What is the product of 3.4 x 10-14 and 1.8 x 10287
O6.12 x 1014
O9.4x 1014
O5.2 x 1042
O6.12 x 1042

The constant of proportionality is a value that relates two quantities that are directly proportional or inversely proportional to each other.

What is the constant?

For example, in the equation y = kx, where y and x are two quantities that are directly proportional to each other, k is the constant of proportionality. It represents the ratio between y and x, or the amount that y changes for a unit change in x.

Similarly, in the equation y = k/x, where y and x are two quantities that are inversely proportional to each other, k is the constant of proportionality. It represents the product of y and x, or the amount that y changes for a unit change in 1/x.

The constant of proportionality is often denoted by the letter k, but it can have other symbols depending on the context. It is also sometimes called the proportionality constant, the scaling factor, or the unit rate.

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Complete question is: The constant of proportionality is a value that relates two quantities that are directly proportional or inversely proportional to each other.

Answer:

Step-by-step explanation:

Answer: C and D respectively

Step-by-step explanation:

To find the sum "n"  consecutive even/odd integers you need to do x + (x+2) + (x + 4) ... for n times. You can just add them and solve.

To find the sum of "n" consecutive integers you need to do x + (x + 1) + (x + 2) ... for n times. In this problem we do x + (x + 1) + (x + 2) = 96; 3x +3 = 96; x = 31. Then we can find the other numbers by plugging in 31 for x. 31, 32, 33.

The two tanks differ in terms of Filling rates and initial volumes.

We can work with the equation for tank A, which represents a linear relationship between the volume of liquid in the tank (y) and the time it has been filling (x).

The equation y = 75x + 110 tells us that the tank A is filling at a constant rate of 75 units per minute, starting with an initial volume of 110 units.

To analyze the data for tank B, we would need to know the volumes of the tank at different times as it is being filled.

If the relationship for tank B is also linear, we could find the equation that represents it by using two points from the table and the slope-intercept form of a linear equation (y = mx + b). Once we have both equations, we can compare them to see how the two tanks differ in terms of filling rates and initial volumes.

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A fair punishment I believe is the person going to prison for their life or a death sentence.

250 adults and 195 children swam at the public pool on that day.

What is the system of linear equations?

A system of linear equations is a set of two or more equations that contain two or more variables. The goal is to find the values of the variables that will satisfy all of the equations in the system.

This is a system of equations problem. We can start by using two variables, x for the number of children and y for the number of adults, and then set up two equations based on the information given.

The first equation is for the total number of people: x + y = 445

The second equation is for the total amount of money collected: 1.75x + 2.5y = 964.75

We can now use the first equation to solve for one of the variables in terms of the other, and then substitute that expression into the second equation.

x + y = 445

x = 445 - y

Now we substitute x = 445 - y into the second equation

1.75(445 - y) + 2.5y = 964.75

after solving this equation we get

y = 250

x = 195

Hence, 250 adults and 195 children swam at the public pool on that day.

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Answer:

Step-by-step explanation:

To find the answer, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of games, r is the number of losses, and n-r-1 is the number of ties (since we already know there are 9 wins).

Substituting the values, we get:

13C3 * 10C1

= (13! / 3!10!) * (10! / 1!9!)

= (13*12*11 / 3*2*1) * 10

= 2860

Therefore, there are 2860 ways the schedule can end with 9 wins, 3 losses, and 1 tie.

Answer:

69.06

Step-by-step:

1 ) Calculate the discount.

15% of 1250 is...

187.5

2 ) Subtract 187.5 from 1250...

1062.5

3 ) Calculate the sales tax.

6.5% of 1062.5 is...

69.06

4 ) Add 69.06 to 1062.5 to get the final answer...

$1131.56

Hope this helps! :)

Answer:

69.06

Step-by-step explanation:

15% of R1250

= R187, 5

R1250 - R187 ,5

= R1062,5

Answer:

75−4(4−2)^3

=43

Answer:

136 cm²

Step-by-step explanation:

Surface area = 2(lw+wh+hl)

l = 7

w = 2

h = 6

so,

2(7×2+2×6+7×6)

= 136 cm²

Answer:

136 cm^2

Step-by-step explanation:

L 7cm

W 6cm

D 2cm

7 x 6 + 6 x 2 + 2 x 7 (x 2) = 68 x 2 = 136cm^2

On the coordinate (0,7) the value of P is maximum 280.

What is a Linear Inequality?

In mathematics, inequality denotes a mathematical expression in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers.

Solution:

First of all to solve the Linear Inequality we need to plot the graph of the given equations.

Kindly find the attached graph

To maximise the equation P = 30x + 40y

we need to find the corner values of x and y.

According to the graph, the corner values of (x,y) are

(5,0), (3,4) and (0,7)

putting the values in the equation P = 30x + 40y

at x = 5 and y = 0

P = 150

at x = 3 and y = 4

P = 250

at x = 0 and y = 7

P = 280

So, on the cordinate (0,7) the value of P is maximum i.e. 280.

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Answer: 0, 4

Step-by-step explanation:

Answer:

60,242

Step-by-step explanation:

86060 = 100%

÷10

8606 = 10%

×7

60242 = 70%

Answer: The answer is 12

Step-by-step explanation:

2.3 slices are two whole units with one decimal in the tenths place. Thus, we have to convert the decimal to a fraction.

As the number 3 is in the tenths place, we can do the following:

Then, the fraction is:

Answer: C)

By using the coordinates of the labeled point, the point-slope equation of the line include the following: D. y + 5 = -3(x - 3)

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

0 5 2 -2

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (4 + 5)/(0 - 3)

Slope (m) = -9/3

Slope (m) = -3

At data point (3, -5) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-5) = 3(x - 3)  

y + 5 = -3(x - 3)

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

She should find the squares between 4.2 and 4.3

Step-by-step explanation:

The square of 4.2 was too low and the square for 4.3 was too high so the answer is between the two.

If two figures are similar, it means that the ratio of their corresponding sides are equal. This ratio also equals the ratio of their area. Considering the given scenario,

Area of figure A = 48

Area of figure B = 75

The ratio of the area of figure B to figure A is

75/48

= 25/16

If the length of one side of figure A is 6 feet, let the length of the corresponding side of figure B be x. Thus,

x/6 = 25/16

By cross multiplying, we have

16x = 25 * 6 = 150

x = 150/16

x = 9.375

x = 9 3/8

The length of the corresponding side is 9 3/8

1.1. Accumulated depreciation:

The accumulated depreciation for the machine bought on 1 July 2013 would be R150,000 as of 31 March 2016.

1.2. Machine realization:

The machine bought in 2013 was sold for R120,000 on 30 June 2015, resulting in a profit/loss on the sale of R10,000.

1.1. Accumulated Depreciation:

To calculate the accumulated depreciation, we need to determine the annual depreciation expense for each machine and then accumulate it over the years.

Machine bought on 1 July 2013:

Cost: R250,000

Depreciation rate: 20% per annum on cost

Depreciation expense for the year ended 31 March 2014: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2015: 20% of R250,000 = R50,000

Depreciation expense for the year ended 31 March 2016: 20% of R250,000 = R50,000

Accumulated depreciation for the machine bought on 1 July 2013:

As of 31 March 2014: R50,000

As of 31 March 2015: R100,000

As of 31 March 2016: R150,000

1.2. Machine Realisation:

To record the sale of the machine bought in 2013, we need to adjust the machine's value and the accumulated depreciation.

Machine's original cost: R250,000

Accumulated depreciation as of 30 June 2015: R100,000

Net book value as of 30 June 2015:  

R250,000 - R100,000 = R150,000.

On 30 June 2015, the machine was sold for R120,000.

Realisation amount: R120,000

To record the sale:

Debit Cash: R120,000

Debit Accumulated Depreciation: R100,000

Credit Machine: R250,000

Credit Machine Realisation: R120,000

Credit Profit/Loss on Sale of Machine: R10,000 (difference between net book value and realisation amount).

These entries will reflect the appropriate balances in the ledger accounts and properly close off the accounts for the years ended 31 March 2016.

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The domain of \(y=4\log_5(x-3)\) is (d) all real numbers greater than 3.

The function is given as:

\(y=4\log_5(x-3)\)

Set the expression in bracket greater than 0

x -3 > 0

Add 3 to both sides

x > 3

Hence, the domain of \(y=4\log_5(x-3)\) is (d) all real numbers greater than 3.

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The angle from the options given that is shown in the drawing is: D. <LIJ.

An angle is a geometric figure that is formed by two rays that share the same endpoint, called the vertex. The rays are called the sides of the angle, and the endpoint is called the vertex.

In the drawing given,  IJ and LI are two segments that have a common endpoint called vertex I.

Points L, I, and J forms an angle whose vertex is at I, as shown in the image given. Thus, the angle shown in the drawing is: D. ∠LIJ.

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Answer:

Step-by-step explanation:

Just substitute any values of x so that you can graph it <33

The rate of each group was 1.86 mph and 3.36 mph.

Given that the two towns are 1150 miles apart.

A group of hikers from each town meet after a total hiking time of 220 hours.

One group travels 1 1/2 mile per hour slower than the other​ group,

We need to find the rate of each group,

So, let use consider, distance travelled by one group = x miles,

Therefore, second group travelled = 1150 - x miles.

Rate of first group = y mph

Rate of second group = y - 3/2 mph

Rate = distance / time

So,

y = x / 220

x = 220y.............(i)

Similarly,

y-3/2 = 1150 - x / 220

220y - 330 = 1150 - x

Using eq (i)

220y - 330 = 1150 - 220y

440y = 1480

y = 3.36

y - 3/2 = 1.86

Hence the rate of each group was 1.86 mph and 3.36 mph.

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Answer:

square root of 25

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

the square root of 25 is 5, and thats the only rational number there

I hope I was helpful! :D

Answer:

X is 1

Step-by-step explanation:

The general form of the equation of the Quadratic function is y = (-1/9) x2-(14/9) x-43/9.

The general form of the equation of the Quadratic function is y = (-1/9) x2-(14/9) x-43/9.    

The general form of the equation of a quadratic function given the vertex and a point on the graph, we can use the vertex form of the quadratic equation  y =  a( x- h) 2 k  where( h, k) represents the vertex of the parabola.  In this case, the vertex is(- 7, 6) and the point is(- 10, 5).  We can substitute these values into the equation to get  5 =  a(- 10-(- 7)) 2 6  Simplifying  farther  5 =  a(- 10 7) 2 6  5 =  a(- 3) 2 6  5 =  9a 6  Now, we can  break for' a'  a =  5- 6  9a = -1  a = -1/ 9  Substituting this value back into the equation, we get  y = (-1/9)( x-(- 7)) 2 6

 Simplifying  farther  y = (-1/9)( x 7) 2 6  Expanding and rearranging, we can write the equation in general form  y = (-1/9)( x2 14x 49) 6  y = (-1/9) x2-(14/9) x-49/9 6  y = (-1/9) x2-(14/9) x-43/9  So, the general form of the equation of the quadratic function is y = (-1/9) x2-(14/9) x-43/9.

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1. The volume of the black bag is 1728 cubic inches. 2. The volume of the blue bag is 2700 cubic inches. 3. The black bag will fit in the Check Box. 4. The bigger suitcase is 27 times larger than the smaller suitcase.

Volume, which is commonly expressed in cubic units, is the amount of space occupied by a three-dimensional object. By multiplying an object's length, breadth, and height, as well as other formulas depending on the shape of the object, one can get the volume of the thing. Volume is a key concept in many practical applications, including calculating container capacity, constructing structures, and estimating the amount of material required for a construction project. Volume is utilised in many branches of mathematics, science, and engineering.

For the given dimensions of the bags we have:

1. The volume of the black bag is:

18 x 12 x 8 = 1728 cubic inches

2. The volume of the blue bag is:

18 x 15 x 10 = 2700 cubic inches

3. The black bag will definitely fit in the Check Box because its volume of 1728 cubic inches is less than the volume of the Check Box, which is 2772 cubic inches.

4. The ratio of bigger suitcase to smaller suitcase is:

75 x 20 x 18 = 27000 cubic inches

25 x 8 x 9 = 1800 cubic inches

27000 / 1800 = 27

The bigger suitcase is 27 times larger than the smaller suitcase.

5. Now, if the watermelons is about 10 inches long and 9 inches wide, then its height would be:

720 = 10 x 9 x H

720 = 90H

H = 8 inches

The maximum amount of watermelons that can fit are:

27000 / 720 = 37.5 watermelons = 37 watermelons.

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Given:

The charge per hour for Bait's shop: $4

The charge per hour for family's shop: charge per hour for Bait's shop

Answer:

8 and 9

Step-by-step explanation