Answer:
A sample size of 2401 is needed.
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 given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
What sample size would be needed to construct a margin of error of 2% with 95% confidence?
This is M for which n = 0.02.
Supposing we have no estimate for the true proportion, we use [tex]\pi = 0.5[/tex].
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.02\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.02}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2[/tex]
[tex]n = 2401[/tex]
A sample size of 2401 is needed.
What line does the point (8,41) lie?
Answer:
There are infinite answers to your question
y= 5x + 1
is one of them
Step-by-step explanation:
In the following diagram, BAC = 46 degrees, and AD is the bisector of BAC. Find BDA
Answer:
67 degrees
Step-by-step explanation:
We have a right triangle with the following known values:
B = 90
A = 23 (46/2=23 since AD is the angle bisector)
D = ?
180 = 90 + 23 + D and we solve
67 = D
Please help me this on the picture
Answer:
Step-by-step explanation:
1. demand can be said to control supply and demand.
(Consumer, Producer)
Answer:
The law of demand says that at higher prices, buyers will demand less of an economic good. The law of supply says that at higher prices, sellers will supply more of an economic good. These two laws interact to determine the actual market prices and volume of goods that are traded on a market.
Supply is generally considered to slope upward: as the price rises, suppliers are willing to produce more. Demand is generally considered to slope downward: at higher prices, consumers buy less. ... The relationship between the supply and demand for a good (or service) and changes in price is called elasticity.
LENGTH OF ARCS. URGENT.
Since the angle of the arc is 90°, we'll plug that in for theta. We're finding the length of the arc, so we'll use the circumference formula.
factor: 3x^(2)-16x+16
Answer:
[tex]3 {x}^{2} - 16x + 16 \\ 3 {x}^{2} - 12x - 4x + 16 \\ 3x(x - 4) - 4(x - 4) \\ (3x - 4)(x - 4)[/tex]
Step-by-step explanation:
I hope it helped U
stay safe stay happy
dilations geometry help please
Multiply x and y by 2:
A. (-6, 4)
B. (2, 2)
C. (-2, -2)
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!!
A teacher takes a random sample of 100 students enrolled at Springfield High School and asks them their opinions about the food served in the school cafeteria. The population of students here is __________________.
A. the 100 students who are asked questions
B. all students enrolled at Springfield High School
C. all high school students in the country
D. all high school students in the world
Answer:
The 100 students who are asked questions.
what is the equation of the axis of symmetry do the quadratic function f(x) = -(x+4) (x-1)
9514 1404 393
Answer:
x = -3/2
Step-by-step explanation:
The zeros of the function are the values of x that make the factors zero:
x = -4, x = 1
The axis of symmetry is the vertical line halfway between these zeros.
x = (-4 +1)/2 = -3/2
The equation of the axis of symmetry is x = -3/2.
31. Which choice describes the value of m when -5(m + 1) = 23?
А
B.
m 2-3
ms-
6 m2
D.ms-
Answer:
The correct choice is Option A. m ≥ -28/5
Step-by-step explanation:
Steve works two different jobs for a total of 60 hours every Monday through Friday schedule is the same each day and he works three hours a day at his first job how many hours a day does he work at his second job
Answer:
Step-by-step explanation:
Steve works:
- 60 hour per week = 12 hours per day (60/5)
- first job: 3 hours per day = 15 hours per week
- x = second job hours per day
equitation:
1st option to calculate:
12 (total hours per day) = 3 (hours per day on first job) + X
9 = X
2nd option to calculate:
60(total hours per week) = 15 (3 hours per day x 5) + x
45 = x
you need to divide 45 / 5 to get the daily hours which is 9
Robi bought a toy car for $x. He sold it at a loss of 10%. Find the expression
for the selling price.
Step-by-step explanation:
loss amount'= loss% × C.P
=10/100 × x
=0.1 x
Again,
S.P = C.P - Loss amount
=$x - $0.1 x
=0.9 x
The expression for the selling price is:
0.9x
What is selling price and cost price and its formula?
Cost Price: The price paid for an item is referred to as its cost price (C.P.). The price at which an item is purchased is referred to as its selling price (S.P.).
Profit or Gain: The seller is considered to have profit or gain if SP exceeds CP.
Solution:
Given, loss percent is = 10%
cost price of the toy car is = $x
Therefore the loss amount is: loss% × C.P
= 10/100 × cost price
= 0.1x
Now, for the selling price expression:
selling price (SP) = Cost price ₋ Loss amount
= $x ₋ $0.1x
= 0.9x
Hence we get the desired expression for the selling price as 0.9x.
Learn more about "selling price questions" here-
brainly.com/question/1153322
#SPJ2
Find the 8th term of the geometric sequence 7,−21,63,
Answer:
8th term is -15309
Step-by-step explanation:
[tex]{ \boxed{ \bf{u_{n} = a( {r}^{n - 1} ) }}} \\ { \tt{u_{8} = 7( {( - 3)}^{8 - 1}) }} \\ { \tt{u_{8} = 7( - 2187)}} \\ { \tt{u _{8} = - 15309}}[/tex]
r is the common difference, r = -21/7 = -3
Answer:
a₈ = - 15309
Step-by-step explanation:
The nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 7 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-21}{7}[/tex] = - 3 , then
a₈ = 7 × [tex](-3)^{7}[/tex] = 7 × - 2187 = - 15309
Chase plans to repaint some classroom bookcases. He has 1 4/7 gallons of paint. All of the bookcases are the same size and each requires 1/3 gallon of paint. How many bookcases will the custodian be able to repaint with that amount of paint?
What are the two square roots of 9/4?
Answer:
3/2
Step-by-step explanation:
3^2=9
2^2=4
3/2 and -3/2
sqr of 9 is 3 or 3
sqr of 4 is 2 or -2
Which equation is in slope-y-intercept form?
Question 1 options:
a) 3x + 4y = 7
b) x = 4y - 2
c) y = 3x -1
d) x + 4y -2
Answer:
C = y - 3x-1
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
C = y - 3x-1 is in slope intercept form
The answer is A.
I took the test.
If A = {1, 3, 5, 6, 7, 9, 10}, B = {3, 5, 7, 9,10,12}, C = {2, 4, 6, 8, 10,12} (a) Find A U B ( b) Find A U C (c) Find B ∩ C
Answer:
Step-by-step explanation:
A ∪ B -----> we have to write all the elements from A & B set without duplicating.
B∩C ------> We have to write only the elements that are found in both B set and C set
A) A ∪ B = {1,3,5, 6, 7, 9, 10,12}
b) A ∪ C = {1, 3, 5, 6, 7, 9, 10,2,4,8,12}
c) B ∩ C = {10,12}
Answer:
a. A U B = { 1,3,5,6,7,9,10,12 }
b. A U C = { 1,2,3,4,5,6,7,8,9,10,12}
c. B n C = { 10.12 }
Step-by-step explanation:
a. A U B — you put all the numbers in set A and B together without repeating anything.
A U B = { 1,3,5,6,7,9,10,12}
b. A U C — you put all the numbers in set A and C without repeating anything.
A U C = { 1,2,3,4,5,6,7,8,9,10,12}
c. B n C — you find a common number in sets B and C.
B n C = { 10,12}
The numbers 10 and 12 are the only common thing in sets B
and C.
Is it equivalent? please show work so i can write it
No, because
2(y + 1,5) = 2 · y + 2 · 1,5 = 2y + 3
2y + 3 ≠ 2y + 1,5
Answer:
No
Step-by-step explanation:
2 ( y + 1.5 ) = 2y + 3. Not 2y + 1.5
find the missing length indicated
Answer:
192
Step-by-step explanation:
According to Euclidian theorem
x^2 = 144*(400-144)
x^2 = 144*256
x^2 = 36864 find the root of both
x = 192
Work out an estimate for the value of
41.2 x 19.8
——————-
0.49
Answer:
820
Step-by-step explanation:
41.2 * 19.8 = 41 *20 = 820
41.2
In this tenth value is 2 which is less than 5. So ignore it and write the whole number alone. 41
19.8
In this tenth value is 8 awhich greater than 5. So add 1 to whole part and write.
19+1 = 20
1 upon sec A -tan a minus one upon cos A is equal to 1 upon Cos A minus one upon sec a + tan a prove it
Step-by-step explanation:
1/(seca-tana) - 1/cosa=1/cosa -1/(seca+tana)
There are many ways to solve this, let's take a look at a simple one
1/(seca-tana) + 1/(seca+tana) =1/cosa + 1/cosa
((seca-tana)+(seca+tana))/(sec^2a-tan^2a)=2/cosa
(seca-tana+seca+tana)/1=2*1/cosa
2seca=2seca
Yet another calculus question :)
Given [tex]y = x^3 - 2x[/tex] for [tex]x \geq 0[/tex], find the equation of the tangent line to y where the absolute value of the slope is minimized.
I have tried taking both the first and second derivatives and setting them equal to 0 and using that as the answer, but they're incorrect. Could somebody please explain how to complete the question correctly? Thank you so much!
Answer: y = (-4/3)*sqrt(2/3)
This is the same as writing [tex]y = -\frac{4}{3}\sqrt{\frac{2}{3}}[/tex]
============================================================
Explanation:
The phrasing "where the absolute value of the slope is minimized" is an interesting way of saying "the tangent slope is 0". This is because absolute values are never negative, so the smallest it can get is 0.
Your teacher has given you
y = x^3 - 2x
which differentiates into
dy/dx = 3x^2 - 2
after using the power rule
The derivative function lets us determine the slope of the tangent. The slope is the dy/dx value. Since we want a slope of 0, we'll set 3x^2-2 equal to zero and solve for x. So you have the correct idea, but you won't involve the second derivative.
dy/dx = 0
3x^2 - 2 = 0
3x^2 = 2
x^2 = 2/3
x = sqrt(2/3)
Notice how I'm ignoring the negative version of this root. This is due to the fact that [tex]x \ge 0[/tex]
-------------------------
Now plug this x value back into the original equation to find its corresponding y coordinate.
y = x^3 - 2x
y = x(x^2 - 2)
y = sqrt(2/3)*( 2/3 - 2 )
y = sqrt(2/3)*( -4/3 )
y = (-4/3)*sqrt(2/3)
Note that x = sqrt(2/3) leads to x^2 = 2/3 after squaring both sides.
-------------------------
Therefore, the equation of this tangent line is y = (-4/3)*sqrt(2/3)
All horizontal lines are of the form y = k, for some constant k. This constant value is basically what number you want the horizontal line to go through on the y axis. That number would be (-4/3)*sqrt(2/3).
Find the first four terms of the sequence given by the following.
an=51 + (n-1).8, n=1, 2, 3...
Answer:
Step-by-step explanation:
a1 = 51 + (1 -1 ) * 0.8
a1 = 51
a2 = 51 + (2 - 1)*0.8
a2 = 51 + 0.8
a2 = 51.8
a3 = 51 + (3 - 1)*0.8
a3 = 51 + 2*0.8
a3 = 51 + 1.6
a3 = 52.6
a4 = 51 + (4 - 1)*0.8
a4 = 51 + 2.4
a4 = 53.4
Provide a rule to describe the relationship between the number in the sequence
1,4,9,16
Answer:
add 3, add 5, add 3
Step-by-step explanation:
1, 4, 9, 12
add 3, add 5, add 3
Answer:
x^2
Step-by-step explanation:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
And so on.
So, the rule is x^2.
One angle of a triangle is 22^0. What is the measurement (in degrees) of the corresponding angle in a similar triangle?
Answer:
22 degrees
Step-by-step explanation:
Corresponding angles in similar triangles are equal
So the corresponding angle would be 22 degrees
Anybody help please ! Step by step
Your answer is -6.
Hope my answer is helpful to you. Stay blessed .
[tex]\\ \large\sf\longmapsto {27}^{x} = {9}^{x - 3} \\ \\ \large\sf\longmapsto ( {3}^{3} ) {}^{x} = ({3}^{2} ) {}^{x - 3} \\ \\ \large\sf\longmapsto 3 {}^{3x} = 3 {}^{2(x - 3)} \\ \\ \large\sf\longmapsto {3}^{3x} = 3 {}^{2x - 6} \\ \\ \large\sf\longmapsto 3x = 2x - 6 \\ \\ \large\sf\longmapsto 3x - 2x = - 6 \\ \\ \large\sf\longmapsto x = - 6[/tex]
please help geometry surface area
Answer: 159
Step-by-step explanation:
We have to find the surface area of two triangles and 3 rectangles
To find the surface areas of the triangles, we use the formula: base x height / 2
6 x 5.5 / 2 = 16.5
Multiply that by 2 since there are 2 of them
16.5 x 2 = 33
To find the surface area of the rectangles, we multiply the length and width
7 x 6 = 42
Multiply that by 3 since there are 3 of them
42 x 3 = 126
Add up all the surface areas
126 + 33 = 159
A cartoon has a length of 1 2/3 feet, width of 1 1/6 feet, and height of 1 1/5 feet what is the volume of the cartoon?
A: 2 cubic feet
B: 2 1/3
C: 4 cubic feet
D: 4 2/3
Density of wood is a very important trait for furniture making. There are two main important mechanical properties: strength and stiffness. Research has shown that a increase density equals an increase strength, hardness and stiffness of sawn timber.
A carpenter has two pieces of wood. He wants to find the density of each piece.
The first piece came from a birch tree. The piece of birch wood measures 2 meters by 4 meters by 3 meters and weighs (mass) 16 kilograms.
The second piece came from a cypress tree. The piece of cypress wood measures 3 meters by 5 meters by 2 meters and weighs (mass) 15.3 kilograms.
Which piece of wood has a greater density? You must show your work in order to receive credit.
Step-by-step explanation:
The Birch tree has a greater density.
worth 10pts if someone can help!
Answer:
y=-x
I found the points then simplified it down
Answer:
hmm maybe trying using 2y=5x-2
Step-by-step explanation:
how i came to this was just looking at point y which was just 2 and then since point x was at 5,-2 all i did was simply it into 2y=5x-2
maybe that's the answer if it is can i get brainlist ?! pretty please if not let me know so i can see what i got wrong
