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Strike441 [17]
2 years ago
12

Fine the sum of the first 8 terms of the arithmetic series 2+7+12+...

Mathematics
1 answer:
ss7ja [257]2 years ago
4 0

Answer:

156

Step-by-step explanation:

s8 = n/2 [2t + (n-1)(d)]

= 8/2 [2(2) + (8-1)(5)]

= 4 [4 + (7)(5)]

= 4 (4 + 35)

= 4 (39)

= 156

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Express the trig ratios as fractions in simplest terms.
Jet001 [13]

Answer:

Step-by-step explanation:

SOH CAH TOA

cos K  = 36/48 = 3/4

SIN L = 36/48 = 3/4

4 0
2 years ago
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
3 years ago
A trapezoid has four sides with two sides that are the same length. Let the two sides have length x. The longest side has a leng
Oduvanchick [21]

Answer:

fx21

Step-by-step explanation:

5 0
3 years ago
What is the first step?
kogti [31]

Answer:

-5x-1/6=3/2

-5×1/6+1/6=3/2+1/6

-5×÷5×=10/6/-5x

x=-10/30

<h3> x=-1/3</h3>

8 0
3 years ago
Factor the following, I will give 5 stars and thanks.
Maurinko [17]

Answer:

17) k=-5,-6

18) x=6,4

19) k=-2,-6

20) v=6,-3

Step-by-step explanation:

6 0
3 years ago
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