Answer:
170
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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
Assume:
[tex]\pi = 0.06[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
What is the smallest sample size required to obtain the desired margin of error?
This is n for which M = 0.03. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.03 = 1.645\sqrt{\frac{0.06*0.94}{n}}[/tex]
[tex]0.03\sqrt{n} = 1.645\sqrt{0.06*0.94}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.06*0.94}}{0.03}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645\sqrt{0.06*0.94}}{0.03})^2[/tex]
[tex]n = 169.6[/tex]
Rounding up, 170.
Estimate the slope of the regression line manufacturer of cases for sound equipment requires drilling holes for metal screws. The drill bits wear out and must be replaced; there is expense not only in the cost of the bits but also for lost production. Engineers varied the rotation speed of the drill and measured the lifetime in thousands of holes drilled of bits at different speeds in surface feet per minute (sfm). Suppose you want to create a model that estimates the drill bit lifetime ( y) based on rotation speed ( x). Summary statistics for 20 observations collected are given below.
20 20 20 20
Σ xi = 2,000 ; Σ yi = 86.6 Σ xi^2= 216,000 Σ xiyi= 8,338
i= 1 i=1 i=1 i=1
Estimate the slope of the regression line.
a. -0.017
b.-0.037
c. -0.057
d.-0.077
Answer:
[tex]b_i = -0.020125[/tex]
Step-by-step explanation:
Given
[tex]\sum x_i= 2000[/tex]
[tex]\sum y_i= 86.6[/tex]
[tex]\sum x_i^2= 216000[/tex]
[tex]\sum x_iy_i = 8338[/tex]
[tex]n = 20[/tex]
Required
Determine the slope (b) of the regression line
This is calculated as:
[tex]b_i = \frac{\sum xy - \frac{\sum x\sum y}{n}}{\sum x^2 - \frac{(\sum x)^2}{n}}[/tex]
Substitute values for each term, we have:
[tex]b_i = \frac{8338 - \frac{2000 * 86.6}{20}}{216000 - \frac{(2000)^2}{20}}[/tex]
Simplify the numerator
[tex]b_i = \frac{8338 - 8660}{216000 - \frac{(2000)^2}{20}}[/tex]
Simplify the denominator
[tex]b_i = \frac{8338 - 8660}{216000 - 200000}[/tex]
[tex]b_i = \frac{-322}{16000}[/tex]
[tex]b_i = -0.020125[/tex]
Help plis I don’t understand ✋✋
Trapezoid Area =
[ ( Sum of the rules ) × ( height ) ] ÷ 2
_________________________________
Area = [ ( 2 + 3 ) × 3 ] ÷ 2
Area = [ 5 × 3 ] ÷ 2
Area = 15 ÷ 2
Area = 7.5 m^2
solve y=x-2 and x+y=12 using substitution
Step-by-step explanation:
y=x-2....eqn1
x+y=12.....eqn2
now,
from eqn 1
y= x-2
again, putting value of y in eqn 2
x+y=12x+x-2=122x=12+2x=14/2x=7in eqn 1
y=x-2y=7-2y=5hope it helps..
A sphere has a radius of 9 in, which means its volume is 972π in3. The sphere is dilated by 2⁄3. What is the volume of the new sphere?
Answer:
08-Oct-2009 — If a spherical balloon has a volume of 972 pi cubic centimeters, what is ... is 4.pi.r^2 (its area remember not volume) as 4/3.pi.r^3=972pi r=9 ... and it is good to know the squares of the next 10 numbers.
Answer:
I have this same question on my math test.
Since the radius is 9, the diameter is 18.
The shape is being dilated by 2/3, so the new radius is 6.
Volume formula: V = 4/3πr^3
So now we plug in the values.
V = 4/3 x π x (6)^3
V = 4/3 x π x 216
V = 288π
If the answers do not have the pi symbol present, then it has been multiplied into the answer.
288 x 3.14 = 904.32
The new volume of the sphere is 904.32 in^3
The Hutton's records for the past six months show that their expenditures totaled $2.768, $3,001, $2,663, $2,471, $2,893, and $2,803. What is their average monthly expenditure for the six months?
Answer
2766.5
Step-by-step explanation:
Well to solve for average all you have to do is add the values together then divide by the number of values you started with. So we add them together(2768+3001+2663+2471+2893+2803) and get 16599. Then, since there were 6 values we divide that by 6 and you get your answer.
WILL MARK BRAINLEST Select the correct answer.
The stem and leaf plot shows the number of coples of a newly released book ordered from several bookstores.
Answer:
the median is 139
Step-by-step explanation:
there are 19 numbers in the data set. Therefore, the 10th number would be the median.
In what direction does the function f(x)=−(14x−1)(4x+1) open? Explain.
Answer: Direction opens downward
Step-by-step explanation:
X-Intercept: (1/14,0),(-1/4,0)
Y-Intercept: (0,1)
Find the vertex using x= -b/2a
Plug it into the vertex form = y=a(x-h)^2 +k
H,K will identify the direction.
a) Expand and simplify (x + 4)(x - 7)
Answer:
X x X=x²
X x -7=-7x
4 x X=4x
4 x -7=-28
-7x + 4x=-3x
x² + -3x -28
hope that helped :)
Step-by-step explanation:
Marking brainliest please help me
Answer:
I think B
Step-by-step explanation:
Not sure but seems like so. Hope I helped U :)
A baseball field is being designed. There is 60 ft between the pitcher and 3rd
baseman and 90 ft between the catcher and 3rd baseman. The half-way
distance from the catcher to the 3rd baseman is 45 ft. How far is the distance
between the pitcher and the catcher?
441 = 21
3600 = 60
5400 = 73.5
7650 = 87.5
1800 = 42.4
Answer:
30ft.
your welcome. ...................
4.
What is the equation of the circle with a radius of 5 and center at (2, 3)?
AO (x + 2)2 + (y + 3)2 = 25
BO (x - 2)2 + (y - 3)2 = 25
CO (x - 2)2 + (y - 3)2 = 5
D. (x + 2)2 + (y + 3)2 = 5
Answer:
the answer is A
Step-by-step explanation: since the radius is 5 and we have (2,3) then we are going into 2 and 3 the x and y represent 5 so the answer wouldn't be 5 then you would have done no work. so it is A. i suck at explaining things hope this helps!
Step-by-step explanation:
[tex]general \: equation \\ {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0 \\ centre : ( - g, - f) = (2,3) \\ g = - 2 \: and \: f = - 3 \\ c = {g}^{2} + {f}^{2} - {r}^{2} \\ c = {( - 2)}^{2} + {( - 3)}^{2} - {(5)}^{2} \\ = - 12 \\ therefore \\ {x}^{2} + {y}^{2} - 2x - 3y - 12 = 0[/tex]
3. The cost of renting a car is $26.50 plus $10 per day. Sales tax is 6%. Select all expressions that represent the cost of renting a car for d days. 1.06(26.50 + 100) 28.09d 26.50 + 6d 28.09 + 10.6d 26.50 + 1.06d
Estimate the product. 3 1/3 x 4 1/8 =
Answer:
13 3/4 or 14 if rounded
Step-by-step explanation:
Answer:
Step-by-step explanation:
55/4
13 3/4
7) Write an inequality that represents 7 more than three times a number, n, is less than 16.
Answer:
3n + 7 < 16
Step-by-step explanation:
7 more than 3 times a number, n, is less than 16 is represented by
3n + 7 < 16 where:
3n = three times a number, n,
+ 7 = 7 more than
and
< 16 = is less than 16.
Answer:
Step-by-step explanation:
12 bars of soap for $8.69
What is the area of this composite figure?
A) 130 in2
B) 280 in2
C) 436 in2
D) 616 in2
Answer:
See explanation. I attached a photo to help visualize and make it easier to understand, but tell me if handwriting was fine :)
Also, C) 436 in² is correct :)
Step-by-step explanation:
the answer is C
Step-by-step explanation:
if we take the 15 from 28
13 will be left
so 13×22=286
and 15×5=75
15×5=75
150+286=436
hopefully its helpful
Answer this question pls!!
Answer:
(6, 7)
Step-by-step explanation:
A rectangle means that opposite sides are parallel to each other and that opposite sides are equal in measurements.
If we look at the opposite side starting at (2, 1), we can count how long the other side should be. Counting the next point of the rectangle is (6, 1) which is a difference of 4. This means if we count from (2, 7) 4 spaces to the right, we will find our missing vertex.
(2 + 4, 7) = (6, 7)
In a lab experiment, 2000 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 23 hours. How many bacteria would there be after 26 hours, to the nearest whole number?
Answer:
4,261
Step-by-step explanation:
after 23 hours, the number of bacteria =
4,000.
so, after 26 hours = 4,000+ (3/23 ×4000)
= 4,000 + 261 = 4,261
HELP ME PLEASEEEEEEEEEE
Answer:
2, - 6 your welcome caubububyvyvybubufwrduvibuvc
3/2 of a number is less than this number?
true or false, justify your answers
Answer:
False because 1/2 would be half the number 2/2 or 1 would be the whole number so 3/2 would be a whole and half or 1 1/2
Answer:
false
if the number is X
3/2 of X= X 1/2
[tex]x \frac{1}{2} > x[/tex]
Round to the nearest hundredth (2 decimal places) when necessary
Answer:
volume = 91 cm²
perimeter = 41.1 in
Step-by-step explanation:
volume = 1/2(b1+b2)(h) = 1/2(11 + 15)(7) = 91 cm²
Please help!
1. What is the perimeter of the triangle below? Show your work.
Answer:
16.73 I THINK
Step-by-step explanation:
my guess is n1 is relating to the 4.9, and if it then you would do the Pythagorean theorem. because the degrees are there to let you know it's a right angle and you are able to use the theorem..... so -
4.9^2 + 4.9^2 =C^2
48.02 =C
√48 = 6.93 (rounded to nearest hundredth)
then you add them all together
4.9+4.9+6.93=16.73
For each expression in the table, select which number line model, If any, can be used to represent the expression. Select all appropriate cells in the
table.
Answer:
I don’t know
Step-by-step explanation:
You didn’t attach a photo lol
NEED HELP DUE IN 2 MINUTES!!!!
A cube has a volume of 64 cubic feet. What is the length of one side of the cube in feet?
Answer:
4 feetStep-by-step explanation:
s³ = 64
Take the cube root of both sides
s = 4
Two trains, Train A and Train B, weigh a total of 243 tons. Train A is heavier than Train B. The difference of their weights is 87 tons. What is the weight of each train?
Answer:
Train A weighs 156 tons, and Train B weighs 78 tons.
Step-by-step explanation:
Given that two trains, Train A and Train B, weigh a total of 243 tons, and Train A is heavier than Train B, with a difference of their weights of 87 tons, to determine what is the weight of each train, the following calculation has to be done:
(243 - 87) / 2 = B
156/2 = B
78 = B
243 - 87 = A
156 = A
Therefore, Train A weighs 156 tons, and Train B weighs 78 tons.
Find the area and perimeter
Answer:
Step-by-step explanation:
Add all 4 sides to get perimeter so the first one is 9+9+2+2=22cm
the area is length x width so the first one is 9 x 2 =18cm ^2
Solve for x
Please help!
Answer:
Hello! answer: x = 20
Step-by-step explanation:
Because 3 multiplied by x which equals 20 gets us 60 then we just add the 2 and get 62 these are vertical angles so they will have the same measure hope that helps!
Find the Find the marginal cost function, given the average cost function AC=100100Q+2arginal cost function, given the average cost function AC=100100Q+2
Answer:
Step-by-step explanation:
a) total fixed cost is 100(derived from total cost function). It is not depended on output.
b)AFC=TFC/Q.AFC=TFC/Q.
AFC(100)=100/100=1.AFC(100)=100/100=1.
AFC(300)= 100/300=1/3.AFC(300)=100/300=1/3
Find the sum of the measures of the interior angles of the indicated covex
Very confused
Answer:
Step-by-step explanation:
Hope it helps u!!
8
The median of 3 numbers is 7. If one of the numbers is 10, which of the following is a possible value for one of
the other numbers?
0/
6
8
ОООО
13
17
Review Questions
Mathematics
9514 1404 393
Answer:
(a) 6
Step-by-step explanation:
The median is the middle number when they are sorted into order. If one of the numbers is 10, the remaining number must be any number less than 7. Of the offered choices, the only one less than 7 is 6.
__
The three numbers are 6, 7, 10.