Suppose P(A)=4/10,P(B)=5/10, and P(AB)=2/10. (a) Compute P(A c
). (b) Compute P(A∪B). (c) Compute P(A∣B). (d) Compute P(B∣A). (e) Compute P(B∣A c
). (f) Are A and B independent? Explain. (g) Are A and B mutually exclusive? Explain.

Answer:

250=15x+10

Step-by-step explanation:

250=y

10=b

15 is how much you are paying consantly

The equation in slope-intercept form to represent the cost of each plan is 250=15x+10.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

A linear equation has the form y = mx + b in the slope-intercept format. X and Y are the variables in the equation. The values m and b represent the line's slope (m) and the value of y when x is 0.

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

It is given that, a $ 250 lifetime online membership was required. The website's membership costs $10 to enroll and $15 each month.

If x is the number of months, the equation in slope-intercept form to represent the cost of each plan is,

y=mx+c

250=15x+10

Thus, the equation in slope-intercept form to represent the cost of each plan is 250=15x+10.

Learn more about the straight line here:

brainly.com/question/3493733

#SPJ2

Answer:

The answer is C which is -3

Step-by-step explanation:

Answer:

B) 3b. 10b

Step-by-step explanation:

B) 3b. 10b = (3x10)(bxb) = 30b²

Reason: The line goes downhill when moving to the right, and when we're between x = -1 and x = 1. You can think of it like a roller coaster.

The probability that the mean weight of the sample babies would differ from the population mean by less than 54 grams is 0.4339.

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

First, solve for the z-score using the formula below.

z-score = (x – μ) / σ

where x = individual data value = 3316 grams - 54 grams = 3262

μ = mean = 3316 grams

σ = standard deviation = 324 grams

z-score = (3262 - 3316) / 324

z-score = -54 / 324

z-score = -0.1667

Find the probability that corresponds to the z-score in the z-table. (see attached images)

z-score = -0.1667

Using interpolation of values,

probability = 0.4339

Learn more about probability here: brainly.com/question/26822684

#SPJ4

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

for such more question on inverses

https://brainly.com/question/15066392

#SPJ8

Lynn used \(47.826\) gallons fuel in each month.

Average is defined as the mean value which is equal to the ratio of the sum of the number of a given set of values to the total number of values present in the set.

Gallon is the unit for measuring liquids (fuel).

Mile is a unit of large distance.

Given,

Lynn drive her car for work an average of \(1100\) miles

Car get \(23\) miles per gallon.

It's mean car covers \(23\) miles distance in \(1\) gallon of fuel.

She used fuel in each month

\(=\frac{Total miles}{miles per gallon} \\=\frac{1100}{23}\\ =47.8260 gallon\)

Lynn used \(47.826\) gallons fuel in each month.

To know more about Lynn

https://brainly.com/question/12877834

#SPJ4

Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

Answer:

option D is correct

Step-by-step explanation:

Given data

From the given expression/options of answers, option D is correct

This is because the given expression in the attached file corresponds to the terms in option D

Answer:

When cooper was 15 years old, he scored an 85 on an iq test. he took the test again when he was 35 years old and scored an 85 again. this indicates that the iq test is highly: __________

Reliable

Because his scores were so close together the test would be considered as Reliable.

Know more about “intelligent iq question” here: https://brainly.com/question/28319133

#SPJ4

Answer:

6

Step-by-step explanation:

What is 1 half (1/2) multiplied by (4+8) equal?

1/2*(8+4) <== add the number in the parenthesis

1/2*12 <== multiply the numbers, half of 12 is 6

6 <== final answer

Hope this helps!

6

Step-by-step explanation:

Hope the pic will help

Answer:

D. 27/16

Step-by-step explanation:

Volume of a cyclinder=πr^2h

Volume of cylinder A=πr^2h

r=3

h=3

π=3.14

=3.14×3^2×3

=3.14×9×3

=84.78

Volume of cylinder B

r=2

h=4

Volume of cylinder B=πr^2h

=3.14×2^2×4

=3.14×4×4

=50.24

Ratio of A to B

=84.78/50.24

Change to fraction

=84.78×100/50.24×100

=8478/5024

=27/16

The preimage of the image after translation are shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The rule of the translation are,

T <2, - 5> (x, y)

Here, The coordinates of the image are,

(- 7, 7) , (- 2, 3) and (2, 7)

Since, The rule of the translation are,

T <2, - 5> (x, y)

Hence, The new coordinates of the pre - image are,

(- 7, 7) = (- 7 + 2, 7 - 5) = (- 5, 2)

(- 2, 3) = (- 2 + 2, 3 - 5) = (0, - 2)

(2, 7) = (2 + 2, 7 - 5) = (4, 2)

Thus, The new coordinates of the pre - image are,

(- 5, 2) , (0, - 2) and (4, 2)

Therefore, The preimage of the image after translation are shown in figure.

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ1

Solution:

Consider the following trigonometric equation:

This is equivalent to:

now, consider the following trigonometric circle and the above equation:

According to this trigonometric circle and the definition of the cotangent function, we can conclude that the general solution would be:

Part A: An open circle on a number line represents an excluded value, indicating that the endpoint is not included in the solution set of the inequality. It is used when the inequality includes the symbols < (less than) or > (greater than), which denote strict inequality.

Part B: A closed circle on a number line represents an included value, indicating that the endpoint is part of the solution set of the inequality. It is used when the inequality includes the symbols ≤ (less than or equal to) or ≥ (greater than or equal to), which denote inclusive inequality.

Part C: The shading on the number line represents the range of values that satisfy the given inequality. It indicates which values make the inequality true. Typically, the shading is done to the right or left of the circle(s) depending on whether the inequality is greater than or less than.

Part A:

For example, if we have the inequality x > 2, we would represent it with an open circle at 2 on the number line. This means that 2 itself is not a valid solution, but any value greater than 2 is included.

Part B:

For example, if we have the inequality x ≥ -3, we would represent it with a closed circle at -3 on the number line. This means that -3 itself is a valid solution, as well as any value greater than or equal to -3.

Part C:

For example, if we have the inequality x > 2, we would shade the portion of the number line to the right of the open circle at 2. The shaded region represents all the values greater than 2 that satisfy the inequality. The shading visually illustrates the solution set and helps identify the range of valid values for the variable in the given inequality.

for more such questions on number line

https://brainly.com/question/24644930

#SPJ8

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the required figure is not attached to the question.

From the question, we can deduce that the telescope is a composite figure made from a cone and a cylinder.

To get the volume of the materials used, you have to calculate the volume of the cone and that of the cylinder.

The sum of these volumes, is your answer.

Assume the following dimensions:

Cone

\(r = 5\\\) --- radius

\(h = 7\) --- height

Cylinder

\(r = 5\\\) --- radius

\(h = 20\) --- height

The volume of the cone is:

\(Volume = \frac{1}{3} \pi r^2h\)

\(V_1= \frac{1}{3} \pi *5^2*7\)

\(V_1= \frac{1}{3} \pi *25*7\)

\(V_1= \frac{175}{3} \pi\)

The volume of the cylinder is:

\(Volume = \pi r^2h\)

\(V_2 = \pi * 5^2 * 20\)

\(V_2 = \pi * 25* 20\)

\(V_2 = 500\pi\)

The total is:

\(Volume = V_1 + V_2\)

\(Volume = \frac{175\pi}{3} + 500\pi\)

Take LCM

\(Volume = \frac{175\pi+1500\pi}{3}\)

\(Volume = \frac{1675\pi}{3}\)

Answer: 64

Step-by-step explanation:

The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

Learn more about capability index on:

brainly.com/question/15734839

#SPJ12

Answer:

120

Step-by-step explanation:

480 total

1/2 = 240 are cows

1/8 = 60 are goats

remaining = 480-240-60 = 180 are chickens & ducks

33.3333% of 180 = chickens  =180/3 = 60 chickens

so ducks = 180-60 =120

Answer:

120

Step-by-step explanation:

given that out of 480 animals 0.5 of the animals are cows . So ,

no. of cows = 0.5*480 = 240

Again, we are given that 1/8 of the animals are goats , so the number of goats would be ,

no. of goats = 1/8*480 = 60

Total no. of goats and cows ,

= 240 + 60 = 300

No. of remaining animals= 480 -300 = 180

Now out of these 180 animals 33⅓ % animals are chickens and remaining are ducks.

Percentage of ducks = (100 - 33⅓ )% = 66.67%

So the number of ducks would be ,

180 * 66.67/100 = 120

And we are done!

Answer:

399 = 313 + d

Step-by-step explanation

Answer:

399 = d + 313

Step-by-step explanation:

Answer:

yeah 13 is the right answerrrrr

Answer:

Step-by-step explanation:

"half of R" it is:   \(\dfrac R2\)

"y cubed" it is:   \(y^3\)

Therefore, half of R subtracted from y cubed is:  \(y^3-\dfrac R2\)

Answer:

x <3

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

Distribute

-10 +8x < 6x-4

Subtract 6x from each side

-10+8x-6x < 6x-6x-4

-10 +2x < -4

Add 10 to each side

-10+2x+10 < -4+10

2x< 6

Divide by 2

2x/2 < 6/2

x <3

Answer: B & D

Step-by-step explanation:

A is not correct because it says "in the city" instead of "in Elan's school"

C is not correct because it says do NOT ....

The formula (kerA)⊥=im(AT) is indeed true.

First, recall that the kernel (or null space) of an n×m matrix A is the set of all vectors x in \(R^m\) such that Ax=0. Geometrically, the kernel of A represents the subspace of \(R^m\) that gets mapped to the origin under the linear transformation represented by A. Similarly, the image (or range) of A is the set of all vectors y in \(R^n\) that can be written as y=Ax for some x in \(R^m\). Geometrically, the image of A represents the subspace of R^n that can be reached by applying the linear transformation represented by A to some vector in \(R^m\).

Now, let W denote the subspace spanned by the kernel of A, that is, W=span{v1, v2, ..., vk} where {v1, v2, ..., vk} is a basis for kerA. By definition, any vector w in W satisfies Aw=0. We want to show that the orthogonal complement of W, denoted by W⊥, is equal to the image of the transpose of A, im(AT). That is, we want to show that any vector y in W⊥ satisfies y=ATx for some x in \(R^m\).

To prove this, let y be an arbitrary vector in W⊥. Then, by definition, y is orthogonal to every vector in W, including the basis vectors {v1, v2, ..., vk}. In other words, we have y⋅vi=0 for all i=1,2,...,k. Now, consider the transpose of A, denoted by AT, which is an m×n matrix. The i-th row of AT is given by the i-th column of A, and the j-th column of AT corresponds to the j-th row of A. Therefore, we have AT=[a1T, a2T, ..., amT], where ajT denotes the transpose of the j-th column of A. Let x be the vector in \(R^m\) given by x=c1a1+c2a2+...+cma m, where {c1, c2, ..., cm} are arbitrary scalars. Then, we have ATx=(c1a1T+c2a2T+...+cmamT)=[c1, c2, ..., cm] [a1T, a2T, ..., amT]=c1v1+c2v2+...+ckvk.

Note that the vector c1v1+c2v2+...+ckvk belongs to the kernel of A, since Aw=0 for any w in the kernel of A. Therefore, we have ATx⋅vi=0 for all i=1,2,...,k. But we also have y⋅vi=0 for all i=1,2,...,k, since y is orthogonal to every vector in W. Therefore, we have (ATx+y)⋅vi=0 for all i=1,2,...,k. Since {v1, v2, ..., vk} is a basis for kerA, this implies that ATx+y is in the kernel of A, that is, A(ATx+y)=0. But this means that ATx+y is orthogonal to every column of A, and hence lies in the orthogonal complement of the image of A.

Therefore, we have shown that any vector y in W⊥ can be written as y=ATx for some x in \(R^m\). This proves that W⊥.

To know more about "Matrix" refer here:

https://brainly.com/question/28180105#

#SPJ11

Answer:

-3

Step-by-step explanation:

     Let x = the number

Then 3x = its triple, and the condition is:

x - 8 < 3x

Subtract x from each side

-8 < 2x

Divide each side by 2

-4 < x

Reverse the inequality

x > -4

The smallest integer greater than -4 is -3.

Check:

-3 - 8 < 3(-3)

-11 < -9

It checks.

Answer:

for the seniors, the answer is $12, and for the children, the answer is 8.

Step-by-step explanation:

Answer:

b. Formal

Step-by-step explanation:

Colloquial is a more casual style of writing, which this text doesn't include.

Answer:

s=750+30W, after 14 weeks she has 1170$

Step-by-step explanation:

Answer:

750+30w=s     750+(30*14)=1,170

Step-by-step explanation:

i think this is it

Answer:

-8x - 1

Explanation:

-7x + 2 - x + 3 – 6

-7x - x + 2 + 3 - 6

Add: 2 + 3 - 6 = -1

= -7x - x - 1

Combine: -7x - x = -8x

= -8x - 1