Find the mode or modes.
Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mode(s).
51 62 59
54 56 66
67 58 50
Question 29 options:
A)
51, 62, 59, 54, 56, 66, 67, 58, 50
B)
No mode
C)
58.1
D)
58
To find the slope of the line, we need to rewrite the given equation in slope-intercept form (y = mx + b), where m represents the slope.
Starting with the given equation:
3x + 5y = 19
We isolate y on one side by subtracting 3x from both sides:
5y = -3x + 19
Now we divide both sides by 5 to solve for y:
y = (-3/5)x + 19/5
Comparing this equation with y = mx + b, we can see that the slope is -3/5.
To sketch the graph, we can plot two points and draw a line through them.
1. Let's choose x = 0:
y = (-3/5)(0) + 19/5
y = 19/5
The point (0, 19/5) is on the line.
2. Now let's choose another value for x, such as x = 5:
y = (-3/5)(5) + 19/5
y = -3 + 19/5
y = -3 + 19/5
y = 2/5
The point (5, 2/5) is also on the line.
Now we can plot these two points on a coordinate plane and draw a straight line passing through them.
The graph will have a slope of -3/5 and will go through the points (0, 19/5) and (5, 2/5).
Here is a rough sketch of the graph:
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0 5
Note that the line is downward sloping from left to right, indicating a negative slope of -3/5.
Solve the equation.
(y - 9) - (y + 5) = 5y
Let's simplify the equation step by step to solve for y:
(y - 9) - (y + 5) = 5y
First, let's simplify the expression inside the parentheses:
y - 9 - y - 5 = 5y
Next, simplify the equation by combining like terms:
-y - 14 = 5y
To get rid of the negative sign in front of y, we can multiply the entire equation by -1:
1y + 14 = -5y
Combine like terms again:
14 = -6y
To solve for y, divide both sides of the equation by -6:
14 / -6 = -6y / -6
-7/3 = y
Therefore, the solution to the equation is y = -7/3.
Find the slope of the line through the given pair of points, if possible. Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.
(-1.7, -2.3) and (1.6, -0.5)
To find the slope of a line passing through two points (x1, y1) and (x2, y2), we can use the formula:
Slope = (y2 - y1) / (x2 - x1)
Using the given points (-1.7, -2.3) and (1.6, -0.5), we can substitute the values into the formula:
Slope = (-0.5 - (-2.3)) / (1.6 - (-1.7))
= (-0.5 + 2.3) / (1.6
The mode is the value(s) that appear(s) most frequently in the data set. In this case, the numbers that appear most frequently are 58 and 51, both appearing twice. Therefore, the mode is 58 and 51.
The correct answer is D) 58.
Solve the problem.
A radio transmission tower is 230 feet tall. How long should a guy wire be if it is to be attached 14 feet from the top and is to make an angle of 27° with the ground? Give your answer to the nearest tenth of a foot.
Question 30 options:
A)
475.8 ft
B)
258.1 ft
C)
506.6 ft
D)
242.4 ft
To solve this problem, we can use trigonometry. The length of the guy wire can be found using the sine function.
The length of the guy wire (h) can be calculated using the formula:
h = 230 / sin(angle)
Using the given information, we can substitute the values into the formula:
h = 230 / sin(27°)
h ≈ 506.6 ft
Therefore, the correct answer is C) 506.6 ft.
Solve the equation.
4m + 6 + 5(4m - 4) = 4(m + 4)
Answers:
A1/10
B 3/2
C15/14
D 21/10
To solve the equation, we will simplify and collect like terms.
Starting with the left side of the equation:
4m + 6 + 5(4m - 4)
= 4m + 6 + 20m - 20
= 24m - 14
Now let's simplify the right side of the equation:
4(m + 4)
= 4m + 16
Now let's rewrite the equation:
24m - 14 = 4m + 16
To isolate the variable m, we can subtract 4m from both sides and add 14 to both sides:
24m - 4m - 14 + 14 = 4m + 16 - 4m + 14
20m = 30
Finally, divide both sides by 20:
m = 30/20
m = 3/2
Therefore, the correct answer is B) 3/2.