(bh) × H

A. Volume = 1/2(bh) × H = 1/2(6)(8) × 5 = 120 units³

B. Volume = 1/2(bh) × H = 1/2(6)(14) × 17 = 714 units³

C. Volume = 1/2(bh) × H = 1/2(12)(8) × x = 2,688 units³

48x = 2,688

x = 2,688/48

x = 56 units (height of the prism)

D. Volume = base area × height of prism

Plug in the given values

27.36 = base area × 2.88

27.36/2.88 = area of triangular base

area of triangular base = 9.5 units².

E. Volume = 1/2(bh) × H = 1/2(8)(15) × x = 3,360 units³

60x = 3,360

x = 3,360/60

x = 56 units (height of the prism)

F. Volume = 1/2(bh) × H = 1/2(17)(4) × 21 = 714 units³

G. Volume = 1/2(bh) × H = 1/2(3)(5) × 16 = 120 units³

H. Volume = 1/2(bh) × H = 1/2(1.9)(2) × 5 = 9.5 units³

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Answer: y=0.2

Step-by-step explanation:

y∝(1/x)

this implies that

y=k/x    eq(*)

when y =0.25 when x =4

0.25=k/4

k=1

for y when x=5

y=k/x

y=1/5

y=0.2

Answer:

C

Step-by-step explanation:

If the graph of a relationship is a line or a ray through the origin, then it is proportional.

The line in graph C goes through the origin (0,0)

Answer:

y=2x+4

Step-by-step explanation:

60 cds - 12 country = 48 cds are not country.

probability of picking one that is not country = total of non country/ total cds

probability = 48/60 which reduces to 4/5

answer: 4/5

Answer:

Lucas has 16 chocolate bars

Step-by-step explanation:

Let x = number of chocolate bars Lucas has

⇒ x - 2 = number of chocolate bars Caidon has

If they have 30 chocolate bars altogether then:

⇒ x + x - 2 = 30

⇒ 2x - 2 = 30

⇒ 2x = 32

⇒ x = 16

Therefore, Lucas has 16 chocolate bars (and Caidon has 14 chocolate bars).

The surface area and the volume of the cone is 816.4 km² and 7536 km³ respectively.

Volume is the capacity of an object.

To calculate the surface area and volume of the cone shown above, we use equation 1 and equation 2 respectively.

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1 and equation 2 respectively.

Also for the volume of tyhe cone

Hence, The surface area and the volume of the cone is 816.4 km² and 7536 km³ respectively.

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The equation to calculate the coordinates of point B is (b) 3 = √(x - 4)²+(y - 2)²

The given parameters are:

A = (4,2)
AB = 3

The distance formula is:

AB = √(x - x1)²+(y - y1)²

So, we have:

3 = √(x - 4)²+(y - 2)²

Hence, the equation to calculate the coordinates of point B is (b) 3 = √(x - 4)²+(y - 2)²

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a. The interest for the first payment is $40.

b. The interest for the seventh payment is $29.27.

In financial accounting and management, interest refers to the finance charge for obtaining or giving a loan or credit.

The interest payment or revenue is based on the interest rate applied to the principal or loan balance.

Loan = $3,200

Monthly payment = $199.68

Interest rate = 15%

Loan balance after 6 payments = $2,341.45

Interest for the first payment = $40 ($3,200 x 15% x 1/12)

Interest for the seventh payment = $29.27 ($2,341.45 x 15% x 1/12)

Thus, while the interest for the first payment is $40, the interest for the seventh payment is $29.27.

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Answer:

n= 5/3 or 1.67

Step-by-step explanation:

9n^2 -9 =16

9n^2 = 16 + 9

9n^2 = 25

n^2 =25/9

n^2 =25/9

[tex]\sqrt{n^2} = \sqrt{\frac{25}{9} }[/tex]

n= 5/3 or 1.67

[tex]~~~~~~9n^2 -9 = 16\\\\\implies 9(n^2 -1) = 16\\\\\implies n^2 -1 = \dfrac{16}9\\\\\implies n^2 = \dfrac{16}{9}+1\\\\\implies n^2 = \dfrac{25}{9}\\\\\implies n=\pm\sqrt{\dfrac{25}{9}}\\\\\implies n= \pm\dfrac 53\\\\\implies n = \pm1.67[/tex]

Answer: A. -$157

Step-by-step explanation:

This is would be much more in debt for his credit card statement, it would take him longer to pay off.

Answer:

Question 6: The cost of a chocolate bar is $1.20 and the cost of a box of gum is $0.75

Question 7:  There were 7 students

Step-by-step explanation:

We will be using system of equations which a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations intersect.

Our Variables:

- chocolate bar which will be represent as b in the equation

- box of gum which will be represent as g in the equation

Forming the equations:

Sally -

bought 2 chocolate bars (b)

bought 1 box of gum (g)

to a total of $3.15

so 2b + 1g = $3.15

Evans -

bought 1 chocolate bars (b)

bought 2 box of gum (1)

to a total of $2.70

so 1b + 2g = $2.70

Solving using substation:

2b + 1g = $3.15              we want to isolate b to input into the other equation

1b + 2g = $2.70                  

2b + 1g = $3.15             subtract 1g from both sides, divided both sides by 2

2b / 2 + 1g - 1g = $3.15 - 1g / 2

b = $3.15 - 1g / 2

Now substation b into the second equation

1b + 2g = $2.70 becomes 1($3.15 - 1g / 2) + 2g = $2.70

simplify,

$3.15 + 3g / 2 = $2.70                isolate g

$3.15 + 3g / 2 x 2 = $2.70 x 2   multiply both sides by 2

$3.15 + 3g = $5.40                     subtract $3.15, divided by 3 from both sides

$3.15 - $3.15 + 3g / 3 = $5.40 - $3.15 / 3

g = $5.40 - $3.15 / 3

g = $2.25 / 3

g = $0.75

Now plug in g to get b into any equation:

If Sally equation is used

2b + 1g = $3.15

2b + 1(0.75) = $3.15    →    2b + 0.75 = $3.15

2b + 0.75 - 0.75 = $3.15 - 0.75

2b = $2.40    →    2b / 2 = $2.40 / 2

b = $1.20

If Evans equation is used

1b + 2g = $2.70

1b + 2(0.75) = $2.70     →    1b + 1.50 = $2.70

1b + 1.50 - 1.50 = $2.70 - 1.50

1b / 1 = $1.20 / 1

b = $1.20

Our Variables:

- adult which will be represent as A in the equation

- student which will be represent as S in the equation  

Forming the equations:

- sample size: group of 30

- Adult cost $5        (A)

- Student cost $2    (S)

- Five members are free

to a total cost is $104

so A + S = 30 - 5

this is how many of each variable from the total group and we subtract 5 as 5 members were free

so 5A + 2S = $104

Solving using substation:

A + S = 25                     we want to isolate a to input into the other equation

5A + 2S = $104

a = 18

s =7

Answer:

12

Step-by-step explanation:

Using Permutation Formula :

The height of the tree whose angle of elevation is [tex]74^{0}[/tex] and 54 feet tall is 188 foot.

Height of the tree= 188 foot (rounding off nearest tenth)

The angle of elevation in math is "the angle formed between the horizontal line and the line of sight when an observer looks upwards is known as an angle of elevation".

We know by trigonometric ratios,

[tex]tan \; \theta = \frac{P}{B}[/tex]

[tex]tan \; 74^0 \;[/tex] = [tex]\frac{P}{54}[/tex]

3.48 = [tex]\frac{P}{54}[/tex]

P= 3.48 x 54

 = 187.92 feet

 ≈ 188 foot (rounding off nearest tenth)

The height of the tree whose angle of elevation is  and 54 feet tall is 188 foot.

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Answer: 188.3 feet tall*

Step-by-step explanation:

Answer:

800 Cm

Step-by-step explanation:

bro typa question is that its common sense that 100 cm = 1 meter

Answer:

3

Step-by-step explanation:

Volume of a cone

V = pi x r^2 x h/3

So plug in the values we have

30pi = pi x r^2 x 10/3

30 = r^2 10/3

9 = r^2

3 = r

Answer: approximately 4478.46096908264 square cm.

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

Explanation:

I'm assuming this is a regular 12-sided polygon

The area formula for regular polygons is

[tex]A = 0.25n*s^2*\cot(180/n)[/tex]

where in this case we have n = 12 sides and each side is of length s = 20

So,

[tex]A = 0.25n*s^2*\cot(180/n)\\\\A = 0.25*12*(20)^2*\cot(180/12)\\\\A = 0.25*12*(20)^2*\cot(15)\\\\A = 0.25*12*(20)^2*\frac{1}{\tan(15)}\\\\A \approx 4478.46096908264\\\\[/tex]

The area of this regular polygon is approximately 4478.46096908264 square cm.

Make sure your calculator is in degree mode when computing that value of cot(15) or 1/tan(15).

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

Explanation:

The circumference is the perimeter of the circle. It's the distance around the circle's edge. Think of it like a fence.

The full circle's perimeter is 6 units. The arc length is a piece of that and it's 1 unit.

1/6 of the full perimeter is the arc length

1/6 of a full 360 degree rotation is (1/6)*360 = 360/6 = 60

The central angle of the arc is 60 degrees.

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

If you want to use a formula, it would be

[tex]A = \frac{L}{C}*360[/tex]

where,

A = central angle of the arc

L = arc length

C = circumference

You would plug in L = 1 and C = 6 to find that A = 60

The increasing order of the complex numbers is (√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ =  (-1 + √3i)¹² < (√3 - √3i)⁴.

The absolute values of the complex numbers are determined as follows;

(sqrt3-sqrt3i)^4 = (√3 - √3i)⁴

[tex]|z| = \sqrt{(\sqrt{3} )^2 + (\sqrt{3 }\times1 )^2} } \\\\|z| = \sqrt{6}[/tex]

(-1+sqrt3i)^12 = (-1 + √3i)¹²

[tex]|z| = \sqrt{(-1)^2 + (\sqrt{3)^2} } \\\\|z| = \sqrt{4} \\\\|z| = 2[/tex]

(sqrt 3-i)^6 = (√3 - i)⁶

[tex]|z| = \sqrt{(\sqrt{3})^2 + (-1)^2 } \\\\|z| = \sqrt{4} \\\\|z| = 2[/tex]

(sqrt2-sqrt2i)^8 = (√2 - √2i)⁸

[tex]|z| = \sqrt{(\sqrt{2} )^2 + (\sqrt{2})^2 } \\\\|z| = 2[/tex]

(sqrt2-i)^6 = (√2 - i)⁶

[tex]|z| = \sqrt{(\sqrt{2})^2 + (-1)^2} } \\\\|z| = \sqrt{3}[/tex]

Increasing order of the complex numbers;

(√2 - i)⁶ < (√2 - √2i)⁸ = (√3 - i)⁶ =  (-1 + √3i)¹² < (√3 - √3i)⁴.

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Answer:

see screenshot below

Step-by-step explanation:

correct on edmentum

Answer:

5/8

Step-by-step explanation:

The longest lizard there is, is 3/4 feet. The shortest lizard is 1/8. The equation to solve this is 3/4 - 1/8. The answer to this is 5/8. I hope this helps :)