The right answer is: E, according to the Central Limit Theorem for proportionality. The statistic is inaccurate.
In probability theory, the central limit theorem establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed.
The Central Limit Theorem establishes that for a proportion p in a sample of size n:
The expected value is μ=р
The standard error is s=[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
In this problem, the expected value is different of the expected of μ=р , hence, the statistic is biased, and the correct option is E.
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8. You have an investment of $20,000 with
4.2% simple interest and weekly payments.
How much money (to the nearest dollar)
will you have after three years?
[A] $23,030
[B] $19,730
IC] $21,200
[D] $24,250
[E] $20,048
Answer:
[D] $ 24,250
Step-by-step explanation:
$24,250 dollar will I have after three years.
what is the probability that out of ten randomly selected 30 year olds in 1970. at least one did not earn more than his or her parents at age 30
Therefore the probability that out of ten randomly selected 30 year old in 1970. at least one did not earn more than his or her parents at age 30 is 0.8448
What is probability?The study of probabilities involves calculating the possibility that an event will occur or that a proposition is accurate. The probability of an event is a number between 0 and 1, where 0 often represents impossibility and 1 typically represents certainty.
Here,
It is found by reading so it says ten so we multiply 0.8300 10 times by one and one example 0.0830,0 0.8300, 0.8300 ,0.8300..... and so forth or else you will not get the correct answer, there is an easier way to put in the calculator but you figure that out
after we found that we get =
1−0.830010^10
Our response is 0.1552, so since it specifies "at least," we deduct 1.
= 1−0.1552
and our answer is :
= 0.8448
Therefore, the probability that out of ten randomly selected 30 year old in 1970. at least one did not earn more than his or her parents at age 30 is 0.8448
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Find values of p, q, r and s such that (2x + 3) (px^3 + qx^2+rx+ s) = 2x^4+ 13x^3 + 7x^2 + 18
Answer:
p = 1q = 5r = -4s = 6Step-by-step explanation:
You want values of p, q, r and s such that (2x + 3) (px^3 +qx^2 +rx +s) ≡ 2x^4 +13x^3 +7x^2 +18.
Find coefficientsMultiplying out the left side of the equation, we have ...
2px^4 +(3p+2q)x^3 +(2r +3q)x^2 +(2s +3r)x +3s
Match coefficientsWhen we match coefficients between the two polynomials, this gives rise to 5 equations in the four unknown values:
2p = 23p +2q = 132r +3q = 72s +3r = 03s = 18The first and last equations tell us ...
p = 2/2 = 1
s = 18/3 = 6
Using these values in the 2nd and 4th equations makes them be ...
3 +2q = 13 ⇒ q = 10/2 = 5
12 +3r = 0 ⇒ r = -12/3 = -4
The values of p, q, r, s are ...
p = 1q = 5r = -4s = 6__
Check
We can use the 3rd equation to check these results:
2r +3q = 7
2(-4) +3(5) = 7
-8 +15 = 7 . . . . . . . true
The zeros for this function are -7, 2, and -3. Verify the zeros. Show all working
(-3)^(3) + 8(-3)^(2) + (-3) - 42
The polynomial p(x) = x³ + 8 · x² + x - 42 contains the zeros - 7, 2 and - 3.
How to derive a polynomial that contains a given set of real roots
Polynomials are algebraic expressions, whose standard form is shown below:
p(x) = Σ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., m}
Where:
cₙ - n-th Coefficientm - Grade of the polynomialAnd whose factor form is:
p(x) = a · Π (x - rₙ), for n = {1, 2, 3, ..., m}
Where:
a - Lead coefficientrₙ - n-th ZeroIn this problem we need to find a polynomial whose zeros are only real and represented by r₁ = - 7, r₂ = 2 and r₃ = - 3, respectively. If we know that a = 1, r₁ = - 7, r₂ = 2 and r₃ = - 3, then the factor form of the polynomial is:
p(x) = 1 · (x + 7) · (x - 2) · (x + 3)
p(x) = (x + 7) · (x - 2) · (x + 3)
p(x) = (x + 7) · (x² + x - 6)
p(x) = x³ + x² - 6 · x + 7 · x² + 7 · x - 42
p(x) = x³ + 8 · x² + x - 42
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Find a formula for RN for the function f(x) = (5x)2 on [1, 5] in terms of N.
Could you please show the work? I was able to get the area but can't exactly figure out what they want for the formula.
The formula for R(N) for the function f(x) = (5x)2 on [1, 5] in terms of N is R(N) = [tex]100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}[/tex] and area is 767(approx).
In the given question, we have to find a formula for R(N) for the function f(x) = (5x)^2 on [1, 5] in terms of N.
The given function is f(x) = (5x)^2 on [1, 5].
∆x = (5-1)/N
∆x = 4/N
X = 1+i∆x
X = 1+i4/N
f(x) = 25X^2
f(x) = 25(1+i4/N)^2
f(x) = 25(1+i8/N+16/N^2 i^{2})
R(N) = [tex]\sum_{i=1}^{N}f(X)\Delta x[/tex]
Now putting the value of f(x) and ∆x
R(N) = [tex]\sum_{i=1}^{N}\frac{4}{N}\left[25\left(1+\frac{8}{N}i+\frac{16}{N^2}i^{2}\right)\right][/tex]
R(N) = [tex]\frac{100}{N}\sum_{i=1}^{N}\left(1+\frac{8}{N}i+\frac{16}{N^2}i^{2}\right)[/tex]
R(N) = [tex]\frac{100}{N}\left(\sum_{i=1}^{N}1+\sum_{i=1}^{N}\frac{8}{N}i+\sum_{i=1}^{N}\frac{16}{N^2}i^{2}\right)[/tex]
R(N) = [tex]\frac{100}{N}\left(N+\frac{8}{N^2}\sum_{i=1}^{N}i+\frac{16}{N^3}\sum_{i=1}^{N}i^{2}\right)[/tex]
R(N) = [tex]\frac{100}{N}\left(N+\frac{8}{N^2}\frac{N(N+1)}{2}+\frac{16}{N^3}\frac{N(N+1)(2N+1)}{6}\right)[/tex]
R(N) = [tex]\frac{100}{N}\times N+\frac{100}{N}\times\frac{8}{N^2}\times\frac{N(N+1)}{2}+\frac{100}{N}\times\frac{16}{N^3}\times\frac{N(N+1)(2N+1)}{6}[/tex]
R(N) = [tex]100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}[/tex]
Now finding the area
[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = [tex]\text{lim}_{N\rightarrow \infty}\left[100+400\times\frac{(N+1)}{N^2}+\frac{800}{3}\times\frac{(N+1)(2N+1)}{N^3}\right][/tex]
[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 100 + 400 + 800/3
[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 766.67
[tex]\text{lim}_{N\rightarrow \infty}[/tex]R(N) = 767(approx)
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What are the domain and range of the function shown on this graph?
Domain is z>0, and range is y ≥ 0.
O Domain is 0 ≤z ≤0, and range is 0 ≤ y ≤ 200.
O Domain is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
O Domain is all real numbers, and range is all real numbers.
and range is y ≥ 0.
Distance
300
275
250
200
175
150
125
100
75
50
2
The domain and range of the function shown on the graph are (a) Domain is x ≥ 0, and range is y ≥ 0
How to determine the domain and the rangeFrom the question, we have the following parameters that can be used in our computation:
The graph
On the graph, we can see that the line is a straight line
This means that the graph is a linear function
However, the function only covers the positive axes
This means that
Domain is x ≥ 0, and range is y ≥ 0
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Please help me!
I need to deliver it tomorrow.
Step-by-step explanation:
10.
-2 < 6x - 2 < 46
0 < 6x < 48
0 < x < 8
so the line goes (with empty dots because of "<") from 0 to 8.
11.
4 + 9r <= 58 or 7r - 3 >= 46
9r <= 54 or 7r >= 49
r <= 6 or r >= 7
the line goes (with filled dots because of ">=" and "<=") from 6 all the way to the left, and from 7 all the way to the right.
12.
filled dot at -4, empty dot at +3.
connecting line between both dots.
-4 <= x < 3
13.
filled dots at -1 and at +6.
lines going away left and right.
x <= -1 or x >= 6
14.
empty dots at +3 and +4.
lines going away left and right.
x < 3 or x > 4
15.
filled dot at +6, empty dot at +8.
connecting line between both dots.
6 <= x < 8
I need help please….
The slope of the line as per the given points will be equal to 7/10.
What is the slope?It is possible to determine a line's direction and steepness by looking at its slope.
Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the given information in the question,
The given points are (25, 24) and (15, 17)
Use the formula to find the slope,
m = (y₂ - y₁)/(x₂ - x₁)
Substitute the values in the above formula,
m = (17 - 24)/(15 - 25)
m = -7/-10
m = 7/10
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The vertices of ABC are A(2,-1), B(0, 4), and C-3,5). Find the coordinates of the vertices of the image after the translation (x, y)-(x-1, y + 3).
Answer:
A(1,2), B(-1,7) C(-4,8)
Step-by-step explanation:
I think that is the answer.
Multiply. –4x(7 – 3x)
–28x – 3x^2
7 + 12x^2
–3x – 7x^2
–28x + 12x^2
Find the volume of the olid cone obtained by rotating the region bounded by the line y=12x, y=0, and x=4 about the x-axi
The volume of the solid cone obtained by rotating the region bounded by the line y=12x, y=0, and x=4 about the x-axis is 38603.89 [tex]unit^{3}[/tex]
We will calculate the volume in the following way,
Given lines are: x=4, y=0, y=12x
First, we make a triangle from the given equation and then rotate it along the x-axis to get the dimensions of the cone.
We, need to put x=4 and y=0 in y=12x to get all the vertices of the triangle.
Points are: (0, 0), (4, 0), and (4, 48).
Now, we rotate this triangle about the x-axis.
Thus, the radius of the cone(r)= 48 and the height of the cone(h)= 4.
Therefore, the formula for the volume of the cone (v)= [tex]\frac{4}{3}*(\pi *r^{2}*h )[/tex]
=[tex]\frac{4}{3} \pi*48^{2}*4[/tex]
=38603.89 [tex]units^3[/tex]
Therefore the volume obtained is 38603.89 [tex]unit^{3}[/tex]
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An airplane is descending from 35600 ft at 3200ft per mile,
what is the equation for altitude? altitude=a time=t
Also, What is the unit rate of change?
I also have to graph please help!
Answer:
Step-by-step explanation:
Let y be the altitude and x the distance the plane travels from the point of the 35600 ft altitude location (x=0 at that point)
y = 35600 - 3200x
It would be nice to use time instad of distance, but there is no speed of the plane give. It's altitude is espressed only on the basis of miles traveled. If the elevation change were given in feet per minute, or some other unit of time, we can write an equation with time as the x variable.
This equations says:
1) the plane starts at 35,600 ft (since x = 0, the result is 35,600 feet).
2) it descends 2,300 ft for every mile traveled from x = 0.
The unit rate of change is 3200 feet/mile.
The graph is attached.
x (2x - 4) = (2x + 1) (x - 2) solve
Answer:
2
Step-by-step explanation:
First distribute the first x into the first parenthesis: x (2x - 4) = (2x + 1) (x - 2)
x times 2x is [tex]2x^{2}[/tex] and x times -4 is -4x
This changes the equation to: [tex]2x^{2}[/tex]-4x = (2x + 1) (x - 2)
Now multiply the other parentheses: [tex]2x^{2}[/tex]-4x = (2x + 1) (x - 2)
Do this by using the Foil method (I attached a picture of the method if you don't know it)
First: (2x + 1) (x - 2)
Do 2x times x which = [tex]2x^{2}[/tex]
Then 2x times -2 which = -4x
Then 1 times x which = x
Lastly, 1 times -2 which = -2
The order you do this is the order that the foil method says.
Now the equation is:
[tex]2x^{2}[/tex]-4x =[tex]2x^{2}[/tex]-4x+x-2 (I just added all the numbers we just got)
Next cancel out the equal terms. To combine like terms you'd usually move the right [tex]2x^{2}[/tex] over to the left one and subtract it. But since they are the same number, subtracting it would leave you with 0. So you can just get rid of both.
You can also do this with both -4x
This leaves you with:
0=x-2
Now you move the variable to the left
you also make it negative since it is going to the other side of the =
this leaves: -x=-2
You can't have a negative x so now you have to change the signs for both. Make them both positive.
Now you have x=2
so your answer is 2
Croissants cost 85p each and pain au chocolate cost 95p each. Didier buys 22 pastries and spends a total of £20. How many croissants and how many pain au chocolat did he buy?
Answer:
croissants: 10 pain au chocolat: 12
Step-by-step explanation:
85c + 95p = 2000
c + p = 22
85c + 95p = 2000
-
85c + 85p = 1870
10p = 120
p = 12
c + p = 22
c + 12 = 22
c = 10
Answer:
Step-by-step explanation: Let C be the number of croissants and P be the number of pain au chocolat that Didier buys. We know that C + P = 22 and 0.85C + 0.95P = 20.
We can solve this system of equations using substitution. First, we solve the first equation for P: P = 22 - C. Then, we substitute this expression for P into the second equation: 0.85C + 0.95(22 - C) = 20. Expanding the expression inside the parentheses and combining like terms, we get: 0.85C + 21.1 - 0.95C = 20.
Then, we can solve for C by moving all the terms to one side of the equation: -0.1C = -1.1. Dividing both sides by -0.1, we get: C = 11.
Substituting this value for C back into the equation P = 22 - C, we get: P = 22 - 11 = 11.
Therefore, Didier buys 11 croissants and 11 pain au chocolat.
a coin has two sides: heads and tails. a die has six sides, numbered through . if you flip the coin and roll the die, what is the probability that you flip ''heads'' and roll a number less than
The probability that you flip 'heads' and roll a number less than 5 is 1/3.
The probability of flipping heads is 1/2, and the probability of rolling a number less than 5 is 4/6.
The probability of both occurring is the product of the two probabilities, or 1/2 multiplied by 4/6, which is equal to 1/3.
This means that the probability of flipping heads and rolling a number less than 5 is 1/3.
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Graph the following equation y-2=1/2(x+5)
Answer: I could be wrong, but I tried my best.
Slope: 1/2
Y-intercept: (0, 6)
Step-by-step explanation:
When an investor considers putting their money into a potentially high rate of return investment, they should understand there will be
risk involved with the investment. Higher potential returns often come with a higher level of risk, as the investor is taking on the possibility of losing some or all of their investment in exchange for the chance to earn a higher return. It's important for investors to carefully consider the level of risk they are comfortable with and to do their due diligence before making any investment decisions. This may include researching the company or investment, reviewing financial statements, and consulting with financial professionals. Investors should also consider the potential tax implications of any investment, as well as how it fits into their overall financial plan.
Work out the circumference of this circle. Take pi to be 3.142 and give your answer to 1 decimal place.
9m
ok i can di it...... ..........
The solution is 28.3 m
The circumference of the circle whose radius is 4.5 m is 28.3 m
What is a Circle?
A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The perimeter of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle
Given data ,
Let the circumference of the circle be represented as C
Now , the equation will be
The diameter of the circle = 9 m
The radius of the circle r = d/2 = 4.5 m
And , the circumference of the circle C = 2πr
Substituting the values in the equation , we get
Circumference of the circle C = 2 x 3.142 x 4.5
Circumference of the circle C = 28.278 m
Therefore , the value of C is 28.3 m
Hence , the circumference of the circle is 28.3 m
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Please help me respond this question. I am struggling!
Viktor is in the 60th percentile, which is 85, while the percentile for 71 is 26.666.
What is percentile?Percentile is defined as the value below which a given percentage falls under. Ben, for instance, is the fourth tallest child in a group of 20, and eighty percent of the kids are shorter than you. As a result, Ben is in the 80th percentile.
We have the data
Sort the data as follows: 58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96
employing the percentile formula,
Percentile is calculated as follows: 71 Percentile
(4 / 15)*100 Percentile
26.666 Percentile = (Number of Values Below "x" / Total Number of Values) 100
Consequently, 71's percentile is equal to 26.666.
Identifying the rank
Thus, the ranking is 0.6.
To find the rank for viktor
Find the percentile using the formula,
Percentile = Rank × Total number of the data set
Percentile = 0.6 × 15
Percentile = 9
Now, counting 9 values from left to right we reach 85, and we can say that all the values below 85 will come under the 60th percentile. In other words, 60% of the values are below 85.
The 60th percentile is 85
Thus viktor is in 60th percentile is 85
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19) Which two integer values is 17 between?
C) 3 and 4
A) 13 and 14
B) 5 and 6
D) 2 and 3
Answer: D
Step-by-step explanation:
The exact answer is 2.571281591, which is between:
D) 2 and 3
Find the 5th term in this sequence n²-4n
Answer: 5
Step-by-step explanation:
(5^2) - (4 x 5)
The shape on the left is transformed to the shape on the right.
Triangle W X Y is rotated to triangle W prime X prime Y prime.
Which of the following statements describes the transformation?
W prime X prime Y prime right-arrow W X Y
W X Y right-arrow W prime X prime Y prime
W X Y right-arrow Y prime X prime W prime
X prime Y prime W prime right-arrow W X Y
Answer:
It seems that you are describing a geometric transformation in which triangle WXY is rotated to form triangle W'X'Y'. The correct statement describing this transformation is: "WXY right-arrow W'X'Y'". In this transformation, the triangle is rotated in some way, resulting in the new triangle W'X'Y'.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Which of the following are possible side lengths
for a triangle?
A. 8, 16,4
B. 3, 6, 9
C. 3, 12, 10
Answer:
C. 3, 12, 10---------------------------
According triangle inequality theorem the sum of any two sides of a triangle is greater than the third side.
Apply this to our options, add up the two shortest sides and compare with the longest side.
Option A8 + 4 < 16, no, it is impossible to build a triangle.Option B3 + 6 = 9, no, it is impossible to build a triangle.Option C3 + 10 > 12, yes, possible triangle.I need help on this Math. It was due so long ago.
Answer:
y-intercept: (0,4)
y-intercept in the coordinate form: (0,4)
The equation in slope-intercept form: y=7x+4
Step-by-step explanation:
The slope is rise/run
We see that the y increase by 28 and the x increase by 4, so the slope is 28/4 = 7
m = 7
We know that the y-intercept is at (0,4)
So the slope-intercept equation will be
y = 7x + 4
Answer:
y- intercept = 0.4
y- intercept in the coordinate = 0.4
so the equation is : y=7x+4
The scores for assessments are displayed in the box-and-whiskers plot below. What is the range of the middle 50% of the data of scores on the assessment?
The range of the middle 50% of the data of scores on the assessment is 10.
Option A is the correct answer.
What is a range in a set of data?The range is the difference between the highest value and the lowest value of a given set of data.
We have,
Median = 80
First quartile = 70
Third quartile = 90
The Middle 50% is from the Median to the First quartile.
Range.
= 80 - 70
= 10
Thus,
The range is 10.
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consider the following birthday problem. if we randomly selected 3 people born in 2001, what's the probability that they all have different birthdays?
Probability that any one of three outcomes will occur: P(A, B, C), plus P(A, B, C'), plus P(A, B', C);
What is the probability that 3 people have different birthdays?
Since there are 363 days still “unused” out of 365, we have p = 363÷365 = about 0.9945. Multiply that by the 0.9973 for two people and you have about 0.9918, the probability that three randomly selected people will have different birthdays.
Poisson Way. The probability of same-birthdays triplet is 1 / (365 * 365), which is very small, and there are C(n, 3) triplets, which is a big number for the moderately high values of n (~>20).
Calculating the likelihood of three events
Probability that at least one of the three events occurs: Probability that each of the three occurrences will occur: P(A, B, C);
Probability that any one of three outcomes will occur: P(A, B, C), plus P(A, B, C'), plus P(A, B', C);
P() is the likelihood that none of the events will occur.
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a sampling technique that is based on the cumulative effect of information that every additional item in the sample adds as it is inspected is called:
A sampling technique that is based on the cumulative effect of information that every additional item in the sample adds as it is inspected is called: sequential sampling.
What is sequential sampling?
Sequential sampling is a non-probability sampling strategy where the researcher selects one or more populations within a time frame, conducts his research, evaluates the findings, and then selects further populations as necessary.
An auditor develops a set of three groups of sampling units, where each successive group contains the same number of units to be sampled. The sampling plan is to continue to the next group of sampling units if the preceding group contains at least one deviation
Simple random sampling, systematic sampling, stratified sampling, and cluster sampling are examples of probability sampling techniques.
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the security system in a house has two units that set off an alarm when motion is detected. neither one is entirely reliable, but one or both always go off when there is motion anywhere in the house. suppose that for motion in a certain location, the probability that detector a goes off and detector b does not go off is 0.25, and the probability that a does not go off is 0.35. what is the probability that b goes off?
The probability that detector B goes off is 0.75
In this question we have been given the security system in a house has two units that set off an alarm when motion is detected.
Here, the probability that detector A will not go off is 0.35
And the probability that A will go off and B will not go off is 0.25
We need to find the probability that B goes off
The probability that detector A will go off would be,
1 - P( detector A will not go off )
= 1 - 0.35
= 0.65
And the probability that both A and B will go off would be,
= P(A will go off) - P( A will go off and B will not go)
= 0.65 - 0.25
= 0.40
Now we find the required probability.
P(B goes off) = P(both A and B will go off) + P(detector A will not go off)
= 0.40 + 0.35
= 0.75
Therefore, the required probability is 0.75
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Enter the value of x below.
x+8=12
Answer:
4
Step-by-step explanation:
x + 8 = 12
Subtract 8 from both sides :
x = 12 - 8
x = 4
Hope this helped and have a good day
Express the height of the tree in terms of
trigonometric ratios. (MGSE9-12.G.SRT.6, MGSE9-
12.G.SRT.7)
A. 90 cos 50°
B. 90 sin 50⁰
C. 90 cot 50°
D. 90 tan 50⁰
Answer:
x = 90 Tan 50
107.1
Step-by-step explanation:
Adjacent = 90
Height of the tree(opposite) = x
so what connects adjacent and opposite is TOA
Tanθ = opposite /Adjacent
Tan 50° = x/90
cross multiply
x = 90 Tan 50°
x = 90 × 1.19
x = 107.1m
:- the height of the tree is 107.1m
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