Answer:
0.64 ± 0.1117 or
Step-by-step explanation:
Sample size (n) = 50
Z-score for a 90% confidence level (z) = 1.645
Proportion of students who read at least one book (p):
The confidence interval is calculated as:
By applying the provided information:
The confidence interval results in 0.64 ± 0.1117
Answer: The unknown values x and y correspond to 8 and 20, specifically;
(x, y) = (8, 20)
Step-by-step explanation: The equation y = 16 + 0.5x represents a linear relationship that can be illustrated with a graph. This indicates that values for x and y can be located at various points on the line.
The ordered pairs signify that for each x value, there exists a matching y value.
The values listed in a two-column format for x and y all fulfill the equation y = 16 + 0.5x. Observing the first example, the pair (-4, 14) is presented.
This reveals that when x is -4, y will be 14.
Where y = 16 + 0.5x
y = 16 + 0.5(-4)
y = 16 - 2
y = 14
Thus, the first pair, similar to the other pairs, satisfies the equation.
Consequently, by reviewing the options provided, we can deduce which one fulfills the equation.
(option 1) If x = 0
y = 16 + 0.5(0)
y = 16 + 0
y = 16
(0, 16)
(option 2) If x = 5
y = 16 + 0.5(5)
y = 16 + 2.5
y = 18.5
(5, 18.5)
(option 3) If x = 8
y = 16 + 0.5(8)
y = 16 + 4
y = 20
(8, 20)
Our calculations confirm that the third option (8, 20) is the correct ordered pair for x and y.
Certainly. 2L = 4680 + 520 2L = 5200 L = 5200 / 2 L = 2600.
Answer:
60.36 steps West from center
85.36 steps North from center
Step-by-step explanation:
Refer to the attached
Musah's starting point and movement are depicted in the image.
- 1. He moves 50 steps towards the North,
- 2. Next, he moves 25 steps towards the West,
- 3. Then he proceeds 50 steps on a bearing of 315°. We now recognize that North is measured at 0°
or 360°, so a bearing of 315° corresponds to North-West 45°.
Note: According to the Pythagorean theorem, a right triangle at 45° with hypotenuse 'a' will have legs equal to a/√2.
What is the distance West of Musah's final position from the center?
25 + 50/√2 ≈ 60.36 steps
What is the distance North of Musah's final position from the center?
Response:
- Refer to the attached graph
Clarification:
To analyze log (−5.6x + 1.3) = −1 − x visually, graph these equations on the same coordinate system:
- Equation 1: y = log (5.6x + 1.3)
The first equation can be graphed using these characteristics of logarithmic functions:
- Domain: values must be positive ⇒ -5.6x + 1.3 > 0 ⇒ x < 13/56 (≈ 0.23)
- Range: all real values (- ∞, ∞)
log ( -5.6x + 1.3) = 0 ⇒ -5.6x + 1.3 = 1 ⇒ x = 0.3/5.6 ≈ 0.054
x = 0 ⇒ log (0 + 1.3) = log (1.3) ≈ 0.11
- Choose additional values to create a table:
x log (-5.6x + 1.3)
-1 0.8
-2 1.1
-3 1.3
- This graph is shown in the attached image: it's represented by the red curve.
Graphing the second equation is simpler as it forms a straight line: y = - 1 - x
- slope, m = - 1 (the coefficient of x)
- y-intercept, b = - 1 (the constant term)
- x-intercept: y = 0 = - 1 - x ⇒ x = - 1
- This graph is indicated by the blue line in the image.
The resolution to the equations corresponds to the points where the two graphs intersect. The graphing method thus allows you to determine the x coordinates of these intersection points. Ordered from smallest to largest, rounded to the nearest tenth, we have:
