What is the inverse of f(x) = 2x − 8?

A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.

Given that are two events P(A) = 1/3, P(B) = 1/3, and P(A ∩ B) = 2/9.

We need to determine if the events are independent or not.

The chance of occurrences A and B intersecting (P(A B)) must be compared to the sum of both events' individual probabilities (P(A) × P(B)) in order to assess if events A and B are independent.

Two events A and B are independent if and only if:

P(A ∩ B) = P(A) × P(B)

Let's check if this condition holds for the given probabilities:

P(A) = 1/3

P(B) = 1/3

P(A ∩ B) = 2/9

Next, add up the odds of each separately:

P(A) × P(B) = (1/3) × (1/3) = 1/9

We can infer that A and B are not independent events because P(A B) = 2/9 and 2/9 is not equivalent to 1/9.

In other words, the likelihood that one event (A) occurs influences the likelihood that another event (B) occurs, and vice versa.

The probability of both events happening at once (P(A B)) would be equal to the product of their individual probabilities (P(A) × P(B)) if A and B were independent, but this is not the case in this situation.

Learn more about Independent Events click;

https://brainly.com/question/32716243

#SPJ12

Answer:D

Step-by-step explanation:

Answer:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Step-by-step explanation:

For this case we have the following confidence interval given:

[tex] 0.345 \leq p \leq 0.895 [/tex]

And for this case we want to find the estimated proportion like this:

[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]

And the margin of error for this case would be given by:

[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

Which relationship in the triangle must be true? Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.

sin(B) = sin(A)

sin(B) = cos(90 – B)

cos(B) = sin(180 – B)

cos(B) = cos(A)

Assuming the angles are in degrees, the second relation is always true.

By definition of sine,

sin(B) = AC/AB

cos(90-B) = cos (A) = AC/AB

therefore the second relation is true, for arbitrary values of B.

Answer:

sin(B) = cos(90 – B)

Step-by-step explanation:

Which relationship in the triangle must be true?

Triangle A B C is shown. Angle A C B is a right angle. The length of side C B is a, the length of side A C is b, and the length of side A B is c.

Answer:

A ∪ B = {1,3,6,9,12,15,18,24}

Step-by-step explanation:

Let A = {3,6,9,12,15}

B = {1,6,12,18,24}

So,

A ∪ B = {3,6,9,12,15} ∪ {1,6,12,18,24}

A ∪ B = {1,3,6,9,12,15,18,24}

Answer:

{1,3,6,9,12,15,18,24}

Step-by-step explanation:

The union is joining of the elements of the sets

{3, 6, 9, 12, 15}U {1, 6, 12, 18, 24}

= {1,3,6,9,12,15,18,24}

Answer:

a. [tex]N(1)=2600[/tex]

b. [tex]N'(a) = 470/a[/tex]

c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)

d. lim a→[infinity] N′(a) = 0

Step-by-step explanation:

a.

the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:

[tex]N(1)=2600 + 470ln(1)[/tex]

[tex]N(1)=2600 + 470*0[/tex]

[tex]N(1)=2600[/tex]

b.

To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:

[tex]N'(a) = 2600' + (470ln(a))'[/tex]

[tex]N'(a) = 0 + 470*(1/a)[/tex]

[tex]N'(a) = 470/a[/tex]

c.

The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).

The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.

d.

When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.

Answer: The width of the garden is 6 Meters

Step-by-step explanation:

3x + x = 24

The length is 3x and the width is x

24 / 4 = 6

x= 6

The width of the garden is 6 Meters

Answer:

x = 6

Step-by-step explanation:

3x + x = 24

24 / 4 = 6

x = 6

Answer: 95 degrees.

Step-by-step explanation:

A quadrilateral has a total combined angle measure of 360 degrees. If you do 360-(80+110+75) it would equal 95.

Answer:

Option C is the correct option

Solution,

The sum of the angles in the quadrilateral is 360°

Let the forth angle be X

X + 80° + 110° + 75° = 360°

Calculate the sum:

X + 265° = 360°

Subtract 265° on both sides

X + 265° - 265° = 360° - 265°

Calculate the difference

X = 95°

Hope this helps...

Good luck on your assignment...

Answer:

ADB = Major Arc

arc measure = 310

Step-by-step explanation:

major arc measure = 360 - 50 = 310

Answer:

(0, 16]

Step-by-step explanation:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

According to the ratio test, if we define L such that:

L = lim(n→∞) |aₙ₊₁ / aₙ|

then the series will converge if L < 1.

aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)

aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)

Plugging into the ratio test:

L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |

L = lim(n→∞) | -n (x−8) / (8 (n+1)) |

L = (|x−8| / 8) lim(n→∞) | n / (n+1) |

L = |x−8| / 8

For the series to converge:

L < 1

|x−8| / 8 < 1

|x−8| < 8

-8 < x−8 < 8

0 < x < 16

Now we check the endpoints.  If x = 0:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° -1 / n

This is a harmonic series, and diverges.

If x = 16:

∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)

∑ₙ₌₁°° (-1)ⁿ⁺¹ / n

This is an alternating series, and converges.

Therefore, the interval of convergence is:

0 < x ≤ 16

Or, in interval notation, (0, 16].

Answer:

0.15 or 15%

Step-by-step explanation:

If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.

To calculate how much the price went up each day on average, we will create exponential equation.

x = price of the stock

y = average daily change

[tex]x*y^{4} =1.75x[/tex]  divide by x

[tex]y^{4} = 1.75[/tex]

We will calculate it using logarithms.

y = 1.15016, rounded to 1.15

We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%

Answer:

The probability of getting even 7 times out of 8 is 1/256. Hope this helps!!

Step-by-step explanation:

21/7 = 3 is the answer of your question

Answer:

B.

Step-by-step explanation:

According to SohCahToa, when using Sin to find a side value, you must use opposite over hypotenuse.

So in this case to find x, you would do the Sin(L)=x/y

Answer:

B.  Sin(L)=x/y  indeed!

Step-by-step explanation:

Answer:

8 is in the hundreds place as well as in the tens place.

Step-by-step explanation:

We use the base 10 system. 880 would represent eight hundred and eighty. So our 0 would be the ones place, 8 in the tens place, and 8 also in the hundreds place.

6 x (10+ 6) = 8 x (8 +x)

Simplify:

96 = 64 + 8x

Subtract 64 from both sides:

32 = 8x

Divide both sides by 8

X = 4

Answer:

k = -10/9 and k = 10/9

Step-by-step explanation:

given y = cos(kt) and the differential equation 81y'' = -100y

y' = -ksin(kt)

y'' = -k²cos(kt)

Substituting the value of y and y'' in the differential equation we have;

81 (-k²cos(kt))= -100 (cos(kt))

-81k²cos(kt)) = -100cos(kt))

-81k² = -100

k² = 100/81

k = ±[tex]\sqrt{\frac{100}{81} }[/tex]

k = ±10/9

k = -10/9 and k = 10/9

Answer:

8 and 4/9 i think... i am sorry if i am wrong

Step-by-step explanation:

Answer:

Length=29.8 inches

Width=11.8 inches

Height=4.6 inches

Volume=1,617.54 cubic inches

Step-by-step explanation:

Let the side of congruent square cut =x inches

So the length of the rectangular box=(39-2x)

width = (21-2x)

height = x

The volume V=Length*Width*Height

= (39-2x)*(21-2x)*x

dV/dx= (39-2x)(21-4x)-2x(17-2x)=0

Simplify the equation above

819-156x-42x+8x^2-34x+4x^2=0

We have,

12x^2 -232 +819=0

Solve the quadratic equation using formula

a=12

b= -232

c=819

x= -b +or- √b^2-4ac/2a

= -(-232) +- √(-232)^2 - (4)(12)(819) / (2)(12)

= 232 +or- √53824 - 39312 / 24

= 232 +or- √14512 / 24

= 232 +or- 4√907 / 24

x= 232 / 24 + 4√907 / 24

=14.6861

Or

x=232 / 24 - 4√907 / 24

=4.64726

x=4.6 inches

Length=(39-2x)

={39-2(4.6)}

= 29.8 inches

Width=(21-2x)

={21-2(4.6)}

= 11.8 inches

Height=x= 4.6 inches

Volume=(39-2x)*(21-2x)*x

={39-2(4.6)}*{21-2(4.6)*4.6

=(39-9.2)*(21-9.2)*4.6

=29.8*11.8*4.6

=1,617.544

Approximately 1,617.54

Volume=1,617.54 cubic inches

Answer:

4+10-284-4819+2948929

Answer:

Solution,

[tex] \frac{ab}{bc} = tan \: 40 \\ ab = bc \times tan \: 40 \\ ab = 10 \times 0.84 \\ ab = 8.4 \: inches \: [/tex]

[tex] \frac{bc}{ac} = cos \: 40 \\ \frac{bc}{cos \: 40} = ac \\ ac = \frac{10}{cos \: 40} \\ ac = 13.05 \: inches[/tex]

Hope this helps...

Good luck on your assignment..

Answer:

The height increase by

20/49π when pile is 14ft high

Step by step Explanation

Given:

rate of 20 ft3/min

To asolve this quest we will be using the volume of a cone then find the partial derivative

CHECK THE ATTACHMENT FOR DETAILED EXPLANATION

Answer:

The range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Step-by-step explanation:

The complete question is:

The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?

Solution:

As the sample size is large, i.e. n = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.

So,[tex]\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})[/tex]

The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.

The critical value of z for 98% confidence level is,

z = 2.33

Compute the 98% confidence interval as follows:

[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]

     [tex]=267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)[/tex]

Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).

Answer:

[tex]\$45[/tex]

Step-by-step explanation:

[tex]20+(2.5*20)=45[/tex]

Marking up means that the new value is added onto the original value.

As we are increasing the original price by 250% of the price, we need to multiply it by 2.5, as that is equal to 250%

Answer:

20*2.5 = $50 Gross margin $70 Selling price

Step-by-step explanation:

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

18-22 = 1

23-27 = 3

28-32 = 3

33-37 = 3

Answer:

9x^4

Step-by-step explanation:

(3x)^2 * x^2

9x^2 * x^2

Add the exponents

9x^(2+2)

9x^4

Answer:

Step-by-step explanation:

Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]

To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;

[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]

As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;

[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]

Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]

Since the limit of the sequence gave a finite number , the sequence converges.

Note that the only case when the sequence diverges id when the limit of the sequence is infinite

Answer:

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Step-by-step explanation:

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

All outcoms of the dices:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

36 in all

Total outcomes:

In this question, we want all with no repetition.

There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.

Desired outcomes:

One landing on six:

(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).

10 desired outcomes.

Probability:

10/30 = 0.3333

33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers

Answer:

13/20<--->65%

21/25<--->84%

3/4<--->75%

2/5<--->40%

3/5<--->60%

To find the matching pairs, divide the fraction and move the decimal point to your answer 2 places to the right to then get a percentage.

Ex:  1/2=   .50->5.0->50.->50%

The image did not show the rest of the answers, but I worked with what information I received from the current image, producing 5 sets of answers. If there are more than 5 sets, please send a second image with your question so we can help you with the rest.

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%

Fractions are written as a ratio of two integers. In order to convert fractions to percentage, we will simply multiply the fraction given  by 100.

For the fraction 13/20

13/20 * 100 = 13 * 5

13/20 = 65%

For the fraction 21/25

21/25 * 100 = 21 * 4

21/25 = 84%

For the fraction 3/4

3/4 * 100 = 3 * 25

3/4 = 75%

For the fraction 2/5

2/5 * 100 = 2 * 20

2/5 = 40%

For the fraction 3/5

3/5 * 100 = 3* 20

3/5 = 60%

Hence the correct match of fractions to their equivalent percentages are;

13/20 = 65%

21/25 = 84%

3/4 = 75%

2/5 = 40%

3/5 = 60%
Learn more on percentages here: https://brainly.com/question/24304697

#SPJ9

Answer:

a. 125.0714; 11.1835.

b. 109.4375; 10.4612.

Step-by-step explanation:

Given the following data;

70, 65, 71, 78, 89, 68, 50, 75.

Mean = 70.75

The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.

We would then find the square of this deviation;

[tex]=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2[/tex]

[tex]=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625[/tex]

= 875.5

Next is to find the population variance;

[tex]V = \frac{875.5}{8}[/tex]

Variance, V = 109.4375

The population standard deviation is the square root of the population variance;

[tex]Sd = \sqrt{109.4375}[/tex]

Standard deviation, Sd = 10.4612

To find the sample variance;

[tex]V = \frac{875.5}{8-1}[/tex]

[tex]V = \frac{875.5}{7}[/tex]

Variance, V = 125.0714

The sample variance is;

[tex]Sd = \sqrt{125.0714}[/tex]

Standard deviation, Sd = 11.1835

Therefore,

a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.

b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.

Answer:

C. 20.67

Step-by-step explanation:

I got it right on edge :)