One painter can paint a room in 2 hours; another painter requires 4 hours to paint
the same room. How long will it take them to paint the room together

A set of n elements has 2ⁿ subsets. One of these subsets is the set itself, so this set would have 2ⁿ - 1 proper subsets.

The given set has 4 elements, so it has 2⁴ = 16 subsets and 2⁴ - 1 = 15 proper subsets.

Just to illustrate the claim, we have

• subsets of size 0 (1 of these):

{ } (empty set)

• subsets of size 1 (4 of these):

{1/6}, {1/7}, {1/8}, {1/9}

• subsets of size 2 (6 of these):

{1/6, 1/7}, {1/6, 1/8}, {1/6, 1/9}, {1/7, 1/8}, {1/7, 1/9}, {1/8, 1/9}

• subsets of size 3 (4 of these):

{1/6, 1/7, 1/8}, {1/6, 1/7, 1/9}, {1/6, 1/8, 1/9}, {1/7, 1/8, 1/9}

• subsets of size 4 (1 of these):

{1/6, 1/7, 1/8, 1/9}

and the last one is the only subset that is not a proper subset, because that subset = the set.

The number of subsets are 16 and number of  proper subsets for the set are 15. So, correct option is A.

The set {1/6, 1/7, 1/8, 1/9} has 4 elements.

To calculate the number of subsets, including both the proper and improper subsets, you can use the formula 2ⁿ, where n is the number of elements in the set.

So, for this set, there are 2⁴ = 16 subsets.

To calculate the number of proper subsets, you subtract 1 from the total number of subsets (to exclude the empty set).

So, the number of proper subsets is 16 - 1 = 15.

Hence, option A is correct, the number of subsets are 16 and number of  proper subsets for the set are 15.

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Answer:

slope = 2, y-intercept = 3

Step-by-step explanation:

» Concepts

All straight lines can follow the slope-intercept form, y = mx + b, where y = y-coordinate, m = slope, x = x-coordinate, and b = y-intercept. The slope is the constant rate of change, and the y-intercept is where the line intersects at the y-axis.

» Application

We are asked to find the slope and y-intercept of the equation, y = 2x +3, given the form y = mx + b. As you can see, in the place of m (the slope), there is the number 2, making the slope 2. Then, in the place of b (the y-intercept), there is the number 3, making the y-intercept 3.

Answer:

find the probability of rolling a 4, take the number of possible ways of rolling a 4 and divide it by the total number of possible outcomes.

Answer:I guess

represent

expression

degree of 4

Answer:

1.2 miles/gal

Step-by-step explanation:

I assume you want miles per gallon

  3/10 mile /  1/4 gallon  =    3/10  *  4/1 =   12/10 = 1.2  miles per gallon

if you want gallons/mile

                  1/4 gallon / 3/10 mile =  .8333  gallon/mile

A: 3

if you subtract 11 from 14 you get three, and the pattern is repeated and works with the other consecutive numbers

Answer:

Here are the examples!

Step-by-step explanation:

15 45 X +3 5x + 1 15 = 45 5x + 1 = 3x + 9 x+3 5x + 1 5x - 3x = 9-1 1 … 5( 5x + 1) = 45(x+3) 2x = 8 5x + 1 = 3( x + 3) x :) ...

The probability that a house in her neighborhood has a pool, given that it has a garage is; A. 58%

By Venn diagram, all houses that have garage have a pool. Thus, since given that households that have garage is 80% and households that garage and a pool is 46%.

Then probability that a house in her neighborhood has a pool is;

P = 46%/80%

P = 57.5% = 58%

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Answer:

480

Step-by-step explanation:

9x9= 81x5= 480

Then the number of the ways that the medals can be awarded will be 165. Then the correct option is D.

A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.

There are 11 runners in a race. Medals are awarded for 1st, 2nd, and 3rd place.

Then the number of the ways that the medals can be awarded.

[tex]\rightarrow ^{11}C_3\\\\\\\rightarrow \dfrac{11!}{(11-3)! 3!}\\\\\\\rightarrow \dfrac{11 \times 10 \times 9 \times 8!}{8! \times 3 \times 2 }\\\\\\\rightarrow \dfrac{11 \times 10 \times 9}{3 \times 2}\\\\\\\rightarrow 11 \times 5 \times 3\\\\\\\rightarrow 165[/tex]

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Step-by-step explanation:

Howdy there :)

To describe the transformation of the parent logarithmic function, you just need to follow these rules

1. A +  on the outside of the parentheses will mean a vertical shift upwards. As such, the transformation is moved 5 units up. If it was -, it would move 5 units down.

2. The inside of the parentheses will result in a horizontal shift right 4 units. The rule to remember is that these kinds of functions follow x(a - b) rules, meaning that when the 4 is subtracted, we are really talking about a positive four, unlike in standard arithmetic. Vice versa, a + 4 will mean a -4 four, since a - -4 is the same as a + 4. As such, we will move in the positive direction (right) on the y axis.

3. Since x is now -2x, we are reflecting about the y axis, meaning the function will switch from left to right or right to left.

4. The 2 in front of it represents a vertical dilation by a factor of 2. This is because our constant, 2, is greater than 1. If the number were in between 0 and 1, it would represent a vertical compression by the constant number.

Answer:

1, 3

Step-by-step explanation:

1. 2.3 - 2.3 = 0

2. -3.7 + -4.1 = -7.8

3. -2.6 - (-12/4) = 0.4 = 4/10 = 2/5

4. 5/2 + (-2.5) = 0

5. 72- (-100)

   72+100 = 172

The length in units of the line segment A'B' in the resulting figure is the same as the length of line segment AB in the previous rectangle.

Form the task content;

The translation which occurs on the rectangle only shifts the whole rectangle leftward and downward and hence, each line segment in the rectangle still retains its length.

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Step-by-step explanation:

The answer is 0.8 as a fraction is 4/5

Answer:

30 square millimeters

Step-by-step explanation:

3 x 3 = 9

3 x 1 = 3

there are two sides with the area 9 therefore...

9 x 2 = 18

There are four sides with the area 3 therefore...

3 x 4 = 12

Therefore the suface area is

12 + 18 = 30

Answer:

0.45 cm

Explanation:

In order to find the height of any shape given the volume and base area.

Simply divide the volume by the base area.

Here given:

Height:

Answer:

-26042

Step-by-step explanation:

sum of a finite geometric series =

[tex]\frac{a_1(1-r^n)}{1-r}[/tex]

here, a1 is the first term, r is the common ratio, and n is the number of terms

a1 = -2

r = -5

n = 7

[tex]\frac{a_1(1-r^n)}{1-r} = \frac{-2(1-(-5)^7)}{1-(-5)} = -26042[/tex]

The equation that can be used to find the time t, in hours,  it would take Johnson and Nathan to tile a 100 square foot area together is 3.9375 hours, which approximates to 4 hours.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,(assume all men have same strength)

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

For this case, we're specified that:

So, we see that strength of Johnson and Nathan are different.

Let the general manpower (from some frame of a general public or any third frame) needed by this work be M.

Then, Johnson delivers M manpower in 7 hours or M/7 manpower in one hour.

In the similar way, Nathan delivers M/9 manpower per hour.

Thus, if Nathan and Johnson work together, they can deliver: [tex]\dfrac{M}{9} + \dfrac{M}{7} = M\dfrac{9+7}{63} = \dfrac{16M}{63}[/tex] manpower per hour.

Let it takes them together h hours to complete the work.
That means, in 'h' hours, their together work power will accumulate to M manpower.

Or, we can say:

[tex]h \times \dfrac{16M}{63} = M\\\\h = \dfrac{63M}{16M} = \dfrac{63}{16} = 3.9375[/tex]

Thus, the equation that can be used to find the time t, in hours,  it would take Johnson and Nathan to tile a 100 square foot area together is 3.9375 hours, which approximates to 4 hours.

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Answer:

4x-5

Step-by-step explanation:

Answer:

It's A. The ability of a muscle group to exert a force against a resistance for an extended period of time.

Answer:

The statement is true

Step-by-step explanation:

Positive numbers are always greater than negative numbers, so the statement would be true

Answer: r = 5

Steps:

[tex]a_n=ar^{n-1}[/tex]

1. add Values to formula

[tex]1250=2r^{5-1}[/tex]

2. get r alone

[tex]\frac{1250}{2}=\frac{2r^{4}}{2}[/tex]  ➜ [tex]625= r^4[/tex]
3. get rid of the exponents

[tex]\sqrt[4]{625}= \sqrt[4]{r^4}[/tex] ➜ [tex]\sqrt[4]{625}= r=5[/tex]

r = 5

Answer:

wE NEED MORE CLARIFICATION

Step-by-step explanation:

What is the equasion
What is the link

Answer:

im passing this concept trust me answer is 34.8

Step-by-step explanation:

The value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1

The limit of a function is the limit of a function as x tends to a value.

From the given graph, you can see that the function g(x) goes large at the point where the arrows orange and purple point down from the x-coordinates -1 and 1.

Hence the value of a where the Limit of g(x) as x approaches alpha not exist are -1 and 1

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