Answer:
The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
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.
We have:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex].
Sample of size n:
This means that the z-score is now, by the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Find the probability that the mean life expectancy will be less than years.
The probability that the mean life expectancy of the sample is less than X years is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean life expectancy, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Need help on last question
Answer:
Step-by-step explanation:
so let the equation equal 13
13 = 3[tex]x^{3}[/tex]-12x+13
so when ever 3[tex]x^{3}[/tex]-12x=0 then this is equation is true, soooo
x (3[tex]x^{2}[/tex] - 12) =0
so when x = 0 this is true, but also when
3[tex]x^{2}[/tex]-12=0 also
3[tex]x^{2}[/tex] = 12
[tex]x^{2}[/tex] = 4
x = 2
so when x = 2 or -2 or 0 , then this is true
Midwest Publishing publishes textbooks. The company uses an 800 number where people can call to ask questions about the textbooks and place orders. Currently, there are 2 representatives handling inquiries. Calls occurring when both lines are in use get a busy signal. Each representative can handle 12 calls per hour. The arrival rate is 20 calls per hour.
Required:
a. How many extension lines should be used if the company wants to handle 90% of the calls immediately?
b. What is the probability that a call will receive a busy signal if your recommendation in part (a) is used?
c. What percentage of calls receive a busy signal for the current telephone system with two extension lines?
Answer:
A. 18 calls
B. 0.9
C. 20
Step-by-step explanation:
Number of representatives=2,
Number of extension lines=2,
Average calls each representative can accommodate per hour = 15 calls,
Arrival rate per hour = 30 calls
(a) 90% of the arrival rate = 0.09 × 20 = 18 calls
To handle 18 calls immediately, 18 extension lines should be used
(b) Probability is given by number of possible outcomes ÷ number of total outcomes
Number of possible outcomes = 18, number of total outcomes = 20
Probability (call will receive busy signal) = 18/20 = 0.9
(c) For one extension line, numbers of calls to receive busy signal = 20 - 10 = 10 calls
Number of calls to receive busy signal for the current telephone system with two extension lines = 2 × 10 = 20 calls
Few drivers realize that steel is used to keep the road surface flat despite the weight of buses and trucks. Steel bars, deeply embedded in the concrete, are sinews to take the stresses so that the stresses cannot crack the slab or make it wavy. The passage best supports the statement that a concrete road
Answer: Is reinforced with other material
Step-by-step explanation:
The options are:
A is expensive to build.
B usually cracks under heavy weights.
C looks like any other road.
D is reinforced with other material.
The passage best supports the statement that a concrete road are reinforced with other material. According to the information given in the passage, steel plays a vital role in keeping the road surface flat.
Steel bars are embedded in concrete so that the stresses cannot crack the slab. Therefore, it indicates that concrete road is reinforced with other material.
Find a power series representation for the function. (Assume a>0. Give your power series representation centered at x=0 .)
f(x)=x2a7−x7
Answer:
Step-by-step explanation:
Given that:
[tex]f_x = \dfrac{x^2}{a^7-x^7}[/tex]
[tex]= \dfrac{x^2}{a^7(1-\dfrac{x^7}{a^7})}[/tex]
[tex]= \dfrac{x^2}{a^7}\Big(1-\dfrac{x^7}{a^7} \Big)^{-1}[/tex]
since [tex]\Big((1-x)^{-1}= 1+x+x^2+x^3+...=\sum \limits ^{\infty}_{n=0}x^n\Big)[/tex]
Then, it implies that:
[tex]\implies \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\Big(\dfrac{x}{a} \Big)^{^7} \Big)^n[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x}{a} \Big)^{^{7n}}[/tex]
[tex]= \dfrac{x^2}{a^7} \sum \limits ^{\infty}_{n=0} \Big(\dfrac{x^{7n}}{a^{7n}} \Big)}[/tex]
[tex]\mathbf{= \sum \limits ^{\infty}_{n=0} \dfrac{x^{7n+2}}{a^{7n+7}} }}[/tex]
PLEASE HELP!!! I tried using different formulas, adding, subtracting, dividing, multiplying you name it and I have yet to find the correct answer. How would I should this problem?
Answer:
19.14
Step-by-step explanation:
You have a half circle and a square, look at them separate then add for the area.
Circle
Your radius is half the diameter, so 4/2
Radius = 2
[tex]A = 3.14 * radius\\A = 3.14 * 2\\A = 6.28[/tex]
This is for the entire circle, half of that would be 3.14
Square
[tex]A = 4^{2} \\A = 16[/tex]
Add them both together for a total area of 19.14 square miles
The product of 2 consecutive even integers is 16 less than 8 times their sum
Answer:
there are two solutions:
x=0
and
x=14
Step-by-step explanation:
lts suppose the numbers are x and x+2, so:
[tex]x(x+2)=8(x+(x+2))-16\\x(x+2)=8(2x+2)-16=16x+16-16=16x\\x^2+2x=16x\\x^2-14x=0\\x(x-14)=0\\x=0,~x=14[/tex]
is y=3x^2-x-1 a function
Answer: Yes it is a function.
This is because any x input leads to exactly one y output.
The graph passes the vertical line test. It is impossible to draw a single vertical line through more than one point on the parabolic curve.
The accompanying data are lengths (inches) of bears. Find the percentile corresponding to 61.0 in.
(Round to the nearest whole number as needed.)
Bear Lengths
36.0 37.0 39.5 40.0 40.5 43.0 44.0 45.5 45.5 46.5 48.0 48.00 49.0 50.0 51.5 52.5 53.0 53.5 54.0 57.3 57.5 58.0 58.5 59.0 59.5 60.0 61.0 61.0 61.0 61.5 62.0 62.5 63.0 63.0 63.5 64.0 64.0 64.0 64.5 65.0 66.0 67.5 67.5 68.5 70.0 70.5 71.5 72.0 72.5 72.5 72.5 73.5 74.5 77.5
Answer:
52nd percentile
Step-by-step explanation:
The sorted data :
36.0, 37.0, 39.5, 40.0, 40.5, 43.0, 44.0, 45.5, 45.5, 46.5, 48.0, 48.00, 49.0, 50.0, 51.5, 52.5, 53.0, 53.5, 54.0, 57.3, 57.5, 58.0, 58.5, 59.0, 59.5, 60.0, 61.0, 61.0, 61.0, 61.5, 62.0, 62.5, 63.0, 63.0, 63.5, 64.0, 64.0, 64.0, 64.5, 65.0, 66.0, 67.5, 67.5, 68.5, 70.0, 70.5, 71.5, 72.0, 72.5, 72.5, 72.5, 73.5, 74.5, 77.5
The total size of the data = 54
The value 61.0 occurs in position ; 27th, 28th and 29th
Taking the position average :
(27+28+29)/3 = 84/3 = 28th position
This means the percentile score of 61 is :
(Position average / total size) * 100%
(28/54) * 100%
0.5185185 * 100%
= 51.85%
This means that 61 inch length falls in the 52nd percentile
If f(x) = 3x^2 - x, find f(-2)
Answer:
14
Step-by-step explanation:
Substitute x for -2
3(-2)^2 - (-2)
3(4) +2
12+2=14
41:41
How many solutions does this linear system have?
y=-6x+2.
-12x - 2y = -4
O one solution: (0,0)
one solution: (1, -4)
O no solution
O infinite number of solutions
Answer is C
Answer:
Answer: B
Step-by-step explanation:
just solve keep up learning!
IF A=[2,4] and B=[0,3] then BUA=?
Answer:
it equal:
answer is : [0234]
Which of the following is an even function?
g(x) = (x – 1)2 + 1
g(x) = 2x2 + 1
g(x) = 4x + 2
g(x) = 2x
Consider that choice B is the same as saying 2x^2+1x^0.
The exponents 2 and 0 are both even, which is sufficient to say that the entire polynomial function itself is also even.
Something like choice A expands out and simplifies to x^2-2x+2, and that's equivalent to saying x^2+2x^1+2x^0. The presence of the x^1 term, with its odd exponent, is what makes choice A not even (it's not odd either).
Similarly, choices C and D also have exponents of 1, so they aren't even either.
Answer:
G(x)=2x2+1
Step-by-step explanation:
Frans paid R9600 as interest on a loan he took 5 years ago at 16% rate. What's was the amount he took as loan?
Step-by-step explanation:
Interest (I)=R9600
Rate(R)=16%
Time (T)=5years
Principal (P)=?
P=100×I÷R×T
P=100×R9600÷16×5
P=R960000÷80
P=R12, 000
Answer:
The amount he took as loan = R12,000
Step-by-step explanation:
Simple Interest
Let loan amount be = P
R = 16%
T = 5years
I = 9600
Find P
[tex]I = \frac{PRT}{100}\\\\9600 = \frac{P \times 16 \times 5}{100}\\\\P = \frac{9600 \times 100}{16 \times 5} = 12,000[/tex]
J. Aitchison collected expenditures data for 20 randomly selected single men and 20 randomly selected single women. He uses the data to conduct a hypothesis test to determine if the mean percent of expenditures that goes toward housing (including fuel and light) is different for men and women. What is the correct alternative hypothesis?
a. Md = 0
b. μα = 0
c. ud > 0
d. Opmen — Вwomen
e. Himen > Mwomen
f. Mmen Mwomen
Answer:
The alternative hypothesis is [tex]H_1: \mu_M - \mu_W \neq 0[/tex], considering M for men and W for women.
Step-by-step explanation:
He uses the data to conduct a hypothesis test to determine if the mean percent of expenditures that goes toward housing (including fuel and light) is different for men and women.
At the null hypothesis, we test if there is not difference, that is, the difference of the mean is 0, so:
[tex]H_0: \mu_M - \mu_W = 0[/tex]
At the alternative hypothesis, we test if there is a difference, that is, the difference of the means is different of 0, so:
[tex]H_1: \mu_M - \mu_W \neq 0[/tex]
f(x) = (x + 1)^2
Determine for each x-value whether it is in the domain of f
or not.
Answer:
All of them are in the domain.
Step-by-step explanation:
The function is f(x)= (x+1)^2. If you simplify this, you get y=x^2+2x+1=0. This is a quadratic that opens upwards. There are no gaps in the x values and no impossible values. The domain is all real numbers and all the answer choices are real numbers.
HELP!!!!!! I need an answer fasttttt
Answer:
see the attachment
Step-by-step explanation:
Hope it helps you
If (3x − 2)(3x + 2) = ax2 − b, what is the value of a?
(3x-2)(3x+ 2)
Multiply each term in one set of parentheses by the other terms:
3x x 3x =9x^2
3x x 2 = 6x
-2 x 3x = -6x
-2 x 2 = -4
Combine to get:
9x^2 + 6x - 6x -4
Combine like terms:
9x^2 - 4
The value of a would be 9.
[tex]\sf{\bold{\blue{\underline{\underline{Given}}}}}[/tex]
(3x − 2)(3x + 2) = ax2 − b⠀⠀⠀⠀[tex]\sf{\bold{\red{\underline{\underline{To\:Find}}}}}[/tex]
⠀what is the value of a?⠀⠀⠀[tex]\sf{\bold{\purple{\underline{\underline{Solution}}}}}[/tex]
At first we have to solve the value of (3x-2)(3x+2)
[tex]\sf{(3x-2)(3x+2) }[/tex] [tex]\sf{3x(3x+2)-2(3x+2) }[/tex] [tex]\sf{9x^{2}+6x-6x-4 }[/tex] [tex]\sf{9x^{2}-4 }[/tex]According to the question,
[tex]\sf{ (3x − 2)(3x + 2) = ax^{2} − b }[/tex] [tex]\sf{9x^{2}-4=ax^{2}-b }[/tex] [tex]\sf{9x^{2}=ax^{2}~and~-4=-b }[/tex] [tex]\sf{a=9~and~b=4 }[/tex]⠀⠀⠀
[tex]\sf{\bold{\green{\underline{\underline{Answer}}}}}[/tex]
Hence,
The value of a is 9
Find the image of the given point
under the given translation.
P(4, -7)
T(x, y) = (x+1, y + 3)
P' = ([?], []).
Answer:
P' (5, -4)
Step-by-step explanation:
P (4, -7)
x = 4 & Y =-7
T(4,. -7) = (4 + 1, -7 +3)
P' = (5, -4)
(3x^3)^2 write without exponent
Answer:
9*x*x*x*x*x*x.
Step-by-step explanation:
(3x^3)^2
= 3^2 * x^(3*2)
= 3^2 * x^6
= 9*x*x*x*x*x*x
A bag has 180 balls. the ratio of red to blue to yellow balls is 8:5:7 how many red balls are there and how many blue balls are there
Answer:
72 red
45 blue
63 yellow
Step-by-step explanation:
8+5+7= 20
180÷20= 9
red = 9*8
blue = 9*5
yellow = 9*7
Angle ABC has A(3-,6), and C(9,55 as it vertices.
What is the length of side AB in units?
Answer:
7.07 units
Step-by-step explanation:
Given
[tex]A = (-3,6)[/tex]
[tex]B = (2,1)[/tex]
[tex]C = (9,5)[/tex]
See comment for complete question
Required
Side length AB
To do this, we make use of the following distance formula;
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]d = \sqrt{(-3 - 2)^2 + (6 - 1)^2}[/tex]
[tex]d = \sqrt{(-5)^2 + 5^2}[/tex]
[tex]d = \sqrt{25 + 25}[/tex]
[tex]d = \sqrt{50}[/tex]
[tex]d = 7.07[/tex]
-6×-5y=6
4x+y=3
What's answer to this equation
9514 1404 393
Answer:
(x, y) = (3/2, -3)
Step-by-step explanation:
Using the second equation, we can write an expression for y:
y = 3 -4x
Using this in the first equation, we have ...
-6x -5(3 -4x) = 6
-6x -15 +20x = 6 . . . . eliminate parentheses
14x = 21
x = 21/14 = 1.5
y = 3 -4(1.5) = 3 -6 = -3
The solution is (x, y) = (1.5, -3).
__
I find a graphing calculator a useful tool for finding solutions quickly.
UNIT CHECKPOINT:
Probability Distributions
Calculator
Suppose a normal distribution has a mean of 18 and a standard deviation of 4.
A value of 24 is how many standard deviations away from the mean?
-3
-1.5
1.5
24 = 18 + 6 = 18 + 1.5*4
so 24 is +1.5 standard deviations away from the mean.
Answer:
The above answer is definitely correct.
Step-by-step explanation:
You work as an office assistant who does data entry for a large survey company. Data entry is performed in two-person teams: one person types and the other checks that person's work for errors. Each two-person team, on average, can enter the data of 520 surveys per day. A huge collection of 7,540 surveys will arrive tomorrow and must be entered by the end of the day. In order to enter all of the survey data, how many total employees, working in two-person teams, must work tomorrow?
Answer:
you just gave your self the answer because you just need to multiply
Step-by-step explanation:
15080 is the answer
Marina spent $13.50 at the grocery store. She bought pears, kiwis, and pineapples. Pears cost $0.50 each, pineapples cost $1.50 each, and kiwis are $0.30 each.How many of each kind did she buy if she bought 9 more pears than pineapples and 2 fewer kiwis than pears? Branliest if correct.
Answer:
Number of pineapples = 10
Number of pears = 10 + 9 = 19
Number of kiwis = 10 - 2 = 8
Step-by-step explanation:
Money = $ 13.5
Cost of a pear = $ 0.5
Cost of a pineapple = $ 1.5
Cost of a kiwi = $ 0.3
let the number of pineapple = p
Number of pears = p + 9
Number of kiwis = p - 2
Cost is
0.5 (p + 9) + 0.15 p + 0.3 (p - 2) = 13.5
0.5 p + 4.5 + 0.15 p + 0.3 p - 0.6 = 13.5
0.95 p = 9.6
p = 10
So, number of pineapples = 10
Number of pears = 10 + 9 = 19
Number of kiwis = 10 - 2 = 8
Answer:
3 pineapples 12 pears 10 kiwis
what is the difference between dot product and cross product?
Answer:
A dot product is the product of the magnitude of the vectors and the cos of the angle between them. A cross product is the product of the magnitude of the vectors and the sine of the angle that they subtend on each other.
Step-by-step explanation:
f(x)=2x1 + 16x2 + 7x3 + 4x4 -> min
Step-by-step explanation:
f(x)=(2x-1)square=0
it can be 0 or greater than 0
Hence,maximum value of (2x- 1)square=0
maximum value of (2x- 1square)+3=0+3=3
A game-show spinner has these odds of stopping on particular dollar values: 55% for $5, 20% for $25, 15% for $50, and 10% for $500. What are the odds of a player winning $5 or $25
Answer: 75%
Step-by-step explanation:
Name the following polynomial based on its degree and number of terms x to the power of 2 plus 6x - 4
Answer:
x²+6x-4 is answer maybe
What is the slope of (-0,-1) and (3,1)
Answer:
Step-by-step explanation:
(0, -1) & (3 ,1)
[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{1-[-1]}{3-0}\\\\=\frac{1+1}{3}\\\\=\frac{2}{3}[/tex]
