Question

1. what is the mean of the data below? 24, 32, 45, 56, 67 a) 44 b) 44.8 c) 45 d) 56 10. simplify the expression. 2(3x + 4) - x 11. solve for x. 3x + 7 + x = 35 12. write an algebraic expression for sixteen decreased by a number a. 13. evaluate the expression 2x - 8 - 3y if x = 11 and y = -2. 14. no calculator. add. 2/3 + 3/5 15. joes seafood charges $12.75 per crabcake plus $26.25 for shipping and handling to send fresh maryland crab cakes anywhere in the continental us. the total cost of shipping your order was $128.25. how many crab cakes did you order?

Explanation:

Step1: Calculate the sum of the data

$$24 + 32+45 + 56+67=224$$

Step2: Calculate the mean

The number of data points \(n = 5\). The mean formula is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). So \(\bar{x}=\frac{224}{5}=44.8\)

Step3: Simplify the expression \(2(3x + 4)-x\)

Use the distributive property \(a(b + c)=ab+ac\). First, \(2(3x + 4)=6x+8\). Then \(6x + 8-x=(6x-x)+8 = 5x+8\)

Step4: Solve the equation \(3x + 7+x=35\)

Combine like - terms: \(4x+7 = 35\). Subtract 7 from both sides: \(4x=35 - 7=28\). Divide both sides by 4: \(x=\frac{28}{4}=7\)

Step5: Write the algebraic expression for sixteen decreased by a number \(a\)

The expression is \(16 - a\)

Step6: Evaluate the expression \(2x-8 - 3y\) when \(x = 11\) and \(y=-2\)

Substitute \(x = 11\) and \(y=-2\) into the expression: \(2\times11-8-3\times(-2)=22-8 + 6=(22-8)+6=14 + 6=20\)

Step7: Add \(\frac{2}{3}+\frac{3}{5}\)

Find a common denominator. The least common multiple of 3 and 5 is 15. Rewrite the fractions: \(\frac{2}{3}=\frac{2\times5}{3\times5}=\frac{10}{15}\), \(\frac{3}{5}=\frac{3\times3}{5\times3}=\frac{9}{15}\). Then \(\frac{10}{15}+\frac{9}{15}=\frac{10 + 9}{15}=\frac{19}{15}=1\frac{4}{15}\)

Step8: Solve the crab - cake problem

Let the number of crab - cakes be \(n\). The cost equation is \(12.75n+26.25 = 128.25\). Subtract 26.25 from both sides: \(12.75n=128.25-26.25 = 102\). Divide both sides by 12.75: \(n=\frac{102}{12.75}=8\)

Answer:

1. B. \(44.8\)
2. \(5x + 8\)
3. \(x = 7\)
4. \(16 - a\)
5. \(20\)
6. \(\frac{19}{15}\) or \(1\frac{4}{15}\)
7. \(8\)