In a random sample of 500 college students, 23% say that they read or watch the news every day. Develop a 90% confidence interval for the proportion of all students who read or watch the news on a daily basis. Interpret your results. If you wanted to develop a 95% confidence interval with a margin of error of .01, how many students would need to be surveyed?
Answer:
The 90% confidence interval is [tex]0.199 < p < 0.261 [/tex]
The sample size to develop a 95% confidence interval is [tex]n = 2032 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n =500
The sample proportion is [tex]\^ p = 0.23[/tex]
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.645 * \sqrt{\frac{0.23 (1- 0.23)}{500} } [/tex]
=> [tex]E = 0.03096 [/tex]
Generally 90% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex]0.23 -0.03096 < p < 0.23 + 0.03096 [/tex]
=> [tex]0.199 < p < 0.261 [/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is given as [tex]E = 0.01[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
=> [tex]n = [\frac{1.96 }{0.01} ]^2 *0.23 (1 - 0.23 ) [/tex]
=> [tex]n = 2032 [/tex]
You have a ribbon that is 7 1/2 inches long you use 1/2 of it on a project how many inches of ribbon are left
Use a half-angle identity to find the exact value of sin 3pi/8
The above answer is correct! The correct response is A.
Just got it right on edge 2020, hope this helps!! Good luck, and have a great day! :)
The solution is, Using a half-angle identity we get the exact value of
sin 3pi/8 is ±√[(2 + √2) / 4].
Here, we have,
The half angle formula of sin in trigonometry is
sin A/2 = ±√[(1 - cos A) / 2].
If 0 < x < π/2 , then cos x > 0.
now, we have,
sin 3pi/8
here, A/2 = 3pi/8 so, A = 3pi/4 = 6π/8
applying this half angle formula of sin in trigonometry
we get,
sin 3π/8 = ±√[(1 - cos 6π/8) / 2]
= ±√[(1 + 1/√2) / 2]
= ±√[(2 + √2) / 4]
so, we get,
sin 3π/8 = ±√[(2 + √2) / 4]
Hence, The solution is, Using a half-angle identity we get the exact value of sin 3pi/8 is ±√[(2 + √2) / 4].
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What are the roots of the equation 3x^2-4x+4=0?
Answer:
[tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]√-1 is imaginary number iStep-by-step explanation:
Step 1: Define
3x² - 4x + 4 = 0
a = 3
b = -4
c = 4
Step 2: Find roots
Substitute: [tex]x=\frac{-(-4)\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]Simplify: [tex]x=\frac{4\pm\sqrt{(-4)^2-4(3)(4)} }{2(3)}[/tex]Evaluate: [tex]x=\frac{4\pm\sqrt{16-4(3)(4)} }{2(3)}[/tex]Multiply: [tex]x=\frac{4\pm\sqrt{16-48} }{6}[/tex]Subtract: [tex]x=\frac{4\pm\sqrt{-32} }{6}[/tex]Factor: [tex]x=\frac{4\pm\sqrt{-1} \sqrt{32} }{6}[/tex]Simplify: [tex]x=\frac{4\pm4i\sqrt{2} }{6}[/tex]Factor: [tex]x=\frac{4(1\pm i\sqrt{2} )}{6}[/tex]Simplify: [tex]x=\frac{2(1\pm i\sqrt{2} )}{3}[/tex]Which number is NOT a common multiple of 4 and 6?
Answer:
8
Step-by-step explanation:
you can multiply 4 by another number to get 8
but you can’t multiply 6 by any whole number to get 8
Answer:
The answer is 8
Step-by-step explanation:
You can multiply 4 by two and get 8, but you can't multiply 6 by any whole number and get 8.
4 times 6= 24
6 times 4=24
4 times 3=12
6 times 2=12
4 times 15=60
6 times 10=60
subtracting decimals
0.89-0.6
Answer:
o.29 answer of this question
Answer:
0.29
Step-by-step explanation:
0 . 8 9
-0 . 6 0
-------------
0 . 2 9
--------------
Hope this helps
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Which equation matches the scenario?
Maggie has $15 to spend. Pinball games cost $0.75 per play and skee-ball games cost $1.25 per play.
Question 4 options:
A. 15x+0.75y≤1.25
B. 0.75x+1.25y≤15
C. (0.75+1.25)x<15
D. 0.75x+1.25y≥15
Answer:
B. 0.75x + 1.25y [tex]\leq[/tex] 15
I WILL MARK BRAINLIST
Answer:
The answer would be c
Step-by-step explanation:
If you look at the vertices you will see that none of them have any of the same vertices.
answer fast and quickly plsss
Answer:
C. 65°, 115°
Step-by-step explanation:
3x - 5 + 2x - 15 = 180
5x - 20 = 180
5x = 180 + 20
5x = 200
x = 200/5
x = 40
5x - 20 = 3*40-5 = 120 - 5 = 115
2x - 15 = 2*40 - 15 = 80 - 15 = 65
determine the intersepts of the lines
Answer:
Y-intercept is (0, 100) and the X-intercept is (-250, 0)
Step-by-step explanation:
For the y-intercept the line from the origin does not move left or right and stays at 0 but it goes up by 100.
For the x-intercept the line does not go up and down but it goes to the left -250.
Input in standard form the equation of the given line that passes through (-1,-3) and (2, 1)
Answer:
y=4/3x-5/3
Step-by-step explanation:
We can use the slope formula, m=(y2-y1)/(x2-1), to find the slope.
1-(-3)/2-(-1)=4/3
We can subsitute now that we have the slope.
y=4/3x+b
-3=4/3(-1)+b
-3+4/3=b
b=-5/3
y=4/3x-5/3
What is the sum or difference?
2x^4 +8x^4
Answer:
10x^4
Step-by-step explanation:
The solution to the given expression is 10x⁴ which represents its sum.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers. Unknown variables, numbers, and arithmetic operators make up an algebraic expression.
The expression is given in the question, as follows:
2x⁴ + 8x⁴
We have to determine the sum or difference of the given expression.
As per the question, we have
2x⁴ + 8x⁴
Combine the likewise terms in the above expression, and we get
10x⁴
Thus, the solution to the given expression is 10x⁴.
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Express into slope form
Answer: y= 3/2x+1
Step-by-step explanation:
A plane begins its takeoff at 2:00 P.M. on a 2200-mile flight. After 12.5 hours, the plane arrives at its destination. Explain why there are at least two times during the flight when the speed of the plane is 100 miles per hour.A) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 303 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 303 mi/hr and decelerating from 303 mi/hr.B) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 152 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 152 mi/hr and decelerating from 152 mi/hr.C) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 88 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 88 mi/hr and decelerating from 88 mi/hr.D) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 117 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 117 mi/hr and decelerating from 117 mi/hr.E) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 176 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 176 mi/hr and decelerating from 176 mi/hr.
Answer:
E) By the Mean Value Theorem, there is a time when the speed of the plane must equal the average speed of 176 mi/hr. The speed was 100 mi/hr when the plane was accelerating to 176 mi/hr and decelerating from 176 mi/hr.
Step-by-step explanation:
In this question we have the average velocity v = 2200/12.5
= 176miles/hr
The function Which describes the velocity of a plane is continuous. At point t, f(t) is equal to 176. So by the mean value theorem we arrive at a conclusion that the velocity is going to attain the speed of 100 miles per hour twice. The first time is during acceleration, and the second time is during deceleration. So by this, the answer to this question is option E.
A tailor charge $560 for a suit of clothes and gives a discount of 12% for cash. Calculate the discounted price for a suit of clothes.
Answer:
$492.80
Step-by-step explanation:
The discount= 12%*$560/100%
= $67.20
The discounted= Selling price- discount
= $560 - $67.20
= $492.80
A die is rolled twice. Find the chance that the ace (single dot) comes up on one of the two rolls, but not both. Record your answer as a percentage rounded to the nearest tenth of a percent.
Answer:
13.9%
Step-by-step explanation:
In order to calculate the probability of this happening, we would need to multiply the probability of one of the rolles being an ace with the probability of one of the roles NOT being an ace. Since the probability of rolling an ace is 1/6 (since there is only one ace in a six-sided die) then the probability of NOT rolling an ace is 5/6
[tex]\frac{1}{6} * \frac{5}{6} = \frac{5}{36}[/tex] or 0.1388 multiply by 100 to get percentage value
0.1388 * 100 = 13.9%
Therefore, the probability of getting one ace and one non-ace roll is 13.9%
A $250 suede jacket is on sale for 20%off how much should you pay for the jacket
Answer: $ 200
Step-by-step explanation:250 * 0.20 = $50 sale
250 - 50 = $200
(Angle relationships) solve this question.
Answer:
21
Step-by-step explanation:
In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within + 8 hours?
Complete Question
In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within [tex]\pm 8 \ hours[/tex]?
Answer:
a
[tex]1206 < \mu < 1228 [/tex]
The reason why a normal distribution was chosen is because the sample size is large enough that is [tex]n > 30[/tex]
b
[tex]n =162 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 80
The sample mean is [tex]\= x = 1217[/tex]
The standard deviation is [tex]\sigma = 52[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 52}{\sqrt{80} }[/tex]
=> [tex]E = 11.395 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]1217 -11.395 < \mu < 1217 + 11.395[/tex]
=> [tex]1206 < \mu < 1228 [/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
Here E = 8
=> [tex]n = [\frac{1.96 * 52 }{8} ] ^2[/tex]
=> [tex]n =162 [/tex]
Figure ABCD is a parallelogram.
Parallelogram A B C D is shown. The length of A B is 3 y minus 2, the length of B C is x + 12, the length of D C is y + 6, and the length of A D is 2 x minus 4.
What are the lengths of line segments AB and BC?
AB = 4; BC = 16
AB = 4; BC = 8
AB = 10; BC = 20
AB = 10; BC = 28
The lengths of line segments AB and BC are AB = 10; BC = 28
What are parallelograms?Parallelograms are shapes with parallel and equal opposite sides
The given parameters are:
AB = 3y - 2
BC = x + 12
DC = y + 6
AD = 2x - 4
The above means that:
AB = DC
BC = AD
So, we have:
AB = DC
3y -2 = y + 6
Collect like terms
3y - y = 2 + 6
2y = 8
Divide by 2
y = 4
Also, we have:
BC = AD
x + 12 = 2x - 4
Collect like terms
2x - x = 4 + 12
x = 16
The lengths AB and BC are given as:
AB = 3y - 2
BC = x + 12
So, we have:
AB = 3*4 - 2
AB = 10
BC = x + 12
BC =16 + 12
BC = 28
Hence, the lengths of line segments AB and BC are AB = 10; BC = 28
Read more about parallelograms at:
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Answer:
D
Step-by-step explanation:
Irene makes 4⅔ cups of pancake batter. She splits the batter into 2 bowls.She mixes blueberries into 2¼ cups of batter and walnuts into the rest of the batter.
Answer:
You have to find the most simple estimation by finding the nearest whole number, but the actual answer in 2 5/12
Select all angles of symmetry.
Answer:
B,C,F
Step-by-step explanation:
Compare. Select <, >, or=.
6.61? 6.610
The awnser is 6.610
Answer:
6.61=6.610
Step-by-step explanation:
6.61=6.610
After point we can increase no. Of zero.
Allyn's room is located at (3, -3). Use words to describe the location on a
coordinate plane.
Will name brainest for the first great answer with a explanation
Her room's location is 3 right from the origin, or (0,0) , and 3 down from the origin. She is in the 4th quadrant.
(I'm not quite sure how I'm supposed to describe it...)
PLEASE ANSWER THIS IN 30 MINUTES ILL GIVE YOU 30
Answer:
can you not just divide by 2 because you want to serve half the people?
Step-by-step explanation:
Callista used 10% off coupon to purchase a band t-shirt from Hot Topic . If the shirt cost $21.00, what is the discount in dollars?
Answer:
The discount is 2.1 dollars
There are 19.3 cups of flour in a bag. The chef uses 2.9 cups for making cookies.
Then, he uses 1.2 cups of sugar and 5.1 cups of flour for making banana bread.
How many cups of flour are left?
Answer:
10.1 cups left
Hope this helps!
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Find the GCF of 32, 64, and 96. The GCF is _______.
Answer:
128
Step-by-step explanation:
If you multiply you get it.
Answer:
The GCF of these numbers are 32.
Step-by-step explanation:
All of these integers are able to be divided, and by the first number.
Hope this helps! :3
What is the distance between (-3,-5) and (-3, 2)?
Answer: 7 units
Step-by-step explanation:
Just plot the numbers, then count the distance between them
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Bobby has 38 dolar and his siter had 92 dolar how much more money sister have?
Answer:
54
Step-by-step explanation:
92 (how much his sister has) - 38 (how much he has) = 54 (how much more money his sister has then him)
Answer: His sister had 54 more dollars than him.
Step-by-step explanation: 92 (sister's amount) -38 (Bobby's amount) = 54 (total difference).