The numbers 1, 2, ... ,10 are to be entered into the 10 boxes shown below, so that each number is used exactly once: P = (\square + \square + \square + \square + \square)(\square + \square + \square + \square + \square). What is the maximum value of P? What is the minimum value of P?

Answer:

k=30

Step-by-step explanation:

The number of mice vary inversely with cats. This is written as:

[tex]Mice \propto \dfrac{1}{Cat} \\Mice = \dfrac{k}{Cat}[/tex]

When there are 3r-19 cats, there are 2r+1 mice

[tex]2r+1 = \dfrac{k}{3r-19}\\$Cross multiply$\\k=(3r-19)(2r+1)[/tex]

When there are 6r-27 mice, there are r-5 cats.

[tex]6r-27 = \dfrac{k}{r-5}\\$Cross multiply$\\k=(6r-27)(r-5)[/tex]

Taking the values of k above, we have:

[tex]k=(3r-19)(2r+1) =(6r-27)(r-5)\\(3r-19)(2r+1) =(6r-27)(r-5)\\6r^2+3r-38r-19=6r^2-30r-27r+135\\$Collect like terms\\6r^2-6r^2+3r+30r-38r+27r-19-135=0\\22r-154=0\\22r=154\\$Divide both sides by 22\\r=7[/tex]

Therefore:

[tex]k=(3r-19)(2r+1) \\=(3*7-19)(2*7+1)\\=(21-19)(14+1)\\=2*15\\k=30[/tex]

This is a example since there is no topic:

Explanatory variable: Could be found on the x axis

Response variable: Could be found on the y axis

Four things need to talk about when you describe a scatter plot:

D.       Direction

O.        Outliers

F.        Form

S.       Strength

Example: The relationship between this graph is strong, positive and linear relationship. There does not appear not be outlines.

How to know if its positive: As the x axis increases so does y axis increases too.

How to know if the chart is linear:

Because it describe the scatter plot. DOFS.

Tell me if you need more help with a pacific thing.

Hope this helps.

Answer:

B and D

Step-by-step explanation:

Age of Student --> Age of student is continues

Time taken to run one mile is also continues

Answer:

B and D

Step-by-step explanation:

Answer:

y = -3/4x - 2

Step-by-step explanation:

You put the equation in the slope-intercept form. Remember that the perpendicular slope is the negative reciprocal. You plug in the slope and the point into the slope-intercept formula. Solve for b then plug it into the final formula.

The equation of the line that passes through the point (8,-8) and is

perpendicular to the line 4x – 3y = 18 is;

⇒ 3x + 4y = -8

Here,

The point is (8, -8)

And, The equation of line is, 4x - 3y = 18

What is Equation of line?

The equation of line passes through points (x₁, y₁) and has slope m is;

y - y₁ = m₂ (x - x₁)

Now,

The point is (x₁, y₁) = (8, -8)

And, The equation of line is, 4x - 3y = 18

Put into the slope form as;

4x - 3y = 18

4x - 18 = 3y

y = (4/3)x - 6

Hence, Slope of the given line = 4/3

The slope (m₁) of perpendicular line relationship is;

4/3 * m₂ = -1

m₂ = -3/4

Hence, slope of perpendicular line (m₂) = -3/4

So, The equation of line by using point/slope form is;

y - y₁ = m₂ (x - x₁)

y - (-8) = -3/4 (x - 8)

y + 8 = -3/4 (x - 8)

4 (y + 8) = -3 (x - 8)

4y + 32 = -3x + 24

3x + 4y = -8

Hence, The equation of the line that passes through the point (8,-8) and is perpendicular to the line 4x – 3y = 18 is;

⇒ 3x + 4y = -8

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Answer: The second endpoint is  (2,6)

Step-by-step explanation:

[tex]\frac{-6 +x}{2}[/tex] = -2  solve for x  

-6 +x = -4

+6        +6

x= 2

[tex]\frac{-6+y}{2} = 0[/tex]  

-6 + y = 0

+6         +6

 y= 6

Answer:

374 feet^2

Step-by-step explanation:

Surface area:

area of cross section x 2 = 110feet^2

area of tope x 2 = 264 feet^2

sum / Surface area: 374 feet^2

Answer:

(QUESTION CORRECTNESS : 2/3 OF MEN ARE MARRIED TO 3/4 OF WOMEN)

Part of Entire Population married = 12/17 = 70.58%

Step-by-step explanation:

Fraction of men married:

[tex]\frac{2}{3}=\frac{4}{6}=\frac{6}{9}=\frac{8}{12}..........[/tex]

Fraction of women married:

[tex]\frac{3}{4}=\frac{6}{8}=\frac{9}{12}=\frac{12}{16} .........[/tex]

To solve the problem, we know that number of husbands should be equal to number of wives.

Number of husbands and wives are represented by the numerators of both fractions.

We have to find such a multiple of each fraction such that there numerator are same.

Let fraction of men married:  [tex]\frac{6}{9}[/tex]

Let fraction of women married:  [tex]\frac{6}{8}[/tex]

Add the numerators and denominator to find the solution:

[tex]\frac{6+6}{9+8}= \frac{12}{17}[/tex]

Answer:

False

Step-by-step explanation:

Flip the equation.

−a<2

Divide both sides by -1.

a>−2

Answer:

In the triangle shown, AB = 11, BC = 61. Find AC. Right Triangle ABC v2. 3,600; 3,842; 60; 62. 4. Using the following measurements, find the length of the leg of the right triangle. leg = 5

Step-by-step explanation:

Not sure if that's helpful, but hope it is.

Answer: i hope this will help you

a^x=y this is a simple equation

where as loga(in the base) y=x this is a logarithmic equation

Answer:

144-36π sq. in.

Step-by-step explanation:

Answer:

[tex]y=\frac{1}{3} x+4[/tex]

Step-by-step explanation:

A linear equation is written as [tex]y=mx+b[/tex], "m" being the slope and "b" being the y-intercept.

The slope is how many times you rise/run in order to get from one point on the line to the next. You rise (go up/down) 1 unit and run (go left/right) 3 units. Plug in the numbers and you get 1/3.

The y-intercept is where the graph lands on the y-axis, which is 4.

y = 1/3x + 4

Step-by-step explanation:

y = ax + b

b = the intercept with the y-as.

In the graph, the linear function (which is a fancy word for a line), you can see that the incline with the y-axis is at point (0,4).

So, b = 4

a = slope or incline.

To easilly find "a", you can follow these steps:

1. You choose two "nice" poins.

2. Starting on one point of the line, you count how many units you need to go in horizontal direction and in vertical direction to end upon the another point on the line.

3. The fraction a = y units/x units

1. Choose two nice point

Starting from (0,4) and going to the next "nice" point for example (3, 5).

2. Horizontal 3 units to the right, and 1 unit up.

3. a = y units/x units

a = 1/3

y = 1/3x + 4

Answer:

Decay factor is 0.75.

Step-by-step explanation:

The given function is  

[tex]y=760(0.75)^3[/tex]     ...(1)

The general form of exponential decay function is  

[tex]y=a(1-r)^t[/tex]    ...(2)

where, a is initial amount, t is the time period, r is decay rate and (1-r) is the decay factor.

On comparing (1) and (2), we get

[tex]a=760, t=3, (1-r)=0.75[/tex]

Therefore, the decay factor is 0.75.

Start with the point-slope formula, shown below in bold.

Our point which in this case is (6, 8) represents (x1, y1) in our formula.

~Substitute

Y - 8 = -2(x - 6)

I will be writing this equation in standard form.

First distribute the -2 through the parentheses.

This gives us y - 8 = -2x + 12.

Next we would move the -8 to the right side of the equation

by adding 8 to both sides to get y = -2x + 20.

Finally we move our x term to the left side of the equation

by adding 2x to both sides and our answer is 2x + y = 20.

Answer:

Diagonals are congruent

Step-by-step explanation:

The diagonals of a parallelogram are not congruent; one is longer than the other

Answer:

(b)

Step-by-step explanation:

This is inverse variation.  As y increases (but not allowed to be zero), x decreases.  Thus, (b) is correct:  y varies inversely with x.

The relation between the variables in the equation x= -3/y. Thus, (b) is correct, y varies inversely with x.

Let there are two variables p and q,

Then, p and q are said to be directly proportional to each other if

p = kq

where k is some constant number called constant of proportionality.

This directly proportional relationship between p and q is written as

[tex]p \propto q[/tex]  

where, that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n are two variables.

Then, m and n are said to be inversely proportional to each other if

[tex]m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}[/tex]

where c is a constant number called constant of proportionality.

This inversely proportional relationship is denoted by;

[tex]m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}[/tex]

As , increasing one variable will decrease the other variable if both are inversely proportional.

Here the relation between the variables in the equation x= -3/y;

This is inverse variation, As y increases (but not allowed to be zero), x decreases.

Thus, (b) is correct, y varies inversely with x.

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Answer:

Kerry = 2/3 * 420 = 280

David = 3/4 * 420 = 315

David read more pages compared to Kerry.

David read 35 more pages than Kerry.

The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.

Given:

Chemistry book contains 420 pages.

Kerry read 2/3 of her chemistry book,

= 2/3 x 420

= 280 pages.

David read 3/4 of her chemistry book,

= 3/4 x 420

= 315 pages.

315 - 280 = 35 pages.

Therefore, David read more pages.

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Answer:

30 and 32

Step-by-step explanation:

No because to be a function, each dot on the graph would need to be located at its own x value. Looking at the graph you see two dots located at x = 5 so it is not a function.

[tex]answer \\ = 15.01 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps[/tex]

Answer: Each friend got 3 cookies.

Step-by-step explanation:

Johann gets three cookies so 24-3=21. Divide it by the seven friends that came. 21/7=3 cookies.

Answer:

Step-by-step explanation:

So 7 of his friends came to the party and 3 cookies were left for himself. To find how many cookies each friend got, first subtract the 3 cookies Johann has from the total.

24-3=21

Then divide 21 by the number of friends.

21÷7=3

So each friend got 3 cookies.

Answer:

a) 72

b) 1/72

c) 1/36

Step-by-step explanation:

a) number of ways she can choose route= 3C1 = 3

   number of ways she can choose parking lots= 4C1 = 4

number of ways she can choose entrances= 3C1 = 3  

number of ways she can choose elevators= 2C1 = 2

number of ways she can go to office= number of ways she can choose route×number of ways she can choose parking lots×number of ways she can choose entrances×number of ways she can choose elevators

      number of ways she can go to office= 3×4×3×2

                                                                      = 72

b) Probability of morning side= number of morning side/ total number of routes=  1/3

probabiltiy of Parking lot A=  number of parking lot A/ total number of parking lot= 1/4

probability of south entrance= number of south entrance/ total number of entrances=  1/3

probablity of elevator 1=  number of elevator 1/ total number of elevator= 1/2

combine probability= 1/3× 1/4×1/3×1/2 = 1/72

c) Probability of Industrial Avenue= number of industrial avenue/ total number of avenue= 1/3

Probability of parking lot D= number of parking lot D/ total number of parking lot after deducting number of parking lots A and B = 1/2

Probability of north entrance= number of north entrance/ total number of entrance= 1/3

probablity of elevator 2= number of elevator 2/ total number of elevator

                                      = 1/2

combine probability= 1/3 × 1/2 × 1/3 ×1/2

                                  = 1/36

Answer:

a ) - 8x^7,

b ) - 4m^2 / nx,

c ) - 11a^2b^18 / 5

Step-by-step explanation:

[tex]a ) (2x^2)(-4x^5),\\-2x^2\cdot \:4x^5,\\-8x^5x^2,\\-8x^7\\\\Solution = -8x^7[/tex]

To solve this problem, I removed ( ), multiplied the terms, and through the " exponential rule " added the exponents to derive the solution - 8x^7

[tex]b ) (36m^2) / (-9nx),\\-\frac{36m^2}{9nx},\\-\frac{4m^2}{nx}\\\\Solution = -\frac{4m^2}{nx}[/tex]

Here I simplified the bit " 36 / 9 " which was found as 4 in the numerator, deriving the solution - 4m^2 / nx

[tex]c ) -11ab^9b^6 / 5b^3a,\\-11b^9\frac{b^6}{5}b^3a^{1+1},\\-11b^9\frac{b^6}{5}b^3a^2,\\-11\cdot \frac{b^6}{5}b^{9+3}a^2,\\-11\cdot \frac{b^6}{5}b^{12}a^2,\\-\frac{b^6\cdot \:11b^{12}a^2}{5},\\-\frac{11a^2b^{18}}{5},\\\\Solution = -\frac{11a^2b^{18}}{5}[/tex]

I applied a combination of " the exponential rule " and the addition of these exponents to receive a simplified solution - 11a^2b^18 / 5.

Answer:

[tex](x - 4)(x - 5)[/tex]

Step-by-step explanation:

x2 − 9x + 20

[tex] {x}^{2} - 9x + 20 \\ {x}^{2} - 5x - 4x + 20 \\ x(x - 5) - 4(x - 5) \\ (x - 4)(x - 5)[/tex]

The factors of the given trinomial are (x-5)(x-4).

The given trinomial is x²− 9x + 20.

To the factor, a trinomial in the form x² + bx + c, find two integers, r and s, whose product is c and whose sum is b.

Rewrite the trinomial as x² + rx + sx + c and then use grouping and the distributive property to factor the polynomial. The resulting factors will be (x + r) and (x + s).

Now, x²− 9x + 20 can be written as x²− 5x-4x + 20

=x(x-5)-4(x-5)

=(x-5)(x-4)

Therefore, the factors of this trinomial are (x-5)(x-4).

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Answer: The missing values represented by x and y are 8 and 20, that is;

(x, y) = (8, 20)

Step-by-step explanation: The function y = 16 + 0.5x is a linear equation that can be solved graphically. This means the values of both variables x and y can be found on different points along the straight line graph.

The ordered pairs simply means for every value of x, there is a corresponding value of y.

The 2-column table has values for x and y which all satisfy the equation y = 16 + 0.5x. Taking the first row for example, the pair is given as (-4, 14).

This means when x equals negative 4, y equals 14.

Where y = 16 + 0.5x

y = 16 + 0.5(-4)

y = 16 + (-2)

y = 16 - 2

y = 14

Therefore the first pair, just like the other four pairs all satisfy the equation.

Hence, looking at the options given, we can determine which satisfies the equation

(option 1) When x = 0

y = 16 + 0.5(0)

y = 16 + 0

y = 16

(0, 16)

(option 2) When x = 5

y = 16 + 0.5(5)

y = 16 + 2.5

y = 18.5

(5, 18.5)

(option 3) When x = 8

y = 16 + 0.5(8)

y = 16 + 4

y = 20

(8, 20)

From our calculations, the third option (8, 20)  is the correct ordered pair that would fill in the missing values x and y.

Answer:

The missing values represented by x and y are 8 and 20, that is;

(x, y) = (8, 20)

Step-by-step explanation:

Answer:

r < 1/3

Step-by-step explanation:

21r<7

Divide each side by 21

21r/21<7/21

r < 1/3

Answer:

[tex] r < \frac{1}{3} \\ [/tex]

Step-by-step explanation:

[tex]21 \: r < 7 \\ \frac{21 \: r}{21} < \frac{7}{21} \\ r < \frac{1}{3} [/tex]

hope this helps

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good luck! have a nice day!

Answer:

Option(1) is the correct answer to the given question .

Step-by-step explanation:

let     [tex]x1, y1=\ (2, 3)[/tex]

[tex](x2,y2)=(\sqrt{15,3} \ )[/tex]

[tex](x3,y3)=\ (4,8)[/tex]

Now we know that

[tex]Area=\ \frac{1}{2} |x1(y2-y3)\ + \ x2(y3-y1)\ + x3(y1-y2)[/tex]

Now putting this value in the formula we get

[tex]\frac{1}{2}|2(3-8)\ +\sqrt{15}(8-3)\ * 4(5-3)|[/tex]

[tex]=\ \frac{1}{2}\ *9.3649[/tex]

=4.6824

Therefore option(1) is the correct answer .

Answer:

Option(1) is the correct answer to the given question .

Step-by-step explanation:

Answer;

Explanation:

CHECK THE COMPLETE QUESTION BELOW:

chemist is studying the properties of a gas under various conditions. He observes that when the gas is at room temperature and low pressure, it behaves as an ideal gas. When the gas is cooled to 10 kelvin and is placed under high pressure, however, it deviates significantly from an ideal gas. Explain these observations.

ideal gas reffered to as one that has the collisions between its atoms or molecules perfectly eleastic and in which there are no intermolecular attractive forces existing between them. The ideal gas concept is important because it obeys the ideal gas law.

Which is PV=nRT

Where P is the pressure

T is the Temperature

V is the Volume

R is ideal gas constant

n is amount of substance

The ideal gas model assumes that gas particles experience no intermolecular attractions. These are the behavior of gases under different condition

✓At low temperature, gas particles move slowly.

-✓At high pressures, gas particles are very close together.

✓ When the particles of gases are close they have low speed and their low speed allow intermolecular forces to become important at high pressure and low temperature.

OBSERVATION S:

At room temperature which is comfortable ambient temperature, generally taken as about 20°C to 25C

Gases behave non ideally at cold temperatures, So when the gas is cooled to 10Kelvin, molecules are moving relatively slowly past one another, then they give room for the repulsive and/or attractive forces between their molecules giving room for deviation from an Ideal Gas.

The intermolecular forces cause the gas to deviate from ideal behavior So, the reason why a gas deviate from ideal behaviour may be due to some two assumptions of kinetic theory of gases. The forces of attraction between gas molecules are negligible. When the gas is placed under high pressure the gas molecules get more crowded and the amount of empty space between the molecules is reduced.

--

Answer:

Ideal gas explains the property of gas that has no inter-molecular attractions irrespective of temperature and pressure.

Explanation:

Ideal gases assumes that the gases would experience no inter-molecular attraction and collision with other gases.

These gases are perfectly exhibiting elastic collision in nature.

The particle of gases moves slowly at lower temperature and the gases would become close when they exhibit high pressure.

The "closeness of the gas-particle" and "low-speed characteristics" are the important observations noted.

The inter-molecular forces deviate the property of gases from ideal gas behavior.

Step-by-step explanation: