Answers:
In other words, only choice C is false while the others are true.
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Explanation:
The height of each bar represents the frequency for each group. It tells us how many students are in a certain interval. For example, the first bar has a height of 3 units to indicate there are 3 students between 140 and 155 cm.
Add up the heights of each bar to find the total number of students: 3+5+6+5+3+2 = 24
Statement A is correct because there are 24 students.
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Statement B is also correct. This is because the highest value on the x axis is 230 and the lowest is 140. The range is the distance or gap between them. Subtract the values: 230-140 = 90.
The distance from the shortest height (140 cm) and tallest height (230 cm) is 90 cm, which is the range.
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Unlike the previous two statements, choice C is not correct. Each bar represents a different interval. There are 6 bars, so there are 6 intervals (not 7).
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Choice D however, is correct. Focus on any single bar. Look at where its left and right endpoints are located. The first bar for instance starts at x = 140 and ends at x = 155. The gap is 155-140 = 15 units wide.
The value of x is 27°.
Solution:
Given .
∠A = 3x – 10, ∠C = 45°, ∠D = 2x + 10
<em>If two triangles are congruent, then the angles are congruent.</em>
∠A = ∠E (Alternate interior angles)
∠C = ∠C (Reflexive property)
∠B = ∠D (Alternative interior angles)
⇒ ∠B = 2x + 10
<em>Sum of the interior angles of the triangle = 180°</em>
In ΔACB,
3x – 10 + 45° + 2x + 10 = 180°
5x + 45° = 180°
Subtract 45° on both sides of the equation.
5x = 135°
Divide by 5 on both sides of the equation.
x = 27°
The value of x is 27°.
Answer:
x=8
Step-by-step explanation:
−2x−40=8(1−x)
Step 1: Simplify both sides of the equation.
−2x−40=8(1−x)
−2x+−40=(8)(1)+(8)(−x)(Distribute)
−2x+−40=8+−8x
−2x−40=−8x+8
Step 2: Add 8x to both sides.
−2x−40+8x=−8x+8+8x
6x−40=8
Step 3: Add 40 to both sides.
6x−40+40=8+40
6x=48
Step 4: Divide both sides by 6.
to get the answer
x=8
Answer: d. $852.96
Step-by-step explanation:
Given: The net pay = $667.17
Since net pay is the amount of money your employees take home after all deductions have been taken out.
We know that gross pay is the amount of money that employees receive before any taxes and deductions are taken out.
Thus to find the gross pay, we need to add all of the deductions to the net pay as:
Gross pay
Hence, D is the right option.
Answer:
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