Margin of error is 4.645% with 95% confidence that the mean number of hours all the residents of the city are watching news on television is 1.8 .
Data given :
A researcher surveyed 220 residents of a city about the number of hours they spend watching news on television each day. The mean of the sample was 1.8 with a standard deviation of 0.35 .
The researcher can be 95% confident that the mean number of hours all the residents of the city are watching news on television is 1.8 with what margin of error,
By formula of margin of error = [tex]M = 1.96 \times S / \sqrt{N} ,[/tex]
[tex]Margin \ of \ error, \ M = z \times \frac{s}{\sqrt{N}}[/tex]
z - represents the z-value for the required confidence level .
s - represents the standard deviation of the sample .
N - represents the sample size .
Now, using the above information, compute the margin of error as -
[tex]\therefore \ Margin \ of \ error, \ M = z \times \frac{s}{\sqrt{N}} \\= 1.96 \times \frac{0.35}{\sqrt{220}}[/tex]
[tex]=0.04625 (rounded \ to \ 5\ decimal\ places) \\\\ =4.625\%[/tex]
Thus, the margin of error, M, is approximately 4.625% .
Know more about margin of error,
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Jerry has $90 in his savings account. The interest rate is 10%, compounded annually. To the nearest cent, how much interest will he earn in 3 years
Answer:
27 cents
Step-by-step explanation:
10% of 90= 9
9x3=27
Answer:
p x t x r / 100
90 x 10 x 3 / 100
=27
9 mi
12 mi
What is the length of the hypotenuse?
miles
find m
135°
125°
55°
100°
Answer:
answer: m = 125
Step-by-step explanation:
parellograms add up to a total of 360 so m = 125 because 125 + 125 + 55 + 55 = 360 Hope this helps!
Step-by-step explanation:
here's your solution
==> sum of corresponding angles of parallelogram = 180°
==> angle J + angle k = 180°
==> 55° + k = 180°
==> k = 180° - 55°
==> k = 125°
[tex]hope \: it \: helps[/tex]
30 POINTS, NO LINKS, AND ANSWER RIGHT.
-15 = 8z + 7. what is the value of z
Paul is selling $2 raffle tickets for his baseball team. He needs to sell at least
$230 worth of tickets to earn a team jacket. If he has already sold $50 worth of tickets, how many more raffle tickets, x, does Paul need to sell to earn a team jacket?
Answer: 90 more tickets
Step-by-step explanation:
230 - 50 = 180
180 divided by 2 = 90 tickets
Kate is 5 feet 2 inches tall.
Alice is 1.57 metres tall.
Alice says that she is taller than Kate.
Use the conversions below to decide if Alice is correct.
12 inches = 1 foot
1 inch = 2.5 centimetres
if someone could help me with this it would be really helpful
Answer:
Alice is wrong kate is taller than Alice
Step-by-step explanation:
because Alice is 5'1 and Kate is 5'2
Help ASAP I’ll mark branliest
Answer:
C - 129
Step-by-step explanation:
180-51=129
14. A cone has twice the base diameter and
three-fourths the height of a cylinder. Can
you tell what the relationship between the
volume of the cone and the volume of the
cylinder is? Explain your reasoning.
Answer:
1+1 is cannot be
Step-by-step explanation:
jajauajhwhahwwhhahwhauwu
Please help me this is for a test. Thank you so much whoever answers this.
Answer: Pretty sure the answer is 3.
Step-by-step explanation:
[tex]\frac{2(4+7)-7}{5}[/tex]
[tex]\frac{2(11)-7}{5}[/tex]
[tex]\frac{22-7}{5}[/tex]
[tex]\frac{15}{5}[/tex]
find the volume of the solid formed by revolving the region bounded by the graphs of y = 4x - x^2 and f(x) = x^2 from [0,2] about the... a) x-axis.
Answer:
[tex]v = \frac{32\pi}{3}[/tex]
or
[tex]v=33.52[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4x - x^2[/tex]
[tex]g(x) = x^2[/tex]
[tex][a,b] = [0,2][/tex]
Required
The volume of the solid formed
Rotating about the x-axis.
Using the washer method to calculate the volume, we have:
[tex]\int dv = \int\limit^b_a \pi(f(x)^2 - g(x)^2) dx[/tex]
Integrate
[tex]v = \int\limit^b_a \pi(f(x)^2 - g(x)^2)\ dx[/tex]
[tex]v = \pi \int\limit^b_a (f(x)^2 - g(x)^2)\ dx[/tex]
Substitute values for a, b, f(x) and g(x)
[tex]v = \pi \int\limit^2_0 ((4x - x^2)^2 - (x^2)^2)\ dx[/tex]
Evaluate the exponents
[tex]v = \pi \int\limit^2_0 (16x^2 - 4x^3 - 4x^3 + x^4 - x^4)\ dx[/tex]
Simplify like terms
[tex]v = \pi \int\limit^2_0 (16x^2 - 8x^3 )\ dx[/tex]
Factor out 8
[tex]v = 8\pi \int\limit^2_0 (2x^2 - x^3 )\ dx[/tex]
Integrate
[tex]v = 8\pi [ \frac{2x^{2+1}}{2+1} - \frac{x^{3+1}}{3+1} ]|\limit^2_0[/tex]
[tex]v = 8\pi [ \frac{2x^{3}}{3} - \frac{x^{4}}{4} ]|\limit^2_0[/tex]
Substitute 2 and 0 for x, respectively
[tex]v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ \frac{2*0^{3}}{3} - \frac{0^{4}}{4} ])[/tex]
[tex]v = 8\pi ([ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ] - [ 0 - 0])[/tex]
[tex]v = 8\pi [ \frac{2*2^{3}}{3} - \frac{2^{4}}{4} ][/tex]
[tex]v = 8\pi [ \frac{16}{3} - \frac{16}{4} ][/tex]
Take LCM
[tex]v = 8\pi [ \frac{16*4- 16 * 3}{12}][/tex]
[tex]v = 8\pi [ \frac{64- 48}{12}][/tex]
[tex]v = 8\pi * \frac{16}{12}[/tex]
Simplify
[tex]v = 8\pi * \frac{4}{3}[/tex]
[tex]v = \frac{32\pi}{3}[/tex]
or
[tex]v=\frac{32}{3} * \frac{22}{7}[/tex]
[tex]v=\frac{32*22}{3*7}[/tex]
[tex]v=\frac{704}{21}[/tex]
[tex]v=33.52[/tex]
Guys help me with this quick pls
Answer:
[tex]117 = 66 + \beta \\ \beta = 51[/tex]
What is the total of 12 monthly payments of 100.00 including tax
Answer:
The monthly payments of said financing plan will be $8.33.
Step-by-step explanation:
To determine what is the total of 12 monthly payments of $ 100.00 including tax, the following calculation must be performed:
100/12 = X
8.33 = X
Therefore, the monthly payments of said financing plan will be $8.33.
Graph the following function on the axes provided.
Answer:
this may help you.look it once
Step-by-step explanation:
.
Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 40 at one school and 13 of 30 at the other had this infection. Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other. Find the test statistic. [Suggestion: try to use a TI 83 or a similar calculator.]
Answer:
The test statistic is [tex]z = -0.28[/tex]
Step-by-step explanation:
First, before finding the test statistic, we need to understand the central limit theorem and difference between 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 between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
A random sample of children in two different schools found that 16 of 40 at one school
This means that:
[tex]p_1 = \frac{16}{40} = 0.4, s_1 = \sqrt{\frac{0.4*0.6}{40}} = 0.0775[/tex]
13 of 30 at the other had this infection.
This means that:
[tex]p_2 = \frac{13}{30} = 0.4333, s_2 = \sqrt{\frac{0.4333*0.5667}{30}} = 0.0905[/tex]
Conduct a test to answer if there is sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other.
At the null hypothesis, we test if there is no difference, that is:
[tex]H_0: p_1 - p_2 = 0[/tex]
And at the alternate hypothesis, we test if there is difference, that is:
[tex]H_a: p_1 - p_2 \neq 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis and s is the standard error
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the two samples:
[tex]p = p_1 - p_2 = 0.4 - 0.4333 = -0.0333[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0775^2+0.0905^2} = 0.1191[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{-0.0333 - 0}{0.1191}[/tex]
[tex]z = -0.28[/tex]
The test statistic is [tex]z = -0.28[/tex]
Find the slope of the line parallel to the line graphed.
My Answer:
a)Solve for x:
y = 130 − 4x
b) What is the value of x when y = 120
Answer:
[tex]x = \frac{5}{2}[/tex]
Step-by-step explanation:
y = 130 - 4x
======================
120 = 130 - 4x
-10 = -4x
x = [tex]\frac{-10}{-4} =\frac{5}{2}[/tex]
PLS HELP ME GIVING OUT BRAINLIEST ANSWER!!
Answer:
4r^2
Step-by-step explanation:
The area of a square is the square of the side length. Since a circle with radius r is inscribed inside the square, the side length of the square is 2r. Therefore, the area of the square is (2r)^2, which is 4r^2.
Note that the area of the circle is [tex]\pi r^2[/tex].
What is the answer to this problem?
Answer:
5 2/3
Step-by-step explanation:
just trust me
Answer:
option b 5.6 is the correct answer
Write each phrase as an algebraic expression.
16 seconds faster than Aya’s time.
Given:
The given phrase is 16 seconds faster than Aya’s time.
To find:
The algebraic expression for the given phrase.
Solution:
Let x be the Aya’s time.
16 seconds faster than Aya’s time. It means 16 seconds less than Aya’s time.
We know that a negative sign "-" is used for less than.
16 seconds less than Aya’s time = [tex]x-16[/tex]
16 seconds faster than Aya’s time = [tex]x-16[/tex]
Therefore, the required algebraic expression is [tex]x-16[/tex].
Which expression has a value greater than 43 ?
PLEASEEE HELP!
Answer:
7^2
Step-by-step explanation:
7*7=49
4^3=43
49>43
Rationalize the denominator and simplify
Select all values of x that make the inequality true: (x ≥ -1)
A. -4
B. -2
C. -1
D. 0
E. 1
F. 4
Answer:
c,d,e,f
Step-by-step explanation:
mark me brainliest
Select all values of x that make the inequality true: (x ≥ -1)
A. -4
B. -2
C. -1
D. 0
E. 1
F. 4
Answer:
C, D, E, F
Step-by-step explanation:
hope this helps! #HappyCheating
x > -3 For each statement list three numbers that would make a solution to the inequality true.
Answer:
x = -2
x = -1
x = 0
Step-by-step explanation:
Find three numbers to the left of -3 on the number line
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
In an isosceles triangle, the base angles measure 65°. Which of the following expressions is a way to calculate the measure of the third angle?
Answer:
its A
Step-by-step explanation:
its A ️ ♀️ ️ ♂️ ️
A box holds 30 tins How many boxes can be filled
with 810 tins
2.52343454 + -34355343.99
NEED HELP PLZZZZZZ ASAP
Answer:
5555555555555555555555555555555555555 trust
Step-by-step explanation:
The question is in le picture below U-U
Answer:
30%
Also I LOVE THE EMMA PIC!!!!!!!!
please help me with this question:(
What’s the answer (no link I give brainly)
Find the radius of the curcle
Answer:
radius=diameter/2
=9/2
=4.5 in.
diameter=radius*2
=3m*2
=6m
Step-by-step explanation:
Step-by-step explanation:
1) r=d/2
r=9in/2
r=4.5in
2) d= r×2
d=3m×2
d=6m