Using the information given, it is found that the 95% confidence interval for the proportion of all U.S. adults who experienced depression in that year is (0.075, 0.081).
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
3156 out of 40467 adults experienced depression, hence:
[tex]n = 40467, \pi = \frac{3156}{40467} = 0.078[/tex]
95% confidence level
So [tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so [tex]z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.078 - 1.96\sqrt{\frac{0.078(0.922)}{40467}} = 0.075[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.078 + 1.96\sqrt{\frac{0.078(0.922)}{40467}} = 0.081[/tex]
The 95% confidence interval for the proportion of all U.S. adults who experienced depression in that year is (0.075, 0.081).
A similar problem is given at https://brainly.com/question/16807970
Please help this is my fifth time asking this question please answer it correctly with explanation
Step-by-step explanation:
There are two attachments to this post. The first attachment shows the numbered angles formed through the intersection of the transversal, t, into the parallel lines, m and n, which will be used to determine how each angle relates to other angles.
First attachment:The corresponding angles in the first attachment are:
∠1 and ∠5
∠2 and ∠6
∠3 and ∠7
∠4 and ∠8
Corresponding angles have the same measure.
The same-side exterior angles are the pair of angles that are outside the parallel lines, and on the same side of the transversal. In the first attachment, the same-side exterior angles are:
∠1 and ∠8
∠2 and ∠7
These angles are supplements of each other, meaning that the sum of their measure equal 180°.
Second Attachment:
Given parallel lines, m and n that are cut by a transversal, t.
The angle that has a measure of ∠(10x + 5)° is a supplement of ∠(5x + 25)°. In order to solve for the value of x, we must establish the following equation:
m∠(10x + 5)° + m∠(5x + 25)° = 180°
10x° + 5° + 5x° + 25° = 180°
Combine like terms:
15x° + 30° = 180°
Subtract 30 from both sides:
15x° + 30° - 30° = 180° - 30°
15x° = 150°
Divide both sides by 15:
15x°/15 = 150°/15
x = 10°
Verify whether we have correct value for x by substituting its value into the established equation:
m∠(10x + 5)° + m∠(5x + 25)° = 180°
10(10)° + 5° + 5(10)° + 25° = 180°
100° + 5° + 50° + 25° = 180°
180° = 180° (True statement).
Therefore, we have the correct value for x = 10°.
m∠(10x + 5)° = 105°
m∠(5x + 25)° = 75°
What is 2x2, I keep on getting it wrong. Can u please help, Thank you
Answer:
4
Step-by-step explanation:
Answer this question for me ASAP
Answer:
Option A: (It's just that the y-intercept and slope are in different spots.)
Line in (y=mx+b) form is y = 2x + 4
Slooe is 2
y-intercept is 4
Step-by-step explanation:
Slope-intercept form is written as y=mx+b, where m is slope and b is y-intercept.
By looking at the graph, we can already tell that the y-intercept is positive 4, since the line crosses the y-axis at that point.
Now use rise/run to find slope. (Remember that rise is movement up or down, and run is movement left or right.) With this in mind, the slope is 4/2, and if we simplify it, it's 2/1 (or basically just 2). Because we go upwards 4 units and to the right 2 units.
Hope this helps :)
You plan on joining a gym. The joining fee is $30 and you must pay $12 a month fee. If you have $100, how many months can you use the gym? Write and solve an inequality to represent the solution.
I need the process for this otherwise I won't get credit for it!!
Answer:
Inequality: 30+12x < 100
x ≈ 5 months
Step-by-step explanation:
To solve, first create the inequality. In this problem, 30 dollars is the flat fee for joining the gym and thus a constant. Additionally, 12 is the monthly payment and thus the coefficient for a variable because it changes with the number of months. Finally, 100 is the most that can be spent (the max), so it should be on the other side of the inequality and the sign should be less than or equal to 100.
This makes the inequality: 30+12x < 100
To find the number of months solve the inequality for x.
30+12x<10012x<70x<5.8So, the inequality equals x<5.8. However, the question asks for the number of full months. And, no more than 100 dollars can be spent. So, while you would normally round up. In this case, you must round down to 5 months.
Identify the restrictions on the domain of f(x) =
X +5
X-2
Ox#5
OX-5
Ox=2
Ox= -2
Find the Area of each triangle. Round intermediate values to the nearest tenth. Use the rounded values to calculate the next value. Round your final answer to the nearest tenth.
Answer: 15!
Step-by-step explanation:
You do 1/2 x (5=base) x (6= height)
Divide.
−4 1/3÷−2 3/5
1 2/3
1 4/5
2 1/5
2 3/5
Answer: 1 2/3
Step-by-step explanation:
10x + 44
8x - 23
It’s solving for X in triangles
Answer:
x=33.5
Step-by-step explanation:
I got an questions for y'all, see if y'all can what do can an cow with no legs
Answer:
eat it can only eat the things around it
Step-by-step explanation:
a cow with no legs has a hard life due to their lack of legs they cant walk or run meaning the cant get water and they can't run away from Predator's
e
Week 6: Culmination Knowledge Check
CLEAR MY CHOICE
Question 8
You buy milk in 1-gallon containers. One portion of waffles requires 2 ounces of milk. How many portions can be made with one container? Select one
a 128
b. 16
c. 32
d. 64
CLEAR MY CHOICE
Question 9
You have 24 quarts of brown stock. You need 75 cups to make one serving of kidney beans. How many servings can you make? Select one
Find the domain and range of the following function f(x) = 51x - 21 + 4
Domain. [4,8) Range: (-00,00)
Domain. (4,00) Range: (-00,00)
Domain (-00,00) Range [4,00)
Domain. (-00,00) Range: (4,00)
Answer:
my gosh, hirap kaya niyan, pareho lang ta u d alam sagot
solve pls brainliest
Answer:
Yes, This is a repeating decimal
No, This is a decimal that neither terminates or repeats
No, This is a decimal that neither terminates or repeats
Yes, This is a terminating decimal
Jessica and her family bought 5 tickets to a
music concert. Tickets for adults cost $5.10 and
tickets for children cost $3.60. Jessica and her
family spent a total of $21. How many tickets
for adults (a) and how many tickets for children
(c) did they buy?
a + c = 5
5.1a + 3.6C = 21
[?] adults [ ] children
Step-by-step explanation:
work is shown and pictured
What’s x?
Answer:
I pretty sure it is F.1cm
16 divided by 5 as a decimal
Answer:
3.2 brainliets
Step-by-step explanation:
(20pts) I need to know who is incorect and why
Answer:
i thig it is hj
Step-by-step explanation:
jk
(4, 7); y = 3x + 6 plz help me
y=3x+6.
y=3x-5
I did it with a parallel line
Caleb has 3 apples and he loses 1 apple how many apples does Caleb have?
Answer:
2 apples
Step-by-step explanation:
he should be more careful next time :)
HURRY PLEASE! Do questions 4,5,6 on paper
This should be right , if any doubt please comment
The domain for f(x) is all real numbers ___ than or equal to 2
Step-by-step explanation:
f(x) = 2x² + 5√(x - 2)
Domain
√(x - 2) ≥ 0
x - 2 ≥ 0
x ≥ 2
x is greater than or equal to 2
Answer: Greater than
Step-by-step explanation:
Solve the math problem
Answer:
1 -66
2. 162
3.11/-2
4. 8/-11
5.12/0
6. 0
7. 15/14
8. 2/-5
Step-by-step explanation:
For which values of x is this function constant?
Answer:
- 2 ≤ x ≤ 0
Step-by-step explanation:
The constant part of the graph is the section between (- 2, 1 ) and (0, 1 )
where the graph is horizontal and parallel to the x- axis, that is the y value is constant at 1
name the congruent triangles
will give brainliest
Answer:
ΔOGD ≅ΔPRC
Step-by-step explanation:
SAS
a number of students are standing in a circle. they are evenly spaced and the fith student is directly opposite the eleventh student. how many students are there all together
Answer:
There would be 12
Step-by-step explanation:
Mali has half of the cost of a day trip to a theme park for two people, and Sarah has one-third of the cost. What fraction of the cost do they have?
Answer:
5/6
Step-by-step explanation:
1/2=3/6
1/3=2/6
2/6+3/6=5/6
.4(x + 7)
.4 + 7x- 5x -6
Answer:6/5x=7/x+2 Two solutions were found : x =(10-√940)/12=(5-√ 235 )/6= -1.722 x =(10+√940)/12=(5+√ 235 )/6= 3.388 Rearrange: Rearrange the equation by subtracting what is to the right
Step-by-step explanation:
I’m wondering if this is a polygon
Answer:
They don't need to have parallel lines or right angles. If you think about that, it means that a triangle is a polygon. So are squares, rectangles and, yes, quadrilaterals, parallelograms and trapezoids. They all are closed shapes with many sides, so they're all polygons!
Have a great day!
Brainliest please :)
make a conjecture (prediction) about the table. what will happen if we continue the table, going down?
Triangle EFG is dilated by a scale factor of \frac{2}{3}
3
2
to form triangle E'F'G'. What is the measure of side FG?
Answer:
B. 36°
Step-by-step explanation:
Dilation does not change the angle measures or the direction of the lines. Angle F is the same as corresponding angle F'.
2. A house costs $30,000. A buyer is given a 1/10 discount. How much money does the buyer save?
Answer:
3000
Step-by-step explanation:
