Answer:
The probability that the sample mean will be between 82.5 and 86 years is 0.8351.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
[tex]\mu_{\bar x}=\mu\\[/tex]
And the standard deviation of the sample means is given by,
[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]
The information provided is:
[tex]\mu=85\\\sigma=6\\n=36[/tex]
As the sample size is large enough the Central Limit Theorem can be used to approximate the sampling distribution of sample mean life expectancy (M) in the United States.
Compute the probability that the sample mean will be between 82.5 and 86 years as follows:
[tex]P(82.5<\bar X<86)=P(\frac{82.5-85}{6/\sqrt{36}}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{86-85}{6/\sqrt{36}})\\\\=P(-2.5<Z<1)\\\\=P(Z<1)-P(Z<-2.5)\\\\=0.84134-0.00621\\\\=0.83513\\\\\approx 0.8351[/tex]
Thus, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.
The probability that the sample mean will be between 82.5 and 86 years is 0.8351.
Standard deviation σ = 6
Sample size n =36
What is the central limit theorem?The central limit theorem (CLT) states that the distribution of sample means approximates a normal distribution as the sample size gets larger, regardless of the population's distribution.
Since the sample size is significant i.e. large, so the given scenario can be treated as normally distributed as per the central limit theorem.
So, the standard deviation of sample means = σ/√n
The probability that the sample mean will be between 82.5 and 86 years:
[tex]P(82.5 < X < 86) = P(\frac{82.5-85}{\frac{6}{\sqrt{36} } } < Z < \frac{86-85}{\frac{6}{\sqrt{36} } } )[/tex]
[tex]P(-2.5 < Z < 1)=P(Z < 1)-P(Z < 2.5)[/tex]
[tex]P(-2.5 < Z < 1) =0.8413-0.0062=0.8351[/tex]
Therefore, the probability that the sample mean will be between 82.5 and 86 years is 0.8351.
To get more about the central limit theorem visit:
https://brainly.com/question/18403552
Cameron spent 32 minutes on Instagram on Friday. The next day
he spent 30% of that on Instagram. In total, how much time did
Cameron spend on Instagram?
Answer:
41.6
Step-by-step explanation:
32 x 0.3 = 9.6
9.6 + 32 = 41.6
41.6
i had the same question
Find the missing angle:
Answer:
40
Step-by-step explanation:
Use this picture as a reference.
So, using remote angles theorem, which states that; the angle formed from the extension of a side in a triangle is equal to the sum of the two angles which it does not make contact with, within the triangle. One can conclude that :
m< BCD = m<B + m<A
substitute:
m<BCD = 80 + 25
Simplify:
m<BCD = 105
Since it is given that m< BCE is 50, then one has to subtract m<BCE from m<BCD to get m<ECD
m<BCD - m<BCE = m<ECD
Subsitute:
105 - 50 = m<ECD
Simplify:
55 = m<ECD
Using the sum of angles in a triangle, which states that the sum of all the angles in a triangle is 180 degrees, one can say that:
m<D + m<ECD + m<E = 180
Substitute:
85 + 55 + m<E = 180
Simplify, inverse operations:
140 + m<E = 180
-40 -140
m<E = 40
Una parte de 25 000 dólares se invierte al 10% de interés, otra parte al 12 % y el resto al 16%. El ingreso anual total de las tres inversiones es de 3200 dólares. Además, el ingreso de la inversión al 16% es igual al ingreso de las otras dos inversiones combinadas. ¿Cuánto se invirtió a cada tasa de interés?
Answer:
$5000 at 10%, $10000 at 12% and 10000 at 16%Step-by-step explanation:
One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?==================
Let the parts be x, y and z
As per given we get below system of equations:
x + y + z = 250000.1x + 0.12y + 0.16z = 32000.1x + 0.2y = 0.16zSubstitute 0.1x + 0.2y in the second equation:
0.16z + 0.16z = 32000.32z = 3200z = 3200/0.32z = 10000Now we have:
x + y + 10000 = 25000 ⇒ x + y = 15000and
0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600Multiply the second equation and then subtract the first one:
10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000x + 1.2y - (x + y) = 16000 - 150000.2y = 1000y = 10000Then
x = 15000 - 10000 = 5000So the parts are:
$5000 at 10%, $10000 at 12% and 10000 at 16%Can someone help me please
===================================================
Work Shown:
For any triangle, the three interior angles always add to 180
(4x-12) + (6x-17) + (2x+5) = 180
(4x+6x+2x) + (-12-17+5) = 180
12x - 24 = 180
12x = 180+24 ..... adding 24 to both sides
12x = 204
x = 204/12 ..... dividing both sides by 12
x = 17
We can use this x value to find the three angles
4x-12 = 4*17-12 = 56
6x-17 = 6*17-17 = 85
2x+5 = 2*17+5 = 39
As a check,
56+85+39 = 180
which confirms we have the right x value.
We see that 56 is the middle angle, so this is the second largest angle.
helppppp please I will give brainliest
Answer:
y=1/3x-2
Step-by-step explanation:
you and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the results by 2 and then add 3. your friend's final answer is 53.
Answer:
It is 5....
Step-by-step explanation:
8. A substance has a half life of 2.347 minutes.
a. If the initial amount of the substance was 110.4 grams, how many half-lives will have passed
before the substance decays to 6.9 grams.
b. What is the total time of the decay?
Answer:
a.) 4 half lives have passed
b) 9.388 minutes
Step-by-step explanation:
Formula for exponential growth / decay is given as:
[tex]A=A_0b^{\frac{t}{c}}[/tex]
Where [tex]A[/tex] is the final population
[tex]A_0[/tex] is the initial population
[tex]b[/tex] is the growth factor
[tex]c[/tex] is the time taken for the growth 'b'
[tex]t[/tex] is the amount of time
Here, we are given that:
[tex]A[/tex] = 6. 9 grams
[tex]A_0[/tex] = 110.4 grams
[tex]b = \dfrac{1}{2}[/tex]
[tex]c = 2.347[/tex] min
To find:
a.) Number of half lives taken for the decay.
b.) Total time in the decay.
Solution:
a.) Number of half lives taken for the decay is nothing but equal to [tex]\frac{t}{c}[/tex].
Putting the values in the formula, we get:
[tex]6.9=110.4\times \frac{1}2^{\frac{t}{c}}\\\Rightarrow 6.9=110.4\times 0.5^{\frac{t}{c}}\\\Rightarrow 0.0625=0.5^{\frac{t}{c}}\\\Rightarrow \dfrac{t}{c} =4[/tex]
Therefore, the answer is:
4 half lives have passed.
b.) Total time of decay. We have to find the value of [tex]t[/tex] here.
From answer of part a.):
[tex]\dfrac{t}{c} =4\\\Rightarrow \dfrac{t}{2.347} =4\\\Rightarrow t =\bold{9.388\ min}[/tex]
Find the equation of the line.
The perpendicular bisector to the line segment with endpoints (-8,5) and (4,1).
The equation of the line is
y =
Answer:
y = 3x + 9
Step-by-step explanation:
The perpendicular bisector to the line segment is passing through the midpoint of the line segment. Coordinates of midpoint are ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
Formula of slope is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Slopes of perpendicular lines are opposite reciprocals. So, if AB ⊥ CD , then [tex]m_{AB}[/tex] × [tex]m_{CD}[/tex] = - 1
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~
(- 8, 5)
(4, 1)
m = ( 5 - 1) / ( - 8 - 4) = - [tex]\frac{1}{3}[/tex]
Opposite reciprocal to ( - [tex]\frac{1}{3}[/tex] ) is 3
Coordinates of midpoint are ( - 2 , 3 )
y - 3 = 3 ( x + 2 )
y = 3x + 9
The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion.Fill in the blanks: We are ________ confident that the population mean is between _______ and _______.a) 1%, 0, 0.583120b) 99%, 0, 0.583120c) 99%, 0.385631, 0.780609d) 1%, 0.385631, 0.780609
Answer:
The following display from a TI-84 Plus calculator presents a 99% confidence interval for a proportion.Fill in the blanks:
We are ____99%____ confident that the population mean is between ___0.385631____ and ___0.780609____.
c) 99%, 0.385631, 0.780609
Step-by-step explanation:
This is the only correct option, given the relevant population mean range. Option B is not correct as the population mean cannot range between 0 and 0.583120 as given by the option. Options 'a' and 'd' are not relevant to the question because they have 1% confidence level, instead of the stated 99% confidence level.
Find the distance of a line given the following points. R(3, 1), W(-1, -2)
Answer:
[tex]\sqrt{13}[/tex]
Step-by-step explanation:
we can solve this using the distance formula: [tex]\sqrt{(x_{2}-x_1)^{2} + (y_{2}-y_1)^{2}}[/tex]
[tex]x_1, y_1[/tex] is (3, 1)
[tex]x_2, y_2[/tex] is (-1, -2)
[tex]\sqrt{(1-3)^2 + (-2-1)^2}[/tex]
which simplifies to: [tex]\sqrt{(-2)^2 + (-3)^2}[/tex]
then: [tex]\sqrt{2^2 + 3^2}[/tex] or: [tex]\sqrt{4+9}[/tex]
your final answer is: [tex]\sqrt{13}[/tex] or about 3.61
Tony rents a bike that costs $4 per hour and $10 for the lock. He has $32 to spend. How long can he rent the bike? Write an equation that represents this situation. Be sure to explain how you got your equation and specify what the variables represent.
Answer:
5 hours; 4x+10=32
Step-by-step explanation:
4x = 4 multiplied by the amount of hours
10 = the cost for the lock
so y = 4x+10
In this case y= 32 so plug it in
4x+10=32
-10 -10
4x=22
/4 /4
x=5.5
So assuming you can only rent whole hours, it would be 5 hours
Hope this helps.
Answer:
he can rent the bike for 5 hours
Step-by-step explanation:
32-10=22
22*4=5
Please help...20 points! And explain
4. If f(x) = 5X + 8, g(x) = 7X -2 Find (f - g)(x)
Answer:
-2x+10
Step-by-step explanation:
f(x)=5x+8
g(x)=7x-2
(f-g)(x)= 5x+8-7x+2= -2x+10
Find: 11 3 ÷ 2 3 The quotient is 5 and .
Answer:
0.5
Step-by-step explanation:
The answer of this problem would be 5.5, so you are missing the 0.5
Answer :
1/2
Explanation :
Completed the assignment on Edge.
Mrs. Wheeler wants to cook a turkey for Thanksgiving dinner she knows that a 20 pound turkey Is enough to feed 16 people at this rate what size turkey will mrs. Wheeler need it 21 people are expected to come over for a dinner .
A fast food chain sells 4,500 hamburgers per hour worldwide. How many hamburgers does the fast food chain sell worldwide in 1 minute?
Answer:
75 hamburgers per minute
Step-by-step explanation:
We’ll it’s 4500 per hour, or every 60 minutes, to find 1 min, you can divide by 60.
4500/60 = 75
Jack wants to attend a private 4-year university that costs $32,500 a year for tuition. His parents said they will give him $15,000 each year towards tuition. If he saves his money over the next four years before college, how much money will he have to save each year?
A $1,750
B $17,500
C $175
D $4375
Answer:
b
Step-by-step explanation:
3. Which number is a distance of 4 units away from 2 and a distance of 2 units from -4?
HH
-6
-5
-4
-3
-2
-1
0
1
2.
3
4
5
6
Answer:
-2
Step-by-step explanation:
Brainliest be good peeps Calculate the missing term in each and for 2 its not 6/7 it cant be okay? thanks tho if you try and get that.
proportion.
2/11= /55
36/42= /
9/ = 21/28
6/9= /15
Answer:
The missing term is 10
Step-by-step explanation:
2/11=x/55
cross multiply
2*55=11x
x=10
I hope this helps :)
The area of a square is 81 m ^ 2 what is the perimeter of the square? How do you know?
Answer:
Square root of 81 is 9
9 multiply with 4 is 36
Permiter is 36cm.
Thank you and please rate me as brainliest as it will help me to level up
There is ounce of yeast in every 2 teaspoons of yeast. A recipe for bread calls for 2 teaspoons of yeast. How many ounces of yeast are needed for this recipe?
For all x in the domain of the function (x+1)/(x^3-x) this func-
tion is equivalent to
Answer:
The function is equivalent to
[tex]\frac{x+1}{x^3-x}=\frac{1}{x\left(x-1\right)}[/tex]
Step-by-step explanation:
Given the function
[tex]f\left(x\right)=\frac{x+1}{x^3-x}[/tex]
Let us simplify this function
[tex]f\left(x\right)=\frac{x+1}{x^3-x}[/tex]
[tex]=\frac{x+1}{x\left(x+1\right)\left(x-1\right)}[/tex] ∵ [tex]Factor\:x^3-x=x\left(x+1\right)\left(x-1\right)[/tex]
Cancel the common factor (x+1)
[tex]=\frac{1}{x\left(x-1\right)}[/tex]
Therefore, the function is equivalent to
[tex]\frac{x+1}{x^3-x}=\frac{1}{x\left(x-1\right)}[/tex]
Answer:
wrong
Step-by-step explanation:
The problems in this lesson review basic arithmetic skills.
Answer:
false
Step-by-step explanation:
There are 60 new houses being built in a neighborhood. Last month, 1/4 of them were sold. This month, 1/5 of the remaining houses were sold. How many houses are left to be sold.
Answer:
36
Step-by-step explanation:
Number of new houses = 60
Number of houses sold last month = (1/4) of 60
[tex]= \frac{1}{4}*60[/tex]
= 15
Remaining houses = 60 - 15 = 45
Number of houses sold this month = (1/5) of 45
[tex]=\frac{1}{5}*45\\\\= 9[/tex]
Number of houses that are left = 45 - 9 = 36
I’ll give you a Brainly if you get this done in 3 mins -Solve each system by substitution
1) y=-3x+5
5x-4y=-3
2)y=-2
4x-3y=18
3)-7x-2y=-13
X-2y=11
4)-5x+y=-3
3x-8y=24
Answer:
1) x = 1 , y = 2
2) x=3, y=-2
3) x=3, y=-4
4) x=0, y=-3
Step-by-step explanation:
I hope this helped! please mark as brailiest
You may use any notes from class or past assignments on this assessment. You may also use a
calculator. You may not look up any answers on the internet or use anyone else's work.
1.
The equation m=40g gives the distance in miles, m, that a car can travel using g gallons
of gas.
a. If the car has gone 140 miles, how much gas was used?
b. Write an equation that represents the inverse function: the gallons of gas as a
function of distance in miles.
Function C is defined by the equation cov) = 50 + 4y It mives the month con
please help, the question says what statement best describes the placement of the lines Carson Drew
Answer:
Only line A is a well-placed line of best fit.
Step-by-step explanation:
I did this on Plato and got it correct.
write the slope - intercept form of the equation. PLEASE HELP. i will mark brainliest
Answer:
Step-by-step explanation: To find the equation of the perpendicular line, take the reciprocal of the slope with the opposite sign.
For example, the reciprocal of 4/3 is 3/4 and if it's negative, the opposite is positive.
The reciprocal of 2 is 1/2. and if it's positive, the opposite is negative.
The reciprocal of any number or fraction is whatever you multiply it by to get 1. 4 times 1/4 is 1 5/4 times 4/5 is 1. What about 1 ? 1 times 1 is 1. So one is its own reciprocal!
I hope this helps. (we're not supposed to give answers to t e s t s.)
Write the equation of the exponential function given two points: (1,6) (3,96)
Answer:
y = 3/2 ⋅ 4^x
Step-by-step explanation:
I hope this helped! please mark as brainliest
A car travels 180 miles in 4 hours. What is
the car’s speed in feet per minute?
Answer:
3,960 feet per minute, brainliest pls
Step-by-step explanation:
Answer:
3960 feet per minute
Step-by-step explanation:
1 mile = 5280 feet
Therefore,
180 miles = 180*5280
180 miles = 950400 feet
1 hour = 60 minutes
So, 4 hours = 240 minutes
Speed if the car
= 950400/240
= 3960 feet per minute