Which expression is Equivalent to the problem in the photo?

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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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:

matrix multiplication is possible in this matrix

Step-by-step explanation:

[tex] ( \frac{1}{ - 1} ) \times (0 \: \: 4)[/tex]

Answer:

D

really sorry if wrong

but I am positive that is the answer

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.

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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Answer:

x = 10

y = 17.321

Step-by-step explanation:

feel free to ask questions !!

I have also attached the trig rules I was using just in case you wanted a general idea

Answer:

[tex]\displaystyle V = \pi \int_0^{1.835}\left[ 4 - y^2\right]^2 - \left[ 4-\sqrt{4(y+1)}\right]^2\, dy[/tex]

Step-by-step explanation:

We can use the washer method. Because the axis of revolution is vertical, our representative rectangle is horizontal. Recall that:

[tex]\displaystyle V = \pi \int_a^b \left[ R(y)\right] ^2 - \left[r(y)\right]^2 \, dy[/tex]

Solve each equation as a function of y:

[tex]\displaystyle \begin{aligned} y & = \sqrt{x} \\ \\ x_1 & = y^2\end{aligned}[/tex]

And:

[tex]\displaystyle \begin{aligned} y & = \frac{1}{4}x^2 - 1 \\ \\ x_2 & = \pm\sqrt{4(y+1)} \\ \\ & = \sqrt{4(y+1)}\end{aligned}[/tex]

The outer radius R is simply (4 - x₁) and the inner radius r is (4 - x₂). The point of intersection is (3.368, 1,835), so our limits of integration are from y = 0 to y = 1.835.

Therefore, the integral that represents the region being revolved around

x = 4 is:

[tex]\displaystyle V = \pi \int_0^{1.835}\left[ 4 - y^2\right]^2 - \left[ 4-\sqrt{4(y+1)}\right]^2\, dy[/tex]

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

Step-by-step explanation:

all bags are mislabeled. that means, whatever is written on either of the 3 bags, is wrong.

so, the bag labeled "green" is NOT the one with 2 green apples. the one labeled "red" is NOT the one with 2 red apples.

and - my favorite - the one labeled "red/green" is NOT the one with the mixture.

so, we pick one apple from the bag that is currently (mis-)labeled as "red/green".

as it cannot be the mixed bag, it must be one of the pure color bags.

whatever color shows up, we know this is the bag with 2 apples of that color.

then the bag that was labeled with that color must be the other pure color (if it were the mixed bag, it would mean that the third bag was labeled correctly, which is not the case). and then the third bag is the mixed one.

for example :

we get a red apple in our first pick.

so, the bag, that was originally (but wrongly) labeled as "red/green" gets the label "red".

then the bag with the original (but again wrong) label "green" gets now the label "red".

and the third bag with the original (but wrong) label "red" gets the "red/green" label.

if the first apple is green, then the same principle just with reversed colors applies.

A: 3

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

Answer:

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

Answer:

Step-by-step explanation:

What is the rule for a reflection across the Y axis? The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the -value the same

Answer:

  A'(-2, 5)

  B'(-6, 3)

Step-by-step explanation:

When a point is reflected in the y-axis, the image is as far from the y-axis on the other side as the original point is on this side. That is, the y-axis is halfway between the original point and its image. The x-coordinate of a point measures how far from the y-axis it is, so reflection in the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y) . . . . . reflection in the y-axis

__

  A(2, 5) ⇒ A'(-2, 5)

  B(6, 3) ⇒ B'(-6, 3)

Answer:

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

Answer:

see below

Step-by-step explanation:

the third one

8m^2-5m^+9m^2-9-4-2m

You add 8 and 9, as they have the same exponents, and as there is only one answer witha positive 17, it is ur answer

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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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:

480

Step-by-step explanation:

9x9= 81x5= 480

When the first two terms and the last two terms are grouped, the common binomial factor is 6x – 7

30x² – 35x + 54x – 63

Group the first two and the last two terms

(30x² – 35x) + (54x – 63)

Factorise

5x(6x – 7) + 9(6x – 7)

Common factor => 6x – 7

Therefore, we can conclude that the common binomial factor in the expression is 6x – 7

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Answer:

4x-5

Step-by-step explanation:

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

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:

The statement is true

Step-by-step explanation:

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

Answer:

$9629.63

Step-by-step explanation:

I assume this is simple interest.

The formula for simple interest is

F = P(rt + 1)

where F = future value,

P = present value

r = annual interest rate

t = number of years

10,400 = P(0.02 × 4 + 1)

10,400 = 1.08P

10,400/1.08 = P

9,629.63 = P

Answer: $9629.63

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