Answer:
The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.95[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{1000}{\sqrt{64}} = 245[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 7500 - 245 = 7255 hours.
The upper end of the interval is the sample mean added to M. So it is 7500 + 245 = 7745 hours.
The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.
A means of the estimate numerical, the variation in that estimate is referred to as the confidence interval, therefore its value is "[tex][7255, 7745][/tex]".
Confidence interval:[tex]95\%[/tex] C.I. for a mean lifetime is given by
[tex]= [ \overline{X} - \tau_{0.975} \frac{\sigma}{\sqrt{n}} , \overline{X} + \tau_{0.975} \frac{\sigma}{\sqrt{n}} ][/tex], where
[tex]\bar{X}[/tex] (sample mean) [tex]= 7500[/tex]
[tex]\sigma[/tex] (standard deviation)[tex]= 1000[/tex]
[tex]n = 64[/tex]
by putting the value into the above-given formula we get the value that is [tex]= [7255, 7745].[/tex]
Find out more information about the confidence interval here:
brainly.com/question/2396419
Find an equation for the nth term of the arithmetic sequence.
a16 = 21, a17 = -1
Answer:nth term=a1 - 27n + 27
Step-by-step explanation:
first term =a1
common difference=d=-1-21
d=-27
Using the formula
Tn=a1 + d x (n-1)
nth term=a1 + (-27)(n-1)
nth term=a1 - 27n + 27
The Senate in a certain state is comprised of 58 Republicans, 39 Democrats, and 3 Independents. How many committees can be formed if each committee must have 3 Republicans and 2 Democrats?
YuAnswer:
Step-by-step explanation:
I really don't know the answer sorry
Ramesh examined the pattern in the table. Powers of 7 Value 7 Superscript 4 2,401 7 Superscript 3 343 7 Superscript 2 49 7 Superscript 1 7 7 Superscript 0 1 7 Superscript negative 1 StartFraction 1 Over 7 EndFraction Ramesh says that based on the pattern 7 Superscript negative 5 = negative 16,807. Which statement explains whether Ramesh is correct? Ramesh is correct because 7 Superscript negative 5 is equivalent to Negative 7 times (negative 7) times (negative 7) times (negative 7) times (negative 7), which has the same value as Negative 16,807. Ramesh is correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = negative 16,807. Ramesh is not correct because 7 Superscript negative 5 is equivalent to StartFraction 1 Over 7 Superscript 5 EndFraction, which has the same value as StartFraction 1 Over 7 Superscript 4 EndFraction divided by 7 = StartFraction 1 Over 7 cubed EndFraction = StartFraction 1 Over 343 EndFraction. Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7 Superscript negative 5 = 1 divided by 7 divided by 7 divided by 7 divided by 7 divided by 7 = StartFraction 1 Over 16,807 EndFraction. NEED HELP NOW PLEASE I HAVE ONLY SEEN WRONG ANSWERS
Answer:
D
Step-by-step explanation:
Answer:
D.- Ramesh is not correct because as the exponents decrease, the previous value is divided by 7, so 7^-5 = 1 ÷ 7 ÷ 7 ÷ 7 ÷ 7 ÷ 7 = 1/16,807.
1.] What is the probability of choosing a king
from a standard deck of playing cards?
Answer:
1/13
Step-by-step explanation:
there are 4 kings in a deck of 52 cards.
4/52 = 1/13
Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
What is the solution to the equation StartFraction m Over m + 4 EndFraction + StartFraction 4 Over 4 minus m EndFraction = StartFraction m squared Over m squared minus 16 EndFraction?
Answer: m = -2.
The given equation is: [tex]\frac{m}{m+4}+\frac{4}{4-m}=\frac{m^{2}}{m^{2}-16}[/tex].
The LCM of the denominators = [tex]m^{2}-16=(m+4)(m-4)[/tex].
We multiply both sides by LCM.
[tex]\left(m+4\right)\left(m-4\right)\left(\frac{m}{m+4}+\frac{4}{4-m}\right)=\left(m+4\right)\left(m-4\right)\cdot\frac{m^{2}}{m^{2}-16}[/tex]
[tex]m\left(m-4\right)-4\left(m+4\right)=m^{2}[/tex]
[tex]m^{2}-4m-4m-16=m^{2}[/tex]
[tex]8m=-16\\m=-2[/tex]
Learn more: https://brainly.com/question/13769924
Answer:
M=-2 B
Step-by-step explanation:
trust me i took the quiz
Jessica bought the ingredients to make chicken soup, and wanted to make a double batch, which would be 18 cups of soup. A quick Google search told her that this was 259.9 cubic inches. She hoped the soup pot below would be big enough. The soup pot is 9 inches tall with a radius of 3.5 inches. What is the volume of the soup pot? Answer choices are rounded to the nearest tenth cubic inch. 169.6 cubic inches 890.6 cubic inches 197.9 cubic inches 346.4 cubic inches
Answer: 346.4 in^3
Step-by-step explanation:
The pot can be thinked as a cylinder:
The volume of a cylinder is equal to:
V = (pi*r^2)*h
where h is the height, r is the radius and pi = 3.1416
Here we have that: r = 3.5in, h = 9in.
Then the volume is:
V = 3.1416*(3.5in)^2*9in = 346.4in^3
When you cough,the radius of your trachea (windpipe) decreases,affecting the speed S of the air in the trachea. If r0 is the normal radius of the trachea, the relationship between the speed S of the air and the radius r of the trachea during a cough is given by a function of the form
S(r) = (r0 - r) ar^2
where a is positive constant. Find the radius r for which the speed of the air is greatest.
Answer: 2r(0)/3.
Step-by-step explanation:
So, we are given one Important data or o or parameter in the question above and that is the function of the form which is given below(that is);
S(r) = (r0 - r) ar^2 -----------------------------(1).
We will now have to differentiate S(r) with respect to r, so, check below for the differentiation:
dS/dr = 2ar (r0 - r ) + ar^2 (-1 ) ---------;(2).
dS/dr = 2ar(r0) - 2ar^2 - ar^2.
dS/dr = - 3ar^2 + 2ar(r0) ------------------(3).
Note that dS/dr = 0.
Hence, - 3ar^2 + 2ar(r0) = 0.
Making ra the subject of the formula we have;
ra[ - 3r + 2r(0) ] = 0. -------------------------(4).
Hence, r = 0 and r = 2r(0) / 3.
If we take the second derivative of S(r) too, we will have;
d^2S/dr = -6ar + 2ar(0). -------------------(5).
+ 2ar(0) > 0 for r = 0; and r = 2r(0)/3 which is the greatest.
Answer:
[tex]r =\frac{2r_{0}}{3}[/tex]
Step-by-step explanation:
We need to take the derivative of S(r) and equal to zero to maximize the function. In this conditions we will find the radius r for which the speed of the air is greatest.
Let's take the derivative:
[tex]\frac{dS}{dr}=a(2r(r_{0}-r)+r^{2}(-1))[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-2r^{2}-r^{2})[/tex]
[tex]\frac{dS}{dr}=a(2r*r_{0}-3r^{2})[/tex]
[tex]\frac{dS}{dr}=ar(2r_{0}-3r)[/tex]
Let's equal it to zero, to maximize S.
[tex]0=ar(2r_{0}-3r)[/tex]
We will have two solutions:
[tex]r = 0[/tex]
[tex]r =\frac{2r_{0}}{3}[/tex]
Therefore the value of r for which the speed of the air is greatest is [tex]r =\frac{2r_{0}}{3}[/tex].
I hope it helps you!
The object below is a cubical lunch box having each edge as 10 cm.
Find its surface area.
A
600 cm2
B
360 cm2
C
300 cm2
D
36 cm2
Answer:
B
Step-by-step explanation:
The total surface area of a cubical lunch box having each edge as 10 cm is 600 square centimeter. Therefore, option A is the correct answer.
What is surface area of a cube?The surface area of the cube all six faces of the cube are made up of squares of the same dimensions then the total surface area of the cube will be the surface area of one face added six times to itself. The formula to find the surface area of a cube is 6a², where a is edge.
Given that, the cubical lunch box having each edge as 10 cm.
Here, surface area = 6×10²
= 600 square centimeter
Therefore, option A is the correct answer.
Learn more about the surface area of a cube here:
brainly.com/question/23273671.
#SPJ2
If h = 85 cm and 1 = 36 cm, what is the length of g?
A. 77 cm
B.
92 cm
C
49 cm
D
75 cm
Answer:A
Step-by-step explanation:
h=85 f=36
Since it is a right angled triangle we can apply Pythagoras principle to get g
g=√(h^2 - f^2)
g=√(85^2 - 36^2)
g=√(85x85 - 36x36)
g=√(7225 - 1296)
g=√(5929)
g=77
Trust me,I will give braineist. I swear to god.
Answer:
= 1696m^3
Step-by-step explanation:
V = πr²h
= 3.14 x 6 x 6 x 15
= 3.14 x 540
= 1695.6 m^3
= 1696m^3
A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the
function has a negative leading coefficient and is of even degree, which statement about the graph is true?
The graph of the function is positive on (-0, 5).
The graph of the function is negative on (-5, 3)
The graph of the function is positive on (-0, 1).
The graph of the function is negative on (3,co)
Mark this and return
Save and Exit
Sabem
Answer:
The graph of the function is negative on (3, ∞)
Step-by-step explanation:
The function starts negative at the left side of the graph, crosses the x-axis at x = -5, touches the x-axis at x = 1, again crosses into negative values at x = 3.
The function is positive on the open intervals (-5, 1) and (1, 3). It is negative on the open intervals (-∞, -5) and (3, ∞). The latter description matches the last answer choice:
the graph of the function is negative on (3, ∞).
Find the compound interest on GHS 50,200 invested at 13% p.a. compounded annually for 3 years ( to the nearest
GHS).
Select one:
A. GHS 19,578
B. GHS 69,778
O
C. GHS 72,433
D. GHS 22.233
Answer:
D
Step-by-step explanation:
First found amount yielded
A = P(1+r)^nt
P is amount deposited 50,200
r is interest rate 13% = 13/100 = 0.13
t = 3
A = 50,200(1+0.13)^3
A = 50,200(1,13)^3
A = 72,433.42939999998
A is approximately 72,433.43
interest = A - P = 72,433.43-50,200 = 22,233.43= 22,233 to the nearest GHS
Identify two Pythagorean triples using the known triple 9, 40 , 41. *
Your answer
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {9}^{2} + {40}^{2} = {41}^{2} \\ 81 + 1600 = 1681 \\ 1681 = 1681[/tex]
Which goes with which
Collete mapped her vegetable garden on the graph below. Each unit represents 1 foot.
Collete plants an 8-foot row of lettuce in the garden. Which points could tell where the row of
lettuce starts and ends?
(-4,-1) and (-4,7)
| (-1, –4) a (
74)
(-1,-6) and (8,-6)
(-6, -1) and (-6,8)
Answer:
(-4,-1) and (-4,7)Step-by-step explanation:
If Collete planted a row of lettuce, that means their coordinates must have the same vertical coordinate, or the same horizontal coordinate. Another important characteristic is that between those points, there must have 8 units of separation, because it's an 8-foot row.
Only the first choice offers these characteristic to properly represent the row of plants with 8 feet distance between the first and the last plant.
Therefore, the answer is (-4,-1) and (-4,7)
Answer:
(-4, -1) and (-4, 7)
Step-by-step explanation:
I did the quiz
................................................
Answer:
V =108 ft^3
Step-by-step explanation:
The volume is found by
V = Bh where B is the area of the base
B = the area of the trapezoid
B = 1/2 (b1+b2)*h of the trapezoid
B = 1/2(4+6)*4 = 1/2(10)*4 = 20
Now we can find the volume
V = 20* 9
V =108 ft^3
what is (4 to the square root of 81)5?
Answer:
1310720
Step-by-step explanation:
Find out the frist part "4 to the square root of 81" 262144
then times it by 5
to get 1310720
plzz help i hav a test after i need the answer quick plzz.
Answer:Oop
Step-by-step explanation:
Please help worth 20 points!!
Answer:I would think u would
Step-by-step explanation:42,500×26
Answer:
1634.62$
Step-by-step explanation:
P=S/n
P=42500/26=1634.62
A bookstore had 60 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 1/4 of what remained. How many copies does the bookstore have left?
Answer:
30
Step-by-step explanation:
1/3 of 60 is 20
40 would be left
1/4 of 40 is 10 so 30 would be left
Daryl wishes to save money to provide for his retirement. He is now 30 years old and will be
retiring at age 64. Beginning one month from now, he will begin depositing a fixed amount into
a retirement savings account that will earn 12% compounded monthly. Then one year after
making his final deposit, he will withdraw $100,000 annually for 25 years. In addition, and after
he passes away (assuming he lives 25 years after retirement) he wishes to leave in the fund a sum
worth $1,000,000 to his nephew who is under his charge. The fund will continue to earn 12%
compounded monthly. How much should the monthly deposits be for his retirement plan?
Answer:
Step-by-step explanation:
Today's Age = 30
Retirement Age = 64
Total Monthly Deposits = ( 64 - 30 ) * 12 = 408
In case of 12% Compounded Monthly , Interest Rate per month = ( 12% / 12 ) = 1%
Effective Interest Rate per year = ( 1 + 0.12/12 )12 - 1 = 1.1268 - 1 = 0.1268 = 12.68%
Present value of Annual 25 Years withdrawal of $100,000 at time of Retirement = $100,000 * PVAF ( 12.68% , 25 )
= $100,000 * 7.4864
= $748,642.20
Present Value of Money for nephew at time of Retirement = $1,000,000 * PVF ( 12.68% , 25 )
= $1,000,000 * 0.050535
= $50,534.52
Now the Present Value of total Amount Required at time of Retirement = $748,642.20 + $50,534.52
= $799,176.70
Now the monthly deposit be X
= X * FVAF ( 408 , 1% ) = $799,176.70
= X * 5752.85 = $799,176.70
X = $138.918
Therefore Monthly Deposit = $138.92
Harris Interactive® conducted a poll of American adults in August of 2011 to study the use of online medical information. Of the 1,019 randomly chosen adults, 60% had used the Internet within the past month to obtain medical information. Use the results of this survey to create an approximate 95% confidence interval estimate for the percentage of all American adults who have used the Internet to obtain medical information in the past month.
Answer:
[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]
[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]
The 95% confidence interval for the true proportion would be given by (0.570;0.630) .
And if we convert this into % we got (57.0%, 63.0%)
Step-by-step explanation:
The information given we have the following info given:
[tex] n = 1019[/tex] represent the sampel size
[tex] \hat p=0.6[/tex] represent the sample proportion of interest
The confidence level is 95%, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
Replacing the info given we got:
[tex]0.60 - 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.570[/tex]
[tex]0.60 + 1.96\sqrt{\frac{0.60(1-0.60)}{1019}}=0.630[/tex]
The 95% confidence interval for the true proportion would be given by (0.570;0.630) .
And if we convert this into % we got (57.0%, 63.0%)
The formula A=12(b+c)h. Write the equation in term of c?
Answer:
[tex]c = \frac{A}{12h} - b[/tex]
Step-by-step explanation:
Okay, so the goal is to isolate c on one side with all the other terms on the other side. So, let's start by dividing both sides with 12h. After we do that, we will be left with [tex]\frac{A}{12h} = b+c[/tex]. Now, we can subtract both sides by b, and we will be left with [tex]\frac{A}{12h} - b = c[/tex]. Yay! We've now isolated c and that is our final answer!
Hope this helped! :)
Round 0.378 to the place underlined digit 3
Answer:
0.38
Step-by-step explanation:
7 is the 3rd digit, so 8 is greater then 5, so you round up, if it is correct, can you give brainiest
Answer:
0.40
Step-by-step explanation:
this is because the number before it is up to five and even more than 5 so we round it up by adding one to the next number and the remaining digit to zero
What is the value of 5x+3 when x = 4?
Answer:
Step-by-step explanation:
5(4)+ 3
20+3
23
Which types of triangles can be formed by taking the cross-section of a rectangular prism like the one shown above?
Answer: Equilateral, isosceles and scalene.
Step-by-step explanation:
A 6-sided die is rolled three times. What is the probability of rolling a 4 each time?
A 0.00463
B. 0.99537
C 0.16667
D. 0.00231
Answer:
a
Step-by-step explanation:
math
The picture shows a cement bag of weight Fg hanging from a rope which itself is supported by two other ropes attached to a ceiling. The latter two ropes make an angle θ1 and θ2 with the ceiling. Determine the tension in each rope. Use the angle addition identity to simplify your result: sin(α ± β) = sin α cos β ± cos α sin β
Answer:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
Step-by-step explanation:
From the free body diagram attached below; we will see that
T₃ = Fg ------ (1)
Thus; as the system is in equilibrium, the net force in the x and y direction shows to be zero
Then;
[tex]\sum F_x= 0 \to T_2 Cos \theta _2 - T_1 cos \theta _1[/tex]
[tex]T_2 Cos \theta _2 = T_1 cos \theta _1 \ \ \ \ \ - - - (2)[/tex]
Also;
[tex]\sum F_y =0 \to T_2sin \theta_2+T_1sin \theta_1 - T_3 = 0[/tex]
[tex]T_3 = T_2sin \theta_2+T_1sin \theta_1[/tex] ---- (3)
From equation (2):
[tex]T_2 = \dfrac{T_1cos \theta_1}{cos \theta_2}[/tex]
Replacing the above value for T₂ into equation 3; we have
[tex]T_3 = \dfrac{T_1cos \theta_1}{cos \theta_2}sin \theta_2+T_1sin \theta_1[/tex]
[tex]T_3 cos \theta_2 = {T_1cos \theta_1}{}sin \theta_2+T_1sin \theta_1 cos \theta_2[/tex]
[tex]T_3 cos \theta_2 = T_1(cos \theta_1 sin \theta_2+sin \theta_1 cos \theta_2)[/tex] ---- (4)
Using trigonometric identity Sin (A+B) = SIn A cos B + Cos A sin B
So ; equation 4 can now be:
[tex]T_3 cos \theta_2 = T_1sin(\theta _1 + \theta_2)[/tex] --- (5)
replacing equation (1) into equation (5) ; we have:
[tex]F_g}cos \theta_2 =T_1 sin (\theta_1+\theta_2)[/tex]
Hence; the tension in the string is:
[tex]T_1= \dfrac{F_gcos \theta_2}{sin (\theta_1+\theta_2)}[/tex]
GIVING BRANLIEST Which prism has a greater surface area?
2 prisms. A rectangular prism has a length of 12 inches, height of 8 inches, and width of 6 inches. A triangular prism has a rectangular base with a length of 6 inches and height of 12 inches. 2 rectangular sides are 12 inches by 10 inches. The triangular sides have a base of 6 inches an height of 8 inches.
The rectangular prism has a greater surface area by 72 square inches.
The rectangular prism has a greater surface area by 88 square inches.
The triangular prism has a greater surface area by 72 square inches.
The triangular prism has a greater surface area by 88 square inches.
Answer:
Rectangular prism
Step-by-step explanation:
