This question is incomplete, the complete question is;
A sociologist wants to construct an 80 confidence interval for the proportion of children aged 8-10 living in New York who own a cell phone.
(a) A survey by the National Consumers League taken in 2012 estimated the nationwide proportion to be 036. Using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.02?
Answer:
the required or needed sample size is 946
Step-by-step explanation:
Given the data in the question;
confidence level = 80%
⇒ 100( 1 - ∝ )% = 80%
100 - 100∝ = 80
100∝ = 100 - 80
∝ = 20/100
level of significance ∝ = 0.2
[tex]Z_{\alpha /2[/tex] = [tex]Z_{0.10[/tex] = 1.2816 { from z-table }
p = 0.36
Allowable margin of error E = 0.02
let n be the required sample size.
we know that
E = √( p( 1 - p) / n )
given that margin of error E = 0.02
⇒ √( p( 1 - p) / n ) × [tex]Z_{\alpha /2[/tex] = 0.02
⇒ √( 0.36( 1 - 0.36) / n ) × 1.2816 = 0.02
⇒ √( 0.2304 / n ) × 1.2816 = 0.02
√( 0.2304 / n ) = 0.02 / 1.2816
√( 0.2304 / n ) = 0.01560549
( 0.2304 / n ) = ( 0.01560549)²
0.2304 / n = 0.000243531318
n = 0.2304 / 0.000243531318
n = 946
Therefore, the required or needed sample size is 946
A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80. Suppose also that exactly 15% of the scores exceed 700. Find the mean of the distribution of scores. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.
Answer:
The mean score is of 617.4.
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.
Suppose that the scores on the questionnaire are normally distributed with a standard deviation of 80.
This means that [tex]\sigma = 80[/tex]
Suppose also that exactly 15% of the scores exceed 700.
This means that when X = 700, Z has a pvalue of 0.85. So X when X = 700, Z = 1.033. We use this to find [tex]\mu[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.033 = \frac{700 - \mu}{80}[/tex]
[tex]700 - \mu = 80*1.033[/tex]
[tex]\mu = 700 - 80*1.033[/tex]
[tex]\mu = 617.4[/tex]
The mean score is of 617.4.
Using first principle find derivatives of x2
Answer:
[tex]\displaystyle f'(x) = 2x[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]Differentiation
DerivativesDerivative NotationDefinition of a Derivative: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = x^2[/tex]
Step 2: Differentiate
Substitute in function [Definition of a Derivative]: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{(x + h)^2 - x^2}{h}[/tex]Expand: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{x^2 + 2hx + h^2 - x^2}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{2hx + h^2}{h}[/tex]Factor: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{h(2x + h)}{h}[/tex]Simplify: [tex]\displaystyle f'(x) = \lim_{h \to 0} 2x + h[/tex]Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle f'(x) = 2x[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
A sprinkler sprays in a circular pattern at a radius of 12 meters. If the degree of the circle that
is covered is 100°, what is the area of the lawn that is covered by the water from the
sprinker? (Round to the nearest hundredth of a meter)
Answer:
The area of the lawn that is covered by the water from the sprinkler is
[tex]125.6[/tex] square meter
Step-by-step explanation:
Given
The radius of the circle is 12 m
Area of the circle is [tex]\pi r^2 = \pi * 12^2 = 144\pi[/tex]
For one complete circle, the degree of rotation is 360 degrees.
Area of lawn covered by rotation of 100 degrees only is 100/360 = 5/18
The area of the lawn that is covered by the water from the sprinkler is
[tex]\frac{5}{18} * 3.14*144 = 125.6[/tex] square meter
A right triangle has a hypotenuse of 15 cm. What is the length for the missing leg if one of the two legs of the triangle is 5?
Answer:
The other leg is 12 cm long.
Step-by-step explanation:
c
2
=
a
2
+
b
2
,
where:
c
is the hypotenuse, and
a
and
b
are the other two sides (legs).
Let
a
=
9 cm
Rearrange the equation to isolate
b
2
. Plug in the values for
a
and
c
, and solve.
b
2
=
c
2
−
a
2
b
2
=
(
15 cm
)
2
−
(
9 cm
)
2
Simplify.
b
2
=
225 cm
2
−
81
cm
2
b
2
=
144 cm
2
Take the square root of both sides.
b
=
√
144 cm
2
Simplify.
b
=
12 cm
Answer:
14.14 cm
Step-by-step explanation:
using the Pythagorean theorem:
?² = 15² - 5² = 225 - 25 = 200
? = √200 = 14.14 cm
Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch. She slipped and spilled 1/4 of the lemonade in the pitcher. What fraction of a gallon of lemonade did she spill?
Answer:
Susan spilled 1/6 of a gallon of lemonade.
Step-by-step explanation:
Since Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch, and she slipped and spilled 1/4 of the lemonade in the pitcher, to determine what fraction of a gallon of lemonade did she spill the following calculation must be performed:
2/3 = 0.6666
0.666666 x 1/4 = X
0.166666 = X
0.166666 = 1/6
Therefore, Susan spilled 1/6 of a gallon of lemonade.
Help!! Will give brainliest and bonus air-hugs!!
Can someone please explain a few steps and try to help me understand this!?!
Part A
Which measurements do you need to know to find the volume of a cylinder?
Part B
Since the base of the refraction cup is a half circle, how can you find the radius? What is the radius?
Part C
If you put two refraction cups together, what three-dimensional shape do you have?
Part D
The formula for the volume of a cylinder is v= 3.14r^2h.
What is the approximate volume of two refraction cups use 3.14 for pi.
Part E
Since one refraction cup is half of a cylinder, how could you change the formula for the volume of a cylinder to calculate the volume of a refraction cup?
Part F
Using the equation from Part E, what is the approximate volume of one refraction? What is the relationship between this value and the value from part D? Use 3.14 for pi.
Answer:
Part A: To find the volume of a cylinder, we need the dimensions of the cylinder such as the radius of the base of the cylinder and the height of the cylinder.
Part B: We have given the base of the refraction cup as a half-circle, we can calculate the radius of the base.
The diameter is given as 8 cm so, the radius would be half of the diameter.
r = 4cm
Part C: If you put two refraction cups together, we get the full three-dimensional shape that is a circle.
Part D: The formula for the volume of a cylinder is V=pi r^2 h.
Part E: The volume of a refraction cup =
= 4/3 (3.14)(8)
= 33.49
Part F: The relationship between the value D and the value from Part D is as follows
The volume of a cylinder = 3 times the volume of a refraction cup
Step-by-step explanation:
Find the f^-1(x) and it’s domain
Answer:
[tex]f^{-1}(x) = (x + 8)^2[/tex]
[tex]x \ge -8[/tex]
Step-by-step explanation:
Given
[tex]f(x) = \sqrt x - 8[/tex]
Solving (a): [tex]f^{-1}(x)[/tex]
We have:
[tex]f(x) = \sqrt x - 8[/tex]
Express f(x) as y
[tex]y = \sqrt x - 8[/tex]
Swap x and y
[tex]x = \sqrt y - 8[/tex]
Add 8 to [tex]both\ sides[/tex]
[tex]x + 8 = \sqrt y - 8 + 8[/tex]
[tex]x + 8 = \sqrt y[/tex]
Square both sides
[tex](x + 8)^2 = y[/tex]
Rewrite as:
[tex]y = (x + 8)^2[/tex]
Express y as: [tex]f^{-1}(x)[/tex]
[tex]f^{-1}(x) = (x + 8)^2[/tex]
To determine the domain, we have:
The original function is [tex]f(x) = \sqrt x - 8[/tex]
The range of this is: [tex]f(x) \ge -8[/tex]
The [tex]domain[/tex] of the [tex]inverse[/tex] function is the [tex]range[/tex] of the [tex]original[/tex] function.
Hence, the domain is:
[tex]x \ge -8[/tex]
Quadrilateral K is the image of Quadrilateral K under a dilation
[tex]16 \div81 \: - 3 \div 4[/tex]
please note that this is exponents
Answer:
16/81-3/4[
=[16×4-3×81]/[81×4]=-179/324 is your answer
Please help ASAP 60 pts!
Write the equation of a circle with endpoints of the diameter at (4, -3) and (-2, 5).
Show your work for credit.
Answer:
(x - 1)² + (y - 1)² = 25Step-by-step explanation:
Find the center, the midpoint of the diameter:
x = (4 - 2)/2 = 1, this is h of the circle equationy = (-3 + 5)/2 = 1, his is k of the circle equationFind the square of the radius by distance formula:
r² = (1 - 4)² + (1 + 3)² = 25Equation of the circle:
(x - h)² + (y - k)² = r²,Substitute the values to get:
(x - 1)² + (y - 1)² = 25Answer:
solution given:
points at (4, -3) and (-2, 5
diameter [d]=
[tex]d = \sqrt{(4 + 2) {}^{2} +( - 3 - 5) {}^{2} } \\ d = 10units \\ radius(r) = 5units [/tex]
centre[h,k]={(4-2)/2,(-3+5)/2}=(1,1)
now equation of a circle
(x-h)²+(y-k)²=r²
(x-1)²+(y-1)²=25 is a required equation
Simplify 79.5-2.58 x (3.63-1.63) to the third power
Answer:
a
Step-by-satep explanation:
Helppppp pleSeeeeeeeee
Answer: C
Step-by-step explanation: Hope this help :D
The coordinates of the following points represent the vertices of a rectangle. W: (3,3) X: (8,3) Y: (8,7) Z: (3,7) What is the perimeter, in units, of rectangle WXYZ?
Answer:
18
Step-by-step explanation:
The answer is B, 18
Answer:
The person above me is correct
Step-by-step explanation:
Which angle is an acute angle?
A. An angle measuring 325°
B. An angle measuring 265°
C. An angle measuring 125°
D. An angle measuring 85°
Answer:
The answer is Option D
Step-by-step explanation:
Option D is the right answer since 85° is a acute angle. Acute angles are angles below 90°
Hope this helps!
Have a good day
can somebody help me please and thank you
1. 12/40 or 30% chance
2. 60
Explanation: 1. Not gonna lie i searched it up
2. x/200 times 12/40 = 2400/40
4. The volume of a certain room is 2016 cubic ft. If the square footage of the
floor is 144 sq. ft., what will the height of the room be?
Answer:
The room is 14ft high
Step-by-step explanation:
Given
[tex]Volume = 2016ft^3[/tex]
[tex]Base\ Area = 144ft^2[/tex]
Required
The height of the room
This is calculated as:
[tex]Volume = Base\ Area * Height[/tex]
Make Height the subject
[tex]Height = \frac{Volume}{Base\ Area}[/tex]
So, we have:
[tex]Height = \frac{2016ft^3}{144ft^2}[/tex]
[tex]Height = \frac{2016}{144}ft[/tex]
[tex]Height = 14ft[/tex]
Identify the smallest of the similar triangles. Then find x
Which expression shows twice the sum of 8 and a number n?
Answer:
A
Step-by-step explanation:
The sum of 8 and a number n represents n + 8
Twice that sum would give us 2(n + 8)
Answer:
A. 2(n+8)
sum of 8 and number = n+8
and twice that means 2(n+8)
If you punched 1 raffle ticket, what is the probability of winning of only 10 tickets are winners and 179 total tickets were sold
Answer:
1 out of 179
Step-by-step explanation:
What is the diameter of a circle that has a radius of 7
inches?
Answer:
d=14in
Step-by-step explanation:
Solution
d=2r=2·7=14in
Hope this helped!!!
Find the value of x.
B
2
X
А A
30°
5
30°
5
Answer:
the x value is 2
because the triangles are similar
i think
The value of x, that is chord CD is 2 cm.
We need to find the value of x.
What is the statement of equal chords of a circle?Equal chords of a circle subtend equal angles at the centre. The converse of the theorem is if two chords subtend equal angles at the centre, they are equal.
In the given diagram chord AB and chord CD subtend the equal angles which are 30°. Therefore, AB=CD=2 cm.
Hence, the value of x, that is chord CD is 2 cm.
To learn more about circle theorems visit:
https://brainly.com/question/19906255.
#SPJ2
Please Help!
Using Heron’s formula, calculate the area of the parallelogram to the nearest tenth of a square unit.
Area ≈ ____ square units
Thank you!
Step-by-step explanation:
Hello! In order to get the best explication for your question, here's the link to a useful website:
https://geometryhelp.net/area-parallelogram-diagonals/
I believe, it's better for you to understand how to use the Heron's formula in other contexts so as to understand deeper into details how to apply it
Hope it helped!
Answer:36.7
Step-by-step explanation:
Would greatly appreciate the help
Answer:
Answer is E but not 100%
Step-by-step explanation:
Answer:
A is correct
E shows an error as the first two values are identical so one cannot be greater than the other.
Step-by-step explanation:
A shows 2.69 is equal to 2.696 which is more than 2.696 which is more than 2.696 which is more than 2.696
As when;
2.696 repeats in bold = 2.696969696 1st greatest
2.696 repeats in bold = 2.696696696 2nd in highest value so 2nd in order.
2.696 repeats in bold = 2.696666666 3rd in highest value so 3rd in order.
2.696 does not repeat = 2.696 so is the least greatest from the list.
Solve the inequality. -4x < 24
Answer:
x > -6
Step-by-step explanation:
1) Divide both sides by -4
x > - [tex]\frac{24}{4}[/tex]
2) Simplify and solve to get answer.
x > -6.
Paul earns twice as much as john
Answer:
Wat?
Mark me as brainlist
Answer:
whats the question
Step-by-step explanation:
Find the coefficient of x^2 in the expansion of (2x - 1)^5.
Answer:
So, the coefficient of the x^2 -term is 80
Step-by-step explanation:
so we need to simplify it:
#10(x^2)(2^3) = 10(x^2)(8) = 80x^2
What is the width of a rectangle with a length of 3/8 ft and and area of
4 square feet?
hewo the whole world that i hate^^
Royston plays a video game 7 times. His scores are 60, 65, 66, 74, 69, 72, and 63. Which is the best measure of center of Royston's performance?
median
middle number
mean
mode
Answer:
Mean: 67
Median: 66
Mode: no mode
Range: 14
Step-by-step explanation:
Answer:
mean
Step-by-step explanation:
Select the correct answer.
In a sequence described by a function, what does the notation f(3) = 1 mean?
OA.
The third term in the sequence has a value of 1.
OB.
The common difference I of the sequence is 3.
O C.
The first term in the sequence has a value of 3.
OD
The common ratio of the sequence is 3.
Answer:
c is correct
Step-by-step explanation:
Answer:
c is right answer
Step-by-step explanation:
HOPE IT HELPS U
FOLLOW MY ACCOUNT PLS PLS
Are these slopes equal? Explain if they are or if there not.
Answer:
Yes
Step-by-step explanation:
When dividing (or multiplying) two negative numbers, you end up with a positive number. The other slope is already positive. So 4/5=4/5