Answer:
The 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is (-0.1078, 0.1702).
Step-by-step explanation:
Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction of normal variables:
When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.
In a random sample of 42 Democrats from one city, 10 approved of the mayor's performance.
This means that:
[tex]p_D = \frac{10}{42} = 0.2381, s_D = \sqrt{\frac{0.2381*(1-0.2381)}{42}} = 0.0657[/tex]
In a random sample of 58 Republicans from the city, 12 approved of the mayor's performance.
This means that:
[tex]p_R = \frac{12}{58} = 0.2069, s_R = \sqrt{\frac{0.2069*(1-0.2069)}{58}} = 0.0532[/tex]
Distribution of the difference:
[tex]p = p_D - p_R = 0.2381 - 0.2069 = 0.0312[/tex]
[tex]s = \sqrt{0.0657^2+0.0532^2} = 0.0845[/tex]
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.
Now, find the margin of error M as such
[tex]M = zs[/tex]
[tex]M = 1.645*0.0845 = 0.139[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 0.0312 - 0.139 = -0.1078
The upper end of the interval is the sample mean added to M. So it is 0.0312 + 0.139 = 0.1702
The 90% confidence interval for the difference between the proportions of Democrats and Republicans who approve of the mayor's performance is (-0.1078, 0.1702).
I need super help with this one.
Which expression is equivalent to 8k+10+9k+1?
-k+11 18k+10
-k+9 or 11+17k
Answer:
[tex]8k + 10 + 9k + 1 = k(8 + 9) + (10 + 1) \\ = 17k + 11[/tex]
Anna drives her car at a speed of 70 km per hour. How much distance will she cover in 3 hours 30 minutes?
Distance» [tex]speed \times time[/tex]
Distance» [tex]70 \times \frac{7}{2} [/tex]
Distance» [tex] \frac{490}{2} [/tex]
Distance» 245
Answer:
245 units
Step-by-step explanation:
Anna drives her car at a speed of = 70 kmph
To Find:
How much distance will she cover in 3 hours 30 minutes.
Solution:
We'll use here the formula of Speed,then plug the values which are given.
Speed = Distance/Time
Speed = 70 kmphDistance = 3 hr 3 mins = 7/2 hrs70 = D/7/2
7/2*70 = Distance
7*35 = Distance
Distance = 245
We can conclude that Anna can cover 245 units in 3 hrs 30 mins.
3 wings cost $2 How many wings for $18?
Answer:
We can get 27 wings
Step-by-step explanation:
We can write a ratio to solve
3 wings x wings
--------------- = --------------
2 dollars 18 dollars
Using cross products
3 * 18 = 2 x
54 = 2x
Divide by 2
54/2 = 2x/2
27 =x
We can get 27 wings
Select the correct answer.
Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina?
A.
The equation that represents this situation is t − 3 = 18. Tina is 21.
B.
The equation that represents this situation is t + 3 = 18. Tina is 15.
C.
The equation that represents this situation is 3 − t = 18. Tina is 21.
D.
The equation that represents this situation is -3 − t = 18. Tina is 15.
In ΔPQR, r = 640 inches, q = 310 inches and ∠Q=30°. Find all possible values of ∠R, to the nearest degree.
Answer:
No Possible Triangles
Step-by-step explanation:
sinA/a = sinB/b
From the reference sheet (reciprocal version).
sinR/640 = sin30/310
Plug in values.
sinR= (640 (sin30))/ 310≈1.0322581
Evaluate.
R=sin −1 (1.0322581)=ERROR
Sine cannot be greater than 1.
PLEASE HELP ME ITS ALGEBRA THANK YOUUUU
Answer:
722 kg
Step-by-step explanation:
551:29=x:38
551*38=29x
20938/29=x
x=722 kg
a(b+c)=a(d-e) solve for b
Answer:
b = - c + d - e
abcdefghijklmnopqrstuvwxyz
Looking for the answer for the second one
Answer:
3 for the left one, and 5 on the right one.
Step-by-step explanation:
The scale factor is 2 because they are scaled from each other, meaning they have proportional side lengths. (The angles are also the same <hint for the next question>)
If the top side is 2.5, and the bottom is 5, then you divide to find the scaled factor since they correlate to each other.
If the side lengths on A is multiplied by 2, you can do that to the missing sides to find the answers.
Simplify
8/9
____
5/6
Answer: 16/15
decimal: 1.0666
mixed number: 1 1/15
Step-by-step explanation:
percent change of 3.25 to 2.95
Answer:
-9.23%
Step-by-step explanation:
.
An airport has an electronic system that randomly selects bags for extra security screening. Each bag has a 14% percent probability of being selected for extra screening, and one bag being selected or not doesn't affect whether or not another bag will be selected. Suppose that 222 bags go through the system, one after the other. What is the probability that both bags are selected for extra screening? Round your answer to two decimal places.
Probabilities are used to determine the chances of an event.
The probability that the two bags are selected for extra screening is 0.02
The given parameters are:
[tex]n = 2[/tex] --- number of bags
[tex]p = 14\%[/tex] --- the probability that a bag is selected for extra screening
The probability that the two bags are selected for extra screening is:
[tex]P(2) = p^n[/tex]
So, we have:
[tex]P(2) = (14\%)^2[/tex]
Express percentage as decimal
[tex]P(2) = (0.14)^2[/tex]
[tex]P(2) = 0.0196[/tex]
Approximate
[tex]P(2) = 0.02[/tex]
Hence, the required probability is 0.02
Read more about probabilities at:
https://brainly.com/question/11234923
Answer:
0.02 i did khan academy pls mark brainliest
Step-by-step explanation:
If y varies directly as x and as the square of z, and y =25/9 when x=5 and z=1, find y when x =1 and z=4
Answer:
y= 80/9
Step-by-step explanation:
Given
" y varies directly as x" and "as the square of z" so y = x* z²* some number
if y =25/9 when x= 5, z= 1 and y = x*z²* some number
then 25/9 = 5 * 1² * some number
5*(5/9) = 5 * some number
therefore y = x* z²* (5/9)
y= ? when x=1 , z= 4
y = x * z² * (5/9)
y = 1 * 4² * (5/9)
y = 16*5 / 9
y = 80/9
Mixed numbers 204/5=
Answer:
Step 1 - Find Whole Number
Calculate out how many times the denominator goes into the numerator. To do that, divide 204 by 5 and keep only what is to the left of the decimal point:
204 / 5 = 40.8000 = 40
Step 2 - Find New Numerator
Multiply the answer from Step 1 by the denominator and deduct that from the original numerator.
204 - (5 x 40) = 4
Step 3 - Get Solution
Keep the original denominator and use the answers from Step 1 and Step 2 to get the answer. 204/5 as a mixed number is:
40
4
5
Improper Fraction To Mixed Number Converter
204/5 as a mixed number is not the only problem we solved. Go here to convert another improper fraction to a mixed number.
What is 204/6 as a Mixed Number?
Here is the next improper fraction on our list that we converted to a mixed number.
Terminology & Explanation
204 above the division line is called the numerator and 5 below the divison line is called the denominator.
We call the line that separates 204 and 5 the division line. It is also known as the fraction bar or vinculum.
204/5 is an improper fraction because the numerator is greater than the denominator.
A mixed number is an integer (whole number) and a proper fraction.
104 18/ 25 divided by 29 7/10
Answer:
Exact form = 476/135
Decimal form = 3.5259
Mixed Number form = 3 71/135
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
Hope this helps. Please mark as brainlist
1. Which of the following should you do first when solving the equation 3x + 2 = 4x – 5(x + 6)?
A. divide both sides by 3
B. subtract 2 from both sides
C. distribute the - 5 through the parenthesis (x+6)
D. subtract 4x from both sides
Answer:
(x+6)
Step-by-step explanation: remember gemdas
Groups
Exponents
Multipy
Divide
Add
Ssubtract
Express 960% as a mixed number
Answer:
9 3/5
Step-by-step explanation:
When we see a percentage, we know that the base is 100. In other words, 960% is equal to 960/100
With this, its just a matter of transforming the improper fraction to a mixed number.
100 fits 9 times in 960 so there will be 9 wholes
the remaining 60/100 can be simplified to 3/5 through this process:
60/100 = 6/10 = 3/5
Answer:
9 3/5
Step-by-step explanation:
Step 1: Write down the percent divided by 100 like this:
960% = 960/100
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As 960 is an integer, we don't have numbers after the decimal point. So, we just go to step 3.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(960,100) = 20. So,
(960÷20)/(100÷20) = 48/5 when reduced to the simplest form.
As the numerator is greater than the denominator, we have an IMPROPER fraction, so we can also express it as a MIXED NUMBER, thus 960/100 is also equal to 9 3/5 when expressed as a mixed number.
Suppose you deposit $200 in a savings account that earns 4% per year. Find the simple interest earned in 2 years. Then find the total of principal plus interest.
9514 1404 393
Answer:
interest: $16account total: $216Step-by-step explanation:
The amount of interest is given by the simple interest formula:
I = Prt . . . . where P is the amount earning interest, r is the annual rate, t is the number of years
I = $200·0.04·2 = $16.00
The simple interest earned in 2 years is $16.00.
__
The total of principal and interest is found by adding those values:
$200.00 +16.00 = $216.00
The total amount is $216.00.
Pleas help thx need asap!
Answer: 2
Step-by-step explanation:
Fill the table so it represents a linear function
Answer:
Hey mate.....can't see the attached picture....please check again
Answer:
what table??
Step-by-step explanation:
what is this answer 6×7/8
Answer:
6
56
this is answer
Step-by-step explanation:
Here we will show you how to calculate 6/7 divided by 8. We will give you the answer in fraction form and in decimal form.
Here is 6/7 divided by 8 displayed mathematically in colors:
6
7
÷
8
The numbers in 6/7 divided by 8 are labeled below:
6 = numerator
7 = denominator
8 = whole number
To make it a fraction form answer, you keep the numerator and multiply the denominator by the whole number to make a new denominator:
6
7 x 8
=
6
56
Thus, the answer to 6/7 divided by 8 in fraction form is:
6
56
-5^2 - (-5)^2 PLS SOLVE FAST!!!!! I WILL GIVE BRAINLIST...... BUT I NEED ANSWER CORRECT
Answer: -50
Step-by-step explanation:
Find the complete factorization of
6x^3 - 15x^2 – 9x.
What is one of the factors of the complete fac-
torization of 6x^3 - 15x^2- 9x?
[tex]6x {}^{3} - 15x {}^{2} - 9x \\ 3x(2x {}^{2} - 5x - 3) \\ 3x( 2x {}^{2} + x - 6x - 3) \\ 3x(x(2x + 1) - 3(2x - 1) \\ (2x + 1)[/tex]
Hence, Proved ✔︎Answer:
the correct answer is D on edge 2020 for me.
Step-by-step explanation:
El cuadrado de un número es igual a 140 + 4
Answer:
12
Step-by-step explanation:
140 + 4 = 144
raíz cuadrada de 144 es 12
(-10) + 3 please help
Answer:
The answer is -7 the answer is-7
Answer:
-7
Step-by-step explanation:
(-10)+3
-10+3=-7
-4-6=-10
-10+7=-3
I really need this last question please anyone's help is very appreciated
Answer:
y = (5/2)x + 13/2
y = 3
y = -2x + 6
Step-by-step explanation:
The left part of the function which is a line sloping up to the right contains points (-3, -1) and (-1, 4) which can be read off the graph.
Since we have two points, we can find the equation.
You can use the slope formula given two points, but I will read it off the graph with rise and run.
Go from point (-3, -1) to point (-1, 4) by going up 5 (the rise) and going right 2 (the run).
slope = rise/run = 5/2
y = mx + b
y = (5/2)x + b
Use point (-1, 4) for x and y and solve for b.
4 = (5/2)(-1) + b
8/2 + 5/2 = b
b = 13/2
y = (5/2)x + 13/2
This is the first answer.
The middle part is a horizontal line in which every point has y-coordinate 3.
The equation is:
y = 3
This is the second answer.
The right part is the line that slopes down to the right. We can read two points easily. Use points (3, 0) and (2, 2).
Start at (3, 0). Go left 1 (run of -1) and up 2 (rise of 2). Now you are at point (2, 2).
slope = rise/run = 2/(-1) = -2
Now we find the y-intercept on the graph. After you get to (2, 2), keep moving with the same run and rise of the slope. Go left 1 and up 2 to point (1, 4). Go again left 1 and up 2 to (0, 6). Point (0, 6) is on the y-axis, so it is the y-intercept.
b = 6
y = mx + b
y = -2x + 6
This is the third answer.
Whats the answer to this question? ( Branliest )
Answer:
3+jk+k^6
j=2 & k=6
substituting the values, we have
= 3+2(6)+6^3
= 3+12+216
= 231
Ans=231
Step-by-step explanation:
j=2 and k=6
Now
(6)³+2(6)+3216+12+3216+15231Luis is buying a 65 inch TV that costs $650. He pays $100 down and will pay the rest in monthly payments over two years. What will his monthly payments be?
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 5.4 years, and standard deviation of 1.2 years.
If you randomly purchase one item, what is the probability it will last longer than 3 years?
Round answer to four decimal places
Answer: bro im sorry ion no but ima look it up lol
Step-by-step explanation: it is what it is
A tugboat goes 72 miles upstream in 9 hours. The return trip downstream takes 4 hours. Find the speed of the tugboat without a current and find the speed of the current.
Step-by-step explanation:
72÷9= 8, so the boat was only doing 8mph going upstream (against the current) the return trip downstream only took 4 hours. 72÷18=4 meaning the boat was traveling at 18mph downstream (no current) there is a 10mph difference between upstream and downstream therefore the current had to be running at 10 mph. so the speed of the tug boat is 8mph without a current and the current is running at 10mph.
A repair team is responsible for a stretch of oil pipeline 2 miles long. The distance (in miles) at which any fracture occurs can be represented by a uniformly distributed random variable, with probability density function f(x) = 0.5.
What is the probability that the next fracture will occur in the last half mile of the two mile interval?
Using the uniform distribution, it is found that there is a 0.25 = 25% probability that the next fracture will occur in the last half mile of the two mile interval.
The uniform distribution has two bounds, a and b.
The probability of finding a value above x is:
[tex]P(X > x) = \frac{b - x}{b - a}[/tex]
In this problem, the distribution is uniform over 2 miles, thus [tex]a = 0, b = 2[/tex].
The probability of a failure on the last half-mile is P(X > 1.5), thus:
[tex]P(X > 1.5) = \frac{2 - 1.5}{2 - 0} = 0.25[/tex]
0.25 = 25% probability that the next fracture will occur in the last half mile of the two mile interval.
A similar problem is given at https://brainly.com/question/17088600