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3 years ago

8

Sarah has an older sister and a younger sister. Her older sister is one year more than twice Sarah's age. Sarah younger sister i

s three years younger than she is. The sum of their three ages is 26. Formulate 3 equations that describes the situation.

1 answer:

Alchen [17]3 years ago

8 0

Sarah has 7 years, sarah's older sister is 15, and sarah's younger sister is 4 because 7+15+4=26 hope this helps

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Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 12 ca

Ksju [112]

Answer:

a) 45 possible outcomes

b) 55 possible outcomes

Step-by-step explanation:

Given:

- Total cavities = 12

- Selection = 3 parts

- Non-conforming cavities = 2

Find:

a) How many samples contain exactly 1 nonconforming part?

b) How many samples contain at least 1 nonconforming part?

Solution:

- The question asks for the use of combinations to express the outcomes for each scenario.

- For first part, we want the inspector to pick exactly one non-conforming part among 3 selected. So let us say that he has already chosen that one non conforming cavity. Now he has to make 2 more selections out of total conforming cavities = 12 - 2 = 10 conforming cavities. Hence, the total possible outcome is to chose 2 randomly from 10 conforming cavities.

( Exactly 1 ) 10C2 = 45 possible outcomes

- The second part entails that at-least 1 non-conforming cavity is selected. To choose exactly 1 non conforming we calculated above. In the similar way calculate for selecting exactly 2 non-conforming cavities. The total possible outcome would be to choose from 10 conforming and we choose 1 from it:

( Exactly 2 ) 10C1 = 10 possible outcomes

- Hence, for at-least 1 non conforming cavity being selected we same the above two cases calculated:

(At-least 1 ) = ( Exactly 1 ) + ( Exactly 2 )

(At-least 1 ) = 45 + 10 = 55 possible outcomes

4 0

3 years ago

An investment firm invested in two companies last year. They invested $40,000 in company A and made a profit of 15%. They invest

alexira [117]

Answer:

A) $8200.

B) 16.4%

Step-by-step explanation:

Here is the complete question: An investment firm invested in two companies last year. They invested $40,000 in company A and made a profit of 15%. They invested $10,000 in company B and made a profit of 22%.

A) What is the investment firms total profit?

B) What is the percent profit of the total investment?

Given: Company A invested $40000 and made profit of 15%

Company B invested $10000 and made profit of 22%

A) First lets find the profit of company A and B.

Company A= $\frac{15}{100} \times \$ 40000= \$ 6000.$

∴ Profit of company A is $6000.

Company B= $\frac{22}{100} \times \$ 10000= \$ 2200$

∴ Profit of company B is $2200.

Total profit= profit of company A+ profit of company B

⇒ $Total\ profit= \$ 6000+\$ 2200$

∴ Total Profit= $\$ 8200$

Hence, the total profit of investment firm is $8200.

B) Now finding the percentage of total profit made by firm.

Total investment by the firm= $\$ 40000+\$ 10000= \$ 50000$

∴ Total investment done by the firm is $50000.

Percent of profit= $\frac{Total\ profit}{Total\ investment} \times 100$

⇒ Percent of profit= $\frac{8200}{50000} \times 100$

⇒ Percent of profit= $\frac{82}{5} = 16.4\%$

Hence, 16.4% is the percent profit of the total investment.

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3 years ago

Joey built a model sailboat that is similar to his real sailboat. The triangular sail on

lord [1]

Answer:

31.25

Step-by-step explanation:

25/12=2.083333

15 x 2.0833333=31.24999999995

round up to get 31.25

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2 years ago

For the polynomial below, what is the coefficient of the term with the power of 1 3? x + x4 +6x +5 3

vazorg [7]

Answer:

c.1

Step-by-step explanation:

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3 years ago

A class rolled number cubes. Their results are shown in the table. What is the experimental probability of rolling the number1?

Amiraneli [1.4K]

Total occurrences = 42 + 44 + 45 + 44 + 47 + 46 = 268

#1 occurs 42 times

The probability of rolling the number 1 = 42/268 = 0.1567 = 15.7%

Answer

A) 15.7%

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3 years ago