A survey conducted by General Motors of 38 drivers in America, 34 indicated that they would prefer a car with a sunroof over one without. When estimating the proportion of all Americans who would prefer a car with a sunroof over one without with 99% confidence, what is the margin of error
Answer:
The margin of error is of 0.1282 = 12.82%.
Step-by-step explanation:
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]1-\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]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
A survey conducted by General Motors of 38 drivers in America, 34 indicated that they would prefer a car with a sunroof over one without.
This means that [tex]n = 38, \pi = \frac{34}{38} = 0.8947[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
What is the margin of error?
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 2.575\sqrt{\frac{0.8947*0.1053}{38}} = 0.1282[/tex]
The margin of error is of 0.1282 = 12.82%.
The average marks for 25 students in a mathematics was was 48.
what was the total marks scored by the students?
A student who scored 84 marks was absent.
what was would be the average of the remaining students?
Answer:
132
Step-by-step explanation:
48
+ 84
--------
132
_____
Can somebody please help
Answer:
Approximately 46.29 feet
Step-by-step explanation:
Hello Plsss ...... this is important
4x^2+4x-14=0 solve and explain then you get brainliest .
Answer:
Step-by-step explanation:
Hope this helps u!!
-2/3×3/5+5/2-3/5×1/6
Answer:
2
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]\frac{-2}{3}*\frac{3}{5}+\frac{5}{2}-\frac{3}{5}*\frac{1}{6}=\frac{-2}{5}+\frac{5}{2}-\frac{1}{5*2}\\\\= \frac{-2}{5}+\frac{5}{2}-\frac{1}{10}\\\\=\frac{-2*2}{5*2}+\frac{5*5}{2*5}-\frac{1}{10}\\\\=\frac{-4}{10}+\frac{25}{10}-\frac{1}{10}\\\\=\frac{-4+25-1}{10}\\\\=\frac{20}{10}\\\\= 2[/tex]
A light bulb consumes 960 watt-hours per day how long does it take to consume 5040 watt-hours?
Answer:
5 hour and 25 mins
Step-by-step explanation:
solve for x to the nearest tenth y completing the square: x^2-5x+7=0
Answer:
does not have a solution because √-0.75 ≠ R
Step-by-step explanation:
x^2 - 5x + (5/2)^2 = -7
x^2 - 5x + 6.25 = -7 + 6.25
(x - 2.5)^2 = -0.75
(x - 2.5) = √-0.75
does not have a solution because √-0.75 ≠ R
Answer:
x = (1/2)(5 ± i√3)
Step-by-step explanation:
x² - 5x + 7 = 0
subtract 7 from both sides
x² - 5x = -7
Use half the x coefficent, -5/2, as the complete the square term
(x - 5/2)² = -7 + (-5/2)²
(x - 5/2)² = -7 + 25/4
(x - 5/2)² = -3/4
Take the square root of both sides
x - 5/2 = ±(√-3) / 2
x - 5/2 = ±(i√3) / 2
Add 5/2 to both sides
x = 5/2 ± (i√3) / 2
factor out 1/2
x = (1/2)(5 ± i√3)
What is the slope and y-intercept of 6x-5y=13
Answer:
The slope is 6/5 and the y intercept is -13/5
Step-by-step explanation:
6x-5y=13
Solve for y
Subtract 6x from each side
6x-6x-5y=-6x+13
-5y = -6x+13
Divide by -5
-5y/-5 = -6x/-5 +13/-5
y = +6/5x -13/5
This is in slope intercept form y = mx+b where m is the slope and b is the y intercept
The slope is 6/5 and the y intercept is -13/5
What is the equation of the line that passes through point ( -5,2 ) and has a slope = 2
The difference between 8 and a number is 5.
Answer:
the answer is 3.
Step-by-step explanation:
Difference between means to subtract.
8 - 5 = 3
Answer:
8- a = 5
Step-by-step explanation:
The table below shows Karen's distance during the marathon. What is a reasonable explanation for what happened between hours 2 and 3.
o
Karen ran backwards for an hour.
Karen ran 2 miles between hours 2 and 3.
Karen decided to rest and stopped running for an hour.
K aren ran at the same speed between hours 2 and 3.
rious
Answer:
C. Karen decided to rest and stopped running for an hour
Step-by-step explanation:
The line of the graph shows a horizontal line between hours 2 and 3 with a corresponding distance that remains the same on the y-axis. This simply means that, only the hours change but distance didn't change. Therefore, it can be concluded that after for 1 hour, Karen decided to stop over and rest.
Answer:
the answer is C
Step-by-step explanation:
8) The sides of a flower garden are shown in the diagram below. What is the perimeter of the flower garden? 4m 2 m
Answer:
18.28 m
Step-by-step explanation:
Given the flower garden in the question :
The shape is composite and can be divided into 2 semicirles and rectangle
The perimeter of a semicircle is the Circumference of the semicircle = πr
Hence, 2 semicirles = 2πr
Radius of semicircle = 2/2 = 1
Perimeter = 2 * 3.14 * 1² = 2 * 3.14 * 1 = 6.28 m
The perimeter of rectangle; length and width are 6m and 2 m respectively :
Perimeter of rectangle = 2(l + w) = 2(4+2) = 2(6) = 12m
Tve perimeter of garden = 6.28 + 12 = 18.28 m
Please answer this: There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest meter, how many meters are in 158 inches?
Answer:
40 m
Step-by-step explanation:
158 · 2.54 = 401.32
401.32/100 = 40.132
40.132 ≈ 40
Somebody help me to solve this inequality:8x-2>15x-6.
Answer:
x< 4/7
Step-by-step explanation:
See image below:)
Ms. Jackson is making book bags for her class. She needs 2 2/3 yards of fabric for each book bag. If she
wants to make 10 book bags, how much fabric should she buy?
Answer:
26 2/3
Step-by-step explanation:
first you want to times the yards which gives you 20 yards.
next you times the 2/3 by 10 giving you 20/3 yards. the fraction converted into a mixed numeral is 6 & 2/3.
add both the 6 & 2/3 and the 20 which gives you 26 2/3
Answer:
26 2/3 is the answer.
Explanation:
Add the wholes first. That will give you 20. Then add the fractions. That will give you 20/3. When you write that in a mixed number, it will be 6 2/3. Add 20 with 6 2/3. That will give you 26 2/3 as the final answer.
да е анан алое вераснята на акту
find the roots of the quadratic equation w+w²/3=0
I assume that the equation you mean is below:
[tex] \large \boxed{w + \frac{ {w}^{2} }{3} = 0}[/tex]
To find roots for this equation, we have to get rid of the denominator. We can do by multiplying both sides by 3.
[tex] \large{w(3) + \frac{ {w}^{2} }{3} (3) = 0(3)} \\ \large{3w + {w}^{2} = 0}[/tex]
Factor w-term out (common factor)
[tex] \large{w(3 + w) = 0} \\ \large{w = 0 \: \: \: or \: \: \: 3 + w = 0} \\ \large{w = 0, - 3}[/tex]
Answer
The roots of quadratic equation are 0,-3what's the easiest way to answer how I know the answer pls?
PLEASE HELP ME!!! I need to simplify these equations, not answer them.
Answer:
Step-by-step explanation:
a= 2qr^3 quotent 6p^2
I need the answers pls!!!!
please
Answer:
[tex](4x - 3)(5x - 8) = 20x^2 -47x + 24[/tex]
Step-by-step explanation:
Given
[tex](4x - 3)(5x - 8)[/tex]
Required
Identify and correct error
The error is when the inner and outer terms are multiplied. i.e.
[tex]4x * -8 = -32x[/tex] not 32x
[tex]-3 * 5x = -15x[/tex] not 15x
So, the expression is:
[tex](4x - 3)(5x - 8) = 20x^2 - 32x -15x + 24[/tex]
[tex](4x - 3)(5x - 8) = 20x^2 -47x + 24[/tex]
Use the disk method or the shell method to find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = √x, y = 2, x = 0.
a. the x-axis
b. the line y = 2
c. the y-axis
d. the line x = -1
Answer:
a) 8π
b) 8/3 π
c) 32/5 π
d) 176/15 π
Step-by-step explanation:
Given lines : y = √x, y = 2, x = 0.
a) The x-axis
using the shell method
y = √x = , x = y^2
h = y^2 , p = y
vol = ( 2π ) [tex]\int\limits^2_0 {ph} \, dy[/tex]
= [tex]( 2\pi ) \int\limits^2_0 {y.y^2} \, dy[/tex]
∴ Vol = 8π
b) The line y = 2 ( using the shell method )
p = 2 - y
h = y^2
vol = ( 2π ) [tex]\int\limits^2_0 {ph} \, dy[/tex]
= [tex]( 2\pi ) \int\limits^2_0 {(2-y).y^2} \, dy[/tex]
= ( 2π ) * [ 2/3 * y^3 - y^4 / 4 ] ²₀
∴ Vol = 8/3 π
c) The y-axis ( using shell method )
h = 2-y = h = 2 - √x
p = x
vol = [tex](2\pi ) \int\limits^4_0 {ph} \, dx[/tex]
= [tex](2\pi ) \int\limits^4_0 {x(2-\sqrt{x} ) } \, dx[/tex]
= ( 2π ) [x^2 - 2/5*x^5/2 ]⁴₀
vol = ( 2π ) ( 16/5 ) = 32/5 π
d) The line x = -1 (using shell method )
p = 1 + x
h = 2√x
vol = [tex](2\pi ) \int\limits^4_0 {ph} \, dx[/tex]
Hence vol = 176/15 π
attached below is the graphical representation of P and h
Write the equation of the line passing through the point (−2, 1) that is parallel to y=−4x+3.
It was some mistake in previous one so i edited this one.
To estimate the height of a skyscraper 1km in the distance, Jenny finds that if her friend Steve stands 2.5 meters away, the top of his head just lines up with the top of the building. Steve is 2 meters tall, and Jenny's eye is 1.5 meters from the ground. How high is the building
Answer:
The answer is below
Step-by-step explanation:
Similar triangle are triangles with the same shape, equal pair of corresponding angles. Also they have the same ratio of the corresponding sides.
From the diagram attached, we can see that triangle ABC and triangle CEF are similar triangles. Hence:
AB/BC = CF/EF
Given that BC = 1 km = 1000 m, CF = 2 m - 1.5 m = 0.5 m, EF = 2.5 m.
Hence:
AB/1000 = 0.5/2.5
AB = (0.5/2.5) * 1000 = 200 m
The height of the building = AB + height of Steve = 200 m + 2 m
The height of the building = 202 m
405, 397,389, ...
Find the 31st term.
plss.. help me po goisss:( BRAINLIEST KO PO YUNG TAMANG SAGOT PLSS:(
I.)
1.) 7N = 50
2.) 35 - 16 = N
3.) 2P + 8 = 24
4.) R/5 = 9
5.) 30 - 10 = 20
II.)
1.) Twinity increased by eight times N
2.) D decreased by eleven
3.) The quotient of X and nine is K
4.) Five times X
5.) Three times a decreased by 5 is thirteen
6.) Nothing
7N = 50
35 - 16 = N
2P + 8 = 24
R/5 = 9
30 - 10 = 20
Twenty increased by eight times N
D decreased by eleven
The quotient of X and nine is K
Five times X
Three times a decreased by 5 is thirteen
a differentiable function g has the values shown below. Estimate f'(2.5).
х
2.0
2.2
2.4
2.6
f(x)
10
14
18
24
I assume you meant to say "a differentiable function f has the values ..." and not g.
Since f is differentiable, the mean value theorem holds, so you can approximate
f ' (2.5) ≈ (f (2.6) - f (2.4)) / (2.6 - 2.4) = (24 - 18) / (0.2) = 30
A basketball player scores 9 points in 12 minutes. How many points per minute does the basketball player score?
Answer:
0.75 points per minute
Step-by-step explanation:
9/12 is 0.75
Construct a data set that has the given statistics.
n = 7
x = 12
S = 0
Answer:
The desired data-set is: {12,12,12,12,12,12,12}
Step-by-step explanation:
n = 7
Data set of 7 elements.
x = 12
Mean of 12
S = 0
Standard deviation of 0.
Desired data-set:
Since the desired standard deviation is 0, all the elements in the data-set will be the same. Since the mean is 12, all elements is 12. 7 elements.
The desired data-set is: {12,12,12,12,12,12,12}
A small engine shop receives an average of repair calls per hour, with a standard deviation of . What is the mean and standard deviation of the number of calls it receives for -hour day? What, if anything, did you assume?
Answer:
Assuming normal distribution, the mean number of calls for a n-hour day is of [tex]m = n\mu[/tex], in which [tex]\mu[/tex] is the mean number of calls per hour, and the standard deviation is [tex]s = \sqrt{n}\sigma[/tex], in which [tex]\sigma[/tex] is the standard deviation of the number of calls per hour.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
N-instances of a normal variable:
For n-instances of normal variable, the mean of the distribution is: [tex]m = n\mu[/tex], and the standard deviation is [tex]s = \sqrt{n}\sigma[/tex]
What is the mean and standard deviation of the number of calls it receives for n-hour day?
Assuming normal distribution, the mean number of calls for a n-hour day is of [tex]m = n\mu[/tex], in which [tex]\mu[/tex] is the mean number of calls per hour, and the standard deviation is [tex]s = \sqrt{n}\sigma[/tex], in which [tex]\sigma[/tex] is the standard deviation of the number of calls per hour.