Answer:
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean life of 82 months with a standard deviation of 7 months.
This means that [tex]\mu = 82, \sigma = 7[/tex]
Sample of 71
This means that [tex]n = 71, s = \frac{7}{\sqrt{71}}[/tex]
What is the probability that the mean monitor life would be greater than 83.8 months?
1 subtracted by the p-value of Z when X = 83.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{83.8 - 82}{\frac{7}{\sqrt{71}}}[/tex]
[tex]Z = 2.17[/tex]
[tex]Z = 2.17[/tex] has a p-value of 0.985.
1 - 0.985 = 0.015
0.015 = 1.5% probability that the mean monitor life would be greater than 83.8 months in a sample of 71 monitors
Part E
1e. Subtract the binomial 12y2 – 4y3 from the trinomial 7y - 2y3 + 5y2
Answer:
2y^3-7y^2+7y
Step-by-step explanation:
7y - 2y^3 + 5y^2 - ( 12y^2 – 4y^3)
Distribute the minus sign
7y - 2y^3 + 5y^2 - 12y^2 + 4y^3
Combine like terms
2y^3-7y^2+7y
Thank you guys fir the help
9514 1404 393
Answer:
A
Step-by-step explanation:
The function f(x) is required in the numerator, eliminating choices C and D.
The restriction is that function g cannot be zero, so we cannot have ...
3x +2 = 0
3x = -2
x = -2/3 . . . . . eliminates choice B; confirms choice A
I need help Plz help
Use the permutation formula to solve a problem when n = 8 and r = 2.
A. 56
B. 672
C. 6,720
D. 40,320
Answer:
Option A. 56
Step-by-step explanation:
From the question given above, the following data were obtained:
Total number (n) = 8
Item taken for permutation (r) = 2
Pemutation (P) =?
ₙPᵣ = n! / (n – r)!
₈P₂ = 8! / (8 – 2)!
₈P₂ = 8! / 6!
₈P₂ = 8 × 7 × 6! / 6!
₈P₂ = 8 × 7
₈P₂ = 56
Answer:
A. 56
Step-by-step explanation:
How is the series 6+13+20+...+111 represented in summation notation?
Notice that
6 + 7 = 13
13 + 7 = 20
so if the pattern continues, the underlying sequence in this series is arithmetic with first term a = 6 and difference d = 7. This means the k-th term in the sequence is
a + (k - 1) d = 6 + 7 (k - 1) = 7k - 1
The last term in the series is 111, which means the series consists of 16 terms, since
7k - 1 = 111 ==> 7k = 112 ==> k = 16
Then in summation notation, we have
[tex]\displaystyle 6+13+20+\cdots+111 = \boxed{\sum_{k=1}^{16}(7k-1)}[/tex]
What is the value of g(-4)?
Answer:
A
Step-by-step explanation:
(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)
[tex]g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1[/tex]
[tex]\sqrt{4+\sqrt{4+\sqrt{4+...+\sqrt{4}[/tex]
Answer:
y=0.5+sqrt(17)
Step-by-step explanation:
Let y=sqrt{4+sqrt{4+...+sqrt(4)}
y=sqrt(4+y). (Since it's an infinite series)
y^2=4+y, y=0.5-sqrt(17) or 0.5+sqrt(17). We will omit the negative since root values are positive.
Naomi invested $3,425 in an account that
pays 3% simple interest. what was the total
balance of the account after 15 years?
Answer:
$4,966.25
Step-by-step explanation:
3 x 15 = 45
After 15 years, Naomi would have earned a total of 45% interest rate.
3,425 x 1.45 = 4,966.25
Don't use .45 as the multiplier
3,425 x .45 = 1,541.25 <- incorrect
Samantha bought m candies at the store. There are n candies in a pound, and each pound costs c dollars. Write an expression for how much Samantha paid.
Answer:
total = m/n * c
m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid
I will give brainliest if you answer properly.
Answer:
See below
Step-by-step explanation:
a)
[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]
[tex]\therefore x=\dfrac{4\pi }{3}[/tex]
But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution
Therefore,
[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]
This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.
Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]
b)
[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]
Once
[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]
As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
[tex]\therefore x=-\dfrac{\pi }{6}[/tex]
c)
[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]
Therefore,
[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]
[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
The solutions are
[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
Solve each system by graphing.
9514 1404 393
Answer:
no solution
Step-by-step explanation:
These lines have the same slope and different y-intercepts, so graph as parallel lines. As such, they will have no point of intersection, so there is NO SOLUTION to this system of inconsistent equations.
5 less than three times a number is 37 what is the number
Answer:
x = 14
General Formulas and Concepts:
Pre-Algebra
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
3x - 5 = 37
Step 2: Solve for x
[Addition Property of Equality] Add 5 on both sides: 3x = 42[Division Property of Equality] Divide 3 on both sides: x = 14If 4 men working 4 hours for 4 days complete 4 units of work, then how many units of work will be completed by 2 men working for 2 hours per day in 2 days.
Answer:
16 days
Step-by-step explanation:
Here,
By the question,
4 men takes 4 days working each day 4 hours to complete 4 units of work..
then..
if 1 man works 1 hour each day then i would take ( 4×4×4 ) days
= 64days
then..
if 2 men work for 2 hours per day then.
it would take
4×4×4 / 2×2 days
= 16 days
The average mileage per gallon for cars built since 1940 approximates to the following curve 0.0075*t^2-.2672*t+14.8 where t is year -1940.
Answer the following questions:
What is the expected MPG in 2025?
How about 2050?
Is this a valid function?
Is there a top end to MPG?
9514 1404 393
Answer:
46.3 in 202576.2 in 2050Step-by-step explanation:
The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.
__
No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.
Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.
A new coffee shop is being built. Its location is the reflection of the arcade's coordinates across
the y-axis. Which procedure will find the correct distance between the arcade and the new coffee shop?( there is more than one answer)
Step-by-step explanation:
mark me brainlist
please mark mep
Use the following data obtained from ages of the last six U. S. Presidents at the time of their inauguration to answer the following questions:
Ages of Last 6 Presidents at Inauguration
Ronald Reagan 69
George Bush 64
Bill Clinton 46
George W. Bush 54
Barack Obama 47
Donald Trump 70
a. Find the mean of the data set. (Round to one decimal place.)
b. Find the standard deviation of the data set. (Do not round until the final answer. Round final answer to 1 decimal place.)
c. What percentage of presidents' ages fall within one standard deviation of the mean
Answer:
a) The mean of the data set is 58.3.
b) The standard deviation of the data-set is of 10.8.
c) 50% of presidents' ages fall within one standard deviation of the mean
Step-by-step explanation:
Question a:
Sum of all values divided by the number of values.
[tex]M = \frac{69 + 64 + 46 + 54 + 47 + 70}{6} = 58.3[/tex]
The mean of the data set is 58.3.
Question b:
Square root of the sum of the difference squared between each value and the mean, divided by the number of values subtracted by 1. So
[tex]S = \sqrt{\frac{(69-58.3)^2 + (64-58.3)^2 + (46-58.3)^2 + (54-58.3)^2 + (47-58.3)^2 + (70-58.3)^2}{5}} = 10.8[/tex]
The standard deviation of the data-set is of 10.8.
Question c:
Between 58.3 - 10.8 = 47.5 and 58.3 + 10.8 = 69.1.
3 out of 6(Reagan, Bush and W. Bush), so:
3*100%/6 = 50%
50% of presidents' ages fall within one standard deviation of the mean
Question 3 of 10
What is the value of p?
V140
140°
90-
A. 50°
ООО
B. 90°
C. 60°
D. 40°
Answer:
A. 50º
Step-by-step explanation:
we are given the exterior angles 140º and 90º
exterior angles + corresponding interior angles = 180º
that means the two other angles of the triangle are:
180 - 140 = 40º
and
180 - 90 = 90º
the sum of interior angles in a triangle = 180
p = 180 - (40 + 90)
p = 180 - 130
p = 50º
A ball is thrown from an initial height of
1 meter with an initial upward velocity of
1 m/s. The ball's height h
(in meters) after t
seconds is given by the following. h=1+30t-5t^2
Find all values of t
for which the ball's height is 11
meters.
Round your answer(s) to the nearest hundredth.
Answer:
Step-by-step explanation:
If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:
[tex]11=-5t^2+30t+1[/tex] and
[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get
t = .35 seconds and t = 5.6 seconds
Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.
Solve triangles: angle bisector theorem
DAC = BAD.
What is the length of CD?
Round to one decimal place.
Answer:
Step-by-step explanation:
CD/6.5 = 2.6/4.9 This is the result of the angle bisector theorem.
The theorem basically says that the side opposite the angle being bisected is divided the ratio of the sides enclosing the angle.
Multiply both sides of the proportion by 6.5
CD = 2.6 * 6.5 / 4.9
CD = 3.4489
CD = 3.4 rounded.
Pls Help ASAP..................
Answer:
1. 8+(30/(2+4)) = 8+(30/6) = 8+5 = 13
2. ((8+30)/2)+4 = (38/2)+4 = 19+4 = 23
Step-by-step explanation:
:)
Answer:
Step-by-step explanation:
23:
(8 + 30) ÷ 2 + 4
13:
8 + 30 ÷ (2 + 4)
please give me the brainliest if u can
The Laplace Transform of a function f(t), which is defined for all t > 0, is denoted by L{f(t)} and is defined by the improper integral L{f(t)}(s) = infinity 0 e-st.f(t)dt, as long as it converges. Laplace Transform is very useful in physics and engineering for solving certain linear ordinary differential equations. (Hint: think of as a fixed constant)
1. Find L{t}. (hint: remember integration by parts)
A. 1
B. -1/s2
C. 0
D. 1/s2
E. -s2
F. None of these
2. Find L{1}.
a.1/s
b. 1
c. 0
d. -s
e. -1/s
f. none of these
(1) D
[tex]L_s\left\{t\right\} = \displaystyle\int_0^\infty te^{-st}\,\mathrm dt[/tex]
Integrate by parts, taking
[tex]u = t \implies \mathrm du=\mathrm dt[/tex]
[tex]\mathrm dv = e^{-st}\,\mathrm dt \implies v=-\dfrac1se^{-st}[/tex]
Then
[tex]L_s\left\{t\right\} = \displaystyle \left[-\frac1ste^{-st}\right]\bigg|_{t=0}^{t\to\infty}+\frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]
[tex]L_s\left\{t\right\} = \displaystyle \frac1s\int_0^\infty e^{-st}\,\mathrm dt[/tex]
[tex]L_s\left\{t\right\} = \displaystyle -\frac1{s^2}e^{-st}\bigg|_{t=0}^{t\to\infty}[/tex]
[tex]L_s\left\{t\right\} = \displaystyle \boxed{\frac1{s^2}}[/tex]
(2) A
[tex]L_s\left\{1\right\} = \displaystyle\int_0^\infty e^{-st}\,\mathrm dt[/tex]
[tex]L_s\left\{1\right\} = \displaystyle\left[-\frac1se^{-st}\right]\bigg|_{t=0}^{t\to\infty}[/tex]
[tex]L_s\left\{1\right\} = \displaystyle\boxed{\frac1s}[/tex]
Point M is the midpoint of CD. What is the value of a in the figure?
Answer:
a=3
Step-by-step explanation:
Given points (a, b) and (c,d), the midpoint of the points will be at
((a+c)/2, ((b+d)/2)
Therefore, given (9, 2) and (a,2a), our midpoint is at
((9+a)/2, (2+2a)/2) = (6,4)
Matching the x values to their corresponding x values and doing the same with the y values, we get
(9+a)/2 = 6
(2+2a)/2 = 4
First, we have
(9+a)/2 = 6
multiply both sides by 2 to remove the denominator
9+a = 12
subtract 9 from both sides to isolate a
a = 3
2a = 2 * a = 6
Confirming this, we have
(2+2a)/2 = 4
(2+6)/2 = 4
8/2=4
The value of a is 3 after using the bisection formula and the coordinate of the C is (3, 6).
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
Point M is the midpoint of CD.
The coordinate of the C is (a, 2a)
The coordinate of the M is (6, 4)
The coordinate of the C is (9, 2)
Using bisection formula:
(a + 9)/2 = 6
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. I
a + 9 = 12
a = 12 - 9
a = 3
Or
(2a + 2)/2 = 4
a + 1 = 4
a = 3
Thus, the value of a is 3 after using the bisection formula and the coordinate of the C is (3, 6).
Learn more about the order double here:
brainly.com/question/10757890
#SPJ2
3.06 as. a fraction PLEASE HELP
Answer:
153/50
Step-by-step explanation:
3.06
Rewriting as
There are two numbers after the decimal so we put the number over 100
306/100
Divide top and bottom by 2
153/50
To write 3.06 as a fraction you have to write 3.06 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.
3.06 = 3.06/1 = 30.6/10 = 306/100
And finally we have:
3.06 as a fraction equals 306/100
7x2 - 4x +10+ 3x2 – 8
Convert the following numbers into scientific notation. ( i did them but I feel like they wrong can y’all correct them if they are?)
Answer:
only 4 is incorrect...
1,450,000 = 1.45 x [tex]10^{6}[/tex] NOT
1,450,000 = 1.45 x [tex]10^{7\\}[/tex]
Step-by-step explanation:
Drag each factor to the correct location on the image.
If p(1) = 3, p(-4) = 8, p(5) = 0, p(7) = 9, p(-10) = 1, and p(-12) = 0,
P(x).
Answer:
(x-7) and (x+12) are the factors and the rest are non factors...
What is 22 x 2 + 6 = x
Answer:
x=50
Step-by-step explanation:
22•2=44
44+6=50
Answer:
50
Step-by-step explanation:
22×2=44+6=50.
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If the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse?
Answer:
13
Step-by-step explanation:
If we have a right triangle, we can use the Pythagorean theorem to find the hypotenuse
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
5^2 + 12^2 = c^2
25+144= c^2
169 = c^2
Take the square root of each side
sqrt(169) = sqrt(c^2)
13= c
Answer:
The length of the hypotenuse is 13.
Step-by-step explanation:
[tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex]
[tex]a^2 = 12^2 + 5^2[/tex]
[tex]a^2 = 144 + 25[/tex]
[tex]a^2 = 169[/tex]
a=[tex]\sqrt{169}[/tex]
a= 13
Here we use the idea of the Pythagoras' theorem. Which suggests that [tex]a^{2}[/tex] = [tex]b^2 + c^2[/tex] in which [tex]a^{2}[/tex] is the hypotenuse of the triangle and [tex]b^2[/tex] and [tex]c^{2}[/tex] are the two other lengths of the triangle.
HOPE THIS HELPED
there is a 400 meter track. tom rides a bike at the speeed of 450 meters/minute. mike runs at the speed of 250 meters/minute. if both of them set out at the same time and same place, how soon will they meet for the first time?
Answer: Distance: 2250
Step-by-step explanation:
Find GCF of 450 and 250
2. How many solutions does this system of equations have? *
y = 5x – 2
y = 5x + 7
Answer:
No solution.
Step-by-step explanation:
[tex]{ \sf{y = ±∞ \: \: and \: \: x = ±∞}}[/tex]
