Answer:
<em>x = - 11 ; m∠B = 132° </em>
Step-by-step explanation:
(33 - 9x)° + 48° = 180°
33 - 9x + 48 = 180
81 - 9x = 180
- 9x = 99
<em>x = - 11</em>
m∠B = [33 - 9(- 11)]° = (33 + 99)° = 132°
<em>m∠B = 132°</em>
Answer:
1.) .399
2.) {.369, .429}
Step-by-step explanation:
The proportion of criminals in this sample that were caught was
=.39944, .399 rounded to three decimal places.
To construct the confidence interval, you need three pieces of information: the statistic, the critical value, and the standard error.
The statistic is given in the first part of the problem with the proportion of criminals in the sample that were caught was .399.
The critical value, we are told, is the z equivalent of 90%, or 1.645. You can find this value using a z table or with the inverse normal function on a calculator.
Finally, we need the standard error. The formula for standard error for a proportion with a single population is
so in this situation it would be
=.0183.
The confidence interval would be .399±.018×1.645 or .399±.030 {.369, .429}
Answer:
x = 5√2
y = 5√6
z = 5√3
ΔABC ~ ΔBDC ~ ΔADB
Step-by-step explanation:
ΔABC, ΔBDC, and ΔADB are all similar triangles to each other.
By definition of similar triangles, the corresponding sides have the same ratios.
CD from ΔBDC corresponds to BD from ΔADB, and BD from ΔBDC corresponds to AD from ΔADB. So:
CD / BD = BD / AD
10 / x = x / 5
x² = 50
x = 5√2
Since ΔBDC is right, we can use the Pythagorean Theorem to solve for y:
CD² + BD² = BC²
10² + (5√2)² = y²
y² = 100 + 50 = 150
y = 5√6
Again, since ΔΔABD is right, we can use the Pythagorean Theorem to solve for z:
AD² + BD² = AB²
5² + (5√2)² = z²
z² = 25 + 50 = 75
z = 5√3
Rectangles<span> and squares are </span>alike<span> in that both have </span>two<span> pairs of parallel sides and four right angles.</span>
Answer:
x = - 2
Step-by-step explanation:
The equation of a vertical line parallel to the y- axis is
x = c
Where c is the value of the x- coordinates the line passes through.
The line passes through (- 2, - 3) and (- 2, 2)
Both of these points have an x- coordinate of - 2, thus
x = - 2 ← equation of line