Question

1. which of the following expressions has a value of 4? (a) (16 - 12)^2 (b) -|-4| (c) (96 / 8) - 2^3 (d) 2^4 - 4^2 2. tais baby brother has a mass of 3,745 grams. what is his mass in kilograms? (a) 0.3745 kg (b) 3.745 kg (c) 37.45 kg (d) 374.5 kg 3. a rectangle on a coordinate plane has vertices at (7, 5), (-7, 5), (-7, -2), and (7, -2). what is the perimeter of the rectangle? (a) 21 units (b) 34 units (c) 42 units (d) 98 units 4. which statement represents the situation described below? the cost c of a shirt is less than $27.50. (a) c > 27.50 (b) c < 27.50 (c) c = 27.50 (d) 27.50 < c 5. jayden uses the net below to design a box. how much cardboard will jayden need to make the box? (a) 60 ft^2 (b) 96 ft^2 (c) 128 ft^2 (d) 144 ft^2 6. kenji earned the test scores below in english class. {79, 91, 93, 85, 86, 88} after his next test, his mean and median scores both change to 88. what does he earn on this test? (a) 86 (b) 89 (c) 91 (d) 94

Explanation:

Step1: Solve question 1

Option A:

$(16 - 12)^2=(4)^2 = 16$

Option B:

$-|-4|=-4$

Option C:

$(96\div8)-2^3=12 - 8=4$

Option D:

$2^4-4^2=16 - 16=0$
So the answer to question 1 is C.

Step2: Solve question 2

Since $1$ kg = $1000$ g, to convert grams to kilograms, we divide by 1000. So $3745$ g=$\frac{3745}{1000}=3.745$ kg. The answer to question 2 is B.

Step3: Solve question 3

The length of the rectangle: The difference in x - coordinates of two points $(7,5)$ and $(-7,5)$ gives the length $l=|7-(-7)| = 14$. The width of the rectangle: The difference in y - coordinates of two points $(7,5)$ and $(7,-2)$ gives the width $w=|5-(-2)| = 7$. The perimeter of a rectangle $P = 2(l + w)=2(14 + 7)=42$ units. The answer to question 3 is C.

Step4: Solve question 4

The cost $c$ of a shirt is less than $\$27.50$, which is written as $c<27.50$. The answer to question 4 is B.

Step5: Solve question 5

The net is a rectangular - prism net. The surface area of a rectangular prism with length $l = 6$ ft, width $w = 4$ ft and height $h = 4$ ft is $S=2(lw+lh+wh)=2(6\times4 + 6\times4+4\times4)=2(24 + 24 + 16)=2\times64 = 128$ ft². The answer to question 5 is C.

Step6: Solve question 6

The original set of scores is $\{79,91,93,85,86,88\}$. Arrange in ascending order: $\{79,85,86,88,91,93\}$. The original median is $\frac{86 + 88}{2}=87$. Let the new score be $x$. The new set has 7 scores. The new median is the 4th - ranked score when the scores are arranged in ascending order. Since the new median is 88, when we add $x$ and arrange the scores in ascending order, $x$ must be such that the 4th - ranked score is 88. The new mean $\bar{x}=\frac{79 + 91+93+85+86+88+x}{7}=88$. Cross - multiply: $79 + 91+93+85+86+88+x=88\times7=616$. $522+x=616$. $x = 94$. The answer to question 6 is D.

Answer:

1. C. $(96\div8)-2^3$
2. B. $3.745$ kg
3. C. 42 units
4. B. $c<27.50$
5. C. $128$ ft²
6. D. 94