If the population variance of the lifetime of a light bulb is 10000 hours, how large of a sample must be taken in order to be 99% confident that the margin of error will not exceed 35 hours
Answers
Answer:
The sample must be greater than 55
Step-by-step explanation:
Confidence = 99% = 0.99
α = 1 - C = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005
The z score of α/2 (0.005) corresponds to the z score of 0.495 (0.5 - 0.005) which is equal to 2.576
\(z_\frac{\alpha}{2} =2.576\)
The margin of error (E) is given by the formula:
\(E=z_\frac{\alpha}{2}*\sqrt{\frac{\sigma^2}{n} }\\ \\n=sample\ size,\sigma=standard\ deviation,\sigma^2=variance\\\\Given\ that:\\\\\sigma^2=10000,E=35,z_\frac{\alpha}{2}=2.576\\\\35= 2.576*\sqrt{\frac{10000}{n} }\\\\35= 2.576*\frac{100}{\sqrt{n} } \\\\35= \frac{257.6}{\sqrt{n} }\\\\\sqrt{n} =\frac{257.6}{35 }\\\\\sqrt{n} =7.36\\\\n=7.36^2\\\\n=54.17\)
n > 55
The sample must be greater than 55 so that the margin of error will not exceed 35 hours
Related Questions
Vertical angles are two angles that are ___ of each other when two intersect. These angles are
Answers
Answer:
The two angles that are directly across the intersection point from each other are called vertical angles. Vertical angles are always congruent.
Step-by-step explanation:
brainliest???
Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.
What are vertical angles?Vertical angles are angles opposite to each other where two lines cross.
When two lines intersect, they naturally form two pairs of vertical angles. Vertical angles share the same vertex or corner, and are opposite each other.
These pair of angles are congruent which means they have the same angle measure.
Hence, Vertical angles are two angles that are opposite of each other when two intersect. These angles are congruent.
Learn more about Vertical Angles with this given link:
https://brainly.com/question/28424551
f f(x) = 3x2 + 1 and g(x) = 1 – x, what is the value of (f – g
Answers
The value of the function operation f - g(x) is 3x² + x
What is Function OperationsFunction operations refer to mathematical operations that can be performed on functions, such as addition, subtraction, multiplication, and composition.
Addition and subtraction of functions:
A function can be added or subtracted with another function if both of them have the same domain. The result is a new function with the same domain as the original functions.
Multiplication of functions:
Two functions can be multiplied together to create a new function. The result is a new function whose value at each point in the domain is the product of the original functions' values at that point.
Composition of functions:
Function composition is the application of one function to the result of another function. The result is a new function that is the composition of the original functions. It is represented by (f ∘ g) (x) = f(g(x)) where f and g are the functions being composed.
In this problem, we have two functions which are;
f(x) = 3x² + 1g(x) = 1 - xThe value of (f - g)(x) = 3x² + x
Learn more on function operations here;
https://brainly.com/question/17121792
#SPJ1
You might need: CalculatorZA=Round your answer to the nearest hundredth.СоMY?ProPro6TeaB4
Answers
∠A = 41.81°
Explanation:To get measure of angle A, we would apply trigonometry ratio SOHCAHTOA:
opposite = side opposite the angle = 4
hypotenuse = 6
adjacent = base = AC = ?
Since we have been given the opposite and the hypotenuse, we would use the sine ratio:
Sin A = opposite/hypotenuse
Sin A = 4/6
sin A = 0.6667
\(A=sin^{-1}(0.6667)\)A = 41.8129 degrees
To the nearest hundredth, ∠A = 41.81°
Choose the equation that is true.
345 – 15 = 15 - 345
18 + 0 = 0 + 18
3 + 8 = 7 + 5
5 + 4 + 2 = 6 + 3 + 1
Answers
the first one is 330=-330
the third is 11=12
the fourth is 11=10
so the first is the only true answer
12. Find the LCD: 27, 54, 9, 108
A. 6
B. 108
C. 27
D. 18
Answers
The LCD of the given number set is; B: 108
How to find the Lowest common denominator?
The least common denominator (LCD) is defined as the smallest number that is a common denominator for a given set of fractions or numbers.
Now, we are given the number set as;
27, 54, 9, 108
Let us break down these into their respective products in terms of the prime numbers to get;
27 = 3 * 3 * 3
54 = 2 * 3 * 3 * 3
9 = 3 * 3
108 = 3 * 3 * 3 * 2 * 2
Thus, the LCD = 3 * 3 * 3 * 2 * 2 = 108
Read more about Lowest common denominator at; https://brainly.com/question/19249494
#SPJ1
based on the graph how many tiles are im figure 0
Answers
For figure {0}, the number of tiles will be equal to 2.
What is a mathematical function, equation and expression?Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function
Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators
Equation : A mathematical equation is used to equate two expressions.
Given is a graph as shown in the image.
The line passes through point -
(3, 8) and (4, 10)
So, the slope of the line will be -
m = (10 - 8)/(4 - 3)
m = 2
y = 2x + c
For the point (3, 8), we can write -
8 = 6 + c
c = 2
For figure {0}, the number of tiles will be equal to 2.
Therefore, for figure {0}, the number of tiles will be equal to 2.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ1
two vectors a and b are inclined at a angle of 60° with each other. its resultant makes angle of 45° with a and value of resultant is 2 sqrt 2 . find the component
Answers
Answer:
\(\blue{\rule{100pt}{999999pt}}\) \(\blue{\rule{100pt}{999999pt}}\)
Anne has 5 pints of milk and is planning to make 6 cakes to sell in fundraising. Each cake will require 112 cups of milk. Does she have enough milk to make the 6 cakes? If so, how many cups of milk will be left, and if not, how many extra cups of milk would she need?
Yes she has enough milk; She will have 1 extra cup of milk.
No she does not have enough milk; She will need 1 more cup of milk.
Yes she has enough milk; She will have 112 extra cups of milk.
No she does not have enough milk; She will need 412 extra cups of milk.
Answers
Answer:
Option (1)
Step-by-step explanation:
Each cake requires cups of milk = \(1\frac{1}{2}\) cups ≈ 1.5 cups
6 cakes will require milk = 6 × 1.5
= 9 cups
Anne has milk = 5 pints
∵ 1 pint = 2 cups
∴ 5 pints = 10 cups
Therefore, Anne has milk = 10 cups
Extra amount of milk Anne has = 10 - 9 = 1 cup
Hence, Answer is yes, she has enough milk. She will have 1 extra cup of milk.
Option 1 will be the answer.
ASAP Find and compare the measures of the base angles, ∠BCA and ∠CAB. What do you notice about the angle measurements?
Answers
Answer:m∠BCA = m∠CAB = 63.43°. The measurements for the two base angles are equal.
Step-by-step explanation: I did it trust me
Answer:
m∠BCA = m∠CAB = 63.43°. The measurements for the two base angles are equal.
Step-by-step explanation:
plato
H
6:00 PM
What is a frostbite?
Answers
Can y’all solve this please
Answers
Answer:
it = my but lol
Step-by-step explanation:
lol sorry just trying to get points
James wants to have earned $6,180 amount of interest in 28 years. Currently he finds
that his annual interest rate is 6.12%. Calculate how much money James needs to invest
as his principal in order to achieve this goal.
Answers
Answer:
$3606.44
Step-by-step explanation:
The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.
To do this, we need to use the formula for simple interest:
\(\boxed{I = \frac{P \times R \times T}{100}}\),
where:
I = interest earned
P = principal invested
R = annual interest rate
T = time
By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:
\(6180 = \frac{P \times 6.12 \times 28}{100}\)
⇒ \(6180 \times 100 = P \times 171.36\) [Multiplying both sides by 100]
⇒ \(P = \frac{6180 \times 100}{171.36}\) [Dividing both sides of the equation by 171.36]
⇒ \(P = \bf 3606.44\)
Therefore, James needs to invest $3606.44.
Consecutive sides of a square are perpendicular; therefore, QR 1 SQ. Find thevalue of x.
Answers
SOLUTION
Since QR is perpendicular to SQ, then,
Let the grdient of the line QR be m1 and the gradient of the line SQ be m2.
Since QR is pendicular to SQ, m1 x m2 = -1
\(\begin{gathered} \text{From m = }\frac{y2\text{ -y1}}{x2\text{ -x1}}\text{ } \\ m1\text{ = }\frac{1\text{ - 3}}{7\text{ - 3 }}\text{ = }\frac{-2}{4} \\ =\text{ }\frac{-1}{2} \end{gathered}\)\(\begin{gathered} m2\text{ = }\frac{3\text{ - }1}{3-\text{ x}}\text{ } \\ m2\text{ = }\frac{2}{3\text{ -x }} \end{gathered}\)\(\begin{gathered} \frac{-1}{2}\text{ }\times\frac{2}{3\text{ -x }}\text{ = -1 } \\ \frac{-2}{2(3\text{ -x)}}\text{ = -1} \\ \frac{-2}{6\text{ - 2x}}\text{ = -1 cross multiplying, we will have } \\ -1(6\text{ - 2x) = -2 } \\ -6\text{ + 2x = -2 } \\ 2x\text{ = -2 + 6} \\ 2x\text{ = 4 } \\ x\text{ = 2} \end{gathered}\)Therefore, x = 2
Find the missing angle using trigonometry
Answers
Answer:
please look at detailed answers below
Step-by-step explanation:
example 1 is correct.
example 2:
x = (12 sin 15) / sin 75 = 3.22.
example 3:
x/sin 90 = 19/sin (180 - 90 -36)
x = (19 sin 90) / sin 54
= 23.5
example 4:
x/sin 53 = 7/sin (180 -90 - 53)
x = (7 sin 53)/ sin
= 9.29
1 equals to how many parts
Answers
if you divide "1" into two equal parts, each part would be 0.5. If you divide it into four equal parts, each part would be 0.25.
The concept of "1" in mathematics typically represents a whole unit or a single entity. However, your question about how many parts "1" equals to requires clarification. If you are referring to dividing a whole into parts, then "1" can be divided into any number of parts, as long as each part is equal.
For instance, if you divide "1" into two equal parts, each part would be 0.5. If you divide it into four equal parts, each part would be 0.25, and so on. In this context, "1" can be divided into an infinite number of parts, depending on the desired level of precision or subdivision.
On the other hand, if you are referring to expressing "1" as a fraction or a ratio, it can be written as 1/1 or 1:1, indicating that there is one part in total, and that one part is the whole itself.
In this case, "1" is not divided into multiple parts but represents the entirety of a single unit.
For more such questions parts,click on
https://brainly.com/
#SPJ8
A map in Connecticut is drawn to a scale where 2 inches on the map represents 35 miles. If Greenwich and stonington are 105 miles from each other how far apart do they appear on a map
Answers
Answer: 6 inches
Step-by-step explanation:
From the question, we are informed that a map in Connecticut is drawn to a scale where 2 inches on the map represents 35 miles.
If Greenwich and stonington are 105 miles from each other, to calculate their distance on the map will be:
Since 2 inches represent 35 miles, then: 1 inch = 35miles/2 = 17.5 inches.
Since 1 inch = 17.5 inches;
105 inches will then be: 105inches/17.5 inches = 6 inches
Therefore, 6 inches represent 105 miles.
If f(x) -V7-3, complete the following statement (round your answer
to the nearest hundredth):
x + 2
Answers
Answer:
- 1.67
Step-by-step explanation:
f(x) = \(\frac{3}{7+2}\) - \(\sqrt{7-3}\)
= \(\frac{3}{9}\) - \(\sqrt{4}\)
= \(\frac{1}{3}\) - 2
= - 1 \(\frac{2}{3}\)
= -1.6666666
= -1.67
What is 2 1/2+3 1/3 pretty please help I need this answer fast
Answers
Answer:
D. 5 5/6
Step-by-step explanation:
2 1/2 + 3 1/3
= \(\frac{5}{2}\) + \(\frac{10}{3}\)
= \(\frac{15 + 20}{6}\)
= \(\frac{35}{6}\) = 5 5/6
Answer:
5 1/3
Step-by-step explanation: i am pretty sure
Tough calculus question I have been struggling with, please help me
Answers
You have the following function:
\(f(x)=9x^{\frac{1}{3}}+\frac{9}{2}x^{\frac{4}{3}}\)The first derivative of the previous function is:
\(\begin{gathered} f^{\prime}(x)=\frac{1}{3}\cdot9x^{\frac{1}{3}-1}+\frac{4}{3}\cdot\frac{9}{2}x^{\frac{4}{3}-1} \\ f^{\prime}(x)=3x^{-\frac{2}{3}}+6x^{\frac{1}{3}} \end{gathered}\)next, equal the previous expression to 0 and solve for x:
\(\begin{gathered} 3x^{-\frac{2}{3}}+6x^{\frac{1}{3}}=0 \\ (x^{-\frac{2}{3}})^3=(-2x^{\frac{1}{3}})^3 \\ x^{-2}=-8x \\ \frac{1}{x^2}=-8x^{} \\ -\frac{1}{8}=x^3 \\ x=-\frac{1}{2} \end{gathered}\)Then, for x=1/2 there is a critical point.
To determine if the critical point is a maximum or a minmum, derivate f'(x) and replace x=1/2=0.5:
\(\begin{gathered} f^{\doubleprime}(x)=-\frac{2}{3}\cdot3x^{-\frac{5}{3}}+\frac{1}{3}\cdot6x^{-\frac{2}{3}} \\ f^{\doubleprime}(0.5)=-2(-0.5)^{-\frac{5}{3}}+2(-0.5)^{-\frac{2}{3}}\approx9.52>0 \end{gathered}\)Now, by considering the second derivative test, you have that if f(xo)>0, then, there is a local minimum at xo.
In this case, there is a local minimum at x = -0.5.
The y-coordinate is found by replacing x=-0.5 into f(x):
\(f(-0.5)=9(-0.5)^{\frac{1}{3}}+\frac{9}{2}(-0.5)^{\frac{4}{3}}=-5.357\)Then, the relative extrema point is (-0.5 , -5.357)
The inflection point is found by making the expression for f'' = 0 and solving for x:
\(\begin{gathered} -2x^{-\frac{5}{3}}+2x^{-\frac{2}{3}}=0 \\ -x^{-\frac{5}{3}}+x^{-\frac{2}{3}}=0 \\ (x^{-\frac{5}{3}})^3=(x^{-\frac{2}{3}})^3 \\ x^{-5}=x^{-2} \\ x^{-5}\cdot x^2=1 \\ x^{-3}=1 \\ x^3=1 \end{gathered}\)Then, for x = 1 there is an inflection point.
By replacing x=1 into f(x):
\(f(1)=9(1)^{\frac{1}{3}}+\frac{9}{2}(1)^{\frac{4}{3}}=9+\frac{9}{2}=13.5\)Hence, the inflection point is (1 , 13.5)
I don’t know what to do, can someone people help me? Thank you
Answers
The correct answer is B) ΔDEF ≅ ΔJKL
Angle D corresponds to angle J, at 38°
Angle E corresponds to angle K, at 46°
Angle F corresponds to angle L, at 96°
Angles are congruent.
Side DE corresponds to side JK, at 8.8cm.
Side FE corresponds to side LK, at 5.4cm.
Sides are congruent.
please provide an answer and explanation for how you do this
Answers
here is the answer..
check the above picture.
step by step explanation...
do u want me to plot the graph too??
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
Step-by-step explanation:
considering A). hemisphere diameter = 48 yd
volume of hemisphere = (2/3)*pi*(r)^3
the radius of hemisphere = diameter/2 = 48/2 = 24 yd
hence, the volume of hemisphere = (2/3)*pi*(24)^3 yd^3
taking pi = 3.14
volume = 28938.24 yd^3 approximately volume = 28940 yd^3
considering B). Circumference of a great circle = 26 m
circumference of sphere = 2*pi*r
therefore r = 4.14 m
volume of sphere = (4/3)*pi*(r)^3
volume of sphere = 297.077 m^3
Answer:
24. A. 28952.9 yd²
B. 297.2 m³
Step-by-step explanation:
24.
A.
diameter=48 yd
radius (r)=diameter/2=48/2=24yd
We have
Volume of Hemisphere= ⅔*πr³=⅔*π*r³
Substituting value
Volume of Hemisphere=⅔*π*24³=28952.9 yd³
B.
Circumference of great circle=2πr=26m
2πr=26
r=26/(2π)
r=4.14
Now
Volume of sphere = 4/3*πr³
Volume of sphere=4/3*π*4.14³=297.2 m³
85% of x is 51. Write an equation that represents the situation.
Answers
Answer:
85/100*x=51
Step-by-step explanation:
85x=5100
What is the ordered pair that represents the point (-8, 7) after a reflection over the y-axis?
A. (-8, -7)
B. (8,7)
C. (-7,8)
(7,-8) D.
Answers
D (8,7)
-8 along the x-axis turns into 8 along the x-axis.
7 doesn’t change.
Think of it this way. If you’re only reflecting over the y-axis, the only number that changes is the x in the ordered pair.
If the only reflection is over the x-axis then the only number that changes is the y in the ordered pair.
Beverly has a bag of marbles that weighs 30 grams. She knows that each marble weighs 1.5 grams and the bag weighs 1.5 grams. Which equation could she use to determine how many marbles are in the bag? Select all that apply. (1.5)x + 1.5 = 30 30 – x = 2(1.5) (1.5)(30) = 1.5x 1.5 + x = 30 1.5x = 30 – 1.5
Answers
Answer:
1.5x = 30 - 1.5
Step-by-step explanation:
30 grams minus the weight of the bag 1.5
1.5x x is the number of marbles and the bag so take 1 out and you have an answer which is 28.5 19 marbles
Find the volume of a cone with radius 5 yards and height 8 yards. Round your answer to two
decimal places
Answers
The volume of a cone will be 209.41 yard³.
What is volume of cone?
The area or volume that a cone takes up is referred to as its volume. Cones are measured by their volume in cubic units such as cm3, m3, in3, etc. By rotating a triangle at any of its vertices, a cone can be created. A cone is a robust, spherical, three-dimensional geometric figure.. Its surface area is curved. The perpendicular height is measured from base to vertex. Right circular cones and oblique cones are two different types of cones. While the vertex of an oblique cone is not vertically above the center of the base, it is in the right circular cone where it is vertically above the base.
So the
V = (1/3)πr²h.
Given, data r = 5yards
h = 8 yards
Volume = 1/3 * π * r ²* h
= 1/3 * 3.141*25*8
=209.41 yard³
Hence, the volume of a cone will be 209.41 yard³.
Learn more about volume of cone, by the following link
https://brainly.com/question/1082469
#SPJ1
The importance of crushing the Whiskey Rebellion was to uphold
Answers
Answer:
Federal Authority should be the answer
Estimate the sum or difference 9.84-1.86
Answers
Answer: The estimated sum or difference would be 8.00. If not estimated it would be 7.98.
Step-by-step explanation:
If we differentiate the given numbers from 9.84-1.86, the answer will be 7.98 exactly.
As 7.98 is closer to 8.00, we can easily estimate the number to be 8.00.
The most frequently occuring value in a set is called the
Answers
Answer:
Step-by-step explanation:
The mode is the correct answer
f(x) = -4x + 10
g(x) = x2 + 7x+ 5
Composition of functions how to solve value of g [f(4)]
Answers
9514 1404 393
Answer:
g(f(4)) = -1
Step-by-step explanation:
Evaluate this the way you would any function. Start with the inner parentheses according to the order of operations. Substitute for the function variable and do the arithmetic.
g(f(4)) = g(-4·4 +10) = g(-6) = (-6)² +7(-6) +5 = 36 -42 +5
g(f(4)) = -1