lesson #33\n1. a 12\×8\ rectangle is divided into two congruent triangles. what is the area of each…

lesson #33\n1. a 12\×8\ rectangle is divided into two congruent triangles. what is the area of each triangle?\n2. 720÷30 =?\n3. write the ratio of buttons to spools. for every 6 buttons, there is/are 2 spool(s).\n4. kim got a present for her birthday. the box measured 4×7×6 feet. what was the cubic volume of the present?\n5. to evaluate an expression means to find its value. evaluate 6⁴.\n6. a survey asks workers about their salaries. will there be a wider range of data if workers give their salaries to the nearest thousand dollars or to the nearest ten thousand dollars?\n7. martine is milking the cow. the milk yield in gallons is listed in the table. fill in the milk yield in quarts and cups.\n8. locate table k in the appendix. what is the range of the data points in this table?\n9. find the prime - factorization of 20.\n10. study the following expression: 3x² + 5x - 7. there are 3 terms: 3x², 5x, and - 7. terms are quantities connected by a plus or minus sign in an algebraic expression. identify the terms in the expression 8t³ - 4t² + 3t - 2.\n11. if 4 cups of ice cream have 1,000 calories, how many calories are in one cup of ice cream? write the unit rate in calories per cup.\n12. 88.36 + 29.421 =?\n13. solve and compare. 25×4 - 3 and 25×(4 - 3)\n14. how many sixths of a pound are in ⅔ pound? use a fraction model. a) ⅑ b) 4\n15. 3⅝ + 2⅗ =?

lesson #33\n1. a 12\×8\ rectangle is divided into two congruent triangles. what is the area of each triangle?\n2. 720÷30 =?\n3. write the ratio of buttons to spools. for every 6 buttons, there is/are 2 spool(s).\n4. kim got a present for her birthday. the box measured 4×7×6 feet. what was the cubic volume of the present?\n5. to evaluate an expression means to find its value. evaluate 6⁴.\n6. a survey asks workers about their salaries. will there be a wider range of data if workers give their salaries to the nearest thousand dollars or to the nearest ten thousand dollars?\n7. martine is milking the cow. the milk yield in gallons is listed in the table. fill in the milk yield in quarts and cups.\n8. locate table k in the appendix. what is the range of the data points in this table?\n9. find the prime - factorization of 20.\n10. study the following expression: 3x² + 5x - 7. there are 3 terms: 3x², 5x, and - 7. terms are quantities connected by a plus or minus sign in an algebraic expression. identify the terms in the expression 8t³ - 4t² + 3t - 2.\n11. if 4 cups of ice cream have 1,000 calories, how many calories are in one cup of ice cream? write the unit rate in calories per cup.\n12. 88.36 + 29.421 =?\n13. solve and compare. 25×4 - 3 and 25×(4 - 3)\n14. how many sixths of a pound are in ⅔ pound? use a fraction model. a) ⅑ b) 4\n15. 3⅝ + 2⅗ =?

Answer

Explanation:

Step1: Find rectangle area

The area of a rectangle is $A = l\times w$, where $l = 12$ inches and $w = 8$ inches. So $A=12\times8 = 96$ square - inches.

Step2: Find triangle area

Since the rectangle is divided into two congruent triangles, the area of each triangle is half of the rectangle's area. So $A_{triangle}=\frac{1}{2}\times96 = 48$ square - inches.

Answer:

48 square - inches

Explanation:

Step1: Perform division

$720\div30=\frac{720}{30}=24$.

Answer:

24

Explanation:

Step1: Identify ratio

From the description, for every 6 buttons, there are 2 spools. The ratio of buttons to spools is $\frac{6}{2}=\frac{3}{1}$.

Answer:

For every 6 buttons, there are 2 spools. The ratio is 3:1.

Explanation:

Step1: Use volume formula

The volume of a rectangular - prism (the box) is $V=l\times w\times h$, where $l = 4$ feet, $w = 7$ feet, and $h = 6$ feet. So $V=4\times7\times6=168$ cubic feet.

Answer:

168 cubic feet

Explanation:

Step1: Evaluate exponent

$6^{4}=6\times6\times6\times6 = 1296$.

Answer:

1296

Explanation:

Step1: Understand data range

If workers give their salaries to the nearest ten - thousand dollars, the values are grouped in larger intervals compared to giving salaries to the nearest thousand dollars. So there will be a wider range of data when giving salaries to the nearest ten - thousand dollars.

Answer:

To the nearest ten thousand dollars

(No table provided, unable to solve)

(No Table K provided, unable to solve)

Explanation:

Step1: Start factoring

We start by dividing 20 by the smallest prime number. $20\div2 = 10$, then $10\div2 = 5$. So $20=2\times2\times5=2^{2}\times5$.

Answer:

$2^{2}\times5$

Explanation:

Step1: Identify terms

In the expression $8t^{3}-4t^{2}+3t - 2$, the terms are $8t^{3}$, $-4t^{2}$, $3t$, and $-2$.

Answer:

$8t^{3}$, $-4t^{2}$, $3t$, $-2$

Explanation:

Step1: Calculate unit rate

If 4 cups of ice - cream have 1000 calories, then for 1 cup, the number of calories is $\frac{1000}{4}=250$ calories per cup.

Answer:

250 Calories per cup

Explanation:

Step1: Add decimals

$88.36+29.421 = 117.781$.

Answer:

117.781

Explanation:

Step1: Calculate first expression

$25\times4 - 3=100 - 3=97$.

Step2: Calculate second expression

$25\times(4 - 3)=25\times1 = 25$.

Step3: Compare

$97>25$.

Answer:

$25\times4 - 3 = 97$, $25\times(4 - 3)=25$, and $97>25$

Explanation:

Step1: Set up division

We want to find out how many sixths are in $\frac{2}{3}$ pound. We divide $\frac{2}{3}$ by $\frac{1}{6}$, which is $\frac{2}{3}\div\frac{1}{6}=\frac{2}{3}\times6 = 4$.

Answer:

B. 4

Explanation:

Step1: Convert mixed numbers to improper fractions

$3\frac{8}{12}=\frac{3\times12 + 8}{12}=\frac{44}{12}$, $2\frac{3}{10}=\frac{2\times10+3}{10}=\frac{23}{10}$.

Step2: Find a common denominator

The common denominator of 12 and 10 is 60. $\frac{44}{12}=\frac{44\times5}{12\times5}=\frac{220}{60}$, $\frac{23}{10}=\frac{23\times6}{10\times6}=\frac{138}{60}$.

Step3: Add fractions

$\frac{220}{60}+\frac{138}{60}=\frac{220 + 138}{60}=\frac{358}{60}=\frac{179}{30}=5\frac{29}{30}$.

Answer:

$5\frac{29}{30}$