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Paul [167]
3 years ago
5

Help please. Thanks in advance

Mathematics
1 answer:
anygoal [31]3 years ago
6 0
Since they want only the coordinates of the vertices. You only care about where the lines intersect, the greater than, less than signs are irrelevant.

Get each equation in 'y=mx+b' form
1)  y = -x + 9
2)  y = 2x-21
3)  y = -4x +15

Now you can set any 2 equations equal to each other and solve for 'x'.
This will be the 'x' coordinate of the point where the 2 lines intersect.
You need 3 points, so you will need 3 different sets of 2 equations:

1) = 2)
2x -21 = -x+9
3x = 30
x = 10  -----> y = -(10)+9 = -1


1) = 3)
-x+9 = -4x+15
3x = 6
x = 2  -------> y = -(2) + 9 = 7

2) = 3)
2x - 21 = -4x+15
6x = 36
x = 6  ---------> y = 2(6) -21 = -9

Therefore the 3 intersecting points are:
(10,-1)
(2, 7)
(6, -9)
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The amount of toothpaste in a tube is normally distributed with a mean of 6.5 ounces and a standard
Anarel [89]

Answer:

a) 266 tubes ,  TC_r = $53.2

b) 266 tubes ,  T.Loss = $13.30

Step-by-step explanation:

Given:

- The sample size of tubes n = 1,000 tubes

- The mean of the sample u = 6.5 oz

- The standard deviation of the sample s.d = 0.8 oz

- Cost of manufacturing a tube C_t = 50 cents

- Cost of refilling a tube C_r = 20 cents

- Profit loss per tube Loss = 5 cents

Find:

a). How many tubes will be found to contain less than 6 ounces? In that case, what will be the total cost of the  refill?

b) How many tubes will be found to contain more than 7 ounces? In that case, what will be the amount of  profit lost?

Solution:

- First we will compute the probability of tube containing less than 6 oz.

- Declaring X : The amount of toothpaste.

Where,                         X ~ N ( 6.5 , 0.8 )

- We need to compute P ( X < 6 oz )?

Compute the Z-score value:

                  P ( X < 6 oz ) =  P ( Z < (6 - 6.5) / 0.8 ) = P ( Z < -0.625 )

Use the Z table to find the probability:

                               P ( X < 6 oz ) = P ( Z < -0.625 ) = 0.266

- The probability that it lies below 6 ounces. The total sample size is n = 1000.

       The number of tubes with X < 6 ounces = 1000* P ( X < 6 oz )

                                                                           = 1000*0.266 = 266 tubes.

- The total cost of refill:

                            TC_r = C_f*(number of tubes with X < 6)

                            TC_r = 20*266 = 5320 cents = $53.2

- We need to compute P ( X > 7 oz )?

Compute the Z-score value:

                  P ( X > 7 oz ) =  P ( Z > (7 - 6.5) / 0.8 ) = P ( Z < 0.625 )

Use the Z table to find the probability:

                               P ( X > 7 oz ) = P ( Z > 0.625 ) = 0.266

- The probability that it lies above 7 ounces. The total sample size is n = 1000.

       The number of tubes with X > 7 ounces = 1000* P ( X > 7 oz )

                                                                           = 1000*0.266 = 266 tubes.

- The total cost of refill:

                            T.Loss = Loss*(number of tubes with X > 7)

                            T.Loss = 5*266 = 1330 cents = $13.30

5 0
2 years ago
Simplify the ratio 24/56
Brrunno [24]
How to solve:
Step 1 :  Note down the given ratio from the questions.

Step 2 :  <span>Find the greatest common factor, and divide the numerator and denominator by that value.
Answer: 3:7</span>
7 0
3 years ago
Round this number to the nearest thousand 7,433,654
Aliun [14]
The answer is going to be 7,434,000. hope that helped
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3 years ago
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nataly862011 [7]

Answer:

78 girls

Step-by-step explanation:

Ratio is 3:4, so that means the total number of 182 can be divided into 7 parts. 182 divided by 7 is 26, so each part is 26. The ratio of girls is 3, so 3 times 26 is 78. You can check this by putting (3*26)/(4*26) simplifies to 78/104 to 3/4 which is the right ratio

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oksano4ka [1.4K]

Answer:

B

Step-by-step explanation:

3.4 x -3.4= -11.56  

3.4 X 3.4 = 11.56 YES

-3.4 X -3.4 = 11.56

-3.4 X 3.4 = -11.56

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