At a university of 25,000 students, 18% are older than 25. The registrar will draw a simple random sample of 242 of the students. The percentage of students older than 25 in the sample has an expected value of 18% and a standard error of:______.

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.

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.

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)

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

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.

The 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.

The 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.

Being 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:

Answer:

5x

Step-by-step explanation:

(75b x)x×2

---------------

(10b x)×3

=75b x×x×2

-----------------

10b x×3

=25x

-------

5

=5x

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.

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.

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

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]

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]

( 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.

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]

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

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

Answer:

gang nem

Step-by-step explanation:

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]

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

Answer:

27 inch

Step-by-step explanation:

Current perimeter=18

New perimeter=18*1.5=27 in

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

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]

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:)

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

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.

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)

Answer:

x = 65

Step-by-step explanation:

x = √(25×(25+144))

x = √(25×169)

x = 5×13

x = 65

Answered by GAUTHMATH

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

Answer: y = 0 and x = -1

Answer:

You dind't include the answer choices but it should look something like

[tex]50000(.8)^t[/tex]

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: