What is the inverse of f(x)=3x-2/6 ?

Answer:

The required sample size increases.

Step-by-step explanation:

The margin of error of a confidence interval is given by:

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which z is related to the confidence level(the higher the confidence level the higher z), [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

In this question:

The confidence level decreases, so z decreases.

For the margin of error to stay the same, the sample size also has to decrease.

The required sample size increases.

Answer:

Step-by-step explanation:

This equation is true in either case, because the expression [tex]\sqrt{2x} +3[/tex] is equivalent to itself, that means the equation is true for all positive real numbers including the zero.

Therefore, the right answers are B and D, both numbers are true solutions of the expression.

Answer:

A: x=1/2  is an extraneous solution.

Step-by-step explanation:

Answer:

u forgot picture

Step-by-step explanation:

if not then define ea

werido modz... up for a laugh? I can't answer a question that is measure ea with no picture nor any info

Answer:

The nth term rule of the quadratic sequence is [tex]2n^{2} +5n-3[/tex].

Step-by-step explanation:

We are given the following quadratic sequence below;

4, 15, 30, 49, 72, 99, 130,...

As we know that the formula for the nth term of the quadratic sequence is given by =  [tex]an^{2}+bn+c[/tex]

Firstly, we will find the difference between the term of the given sequence;

1st difference of the given sequence;

(2nd term - 1st term), (3rd term - 2nd term), (4th term - 3rd term), (5th term - 4th term), (6th term - 5th term), (7th term - 6th term)

= (15 - 4), (30 - 15), (49 - 30), (72 - 49), (99 - 72), (130 - 99),....

= (11, 15, 19, 23, 27, 31,.....)

Now, we will find the second difference of the given sequence, i.e;

= (15 - 11), (19 - 15), (23 - 19), (27 - 23), (31 - 27),....

= (4, 4, 4, 4, 4)

Since the differences are same now, so to find the value of a we have to divide the value of second difference by 2, i.e;

The value of a  =  [tex]\dfrac{4}{2}[/tex] = 2

SO, the first term of the nth term rule equation is [tex]an^{2}[/tex] = [tex]2n^{2}[/tex].

Now, in the term [tex]2n^{2}[/tex], put the value of n = 1, 2, 3, 4 and 5 and then form the sequence, i.e;

If n = 1, then [tex]2n^{2}[/tex] = [tex]2 \times (1)^{2}[/tex] = 2

If n = 2, then [tex]2n^{2}[/tex] = [tex]2 \times (2)^{2}[/tex] = 8

If n = 3, then [tex]2n^{2}[/tex] = [tex]2 \times (3)^{2}[/tex] = 18

If n = 4, then [tex]2n^{2}[/tex] = [tex]2 \times (4)^{2}[/tex] = 32

If n = 5, then [tex]2n^{2}[/tex] = [tex]2 \times (5)^{2}[/tex] = 50

SO, the sequence formed is (2, 8, 18, 32, 50).

Now, find the difference of this sequence and the original quadratic sequence, i.e;

= (4 - 2), (15 - 8), (30 - 18), (49 - 32), (72 - 50)

= (2, 7, 12, 17, 22)

Now, as we can see that the above sequence resembles the general form of (5n - 3) because:

If we put n = 1, then (5n - 3) = 5 - 3 = 2

If we put n = 2, then (5n - 3) = 10 - 3 = 7 and so on....

From this, we concluded that the value of b and c are 5 and (-3) respectively.

Hence, the nth term rule for the given quadratic sequence is [tex]2n^{2} +5n-3[/tex].

Answer:

921.165 feet

Step-by-step explanation:

Ok we are looking for the length of the base.

Now let's take the question and picture it as a triangle, we will find out that it looks like a right angle triangle.

The height= 645 feet

Angle of elevation= 35°

Base is unknown

To find the base

We recall that tan of angle

= opposite/adjacent

In this case

Angle= 35°

Opposite= height= 645

Adjacent= base

Tan 35 = 645/adj

Adj =645/tan 35

Adj =645/0.7002

Adj = 921.165

The base is 921.165 feet

Answer:

Step-by-step explanation:

Let x represent the rate of the freight train. If the rate of the passenger train is 15 MPH faster than the rate of the frieght train, it means that the rate of the passenger train is x + 15

Time = distance/speed

Time that it will take a passenger train to travel 245 miles is

245/(x + 15)

Time that it will take a fright train to travel 200 miles is

200/x

Since both times are the same, it means that

245/(x + 15) = 200/x

Cross multiplying, it becomes

245x = 200(x + 15)

245x = 200x + 3000

245x - 200x = 3000

45x = 3000

x = 3000/45 = 66.67 mph

Rate of freight train is 66.67 mph

Rate of passenger train is 66.67 + 15 = 81.67 mph

Answer:

y = 4x - 9

Step-by-step explanation:

Use the formula:

y = mx + b

Where m is the slope, b is the y-intercept.

The slope is 4.

y = 4x + b

The y-intercept is -9 because it passes through (0, -9).

y = 4x - 9

Answer:

70% of the reports will take 525 minutes (8 hours, 45 minutes) to file.

Step-by-step explanation:

Given;

total number of Meredith's report, N = 10

average time taken for each report to be filed is, t = 75 minutes per report

let the total time for the 10 reports = T

[tex]\frac{T}{N} = t\\\\T = N*t \\\\T = 10 *75\\\\T = 750 \ minutes[/tex]

The total time for the 10 reports is 750 minutes.

Time taken to file 70 % of 10 reports = (0.7 x 10) x (75 mins)

                                                             = 0.7 x 750

                                                             = 525 minutes (8 hours, 45 minutes)

Therefore, 70% of the reports will take 525 minutes (8 hours, 45 minutes) to file.

To solve this system, I would use substitution.

Since our first equation tells us that y = 2x - 3, we can substitute a

2x - 3 in for the y in our second equation to get 2x - 3 - 9 = -x.

Simplifying on the left we get 2x - 12 = -x.

Moving the 2x to the right, we have -12 = -3x.

Now divide both sides by -3 and we have 4 = x.

To find y, plug 4 back into either one of the original equations.

I'll go with the first one.

So we have y = 2(4) - 3.

Solving from here, we find that y = 5.

So the solution to this system is (4,5).

Answer:

Step-by-step explanation:

3n + 7

n = 3

Substitute the value of n into the expression

That's

3(3) + 7

= 9 + 7

Hope this helps you

Answer:

[tex]16[/tex]

Step-by-step explanation:

[tex]3n+7[/tex]

The value of [tex]n[/tex] is given 3.

Plug [tex]n[/tex] as 3.

[tex]3(3)+7[/tex]

Evaluate.

[tex]9+7[/tex]

[tex]=16[/tex]

Answer: 420 words

Step-by-step explanation:

First find how much he did the first day by doing 1/5*2400=480.

Then find out how much he did the second day by doing 2400-480=1920, then doing 1920*(2/3)=1280.

Then, because he did 220 words the third day, simply do 2400-480-1280-220=420.

Hope it helps <3

Ans420 words per min

Step-by-step explanation:

Answer:

[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]

The expected values for all the categories is :

[tex] E_i =\frac{150}{3}=50[/tex]

And then the statistic would be given by:

[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]

And the best option would be:

b. 4

Step-by-step explanation:

For this problem we have the following observed values:

Yes 40 No 60 No Opinion 50

And we want to test the following hypothesis:

Null hypothesis: All the opinions are uniformly distributed

Alternative hypothesis: Not All the opinions are uniformly distributed

And for this case the statistic would be given by:

[tex]\chi^2 = \sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]

The expected values for all the categories is :

[tex] E_i =\frac{150}{3}=50[/tex]

And then the statistic would be given by:

[tex]\chi^2 = \frac{(40-50)^2}{50}+\frac{(60-50)^2}{50}+\frac{(50-50)^2}{50}=4[/tex]

And the best option would be:

b. 4

Answer:

Hey!

69/8 as a mixed number is...

8 5/8!

To get this answer, simply divide 69 by 8, then subtract the WHOLE NUMBER from 69 and then the left over number is the numerator over 8

Hope this helps!

Answer:

8 5/8

Step-by-step explanation:

Answer:

20% probability that a box weighs more than 32.2 ounces

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X higher than x is given by the following formula.

[tex]P(X > x) = \frac{b-x}{b-a}[/tex]

Uniform distribution ranging from 31 to 32.5 ounces.

This means that [tex]a = 31, b = 32.5[/tex]

What is the probability that a box weighs more than 32.2 ounces?

[tex]P(X > 32.2) = \frac{32.5 - 32.2}{32.5 - 31} = 0.2[/tex]

20% probability that a box weighs more than 32.2 ounces

Answer:

To the RIGHT

Step-by-step explanation:

The parabola will open right if the y^2 is positive and will open left if the y^2 is negative.

The mass of the lamina is 6 units.

The center of mass of the lamina is (X,Y) = (-3/2, 9/2).

Here,

To find the mass and center of mass of the lamina, we need to integrate the density function ρ(x, y) over the triangular region D.

The mass (M) of the lamina is given by the double integral of the density function over the region D:

M = ∬_D ρ(x, y) dA

where dA represents the differential area element.

The center of mass (X,Y) of the lamina can be calculated using the following formulas:

X = (1/M) ∬_D xρ(x, y) dA

Y = (1/M) ∬_D yρ(x, y) dA

Now, let's proceed with the calculations:

The triangular region D has vertices (0, 0), (2, 1), and (0, 3). We can define the limits of integration for x and y as follows:

0 ≤ x ≤ 2

0 ≤ y ≤ 3 - (3/2)x

Now, let's calculate the mass (M):

M = ∬_D ρ(x, y) dA

M = ∬_D 2(x + y) dA

We need to set up the double integral over the region D:

M = ∫[0 to 2] ∫[0 to 3 - (3/2)x] 2(x + y) dy dx

Now, integrate with respect to y first:

M = ∫[0 to 2] [x(y²/2 + y)] | [0 to 3 - (3/2)x] dx

M = ∫[0 to 2] [x((3 - (3/2)x)²/2 + (3 - (3/2)x))] dx

M = ∫[0 to 2] [(3x - (3/2)x²)²/2 + (3x - (3/2)x²)] dx

Now, integrate with respect to x:

[tex]M = [(x^3 - (1/2)x^4)^2/6 + (3/2)x^2 - (1/4)x^3)] | [0 to 2]\\M = [(2^3 - (1/2)(2^4))^2/6 + (3/2)(2^2) - (1/4)(2^3)] - [(0^3 - (1/2)(0^4))^2/6 + (3/2)(0^2) - (1/4)(0^3)]\\M = [(8 - 8)^2/6 + 6 - 0] - [0]\\M = 6[/tex]

So, the mass of the lamina is 6 units.

Next, let's calculate the center of mass (X,Y):

X = (1/M) ∬_D xρ(x, y) dA

X = (1/6) ∬_D x * 2(x + y) dA

We need to set up the double integral over the region D:

X = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] x * 2(x + y) dy dx

Now, integrate with respect to y first:

X = (1/6) ∫[0 to 2] [x(y² + 2xy)] | [0 to 3 - (3/2)x] dx

X = (1/6) ∫[0 to 2] [x((3 - (3/2)x)² + 2x(3 - (3/2)x))] dx

X = (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x² + 6x - (3/2)x²)] dx

X = (1/6) ∫[0 to 2] [(9/4)x³ - (3/2)x⁴ + 15x - (3/2)x³] dx

Now, integrate with respect to x:

[tex]X = [(9/16)x^4 - (3/8)x^5 + (15/2)x^2 - (3/8)x^4] | [0 to 2]\\X = [(9/16)(2)^4 - (3/8)(2)^5 + (15/2)(2)^2 - (3/8)(2)^4] - [(9/16)(0)^4 - (3/8)(0)^5 + (15/2)(0)^2 - (3/8)(0)^4]\\X = [9/2 - 12 + 15 - 0] - [0]\\X = 15/2 - 12\\X = -3/2[/tex]

Next, let's calculate Y:

Y = (1/M) ∬_D yρ(x, y) dA

Y = (1/6) ∬_D y * 2(x + y) dA

We need to set up the double integral over the region D:

Y = (1/6) ∫[0 to 2] ∫[0 to 3 - (3/2)x] y * 2(x + y) dy dx

Now, integrate with respect to y first:

Y = (1/6) ∫[0 to 2] [(xy² + 2y²)] | [0 to 3 - (3/2)x] dx

Y = (1/6) ∫[0 to 2] [x((3 - (3/2)x)²) + 2((3 - (3/2)x)²)] dx

Y= (1/6) ∫[0 to 2] [x(9 - 9x + (9/4)x²) + 2(9 - 9x + (9/4)x²)] dx

Y = (1/6) ∫[0 to 2] [(9x - 9x² + (9/4)x³) + (18 - 18x + (9/2)x²)] dx

Now, integrate with respect to x:

[tex]Y= [(9/2)x^2 - 3x^3 + (9/16)x^4) + (18x - 9x^2 + (9/6)x^3)] | [0 to 2]\\Y = [(9/2)(2)^2 - 3(2)^3 + (9/16)(2)^4) + (18(2) - 9(2)^2 + (9/6)(2)^3)] - [(9/2)(0)^2 - 3(0)^3 + (9/16)(0)^4) + (18(0) - 9(0)^2 + (9/6)(0)^3)]\\Y = [18 - 24 + 9/2 + 36 - 36 + 12] - [0]\\Y= 9/2[/tex]

So, the center of mass of the lamina is (X,Y) = (-3/2, 9/2).

Learn more about mass here

brainly.com/question/17137444

#SPJ4

Answer: 13.5

Step-by-step explanation:

30% = 0.3.

Thus, simply do 0.3*45 to get 13.5.

Hope it helps <3

Answer:

Numbers 1,0,8,2 would lie on y-axis.

Step-by-step explanation:

This is because for example, (0,1)

we must prefer 0 as x-axis and 1 as y-axis. That's means left number or side will always be x-axis and right side will always be y-axis.

Answer: (0, 1)

Step-by-step explanation:

When the x is 0 is lies on the y axis.

Answer:

307 members

Step-by-step explanation:

Relative growth rate= Growth rate/population

Given: constant relative growth rate=0.7233

0.7233=[tex]\frac{dP/dt}{P}[/tex]

[tex]\frac{dP}{dt} =0.7233 P[/tex]

Theorem 2 states that solutions of the differential equation dy/dt = ky are in the form:    y(t)=y(0)[tex]e^k^t[/tex]

Writing the soltuion of our dif. equation as:

P(t)=P(0)[tex]e^{0.7233t}[/tex]

since on day zero the population consists of four members.

P(t)=4[tex]e^{0.7233t}[/tex]

next is to find the population size after six days. i.e t=6

P(6)=4[tex]e^{0.7233\times 6}[/tex] ≈ 307 members

Answer:

4. 9.1 – 10 = 0.2x

X= -4.5

Step-by-step explanation:

Let's solve for x in the equations given below

1. 9.1 = -0.2x + 10

9.1 - 10 = -0.2x

-0.9= -0.2x

-0.9/-0.2= x

4.5 = x

2. 10 = 9.1 + 0.2x

10-9.1 = 0.2x

0.9= 0.2x

0.9/0.2 = x

4.5 = x

3. 10 – 0.2x = 9.1

10-9.1= 0.2x

0.9= 0.2x

0.9/0.2= x

4.5 = x

4. 9.1 – 10 = 0.2x

-0.9 = 0.2x

-0.9/0.2= x

-4.5 = x

The different equation is equation 4

Reason because it's answer gave a negative value of x while others gave a positive value of x.

But in magnitude they all have same value of x

Answer:Its D

Step-by-step explanation:

I just did it on ed

Answer:

45

Step-by-step explanation:

We are using sigma notation to solve for a sum of arithmetic sequences:

The 5 stands for stop at i = 5 (inclusive)

The i = 1 stands for start at i = 1

The 3i stands for expression of each term in the sum

Answer: 1/35

Step-by-step explanation:

1/5 = 0.2

0.2/7= 1/35

Answer:

Step by step explanation

[tex] \frac{1}{5} \div 7[/tex]

Dividing is equivalent to multiplying with the reciprocal:

[tex] \frac{1}{5} \times \frac{1}{7} [/tex]

Multiply the fraction

[tex] \frac{1 \times 1}{5 \times 7} [/tex]

[tex] = \frac{1}{35} [/tex]

Hope this helps...

Good luck on your assignment.

Step-by-step explanation:

let the larger number be x and smaller number be y

according to this question

x=y+33----------(1)

y+33+5y=129----------(2)

6y+33=129

y=16

x=16+33(takimg equation (1)

x=49

Answer:

Larger number: 49.

Smaller number: 16.

Step-by-step explanation:

Let's say that the larger number is represented by y, and the smaller is represented by x.

y = 33 + x

y + 5 * x = 129

(33 + x) + 5x = 129

6x + 33 = 129

6x = 96

x = 16

y = 33 + 16

y = 49

Check our work...

49 + 5 * 16 = 49 + 80 = 129

49 = 33 + 16 = 49

Since it all works out, the larger number is 49 and the smaller number is 16.

Hope this helps!

Answer:

Cube

Step-by-step explanation:

A cube is a 3-D shape that consists of 6 squares. A cube is the correct following shape that must have a square base or a square bottom since all of it's sides are the shape of a square.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

Answer:

Step-by-step explanation:

The cube is the only one there that must have a square base.

The rectangular prism might have a square base, but most likely it does not. T

The pyramid can have a square base like the ones in Egypt but it can also have a triangular base.

A cone has a circular base.

Answer:

A. 2x

Step-by-step explanation:

Step 1: Factor out a 2

2(2x³ - x² + 4x)

Step 2: Factor out an x

2x(2x² - x + 4)

So our answer is B.

Step-by-step explanation:

use length x width x height

Answer:

[tex]\boxed{\sf \ \ \ a = 1 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

saying that [tex]x-\sqrt{a}[/tex] is a factor means that [tex]\sqrt{a}[/tex] is a zero which means

[tex]2(\sqrt{a})^4-2a^2(\sqrt{a})^2-3*\sqrt{a}+2a^3-2a^2+3=0\\\\<=> 2a^2-2a^3-3*\sqrt{a}+2a^3-2a^2+3=0\\\\<=>3-3*\sqrt{a}=0\\\\<=>\sqrt{a}=\dfrac{3}{3}=1\\\\<=> a = 1[/tex]

so the solution is a = 1

Do not hesitate if you have any question

Answer:

39.16% probability of selecting three Democrats and three Republicans

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the people are selected is not important. So we use the combinations formula to solve this question.

Combinations formula:

[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]

Desired outcomes:

3 Democrats, from a set of 8.

3 Republicans, from a set of 8.

[tex]D = C_{8,3}*C_{8,3} = (C_{8,3})^{2} = (\frac{8!}{3!5!})^{2} = 56^2 = 3136[/tex]

Total outcomes:

6 people from a set of 16.

[tex]T = \frac{16!}{6!10!} = 8008[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{3136}{8008} = 0.3916[/tex]

39.16% probability of selecting three Democrats and three Republicans