Answer:
Standard error of: 2.47%
Step-by-step explanation:
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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
18% are older than 25.
This means that [tex]p = 0.18[/tex]
Simple random sample of 242 of the students.
This means that [tex]n = 242[/tex]
Standard error:
By the Central Limit Theorem:
[tex]s = \sqrt{\frac{0.18*0.82}{242}} = 0.0247[/tex]
0.0247*100% = 2.47%
Standard error of: 2.47%
Charlie puts $50000 in a stock account, but it loses money at a rate of 20%
every month. Which of the expressions below models the number of dollars
Charlie's account has after t months?
Answer:
You dind't include the answer choices but it should look something like
[tex]50000(.8)^t[/tex]
Instructions: Find the missing length indicated.
Answer:
x = 65
Step-by-step explanation:
x = √(25×(25+144))
x = √(25×169)
x = 5×13
x = 65
Answered by GAUTHMATH
Tay–Sachs Disease Tay–Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, the probability that their offspring will develop the disease is approximately .25. Suppose a husband and wife are both carriers of the disease and the wife is pregnant on three different occasions. If the occurrence of Tay–Sachs in any one offspring is independent of the occurrence in any other, what are the probabilities ofthese events?
a. All three children will develop Tay–Sachs disease.
b. Only one child will develop Tay–Sachs disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.
Answer:
a) 0.0156 = 1.56% probability that all children will develop the disease.
b) 0.4219 = 42.19% probability that only one child will develop the disease.
c) 0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.
Step-by-step explanation:
For each children, there are only two possible outcomes. Either they carry the disease, or they do not. The probability of a children carrying the disease is independent of any other children, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The probability that their offspring will develop the disease is approximately .25.
This means that [tex]p = 0.25[/tex]
Three children:
This means that [tex]n = 3[/tex]
Question a:
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]
0.0156 = 1.56% probability that all children will develop the disease.
Question b:
This is P(X = 1). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.25)^{1}.(0.75)^{2} = 0.4219[/tex]
0.4219 = 42.19% probability that only one child will develop the disease.
c. The third child will develop Tay–Sachs disease, given that the first two did not.
Third independent of the first two, so just multiply the probabilities.
First two do not develop, each with 0.75 probability.
Third develops, which 0.25 probability. So
[tex]p = 0.75*0.75*0.25 = 0.1406[/tex]
0.1406 = 14.06% probability that the third children will develop the disease, given that the first two did not.
what fraction of 1 day is 48 minutes
Answer:
48 ÷ 60 = 4/5
Step-by-step explanation:
4/5 is the answer
Answer:
[tex]\frac{1}{30}[/tex]
Step-by-step explanation:
We require the number of minutes in a day.
i hour = 60 minutes
24 hours = 24 × 60 = 1440 minutes ( 24 hours in 1 day )
Then
fraction = [tex]\frac{48}{1440}[/tex] ( divide numerator/ denominator by 12 )
= [tex]\frac{4}{120}[/tex] ( divide numerator/ denominator by 4 )
= [tex]\frac{1}{30}[/tex]
PLEASE HELP!!!!!!!!! DUE ASAP I WILL GIVE BRAINLIEST!!!!!!!!
Explanation:
A = values on the die greater than 1
A = {2,3,4,5,6}
B = values on the die less than 5
B = {1,2,3,4}
Union those two sets together
C = A u B = {1,2,3,4,5,6}
Effectively, we get every possible value on the die. This is due to the "or" keyword. If it was "and", then it would be a difference story.
So the probability of getting anything in set C is 100% or just 1. We have guaranteed certainty we'll have this event happen.
Question 6 of 10
The domain of a function f(x) is x = 0, and the range is ys -1. What are the
domain and range of its inverse function, '(x)?
Answer: y = 0 and x = -1
Pls solve this for me ryt now wai abeg
...The first three terms of an arithmetic progression (A.P) are (x+1),(4x-2) and(6x-3) respectively .If the last term is 18,find the
a.Value of x b.Sum of the terms of the progression
Answer:
[tex]x = 2[/tex]
[tex]S_n = 63[/tex]
Step-by-step explanation:
Given
[tex]a_1 = x + 1[/tex]
[tex]a_2 = 4x -2[/tex]
[tex]a_3 = 6x -3[/tex]
[tex]a_n = 18[/tex]
Solving (a): x
To do this, we make use of common difference (d)
[tex]d = a_2 - a_1[/tex]
[tex]d = a_3 - a_2[/tex]
So, we have:
[tex]a_3 - a_2 = a_2 - a_1[/tex]
Substitute known values
[tex](6x - 3) - (4x - 2) = (4x - 2) - (x + 1)[/tex]
Remove brackets
[tex]6x - 3 - 4x + 2 = 4x - 2 - x - 1[/tex]
Collect like terms
[tex]6x - 4x- 3 + 2 = 4x - x- 2 - 1[/tex]
[tex]2x- 1 = 3x- 3[/tex]
Collect like terms
[tex]2x - 3x = 1 - 3[/tex]
[tex]-x = -2[/tex]
[tex]x = 2[/tex]
Solving (b): Sum of progression
First, we calculate the first term
[tex]a_1 = x + 1[/tex]
[tex]a_1 = 2 + 1 = 3[/tex]
Next, calculate d
[tex]d = a_2 - a_1[/tex]
[tex]d = (4x - 2) - (x +1)[/tex]
[tex]d = (4*2 - 2) - (2 +1)[/tex]
[tex]d = 6 - 3 = 3[/tex]
Next, we calculate n using:
[tex]a_n = a + (n - 1)d[/tex]
Where:
[tex]a_n = 18[/tex]
[tex]d = 3; a = 3[/tex]
So:
[tex]18 = 3 +(n - 1) * 3[/tex]
Subtract 3 from both sides
[tex]15 = (n - 1) * 3[/tex]
Divide both sides by 3
[tex]5 = n - 1[/tex]
Add 1 to both sides
[tex]6 = n[/tex]
[tex]n = 6[/tex]
The sum of the progression is:
[tex]S_n = \frac{n}{2} * [a + a_n][/tex]
So,, we have:
[tex]S_n = \frac{6}{2} * [3 + 18][/tex]
[tex]S_n = 3 * 21[/tex]
[tex]S_n = 63[/tex]
6.(a) A laptop was bought at Canadian $ 770. If the tax of 20% and 13% VAT should be paid, find the least selling price of it in Nepali rupee that prevents the shopkeeper from loss?
The LEAST selling price of the laptop should be ;
$1024.1 in other to avoid loss.
Price of laptop = $770
Tax = 20%
VAT = 13%
TO avoid loss ;
both the VAT percentage and TAX must be added to the price of the laptop:
Total percentage = VAT + TAX = (20 + 13) = 33%
THEREFORE, Least selling price should be :
Price of laptop * (1 + 33%)
770 * 1.33
= $1024.1
Learn more about TAX :
https://brainly.in/question/31818297
Solve using the addition principle. 3y - 11 ≤ 2y - 2
Answer:
y ≤ 9
Step-by-step explanation:
3y - 11 ≤ 2y - 2
Subtract 2y from each side
3y-2y - 11 ≤ 2y-2y - 2
y - 11 ≤ - 2
Add 11 to each side
y - 11+11 ≤ - 2+11
y ≤ 9
Answer:
[tex]y \leqslant 9[/tex]
Step-by-step explanation:
[tex]3y - 11 \leqslant 2y - 2 \\ 3y - 2y \leqslant 11 - 2 \\ y \leqslant 9[/tex]
some1 help please :) dont answer if u are not 100% sure thank you
Answer:
Step-by-step explanation:
It's never negative.
D is indeed correct, the function's values never go below 0, meaning never below the x-axis
I need help please thank you
Answer:
A
Step-by-step explanation:
in the question given, the goal is to rationalize the denominator, or in other words get rid of any square roots.
recall this formula :
(a-b)(a+b) = a^2 - b^2
in this case, to rationalize the denominator of 3 - [tex]\sqrt{6x}[/tex] , we will multiply it and the numerator by its conjugate. the conjugate of 3 -
after multiplying the denominator by its conjugate, we get:
(3 - [tex]\sqrt{6x}[/tex]) (3 +
at this point there is no need to solve the numerator as there is only one answer with this denominator.
hope this helps :)
Answer:
Step-by-step explanation:
(x2 + 3x + 1) + (2x2 + 2x)
HINT
Answer:
3x^2+5x+1
Step-by-step explanation:
(x^2 + 3x + 1) + (2x^2 + 2x)
Combine like terms
x^2 + 2x^2 + 3x +2x +1
3x^2+5x+1
Answer:
[tex]3x^{2} + 5x + 1[/tex]
Step-by-step explanation:
Step 1: Combine like terms
[tex](x^{2} + 3x + 1) + (2x^{2} + 2x)[/tex]
[tex](x^{2} + 2x^{2} + (3x + 2x) + (1)[/tex]
[tex]3x^{2} + 5x + 1[/tex]
Answer: [tex]3x^{2} + 5x + 1[/tex]
Estimating Mean SAT Math Score
Type numbers in the boxes.
aby Part 1: 5 points
The SAT is the most widely used college admission exam. (Most community
aby Part 2: 5 points
colleges do not require students to take this exam.) The mean SAT math score
varies by state and by year, so the value of u depends on the state and the year. 10 points
But let's assume that the shape and spread of the distribution of individual SAT math scores in each
state is the same each year. More specifically, assume that individual SAT math scores consistently
have a normal distribution with a standard deviation of 100. An educational researcher wants to
estimate the mean SAT math score (u) for his state this year. The researcher chooses a random
sample of 661 exams in his state. The sample mean for the test is 494.
Find the 99% confidence interval to estimate the mean SAT math score in this state for this year.
(Note: The critical z-value to use, zc, is: 2.576.)
Your answer should be rounded to 3 decimal places.
Answer:
(483.981 ; 504.019)
Step-by-step explanation:
Given :
σ = 100
Sample size, n = 661
xbar = 494
We use the Z distribution since we are working with the population standard deviation ;
C.I = xbar ± (Zcritical * σ/√n)
Zcritical at 99% = 2.576
C.I = 494 ± (2.576 * 100/√661)
C.I = 494 ± 10.019
Lower boundary = (494−10.019) = 483.981
Upper boundary = (494+10.019) = 504.019
C.I = (483.981 ; 504.019)
All of the following are equivalent except
x-7
X-(-7)
-7+x
x+(-7)
Answer:
X-(-7)
Step-by-step explanation:
If you are subtract by a negative number it turns it into a positive. It would look like this: X+(+7)
(x)=4log(x+2) Which interval has the smallest average rate of change in the given function? 1≤x≤3 5≤x≤7 3≤x≤5 −1≤x≤1
Answer:
5≤x≤7
Step-by-step explanation:
For a given function f(x), the average rate of change in a given interval:
a ≤ x ≤ b
is given by:
[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]
Here we have:
f(x) = 4*log(x + 2)
And we want to see which interval has the smallest average rate of change, so we just need fo find the average rate of change for these 4 intervals.
1) 1≤x≤3
here we have:
[tex]r = \frac{f(3) - f(1)}{3 - 1} = \frac{4*log(3 + 2) - 4*log(1 + 2)}{2} = 0.44[/tex]
2) 5≤x≤7
[tex]r = \frac{f(7) - f(5)}{7 - 5} = \frac{4*log(7 + 2) - 4*log(5 + 2)}{2} = 0.22[/tex]
3) 3≤x≤5
[tex]r = \frac{f(5) - f(3)}{5 - 3} = \frac{4*log(5 + 2) - 4*log(3 + 2)}{2} = 0.29[/tex]
4) −1≤x≤1
[tex]r = \frac{f(1) - f(-1)}{1 - (-1)} = \frac{4*log(1 + 2) - 4*log(-1 + 2)}{2} = 0.95[/tex]
So we can see that the smalles average rate of change is in 5≤x≤7
A rectangle has a length of 7 in. and a width of 2 in. if the rectangle is enlarged using a scale factor of 1.5, what will be the perimeter of the new rectangle
Answer:
27 inch
Step-by-step explanation:
Current perimeter=18
New perimeter=18*1.5=27 in
Simplify the following expression:
(15b^5)^2
—————-
(5b^2)^3
Answer:
5x
Step-by-step explanation:
(75b x)x×2
---------------
(10b x)×3
=75b x×x×2
-----------------
10b x×3
=25x
-------
5
=5x
answer this question ASAP
Answer:
972pi in ^3
Step-by-step explanation:
We need to find the volume of the sphere
V = 4/3 pi r^3
The diameter is 18
r = d/2 = 18/2 = 9
V = 4/3 pi ( 9)^3
V = 972pi in ^3
What's the next number in the sequence 16, 4, 1,
Answer:
0.25
Step-by-step explanation:
16/4 = 4
4/4 = 1
1/4 = 0.25
0.25/4 = 0.0625
0.0625/4 = 0.015625
give me brainliest please:)
Translate and solve: fife less than z is 4
Answer:
z=9
Step-by-step explanation:
z-5=4. /+5
z=4+5
z=9
Answer:
z<-1
Step-by-step explanation:
5<z=4
collect like terms
z=<4-5
z<-1
If f(×)=16×-30 and g(×)=14×-6, for which value of x does (f-g)(x)=0
Answer: [tex]x=12[/tex]
Step-by-step explanation:
[tex]f(x)=16x-30\\g(x)=14x-6[/tex] are the equations that you've given us.
Now if we plot these two equations on the graph we notice there's an intersection at (12,162). Therefore meaning that [tex]x=12[/tex].
We can prove that by doing the following calculations to prove that both sides are equal to each other.
The left side of the equal sign:
Step 1: Write the equation down:
[tex]16x-30[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]16(12)-30[/tex]
Step 3: We will multiply [tex]16*20[/tex] first, giving us 192.
[tex]192-30[/tex]
Step 4: Subtract 192 from 30. Which gives us 162.
[tex]162[/tex]
The right side of the equal sign:
Step 1: Write the equation down:
[tex]14x-6[/tex]
Step 2: Substitute x for the numerical value we found.
[tex]14(12)-6[/tex]
Step 3: We will multiply [tex]14*12[/tex] first, giving us 168.
[tex]168-6[/tex]
Step 4: Subtract 168 from 6. Which gives us 162.
[tex]162[/tex]
We know that [tex]x=12[/tex] because when substituting x with 12, we get 162 on both sides. Therefore making this statement true and valid.
[tex]162=162[/tex]
Last question I need help on
( x + 1 )( x )( x - 5 ) =
( x + 1 )( x - 5 )( x ) =
( x^2 - 4x - 5 )( x ) =
x^3 - 4x^2 - 5x
Step-by-step explanation:
the other answer is basically correct.
as the simplest form you create 3 terms for the three given solutions (= the values for when the equation equals 0).
but maybe you need to add " = 0" for the full equation.
Make x the subject
5y + 2x = 25
Answer:
x = -5/2 y +25/2
Step-by-step explanation:
5y + 2x = 25
Subtract 5y from each side
5y + 2x -5y= -5y+25
2x = -5y +25
Divide by 2
2x/2 = -5y/2 +25/2
x = -5/2 y +25/2
How many numbers multiple of 3 are in the range [2,2000]?
Answer:
There are 666 numbers multiple of 3 in the interval.
Step-by-step explanation:
Multiples of 3:
A number is a multiple of 3 if the sum of it's digits is a multiple of 3.
Range [2,2000]:
First multiple of 3 in the interval: 3
Last: 1998
How many:
[tex]1 + \frac{1998 - 3}{3} = 1 + 665 = 666[/tex]
There are 666 numbers multiple of 3 in the interval.
You have collected data about the fasting blood glucose (FBG) level of participants in your study. You are delighted to find that the variable is normally distributed. If the mean FBG is 82 and the standard deviation is 2.8 in what range would you expect to find the FBG of 68% of your study participants
Answer:
Between 79.2 and 84.8.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean of 82, standard deviation of 2.8.
In what range would you expect to find the FBG of 68% of your study participants?
By the Empirical Rule, within 1 standard deviation of the mean, so:
82 - 2.8 = 79.2
82 + 2.8 = 84.8
Between 79.2 and 84.8.
Test scores are normally distributed with a mean of 68 and a standard deviation of 12. Find the z – score for a grade of 74. Round your answer to two numbers after the decimal.
Answer:
gang nem
Step-by-step explanation:
Companies are starting to use 360-degree surveys to evaluate the performance of their employees. This approach uses annonymous feedback from a variety of people who work closely with the employee. People who fill out the survey could be coworkers, supervisors, subordinates, or even customers. It is different from a traditional performance review, which relies only on feedback from an employee's supervisor. Many prefer the 360-degree approach because it provides a more well-rounded perspective on how the employee performs in their job role. Supervisers can be biased because they do not interact with the employee in the same way that a customer or co-worker might. However, the 360-degree survey approach still relies only on subjective feedback, which does not always give a fair representation of the employee's work?
Answer:
the study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural lawsthe study of and knowledge about the physical world and natural laws
Instructions: Given the vertex of a quadratic function, find the axis
of symmetry.
Vertex: (5,7)
Taking into account the definition of axis of simmetry and vertexn the axis of symmetry is x = 5.
So, first of all, you must know what a quadratic function is. Every quadratic function can be expressed as follows:
f(x) = a*x² + b*x + c
where a, b and c are real numbers.
Axis of symetryThe graph of a quadratic function is a parabola. Every parabola is a symmetric curve with respect to a horizontal line called the axis of symmetry.
That is, the axis of symmetry is an imaginary line that passes through the middle of the parabola and divides it into two halves that are equal of each other.
In other words, the axis of symmetry of a parabola is a vertical line that divides the parabola into two equal halves and always passes through the vertex of the parabola.
VertexThe point of intersection of the axis of symmetry with the parabola is called the vertex.
The axis of symmetry always passes through the vertex of the parabola. The x-coordinate of the vertex is the equation of the axis of symmetry of the parabola.
SummaryBeing the vertex of the quadratic function (5,7), where the vertex on the x-axis has a value of 5 and on the y-axis a value of 7, the axis of symmetry is x = 5.
Learn more with this examples:
https://brainly.com/question/2799442?referrer=searchResultshttps://brainly.com/question/20862832?referrer=searchResultshttps://brainly.com/question/15266651?referrer=searchResultsSamantha 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
Knowing that AQPT - AARZ, a congruent angle pair is:
Answer:
Angle T is congruent to Angle Z
Step-by-step explanation:
Since the 2 triangles are equal, that means that each pair of angles are also congruent. To know which angles are congruent, you check th order of how the triangles are named. Ex. Angle Q is congruent to Angle A, Angle P is congruent to Angle R, and Angle T is congruent to Angle Z.
