Scores on the ACT exam have a N(μ = 18,σ = 6) distribution, while scores on the SAT
exam have a N(μ = 500,σ = 100) distribution. Suppose Xiaoyu got a 27 on the ACT
exam, while Emily got a 720 on the SAT exam. Who has the higher relative score? Why?

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that,

In triangle TPQ,

As it is given that, RS || PQ

So, it means

⇛∠TRS = ∠TPQ [ Corresponding angles ]

⇛ ∠TSR = ∠TPQ [ Corresponding angles ]

[tex]\rm\implies \: \triangle TPQ \: \sim \: \triangle TRS \: \: \: \: \: \: \{AA \}[/tex]

Now, We know

Area Ratio Theorem,

This theorem states that :- The ratio of the area of two similar triangles is equal to the ratio of the squares of corresponding sides.

[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{ar( \triangle \: TRS)} = \dfrac{ {PQ}^{2} }{ {RS}^{2} } [/tex]

[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = \dfrac{ {6}^{2} }{ {3}^{2} } [/tex]

[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = \dfrac{36 }{9} [/tex]

[tex]\rm\implies \:\dfrac{ar( \triangle \: TPQ)}{15} = 4 [/tex]

[tex]\rm\implies \:ar( \triangle \: TPQ) = 60 \: {cm}^{2} [/tex]

Answer:A manufacturing company makes two types of water skis, a trick ski and a slalom ski. The relevant manufacturing data are given in the table. (A) If the profit on a trick ski is $40$ and the profit on a slalom ski is $30,$ how many of each type of ski should be manufactured each day to realize a maximum profit? What is the maximum profit? (B) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski decreases to $25$ and all other data remains the same. (C) Discuss the effect on the production schedule and the maximum profit if the profit on a slalom ski increases to $45$ and all other data remain the same.

Step-by-step explanation:

The optimal production plan for maximizing profit is to manufacture 48 slalom skis and 0 trick skis each day, resulting in a maximum profit of $2880.

Given data:

To solve this problem, we can use linear programming techniques to find the optimal number of trick skis and slalom skis that should be manufactured each day to maximize the profit.

x = number of trick skis

y = number of slalom skis

We need to maximize the profit function: P = 40x + 60y

Subject to the following constraints:

1x + 1y ≤ 336 (Fabricating department constraint)

1x + 1y ≤ 48 (Finishing department constraint)

x, y ≥ 0 (Non-negativity constraint)

We can graphically represent these constraints on a coordinate plane and find the feasible region, which is the region where all constraints are satisfied. Then, we can evaluate the profit function at the corner points of the feasible region to find the maximum profit.

After solving this system of linear inequalities, we find that the feasible region is a triangle with vertices at (0, 48), (0, 48), and (48, 48).

Evaluating the profit function at these vertices:

P(0, 48) = 40(0) + 60(48)

= $2880

P(0, 0) = 40(0) + 60(0)

= $0

P(48, 0) = 40(48) + 60(0)

= $1920

The maximum profit is $2880, which occurs when they produce 48 slalom skis and 0 trick skis.

Hence, the optimal production plan for maximizing profit is to manufacture 48 slalom skis and 0 trick skis each day, resulting in a maximum profit of $2880.

To learn more about linear programming, refer:

https://brainly.com/question/28579054

#SPJ3

Answer: Total cost = 4m

Step-by-step explanation:

Each meal is $4, so the total would be the number of meals times $4/meal: Total = 4m

Answer:

dₙ = (m-1)*4

Step-by-step explanation:

d1: initial dollar   d1=0

dₙ = (m-1)*4

d₁ = (1-1)*4 = 0

d₂ = (2-1)*4 = 4

d₃ = (3-1)*4 = 8

Answer:

n=-10

Step-by-step explanation:

n+3=-7

n=-7-3

n=-10

this helps thank you

branlist please

Answer:

n = -10

Step-by-step explanation:

solving a one step equation with a missing variable

step 1: subtract 3 from both sides of the equation then simplify

ex: n + 3 - 3 = -7 - 3   (n = -10)

step 2: take your answer of n which is -10 and add plug it in into your original equation n + 3 = -7 and solve to check your answer

ex: n + 3 = -7   (-10 + 3 = -7)

add

-10 + 3 = -7

-7 = -7   (if both sides of the equation are the same numbers like -7 = -7 then your answer is true making n = -10 your answer) i would love to get brain if this is correct and helps <(^w^)>

Answer:

You would have a 80% chance.

Step-by-step explanation:

16 out of 20 is equal to 80%. ( I can't really explain how I got 80% -_-. ) Let me know if I'm wrong.

[tex] = 2ac \: + ab \: + 3a \: - 2bc[/tex]

see the attachment!!

hope it helps

Answer:

7/16

Step-by-step explanation:

please give brainliest

Add 14 and 13+14=27...ans

D.

I am so sorry if it is wrong

Answer:

The answer to the question is (2,-3).

Answer:

origanal

Step-by-step explanation:

origanaol

Answer: The measurement of ∠EFG is equal to 70°.

Step-by-step explanation:

Two interior angles who are always opposite to an exterior angle sums to that exterior angle. So we would start as the following:

(6x - 10) + 38 = 7x + 18

In order to find m∠EFG, we must first isolate x. In order to do that, we first add like terms together on both sides.

(6x - 10) + 38 = 7x + 18

6x + 28 = 7x + 18

We then substract 18 on both sides.

6x + 10 = 7x

We finally substract 6x from both sides in order to have the value of x.

x = 10

Now that we know the value of x, we substitute it in our the equation in order to find m∠EFG.

m∠EFG = 6x + 10

m∠EFG = 6(10) + 10

m∠EFG = 60 + 10

m∠EFG = 70

Answer:

50°

Step-by-step explanation:

( 7x + 18 )° = ( 6x - 10 )° + 38°

7x + 18 = 6x - 10 + 38

7x - 6x = 28 - 18

x = 10

m∠EFG = 6(10) - 10

m∠EFG = 50°

Answer:

Add 8 and 8 and then add 5and 5 and get answer 16

Step-by-step explanation:

Answer:

a^8

I hope this is the correct answer

have a great day

Answer:

a³

Step-by-step explanation:

(a².a³.(a-¹)²)

a²+³.a-¹×2

a⁵.a-²

a⁵+(-²)

a⁵-²

a³

Answer:

1 is equal

2 is greater

3 is greater

Step-by-step explanation:

2^3 x 2^5 is 32, and 2^5 is 32, meaning these are equal.

2^2 x 3^2 is 36, and 6^3 is 216, meaning 6^3 is greater.

2^3 x 3^2 is 72, and 6^2 is 36, meaning that 2^3 x 3^2 is greater.

Answer:

15×15×16=3600

15×15=225

225×16=3600

Answer:

Step-by-step explanation:

cost of 6 potatoes=24.65-18.95=5.70 $

cost of 1 potato=5.70÷9=0.95 $

Answer:

Step-by-step explanation:

6x + 7 + 3x - 16 = 180    {Supplementary}

6x  + 3x + 7 - 16 = 180

9x   - 9 = 180

      9x = 180+ 9

      9x = 189

         x = 189/9

x = 21

6x + 7 = 6*21 + 7 = 126 + 7 = 133

11y - 32 = 6x + 7    {Vertically opposite angles}

11y - 32 = 133

      11y = 133 + 32

      11y = 165

y = 165/11

y= 15

Answer:

A) Perimeter

Step-by-step explanation:

Answer:

A perimeter is the answer

Answer: can you show the selections?

Step-by-step explanation:

Answer:

you need 8 bins because 150/20 is 7.5 but you can't have half a bin and you need somewhere to put the other books

Answer:

<BAC=100°

Step-by-step explanation:

<ACB = <DCE - vertical angles are congruent

<ACB = 45° - substitute <DCE = 45° <ACB = <DCE

<ABC + <ACB + <BAC = 180° - angle sum theorem

35° + 45° + <BAC = 180° - substitute <ABC = 35°, <ACB = 45° INTO <ABC + <ACB + <BAC = 180 °

35°+ 45° + <BAC = 180°

180° - 80° = 100

Answer:

The answer that you are looking for is b

Answer:

13in

Step-by-step explanation:

remember it's the same angle width.

Answer:

Step-by-step explanation:

∠8 = ∠6

∠8 = 7x - 36

∠8 +∠9 = 180   {Linear pair}

7x - 36 + 5x + 12 = 180

7x + 5x - 36 + 12 = 180

   12x  - 24 = 180

            12x = 180 + 24

           12x   = 204

               x = 204/12

x = 17

∠6 = 7x - 36  = 7*17 - 36 = 119 - 36 = 83

∠11 = ∠6    {Vertically opposite angles}

∠11 = 83

give us a problem or somen

Step-by-step explanation:

Answer:

x=4, i did the other one on ur acc, sad to see these points go to waste.

Step-by-step explanation:

Answer: 83 meters

Step-by-step explanation:

The perimeter of a rectangle is 2l + 2w, where l is the length and w is the width.

2(96) + 2w = 358

192 + 2w = 358

2w = 166

w = 83

Hope it helps :) and let me know if you want me to elaborate.